Dissipative Processes in Tribology

DISSIPATIVE PR0CESSES IN TRIBOLOGY

TRIBOLOGY SERIES, 27 EDITOR: D. DOWSON

DISSIPATIVE PROCESSES IN TRIBOLOGY edited by

D. Dowson, C.M. Taylor, T.H.C. Childs, M . Godett and G. Dalmaz Proceedings of the 20th Leeds-Lyon Symposium on Tribology held in the Laboratoire de Mecanique des Contacts, lnstitut National des Sciences Appliquees de Lyon, France 7th-10th September 1993

ELSEVIER Amsterdam

London New York Tokyo

1994

For the Institute of Tribology, The University of Leeds and The lnstitut National des Sciences Appliquees de Lyon

ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 21 1,1000 AE Amsterdam, The Netherlands

L i b r a r y o f Congress C a t a l o g i n g - i n - P u b l i c a t i o n

Data

Leeds-Lyons Symposium on T r i b o l o g y ( 2 0 t h : 1993 : I n s t l t u t n a t i o n a l des s c i e n c e s a p p l i q u i e s de L y o n ) D i s s i p a t i v e processes i n t r i b o l o g y : p r o c e e d i n g s o f t h e 2 0 t h Leeds -Lyon Symposium on T r i b o l o g y h e l d i n t h e L a b o r a t o l r e de mecanlque des c o n t a c t s , I n s t i t u t n a t i o n a l des s c i e n c e s a p p l i q u i e s de Lyon. France, 7 t h - 1 0 t h September 1993 1 e d i t e d by D. Dowson [et al.1. p. cm. -- ( T r i b o l o g y s e r i e s ; 27) I n c l u d e s b l b l i o g r a p h i c a l r e f e r e n c e s and i n d e x . ISBN 0-444-81764-6 ( a c i d - f r e e p a p e r ) 1. Trlbology--Congresses. I.Dowson. D. 11. U n i v e r s i t y o f Leeds. I n s t l t u t e of Tribology. 111. I n s t i t u t n a t i o n a l des s c i e n c e s IV. Tltle. V. S e r i e s . a p p l i q u e e s de Lyon. TJ1075.A2L43 1993 621.8'9--d~20 94- 18428 CIP

...

ISBN 0 444 81764 6 (Vol. 27)

0 1994 ELSEVIER SCIENCE B.V. All rights reserved. No part of this publication may be reproduced, stored i n 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), Salem, Massachusetts. 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 t o the copyright owner, Elsevier Science B.V., 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 i n the material herein. This book is printed on acid-free paper Printed i n The Netherlands

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Proceedings of the 20th Leeds-Lyon Symposium on Tribology INTRODUCTION The twentieth Leeds-Lyon Symposium on Tribology was held at the Institut National des Sciences AppliquCes de Lyon from Tuesday 7th to Friday 10th September 1993. It discussed dissipative phenomena and particularly the origins of fiction at all scales, fiom all points of view coming fiom mechanics, physics and chemistry, encountered in all fields of Tribology, from thick film lubrication to dry friction. The Symposium opened on the Tuesday afternoon with two keynote lectures delivered by Dr Irwin Singer fiom the US Naval Research Laboratory, Washington DC, U S 4 on "Energy Dissipation during Friction : Interfacial Processes" and by Professor Kenneth Johnson from Cambridge University, UK, on "The Mechanics of Adhesion, Deformation and Contamination in Friction". They clearly showed the hndamental and pluridisciplinary aspects of dissipative processes in tribology. The meeting was attended by some one hundred and forty delegates from sixteen countries of North America, Asia and Europe and by fourteen accompanying persons. Thirty per cent of the delegates were from industry. It was again pleasant to welcome a large and active group from the University of Leeds, our sister institution. The Symposium Review Board had examined and selected the abstracts of more than eighty submitted papers. The organisers decided for the second time, instead of parallel sessions, to have classical sessions reserved for twenty minute paper presentations and hybrid sessions which included a five minute oral presentation followed by a poster session. The twentieth Symposium was dedicated to Professor Duncan Dowson, in honour of his retirement as a member of the staff at the University of Leeds. The Vice Lord Mayor of Lyon, hosted the delegates at a reception in the Lyon Town Hall to honour and recognise through the 20th LeedsLyon Symposium anniversary, the international scientific activity in the field of Tribology of the two co-founders of the Leeds-Lyon Symposia. Professor Duncan Dowson from the Institute of Tribology of the University of Leeds and Professor Maurice Godet, from the Laboratoire de Mecanique des Contacts of INSA of Lyon. The traditional Symposium banquet was held in the "Salle de la Corbeille du Palais de la Bourse" in Lyon. The dinner was prepared by one of the well known Chef of Lyon, Gilles Troump. On the Thursday evening, the delegates were invited the celebrate the 20th Leeds-Lyon anniversary in the Conservatoire National Superieur de Musique de Lyon. In this famous place, they discovered eight centuries of music in Lyon and the pleasure of listening to 500 years of fanfares played by the "Ensemble Cuivres et Percussion" of the "Orchestre National de Lyonll.

vi

The concert programme had been specially chosen by Maurice Godet to show how music can magnify science. It was a superb musical evening with Maurice. The usual Friday evening barbecue party was arranged by the Laboratory staff. The Saturday tour took some delegates on a trip through the Jura in Franche Comte to visit the fabulous Arc-etSenans Royal salt-works, to see the beautiful valley of the River Loue and test yellow wines. The success of the Symposium must be attributed to all members of the Laboratoire de Mecanique des Contacts. They are individually congratulated for their contribution and active participation in the Symposium organisation. Warmest thanks to all. Thanks are also due to the Direction des Recherches Etudes et Techniques, Direction GenCrale de I'Armement, Ministere de la Defense, Paris, France, for his financial support for the 20th LeedsLyon Symposium on Tribology. The topics covered by the Leeds-Lyon series of Tribology symposia are listed below: 1. 2. 3. 4.

5. 6. 7. 8. 9. 10. 11. 12. 13.

14. 15. 16. 17.

18. 19. 20.

Cavitation and Related Phenomena in Lubrication SuperlaminarFlow in Bearings The Wear of Non-Metallic Materials Surface Roughness Effects in Lubrication Elastohydrodynamic Lubrication and Related Topics Thermal 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 - Osborne 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

Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds

1974

Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon

1985

1975 1976 1977 1978 1979 1980 1981 1982 1983 1984

1986 1987 1988 1989 1990 1991 1992 1993

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Delegates to the Symposium and the international community of tribologists were deeply saddened by the news, so soon aRer the Symposium, of the untimely death of our dear friend and colleague Professor Maurice Godet on October 9th 1993. The 21st Symposium, to be held in Leeds from September 6th - 9th 1994 on the subject of "Lubricants and Lubrication", will be dedicated to the life of Maurice Godet. Gerard Dalmaz

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CONTENTS Introduction Session I

Session II

V

Opening Session Friction and Energy Dissipation at the Atomic Scale A Review I.L. SINGER The Mechanics of Adhesion, Deformation and Contamination in Friction K.L. JOHNSON

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Liquid and Powder Lubrication A Rheological Basis for Concentrated Contact Friction S. BAlR and W.O. WINER On the Theory of Quaisi-Hydrodynamic Lubrication with Dry Powder : Application to Development of High-speed Journal Bearings for Hostile Environments H. HESHMAT The Influence of Base Oil Rheology on the Behaviour of VI Polymers in Concentrated Contacts P.M. CANN and H.A. SPIKES Temperature Profiling of EHD Contacts Prior to and During Scuffing J.C. ENTHOVEN and H.A. SPIKES Computational Fluid Dynamics (CFD) Analysis of Stream Functions in Lubrication D. DOWSON and T. DAVID Shear Properties of Molecular Liquids at High Pressures A Physical Point of View E.N. DIACONESCU

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Session 111

Session iV

1 3 21 35 37

45 65 73 81 97

Surface Damage and Wear Magnetic Damage in Mn-Zn and Ni-Zn Ferrites Induced by Abrasion Y. AHN, R. HEBBAR, S.CHANDRASEKAR and T.N. FARRIS Effects of Surface Roughness Pattern on the Running-In Process of Rolling/Sliding Contacts J. SUGIMARA, T. WATANABE and Y. YAMAMOTO Influence of Frequency and Amplitude Oscillations on Surface Damages in Line Contact J. PEZDlRNlK and J. Vlz NTlN Effects of Surface Topography and Hardness Combination Upon Friction and Distress of Rolling/Sliding Contact Surfaces A. NAKAJIMA and T. MAWATARI Anti-Wear Performance of New Synthetic Lubricants for Refrigeration Systems with New HFC Refrigerants T. KATAFUCHI, M. KANEKO and M. IlNO

115

Miscroscopic Aspects A Molecularly-Based Model of Sliding Friction J.L. STREATOR Friction of Dielectric Materials : How is Energy Dissipated? B. VALLAYER, J. BIGARRE, A. BERROUG, S. FAYEULLE, D. TREHEUX, C. Le GRESSUS and G. BLAISE

171

117 125 139

151 163

173 185

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Friction Energy Dissipation in Organic Films B.J. BRISCOE and P. THOMAS Session V

193

Polymers Interfacial Friction and Adhesion of Wetted Monolayers J.-M. GEORGES, A. TONCK and D. MAZUYER Effect of Thickness on the Friction of Akulon A Problem of Constrained Dissipation L. ROZEANU, S. DIRNFELD and J. YAHALOM Interface Friction and Energy Dissipation in Soft Solid Processing Operations M.J. ADAMS, B.J. BRISCOE and S.K. SHINA The Effect of InterfacialTemperature on Friction and Wear of Thermoplastics in the Thermal Control Regime F.E. KENNEDY and X. TlAN

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Session VI

Session VII

Session Vlll

Friction in Specific Applications The Relation Between Friction and Creep Deformation in Articular Cartilage K. IKEUCHI, M. OKA and S. KUBO Characteristics of Friction in Small Contact Surface Y. ANDO, H. OGAWA and Y. ISHIKAWA Sliding Friction in Porous and Non-Porous Elastic Layers: The Effect of Translation of the Contact Zone Over the Porous Material L. CARAVIA, D. DOWSON, J. FISHER, P.H. CORKHILL and B.J. TIGHE The Effect of Additive of Silane Coupling Agent to Water for the Lubrication of Ceramics K. MATSUBARA. S. SASANUMA and K. NAGAMORI The Origin of Super-Low Friction Coefficient of MoS2Coatings in Various Environments C. DONNET, J.M. MARTIN, Th. le MOGNE and M. BELIN

203 205 213 223 235 245 247 253 26 1 267 277

Coatings and Thin Films (Short Oral Presentations Associated with Posters) Characterisation of ElastioPlastic Behaviour for Contact Purposes on Surface Hardened Materials P. VIRMOUX, G. INGLEBERT and R. GRAS On the Cognitive Approach Toward Classification of Dry Triboparticulates H. HESHMAT and D.E. BREWE Surface Chemistry Effects on Friction of Ni-P/PTFE Composite Coatings E.A. ROSSET, S. MISCHLER and D. LANDOLT Transfer Layers in Tribological Contacts with Diamond-Like Coatings J. VIHERSALO, H. RONKAINEN, S. VARJUS, J. LIKONEN and J. KOSKINEN Surface Breaking Crack Influence on Contact Conditions. Role of Interfacial Crack Friction. Theoretical and Experimental Analysis M.-C. DUBOURG, T. ZEGHLOUL and B. VILLECHAISE

285

Macroscopic Aspects, Friction Mechanisms The Generation by Friction and Plastic Deformation of the Restraining Characteristics of Drawbeads in Sheet Metal Forming Theoretical and Experimental Approach E. FELDER and V. SAMPER

359

287 303 329 337

345

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36 1

X

A Model for the Estimation Of Damping In Helical Strand Under Bending Vibration A. HADJ-MIMOUNE and A. CARDOU Energy Dissipation and Crack Initiation in Fretting Fatigue D. NOWELL, D.A. HILLS and D.N. DAI

Session IX

Session X

Session XI

Session XI1

373 389

Energy and Friction : Theoretical and Numerical Aspects Friction in Partially Lubricated Conjunctions 1.1. KUDISH and B.J. HAMROCK Third Body Theoretical and Numerical Behaviour by Asymptotic Method G. BAYADA, M. CHAMBAT, K. LHALOUANI and C. LICHT Thermomechanical State Near Rolling Contact Areas K. DANG VAN and M.H. MAITOURNAM

397

Thermal Power Dissipation in Machines Thermal Dissipation in Elliptical Bore Bearings M.T. MA and C.M. TAYLOR Material Dissipative Processes in Automotive Engine Exhaust Valve - Seat Wear Z. LIU and T.H.C. CHILDS Thermal Matching of Tribological Systems A.V. OLVER Power Loss Prediction in High-speed Roller Bearings D. NELIAS, J. SEABRA, L. FLAMAND and G. DALMAZ Power Dissipation in Elastohydrodynamic Traction Drives I.M. CIORNEI, E.N. DIACONESCU, V.N. CONSTANTINESCU and G. DALMAZ

429

General Aspects of Friction (Short Oral Presentations Associated with Posters) Frictional Heating of Elliptic Contacts J. BOS and H. MOES Soil-Structure Interface Friction in Reinforced Soils F. BAHLOUL, Y. BOURDEAU and V. OGUNRO Diagrams for Estimation of the Solidified Film Thickness at High Pressure EHD Contacts N. OHNO. N. KUWANO and F. HIRANO

489

Fatigue and Damage Fracture Modes in Wear Particle Formation A.A. TORRANCE and F. ZHOU The Influence of Lubricant Degradation on Friction in the Piston Ring Pack R.I. TAYLOR and J.C. BELL High Speed Damage Under Transient Conditions 0. LESQUOIS, J.J. SERRA, P. KAPSA and S. SERROR Incipient Sliding Analysis Between Two Contacting Bodies. Critical Analysis of Friction Law T. ZEGHLOUL, M.C. DUBOURG and B. VILLECHAISE

519

399 41 5 423

431 445 453 465 479

491 501 507

521 531 537 549

Written Discussion

559

List of Delegates

567

SESSION I OPENING SESSION Chairman:

Professor M Godet

Paper I (i)

Friction and Energy Dissipation at the Atomic Scale A Review

Paper II (ii)

The Mechanics of Adhesion, Deformation and Contamination in Friction

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Dissipative Processes in Tribology / 1994 Elsevier Science B.V.

D.Dowson et al. (Editors)

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Friction and energy dissipation at the atomic scale - a review I.L. Singer Code 6170, U.S. Naval Research Laboratory Washington DC 20375, USA ABSTRACT Discussions of energy dissipation during friction processes have captured the attention of engineers and scientists for over 300 years. Why then do we know so little about either dissipation or friction processes? A simple answer is that we can not see what is taking place at the interface during sliding. Recently, however, devices such as the atomic force microscope have been used to perform friction measurements, characterize contact conditions and even describe the "worn surface." Following these and other experimental developments, friction modelling at the atomic level -- particularly molecular dynamics simulations -- has brought scientists a step closer to "seeing" what takes place during sliding contact. With these investigations have come some answers and new questions about the modes and mechanisms of energy dissipation at the sliding interface. This paper will review recent results of 1) molecular dynamics and other theoretical studies that have identified modes of energy dissipation during friction processes and 2) friction experiments that have added to our understanding of dissipation processes and friction behavior. Finally, several approaches for addressing the questions of dissipation mechanisms will be presented. 1. INTRODUCTION.

Friction can now be studied at the atomic scale, thanks to developments in the past decade of a variety of experimental techniques [I]. The most well known techniques, often referred to as proximal probes, have been derived from Scanning Tunneling Microscopy (STM)(21; they include Atomic Force Microscopy (AFM) [3] and its sliding companion Friction Force Microscopy, (FFM) (4-61. These probes allow friction to be studied with atomic resolution in all three dimensions. Another proximal probe, generically known as a Surface Force Apparatus (SFA), affords atomic resolution only in the vertical direction, but allows direct measurement and/or control of micrometer-sized areas of contact in the lateral direction (7-121. A very recent technique, based on the Quartz Crystal

Microbalance (QCM), permits sliding friction processes to be studied at the Angstrom level and at time scales in the nanosecond range [13-

IS]. Although friction processes may originate at the sliding interface, the measurement of friction is usually performed by macroscopic devices -springs, levers, dashpots, etc -- often located far from the interface. In order to link measured frictional forces with theory, it has been necessary to examine the influence of mechanical parameters, such as stiffness, on friction measurements, not an unfamiliar problem to tribologists [I6,17]. Unlike traditional friction devices, however, proximal probes are sensitive to mechanical properties of the device at distances as close as the first atomic layer of the tip and as far away as the compliant lever arm (18-201.

4

The opening of experimental studies of friction at the nanometer and nanosecond scale has attracted theorists equipped to model physical and chemical processes at these scales. Surface scientists are now using sophisticated solid-state potentials to calculate mechanical interactions between surfaces [20]. Friction force calculations are performed either analytically or by molecular dynamics (MD) simulations [22,22/. MD simulation affords the added opportunity of using video animation to study friction processes. For the first time, scientist can "see what is happening" at the otherwise buried sliding interface. As you will read shortly, they see atomic and molecular excitation modes (vibrations, bending and rotations), electron-hole excitations, density waves and molecular interdigitation, to name a few. Once the modes are identified, physicists and chemists can address perhaps the most fundamental but least understood aspect of friction: energy dissipation processes. While it has been known for centuries [23,24] that most frictional energy dissipates as heat, neither the macroscopic nor microscopic mechanisms of energy dissipation have been fully explained. In a companion paper presented at this Leeds-Lyon conference, Ken Johnson discusses adhesion and deformation contributions to energy dissipation in friction. Here I review some recent theoretical and experimental studies of atomicscale friction behavior and modes of energy dissipation. Before launching into the studies, it is useful to review the thermodynamic criteria used to study energy dissipation. Clearly, if friction processes generate heat, they are irreversible and cannot be treated by classical thermodynamics. If, however, each step in a sliding interaction is executed with infinite slowness and with the two couples always in equilibrium (never an unbalanced force), then the process may be considered reversible. In such a quasi-static process, sliding can be achieved with zero

friction. Real systems can approximate such reversible, adiabatic processes so long as the rate at which each step is taken is much slower than the relaxation time of the system [25]. However, any instability in the mechanical system that leaves unbalanced forces will result in an irreversible process in which energy is lost (or, more precisely, unrecoverable). In a mechanical system, where force, F, acts over a distance, r, the fraction of energy, U, lost over a cycle is given by

AU

=

fF*dr.

In an atomic sliding calculation, a cycle can be a translation across some periodic distance of the lattice, e.g., one atomic spacing. In an experiment, one cycle can be a single pass over a surface, including the making and breaking of the contact. This paper is presented in the following sequence. The second section deals with theoretical approaches used to examine friction processes and friction measurements at the atomic scale. Conditions that can give zerofriction and finite friction in simple systems are presented. Two molecular dynamics simulations of more realistic yet "wearless" friction studies are described and modes of energy dissipation are identified. The third section presents two experimental approaches that have succeeded in identifying microscopic friction process; in both cases, energy losses are identified with hysteresis losses in the system. The fourth section summarizes our understanding of interfacial friction processes and energy dissipation mechanisms, and the fifth section considers ways that atomistic approaches can be used to solve practical problems in tribology.

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Fig. I . Two representations of the motion of atom Bo in the independent oscillator model: atom-on-spring and atom-in-potential. Top and bottom rows depict strong and weak inter$acial interactions, respectively. i%e left-most diagrams display the relevant potentials (see text); subsequentpanels illustrate the response of Bo to progressive sliding of the lower layer of atoms. B, in the combined potential, V', is represented by a black dot plotted below each atom-on-spring diagram. From [26,27]. 2. THEORETICAL APPROACHES

2.1. Frictionless Sliding. Two analytical studies that identify conditions for zero friction behavior and the transition to finite friction are reviewed. The first investigates the potential seen by a moving atom, while the second examines the force experienced by the tip of a FFM. Although both present surface interactions at zero degrees Kelvin, they establish baseline criteria for zero friction systems and measurements of zero friction by which more general calculations can be evaluated. McClelland [26,27] describes the sliding friction behavior of a simple two-dimensional couple consisting of two substrates: the stationary upper substrate has an atom, $, attached to a spring while the moving lower

substrate consists of equally-spaced, rigid atoms (see Fig. 1). Because of the periodicity of the lower layer, the entire sliding behavior can be analyzed by following the motion of atom B, across one atomic spacing. According to this independent oscillator (IO) model, atom B, experiences forces exerted by a spring above and the atoms below; the forces are derived from potentials VBB and Vm, respectively. As the lower substrate moves, the combined interaction potential, Vs, changes. The changing potential and the atomic trajectory of atom B, are depicted in the five sketches running left to right across the figure. The upper sketches represent a "strong" interaction and the lower, a "weak" interaction. The atom's position on a spring is shown as an open circle and its position in the potential V, by a solid circle. In a "strong" potential, the atom is initially repelled to the

6

right; then beyond half an atomic spacing, it "snaps" back to the left, the atomic equivalent of "stick-slip." The snap back, or "plucking" motion, can be understood in terms of the evolving shape of potential Vs. In an adiabatic process, an atom must always sit at a minimum in the potential well. As can be seen, however, the position of the atom at (d) is only a local minimum, which disappears by position (e). At the moment the local metastable minimum "flattens out," there are unbalanced forces on atom B,; to regain an equilibrium state, the atom falls to the position of the stable minimum. Since this transition doesn't occur under equilibrium conditions, the process is irreversible and the energy lost in the fall cannot be reused to assist the sliding process. Stated in more physical terms, the strain energy put into stretching the spring at B, is not recovered locally; instead, it is converted into vibrational motion which dissipates into the substrate (as heat). This instability can be avoided by using a "weaker" interaction potential. As shown in the lower sequence of sketches in Fig. 1, the weaker potential does not develop a local minimum. The atom moves smoothly through a repulsive then an attractive force field, first being repelled by, then pushing, the lower substrate. Since the system remains in equilibrium throughout the cycle, no energy is dissipated and the friction force is zero. McClelland then gives more precise criteria for stability and shows that qualitatively similar friction behavior occurs with other more complex sliding couples. Tomanek, et al. [28,29] also describe conditions associated with frictionless sliding, emphasizing the mechanical properties of the apparatus as well as the

L

Fig. 2. Model of a Friction Force Microscope. External suspension M is guided along a horizontal suvace in the x direction. m e load Fa, is kept constant along the trajectory shown by arrows. The spring-tip assembly is elastically coupled to the suspension M in the horizontal direction by a spring of constant c. 7hefriction force FJ is related to the elongation x,-x, of the horizontal spring from its equilibrium value. From [28,29].

strength and shape of the interatomic potentials. They present two idealized models for a FFM tip interacting with an atomic surface, only one of which is presented here. Called a "realistic-friction microscope" by the authors, the model accounts for the elasticity of the FFM as well as the external load, F,,,, and the surface interaction potential. Fig. 2 shows a FFM, with a horizontal spring that pulls the spring-tip assembly along the interface potential of the substrate. The tip experiences the combined force of the interface potential and F,,,. As the tip moves across the surface, the horizontal spring elongates by an amount, xM - x,, which depends on the stiffness, c, of the horizontal spring. For a "hard" spring (c > ccriJ,both the tip trajectory and the Ff

7

-

1.5

'hardj

pfl"

1.o

0.5 0.0 c

Li -0.5 -1.0

1

-1.5 -2.0

9

0

AX XU

Fig. 3. 'Ihefriction force F, as a function of the FFM position x, and the average friction force for a hard and a sop spring. From (28,291.

3 00

200 A

7

E

z

v

U

100

0

2

6

8

10

Fig. 4. Contour plot of the average friction force < F,> per atom as a function of the load Fat and the horizontal spring constant, c. for monoatomic Pd tip on graphite, from /28,29])

curve are single-valued functions of x,; an example of the latter curve is labeled "hard" in Fig. 3. Since the positive and negative excursions of Ff are the same over a cycle, the average friction force C Ff> is zero. When c falls below ccri,,both the tip trajectory and the Ff curve are triple-valued functions of x,; an example of the latter is labeled "soft" in Fig. 3. In this "soft" spring case, the tip snaps forward at the point of "instability," as in the "strong" 0 model above, giving the spring case in the I asymmetric Ff vs X, curve shown by the curve with arrows. The average friction force, < Ff > , is therefore non-zero, as given by the dashed line. The energy dissipated by the collapse of the elongated spring is represented by the shaded area under a portion of the Ff vs X, curve. Fig. 4 gives the average friction for a range of values of horizontal spring constant, c, and Two results are apparent. external force, F,. First, the ability to measure zero friction depends on the value of c. Secondly, the friction coefficient p= < Ff> /Fea for atomic contacts is not independent of load. Further discussion of friction vs load behavior for atomic sliding is given elsewhere [28,29]. These simplified models of friction between atomic couples provide analytical criteria for transitions to zero friction, thus zero energydissipation conditions at T = OK. Zero friction requires "weak" interaction forces (low atomicscaled corrugations) for adiabatic motion and "hard" horizontal springs to measure the effect. An atomic "stick-slip" phenomena is predicted when these criteria are not met. The models are, in fact, consistent with atomic scale FFM measurements [4]. 2.2. Molecular Dynamics Simulations of Monolayer Films. Molecular dynamics (MD) simulations of friction behavior go beyond the simple analytical models. They use more realistic interaction potentials that exhibit anisotropy in two or three

8

dimensions; they account for effects of temperature and sliding velocity. Moreover, video animations of the simulations allow us to visualize the trajectories of the atoms at and near the interface. MD thereby gives us our "first look" at what happens at the buried interface during sliding contacts. Early examples of MD studies of frictional contact between solid surfaces depicted wear and transfer of material in the sliding contact (22,301. More recently, two studies of "wearless" friction have been reported; "wearless" friction, meaning that no atoms are lost from or transferred to either couple. In both cases, the solid surfaces were terminated with a monolayer of a simple hydrocarbon or hydrogen. This section presents these studies, which begin to address the role of surface films in friction processes. 2.2.1. monolayers of alkane chains McClelland and Glosli [27,31] have performed MD simulations of friction between two monolayers of alkane chains. The chains, six C atoms long, are initially ordered in a herringbone pattern. Chain bonds are allowed to bend and twist, but not stretch. C and H atoms on each chain interact with atoms of other chains by a Lennard-Jones potential of interaction strength, E,. The interaction strength at the interface, E , , is adjustable in order to study friction behavior as a function of interface interaction strength. The temperature of the layers is held constant by means of a heat bath; energy losses in the chains can thus be followed as heat losses in the layers. MD calculations are performed over a temperature range of 0 < T < 300K and sliding velocities up to v, = 204 mlsec. The friction force is calculated as the shear stress, T , averaged over several cycles of sliding. Fig. 5 shows two sets of friction vs temperature data for the case of strong ( E , / E , = 1.0) and weak ( E , / E , = 0.1) interactions at sliding speed of v = 20 m/sec. For both cases,

2.0

015 .

e A 6V t 0 ._

1.0

L

0 .L

0.5

0

1

2 3 Temperature T/E,

4

5

Fig. 5. Friction vs temperature data in normalized units for the case of strong (& = 1.0) and weak ( E ~ / C ~ = 0.1) inte@acial interactions at a sliding speed, v = 20 m/sec. Ihe solid line represents afit to the data using a thermal activation model. From [31]. the friction force exhibits different behaviors in the three (low, medium and high) temperature regimes; in addition, for the case of weak interactions, the friction vanishes at low and high temperatures. In order to interpret the friction behaviors and energy dissipation processes, McClelland and Glosli relied on video animations of the molecular dynamics and calculations of both shear stress and heat flow vs displacement curves. At low temperatures, the trajectories of the alkane chains are very much like that of the atom-on-a-spring in the I 0 model discussed earlier. For strong interactions, the ends of the chains are strained until the local minimum in the potential disappears. At that moment, the ends of the chains are released abruptly and the chains oscillate with a pivoted-hinge motion. As the two chains oscillate synchronously but in opposite directions, CH, groups on the backbone of the chains begin to vibrate but the chains themselves do not twist; the chains retain their initially ordered, herringbone pattern, indicating that vibration and twisting modes are decoupled at this temperature. Friction force vs distance

9

-22

3

4

5

0 0.25 0.5 0.75 1.0

Displacement (D/a)

Fig. 6. Shear stress (leji) and heat flow (right) vs sliding displacement for strong ( ~ J E , = , 1.0) and weak = 0.I ) intevacial interactions at T = 20K. From 1311. curves exhibit atomic stick-slip, as seen in the upper left of Fig. 6. At slip, strain,energy is released abruptly (25 psec), which caused the heat flow shown in the upper right of Fig. 6. Because the energy dissipation is associated with a plucking instability, the friction is expected to be independent of velocity; this was confirmed by MD calculations at several velocities for T = 20K. Plucking motion and energy dissipation occur until the interfacial interaction falls below E J E ~ = 0.4. Below this value, the friction force vs distance curves vary smoothly and symmetrically about Ff = 0 and there is no measurable heat flow (see lower left and right parts of Figs. 6 , respectively). Like the weakly0 model, the weaklyinteracting atom in the I coupled alkane chains exhibit harmonic motion as the two substrates slide past each other. As the temperature increases, the friction in both interaction ranges increases, reaching maximum values around T = 80K. At this temperature, video animations depict very complex dissipation modes. The strain energy released by the bent chain now couples into chain oscillations, CH, group vibration and, for the first time, a torsional mode in which chains

twist about their backbone. Torsional modes, which are "frozen" at lower temperatures, become excited at intermediate temperatures; this process is sometimes referred to as "rotational melting." With all three modes now anharmonically coupled, excitations damp out quickly by transferring energy to the lattice vibrations in the substrate. Hence, the increase in friction at intermediate temperature can be attributed to the excess energy associated with the unfrozen torsional modes. As the temperature increases above the rotational melting temperature, a third mechanism comes into play: molecules vibrate so actively in all directions that an increasing percentage of the chains can hop and slide over the opposite surface without introducing strain. This reduces the net frictional force in both weak and strong interaction cases; in fact, in the weak interaction system, the friction force goes to zero at highest temperatures. Glosli and McClelland then demonstrate that the friction behavior at high temperatures is consistent with classical behavior of polymeric films. MD calculations of strongly interacting couples showed increasing friction (sub-linear) with sliding velocity (not shown here) and decreasing friction with temperature (Fig. 5 ) . The latter curve was fitted to the Eyring thermal activation model that Briscoe and Evans /32] used to describe the shear behavior of thin polymeric films. The straight-line fit, drawn in Fig. 5 , required only one adjustable parameter, the activation energy, Q; it was determined to be Q = 70K. The shear strength (at T = 0) derived from Q was 7 = 32 MPa, about the same value obtained from experimental data for stearic acid (C18) and behenic acid (C22). In summary, MD simulations of friction behavior between monolayers of alkane chains show that the simple harmonic vs plucking friction behavior applies to more complicated systems; in addition, the simulations enumerate the modes of dissipation that arise with

10

increasing molecular complexity and increasing thermal activation. 2.2.2. H- and (H+C,H,,)-terminated diamond (111) surfaces

Harrison, White, Colton and Brenner /33-351 have simulated the friction behavior of H- and (H + C,H,)-terminated diamond (1 11) surfaces placed in sliding contact. The forces are derived from an empirical hydrocarbon potential capable of modeling chemical reactions in diamond and graphite lattices as well as small hydrocarbon molecules /36]. Two diamond (1 1 1) surfaces, each terminated in a (1 x 1) pattern, are placed in twin (mirror-image) contact; the distance of separation depends on the repulsive interaction potential and the load.- Sliding is performed-in two directions: the [ 1121 direction and the [ 1101 direction. In the [ 1121 direction, the opposing H atoms can make "head-on" contact at very high loads because their velocity vectors lie in a common plane perpendicular to the surface; wg'll call these "aligned trajectories." In the (1101 direction, the H atoms can only pass adjacent to each other (across each others' diagonals) because their velocity vectors do not lie in a common perpendicular plane. The lattice temperature is set at 300K, unless otherwise stated, and sliding velocities are 50 or 100 m/sec. Normal loads are varied up to 0.8 nN/atom, corresponding to mean pressures up to 20 GPa. Friction coefficients are averaged over a unit cell, and friction coefficient vs load data are presented for both sliding directions. Their first study examines two (1 x 1) Hterminated diamond (1 11) surfaces /33]. Along the [ 1121 direction, the friction coefficient begins near zero for lowest loads, increases nearly linearly with load up to 0.6 nN/atom, then levels out at p = 0. ( see Fig. 7). Video animation sequences of sliding along the "aligned" [ 1121 direction show different interaction mechanisms at low and high loads.

0.6

0.4

1

CH,CH,

1c

__

0.2 - J

a

A'

-

za

-.I I

I

-- dh I

1

1

I

Fig. 7. Averagefriction coeflcient a; a function of normal load for sliding in the I1121 direction at v = I k/psec and at T = 300K. Curves are for hydrogen, methyl, ethyl and n-propylterminated systems, respectively. From /35/. At lowest loads, opposing H atoms first repel each other backwards. Then as strain develops, they pivot sideways and revolve past each other at closest approach, finally pushing each other forward. With these trajectories, the net frictional force, averaged over a unit cell, nearly cancels and almost no energy is dissipated. At higher loads, atomic-level stick-slip occurs: instead of gently revolving by each other, opposing H atoms collide and momentarily become "stuck," then suddenly "slip" and revolve around one another. (Slip is definitely assisted by thermal motion, as will be made clear later.) The pivoting-then-revolving motion excites both vibrational and bending modes in the C-H bonds. These excitations are passed on to the lattice as vibrations (phonons) then heat. In this way, potential (strain) energy developed at high loads is transformed into kinetic energy

11

(mechanical excitations), leading to non-zero values of the friction coefficient. Friction coefficient vs load data for sliding along the [110] direction (not shown here) are about !a order-of-magnitude lower than along the [ 1121 direction. Animations show that H atoms, instead of meeting along aligned trajectories, "zig-zag" through channels of potential minima that run between adjacent rows of H atoms on the opposing surfaces. Since the opposing H atoms do not encounter each other directly, strain levels are lower and thus the frictional forces are lower. Hence, different sliding directions on identical surfaces lead to anisotropy in both atomic trajectories and friction coefficients. Perhaps these trajectories can account for the well-know frictional anisotropy of single crystals [37,38]. The friction coefficient of the H-terminated surface shows a temperature dependence that is qualitatively similar to that found with alkane chains. At a modest pressure of 3 GPa, the friction coefficient drops from p=0.4 at OK, to p=0.25 at 70K, then to p=0.15 at 300K. The friction coefficient is larger at low temperatures because opposing H atoms cannot rotate out of the way of aligned-trajectory collisions without the help of thermal motion. Harrison et al. [34] next examined the friction behavior of the same sliding configuration of H-terminated diamond but with two methyl groups substituted for two H atoms on one surface. Along the [ 1121 direction, the friction coefficient vs load data rise quicker than on the fully H-terminated surface, but reach lower steady-state values (p = 0.35 vs p = 0.4) (see Fig. 7). These differences can be attributed to the large volume occupied by a methyl group. Instead of easily "revolving" around the H-atoms during low-load, aligned-trajectory collisions, the methyl group gets stuck, then "slips" with a ratcheting motion. The ratcheting motion, analogous to the motion of a "turnstile," rotates the methyl group alternately clockwise then

counter-clockwise 120" around the C-C bond. The turnstile motion, accompanied by C-H bond excitations, is responsible for higher friction at low loads. At high loads, the size of the methyl groups keeps the two surfaces further apart than comparably-loaded H-terminated pairs. Harrison (391 speculates that the "flattening" out of the friction coefficient vs load data may be due either to screening of the interaction potential or to constraining the excitation modes. Sliding the methyl-substituted surface along the [110] direction (not shown) produces the same, strong loadd2pendent friction coefficients found in the [112] direction (see Fig. 7). Remarkably, the substitution of two CH, molecules for two H atoms produces an order of magnitude greater friction coefficient. Why? Unlike the terminal H atoms, which can "zigzag" freely through the adjacent H atom channels, the larger methyl groups exhibit "turnstile" rotations like those found in [ 1121 sliding. The rotations are accompanied by "zigzag" motion, which becomes more pronounced as the load increases. The increased energy expended by the larger molecules in this turnstile and zig-zag trajectory is responsible for the increase in friction coefficient with load. In their latest study, Harrison et al. [35] have substituted two ethyl and two n-propyl groups for two H atoms; friction coefficient vs load data are seen in the right two panels of Fig. 7. The larger, more flexible hydrocarbon groups reduce friction at high loads by a factor of 1.5 to 2 compared with the fully H-terminated diamond slider. Center-of-mass trajectories of the CH, portion of the ethyl groups, plotted on potential energy contour maps of a H-terminated diamond (1 11) surface, give insight into how the motion of an ethyl molecule affects the friction coefficient (not shown here). At low loads, the ethyl molecule bends over, lies down and is dragged almost straight across the repulsive potentials, like the trajectory a chain would have if one end were tied to the upper surface. At

12

high loads, however, the ethyl molecule uses its flexibility and length to "snake" (detour) around high potential energy barriers; this trajectory expends less energy and produces a lower friction coefficient at higher loads. In summary, Harrison et al. have identified several mechanisms which may account specitically for the friction behavior and energy dissipation of H- and hydrocarbon-terminated diamond surfaces, and, more generally, for boundary film lubrication. They have shown that, at 300K, H- and h ydrocarbon-terminations follow different trajectories when sliding along "hard" (aligned-trajectory) and "soft" (channels) directions of H-terminated diamond, and thereby explain the strong frictional anisotropy of Hterminated diamond pairs along selected lowfriction channels. They have cataloged numerous excitations modes (rotations, turnstiles,.. .) by which frictional energy is dissipated. In addition, they have shown that, at high contact stresses, larger hydrocarbon groups reduce friction even further because of size and steric effects.

changed by varying the atmosphere, temperature, velocity or related parameters. The main conclusion of the study is that the friction force does not correlate with the adhesion force (or adhesion energy, y), but rather with hysteresis in the adhesion force. As an example, Fig. 8 shows friction and adhesion measurements for loading and unloading two calcium alkylbenzenesulfonate (CaABS) monolayers at 25°C. The curves to the left (A and C) represent behavior of a liquid-like monolayer: quite a low friction coefficient and some hysteresis in the adhesion during the loading-unloading cycle. The curves to the right (I3 and D) show that after exposing the surfaces to decane vapor, the already low friction coefficient in dry (inert) air decreases even more and the adhesion hysteresis disappears. Previous studies [42,42] had shown that when hydrocarbon vapors condensed onto CaABS, the molecules penetrated the outer chain regions and fluidized the surface. Thus, it was hypothesized that if a monolayer were made more liquid-like, Inert Alr 10

A

Dacana Vaoor 10

I

3. EXPERIMENTAL APPROACHES

3.1. Friction and Adhesion Hysteresis Israelachvili and co-workers [40] have recently discovered a new relationship between adhesion and friction, based on experimental studies of surfactant monolayers. Experiments are performed with a SFA, in which both adhesion and friction are measured. Adhesion behavior is examined in contact radius vs load curves during loading-unloading cycles and in pull-off force measurements; friction behavior, in unidirectional and reciprocating sliding. The surfactant monolayers studied exhibit one of three phases: solid-like, amorphous or liquidlike. The amorphous state is a phase in between the solid-like and liquid-like state. Moreover, the phases of each of the layers could be

-L.

-La

Load, L (mN)

Fig. 8. (A and B) Friction traces of two CaABS monolayers at 25°C exposed to inert air and to air saturated with decane vapor. (C and 0) Adhesion energies on loading, unloading and pull-ofl measured under the same conditions as the upper friction traces. From [40].

13

Increasing load, organic vapors. Increasing chain fluidity, branching

Temperature, T

Longer, more saturated chains

("C)

Fig. 9. A schematic 'piction phase diagram" representing the trends observed in the friction forces of five different suvactant monolayer types studied. The curve also correlates with adhesion hysteresis of the monolayers but not with the adhesion per se. From [40]. the friction and adhesion hysteresis would be reduced. Many other correlations between friction and adhesion hysteresis and the phase of surfactant monolayers have been observed. Both friction and adhesion hysteresis increase when solid-like monolayers or liquid-like monolayers are made amorphous-like. Conversely, when amorphouslike monolayers are made more fluid-like or solid-like, both the friction and adhesion hysteresis decrease. Observed trends in friction and adhesion hysteresis behavior are summarized in the schematic "friction phase diagram curve" shown in Fig. 9. Maximum values of friction and adhesion hysteresis (but not adhesion values) are found around a "chain-melting"temperature, T,; this is the temperature at which the monolayer is in between the solid-like and liquid-like state -i.e., the amorphous-like state. Lower values of friction and adhesion hysteresis are found at temperatures above or below T,. It is seen that the amorphous-like state represents the highest friction and highest adhesiun hysteresis. Factors

that can change the phase state of monolayers, such as vapors, speed, etc.. . can effectively shift the curve in directions indicated by the arrows in Fig. 9. Israelachvili et al. give a physical basis for this behavior. Adhesion hysteresis is the "irreversible" part of the adhesion energy, and is related to the energy dissipated during the A likely loading and unloading process. molecular origin of adhesion hysteresis is the extent of interpenetration and subsequent ease of disentanglement of the molecules across an interface. If there is little interpenetration, as with solid-like layers, the friction is smooth and no additional energy is expended separating surfaces. If there is significant interpenetration, as with liquid-like layers, but also ease of disentanglement on separation, the friction is again low and little extra energy is expended A thermodynamic separating surfaces. description of the liquid-like case would conclude that the time to separate the chains is slower than the Telaxation time of the molecules and, therefore, that separation approximates a reversible process. In both the above cases, the systems are physically in similar states going into and coming out of contact. By contrast, with amorphous-like layers, there is significant chain interpenetration but separation occurs faster than the molecular relaxation time. Thus, amorphous-like layers will be in different states going into and coming out of contact, and consequently, more energy will be expended to separate them than would be needed for the two other phases. Thus, we add a new mechanism of friction in boundary film lubrication. This mechanism is associated with the time it takes a molecule to adapt its trajectory to the lowest possible interaction potential, relative to the timedependence of the potential. In term s of the MD studies of large hydrocarbon-terminated surfaces [35], the low friction achieved with npropyl groups at high loads requires that they

14

"follow" the lowest energy trajectories by following the contours of minimum energy. In monolayer film studies [40],we see examples of one state, liquid-like, in which the chains can follow minimum force trajectories; but a second state, amorphous-like, in which the slower moving chains cannot follow. The energy differences are seen, therefore, in both adhesion hysteresis and friction. 3.2. Friction and Slip of Monolayer Films Krim et al. [13-15] are studying the frictional forces for solid-like and liquid-like films adsorbed on conducting (metal) and insulating (oxidized metal) substrates. Their approach is quite novel. Films of gases such as Kr and Ar or C2H4 and C,H6 are condensed onto surfaces to thicknesses up to several monolayers. The thickness of the film is determined in a straightforward manner with a quartz crystal microbalance (QCM). In addition, the QCM monitors sub-Angstrom shifts in the vibrational amplitude caused by gas adsorption. These shifts are due to frictional shear forces between the condensing film and the oscillating surface. Krim et al [I31 have shown that the "slip time" 7 of a monolayer film can be determined with sub-nanosecond accuracy from these shifts. Note that the time and length scales, nanoseconds and Angstroms, makes these experiments unique in the field of tribology. Since slip is fundamentally an energydissipative process, the technique allows energy dissipation to be measured and the mechanisms of energy dissipation to be studied. Experiments with rare gas atoms have shown that (1) the slip times for monolayers physisorbed on smooth gold surfaces are on the order of nanoseconds and (2) solid-like films exhibit longer slip times than liquid-like films. These results are consistent with a frictional force proportional to the sliding velocity, indicating a viscous friction mechanism. Three models have been proposed to account

for energy dissipation of the sliding monolayers. The first two postulate that phonons carry away the energy. Sokoloff, using an analytical model of friction [43,44/, suggests that defects between the incommensurate monolayer-solid interface can account for the slip times. Robbins et al. [45] have used molecular dynamic simulations to determine the viscous coupling between a driven substrate and an adsorbed monolayer film. Requiring no arbitrary parameters, the model gives excellent agreement with many of the experimental observations; it gives the correct magnitude of slip time, 7 , a friction force proportional to 7 for physisorbed films, and less slip in liquid films than in solid films. They have also shown that their results agree with a simple analytic model, closely related to that of Sokoloff. The slip time is directly related to it is equilibrium properties of the film; proportional to the lifetime of longitudinal phonons and inversely proportional to the square of the density oscillations induced by the substrate. A third model, presented by Persson et al. (461, postulates energy dissipation by electron-hole scattering. It assumes that electrons in the metal substrate experience a drag force equal in magnitude to the force required to slide the adsorbed film. This force is estimated from measurements of the change in resistivity of metal films as a function of gas coverage. Slip times calculated from the forces are in good agreement with experimental values for adsorbed rare gases and hydrocarbon molecules. The electron-hole scattering model also predicts different slip times for C2H4and C2H6 adsorbate films, but only if electronic contributions are present e.g., with metals but not insulators. Krim's group [47] has recently tested this prediction by measuring slip times for C2H4 and c& on silver and on oxygen-coated silver. They find different slip times on Ag, but the sume slip time on oxygen-coated silver, consistent with the

15

predictions. Thus, based on these rather unique studies of friction, it appears that both phonon and electron mechanisms contribute to energy dissipation. 4. SUMMARY AND DISCUSSION

From studies just reviewed and others in the literature, our understanding of interfacial friction processes and energy dissipation mechanisms can be summarized as follows. Low friction, including zero friction, can be achieved at low loads, with weak interface interactions and with "small" atoms at the interface. The mechanical principle that explains this behavior follows from the simple, onedimensional, I0 model: the strain energy transmitted by interfacial atoms during the first half of the cycle is returned to them during the second half cycle. This behavior is also observed in the more realistic, three-dimensional MD simulations. The third dimension itself contributes an additional friction reduction channel; it provides the interfacial atoms an extra degree of freedom -- to move out of their common plane -- to escape "stick" events along aligned trajectories. For example, H-terminated atoms can rotate around each other in aligned collisions or "zig-zag" along potential minima channels; these trajectories are not available to atoms described in two dimensional models. In principle, many "low friction trajectories" can be found along selected directions in real crystals having anisotropic interaction potentials (corrugations); these possibilities are treated more quantitatively by Hirano and Shinjo [48'. In practice, however, too soft a spring in the measuring device can lead to friction force instabilities, resulting in measured friction forces that are higher than expected. Friction is increased by many factors. Strong interfacial interactions (corrugations), according to the simple I 0 model, give a finite static friction force, then stick-slip motion between atoms. Three-dimensional potentials also show

atomic-scale stick-slip processes, but the modes equivalent to twodimensional plucking, e.g. turnstile motion, are novel and more complex. Atomic-scale stick-slip processes have been seen in FFM measurements, but at present the modes responsible have not been identified because of the relatively slow response time of friction devices [49]. Anharmonic coupling of excited modes establishes multiple pathways for energy dissipation, thereby increasing friction coefficients. An example is the MD simulation of alkanes at intermediate temperature, where torsional modes become allowed, providing a new pathway for energy dissipation. Other excitation modes that enhance friction and dissipate energy are density oscillations, defects at interfaces and electron-hole coupling in metals. Commensurate lattices have been shown to increase friction forces by many orders of magnitude [44]. Friction force is expected to increase with increasing external force (load). However, as Zhong and Tomhek [SO] have shown, surface interactions can be perturbed over a selected load range, thereby lowering the friction coefficient as the load increases. Temperature can influence friction behavior in several ways. Thermal activation of an energydissipating mode, like rotational melting, increases friction. In contrast, thermalactivation can lower potential barriers and increase tunneling, thereby reducing friction. At high temperatures, thermal effects can dominate friction processes, giving liquidlike (viscous) friction instead of solid friction (finite static friction at all velocities). The MD simulation of alkane chain friction showed this transition from solid to viscous behavior with increasing temperature. The size and shape of molecules can also influence friction behavior. Small atoms or molecules may follow low-friction trajectories whereas larger atoms or molecules may not "fit" into the same channels, resulting in higher friction. The H- vs CH,-terminated diamond

16

along the [110] direction is such an example. By contrast, larger molecules can reduce friction more effectively than smaller molecules at higher loads if they have sufficient flexibility to spread across the surface; an example is the high load behavior of the hydrocarbon-terminated diamond surfaces. This steric accommodation, however, can increase friction if the molecule cannot follow the minimum-energy trajectory as fast as the surfaces move apart. Chain entanglement between amorphous-like films observed in SFA studies is an example of steric effects causing increased energy dissipation. A new concept of friction behavior has been demonstrated by Israelachvili et al. -- that energy dissipation is maximum when the time (and length) scales of contact (externally controlled) match the intrinsic time and length scales of molecular interactions. This concept is consistent with thermodynamic considerations of two bodies coming into contact. As mentioned in the introduction, the degree to which the contact process approximates a reversible, quasi-static process depends on the rate at which each step is taken compared to the relaxation time of the system. Put in terms of the driven oscillator analog, deviations from equilibrium and energy dissipation are maximum when time and length scales of the system and driver are matched. However, classical thermodynamics is not really suitable for the treatment of contacting surfaces let alone sliding surfaces. Even in the mildest contact circumstances, in which the two bodies retain their identity after separating, equilibrium was never achieved; at best, the two bodies reached metastable equilibrium. A more precise description of the thermodynamics of contacting surfaces is needed. Finally, these studies can give us some new insights into the role of surface films in friction processes. Generalizing the studies of Harrison et al, we see that films in which "small" atoms chemisorb one-to-one with the substrate lattice might provide the screening needed to prevent

interface "welding" and give low-friction trajectories along weak corrugation channels. Films made of larger molecules, with lower compressibility, might reduce friction at high loads by providing atomic screening as well as steric accommodation. 5. RECOMMENDATIONS

This review was meant to introduce tribologists to some of the more recent investigations of energy dissipation processes in interfacial friction. Many recommendations for future research in atomic-scale tribology can be made based on these preliminary investigations. For example, the remarks in the previous paragraph suggest two approaches for modeling boundary lubricant films: 1) gas or solutehdditive interactions with surfaces can be modeled with small, single-atom terminations and 2) "run-in" boundary films can be modeled by more complex molecular attachments. Many of the ideas in this paper were presented at a two week long NATO AS1 meeting held in Braunlage, Germany in August 1991. Considerable time was spent discussing "future issues" and suggested approaches for research in this field; these have been published in the Epilogue to the conference proceedings [52]. Here I summarize only a few of these items: How can atomistic modeling continue to make an impact on understanding friction? on understanding lubrication? Can algorithms (e.g. hybrid methods) be developed to simulate friction processes at time and length scales longer than can be treated in molecular dynamics calculations alone? e.g. that extend computational simulations from the nmjfemtosec scale to the pm/psec scale. Can lubricants be tailored to take advantage of the dynamic properties of certain fluids,

17

e.g., the "chemical hysteresis" of monolayer films Israelachvili, et al. o In practical machines, sliding is sustained on surface films -- whether organic lubricants, oxides or other solid films. Can molecular simulations help us to understand the chemistry of film formation, the mechanical properties of these films and how the films break down? One of the newest issues that tribology must deal with is the concept of matching time and lengths scales in friction studies. As we saw above, energy dissipation hence friction is intimately linked to time and length scales. Moreover, the atomidmolecular modes of interfacial interactions operate at time and length scales far shorter than traditional tribology measurements. In the section of the Epilogue [SlJ entitled New wavs of probing friction processes, we asked "How can we use the power of microscopic modeling to gain new insights into macroscopic friction processes and, ultimately, to solve technological problems?" Bill Goddard [52/ suggests that this can be done by progressing along the "chain-linked" ladder, illustrated in Fig. 10, from quantum-level studies to engineering design. His "hierarchy of modeling tribological behavior" unites atomistic models, which operate in very short length-time scales, with engineering models, which describe tribological behavior in length-time scales observable by more traditional measuring equipment. This approach "...allows consideration of larger systems with longer time scales, albeit with a loss of detailed atomic-level information. At each level, the precise parameters (including chemistry and thermochemistry) of the deeper level get lumped into those of the next. The overlap between each level is used to establish these connections. This hierarchy allows motion up and down as new experiments and theory lead to new understanding of the higher levels, and new

I

DISTANCE 1A

W)A

lOOA

!p

lcm

yofdt

Fig. 10. lime and length scales of present-day models and experiments in Tribology. From [51J.

problems demand new information from the lower levels." But where are the experimental approaches for investigating the "lower (short scale) levels?" As illustrated in Fig. 10, most "friction machines," including the proximal probe devices, are operated at long time scales. An abbreviated search of recent literature produced only three "tribology" tests and a fourth proximal probe method that come close to investigating friction behavior at short time and length scales. Labeled 1 through 4 in the Fig. 10, they are described briefly here: 1. Bair et al. I531 have used fast IR detectors to measure flash temperatures during high speed frictional contacts of asperities of length 10 pm and greater, with time resolution of about 20 psec. 2. Spikes et al. have developed real time optical techniques for investigating the physical behavior of EHL films down to 5 nm thick [54J and chemical processes occurring in contacts 10 pm wide by 80 nm thick (551. 3. Krim et al. [13,14] have used the quartz crystal microbalance experiments (described earlier) for probing atomic vibrations amplitudes between 0.1 to 10 nm and time

18

scales from 1W2 to sec. 4. Hamers and Markert /56] have shown that STM images are sensitive to the recombination of photo-excited carriers whose lifetimes are in the picosecond range. Clearly, innovative experimental approaches for measuring friction processes at short and intermediate time-length scales are needed to assist the modelers who are already there. Tribologists should seek out physicists and chemists working in these time-space domains and form collaborations to carry out tribologyoriented experiments. As I've tried to emphasize in this article, much of the progress in the field comes when experiments and theories can overlap on the same time-length scales. Finally, there is another time scale to consider, and that is "the question of time to translating this (fundamental) knowledge into engineering practice. Duncan Dowson, to whom the XXth Leeds-Lyon session on "dissipativeprocesses in Tribology" is dedicated, told us how this can be accomplished in the final part of the Epilogue [57]. I'

"We have heard quite a lot about the subject of friction from the atomic scale up to the macroscopic scale.. .. 7here are other aspects of scale I think we should reject on. One is the question of time in terms of translating this knowledge into engineering practice.. ..'Ihe time scales are generally enonnous. ... I think you should take note that it is going to be about A DECADE IF NOT A GENERATION before that impact will be seen fully in engineering. m i s makes it all the more importantfor ... physicists, chemists and engineers (to meet), so that the engineers can absorb by osmosis the concepts that you are revealing.. .. It is important that these ideasfeed into our consciousness so that we apply them sensibly in future developments. ...I hope equally that scientists will not be

toofrustrated by the fact we take 10 to 20 years to incorporate their bright new ideas in designing better skis or whatever it might be. Let us perpetuate this interaction between groups of people who all have one objective and that is to understand the laws of physics in order to apply them as eflectively as we possibly can for the good of society through the manufacture of reliable, eflcient and sensible products. " ACKNOWLEDGEMENTS. I am most grateful to the following colleagues for providing reprints and preprints and their willingness to engage in discussions of their results: J.A. Harrison, J.N. Israelachvili, J. Krim, G.M. McClelland, H.M. Pollock, M.O. Robbins, J.B. Sokoloff and D. TomiInek. I am also grateful to my hosts at the Laboratoire de Technologie des Surfaces, Ecole Centrale de Lyon, where this paper was conceived. REFERENCES 1.

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6. 7.

8.

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A.M. Homola, Science, 240 (1988) 189; A.M. Homola, J.N. Israelachvili, P.M.McGuiggan, and M. L. Gee, Wear, 136 (1990) 65. 9. Israelachvili, in Ref. 1, p. 351. 10. A. Tonck, J.M. Georges and J.L. Loubet, J. Colloid Interface Sci., 126 (1988) 150. 11. J-M. Georges, D. Mazuyer, A. Tonck and J.L. Loubet, J. Phys. Cond. Mat., 2 (1990) 399. 12. J-M. Georges, D. Mazuyer, J-L. Loubet and A. Tonck, in Ref. 1, p. 263. 13. J. Krim and A. Widom, Phys. Rev., B38 (1988) 12184. 14. J. Krim, D.H. Solina and R. Chiarello, Phys. Rev. Lett., 66 (1991) 181. 15. J. Krim and R. Chiarello, J. Vac. Sci. Technol., A9 (1991) 2566. 16. Ernest Rabinowicz, Friction and Wear of Materials (Wiley, New York, 1965) pp. 94107. 17. I.V. Kragelskii, Friction and Wear (Butterworths, Washington, 1965) pp. 208218. 18. J.B. Pethica and A. Sutton, J. Vac. Sci. Tech., 6 (1988) 2494. 19. J.R. Smith, G. Bozzolo, A. Banerjea and J. Ferrante, Phys. Rev. Lett., 63 (1989) 305. 20. J. Ferrante and G. Bozzolo, in Ref. 1, p. 437. 21. U. Landman, W.D. Luedtke and E.M. Ringer, Wear, 153 (1992) 3. 22. U. Landman, W.D. Luedtke and E.M. Ringer, in Ref. 1, p. 463. 23. J. Leslie, An Experimental Inauirv into the

G.

Nature and Propagation of Heat (Bell and Bradfute, Edinburgh, 1804). 24. Duncan Dowson, Historv of Tribology (Longman, London, 1979). 25. H.B. Callen, Thermodvnamics (Wiley, New York, 1960), p. 63. 26. G.M. McClelland, in Adhesion and Friction edited by M. Grunze and H.J. Kreuzer (Springer Verlag, Berlin, 1990) p. 1.

27. G.M. McClelland and J.N. Glosli, in Ref. 1, p. 405. 28. D. Tomdnek, W. Zhong and H. Thomas, Europhys. Lett., 15 (1991) 887. 29. D. T o m h e k , in Scanning Probe

Microscopy, edited by H.-J. Guntherodt and R. Wiesendanger (Springer-Verlag, Berlin, 1993). Chapter 11. 30. J. Belak and I.F. Stowers, in Ref. 1, p. 511. 31. J.N. Glosli and G.M. McClelland, Phys. Rev. Letts., 70 (1993) 1960. 32. B.J. Briscoe and D.C. Evans, Proc. Roy. SOC.London, A380 (1982) 389. 33. J.A. Harrison, C.T. White, R.J. Colton and D.W. Brenner, Phys. Rev., M (1992) 9700. 34. J.A. Harrison, R.J. Colton, C.T. White and D.W. Brenner, Wear, 168 (1993) 127. 35. J.A. Harrison, C.T. White, R.J. Colton

and D.W. Brenner, J. Phys. Chem., J. Phys. Chem. fl (1993) 6573. 36. J.A. Harrison, C.T. White, R.J. Colton and D.W. Brenner, Surf. Sci., 271 (1992) 57. 37. Donald H. Buckley, Surface Effects in

Adhesion. Friction. Wear. and Lubrication (Elsevier, New York, 1981). pp. 357-373. 38. M. Hirano, K. Shinjo, R. Kaneko and Y. Murata, Phys. Rev. Lett., 67 (1991) 2642. 39. J.A. Harrison, private communication, 1993. 40. H. Yoshizawa,

Y-L. Chen and J. Israelachvili, J. Phys. Chem., 97 (1993) 4128.

41. Y-L.

Chen, C.A. Helm and J.N. Israelachvili, J. Phys. Chem., 95 (1991)

10736. 42. Y.L. Chen and J.N. Israelachvili, J. Phys. Chem., p6 (1992) 7752. 43. J.B. Sokoloff, Phys. Rev., B42 (1990) 760; Wear, 167 (1993) 59. 44. J.B. Sokoloff, Thin Solid Films, 206 (1991) 208; J. Appl. Phys., 72 (1992) 1262.

20

52. "Tribology of Ceramics" National Materials Advisory Board Report 435, National Academy Press, 1988, Washington DC, p. 88. 53. S. Bair, I. Green and B. Bhushan, J. Tribology, 113 (1991) 547. 54. G.J. Johnston, R. Wayte and H.A. Spikes, communication. Tribology Transactions, 2 (1 99 1) 187. M. Hirano and K. Shinjo, Phys. Rev. !&l 55. P.M. Cann and H.A. Spikes, Tribology (1990) 11837. Transactions, 34 (1991) 248. I.L. Singer and H.M. Pollock, in Ref. 1, p. 56. R.J. Hamers and K. Markert, Phys. Rev. 582. Lett., 64 (1990) 1051. W. Zhong and D. TomBnek, Phys. Rev. 57. I.L. Singer and H.M. Pollock, in Ref. 1, p. Lett., B64 (1990) 3054. 586. I.L. Singer and H.M. Pollock, in Ref. 1, p. 569.

45. M. Cieplak, E. Smith and M.O. Robbins, submitted to Nature, 1993 46. B.N.J. Person, D. Schumacher and A. Otto, Chem. Phys. Letts., 28 (1991) 204; Phys. Rev. B, 44 (1991) 3277. 47. C.H. Mack, C. Daly and J. Krim, private 48. 49.

50. 51.

Dissipative Processes in Tribology / D. Dowson et al. (Editors) 1994 Elsevier Science I3.V.

21

The Mechanics of Adhesion, Deformation and Contamination in Friction K.L. Johnson 1, New Square, Cambridge CBl lEY, United Kingdom It is now half a century ago that Bowden & Tabor, first in the Laboratory for Tribophysics in Melbourne and then in the Cavendish Laboratory in Cambridge, revived an interest in friction as a respectable subject for scientific study. They rejected Coulomb's proposition that energy is dissipated in sliding by lifting the asperities of one surface over those of the other and identified adhesion at the interface, inelastic deformation of the solids and contamination of the interface as the principal factors influencing friction. In this paper the present status of these pervading concepts will be reviewed from a macroscopic point of view and, where possible, related to the present microscopic studies of surface interaction described by Singer in the accompanyingpaper. 1. THE COULOMB THEORY AND THE TIME FACTOR

The Coulomb theory of friction, in which the energy expended is attributed to lifting the asperities of one surface over those of the other, is normally discredited by the argument that the work done against the contact load in lifting is recovered when the surfaces move together. Although the model of an asperity encounter shown in Fig.1 is usually illustrated by rigid asperities, even if they are elastic there will be a normal impulse produced by the encounter which will generate wave motion and vibration. What then is the probable magnitude of this so called 'acoustic loss'?

circular area of the surface, of radius a, like a spring in parallel with a dashpot, in which the energy dissipated in the dashpot corresponds to the acoustic loss. The time constant T of this system is given by T

2a/c0

(1)

where co (= E/p) is the speed of longitudinal waves in the solid. Referring to Fig. 1, if an asperity encounter takes place in*a sliding distance L, the time of the encounter t = L/V, where V is the velocity of sliding. Assuming the impulse to be sinusoidal with a period 2t* , the ratio of the energy dissipated in the dashpot i.e. acoustic loss, to the maximum strain energy stored in the spring i.e. strain energy of deformation of the asperity, is given 3Y

V L co

2a.T - n--a -2t*

Figure 1. Interacting asperities in sliding contact. Interaction time 2t* = interaction distance L/sliding speed v. It is explained in ref.[ 13 that an elastic half-space responds to a sinusoidal impulse applied to a

The acoustic loss is therefore clearly negligible provided the sliding speed V is small compared with the elastic wave speed c,. Similar considerations of the time factor apply to other mechanisms of energy dissipation. Plastic deformation involves dislocation movement. The strain field and energy of a dislocation is unaffected by its speed of movement until the speed approaches the elastic wave speed c, . This means that plastic flow of asperities is fully dissipative and independentof rate effects provided V << c,. The case of viscoelastic materials is more complicated. The simplest viscoelastic material -

22

the 3-parameter solid - has an instantaneous modulus E,, a relaxed modulus E, and a time constant (relaxation time) T = / E,, where q is the viscosity of the dissipative element. In this case maximu2 dissipation occurs when the time of loading t coincides with the relaxation time T of the material

circumstances adhesion between the solid surfaces plays a minor role in the frictional process.

I min

--

/

I I

/ > /ENGINEERING COMPONENTS

Is

i.e. when

V

= L/r

(3)

At sliding speeds either much greater than or much less than this value, the deformation will be elastic with modulus E, or E, respectively. This behaviour has been demonstrated very effectively in rolling friction by Greenwood & Tabor [2]. Many polymers, of course, have a more complex relaxation spectrum with more than one relaxation time. The 'time factor', discussed above in continuum terms in relation to the macroscopic interaction of sliding asperities, carries over to the microscopic studies of friction with the atomic force microscope or through molecular dynamics simulations. In this case the characteristic sliding distance is the atomic spacing: the characteristic time is the period of oscillation of the atoms about their minimum energy positions (e.g. McClelland & Glosi [3]). The map displayed in Fig.2 is adapted from Goddard [4]. For the practical range of sliding speeds, it shows the length and time scales of the different regimes of behaviour. Whether or not an event is dissipative depends upon the relation of the time of the event to the characteristic time of the dissipative process.

wf

('

o

n t 1n uu m

+

IN

1UUl

1-

lttlln

I m

LENGTH

Figure 2. Length and time scales in sliding contact at different speeds. We will start by considering the stationary contact of a sphere (radius R) with a plane, under a normal load, as a model of an asperity contact in an extended surface. According to the Hertz theory a load PI will result in a circular contact area of radius a given by

2. ADHESION AT THE CONTACT OF SOLIDS

a3 = 3RP1/4E*

Bowden & Tabor proposed that contaminant free surfaces form adhesive 'junctions' at the tips of the contacting asperities and that, during sliding, friction predominantly comprises the force to shear those junctions. Not surprisingly this proposition has met with considerable scepticism on account of the observation that such surfaces do not generally remain in adherence when the compressive load is removed. Some, but not all, of the difficulties involved in this proposition have been resolved by subsequent developments in contact mechanics, which have shown that in most practical

where 1/E* = [(1-vl2)/E1 + (1-~2~)/E2 ] ; E and v are Young's modulus and Poisson's ratio respectively. If the load is reduced to P(< PI), while the surfaces remain adhered together at the initial radius a , the pressure distribution takes the form shown in Fig.3a, having an infinite tension at the periphery. This result was used by me in 1958 [5] to explain why, in spite of initial adhesion, asperities would separate when the load was removed. But that was before fracture mechanics had taught us to live with stress singularities. In 1971 Johnson, Kendall & Roberts

(4)

23

[6] used the Griffiths' concept of balancing the rate of release of elastic strain energy with the change in surface energy w to obtain an equilibrium relationship between load P and contact radius a. Their results can be obtained more directly by using fracture mechanics concepts.

from which the graph of x(=nZ2)against P is plotted as curve I in Fig. 4. We note that when the load is reduced to zero the surfaces remain in contact with an area A, = 1 ~ 2 ~ They 1 ~ . snap apart when A has decreased to nn2I3, which requires a tensile (negative)force F, = -1 / 2 to pull them apart. i.e.

P, = 3nwR/2

(8)

Figure 3. Pressure distributions in adhesive contact. (a) JKR theory [6]; (b) DMT theory [12]. We hrst introduce non-dimensionalvariables:

P = P/(3mR) B = d(9wR2/4E*)lB and Pi = Z 3 The singularity in tension at the edge of the contact in Fig.3a can be expressed in terms of a stress intensity factor:

KI = P&d(m)

(3

where Pa is the effective force of adhesion. The strain energy release rate G is then given by

which, when equated to the surface energy w, gives

from which

Hence the net load F(= Fl - Fa) can be written

These results have been confirmed by many exueriments with low modulus elastic solids such as gehne [a]. The second term in eauation (7). i.e. (2F1)ln is Fa when &e iontact the effectiveforce of &ion size is a. It appears as the horizontal segment between curve I (JKR) and curve II (Hertz) in Fig.4. Thus the contribution of adhesion, expressed by the ratio of Pa to P1 ,decreases with the square root of the nominal Hertz load P1 . For metals the surface energy w has a value of about 1.0 J /m2. For an elastic sphere of radius 5mm, the ratio PJP1 will be less than 1.0% when the load P exceeds 10 N. The pull-off force P, is only 0.024 N. In these circumstances adhesion is clearly an effect confiied to light- load situations such as particle-particle interaction in colloidal suspensions. In the multi-

;

G = K~DE*

Pz= 8pwaE* = 6pwRP1

Figure4. Area - Load relationships in adhesive contact. I: JKR theory (reversible): 11: Hertz theory (no adhesion): III-IV: Loading-unloading cycle ABCD.shows effect of inelastic deformation.

(6)

24

asperity contact of rough surfaces,during unloading, the higher asperities progressively break the lower adhesive junctions until there are only a few junctions left and the final 'snap-off force is negligible [7]. It is not surprising that the presence of adhesion between contacting bodies is not readily detectable. There are circumstances,however, which lead to an enhanced effect of adhesive forces. First, if initial loading of the sphere (hard) against a plane (soft) produces a significant plastic indentation, the subsequent elastic recovery and pull-off force is governed by the relative radius of curvature R' between the sphere and the indentation [8], where

R = 4E* a/3xH = 4E*P1n/3(~H)3n (9)

P is the initial load and H is the hardness of the softer surface. Substituting R' for R in equation (8) gives the pull-off force Pd =2wE*(P/xH3 )1/2

G'= w + D'= w + a'G

(10)

where G is the elastic strain energy release rate during 'crack extension. In the perfectly elastic situation (the Griffith crack) G = w, which should

(1la)

With a closing crack (increasing contact area) the work done by surface forces w is reversed and the elastic strain energy increases so that in this case 4"= -W + D" = -W + a"fl

(1 1b)

from which the effective surface energy during opening wi may be written

wi =G'=w/(l-a')= and during closing

Large adhesion would be expected therefore when the hardness is small. This was found to be so by Tabor [9] in experimentsusing tin, lead and indium. Another, more subtle, effect acts to enhance adhesion. It was observed during experiments with rubber that the contact area varied with load according to equation (7) but that the effective work of adhesion during separation wi increased with velocity of separation and greatly exceeded that during compression wf. The reason for this effect lies in the infinite stress and strain predicted by the JKR theory at the edge of the contact area (Fig.3). Of course the actual stress will be finite, but it is still large, and equal to the ultimate strength of the material, of order E/30 for a crystalline solid. Consequently as the contact area changes there will inevitably be some internal dissipation viscoelastic or plastic - in this zone. The configuration of Fig.3a may be regarded as an external crack penetrating a ligament of material radius a. The stress singularity corresponds to a mode I stress intensity factor

KI= (2GE*)lR

be perfectly reversible, whether the crack is opening or closing, i.e. whether the contact area is shrinking or growing (Fig.4, curve I). If the zone of inelastic deformation is very local to the crack tip, i.e. small compared with a, we can use linear elastic fracture mechanics concepts. Assume that a fraction a of the elastic strain energy released G is dissipated, so that if D is the dissipation rate, with an opening crack (decreasing contact area) we can write

wi =G"=w/(l+a")=

k'w k " ~

Wb)

where k' > 1.0 and It'< 1.0. The correspondingcurvesof increasing (119 and decreasing (IV) area A as a function of load P are added to the non-dimensional plot in FigA When the surfaces first touch they snap into contact at point A. During compression the area increases, following curve I11 to pt.B, with w?= k" w. When the load is reduced, at first the contact area remains unchanged until, at C, the energy release rate is sufficient to peel the surfaces apart with an apparent surface energy wi = k' w. Peeling continues until the surfaces snap apart at D where the (tensile) load = -Pc. Greenwood & Johnson [lo] have analysed this behaviour for a linear viscoelastic solid and shown that k' is related to the ratio of the instantaneous elastic modulus E, to the relaxed modulus E,, which can have a value of two or three orders of magnitude, while k" is so small that the surfaces come together as though there were no adhesion. Since viscoelastic dissipation is rate dependent,k' is found to be an increasing function of peeling velocity. These conclusions are well supported by experiments using rubber [ll]. When the inelastic

25

dissipation is by plastic flow, as in metals, the conclusion is the same: when peeling the work of adhesion is enhanced by a factor k' (>LO), which is a function of ( & l o y )where 6 is the maximum adhesive stress in the adhesive zone and or is the yield stress of the material. This effect is well known in the fracture of metals, where the work of fracture greatly exceeds the surface energy of cleavage. When the length of the 'process zone' at the edge of the contact over which the adhesive forces act is no longer small compared with the radius of the contact a, the JKR theory becomes inappropriateand a better approximationis provided by the DerjaguinMuller-Toporov (DMT) theory [12]. In this model the deformed shape is assumed to be that given by Hertz and the adhesive forces act o_utside the contact area, as shown in Fig.3b. The P :Z relationship, equivalent to equation (7) of the JKR theory, is

F = F1 - 213 = Z3 - 213 Using the Dugdale model of elastic-plastic fracture, Maugis [13] has shown that the transition from JKR to DMT conditions depends upon the parameter

h=

26 ( 1 6 n ~ E/*9R)'I3 ~

where 6 is the peak adhesive stress. For the JKR model to apply h > 1.0. Taking 6 to be the yield stress this condition requires R to be greater than about 20 p m for a polymer sphere and about 2 pm for a metal sphere. 3. STATIC FRICTION AS MODE I1 FRACTURE

We shall start this section by accepting Bowden & Tabor's proposition that clean surfaces,

particularly in an out-gassed environment, adhere together with a strength (yield stress) approaching that of the bulk solids. An asperity contact is again modelled by a sphere pressed into contact with a plane by a normal force P, giving rise to a contact area of radius a, given by the JKR theory equation (7). The normal traction is that shown in Fig.3a. A monotonically increasing tangential force Q is

now applied, which gives rise to the tangential traction shown in FigSa:

The singularity at r = a corresponds to a mode I1 stress intensity factor KII= Q / (4m3 )In

(16)

in addition to the mode I factor KI given by equation (5). There has been considerable interest recently in mixed mode interfacial fracture in connection with debonding of composite materials. There it is usually assumed that an interfacial fracture will proPogate when

K: + W * I l2 = K,:

(17)

where KI, is the fracture toughness in tension and , found by experiment to be less than unity. When this criterion is applied to the adhesive contact of a sphere with a plane [14], it predicts that the application of a tangential force causes the surfaces to peel apart until the radius a and pressure distribution are Hertzian. This initial peeling, caused by the application of a tangential force to an adhesive contact, has been observed in rubber by Savkoor & Briggs 1141 but not by Israelachvili with mica surfaces [15]. It is difficult to be precise about what happens next. By analogy with a mode I crack, linear elastic fracture mechanics would say that Q could be increased until KII ,given by equation (16), reaches the value of the fracture toughness in shear KII,. whereupon the junction would shear in an unstable way (FigSa). But this picture ignores the fact that in mode I1 the crack faces remain pressed together behind the crack front ,which will resist slipping by a shear stress s. This situation, depicted in FigSb, has been analysed by Savkoor [161. If the tangential force is controlled, the junction fractures catastrophically when Q = Q,. With a large number of such junctions in an extended surface, each junction will be 'displacement controlled by the hinterland, thereby delaying unstable slip until the critical displacement6, is reached. The contact then slips until Q falls from Q, to Qs(= xa2s). This

p = KIJKII,

26

I

I

I F a - -

Q~= 2 a 6 a

KII~

ai

Figure 5. Static friction as mode I1 fracaUe. (a) Simple mode I1 fracture (unstable); (b) Savkoor's model (unstable if Qs< Qc); (c) stable sliding (Qs > Qc). stick-slip behaviour will only occur if the initial strength of the interface is greater than that after slip

Q,= rca2 > > Q ~= (4m

3 112 K~~~

hasoccurred.

Before accepting this model, we must consider the conditions in which elastic fracture mechanics is appropriate, i.e. that the process zone size at the crack tip should be small compared with the contact radius a. For this to be so,

i.e.

(18)

in which the maximum value of s is the yield stress k in shear of the softer material. There is little data

27

for KII, ,but if it is approximated by KI,,we have K1Jk for metals = 5-50 (pm)1/2;for polymers = 0.5-5Q~m)~”; and for ceramics = 0.04-0.1(pm)1~. The mean radius a of asperity contacts is estimated to be about 20 pm, from which it may be deduced that only ceramics clearly satisfy the condition (18) and metals do not. In the case of an eWtic-perfectlyplastic material (metal), with a strong adhesive bond (s=k), the sequence of events depends upon the intensity of the normal load. If the parameter (aE*/Ray)is less than about 2.0 the stresses due to the normal load will lie within the elastic limit [l]. The subsequent application of a tangential load causes a thin plastic layer to spread across the interface from the sides until complete ductile fracture occurs when Q = na2k (Fig.5~).At the other extreme, if (a E*/ Roy) exceeds about 30, the contact will be fully plastic. On first loading, the contact area increases as the tangential force is increased, until the contact pressure has dropped from about 5.6k (i.e. 2.8 ay) to k and the shear traction has increased to the value k. Shearing of the junction then takes place at a , agreement with coefficient of friction ~ 1 . 0 in experiments on clean ductile metals. This is the process of junction growth, proposed by Tabor [171 and analysed in plane strain by Johnson [181. If s < k this process is interrupted, and steady sliding takes place, when the mean shear stress Q/m2reaches the value s. The material for which the Savkoor model is appropriate, indeed for which it was conceived, is rubber, which has no yield strength in the conventional sense. The low elastic modulus enables it to mold itself to irregularities on the mating surface, so that the real area of contact approaches the nominal area. High adhesion at rapid peeling rates results in the high friction associated with dry rubber. Savkoor [161 conducted friction experiments with interacting model asperities in tangential motion. The surfacesadhered as the contact area grew, followed by large shear deformation. Frequently the rubber fractured in bulk before slip occurred at the interface. Low modulus rubber displays a unique mechanism of frictional ‘slip’ and energy dissipation, which depends directly upon its adhesion Properties described above. A rubber sphere in contact with a harder plane surface undergoes large deformations under the action of a tangential force. The region of singular compression just at

the rear of the contact buckles, as shown in Fig.6, to form a fold in the rubber surface. This then travels through the contact as a ‘wave of detachment’ (Schallamach wave [19]). Thus the sphere quires an apparent sliding velocity V without any actual slip at the interface. The wave moves through the contact area with velocity v by peeling at its leading edge and reattachment at its trailing edge. Thus the material is taken round the cycle shown in Fig.4; the difference in the work of adhesion during peeling from that recovered during reattachment accounts for the frictional energy dissipation. It follows that the correspondingfriction force Q is given by

Q = (k‘- k“) w v/XV

(19)

where 5 is the spacing of the waves and v >> V.

-

LI o Bulk wl.

v

I

Figure 6. Sliding of rubber: Schallamach waves of detachment. Wave speed v >> sliding speed V. 4. STEADY SLIDING : THE EFFECT OF

CONTAMINATION

In most practical situations, unless the sliding speed and/or temperatureare high, the conditions of high adhesion leading to seizure do not arise. This is the consequence of contamination, natural or artificial. Natural contaminants include oxide films on metals, adsorbed water vapour and organic matter. Artificial contaminants consist of lubricant films, surface layers and surface treatment. As we are always being reminded in this institution (INSA), in service the interfaceacquires debris from wear and from the environment. Modelling all this still has a long way to go. For lubricant films between smooth surfaces the frictional resistance to sliding (traction) is governed by the shear properties of the lubricant at the ambient conditions of pressure, temperature and shear rate (see Fig. 7). We note that, at a given

28

sliding speed, the shear rate increases inversely as the film thickness. This introduces a transition from the Newtonian relationship in classical hydrodynamic conditions, through the nonNewtonion equationsof EHL, to the equation which is found to govern boundary lubrication by organic liquids i.e.

s = so + up

I mm 10-3

+

1 7

(20)

where p is the pressure, and and u are constants. When the film thickness is reduced to a few molecular layers (order 1.0 nm) the properties of the fluid depart appreciably from those measured in bulk. There is a marked increase in viscosity and a tendency for organic surfactants to arrange themselves in a regular molecular pattern, i.e. to adopt the structure of a solid. The apparatus developed by Israelachvili [15], in which very thin films are sheared between molecularly smooth crossed cylinders of mica, are particularly revealing of the interaction of adhesion and fluid properties in sliding friction. During sliding in dry air at light loads, the presence of adhesion is apparent from the fact that the measured contact area A (= na2) follows the JKR relationship (7), rather than that of Hertz. By fitting equation (7) to the area measurements, values of the surface energy w and the effective elastic constant E* for the mica surfaces can be obtained. Friction measurements in this region give values which are directly proportional to the measured area, implyin a constant interfacial shear strength so = 2 x 10 N/m2 (p > 2). Due to the effect of adhesion, a friction force could be measured at a negative load (Fig.8). At a high load the surfaces became rough and s e w by flakes of wear debris: adhesion vanished and friction varied with load according to Amontons' law (p = 0.44). At high humidity, when a water film condensed on the surfaces of the mica, adhesion vanished and the friction became very low. This experiment illustrates the common features of unlubricated sliding: roughening of the surfaces and/or contamination, which destroys adhesion between them and replaces it by shear in the interfacial layer. A further effect of adhesion was found by Israelachvili [15]: with certain surfactant films the effective surface energy was found to be greater when the surfaces were being pulled apart (receding contact) than when they were coming together

1-

10-6

.-

ER L

( N e v to ni anI

-

T =

'ol

ti

e.9. Z

N on N ev ~

t.)

7(P>Tj.f(l)

T, sinh-'(TP/T.)

Bonndary Lubrication

104

I i

Enbancnd viscosilg, liquidlrolid transitions

Figure 7. Lubricant film thickness chart, showing regimes of behaviour. Note that the shear rate 9 is inversely proportional to film thickness leading to non-Newtonian response of thin films.

I

I

I

I

I

N

9

Normal Load. L (x 10N)

Figure 8. Friction experiments with crossed cylinders of dry smooth mica [HI.Undamaged surfaces: contact area follows JKR, interfacial stress sc = constant (p > 2). Damaged surfaces: no adhesion, friction follows Amontons' law (p= 0.4).

29

(advancing contact), much as described in 12 with viscoelastic solids. In this case however, the cause would appear to be different. The bond between the films on each surface strengthens with time through the process of 'interdigitation' of the organic molecules, which leads to an increase in adhesion energy with contact time. Returning to the more practical situation of high loads and thicker films, liquid, solid or both, it is clear that adhesive forces do not influence directly the deformation of the solid surface or the force of friction. From the point of view of contact mechanics it is sufficient to know or to idealise the shear strength of the film in the form s=f@,T,j)

(21)

where is the shear rate. Of course, adhesion forces may influence the details of the shear process such as slip at boundary or interaction between solid 'third body' particles. We shall hear a lot more about this central aspect of frictional behaviour during the remainder of the Symposium. 5. DEFORMATION LOSSES

In most circumstances losses through inelastic deformation of the sliding solids is appreciably less than the dissipation in the interfacial film. In fact deformation losses are probably more important in relation to wear and surface fatigue than they are in relation to friction. An exception is provided by a skidding tyre on a wet road, where the interfacial friction is low and deformation losses arise from ploughing of the tyre by the asperities on the road surface. Thus, in a tyre, high hysteresis is required in response to ploughing of asperities, combined with low hysteresis in the bulk deformation in normal rolling contact. Following the reasoning which led to equation(3), Bond [21] showed that a rubber could be formulated whose relaxation time would be close to the time of passage of the material through an asperity contact, but far from the time of passage through the bulk contact patch with the road. The discussion in the remainder of this section will be confined to materials in which inelasticity is due to plastic deformation in one or both surfaces. To assess the severity of plastic deformation when the asperities of a hard surface plough a softer one

we consider the map shown in Fig9 which refers to a rigid cylinder sliding perpendicular to its axis over the surface of an elastic-plastic solid. The abscissa of the map is the non-dimensional parameter (aE*/Rk), which has been shown to correlate the transition from elastic to plastic behaviour in a static indentation [l]. The ordinate is the friction factor f = s/k, where s is the interfacial shear stress and k is the yield stress in shear. At the left of the diagram the deformation is perfactly elastic and specifiedby the Hertz theory. At the right hand side in the 'fully plastic' zone - the stresses and deformation approximate to rigid-plastic models of the type proposed by Challon & Oxley for a sliding wedge [22,23]. In the intervening zone both elastic and plastic strains contribute to the overall deformation. The boundary between the elasticplastic and fully plastic zones has been sketched in and awaits further analysis in order to fix its position more precisely. For a random rough surface the Greenwood & Williamson theory gives the mean contact size a to be ( O $ I C , ) ~ ~ where 6, and K, are the r.m.s. height and curvature respectively. Thus for multi-asperity contact of a random rough surface, the parameter (a E*/Rk) becomes (E*/k)(o, IC,)'~.This will be recognised to be Greenwood & Williamsons' plasticity index (with H replaced by k = W6). The ranges of this parameter for surfaces of different materials and differentroughnesses are superimposed on the map. The region of the map which has received most attention m n t l y , on account of its importance for wear and surface fatigue, is the zone in the vicinity of the shakedown boundary. Surfaces in continuous sliding experience many repeated asperity interactions so that it is the steady 'run-in' state which is relevant. The running-in process has been analysed on the basis of shakedown theory. The hypothesis is made that those asperities which deform plastically change their profile in such a way as to carry the maximum load whilst not exceeding the shakedown limit. If such a state cannot be found then the surfaces will not shakedown, and continuous plastic deformation would be expected The unit event consists of an encounter in tangential motion of two individual asperities, as shown in Fig.10 [N]. Asperities of equal hardness can always reduce their height and curvature to reach a mutual shakedown profile but if one surface is hard the limit for the other is reached when it is completely flattened. Starting from the unit event,

30

of the model and the experiments of Williamson et al. [26]is remarkably good. The shakedown limit is reached when the soft surface is deformed into a flat (zero height deviation).

I

-

Load

3

.g LL

0.1 0.05

-

4-4 madm

--ELASTIC

t h c - p u s n c

',

I---+ Cerodcs Noh I

-A- ~ U YPMC

--

100

10

Figure9. Deformation map of sliding rough surfaces. os & K~ are mean summit height & curvature. Low values of Y : shakedown model [27]; high values of Y :slip-line models [2223].

Figure 11. Running-in by plastic shakedown of a random rough surface [23. Note reduction in height variation with increasing load. Theory compared with experiments of Williamson et al. [%I. tb)

um

II

Figure 10. Plastic shakedown in a repeated asperity encounter. Note height and curvature are reduced; the shakedown limit is reached when one surface is flattened.

the running-in of two nominally flat, randomly rough surfaces, one hard and one soft, has been modelled. If the soft surface initially has a Gaussian height distribution, this appears on 'normal' probability paper as a straight lineofgradient proportional to the standard deviation (Fig.11) [25]. After repeated sliding the height distribution becomes bi-modal; the plastically deformed asperities show a r e d u d variation in height (and curvature). The effect becomes more pronounced as the load is increased and the shakedown limit is approached. The agreementbeween the predictions

If the load is increased above this limit plastic deformation will take place with the passage of every asperity, causing plastic dissipation and eventual surface damage. The mechanics of accumulating plastic strain i.e. ratchetting, which occurs in these circumstances has been analysed by Bower & Johnson [27]. At friction coefficients in excess of 0.25 plastic deformation is confined to the near-surface layer. The stress cycle due to the frictionaltraction experienced by surface elements in sliding contact is shown in Fig.l2a&b. (The stresses due to the normal pressure p are hydrostatic, i.e. oxx= ozz = -p, and so do not appear). The plastic strain cycles are shown in Fig.12~. The direct strain increments, A E ~ :in the compression and tension sectors cancel out, but the shear increments A E are ~ cumulative, leading to the large plastic stnu observed in the tracks of sliding surfaces. The strain increment acquired in each cycle AeL , however, is small: only a few

31

s-'

Figure 12. Plastic ratchetting of a surface layer by a hard cylindricalasperity in sliding contact. (a) Elastic stresses at surface; (b) stress c cle OABCO at yield in am - ra stress space: (c) plastic strain cycles, showing accumulation of shear E, .

4

times the elastic yield strain. In the example shown

in Fig.12 the energy dissipated in this plastic deformation is less than 1.0% of the dissipation by friction at the interface.

(3)

With perfectly elastic solids wf = w = the thermodynamic work of adhesion (surface energy) which is reversible. Inelastic deformation, plastic or viscuelastc, in the zone of separation enhances wf during separation and attenuates it when the contact area is inclt-asing.

(4)

Clean smooth surfaces do adhere strongly. For the static friction of such surfaces to be modelled as a mode II fracture it is necessary for the contact size a >> (4/7C)(KIIdS)2 where s represents the interfacial shear strength s = f x yield stress k. This condition is satisfied for rubber and hard ceramics, but polymers and metals 'slip' by bulk shear. When s = k shear takes place in the solid, when s < k slip occurs at the interface.

6. CONCLUSIONS Acoustic losses are negligible at sliding speeds which are small compared with elastic wave speeds. Rate-dependent friction arises from rate dependent Properties of the solids or the interfacial film. Adhesion in Hertz contact increases the contact area and requires a tensile ('pull-off') force to separate the surfaces. It can be characterised by a work of adhesion wf or by a fracture toughness kIc = (2 wf E*)ln.

32

(5)

Fluid films of a few molecular layers may exhibit properties which differ from those in b u k enhanced viscosity and attachment to the substrate in an ordered way characteristic of a solid. Adhesion forces increase the contact area and give rise to a detectable friction force at negative loads. The adhesion effect becomes negligible at high load, i.e. P >> WfR.

(6) With thicker films between smooth surfaces friction is determined entirely by the shear strength of the film s . In boundary lubrication (10-100 nm), s = + up.

(7) The contribution to friction from inelastic deformation ,viscoelastic or plastic, of the solid surfaces is generally small compared with that arising from shear of the interfacial layer. (8)

In continuous sliding rough surfaces tend to run-in to a steady elastic (shakedown) state. In theory this is always possible with surfaces of equal hardness. If one suface is comparatively hard (under forming) a limiting pressure for shakedown exists; if this is exceeded plastic ratchetting occurs leading to large accumulatedplastic strains.

(9)

In attempting to relate molecular friction, measured by the atomic force microscope or modelled by molecular dynamics, to continuum models on the macroscopic scale, it must be recognised that there is an intermediate length and time scale (see Fig.2) with independentphysical phenomena. This is the scale of dislocations and microstructure: 10 - 103 nm.

REFERENCES 1. K.L. Johnson, Contact Mechanics. C.U.P. 11, 1985. 2. J.A. Greenwood & D. Tabor, The friction of hard sliders on lubricated rubber, Roc.Phys. Soc. 71 (1958 ) 989.

3. G.M. McClelland & J.N. Glosi, Friction at the atomic scale, in Fundamentals of Friction, NATO ASI, Ser.E, 220, (1992) 405 Khmer. 4. W. Goddard, Tribology of ceramics, Nat.Mat.Ad.Bd.Rpt.435, Nat.Acad.Press, Washington DC, (1988) 88. 5 . K.L. Johnson, A note on the adhesion of elastic solids, Brit.J.Appl.Phys. 9, (1958) 199. 6. K.L. Johnson, K. Kendall & A.D. Roberts, Surface energy and the contact of elastic solids, Proc.Roy.Soc.London, A 324 (1971) 301. 7. K.N.G. Fuller & D. Tabor, The effect of roughness on the adhesion of elastic solids, Proc.Roy.Soc. London, A 345 (1975)T 327. 8. K.L. Johnson, Adhesion at the contact of solids, Roc.Congress Th. & Appl. Mech. Ed. Koiter, North Holland. 1976. 9. D. Tabor, Hardness of Metals, Oxford 1951. 10. J.A. Greenwood & K.L. Johnson, The mechanics of adhesion of viscoelastic solids, Phi1.Mag.A 43 (1981) 697. 11. D. Maugis & M. Barquins, Fracture mechanics and the adherence of viscoelastic bodies, J.Phys.D. 11 (1978) 1989. 12. B. Derjaguin, V. Muller & Yu Toporov, Effect of contact deformations on the adhesion of particles, J.Col1. & Interface Sci. 53 (1975) 314. 13. D. Maugis, Adhesion of spheres: The JKRDMT transition using a Dugdale model, J.Coll. & 1nt.Sci. 150 (1992) 243. 14. A.R. Savkoor & G.A.D. Briggs, The effect of a tangential force on the contact of elastic solids in adhesion, Proc.Roy.Soc. A 356 (1977) 103. 15. J.N. Israelachvili, Adhesion, friction and lubrication of molecularly smooth surfaces, in Fundamentals of Friction, NATO AS1 Series E v 220,1992. 16. A.R. Savkoor, Dry adhesive friction of elastomers, Doctoral dissertation, T U Delft, 1970. 17. D. Tabor, Junction growth in metallic friction, Proc.Rov.Soc.A 251 (1948) 378. 18. K.L. Johnson, Deformation of a plastic wedge by a rigid flat die under the action of a tangential force, J.Mech. & Phys.Solids, 16 1968 395. 19. A. Schallamach,How does rubber slide?, Wear 30 (1971) 301.

33

20. A.D. Roberts & A.G. Thomas, Adhesion and friction of smooth rubber surfaces, Wear, 33 (1975) 45. 21. R. Bond, A new tyre polymer improving fuel economy and safety, Proc.Roy.Soc.A, 399 (1985) 1. 22. J.M. Challen & P.L.B. Oxley, The different regimes of friction & wear, Wear 53 (1979) 229. 23. J.M. Challen & P.L.B. Oxley, Slip line fields for polishing & related processes, 1J.Mech.Sci. 26 (1984) 403. 24. K.L. Johnson & H.R. Shercliff, Shakedown of 2-D asperities in sliding contact, 1nt.J.Mech.Sci. 34 (1992) 375.

25. A. Kapoor & K.L. Johnson, Steady state topography of surfaces in repeated boundary lubricated sliding, Proc. 19th.Leeds-Lyon Symp.on Tribology, Leeds, 1992. 26. J.P.B. Williamson, J. Pullen & R.T. Hunt, The shape of solid surfaces, in Ling F.(ed.) Surface Mechanics,New York, 1969. 27. A.F. Bower & K.L. Johnson, The influence of strain hardening on cumulative plastic deformation in rolling and sliding line contact, J.Mech. & PhysSolids, 37 (1989) 471.

This Page Intentionally Left Blank

SESSION II LIQUID AND POWDER LUBRICATION Chairman:

Professor J M Georges

Paper 11 (i)

A Rheological Basis for Concentrated Contact Friction

Paper 11 (ii)

On the Theory of Quasi-Hydrodynamic Lubrication with Dry Powder: Application to High-speed Journal Bearings for Hostile Environments

Paper 11 (iii)

The Influence of Base Oil Rheology on the Behaviour of V1 Polymers in Concentrated Contacts

Paper 11 (iv)

Temperature Profiling of EHD Contacts Prior to and During Scuffing

Paper 11 (v)

Computational Fluid Dynamics (CFD) Analysis of Stream Functions in Lubrication

Paper 11 (vi)

Shear Properties of Molecular Liquids at High Pressures a Physical Point of View

-

This Page Intentionally Left Blank

Dissipative Processes in Tribology / D. Dowson et al. (Editors)

37

CP 1994 Elsevier Science B.V. All rights reserved.

A RHEOLOGICAL BASIS FOR CONCENTRATED CONTACT FRICTION

Scott Bair and Ward 0. Winer Georgia Institute of Technology, School of Mechanical Engineering, Atlanta, GA 30332-0405 It has been observed in boundary lubrication and in some aspects of elastohydrodynamic lubrication that friction is nearly Coulombic in nature - the friction coefficient is only weakly dependent upon load and sliding velocity. In some instances the friction coefficient may be so similar in the boundary and EHD regimes that friction alone does not clearly discriminate the transition from one to the other. These attributes of liquid lubrication would seem enigmatic. However, recent observation of slip planes (shear bands) within a pressurized liquid film suggest that a low molecular weight viscous liquid possesses a "material internal friction coefficient" which is a material property of the lubricant and represents the ratio of shear stress to compressive normal stress at which slip within the film is incipient. The friction coefficient of the contact is then a consequence of and quantitatively related to the lubricant material internal friction coefficient. The Mohr-Coulomb failure criterion is introduced as a predictive method for slip. Mohr-Coulomb defines two possible orientations for stress induced shear bands. Both are experimentally observed in a highpressure flow visualization cell and the measure of the included angle between the types of bands is consistent with theory. The concept of a first normal stress difference (once the subject of much speculation in lubricated contact studies) must be introduced to account for the orientation of the shear bands with respect to the principal shear directions. 1. INTRODUCTION

In spite of the great progress made in understanding hydrodynamic lubrication and particularly the quantitative prediction of film thickness, the coefficient of friction in concentrated contact is still often dealt with as a disposable parameter in numerical analyses. Boundary and elastohydrodynamiclubrication have been recognized as separate regimes of concentrated contact lubrication since the EHD solution of Ertel-Grubin. However, the delineation of these regimes is neady always in practice based on the magnitude of the film thickness relative to surface roughness rather than a transition in friction. Friction in boundary lubrication is usually modeled as Coulombic with a coefficient of about 0.10 to 0.15. Friction in sliding EHL can also reasonably be modeled as Coulombic except at very high sliding velocity with a coefficient of about 0.03 to 0.12. In some experiments the friction coefficient varies continuously and smoothly as the lambda ratio is reduced from very high values to much less than unity. Recent EHD analyses

which address roughness (eg. Ref [l]) have pointed out that lubricant rheology is active in separating solid boundaries and transmitting shear force even when roughness interactions are important. Johnson [2] recognized boundary and EHD regimes as manifestations of the same lubricant rheological response. Much attention has been paid in the literature to the search for a general rheological constitutive equation for liquid lubricants at high pressure [3,4]. The task is further complicated by rhe observation of mechanically induced (not be confused with thermal or "adiabatic" shear bands which are simply a solution to the combined energy and momentum equations [S]) shear localization in liquids [a] under combined pressure and shear stress. Constitutive behavior by definition excludes localization. It is now apparent that much of the departure from Newtonian behavior which has been attributed to constitutive behavior is actually a result of localization in the form of shortlived shear bands. This paper will attempt to bridge the gap between constitutive modeling and recent observations of localization by offering a reasonable

38

rheological constitutive equation and introducing a failure criterion for predicting localization. 2. NEW OBSERVATIONS OF MECHANICAL SHEAR BANDS

The High-Pressure Flow Visualization Cell which we use to optically observe shear bands has been described in detail in Ref. [6] as well as the experimental procedures and preliminary results. It was shown that at a critical shear stress which marked the limit of linear response, an intermittent slip occurred across visible bands. Evidence has been introduced [7] which supports the existence of a mechanism within an operating EHD film, which scatters light in directions consistent with bands observed in flow visualization. In the same paper the existence of two types of bands with differing orientation was introduced. Figure 1 is reproduced from that paper to illustrate the orientations of the two types. New observations which give insight into the slip mechanism are presented in the next sections.

Figure 1. Two types of mechanically induced shear bands

Molecular orientation under stress gives rise to optical anisotropy - the refractive index, n, is different in different directions. Birefrigence observationscan be used to determine the principal normal stress difference, Ao, and the orientation of the principal stress axes if a suitable calibration of the birefrigence, An, can be obtained. Such a calibration is not possible with the flow cell. However, some generalizations regarding the stress distribution in the flow field may be obtained. The High-Pressure Flow Visualization Cell was placed between crossed polarizes See Figure 2. White light was filtered to produce a narrow band at 605 nm. The polyphenyl ether, 5P4E, was the model lubricant. Temperature was 23°C and pressure was 241 MPa. The shearing force was increased with time until shear bands were observed. The interference pattern shown in Figure 2 was obtained just before the shear localized. This fringe pattern disappeared at the time the shear bands formed. Similar experiments were performed with the crossed polarizers placed at eight different angles with respect to the shear direction equally spaced over a span of 180" in an attempt to determine the extinction angle. No effect of orientation of the polarizer/analyzer pair was noted on the contrast or geometry of the fringes or shear bands.

Figure 2. Flow birefringence in 5P4E at 23°C. 241 MPa.

2.1 Birefrigence

Flow birefrigence has been useful for stress analysis in flowing liquids in a manner analogous with photoelasticity in transparent solids [8].

Apparently, the high-pressurewindows which are sapphire are performing as fractional wave plates to eliminate the extinction angle effect [8] and so it

39

was not possible to obtain the principal stress directions. It is possible to obtain the stress distribution in a qualitative sense. If the stress-optic function is monotonic [9], then the fringe order is a representation of the relative magnitude of the principal normal stress difference (and the principal shear stress). Referring again to Figure 2, the zeroeth order fringe occurs in the liquid reservoir far to the right in the figure. The principal shear stress should be a maximum within the highest order fringe in the region marked A. Notice that the shear stress is uniform in the shearing gap at positions fartlier than about 3 times the film thickness into the gap. It was noted previously [lo] that the first band nucleates at the point A and runs to the point marked B in Figure 2. Two conclusions may be drawn from this observation. 1) The reason for the observation of the first bands near the entrance is that the shear stress is greatest there. 2) A band which nucleates within a region, A, of locally high stress (compared to the average stress within the field) will continue to run through a region of locally lower (than the average) stress. The significance of the latter is important. Once initiated the shear band defines a plane on which slip is more easily accommodated than in the bulk of the material - it becomes a "weak spot" and tlie slip is arrested only by pinning at the solid boundaries of the film. 2.2 Persistence of Shear Bands When mechanically induced shear bands are studied in solid amorphous polymers, the observations are usually made on sectioned specimens [lll long after the deformation responsible for the bands has ceased. This is possible because the image of the band, which is probably a result of damage or dilatation, persists. In the liquid lubricants this persistence time is shorter. In Figure 3 we have plotted tlie length of time for which a shear band was visible in 5P4E after shearing (persistence time) versus the viscosity at test conditions. If we define the mechanical shear relaxation time as the ratio of viscosity, 1.1, to shear modulus, G, then the straight line plotted in Figure 3 is the mechanical relaxation time for G = 1 GPa. We may define a characteristic time for thermal diffusion as h2/D where h is the thickness of the

band and D is thermal diffusivity. D is essentially independent of p and is typically about l o 7 m2/s for liquid lubricants. If a shear band is at most 2p.m thick, then the characteristic time for thermal diffusion is at most 40p. The correlation of persistence (of the order of seconds) with mechanical relaxation is much better than for thermal diffusion. Clearly the image of the shear band is a result of mechanical damage or dilatation and not temperature.

a

4 hhr.tlon 0 : 1 OP.

tima

-1

7.6

0.0

0.4 LOO

O.B

0.2

B.6

10.0

vlaco~ltv( h . * l

Figure 3. Time for which a shear band is visible. 2.3 Dilatation A related observation concerns the degree of contrast of the shear band images. Among the liquids in which we have observed shear bands is the perfhoropolyakyl ether, 143AD. In this material the bands appear so faint that it is difficult to reproduce them on a video print, The refractive index, n, is related to density, p, through the Lorenz-Lorentz equation.

1 n2-1 = constant P n2+2 From tliis we can obtain

where

E

is the dilatation. The refractive index of

40

143AD is 1.30 and the refractive index of 5P4E is 1.63. Inserting these values into eqn. (2) we find that the rate of change of n with respect to & is 0.3 for 143AD and -0A for 5P4E. So for the same dilatation the refractive index changes three times less for the perfluoropolyalkyl ether than it does for the polyphenyl ether. Thus the relative degree of contrast in shear band images is consistent with an argument that a persistent dilatation has occurred along the band.

-

reports that m = 0.027 for polycarbonate with shear bands. Such a low rate sensitivity (6%per decade) would possibly be undetectable in high-pressure rlieometers and disc machines; hence the limiting shear stress idealization. Glassy polymers are known to exhibit a pressure dependent shear strength which at high pressure follows the rule [ 113 ty = tyo+

Ap

(3)

2.4 Surface Roughness Effect It miglit be argued that the roughness of the

solid boundary provides a nucleation site for shear bands. The moving shaft which performs as one (the moving one) of the solid boundaries lins two sides each of which may be utilized in an experiment. One side was left as machined with an rms roughness of 1.Opm. The other side was polished to a roughness of 0.03 pn. The stationary surface has a roughness of 0.3 pn rms. Both sides of the moving shaft have been utilized. No difference in the character of the b'ands or die manner in which they developed was noted. We, therefore, cannot associate surface roughness, at least up to 1 pn, with shear localization in liquid films. 3. SLIP CRITERION

where 3iy varies from 0.1 to 0.25 and p is pressure. A similar rule is known to apply to the limiting shear stress of liquid lubricnnts, although with a lower proportionality constant. 3.2 Mohr-Coulomb Criterion The Mohr-Coulomb criterion predicts that slip will occur along any plane on which the ratio of shear stress, f0, to compressive normal stress, -oe, attains the magnitude of a material friction coefficient, T. Referring to Figures 4 and 5 , 78 and may be resolved from the shear stress, f, and normal stresses oxand o,,which are oriented along and perpendicular to the solid boundaries in a plane shear experiment. The mean mechanical pressure, p, is defined by p = -%(ox+ oJ and h = f/p.

3.1 Analogy to Glassy Polymers In a previous paper [6], tlie authors have

associated mechanically induced shear bands with the rate-independent shear stress which is observed in liquid lubricants under pressure in disc machines and rheometers. As a critical stress which is roughly proportional to pressure is approached, increasing amount of the deformation in an otherwise ratedependent matrix is accommodated by intermittent slip along inclined shear planes. When this critical (limiting) stress is reached, any increase of the apparent rate of shear can be accommodated by an increased production of sliear b'mds without changing the stress: the response is rate-independent. In practice, for glassy polymers, the strain rate sensitivity coefficient m = dPnf/dPnf, can be quite low when shear bands are operating. Here, z is shear stress and f is rate of shear. G'Sell [123

Figure 4. Definitions of angles and stresses.

41

which leads to

/ 0

/

0

Figure 5. Mohr's circle representation of slip criterion.

The two solutions for 8, are the shear band angles 8, and €I2for the fvst and second types respectively. The material friction coefficient is

In general, the nonnal stresses will not necessarily be equal and we will quantify the first normal stress difference, N, = ox - aY by 5 = N,/2p. The parameters h and 5 are dimensionless. We may resolve

(5) The slip criterion can be represented graphically on the Mohr's circle plot in Figure 5. The Mohr's circle of stress must fit within the envelope defined by the broken lines. These lines must curve away from the Q axis near p = 0 to allow a non-zero shear stress there. The included angle of he envelope is twice the material friction coefficient, q. Now, slip will occur when the circle of stress increases to tangency with the envelope and the orientation of the band will be such that I 7, / o0I is maximized. This is satisfied by the two radii of the circle drawn to the points of tangency. These radii represent the two shear band angles, 8, and 8, in Figure 4. Analytically, the shear band angles can be found by setting

If the first normal stress difference N, were zero, then the two shear band angles would be complimentary angles (sum to 90") defined by solutions of 8, = l/i sin-' h. Clearly the shear band angles in Figure 1 are not complimentary. It will be necessary to invoke the first normal stress difference to reconcile theory with observation. For example, from Figure 1 for the polyphenyl ether, 8, = 19" and O2 = 103". Then h = 0.089 and 5 = 0.056 are obtained from equation (7). This value of h is in agreement with the measured [13] limiting shear stress if h is applied to a linear equation like (3). The first normal stress difference obtained is a little more than the shear stress. This may seem excessive, since consideration of the normal stress difference has not been necessary to predict bearing load capacity; however, Tanner [141 showed that for typical lubrication flows the fractional increase in load capacity is unaffected by N, of the order of 2. The experimental measurement of N, at high pressure is challenging and has not previously been attempted - possibly because of the expected irrelevance to bearing load capacity. Measurement of N, could confm the applicability of Mohr-Coulomb and might be considered a research priority. In the example above, the material friction

42

coefficient, q = 0.106. Tlie value of q is simply tlie difference between d 2 and tlie included angle between the two types of band (in radians). Since this included angle is very nearly x/2, the determination of q (and h) from observations of bands is sensitive to tlie accuracy of the shear band angle measurement.

4. RHEOLOGICAL MODELS

In previous work [4] the authors showed from experimental measurements that the Maxwell Model, which sums elastic and viscous strain components, correctly describes tlie transient liquid response under pressure. The simplest incompressible fonn of tlie Maxwell model requires two rheological properties - for example: the limiting elastic shear modulus, G, and the limiting low shear viscosity, p. A f u l l rheological model for elastohydrodynamic lubrication was developed from observations of the liquid lubricanl response observed in high-pressure rlieometers. Here, 4, is the rate of deformation tensor, T,, is the deviatoric stress tensor and .re is the von Mises stress. In formulating this equation we adopted tlie Stokes' Condition - the mean mechanical pressure, p, being set equal to the tliemiodyn:unic pressure, p,.. However, in writing the full model in Ref [4] we also set the second coefficient of viscosity equal to zero atid this is inconsistent witli Stokes' Condition. We suggest tentatively tliat a knn be added to the right-h,md side of the equation so that tlie full model now reads

..3pK]

dij = d [r i j - 6r~dt 2G

;:

equation of state. Stokes' Condition is now ab'andoned 'and conipressional viscoelasticity is addressed explicitly. The second coefficient of viscosity is zero which sets the bulk viscosity equal to 2/3p. This choice is made so tliat the short time isothermal compressibility is 1/K and tlie long time compressibility is obtained from Uie state equation. The function F(T,~,T,)is an empirical rate relation. Equation (9) represents unfinished business in two respects. A first normal stress difference is not explicitly introduced. Tlie use of the Jaumann time derivative in (9) will result in N,/T of the order of T/G if F = 1 [15]. Thus the magnitude of shear stress, T, must be close to that of the shear modulus, G , to yield tlie first normal stress difference required by the Mohr-Coulomb theory and observed shear band angles. This is too great a value of T since z,/G is approximately 1/30 [2]. Secondly, we now know Chat tlie non-linear (in TJ form of F(T,p,z,) is at least in part due to shear localization. Constitutive behavior, by definition, excludes localization. Iliat is to say that only the behavior of the matrix between shear bnnds can be described by a constitutive law. For many simple, low molecular weight base stocks it may be most correct to set F = 1 and apply a slip criterion such as Molu-Coulomb. Then the non-linear behavior which was introduced previously through F is a consequence of the distribution of q through tlie material and tlie slip velocity. For simple cases where the flow is steady simple shear, an empirical stress equation such as we have advanced

t =

t,(l-e -CIflr')

+ -F(Tg,t,)

(9)

where K is now the bulk modulus of the glass and p,. is that pressure which yields tlie inst'antnneous density of the liquid when used in the equilibrium

is sufficient. Here the rate sensitivity coefficient, m, goes to zero as py/zL becomes large. For solid polymers where shear bands are operating, m is small but not zero. Also, recent measurements [ 131 indicate tliat the transition from Newtonian to "rateindepcndent" behavior for high molecular weight lubricants is broader in shear mte tlian Uiat which is described by equation (10). These deficiencies may be removed by using the Carreau-Yasuda form

43

Leeds-Lyon Symposium, (1993).

3.

Johnson, K. L. and Tevaarwerk, J. L., "Shear Behavior of Elastohydrodynaniic Oil Films," Proc. R. SOC. Lond., A-356, pp. 215-236, (1977).

The dimensionless exponent, a, controls the breadth of the transition and rate sensitivity coefficient, m, appears explicitly. Note that equation (11) is equivalent to the Elsharkawy and Hamrock [16] model when m = 0. For m very small (-0.01) but not zero, equation (11) fits experimental results well while removing Uie singularity which causes problems in numerical simulations.

4.

Bair, S. and Winer, W. O., "The High Pressure High Shear Stress Rheology of Liquid Lubricants," Trans. ASME, Journal of Tribology, Vol. 114, 1, pp. 1-13, (1992).

5.

Bair, S., Qureshi, F., and Khonsari, M., "Adiabatic Shear Localization in a Liquid Lubricant Under Pressure," ASME Journal of Tribology, 93-Trib 29, (1993).

5. CONCLUSIONS

6.

Bair, S., Qureshi, F., and Winer. W. O., "Observations of Shear Localization in Liquid Lubricants Under Pressure," ASME, Journal of Tribologr, 115, 3, pp. 507-514, (1993).

7.

Bair, S., Winer, W. 0. and Distin, K. W., "Experimental Investigations into Shear Localization in Operating Concentrated Contact," Proc. 19th Leeds-Lyon Symposium, (1992).

8.

Harris, John, Rheology and Non-Newtonian Flow, Longman Group, London pp. 63-64, (1973).

9.

Janeschitz-Kriegl, H., Polymer Melt Rheology and Flow Birefringence, Springer, Verlag, Berlin, p. 118, (1984).

Tlie Coulombic nature of concentrated conk?ct friction is apparently the result of an interniittent slip mechanism operating wilhin an otherwise linear viscoelastic liquid lihn under highpressure. A rigorous analysis of the response of lubricant films with a non-uniform stress field will require a Maxwell model for constitutive behavior coupled with a failure criterion for slip. Tlie MoluCoulomb Model is the appropriate criterion when a first normal stress difference is assumed.

6. ACKNOWLEDGEMENTS

This work was supported by a grant from the Office of Naval Research, Materials Division, Peter Sclunidt, Scientific Officer.

REFERENCES 1.

2.

10. Qureshi. F., "Kinematics of Shear Deformation of Materials Under High Pressure and Shear Stress," P1i.D. Thesis, Georgia Institute of Technology, (1992).

Cheng, L., Webster, M. N. and Jackson, A., "On the Pressure Rippling and Roughness Deformation in EHD Lubrication of Rough Surfaces," ASME Journal of Tribology, 115, No. 3, p. 44, (1993).

11. Bowden, P. B., "Yield Behavior of Glassy Polymers," Physics of Glassy Polymers, Wiley, New York, Edited by R. N. Haward, p. 313, (1973).

Johnson, K. L., "Non-Newtonian Effects in Elastohydrodyn,amic Lubrication," Proc. 19th

12. G'Sell, C., "Plastic Deformation of Glassy Polymers: Constitutive Equations and

44

Macromolecular Mechanisms," in Strength of Metals and Alloys, Pergramon Press, Oxford, p. 1955, (1986).

Contacts," Trans. ASME, Journal Tribology, 113, 3, p. 647, (1991).

of

13. Bair, S. and Winer, W. 0.. "A New HighPressure, High Shear Stress Viscometer and Results for Lubricants," STLE Tribology Trans., 36, 4, (1993).

FIGURES

14. Tanner, R. I., Engineering Rheology, Clarendon Press, Oxford, p. 237, (1985).

Figure 2. Flow birefrigence in 5P4E at 23"C, 241 MPa.

15. Hutton, J. F., "Theory of Rheology," Interdisciplinary Approach to Liquid Lubricant Technology, Edited by P. M. Ku, NASA, p. 206-207, (1972).

Figure 3. Time for which a shear band is visible.

16. Elsharkawy, A. A. and I-Ianuock. B. J., "Subsurface Stresses in Micro-EML Line

Figure 1. Two types of meclianically induced shear bands.

Figure 4. Definitions of angles and stresses. Figure 5 . Mohr's circle representation of criterion.

slip

Dissipative Processes in Tribology / D.Dowson e l al. (Editors) 0 1994 Elsevier Science B.V. All rights reserved.

45

On the Theory of Quasi-Hydrodynamic Lubrication with Dry Powder: Application to Development of High-speed Journal Bearings for Hostile Environments Hooshang Heshmat, Ph.D. Mechanical Technology Incorporated 968 Albany-Shaker Road Latham, New York 12110 USA

This paper describes a series of experiments aimed at the demonstration of the basic feasibility of developing a powder-lubricated, quasi-hydrodynamic (PLQH) journal bearing for high-temperature and hostile environments, where the use of liquid lubricants is impractical. A PLQH bearing has demonstrated operation at speeds to 2 x lo6 DN (58,000 rpm), and it may be the only bearing capable of meeting the ever-demanding tribological goals of a solid lubrication scheme for extreme environments. The work described exceeds the current state of the art (1.5-million DN) in solid-lubricated ceramic rolling element bearing technology, and there is great promise for integrating this technology in outer space systemdmechanisms and in other hostile-environment applications. Experimental evidence shows that powder lubricant films behave much as fluid films do, whereby mechanisms are provided that lift and separate bearing surfaces and cause side leakage. These mechanisms reduce the friction coefficient and, consequently, the heat generated in the bearings, which drastically reduces wear of the tribomaterials. Further, bearing side leakage provides a significant mechanism for heat dissipation because it carries away most of the heat generated by shear, reducing the heat to the critical bearing surfaces (see Figure 1). Experimental parametric studies have delineated the hydrodynamic effects of powder lubrication (MoS,) on bearing performance criteria, such as load, temperature, and power loss as a function of speed, including the effect of powder flow rate on bearing performance characteristics. Comparison with a liquid lubricant provides evidence for the continuum basis for the phenomenological unification of solid particulates and liquid.

- - v,

2v2

u v

Surface 1

I

1

L

U

"

i

= Velocity of Powder Lubricant = Velocity of Independent Bodies

6

= Surface Roughness

O(6) H h, -T Y

On the order of (6) = Heat Flow = Minimum Film Thickness = Total = Reference Coordinate =

!

911045

Figure 1. Quasi-Hydrodynamic Model for Powder Lubrication

46

wn

= 35 Ib (155.7 N)

N

= 8.87 rps

"0

Figure 2.

= 4.6 mlsec

Pivot Point 1, - 6

=

1 Volt

=

60% from Leading Edge of Pad

= 5sec

10013 psi (230 kPa)

Pressure Profiles for Powder-Lubricated Pivoted-Pad Thrust Slider

Wn = 155.68 N (35Ib)

m

a

Oil: SAE 10 wt

U

Figure 3.

Comparison of Lubricant Pressure Profiles for SAElO Oil and TIO, Powder vs. Extent of Pad

47

INTRODUCTION

Ideal rigid particles have been used in almost all attempts to build fundamental hypothesesdescribing the dynamics of powders. These particles have generally been assumed to be both smooth and spheroidal, when in fact actual media composed of nearly rigid particles rarely exist in such simple shapes, as evidenced by sand and many lubricating powders [6, 161. All these media are influenced by friction between the particles. The dynamic properties of media composed of ideal smooth particles in a high state of agitation have been the subject of many investigations. The first to mention particulate flow was Osbome Reynolds (1885) [ 11. Based on a series of other investigations [ 17-19], Heshmat conceptualized in 1988 [2] that the dynamic properties of a medium consisting of fine particulates of unrecognizable shapes, sheared in a narrow gap by forces transmitted through the medium, would be akin to fluid film properties. This unique property is called "quasi-hydrodynamiclubrication with dry triboparticulate matter" [2] because the fluid-like bulk property may change as a consequence of distortional strains or any disturbance that causes a change of volume, density, or temperature of the medium. A sound theoretical basis has now been established based on a series of systematic analytical and experimental investigations that demonstrate the similarity between the velocity, density, pressure, and temperature profiles produced by liquid-lubricated and powder-lubricated bearings [3,4, 5,241. Thus, a lubricant consisting of a fine powder either inserted deliberately or generated by the wear of the mating surfaces constitutes a viable lubricant that generates the required flows and pressures to prevent contact between the surfaces. RHEODYNAMICS OF POWDER LUBRICATION A recent series of investigations aimed at providing evidence of the quasi-hydrodynamic nature of a powder lubricant and which led to the first demonstration of a powder-lubricated journal bearing was completed in three stages. The first stage concerned the rheology and hydrodynamics of dry powder lubrication, in which Heshmat [2, 61 conceptualized the mechanism of powder flow that possesses some of the basic features of hydrodynamic lubrication. The

dynamics of the particles, provided they are of the proper size (1 to 10 pm), function not as aggregates or compacted individual bodies, but rather like a continuum with many of the velocity and shear characteristics analogous to hydrodynamic fluid films. While they also exhibit substantial differences, on the whole, they are closer to the nature of a lubricant film than to the behavior of an aggregate volume of discrete particles. The basic feature of the quasi-hydrodynamic flow is an in-situ, layered flow of the powder film, which is portrayed schematically in Figure 1. Thus, the hydrodynamic behavior of a powder lubricant can be described as a sheared layer that adapts itself to the adjacent layer, so as to cause the least possible discontinuity in the flow of the lubricant film. The basic model of powder lubrication (Figure 1) parallels other established tribological disciplines and permits an evaluation of powder lubrication performance in quantitative terms. Referring to Figure 1, in a sliding contact with powder lubrication, the film can be divided into regions of intermediate films and powder lubricant film. The thickness of the intermediate films is expected to be on the same order as the surface roughness O(6,) and O(6,). In fact, the surfaces of the sliders and counterfaces (surfaces 1 and 2) have been observed to have thin, adhered layers of extremely fine powder after a short period of testing with powder lubricants. This adhered layer plays a major role in terms of protecting the tribomaterial surfaces and dictating the magnitude of slip velocity in the boundaries. There were two main postulates resulting from this early work [2]: In the dry friction regime, the powder constitutes a lubricant, imparting to the interface many of the characteristicsand effects of a hydrodynamic film. Such a hydrodynamic regime holds only for a certain range of particle size (or wear debris) with respect to the nature of tribomaterial combinations. Based on these postulates, a theoretical, rheological model for quasi-hydrodynamiclubrication with dry triboparticulate matter was developed and some solutions were obtained [6, 8, 9, 16, 20-22, 241. The second stage of the investigations dealt with lubricant flow visualization studies conducted by Heshmat [4]. During these studies, a lubricant consisting of micron and submicron size powders was used that offered visual evidence of the theorized velocity

48

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w $-u

-

Lubricant

i--i'P-.-I A(b)

I

1000

I

0,

C

c 0)

0

100

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10

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L

3

,

lo-'

Lubrication

t

\ \

\

/

\

\

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1

I I

v)

(d) Hydrodynamic Lubrication

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---

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Figure 4.

-

881604-1

Film Thickness/Surface Roughness

Traditional Stribeck Curve for Conventional Liquid-Lubricated Bearings

Conlrollable

WaIer-CooIeclI I . Support Splndk

Eleclric

Frictional Torque

Torque Arm

I

.

View A-A Tesl Load

Figure 5.

91889

Powder-Lubricated Hydrodynamic Journal Bearing Test Rig and Instrumentation

49

and shear characteristics of a powdered layer in the interspace of a journal bearing. The main results of this series of experiments conducted with a journal bearing having a D x L x C = 64.4 x 12.7 x 6.6 mm (2.5 in. x 0.5 in. x 0.26 in.) at an eccentricity ratio of E = 0.98 showed the following fluid-like behavior of the powder film: A boundary-layer-like flow occurs along the moving surface. A shear stress is distributed across the film. Compressive and tensile stresses are generated in the film due to journal rotation. The converging part of the film produces compressive stresses and forms fractures in the radial direction; the diverging region produces tensile stresses. Unique boundary conditions that are dependent on the nature, properties, and interaction between the powder and the walls prevail at the two solid surfaces. The originally circumferential flow of powder assumes an axial motion as minimum film thickness, hmin,is approached, indicating the formation of an axial pressure distribution and producing side leakage, analogous to hydrodynamic lubrication. Past hmin,a powder film shows chaotic motion akin to turbulent flow, or cavitation. The third stage in the investigations focused on experimentally determining the pressures generated in the powder film and their kinship with hydrodynamic pressure profiles associated with fluid lubricants. The experiments were conducted with a pivoted pad thrust bearing having an OD of approximately 200 mm (8 in.). Figures 2 and 3 show the nature of the pressure profile that was generated with a powder lubricant and compares it with a comparable oil film pressure profile [5]. As seen, the longitudinally skewed pressure profile generated with a powder film is typical of a hydrodynamic oil film. Following the series of powder lubrication efforts, an appropriate theoretical formulation of the quasihydrodynamic process of powder lubricants was established [6,16,24]. This theory was supported by experimental results, i.e., finding an adhered powder layer, observing the velocity and shear characteristics in a journal bearing, and measuring a pressure profile similar to that found with conventional liquid lubricants. Additional fundamental experiments investigating powder rheology [ 8, 9, 20-221 have been conducted which complement the work discussed above.

PROTOTYPE JOURNAL BEARING TESTING

Of the many items that typify hydrodynamic lubrication, e.g., a wedge-shaped film and the shape and magnitude of the pressure distribution, probably the most telling feature is the decreasing friction coefficient as a function of load parameter (Sommerfeld number). This is presented in classical hydrodynamic lubrication theory by the Stribeck curve, shown in Figure 4, which plots the friction coefficient versus the Sommerfeld number. The Stribeck curve is used to delineate the respective regimes of hydrodynamic, boundary, and dry lubrication as they apply to fluids or solids in direct contact. Having previously demonstrated powder flows and film pressures akin to liquid lubricants, it remained to demonstrate friction characteristics similar to those observed in classical hydrodynamic lubrication as shown on the Stribeck curve for a prototype powderlubricated journal bearing. An experimental program was conducted with the primary purpose of demonstrating the feasibility of powder-lubricated journal bearing operation in advanced turbine engines. These tests documented the friction performance of journal bearings under both oil and powder lubrication. The effects of bearing clearance and powder (MoS,) flow rate on bearing power loss as a function of load parameter were also investigated. Experimental Test Rig

A schematic and a photograph of the experimental setup are shown in Figures 5 and 6, respectively. The test journal bearing consisted of five equally spaced pads with the following dimensions: Bearing diameter: 34.1 mm (1.3438 in.) Bearing length: 20 mm (0.788 in.) Projected pad area: 682 mm2 (1.058 in.,) A novel powder-lubricated hydrodynamic journal bearing concept was designed and fabricated (Figure 7). The bearing pads are attached to the bearing cartridge via sets of adjustable compliant pad mounts that were designed to provide radial, pitch, and roll stiffness. The bearing diametral clearances of 0.1 and 0.2 mm (0.004 and 0.008 in.) were achieved by placing a shim of the proper thickness under the compliant mount elements and bearing cartridge. Special care was taken to maintain the designed structural stiffness of the bearing

50

Figure 6 .

Powder-Lubricated Journal Bearing High-speed Test Rig

I Powder B+

Figure 7.

Outlet

Powder-Lubricated Hydrodynamic Journal Bearing

911046

51

when the bearing clearance was altered. The instrumentation used consisted of the following: Fiber-optic-type sensor probe to monitor rotor speed. Strain gage load cell to measure frictional torque on the bearing. Thermocouples mounted on the back side of the bearing pads: one on the loaded pad, and the other on the unloaded pad at 250" with respect to the load vector. The location of the thermocouples, which were mounted on the back side of the bearing pads, was chosen to be at the centerline of the bearing (radially and axially). One thermocouple was mounted at the top of the pad (Pad No. 1) opposite the bearing load. The other thermocouple was mounted in the same manner on Pad No. 4 (pads were numbered in the counterclockwise direction starting from the top). The thermocouple junction was about 2.9 mm (0.116 in.) from the bearing pad contact surface. The supply powder flow temperature and bearing ambient temperatures were also monitored with additional thermocouples. Lubricant flow rates were calibrated prior to test and remained consistent during the test. Figures 5 and 6 show the instrumented test rig. The torque arm is bolted to the bearing cartridge with its centerline passing through the center of the bearing. The torque arm,in a vertical position opposite the bearing load direction, is restrained via a force transducer fixture. The test load was applied via graduated standard lab weights in various increments to a desired test load level through a cable and tray connected to the bearing cartridge. The bearing assembly, including torque arm,loading cable, and tray, weighed about 17.75 N (3.99 Ib). The test bearing cartridge and compliant mount elements were made of nickel-base alloy, Inconel 718. The test journal with a radius of 17.0 mm (0.669 in.) and bearing pads were made from bearing quality, M2 tool steel. The test journal and pad surfaces were ground after proper heat treatment and then lapped to obtain a surface finish better than 0.1 pm (4 pin.) rms. Test Lubricants Baseline performance data were obtained for liquid lubricant conditions. A petroleum base liquid lubricant spindle oil, Mobil Velocite No. 6, having kinematic

viscosity of 9.4 centistrokes at 40°C and 2.6 centistrokes at 100°C was used. The reference viscosity at the oil inlet temperature of 22°C was considered for data analysis; po = 9 cps, (1.305 preyn). The liquid lubricant was squirted through a nozzle at the beating end. The nozzle was aimed axially and directed at a gap, approximately at the leading edge of the load pad, between test bearing pad numbers 5 and 1. Molybdenum disulfide (MoS,), commercially available and suspension grade, was selected as the powder lubricant. This powder had a reported 50% cumulative particle size distribution of 1 to 2 pm with a purity level of 99.99%, a pour density of 1.125 g d c c , and a solid density of 4.8 g d c c [7]. The delivery of powder lubricant to the inlet zone of the pads was by means of a powder spray device, as shown in Figures 5 and 6. The powder spray nozzle discharged a (dryadpowder) mixture approximately 10 mm from the bearing pad axial end. Powder was blown through the bearing gaps axially via dry air which was supplied to the unit at 70 to 170 kPa (10 to 25 psi). The powder discharge flow rate was adjusted via a powder supply control system which was precalibrated to achieve 15 cc/min (0.28 gdsec) and 30 cc/min (0.56 gdsec). Experimental Results Preliminarv Runs. A number of runs was made with Velocite No. 6 oil lubricant at several loads and speeds in order to establish a reference set of bearing performance data and to check out the instrumentation and operation of the test assembly. This information could then be compared with known bearing inputs and, if necessary, adjustments made in the equipment used. The experimental data were analyzed and nondimensionalized for the generation of parametric plots showing both friction and power loss as functions of load parameter or bearing DN. Figure 8 is a plot of the measured coefficient of friction as a function of nondimensional load parameter, W = [p,, (N/P)(WC)* 1, for four different normal loads of 26.7 to 222.4 N (6 to 50 lb) at various journal speeds up to 20,000 rpm. The two curves on Figure 8 show that, within the limits of test rig operation, some deviation could be seen among the test data. The reference viscosity of the oil was kept constant at po = 1.3 preyn for all calculated nondimensional load parameters. Superimposing the

52

Powder Flow = 20 cc/rnin Bearing Clearance (C,)= 4 mil

1

0 Load- 61b

0.35 0.30 r

Load= 161b Load=36Ib Load=50Ib

Q Q

-

0.15

0.10 3

0.05

-

01

I

I

I

I

I

I

-

10-1

I l l

W = Po

I

0

-(-) N R

1

1

-

10‘

2

91801

P C

Figure 8.

Coefficient of Friction as a Function of Load Parameter @) for a Journal Bearing Lubricated with Oil

40 0

Lubricant: Oil

35 -

-

-

I

20 15 10 -

50

-’

Figure 9.

d mil

Lubricant Flow (0) = 20 cc/rnin Load: o -61b x 16 Ib 0 36 Ib a = 50 Ib

30 25

-

Bearing Claarance (C,)

I

I

I

I

I

I

Power Loss as a Function of Speed and Load for a Five-Pad Journal Bearing Lubricated with Oil

53

curves of Figure 8 on Figure 4, the dry friction, boundary, mixed, and hydrodynamic lubrication regimes become evident. Further data analysis of the nondimensional power loss as a function of speed and load (Figure 9) and comparison with the relevant data available in the literature confirmed the soundness of the test data acquisition procedure and instrumentation [25]. Powder Lubrication Tests. The remaining tests were conducted at what amounts to two different bearing diametral clearances and two powder flow rates, at speeds up to about 60,000 rpm (2 million DN) with applied normal loads up to 227 N (51 lb). The dry air supply delivered MoS, powder axially to the bearing from the outboard side. The powder was introduced prior to loading the bearing completely against the runner. The dry air supply and ambient temperatures were about 22°C. The tests were conducted with powder MoS,, a bearing diametral clearance of 0.102 mm (0.004 in.), and a constant powder flow rate of about 15 cc/min throughout the test operation. The reference viscosity (po)for MoS,, which was based on experimental data reported in Reference [6], was kept constant at 10 preyn for all parametric data analyses. This value was an order of magnitude higher than that of the test oil viscosity. Figure 10 is a plot of nondimensional power loss as a function of speed and load. Comparing Figure 10 with the data shown in Figure 9, a striking similarity with the conventional liquid lubricant power loss is seen. After completing the second series of tests, the bearing diametral clearance was increased from 0.1 to 0.2 mm (0.004 to 0.008 in.) in preparation for the thud test series. The powder flow rate and bearing loads were kept the same. The main purpose of the third test series was to study the effect of bearing clearance on the bearing operating performance. When the friction signatures from the second and third test series were compared, the coefficient of friction and, consequently, power loss, were found to be a weak function of bearing clearance. In the fourth test series, which was undertaken to study the effect of powder flow rate, Q, on bearing performance, the powder flow rate was changed to 30 cc/min. The remaining test conditions were kept the same as for the third series of tests. In general, the trend of measured bearing power loss as a function of

speed indicated an exponential relationship (Figure 1la and 1lb) as called for in classic hydrodynamic theory. COMMON TRIBOLOGICAL MECHANISMS

Figure 12 depicts the friction behavior of the powder-lubricated journal bearing as a function of normalized load parameter, G, for clearances of 0.10 mm (4 mil) and 0.20 mm (8 mil) and powder flow rates of 15 and 30 cc/min. In Figure 12, a set of curves is fitted to their upper and lower boundaries to represent the trend of friction coefficient versus load parameter. The most significant aspect of the frictional behavior of dry powder-lubricated bearings is that it closely resembles hydrodynamic behavior rather than the elastic behavior of dry contacts. Another example of the quasi-hydrodynamic behavior functioning in a powder-lubricated bearing is shown in Figure 13 which shows a drop in dimensionless power loss with increasing load parameter, (G). In particular, data obtained from the liquid lubricant tests are superimposed over the test powder data. As can be seen from this figure, excellent correlation has been achieved. This clearly is more direct proof of the quasi-hydrodynamic action of solid particles in a self-acting converging wedge. During the powder lubrication tests, the bearing pad temperature was measured at approximately 177°C (350°F). Considering the test speeds, this temperature was considerably lower than would be expected from solid lubrication with MoS, coating. Other key features of the powder-lubricated bearing test results presented in Table 1 are the range of measured bearing power loss, achieved DN value, total operating time, and wear distance. From this table, it is seen that operation above 1.3-million DN was achieved and maintained for up to 1080 sec. The low power loss and pad temperature rise are further evidence of the similarity of powders to oils and the ability of powder to carry heat away from the contact. One consequence of the friction in the powderlubricated hydrodynamicjournal bearing is the resulting heat generation. While the low friction coefficient provided by a powder lubricant film goes a long way to limiting the heat that is transmitted to the bearing journal and pads, without some mechanism to carry the heat away from the bearing, the local pad and journal temperatures would quickly rise and components would

54

.d."

Lgbricant: MoS, Bearirlg Clearance (C,) = 4 mil Lubricant Flow (0) = 15 a ' m i n Load: o = 61b i = 161b o = 32Ib

0

0.1

0.2

0.3

0.4

DN x lo6

0.5

0.6

0.7 91%

Figure 10. Power Loss as a Function of Speed and Load for a Five-Pad Journal Bearing Lubricated with Powder MoS,

55

melt. As with conventional hydrodynamic lubrication theory, the quasi-hydrodynamic powder lubrication theoretical model includes heat transfer via the lubricant. As shown in Figure 1, the generated heat is transmitted to the three elements comprising the bearing, namely the journal, the bearing pads, and the powder. The bulk of the heat is carried away from the bearing by the powder in a manner similar to liquid lubricant side leakage. Following an accumulated test time of 2730 sec under various loads and speeds, the test specimens were examined, and the bearing and shaft were observed to be in excellent condition. Figure 14 shows the posttest condition of the pads and test journal. A close examination of the surfaces revealed that a thin layer of powder about 2.5 to 7.5 pm (0.1 to 0.3 mil) had adhered to the surfaces of the test journal. This phenomenon has been observed following tests with various other types of powder, as reported in [8, 9, 14, 15, 20-221. The adhered layer is believed to play a major role in terms of protecting the tribomaterial surfaces and dictating the magnitude of slip velocity at the boundaries. The Quasi-Hydrodynamic Nature of Powder Lubrication

Two of the basic determinants of the mode of hydrodynamic lubrication are the pressure profile produced and the behavior of the coefficient of friction as a function of load (Stribeck curve). Based on the experiments conducted with the powderlubricated films, the results show a striking kinship of the powder film with that of a conventional liquid lubricant. Based on the friction data generated by an oil and a powder, Figure 15 shows that in all essential aspects the powder lubricant behaved as expected of a hydrodynamic bearing. The values of the coefficient of friction consistently showed that hydrodynamic effects are at work in all powder film interactions for all imposed loads and speeds. Thus, the analogy presented earlier that powders may be treated as continuum media in an analytical model based on continuum theory appears valid [2,6,24]. Therefore, a basis has been established which permits the engineering design of practical powder-lubricated bearings for hostile-environment applications. Further examination of the results strongly indicates that the mechanism of powder flow seems to

follow some of the basic features of hydrodynamic lubrication by exhibiting a layer-like shear, reminiscent of fluids. This shear is deemed responsible for the reduction in friction coefficient. The nature of the sheared flow causes the least possible discontinuity between the various laminae of the powder film. While a dry particulate film has no true viscosity as it is understood in liquids, it exhibits a strainstress relationship with a proportionality constant, po, which represents a resistance to flow or an "effective viscosity" [2, 5, 16, 19,231. The motion of the particles in this concept resembles molecules in a liquid. Thus, given an appropriate tribosurface geometry, the dry particulate film will generate a lift. Using po, friction and film thickness, and consequently wear, can be related to the group of variables [p,, (N/P)(R/C)*], much as the Sommerfeld number, S, is related to friction, film thickness, and wear in hydrodynamic lubrication. The results of the testing allow the conventional hydrodynamic lubrication Stribeck curve to be extended to include powder lubrication and limiting shear stress regimes. As shown in Figure 16, powder lubricants are included at both wings of the f-S spectrum, where the poin the Sommerfeld number is a properly defined viscosity equivalent of the powder. Figure 16 shows qualitatively the five operating regimes of lubrication, dry, boundary, mixed, hydrodynamic, and limiting shear stress. At low values of the speed parameter, there is intimate contact between the surfaces, and the conditions are essentially the same as those with dry friction, which results in high friction and wear. As the speed increases, a thin boundary layer of film is formed with a thickness of the same order as the composite roughness of the two surfaces. With a further increase in speed, the system moves into the mixed regime where the lubricant film thickness increases progressively to the level typically regarded as hydrodynamic and boundary lubricated. As the film increases, asperity contact declines rapidly, giving a significant reduction in both friction and wear. When full hydrodynamic lubrication is achieved, it is believed that the surfaces are completely separated by the lubricant film and that no wear due to asperity contact occurs. In the full hydrodynamic region, friction increases with speed due to viscous drag. For a finite value of an applied load, W, slip may occur at the

56

3 Powder Lubricant: MoS, C, = 0.2 m m (8 mil) L=20mm UD = 0.59 Wn = 71.2 N (16Ib)

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a =u) 2

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61

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1.2

0.9

lo6

93330

Powder-Lubricated Journal Bearing Power Loss as a Function of DN and Powder Flow Rate

Lubricant: MoS, Bearing Clearafica (C,) = 8 mil Lubricant flow (Q) I 15 Wmin Load: o = 41b x o

-

l6lb

= 32ib 51 Ib

/

Lubricant flow (Q) = 30 d m i n Load: o 16 Ib + 32 Ib

/

/ /

/ /

/

/

/'

= 30 cc/min;

Q -,

W=161b

0.2

0.4

0.6

0.8

1.0

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Figure 1 lb.

0

a = 15 cc/rnin;

2

0

/1

1

I

I

I

1.2

1.4

1.6

1.8

2.0 QlQW

Journal Bearing Power Loss as a Function of Bearing DN

57

boundary or near the contact surfaces for increases in the relative sliding speed, U, beyond the full hydrodynamic region where the limiting shear stress may prevail. For powder, this phenomenon has been experimentally observed and reported by Heshmat [3, 8, 9, 20, 221, and for liquids, particularly in EHD lubrication, by Scott and Winer [ 10, 111, Tevaarwek and Johnson [12] and recently by Kaneta et al [13]. As a result of the slip between the film and the bearing surfaces, wear will increase rapidly and lubricant film thickness along with friction value will approach a limiting value [ 5 , 6, 161. Indeed, in the limiting shear region, wear of the tribomaterial is due to the tribological action taking place between the "lubricant" and the tribosurfaces, rather than asperityto-asperity or surface-to-surface contact. Note that the wear rate in Figure 16 is normalized with respect to the maximum wear rate believed to be occurring at the dry contact regime. SUMMARY AND CONCLUSIONS

Powder lubricant films behave much as fluid films do in their ability to generate lift, separating bearing surfaces and causing side leakage. In this way, the power loss or friction coefficient and, consequently, the heat generated in a bearing are reduced. Further, the side leakage provides the mechanism to carry the generated heat away from critical bearing surfaces. A series of experiments has demonstrated the basic feasibility of developing a powder-lubricated quasi-hydrodynamic bearing for advanced rotating machinery and extreme environments. In fact, based on the demonstrated operation of a powder-lubricated journal bearing at speeds to 58,000 rpm, these may be the only bearings capable of meeting and complementing the ever demanding tribological goals of a solid lubrication scheme for extreme environments. The specific conclusions of this investigation are as follows: A flexibly mounted five-pad journal bearing with a 60% pivot position capable of operating at speeds about 60,000 rpm (2 million DN) with dry MoS, powder lubricant was developed. Powder lubrication friction curves compare favorably with liquid lubrication friction curves, providing additional evidence for the validity of quasi-hydrodynamic theory.

The present work has extended the classical regimes of fluid and boundary lubrication in the conventional Stribeck curve to include the regimes of powder lubrication and limiting shear stress. NOMENCLATURE

4

Area under pressure curve Length of slider pad Radial clearance Diameter Speed parameter; D = mm; N = rpm fi Power loss H W [ npo L U, (WC)]; dimensionless power loss HP Bearing power loss (hp) L Bearing axial length P W/(LD); Bearing unit load (psi) Q Flowrate R journal radius S Sommerfeld number; { (po NAp/w,)(WC)2} U Linear surface velocity at R, wR W Bearing normal load \ij (poN/P)(R/C)*; dimensionless load W, Normal applied load e Journal bearing eccentricity f Friction force f Friction coefficient h Powder film thickness hmiominimum film thickness E e/C; eccentricity ratio po Reference viscosity o Angular velocity; radidsec B C D DN

REFERENCES

1. Reynolds, Osbome. "On the Diletancy of Media Composed of Rigid Particles in Contact - With Experimental Illustrations." London, Edinburgh and Dublin Phil. Mag and Journal of Science 55, 20, 127 (1885): 469-81. 2. Heshmat, H. "The Rheology and Hydrodynamics of Dry Powder Lubrication." STLE Tribologv * 34, NO. 3 (1991): 433-39. 3. Heshmat, H., 0. Pinkus, and M. Godet. "On a Common Tribological Mechanism Between Interacting Surfaces." 43rd Annual STLE Meeting, 912 May 1988, Cleveland, Ohio, STLE Transactions 32 (1989): 1, 32-43.

58

0.45-

o Bearing Clearance (C,) = 4 mil Lubricant Flow (a)= 15 d m i n

1o3

Dimensionless Load Parameter ( i )

91 1048

m, for a Powder-Lubricated

Figure 12. Friction Coefficient vs. Load, Hydrodynamic Journal Bearing

1o2

-

‘.r-

Lubricant: MoS,

v) v)

0 L I

Bearing Clearance (C,) = 4 mil Lubricant Flow (Q) = 15 d m i n

10’

a

3

W

0 a

Lubricant: MoS, Bearing Clearance (C,) E 8 mil Lubricant Flow (Q) = 15 W m i n

v) v)

-a L r.

.-0

!g

0

loo

E

B

Lubricant: MoS, Bearing Clearance (C,) = 8 mil Lubricant Flow (a) 30 d m i n

0

0

I

I

I

I

1

I

I

5

10

15

20

25

30

35

Dimensionless Load Parameter (fi)

Figure 13. Power Loss vs. Load Parameter for Oil- and Powder-LubricatedJournal Bearings

40 91863

59

4. Heshmat, H. "The Quasi-Hydrodynamic Mecha-

14. Heshmat, H. "Wear Reduction Systems for Coal-

nism of Powder Lubrication--Part I: Lubricant Flow Visualization." STLE 46th Annual Meeting, April-May 1991, Paper No. 9 1-AM4D- 1, Journal of STLE 48, No. 2 (February 1992): 96-104. 5. Heshmat, H. "The Quasi-Hydrodynamic Mechanism of Powder Lubrication: Part 11: Lubricant Film Pressure Profile." STLE/ASME Tribology Conf., St. Louis, Missouri, October 14-16, 1991, Journal of STLE 48, No. 5 (1992): 373-383. 6. Heshmat, H. "Development of Rheological Model for Powder Lubrication." NASA Lewis Research Center CR- 189043 (October 199 1). 7. Risdon, T. J. "Propertiesof Molybdenum Disulfide - MoS2 (Molybdenite)." Chemical Data Series Bulletin C-5C of Climax Molybdenum Co., a unit of AMAX Inc. (Aug. 1989). 8. Heshmat, H., and J. F. Walton. "The Basics of Powder Lubrication in High-Temperature PowderLubricated Dampers." International Gas Turbine and Aeroengine Congress and Exposition, Orlando, Florida, June 3-6, 1991, ASME Preprint Paper 9 1GT-248, ASME Transactions of the Journal of Engineering for Gas Turbine and Power 115, No. 2 (April 1993): 372-82. 9. Heshmat, H. "High-Temperature Solid-Lubricated Bearing Development: Dry-Powder-Lubricated Traction Testing." AIAA/SAE/ASME 26th Joint Propulsion Conference, Paper 90-2047 (July 1990), Journal of Propulsion and Power 7, No. 5 (199 1): 8 14-820. 10. Scott, B., and W. 0. Winer. "Shear Strength Measurements of Lubricants at High Pressure." ASME Journal of Lub. Tech. 101, No. 3 (1979):

Fueled Diesel Engines--Part I: The Basics of Powder Lubrication." 9th International Conf. on Wear of Materials, April 1993, San Francisco, California; Wear Elsevier Seauoia 162-164

25 1-57. 11. Scott, B., and W. 0. Winer.

"A Rheological Model for Elastohydrodynamic Contacts Based on Primary Laboratory Data." ASME Journal of Lub. Tech. 101, NO. 3 (1979): 258-65. 12. Tevaarwek, J. L., and K. L. Johnson. "The Influence of Fluid Rheology on the Performance of Traction Drivers." ASME J o u d of Lub. Tech. 101, NO. 3. (1979): 266-74. 13. Kaneta, M., H. Nishikawa, and K. Kameishi. "Observations of Wall Slip in Elasto-hydrodynamic Lubrication." Journal of Tribolom, Trans. ASME 112, NO. 3 (1990): 447-452.

(1993): 508-517. 15. Heshmat, H. "Wear Reduction Systems for CoalFueled Diesel Engines--Part 11: The Experi-

mental Results and Hydrodynamic Model of Powder Lubrication." 9th International Conf. of Wear of Materials, April 1993, San Francisco, California; Wear Elsevier S e 'w 162-164 (1993): 508-5 17. 16. Heshmat, H. and Brewe, D.E. "On Some Experi-

17.

18. 19.

20.

mental Rheological Aspects of Triboparticulates." Proceedings of the 18th Leeds-Lyon Symposium on 'WEARPARTICLES: From the Cradle to the Grave, ' Lyon, September 3-6, 199 1, Elsevier Science Publishers, Tribology Series 18 (1992). Berthier, Y., Vincent, L. and Godet, M. "Velocity Accommodation Sites and Modes in Tribology" Eur. J, Mech.. NSolid 11, No. 1, (1992): 35-47. Berthier, Y."Experimental Evidence for Friction and Wear Modelling." Wear 139 (1990): 77-92. Heshmat, H.,Godet, M. and Berthier, Y."Technical Surveillance on the Role and Mechanism of Dry Triboparticulate Lubrication." STLEIASME Joint Trib. Conf, 1992, submitted for publication as an RCT paper in ASME Transactions. Heshmat, H., and Dill, J. F. "Traction Characteristics of High-Temperature, Powder-Lubricated Ceramics (Si,N,/aSiC)." ASWSTLE Tribology Conference 1990, STLE Transactions 35, No. 2

(1992): 360-366. 21. Heshmat, H. and Walton, J. F. "High-Tempera-

ture, Powder-Lubricated Dampers for Gas Turbine Engines." AIAA/SAE/ASME 26th Joint Propulsion Conference Proceedings,Paper No. 90-2046, (July 19901, U P r O P U l sion and Power 8, No. 2, Mmh-April(1992): 449-456. 22. Heshmat, H. "Rolling and Sliding Characteristics of Powder-Lubricated Ceramics at High-Temperature and Speed." 47th Annual STLE Meeting, Philadelphia, Pennslvania, May 1992; to be published by STLE Lub. E w (1993).

60 Table 1 Summary of Powder-Lubricated Hydrodynamic Journal Bearing Performance with MoS,

M2 Tool Steel, Pad Dimensions:L = 20,6 = 17.8,D = 34 mm; Total Number of Pads = 5 Pads

1 DN Average (mm x rpm) x 1o6

Average Tlme (set)

1.3to 2.0

FxD (lb-In.) x 10

1020

1.37 0.31 15.70 3.34 0.15

2730

20.87'

0.27

Maximum Power Loss (hP)

Maximum Pad Temperature

0.24 0.23 2.5 1 .o 0.16

146 188 250 to 300 275 to 350 200 to 250

(OF)

1

-

a1- 193-1

'Total work done on bearing = 1.75x

lo6 ft x Ib z 0.655kWh.

61

23. Walton, O.R. and Braun, R.L., "Viscosity, Granular-Temperature, and Stress Calculations for Shearing Assemblies of Inelastic, Frictional Disks." John Wiley & Sons, Inc., Journal of Rheology 30(5), (1986): 949-980. 24. Heshmat, H. "The Quasi-Hydrodynamic Mechanism of Powder Lubrication: Part 111: On the Theory and Rheology of Triboparticulates." STLE Annual Meeting, Calgary, Canada, May 17-20, 1993; submitted for publication in STLE Transactions.

25. Heshmat, H. "Starved Bearing Technology: Theory and Experiment." Ph.D. thesis, Mechanical Engineering Department, Rensselaer Polytechnic Institute, Troy, New York, December, 1988.

62

Figure 14. Post-Test Condition of Journal Bearing Showing Thin Adhered Layers of MoS, Film

63 0.55

0.50 0.45 -

Lubricant: Oil Bearing Clearance (C,) = 4 mil Lubricant Flow (a)= 20 d m i n Lubricant: MoS, 0 Bearing Clearance (C,) = 4 mil

Figure 15. Experimental Data Correlation Between an Oil- and a Powder-Lubricated,Five-Pad Journal Bearing

64

1

z

s U Y

? I

2

o3

1

Speed Farameter, po

-

T:(

(UP)

(b;

Figure 16. Extension of the Stribeck Curve to Include Powder Lubrication

901686-1

Dissipative Processcs in Tribology / I). I>owson et al. (Editors) 1994 Elscvier Science I3.V.

65

The Influence of Base Oil Rheology on the Behaviour of VI Polymers in Concentrated Contacts P.M.Cann & H.A.Spikes Tribology Section, Department of Mechanical Engineering, Imperial College, London SW7 2BX Whereas elastohydrodynamic (EHD) film thicknesses for simple base stocks can be predicted with some confidence from their bulk properties this is not so for polymer-containing fluids. The behaviour of such fluids in an EHD contact is extremely complex and can include elements of shear thinning, viscoelasticity and boundary properties. In this paper polymer solution behaviour in a concentrated contact has been investigated through detailed EHD film thickness measurements. A series of model polymers; polyisoprenes in the molecular weight range 27-86,000, have been studied in two different basestocks, the intention being to examine the effectof base stock rheology and solvation properties on polymer behaviour. 1. INTRODUCTION

The rheology of a simple basestock in the EHD inlet is usually assumed to be Newtonian even at the extreme strain rate conditions found in this region. Film thickness can therefore be predicted generally from low shear viscosity measurements. This is not the case for polymer-containing fluids which do not obey Newtonian rheology, particularly at high strain rates. It is difficult to measure viscosities at the required strain rates and it is not possible to predict polymer solution behaviour from the usual inelastic flow models. Estimation of EHD film thicknesses therefore for polymer containing fluids is currently impossible. The rheology of these fluids is extremely complex. At low shear rates ( < l d ~ polymer-~) containing fluids are essentially Newtonian. As the strain rate increases viscosity loss occurs. This is usually attributed to alignment or orientation of the polymer coils within the shear field and is reversible once shearing has stopped. A second Newtonian rcgion is observed at very high shear rates (>lo6,l). Rhcological expressions have been developed to describe such behaviour and they are usually in the form of power (1) or doubly truncated power law (2) relationships. Only one (3) is based on a physical model of polymer behaviour. However these models have never been fully investigated at the strain rates associated with an EHD contact, which are often greater than 1 0 V . The viscosity enhancement due to the polymer depends upon both polymer and base stock

properties. Polymer solution viscosity increases with molecular weight and concentration. The solvation properties of the base stock influence the polymer coil size in solution. The larger the coil size the greater the viscosity enhancement. However this is counter-balanced by a greater susceptibilityto shear alignment since the shear stress experienced by the polymer is proportional to coil area. At high stress levels; polymer molecular rupture takes place resulting in permanent viscosity loss. This is thought to occur in the centre of the contact (4), in the high pressure region, and is not the primary cause of viscosity loss in the inlet. It is not therefore considered in this paper. Polymer solutions are also thought to possess viscoelastic properties which, by the generation of forces normal to the direction of shear, will increase film thickness. This has not been measured directly in an EHD contact and has only been inferred from anomalous results for polymer containing fluids in hydrodynamic bearing tests (5). There has also been speculation that polymer containing fluids form boundary layers and, again, this has been inferred from engine wear tests (6). No direct evidence has been offered probably because such films are too thin for normal detection methods. EHD film thickness measurements have been used extensively to investigate polymer solution behaviour (7)(8). Most workers conclude that the film thicknesses are significantly less (60-701(8))

66

than predicted by low shear rate viscosity measurements. Hirata (8) also reports that they are 20% less than predicted from high shear rate measurements. Polymer solutions therefore, within an EHD contact, can exhibit viscosity loss, viscoelasticity and boundary layer formation. All of these will influence EHD film formation. In this paper, detailed film thickness measurements have been made for a series of simple polymers in hydrocarbon solution. The film thickness range studied was 2-200 nm; the intention being to examine the contribution of the polymer to both boundary and hydrodynamic performance. The base stocks were chosen to give a range of pressure viscosity coefficients since this determines the shear stress level experienced by the polymer in the inlet region. In addition the polarity and, hence, solvation properties of the fluids will differ. The low shear rate viscosities of the solutions were measured on a cone-on-plateviscometer. These values were used to calculate the predicted EHD film thickness for each of the base stocks and solutions. These results could then be compared to the measured EHD films. In this way it was possible to estimate the viscosity contribution of the polymer in the inlet region. 2 EXPERIMENTAL

EHD film thicknesses were measured using thin film interferometry,a technique described in detail in earlier papers (9). This method measures EHD film thicknesses down to 2 nm with a resolution of 2 nm. A simple bearing contact simulation device was used (9). The contact is a steel ball driven in pure rolling by a rotating glass disc. The load was 16N giving a maximum Hertzian pressure of 0.47 GPa All tests were run at 22°C. The polymers were monodisperse cis-cis polyisoprenes. Their molecular weights are listed below in Table 1. Table 1 Polymer properties Polymer Molecular weight A 27000 B

c

63000

m

The base stocks used were a synthetic cycloaliphatic hydrocarbon traction fluid ( S A N 40), and a poly-a-olefin hydrocarbon (SHC). Their viscosities and pressure-viscosity (a)values are given in Table 2. The polymer solutions were prepared as 2% weighvweight concentration. Table 2 Lubricant basestocks Basestock Viscosity Pas woe)

0.0485 0.048

S A N 40 SHC

a Value GPa-1 (22°C) 36 13

3 RESULTS & DISCUSSION

The viscosities of the base stocks and solutions were measured on a cone-on-plate viscometer at 22°C. The results for the polymer solutions are shown in Table 3 for a shear rate of 8500 s-l. Table 3 Viscosity results for 2% polymer solutions (Pas) Polymer SAN40 SHC A 0.073 0.064

B

0.1009

C

0.117

2*4

0.071 0.080

1 SAN40 0

SHC

0

1.4

1.2

0

n

20000 4oooO

60000 8oooO 1OOOOO

Molecular weight Figure 1 Relative viscosity as a function of molecular weight These results are plotted in figure 1 in a different form: as viscosity relative to the base oil ie viscosity (solution)/viscosity (baseoil). In this way

67

the different viscosity enhancement for each of the base stocks can be seen. This is larger for the traction fluid which probably reflects the latter’s better solvation properties and hence a greater polymer coil size. EHD film thickness was measured with increasing rolling speed for each of the base stocks and solutions. Representative results are shown plotted in log-log form in figures 2 and 3 for both the base stocks and 2%C solution. The film enhancement due to the presence of the polymer can clearly be seen, particularly at low rolling speeds.

The second effect can be seen in figure 2 where the result for 28C appears to approach an asymptote at low speeds indicating the existence of a speedindependent, boundary film. This result is typical for polymers in the ply-a-olefin solution. It was not found with the traction fluid (see figure 3 below).

.001

.o 1

.1

1

Rolling Speed ( 4 s ) Figure 3 EHD film thickness results for SAN40 and 2%C

.oo1

.01 .1 Rolling Speed (mh)

1

Figure 2 EHD film thickness results for SHC and 2%C Figure 2 shows that, whilst the measured gradients for the base stocks show reasonable agreement with the predicted value of 0.7 (lo), values for the polymer solutions were significantly lower, often less than 0.5. This can be seen in the curve for 2%C which approaches that of the base stock at high rolling speeds. Two factors may cause this; (i) shear thinning of the fluid occurs so that the effective viscosity in the inlet is progressively reduced with increasing speed. (ii) a boundary layer forms at the solid surfaces. This results in an anomalously thick film at low rolling speeds.

It is probable that both shear thinning and boundary film formation occur within an EHD contact. The relative magnitude of these effects and the resulting EHD film thickness will depend on polymer size and inlet shear rate. The raw data of the EHD tests was therefore analysed in the following way to try and understand these two effects. Most tests were repeated twice and a large number of data points generated. Some scatter was observed in the results and to aid interpretation the data was curve fitted using a high order polynomial. Typical results generated by such curve fitting are shown in figures 4 and 5. The film thicknesses predicted using EHD theory (10) are also shown. In both figures the fitted results are shown as the solid line, the predicted result as the dotted line. For both additive-freebase fluids (bold lines) the curve fitted experimental film thicknesses are close to film thicknesses predicted from EHD theory. For the polymer solutions there are however striking

68

differences. Polymer solutions in SHC gave film thicknesses greater than predicted from the viscosity of the polymer solutions. For SAN40, by contrast, the measured film thicknesses were lower than predicted.

1 .001

.o 1

.1

1

.01 .1 Rolling Speed (m/s)

It can be seen that polymers in SHC form boundary films of approximately 13 - 16 nm, but the same polymers in SAN40 form much thinner films. In an earlier paper (1 1) these boundary fdms have been ascribed to the adsorption of polymer molecules at the solid surfaces. Similar results have been presented for polyisoprenes from surface force measurements (12). The thickness of the film increases with molecular weight and was related to the polymer coil dimensions (11)(12). It is noteworthy that polymers in SAN40 solution give only thin boundary films. The existence of a high viscosity surface layer is supported by the observation that when motion of the disc is halted that a separating film persists in the contact. This was not observed for the base stock tests. Residual film thickness is seen to decay with time in the stationary contact. A typical result is shown in figure 6. Table 4 Boundary film thickness (in nm) from EHD tests Test Fluid SAN40 SHC Basestock 2 3 + 2%A 8 13 +2%B 0 16 + 2%C 2 13

Rolling Speed (mh) Figure 4 Generated and predicted film thickness curves for SHC and 2%C solution

.oo1

made for both base stocks and polymer solutions. These results are shown in table 4.

1

Figure 5 Generated and predicted film thickness curves for SAN40 and 2%Csolution 3.1 Boundary Film Component

By extrapolating the curve fits to zero speed then an estimate of the boundary film thickness can be

0

200 400 600 800 lo00 Time (secs)

Figure 6 Residual film decay at zero speed for 2%C in SHC

69

The low shear rate viscosity results suggest that in the traction fluid polyisoprene adopts a more open conformation and has a relatively large coil size. This should result in a thicker residual film however this is not observed in the film thickness results for S A N 40.

and C in SAN40 do not form boundary films so that the effect of shear thinning can be seen directly.

From these results it is also possible to estimate the “effective viscosity” of the polymer solution relative to that of the base oil in the inlet regiona. Effective relative viscosity is calculated from the measurd film thickness results where:

3.2 EHD Film Component To deduce the hydrodynamic contribution of the polymer solutions it is necessary to remove the effect of the boundary layer. The generated film thickness curves have been replotted with the calculated boundary film thickness subtracted. This is shown in figure 7 which is a linear film thickness/speed plot for 2%C in SHC. Curve A corresponds to the original curve-fitted film thickness results, B when the boundary film (13 nm) has been subtracted. Curve C is the theoretically predicted film result calculated from the low shear rate viscosities. Even with the boundary film subtracted,thepolymer solution still appears to give a thicker EHD film than its low shear rate viscosity would suggest.

effectiverelative viscosity = (hsolutionhbase stock) 1P.67 h is the film thickness generated from the curve fit

Any adsorbed boundary film would distort the relative viscosity results calculated this way. Relative viscosity has therefore been calculated both with ((i)) and without ((ii)) the boundary film present. These are plotted as a function of rolling speed for both fluids in figures 8 and 9. The relative viscosity for the solution measured on the cone-onplate is also shown as (iii),

n

E

: 100 3

8

E f

50

0

0.00 0.05 0.10 0.15 0.20 0.25 Rolling Speed ( 4 s ) Figure 7 Film thickness curves for 2%C in SHC effectof boundary layer The film thicknesses for the polymers in S A N 40 are lower than predicted, although the agreement between predicted and measured for the base stack was very good. This would suggest that significant shear thinning is occuring in the inlet. Polymers B

0.00

0.05

0.10

0.15

0.20

0.25

Rolling Speed ( 4 s ) (a)2%A Figure 8 Effective relative viscosity for polymer solutions in SHC against rolling speed

I

0 k ' ul

in

t

I

in

8

h

.3

0

8

LA

c 0

w

.

I I

z

I

2

.

I

Effective Relative Viscosity

- 0

c

c

z

LA

!Q

Effective Relative Viscosity

P

w N L

- 0

Effective Relative Viscosity Effective Relative Viscosity

Figure 8 (cont.) Effective relative viscosity for polymer solutions in SHC against rolling speed

Figure 9 Effective relative viscosity for polymer solutions in SAN40 against rolling speed

71

3

x

.I

2*6 viscometer

00

1.o 1 : 0.00

.

I

I

.

0.05

0.10

.

1

0.15

'

l

.

I

0.25

0.20

Rolling Speed ( 4 s )

EHD result

1

o.ooe+o

1.OOe+6

2.OOe4

Shear Rate (s-1) Figure 11 Effective relative viscosity plotted against shear rate for 2%Cin SAN40

(c) 2%C Figure 9 (cont.) Effective relative viscosity for polymer solutions in SAN40 against rolling speed The effective viscosities of both SAN40 and

SHC solutions clearly decrease with increasing rolling speed. These results can also be plotted as a function of maximum inlet shear rate (7) as illustrated in figures 10 and 11 where the results from viscometer measurement is also shown.

For polymer solutions in SHC at low shear rates (low rolling speeds) the solutions are showing effective relative viscosities greater than their low shear viscosities determined by a cone-on-plate viscometer. As the shear rate is raised,the effective relative viscosity falls presumably due to shear thinning The effective relative viscosity results for S A N 40 solutions are very different to those seen for

SHC. Only A formed a significant boundary film and the relative viscosity results are thus greater than expected when this is present. For polymers B and C the results are far lower signifying considerable viscosity loss in the inlet. 0

8

EHDresult

result

O.OOe+O

1.OOe+6

2.OOe+6

3.OOe+6

S h a Rate (s-1) Figure 10 Effective relative viscosity plotted against shear rate for 2%C in SHC

The film thickness results presented have shown that polymer-containing fluids do not inevitably give lower EHD films than predicted. At low rolling speeds far greater films are seen, even when the boundary films have been taken away a substantial viscosity enhancementcan be seen. This effect is greatest for the lower molecular weight polymers. It is interesting that SAN40 does not appear to form boundary films under rolling conditions, or at least they do not survive. It is possible that the high shear stresses associated with the traction fluid at the surface prevent the formation of a stable adsorbed layer. The behaviour of polymer solutions in SAN40 is quite different. From the lowest attainable shear rate the effective relative viscosity of these fluids are

12

less than measured in the cone-on-plate viscometer. This is attributed to shear thinning of the solutions which is more likely in SAN40 than SHC due to the following; (i) greater polymer coil size due to better solvation properties (ii) greater shear stresses in inlet due to higher avalue. The additional ftlm thickness enhancement over and above that predicted by the adsorbed layer is intriguing and it is interesting to speculate on its origins. This effect is only seen when the layer is present, this observation would suggest that the adsorbed polymer coils at the metal surface induce a localised change in the fluid structure immediately above the boundary layer. This might take the form of local ordering or structuring of base fluid and polymer or increase in the polymer concentration. This would result in an increase in viscosity or a viscoelastic effect due to the loss in mobility of the polymer molecules in the ordered region. Both of these effects would contribute to an EHD film enhancement. 4. CONCLUSIONS

The film thickness results presented have demonsmted the complexity of polymer solution behaviour in EHD contacts. Depending upon the film thickness range studied this behaviour can be dominated by either a boundary or rheological response. This study has demonstrated, through direct measurement, that polymer solutions contribute to EHD film formation in the following manner; (i) Polymer solutions form boundary surface films in rolling contacts and these maintain separation even at zero speed. (ii) These films, probably of adsorbed polymer molecules, have viscoelastic properties which further enhance EHD film thickness. The degree of the enhancement represents a balance between increasing polymer size and the resultant increasing susceptibility to shear alignment.

(iii) Both these effects are dependent upon the solvation and rheological properties of the basestocks.

REFERENCES

1. Whorlow, R.W., “‘RheologicalTechniques.” 2nd

edition Ellis Horwood. 2. Wu, C.S., Melodick, T., Lin, S.C., Duda, J.L. and Klaus, E.E., “The Viscous Behavior of Polymer-Modified Oils Over a Broad Range of Temperature and Shear Rate.” J. Trib., 112, pp417425, (1990). 3. Cross, M.M., J. Colloid Sci., 20, pp417-437, (1965). 4. Walker, D.L., Sanborn, D.M.and Winer, W.O., “Molecular Degradation of Lubricants in Sliding Elastohydrodynamic Contacts.” ASME Trans. J. Lub. Tech., 97, ~~390-397, (1975). 5. Bates, T.W., Williamson, B., Spearot, J.A. and Murphy, C.K. “The Importance of Oil Elasticity.“, Ind. Lub. & Tech., 40, pp4-19, (1988). 6.0krent, E.H. “The Effect of Lubricant Viscosity and Composition on Engine Friction and Bearing Wear.’’ ASLE Trans., 4, ~~257-262, (1961). 7. Foord, C.A., Hamman, W.C. and Cameron, A. “Evaluation of Lubricants Using Optical Elastohydrodynamics.” ASLE Trans. 11, pp 31-43, (1968). 8. Hiram, M. and Cameron, A. “TheUse of Optical Elastohydrodynamics to Investigate Viscosity Loss in Polymer-thickened Oils.” ASLE Trans. 27, pp 114-121,(1984). 9. Johnston, G.J., Wayte, R. and Spikes, H.A. “The Measurement and Study of Very Thin Lubricant Films in Concentrated Contacts.” STLE Trans. 34, pp. 187-94, (1991). 10. Hamrock, BJ, and.Dowson, D.D.. “Ball Bearing Lubrication. The Elastohydrodynamicsof Elliptical Contacts.” Pub. John Wiley & Sons (1981). 11. Cann, P.M. and Spikes, H.A., “The Behavior of Polymer Solutions in Concentrated Contacts: immobile Surface Layer Formation.” STLE Preprint 93-TC-1B-1 12. Georges, J-M., Millot, S.. Loubet, J-L. and Tonck, A., “Drainage of Thin Liquid Films Between Relatively Smooth Surfaces.”, J. Chem. Phys., 98, ~~7345-7360, (1993). 13. Bair, S. and Winer, W.O. “Shear Rheological Characterisation of Motor Oils.” STLE Trans. 31, pp 316-323, (1988).

Dissipative Processes in 'I'ribology / D. Dowson et al. (Editors) 1994 Elsevier Science B.V.

73

Temperature Profiling of EHD Contacts prior to and during Scuffing. J C Enthoven & H A Spikes

In this paper a novel "nodding mirror" infra-red line scanner is used to study the effect of additives on contact temperatures and hence scuffing in a sliding point contact. The "nodding mirror" line scanner is capable of taking temperature profiles across the contact in a very short time (less than 30 msec). The objective is to capture the temperature history across the contact just prior to and during scuffing using lubricants with and without additives. Tests were carried out in a device consisting of a steel ball loaded and sliding against a stationary sapphire window. The lubricant basestock used in this study was purified hexadecane. This was chosen as it is a simple, low viscosity lubricant that forms a negligible EHD film under the conditions of these tests. This was important as one of the aims was to study boundary additive response to contact temperatures and their effectiveness in postponing or preventing failure. Temperature profiles prior to and during scuffing have been taken in tests with pure hexadecane and with hexadecane containing (i) 1.0 wt% dibenzyldisulfide, an EP additive, and (ii) 0.1 wt% stearic acid, a friction modifier. 1. INTRODUCTION Practical components in which a high degree of sliding exists, such as gears, and cams and tappets, often fail duc to scuffing. Although this catastrophic failure mode has been the subject of research for many years, the exact mechanisms are still not clearly understood. Many scuffing theories have been proposed which try to predict the onset of scuffing [1,2]. The best known are Blok's critical temperature hypothesis [3,4], the failure of elastohydrodynamic lubrication as proposed by Dyson [5,6], and the frictional power intensity model [7]. In each of these models a different thermal criterion is used to predict the onset of scuffing. Blok postulated that the transition from smooth running to scuffing would occur when the contact temperature exceeds some critical value. This critical tempcrature is assumed to be independent of load, sliding speed and test history. His postulate has been the subject of much testing and is generally considered to only be valid for un-doped mineral oils. In Dyson's theory, failure is based upon the breakdown of the main elastohydrodynamic lubrication film in sliding contacts. According to this modcl scuffing will occur when the lubricant inlet viscosity is insufficient to generate the large pressures needed for successful operation of the main and micro EHL films. Since the inlet viscosity is dependent upon the inlet tcmpcrature, Dyson's criterion can be related to a critical inlct tcmpcrature.

In the Frictional Power Intensity model, the amount of frictional heat generated in the contact area is assumed critical. Despite our current lack of detailed understanding of its origin and mechanism, the occurrence of scuffing is generally regarded as resulting from thermal feedback. Under a particular combination of load, speed and friction, a critical temperature is reached somewhere in the vicinity of the contact. At this temperature the lubricant film weakens, resulting in an increase in asperity contact friction. If this increase in friction causes a still higher temperature then the consequence can be the collapse of the lubricant film. The magnitude of the temperatures within and in the vicinity of the contact depends upon the amount of heat generated and dissipated. It is apparent from the above that for a complete analysis of scuffing, information about contact temperatures is vital. However traditionally, scuffing tests are conducted using actual gears or discs. In these experiments, contact temperatures are either measured using embedded or trailing thermocouples, or calculated theoretically from the contact conditions at which scuffing takes place. The transition to scuffing occurs very suddenly and the actual contact temperatures just prior to failure can not be found in this way. In previous work [8] infrared temperature profiles were taken across the point contact formed between a steel ball loaded and sliding against a stationary sapphire window. In these tests purified hexadecane

74

was used as a lubricant. The profiles were taken by moving an infrared microscope across the contact area using a x-y table controlled by a stepper motor. Some temperature profiles taken by this means are shown in Figure 1. In this figure, the temperatures across the contact area at each load stage up to scuffing can be seen. Scuffing occurred at a maximum contact pressure of 1.77 GPa, shortly after the last temperature trace had been taken. The authors compared their data with Blok’s critical temperature hypothesis and with Dyson’s theory but no agreement was found. The authors did find that scuffing between a steel ball and sapphire window was similar to that observed between a steel ball and a steel flat. 250

I

-

d

-

I

-

-

-

I

i * 200 ..................... .;.............. r... i.77GPa

:

_ - -

1

-

-

-

I

-

under the conditions of these tests. This was important as one of the aims was to study the response of boundary additives to contact temperatures and their effectiveness in postponing or preventing failure. 2. EXPERIMENTAL APPARATUS

A schematic diagram of the sliding test rig used is shown in Figure 2. A 25.4 mm diameter AISI 52100 steel ball is loaded against a 2 mm thick sapphire window. The loading mechanism is such that the plane of the applied load passes through the centre of the nominal point contact. A strain gauge beam is then used to monitor the friction force accurately.

- -

Hexadecane Tbulk=6OOC “s = 1 m’s Pscuff = 1.i7 GPa ”’:

.w

n 150

3

I

’=

.e5

100 50

c -600

-400

-200

0 200 X-AS, micron

400

600

Figure 1 Temperature traces for a scuffed run, from reference [8]. One of the limitations of the work reported in [8] was the amount of time needed to take one temperature trace, which was about 30 seconds. Since the transition from “smooth” running to scuffing occurs very suddenly, it was clear that in order to be able to study boundary additive response, the time required to take one trace needs to be reduced considerably. This has been achieved in the work describcd in this paper by converting an infrared microscope into a ‘nodding mirror’ infrared line scanner. This is capable of taking successive temperature profiles across the contact in less than 0.03 seconds. The objective is to capture the temperature history across the contact just prior to and during scuffing. Tests were carried out in a point contact device consisting of a steel ball loaded and sliding against a stationary sapphire window. The lubricant basestock used in this study was purified hexadecane. This was chosen as it is a simple, low viscosity lubricant that forms a negligible EHD film

Figure 2 Schematic diagram of sliding test rig. The infrared microscope is mounted in a fixed position above the ball. The microscope focuses the radiation from a 36 pm diameter spot from the contact zone through a x15 reflecting objective onto a liquid nitrogen cooled indium antimonide detector. The detector has a spectral response of 1.8 to 5.5 pm. The microscope is also fitted with a parfocal channel, with a lox eycpicce to permit simultaneous viewing of the area being studied. Positioned between the microscope objective and the sapphire window is the ‘nodding mirror’ assembly. This is mounted on a solid steel block to limit vibrations. The ‘nodding mirror’ is driven by a

75

rotating steel shaft, which is connected to a gear box and a high speed electric motor. A more detailed picture of the workings of the ‘nodding mirror’ is shown in Figure 3. Two reflective mirrors can be seen. One 17 mm square mirror is mounted on the x15 reflecting objective which is attached to the infrared microscope. A smaller, 7 mm square mirror is attached to the nodding mount. This mount consists of a thin piece of carbon fibre tubing with a 45’ flat face on which a very thin and lightweightmirror is glued. The mount can pivot about a 1 mm diameter shaft marked “0” as seen in Figure 3. A horizontal slot is machined in the carbon fibre tubing and the cam on the rotating shaft fits in this slot.

c)

Figure 3 Nodding mirror assembly. The principle behind the approach is that it is easier to deflect an infrared beam rapidly using a low inertia mirror, than to move either the test rig rapidly beneath the microscope, or the microscope over the test rig. The radiation from the 36 pm diameter focal point is reflected off the small nodding mirror on the mirror attached to the objective. The objective in turn will then focus the radiation onto the detector. By rotating the steel shaft the cam inserted in the mirror mount will pivot the mirror backwards and forwards about the shaft marked “0”.This in turn will move the focal point from left to right in a horizontal plane as shown in Figure 3. Thus by “nodding” the small mirror, the infrared microscope can scan the surface and therefore now operates as an infrared line scanner. The distance the focal point will move depends on the eccentricity of the cam on the rotating shaft. Different s h a h were made but the one used in this work moved the focal point by about 1200 mm, which is well across the contact zone. Shown very schematicallyin Figure 2 is the optical pick-up mounted on the rotating shaft. This triggers data acquisition at the beginning of the movement of

the focal point from left to right, i.e. from the contact inlet to outlet. The microscope takes 150 data points at a frequency of loo00 Hz when scanning. No data is taken whilst the focal point moves back to the inlet. In the current study, experiments were carried out with the shaft rotating at lo00 rpm. This means that it takes 0.03 seconds to complete one trace. In this time, all 150 data points need to be first measured by the microscope, then converted into digital values and finally stored in a buffer of the microcomputer. To do this, a fast analogue to digital converter was needed, and a 12 bit linear converter which can sample analogue voltages at rates up to 160000 Hz was employed. The result of each conversion was stored in a buffer, sited on the A D board of a microcomputer. The host computer then accessed these intermediate results simultaneouswith the ADC starting the process of converting the next analogue sample. In this work a clock speed of 10000 Hz was used for collecting the detector data. In order to allow for fast data acquisition a buffer was created on the microcomputer large enough to contain 50 traces each containing 150 data points (50 traces x 150 points x 4 bytes = 30 kbytes). After 50 traces had been taken, the 5tst trace was written over the 1st trace, the 52nd trace stored in place of the 2nd trace, etc. At the end of the experiment, when the space bar was touched, the buffer was written to an array and stored onto the hard disc. This way a series of 50 temperature profiles over the last 3 seconds of any test were available for subsequent analysis. 3. CALIBRATION

In these experiments, the infrared microscope was used in “transient mode”. In this mode, the incoming radiation is not chopped as in earlier work [8], but instead the signal is amplified and demodulated inside the microscope housing before being send directly to thc microcomputer. Two probIems arise in the calibration procedure. Firstly, since in AC mode the measured radiance is not compared with the background radiation of the chopper, the microscope electronics positions the incoming signal around a floating base line rather than relative to the chopper background value. This is done in such a way that the area below the base line equals the area above, as can be seen in Figure 4.The second problem is that the base line drifts. This means that

76

there is no reference point or line which is present when the microscope is used in DC mode. Both problems are a result of the electronics inside the microscope housing and could not be changed easily.

I

4

I

time I Figure 4 Input voltage versus time in AC or transient

I

mode. The drift was measured and found to be insignificant in the first 7 minutes of the test, but considerable after 150 minutes. This means that the drift did not affect the results obtained over 50 uaces or 3 seconds. In order to convert the measured radiance values into temperatures, a new baseline needed to be determined. This was achieved by measuring the track temperature of the ball with the microscope in chopped mode in a separate experiment. Once the track temperature was known, the radiance traces could be converted into temperature profiles following the calibration procedure used in [8]. The reader is referred to this paper for a complete radiation analysis. The error in determining the track temperature for the transient traces is about f 15 %. Due to the shape of the calibration curve, the resulting error in the maximum contact temperature will be less than this. 4. EXPERIMENTAL RESULTS

All experiments reported in this work wcre carried out with polished stcel balls having a roughness of 0.016 RMS.A new ball was used for each test. Each sapphire window was used several times but the window was mounted off-centre in its stainless steel holder so that rotation of the holder enabled a new region of the sapphire surface to be cmploycd for each run. Prior to a test, the lubricant bath, ball and sapphire window were thoroughly cleaned with toluene and then analytical grade acetone. The oil bath was filled with lubricant so that the ball was just over halfimmersed. The rig was then allowed to heat up to the desired bulk oil temperature. During this time, the stcel ball was lightly loaded against the window at a contact pressure of 0.80 GPa whilst sliding at 1.0 m/s.

In all the tests reported in this work, the operating temperature was 80 ‘Cand the sliding speed equalled 1.99 mls. After a test was started, the load was increased in steps of two minute intervals until scuffing occurred or until the 500 N load limit of the rig was reached. The starting load was 50 N and the load was increased in 50 N stages. The surface was scanned continuously during a test but, as was mentioned above, only the temperature history of the last 50 traces or last 3 seconds was saved. This meant that the results presented in this paper only show the temperature traces taken at the last load stage. Figure 5 shows ten consecutive temperature traces taken with the infrared line scanner. The nodding mirror drive shaft rotated at a speed of 1000 rpm, thus each trace in Figure 5 was taken at an interval of 0.03 seconds. Every profile contains 150 data points, sampled at a frequency of 10,000 Hz.

400

u

350

150 100

50

inlet

outlet

Figure 5 Tempcrature traces taken at 0.03 seconds interval up to scuffing. The horizontal axis in Figure 5 shows the position, with the inlct on the left and the outlet on the right hand side. The scanning distance is approximately 1200 pm. The vertical axis shows the stecl ball surface temperature in ‘C. The lubricant in this experiment was purified hexadecane and scuffing occurred at a contact load of 250 N. The traces shown in Figure 5 were all taken at this load and show the transition from “smooth” running to scuffing. Within the 10 traces, or 10 x 0.06 = 0.6 seconds, failure occurred, and in this time the maximum contact temperature increased from about 170 ‘C to more than 420 ‘C. No temperatures could be measured above 420 ‘C since the voltage input to the

77

computer was then outside the range of the A-to-D converter. In Figure 6 the maximum contact and inlet temperature is shown for the 50 saved traces. The horizontal axis shows the time in seconds. Time equals zero and 3 seconds do not correspond to the beginning and end of the test, respectively, but merely to the first and 50th trace, respectively. 450 400

P

350

150

100 50

Time, seconds

Figure 6 Maximum contact and inlet temperature at last load stage, from Figure 5. Looking at Figure 6, one can again see the sudden transition in both maximum and inlet temperature. Up until scuffing the inlet temperature is about 125 ‘C and the maximum contact temperature is about 170 ‘C, except for the peak at 1.5 seconds. This trace, and the traces before and after this peak are shown in Figure 7. 250

to be influenced by this event. The trace taken before and after the peak are very similar in shape. The behaviour seen in Figure 5 and 6 was typical for scuffing test with pure hexadecane. The transition occurs very suddenly (within one second) and without any warning, and this emphasises the need for a very rapid measuring technique, in order to follow the development of scuffing failures. A different response was seen in experiments carried out with hexadecane + 1.0 wt% dibenzyldisulor phide ( C ~ H ~ C H ~ S S C H ~ CDibenzyldisulfide ~HS). “DBDS”, is a sulphur-based anti-wear additive, and its addition increased the failure load of hexadecane considerably. Scuffing occurred at a contact pressure of 2.31 GPa. Figure 8 shows the maximum and inlet temperature at the last load stage. Looking at this figure, one can see that both temperatures vary by large amounts from trace to trace. Until the onset of scuffing, differences of almost 100 “C in maximum contact temperature were found between traces. This behaviour stands in contrast to what was seen in experiments with pure hexadecane, where up until the transition, the maximum contact temperature remained fairly constant. . . . . , - - - . I . ..

. I

.... I ....

400

[

350 300

8 5 c 250

2

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

200 150

‘

’

t . . . . ....I .... .... I . . . . I . . . .

0

0.5

1

1.5

2

2.5

3

Time, seconds

..................................................................... inlet

outlet

Figure 7 Temperature traces at around 1.5 seconds. Looking at this figure one can see that the maximum contact temperature suddenly increased to more than 220 ‘C. The inlet ternperaturc does not seem

Figure 8 Maximum and inlet temperatures for a test with hexadccane with 1.0 wt% DBDS. In Figure 9, six temperature profiles are shown from the results of a test with hexadecane + 1.0 wt% DBDS. Five of the traces are marked from A to E and one trace is marked “scuffed”. Up until scuffing, the shape of the profiles rapidly changed from A to E and back to A again. It can be seen in Figure 9 that in between traces, the temperatures changed by large amounts. Profile B is very irregular of shape, with a maximum temperature of 400 “C.On the other hand,

78

450

_.....................................I..,~.,,.,.,,.,..,..,..,.~....................~..~..~..~..~~~ 450 ...................................................................................................

400

_............. .....................................................................................

350

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

100

450

400

350

100

450 400

,

.

1

inlet

.

1

.

'

-

1

inlet

ouuet

A

_..................................................................................................

450

outlet

B

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

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

~.,,.,,.,,.,...............(............,,,,...,....,,,,,,,..,....,.,,,.....,,......

_...............................................,,.,.,...,..,,..............,.....................

l

inlet

.

l

.

C

I

.

1

-

I

l

inlet

outlet

_..................................................................................................

450

.

I

.

l

.

(

oudet

D

-................,....(................~.....,......................................................

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

1

inlet

E

outlet

inlet

.

1

.

1

SCUFFED

-

1

outla

Figure 9 Six temperature profiles from a test with hexadecane + 1.0 wt% DBDS.

-

1

79

the next race taken 0.03 seconds later is very smooth and the contact temperature is about 80 ‘Clower. This rapid changing of shape of the temperature profiles was increasingly seen at load stages above the failure load of pure hexadecane. It appears that the addition of 1.0 wt% DBDS to hexadecane increases the failure load by responding to incipient failure, allowing for recovery. When the conditions become too severe, no recovery takes place and the scuffing occurs, as seen in the trace marked “scuffed” in Figure 9. In the last experiment to be discussed, 0.1 wt% stearic acid was added to the hexadecane. Stearic acid (CH3.(CH2)16,COOH) is a boundary additive which adsorbs onto the surface. The molecules are thought to desorp from the surface at a certain temperature depending upon the contact pressure and additive concentration [91. Stearic acid proved to be a very effcctive additive in the conditions of this test. In an experiment with hexadecane + 0.1 wt% stearic acid no scuffing occurred, the test was terminated when the maximum load of the rig was reached instead. At this load, the maximum contact pressure equalled 2.39 GPa. Shown in Figure 10 are the maximum and inlet temperature at the last load stage. Looking at this figure one can see that the maximum contact temperature equals about 220 ‘C,with every fifth trace having a contact temperature about 30 ‘C higher. The inlet temperature averages about 150 ‘C. 300

~

I.............

250

P

$ 225

- .

- .~.

J ...............6 .......... 6 I...

. ..........I....

-.

.. .

......

i

I,......

-. t .............

appears around the point of the maximum Hertzian contact pressure. The inlet temperature does not seem to be affected. The reason for the observed cyclic behaviour shown in Figure 10 is not yet clear. The effect was not seen in another experiment in which thc nodding mirror line scanner was used. The failure load for hexadecane + 0.1 wt% stearic acid is much higher than for pure hexadecane and stearic acid as an additive seems to outperform DBDS as well. 250 220

P

4

I90

er.

8 160

b

130

---

inlet

OUtlCl

Figure 1 1 Three temperature profiles for hexadecane + 0.1 wt% stearic acid. This is surprising. However, one plausible explanation is that besides the absorbed layer, stearic acid might react with the sapphire (AI203) to form (basic) aluminium stearate, which is a metal soap. This in turn might form a very protective layer covering both the steel and sapphire surface.

5. CONCLUSIONS

Temperature profiles prior to and during scuffing have been taken at 0.03 seconds intervals across the 175 contact area. A single basestock with two boundary b 150 additives has been studied. In scuffing tests with pure hcxadecane, the 125 transition from smooth running to scuffing occurred 1 M L : : i : : : : !::::!::::!:::A:::-! very suddenly (within 0.6 seconds). This emphasises 0 0.5 I 1.5 2 2.5 3 the nced for a very rapid measuring technique, in order Time, seconds to follow the development of scuffing failure. Figure 10 Maximum and inlet temperature for The temperature profiles taken in experiments with hexadecane + 0.1 wt% stearic acid. hcxadccane + 1.0 wt% dibenzyldisulphide were very irregular of shape, with large fluctuationsin maximum Figure 11 shows thrce successive tcmperature profiles temperature. The addition of DBDS to hexadecanc taken with the infrared line scanncr. It can be seen in seems to increase the failure load by responding LO this figure that the increase in maximum tcmperature

E$ m

80

incipient failure allowing recovery. This possibly provides further insight into the mechanisms of action of EP and anti-wear additives. No failure could be obtained with hexadecane + 0.1 wt% stearic acid. Stearic acid might react with the sapphire to form a metal soap, which protects the surfaces very effectively.

REFERENCES 1 Dyson, A., "Scuffing - a review, part l", Tribology

International,April 1975, pp. 77-87. 2 Dyson, A,, "Scilffing - a review, part 2",Tribology International,April 1975, pp. 108-122. 3 Blok. H., "Surface temperatures under extreme pressure conditions",Congres Mondial du Peuole, pp. 471-486, Paris, 1937. 4 Blok, H., (1969), "The postulate about the constancy of scoring temperature", Interdisciplinary Approach to the lubrication of Concentrated Contacts, Troy, N.Y.. Vol. SP-237, pp. 153-224. 5 Dyson, A., "The failure of elastohydrodynamic lubrication of circumferentially ground discs", Proc. Inst. Mech. Engrs., 190,52/76, 1976. 6 Dyson, A., "Elastohydrodynamiclubrication of rough surfaces with lay in the direction of motion", 4th Leeds-Lyon Symp., pp. 201-209.1977. 7 Bell, J. C., Dyson, A., "The effect of some operating variables on the scuffing of hardened steel discs", Roc. Inst. Mech. Engrs., Symp. on EHL, 1972, Paper C11P2, pp. 61-67. 8 Enthoven, J. C., Cann, P. M., Spikes, H. A., "Temperature and Scuffing", Tribology Transactions, 36, 1993, p. 258-266. 9. Spikes, H. A., "Boundary lubrication and boundary films", XIXth Leeds-Lyon Conference, 1992, Leeds.

Dissipative Processes in Tribology / D. Dowson CI al. (Edilors) 0 1994 Elscvier Scicnce R.V. All rights reserved.

81

Computational Fluid Dynamics (CFD) Analysis of Stream Functions in Lubrication D Dowson and T David Department of Mechanical Engineering The University of Leeds, Leeds LS2 9JT, United Kingdom In fluid mechanics streamlines are widely used in association with ideal fluid flow, but less frequently for slow viscous flow. They can nevertheless indicate details of lubricant behaviour of considerable value to the tribologist and the purpose of this paper is to demonstrate the way in which streamline solutions for simple bearing forms can be derived and interpreted. It is now possible to apply versatile computational fluid dynamics (CFD) software to bearing problems as an alternative procedure for the generation of streamline solutions and this is demonstrated in the present paper. 1. INTRODUCTION

The basic equation of fluid film lubrication is a second order partial differential equation in pressure formed from an amalgamation of the equation of continuity and the Navier-Stokes equations of motion. Analytical and numerical solutions to this equation have provided the foundations for studies of bearing performance and design ever since it emerged from the classical analysis by Osborne Reynolds [ 11 in 1886. Once the pressure distribution in a bearing has been established, the cross film variation of lubricant velocity parallel to the entraining surface (u) can readily be derived to reveal important illustrations of fluid motion, as shown by Reynolds in his most effective illustrations. Likewise, contours of constant fluid velocity in the lubricating film (isotachs) and of constant pressure (isobars) can be constructed to reveal further details of the field of viscous flow. Michell [2] presented isotachs for the plane inclined or tilting pad bearing in his book published by 1950. Whereas streamlines are normal features of solutions to ideal fluid flow problems, they are less frequently represented in viscous flow analysis. They can, nevertheless, convey important information on the nature of slow viscous flow in fluid-film lubricated bearings, particularly in relation to cross film velocity components, perpendicular to the entraining bearing surfaces and

one of the purposes of this paper is to focus attention on the merit of recording streamlines in many lubrication problems. Some authors have adopted this approach to good effect for both hydrodynamic and elasto-hydrodynamic conjunctions. Two notable and early solutions to bearing problems were recorded in the 1950's by Wannier [3] and Milne [4], who analysed infinitely long journal and plane inclined thrust bearings respectively. Jeffery [5] provided a classical solution for stream functions between submerged rotating cylinders as early as 1922. This was later extended to circumstances more akin to journal bearings by Diprima and Stuart [6], while Kamal [7] examined flow separation in such configurations. Simuni [8] and Putrie [9] used numerical methods to reveal stream functions in stepped parallel slider bearings while Jinn-An Shieh and Hamrock [ 101 considered the stream function in elastohydrodynamicconjunctions.

For the slow viscous flow of an isoviscous, incompressible fluid, the stream function (y) is governed by the bi-harmonic equation, as is the stress function (0) in plane strain elasticity problems. For this reason, solutions to the biharmonic equation have attracted considerable attention and in some cases analytical solutions exist for simplified bearing configurations. In general, however, numerical solutions are required for realistic bearing configurations and initially finite-difference representations and relaxation procedures were adopted. Some early solutions based upon this approach will be noted. When

82

inertia terms in the equations of motion are considered, numerical solutions are invariably required, but the influence of flow reversal and circulation within lubricating films has nevertheless been explored through this approach. In recent years advances in computational fluid dynamics (CFD) have led to the development of robust software for the solution of a wide range of fluid flow problems. In the present paper we demonstrate how one such CFD package can be adapted to solve plane-flow lubrication problems. Simple solutions for plane-inclined and Rayleigh step bearings are compared with earlier finitedifference results, but the CFD package is then used to investigate features of lubricant flow into a bearing groove or pressurised recess. 2. THEORETICAL BACKGROUND

The plane flow of an incompressible, isoviscous Newtonian fluid is governed by the equations of continuity and momentum (NavierStokes).

It follows at once from equations (1,2) that if inertia can be neglected, the pressure in the field of flow is governed by the Laplace equation.

(4)

- (v)automatically satisfies the continuity equation (1).

Furthermore, the stream function ( y ) satisfies the biharmonic equation,

Solutions to equation ( 5 ) for the stream function (v), with boundary conditions appropriate to a particular bearing geometry and operating conditions, will thus satisfy the requirements of both mass and momentum conservation. Whereas a limited number of analytical solutions to the biharmonic equation ( 5 ) exist which are of interest in the analysis of fluid-film bearings (Jeffrey [ 5 ] , Jaeger [ 1l]), numerical solutions have been obtained by both finite difference and finite element procedures. When inertia is considered, numerical solutions to equations (1) and (2) are inevitably required. Such solutions enable Reynolds number effects to be explored and although these do not often influence the overall performance of bearing systems, they can materially influence the local behaviour of lubricant within a bearing. 3.

In addition, if a function ( y ) exists such that,

NUMERICAL COMPUTATION

ANALYSIS

AND

Early numerical solutions for stream functions in lubricating films were based upon finitedifference representations of the governing equation. More recent approaches have adopted finite element formulations in general CFD solvers. 3.1 Finite-Difference Solutions Much has been written about the use of finite difference representations to the governing

83

equations and the adoption of relaxation methods in studies of fluid-film bearings. In general there are familiar problems of mesh sizing; the failure of grids to coincide with realistic bearing boundaries; the selection of over and under relaxation factors and convergency problems, particularly when reverse flows are encountered. Since this is a long established procedure it is not necessary to dwell on the technique at this stage. 3.2 CFD Approach based upon Finite Element

Formulation

Once again the approach to numerical solutions of general fluid flow problems for incompressible, isoviscous fluids and steady state

:(

=0)

conditions is based upon the discretisation of the conservation equations for mass and momentum (equations (1) and (2)).

I u.vu = - v p + - v*u

Re

FIDAP uses the Galerkin form of the method of weighted residuals [13], allowing the residuals to be orthogonal, in an integral formulation, to the interpolant functions of each element. A matrix equation results from the assembly of the element formulations. This matrix may be solved in a number of ways, but is usually accomplished, as was the case for the solutions presented here, by a Newton iterative scheme. Inspection of equations (7) and (2) shows that for the nondimensional equation set FIDAP can accept a density of unity and a viscosity proportional to the inverse of the Reynolds number characteristic of the flow regimes. Hence, in specifLing the input data, various dimensionless flow solutions may be obtained readily for a variety of Reynolds numbers by simply changing the adopted value of viscosity. 4.

For the results presented in the next section we have adopted a finite element formulation utilising a commercially available solver, FIDAP. The fluid domain is sub-divided into discrete elements fixed in space and mesh generation schemes can be adopted to represent the domain geometry in the most effective manner for discretisation purposes. Within each element the dependent variables of pressure and velocity are interpolated by functions of known order whose coefficients are to be determined. For a valid and robust scheme the order of interpolation is such that the pressure interpolant needs to be one order lower than that of the velocity interpolant, the so called LBB condition [121.

By choosing a characteristic velocity, normally that of the moving surface if onc of the bearing solids is stationary, and a characteristic length scale, normally the minimum or outlet film thickness, the conservation equations can be reformulated into their non-dimensional equivalents and written in vector form as; v.u = 0

(6)

(7)

RESULTS

Initially solutions for streamlines in lubricating films were obtained analytically for simple configurations, or numerically by means of finite difference representations and the use of relaxation methods for realistic configurations. A range of numerical solutions obtained in this way will be presented for simple bearing forms, before the application of CFD solvers to this field is discussed. 4.1 The inlet region between rigid rotating cylinders An illustration of the streamlines in the inlet region to the nip between two rotating rigid cylinders with parallel axes obtained by Oteri [14] was included in a paper [15] presented to the first Leeds-Lyon Symposium on Tribology. It is reproduced have as Figure l(a), together with additional information in the form of contours of uniform velocity (isotachs) and uniform pressure (isobars) in Figures I@) and l(c).

An interesting feature of the solutions shown in Figure 1 is the reverse flow in the inlet region and the formation of a free boundary between the oil and the air. Oteri [ 141 was able to show that surface

84

tension played a negligible role in determining the form and location of this free surface in the case considered. 4.2 The Rayleigh step bearing

Details of the viscous flow in a step bearing were considered in detail by Toyoda [16] through the use of finite difference and relaxation methods. An important issue was the specification of the velocity and pressure boundary conditions at entry to and exit from the bearing. The Dirichlet (no slip) boundaq~conditions on velocity were adopted on each of the solid bearing surfaces, while the von

(

:-I

Neumann condition on pressure p = - - 0 was applied across the inlet and outlet sections to the lubricating film. In reality, the pads in a thrust bearing ring will experience the formation of a ram pressure effect, but this can readily be taken into consideration if the external flow field upstream of the bearing pad is also analysed. The well known linear pressure profile for the complete step bearing is readily revealed by the numerical solutions as shown in Figure 2(a). Perturbations to the pressure in the vicinity of the step were revealed by Toyoda [16] employing finite difference methods and isobars are portrayed in Figure 2@) for a Rayleigh step bearing with the step located half way along the bearing and Reynolds numbers of R, = 10 and R, = 100. It is evident that cross film presusre variations are of greatest magnitude in the vicinity of the step. A solution based upon the CFD code FIDAP revealed the crossfilm pressure variation shown in Figure 2(c) for a step located mid-way along the bearing and a step height ratip = h, / h o ) of 1.8. It should be noted, however, that the pressure variation across the film is only about 2 percent.

(6

Figure 1Finite difference solutions for the flow in the inlet region to two rigid, rotating cylinders (a) Streamlines (b) Isotachs (c) Isobars

It is, however, the details of the flow in the vicinity of the step which generally attracts attention in the analysis of the Rayleigh step bearing. This can be analysed by either finite difference and relaxation procedures or by the application of a CFD solver. The influence of step height ratio

85

0.3

P

0.2

- U0.1

0

I

U-

p

I

liil

i

0.5

(PI

1

Figure 2(a) Linear pressure profile for Rayleigh Step Bearing ( n = 0.5, 6 = 1.5))

(h, - hi/h,)

upon the flow in the vicinity of the

step, as revealed by the CFD solver FIDAP, is shown in Figure 2(d). Most of the lubricant entering the step bearing is drawn into the region of minimum film thickness beyond the step if the step height is small, albeit with a pocket of recirculation in the comer of the step in most cases. For larger step height ratios it is essentially only the lubricant in the lower part of the inlet film which is transported beyond the step, while the remainder forms a reverse flow stream in the inlet land region. Such details, which are readily revealed by the stream functions, are particularly important when viscous dissipation and thermal balances are considered.

Figure 2(b) Isobars in the vicinity of the step in a Rayleigh step bearing (n = 0.5, (i) R, = 10, (ii) R, = 100) While numerical solutions readily reveal the overall features of viscous flow in standard bearing configurations, such as plane inclined and Rayleigh step bearings, it is for the less standard lubrication problems that CFD solvers are likely to find greatest appeal. In order to illustrate this point we turn to the age-old problem of lubricant entering a bearing via a supply slot and a groove in the next section. 4.3 Lubricant flow in a supply slot and groove.

The general configuration of the problem considered is shown in Figure 3, Lubricant enters a relatively deep groove from a supply slot with pressure (pS)before being entrained into the bearing clearance by the surface moving with velocity 0. Much of the lubricant circulates within the groove, with only a small amount being drawn into the clearance space. Details of the flow patterns, which are influenced by Reynolds number in the groove, are readily revealed by FIDAP solutions to the problem.

86

0

0.-3

0.6

0.9

I.?

1.5

14

1hlh.l

Figure 2(c) Cross film pressure distribution at the step in a Rayleigh step bearing ( n = 0.5, h, = 1.8) The finite element mesh for the groove domain in the vicinity of the supply slot, groove inlet and groove outlet regions are shown in Figure 4. A summary of the conditions considered is given in Table 1.

Depth of supply groove Chamfer radius in groove Groove width (L) Supply pressure (P,) Lubricant viscosity (q) Lubricant density (p) Surface velocity cu)

2mm 1 mm 128 mm 3.5 MPa 0.037 Nm2/s 880 kg/m3 0 - 21.21 m/s

\

I

Figure 2(d) Streamlines for various step height (Ki = hi/h,) and the ratios development of reverse flow in a Rayleigh step bearing (FIDAF').

87

n.Vu = 0

n.Vu = 0

/ -

\

u-

'I

I'

Figure 3 Lubricant supply configuration.

slot

and

groove

The Reynolds number (RJ was defined in relation to the surface velocity 0, the groove width (L) and the lubricant properties (q, p) as; Re = -P

a

q Streamlines in the vicinity of the central lubricant supply slot are shown for Reynolds numbers of 0,50, 100 and 200 in Figure 5 .

The streamlines for the same range of Reynolds numbers, but in the regions of the upstream inlet and downstream exit from the groove, are shown in Figures 6 and 7. 5. DISCUSSION

The results obtained for the Rayleigh step bearing have shown that current CFD tools can not only predict overall features of fluid film bearing performance characteristics, but also reveal fine detail of the flow patterns, velocity distributions and cross film pressure variations. A range of solutions for different step height ratios has been used to illustrate the recirculation that occurs in the vicinity of the step and the substantial recirculation in the inlet zone under certain conditions. The normality of one particular package, FIDAP, has been demonstrated by considering the flow conditions in

a lubricant supply slot and groove for various Reynolds numbers. Analytical solutions do not exist for the geometry and flow conditions considered, but the CFD package enables the effect of operating conditions upon flow parameters to be explored with ease. Since the overall geometry has been assumed to be fixed in the case considered, the solutions for various Reynolds numbers represent different sliding speeds 0. When both the bearing surfaces are stationary flow through the supply slot and groove into the bearing films is symmetrical and dominated by the supply pressure (Pa. As the bearing surface starts to move with velocity 0,all the lubricant entering the groove from the supply slot initially flows upstream in the reverse flows shown in Figures 5@), (c) and (d). At the higher Reynolds numbers of 100 and 200 a recirculation of lubricant takes place within the supply slot. As the reverse flow in the upstream part of the groove approaches the inlet region, it is entrained by the rapidly flowing lubricant adjacent to the moving bearing surface. Recirculating flows are in evidence in the outlet regions of the groove and it is interesting to note that much of the lubricant recirculates, while a substantial proportion of the fluid drawn into the groove by the moving surface is 'curried out' into the lubricating film formed beyond the groove. Once again, the importance of this feature of the flow becomes even more significant when thermal aspects of the problem are considered and the phenomenon of 'hot oil carry over' is an important issue in thrust bearing design. The role of the Reynolds number upon the flow patterns is significant, but it was found that changes in the supply pressure had only a modest impact upon the streamline patterns.

6. CONCLUSIONS

The major objective of the paper has been to draw attention to the value of the additional information revealed by stream function solutions to lubrication problems, rather than the conventional solutions to the Reynolds equation. This has been illustrated by examples from the flow at the inlet to lubricated rigid cylinders; the Rayleigh step bearing and the lubricant supply to a bearing through a slot

88

I

Figure 4 Finite element mesh for lubricant supply groove domain. (a) Central supply slot (b) groove inlet (c) groove outlet

89

U-

P

Figure 5 (a), (b) Streamlines in the vicinity of the central lubricant supply slot Ps= 3.5 MPa (a) & = O (b) & = S O

90

Figure 5 (c), (d) Streamlines in the vicinity of the central lubricant supply slot Ps= 3.5 MPa (c) = 100 (d) R,= 200

91

u=o

u-

Figure 6(a), (b) Streamlines near the upstream inlet into the lubricant groove P,= 3.5MPa (a) % = O (b) % = 5 0

I

92

I

p

u-

P

U-

Figure 6(c), (d) Streamlines near the upstream inlet into the lubricant supply groove Ps= 3.5 MPa (c) % = 100 (d) %=200

I

93

u =o

Streamlines near the downstream exit from the lubricant supply groove Ps= 3.5 MPa (a) R, = 0 @) R, = 50

94

Figure 7(c), (d) Streamlines near the downstream exit from the lubricant supply groove P S = 3 . 5 M P a (c) % = 100 (d) %=200

95

and groove. Furthermore, it has been shown that current CFD solvers, such as FIDAP, can be used effectively to solve realistic bearing problems.

Basic Engineering, Series D, Vol. 88, No. 4, 717-724.

8. L M Simuni, The numerical solutions of some

problems in the flow of a viscous fluid, Inzhen. Zhur. (1964), 4 446-450.

ACKNOWLEDGEMENTS

The authors are pleased to acknowledge the numerical solutions to lubrication problems by former PhD students (Oteri [14], Toyoda [16]) and by recent MSc project students (Y M Zhou (1991) and K Roberts (1992)).

9. H A Putre, Computer solution of unsteady

Navier-Stokes equations for an infinite step bearing (1970), NASA TN D-5682. 10. Jinn-An Shieh and B J Hamrock,

REFERENCES 1. 0 Reynolds, On the theory of lubrication and its

application to Mr Beauchamp Tower's experiments including an experimental determination of the v i s p i t y of olive oil, Phil. Trans. Roy. SOC.(1886), 177, 157-234. 2.

A G Michell, Lubrication Its Principles and Practice, (1950), Blackie, London and Glasgow, I

1-317. 3.

G H Wannier, A contribution to the hydrodynamics of lubrication, Quarterly of Applied Mathematics, (1950), Vol. 8, No. 1, 132.

Stream

functions in fluid film lubrication, US/Taiwan Joint Symposium, on Tribology, (1989), Proceedings, 69-78. 11. J C Jaeger, Elasticity, Fracture and Flow, with

Engineering and Geological Applications, (1956), Methuen & Co Ltd., London 1-152. 12. I Babushka and A K Aziz, Lectures on the

Mathematical Foundations of the Finite Method, Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, (Ed. A K Aziz), Academic Press, New York, pp 135, (1972). 13. FIDAP Manuals 1-4 (Version 6.03). pub.: Fluid

Dynamics International Inc. 4.

A A Milne, A contribution to the theory of

hydrodynamic lubrication. A solution in terms of the stream function for a wedge shaped oil film, (1957), WEAR, Vol. 1,32. 5.

G B Jeffery, The rotation of two circular cylinders in a viscous fluid, Proc. Roy. SOC. (1922), A, 101.

6. R C Diprima and J T Stuart, Flow behveen

eccentric rotating cylinders, Trans ASME, Journal of Lubrication Technology, (1972), Series F, Vol. 94, No. 3, pp 266-274. 7. M M Kamal, Separation in the flow between eccentric rotating cylinders, ASME Journal of Basic Engineering, Series D, Vol. 88, No. 4, 717-724. 7. M M Kamal, Separation in the flow between

eccentric rotating cylinders, ASME Journal of

14. B J Oteri, A study of the inlet boundary

condition and the effect of surface quality inb certain lubrication problems, (1972), PhD thesis, The University of Leeds. 15. D Dowson, The inlet boundary condition, Proceedings of the 1st Leeds-Lyon Symposium

on Tribology, 'Cavitation Phenomena', Mechanical Publications, pp 143-152.

and Related Engineering

S Toyoda, A study of the effect of fluid inertia and lubricant starvation upon fluid film lubrication, (1977), PhD thesis, The University of Leeds.

16. D Dowson and

This Page Intentionally Left Blank

Dissipative Processes in Tribology / D. Dowson et al. (Editors) 1994 Elsevier Science I3.V.

97

Shear properties of molecular liquids at high pressures - a physical point of view E.N. Diaconescu

University of Suceava, 1 University Street, 5800, Romania A liquid at high pressures is regarded as an overheated solid having a Lennard-Jones-London molecular interaction potential. Jump frequency of a molecule, established by using the concepts of disturbed and activated lattice oscillators, is applied to derive the net frequency of molecular jumps along an applied shear stress. Two molecular displacements, elastic and viscous, are found to take place as it is implied by a Maxwell rheological model. The solid like behaviour of liquid state is then justified. A general expression for intrinsic viscosity of a liquid is derived. This is found to reduce, in certain circumstances, to various known formulae for viscosity. Then shear viscosity is deduced, which is found to follow a hyperbolic sine law. An expression for piezoviscous coefficient is worked out by taking into account the effect of pressure upon interaction potential. It is shown that intrinsic viscosity changes exponentially after a pressure step and, if molecules are plane or linear, it decreases with increasing shear duration as a result of molecular alignment. Tangent shear modulus is found to decrease with shear strain and to depend nearly linearly on pressure. Limiting shear stress occurs at a critical value of shear strain which changes little with pressure. A linear dependence of this stress on pressure can be accepted as a satisfactory approximation of actual variation. 1. INTRODUCTION

It is nowadays widely accepted that, at moderate shear rates, the lubricant exhibits non-linear viscoelasticity inside an EHD oil film, [l-41. The response of an oil film to shear depends on viscosity, 7 , usually a function of shear rate, i ,and on elastic shear modulus, G. A non-linear Maxwell model is often used to describe this behaviour, [1,2,4-61:

z being the applied shear stress. At large shear rates, increasing shear stress under increasing shear rate is limited by solid like shear strength of lubricant, z - ~ , [ 1-1 11. Various relations between viscosity and shear rate or shear stress have been proposed, widely acccpted being Eyring hyperbolic sine law, [ 1,4,6], and Winer logarithmic law, [5-121. In the former law, a reference shear stress of liquid.?,, called Eyring stress, and an initial viscosity of the fluid, qo,defined for a shear rate tending towards zero are used. The most widely used dependence of viscosity

on pressure is expressed by Barus equation, which is based on a piezoviscous coefficient, a. Up to date, shear modulus is determined experimentally by high frequency oscillatory shear, [I 1,13,14], light scattering, [15,16], stress-strain investigations, [2,5,8] and traction tests, [4,11,17251. Most results suggest a linear dependence of this modulus on pressure:

where Go=(O...0.8)GPa i s the valuc of modulus at zero pressure and A=0.5...5 is a dimensionless coefficient, [1,2,13,15,19,26]. Traction experiments systematically yield smaller values of Go and A than physical investigations. Limiting shear stress, measured by various procedures, such as static shear in especially devised apparatus, [2,3,8,27], pressure shear plate impact experiments, [9,28], dynamic shear by a jumping ball, [3,29], temperature mapping of an EHD contact by infrared radiometry, [30,31], or traction experiments, [ 1,7,10,11,18-251, seems to vary linearly with pressure:

98

where rto is the shear strength of the fluid at p=O and p is the slope d r , / d p . Jacobson, [3,27], found values of 15 MPa for rto in the case of mineral oils and of 0.026 ... 0.14 for p . The ratio of shear modulus to limiting shear stress depends on oil, pressure, temperature and on actual measuring procedure. Traction experiments yield lower values of this ratio, of up to 12.5, whereas physical results show values of 26 to 4 1. Excepting some works upon viscosity, [32-351, and simple attempts to explain shear behaviour of liquids, [36,37], no other physical explanation has been advanced for shear properties of lubricants. Present work aims to improve physical knowledge on the subject by taking into study, for a start, only simple molecular liquids. 2. SIMPLE MOLECULAR LIQUIDS

A simple molecular liquid results from the melting of a simple molecular crystal. Spherical or nearly spherical molecules are placed in the lattice sites of such a crystal. These are bound by weak, non directional van der Waals' forces. The stability of a crystalline structure held by weak forces requires it to bc close packed, [38-413. If the molecules are spherical, the lattice cell is facecentred cubic. A similar arrangement is preserved if the molecules are not spherical, but have comparable dimensions on all three directions. The forces a molecule exerts upon its neighbours are supposed to have the same origin, called centre of interaction of that molecule. At equilibrium, these centres are placed in the lattice sites. Due to dimensional homogeneity of the molecules, molecular crystals contain mainly Shottky point defects, called vacancies or holes, and dislocations. At the melting temperature, T,, a critical value of vacancy concentration is reached, the holes having a homogenous distribution over the volume. Latent heat of hsion generates nm additional vacancies which destroy the stability of the crystal and confer fluidity on the substance. New holes are formed at even higher temperatures. Regarded instantaneously, a molecular liquid maintains locally the original close packed arrangement of the originating crystal, but the long range order is disturbed by the presence of vacancies. The molecules oscillate around the lattice sites for very short times, until they gain

enough energy to jump into neighbouring holes, leaving vacancies in the initial positions. These jumps confer a great mobility on the molecules and, consequently, produce the fluidity of the substance. This fluidity does not allow the persistence of dislocations. The concentration of vacancies in the liquid state is given by a Bose-Einstein distribution, [37,42]:

(4) n being the number of vacancies in a mole of liquid, N the Avogadro's number, k the Boltzmann's constant, T the absolute temperature and dg, the Gibbs free energy of a hole formation in the liquid state, dcduced in [42]. A mole of liquid substance containing N molecules is studied further down. It contains n vacancies and, consequently, N + n lattice points. The average molecular volume is w = V/N , where V denotes the molar volume of the liquid. In fact, a molecule placed in one of the lattice sites, surrounded by other molecules, occupies a smaller volume, w,. This is the molecular volume in a hypothetical perfect solid lattice of the same substance, subjected to the same pressure and temperature as the liquid is. The volume of ideal crystalline component of the liquid is V, = N u , , and V f represents the free molar the difference V -V, volume. The free volume per molecule is w / = V / / N = w -w , . Above it has been assumed that although locally, in the neighbourhood of a vacancy, the crystal latticc is strained, this strain vanishes at a few intermolecular distances. Consequently, a vacancy increases both, the free and the total volumes by the same amount w,, although its actual volume is slightly smaller. The following relations hold between these volumes

Owing to a rather solid like structure of a liquid subjected to such high pressures as encountered inside EHD films, thc oscillations of molecules around lattice sites can be assessed by applying the theory of solid state. According to this theory, the oscillatory motions of individual molecules are replaced by a collective movement of all lattice elements. A system of coupled harmonic oscillators

99

is formed, which can be de coupled by conveniently transforming the equations of motions and by using generalised co-ordinates, called normal coordinates. Thus, in a mole of substance there are 3N independent harmonic oscillators, called normal oscillators of the lattice. They belong either to an acoustic or to an optical vibration mode of the lattice, each of these being longitudinal or transverse. Because the reciprocal lattice of a face centred cubic molecular lattice contains a single molecule, acoustic vibration modes, longitudinal and transverse, occur only. Acoustic vibrations of low frequencies, having a maximum wave length twice the length of the crystal, exist at a very low temperature. As the temperature rises, acoustic vibrations of higher frequencies occur. When the temperature reachcs a characteristic value, called Debye temperature of the substance, T, , two neighbouring molecules oscillates in counterphase. This vibration mode defines the smallest length of wave excited in a crystal. Corresponding maximum frequency of acoustic oscillations is called Debye frequency of that substance, v,. The following equation holds between v, and 7‘’ : kT,

= hv,,

h being Planck’s constant. If the temperature rises above T,, no new vibration modes occur but the additional energy increases the amplitude of existing oscillations. The above defined Debye parameters, T,, and v D , are valid for a perfect lattice. In a real lattice, in immediate neighbourhood of a vacancy, the stiflness of the lattice is considerably lowered and the vibration frequency is diminished. According to Mott and Gurney, [43], this effect is significant only for molecular vibrations along directions joining the hole centres with neighbouring, occupied lattice sites. Therefore, a hole lowers the Debye frequency of normal oscillators which contain molecules neighbouring a hole, to a value i, 4 v,. Such oscillators are called disturbed oscillators and is called disturbed Debye frequency of that substance. This is another characteristic frequency of observed substance. The normal oscillators, attached to lattice vibrations, can be regarded as quantum oscillators. From this point of view, the energy of an oscillator,

which is identified by a wave vector in the reciprocal lattice, g , and by a vibration branch, s, takes discrete values only, E + , called energy levels:

where v+ is the frequency of considered oscillator and nis is an integer, known as a quantum number. The smallest value of energy level, cGS= 0.5hvqS, is called zero energy, and it represents the vibration energy at absolute zero. Energy difference between two adjacent levels corresponds to a change of quantum number by unity, and it is Asqs = hvis. It represents the quantum of vibration field of a crystalline lattice, and bears the name of phonon. The phonon is a quasi- particle because it has no mass and, unlike ordinary particles, it cannot appear in vacuum since it needs a material medium to appear and to exist. Like the vibration mode, q s , to which a phonon is attributed, the latter can be acoustic or optic, and longitudinal or transverse. Between phonons there no interactions because they stem from harmonic and independent oscillators. The phonons travel through the lattice with the phase velocity of the corresponding wave. Consequently, the lattice oscillations can be represented as a gas of phonons, confined within the limits of the crystal. The interactions between the crystalline lattice and phonons can be visualised as simple collisions between phonons and molecules. If a molecule belongs to a normal oscillator having a frequency vqs,equal to or less than the frequency of the phonon, the latter is absorbed by oscillator and the energy of the oscillator increases by /lvis. The difference / I (vp - vqs), vp being the frequency of the phonon, is freed as a lower frequency phonon. If the frequency of the phonon is less than that of the oscillator, the phonon is elastically reflected without energy exchange. At thermal equilibrium, the phonons, having no spin, obey a Bose-Einstein distribution with zero chemical potential, the average number of phonons in the state qs being:

100

Therefore, the average energy of the oscillator is: (9)

The Debye temperature of a molecular crystal is less than 100 K. Thus, practical operating temperatures are much higher than TD. Therefore, the argument of hyperbolic cotangent function is much smaller than the unity, and by using the approximation coth x s If x , when x +*1 , the average energy of an oscillator becomes:

The potential energy of interaction bctween two molecules in a molecular solid or liquid can be accepted to be given by a Lennard-Joncs-London potential, of 6-12 kind:

L

J

where r is the distance between interaction centres of adjacent molecules, cr is that value of r which yields q ( r ) = 0 and E is the minimum valuc the potential reaches at equilibrium. Values of E and cr, taken from [44], can be seen in Table 1. The intermolecular force is equal to the negative

Table 1 Potential paramcters and calculated piezoviscous coefficients for sevcral hydrocarbons Substance Molecular weight a, (Angsfr) E/ k, ( O K ) i -C,H,, 58.12 5.311 3 13 n - C5HI2 72.15 5.769 345 n -C,H,, 86.17 5.909 413 n - C8H18 114.22 7.451 320 Cyclohexnne 84.16 6.093 324 C6 H6 78.11 5.270 440

a,,( l / G P a ) 21.55 27.15 29.20 58.50 32.00 20.70

derivative of thc potcntial: F ( r ) = --

dr

I sL

A

This force becomes equal to zero at equilibrium, when the potential energy is at a minimum. In this situation the intermolecular distance reaches the equilibrium value v = ro = 21’6 0. A structural unit, as shown in Figure 1, consisting of four neighbouring nioleculcs is considered. The centres of interaction of these four molecules are the vcrtices of a regular tetrahedron. If a pressure p is applied to the liquid, a forcc F, directcd towards the centre of the tetrahedron acts upon each molecule. As a result, the equilibrium intcrniolccular distance r,, decreases to a valuc r, I r , in order to produce the repulsion required to As the area balance thc prcssurc force F,. attributcd to each niolccule in a plane pcrpcndicular on I;, is (&/2)vi, the force F, takes the following value:

Equilibrium intermolecular distancc under pressure, r,, is, therefore, the solution of equation F(r,) = F, which can be expressed as:

Figure 1 Molecular structural unit under pressure

101

Table 2 Dependence of solid like shear properties on pressure for a simple liquid p=pd/E F=r,/o G=Gd/E r1 = r,d / E 0 1.1224620 24.00 1.99 5 1,0941643 36.87 2.91 10 1,0764083 48.32 3.72 25 1.0441497 79.35 5.91 50 1.0142835 126.41 9.19 100 1.0441497 213.38 15.25 297.27 20.99 150 0.9608 17 1 200 0.94708 10 378.46 26.56 300 0.9250444 536.87 37.38 691.95 400 0.9100070 47.95 500 0.8983152 844.86 58.34 Dimensionless distances 7 = rp/ o,computed from equation 14, are given in Table 2 for different values of dimensionless pressure p = p d / E .

3. MOLECULAR JUMPS

Each vacancy is surrounded by z neighbouring molecules, z being the co-ordination number. Consequently, a vacancy introduces z disturbed Debye oscillators. This means that in a mole of liquid there is a number Nd = nz of disturbed oscillators, which vibrate on a diminished Debye frequency, vD. As the total number of oscillators is 3 N , the probability that a given oscillator is disturbed is given by

Pd = N d / 3 N = n z / 3 N .

(15)

According to equation 10, the average energy of a disturbed oscillator equals k T . A disturbed oscillator can change energy only when interacts with phonons having a frequency equal or superior to t i , that is only with phonons of frequencies vD and vD. The absorption of such phonons increases the oscillator energy. Once a certain level of this energy, called jump activation energy, s J , is reached, a molecule of this oscillator is able to jump into a neighbouring vacancy. This activation energy corresponds to an activation number of phonons, tiJ

After each jump, the surplus energy is freed as heat,

YCI.

0.189 0.171 0.164 0.155 0.150 0.145 0.143 0.142 0.140 0.139 0.138

that is as phonons of frequency GD, freely moving through the lattice. As shown by Planck, [45], the quantum number obeys a Boltzmann distribution. Consequently, the number of activated oscillators, N,, having an energy superior to E, , is

N,

=

3 Nexp(-gj / kT) .

(17)

The activation probability for a given oscillator can be written as:

The jump probability, defined as the probability that a given molecule is performing a jump, is the product of both independent probabilities that the considered oscillator is disturbed, Pd, as well as activated, p0,:

3N Obviously, the jump is performed when the oscillator elongation is at a maximum. This situation repeats itself with a frequency v,. Consequently, the jump frequency of a molecule is given by the following equation:

znvD E. v . = P . v =-exp(---?-). ’ ” 3N kT I

In a liquid at rest, these jumps appear with the same frequency on all directions. As a result, no

102

definite flow occurs. If the components of these jumps on three rectangular directions are considered, then the jump frequency along one of these directions is:

given instant, i.e. flowing at that instant, can be estimated by using the following obvious equation: NI , = N P

"

v

'J

- znvD

3

9N

= _ -

zn =_

18

&

exp(--L)sinh(-).7Ws

kT

2kT

(24)

&

-exp( -1)

kT

Usually, a liquid is not at rest, but flows on certain surfaces, along certain lines, under the action of applied external forces. A shear stress t acts in any point of a flow line. This generates a shear rate i . Under the action of this shear stress, a molecule that jumps performs, by displacing itself to the potential barrier, a work w = 0 . 5 ~ This ~ ~ . work is subtracted from activation energy for the jumps along the flow and is added to it for the jumps against the stress. The jump frequencies along the flow, denoted by +, and against it, denoted by -,become different:

The factor 1/2 multiplying the frequency v, takes into account the equal jump frequencies on both directions on a straight line in a liquid at rest. The net frequency of molecular jumps along the shear stress is:

In a sheared liquid, any molecule oscillates around its equilibrium position in a time interval equal to the period of jump, P = 1 1 v,, and then jumps in a new position, where it oscillates again. The displacement of a molecule along the flow can only be performed during a jump. For the duration P the molecule behaves as in a solid state. The effect of a shear stress depends on its duration, t . If t 4 P , the mean position of the observed molecule is displaced elastically only, by a very small distance A,. If t + P , the molecule jumps integer [ t / P ] intermolecular distances R. along the flow, that is it flows, and then, in the new position, as wcll as in each of the intermediate positions, becomes elastically displaced by A, . The number of molecules performing the jump at a

Because NJs44 N , it can be stated that, at any instant, the great majority of molecules behaves in a solid like manner. The elastic shear strain, y e , has the value ye = Arctun(A, / A,), A, being the distance between two adjacent molccular layers, parallel to the shear plane. Net flow or viscous displacement of a molecule during a time interval t is S, = [ t / P ] A . At large values of t it increases nearly linearly in time because an integer part becomes practically equal to its argument. Elastic and viscous displacements add together to give the total displacement of a molecule. This justifies the use of a Maxwell model for shear behaviour of molecular liquids. If shear duration is large in comparison to jump period, the solid like deformation is overwhelmed by viscous flow and it cannot be observed. Although unnoticeable in the presence of a large viscous flow, this solid like behaviour is of utmost importance because the increasing shear stress under increasing shear rate can reach the shear strength of the instantaneously "solid component" of the liquid and the latter shears as in a solid state. Therefore, the limiting shear stress of the liquid is the shear strength or the ultimate shear stress of its instantaneously "solid component", consisting of Nss = N - N,, molecules. As a consequence, the solid like properties of a liquid can be determined if the viscous flow is disregarded and the instantaneous liquid lattice, made of N , molecules, is seen as being "frozen".

4. VISCOSITY

4.1. Intrinsic viscosity As stated above, in a liquid at rest there is not a net flow. Nevertheless, there is an internal mobility of molecules, caused by molecular jumps. Jump frequency of a molecule on a certain direction is L;, given by equation 29. An average energy kT is available for jump on that direction. This can be visualised as generating, at a molecular level, an average shear stress 7,, directed along the jump. If

103

intermolecular interaction is elastic, r, yields from rows= 2kT and it is I , = 3 k T / w , . This average shear stress z, .available in a liquid at rest on the direction of a molecular jump, is in fact the Eyring stress, a liquid parameter. Introduced this way, Eyring stress acquires a physical meaning. As shown by Tabor, [46], an average velocity gradient, grad u = RV, / Ro, occurs between a molecule performing a jump and its neighbours. By definition, the viscosity is the ratio of applied shear stress to the velocity gradient it produces. Accordingly, the intrinsic viscosity of a liquid, a measure of the resistance a fluid at rest opposes to a molecular jump, is expressed by the equation:

The jump activation energy, E ~ ,is, under constant temperature and pressure, a measure of useful work done against intermolecular forces. Consequently, it represents the free Gibbs energy of activation of a molecular jump, that is E, = Ag,, and the intrinsic viscosity becomes:

Ro 18kT

17, ==

4,

exp -. R w,zdvD kT

-~

By using expression 4 of vacancy concentration, this equation takes the form:

which is the empirical formula proposed by Batschinski, but with an explicit constant. If w, is replaced by w / ( l + d ) and d by its relation 4 in equation 26, the latter takes the following form:

2, 18kT R wvD

qi = --exp-,

As, kT

where dga = Ag, +dg, is the Gibbs free energy of flow activation, introduced by Eyring, [32]. By taking into account that Eyring used a molecular vibration frequency v = kT/h instead of vD and that (182, / z R ) e l , the above expression transforms into a well known formula for viscosity, deduced by Eyring:

4% h qi = -exp-, w kT As found experimentally, [32], molecular Gibbs free energy of flow activation is a fraction of latent heat of vaporisation,h, , or of lattice energy, E, :

By regarding the latent heat of vaporisation as work done against internal pressure, hv = copi,and by using van der Waals' expression for thermal pressure, p, = kT / w then, at low pressures, when p 44 p, , p, z p , and equation 29 takes the form: f ,

R 18kT

w

R zwv,

wf

11, = o-exp(c-).

Equations 26 and 27 take into account both, the activation energy for a jump and the free volume of a liquid, and therefore they can be considered as general equations of viscosity of simple liquids. Under certain circumstances they reduce to other well known viscosity equations. For instance, if Ag, is only marginally superior to the average energy k T , that is, kT S A g J 1 1 . 1 5 k T , then the obvious approximation exp(dgJ / k T ) z e A g J / kT holds with less than 1% error. This transforms equation 26 as into:

This is a formula proposed experimentally by Doolittle, [47], and deduced theoretically by Cohen and Turnbull, [48], but having now an explicit constant. Other known formulae, such as those of Williams-Landel-Ferry, Fulcher-Tamman, [48], or Vogel, [49], can easily be derived. 4.2. Shear viscosity

The viscosity of a sheared liquid depends on applied shear stress or shear rate. At zero value of this rate, shear viscosity, denoted by q,, is called initial viscosity. The name of final viscosity, q,, is used when shear rate tends towards infinity. As the flow proceeds along a shear stress, t , the

104

net jump frequency along direction of shear, v,, is given by equation 23 and velocity gradient becomes grad u = Av, / A,. Consequcntly, the shear viscosity can be written as:

E! =

(38)

1.0147pri + 8 . 6 1 ~ .

If one assumes w go, in equation 29 and takes into account equations 31 and 38, the following expression for viscosity at high pressures is obtained:

(33) which is the hyperbolic sine Eyring law. When r+O, q + i i 0 and if r j a , q + q , = O , that is initial viscosity is equal to intrinsic viscosity of that liquid and final viscosity is zero. Equation 33 can be rewritten as:

'

7/ 7,

'lo sinh( P/

70)

(34)

This formula prcdicts a non-Ncwtonian behaviour of a simple liquid, its shear viscosity decreasing with increasing shear rate. This behaviour is usually called a "shear thinning effect". 4.3. Effect of static pressure upon viscosity A pressure p applied to a liquid reduces the intcrmolccular distances from ro to 1 ; . A force F,, given by equation 13, acts upon each molecule towards the centrc of tctrahedron shown in Figure 1. This generates an intermolecular repulsive force:

By dividing this equation by v,(O),by assuming that z, vD,and A,(p) / A ( p ) do not depend on pressure and by replacing w , ( p ) w,(O) = (rp/ r0)3, the following final exprcssion is found for intrinsic viscosity at high pressures:

A direct comparison of equation 39 with Barus equation yields the following expression of piezoviscous coefficient:

where c has been considered to be 0.408. This equation can be expressed in terms of Lennard-Jones parameters as follows:

"1

a(p)=The force hy stems from an intcrmolccular potential which is modified by applied pressure:

Thc solution of this differential equation under initial condition qp= -E when p = 0. is: J2 pP = --prP 12

&

0.414(-) rp 3 -+-InE 3 Q kT

ro] , rP

(41)

where ji = pa / E is the dimensionless pressure. The second term in right hand members of equations 40 and 41 is much smaller than the first. This leads to a simple, but sufficiently precise formula for piczoviscous coefficient:

a ( p ) = O . 4 1 d Lr3 kT

--E.

(37)

For a 6-12 Lennard-Jones potential, molecular lattice = 8 . 6 1 ~ . By energy under zero pressure is assuming a similar proportionality under pressure, the following cspression can be written:

and justifies the assumption w z 0,. Piezoviscous coefficient decreases with incrcasing prcssure due to decreasc of intcrmolecular distance. Variation of dimensionless piezoviscous coefficient, E = a ( p ) / a(O), computed by using equation 42 and Table 2, is shown in Table 3.

105

Table 3 Variation of piezoviscous coefficient with pressure 4

0

5

25

50

a

1

0.926

,805

0.738

-

100 0.668

Computed values of piezoviscous coefficients at zero pressure for several simple hydrocarbons can be seen in Table 1. 4.4. Viscosity under transient pressure A vacancy is formed when a molecule from volume jumps on interface and vanishes by a reverse jump. The frequency of vacancy formation, vht , is equal to frequency of molecular jumps from volume on interface, whereas the frequency of hole vanishing, vh- , equals the frcquency of jumps from interface into volume. Total frequency of jumps that influence the number of vacancies is vhr= vht + vh-, whereas net frequency of hole formation is vh = vh+ - vh-. At equilibrium, the number of vacancies is

constant, that is net frequency of vacancy formation is zero, 4h = O, Or 4h+ = 4h-> and the frequency a molecule performs jumps is given by equation 20. Total frequency of jumps, on and from the interface, is N , times larger than vJ, N , being the number of holes sited on interface: znN, vD 3N

A

4, = -exp( -A). kT

Equilibrium frequencies

4h t = 4 h-

=

(43)

<+and $- are:

znN, vD exp( --)A 8, 6N kT

.

vh+ = z n ~ N * v D

6N

300 0.560

400 0.533

(44)

500 0.513

[

exp -~ A@;)]

(45)

Vacancies disappear by jumps against the same Gibbs free energy, but their frequency corresponds at any instant to the actual number of holes existing in liquid, n = n ( t )

[

znN v vh- = exp -~ Agi;)].

6N

(46)

The rate of change of vacancy number is: dn _ dt

vh+

- v&.

(47)

Relationships 45 to 47 yield the following differentia] equation with respect to n: dn = KvD(np- n ) d t ,

(48)

where K = zNs exp[ -Ag[( p ) / kT] / 6 N is a liquid constant. The solution of equation 48 for n = no when t = 0 is:

n = ( n o -np)exp(-Kvbt)

a pressure step from to p , the frequencies of formation and disappearance of holes are no longcr equal. As a result, the nunibcr of holes changes bctween equilibrium values no and n,,, which arc given by equation 4 for Ag, = Ag,(p,) and Ag, = A g , ( p ) , respectively. As shown in [32], at zero pressure, the approximation Ag, G 0 . 2 5 ~ ~ holds. This means that under pressure it can be writtcn & ( p ) EO. 25(8.61& + I.Old7pr;). The Jumps that gcncrate vacancies take Place against applied pressure; p , and, consequently, their frequency can be written as: ~f~~~

200 0.599

(49)

Equation 49 shows that after a pressure step the number of vacancies varics exponentially between equilibrium values no and t i p . Relasation time of this transition is given by following equation: t,

=

I 6N --, e x p [ y ] . Kv,

zN,v,

(50)

It depends on the ratio N / N , , that is on the configuration of liquid volume, decreasing as its limiting surface increases with respect to the volume. Intrinsic viscosity at an instant t after the pressure step is derived by expressing the vacancy concentration entering equation 26 in terms of n :

106

q,,being intrinsic viscosity at initial pressure. It is obvious that the viscosity changes exponentially in time between initial, 77i,, and final, 5, equilibrium values. These arc rclated by following equation:

t , as shown in Figure 2. The motion of this molecule consists of a translation with the velocity u

-

4.5. Effect of shear duration upon viscosity

In the abovc model of flow, molecules are assumed to be spherical or nearly spherical. The viscosity of a liquid made of such molecules does not depend on shear duration. Many liquid lubricants possess kinetic structural units, nioleculcs or part of molecules, which arc far of having a spherical shape. For esaniplc, the paraffins have simple or branched linear molecules. The cycloparaffins and the aromatics have molecules consisting of atoms placed in a single plane. Such molecules show a different resistance to flow, according to their orientation with respect to the flow planc. This resistance is at a maximuill whcn major dinicnsion of the molecule is perpendicular to the flow plane and it is at a minimum when tliis dimension is placcd in the planc of flow. Initially, \vhcn cntcring tlie contact, the molecules havc a random orientation. Statistically, it can be acccptcd that one third of them arc parallcl to each co-ordinatc axis (x axis chosen along thc flow, y axis containcd in the flow plane and z axis perpendicular on thc flow plane). Conscqucntly, two thirds of the kinctic structural units arc aligncd in thc flow planc and one third is perpcndicular on this planc. The fluid possesses a rclativcly high initial viscosily. 17". The velocity gradicnt tciids to align all structural units in tlie flow plane. Conscqucntly, the viscosity tends to dccrcase i n time. Such alignnicnt has bccn observed experimentally by infrarcd spcctroscopy, [SO-521. This orientation of structural units of flow does not take place instantaneously. As a rcsult, the kinematics of alignmcnt nccds to be cstablislicd. To this end, a structural unit of flow of lincar shape, having a lcngth C , is considered to havc initially, at the entry into the contact, a position parallel to z axis. Entering thc contact, the upper cnd of tliis unit niovcs fastcr than the lower as a rcsult of vclocity gradicnt through tlie oil film and, conscqucntly, the unit rotates around thc y axis. Lct B bc thc anglc bctwccn the initial and thc actual position of obscrvcd niolecule at a certain niomciit

U

2

Figure 2. Alignment of a linear molecule of lower end and a rotation of angular vclocity R around this end. This angular velocity is: (53)

where du, is the difference between the vclocities of molecule ends along x axis, in the position B :

Equations 53 and 51 yield the following differcntial equation with respect to 0 : dB= jcos'8dt.

(55)

This yields as an immediate solution:

Integration constant c is zero because initially the anglc B is zero. The time required by this molecule to reach this angular position B is: (57)

The perfect alignment in the flow plane, that is

8 = XI,?,requires an infinite time. As a result, the minimum, final viscosity, reached in a case of perfect alignment of all molecules in the flow plane, can be denoted by 7'., The viscosity at a moment t can be written as a sun1 of two terms: a constant one, related to final

107

viscosity, and a variable one, proportional to cost9 because the momentum transfer between molecular layers is proportional to the projection of molecule length on z axis:

77 = a + bcosB= a +

b

Jm'

derive these properties, a shear structural unit shown in Figure 4 is used. The composing molecules belong to two neighbouring slip planes.

(58)

By taking into account that 17 = r7, when t = 0 and 7 + 11, when t + co,formula 58 becomes:

This equation shows the variation of viscosity with the duration of shear. It can also be written as: Figure 4. Structural unit under shear

This relation indicates that the transition from initial to final viscosity proceeds rapidly with the parameter Y t , as shown in Figure 3.

rl

f'lo

Three of the molecules, of interaction centres B,C,D belong to the lower slip plane and the fourth, of centre A, is placed in the upper slip plane. A pressure force Fp acts upon each molecule. The pressure force acting upon molecule A can be A written vectorially as Fp= - ( p r ; & Z ) i . shear force F = 4 7 +F,J, parallel to the slip planes, acts then upon this molecule. Above, 7 , j , i are the axes unit vectors. The force F displaces the centre A in a new position A' by a displacement vector >= a7 + b j , a and b being displacement along x and y axes, respectively. Lateral edges of deformed tetrahedron, BA' = r,, CA' = r, , DA' = r3, are given by following equations: =

r;'

= r;

r,'

=

Figure 3. Variation of viscosity with shear duration It is thus obvious that if one or two molecular dimensions are small in comparison to the remaining, the fluid exhibits thisotropy, that is, its viscosity decreases under increasing shear duration. 5. SHEAR MODULUS

As shown above, the solid like properties of a liquid are determined by the behaviour of its instantaneously "solid component". In order to

ri +a2 +b2 +2-brp; J3 3

r:

+a2 +b2 --brp J3 3

-arp;

r ++a2 +b2 --brp & 3

+arp.

Supplementary interaction forces which occur between upper and lower molecules are given by:

108

where F; are vectors originating from B,C,D and terminating in A’ and force intensitics F; can be determined by using formula 35. Equilibrium condition for molecule A yiclds:

Tangent shear modulus will be considered only herein. Equations 61, 65, 66 and 67 yield:

6 F -+A rl r2

Shear modulus on y direction increases with b . Its greatest valuc is reached initially, when b is zero:

+-6

-- 3- f i p r p .

r3

J

Two particular cases are of intercst, when either F, or F, is equal to zero. If F, = 0, symmetry with respect to yz plane exists. Conscqucntly, A’ remains in this plane and a = 0, r;, = r3, & = 4 . Equilibrium on s direction is satisfied identically and second of equations 63 leads to following rclation between F, and b , by means of rl = r , ( b ) :

L?J5

[; [$ 7 -

Gym,=32fi-

-2 -

(69)

According to equation 14, expression 69 becomes: Gym, = 9 6 f i -

;[$ ; -

+-p.

t; = -(-r -3b)prb 4 Z P

If F, = 0, the system is not symmetrical; the second of equations 63 implics a displacement b of molecule A on y direction, as a solution of equation:

The shear stress produced by F, is given by:

F , --&-prp

-fipb.

r1 which, is satisfied if rl

and the corresponding shear strain is: y,,:

h

=

nrctflnh

=

=

rp - 2 J 5 6 ,

Finally, equations 71 ani. &.:st of 61, yield:

arctan(

Equations 65 and 66 show that relationship between shear strcss and shear rate is non-linear and shear modulus is not constant. Thcrcfore, it must bc dcfined locally, either as a tangent modulus, GI, or as a secant modulus, G,:

Equation 72 shows that Fr makes the molecule describe an arc of hyperbola contained in a plane z = rPm. At equilibrium, F, is:

109

This force produce a shear stress and a shear strain, as follows:

(74) y,

a

=

arctanh

=

arctan

(75)

Tangent shear modulus along x direction becomes:

results concerning the dependence of shear modulus on pressure fall on a line of equation 2. The slope of actual curve can be derived from equations 14 and 78. It is:

dG dp

-

30 dG drP - 1 + drp d p 3 30-9(rp/o)"

(79)

The initial slope of this curve, at zero pressure, can be obtained for rp = r, This value, 2.833, compares favourably with the values quoted for A in introduction. As the pressure increases, the slope slightly decreases.

=Go.

where

Maximum value of G, is reached at initiation of shear, when a = 0 :

As equations 70 and 77 show, at small deformations, tangent shear modulus does not depend on shear direction. This unique value, G , is given by following relation:

When the pressure is zero, maximum shear modulus becomes Go= 246,' d . Computed values of dimensionless shear modulus G = G d / E for several dimensionless pressures j? are given in Table 2 and plotted in Figure 5. Their departure of these from a straight line is small and this explains why experimental

I

100

'

LOO

500

1

J

Figure 5. Solid like parameters of molecular liquids Values of ~ / and d of computcd shear moduli for several hydrocarbons can be found in Table 4. A good agreement with experimental data can be observed. The decrease of shear modulus with shear strain or shear stress explains the discrepancies found between the results obtained by physical methods and those derived from traction experiments. Physical investigations produce very low shear strains and therefore they yield the maximum values of shear modulus. Shear rates encountered in traction experiments are much larger and, consequently, shear modulus values are lower.

110

Table 4 Computed values of shear modulus and limiting shcar strcss for several hydrocarbons Hydrocarbon E / d , MPa p, GPO G, GPO 0 0.256 0.534 1.350 1.068 2.280 nCgHi, 10.68 2.136 4.040 3.204 5.730 4.272 7.390 5.340 9.020 0 0.474 0.494 1.570 0.988 2.500 Cyclohcxane 19.77 1.977 4.230 2.965 5.880 3.954 7.480 5.930 10.610 0 0.996 0.207 1.530 0.415 2.000 '6 H6 41.50 1.037 3.290 2.075 5.250 4.150 8.880 6.225 12.340 These theoretical expressions of shcar modulus arc valid for a perfect lattice. Vacancics lowcr the stiffncss of the lattice. To a first approximation, shear modulus can be assumed to dccrcasc As vacancy conccntration proportional 1-d. decreases cxponcntially with increasing prcssurc, the effcct of holes upon shear modulus bccomes unimportant at such high pressures as encountered in EHD oil films. 6. LIMITING SHEAR STRESS

Thc samc niodcl of four molecules, shown i n Fibwrc 4, can bc uscd to derive the limiting shcar stress of a fluid. It is known that plastic deformation is causcd by shear forces acting on slip planes. In a crystal lattice, slip planes arc those that possess the highcst degree of lattice sitc packing. Thc dircctions of slip, within a slip planc, arc the directions of greater lattice sitc dcnsity, [38]. According to these rulcs, lower and upper plancs of Figure 4 are slip planes for a face-centred cubic lattice. The slip directions are parallel to tlic lincs BC, CD, DB. Thcrcforc, x axis is a slip direction and the slip along it is produced by Fx. AS shown

T(,AIPn

21.2 98.1 162.8 283.7 399.2 512.1 623.1 39.3 116.7 181.7 301.5 415.0 525.1 739.0 82.6 120.8 154.4 245.0 381.4 623.9 871.1

above, F, cannot displace a niolccule parallcl to s axis, because this tends to follow a hyperbolic trajectory. The value of F, required to maintain the equilibrium of a molecule along such a trajectory is, according to equation 73, very high. Therefore, the slip of a niolccule strictly along x direction is highly improbable. Consequently, a new nicchanisni of molccular slip along a direction is advanccd herein. This is shown in Figure 6. In order to slip along x direction, an upper molecule, denoted in initial position by 1, must occupy intermediate ccntral positions 1, l', l", ..., on top of succcssivc groups of 3

Figure 6. Model of slip along a line

111

three neighbouring molecules in the lower layer, let them be 2,3,4; 3,4,5; 4,5,6; ... . The easiest way to displace a top molecule between successive central positions is to move it along the straight lines l l ' , l'l'', l"l"',... . Such a displacement approximates the slip along x direction by a zigzag trajectory having this shear direction as a medium line. Each segment of zigzag line is contained in a symmetry plane of molecular tetrahedron. The force needed to produce this displacement is always minimum, being equal to F,. Maximum value of this force, 6 ,is a component of external force F, = F , that is F, = & F / 2 . Limiting shear stress is generated by F acting on a molecular area:

As defined above, F, is the maximum value of F, , which is reached when tangent shear modulus G, becomes equal to zero. This condition yields the following equation with respect to b :

Limiting shear stress is obtained by substituting solution bo of this equation in equation 65:

where ri

=

ri t bz +2&rpb0 / 3

When the shear stress equals its limiting value, corresponding shear strain reaches a critical value, ycr,which stems from equation 66:

Some computed values of r! and y,, are shown in Table 2 and are plotted in Figure 5. A straight line closely fits the computed points for T!. The use of a linear dependence of limiting shear stress on pressure is thus theoretically justified, although, as in case of shear modulus, the actual variation is non-linear. The slope of this curve, derived from Figure 5, is 0.09, a value consistent with data mentioned in introduction. The ratio G / rt increases slightly from 12, when no pressure is applied, to 14.5 at highest pressure. These values are smaller than those obtained by physical procedures, but are consistent with results of traction experiments, [ 181. The discrepancies between this model and physical experiments are caused by two elements. Firstly, when writing equilibrium equations, molecules are assumed to be fixed. In fact, they undergo a complex oscillatory motion of amplitudes of about 0.Jo. When a molecule oscillates on directions ll', l'l", ..., external force necessary to produce slip is only the difference between 6 and the value of F,, , corresponding to a displacement b equal to the amplitude of vibration. Secondly, vacancy density must be taken into account because it is responsible for a hrther diminution of limiting shear stress. The combination of these factors yields a limiting shear stress representing 0.7, or less, of above theoretical value. Very interesting is the pressure insensitivity of critical shear strain. This strain decreases from 0.189 at zero pressure to 0.138 at highest pressure considered above. In an EHD regime, the variation is even smaller. For rough estimations, especially at high pressures, critical shear stress can be considered as a constant parameter of shear strength of a liquid. Due to moderate values of ycr the approximation tgy, E ycr is valid with little error. Typical stress-strain curves are traced in Figure 7. Dashed descending parts of these curves at larger shear strains than ycr yield from equilibrium condition. In fact, once the limiting shear stress is reached, the fluid shears in a solid like manner, the strain increasing under constant stress. Such curves are similar to those obtained in a pressure-shear plate impact experiment, [9,28]. Critical shear strain in these experiments is larger than in this theory, reaching 0.3 instead of 0.14-0.19. Computed values of limiting shear stress for several hydrocarbons are shown in Table 4. Taking

112

into account the discussed overestimation implied by this theory. predicted shear stresses are consistent with results reviewed in introduction.

I

T = 200

-

\

7T = 100

1/55

\

\

T = 50

-0.1

0.2

F

0.3

Fig. 7. Stress-strain curves Although the thrcc hydrocarbons have much different values of E / d and, consequently, at low pressures their shear parameters are very different, at high pressures these differences are considerably diminished. It is also worth to note that 0 . 7 for ~~ 17C8H,, is 14.81 MPa, which is very close of 15 MPa, an esperimental value found by Jacobson, [3], for mineral oils. 7. CONCLUSIONS

This work investigates physically the effect of pressure upon shear properties of molecular liquids, namely viscosity, shear modulus and limiting shear stress. Most important results can be summarised as follows: A physical model for the liquid state at high pressures has been advanced by regarding a liquid as an overheated solid having a much higher concentration of vacancies than the solid state. The equilibrium intermolecular distance under pressure is given by a solution of equation 14, which has been deduced by using a Lennard-Jones-London molecular interaction potential.

The frequency of jump of a molecule. either on all directions or along a given direction, in a liquid at rest, is established by using the concepts of disturbed and activated lattice oscillators. This is used to derive net jump frequency along an applied shear stress. This is found to follow a hyperbolic sine law. Two molecular displacements are found to exist, elastic and viscous, which add together to yield the total displacement of a molecule. This justifies the use of a Maxwell model to describe shear behaviour of a liquid. It is found that, instantaneously, the great majority of molecules acts as in a solid state. vibrating around lattice sites; only a few perform a viscous flow at a given instant. Therefore, solid like bchaviour of a liquid can be assessed by regarding the liquid lattice as bcing "frozen" and disregarding all molecular jumps performed instantancously. An average shear stress equal to Eyring stress of that liquid is found to be responsible for a molecular jump. Then, a general expression for intrinsic viscosity of a liquid is derived as the ratio of this shear stress to the velocity gradient which occurs between a molecule that jumps and its ncighbours. Under certain circumstances, this formula reduces to various known viscosity formulae, such as those of Batschinski, Eyring. Doolittlc, Cohen and Turnbull and others. The shear viscosity , defined as the ratio of applied shear stress to velocity gradient it produces, is found to be described by a hyperbolic sine law, as Eyring predicted. The effect of static pressure upon viscosity is approached by taking into account the changes of interaction potential the pressure produces. Deduced expression of viscosity under static pressure yields then the piezoviscous coefficient. This is found to decrease under increasing pressure. Viscosity variation following a pressure step is derived by assessing the net rate of variation in the number of vacancies after the step. Intrinsic viscosity varies exponentially between equilibrium values corresponding to initial and final pressurcs. Relaxation time of this transition depends on the ratio of the number of molecules sited on liquid interface to that of molecules esisting in the volume of that liquid. If the molecules, as kinetic units of flow, have spherical or nearly spherical shapes, the duration of shear does not affect the viscosity. If the molecules have one or two dimensions large in comparison to the remaining, the viscosity decreases with

113

increasing shear duration owing to a molccular alignment and thus the liquid eshibits thixotropy. A very simple model, consisting of four molecules, bound by weak van der Waals' forces, has been advanced in order to derive the solid like shear properties of a liquid. Tangent shcar modulus decreases with increasing shear stress or shear strain. Its maximum value is reached initially, when shear strain tends towards zero, and does not depend on direction of shear force in the shear plane. At zero pressure, the shcar modulus has a finite value, dependent on the parameters of molecular interaction potcntial. The increase of shear modulus with pressure can be approximated by a linear variation, although the actual slope decreases slightly with pressure. Limiting shear stress occurs at a critical value of shear strain which has a small variation with pressure. Although the actual value of the slope of this curvc tcnds to decrease at high pressures, a linear dependcncc of limiting shear stress on pressurc can be accepted. Theoretical values of limiting shear strcss must be corrected for the amplitude of molccular oscillations and for vacancy concentration, by multiplying the results by a factor equal to or sniallcr than 0.7. At high pressures, the critical shear strain can be considcrcd as a constant paranictcr of shcar strength of a fluid. The valucs herein predicted by this model for shcar modulus and limiting shear stress are consistent with espcrimental results found by other authors, espccially if the correction for limiting shcar strcss is taken into account.

7. 8.

9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

REFERENCES 24. 1.

2. 3. 4. 5.

6.

C.R. Evans and K.L. Johnson, Proc. Inst. Mcch. Engrs., 200, C5 (1986) 303. S. Bair and W.O. Winer, ASME J. Trib., 114 (1992) 1. B.O. Jacobson, Rhcology and Elastohydrodynamic Lubrication, Elsevier, 1991. K.L. Johnson and J.L. Tevaarwerk, Proc. Roy. SOC.Lond. A356 (1977) 215. S. Bair and W.O. Wincr, ASME JOLT, 101 (1979) 258. W. Hirst and A.J. Moore, Proc. Roy. SOC. Lond., A360 (1978) 403 and A365 (1979) 537.

25. 26. 27. 28. 29. 30.

D. Berthe, L. Flamand and L. Houpert, EHD and Related Topics, MEP, (1978) 188. S. Bair and W.O. Winer, ASME JOLT., 101 (1979) 251. K.T. Ramesh and R.J. Clifton, ASME J. Trib., 109 (1987) 215. D. Berthe, L. Houpert and L. Flamand, Thermal Effects in Tribology, MEP, (1979) 241. L. Houpert, L. Flamand and D. Berthe, ASME JOLT, 103 (1981) 526. S. Bair and W.O. Winer, ASME JOLT.,102 (1980) 229. A.J. Barlow, G. Harrison, J.B. Riving, M.G. Kim, J. Lamb and W.C. Pursely, Proc. Roy. Soc.Lond., A327 (1972) 403. R.G. Rein, J.R. Asle, T.T. Charng, C.M. Sliepchevich and W.J. Ewbank, ASLE Trans. 18 (1975) 123. J.F. Dill, P.W. Drake and T.A. Litovitz, ASLE Trans., 18 (1975) 202. P. Bezot, C. Hesse-Bezot, G. Dalmaz, P. Taravel, Ph. Vergne and D. Berthe, Wear, 123 (1988) 132. K.L. Johnson and A.D. Roberts, Proc; Roy. SOC.Lond., A337 (1974) 217. L. Houpert, ASME J. Trib., 107, (1985) 241. S.H. Loewenthal and D.A. Rohn, ASLE Trans. 27 (1984) 129. G. Dalmaz and P.P. Chaomleffel. EUROTRIB, (1985), IV, 5.2.1. G. Dalmaz, in EHD and Relatcd Topics, MEP, 1978, 71. G. Dalmaz and P.P. Chaomleffel, in Fluid Film Lubrication -0sborn Reynolds Centenary Elsevier, 1987, 207. G. Dalniaz and N. Gadallah, AGARD Conf. Proc. 323 (1982) 11.1. D. Berthe and L. Flamand, AGARD Conf. Proc. 323 (1982) 15.1. B.K.Daniels, ASLE Trans. 23 (1980) 141. P. Bezot, C. Hesse-Bezot, D. Berthe, G. Dalmaz and Ph. Vergne, ASME JOLT, 108 (1986) 579. E. Hoglund and B. Jacobson, ASME J. Trib., 108 (1986) 571. K.T. Ramesh, ASME J. Trib., 111 (1989) 614. B.Jacobson, ASME J. Trib., 107 (1985) 220. P.M. Cann and H.A. Spikes, STLE Tribology Trans., 32 (1989) 414.

1 I4

31.

H.S. Chang, H.A. Spikes and T.F. Bunemann, Proc. 7 Int. Coll., Esslingen,

42.

1992, 9.4.1.

43.

32.

S. Glasstone, K.J. Leidler and H. Eyring, The Theory of Rate Processes, McGraw-Hill,

33. 34.

35. 36. 37. 38. 39. 40. 41.

1941. T. Rce and H. Eyring, J. Appl. Phys., 27 (1955) 793 and 800. H. Eyring and M.S. Jhon, Significant Liquid Structurc, John Wiley & Sons, 1969. H.A. Spikes, STLE Trib; Trans. 33 (1990) 140. E.N. Diaconescu, Proc. 5 Symp. Stress Anal., Galati, 1989, 4, 176. E.N. Diaconescu, EUROTRIB'89, 5. 136. V.B. John. Introduction to Engineering Materials, Macmillan, 1983. L. Georgcscu, I. Petrea and D. Borsan, Physics of Liquid State, EDP, Buch. 1982. Z.D.Jastrzcbski, The Nature and Properties of Engincering Materials, John Wiley, 1976. M.C. Lovell, A.J. Avery and M.W. Vernon, Physical Properties of Materials, Van Nostrand Reinhold, 1977.

44. 45. 46. 47. 48. 49.

50.

51.

52.

E.N. Diaconescu, Acta Tribologica, 1 (1992) 49. I.G. Murgulescu and E. Segal, Introduction in Physical Chemistry, vol.11, 1 , Ed. Acad., Bucharest, 1979. R.B. Bird, W.E. Steward and E.N. Lightfoot, Transport Phenomena, John Wiley, 1960. T. Cretu, General Physics, vol.11, Ed.Tehnica Bucharest, 1979. D. Tabor, Gases, Liquids and Solids, 2Edn., Cambridge University Press, 1983. A.K. Doolittle, J. Appl. Phys., 22 (1951) 1471. G.V. Vinogradov and A.Ya. Malkin, Rheology of Polymers, MIR, Moscow, 1980. A. Cameron, Basic Lubrication Theory, 3rd Edn., Ellis Honvood, 1983. V.W. King andJ.L. Lauer, ASME JOLT, 103 (1981) 65. J.L. Lauer, L.E. Keller, F.H. Choi and V.W. King, ASLE Trans. 25 (1982) 3 19. P.M. Cann, M. Aderin, G.J. Johnston and H.A. Spikes, in Wear Particles - From the Cradle to the Grave, Elsevicr, 1992, 209.

SESSION 111 SURFACE DAMAGE AND WEAR Chairman:

Professor C M Taylor

Paper 111 (i)

Magnetic Damage in Mn-Zn and Ni-Zn Ferrites Induced by Abrasion

Paper 111 (ii)

Effects of Surface Roughness Pattern on the Running-In Process of RollinglSliding Contacts

Paper 111 (iii)

Influence of Frequency and Amplitude Oscillations on Surface Damages in Line Contact

Paper II (iv)

Effects of Surface Topography and Hardness Combination Upon Friction and Distress of RollinglSliding Contact Surfaces

Paper 11 (v)

Anti-Wear Performance of New Synthetic Lubricants for Refrigeration Systems with New HFC Refrigerants

This Page Intentionally Left Blank

Dissipative Processes in Tribology / D. Dowson el al. (Editors) 0 1994 Elsevier Science R.V. All rights reserved.

117

Magnetic Damage in Mn-Zn and Ni-Zn Ferrites Induced by Abrasion Y . Ahn, R. Hebbar, S. Chandrasekara and T . N . Farrisb aSchool of Industrial Engineering, Purdue University, West Lafayette, IN, USA 47907-1287 bSchool of Aeronautics and Astronautics, Purdue Univesity, West Lafayette, IN, USA 47907-1282 The thickness of surface damaged layers in lapped surfaces of ferrite ceramics has been estimated by measuring the magnetostrictive response. Both Mn-Zn and Ni-Zn ferrite surfaces are found to have damaged or dead layers extending from 5 to 100 micrometers into the surface. In general, Mn-Zn ferrite is found to have a shallower surface damaged layer compared to Ni-Zn ferrite which is most likely due to the smaller magnetostriction of Mn-Zn ferrite. The dead layers are shown to arise due to the deformation and residual stresses generated by the lapping process.

1. Introduction Manganese-Zinc and Nickel-Zinc ferrite ceramics are widely used as slider materials in magnetic recording head systems in computers. The magnetic properties of these ferrites are altered by deformation and stress, both residual and externally applied. Figure 1 shows the changes in the initial permeability of ferrites due to an externally applied stress. Magnetostriction is the term commonly used to describe this effect. When Mn-Zn or Ni-Zn ferrites are diced, ground or lapped, the finished surface is found to have a shallow magnetically inactive layer usually a fraction of a micrometer to several micrometers thick [l-41. This layer, often termed the ‘dead’ layer, increases the effective spacing between the magnetic-head slider and medium, thereby adversely affecting the storage capacity and resolution of the drive. If the efficiency of conventional magnetic recording systems is to be improved, it is critical that the dead layers be minimized and, if possible, eliminated. In this paper, the dead layers in lapped surfaces of ferrites are characterized by measuring the magnetostrictive response-before and after abrasion-of Mn-Zn and Ni-Zn ferrite specimens. From this response, the thickness of the magnetically inactive layers is estimated. This measurement technique provides a simple and effective tool for quantifying the influence of surface finishing processes (and process variables) on the surface damaged layers in magnetic ceramics.

0.2

I

1

1

I

..-.3.

I

a

c 1

0.0

rn

9

I a

w a

-0.2

-1

9 k

z

z,,,

-0.4

CJ

\

_---

z

U I

\ \

Compression Tension

-

0

-0.6

\

I

I

I

I

2

4

6

8

\

0

STRESS MNm-*

Figure 1. Changes in initial permeability ( p i ) as a function of the applied longitudinal stress

in ferrites: (a) Ni-Zn ferrite, pi = 100; (b) MnZn ferrite, pj = 4850; and (c) Ni-Zn ferrite, pi

= 1650 [5].

118

2. Experimental Specimens of Mn-Zn and Ni-Zn ferrites in the form of rectangular plates, 50 x 10 x 0.8 mm which are referred to as length, width, and thickness, respectively, were used in the experiments. Each specimen was coated on one side with an aluminum film approximately 500 A thick to protect that side from the enchant. The specimen was then mounted on a magnetostrictometer and the magnetostrictive response was obtained as a function of the applied magnetic field. This method is an extension of a technique originally used by Klokholm [6]. Figure 2 shows a schematic of the measurement apparatus used to determine the magnetostrictive response. The rectangular sample is cantilevered by clamping one end while the free end of the sample is kept close to adjustable capacitance plates. The specimen, including the capacitance plates, is mounted between the poles of an electromagnet and in a magnetometer an external magnetic field is applied. In the presence of this field, the specimen bends up if the magnetostriction X is negative arid down if X is positive. As a consequence, the spacing between the free end of the sample and the capacitance plates changes. The change in spacing in turn changes the capacitance which is detected by the RF bridge. Thus the deflection of the free end is measured as a function of the externally applied magnetic field, €1. The system was calibrated by hanging known weights from the free end of the sample and also independently by loading it by applying an electric field at and near the free end. In order t o measure the magnetostrictive response of the damaged layer, it is assumed that the layer is ferromagnetic [GI, with the surface damage produced by finishing causing a stress induced anisotropy in the dead layer. Therefore, the magnetostrictive response of the dead layer will not be the same as that of the bulk of the ferrite specimen. This causes the specimen to deflect in the presence of the magnetic field and the deflection is measured. The deflection of the free end is proportional to the product of the dead layer thickness, d , and the magnetostriction A. Notmethat this X is not the saturation magnetostriction, A,, but the linear change in length, A, caused by the application of a magnetic field H . When no dead layers are present on either side of the specimen, there is still some niagne-

Capacitance

A

I

I

Measurement System r l orlage ampli',er

.

Clamp

F e r r i t e Sample

I

Recorder

I

Figure 2. Schematic of the apparatus used to determine the magnetostrictive response. T h e cantilevered ferrite sample has a 500 thick A1 film on the upper side.

tostrictive response due to the presence of the A1 film. This response is caused by X of the bulk ferrite. The deflection of the free end A in this case is given by [6]

where d is the thickness of the Al-film, 1 and t are the length and thickness of the ferrite specimen, EA and EF are the Young's modulii of the aluminum and ferrite, respectively, and V A and VF are the corresponding Poisson's ratios. For the specimens used in the present experiments: 1 = 50 mm; w = 10 m m ;and t = 0.8 mrn giving

A

-

2.6 x 103dA

-

If d = 500 A and X then A 0.1 x pm which is too small to be measured with the capacitance gauge used in the present experiments. Now, if dead layers of t,hickness d l and dz exist at the upper and lower surfaces of the ferrite specimen having magnetostriction X I arid Xz, respectively, then when a magnetic field H is applied the magnetostrictive response is due to the net effect of X I and Xz. Figure 3 shows a schematic of the cross section of a ferrite specimen with upper and lower dead layers. ' l h e deflection of the free end is now given approximately by N

+

+

A = 7.5 x lo3 [(XI A,) d l - ( A 2 A o ) d2] (2) where A0 is the magnetostriction of the bulk ferrite. Here the aluminum properties in Equa-

119

Al-f”rn

------------top dead l a y e r

bulk f e r r i t e

Figure 3. Schematic of the cross-section of a ferrite specimen showing dead layers. X i is the magnetostriction in a layer of thickness d i . tion (1) are replaced by ferrite properties with VF = 0.22. It is assumed that the thickness of the bulk ferrite, 1, is substantially greater than either of these dead layers. In the experiments the specimen was magnetically saturated by a field of about 1400 Oe and the deflection determined as the field was reduced t o 0. The measured X is then the dependence of X upon H between magnetic saturation and magnetic remanence. Before surface damage is caused, the X vs H will be small and after the finishing process induces surface damage the X vs H will be considerably larger. When a ferrite plate with dimensions similar to those used in this study is cantilevered and subjected to a magnetic field H , there will be a deflection of the free end as the field is increased; this deflection arises from a magnetic torque induced by the non alignment of the length of the specimen with the external magnetic field and is not related to the magnetostriction. The force caused by this torque and the consequent deflection, A , vary linearly with H . This deflection is given as

A = K H sin 0 = K‘H

(3)

where 0 is the angle between the long axis of the specimen and the direction of the applied few magnetic field. For H -1000 Oe and 0 milliradians this deflection (Equation 3) will be larger than that caused by the magnetostriction. But since this effect is linear with H , the data can be corrected by extrapolating the linear portion at large H to zero H and then subtracting this from the total response to give the

-

response due to magnetostriction alone. This correction is applied to the experimental data reported later in this paper. The as received specimens of Ni-Zn and MnZn ferrites were cleaned and 500 8, of A1 was deposited on one side of each specimen. A thin 500 8, layer of aluminum was also deposited on the other side of the specimen but only near the tip of the cantilever. The specimens were then mounted one at a time in the magnetometer and magnetostrictive response was determined as the field H was reduced from magnetic saturation to magnetic remanence. After the initial measurement, the specimen was lapped on the side opposite the A1 coating on a tin lapping block using 1 micrometer diamond abrasive. The lapping pressure w a s maintained at 0.015 M P a and the lapping was carried out for 20 minutes. The magnetostrictive response of the lapped specimens was measured. Some of the lapped specimens were etched using hot orthophosphoric acid for 3 minutes and their magnetostrictive response again determined. The saturation magnetostriction of Mn-Zn and Ni-Zn ferrites is negative and relatively small; -1 x and -2 x respectively [6, 71. If there were no dead layers on both the top and bottom sides of the specimen, there would still be a small negative response in the presence of the external magnetic field because of the mechanical constraint imposed by the A1 film. On the other hand if there was a dead layer on the underside of the specimen there would be a positive response. For dead layers on both sides, the net response may be positive or negative depending upon the relative layer thickness.

-

-

3. Results Figures 4, 5 , and 6 show the magnetostrictive response of Mn-Zn and Ni-Zn ferrite specimens subjected to various treatments. The magnetostrictive response shown in the figures has been obtained from correction of the total response. The deflection at magnetic saturation, A s , is the net deflection of the free end of the beam when the externally applied magnetic field is varied between 1400 Oe and 0. Examination of Figure 4 shows that the deflections at magnetic saturation for the as received Mn-Zn and Ni-Zn ferrite specimens are -3 pm and -0.19 pm, respectively. These values are small and indicate either that the ini-

-

-

120

1.001

I

Magnetic Field (Oersteds)

Figure 6. T h e variation of the cantilever-tip deflection with applied magnetic field for lapped Mn-Zn and Ni-Zn ferrite after etching for 3 minutes with hot orthophosphoric acid. Figure 4. The variation of the cantilever-tip deflection with applied magnetic field for as received Mn-Zn and Ni-Zn ferrite specimens.

tial surface damage is small or that the upper surface has slightly more damage than the lower surface. When the lower surface (the side opposite the Al coating) of these ferrite specimens is lapped and the magnetostrictive response measured, there is a large positive deflection and A, is 0.38 pm for Mn-Zn ferrite and N 2.9 p m for the Ni-Zn ferrite (Figure 5). This shows that the lapping process has introduced considerable surface damage on the lower surface which now has a thicker dead layer than the upper surface. The thickness of the dead layer created by lapping can be estimated if it is assumed Lhat at Z XO = A. Equamagnetic saturation X1 S tion (2) becomes

-

3.50

I

A, = 15 x 103X(dl - dz)

Assuming a value of X = for Mn-Zn ferfor Ni-Zn ferrite [8], rite and X = - 2 x the difference between the thickness of the dead layer at the top and bottom surface of the specimen can be obtained by using the measured value of A, and Equation (4). In as received Mn-Zn ferrite, this gives ( d l - d2) 20 p m while in the as received Ni-Zn ferrite ( d l - d z ) 6.3 pm. When the side opposite the A1 coating is lapped, the dead layer thickness on this side increases by a n amount d, while the dead layer thickness of the upper side remains unchanged at d l . Using the value of A, = 0.38 pm from Figure 5 in Equation (4)

-

Figure 5. T h e variation of the cantilever-tip deflection with applied magnetic field for lapped Mn-Zn and Ni-Zn ferrite Specimens.

(4)

-

121

for lapped Mn-Zn ferrite leads to

( d l - d 2 - d l ) Z -25.3pm and for lapped Ni-Zn ferrite with As = 2.9 pm (Figure 5 )

( d l - d 2 - d l ) E -97pm From the values of ( d l - d2) measured on the two as received ferrites and the two equations above, the dead layer induced by lapping of MnZn ferrite is

dr

45pm

and for Ni-Zn ferrite

dl

% !

103pm

These are the thicknesses of the dead layers induced by lapping in Mn-Zn and Ni-Zn ferrites, respectively. Since the latter thickness is more than twice that of the former, it appears that lapping causes more surface damage in Ni-Zn ferrite than in Mn-Zn ferrite. In order to remove the surface damaged layer, the lapped surfaces of the Ni-Zn and Mn-Zn ferrite specimens were etched for 3 minutes in hot orthophosphoric acid at 8OoC. The Al-coated surface was protected from being etched by a thin layer of glycol phthalate. Figure 6 shows the magnetostrictive response of the etched specimens of Mn-Zn and Ni-Zn ferrites. From the figure As = -0.8 p m for Mn-Zn ferrite and this gives ( d l - d 2 ) = 53 pm for the etched specimen. Recall that d l and d2 are the thickness of the dead layers on the top and bottom sides of the ferrite (Figure 3). If it is assumed that the etching has completely removed the damage on the lapped surface then dz E 0 so that dl E 53 pm. This is the thickness of the dead layer on the top surface of the as received Mn-Zn ferrite sample. Using the data of Figure 6, the thickness of the damaged layer on the bottom face of the as received Mn-Zn ferrite sample can be calculated as 33 p m . It is also clear from Figures 5 and 6 that etching the lapped surface of the Ni-Zn ferrite specimen has caused a reduction in As but not to the same extent as in Mn-Zn ferrite. This indi-

cates that etching has a t least removed part of the surface damaged layer present in the lapped Ni-Zn ferrite surface. Figure 7 shows the magnetostrictive response of the lapped Mn-Zn ferrite and Ni-Zn ferrite specimens after they were re-etched for three minutes in the same orthophospheric acid solution. During this etching, the Al-coating was not protected so that both sides of the specimens were etched. From Figure 7 , the As values are estimated as -0.07 pm and 0.92 pm, respectively, for the Mn-Zn and Ni-Zn ferrite specimens. Using Equation ( 4 ) , the values of ( d l - d 2 ) are obtained as 4.7 p m for Mn-Zn ferrite and -31 pm for Ni-Zn ferrite. The bottom face of the etched specimens were again lapped using the same diamond abrasive and their magnetostrictive was measured. T h e lapping should produce dead layers of depth dl on the bottom faces of the ferrite specimens. Figure 8 shows these results. From the deflections (A,) of the specimens a t saturation (Figure 8), Equation (4)can be used to estimated dl - d2 - dl = -45pm,

Mn - Znferrite

and

dl - d2 - dl = -47pm,

Ni - Zn ferrite

From the values of ( d l - d 2 ) calculated before lapping, the thickness of the dead layers ( d l ) are obtained as -50 pm in the lapped Mn-Zn ferrite and 16 p m in the lapped Ni-Zn ferrite specimens. T h e thickness of the dead layer induced by lapping Mn-Zn ferrite is similar to that obtained during the original lapping while that for Ni-Zn ferrite is not. Perhaps this is due to the original dead layer induced by lapping not being completely etched away. This will be the subject of further experiments.

-

4. Discussion

The magnetostriction measurements have demonstrated that lapping introduces dead layers on the surface of Mn-Zn and Ni-Zn ferrite ceramics. Based on measurements described above, the thickness of the dead layers introduced by mechanical lapping processes are

122

201... . , . . . . , . . . . , . . ;

s o.50 -

h

Y

.oo /

Mn-Zn ferrite I

-

0

5

O

A

A

'

O

o

Magnetic Field (Oersteds)

Figure 7. T h e variation of the cantilever-tip deflection with applied magnetic field for the lapped Mn-Zn and Ni-Zn ferrite after a further 3 minute etch with hot orthophosphoric acid (A1 coating not protected).

2.00 . . '

'

1

' .

'

'

I

'

'

' . *

'

.

'

I

.

. '

.

'.

]

Ni-Zn ferrite v

C

.g

1.00

o'ooO.

'

250 . .500 .750 '

1000' 1250 l5lOO

Magnetic Field (Oersteds)

Figure 8. T h e variation of the cantilever-tip deflection with applied magnetic field for lapped Mil-Zn and Ni-Zn ferrite after lapping following the 6 minute etch with hot orthophosphoric acid.

-

6

0

15 20 Depth Below Surface (Fm)

5

10

1 1 25

Figure 9. Typically measured residual stress distributions in lapped Ni-Zn ferrite surfaces for a lapping pressure of 0.03 MPa and 1 p m and 3 p m diamond abrasive [4]. found to vary between 5 p m to 60 p m in MnZn ferrite and 9 p m to 100 pm in Ni-Zn ferrite. These values are obtained from a simple model applied to the data from the magnetostrictive response. In general the deformation produced under nominally identical lapping conditions induces a larger dead layer in Ni-Zn ferrite than in Mn-Zn ferrite. This is probably a reflection of the larger magnetostriction of Ni-Zn ferrite [5]. T h a t the origin of the dead layers lies in the deformation and residual stresses produced by lapping is clearly borne out by the following. Measurements of the residual stress on mechanically lapped surfaces of ferrites show the presence of a surface compressively stressed layer extending 5 - 10 pm into the surface underlying which is a zone of residual tensile stress. Figure 9 shows a typical residual stress profile measured on a lapped Ni-Zn ferrite specimen. When this layer of residual stress is removed by chemical etching, the depth of the dead layers are also found to decrease, see Figures 5 and 6. Recent measurements of the rnagnetostrictive response of mechanochemically lapped Mn-Zn and Ni-Zn ferrite specimens show that t,he dead layers in these samples are considerably smaller than in mechanically lapped ferrites. The mechanochemically lapped ferrite surfaces are also found to have a much smaller residual stress (deformation) compared to mechanically lapped

123

ferrite surfaces [4]. A considerable reduction in the dead layer thickness has also been observed when lapped ferrite samples have been annealed to relieve the residual stress. 5. Conclusions

In conclusion, the presence of magnetically damaged (dead) layers in lapped surfaces of Mn-Zn and Ni-Zn ferrites have been demonstrated by measuring the magnetostrictive response. Using a simple model, the thickness of the dead layers has been estimated from the measurements. Furthermore these layers are shown to be a consequence of the deformation and residual stresses induced by lapping. In general lapping is found to introduce a thicker dead layer in Ni-Zn ferrite compared to Mn-Zn ferrite which is probably due to the larger magnetostriction of Ni-Zn ferrite. Acknowledgment The research was supported in part by the National Science Foundation through grants DDM 9057916, Bruce Kramer, Program Director and MSS 9057082, Jorn Larsen-Base, Program Director.

REFERENCES

1 . E. Sterne and D. Temme. Magnetostriction effects in remanence phase shifters. I E E E Transactions on Microwave Theory and Techniques, 13:873-874, 1965. 2. J.E. Knowles. The effect of surface grinding upon the permeability of manganesezinc ferrites. Journal of Physics D: Applied Physics, 3:1346-51, 1970. M. Kinoshita, T. Murayama, N . Hoshina, 3. and A. Kobayashi. The surface damaged layer study of mn-zn single crystal using magnetic domain observation technique. Annals CIRP, 25:449-454, 1976. 4. S. Chandrasekar, T.N. Farris, M.C. Shaw, and B. Bhushan. Surface Finishing Processes for Magnetic Recording Head Ceramics . A S M E Advances in Information Storage Systems, 1(1):353-373, 1991. 5. E.C. Snelling and A.D. Giles. Ferrites for Inductors and Transformers. Research

Studies Press, England, 1983. Chapters 3 and 4. 6. E. Klokholm. The measurement of magnetostriction in ferromagnetic thin films. IEEE Transactions on Magnetics, MAG12(6):819-821, 1976. 7. E.G. Visser. T h e stress dependence of the domain structure and the magnetic permeability of monocrystalline MnZnFe" ferrite. Journal Magnetism & Magnetic Materials, 26(1-3):303-305, 1982. 8. R.O. Handley, August 1984. IBM Watson Research Center, Private Communication.

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Dissipative Processes in Tribology / D. Dowson el al. (Editors) B.V. AU rights reserved.

125

0 1994 Elsevicr Science

EFFECTS OF SURFACE ROUGHNESS PATTERN ON THE RUNNING-IN PROCESS OF ROLLING/SLIDING CONTACTS J. Sugimura, T. Watanabe and Y. Yamamoto Kyushu University, Department of Mechanical Engineering 6-10-1, Hakozaki, Higashi-ku, Fukuoka 812, Japan Effects of surface roughness pattern on the lubricated running-in process of pure rolling and rollinglsliding contacts were studied using a twin-disk machine. Three roughness patterns, i.e. longitudinal, isotropic and transverse roughness, showed different running-in processes. A simple model of surface truncation was introduced, and the roughness leveling depth was employed as a parameter to represent heights of surface microasperities. Plastic deformation was proved to be dominant in surface microtopographical change. It was shown, however, that wear was essential to the decrease in metal-to-metal contacts. Discussion was made on the formation of lubricating films in the running-in process, and it was suggested that the average effects of roughness in combination with local microscopic effects of roughness contributed to the process. In the rollinglsliding contact with the longitudinal roughness, very thin and steady lubricating films were developed. 1. INTRODUCTION

Many lubricated machine parts operate in the mixed lubrication regime where the so-called lambda value is close to or less than unity. Their surfaces are often expected to run-in by geometrical and chemical modification during early stages of operation. With proper running-in, they will be prevented from problems such as power loss, excessive wear and early failure. Because of its practical importance, running-in has been studied by many investigators [ 1,2]. We are, however, far from understanding the mechanisms of running-in. As to the microtopographical aspects, which is the subject of this paper, comprehensive treatment of surface roughness in the running-in has not yet b t w established. It is necessary to clarify how lubricating films are formed between rough surfaces and how asperities contact, deform and wear. Surface roughness effect in lubrication has long been a fundamental subject in tribology, and theoretical works have revealed basic functions of surface roughness in hydrodynamic and ehd lubrication. In particular, effects of directional patterns of surface irregularities are well explained with stochastic theories represented by the average flow model of Patir and Cheng [3], and subsequent studies based on this model [4,5]. Deterministic approaches with sophisticated numerical computation have also made success in demonstrating behavior of individual

asperities in ehd contact [6,7]. Recent developments include theories incorporating non-Newtonian property of lubricants [8-101 and utilization of real surface profile data in computation [lo-121. Although the mechanisms of formation and breakdown of lubricating films in low-lambda conditions are still unsolved, the knowledge we have on full hydrodynamic lubrication is useful in understanding the running-in. In low-lambda conditions, hydrodynamic pressure and film thickness on the average will still depend on roughness patterns. Therefore, the number of asperity contacts, their size, and pressure on each asperity will also depend on roughness patterns. Asperities deform elastically, or plastically, and eventually wear out. Resulting microtopography then affects formation of hydrodynamic film in a manner that is not exactly the same as it did before the modification. Under a new condition, deformation and wear of asperities continue to occur. This process will be repeated until modified microtopography allows hydrodynamic film to form on every asperities. This is a process of running-in. It is expected that transverse roughness, which promotes formation of hydrodynamic film, runs in with lesser surface topographical change in a short time, while longitudinal roughness is less likely to run-in. Accordingly, changes in surface roughness will be greatest for the longitudinal roughness. In the present paper, results of pure rolling and

126

Lever

TIMING CIRCUIT-2

ROTARY ENCODER

-

toMotorII, DISKS

-

ENCODER

TRIOCER W

I

DIGITAL SCOPE

I

E

I

TIMING CIRCUIT-1

I

I Weight Loading Ar

RESISTANCE

-v

BOX

I-!

COMMAND

MICRO C O M PUTER

to Timing Circuits

Figure 1. The twin-disk machine rolling/sliding disk experiments of steel are presented in which running-in processes for three different roughness patterns are studied by measuring changes in electrical contact resistance, surface microtopography, and wear. Attention is drawn to the result that higher wear rate does not always lead to faster running-in. This is explained in terms of the average separation of the disks, which depends on ehd film formation mechanisms and is shown to affect surface microtopographical changes. A simple model of surface truncation is introduced in order to evaluate the volumetric loss of surfaces by we& and that by plastic deformation.

2. RUNNING-IN EXPERIMENT 2.1. Twin-disk machine Running-in experiments were conducted on a twin-disk machine. Figure 1 schematically shows an arrangement of its main part. Both the driving disk and the specimen disk had the same diameter of 60 mm. The driving disk was fixed to a driving shaft which was driven by an AC motor. The specimen disk shaft was driven by the driving shaft via a set of gears. Two sets of gears were used for the experiment. One gave a gear ratio of 1:1 to provide pure rolling contact. The other gave a ratio of 2: 1 to provide rolling/sliding contact with a slide-to-roll ratio of 0.667. The disks were loaded using dead weights and a loading arm. Though not shown in the figure, lubricant of constant temperature was supplied from a tank above the disks with a constant feed rate, and collected below the disks for the parti-

Figure 2. The computer controlled system for measuring electrical contact resistance cle analysis. In order to collect the lubricant scattering in all directions, the disks were covered with shields and oil guides made of transparent acrylic resin. Both the disks were electrically insulated from the shafts in order to determine variation of electrical contact resistance between the disks during experiments. Lead wires ran through the shafts and connected the disks with slip rings. Wires from the slip rings were connected to a circuit. The circuit is diagrammatically shown in Fig. 2. It is basically of the same type as the circuit originally developed by Furry [13]. It had two resistances and a 1.5 V dry cell. The resistance Ri was called the parallel resistance, and the resistance R2 was always set to 14 times R1 so that a voltage of 100 mV was applied to the disks when they were completely separated. Six sets of resistance were available from R i = l R to Ri=100 kR. Selection of the parallel resistance R1 depends on what range of electrical resistance variation is of interest. In the present experiment, 100 R was used for R1 so that it could detect formation of thin lubricating films. The output voltage from the resistance circuit was stored in a digital storage scope with a sampling interval of 1 microsecond. The storage scope stored 16,000 words of data at one time so that voltage variation of 16 ms duration was obtained at one measurement. The data were fed into a microcomputer just after A/D conversion was completed, and stored in a harddisk. Then next 16,000 data were to be acquired. In order to determine the contact resistance variation at the predetermined position of the specimen disk throughout the

127

Correlation distances, defined as the distance at which the normalized auto-correlation function decays to l/e, were determined from three dimensional roughness data. For the ground surfaces, the correlation distance in the direction of grinding lays was 1.3 mm and that in the direction perpendicular to the lays was 13 pm. For the isotropic surfaces, correlation distance was 13 pm in all the directions. The prepared surfaces thus had the surface pattern parameters y [3] of 100,0.01, and 1. The driving disks were also made of 0.45% C steel but hardened by induction hardening to 650 HV. They had a crown radius of 500 mm perpendicular to the circumferential direction. Surfaces were ground and then polished by fine diamond paste to an rms roughness of 0.04 pm. Use of the hard polished disk as the driving disk aimed at confining topographical changes during the running-in only to the specimen disks.

(a) Longitudinal roughness "'1

(b) Isotropic roughness

' I

Figure 3. Surfaces of the specimen disks before experiments experiment, timing circuits were developed to determine rotational position and generate trigger pulses for A D conversion. The circuits operated in conjunction with rotary encoders connected to the disk shafts. The circuits were also used in threedimensional roughness measurement. As shown in Fig.2, all the devices described above were controlled by the computer. Response of the resistance measurement circuit including the storage scope was checked by feeding high frequency oscillation signal, and it was proved that it could detect voltage variation of frequencies up to 1 MHz. This would allow the circuit to detect contacting asperities that ran through an elliptical ehd conjunction in the present experiments. 2.2. Roughness patterns The specimen disks used were made of 0.45% C steel annealed to a hardness of 200 HV. Preparation of the disk surfaces was made in three ways: circumferential grinding, axial grinding, and sand blasting. These processes provided longitudinal, transverse, and isotropic surfaces, respectively. Figure 3 shows the three dimensional representation of the longitudinal roughness and the isotropic roughness. The rms roughness values were within the range 1.0 to 1.4 pm for all the three finishing processes.

2.3. Experimental procedure With the combination of the rough/soft disk against the smoothhard disk, lubricated pure rolling and rolling/sliding experiments were conducted. Total of the six sets of experiments will be shown here, all of which were performed under the same load of 277 N, at a room temperature of 15 "C, for the running time of 180 minutes. The oil used was a paraffinic mineral base oil P500 which have a viscosity of 88 cSt at 40 "C. The oil was fed from the tank at a rate of 10 ml/sec. Rotational speed of both the disks was 180 rpm in the pure rolling experiments; the peripheral speed was 0.565 m/s. In the rolling/sliding experiments, the driving disks rotated at 240 rpm while the specimen disks rotated at 120 rpm; the slide-to-roll ratio was 0.667 as already described. In either of the rolling or the rolling/sliding experiments, the average speed was 180 rpm, which implied that the same minimum film thickness would be expected if there were no roughness effect. With these conditions, the Hertzian ellipse had a semimajor (axial) axis of 1.46 mm and a semiminor (circumferential) axis of 0.153 mm, and the maximum Hertzian contact pressure was 0.603 GPa. This is about half the level for the onset of plastic flow of the softer disk. Therefore, large bulk plastic flow would not be expected, although there could be local plastic deformation of asperities. The ehd minimum film thickness hmin for smooth surfaces were calculated with the formula by Hamrock and Dowson [14] to be about 0.9 pm. This obviously indicates that all the experiments started with lambda

128

values below unity. During the run, variation of electrical contact resistance was measured with the devices described above. Data of 16 ms length were obtained from two peripheral position of the specimen disk at every 20 seconds in the first 30 minutes of run; the interval was set to one minute in the next 30 minutes, and 5 minutes thereafter. Oil used for each thirty minutes of run was collected separately in glass beakers, from which wear particles were collected. Also, the outlet oil temperature was continuously monitored with a chromel-alumel thermocouple. Temperature data were used in the calculation of the theoretical film thickness. After three hours of run, the specimen disk assembly including the rotary encoder was removed, and set on a three-dimensional roughness measuring system. The system consisted of a conventional stylus profilometer, a stepper motor with a harmonic-geared reduction unit for rotating the disks, and a microcompu'ter which controlled the profilometer and the motor and acquired profile data in digital form. As mentioned above, the position of roughness measurement was set at the position where electrical contact resistance was measured using the timing circuits.

2.4. Wear particle analysis Wear particles generated were collected on membrane filters with pores of 0.45 pm diameter. Particles on the filters were observed under a microscope and analyzed with a particle image processing system [15]. The system counts the number of particles, measures parameters such as size, shape factors, roundness, thickness, reflectance of each particle, and determines distribution of these parameters. Particles having representative diameter less than 0.5 pm are excluded from the analysis. The representative diameter here is defined as a squareroot of the projected area of a particle. In the present experiments, particles from fifty views on the microscope randomly selected were analyzed, and the number of particles generated N, the average projected area s, and the average elongation L of the particles were used to estimate volumetric wear. The total number of particles N generated in a specific thirty-minute duration was estimated from the particle count N' in the analyzed area of the filter. Each particle is assumed to have an ellipsoidal shape with axes of a, b and c so that its volume is nabc/6. Axes a and b corresponds to width and length of the projected contour of the particle, while c is the thickness. If we assume b = La, then the projected area S

Table 1 Changes in roughness; pure rolling

Longitudinal

0.69 0.90

1.86

Isotropic

0.65 0.78

1.84

Transverse

0.93 0.96

2.12

A = hmin/a

hmin : Film thidmess by Hamrock 8 Dowson's formula

Table 2 Changes in roughness; rollinghliding

Longitudinal

0.91

1.09

1.68

Isotropic

0.68 0.74

1.89

Transverse

0.67

2.70

0.71

= nab = nLa2. A typical particle in the present experiments seems to have thickness, though not measured, less than its width, but here we tentatively assume that thickness is equal to its width, i.e. c = a; this will overestimate the volume of the particle. From these relations we can calculate total volume of particles from N, S and L by

V = N (S3/r~L)1/216.

(1)

The method of obtaining wear curve from the volumetric wear data thus calculated for every periods of thirty minutes will be described in the next section.

3. EXPERIMENTAL RESULTS Tables 1 and 2 show the lambda values before and after the experiments. The lambda is defined here as the theoretical minimum film thickness hmin divided by the root-mean-square roughness o of the specimen disk; the formula by Hamrock and Dowson [14] is employed to compute hmin. It should be noted here that no significant change was found on surfaces of the driving disks after the experiments. Also shown in the tables is the roughness leveling depth Rp after the run normalized by hmin.

129

I

I 1min

lmin

hin

4in

m1n

m m

1m1n

120min

120min I

I

1mm

180min

0

4

8 Tim,

12

00

g 3 0Q

16,

0

4

8

1

2

1

6

0

Tim?, ms (b) Isotropic roughness

ms (a) Longitudinal roughness

4

8

12

16

Time, rns

(c) Transverse roughness

Figure 4. Changes in electrical contact resistance with time; pure rolling Omin

Clmin

Chm

lmin

1min

lmin

5min

min

5m1n

lmln

1Cfnin

lomm

m 1 n

m1n

mm

30min

mm

30rmn

4mln

40mlfl

4omm

m m

m1n

6cmm

9omm

9omm

9omM

1mM

1mm

1XlWl

1mm

1 m 1 n

1mm

0

4

8 1 2 1 5 Time, ms

(a) Longitudinal roughness

300Q

180min

0

4

8

1 2 1 6

0

4

8

1 2 1 6

Time, rns

Tim, rns

(b) Isotropic roughness

(c) Transverse roughness

Figure 5. Changes in electrical contact resistance with time, rolling/sliding

130

Most of the experiments started and finished with lambda's below unity. The reason for employing Rp is that the topography after the experiments, though not shown, has the feature that is characterized by asperities whose peaks are truncated at a certain level. Aligned peaks must help the formation of lubricating films in the run-in state. The leveling depth Rp is equal to this height, and when two surfaces are brought into contact without lubricant, or with film of negligibly small thickness, the average approach between them is equal to Rp if deformation of asperities are ignored. Figures 4 and 5 show variation of electrical contact resistance in the form of contact voltage plotted against time. Eleven data are selected from each experiment so as to depict changes which occurred during the running-in. The upper bound for each plot is the full applied voltage of 100 mV representing infinite resistance, whereas the lower bound 0 mV indicates metallic contact with a resistance of almost zero. At right bottom of the figures is shown a scale giving levels of some resistance values. A data length of 16 ms corresponds to a distance of 9.04 mm travelled by a disk surface when the rotational speed is 180 rpm. The electrical resistance in general tends to rise in the present experiments. However, the way it rises differs from experiment to experiment. The transverse roughness gives the fastest and the simplest rise. In the initial periods, there is oscillation of resistance between the two extremes of infinity and a very low value, representing the mixed lubrication condition in which contact of microasperities and formation of hydrodynamic film both occur. The running-in proceeds with the decrease in asperity contact, and finally there is no contact and the surfaces are separated by coherent lubricating film. The data indicate that full film has been established by as early as 20 minutes in the rolling/sliding of the transverse roughness. The rolling/sliding with the isotropic roughness shows slower but definite rise in resistance before 90 minutes, while in the pure rolling of the longitudinal roughness, running-in is much slower, but almost full lubricating film appears to have formed at the end of the three hours of run. On the other hand, the pure rolling with the isotropic roughness gives continuous oscillation in intermediate range of resistance and never reaches the full lubrication condition. Another unusual result is provided by the rolling/sliding experiment of the longitudinal roughness, in which uppermost part of the oscillation

aligns at a finite level and this level gradually rises with time. The fastest running-in of the transverse roughness as seen in the contact resistance agrees with the roughness change shown in Tables 1 and 2; the final R p values for the transverse roughness are larger than those for the other roughness patterns. This is in accordance with the prediction based on the average action of rough surfaces in hydrodynamic film formation. It is not likely, however, that this holds for the cases of the isotropic roughness and the longitudinal roughness. The latter would have given the smallest separation with hydrodynamic film, thus giving longer running-in time and the smallest run-in roughness. The experimental results, on the contrary, demonstrate that longitudinal roughness gives shorter running-in time in the pure rolling, and the final Rp values are almost the same for both roughness patterns. Tables 3 and 4 show the number and the average representative diameter of wear particles generated per minute for each period of 30 minutes. It can be seen that, in all the experiments, both the number and the average diameter have a tendency to decrease with time. The average elongation of particles, not shown, mostly lies in the range from 1.4 to 1.8 and also has the decreasing trend: only isotropic surface gives small elongation less than 1.6 in the first period, but it also decrease slightly with time. Table 3 Number of wear particles; pure rolling 0-30min

30-60rnin

60-90rnin 150-18Omin

Longitudinal

2.1 8 2.60 1 3 . 2 2 ~ 1 0 ~9 . 9 0 ~O3

1.48 1.80 7 . 2 8 ~ 1 0 ~4 . 0 1 ~ 1 0 ~

Isotropic

2.19 2.40 4 . 2 5 ~ 1 0 ~8 . 5 6 ~ 1 0

1.74 7 . 2 8 ~O13

Transverse

2.45 1.73~10

1.29 2.39~10~

1.so 1 .so 1.88 7 . 6 1 ~ 1 0 ~5 . 1 9 ~ 1 0 ~2 . 8 0 ~ 1 0 ~ Upper: Average diameter. p m Lower: Number. lmin

Table 4 Number of wear particles; rolling/sliding

Long'udina'

isotropic Transverse

0-3Omin

30-60min

2.61

2.38

60-90min 150-180rnin 1.67

1.63

2.07~10~6 . 2 6 ~ 1 0 ~3 . 8 2 ~ 1 0 ~2 . 9 2 ~ 1 0 ~ I.39 1.52 1.56 1.69 2 . 4 5 ~ 1 0 ~2 . 9 0 ~ O1 4 7 . 0 4 ~ 1 0 ~2 . 5 7 ~ 1 0 ~ 1.84 1.44 2.12 2.44 7 . 9 3 ~ 1 0 ~4 . 1 8 ~ 1 0 ~2 . 0 9 ~ 1 0 ~1 . 1 9 ~ 1 0 ~

Upper: Average diameter, p m Lower: Number, lmin

131

0.004

0.0°4

*

E E

t

Isotropic

~

0.003

Longitudinal \

IsotroDic

-I

I

/

I I

s 3

Longitudinal

I

Transverse

.-._._._.-.-._._._..

0.oc

I

0

30

60

90

I

120

Transverse *-.-.-.-.-.-.-.-.-..

I

150

180

0

From these data, wear volume in each period is computed using eq.(l), and cumulative wear is obtained for time 30, 60, 90 and 180 minutes. It is to be noted that this gives upper estimation of wear volume because eq.( 1) assumes that the thickness of particles is equal to their width. Since wear volume appears to decrease exponentially with time, curves having the form:

60

I

I

I

90

120

150

180

Time, min

Time, min Figure 6. Variation of wear with time; pure rolling

30

Figure 7. Variation of wear with time; rollinpjsliding cating films. Also, plastic deformation of surface layers has to be considered for such soft materials as the mild steel in the present experiments. In the next section, a simple model of surface roughness modification will be introduced, and contribution of wear and plastic deformation will be discussed. 4. ANALYSIS OF TOPOGRAPHICAL

CHANGE where t denotes time and, A and B are constants, are fitted to the cumulative volume. The results are shown in Figs. 6 and 7. Although the decrease in the wear rate may account for the gradual rise in the electrical contact resistance in each individual experiment, it is difficult to find any quantitative relationship between wear and the running-in. For example, the longitudinal and the isotropic surfaces give the similar wear curve in spite that the former shows the gradual running-in while the latter does not. The transverse roughness gives the smallest wear leading to fast running-in, but the isotropic roughness gives the heaviest wear leading also to good running-in. These results obviously suggest that the amount of wear does not always reflect the running-in behavior. Wear, however, must contribute to changes in surface microtopography. In order to explain the role of wear, it is necessary to clarify how wear modifies microtopography, and how modified topography affects the formation of lubri

4.1. Simple truncation model A model of simple truncation is introduced here which was originally applied to wearing surfaces by King et a1.[16]. The model was extended by themselves to include contact of two rough surfaces using numerical method. One of the present authors expressed the basic relations in analytical form [ 171 in order to deduce the correlation coefficient between worn mating surfaces, and proposed the segmented surface model to simulate changes associated with sliding [18]. We are concerned here with the simplest case where changes occur only on one of contacting surfaces, and also the changes can be approximated by simple truncation of microasperities. Consider truncation of a random surface whose height obeys Gaussian height distribution with a standard deviation 00, as illustrated in Fig.8. Height h of the truncation is measured from the original center line. The truncated part of the height probability density function is replaced by a delta function

132

I

Initial center line

Pure Rolling 1

Wear

Center line after truncation

Figure 8. A simple model of truncation at h, and its original shape remains for heights less than h. Height reduction 6 of the center line is written as

Rolling/ Sliding 0

roo

This is identical with the average amount of height loss of the surface by the truncation. The leveling depth Rp of the truncated surface is then given by Rp = h

+ 6.

(4)

Using eqs.(3) and (4),we can obtain 6 and Rp for a given h straightforwardly, or obtain Rp for a given 6. The latter corresponds to obtaining the leveling depth Rp from the height loss. 4.2. Volumetric loss

The model provides an easy way of making a rough simulation. It only requires that an initial surface have a Gaussian height distribution and its change, whether due to wear or due to deformation, can be approximated by truncation of asperities. Requirement for the change to be truncation means that topographical changes are confined to the upper portion and do not affect the remaining part. This is sometimes violated, because thicknesses of wear particles are usually distributed; the distribution is taken into account in the "Running-in Equation" model [19]. Also heavy plastic deformation with side flow may cause some rise of valleys. Since the topographical changes in the present experiments are not so heavy, the model is applied here as a first approximation. As an example, calculation is made on the rolling/sliding experiment with the isotropic surface. From Table 2, the initial standard deviation GO is 1.32 pm and the final leveling depth Rp is 1.70 pm. The total wear volume estimated in the previous

0.01 0.02 Volumetric Loss, mm3

0.03

Figure 9. Contribution of wear and plastic deformation to total volumetric loss section is 3.10~10-3mm3. Dividing this by a product of the periphery of the disk and the major axis of Hertzian ellipse, which is assumed to represent the area of the wear track, we obtain the average ~ pm. height reduction by wear 6w of 5 . 6 5 10-3 Using the above equations, Rp is calculated by . result is Rp = 2.53 pm, which is giving 6 ~ The much greater than the measured value, and this implies that the wear is not enough to cause the changes in microtopography. If we give the measured Rp, calculation yields the total height loss 6t of 0.0376 pm. The discrepancy 6, between 6t and 6w is about 0.032 pm, and this should be attributed to plastic deformation. Plastic deformation of asperities include normal compression as well as shear deformation. It is, however, height reduction that is of interest here. The loss of height 6p multiplied by the area of the wear track is the volume lost by plastic deformation. Actually, materials of this volume has not vanished nor been removed, but is accommodated by elastic deformation of surroundings. For this reason, we simply call it the volumetric loss. Figure 9 shows the volumetric loss calculated with the model for the six experiments. It can readily be seen that the loss by plastic deformation dominates microtopographical changes; ten percent or less is due to wear all the cases. The percentage of the wear volume, however, could be even much smaller since the data from the particle analysis are the greatest estimation for the wear amounts.

133

4

I\ No plastic deformation

a

Initial deformation followed by gradual wear

Q)

3 1

-

No plastic deformation

n

n

a

0

0

30

60

90 120 Time, min

150

Final Rp

-

+ Final Rp

.-

a,

3

-I

Initial deformation followed by gradual wear

1 -

01 0

180

I

30

I

60

I

I

90 120 Time, min

I

150

'

10

(a) Longitudinal roughness

(a) Longitudinal roughness

t,

Initial deformationfollowed by gradual wear

0

0

30

60

90 120 Time, min

150

+ Final Rp

Initial deformation followed by gradual wear

Ob

180

$0

A

1bo

1Qo

\.

\.

5ti

t-

.-c

Initial deformation followed by gradual wear

Final Rp

30

60

90 120 Time, rnin

150

plastic deformation

!<-'-'\

-.-a,

Initial deformation followed - z R P by gradual wear

RPP

l -

0 0

N 'o

.-.-.-.-.-.-.-.-.-.

t,? e 2 U cn c

3

..-.-.-.-.-.-._._._.-.-..

3 -

LT

0

do 1o; Time, min

(b) Isotropic roughness

(b) Isotropic roughness

-

o;

I

I

I

1

I

180

(c) Transverse roughness

Figure 10. Simulation results for the leveling depth of surfaces; pure rolling

Figure 1 1. Simulation results for the leveling depth of surfaces; rolling/sliding

134

4.3. Role of wear and plastic deformation The above result suggests a great contribution of plastic deformation of asperities to the topographical changes. A question arises as to when the deformation occurred. It is widely accepted that plastic deformation of contacting asperities will lead to elastic contact after repeated contact [20]. This holds when load applied to an asperity is constant or decreasing. In the case of heavy wear in which plastically deformed asperities are removed and new asperities come up to contact one after another, loads on the new asperities will always be increasing and rhcy will soon or later experience plastic deformation. On the other hand, when topographical changes are confined to uppermost portion of asperities, such as in the present experiments, wear and plastic deformation of higher asperities will never lead to heavy plastic deformation of other asperities. In addition, it is expected that microtopographical changes increase load carrying capacity of hydrodynamic films, making the load supported by each asperity lower. The plastic deformation, therefore, can be assumed to have occurred during early period in the present experiments. In order to make the story simple, a hypothesis is made that all the volumetric loss due to plastic deformation occurs in a short period just after the start of the run, and topographical change thereafter is caused only by wear. Duration of the initial period is not specifically given here, but it is considered to be very short, say less than one minute. Simulation of truncation is conducted based on this assumption. The results are shown in terms of the variation of leveling depth in Figs. 10 and 11; also in the figures are plotted the results with no plastic deformation. The resulting curves have initial rapid drop by plastic deformation followed by gradual decrease by wear. The smaller decrease in Rp compared with the decrease seen in the case of no plastic deformation is due to the form of height distribution, in which higher part has lesser probability density. The same amount of wear results in different amount of height reduction according to the initial level. Contact of asperities occurs as a result of insufficient load carrying capacity of hydrodynamic lubricating films. This is illustrated in Fig. 12(a). The insufficient capacity gives rise to larger area of asperity contacts, giving smaller average distance between the surfaces. The results shown in Figs. 10 and 11 suggest that the leveling depth Rpp just after the initial plastic deformation is slightly higher in the rolling/sliding contact than in the pure rolling,

Macroscopic EHL pressure

-

Local pressure

‘Asperity contacts

Thin film

Figure 12. EHD conjunction (a) with asperity contacts before running-in, and (b) with thin film after running-in

and also higher with the transverse roughness. This generally agree with predictions of the existing theories [3-91 that transverse roughness gives a greater average load carrying capacity than longitudinal roughness, and a stationary rough surface gives a higher load carrying capacity than a moving rough surface. As seen in Section 3, the difference between the isotropic roughness and the longitudinal roughness is not so great as expected from the theories. Nevertheless, the leveling depth Rpp is interpreted as a distance between the surfaces that is determined from the balance between the average, macroscopic actions of hydrodynamic films and asperity contacts. Asperities left after plastic deformation will continue to make contacts and deform elastically. The resulting wear will modify them, and eventually allow lubricant to form films on them, as illustrated in Fig. 12(b). It is likely that the roughness leveling depth Rp when films are formed is smaller than a leveling depth at which there are still asperity contacts. It seems, therefore, that a critical Rp

135

exists at which lubricating films begin to form. This critical value may depend on the roughness patterns and the running conditions. The results shown in Figs. 4 and 5 indicate that asperity contacts almost disappear by the end of the run, except for the pure rolling with the isotropic roughness. This follows that the leveling depth has decreased from a level above the critical value to a level below the critical value in the course of the running-in. In order to examine the variation of Rp after the plastic drop in detail, the results are replotted in Fig. 13; the ordinate is taken as the relative change in Rp after the initial drop to Rpp. The figure shows that the reduction of leveling depth is large for the transverse roughness in spite of the small amounts of wear, while the reduction is rather small for the longitudinal roughness which had larger amount of wear. This is because of the difference in the height on the surfaces at which wear has started. From Figs. 4, 5 and 13, the critical leveling depth is determined as the leveling depth at a point when the electrical resistance almost finishes rising to infinity. For the transverse roughness, the critical R p is about 0.02 pm below Rpp. For the isotropic roughness, the threshold is about 0.07 pm in the rolling/sliding experiment. The pure rolling of the isotropic roughness does not attain this level up to the end of the run, and this may be the reason for the persistent asperity contacts. For the longitudinal roughness, the threshold may be 0.03 pm. Though this level is not reached in the rolling/sliding experiment, the finite electrical resistance without any sign of direct asperity contact is regarded as an indication of thin lubricating films as will be discussed later. These critical values are of the same order as the rms roughness of 0.04 pm of the driving disks. This implies that microtopography on tops of contacting asperities is crucial in the running-in process. Since the topography of the driving disk surface does not substantially change, the specimen disk wears such that it improves surface microconformity with the mating surface. The reduction of asperity heights in the idealized truncation model should, therefore, be interpreted as the decrease in composite roughness of local contact region on asperities. This allows wear to include large particles of thickness of the order of a tenth of microns. In fact, data used in obtaining the wear rates are from particles of at the least that size, though there must have been smaller particles that were neglected in the particle analysis. From the above argument, the critical value for

0

R-Trans RIS-lm --------________

0.08

o

30

60

90 120 Time, min

150

180

Figure 13. Decrease . in .leveling depth after initial abrupt mop by plastic deformation -

9

.

I

height reduction of asperities depends on the roughness pattern and probably on rolling or sliding conditions. The isotropic asperities have to wear more than the transverse asperities to form local hydrodynamic films. This may be explained by microelastohydrodynamic action of asperities. On the other hand, the longitudinal asperities need lesser wear than the isotropic asperities. This suggests that the longitudinal asperities have greater ability to form local lubricating films than the isotropic ones do. The mechanism of local film formation, therefore, should not be separated from the macroscopic ehd action.

5. DISCUSSION The present experiments suggest that hydrodynamic film formation and asperity contact in the low lambda regime, and the associated modification of surface microtopography, can be qualitatively explained with the macroscopic ehd mechanism for the transverse and the isotropic roughness. The final leveling depth, which is close to the average film thickness between the disks if elastic deformation of asperities is ignored as shown in Fig. 12(b), can be correlated with the minimum film thickness from the average flow model. For example, Zhu and Cheng's results for the elliptic contacts of an ellipticity parameter of about 4 [5] are examined, though direct comparison cannot be made between data from different conditions. The ratio of the mini-

136

mum film thickness to the thickness by Hamrock and Dowson's formula is of the same order as the ratio Rp/hmin in Tables 1 and 2 for the transverse roughness, but the theory would give smaller values for the isotropic and the longitudinal roughness. In particular, their prediction of the ratio to be under unity for the longitudinal roughness contradicts with the present results. The deterministic approaches to ehd contacts have revealed that the longitudinal roughness provides a film thickness greater than that for smooth surfaces if there are not so many asperities in the Hertzian region [6-lo]. The calculations also predict that asperities are flattened, which maintains bulky ehd film with pressure ripples. These may partly support the present results. The existing analyses, however, do not take into account the asperity contacts. The present experiments demonstrate the behavior of a very thin film which works to separate the surfaces in a run-in condition but also fail to separate them to afford asperity contacts under a slightly different condition. The analysis in the preceding section demonstrates that, for all the roughness patterns, a height reduction of several tens of nanometer allows the formation of lubricant films. This implies that the films formed on asperities may have thickness of that order or less. Particularly thin films are clearly observed in the rolling/sliding experiment with the longitudinal roughness. The electrical contact resistance does not have a form of contacthon-contact signal as Furey [ 131 considered, but shows intermediate voltages, indicating thin films having resistance of several thousands of ohms. This cannot directly be explained from resistance of usual conductor materials. The specific resistance of the oil used is in the range from 1015 to 1017 Rcm, which predicts the resistance in the present Hertzian area to be from 1013 to 1015 R. Even if the separation of the whole area is assumed to be 1 nm, the resistance would be as large as ten gigaohms. In order to confirm the occurrence of unpredictably low resistance under thin films, another experiment was conducted. A specimen disk had a crown radius of 3 mm, and surfaces were finished to an rms composite roughness of 14 nm. Using low viscosity oil P60 (10.5 cSt @ 30 "C), the 2:l rolling/sliding experiment was conducted under a load of 10 N; which would give the minimum film thickness of 30 nm. As a result, finite electrical resistance of the order of 100 kR was obtained. This implies that, if thirty asperities are assumed to form the similar conjunctions in the longitudinal

surface, they might provide a composite resistance of 3 kR. Although this result may need further verification, it suggests that electrical resistance of very thin film cannot directly be related with the bulk specific resistance. It is likely that such thin films are formed under very high and stable shear on asperities whose peaks are smoothened by runningin. Thus, the prolonged shape and orientation of the longitudinal asperities give rise to the thin persistent films as observed in the electrical contact resistance. It is found that thin film lubrication allows wear even after the contact resistance rise up to sufficiently high levels, though the wear rate decreases. This suggests that the most probable cause of wear is fatigue in the present experiment. Wear particles generated by fatigue are considered to have flat shape; the lubricated sliding of steel showed that the ratio of thickness to width of particles ranges from 0.1 to 0.2 [21]. Therefore, the wear amount used in the simple analysis of truncation is the upper estimate, and the reduction of height predicted would be smaller than those shown. It is expected that sliding promotes wear. However, the wear amounts are lesser in the rolling/sliding experiments than those in the pure rolling experiments, except for the isotropic roughness. This may be partly due to lesser asperity load provided by higher average hydrodynamic pressure with the lower speed of the specimens as mentioned earlier. Another very important reason will be shear plastic deformation of asperities, which will effectively modify microtopography on asperity peaks to improve microconformity without volumetric loss.

6. CONCLUSIONS Effects of surface roughness pattern on lubricated running-in were studied by the pure rolling and rolling/sliding twin-disk experiments and the simple simulation of surface roughness change. It was shown that changes in electrical contact resistance, wear rate, and surface roughness depended on the roughness patterns. The difference in the running-in process was shown to be caused by the combinatory effect of hydrodynamic film formation and surface microtopographical changes. The roughness leveling depth Rp was employed as a parameter to represent asperity heights. Plastic deformation of asperities provided rapid reduction of Rp in the initial stage of run, which was followed by gradual modification of microtopography by wear. It was demonstrated that about ninety percent

137

of the total volumetric loss was caused by the initial plastic deformation. The leveling depth after the plastic deformation depended mainly on the development of macroscopic ehd film, which was greatly affected by the roughness patterns as the existing theories predict. Wear was shown to be essential to the decrease in metal-to-metal contacts. Time to complete the running-in depended not only on the wear amount, but also on Rp after the initial plastic deformation. The formation of local, microscopic lubricating films also affected the running-in process. In the rolling/sliding contact with the longitudinal roughness, very thin and steady lubricating films were developed.

ACKNOWLEDGMENT The authors wish to thank Dr. K. Kiryu of the Eagle Industry Co. Ltd., for supplying specimens of isotropic roughness.

REFERENCES

D. Dowson et al. (eds.), The Running-in Process in Tribology, Proc. 8th Leeds-Lyon Symposium, Butterworths, 1982. 2. P. J. Blau, Friction and Wear Transitions of Materials, Noyes Publications, 1989. 3. N. Patir and H. S. Cheng, ASME J. Lub. Tech., 100 (1978) 12. 4. J. Prakash and H. Czichos, ASME J. Lub. Tech., 105 (1983) 591. 1.

5. D. Zhu and H. S. Cheng, ASME J. Tribol., 110 (1988) 32. 6. A. A. Lubrecht et al., ASME J. Tribol., 110 (1988) 421. 7. C. C. Kweh et al., ASME J. Tribol., 1 1 1 (1989) 577. 8. L. Chang et al., ASME J. Tribol., 1 1 1 (1989) 344. 9. I. A. Greenwood and K. L. Johnson, Wear, 153 (1992) 107. 10. F. Sadeghi, ASME J. Tribol., 113 (1991) 143. 1 1 . C. C. Kweh et al., ASME J. Tribol., 114 (1992) 412. 12. C. H. Venner and W. E. ten Napel, ASME J. Tribol., 114 (1992) 616. 13. M. J. Furey, ASLE Trans., 4 (1961) 1 . 14. B. J. Hamrock and D. Dowson, Proc. 5th Leeds-Lyon Symp. on Tribology, (1 979) 22. 15. J. Sugimura and Y. Yamamoto, Proc. JSLE Tribol. Conf. Fukuoka, (1991) 365 (in Japanese). 16. T. G. King et al., Proc. 4th Leeds-Lyon Symp. on Tribology, (1978) 333. 17. J. Sugimura, Proc. JSLE 33rd Conf., Tokyo (1989) 121 (in Japanese). 18. J. Sugimura, Wear of Materials, ASME (1991) 627. 19. J. Sugimura et a]., J. JSLE Int. Ed., 8 (1987) 69. 20. J. F. Archard, Proc. Roy. SOC.Lond., A243 (1957) 190. 21. Y. Kimura and J. Sugimura, Wear, 100 (1984) 33.

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Dissipative Processes in Tribology / 1994 Elsevier Science B.V.

D.Dowson

et

al. (Editors)

139

Influence of frequency and amplitude oscillations on surface damages in line contact J. Pezdimik and J. Viiintin Faculty of Mechanical Engineering, University of Ljubljana, ASkerEeva 6,6 1000 Ljubljana, Slovenia

According to parameters, that are usual at hydraulic control spool-sliding type of valves, the influence of frequency and amplitude axial oscillations on the coefficient of friction and surface damages has been researched. Specimens of some various materials were used for tests. As a result, differences in Coefficient of friction are very apparent among various normal forces and among various combinations of frequency and amplitude. The surface damages on sliding surfaces look like welded points and they occur mostly and are more distinctive at lower frequencies and greater amplitudes of our testing range.

1. INTRODUCTION Hydraulic valves are mostly sliding type valves. For the great majority of them the working fluid is still hydraulic mineral oil. Spool in a bushing or directly in a housing moves linear oscillating in axial direction. The frequencies change from near zero up to some hundreds of Hz, and amplitudes, on the other hand, from some millimeters to some microns, depending on various hydraulic parameters and types of valves. At hydraulic spool type valves very interesting are working as well as dither frequencies and amplitudes. Knowledge about friction, phenomenon of surface damages and wear on sliding elements is one of the basics necessary for optimal design of reliable hydraulic control components. Influence of frequency and amplitude oscillatory movements at different load forces, materials and parameters on the friction coefficient, wear and occuring of surface damages, have been published in papers of various authors; 111, 121, 131. But some parameters of the hydraulic components are much different from those used at the published research works. For instance the range of frequencies and amplitudes, the ratio of normal load to contact area, then shape of contact area, differ from those that are usually used at tribological researches. The great majority of experiments was made using

lubricated sliding surfaces. But, for the comparison of the results for friction coefficient and surface damages formation, we have carried out some tests also with dry friction. The results for lubricated friction and dry friction show us some equal relations among some parameters. The purpose of our research is to find out the influence of oscillating frequency, slip amplitude, normal force, hardness of sliding surfaces, geometry of sliding area, material and shape of sliding elements on the formation of surface damages and coefficient of friction. This paper presents some results for friction coefficient for nine combinations frequency amplitude at three values of normal forces. Furthermore it presents some examples of formation the surface damages. Some important parameters at which they occur are stated too.

2. EXPERIMENTAL CONDITIONS AND PROCEDURES

2.1. Material and operating procedures For the experiments the test elements, that are by shape, dimensions, materials, surface parameters and geometry adequate to spool and bushing of hydraulic valves, have been made. They were made on the

140

machines for series production and with the same quality as industrial valves. Experiments were carried out with specimen pairs consisting of piston and half bushing shown in

_ .

Figure 1. Concave-convex contact between piston and bushing is only theoretically line contact. Actually it is an area contact or more exactly a contact in a number of very small areas. Tests were carried out with significant differences in contact areas. A part of contact area between piston and bushing, respectively configuration of contact area consi

Figure 2. Configuration of contact area and dimensional relations between piston and bushing.

Figure 1. Specimens as testing pair. F ... normal force f ... oscillating frequency a ... slip amplitude dering surface roughness, is presented in Fig. 2. Tests were made using half bushings of radius r1 in the range from 1 1,000 mm to 1 1,050 mm and pistons with the radius 1-2 in the range from 10,990 mm to 11,045 mm. That way it has been tested for the range of clearance between piston and bushing from 6 microns to 123 microns, considering theoretically maximal possible eccentricity 'le", tolerances and the possible combinations of available pistons and half bushings. Clearances are referring to ideal circular line, not considering the roughness and unexactnesses of the shape of piston and bushing. Actually so great range of clearances is not real for

the hydraulic components. Yet they have been tested to see the influence that the largeness of contact area has on the friction coefficient and on the formation of surface damages. As from Figure 2 evident is, we have made calculations of macro contact area considering the differences in radius of piston and bushing and considering the, through measuring obtained, surface roughness and unexactness of circular shape. Specimens were produced of some various materials, all of them are standard materials for elements of hydraulic valves. So the testing pistons are made of 5 different materials and bushings of 4 different materials. The surface hardnesses of test elements - pistons and half bushings - varied from 24 HRc up to 62 HRc. Every test lasted 20 minutes. All experiments with lubricated sliding surfaces were carried out using hydraulic oil according to IS0 VG 46 as lubricant between sliding surfaces of piston and half bushing.

141

2.2. Apparatus and procedures The exactness of circular line of half bushings has been measured with a three coordinate laboratory measuring machine. To simulate linear oscillatory movements we have used a laboratory testing machine, that enables us to predefine frequency, amplitude and normal load on specimens. Schematic view of testing ring of this testing machine is shown in Fig. 3 .

a

Loading system (6)

Figure 3. Schematic view of a part of testing machine with both testing pieces: small piston and half bushing.

In testing cell the vibrating specimen - piston (1) is mounted in the upper holder (3), which is connected with horizontal oscillating rod (5) to an electromagnetic exciter sine generator and power amplifier for controlling amplitude and frequency of oscillations. The frequency range of the test ring depends on the range of the displacements amplitudes of interest. In order to ensure stable testing conditions, a measuring accelerometer is mounted inside the specimen holder and the signal is used in a feedback loop. The loading system consists of push rod where the normal load is applied by an electronic loading system ( 6 ) and piezo measurement (7). Lower specimen - half bushing (2) is fixed in

lower holder (4) which is hrthermore fixed stationary on a piezo measurement cell (7). Friction measuring and at the same time eventual surface damage occuring tests were carried out by first loading the piston specimen by loading system shown in Fig. 3 against the half bushing specimen. After this an oscillation motion is transmitted to the piston from the electromagnetic exciter. As the half bushing is fixed stationary, the oscillatory motion is limited to the piston. This produces slip in the piston -bushing contact area, that is concave-convex contact. Loading of the piston against the half bushing is achieved by the loading system and the load is determined and maintained constant by means of the piezo measurement cell. This way the motion circumstances are the same as in a hydraulic spool valve. Only normal force on the spool in a valve is not always constant. The heating system (8) in testing machine held at our tests the temperature of specimen constant at 50 OC. The variations of values for coefficient of friction during test were recorded and memorized using a computer system. 210 experiments have been made. 192 of them using hydraulic mineral oil as lubricant on sliding surfaces, Other 18 experiments were made with dry friction of sliding surfaces. For every test testing elements were heated to 50 degrees Celsius, because being that normal temperature of hydraulic oil in stationary hydraulic systems, often working with more sophisticated hydraulic valves operating on working and dither frequencies simultaneously. We have tested at following combinations of frequencies1 amplitudes (Hdmicrons): 10/5, 3015, 20015, 40015, 10120, 30120, 200120, 101100, and 301100. With these 9 combinations we cover the range from working to dither frequencies and amplitudes (14/,154, respecting at the same time also the possibilities of testing machine. Three different normal forces were applied to load the testing oscillating piston: 5 N, 50 N and 200 N. Because of not ideal shape of piston and bushing, respectively because it is not possible to manufacture hydraulic elements with total exactness of dimensions, transversal forces on spool in hydraulic valves occur 161. According to calculations the chosen normal forces are in the range that is to

142

expect in operating hydraulic spool type of valves. Before and after testing specimens were analyzed using optical microscope (OM). Especially sliding surfaces were examined thoroughly.

3. EXPERIMENTAL RESULTS

3.1. Coefficient of friction Figures 4, 5 and 6 show the ranges of values for friction coefficient versus frequency and amplitude.

F= 5

F = 50 N

N

-

30

3

5 frequent arnpiitud:

These ranges of values for friction coefficient are shown for normal forces $ 5 0 and 200 N. The diagrams show the density of values for friction coefficient. Denser hatching means more values of the results of testing in a certain range. It is obvious that greater normal forces give mostly lower values for friction coefficient than small forces. At the same normal force the most significant differences among values for friction coefficient are among some proportions frequency/amplitude. The most obvious difference is between values for friction coefficient at proportions frequency I

20

'f' .a.

[51

Figure 4. Ranges of values for the coefficient of friction at normal force 5 N.

Figure 5. Ranges of values for the coefficient of friction at normal force 50 N.

143

amplitude 200/5 and 400/5. This significant difference for friction coefficient between stated two proportions frequency / amplitude is obvious for all three used normal forces (Fig. 4, 5 and 6).

F = 200 N

constant, or decreased and then stayed constant. All 4 pairs of specimens had the same contact area, considering production tolerances minudplus 1 micron for single element. According to Figure 2 the difference between both radii was r1 - 1-2= 0,005 mm. It defines contact area. Single curves (cl ... c4) in diagram Figure 7 were obtained with pairs of specimens of material and with parameters shown in Table 1. Furthermore Figure 8 shows the diagram of friction coefficient versus time, again for 200 N and 400 HA5 microns for another 4 pairs of specimens

-c ._ .

1--

- - -. c3..- ............

.

c2 0

0.16

?

I

I , I . . . . ' :

, . 20,12+:: ,

, ;

.-

/

g o mf ICI

u

,

. .

:; I

:

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

c4 ...........................

,, .

0.04

0,OP

''

I

I

Figure 7. Coefficient of friction -time diagram for 4 pairs of specimens at F = 200 N and f/a = 400 HA5 microns (lubricated friction).

130 0 100

Figure 6. Ranges of values for the coefficient of friction at normal force 200 N. Diagram of friction coefficient versus time for normal force 200 N, frequency 400 Hz and amplitude 5 microns for 4 pairs of specimens is shown in Figure 7. This one shows, that the coefficient of friction increased in the first few minutes to maximal values. After that it stayed

with a little smaller contact area. The difference between radii for these pairs was in the range r1 - r2 = 0,010 ... 0,020 mm (Fig. 2). The material and other parameters for these pairs of specimens are evident from Table 1. Though parameters and materials are different from those of first four pairs, the results for friction coefficient also for them lay in the same range. At normal force 200 N we have made also 8 tests with dry friction for the already mentioned two interesting proportions frequency/amplitude. There were 4 tests for 200 HA5 microns and other 4 tests for 400 HA5 microns. The obtained values for friction coefficient are shown in Figure 9.

144

Table 1. Parameters and material of specimens

c7

ETG 100

24

0,08

100Cr6

61

0,12

C8

45S20

51

0.09

100Cr6

61

0,12

c9

90MnV8

45

091

16MnCr5

62

0,05

c10

90MnV8

45

0.1

16MnCr5

62

0.1

~

~-

c11

90MnV8

62

091

16MnCr5

62

0,05

c12

90MnV8

62

051

16MnCr5

62

091

C13

90MnV8

45

091

16MnCr5

62

091

C14

45820

51

0,09

100Cr6

61

0,12

0

5

10

Time

15

20

[min]

Figure 8. Coefficient of friction -time diagram for another 4 pairs of specimens at normal force F = 200 N and Wa = 400 H d 5 microns (lubricated friction).

Already visual comparison for the values of friction coefficient for lubricated (Fig. 6) and dry friction (Fig. 9) shows, that the relation between friction coefficients for both types of friction at both f/a is approximately the same. The values for friction coefficient at dry friction are higher than those at lubricated friction. The diagram of friction coefficient versus time for 4 pairs of specimens at dry friction is shown in Figure 10. Single curves in diagram Fig. 10 are obtained with pairs of specimens with parameters and materials as shown in Table 1. Concerning contact area, the difference between radii of piston and half bushing for all 4 pairs of specimens at dry friction was r1 -9 = 0.005 mm (Fig. 2). What could be unexpected is that also at dry friction the values for friction coefficient in time 20

145

minutes are approximately constant if we do not consider first minutes of testing time, needed for stabilization of friction coefficient. For other tests at dry friction, 200 N and f/a = 200 H d 5 microns, the diagrams for friction coefficient are similar to Fig. 10, but values for friction coefficient are higher. That is obvious already from Fig. 9.

0,40 1

.- 0 2 0

10

Time [min]

I5

20

The coefficient of friction was not always constant or nearly constant during the testing time. In some cases we have obtained very changeable values for friction coefficient. Such case is shown in Figure 1 1. The materials of specimens and parameters, at which curve c 13 in diagram Fig. 1 1 is obtained, are given in Table 1. Contact area: r1 - 1-2= 0,005 mm. Another case for changeable friction coefficient during the testing time 20 minutes is shown in Figure 12, curve c 14. It was obtained with contact area, respectively difference of radii of both specimens r1 - r2 = 0,013 mm. The materials and parameters, at which curve 14 in Fig. 12 is obtained, are given in Table 1.

0.8a

0.7-

'C

L

-

I

5

Figure 10. Coefficient of friction - time diagram for 4 pairs of specimens at dry friction for normal force F = 200 N and f/a = 400 Hd5 microns.

0.9-

s 0.6.c ._ "

I 0

1 .o.-

._ c

................... ._.. .................................

3

0,oc

F = 200 N (dry friction)

I

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

-

0.5.-

a

0.4-

0.3.0.2-

0.1 .~

3.2. Surface damages 400 10 5

20

30 200 20

rn

frequency amplitude

c

30 100 100 [HZ] wn

1::

Figure 9. Ranges of values for the coefficient of friction for 2 proportions f/a at normal force 200 N and dry friction.

Carrying out our experiments at some of them the surface damages occured. It can happen that at one experiment two or more surface damages on half bushing and/or on piston are formed. Figure 13 shows the location of three surface damages (drawn magnified) on a half bushing. All three of them occured at the same experiment for which the diagram is presented in Figure 12. Material and parameters of both specimens for this test are obvious from Table 1 for curve C14.

I46

0.50-

I

I,..

I

3 0.25c)

-

B 0.20-

I

5

0.157

V

0.lO-L 0.05

1

-

O i i - r r 0 2 4

I 6

I 8

I

10

I 12

I 14

I 16

I

I

18

20

Time [min]

Figure 11. Coefficient of friction - time diagram at normal force F = 200 N and f/a = 30 Hd100 microns (lubricated friction).

1 1

0

2

4

6

8

Time

I

I

I

I

I

I

10

12

14

16

18

20

[mm]

Figure 12. Coefficient of friction - time diagram at normal force F = 200 N and f/a = 200 Hd20 microns (lubricated friction).

Figure 13. Location of surface damages on a half bushing. At our experiments two different types of damages occured. The first one is an abrasive type of surface damage (Fig. 14 and Fig. 13, damage "C"). At this type the damaged part of surface looks only more harsh as the initial surface. The second type of damage (Fig. 15, Fig. 16 and Fig. 13, damages "A" and "B") looks like a welded point on the surface. Both types of damages can occur on the same half bushing (Fig. 13) and at the same experiment. We have found out, that friction coefficient at experiments, at which damages occur, is not necessarily higher than that at experiments at which formation of damages does not occur. Yet the values for friction coefficient at experiments which form surface damages are never constant during testing. Anyway, the formation of surface damages causes the changing of the value of friction coefficient. At the experiment, for which the diagram friction coefficient - time is shown in Figure 1 1, two surface damages of the shape of welded points occured on the sliding area of the half bushing. Microphotograph of the greater surface damage is shown in Figures 17 and 18 and the microphotograph of the smaller surface damage is shown in Figure 19. Material and other parameters of both specimens for this test (testing diagram Fig. 11) are obvious from Table 1 for curve C13. The difference of radii of both specimens is already quoted too.

147

Figure 14. Magnification 100 -times of an abrasive type of surface damage on half bushing (Damage "C"in Fig. 13).

Figure 15. Magnification 100 -times of a point welded type of surface damage on a half bushing (Damage "A" in Fig. 13, testing diagram Fig. 12). At the same tests, when surface damage on a half bushing occured, mostly occured also surface damage alike to welded points on pistons. At our experiments the surface damages, that occured on testing pistons, were not so significant as those on half bushings. But they are, anyway, similar to those

Figure 16. Magnification 40-times for the same damage as shown in Fig. 15 (Damage "A" in Fig. 13).

Figure 17. Magnification 100 -times of a point welded type of surface damage (greater damage) on a half bushing (testing diagram Fig. 11). point welded points like looking surface damages on half bushings. The experiments, at which surface damages does not occur, show us that friction coefficient is mostly constant (Fig. 7, 8, 10). In the cases, where surface damages occur, the friction coefficient is not considerably or is not at all higher, but it is always

148

4. DISCUSSION

Figure 18. Magnification 40 damage as shown in Fig. 17.

- times for the same

Figure 19. Magnification 100 -times of the smaller point welded type of surface damage on the half bushing (testing diagram Fig. 11). changeable (Fig. 1 1 and Fig. 12) at least for the time, when, as we presume, damages form and the rands of the damage scar are at least a little smoothed (arrow in Fig. 15).

From diagrams - Figures 4, 5 and 6 appears, that greater normal forces give mostly lower values for friction coefficient than small forces. For that we have not yet any reliable explanation. We suppose it can be explained through different influence of adhesion forces at various normal forces. Varying with different pistons and half bushings we have had various materials in sliding contact and have got various contact areas. As for the results, no significant influence of various materials and various contact areas on the values for friction coefficient has been found. Additional research work and testing will be necessary for more accurate determination of the influence of these parameters on the friction coefficient. As already mentioned, 18 tests were made with dry friction. Figure 9 shows the ranges of values for Coefficient of friction at dry friction versus two combinations for frequency and amplitude at normal force 200 N. The comparison with Fig. 6 for lubricated friction at the same normal force shows, that friction coefficient for dry friction is higher, what is to be expected. Interesting is, that the relation for friction coefficient between proportions frequency/ amplitude 20015 and 40015 is about the same for both types of friction. We have found more interesting and extraordinary the surface damages that are alike to welded points, than those of abrasive type. The possibility for the formation of welded type of damages is greater at greater normal forces. But we have not yet found any influence of kind of steel, hardness and smoothness of sliding surfaces in the range of usual values, respectively parameters, for hydraulic elements on the possibility for formation of surface damages. At lubricated friction between two surfaces of sliding elements a thin oil lubrication layer normally exists. Yet, we suppose, because of normal forces on the sliding elements and because of some other effects too, the lubrication film can be destroyed and it comes to direct metallic contact, at first on some small point areas. With the thinning of the oil layer the molecular forces between surfaces become more significant. Herein, we presume, is the reason, why

149

the relations for friction coefficient for the same proportions frequency/amplitude are the same for lubricated and dry friction. It is also necessary to note, that we have, at our experiments, not noticed the formation of surface damages at higher frequencies and low amplitudes, especially not for proportion 400 H d 5 microns. It is important to emphasize, that for all 8 experiments with 200 HA5 microns and 400 HA5 microns also at dry friction we have obtained no surface damages. It is pity we until now didn't succeed to make more experiments at dry friction with other frequencies, amplitudes and materials too.

5. CONCLUDING REMARKS A lot of producers of hydraulic spool valves, with the main regard to producing proportional- and servo-valves, use dither frequencies at about 200 Hz. With the respect to our present results it would be suitable to examine and testify if higher dither frequencies were not reasonable, as coefficient of friction is significantly lower at higher frequencies. From our experiments we can conclude that various kinds of steel, various contact areas, surface hardnesses and roughnesses in the range that is usual for the elements of hydraulic components have not so great influence on friction coefficient as proportion of frequency/amplitude especially at normal force about 50 N. To avoid or at least to minimize the possibility of the formation of surface damages on the surfaces of sliding elements, the occur of damages at our present experiments show, that it is very important to minimize normal forces. At hydraulic components it is possible to achieve that with more accurate manufacturing (higher quality of manufacturing machines) and better construction

design of components. - According to the results of our experiments we can conclude, that high frequencies and low amplitudes of our testing range also minimize the danger for formation of surface damages of welded points type.

6. ACKNOWLEDGEMENT The authors of this paper are grateful to Ministry for Science and Technology of the Republic Slovenia for financial support at present work.

REFERENCES 1 . Kennedy, L. Stallings and M.B. Peterson, A study of Surface Damage at Low-Amplitude Slip, Asle Transactions, Volume 27, 4, 305-312, (1 983)

2. Soederberg, U. Bryggman and T. McCullough, Frequency Effects in Fretting Wear, Wear, 110 (1986) 19-34 3. Viiintin, L.K. Ives, F. Vodopivec, The Effect of Slip Amplitude on Fretting in Metal-Metal Contact, Proceedings 6th International Congress on Tribology, Volume 5, Eurotrib '93, Budapest, 198-203, 1993

4. Ebertshaeuser (editor), Fluidtechnik von A bis Z, Vereinigte Fachverlage, Mainz, 1989 5 . Niemas, Understanding servovalves and using them properly, Hydraulics & Pneumatics,

Sept./Nov. 1977 6. Will and H. Stroehl, Einfuehrung in die Hydraulik und Pneumatik, VEB Verlag Technik, Berlin, 1981

This Page Intentionally Left Blank

Dissipative Processes in ’l‘ribology / I). Dowson et al. (Editors) 0 1994 Elscvicr Scicncc I3.V. All rights rcscrvcd.

151

Effects of surface topography and hardness combination upon friction and distress of rolling/sliding contact surfaces A.Nakajima and T.Mawatari Dept.of Mechanical Engineering, Faculty of Science and Engineeering, Saga University, 1, Honjo-machi, Saga-shi, Saga 840, Japan

Using circumferentially, axially, and obliquely ground steel discs, the changes in the frictional force during the running-in process have been examined under the lubricated rolling with sliding contacts. The results obtained were much different depending on the surface topography, the hardness combination, the slip ratio, etc. Especially, the circumferentially ground discs showed a considerably high friction and severe wear occurred in the different hardness combination. Based on the results of experiments and measurements of the surface temperature, the surface hardness, the surface profile, the state of oil film formation, etc., the authors discuss the mechanisms which cause such differences.

1. INTRODUCTION Friction is the resistance to motion which is experienced whenever one body moves relative to the other body in contact, and the running performance or the durability of machinery with many tribo-components is decisively affected by its behavior. Especially, excessive friction in concentrated contacts such as gears, cams and rolling element bearings causes not only an energy dissipation or a lowering of mechanical efficiency but also surface damages like severe wear, scuffing and rolling contact fatigue. Concerning this kind of problem, it is generally considered that one of the dominating factors is the relative configuration between the EHD oil film thickness and the surface roughness which is represented by Dawson’s D value[l] or Tallian’s film parameter A[2]. For example, Bair and Winer[S] and Evans and Johnson[4] clarified that roughness effects on traction (friction) become negligible at values of A exceeding about 3 5 , while in the mixed lubrication regime where the 2, the behavior value of A is less than 1 is strongly influenced by the parameter A.

-

-

Furthermore, Johnson and Spence[5] showed that there is a difference in the friction between circumferentially ground discs and transversely ground ones even though they are compared at the same value of A, but tooth friction loss in gears can be confidently predicted from disc machine tests provided that the surface finish of the discs is representative of the gears in magnitude and orientation. Certainly, the parameter A defined by the ratio of the oil film thickness to the combined surface roughness gives a criterion for judging the degree of asperity contacts or the duration of oil film formation. In the partial EHD or the mixed lubrication regime, however, depending on the running conditions, the characteristics of surface topography, the hardness combinations, etc., the severity of asperity interactions can change significantly during operation, and it thus appears that not only the initial surface roughness but also the running-in effects become an extremely important factor. In the present paper, the authors have investigated this problem using a disc machine.

152

2. EXPERIMENTAL METHOD 2.1. Testing machine and test discs Experiments were carried out using a disc machine having a center distance of 60mm. The main part is shown in Fig.1. A pair of discs D and F were driven by gears with the gear ratios of 28/29 (slip ratio s = -3.6%) and 26/31 (s = -19.2%). The outside diameter of discs was GOmm and the effective track width was 1Omm. As disc materials, a carburized and hardened alloy steel (SCM415 according to JISG4105, Hv 2760) aiid a thermally refined carbon steel (S45C according to JISG4051, Hv 2~320)were used. Disc surfaces were finished using a cylindrical grinding machine or a cup wheel on a universal tool & cutter grinder. According to the direction of grinding and the surface roughness, test discs were classified as follows. 0 Relatively rough discs ground circumferentially (c), axially ( a ) , and obliquely at the angle of about 45" with respect to the axis of disc (0). (Rmax -1 -2 p m , Ra -0.20 -0.44 pum) 0 Smooth discs finished by precision cylindrical grinding ( p ) . (Rmax =0.1 -0.2 pum, Ra -0.02 -0.04 Pm)

Fig.2 shows the three dimensional views of disc surfaces before running. As test discs, c/p, a/p, o/p, a / a , p/p, etc. were mated in equal hardness (760/760 Hv) or different hardness (760/320 Hv) combinations.

Circurnferentially ground (c)

Axially ground (a)

lo

01

Fig.1. Main part of testing machine 2.2. Experimental conditions

and procedure A summary of the present experiments is given in Table 1. The rotational speed was 3583 f 1Orpm on the driving D disc and a maximum Hertzian stress of PH = 1.2GPa was applied in line contact. As lubricant, a nlineral gear oil without EP additives (vis-

Obliquely ground

(0)

Fig.2. Three dimensional views of surfaces (D disc before running)

Precision cylindrical grinding ( p ) 2 20prn

/Lx 0.2mrn

Y 0.2mm

153

Table 1

Suiniiiary of experiments and main results $1 Surface Hardness finish

Exp.

No.

Hv

Roughness Rmax, Dm Before After

D c

A-1

F

D

A- 2

F

p p p

D c

A-3

F

p

D c

A-4

F

D F D

A-5 A-6

F

p p p p p

D c

A-7

F

p

D F D B-2 F D B-3 F D 0-4

a a a

B-l

p

a a a F a D a

B - 5 F p

D a

B-6

F

p

D a

B-7

F

p

D o F p D o

c-1 c-2

F

p

D o c-3 F P

N.B.

756 758 765 760 754 319 775 326 757 329 777 773 777 331 756 757 754 756 771 322 769 312 778 321 778 332 792 332 767 768 779 322 784

320

1.0 0.2 0.1 0.1 1.0 0.2

0.8

0.2 0.1 0.1 2.0 0.8

0.8

0.8

0.2 0.1

0.4 0.1 0.1 0.1 0.1 0.8 0.5 1.5 2.0 1.0 0.2 2.0 0.8 2.0 0.3

0.2

0.1 0.1 0.8 0.5 2.0 2.5 1.0 0.1 2.0 2.5 2.0 3.0 2.0 0.1 1.0 0.2

1.8

0.9 1.0 0.3

1.0

1.0

0.5 1.0 0.1 1.0 0.2 0.8 0.5

0.2 1.0 0.1 0.8 0.2 0.8

0.5

Slip ratio s,

x

-19.2 -19.2 -19.2

-19.2 -19.2 -3.6 -3.6 -19.2 -19.2 -19.2

-19.2 -19.2 -19.2 -3.6

-19.2 -19.2 -3.6

Coeffi.of friction

$2 hmin

,,urn

$3 A

*4 A h

Weight

loss

LL

0.051 -0.030 0.027 -0.019 0.098 -0.061 0.061 -0.033 0.027 -0.014 0.035 -0.029 0.042 -0.036 0.038 -0.037 0.032 -0.026 0.041 -0.022 0.036 -0.022 0.038 -0.019 0.030 -0.021 0.040 -0.037 0.041 -0.027 0.047 -0.023 0.040 -0.037

(45°C) 0.30 (1.30) 0.51 (1.30) 0.13 (1.30) 0.12 (1.30) 0.42 (1.30) 0.98 (1.36) 0.76 (1.36) 0.32 (1.30) 0.32 (1.30) 0.36 (1.30) 0.29 (1.30) 0.31 (1.30) 0.32 (1.30) 0.80

(1.36) 0.25 (1.30) 0.26 (1.30) 0.80

(1.36)

,g

(45T) 1.01

(4.38) 19.3 (49.2) 0.46 (4.62) 0.52 (5.84) 6.48 (20.1) 30.8 (42.7) 1.60 (2.87) 0.43 (1.74) 1.24 (5.03) 0.39 (1.42) 0.43 (1.91) 0.58 (2.43) 1.20 (4.87) 2.40 (4.07) 0.84 (4.38) 0.80 (3.98) 1.85 (3.14)

19 18 12 13 15 112 2 114

0.01 0.00 5.10

& severe wear

F:pitt ing(L2) & severe wear

0.01

3

0.00 0.00 0.00 0.01 0.01 0.00 0.01 0.01 0.00 0.54 0.01 0.52 0.01 0.64 0.00 0.01 0.00 0.02 0.00 0.00 0.00 0.05 0.00 0.00

5

F : rippling

l3

0.01

0

149 6 10

xi04

Ojl

10

12 36 24 26 24 8 15 251 22 262 29 259 14 126 2 2 12 28

N,

0.00 0.02

1.10 0.01

1

$5 Number. Remarks of cycles

61 78

F:pit t ing (11) F :pi t t ing

(L2,MZ) F :pit t ing (M3,S3)

loo F :p i t t ing

loo

(S1)

F:p i t t ing 63

(M1,SZ)

* 1 c : Circumferentially ground, a : Axially ground, *2 * * *

o : Obliquely ground at the angle of about 45" with respect to the axis of disc, p : Precision cylindrical grinding.

hmin : the oil film thickness caluculated using the oil viscosity at the disc surface temperature. ( ) is hmin for the inlet oil temperature 45°C. : the combined root mean square roughness of two surfaces. 3 A = hmin/a , u = ( ) is A calculated using hmin for the inlet oil temperature 45°C . 4 Increase in micro-Vickers hardness of disc surface after running. 5 Number of pits . . . L pit : > 43, M pit : 42 3, S pit : 40.5 2

d

m

N

-

154

cosity v , 66.3mm2/s at 40"C, 8.9mm2/s at lOO"C, pressure viscosity coefficient a ; 16.6GPa-', specific gravity 15/4"C : 0.877) was supplied at a flow rate of 15cni3/s. The oil temperature was kept at 45°C and the corresponding oil viscosity v was 52.5inm2/s. The state of oil formation between discs was continuously monitored by means of an electric resistance method. The voltage of 150mV was impressed between discs (the resistance of about 1 . l l k R was connected in parallel in the measuring circuit), and the variation of the voltage during operation was observed. When the oil film is developed fully, the voltage Eab recorded on a chart reaches 15mV. The frictional force between discs was measured using strain gauges stuck 011 the driving shaft (via slip rings), and the actual surface temperature on the track was also measured successively using trailing thermocouples. The theoretical oil flni thickness hmin[6] was calculated using the oil viscosity a t the actual temperature of the disc surfaces. For reference, the value for the viscosity at the inlet oil temperature (45°C) was also calculated. 3. RESULTS AND DISCUSSION 3.1.F'riction and surface temperature Experiments were all carried out at a constant normal load giving a maximum Hertzian stress O f pH = 1.2GPa and a t a designated slip ratio of s = -3.6% or -19.2%. The testing machine is equipped with an automatic stopping device which is worked by the vibration induced. In the present experiments, each test was continued up to N=106 cycles unless any serious surface damages occurred. The main results are summarized in Table 1. Figs.3 to 5 show some results of the friction measurements. On the whole, the frictional force had a tendency to be large immediately after the start of ruiiiiing, then decrease monotonously and settle down. However, if examined in detail each result, considerably different behaviors were recognized depending on the combination of discs and

0.10

Hv: 760/760,760/320

\

0.08

Axial/P

A-3

8-2

8-5

A

A

c-l

c-2

-1

---

Oblique/P---

; I

B'

c 0

.r

A-1

0.06

.r

YL

+0

1

c, C

.r

.,U 0.04 Y'c 0) V 0

0.02 S=

I

0 104

-19.2%

I

I

I I I l l 1

I

105 Number o f cycles

I

1

1

1

1

lo6 N

Fig.3. Changes in coefficient of friction ( S = -19.2%) the running condition. Fig.3 shows the results of pairs of a relatively rough D disc and a smooth F disc (tested at s = -19.2%). As is apparent from the figure, the circumferentially ground discs showed a higher friction than both the obliquely ground discs and the axially ground discs. Furthermore, a t the initial stage of running, the discs of different hardness combination (760/320Hv) showed a higher friction compared with the pairs of equal hardness (760/760Hv). Especially, in Exps.A-3 and A-4, where circumferentially ground discs were used in the different hardness combination, considerably high friction, high surface temperature and severe wear were observed. Fig.4 shows the results of axially ground rough discs tested a t s = -19.2%. Although two surfaces were equally rough and the value of A was less than 0.5, the friction in

155

I

0.06

c

:

1 01

1 o4

I

1 I 1 1 1 1 1

I

a)

8-1, a / a

IZI 8-3, a / a

I

1

I 1 1 1 1 1

I

A-7, c l p

A C-3, O/P

1

s = -19.2%

I

I

I

I I I I I I

I

I

105 Number o f c y c l e s N

I l l l l l l

1 O6

Fig.4. Changes in coefficient of friction ( S = -19.2%) Exp.B-1 of equal hardness combination was not so high, and there was hardly change during operation. On the other hand, the friction in Exps.B-3 and B-4 of different hardness combination was high at first, then dropped gradually in the same manner as Exp.B-5 shown in Fig.3. The results tested at s = -3.6% are shown in Fig.5. As seen from the data in Table 1, the coefficient of friction increased to some extent with the change of the slip ratio from s = -19.2% to -3.6% in the combination of smooth discs (compare Exps.A-2 and A-5 with Exp.A-6). In Exps.A-7, B-7 and C-3, where relatively rough D disc and smooth F disc were combined ( A = 1.6 2.4), the difference in the friction among discs with different topographies became very small in contrast with the case of s = -19.2%. Figs.6 to 8 show the surface temperatures of discs during operation. The temperatures were measured on the track of D disc side with a faster peripheral velocity. Except for a few cases, the variation of surface temperature during operation was relatively small in each test, and the temperatures were in the range of approximately 100 130°C with rough discs and 75 95°C with smooth discs when tested at s = -19.2%. Of course, some differences were observed depending on the

0 104

105 Number o f c y c l e s

106 N

Fig.5. Changes in coefficient of friction (S = -3.6%)

-

-

“I

104

5x104 lo5 Number o f c y c l e s

5x105

lo6

N

Fig.6. Temperature of disc surfaces (S = -19.2%)

N

surface topography, and the axially ground discs generally showed a lower temperature

156

150

Y 01

a +.' m

01

8100 #

c,

q 9

01 U

I I

c-1

S=

a

5

0

1

a)

A-7

A

C-3

UI 8-7

c, 3

m W L

El00 42 #

.

aJ

c

-19.2%

v)

B-2

50 104

1

01 L

m

Y-

V

5x104 l o 5 Number o f c y c l e s

I I 5x105

v) 3

104

N

Fig.7. Temperature of disc surfaces (S 1-19.2%) than the obliquely ground discs or the circumferentially ground discs. Among the rest, the temperature was extremely high when the circumferentially ground rough D disc with higher hardness and the F disc with lower hardness were combined. In fact, in Exps.A-4 and A-3, the maximum temperature reached easily even 200°C 225°C immediately after the start of running as shown in Fig.6. In the experiments tested at s = -3.6%, however, the temperature increased a little but 75"C, and the differremained about 55 ence among discs became smaller or negligible as shown in Fig.8.

-

-

3.2. Changes in surface As shown in Table 1, some experiments of the pairs with different hardness were discontinued before N = lo6 cycles owing to the occurrence of surface damages such as rippling (i.e. corrugation), pitting and severe wear. In Exps.A-3 and A-4 of circumferentially ground discs, the disc surfaces became discolored noticeably, possibly owing to the extremely high temperature and the ensuing oxidation, arid it is not unimaginable that scuffing caused severe wear. In Exps.B-3, B-4 and B-5, where axially ground discs were used in the different liardness coinbination, pitting occurred a t an earlier stage on the slower F disc with lower hardness. This is consistent with previous work on the effect of asperity interaction

I

50

lo6

5x10" 1 Number o

5x105 cycles

I

10'

N

Fig.8. Temperature of disc surfaces ( S 1 -3.6%) pitting[7] which shows that the asperity interactions accompanied with sliding become severe when the directions of sliding and machining marks cross each other, and consequently the pitting life of axially ground discs is generally short compared with that of circumferentially ground discs. In the experiments where the same high hardness discs were combined, neither serious daniage like pitting nor scuffing occurred except for a slight discoloration on the track. AHv in Table1 shows the increase in microVickers hardness of disc surfaces after running. In Exps.A-3, A-4, B-3, B-4, B-5, B-6 and C-2 tested at s = -19.2%, work hardening was remarkable on the F disc surfaces with lower hardness. In the experiments tested at s = -3.6%, however, the increase in hardness was only a little as shown in Exps. A-7, B-7 and C-3. Figs.9, 10 and 11 show some of the profile curves, the three dimensional views and the photographs of contacting surfaces, respectively. When there is a large difference in the hardness between two surfaces, the roughness of the harder surface remains almost 1111changed and plays a dominant role on the running-in or the occurrence of surface damage and wear of the mating surface with lower hardness. Some results are shown in the figure (Exps.A-4, B-3, C-2, etc.). On the other hand, in the case of almost the same hardness

on

157

rD Before runnning

L

After runnning EXp.A-1

Before runnning

[r

rD

,

-

Before runnning

Exp.B-1

,

.

.

.

. . . . , . . _ _ . .

After runnning

-

I

,

Before iunnning

-

Exp.B-2

After runnning

Before runnning

-

Before runnning 7

After runnning Exp.B-5

L‘

-

Exp.B-3

Before runnning

!

After runnning

Before runnning

E ~ ~ . c After - ~ runnning D///////// F m Axial direction

:L

c,

l.Ornm

Fig.9. Profile curves of mating surfaces

Exp.B-5

After runnning

Circumferential direction

ET

158

EXp.B-1

EXP.B-3

Fig.10. Three dimensional views of contacting surfaces after riinning

.-.

1W m r n y 0 . 2 ~ ~

159

Fig.11. A pair of disc surfaces after running (Exp.A-4)

Fig.12. Contour maps of contacting surfaces (D disc)

I60

combination, the roughness has a tendency t o diminish on both sides when two surfaces are equally rough. However, when two surfaces with a large difference in the roughness were combined, the decrease in the roughness of the rougher surface becomes modest[8]. For example, in Exp.B-1 of equally rough discs (ground axially) , the asperities became blunt and the roughness diminished to some extent on both surfaces. However, in Exps.A-1, B-2 and C-1, where a relatively rough disc and a smooth disc were combined, the magnitude of surface profile curves of rougher disc hardly changed but only the tips of asperities flattened slightly. In order t o understand easily such a slight change in surface, the authors drew contour maps of contacting surfaces based 011 the digital data of surface profile measured threedimensionally. A few examples of them are shown in Fig.12, where depth levels are classified by shading (the original one was displayed by color). We can see the increase or the extension of higher flattened areas after running.

3.3. States of oil film formation Fig.13 shows some examples of the progress of oil film formation during operation. In most cases, immediately after the start of running, the voltage between discs showed nearly zero or a very low value owing to the

104 15

r

5x104 lo5 5x10' Number o f cycles N

lo6

5x1 0'

1 O6

f4 B-1, a / a

1 o4

5x104 lo' 5x10' Number o f cycles N

1 Number o f cyc l e s N

Fig.13. Changes in voltage between discs (Eab=OmV:contact, 15mV:separation)

161

metallic contacts, then the oil film came to be built up and the voltage rose gradually. However, as shown in the figure, the processes of oil film formation were considerably different according to the combination of discs and the running condition. In the combination of rough and smooth discs with equally high hardness, the voltage rose rapidly when they were tested at s = -19.2% (Exps.A-1, B-2 and C-1). Among the rest, the circumferentially ground one (Exp.A-1) showed a most rapid increase contrary t o the order expected from the friction measurements. Such a result may be explained partly by the formation of oxide film, possibly accelerated during operation. Also in the combination of equally rough discs, the progress was rather slow but the oil film came to be built up steadily (Exp.B-1). As shown in Fig.9, the total roughness depth (peakto-valley height) after running was still large enough although the crests of asperities flattened out, and thus it is supposed that the micro-EHL action[9] plays an important role in the oil film formation between such rough surfaces. Meanwhile, in the combination of discs with different hardness, the voltage rise was hardly observed or showed a very slow progress when the harder disc was rough and tested at s = -19.2% (Exps.A-3, A-4, B-6, C-2, etc.). Especially, in Exps.A-3 and A-4 of circumferentially ground discs, the voltage remained almost zero during the operation, and this corresponds well to the results of friction measurements . When a rough harder disc and a lower hardness disc are rotated in company with sliding, asperities on the harder surface penetrate into the lower hardness surface and plastic deformation due to the indentation and ploughing is repeated there, although the condition of asperity contacts varies with work hardening of the lower hardness surface and ensuing deformation of asperities on the harder surface. That is possibly the main cause for the high friction and the poor oil film formation in the different hardness combination. However, when they were tested at s =

-3.6%, owing to the less surface temperature rise, the states of oil film formation were improved evenly although some differences among discs were still observed ( Exps. A-7, B-7, C-3, etc.). 4. CONCLUSIONS

Using carburized alloy steel discs (760Hv) and thermally refined carbon steel discs (320Hv) ground circumferentially, axially, and obliquely, the effects of surface topography and hardness combination on the behavior of friction and the occurrence of surface distress were investigated under the lubricated rolling with sliding conditions of two fixed slip ratios (s = -3.6% and -19.2%). The main results are summarized as follows:

(1) Generally, the friction had a peak at first, then decreased gradually and settled down at a certain value. However, significant differences in the behavior were recognized depending on the combination of discs and the running condition. (2) The circumferentially discs showed a higher friction than the axially ground discs, and the obliquely ground discs showed an intermediate value between these two when they were tested a t s = -19.2%. (3) And then the discs of different hardness combination (760 / 320Hv) showed a higher friction compared with those of equal hardness combination (760/760Hv) at the initial stage and showed a gradual decrease with the progress of running. Especially, considerably high friction, high surface temperature and sever wear were observed with circumferentially ground discs. (4) By changing the slip ratio from s = -19.2% to -3.6%, the friction increased t o some extent with smooth discs. Although a little more higher friction was obtained with relatively rough discs, the effect of difference in the topography became very small owing to the formation of thick oil film.

162

(5) The mechanisms which caused such different behaviors in the friction were discussed based on the observed surface temperatures, the changes in hardness, the surface profiles, the states of oil film formation, etc. (6) Even when the friction decreased and the oil film came to be built up significantly, the changes in the magnitude of roughness were relatively small in the present experiments. Therefore, in order to understand such a situation, it is necessary t o take into account microtopographical changes of asperities which engage in contact.

REFERENCES 1. P. H. Dawson, J . Mech. Engng. Sci., 4 , 1

(1962) 16. 2. T. E. Tallian, ASLE Trans., 10, 4 (1967) 418. 3. S. Bair and W. 0. Winer, Trans. ASME, J. Lub. Tech., 104, 3 (1982) 382. 4. C.R.Evans and K.L.Johnson, Proc. Inst. Mech. Eng., 201, C2 (1987) 145. 5. K. L. Johnson and D. I. Spence, Tribology Int., 24, 5 (1991) 269. 6. D. Dowson, Proc. Inst. Mech. Eng., 182, Pt 3A (1968) 151. 7. K. Ichimaru, A. Nakajima and F. Hirano, Trans. ASME, J.Mech.Des., 103, 2 (1981) 482. 8. A. Nakajima and T. Mawatari, Proc. 6th Int. Cong. on Tribology, Budapest, Vo1.5 (1993) 290. 9. M.Kaneta and A.Cameron, Trans. ASME, J. Lub. Tech., 102, 3 (1980) 347.

Dissipative Processes in l'ribology / D. Dowson e[ al. (Editors) 0 1994 Elsevier Science B.V. All rights reserved.

163

Anti- wear Performance of New Synthetic Lubricants for Refrigeration Systems with New HFC Refrigerant. T.Katafuchi'

,

M. Kaneko'

,

M. Iinob

'Lubricants Research laboratory, Idemitsu Kosan Co. Ltd. 24-4 Angasaki-kaigan, Ichihara, Chiba, Japan 'Lubricating Oils Division, Idemitsu Kosan Co. Ltd. 3-1-1 Marunouchi, Chiyoda, Tokyo, Japan

The influence of new synthetic lubricants for use with HFC134a on the wear between aluminum-alloy and steel, which are used as mechanical parts in the compressor of automotive air conditioning systems refrigerated by HFC134a under severe lubricating conditions, was studied using a flat ring on flat ring friction apparatus equipped with a newly developed in situ wear sensor. It was clarified that a PAG type lubricant had excellent anti-wear properties compared with an ester type lubricant during the break-in stage for practical compressors with HFC134a..

1. Introduction The charge of refrigerant in automotive air-conditioning systems from CFClZ t o HFC134a is underway in compliance with the CFC phase-out program[l. 2,31. The main problem to be solved is the reduction of wear of mechanical parts in compressors in order to make this replacement. A sensor was developed for in situ monitoring of

the wear between aluminum-alloy and steel which are used asmechanical parts in compressors. The wear characteristics of ester and PAC type lubricants, which were recently commercialized as refrigeration oils for HFC134a, were evaluated using a flat ring on flat ring friction apparatus[41 equipped with the in situ wear sensor.

164

2. Test apparatus and lubricants 2. 1 Test apparatus

A rotating flat ring on a stationary flat ring type friction apparatus was used for the evaluation. This friction apparatus was adopted in order to reproduce the lubricating conditions in practical compressors, because the flat face to face contact keep the contact pressure constant during the wear test. The upper rotating ring was made of bearing steel, and the lower stationary ring was aluminum-alloy(Si:14%). The design of these rings is shown in Fig. 1.

contact pressure at 500 rpm with a continuous supply of gaseous HFC134a. The oil tempreature was kept at 50 "C. The applied load, frictional force, electric resistance between sliding surfaces under 15mV of applied voltage and 100 ohm of parallel resistance, and wear traced by the in situ wear sensor were measured during the wear test. 2.2 In situ wear sensor. Wear particles of aluminum-alloy, which are stably dispersed in the test lubricants, increase with test duration. Therefore, it is possible to trace the wear continuously by measuring the light transmittance of the test lubricant during the wear test, which changes with the concentration of dispersed wear particles.

Lower stationary ring Upper rotating ring aluminum - Alloy) (Bearing steel)

Fig. 1 The design of Test Ring

The test conditions were as follows. After gaseous HFC134a had been supplied to the test lubricant at 54!/hr for 30 minutes through a hole drilled near the center of the stationary flat ring, the wear test was conducted under the selected

i 6 t Fig. 2 The cornfiguration of the detector part of the wear sensor

The newly developed in situ wear

165

monitoring sensor utilizing an optical fiber cable was based on this concept. The configuration of the detector part of the wear sensor, which is set near the test specimen in the test lubricant during the wear test, is shown in Fig.2. 2.3 Test lubricants. Commercially available ester and PAG type refrigeration oils for automotive air conditioning systems with HFC134a were used for the evaluation. The properties of these lubricants are shown in Table 1. The base fluid of the PAG type lubricant is an end-capped polyalkyleneglycol. The ester type lubricant is composed of a di-pentaerythritol carboxylic acid

ester. Both lubricants can be completely dissolved in liquid HFC134a in compressor systems at 50 "C. I t was difficult to evaluate the difference i n lubricity between the ester and the PAG type lubricants from the load carrying capacity using the Falex Test, because these two lubricants gave almost the same failure load with the supply of gaseous HFC134a as shown in this table.

3. Resu I t s and discuss ion 3 . 1 Performance of the newly developed

in situ wear sensor. The relationship between aluminum content in the test lubricants analyzed by

Table 1 The properties of synthetic test lubricants Ester type Kinematic Viscosity

@ 40"C

PAG type

80.88

49.99

10.40

10.34

112

214

Total Acid Value (mgKOH/g)

0.01)

0.01)

Saponification Value (mgKOH/g)

337

5)

- 50)

- 50)

(mm2/s>

@ 100°C

Viscosity Index

Pour Point ("C)

Phase Separation Temp. ("C) HFC134aAubricant = 80/20 Failure Load by Falex Test (lbs.) with supply of gaseous HFC134a at 52! /hr

-4O),

80 (

1250

- 40 )

, 80

1080

I66

an ICP emission spectrometer and the transmittance measured by the developed wear sensor is shown in Fig. 3. .00

80

R

=-

0.926695

3 . 2 Test results under stepped-up load

conditions. Average friction coefficient, electric resistance and light transmittance versus contact pressure are shown in Fig.4, 5 and 6, respectively, The wear tests for both PAG and ester type lubricants were

60 40

lKt

20 0 ' 0

I

I

3

6

I

I

9 12 A1 content (ppm)

I P

Fig. 3 Relationship between A1 content of test lubricants and light transmittance

0

A good correlation was obtained as shown in this figure. It can be seen that the n e w l y d e v e l o p e d w e a r s e n s o r is satisfactory for practical use.

1.5 3.0 Contact Pressure (MPa)

Fig. 5 Relationship between average electric resistance (R) and contact pressure 100 -

0.2 -

T (%)

,u

50 -

0.1 -

1 PAG 0. 0

I

Fig. 4 Relationship between average friction , ) and contact pressure coefficient ( u

I

0

I

1.5

Fig. 6 Relationshiup between average light transmittance (T) and contact pressure

I

3.0

167

conducted by stepping up the load every 3 minutes. The ester type lubricant decreased the electrical resistance and light transmittance with an increase of the friction coefficient at low contact pressure compared with the FAG type lubricant. These test results were noticeably different from those from the Falex test. The load carrying capacities of these two lubricants by Falex test were almost the same, as mentioned before. 3. 3 Test results under constant

load conditions. Wear tests were conducted at 1.2 MPa for the PAC type lubricant and 0.75 MPa for the ester type lubricant f o r 3 minutes, respectively.in order to determine the wear behavior at an early stage of the wear test at low contact pressure. The selected load was the load at which the wear started to be observed and the average light transmittance of the test lubricants decreased to about 85% of the new oil. These test conditions were considered to be reasonable to evaluate the wear characteristics of refrigeration oils at the break-in stage of practical compressors. The relationship between friction

OL OL

o w * 0

.

I

Fig. 7 Relationship between friction cient ( D O , electric resistance light transmittance (T),and duration with the PAC type

0

I

1 Test duration 2 (mid3

1

2

coeffi (R) and test lubricant.

3

Test duration (min)

Fig. 8 Relationship between friction coeffi cient (D),electric resistance (R) and light transmittance (T),and test duration with the ester type lubricant

coefficient, electric resistance and light

168

transmittance, and test duration for each test lubricant is shown in Fig.? and 8. The P A G type lubricant slightly decreased the light transmittance, in other words, the wear was slightly increased with decrease of friction coefficient and rapid increase of the electrical resistance after 1 minute from the start of the wear test. The wear did not increase after that and the friction coefficient became stable at about 0.03, which indicated a regime of fluid lubrication. Meanwhile, the electrical resistance reached a maximum, which meant that the sliding surfaces were electrically insulated by the oil film. On the other hand, the ester type lubricant continuously increased the wear with a slight increase of friction coefficient from 0.12 to 0.14 over the test durat ion. The electrical resistance stayed around zero, which meant that metal contact continously occurred between the sliding

(1)

-.. '

I

.. . ,:

New Specimen

'-"-

.

..

.

. .

. ...... .

i

.

.

.

- 1

(2) Tested with PAC type lubricant

'- T .I

-

:

1

.._

-- .

'(3) Tested with &ter type lubricant

Fig. 9 Surface roughness of test specimens

surfaces. In order to clarify the difference in wear behavior between PAC and ester type lubricants, the surface roughness of the aluminum-alloy test specimen after the wear test at constant load for 3 minutes were measured in comparison with that of a new specimen, as shown in Fig.9. Micro scuffing was partially observed on the sliding surfaces tested by ester type

Table 2 Elements on the sliding surfaces

I Smoothly worn surface I

Micro scuffed surface

A1 on steel

1.5

1.4

F e on Al-alloy

2.8

2.8

A1 on steel

1.5

1.7

101.1

F e on A1 - alloy

4.7

3.0

12.5

PAG type lubricant ~~~

107.4

Ester type lubricant 15.2

I

169

lubricant. On the other hand, the PAG type lubricant did not generate micro scuffing, the surface being perfectly smooth like a new specimen. Furthermore, the concentration of related elements on the sliding surfaces were analyzed using EPMA. The analytical results are shown in Table 2 as a ratio of the element on the sliding surface to that of a new specimen. A larger amount of metal transfer between the micro scuffed surfaces was observed, compared with smoothly worn surfaces. I t indicated that the PAG type lubricant had excellent anti-wear performance at the break-in stage of practical compressors for HFC134a compared with the ester type lubricant.

4. Conc I us i on

The summary and conclusions obtained from these test results are as follows: (1) The newly developed in situ wear sensor has a good performance for practical use. (2) The in situ wear behavior of refrigeration oils at the break-in stage of practical compressors for HFC134a can be precisely traced by using a flat ring on flat ring friction apparatus equipped with the sensor.

(3) The PAG type lubricant is considered to have excellent anti-wear performance compared with the ester type lubricant at the break-in stage of practical compressors for HFC134a.

Reference

1. Montreal Protocol on Substances that Deplete the Ozone Layer. 1987 2. Helsinki Declaration on the Protection of Ozone Layer. 1989 3.Copenhagen Agreements and Amendments to a Phase-out of Ozone Depleting ubstances. 1992 4. Subcommittee on Wear, Lubrication Fundamentals Committee, ASLE (eds.) . Friction and Wear Devices. 1976. 223 5.H.A.Hanna and F. Shehata. J. of Lub. Eng. Vo1.49. No.6. 1993. 473

This Page Intentionally Left Blank

SESSION IV MICROSCOPIC ASPECTS Chairman:

Dr I L Singer

Paper IV (i)

A Molecularly Based Model of Sliding Friction

Paper IV (ii)

Friction and Dielectric Materials : How is Energy Dissipated?

Paper IV (iii)

Friction Energy Dissipation in Organic Films

-

This Page Intentionally Left Blank

Dissipative Processes in Tribology / D. Dowson el al. (Editors) 0 1994 Elsevier Science B.V. AU rights reserved.

173

A molecularly-basedmodel of sliding friction J. L. Streator

G. W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332-0405 Kinetic friction is well known to be a dissipative process. The key to understanding friction, then, is to discover the mechanisms by which mechanical energy is dissipated when one body slides upon another. Some recent reports in the literature have discussed the source of dissipation in the context of several models of atomic interaction, including the Frenkel-Kontorova(FK) and the Independent Oscillator (10) model. In the current work, aspects of the FK and I 0 models are incorporated to model the interaction between a solid asperity and an adsorbed interfacial film. As predicted by the I 0 and FK models, calculations indicate that the existence of an appreciable dissipative component of friction depends on the occurrence of an instability in the configurations of the molecules. It is also found that this dissipative component is influenced by whether or not there exist mechanisms for energy to continually propagate away from the interface. When such avenues exist, the friction force is found to be significantly greater than under conditions where the energy can return to the interface. To provide additional insight into the mechanism of dissipation, an analogy is made between the discrete, molecular model and that of a string on an elastic foundation. The conditions governing the propagation of waves with the continuous model suggest that significant dissipation requires a frictional instability. 1. INTRODUCTION Kinetic friction has long been recognized as a dissipative process, but the mechanism by which mechanical energy is lost remains a point of investigation [l]. It is known that the kinetic friction between two bodies results from interactions that occur on the atomic level. It follows, therefore, that the elucidation of frictional dissipation should result from consideration of atomic and/or molecular interactions. Probably the first atomic account of kinetic friction was due to Tomlinson [2]. Tomlinson proposed that when an atom of one body moves tangentially past an atom of another body, the lateral component of force may be different between approach and separation. The non-symmetry in this lateral force arises because, at a certain point, the atoms attain a position of unstable equilibrium. This condition leads to the sudden motion of the atoms toward the nearest stable equilibrium configuration. Tomlinson assumes that this "jump" phenomenon irreversibly transforms all of the stored energy into molecular kinetic energy or heat, thereby accounting for

mechanical losses. Thus the mechanism involves the nonadiabatic motion of atoms. Tomlinson's mechanism appears in the context of the Independent Oscillator (10) model [3, 41, shown schematically in Fig. l(a). Here the atoms of one surface are modeled by masses which are independent of one another but are harmonically coupled to a rigid base. The influence of the opposing surface is modeled by a sinusoidally varying force which translates quasistatically in a direction parallel to the interface. Although drawn vertically, both the interaction force and springs act tangential to the interface. Above a certain magnitude of interaction force the model atoms are displaced by the force in the direction of sliding until they reach a point of unstable equilibrium. Further translation of the upper surface causes the atoms to suddenly spring back. Assuming that this release of energy is irreversible, the instability in the I 0 model accounts for the Occurrence of friction. If, however, the interaction force is low, it can be shown that the molecules remain in positions of stable equilibrium throughout the sliding process. In this case the average tangential force vanishes so

174

L

k

/// Figure 1 : Previous models of dissipation. (a) Independent Oscillator (10) model. (b) Frenkel-Kontorova (FK) model. that the dissipcltive component of friction force is zero [3.4]. Similar effects can be seen in the FrenkelKontorova (FK) [S] model, shown schematically in figure I@). In this model, the atoms are modeled In the by a set of harmonically coupled masses. classical treatment, the system is analyzed for static configurations which lead to instability in the positions of the model atoms. It has been shown that this instability occurs at a critical value of the interaction force between the two surfaces. In the quasi-static analysis, the occurrence of this instability has heen identified as the source of friction. Since the masses of the surface are mutually coupled, the system behavior is influenced by their average spacing as compared to the wavelength of the translating force [ 6 ] , which is taken to be the lattice spacing of the upper surface. It has been found that when the ratio a/b is irrational, yielding incommensurate lattices, the friction force is considerably less than when a/b is a rational number [3.4].

In both the (quasistatic) FK and I 0 models. the Occurrence of friction depends on the existence of unstable equilibrium positions during the translation of one body over another which leads to sudden displacement or "plucking" of the atoms. In contrast. Hirano and Shinjo (1990) [7] performed calculations based on the Morse potentials for selected metals and found that, for these materials, such an instability should not occur. In a separate investigation [8] the authors analyzed a one-dimensional FK model with kinetic energy terms and found that friction could arise under dynamic conditions in cases where the quasistatic analysis would predict no instabilities of the atoms. The authors associated the Occurrence of friction with the transformation of macroscopic kinetic energy into internal motions of the body. Sokoloff (1992) [9] studied the interaction of a translating sinusoidal force with a layered crystalline lattice, modeled by a collection of springs and masses. In this investigation, the author emphasized the importance of internal damping on the generation of friction force for any finite-sized crystal. The Same author also compared frictional forces between commensurate and incommensurate sliding and found the former values to be 12 orders of magnitude greater than the latter [ 101. In the present work. we investigate a simple model of surface interaction which incorporates aspects of the both the 10 and FK models. I n contrast to previous studies, however, we consider directly the role that energy propagation plays i n influencing the kinetic friction. The motivation for this investigation comes from the observation that. when two macroscopic bodies slide. there is an appreciable amount of energy which propagates away from the interface in the form of acoustic waves. The question arises how this mechanism of energy loss affects the magnitude of friction. 2. MOLECULAR MODEL The physical system to be modeled is schematically shown in Fig. 2a. The upper surface is a hard asperity which slides against an adsorbed film of an opposing surface. The mathematical model is shown in Fig. 2b. Since the molecules of the film are anchored to the surface, the masses of

175

vo 0

(a)

*

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

into the contacting bodies, supporting structures. etc.

0

2.1 Governing Equation

With reference to Fig. 2b. the equation of motion for each of the masses of the model is written

with

Q(x, ,I ) = [H (X, - x, - V,I)- H ( X, - (X, + L ) - V,I )] x

Figure 2: Model of interface. (a) Asperity sliding on adsorbed film. (b) Mathematical model. the model (Fig. 2b) are connected to springs which resist absolute displacement relative to the base. The set of molecules are also assumed to prefer a certain equilibrium spacing which is modeled by the coupling between the masses. Since the upper surface is assumed to be that of a hard solid, it is modeled by a rigid sinusoidal force. All of the couplings are harmonic in nature. Following Shinjo and Hirano (1993) in their application of the FK model [8], we integrate the dynamical equations of motion for each of the masses. To directly investigate the role of energy propagation. the extent of the adsorbed film is taken either to be ( I ) just large enough to cover the contact length over the sliding distance, or (2) effectively unlimited in each direction. In practice, this latter condition means that the surface extent is sufficiently large that, over the duration of the sliding. elastic waves propagate outward and do not return. Physically, this feature is used to model what happens when real 3D bodies experience sliding Contact. In this case, acoustic waves generated at the Contacting interfaces propagate away from the interface region

where m is the mass, k and ke are the spring constants (Fig. 2b), ui is the displacement of the ith mass from its unforced static equilibrium position, xi is the absolute position of the ith mass, Q(xi.1) is the interaction force on the ith mass. Qo is the force amplitude, V, is the sliding velocity, xo is the initial position of the left end of the contact region. L is the length of the contact, a is the wavelength of the periodic force. The function Hc.>is the unit step function. From consideration of the arguments of the step function. it is seen that the interaction force translates from left to right with speed Vo. We can nondimensionalize the governing equation by selecting appropriate length. time and force scales. The parameter b, which gives the equilibrium spacing between the molecules when there is no interaction force (Fig. 2a) is chosen as the length scale, b/Vo is chosen as the time scale, and kb is chosen as the force scale. We also make the following definitions ,41

=by,

t=--'S b

v,

co = b

g

The parameter co has the dimensions of velocity and is nominally the velocity of sound for the medium [ 111. Using the above definitions we have

176

=i'

2.2 Simulation Procedure Equation (2) governs the motion of the ith particle. To study the frictional force we integrate equation (2) for all of the particles in the system using the classical 4th-order Runge-Kutta method [12]. The integration is begun from a position of static equilibrium, which itself is determined by iterative relaxation from an assumed configuration. Starting from this initial static equilibrium position, we sum the interaction force. Q. over all of the particles at each time step. This summation provides the friction force exerted by the translating force field upon the lower surface. The time step was selected to be 0.02 b/co As a check on computational accuracy. we compared the power input to the stored energy of the system. The rate of work performed on each particle is calculated by forming the product of the interaction force on the particle and the particle velocity. After summing over all of the particles in the system at each time step. the power was Integrated in time using Simpson's Rule to provide the total work done by the interaction force at a given instant. The total energy of the system was calculated by summing the kinetic energies of all of the system particles along with the potential energies stored in each of the springs. It was found that there was good agreement between the calculated work done and the energy stored in the system. At the end of the simulation. the relative difference in the two quantities was consistently found to be less than 0.1% .

3.0 RESULTS AND DISCUSSION The governing equation (2) was integrated for a number of parameter combinations. The following values are applicable to all of the calculations to be discussed: a/b = 1, Vdco= 0.02, k& = 0.8. The ratio a/b defines whether or not the interface is commensurate, and the ratio Vdco is the ratio of sliding speed to the nominal acoustic wave speed. With the value of this ratio set to

d

W

OS3

v3

y

d b rn I J

l1 -

-I

Qo/kb=0.05 L h - 5 Qo/kb = 0.1 Qo/kb=0.2

0.2 0.1

d

z 0 F

0.0

u

U

-0.1

-0.2 0

1

2

TIME (Vot/b)

3

Figure 3: Frictional stress vs. time for three force amplitudes. 0.02, the sliding process is slow compared with the speed of relaxation in the interface. 3.1 Effect of Interaction Force Figure 3 shows the (dimensionless) frictional stress vs. (dimensionless) time for three values of the interaction force amplitude and for a (dimensionless) contact length of L/b = 5 . The extent of the model surface film was taken to be unlimited in each direction. The frictional stress is defined to be the friction force, F, per dimensionless contact length L/b, normalized by kb. Thus frictional stress has the form F/kL. Since there is one particle per b spacing. the frictional stress gives a measure of the force per particle in the conlact region. Similarly, one unit of dimensionless time corresponds to the force field translating the equilibrium distance. b, between the molecules. As observed in Fig. 3. For Q&b = 0.05, the frictional stress is nearly sinusoidal being slightly distorted due to some displacement of the masses in the direction of sliding. Moreover, the

177

n

d

w

-

Qo/kb=0.05 ~ b - 5 - Qo/kb=O.l 0.03 - - Q$b ~ 0 . 2

*

W

u g 0.02 zw

u

p

I

-

0.01 -

2

2

0.00

I

I

Figure 4: Kinetic energy within contact for three force amplitudes. amplitude of the frictional stress (0.05) is equal to the amplitude of the normalized interaction force. Since the force profile is nearly symmetrical with respect to the origin, the average frictional stress over the sliding distance is quite small (.OOOOl). When the normalized force amplitude, Q&b, is doubled to 0.1, the friction trace shows a much greater deviation from sinusoidal behavior. Once the frictional stress reaches its peak, there is a faster drop to the minimum value after which some high-frequency oscillations are observed. The average frictional stress remains small but increases to 0.001. When the interaction force is increased to 0.2 kb. there is a sudden drop in the friction force followed by substantial oscillations in the force. In addition, the average frictional stress increases to 0.03. The degree of excitation in the interface can be measured by the amount of kinetic energy generated. Fig. 4 shows the amount of kinetic energy generated in the contact as a function of time. The energy is normalized by kb2 and the dimensionless sliding length L/b. For the case of

Q@b = 0.2, substantial kinetic energy is produced after each drop in the force (see Fig. 3). When the interaction force is reduced to 0.1 kb, the amount of kinetic energy generated is more than order of magnitude less. When Q$b = 0.05. the amount of kinetic energy produced is negligible, as indicated by the horizontal line at the origin. The differences in kinetic energy observed in Fig. 4 compared with the frictional profiles of Fig. 3, indicate the role of frictional instabilities in exciting the interface.

3.2 Effect of Surface Extent Figure 5a shows the frictional stress vs. time for the case of Q&b = 0.5 and L/b = 0.5. Here the surface is unlimited in extent (in each direction). In other words, a sufficient number of surface particles is selected to insure that. during the duration of the simulation, no waves originating from the interface can return to the interface upon reflection from the surface boundaries. As observed in the figure. the friction force demonstrates the plucking instability identified in Fig. 3. Again there is a sudden drop in the friction force followed by substantial oscillations. Fig. 5b shows the (normalized) energy delivered to the surroundings-that is the amount of energy, potential plus kinetic. possessed by the particles ourside of the contact region. The energy is normalized in such a manner that the graph provides the amount of energy lost per particle in the contact region. The figure shows that the energy in the surroundings accumulates with time. As the contact region translates to the right (see Fig. 2b), the particle at the left edge of the contact eventually leaves the contact region while, at the same time, a particle enters the contact from the right. If the particle leaving the contact has been excited by plucking. then its departure will generally result in a greater loss of energy from the contact than is gained from the particle which enters. The key observation here is that once the energy is lost from the contact, it does not return: the energy accumulated outside of the contact increases almost monotonically in time. This steady increase in the energy of the surroundings indicates that energy is continually propagated away from the interface. We compare the foregoing results to those of Fig. 6. In Fig. 6a, frictional stress is computed for

178

the same conditions as those in Fig. Sa. except thal thc surface extent is limited to 10 particles. This number of particles is just enough to cover the contact region for the duration of the simulation (4 units of time). As observed in the figure. the friction reaches an initial peak as in Fig. 5a, but the "stick-slip'' cycle is not repeated to the same degree. Instead. following the initial slip. the force essentially oscillates between positive and negative values. with an average near zero. In fact if we compare the average friction forces in Fig. Sa and Fig. 6a, after time = 1 (i.e.. after the initial stickslip). we find a substantial difference: Fig. 5a corresponds to an average frictional stress of 0.194. while Fig. 6a gives a negative value of -0.03 Clearly, then. the surface extent has a profound effect on the friction force. Consideration of the energy explains the foregoing friction behavior. Figure 6b shows the energy accumulated in the surroundings for the sliding conditions of Fig. 63. In this figure it is observed that the energy of the surroundings initially rises but afterwards does not appreciably increase. This result contrasts that of Fig. Sb i n which the energy lost to the surroundings steadily increases with time. When the surface is unlimited in extent. the energy is continually lost by propagation to the particles surrounding the contact, thus providing a source of dissipation. On the other hand. when the extent of the system is limited. energy does not continually flow out of the contact and dissipative effects are small. 3.3 Effect of Contact Length The role of energy propagation can also be seen when the contact length is varied. Figure 7a shows the amount of energy, per particle in thc contact region. that goes to the surroundings for several values of the contact length: L/b = 5. 10.20, and 40. The surface is of infinire extent. As the contact length increases. the amount of energy lost (per particle in the contact region) decreases, indicating that there is proportionately more energy delivered to the surroundings when the contact length is small than when it is large. This result is expected since, for a shorter contact, a greater percentage of the particles are at the boundary of the contact region. The longer contact length also affects the nature of the friction force. as observed in Fig. 7b.

-0.5 0

3

1

4

TIME~V 0t/b) Figure 5a: Frictional stress vs. time for Q J k b = 0.5 and L/b = 5. n

stf!

0.6

0.5

Pi

d

3

0.4

rn 0

b

cl

0.3

0.2

$(

u

g 0.1 z W

I

0

1

I

I

I

4

T I M E ~ 0Vt/b; Figure 5b: Energy to surroundings for QJkb = 0.5 and L/b = 5 .

179

This figure provides the friction trace for the same interaction force amplitude as i n Fig. Sa. but with a dimensionless contact length. L/b = 40 instead of L/h = 5 . Initially the friction peaks. as in Fig. Sa. but after the sudden drop, the friction force remains low. Since there is a greater proportion of energy which remains in the contact, the amount of dissipation is less and the average friction is small. Figure 8 shows the time average frictional stress as a function of contact length for several amplitudes of the interaction force. The average is taken over the duration of the sliding which is 3 units of time. In each case the frictional stress is observed to decrease with increasing contact length. The consistency of the trend provides further support for the previous conclusion--namely that the magnitude of the average frictional stress is influenced by the tendency for energy to propagate away from the contact. With a smaller contact region, the energy is more readily lost to the surroundings and the average frictional stress is greater.

3.4 Continuous Approximation Inspection of the governing equation (2) reveals that an analogy can be made between the model of Fig. 2b and that of a string on an elastic foundation. In this regard, we introduce u(x.1) as the transverse string displacement and make the following associations:

0.7

3b Y

R

0.3

b m A

0.1

< z 0 i?

-O.l

W

2

-0.3 -0.5

I

I

I

I

0

1

2

3

TIME(V0t/b)

Figure 6a: Frictional stress vs. time for finite surface extent.

0.5

d

at-

m

3

0.4 L

0

b 0.3 b

-

-

0.2

-

-

8 A

We also let

surface extent: 10 particles

0.5

m

a4

ii, e 7

2 Q#b=0.5 L/b=5

Using the above definitions, equation (2) becomes

a h c, ?+ a% pu = (I

--

at?

as-

0.0

0

(3)

1

3

4

TIME t V 0 t/b) Figure 6b: Energy to surroundings for finite surface extent.

I80

Equation (3) is recognized as the governing equation for a string on an elastic foundation. There are two characteristic homogenous solutions to this equation, given by [ 131:

I

sw

d

I

1

0.4

d

3

cn

0.3

0 where w is the frequency of vibration, y is the wavenumber. and 7 is magnitude of the wavenumber when the wavenumber is imaginary. Equation (4a) represents a propagating solution and applies when w2 > p. Conversely. equation (4b) represents a non-propagating solution and the applies when w2 5 p. Recalling that 0 = conditions on w indicate that energy will propagate away from the contact region when frequencies are excited that exceed some critical value characteristic of the system. This result indicates that continuous energy loss to the surroundings requires some excitation at the interface. We expect therefore that a plucking instability should be associated with the Occurrence of dissipation and should increase the friction force. We observed this effect in Fig. 3. When Q&b = 0.05 and there is no plucking. the average frictional stress is very low (.ooOOl). On the other hand. with Q&b = 0.2 there was a clear instability and the average frictional stress was markedly higher (.03). Thus a fourfold increase in the interaction force increased the average frictional stress by more than three orders of magnitude.

urn.

3.5 Relation to Other Mechanisms It was shown in previous sections that the magnitude of the dissipative component of friction is influenced by the efficiency with which energy is propagated away from the contacting interface. We now discuss this result in light of other mechanisms of dissipation identified in similar studies. Sokoloff (1992) [HI finds that internal damping within a (finite) crystal lattice is critical for the Occurrence of frictional losses at the interface. In fact, for a purely elastic model. the dissipative component of friction is found to be virtually zero. When damping is present, the elastic waves which emanate from the contact return to the interface

EE-

rn 0 cl

0.2

*u

d 0.1

W

zW 0.0 0

T~ME(V 0t i )

3

Figure 7a: Energy to surroundings for variable contact length.

m

cn

0.3

cn

<

0.1

z F1 -O.l

0

u

U

-0.3

v t

0

1

TIME (V0t i )

3

Figure 7b: Frictional stress vs. time for QJkb = 0.5 and L/b = 40.

181

diminished in energy. In effect some of energy has propagated away from the interface and has not returned. Damping, therefore, can be viewed as a means of facilitating energy propagation away from the contact. Shinjo and Hirano (1993) [9]. studied the FK model with kinetic energy terms. In their work, a set of masses was given an initial velocity and then allowed to move under the influence of a harmonic potential fixed in space. For certain combinations of interaction force and initial velocity. a friction force arose which caused the velocity of the center of mass to decrease to zero. Since the system in question conserved energy with all of the particles comprising the interface, their results demonstrate that dissipation can exist even when no energy is propagated away from the interface. This mechanism, therefore, appears to contradict our observation that energy propagation is primarily responsible for the dissipative component of friction. We may resolve this apparent discrepancy by comparing the macroscopic work done to the net work done. In the study of Shinjo and Hirano. the total energy of the system is conserved. Since any net work done on the system must change the energy of the system, the net rate of work done on the system by the interaction force is identically zero for all time. On the other hand, there is a finite friction force which opposes the translation of the center of mass. This friction force does macroscopic work at a rate equal to -FV,where F is the friction force and V is the velocity of the center of mass. Again, since the net rate of work remains zero, the loss in macroscopic translation energy is exactly balanced by the increase in the internal kinetic and potential energies [9]. Analogous effects are found in our calculations which correspond to the case of a force translating over a stationary surface (Fig. 2). Fig. 9a shows both the macroscopic work and net work done by the interaction force for the operating conditions of Fig. 5a. Each of the work terms is normalized in the usual manner. The macroscopic work done is just the time integration of the product of the friction force and velocity. and defines the degree of dissipation. The net work done is the time integration of the rate of work done on each particle of the system by the interaction force. This

3 0.3 W

m m W

p?

b

r A 0.2 Cll

6 z 0

F: 0.1 u

Ed >

,

6 0.0 0

I

10

1

,

20

I

30

I

I

40

CONTACT LENGTH (L/b) Figure 8: Average frictional stress vs. contact length for several force amplitudes. difference between the two forms of work, therefore, reveals the component of friction which is not associated with energy changes in the system. Hence, there are two components of dissipation: one component of dissipation depends on the flow of energy away from the contact to the rest of the system, while the other occurs even when no net energy is lost. Our concern here is upon which of these mechanisms is predominant. In Fig. 9a. it is seen that the bulk of the frictional loss (i.e.. the macroscopic work) is associated with the increase in the energy of the system (i.e., the net work). The same result is observed in Fig. 9b, where the extent of the surface is limited to 10 particles. Hence, while frictional losses do not necessitate the flow of energy from the contact region, they are greatly enhanced by it. 4.0 CONCLUSIONS A simple model of frictional contact was presented which focuses on the energetics of sliding at the molecular scale. The model. which

182

macroscopic work

0.9

2 0.8

-

9

0.7

-

0.6

-

z0 0.5

-

w

W

n 0.4 d 0

*

contains aspects of the I 0 and FK models. was used simulate the frictional interactions belween a rigid asperity and an adsorbed film. The rigid asperity was modeled as a translating sinusoidal potential. while the adsorbed film was modeled by a set of harmonically coupled masses which were attached by springs to a rigid base. The frictional behavior of the system was determined by numerical integration of the equations of motion for each of the model molecules. Three key observations werc made:

-

0.3

-

0.2

I I

0

I

I

I

1

4

3

1

T I M E ~ 0Vt/b)

Figure 9a: Macroscopic work vs. total work done on system. 0.5

~

~- 1

- 1

1

1

e W

W

These three observations can hc attributed to the same mechanism: energy propagation away from the region of conhct. First, an instability in the motions of the molecules is needed to excire the molecules in the interface. Second. for significant dissipation to occur, an avenue is required through which energy can be lost from the contact. Third. when the contact length is large, there is less availability for energy to propagate away from the interface, yielding lower frictional stress. Although the results presented here correspond to a limited number of cases investigated by simple model, they provide evidence that frictional losses depend, to a great extent. on the way in which energy propagates away from the contact.

Q0/kb = 0.5 L/b=5

9 -

0.3

z n 0.2

surface extent: 10 particles

0

d 0

*

0.1

0 .o 0

I

I

1

2

1

TIME(V 0t/b)

The average frictional stress was found to hc much higher when the surface was unlimited in extent than when it was finite. The average frictional stress decreased as thc lengrh of contact increased.

- net work - - macroscopic work

2 0.4

An appreciable dissipative component of friction was found to occur only when the interaction force was of sufficient magnitude. This effect corresponded with the onset of an instability in the positions of the model particles.

1

3

Figure 9b: Work comparison for surface of finite extent.

4

ACKNOWLEDGMENT The author would like to thank the Narional Science Foundation for support of his work.

183

REFERENCES 1. Tabor, D., in Fundamentals of Friction: Macroscopic and Microscopic Processes, I. L. Singer and H. M. Pollock, eds., NATO AS1 Series, vol. 220, Kluwer Academic Publishers, The Netherlands, p. 3 (1992).

2. Tomlinson, G. A., Phil. Mag., vol. 7, n. 46, p 905 (1929). 3. McClelland, G. M., in Adhesion and Friction, M. Grunze and H. J. Kreuzer, eds., Springer Series in Surface Science, vol. 17, Springer Verlag, p. 1 (1989). 4. McClelland, G. M., and Glosli, I. N., in Fundamentals of Friction: Macroscopic and Microscopic Processes, I. L. Singer and H. M. Pollock, eds., NATO AS1 Series, vol. 220, Kluwer Academic Publishers, p. 405 (1992). 5. Frenkel Y. and Kontorova T. ,Zh. Eksp. Teor. Fiz., vol. 8, p. 1340 (1938).

6. Peyrard M., and Aubrey, S., J. Phys. C: Solid State Phys., vol. 16, p. 1593 (1983).

7. Hirano, M. and Shinjo, K., Phys. Rev. B. , vol. 41, n. 17, p. 11837 (1990). 8. Shinjo, K., and Hirano, M., Surface Science, vol. 283, p. 473 (1993). 9. Sokoloff, J. B., J. Appl. Phys., vol. 72, n. 4, p. 1262 (1992). 10. Sokoloff, J. B., Phys. Rev. B., vol. 42, p. 760 (1990). 11. Tabor, D., Gases, Liquids, and Solids, 3rd edition, Cambridge University Press, p. 181 (1990). 12. Gear, W. C., Numerical Initial Value Problems in Ordinary Differential Equations, PrenticeHall, New Jersey, p. 47 (1971). 13. Graff, K. F, Wave Motion in Elastic Solids, Ohio State University Press, p. 51 (1975).

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Dissipative Processes in Tribology / D. Dowson et al. (Editors) 0 1994 Elsevicr Sciencc U.V. AU rights reserved.

185

FRICTION OF DIELECTRIC MATERIALS: DISSIPATED ?

HOW IS ENERGY

B. Vallayera, J. Bigarrea, A. Berrouga, S. Fayeullea, D. Treheuxa, C. Le Gressusb, G. Blaisec Laboratoire Matiriaux-Mtcanique Physique URA CNRS 447 Ecole Centrale de Lyon, 69131 Ecully FRANCE

a

CEA-DAM, Centre d'Etudes d e Bruykres-le-Chatel BPI 2 91 680 Bruykres-le-Chatel FRANCE

b

Laboratoire de Physique du Solide Universitt Paris Sud 91405 Orsay FRANCE Abstract

Storage and dissipation of energy in a dielectric material are discussed using the results of the space charge physics. In this model, polarization of the medium is related to trapping of electrical charges in the lattice. This allows the storage of high amount of energy (5eV or more per charge) which, when dissipated, can lead to transfer to the phonon bath, creation of defects, exoemission or even fracture. During friction of dielectrical materials, electrical charges and sites of trapping are created. Therefore, the space charge physics can be applied to explain some aspects of t h e tribological behavior of materials such as ceramics or polymeres. Examples are given using experimental results obtained with sapphire.

1. INTRODUCTION It has been guessed for a long time that electrical and mechanical properties of die lect rical m ate rials are close 1 y related. Experimental evidences have been provided

to correlate electrical breakdown and fracture of insulators. The role of electrical Phenomena has also been underlined during friction of ceramic or polymer mate rials: t riboe lectrification and electrical component of the adhesion force

186

have been partly recognized. From a macroscopic point of view, the theory of elasticity in which forces acting at a point are determined by local deformation, is generally not applicable in dielectrical crystals as soon as it is necessary to take into account the polarization of the medium (i.e. the electrical fields acting on particles) in determining the equilibrium of a point. Therefore, a microscopic approach can provide useful guidelines to understand some mechanical behavior. In order to understand the mechanisms of energy dissipation in dielectrics, we propose to apply the new concepts of the space charge physics (1,2). The mechanisms of storage and of dissipation of energy are related to electrostatic interactions: polarization of the material and displacements of electrical charges. Polarization is quickly achieved and increased during friction because of the built-up of a space charge in the material owing to trapping of charge carriers. This trapping on defects already present in the material before testing or created during friction allows the storage of very high amount of energy (5 eV or more per charge) which, when dissipated, can lead to catastrophic failure. Experimental results obtained on single crystal alumina slid against itself in dry conditions are used to illustrate the discussion of t h e d i e l e c t r i c a l mechanisms. X-ray irradiation is used to modify the dielectrical properties of the superficial layers. Results are discussed in view of the space charge physics model. 2. STORAGE AND DISSIPATION OF ENERGY IN A DIELECTRIC MATERIAL: SPACE CHARGE P H YS I C S

A major characteristic of a dielectric material is that electrical charges can be trapped in some sites of the lattice, leading to the appearance of local intense electrical fields. Therefore, polarization of the medium can be induced locally around these charges. Its value can be calculated owing to microscopic determination of the local electrical fields (1,2). Generally, trapping of charges is achieved in a crystal as soon as the polarisability (from a microcoscopic point of view) or the permittivity (from a continuum point of view) of the medium is modified. This variation can result from the presence of defects (vacancies, interstitials, chemical impurities, dislocations, grains -boundaries...) (1). The possibility of self trapping of electrons by their own potential (polarons) has also to be considered (3-4). The potential energy of these traps has been estimated to range from a few meV to some eV. The total energy of polarization stored around a trapped charge is much greater and can reach 5 eV or more (2). This energy i s mainly stored as mechanical energy in the lattice all around the trapped charges (displacement of the ions from their equilibrium site). Since storage of energy is linked with trapping of charges, detrapping leads to dissipation. Relaxation of t h e mechanical energy associated with trapped charges occurs through a two step process. First, charges are detrapped. This does not release a lot of the stored energy. This detrapping can be obtained for example if a critical number of trapped charges (i.e. a critical value of the local electrical field) is reached. Then, the lattice around the location of t h e charges g e t s depolarized, i.e. comes back to its equilibrium configuration. The

187

relaxation process has been theoretically described owing to a many-body universal model involving the whole dielectric material (5-7) and implies a transfer of the polarization energy to the phonon bath. Dissipation of the mechanical energy corresponding to this transition can lead to breakdown of the material through flashover with treeing, thermal shock waves or exoemission. 3. APPLICATION OF THE SPACE CHARGE PHYSIC TO FRICTION AND WEAR PROCESSES

In order to apply the space charge physics to study the tribological behaviour of dielectric materials (ceramics, polymeres ...), it is necessary to show that electrical charges and sites of trapping do exist during friction experiments. 3.1 Electrical charges On figure 1 is shown the contact area after friction of a diamond tip against a quartz sample. The micrograph has been obtained in a SEM with low voltage. Electrical charges are clearly detected, leading to a potential of several hundreds of volts (8). This kind of phenomena, i.e. the charging of originally uncharged materials when brought into contact has been recognized for a long time and called triboelectrification. It has been assumed to be due to charge transfer by tunneling from delocalized states in the metal or from extrinsic states in the forbidden gap of the dielectric to extrinsic states of the counterface dielectric (9). This has been widely studied for various materials (1 0-14). During tests performed with polymers in contact with metals, surface charge density of some 10-7 C.cm-2 has been

measured (1 0,ll).Electron transfer has also been observed during contact between ceramics (mica-silica ): charge density of 10-6 C.cm-2 has been detected (1 5). When contact and friction are achieved in a polar environment, electrification can result from the formation of an electrical double layer in the interface (1 6,17).This has been observed even when the interfacial polar film is very thin, e.g. adsorbed water layers on surfaces (18). When surfaces in contact are separated, electrical charge of about 10-7C.cm-2 has been measured on various polymeric materials (1 9,20). When sliding occurs, further electrification can result from the exoemission of charged particles. Emission of electrons and ions (positively and negatively charged) has been detected in addition to t ri bo lu mi nescence (emission of photons). This phenomenon is much more intense on ceramics than on metals (21-23). It depends on the type of ceramics, atmosphere, temperature, speed and illumination (24).

3.2 Sites of trapping In order to characterize the polarization properties of a material and to determine if trapping sites exist in the lattice, an experimental method is needed. Such a method, called the mirror method, has been recently developped in which the possibility to create trapped electrical charges in a given sample was measured experimentally owing to a Scanning Electron Microscope. In this method which has been fully explained previously (25,26), samples were bombarded using the electron beam of the microscope at high voltage Vo (usually 30 kV). If defected areas (where polarisability is changed) exist

I88

Figure 1 : Electrical charges observed on a quartz sample after friction with a diamond tip.

Figure 2: The mirror method: image of the chamber of the microscope and of the diaphragm

189

in the superficial layers, the incoming electrons were trapped, leading to the formation of a space charge in the material. This charge was characterized by measuring the distribution of the elect rostatical potential around it. This was achieved by performing further observations of the sample in the SEM with low voltage beam (300-1000 V): in this case, image of the microscope diaphragm was formed because the electron beam of lower voltage was reflected by the potential of the trapped charges (figure 2). The radius R of the observed equipotential was calculated from the diameter D of the diaphragm image and the curve 1/R = f(V) was then plotted. This curve gave information on the charging capacity of the material: the lower the curve, the higher the charging capacity (more precise measurement can be deduced from this kind of curve but this will not be discussed in this paper). Indeed, it has been clearly shown with this kind of experiment that charges are trapped on the intrinsic traps of the material, not on defects created by the electron bombardment. Moreover, in order to remove contamination layers such as adsorbed water that could affect charging capacity, samples were heated in SEM at 200°C before measurement at room temperature. Using this method, it is easy to show that traps exist in most insulators materials as soon as exist grains boundaries, impurities ... In these cases, the role of friction of trapping is more difficult to characterize. More interesting is to study material without such sites of trapping. For example, highly pure sapphire (single crystal alumina) samples are free of such sites and no charging effect is detected at room temmperature in the mirror method before friction. But after a short friction

test (five cycles in very low load conditions), charging is observed in and out of the contact area (figure 3) revealing that sites of trapping now exist everywhere in the sample, that is that storage and relaxation of polarization energy has already been achieved in the bulk material, not only in the surface films. 4. DISSIPATION ENERGY IN MATERIALS

OF FRICTION DIELECTRIC

Since electrical charges and traps are associated with friction and wear processes, the results of the space charge physics can be applied to understand the mechanisms of dissipation of energy. For example, the dielectric constant is proportionnal to the inverse of the trap energy and thus is a major parameter to characterize a material in the space charge physics. Therefore, it should have a major role in friction. One way to modify the dielectric constant of sapphire is to irradiate samples with X rays (ref). Figure 4 shows the variation of the friction coefficient versus time for pure and irradiated sapphire tested in dry conditions (with very low load). The coefficient of friction of irradiated samples is always higher than the one for non irradiated samples. This can be explained by an easier dissipation of energy in the non irradiated samples. Indeed, at room temperature, pure sapphire does not charge in the mirror experiment: electrical charges are not trapped and move easily in the lattice. Parallely, in the friction experiment, the material is easily polarized and depolarized when the strain field is moving through the sample (displacement of the pin on the flat sample fo'r example). Only small

Figure 3: charging effect before friction (curve a) and after a 5cycle friction test in (curve b) and out (curve c) of the friction track

Figure 4 : Friction coefficient of pure (curve a) and X-ray irradiated (curves b) sapphire samples

191

amount of the friction energy is stored as trapped charges and most of it is diss i pated t hrough "soft" mec hanis ms (transfer to the phonon bath, exoe missio n.. .). On the contrary, irradiated samples are more easily charged in the mirror experiment: traps are deeper. During friction, the energy is no more dissipated but is stored as trapped charges in the material: polarization and depolarization are much more difficult and electrostatic forces due to electrical charges are increased: the friction coefficient is higher. In both cases, the steady state period during which the friction coefficient is constant corresponds to an equilibrium between storage and dissipation. During all this stage, defects are created in the samples because of dissipation and the material is progressively weakened. Finaly, when a critical threshold is reached, macroscopic wear is observed. This means that dissipation occurs now through more violent phenomena such as cracking. The exact nature of the threshold is not yet well known but is probably related to a critical amount of trapped charges in the lattice (i.e. a critical amount of energy stored in the material) or to a critical level of degradation of the lattice (i.e. a critical state of the weakened material). It leads to detrapping of a lot of charges, that is to a very high amount of energy (5 eV per charge) in the material: failure of the sample is observed. 5. CONCLUSION

Results of the space charge physics have been used to provide new insights in the friction and wear behavior of insulators. The main results can be summarized as follows:

- Storage of energy in dielectrics is related to the trapping of electrical charges on some sites of the lattice. Relaxation occurs when the charges are detrapped. The amount of energy can reach 5eV or more per charge and its relaxation can be soft (phonon, defects...) or hard (fracture, breakdown, ...) - During a friction test, defects are created everywhere in the samples, i.e. inside and outside the wear tracks. Formation of these defects is explained by the relaxation of polarization energy which is a many body phenomenon. These defects can be detected owing to the mirror method. - X-ray beam irradiation of sapphire samples increased both charging capacity and friction coefficent. This has been related to the fact that energy of traps after irradiation is higher. Charges are thus less mobile and dissipation of energy is more difficult. - Wear (i.e. detachment of particles) is interpreted as the result of the relaxation of high amount of polarization energy stored in the lattice during friction. It depends on the energy and number of traps.

REFERENCES 1. G. Blaise, in Dielectrics, Properties , characterization and Applications (Societe FranGaise du Vide, Paris, 1992) 1 2. G. Blaise, in Dielectrics, Properties, characterization and Applications (Societe FranGaise du Vide, Paris, 1992) 417 3. C. Kittel, Introduction to Solid State Physics (John Wiley, New York, 1976) 4. I.G. Austin and N.F. Mott, Adv.

192

Phys. 18 (1969)42 5. L.A. Dissado and R.M. Hill, Nature 279 (1979) 685 6. L.A. Dissado and R.M. Hill, Phil. Mag. 841 (1980) 625 7. A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics Press, London, 1983 8. A. Berroug, these de doctorat, Ecole Centrale de Lyon, 1993 9. T.J. Lewis, IEEE Trans, El. 19 (1984) 210 10. D.K. Davis, in Static Electrification, Institute of Physics, London, 1967 11. D.K. Davis, in 1972 Annual Report Conf. Electr. Insul. and Diel. Phenom. (NAS, Washington, 1973) 12. J.J. Ritsko, in Electronic Properties of Polymers Eds J. Mort, G. Pfister (Wiley, New york, 1982) 13 13. K. Ohara, J. Electrostatics 15 ( 1 984)249 14. W.R. Harper, Contact and Frictional Electrification , Oxford University Press, London, 1967 15. R.G. Horn and D.T. Smith , Proc. Int. Conf. on Electronic Structure, of Bonding a n d Properties Ceramics, Florida, Oct. 1991 16. B.V. Derjaguin, N.V. Churaev and V.M. Muller, Surface Forces, Plenum Press, New york, 1987 17. B.V. Derjaguin, V.M. Muller, N.S. Mikovich and Yu. P. Toporov, J. Colloids Interface Sci. 118, 2 (1987) 553 18. B.V. Derjaguin and N.V. Churaev, Colloids and Surfaces 41 (1989) 223

19. B.V. Derjaguin, Yu. P. Toporov and I.N. Akinikova, J. Colloids Interface Sci. 54 (1976)59 20. B.V. Derjaguin, V.M. Muller, Yu. P. Toporov and I.N. Akinikova, Powder Technol. 37 (1984) 87 21. A.J. Walton, Adv. Phys. 26 (1977) 887 22. Y. Enornoto, Proc. Eurotrib 85 (Elsevier, 1985) paper 5.1.11 23. K. Nakayama, H. Hashimoto, Wear, 147 (1991) 335 24. S. Sasaki, Proc. 18th Leeds Lyon Symp. Ed. D. Dawson, M. Godet (Elsevier, 1991) 25. C. Le Gressus, in Dielectrics, Properties, characterization and Applications (Societe FranGaise du Vide, Paris, 1992) 149 26. A. Berroug, S. Fayeulle, B. Hamzoui, D. Treheux, C. Le Gressus, IEEE Trans. Elec. Insul. 28, 4 (1993) 528 27. K.H. Oh, C.K. Ong, B.T.G. Tan, C. Le Gressus in Dielectrics, Properties, Characterization and Applications (Societe FranGaise du Vide, Paris, 1992) 320

Dissipative I'rocesscs u1 Tribology / D. Dowson ct al. (Editors) 0 1994 Elsevicr Science U.V. AU ngh& reservcd.

193

Friction Energy Dissipation in Organic Films B.J. Briscoe and P.S. Thomas Department of Chemical Engineeringand Chemical Technology, Imperial College of Science, Technology and Medicine, London, SW7 2BY.

The paper speculates upon the molecular relaxationand dissipation mechanisms which may be responsible for the interfacerheological characteristicsof thin organic films. The molecular structureand interfacerheology of a homologous series of poly(n-alkyl methacrylate)s are characterised for this purpose. These rheological properties are identified by the measurement of the interface shear strength, z as a function of the contact pressure. 'Ihe molecular structure is deduced using vibrational spectroscopy. The Eyring model for molecular plastic flow is then applied and a correlationis drawnbetween the rheological and structural properties which are discussed in terms of possible mechanisms for the dissipation of the frictional energy.

1. Introduction Credible microscopic mechanisms for energy dissipation in friction processes have been sought for at least the past four centuries. Several models have been derived and proposed to explain the mechanisms of frictional motion from the gross surface ratcheting action offeredby Coulomb to the apparently more sophisticated molecular models of the present day [1-91. All of these models essentially describethe relative motion of entities between, or over, physical barriers, but few have truly adchessed the nature of the energy dissipation mechanism itself. A short, but selective, history is shown in Table 1. The present paper concentratesmainly on the discussion of molecular pathways for molecular rearrangement in plastic flow induced by shear deformationin the context of friction processes.The types of mechanisms involved in the dissipation of frictional energy are also discussed. For these purposes, the application of two diverse techniques to the characterisation of thin polymer films ~ I C reported. The rheological macroscopic properties of thin polymer films are characterised by the measurement and rationalisation of the interface shear strength. The intrinsic molecular architectures are characterised directly by using infrared light as the molecular probe to monitor the vibrational spectrum of a variety of thin polymer films using Fourier Transform Infiared (FTIR) spectroscopy. A correlation between the macroscopic and the microscopic responses is then made using a

molecular model which introduces a molecular scale interpretation into the macroscopic contact mechanical parameterswhich are used to describethe friction experiment.

1.1 Rheology The rheological properties of thin poly(n-alkyl methacrylate) films have been characterisedby the measurement of the interface shear strength, 2, which is defmedas the frictional force, F, per unit area, A, of contact. It is synonymous to the magnitude of the energy dissipatedin sliding friction per unit areaof contact per unit sliding distance.z is a strong function of several contact mechanical variables including: the mean contact pressure, P, the temperature, T, and the sliding velocity, V, or the contact time. These functionalities have been observed to have, within experimental error, the following approximate forms [4-6]:

z=zo+aP z = io exp -

(2) (3)

where zo, T ~ ' ,and zO",are material constants, 01 is

194

Table 1. A brief chronology of the advances in the modelling of the friction process.

da Vinci Amontons

1470 1699

Greasy surfaces Low Friction

F=pW

Coulomb

1785

ShipsNood

Leslie

1804

Friction Energy Dissipation: subsurfacedeformation

Hady/Doubleday

1922

Boundary Friction: molecular friction

Deryagin

1934

Adhesion Model: interface (bulk) shear

ratchet friction

P=

P=*

Bridgman

1935

Anvil Technique: bulk shear bands

Bowdeflabor

1950

Asperity Contact Model: molecular shear

Bailey/Courlney-Pratt

1955

Mica Cross Cylinders: methyl friction

Bowers/Zisman Pooleynabor Briscoe/Amuzu Evans SutcliffdCameron

1954 1972 1976 7976 1972

Molecular TopographicalModel Molecular TopographicalModel Eyrins Approach Dislocation Model Methyl Isomerism

BowerdTowle

1972

Anvil Technique

BriscoelScruton Briscoe/Tabor Briscoe/Smith

1973 1977 1983

Model Contact Contact Time Effects

Briscoe/Smith

1984

BriscoeDbomas Israelachvili/Klein/ Grannick

1993

Solvent Effects: ductilehrittleresponse Molecular Environment Static Molecular Topography

the pressure coefficient, Q is an 'activation energy', R is the gas constant and 8 is the velocity index. These functionalitiesare observedto be quite general for polymers [1,4-81, although there are some exceptions which have been fully discussed elsewhere [7,8]. In addition to the contact variable dependencies,z is also known to be a function of the morphological properties of polymer films which are governed by the various processing

1 chain length F + PO)

F = kWn

z=zO+aP

z =
(&) (8+ ~n

ap exp -

(-Q)

(2)

variables available in thin film preparation [7,9]. These include, most importantly, the solvent axl the thermal history. These variables are outside the scope of the present paper which intends to concentrate upon the effects of the molecular structure as a mode for altering the molecular architectureof the polymer during interface shear.

195

1.2 Rheological Model If the flow process is recognised as a thermally activatedkinetic process then the contactmechanical variables of Equations 1 to 3 may be described in terms of a stress modified thermally activated rate limiting process (Eyring Theory) [lo]:

v = VO

exp - (E

+ s2p kT -

(4)

where VO is the preexponetialfactor (a characteristic velocity), E is the activation energy for the process, k is Boltzmann’s constant and R and v are the pressure and the stress activation volumes respectively ascribed to the microscopic entities which migrate in the shear field. The application of the Eyring equation to the deformation of thin solid films has been fully described elsewhere [4,7,9]. However, here it is worth noting that the Eyring equation successfully predicts the form of the empirically derivedrelationships for the variation of z with the contact variables (Equations 1 to 3):

~=--ln

:k

-

+I(E+RP] v

Comparing Equations 1 and 5 , the significance of the pressure coefficient, within the context of the Eyring approach, may be interpreted:

representative of certain conformational isomers. These modes, which correspond to molecular relaxations, are envisaged as the processes which facilitate shear at the microscopic level and we will later assume that the microscopic strain is facilitated by certain conformational relaxations identified by this method. If the population distribution between two conformations is perturbed, say by thermal or stress activation then the energy, AH, between the conformationsmay be estimatedusing a form of the van’ t Hoff equation [ 1 13:

where R is the gas constant, T is the temperature and K is the equilibrium constant for the population distribution of between conformational isomers:

where 4 and a& are the peak absorbancesand the extinction coefficients of the increasing and decreasing bands respectively. The absorbance of a vibrational mode is proportional to the population of that mode. Therefore, by measuring the rate of changeof absorbancewith temperatureit is possible to determine the relative conformationalenergy.

1.4 Frictional Energy Dissipation

a is found to be a ratio of two volumes which are attributed to: R; the local volume which must be created in order that a molecular entity of the volume v may move from one ‘site’ in the moleculararray to a neighbouring ‘site’, to v; the volume of a molecular entity set in motion. Tbe significanceof these parameters is discussed in later.

1.3 Molecular Characterisation The molecular architectures of the thin solid films presented in this paper are characterised by the use of vibrational spectroscopy. The purpose of employing vibrational spectroscopy is to characterise the molecular environment directly. In this paper we have selected a number of vibrational modes, which are describedfully below, that ine

The paper also deals with a possible mechanism for the frictional dissipation of energy. In the present work there is no direct identificationof the relaxation modes responsible for the dissipation of frictionalenergy. However, from a knowledge of the mechanisms of friction at the molecular level an intuitive model is proposed. The magnitude of z is proportional to the magnitude of the frictional energy dissipated in the contact zone in shear. The notion of an interfax shear stress does not, however, convey the notion of any particular shear plane or zone or their locations. The whole film within the contact is regarded as a potential dissipation zone. It is from this incoherent rearrangementof molecular entities in the contact zone that a basis of a dissipation model at the molecular level is evolved.

196

PMMA

PEMA

PBMA

PNMA

PLMA

PCSMA

Figure 1. The chemical structures of the repeat units of the PNAMAs characterised in the present study.

2. Experimental Methods and Materials The experimental data that are discussed below are taken from the investigations of Amuzu et d [5 ] for the rheological properties andBriscoe et a1 [12] for the spectroscopic characterisation. Both groups of authors have published data for a homologous series of poly(n-alkyl methacry1ate)s (PNAMA). The polymers studied were poly(methy1- (PMMA), poly(ethy1- (PEMA), poly(buly1- (PBMA), poly(octy1- (POMA), poIy(nony1- (PNMA), poly(laury1- (PLMA) poly(octadecy1- (PODMA) and poly(cetosteary1 methacrylate) (PCSMA). Figure 1 shows the molecular structures of these materials.

2.1 Rheology The interface shear strength of the above materials was measured using a model contact geometry of a sphere on a flat. The apparatus has been fully dexxibedelsewhere[4,71. The description is only briefly repeated here. The polymer films were cast onto smooth float glass slides by dip coating in a dilute solution of toluene. An hemispherical indenter, of known radius, was loaded against the organic layer which was subsequently slid over the film under load, W, at constant velocity and the frictional force, F, was measured.In the loading regime (107 to 108 Pa), the deformation of the glass substrates is wholly elastic. It is assumed that the presence of the organic layer does not significantly affect the deformation of the substrates and the area of contact, A, is calculated using classicalelasticity equations [ 131. It is further assumed that this areais equal to the molecular am

of the film in the contact and that there is no indenter-substratecontact which was borne out by the fact that on carefulexamination of the slider, no damage was apparent. Thus, the mean contact pressure (=W/A) and the interface shear strength (=F/A) may be calculated. The sliding velocity was maintained constant at 0.2 mm/s and was found not to induce frictional heating within experimental error.

2.2 Spectroscopy The spectroscopic characterisation was &ed out using a Bomem Ramspec 152 spectrometer in which was placed a modified Linkam THMS 600 microscope temperature stage. The polymer films were cast from dilute toluene solution onto potassium bromide discs which were placed in the temperature stage for spectral acquisition over the temperature range 30 to 100°C in increments of 10°C. The temperaturedependence of the intensity of the adsorption bandsof the PNAMAs were measure by spectral subtraction of the 30°C spectra from those at the elevated temperatures. The subtractions were made using the raw data. The spectra acquired, at 30 "C for each polymer, were also baseline corrected for curve fitting purposes so that the absolute rate of change of peak intensities of the analysed modes could be estimated.

197

Table 2. List of values of a,70 and Q for thin P(n-AMA) films (Equations 1 and 2). ~

" 1

0

1

1

I

100 200 300 Contact PressureMPa

4

Figure 2. The contact pressuredependenceof the z for P(nAMA)s; PMMA (A), PEMA, ( O ) , PBMA (0), PNMA (+), PCSMA ( O ) ,LDPE (H) and HDPE ( A ) .

3. Results 3.1 Rheology The pressure dependenceof the z is shown in Figure 2 for the PNAMA homologous series. Without exception, z is found to be a strong function of the mean contact pressure. The general form of the contact pressure dependencecorrelates with the empirical relationshipgiven by Equation 1 and with previously reported data [4,5,7,9]. The correspondingvalues of the parameters of Equation 1 are listed in Table 2. It can be seen, from Table 2, that the value of a increases with the increasing chain length of the n-alkyl substituent. The maease occurs from PMMA to PBMA. Extending the chain length further leads to a decreasein the value of a although it is not until PCSMA that the length of the chain reducesa to a value comparableto that of PMMA. Thus, although the substituent chain initially increases the value of a, the effect of extending the substituent chain length to infinity is expected to approximate the interface shear characteristicsof a branched poly(ethy1ene). The values of the activation energies, Equation 2, listed in Table 2 (taken from ref [14]) are typical for organic films and are indicative of the activation

Material

a

z0/107Pa

HDPE PMMA PEMA

0.25 2.0 2.0

PBMA

0.10 0.24 0.77 0.95

POMA PNMA PLMA PCSMA

0.81 0.72 0.51 0.39

2.2 2.5 0.30 0.7

1.o

Q/kJmol-' 16 14* 14* 10* 10 9 10 9

*These values are measured above the Tg. At sub Tg temperatures the values of Q are zero and ate associated with a shear mechanism of interfacial brittle fracture. energy for the flexing of the carbon backbone chain. Thus, although the mechanism of transport of the flow entities for each polymer in shear is associated with motion of the backbone chain, by increasing the length of the substituent chain it is found that the work involved in such a transport process is increased. The indication is that the change in the substituent chain length is responsible for the change in the value of a.

3.2 Spectroscopy The spectra for five PNAMAs in the region 1300 to 1080 cm-lare shown in Figure 3. These spectra are for the raw data and are those which are used for the spectral subtractions.These curves have also been analytically deconvolved. The activation energies for two conformationally sensitive modes have been tabulated in Table 3. The two modes are the trans-frms/rrans-gauche skeletal modes at 1270 and 1260 cm-*and a C-OR stretching mode split into geometric isomers around the carbonyl group at 1150 and 1130cm-l(Figure 4). The assignment of these modes has some uncertainty. From normal mode analysis [15], the 1270/1260 cm-lmode is

198

Table 3. The effect of chain length on the conformational energy, AH (kJ/mol), of two pairs of modes; the 1270/1260 an-’skeletal and the 1150/1130 an-’ C-OR svetching mode. ~~

AH

PBMA POMA PNMA PLMA PCSMA

0

1250

1200 1150 Wavenumber

ROCII

0’

1270/1260 1150/1130 4.48 5.7 4.80 11.5 4.81 18.4 0.72 0.51 0.39

7.1 6.7

5.09 5.41

1100

Figure 3. The 30.C spectra of PNAMAs which have been baseline corrected for curve fitting purposes.

0

AH

R

F + = *. O

)(C(O)OR

found to be a combination of skeletal C-C stretching and bending modes; a main chain relaxation mode. The 1150/1130 cm-’ doublet assignment is more obscure as it is a combination of the C-OR stretch (side group) and a variety of CH bending modes. It is strongly apparent, however, that for each pair of modes it is the conformational state of the polymeric methacrylatemolecule which produces the complexity of this region [ 1 1,161. It is notable, however, that the main chain mode (1260A270) has a conformational energy which is a strong function of the molecules position within the homologous series. The other mode is less sensitive to the chain length of the side group functionality.

I

4. Discussion R-

11

Figure 4. The conformational structures associated with the two pairs of modes; structure I: 1270 cm-ltrmgauche and the 1 130 cm-lC-OR mode, and; 11:1260 cm- trans-trm and the 1150 cm- C-OR mode.

The first purpose of characterising the structural andrheological propertiesof a series of PNAMAs is to identify a correlation between the structural properties and the rheological properties. From the contact pressure dependence of z, it is apparent that by increasing the chain length of the substituent group attached to the backbone chain, it is possible, initially, to increase the value of a. If the Eyring model is taken as a viable model for the description of the mechanistic process for flow, then it is found that a is a ratio of two volumes (Equation6): the pressure activation volume, R , to the stress activation volume, v. Therefore, for the value of a to increase, the increase in R must be greater than

199

the corresponding increase in v. For the shear of polymeric materials it has been commonly found that by increasing the ‘bulkiness’ of the pendant group, the friction coefficient, p. increases [1,14]. Actually, p is related to the parameters in Equation 1 by:

p = -70 +a P

(9)

and hence an increase in p cannot be wholly associated with an increasein a. However, it has been generally shown that the differences okwed in p are mostly due to changes in the pressure coefficient. From these observations, molecular topographical models have been proposed where, in a similar manner to the process attributed to Coulombic friction, the pendant groups interact with the neighbouring chains to impose physical barriers which have to be overcometo accommodate the frictional strain [l]. This study finds that it is not the activation of the C-OR mode that is affected by the increasing the chain length, showing the flexibility of the COR group, but the skeletal mode of the main chain itself which has the most marked effect(Figure 5). Hence, it is the combination of the main chain and the substituent group ‘bulkiness’ which increases the magnitude of the rotational energy barriers between the skeletal mode conformations. The Eyring interpretation of the significance of a involves the transport of a molecular entity of volume v by the process of creating a space fluctuation of volume R in the molecular lattice. In amorphous polymers of the present sort, a significantvolume fraction is available. Therefore,a reduced volume needs to be created locally which is nominally given by: Q=V-Q‘

R ’ is the mean ‘free volume’ of the system. If it is assumed that by increasing the side group chain length of the PNAMA from a methyl (1 carbon atom) to an ethyl (2 carbon atom) group, the size of the transport unit, v, is doubled, then:

i21=V-i2’

,

1

1

1

1

1

1

1

Figure 5. Comparison of the variation of a (0) and AH of the 1270/1260~m-~ (W) and the 1150/1130~m-~ (0) with length of the alkyl chain ((2”). i22 = 2v

- i2’

where the subscript denotes the number of carbon atoms in the substituent chain, then by simple algebraic substitution:

whereR’/v = 0.82 which suggests that for the shear of PMMA, approximately 80% of the volume required to be mted to set a flow entity in motion under shear is available in the system in the unstressed state. If this argument is applied to the longer chain methacrylates then the relationship becomes:

200

p Table 4. Values of the number of carbon atoms, C,, in the n-alkyl substituent chain and the calculated effective number of carbon atoms, ncalc, for a filled volume, R’lv, set at 0.80 (Equation (15)). Polymer PEMA PBMA POMA PNMA PLMA PCSMA HDPE

C” 2 4 8 9 12 17,18

ncalc 2.2 3.8 2.5 2.0 1.4 1.2 0.9

where n is the actual number of carbon atoms in the substituent chain. If the R’/v is set at 80% then it is possible to calculate a value of n, that is the “effectivesubstituent chain length”, for each of the series of PNAMAs:

n -0 . 8 0 1- 0 . 2 0 ( 3 The values of n calculated from this expression ipe listed in Table 4. The values of n are found to increasein line with the number of carbon atoms in the substituent chain for PEMA andPBMA. For the higher n-alkyl chain lengths the value of n reduces. The value of n may therefore be considendto be the effective ‘bulkiness’ of the alkyl substituent. In effect, two processes govern the rate of change of a with the size of the substituent group; the intramolecular resistance to motion (the v term), defined by the increase in the flex energy of the carbon backbone chain, and the intermolecular distance (the R term). For the shorter chain lengths, extension in the chain length ‘fills’the available fire volume, thus increasing the resistance to intramolecularmotion. It can be seen from Figure 6 that, up to an alkyl chain length of four methylene groups, the substituent chain lengths do not

PMMA

iPEMA

iPBMA

()

sPBMA

Figure 6. A schematic representation of the effect of the size of the akyl substituents on the their neighbouring acrylate groups. The prefixes denote the stem regularity of the backbone chain. For PEMA either conformation allows minimum substituent interaction. In the case of PBMA only the syndiotactic conformation allows minimum substituent interaction. It is assumed, hence, that, for the higher homologues, the substituent chain interactions force an increase in the sweeping volume of the polymer chain. necessarily interact. The substituents chains may therefore fill the free volume available in PMMA between the substituent groups. Therefore, the volume required to be created, R , is increased while the effective volume of the flow entity, v, relative to PMMA, is constant. Above four methylenes, the sweeping volume of the chain extension must occur away from the backbone thus increasing the magnitude of v and, in the same manner, decreasing the magnitude of R , due to the relative increase in free volume. Essentially now, larger units flow with a lesser volume expansion.

5. The Dissipation Model The combination of investigating the effect of molecular structure on the interfacerheology and the effect of molecular structureon the rotational energy barriers between conformational isomers has aided the understanding of the processesof molecular flow in a shear stress gradient. It has been found possible to identify the most likely molecular entities or relaxation modes which are stress activated in the interfaceshear process. These have been identified as the backbone chain relaxation modes. This understandingonly allows an intuitive evaluation of

20 1

the processes responsible for the dissipation of frictional energy. It is from the understanding of the processes of molecular flow that an intuitive model of the frictional energy dissipative processesmay be evolved. The process of molecular flow is associatedwith the transport of molecular entities from one isoenergetic site to a neighbouring isoenergetic site by microscopic shear work (vz). For this to occur, an instantaneous local volume must be createdin the molecular lattice (R ). The creation of this local volume naturally rearranges the molecular architecture. The dissipation of frictional energy must be at least in part associated with this process and hence with the R P ‘work’ term. The creation of a local volume of the size of a molecular entity requires the structural rearrangement of the local molecular architectureto a possible radius of ten molecular entity volumes. It is therefore proposed that, in this microscopic rearrangementprocess, the dissipation of frictional energy occurs. The process is essentially viscoelastic in nature (a parallel may be made here with models for viscoelastic rolling friction for elastomers which is the macroscopic analogue of this microscopic model [ 173). In the process of creating a local activation volume, R , for the transport of a molecular entity, the surroundingmolecular environmentis elastically activated. Once the entity in transport has passed on to the new site the system relaxes. It is in this process that the dissipation of frictional energy is proposed to occur. The energy involved in this elastic activation is dissipated in long range phonon damping relaxations away from the stress activation sites and is hence ‘‘lost’’as heat. This process is associated with the R P term, as the activation associated with the v z term is recovered on relaxation (activation from one isoenergeticsite to a neighbouring site). This type of model was Fist proposed in 1804 by Leslie [ 181. It was realised that in the act of surmounting a Coulombic asperity the potential energy gained would be recovered in kinetic energy once asperity had been surmounted. Hence energy dissipation could not be attributed to this process. Leslie proposed that the dissipation occurred in the surface layers in the form of plastic deformation. The main chain relaxation of the 1270/1260 mode, identified in the spectra, is a possible candidate for the accommodation of microscopic

shear stresses. For the case of the PNAMA homologous series the magnitude of the activation barrier is associated with the effective bulkiness of the substituent chains which determine the amount of R needed to be created relative to the magnitude of v. For the longer substituent chain length PNAMAs, the substituent chains themselves may be involved in the work process possibly acting as ‘pseudoboundary lubricants’ in the sense that they move the dissipation zone away from the substrate (the main backbone chain) complicating the identificationof particular dissipation mechanisms. The size of the energy barrier associated with the work process is in part determinedby the magnitude of the intramolecular rotational energy barriers identified in the spectroscopy, although intermolecularinteractions are also contributors [7]. The substituent groups sterically hinder the flexing of the backbone chain increasing the activation energy for rotation and hence the size of the shear activation barrier(both R P and vz). Although, this is of course a simplification of a complex number of inter- and intramolecularinteractions, it is a mechanism indicative of the sorts of processes which occur in the frictional dissipation of energy. It is worth noting that the dissipation or degradation of specific photon adsorptionfiresuencies has been addressed [ 191. An interesting comparison may be drawn between shear and photon activation and the subsequentenergy dissipation process in the two cases. In both cases, the activation of specific molecular relaxation modes occurs. The degmdation process is associated with that of the conjugation of lower energy, long wavelength, relaxation modes delocalising the initial high energy activation.

Conclusions The paper has exploreda possible mechanism for the molecular dissipation in shear process as an origin for describingthe frictional work. The model is initiated by the identification of the sorts of molecular relaxations responsible for the accommodationof macroscopic shear stresses. By a considerationof the energeticsof molecular isomeric states and the implications of the Eyring parameters, the paper speculates upon a possible mechanism for the dissipation of frictional energy. In final conclusion, it must be emphasised that these deductions are quite speculative.The main aim of the paper was to explore the correlationsbetween

202

shear induced and photon activated molecular relaxations and to consider the origins of such correlations. The fact that such correlations between spectra and frictional responses exists does not of course mean that the deductions drawn, in terms of molecular models, are causal. However, it is interesting that the dissipation processes involved in friction are also apparently accessible in photon activation which are processes readily monitored using infrared spectroscopy.

Acknowledgements The authors are pleased to acknowledge the financial support provided by E.I. Du Pont de Nemours during the implementation of this work and for the useful discussions with Dr.D.R. Williams.

References 1. Pooley and Tabor D. (1972) Proc. Roy. Soc. Lond. A329, 251

2. Sutcliffe M.J., Taylor S.R. and Cameron A. (1978) Wear 5 1, 181 3. Gee M.L., McGuiggan P.M., Israelachvili J.N. and Homola A.M. (1990) J. Chem. Phys. 93(3), 1859 4. Briscoe B.J., Scruton B. and Willis R.F. (1973) Proc. Roy. Soc. Lond. A333, 99 5. Amuzu J.K.A., Brisc0eB.J. andTaborD. (1977) Trans. ASLE 2 0(2), 152 6. Briscoe B.J.. Thomas P.S. and Williams D.R.

(1992) Wear 153. 263; Briscoe B.J. and Smith A.C. (1982) J. Phys. D: Appl. Phys. 15, 579 7. Briscoe B.J., Thomas P.S. and Williams D.R. (1993) in “Thin Films in Tribology”, Tribology Series 2 5 (Leeds-Lyon 19). 453 8. BriscoeBJ. andSmith A.C. (1982)J. Phys. D.: Applied Phys., 15, 579 9. Brisc0eB.J. and Smith A.C. (1983) J. Appl. Polym. Sci. 28, 3827 10. Eyring H. (1936) J. Chem Phys. 4 283 11. O’Reilly J.M. and Mosher R.A. (1981) Macromolecules 14, 602 12. Briscoe B.J., Thomas P.S. and Williams D.R. (1993) in preparation. 13. Timoshenko S.P. and Goodier J.N. (1951) ‘Theory of Elasticity’ (New York M a w - H i l l ) 14. Brisc0eB.J. andTaborD. (1976)ACS Prepriru 21.10 15. Dybal J. andKrimm S. (1990) Macromolecules 23, 1301 16. Havriliak S. and Roman N. (1966) Polymer 7, 387 17. TaborD. (1955) Proc. Roy. Soc. Lond., A229, 198. 18. Dowson D. (1979) “History of Tribology” Longman pp223-5 19. Seisler H.W. and Hollander-Moritz K. (1980) “Infrared and Raman Spectroscopy of Polymers” Marcel Dekker, New York.

SESSION V POLYMERS Chairman:

Professor D Dowson

Paper V (i)

Interfacial Friction and Adhesion of Wetted Mono1ayers.

Paper V(ii)

Effect of Thickness on the Friction of Akulon A Problem of Constrained Dissipation.

Paper V(iii)

Interface Friction and Energy Dissipation in Soft Solid Processing 0perations

Paper V(iv)

The Effect of Interfacial Temperature on Friction and Wear of Thermoplastics in the Thermal Control Regime.

-

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Dissipative Processes in ‘l’ribology / I). Dowson ct al. (Editors) 1994 Elscvicr Science R.V.

205

Interfacial friction and adhesion of wetted monolayers J.-M. Georges, A. Ton&, D. Mazuyer Laboratoire de tribologie et dynamique des systkmes, URA CNRS 855 Ecole centrale de lyon, B. P. 163,69131Ecully Cedex, France

In this paper, the first observations with a new molecular tribometer, where the interfacial friction work necessary to create initial sliding is simultaneoualy measured with interfacial adhesion are reported. In particular, the frictional and adhesion energy between two stearic acid monolayers adsorbed on cobalt surfaces have been observed. It is shown that the anisotropic thin bi-layer is more compliant than the contact, reduces the apparent shear modulus of the contact zone and controls the shear process. The critical yield strength of the two squeezed monolayers which support moderate pressure (20-60 MPa) is reached after a critical sliding distance corresponding to a lattice parameter independent of the normal load. These results are discussed in terms of interactions between molecules due to collisions between molecules of opposite layers. The energy spent in a lattice displacement corresponds to a viscous-like behaviour.

1. INTRODUCTION

Understanding of the mechanisms of adhesion and friction is now possible with the recent development of surface force equipment. Measurement, at molecular scale, of the normal and tangential forces between two surfaces [l-41 is now feasible. In the absence of ploughing friction due to the solid asperities, the fictional force between two smooth solids arises from adhesive bonding and hence from the mechanical shear strength of the sliding interface. Generally, a molecularly thin film present in the interface controls the interfacial friction 151 and gives viscous or frictional forces [l]. These energydissipating forces are important as they determine the performance of boundary lubricants. We have constructed a new device [6] that measures directly and with great accuracy the forces and the displacements that act

between metallic surfaces bearing organic layers in a liquid medium, as they slide past each other. Its originality is due to its low compliances ( C; = 2 x m/N for the normal direction, Ck = C$ = 2 x 104 m/N for the two others), which permit the mechanical control of the thin layer. In this work, it is shown that an anisotropic thin monolayer of stearic acid in n-dodecane adsorbed on each cobalt surface is more compliant than solid surfaces and hence reduces the apparent shear moduli of the contact zone and governs the shear process. The interfacial fiction depends on the sliding speed and is very sensitive to small variations of the film thickness. Two competitive and opposite processes occur during sliding : crushing and lifting of the monolayer. It is suggested that the crushing appeara at very low speeds when the transit time is close to that of molecules in the monolayer. Our findings have direct

206

applications for the properties of boundary lubricant and for the rheological behaviour of both surfactant and polymer molecules.

2. EXPERIMENTAL PROCEDURE A molecular tribometer has been constructed [6], whose principles are shown schematically in Figure 1. An existing surface force apparatus [7-81 was modified so that a sphere can be moved towards and away h m to a plane and transversely at constant normal load. With this equipment, two successive experiments have been made. Adhesion and deformation of the adsorbed layers are studied in normal approach (motion along the 2 axis). Sliding motion (displacement along the X direction) at a constant normal load (see Figure 1.)is used to study friction. The use of three piezoelectric elements controlled by three capacitance sensors permits accurate motion control along three orthogonal axes (sensitivity 0.01 nm). The forces are measured along 2 and X axis by two capacitance sensors (sensitivity 10 nN). The surfaces used in this work am cobalt coatings on fused born-silicate glass for the sphere (radius R = 2.95 mm) and on silicon wafer for the plane. This cobalt layer is deposited under a low argon pressure ( 5 x 1o - ~Pa ) using cathodic sputtering. Before deposition, the chamber is pumped for 8 hours at a p r e ~ ~of~ r e Pa. Atomic force microscopy observations show that the surfaces consist of irregular connected clusters leading to a corrugated %lackberry"like roughness (0.8 n m peak to valley with a wave length of 70 nm). A droplet of 1 mM solution of stearic acid (Aldrich)in anhydrous n-dodecane (pure grade h m Aldrich Sure Seal : grade 99 8)is deposited between the two cobalt surfaces. This droplet forms a meniscus of radius r = 1-2 m m in the sphedplane interface. A monolayer of stearic acid is obtained after one hour adsorption [9-101. AU the experiments were performed in dry air with a drying agent P2O5 at a temperature of 23.5 0.2"C.

*

Figure 1.Schematic picture of the three-axial surface force apparatus used for the experiments. A sphere is fixed to piezoelechic device which enables the motion in 3 directions. Three capacitance sensors control the relative displacements of the sphere with an accuracy of lom2nm. A plane is fixed to an assembly of two sensors measuring both normal and tangential forces with a resolution of 10 nN. The direct measurement of the electrical capacitance of the sphereplane contact gives the sphere-plane separation D. This distance D may be controlled by the capacitance, the normal force or the normal displacement Z. 3. SQUEEZE OF THE LAYER The sphere-plane separation D is measured in normal approach with a speed of 0.1 d s (Figure 2.)as described in previous

207

studies [71, [8], [ill. The electrical capacitance C of the sphere-plane interface is a function of displacement Z and is measured for high frequency. The measured function dZ/dC is proportional to separation D between the two conducting surfaces 1111. Thus, the plot of dZ/dC against Z gives the origin Oe as shown in figure 2. If the surfaces are not deformed and if the intedacial ijlm is absent the origin, 0, corresponds to the contact of the two metallic surfaces. Actually, the cobalt surfaces are covered by an oxide layer whose thickness is D,, = 0.3nm [8]. 20 1

I

I

1

f

zt 1 distance

be

I

&I

/

large, the ratio 1/A is proportional to D and gives a mechanical origin of the contact 0,.

In consequence, the thickness DS =

Oq

-0e

2 of the "immobile layer" on each surface 181 may be determined by extrapolation. We found, for two monolayers of stearic acid, D, = 2.4nm. The thickness of the monolayer measmd by this method is then equal to D, - D,, = 2.4 -0.3 = 2. lnm, a value comparable to the 2.4 nm given in the literature [12], for the case when the adsofbed stearic acid molecules are perpendicular to the surfaces. We conclude that the n-dodecane molecules located on the top of the monolayera are not "immobile" as they are for cobalt surfaces [8] and the monolayers may be heterogeneous. The force-distance curves Fz(D) of the Figure 3. rn the same for the inward and outwad displacement i. e. there is no adhesion hysteresis.

NORMAL DISPLACEMENT Z (nm)

2Ds = 4.8run4

Figure 2. Plot of the electrical distance (deduced from the measured function dZ/dC ) and the hydrodynamic distance (deduced from the measurement of the inverse of the damping h c t i o n l/Al These curves are obtained t h a n k s to dynamic measurements, by superimposing a sinusoidal motion in the Z-direction with a frequency of 37 Hz and an amplitude of 0.1 nm r m s The difference between the origins Oe and O,, is twice the thickness of the immobile layer (2D8) The mechanical damping function A of the interface is also measured. It has been shown [8] that when the liquid is purely viscous and the sphere-plane separation D sufliciently

W

u

E

2

2oo'

100

THICKNESS

OF

-

p:

0

z

o -

I

-100 0

I

I

2

4

1

1

I

I

6

8

SPHERE-PLANE DISTANCE D (nm)

Figure 3. Evolution of the normal force FZ against the sphere-plane separation D, accounting for the elastic deformation of the solids deduced f h m the Hertz theory. For FZ 2 lOOpN, the distance D stays constant and equal to about 5 nm. This shows the presence of rigid wall whose thickness is twice the length of stearic acid molecule.

208

The sphere -plane distance D is given by the law :

4. FRICTIONAL BEHAVIOUR OF THE MONOLAYERS

D=Z+6

The second experiment is performed in sliding mode. The variations of the tangential force FX are plotted against sliding distance X in Figure 4. The fiction experiment is conducted by keeping the normal force at FZ = 1000 * 0.2pN corresponding to a contact radius a = 3.4pm, an elastic deformation of the solids 6 =3.9 nm, a mean contact pressure of 27 MPa and a film thickness D = 5 nm. The values of a, D and 6 are computed from the Hertz’s theory considering the monolayers as a rigid solid.

(0)

where Z is the relative normal displacement between the sphere and the plane, and 6 is the elastic deformation of the a’ solid. b is close to - where a is the contact R radius. In the case of stearic acid for which no adhesion hysteresis is observed, a is given by Hertz’stheory. For a normal force FZ z lOOpN,Figure 3. shows that the thickness of the interface remains almost constant (D = 5nm). According to the value of the roughness of the surfaces, this thickness is compatible with the presence of one stearic acid monolayer on each surface (4.8 nm). It is concluded that for D=Bnm, the n-dodecane molecules are expelled from the contact. The adhesion energy WSLS which is the positive work done for separating two unit areas of solid surfaces (S) from the contact in the n-dodecane liquid (L) can be obtained from the adhesion force Fi , corresponding to the minimum of the curve Fz(D) (Figure 3.) by the following relation [131:

I

I

I

Spherelplane distance D z 5 nm

Stitfness : 2.2 10 N/m

I 5

u = 0.05n m l s

0 1.5 3 SLIDING DISTANCE X (nm)

4.5

3

WSLS = 2JcR

-

This yields a value of W SLS 0.12mJ/m2. If only dispersion forces are responsible for the interadions then there is the following relationship between the adhesion energy and the surface energies per unit area [14] : ~ 2 W S L S= Y s + Y L - 2

JG

(2)

The surface energy for solid surfaces mainly composed of Cy3 groups is y s = 23mJ/m2, the surface tension of ndodecane y L is 25.4 mJ/m2. Equation (2) then gives the same value of W SLS = 0.12 mJ/m2.

Figure 4. Evolution of the tangential force with the sliding distance in a fiction experiment at a normal constant load FZ = 1000 pN.Two periods are observed :

X5 X*: elastic period where the tangential force is proportional to the displacement. The behaviour of the film is characterised by a tangential stif€ness leadmg to a shear modulus of 3 MPa, * X > X : non-linear period where the tangential force increases until an equilibrium value leading to a low friction coefficient (= 0.01) independent of the applied normal load.

209

Due to the very low tangential compliance -6 of the apparatus ( C $ = 2 x l O m/Nl and the large displacement resolution, the tangential compliance of the film itself and the variations of the tangential force F'x can be detected. Indeed, the measured tangential compliance is

(K'

Id ~ I x-0 x

= 4.5x

lodm/N.

Besides this compliance is given by :

as long as v does not exceed vc = 5nmls. The friction force reaches a stabilised value after a sliding distance of about 9 nm (Figure 5. b). When the sliding speed is increased by step (Figure 5. c-d-e), aRer a small and fast increase, the friction force reaches an equilibrium all the more rapidly because the speed is high. This suggests that the relevant parameters to describe that speed-dependent behaviour (parts b-c-d-e in Figure 5.) of the interface are a distance and time.

(3) w

I/

I

0

10 20 30 40 SLIDING DISTANCE X (nm)

50

0

10 20 30 40 SLIDING DISTANCE X (nm)

50

I

I

I

where C,f and C?" are the tangential A

A

compliances of the thin film and the Hertzian He and c;e are contact respectively. As Cx related [151:

cp

PI

2.4 x cFe = 3.2x 10-6

L d N

(4)

tangential compliance is assumed to be :

where Gf is the elastic shear modulus of the film in the XOY plane and is equal to 3 x lo6 N/m2, according to relation (5). Therefore, for small tangential forces, (part a in Figure 4.), the tangential compliance of the thin layer leads to a linear relation between the tangential force and the displacement X : FX = ; c a 2 G f x X D

As the tangential displacement exceeds a critical value X* = 0.4 nm, the tangential force Fx is no longer linearly related t o sliding distance X indicating a sliding process and now depends on the sliding speed v = X

Figure 5. Influence of the sliding speed on the evolution of the tangential force FX related to the variations of the thiclmess of the interface. The friction experiment is carried out for 4 successive sliding speeds (b-c-d-el. The increase in speed causes, first, a steep increase of f i and then a slow decrease to a limiting value. The interface accommodate the sliding process by small variations of its thickness (= nm) correlated to the variations of the fictional force. These speed effects (b-c-d-e)are characterised by a "length constant" of about 4.5 nm.

210

Besides, the friction force variations due to s l i k (part b in Figure 5 . ) or to change in the slidmg speed (part c-d-e in Figure 5 . ) are accommodated by small but sigmficant film thickness variations AD deduced fkom the electrical sphere-plane 'apacitance, assuming no variation of the contact area at constant normal load Fz. When the tangential force increases, a decrease of the thickness of the film is observed (see Figure 5 . ) and vice versa. For every sliding speed, the thickness of the interface reaches a stabilised value in the same time as the fictional force with the same "length constant" of about 4.5 nm. If the very low values of AD are supposed to be due t o a variation of the orientation of the stearic acid molecules relative to the tangential plane of the contacting surfaces, a variation AD = 0.01 nm of the thickness of the film would correspond to an angle of 4" between the normal of the solid surface and the principal axis of the molecule. As the sliding speed exceeds the critical value vc, the tangential force becomes constant and is completely determined by relation (6) in which x = x * . It is interesting to consider the transit time t which is the time taken by a C a group to overcome another CH3 group on the opposite surface, t

3 :

X* . In this experiment, V

there is one critical transit time & under which the molecules are not sensitive to the speed :

X*

tc=-=80ms

(7)

VC

This critical time tc is long compared to the relaxation of a molecule, suggesting the sliding process involves a set of molecules. Indeed, complementary experiments for different applied normal loads show, first, that the distance X* is independent of the normal load FZ and therefore of the mean contact pressure p and second, that,, according to relation (61, the shear modulm,

Gf is proportional to the mean contact pressure p:

Therefore, the friction coefficient p defined as the ratio of the tangential stress t to the pressure p is simply given for a sliding speed v E vC:,by the relation : p =$=1~-=0.009 G X*

P

D

It can be deduced h m relation (9) that p is also independent of the normal load. The value of X* is close to 0.45 nm which corresponds to the average distance between two CH3 p u p s in a monolayer in crystalline condensed state [161. 6. CONCLUSION Our results show that the frictional behaviour of the stearic acid monolayer presented, in this paper, is similar to that of solid-like monolayers observed in previous experiments [l]. In particular, for sliding speed v < vc, the fiction force decreases as v increases. The low compliance of our apparatus leads to friction experiments without stick-slip phenomenon and permits a better description of relaxation processes. The studies of these effects which are comparable to that observed for adsorbed polymers [3], may provide a new approach for relating the chain-like aspects of surfactants or polymer molecules to the macroscopic theory of lubrication like elastohydrodynamic lubrication.

6. ACKNOWLEDGEMENTS The authors are indebted to Shell Research Limited for financial support. We also thank the C. N. R. S. and the members of the GDR 936 "mesure de forces de surfaces en milieu liquide" for helpful discussions.

211

REFERENCES

9.

M. Jacquet and J. M. Gorges, J. Chimie Physique (Paris), 11(1974) 1529

1. H. Yoshizawa, Y. L. Chen and J. N. Israelachvili, J. Chem. Phys., 97, 2 (1993)4128. 2.

J. Van Alsten and S. Gmnick, Phys. Rev. Lett.,61 (1988) 2570

3.

J. Klein, D. Perahia and S. Warburg, Nature, 352 (1991) 143

4.

M. L. Gee, P. J. Mac Guiggan and J. N. Israelachvili, A. M. Homola, J. Chem. Phys., 93, 3 (1990) 1895

5.

A. M. Homola, J. N. Israelachvili, M. L. Gee and P. J. Mac Guiggan, Tribology, 111(1989) 675

6.

A. Tonck, D. Mazuyer and J. M. Georges, to be published

7.

A. Tonck, J. M. Georges and J. L. Loubet J. of Coll. and Inter. Sci.,126, 1 (1988) 1540

8.

J. M. Georges, S. Millot, J. L. Loubet and A. Tonck, J. Chem. Phys., 98, 8 (1993) 7345

10. E. L. Smith,C. A. Alves, J. W. Anderegg, F. Porter and M. D. Siperko, to be appeared Langmuir (1993) 11. A. Tonck, F. HouzB, L. Boyer, J.L. Loubet and J. M. Georges, J. Phys. Condensed Matter 3 (1991) 5195 12. A. S. Akmatov, Molecular Physics of Boundary Lubrication, Israel Prog. for Sci. Trans., Jerusalem, 1966 13. B. V. Derjaguin, V.M. Muller and Y. P. Toporov, J. of Coll. and Inter. Sci., 53 (1975) 314 14. J. N. Israelachvili, Intermolecular and Surface Forces, 2nd Edition, Academic Press, 1992 15. R. D. Mindlin, J. of Appl. Mechanics, 16 (1949) 289 16. D. Tabor in Microscopic Aspects of Adhesion and Lubrication, J. M. Georges (Ed..),Tribology Series 7, Elsevier, 1982

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Dissipative I'roccsscs in Tribology / 1). I)owsoii ct al. (Editors) 1994 Elsevier Science R.V.

213

EFFECT OF THICKNESS ON THE FRICTION OF AKULON A PROBLEM OF CONSTRAINED DISSIPATION L.Rozeanu, S.Dirnfeld and J.Yahalom Dept. Materials Eng., Technion, Haifa, ISRAEL

This paper describes friction experiments with steel balls sliding on Akulon disks of various thicknesses. It is found that the friction torque does not vary monotonously with the specimen thickness. This unusual friction behavior is assumed to be due to a mechanical constraint which prevents the free motion of the entangled molecular chains and to a thermal constraint which prevents free cooling. When these constraints are active the material strength increases, there is less volume work performed and the friction torque decreases.

1. INTRODUCTION The friction of polymers has been extensively studied and it is difficult to find a practical detail or a functional feature which has escaped the attention of researchers. The fast initial R&D progress, has followed the usual trend toward a plateau as regards application know-how; competent review papers written 20 years ago [l] are still useful to-day. The more recent progress aims rather at building up a consistent theoretical frame for the facts already known and at designing new materials. For this reason the finding that the thickness of Akulon does not affect monotonously the friction wass a surprise. The results reported in the present paper show that the resistance to friction follows an initial zigzag variation with the specimen thickness: at least in certain working conditions (loads of 0.2-0.8 Kgm, velocities of 0.5-2.5 m/s and temperatures of 30-60 "C): the friction is maximum in a narrow thickness range of about 1 to '3 n m . In order to explain this it is assumed that the macropolymer is subject to two constraints: A mechanical constraint (the bond to the metallic base) which interferes with the free motion of the entangled chains under stress as if the bulk strength has increased. a thermal constraint (the greater thickness

of the specimen). This slows down the heat flow out of the system promoting adiabatic behavior, less strain for the Same stress.

1.1 NOTATIONS A Free Work (Helmholz) F Applied force G Free Energy (Gibbs) L Nominal length of reference system P Pressure R Radius of thermally driven agitation S Entropy T Temperature V Volume (other notations are explained in Fib. 6) 2. GENERAL

Usually the friction behavior of plastic materials is considered a generic attribute of the material or of the material couple. The sliding interaction between the members of the friction couple is assumed to be confined to the surface and the surface is considered an indistinguishable part of the bulk, the two acting as a single entity. If two factors act in the Same direction, but the contribution of one is very small, its omission is justified, even necessary. Indeed

214

many details can be omitted without harm. The omission of some details, however, can penalize the research. One such detail in friction experiments is the thickness of the specimen which, in certain working conditions, affects substantially, both mechanically and thermally, the friction behavior of plastic materials. The conclusions to be presented refer to one material, Akulon. There are good reasons to believe that other plastic materials behave similarly and that the thickness must be specified except when the friction behavior presents no interest. The fact to retain is that the variation of the friction force of Akulon in sliding interaction with steel does not vary monotonously with specimen thickness: it is low for thin and thick specimens and high in the middle thickness range ( 5 1 to 2 3 rnm). Load, sliding velocity and temperature affect the friction sensitivity to thickness but at a smaller scale. 3. EXPERMENTAL SET-UP

The testing unit (Fig. 1) consists of a rotating disk driven by a variable speed electric motor. On top of this disk is mounted another disk with complete axial and radial degree of freedom, provided with means for applying the load and for ineasuring the friction torque. On the lower disk are fixed 3 steel balls (6 mrn diameter) at 120" and at 17.5 mrn from the center. On the upper disk, made of aluminium, are fixed the Akulon specimens with a cyano-acrylic glue, few p m thick when dry. The Akulon disks were brought to the final thickness by grinding following an adhoc but strictly respected procedure. The active part of the apparatus was enclosed in a thermostatic container were it was kept for 30 min., for thermal conditioniiig prior to each test. The loads (up to 785 gm) and velocities (0.5 to 2.5 m/s) were in the medium range generally encountered in service. 4. RESULTS

The results of over 100 tests are presented in FIG. 2 as averages of torque-vs.disk thickness, indiscriminately, over all loads, velocities and temperatures adopted.

THICKNESS , m m

-

Fig. 2 Torque-vs.-Thickness Averages over all L,T and v

Fig. 1 'I'ES'I'ING U N I T

This rough presentation indicates that the torque for the disks in the thickness range of about 1 to 4 mm is almost twice as high as those outside this range.

215

More information is provided by the following bar graphs which show tile effect of each experimental condition individually (load, temperature and velocity) within each thickness range. Fig. 3 shows the effect of load; for each thickness; as expected, the torque increases with load. The disks of medium thickness continue to give the higher torque results.

In the case of the medium thickness disks the experimental errors (no attempt was made to discard them) or other factors lead to apparently abnormal results without altering the conclusions emphasized by Fig. 2. 400

l250rpm

B600rpm

I1000rpm


1-3

-4

50 I190gm

2 .-0

300

2;

200

W 380gm

I 785gm

E

THICKNESS ,mm

3 0

5

100

I-

n

r4

1-3

Fig.5 Torque-vs.-Thickness and Velocity. Averages over all L and T.

THICKNESS, mm

Fig.3 Torque-vs.-Thickness arid Load. Averages over all T and v.

Fig. 4 presents the effect of temperature: It sliows that the thin and thick disks respond more coherently to temperature.

-.m

c

e

1""

P 45c

I 60C

4oo[ I 30c

c

(d

-

300

.Y

E

w 200 3

0

5

too

I-

-

n
1-3

>4

THICKNESS ,mm

Fig.4 Torque-vs.-Thickness and Temperature. Averages over all L and v.

Fig. 5 shows the effect of velocity. Now the most susceptible appear to be the disks in the medium thickness range. The anomalies in results for the thin disks and the lack of sensitivity of the thick disks will be discussed later. Again the abnormalities within each thickness range are small and do not affect the general conclusion. Another detail to be noted is the width of grooves made by the steel balls during sliding on the Akulon disks. They were between a fraction of one mm and one mm, according to load; this is much less than the diameter of the circular area developed by a quasi-static Hertz contact which, for the same loads, should be 1.5 to 2.5 mm. It means that the strain is not fully reversible, slow relaxatioii taking place. This corroborates Tanaka's assumption 121 adopted in the present paper that for such materials the Poisson Coefficient is about 0.4. 5. INTERPRETATION OF RESULTS

5.1 Theoretical background MeWplastics friction is likely to involve two modes of interaction, one engaging

216

the surface, one reiated to volume work. The surface interaction during friction should be independent of specimen thickness if this exceeds few p n and the material properties do not vary. If they do vary, they will affect far more the volume work. Furthermore lhe effect should be monotonous, one way or another. The problem of main interest is: how the thickness affects , reversible or irreversible, the bulk properties of plastic materials. By this it is implied that the surface contribution to friction is acknowledged but omitted from the present discussion. Also is omitted the role of the metallic part of the friction couple which, being much harder than the plashc, its contribuhon acts as a constant factor. Dissipation of energy means elimination of gradients or entrop production, resulting either heat or intern disorder (for ex. stress relaxation). Deformation in general, stretching in particular, creates internal order (stress gradient) and takes the material system off equilibrium condition; its energy increases.

air

The thermodynamic expression for the increase of energy is given [3] by eq.1: dU = TdS - PdV FdL .... (1) If the Poisson Coefficient is 0.5, the volume does not vary during stretching. it is the case of rubber ((dV=O) for which: dU = TdS FdL (1') Other useful thermodynamic potentials are the Helmholz Free Work (eq.2) and the Gibbs Free Energy (eq.3) : dA = -SdT - MF (2) dG = -SdT FdL (3) According to the properties of exact differentials it follows that: i/ (dUdT) = (dS/dF) ii/ (dF/dT) = -(dS/dL) The last two equalities must be interpreted by refering to Fig. 6 showing a segment of a polymer chain; At 0 K (Fig. 6a), there is no thermal energy to agitate the atoms or the radicals forming the chain. The chain is straight, its configuration entropy is zero. Neglecting the wriggling in space, if the temperature rises to T1, (Fig. 6b), each node of the chain agitates while attached

+

+

+

-'I 1

- FO

+

T=O°K ~ = 4 ~ e

so=o

Fig. 6 Thermoelasticity of rubber

217

to its nearest neighbors by chemical bonds of length "1". In this situation the agitation manifests as rotation within the space constraints imposed by the nearest neighbors. The radius of the rotation circle measures the level of agitation or the thermal energy feeding It. Fig. 6b shows that, in order to increase the radius at constant bond length "1" between nodes, the nearest neighbors depart from the initial alignment by an angle a, contributing to the length of the segment with l'=l*cosa, 0 meaning that if the temperature is increased the force needed in order to keep constant tant

the length of the chain must also increased. From this it follows that the tensile strength (and the modulus of elasticity) of the stressed polymer increases with temperature, just the opposed of what is known for metals. The above picture also gives clear meaning to the representation of the stressstrain relationship in adiabatic and isothermal conditions given in most textbooks, for ex., i4], as shown in Fig. 7.

I 7

STRAIN-*

Fig.7 Slress iiiitler fast (adiab.) aiid slow (isollierni.) strain Almost adiabatic conditions correspond to very fast strain while isothermal conditions correspond to very slow strain. In the isothermal case there is a continuous heat interchange with the environment such that for all practical purposes the thermal equilibrium is maintained; by reference to Fig. 6, it corresponds to the change from T=T1, F=Fo (Fig. 6b) to T=Tl, F1 >Fo (Fig. 6c left). In the adiabatic case the tensile stress rises fast for a small strain, as if passing in Fig. 6 from T=T1, F=Fo to T3 >T1, F1> Fo (Fig. 6c right) the material warms up (if polymer), and the strain continues at constant stress until it reaches the iso-thermal end point (Fig. 7). The horizontal strain segment is completed during a time depending on the heat exchange conditions, Effective thermal isolation of the stressed specimen will inhibit the strain.

218

5.2 Prevailing constraints The thermodynamic picture is essential inasmuch as it indicates the possible paths by which a system can recover equilibrium but is unable to specify the rate at which a change will occur. Moreovere it places the change under the control of the prevailing constraints. The experimental conditions adopted can be redefined such as to take into account the unusual properties of rubber-like p;astics in terms of constraints and degrees of freedom. The applied stress is a constraint. Without a path (degree of freedom) for stress relies (for example by strain) the materid will remain under that stress constraint for ever just as humans live under the " 1 Atm" pressure constraint for ever. Ignoring the contribution of surface interaction, the friction of polymers can be described by the sequence: perform volume work, produce heat, dissipate heat. If the process occurs in cycles and at the end of each cycle all intensive properties return to the values they had the previous cycle, the system has reached steady state friction. Next the thickness of the material is added as supplementary specification. At first sight this does not alter the reasoning based on the indicated sequence. Then an additional statement is made: the polymer specimens are attached to an aluminium plate with a hard glue. The entangled molecular chains are anchored at various points to the surface. This is a mechanical constraint for the free motion of the chains like crosslinking or vulcanization. The result will be less strain for the same stress, less volume work and smaller friction torque. But the chains have a limited space occupancy and the effect of the "wall" constraint decays until it becomes negligible. The connection with the thickness is obvious. The plate supporting the specimen can be considered a good "heat sink" and the glue, although a poor heat conducting material, too thin to affect the heat transfer. Now add the statement: The volume work is performed near the surface (like a hardness test), the surface temperature is high due to friction interaction and the heat produced by volume

work can be dissipated only through the metallic support. The heat transfer efficiency depends on the distance between heat source and heat sink. As long as the distance is short the system can develop a temperature gradient adequate for thermal steady state. If the distance exceeds a certain limit thermal steady state cannot be reached. The specimen thickness had become a thermal constraint. As a result the temperature, in the upper layer where volume work is performed, goes up arid the stressed polymer behaves as indicated by the adiabatic path in Fig. 7. Comments on surface Contribution. The interpretation of the results in terms of constraints and degrees of freedom for volume work is based on the assumption that the surface contribution to the friction torque is constant or not very sensitive to the same service variables, Load, Temperature, Velocity. In order to get a clearer picture, after the friction torque experiments the disks of Akulon were subjected to hardness measurements using the Durometer Hardness Tester (ASTM C 2240-85). An indenter produces its imprint at a specified speed and the hardness is read on a 0-100 scale The measurements were made inside the grooves (produced by the steel balls during friction) and outside the grooves, on the free surface of the disks . The depth of the groove is so small that the nominal thickness of the disks inside and outside the groove could be considered the same. The difference between the results for the same disk would indicate the effect of the changes produced by friction. There were no significant differences; as can be seen in Fig. 8, the same hardness values were found on the same disk, wherever they were measured. As regards hardness variation with disk thickness, it followed the friction torque variation: high for thin and thick disks, small for the intermediate range disks. Of interest is the fact that the change of hardness just above 1 mm thickness is very rapid showing an almost step-like decay of the mechanical constraint.

.

219

5.1 The mechanical constraint,

HARDNESS v s THICKNESS

"I-

*FLAT

79

0''

I

2

3

4

I

OPATH

5

6

7

8

9

THICKNESS,mm

Fig.8 Hardoess-vs.-Plate 7liickiiess iriside arid outside grove. Average and iiidiviuduai points

6. DISCUSSION In the particular case of metal sliding on Akulon (Nylon 6.6) plates glued on metallic supports: - The friction is not a monotonous function of thickness, showing a maximum in a narrow range, not less than about 1 mm and not more than about 3 mm. - In the same thickness range the material hardness is the lowest. The correlation between friction and hardness was expected according to the experimental results but was not necessarily evident. It follows that the thickness of plastic materials is a design detail which should not be neglected. - Although there is no experimental evidence to justify extension of the conclusions reached for Akulon to other plastic materials, there are good reasons to believe that the same functional interactions will control the behavior of all polymeric materials obeying the same thermodynamic relations. In the present paper it was assumed that the friction work involves a surface interaction independent of disk thickness, and a volume work subject to constraints, some of them controlled by the thickness of the polymeric material. Two such constraints were discussed:

- The attachment of polymer chains to the hard interface glue; this prevents them from yielding freely under the applied stress. The strain is completely prevented at the wall and gradually less away from the wall until the constraint ceases to operate at the depth reached by the volume work. The depth of THIS work can be calculated knowing the width of the groove created by friction and the radius of the sphere which has produced it. In the present case it is found that the depth of the groove does not exceed 0.2 mm. Therefore there is plenty of space available for volume work and the higher strength of the polymer is due to the decreased mobility of the entangled chains anchored to the wall. Next it is the case to ask if there is a property related to the friction behavior of thin polymeric materials. There are two aspects to consider: - the rate at which the wall effect decreases with the distance from the wall, and - how far in depth spreads the volume work. It is helpful at this stage to refer to the Poisson Coefficient. If its value is 0.5 all the mass is involved equally in the deformation process and all deformations occur at constant volume. As the Poisson Coefficient decreases the deformation involves smaller fractions of the loaded mass, local1 the stress and strain increase and the defyormation is accompanied by volume increase. For practical purposes The Poisson Coefficient of plastics can be considered equal to 0.4 [2]. n the present context a more precise scale is necessary. Then, materials with a high coefficient will perform more volume work than those at the bottom of the scale so that using this criterion it should be possible to anticipate the friction behavior of plastics. Also worth considering is the quality of the glue and/or support. It is reasonable to expect that the effect of such a mechanical constraint on friction will be observed only when the hardness of the glue is higher than the hardness of the polymeric material.

220

4.2 The thermal constraint - The heat flow out of the system. The surface temperature is high due to friction heating [2] so that the heat produced by volume work must flow out of the plastic material through the aluminium base. The rate at which heat flows out, according to Fig. 7, controls the rate at which lhe strain follows the application of stress. The heat flux varies with the distance, therefore the thickness acts as a thermal constraint; increasing the thickness at constant thermal conductivity has the same effect as reducing the thermal conductivity at constant thickness. Again, there is no reason why this conclusion would not be valid for other polymeric materials. One can go a step farther and conceive another thermal constraint: Preventing the base to act as heat sink. This can be done in various ways according to the desired effect. - A thicker, thermally isolating, glue layer should decrease friction (in the present experiments the glue thickness was 2-3 pm). - In the same direction should act a poor thermally conducting base material or a small mass (thickness) heat sink. - Isolating or deliberately heating the support material should create the same thermal constraint. By reverse actions one could reduce the thermal constraint, increase volume work and energy dissipation, effects which would be of interest in damping problems. In this spirit it is the case to look once again at the effects of the friction variables on the torque. Fig. 3 displays the monotonous effect of load, in all cases as expected. Fig. 4 suggests that the thermal constraint operates in the case of both, thin and thick disks. The controlling variable is the heat flow rate. Observing that the main heat source is the volume work (Jq+) performed near the surface it follows that the temperature rise has two effects: it reduces the strain for a given stress and by this reduces the volume work; it rises the temperature of the heat sink reducing the temperature gradient and the heat flow rate (Jq-). Thermal steady

state can be expressed as Jq+/Jq-= 1 . Now the three thickness alternatives can be evaluated. Thin disks. As the temperature increases, Jq+ (the volume work) decreases. At the same time the temperature gradient decreases because it has less Jq+ to dissipate while the sink temperature rises (independent variable). A further rise of temperature and increase of polymer hardness ma follow. The overall result must be a smaier friction torque. 2-3 mm disks, In the absence of the mechanical constraint much more volume work is performed and a greater temperature gradient develops. Probably, up to '3 mm thickness the heat flow rate is sufficient to maintain Jq+ =Jq-. The externally controlled rise of temperature has only one effect: to rise equally the upper temperature of the gradient. Thick disks, Increasing the length of the path (disk thickness) for heat flow is the same as thermally isolating the material, more or less efficiently. A thermal constraint acts on the system; the temperature of the material rises at a rate which depends on the isolation efficiency and adiabatic conditions develop. Reference to Fig. 7 shows that this means less volume work and lower friction torque. The effect of velocity presented in Fig. 5 is significant in two respects; The amount of volume work (number of loading cycles per revolution) increases while friction heating increases the material strength to a certain extent so that the volume work per each cycle is reduced, independent of the cooling conditions. Beside, there is the surface contribution about which little is known. If hard plastic materials (in adiabatic conditions) behave (in this respect) like metals, the friction torque should decrease with increasing velocity. To conclude: Thin disks, The velocity effect should be small and go either way. At low temperature and small velocity increase the effect of more volume work cycles per unit time may exceed the effect of the diminished volume work per cycle. Then the friction torque will increase. As the velocity increases the magnitude of the effects may reverse and the friction torque will decrease, more so if

22 1

the surface contribution acts in the same direction. -2-3 mm disks, .Inthe absence of the thermal constraint the effect of volume work should prevail , more loading cycles per unit time increasing the friction torque accordingly. Thick disks, The thermal constraint is present. The stress/strain relationship shifts slowly to the adiabatic mode. Apparently there is more volume work per loading cycle than in the case of thin disks but another factor intervenes, the available time for stress relaxation between loading cycles. The time available for relaxation is -0.08 s at low velocity and only 0.02 s at high velocity. Assuming maximum material strength 1s reached and the maximum strain during each loading cycle is constant, the stress (relaxation) decreases as the velocity increases and so does the volume work per loading cycle. Therefore, the friction torque should not be too sensitive to the velocity. Although the paper discusses a very particular polymeric material, the reasoning refers to properties , thermodynamic interpretations, experimental conditions and assumptions similar to those adopted by other authors [2]. This justifies the hope that the conclusions reached for Akulon (Nylon 6.6) will prove valid for other alike materials.

7. SUMMARY AND CONCLUSIONS It was found that when metal balls slide on plates of Akulon (Nylon 6.6) glued on a etal support, the power dissipated by friction varies with the thickness of the plate: low for plates up to -1 mm or more than ‘3 mm thick and about twice as high in the intermediate thickness range. This behavior suggests that the effect is due to the volume work contribution to friction and if for some reasons the strength of the polymeric material is higher, less volume work is performed and the friction is lower. Therrniodynamic considerations show that there are two constraints controlling the volume work. For thin plates the constraint is mechanical, the hard glue preventing the polymer chains from moving freely under

the applied load. For the thick plates the constraint is thermal, it prevents rapid heat flow out of the system allowing the temperature to rise, the strength of the polymer to increase and the volume work to decrease. It is expected that the conclusions presented in this paper can be extended to other applications and to other polymeric materials.

REFERENCES 1. Lancaster J.K., Friction and Wear, Polymer Science, A.D. Jenkins (ed.) North-Holland Publishing Comp. ,( 1972) 959-1046 2. Tanaka K.,Kinetic Friction and Dynamic Elastic Contact Behaviour of Polymers, Wear, Elsevier, Lausanne, 100 (1984) 243-262 3 diBenedetto A.T., The Structure and Properties of Materials, McGrow-Hill Book Company, N.Y., International Students Edition, 1967 4 Jastrzebski Z.D., The Nature and Properties of Engineering Materials, J.Wiley & Sons, New York, N.Y.,1976

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Dissipative Processes in l'ribology / I). Dowson et al. (Editors) 0 1994 Glsevier Science B.V. All rights reserved.

223

Interface friction and energy dissipation in soft solid processing operations

M. J. Adamsa, B. J. Briscoe and S. K. Sinha Department of Chemical Engineering and Chemical Technology Imperial College, London SW7 2BY, U.K. a Visiting Lecturer from Unilever Research, Port Sunlight, Bebington, L63 3JW, U.K.

The paper considers the interactive influences of the bulk rheology and interface friction boundary condition of plastic solids where they are deformed by rigid walls. Various experimental data and analyses are presented which indicates that the wall friction has a pronounced influence upon the nature of the flow induced in the soft solid and as a consequence greatly controls the extent of the energy dissipated during the deformation process. 1.1 INTRODUCTORY REMARKS available commercially and is marketed with the Soft solids constitute an important generic class of materials in so far as many manufacturing operations use materials of this type of rheological fom as part of routine manufacturing operations. These systems are diverse in types and include hot metals, ceramic pastes and food doughs as well as a variety of polymeric composites. Since these materials do not flow appreciably under gravitational forces they must be deformed by the action of solid walls which are nominally rigid. The commonalty is in the form of the rhological response with which these materials are endowed. They are soft, and thus readily deform, plastically deforming solids which have the intrinsic capacity to flow in a coherent way and retain their external form after processing. This paper is concerned with a description of the stresses which are at the plastic solid/rigid wall interfaces and the influence of these stresses upon the energy dissipation and the consequentflow of the deforming solid. 'Ibe main focus is upon the role of the interface friction (the boundary condition) upon bulk flow behaviour which will define the overall energy dissipation during the deformation. The studies to be described here used a model paste system which is constructed with a mixture of clay particles dispersed in a hydrocarbon liquid. The material is readily

trade name "Plasticine". It emulates all of the known bulk and interfacial rheological properties ' soft solid materials at relatively of low temperatures; these materials are often described as pastes. ' h e paper briefly reviews the accepted and aspired for methods of describing these two rheological characteristics. Several experimental methods for obtaining the interfacial and rheological characteristics of these paste systems are described. There are two generic groups. One in which the boundary friction arrests flow. Examples are provided for cylindrical upsetting or squeeze film deformation, ring compression and wedge indentation hardness. The other is where the interface traction is responsible for actually inducing the flow. The example chosen here is for the twin roll configuration. Data are provided for each example and a range of analyses, of various degrees of sophistication,are applied. These results provide first order estimates of the intrinsic rheology of the paste and the prevailing boundary conditions. These data serve to illustrate the pronounced influence of the interface friction, between the paste and the wall, upon the work required to institute flow in these systems. For example, a madest reduction in the wall fiiction leak to a matked reduction in energy dissipated during the deformation process.

224

1.2 Boundary Conditions The viscoplastic deformation or flow of solid materials invariably involves interactions at the interface or the boundary between the material and the processing equipment walls. 'he nature of the boundary is important in the paste processing context because of the fact that the material flow response is extremely dependent upon the interface frictional characteristics. Conversely, the interpretation of most experimental data is not generally viable, to any degree of accuracy, without some knowledge of the interface rheology. The interface characteristics determine the mechanical and thermal energy dissipations across the boundary between the paste and the equipment. It thus actually plays an important role in material processing operations in terms of the optimisation and the efficiency. These effects arise, in the main, because, during paste deformation the interfacial resistance induces inhomogeneity in the flow of the bulk. The flow inhomogeneity produces complex displacement, stress and strain rate fields in the bulk of the deforming paste material. Hence, the reaction or pmcming forces involved during deformationare also greatly influenced by the inhomogeneous flow conditions.

Figure 1: Grid distortion (quarter symmetry) at 6Wo compression of a cylinder with an initial aspect ratio (diameterheight) = 1 and boundary friction p = 0.4. The figure shows the displucement vectorfields of an initial square grid afer compression, and the inhomogeneitiessuch as rigidzone development, shear bandsfoMation geometric barrelling and 'Ifokiing which arise during compression. When the friction is zero a rectangular grid is developed I'

Wall Boundary Conditions 2 , = mz,:O 5 m 5 1

H 2 , 2,

=W =pv

Coulombic

W

Mooney

Biilklev

Table 1: Examples of wall boundary conditions : m, friction factor: p, coeflcient of friction; j, slip coeflcient; v, wall slip velocity; a, wall pressure coeficient; q, wall velocity index and 7 ~ 0wall , yield

stress.

Figure 1 illustrates the flow field inhomogeneity in the bulk of a cylinder specimen undergoing uniaxial compression between parallel platens when the wall friction is finite. The flow field shown by the grid distortion was obtained using a finite element analysis [l]. Similar data may be obtained by flow visualisation. An accurate knowledge of the boundary conditions provides, in principle, a means to obtain a m e estimation of the bulk rheology. A number of boundary conditions have been proposed by various authors [2]. In metalforming, generally, two types of slip boundary conditions are considered. They are referred to as the Coulombic and the Tresca boundary conditions. These boundary conditions define the wall tractional stress as fractions of the normal pressure (Coulombic) or the bulk shear yield stress of the material (Tresca). In the field of fluid rheology, the wall stress has been generally related to the slip velocity or the shear rate at the wall. Table 1 lists the commonly accepted relationships for the wall boundary conditions [2].

225

1.3 Intrinsic Bulk Ftheology

Table 2 lists the commonly adopted constitutive relationships for ideal and engineering materials. The viscoplastic constitutive relationships, which have been used for highly concentrated particulate dispersions, exclude the elastic components as well as the strain hardening process. A real paste material will show elastoplasto-viscous behaviour. To overcome this problem Lipscomb and Denn [5] proposed a biviscosity model which assumes that paste materials show a higher viscosity prior to yielding. The other limitation of these existing constitutive relationships is that they can be implemented only for a two dimensional flow condition. This restricts their applicability to real flow problems, where flow occurs in three dimensions. These points will be discussed in detail in the l a m part of this paper.

The rheological response of paste materials has been, in general, described by a combination of a yield criterion and a postyielding constitutive relationship. 'Ibis choice is based on the fact that the material shows a definite yield point when acted upon by normal or shear stresses. Like ductile metals, pastes exhibit a arguably clear plastic yield phenomena. The Herschel - Bulkley constitutive relationship assumes that the material behaves as a rigid body in the pre-yielding regime and then as a power law fluid after yielding. Similarly, the Bingham model assumes Newtonian flow after yielding

WSI. 3hMLZ Constitutive relationships ~ = G Y

2. ANALYSES

TYPe Hookean solid

2.1 Yield Criterion L

The idea of a yield criterion for ductile solids, such as metals, is well established. It defines a critical combination of stresses at which elastic deformation terminates and plastic deformation is initiated. Certain fluids, such as concentrated suspensions, also exhibit a quite distinct yield phenomena. The most commonly used yield criterion for plastic fluids is the von Mises yield criterion which is defined by the following equality [7];

where 1/2 r* :r* is is the second invariant of the deviatoric stress tensor. 70 is the shear yield stress and r* is the deviatoric stress tensor.

Table 2 I&alised shear constitutive relationships for engineering materials. The parametrs are as follows: .r, stress; strain; ;J, strain rate: G, elastic modulus: 70, yield stress: q, viscosity: Q, plastic viscosity; k, flow consistency: k p plastic flow consistency: n, flow index: z, strain exponent; a, material constant: p, pressure and a,pressure coeflcient.

2.2 Cylinder Upsetting (Squeezefilm Test) The axial compression of a cylindrical specimen bas been studied both in plasticity and in fluid mechanics. In plasticity, the equilibrium stress analysis for the upsetting of rigid-plastic solids is commonly used [8]. Here, the wall boundary condition at the interface is characterised by the Coulombic coefficient of friction, p. The method assumes homogeneous

226

following result for the mean pressure for a plastic fluid between parallel platens as [91;

- 27,R

(a)

I I I

Ro

J++(

* + 6 + -

t

+

I

'=

--

+

where '50 is the shear yield stress of the material; for a von Mises material, the shear yield stress is given by CJo/ff. Equation (3) is not valid when 2R/h tends to zero as it predicts a zero yield stress of the material which is not physically realistic. A full stick wall boundary condition is assumed in this fluid mechanics analytical treatment of cylinder upsetting. However, this condition is not applicable when a highly concentrated paste material is deformed at high shear rates [lo]. Presently, there is no analytical solution available for the slip wall boundary condtion with limited traction.

(b)

.

(c)

I

deformion behviour o f a ring specimen under axial compression between parallel platens. (a) Original ring before compression: (b) ring afrer compression with low wall friction; (c) ring after compression with high wallfrictwn. The arrows show the direction 5 ofjlow of the material. e FIGURE 2:

5 E

(3)

3h

75 5o m

fa deformation. However, in actual practice the a 0 deformation, for the majority of the cases with $ tractional interfaces, is highly nonhomogeneous; E note figure 1. This leads to an overestimation of 2 the yield stress of the material as the measured g, $ -25 mean compressive pressure is greater than that 5 predicted using the classical solution based upon 6 homogeneous deformation. The solution for the critical deformation pressure in this case, -75 assuming homogeneous deformation, is given 0 by (see ref. 8);

3

-

(2)

where

is fhe mean reaction pressure, 60is the

uniaxial yield Of the material* is the radius and h is the height of the cylindrical specimen. This solution predicts that the mean D ~ ~ S S U Rwhen . extrapolated to a zero aspect ratio i2R/h), is non-zeroand equal to the-uniaxial yield stress of the material. Using the lubrication approximation, which is employed in the fluid mechanics treatment, Scott obtained the

1

I

25

50

75

Compressive Slraln Ok

FIGURE 3: The calculated change in the inner diameter of 6:3:2 (Ro:Ri:h, figure 2) ring specimen as a function of compressive strain at dgerent magnitude of wall jiction for Upper Bound solution with a Tresca wall boundary condition. (Tk curves represent results for (jgerent values of m; where is the piction factorWafter Avitzur [Ill)

2.3 Ring The conventional plasticity analysis for ring compression utilises the Upper Bound

227

theorem (Avitzur [ l l ] ) . This analysis incorporates the friction factor (m) as the boundary condition ('Tresca). The friction factor is given by T~ = m ro,where rw is the wall shear stress and again rois the shear yield stress of the material. Hence, the maximum value of m is unity when the wall shear stress is equal to the shear strength of the material. It is possible to correlate the friction factor, m to the Coulombic friction coefficient, p using Kudo's approach. The relationship between p and m is then given as [111;

When a ring specimen is compressed between two parallel platens the direction in which the material flows is solely determined by the interfacial friction condition ( as shown in the figure 2). For each interface friction condition there is a neutral radius; the location where the deforming ring material flows in opposite directions. The Upper Bound theorem relates the neutral radius Rn, with the outer radius, Ro, the inner radius Ri, and m by the following tXpMi0n;

(4)

Equation (4). in combination with the continuity equation, can be used to obtain a plot of the fractional change in the inner radius of a ring specimen against the height reduction for different values of the friction factor, m. This plot is also known as the "calibration curve". Figure 3 shows a calibration curve for ring compression.

Slipline Theory of Wedge Indentation 2.4

In the wedge indentation hardness experiment, tbe material is indentated with rigid wedges and the indentation pressure is measured as a function of the depth of the indentation. Slipline analyses of wedge indentation are available for the cases, with and without the interfacial friction between the rigid wedge face

and the deforming material. Figure 4 shows the penetrarion of a smooth rigid wedge into a semiinfinite mass of a rigid - perfectly plastic material so that the bisector of the wedge angle 2y is perpendicular to the plane surface of the medium.

FIGURE 4: Indentation of a semi-infinite rigid perfectly plastic material by a rigid wedge. w is the semi wedge angle and h is the depth of indentation. a and b are the orthogonal sliplines. p is the indentation bod. Using the continuity equation and the force equilibrium analysis, the indentation pressure pm may be related to the coefficient of friction, p, between the wedge face and the material and the deformation geometry (semi-included wedge angle w) as WI;

pm = JL= p w (I+ p cosy) 2a

(5)

where p is the indentation load per unit width of the wedge, mh, is the pressure at the wedge face and is given by

where rois the shear yield stress of the material.

v and X are related by the following equation;

228

Using equations (3, (6) and (7) it is possible to plot pm/270 against semi wedge angle for different coefficientsof Hction [12].

I

Ap

' I / ' : I

where R2 is the radius of the rolls, h ( = ( ho + hi )/2 ) is the mean sample thickness in the flow field and, a, is the projected linear contact length of a specimen with the rolls ( see Fig.5); hi and ho are the initial and final thicknesses of the sample respectively. The geometric factors in equation (9) define the mean imposed strain and, together with the roll velocity, also define the mean s W n rate. Numerically evaluated integral mean strain and strain rates are employed in practice (see ref. 13 ).

3. EXPERIMENTAL METHODS I I

FIGURE 5: Geometry of hvo roll milling. R2 is the roll radius and hi and ho are the initial and j i ~ thicknesses l of the sample respectively. P is the roll separating force per unit width of the

specimen.

2.5 Rolling In rolling, a hot metal rolling theory may

be applied which assumes a stick wall boundary condition. In this analysis, elements of material are assumed to undergo homogeneous plane strain compression: ( see fig, 5). That is, the mean vertical and horizontal stresses are taken as the principal stresses and, hence, are

interrelated by the following yield criterion;

where 3 is the mean uniaxial flow stress. A mean value description is employed since the stress will be a function of the strain and snain rate and these quantities will vary along the flow field. This model leads to the following expression for the total roll separating force per unit width, P [12]

3.1 Material The experiments were carried out on a model paste material known as "Plasticine". This material is a dispersion of clay particle (Kaoline, A14Si4010(OH)g) in a liquid (hydrocarbon) medium (78% wt. solid particle). The "Plasticine" was homogenised in a z-blade mixer before making specimens. Cylindrical and ring specimens of specified dimensions were prepared by mould cutters from slabs of material. These slabs were prepared using an Instron universal testing machine (model 1122). In order to facilitate removal of the sheets from the die, waxed paper inserts were used. For the rolling and wedge indentation experiments, slabs of accurately defined geometries were used. The specimens were themally equilibrated for at least 2 hours at 21 OC prior to the measurements. The interface traction was changed by introducing lubricants between the model paste and the steel surface of the platens. Talcum powder (MggSig020(0H)4) and a proprietary silicone grease were used as lubricants. The unequivocal stick boundary condition was achieved by utilising emery paper as the interface.

3.2 Experimental procedure

3.2.1

Cylinder Upsetting

Cylinder specimens of 80 mm diameter and 15 m m height were prepared. The cylinders were compressed between two over-hanging parallel steel platens. Experiments were carried

229

out under lubricated and unlubricated interface conditions. The mean compressive stresses as functions of aspect ratio and the natural strain were recorded. In addition, pressure distributions using unlubricated platens were measured for a number of strains. The experimental procedure involved the use of a local pressure transducer mounted in the lower platen [2].

3.2.2

Ring Compression

Specimens with an initial ring geometry of 63:2 (external radius : inner radius : height) and height of 10 mm were prepared. These samples were compressed between parallel platens at nominal strain rates of 0.1 and 0.4 s-l and the inner diamem were measured fora range of imposed compression strains. This was achieved by containing the specimens between "acetate" (poly (ethyleneterephthalate)) sheets which could be peeled away after each increment of strain. Measurements were made for both the unlubricated and the lubricated interface conditions.

3.2.3

Rolling

"Plasticine" slabs of width 80 mm, length 70 mm and thickness 7 mm were used to feed a two roll mill which had 78 mm diameter rolls, a roll speed range of 0.5 - 150 rpm and a minimum gap of 7 mm. Transducers were fitted to the roll bearings in order to measure the roll separation force which is tenned subsequently the "rollforce".

3.2.4 Wedge Indentation Wedge indentation tests were performed on thick "Plasticine" slabs and the ratio of the width of the sample to the indentation depth was kept more than 15. This was done to ensure that the condition of almost plane strain deformation was present during the wedge indentation. Stainless steel wedges of included angles 30°, 60°, 90°, 120° and 150° and of widths 180 mm were used for the indentation experiments. The wedges were driven into the samples to a fixed indentation depth of 6 mm. The indentation loads were recorded during the indentation process. Finally, the samples were removed from the wedges and the actual area of the contact was measured by

observing the residue impressions of the "Plasticine" on wedge faces; "Plasticine" naturally transfers a film of oil and particulate material to contacting surfaces. The indentation pressure was recorded against wedge included angles. For the "hot wedge test", the wedges were heated using heating caruidges. The wedge indentation experiments were carried out on an Instron universal testing machine.

4 RESULTS AND PRELIMINARY DISCUSSION 4.1 Traction Arrested Flows 4.1.1

Cylinder Upsetting

Figure 6 shows the uniaxial compressive stress against the natural strain for lubricated and unlubricated interface conditions. Obviously, the flow stresses obtained under perfectly lubricated conditions should correspond to the yield stress of the material provided that the wall traction is zero. A stick condition at the interface (i.e. emery paper, p=0.577) gives the highest apparent flow stress whereas, the recorded flow stress is the lowest for the lubricated case. Data for the lubricated interface show only slight strain dependence of the flow stress.

0.3

02

0.1

0.0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

FIGURE 6: Mean compressive stress as a function of the natural strain in cylinder upsetting of "Plasticine The interfaces employed are; a, emery paper (400); b, polished steel surface; c, talcum powder; d, silicone grease. 'I.

230

Figure 7 shows the measured local n o d pressure distribution against the position from the centre for cylinder upsetting recorded using small (2 mm diameter pin) normal stress transducers. This figure shows the variations in the lccal normal pressure at the wall for different 0 strains. The edge pressure is equal to the yield lf3 stress which is about 0.13 MPa for this case CE c-r [14]. This result is consistent with those 5 obtained in the tensile measurements [15]. Figure 8 shows the deconvoluted coefficient of 2 friction from these upseaing data obtained using 8 equation (2); assuming homogeneous deformation. The cylinder upsetting experiment, which is a case of the traction arrested flow condition, shows that the interface boundary conditions influence the material flow characteristics. A lubricated or frictionless boundary induces a relatively homogeneous deformation which is basically an extensional flow. Finite traction at the interface produces inhomogeneity and complex flow field. Hence, a large amount of redundant work is done at the boundary as frictional work and also extra energy is needed for the generation of the inhomogeneousdeformation of the bulk.

1.o

Unlubricrted

.s " 0.0

I

0.0

0.2

.

I

0.4

.

I

0.6

.

'

0.8

.

1 -r/n

FIGURE 7: Wall pressure distribution as a function of position during unlubricated upsetting of '~Plasticine"at strain rate of0.1 s-1 for the following uniaxial strains; JC 0.6,, b 0.47, o 0.33, 0 0.22, 0 0.066. a is the current contact radius of the cylinder and r is the radial positionsfrom the centre of the cylider.

1 .o

0.4

0.6

0.8

1.0

Compressive Natural Strain FIGURE 8: Experimentally obtained coefficients offriction against the natural strain during upsetting of a "Plasticine" cylinder for lubricated and unlubricated interfaces. p is &convolutedfrom using equation (2).

4.1.2

0.0

0.2

Ring Compression

Figure 9 shows the measured and theoretical values of the fractional change in the internal radius against the fraction compressive strain. This figure gives a good initial estimate of the prevailing interface friction. For the silicone grease lubricated case, the interface friction factor, m is of the order of 0.04. For talcum powder interface the friction coefficient is around 0.6 and the unlubricated case gives the value m of around unity i.e. the stick condition. For the finite friction cases, it is seen that the friction coefficient starts to reduce at beyond around 30% of strain. This indicates a change in the boundary condition from Tresca to a more complex case. The ring compression test provides an excellent example of a friction retarded flow process. A change in the interface condition can induce an entirely different flow field. As is shown in the figure 9, the change in the internal radius is dependent only upon the friction conditions at the interface between the platen and the material.

23 1

condition upon the material flow characteristics and the overall response of the material.

\ I

1

0

.

1

.

20

1

40

'

1

60

'

1

'

80

100

1

% Height Reduction

frictionless

0.0

FIGURE 9: % decrease in internal radius as a function of % decrease in height during ring (initial geometry 6:3:2) compression for "plasticine",Interfaces are emerypaper, o talcum powder and x silicone grease.

4.1.3

Wedge Indentation

The "hot wedge indentation" experiments were carried out to investigate the effect of interface temperatures on the boundary condition and the bulk flow characteristics. Hot wedges also provide a suitable means of generating the desired amount of slip at the interface, which is, often, a problem in many cases using external lubricants. Many effective lubricants induce plasticisation in pastes of this type. Figure 10 shows the effect of interface temperatures on the pmnq, characteristicsof the material against the wedge semi included angle. The value of T~ was taken as 0.08 MPa. which was obtained from the cylinder upsetting results using the von Mises yield criterion. It is observed, from this figure, that the main influence of the interface temperature is to reduce the wall traction which leads to a lubrication effect. The contact times are relatively short in these experiments; ca 7 s. Although the heat transfer characteristics have not been studied in detail we may reasonably assume that a relatively thin "hot" lubricating region is produced at the paste surface. The "hot wedge" experiment provides a simple means of investigating the effect of the interface boundary

20 40 60 80 SEMIWEDGEANGLE degree FIGURE 10: P d 2 T~ us a function of the 0

semi wedge angle in hot wedge indentation of "Plasticine". The bulk "Plasticine temperature was kept at 21 0C.The intelface temperatures are in OC; Z 40, o 50, o 60, b 70, 80.

4.2 Traction Induced Flow 4.2.1

Rolling

The mean flow stresses calculated from the roll forces using equation (13) are plotted as a function of the mean natural strain in figure 11. Each data set was obtained at different mean strain rates [15]. The tensile data, at corresponding strain rates are also displayed, for strains upto 0.1. These data points clearly show dependence of the flow stress Dpon strain and strain rate. A common practice in metal plasticity is to use a relationship of the form;

a .B

G,=BE

E

where uo is the uniaxial yield stress, & and & are the mean extensional strain and strain rate respectively and, B, a and p are material parameters. The figure also shows data from uniaxial tension experiments. The best fit of

232

equation (10) to the rolling data produces B, a and p as 0.69 MPa, 0.26 and 0.21 respectively. It is interesting to note that the material is almost equally sensitive to the imposed strains and strain rates; in this respect it shows combined "solid" and "liquid" behaviom.

0.0

0.2

0.4

0.6

0.8

1.0

MEAN STRAIN

1.2

dissipated in other deformation geometries. Improvements in experimentation and analytical methods will progressively provide better approximations. The central difficulty is that the wall friciton is responsible for the creation of highly inhomogeneous flow fields within the soft solid and these conditions are not readily pred~cted,UIany degree of accuracy, by ftrst order analytical methods. Hence, the external reaction forces and energy dissipation can not be predicted even if the necessary bulk and interface rheological data are known to a high degree of precision. Naturally the converse situation also applies; knowing the energy dissipation in a given situation does not readily provide a means for an accurate description of the bulk and interface characteristics. These comments apart, the present data and the supplementary analyses serve to emphasise the critical influence of wall friction on the energy dissipation involved during the deformation of soft solid materials.

6. FINAL REMARKS FIGURE 11: ElongatioMl stress as ofunction of mean natural strain for "Plasticine"comparing the rolling and fensile results. (Solid lines show the tensile &a and the dotted lines are calculated using equation (10)for the roll mill data) The mean strain rates in rolling are; 1.0; x 0.5; o 0.1; A 0.05.

5. CONCLUDING DISCUSSIONS A variety of experimental data, derived from several types of experiments, have been described which demonstrate the way in which the interface friction, between a soft solid and a rigid wall, influences the energy dissipation when flow is induced in the soft solid by the action of forces imposed by a rigid wall. The scientific challenge is to uniquely abstract, from a given experiment, the constitutive relationships which accurately prescribe the boundary friction conditions as well as the intrinsic rheology of the soft solid. The methods for achieving this result, offered in this paper, must be regarded as only satisfactory approximations in so far as they provide useful data for the numerical simulation of the energy

Interface friction has a profound influence upon the flow behaviour of soft plastic solids when they are deformed by rigid counterfaces. Modest changes in the wall friction lead to large changes in the energy dissipated by the system. The behaviour of these systems is not accurately described by the available fvst order analytical treatments although a number of experimental configurations and the associated first order models do provide an indication of the extent of the influence of boundary friction upon the magnitude of energy dissipation during plastic flow.

ACKNOWLEDGEMENTS The authors wish to acknowledge the financial and organisational support provided by the MAFFDTI LINK Scheme for the project on "The optimisation of' soft solid processing operations".

List of notations TO = shear yield stress of

the deforming m a t e d -T* = deviotoric stress tensor p = mean compressive pressure in upsetting and ring compressions.

233

00 = uniaxial yield stress h = thickness of the cylinder specimen. R = radius of the cylinder. p = Coulombic coefficient of friction m = friction factor zw = wall shear stress Ri = inner radius of ring = outer radius of ring Rn = neutral radius pm = mean indentation pressure in wedge indentation. pw = wall pressure at the wedge face. 2y = included wedge angle P = roll separating force per unit width of the - specimen h = mean sample thickness in rolling.

REFERENCES

5. S.D.Holdsworth, Trans. IChemE, Part C, Food and Bio product processes, vol. 71, (1993)139,

6. G.G.Lipscomb and M.M.Denn, J . N o n Newtonian Fluid Mech. 14(1984)337. 7. M.J.Adams, B.J.Briscoe and M.Kamyab, Adv. Colloid lnte$ Sci., 44(1993), 141. 8 . G.W.Rowe, Principles of Metal Working Process. Edward Arnold, London, 1977.

9. J.R.Scott; Trans. Inst. Rubber Ind. , 7(1931)169. 10. U.Yilmazer and D.M.Kalyon, 33(8)( 1989)1197.

J Rheo.,

11 B.Avitzur in "Metal forming: Processes and Analysis", Mc Graw - Hill Book Co. NY,(1968) 12. K.L.Johnson, in "Contact Mechanics", Cambridge University Press, Cambridge, 1985.

1. M.J.Adams, S.K.Biswas, B.J.Briscoe and S. Shamasundar, proc. The 1993 IChemE Research Event' IChemE, Rugby (1993)61.

13.J.Chakrabarty in "Theory of Plasticity", Mc Graw Hill Book Co.,NY (1987) p.582.

2. M.J.Adams, S.K.Biswas, B.J.Briscoe and M.Kamyab, Powder Tech., 65(1991)381.

14. M.J.Adams, B.Edmondson, D.G.Caughy and R.Yahya, J.Non Newtonian Fluid Mech. in press.

3. M.J.Adams and B.J.Briscoe, Trans. IChemE, Part C, Food and Bio product processes, in press.

15. M.J.Adams, S.K.Biswas, B.J.Briscoe and S.K.Sinha, Mat. Res. SOC.Symp. Proc., Material Research Society, (eds: L.J.Stuble, C.F.Zukoski and G.C.Maitland, Flow and Microstructure of dense suspensions) USA, 289 (1993)245.

4. R.Byron-Bird, G.C.Dai and B.J.Yarusso;

Reviews in Chemical Engineering, Vol.1, No. 1, (1983)l.

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Dissipative Proccsses in Tribology / D. Dowson et al. (Editors) 0 1994 Elsevier Science B.V. All rights rescrved.

235

The Effect of Interfacial Temperature on Friction and Wear of Thermoplastics in the Thermal Control &@me Francis E. Kennedy and Xuefeng Tian Thayer School of En 'neering Dartmouth Col ege Hanover, NH 03755, USA

P

ABSTRACT This paper describes an experimental study of the sliding behavior of two thermoplastic polymers, polymethylmethacrylate (PMMA) and ultra-high molecular weight polyethylene (UHMWPE),in oscillatory sliding contact. Sliding surface temperatures were measured with the aid of miniature thin film surface thermocouples, and the results were related t o friction and wear behavior. The temperature measurements were also correlated with predictions of a recently-developed surface temperature model for finite bodies in oscillatory sliding contact. The experimental results showed that the contact temperature rise is dominated by a steady state nominal temperature rise, upon which is superimposed a cyclic local temperature rise. When the sliding speed and normal load were high, the measured peak surface temperature reached a ceiling value for the thermoplastic materials. The critical temperatures for PMMA was the temperature at which it softened while under compressive stress, approximately 30-35°C below the melting temperature of the material, whereas UHMWPE's critical temperature was found t o be very close to its melting temperature. At the critical temperature, the wear rate drastically increased and there was a large increase in the real area of contact, but there was not a large change in friction coefficient. The increase in contact area caused a decrease in frictional heat flux, thus limiting the surface temperature rise. Owing t o the large changes in wear and contact area which occur at the critical surface temperature of thermoplastic polymers, conditions which would result in such temperatures must be avoided in sliding components using those materials. In-situ surface temperature sensors could help insure that the sliding temperatures don't reach the critical values. 1. INTRODUCTION

I t is well known that the dissipation of frictional energy results in an increase in the surface temperature of sliding bodies. In many cases those surface temperatures can, in turn, influence the friction that occurs a t the interface. This re 'me of tribological behavior has been ca led by Ettles the 'thermal control regime' 111. Thermal control of friction could be particularly important for materials that melt at a low temperature, such as ice and snow, and for materials such as thermoplastic polymers which soften at temperatures which can be attained on sliding surfaces. For those cases, it was postulated that the interfacial temperature

T

rise due to frictional heating could reach a limiting value which is related t o the melting or softenin temperature or the contacting materia s 121. Accordin t o Ettles' theory, since the temperature f m i t could not be exceeded, this resulted in a limit on the coefficient of friction in severe sliding conditions. As it was formulated, the thermal control theory had several limitations: 1)it was limited t o friction and said nothing about wear; 2) i t is difficult t o predict the actual contact temperature in sliding contacts, so the theory could not be used easily to predict when failure will occur. The objective of this work is t o extend the thermal control theory so that it can be used in predicting wear failure of thermoplastic components.

f

236

It has long been known that sliding surface temperatures have a strong influence on both friction and wear of thermoplastics [3]. The relationship between tem erature and friction or wear is not simple, owever but also depends on such parameters as siiding velocity, contact pressure, and the materials themselves [471. Lancaster and his co-workers found that the wear rate of many thermoplastics increases si nificantly when t h e temperature o f t e polymer surface exceeds a critical value 13, 81. They also found that p a r a m e t e r s which affect surface temperature, particularly sliding velocity, normal load, and ambient temperature, can all cause the surface temperature to reach the critical value [31. In fact, Lancaster showed that the 'PV limit', which is often used in the design of dry plastic bearings, is in reality a 'critical surface temperature limit'; the combination of pressure and velocity which causes severe wear of the polymer is that which causes the surface temperature to reach a critical temperature related t o the softening temperature of the material [81.

R

5

In most of the past research reports, the temperature of interest was either the ambient temperature or the local or "flash" temperature rise due to frictional heating. It has been found, however, t h a t the maximum surface temperature actually has three contributions: background temperature, local temperature rise and nominal surface temperature rise of the contacting materials [91. The background temperature is affected by ambient temperature and any temperature increases caused by the bearing support or housing, while the nominal temperature rise is a general change in the temperature of the entire contactin surface brought about by movement o the real area of contact. The local temperature rise occurs within the real area of contact and is due to frictional heat generated there.

P

Man models have been created to determine t e total contact temperature ratter rise in sliding contacts [8-101, but all such models require knowledge of friction force and the dimensions of the real contact spots. Since such information is not generally known a priori, the models cannot be easily used in a design situation

K

when polymer components a r e to be designed against tribological failure. An alternative approach is proposed in this paper. 2. METHODOLOGY

A combination of experimental and analytical methods was used in this work. 2.1 Experimental Study The objective of the experimental study was to measure the actual sliding contact temperature for several different thermoplastic materials in contact with ceramic and metallic counterfaces, and t o relate the peak contact temperature to the measured friction a n d wear of the polymers. Oscillatory sliding tests were carried out using a test apparatus which had been used in earlier studies of polymer wear [71. The tester has stationary polymer pins in contact with a n oscillatin flat specimen. In this work, the flat-ende pins had 2 mm x 4 mm cross-section (4 mm direction in the sliding direction). The oscillation amplitude was 4 mm and the fre uency ran ed from 0 to 20 Hz.Normal loa s ranging rom 9.8 to 52.4 N were used in the study. The specimen holders for both pin and flat s ecimens were fitted with thermoelectric eaters which enabled their background (or bulk) temperature to be controlled at temperatures ranging from 15OC below room temperature t o 50°C above room temperature. All tests were run in air.

8

a

7

R

To enable contact temperature to be measured, thin film thermocouples (TFTC) were fabricated on the contact surface of the flat specimens. TFTC are extremely small temperature sensors which are deposited on the surface of a sliding component a n d enable t h e accurate determination of actual sliding surface temperatures without requiring any further modification of the sliding components [ l l l . The structure and fabrication procedures of the thin film thermocouples are described elsewhere [lll. For this work, nickel-copper TFTC were used and they generally were about 0.5 pm thick with a measuring junction about 100 pm square. To protect the TFTC from damage, a thin (0.2 pm thick) layer of A1203 was deposited over

237

the thermocouples. The measuring junctions were located at the center of the nominal contact area between pin and flat when the test system was at rest.

developed model [91. The model assumes that total contact temperature is composed of three contributions, as in the following equation:

During a test, a chosen normal force was applied to the top of the polymer pin, background temperatures were set to their desired values, and the flat specimen was set in motion at the chosen oscillatory frequency. The friction force was measured by a piezolectric force transducer and the linear wear of the pin specimen w a s monitored using a displacement transducer (LVDT). Contact temperature, friction force, and linear wear were all monitored continuously with the aid of a computerized data acquisition system a n d a chart recorder.

TtOtal= ATlocal+ ATnominal+ Tbackground

2.2 Materials

Two quite different thermoplastic polymers were tested in the work reported here. One was polymethyl methacrylate (PMMA), an amorphous polymer with a glass transition temperature of about 105°C. A cast grade of PMMA without impact modifiers was used in this study. With the aid of a differential scanning calorimeter (DSC), the meltin point of the PMMA material was found to e 195-203OC. The second material was ultra-high molecular weight polyethylene, a linear, semi-crystalline polymer with a molecular weight ranging between 3 and 4 million. Its melting temperature range was measured to be 138-141OC.

%

For most tests the counterface was a flat glass slide, but stainless steel (304 SS) were used in some tests. The sliding surface of the stainless steel specimens was coated with a thin (approximately 2 - 5 pm thick) dielectric layer of Al2O3 to insulate the surface thermocouples from the stainless steel s u b s t r a t e . Thin film Ni-Cu thermocouples were deposited on the slidin surfaces of glass and stainless stee specimens for surface temperature measurement, as described above.

7

2.3 Analytical Study To accompany the experimental study, analytical predictions of surface temperature were made using a recently-

(1)

a

The back round temperature is assumed to be nown, while the nominal and local (or flash) temperature rises can be calculated as long as contact area, specimen eometry, velocity, and friction force are fnown, as are the thermal properties of the contacting materials. Following t h e procedures developed in reference [91, the nominal t e m p e r a t u r e increase was determined in this work by assuming that a percentage of the frictional h e a t is distributed uniformly over the area on the flat specimen which is swept out by the oscillating pin. The remaining frictional h e a t was assumed t o be uniformly distributed over the nominal contact area of the pin. Steady-state h e a t conduction solutions were used to find ATnominal for both flat and pin specimens. The maximum local temperature rise (ATl, ) was calculated using expressions for ?lash temperature described in a recent paper [121. Measured values of friction force and real contact area were used in the expressions, and the peak sliding velocity was used. The same heat partitioning coefficient was used in the expressions for both nominal and local temperature rise, and that coefficient was determined by setting the maximum total temperatures on the pin and flat s ecimens equal to each other (the Blok postu ate).

Y

3. RESULTS A typical plot of measured surface as a temperature rise ( ATl-1 + ATqominal) function of time during a test IS shown in Figure 1. The test in question had a UHMWPE pin in contact with an oscillating glass flat s ecimen. The measured friction coefficient uring the test was 0.14 and the background temperature was constant at 25OC. It can be seen that the temperature rise consists of a steady nominal temperature rise (ATnominal = 73.9'0 upon which a cyclic local temperature rise was added. The tem erature reached a peak twice during eac cycle, at the times when the absolute value of the sliding velocity

s

R

238

was at a maximum. The Deak measured surface temperature in this 'case was Tm 1 = 117.8"C (= 25" + 73.9" + 18.9'). T%is temperature is well below the melting temperature of UHMWPE a n d t h e measured wear rate in this case was rather low; the conclusion was that the sliding conditions were not severe enough to be in the thermal control regime.

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i

.

! .

:

:

!

:

C

i

;

;

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90.9 1 68.18

.

22.5

.

22.6

.

.

.

22.7

.

.

.

22.8

8

22.9

Seconds

Figure 1. Measured surface temperature in oscillatory slidin test of UHMWPE in against glass flat. scillation amplitu e = 4 mm, frequency = 10.8 Hz, normal load = 52.4 N.

B

8

To test the ability of the surface temperature model to determine the surface temperature, the measured value of friction coefficient was used, along with a post-test measurement of contact area. (The contact area was estimated by measuring the area of the wear scar on the pin surface.) Using those values, the following temperature rises were calculated:

= 71.4"C ATno,.,.,ina,

AT1i,

= 18.3"C

Using these values in equation (11, along with the known back ound temperature of = 114.7"C. 25"C, one gets a pre icted T, This value differs by less than 3% from the measured value. The heat artitionin factor was also calculated for t is case an it was found that over 94% of the generated frictional h e a t entered the flat glass specimen. This was due in large part to the low thermal conductivity of the polymer.

f

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that during the first second of testing the surface temperature rose steadily owing to a steady increase i n t h e nominal was rather large temperature rise. during the first few oscillations, due to the large oscillations, due t o the large friction coefficient of this material combination (approximately 0.5). After about 1 second, however, the local temperature rise became smaller, even as the nominal temperature continued t o rise. This led t o a total temperature which remained approximately constant at about 1625°C 25°C). Continued testin of the (Tbac PMl!@?$i under the same con itions showed t h a t t h e peak temperature remained relatively constant at a value near or just below the 162°C level. There was a very high wear rate of the polymer pin d u r i n g t h i s t e s t , along with considerable evidence of softening and deformation of the pin (to be described later).

i

A test of PMMA under conditions even less severe than those used in Figure 1 led to quite different results. Figure 2 shows the measured surface temperature rise during the first 3.5 seconds of a test of PMMA pin vs. glass flat. It can be seen

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Figure 2. Measured surface temperature during first 3.5 seconds of oscillatory sliding test of PMMA pin against glass flat. Oscillation amplitude = 4 mm, frequency = 8.0 Hz, normal load = 52.4 N. Tests of both PMMA and UHMWPE materials were run at a large number of operating conditions leading t o a wide r a n e of surface temperatures. The resu ting wear rates are shown in Figures 3 and 4 as a function of the measured total surface tem erature. The wear coefficient used in the igures is defined as the volume lost per unit sliding distance per unit normal load, and it has units of m2/N. I t is evident from the figures that both materials experienced relatively low wear until the peak surface temperature reached a critical value. For the PMMA material, as noted above, the critical temperature was about 162"C, whereas for the UHMWPE material the critical temperature was about 137°C.

7

P

2 39

The critical temperature for UHMWPE is approximately equal t o the melting temperature of that material. For PMMA, however, the critical temperature is about 30-35°Cbelow its melting temperature and is determined by the temperature at which the PMMA material softens while under compressive stress. It might also be noted that the wear coefficient of UHMWPE was much lower than that for PMMA, even in the severe wear regime at Tdtical.

* + + ++

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120

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Figure 4. Wear data for PMMA pins in oscillatory sliding against glass flats at different contact temperatures. The wear coefficient is defined as volume lost per unit jliding distance per unit normal load.

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0.060

1 .o

,

160

Ternprnture. "C

Figure 3.Wear data for UHMWPE pins in oscillatory sliding against glass flats at different contact temperatures. The wear coefficient is defined as volume lost er unit sliding distance per unit normal oad.

P

For many of the test points shown in Figures 3 and 4,the surface tem erature was varied by changin the bac ground temperature. It was Eund that small changes in background temperature had a great influence on wear rate when the total surface temperature was close t o the critical value. An example of this is shown in Fi re 5, which shows linear wear of a UH&PE pin a s the background temperature was varied and all other test conditions were held constant. In this case the total surface temperature reached Tcritical when the background temperature was about 51°C. If the temperature was just 3" below this value (the segment from a to b) the wear rate wasn't too severe. A 5°C rise in background temperature above that value, however, was sufficient to cause a transition t o very severe wear (segment from b to c). When the temperature was then dropped back down t o 50°C, the wear rate decreased back to the same value i t had at th a t tern erature at the beginning of the test. There ore, the increase in wear

R

f!

Time, hr

Figure 5. Wear rate as function of for UHMWPE pin in test against glass flat. Oscillation amplitude = 4 mm, fre uency = 11.3 Hz, normal load = 36.5 . = 50°C;a<>b, "background =
%

240

rate that occurs when the temperature reaches the critical temperature is not permanent, but can be brought down by dropping the surface temperature below the critical value.

Other tests demonstrated that the same chan es shown in Figure 5 could also be broug t about by variation of any of the test parameters which controlled surface temperature, This is shown in Figure 6a,in which the surface temperature was varied by changing either t h e background tem erature or the oscillation frequency ( s l i g n g speed). High wear occurred in segment from b t o c, in which t h e background temperature was high but the sliding velocity was moderate, and in the final segment, in which the background temperature was moderate but the sliding speed was high. In both cases the surface temperature was equal t o Tcritica, for the PMMA material.

5

Friction, N

Time. hr

Figure 6a. Wear rate as hnction of £ for PMMA pin in oscillatory ing test against glass flat. Oscillation amplitude = 4 mm, normal load = 9.8N. c, Tbsckground = 53"c,f = 9.3HZ;c o d , Tbackground = 48"C, f = 9.3 Hz; d<, Tbackground = 36"C, f = 12 HZ.

Time, hr

Figure 6b. Measured friction force as function of T @ground for PMMA pin in oscillatory s d m g test against glass flat. Same conditions as in Figure 6a.

24 1

8

While the wear test data of Figure 6a were being gathered, the friction force was measured and the data are shown in Figure 6b. It can be seen that the transition t o severe wear was not necessarily accompanied by a significant change in friction. In some cases (after d) the friction was lower than had been measured under less severe conditions, while in some other cases (e.g., from b to c) the friction was a bit higher in the thermal control regime (at o r above Tcritical). Examination of the pin surfaces showed that in some cases the contact area broadened considerably in the thermal control regime, and this led to enough of a decrease in heat flux to keep the temperature from exceeding T&tical.In other cases, for example after most of the softening and creep had already occurred, another transition into the thermal control re ime required a decrease in friction in or er for the heat flux to be lowered enou h t o keep the temperature from exceeding t e critical value. Therefore, the decrease in friction postulated by Ettles does not always occur when thermoplastic materials enter the thermally controlled sliding regime, although the surface temperature in any case is limited to the critical temperature value for the material.

%

f

Figure 7a. Worn surface of PMMA pin after sliding in thermal control regime. Oscillation amplitude = 4 mm, frequency = 4.0 Hz,normal load = 26.7 N.

4. DISCUSSION

It is evident from the results reported above that the wear behavior of the thermoplastic pins changed drastically when the surface temperature (Tbta) reached the critical value for the materia\. To see what was happening on the pin surface under that condition (the thermal control regime), the pin surfaces were examined using optical and scanning electron microscopy.

A typical surface of a PMMA pin which had encountered oscillator sliding at a surface temperature equa t o Tcritic1 is shown in Figures 7. The entire pin surface is shown in Figure 7a, with section a being Re 'on the re 'on which had been at Trritical. b in t f a t figure designates material wEch had extruded to the side of the pin owin to softening in region a. A h i g f e r magnification view of the central region is shown in Figure 7b, and it is seen that the softened region (a) has become smoother. A small crack (b) is noted in the material

v

Figure 7b. Enlarged view of area a of Figure 7a.

242

Figure 7c. Cross-section in sliding direction of pin shown in Figure 7a. which s e p a r a t e s the softened a n d unsoftened regions. That crack is seen more clearly in Figure 7c, which is a cross-section through the pol mer pin. Two slanted surface-originate cracks (a) are seen on either side of the softened section of the surface. The slidin surface of the pin is desi ated by point . From these f i res it can e concluded that considerable t ermal expansion and deformation had occurred in the central re 'on of the PMMA pin surface. This is even c earer in a high magnification ima e of the softened region of a PMMA sur ace after an sliding test (Figure 8). Some of the softened material had extruded above the glassy material adjacent to it. It is likely that the soft material would have been removed by wear in future passes over the hard counterface if it had continued to remain in contact.

K

%

i?

8"

ff

B

The surfaces of all thermoplastic pins which had not softened appeared rather rough, with wear grooves oriented in the sliding direction. On the other hand, those surfaces which had reached Tcrit.calwere relatively smooth and showed some evidence of having experienced large flows

Figure 8. Higher magnification view of worn surface of PMMA pin after sliding in thermal control regime. Oscillation amplitude = 4 mm, frequency = 4.0 Hz, normal load = 52.4 N. Friction force = 27.1 N. of material in the softened regions. An example of this is given in Figure 9, which shows the worn surface of a UHMWPE pin after a sliding test in the severe wear regime. Section a is quite smooth and has a liquid-like appearance, as if it had melted and resolidified. Section b still shows the wear tracks and evidently did not melt ors often significantly. Therefore, melting o r softening did not occur over the entire surface of the s ecimens in the thermal control regime, u t only within the real areas of contact. In general, the size of the real area of contact increased after running at the critical temperature owing t o spreading of the softened material.

E

When softenin occurred, substantial gross deformation o the surface material occurred. This resulted in the extrusion or spreading of the soft material, causing an enlargement of the real area of contact. In some cases, as in Figure 7a, there was extrusion of material to the sides of the pin. There was also extrusion of the material in the sliding direction, as is shown in Figure 10, which is a cross-sectional view of a UHMWPE pin along the sliding direction after a oscillatory test in which the critical

f

243

Fi re 10. Cross-section of UHMWPE pin a$-' ong sliding direction after test in the thermal control regime.

Fi re 9. Worn surface of UHMWPE pin afl-l ter sliding in thermal control regime. Oscillation amplitude = 4 mm, frequency = 9.4 Hz,normal load = 36.5 N. Friction force = 10.5 N. temperature was reached. The slidin surface is designated by a in Figure 10 an the sliding direction is vertical. Substantial visco-plastic deformation of the material resulted in the extruded lip.

%

It is apparent from the evidence presented above that si ificant surface damage and wear o$thermoplastic materials can occur if the sliding surface t e m p e r a t u r e reaches t h e critical temperature for the material. I t i s i m p o r t a n t t h a t such t e m p e r a t u r e excursions not occur in practice. The actual peak surface temperatures are dependent on the actual friction coefficient and the real area of contact during sliding, and those quantities are seldom known with any certainty, especially durin the design phase. One way t o overcome t is problem and avoid the thermal control regime for thermoplastic components during operation is the following:

a

1. When designing thermoplastic sliding components, use the best available information about friction coefficient, hardness, and sliding velocity t o predict real area of contact and frictional heat generation. Use this in surface temperature models of the type described in [91 and embodied in equation (1) to estimate the surface temperatures t h a t will be encountered in service. This step had been recommended by Floquet, et a1 [131, among others.

Determine the critical surface temperature for the polymers being used in the sliding com onents. In many cases, such as for UHhWPE under reasonable contact pressures, the critical temperature can be approximated by the meltin temperature, whereas for some others, SUC as PMMA, it might be a lower softening temperature [31. In cases with very high contact pressures, the critical temperature of the thermoplastic material could be even lower than t h e melting o r softenin t e m p e r a t u r e [141, so t h e critica temperature should be measured for simulated operational contact pressures. 2.

a f

244

Use in-situ temperature sensors t o determine t h e actual surface temperatures in service. A thin film thermocouple would be a very appropriate sensor for such a measurement. The sensors could provide a warning when the critical temperature is approached, and can therefore enable failure to be avoided. This could be especially helpful when sliding conditions occur which are more severe than anticipated in the design stage. 3.

5. CONCLUSIONS

It was found that the wear rate of thermoplastics will increase drastically when the contacting surface of the material reaches a critical temperature which is related to its melting or softening temperature. This holds true whether the material is amor how, like PMMA, or semi-crystalline, li e UHMWPE.

K

Research under contract number N00014-905-1748. Dr. Peter Schmidt is the ONR contract monitor. REFERENCES 1. C.M.M. Ettles, ASME J. of Tribology, 108 (1986), 98. 2. C.M.M. Ettles, ASLE Transactions, 30 (19871, 149. 3. D.C. Evans and J.K. Lancaster, Treatise on Materials Science and Technology, 13 (1979),85 4. S.B. Ratner and V.P. Yartsev, Russian Engineering Journal, 54 (1974),45.

5. K. Tanaka and Y. Uchi ama, in Advances in Polymer Friction an Wear, L H. Lee (ed.), Plenum Press, New York, 1974, p. 499.

i

When operating conditions are such that the critical temperature is reached, changes occur in real area of contact and/or friction coefficient to keep the maximum surface temperature from exceeding the critical value.

6. H. Uetz, K. Richter and J. Wiedemeyer, Wear, 88 (19831, 103.

The sliding surface temperature can be predicted accurately as long as the actual friction coefficient and contact area are known. Both quantities may, however, change a s the critical temperature is approached (the thermal control regime). A t e m p e r a t u r e model which involves calculation of both the nominal and local surface temperature rises must be used to achieve accurate surface temperature predictions.

8.

An in-situ temperature sensor, such as the thin film thermocouple employed in this study, is the best way t o accurately determine a c t u a l sliding surface temperature during operation. Such a sensor could be used to warn of impending surface f a i l u r e of t h e r mo l a s t i c components, and would aid in avoic rance of the thermal control regime.

ACKNOWLEDGMENT The work re orted here was supported by the U.8. Ofice of Naval

7. F.E. Kennedy, S.C. Cullen and J.M. Leroy, ASME J of Tribology, 111 (1989), 63.8. Lancaster, J . K , Tribology, 4 (1971),82.

Lancaster, J.K., Tribol,ogy, 4 (1971), 82.

9 X. Tian and F.E. Kennedy, ASME J. of Tribology, 115 (1993), 411. 10 R.S. Cowan and W.O. Winer, in Friction, Lubrication and Wear Technolo ASM Handbook, v. 18, P.J. Blau (ed), Int'l., Cleveland, 1992, p. 39.

&

11 X. Tian and F.E. Kennedy, Tribology Transactions, 35 (19921,491. 12. X. Tian and F.E. Kennedy, ASME Paper No. 93-Trib-26, ASME J. of Tribology, in press. 13. A. Floquet, D. Play, and M. Godet, ASME J. of Lubrication Technology, 99 (19771,277. 14. Watanabe, M. andYamaychi, H., Proc. JSLE Intl. Tribology Conf., Tokyo, Elsevier, 1985, p. 483.

SESSION VI FRICTION IN SPECIFIC APPLICATIONS Chairman:

Professor B J Briscoe

Paper VI (i)

The Relation Between Friction and Creep Deformation in Articular Cartilage.

Paper VI (ii)

Characteristics of Friction in Small Contact Surface.

Paper VI (iii)

Sliding Friction in Porous and non-Porous Elastic Layers: The Effect of Translation of the Contact Zone over the Porous Material.

Paper VI (iv)

The Effect of Additive of Silane Coupling Agent to Water for the Lubrication of Ceramics.

Paper VI (v)

The Origin of Super-low Friction Coefficient of M,S2 Coatings in Various Environments.

This Page Intentionally Left Blank

Dissipalive I'roccsscs in 'l'ribology / I). 1)owson cl al. (Iidilors) 0 1994 Elscvicr Scicncc U.V. All rights rescrvcd.

247

The relation between friction and creep deformation in articular cartilage K. Ikeuchi, M. Oka and S. Kubo Research Center for Biomedical Engineering, Kyoto University, 53 Kawahara-cho, Shogoin, Sakyo-ku, Kyoto 606-01, Japan This paper presents the experimental results of compression and sliding tests and discusses the relationship between the lubrication conditions and deformation of the cartilage in a synovial joint. The compression test simulating fluid lubrication conditions resulted in no cartilage deformation. Creep deformation was detected only in the test which simulated direct contact conditions. Friction and deformation were measured with a thrust collar apparatus. It was found that water, which exudes from the cartilage under direct contact, lubricates and suppresses the increase in friction. It was also determined that, as the creep deformation accompanying water exudation is related to the contact pressure, the deformation rate of the cartilage is a good index of the lubrication condition. 1. INTRODUCTION As articular cartilage is very compliant, joint lubrication depends on its elastic deformation as described by soft elasto-hydrodynamic lubrication (soft-EHL) theory [l-71. It is also believed, vice versa, that deformation of the cartilage is effected by lubrication conditions. In several previous compression tests, porous indenters [8-101 were used to minimize the squeeze film effect. Non-porous indenters [ l 1131 were also used to simulate the lubrication condition with squeeze film effect. However, no experimental verification of the dependence of the deformation on lubrication has yet been reported. Therefore, compression tests were performed which simulated fluid film and direct contact conditions under identical pressure distributions and the results were compared. The experimental results confirm the prediction [14] that creep deformation of cartilage is independent of fluid pressure and that only direct contact causes creep deformation. In a synovial joint, the conditions are close to fluid film lubrication, however slight contact is inevitable [I, 15-17], because the opposing cartilage surfaces do not conform perfectly and loading of the joint is not systematic. This situation [l, 181 is appropriately called adaptive multi-mode lubrication. When direct contact occurs, fluid weeps from the cartilage [8-10, 19, 201. This exudation causes creep deformation and the exuded water contributes to maintain a low coefficient of friction.

As the coefficient of friction is the most general index of the lubrication conditions, we measured the deformation and coefficient of friction experimentally using a thrust collar apparatus for cartilage-cartilage and cartilageartificial material combinations. The experimental results for the time dependent changes in the lubrication conditions will be presented and discussed.

2.DEFORMATION UNDER SIMULATED LUBRICATION CONDITIONS 2.1. Materials and methods Figure 1 shows a schematic of the experimental setup used to simulate fluid film lubrication conditions. The specimen (14 mm square and 5 mm thick) was cut from a porcine femoral condyle, which had been stored at -20°C. The thickness of the cartilage was approximately 1 mm. It was then glued to the base. The upper part of the apparatus has a 2 mm inside diameter hole to supply pressurized fluid, a cavity of 10 mm diameter to hold the fluid and a transparent window of polymethylmethacrylate (PMMA) resin. A laser beam displacement pickup with a charge-coupled device (CCD)line sensor was used to measure the surface deflection through the window. As cartilage is translucent, not only the surface but also the interior reflects the beam and results in a large error. To accurately detect the surface, a steel marker (2 mm square

248

and 20 p m thick) was attached to the cartilage surface as the laser beam target. The upper part of the apparatus was bolted to the base. After the cavity was filled with ambient pressure saline, the system was left for 30 minutes to attain an equilibrium condition in the deformation. Then, the saline in the cavity was pressurized suddenly to 0.4 MPa by air from a tank. The cartilage surface was thus pressed only by saline without any direct contact. Another apparatus (Fig. 2) was used to simulate direct contact conditions. The cartilage surface was covered with nylon and a low density polyethylene film, the latter to seal the air in the cavity. The laser beam target was attached to the polyethylene film. The film was pressurized to 0.1 MPa, 0.2 MPa and 0.4 MPa with air. The experimental method was identical to the previous case except for the method of I compression. Laser displacement sensor

2.2. Results No deformation was detected when the cartilage was pressured with saline. As the detectable limit of the displacement sensor was lpm, the deformation was estimated to be less than this value. The reasons may be: (1) Cartilage is incompressible [21]. (2) As the cartilage is thin and attached firmly to the subchondral bone plate, the tangential displacement is restricted. (3) As the elastic modulus of the subchondral bone is high, deformation of the bone was also less than the detection limit. This result confirms that substantially no creep deformation occurs when full fluid lubrication conditions are maintained. Elastic deformation may arise in a well-lubricated joint. Hence, elasto-hydrodynamic lubrication effect is predominant in diarthrodial joints. Figure 3 shows that creep deformation occurs in cartilage in relation to the contact pressure. The deformation rates, which were high just after the beginning of compression, gradually decreased. The results for a rubber specimen (thickness: 3 mm, elastic modulus: 11 MPa) are also shown for comparison. The deformation of the rubber over the first three seconds was mainly due to squeezing of saline from the nylon cloth. Thereafter, the deformation stopped because the permeability of the nylon cloth is high whereas the rubber is not porous. These results suggest that the deformation of the cartilage after the first three seconds are not elastic but rather due to creep.

Figure 1. Schematic of the experimental apparatus €or compression by a fluid. Laser be am

lylen Air

a!

P

.? "1

II)

a

!-I

a

8

0

I

I

I

I

20 40 60 T i m e after compression ( s )

V

Figure 2. Schematic of the experimental apparatus for compression by a solid.

Figure 3. Deformation due to solid contact.

249

3. DEFORMATION AND FRICTION UNDER SLIDING CONDITIONS

3.1. Materials and methods Figure 4 shows the thrust collar apparatus used in the sliding test. The lower shaft, supported by ball bearings, is driven by a variable speed motor. The upper shaft, supported by a slide-roll bearing, can move vertically and rotate with negligible friction. Load is applied with dead weights which are attached on the upper end of the shaft. Deformation of the specimen was measured at the end of the upper shaft with the laser beam displacement sensor. Tension transmitted by a thread wound around the shaft was measured with a leaf spring mounted with strain gauges. Frictional torque, which was proportional to tension, was calculated from the output of the strain gauges. The accuracy of the displacement transducer was 1 pm, and the error for the coefficient of friction due to the friction in the slide-roll bearing was estimated to be 0.002. The specimens, cut from a porcine femoral condyle, were immersed in saline during the sliding tests. In some tests, the upper specimen was replaced by a disc of artificial material. The shapes and the dimensions of the specimens are shown in Fig. 5 with the standard experimental conditions. Load Deformation

J2

In the next experiment, a 'wavy' disc of PMMA was used instead of a flat one. Figure 6 shows a circumferential cross sectional view of the disc at the mean radial position. Due to the 'waves' in the disc with rotation, the cartilage is exposed to alternating periods of direct contact and non-contact conditions. Though most of the applied load is hydrodynamically supported in a joint, the present study focuses on other supplementary lubrication mechanisms which support a small portion of the total load. For this reason, we used small specimens and applied low pressures to the cartilage.

Upper specimen -Articular cartilage Thicknss:lmm \ Bone

Specimen:Fomoral condyle of a Pig Inside diameter: 2 r i = 4 m Mean diameter: 2 r m = 3 . 2 5 m Velocity: u=30mm/s

Figure 5. Specimen geometry and experimental conditions.

-Tension (Friction) Specimens

/

Sub-chondral bone

c) Rot at ion

Figure 4. Cross-sectional view of the thrust collar apparatus.

Figure 6.Cross sectional view of the wavy disc.

250

If contact pressure (p) and coefficient of friction @) are approximately uniform, the applied load (W) and frictional torque Q, respectively, are expressed as follows:

T=

2 23d 23a. ppdr = -(To 3

3

-r?)pp

continued to deform slowly. In this case, a cyclic load was applied to the cartilage and fluid exudation and absorption occurred alternately on the cartilage surface and hence equilibrium conditions were not reached. In addition, EHL due to the hydraulic wedge effect might contribute to maintain a low coefficient of friction.

(2) 0.6

0.3

Eliminating p from the above equations, the coefficient of friction is related to T and W as follows.

c

0

-4 4J

u

.4

!-

0.2

Deformation

w w 0

6

4J

0.2

0

w

coefficient of friction- 0.1 $

al

U .-i

Q

(3)

I

I

I

I

0

5

Where r m is the effective mean radius as defined by the following equation.

20

Figure 7. Deformation and coefficient of friction for the cartilage-flat disc combination.

(4)

3.2. Results Figure 7 shows the variation with time of the deformation and the coefficient of friction for cartilage-flat PMMA disc combination. At the onset of loading, friction was close to zero due to the squeeze film effect. Thereafter, the coefficient of friction increased and reached 0.28 after two hours. The deformation rate, which was initially high, decreased gradually, whereas the deformation stopped after one hour from the start of the experiment. From these results, it is probable that non-contacting conditions occurred only for a short term. Then, with contact, weeping took place and continued for one hour until the internal pressure gradient and the exuding rate approached zero. Thereafter, boundary lubrication by the absorbed layer occurred and continued for the next hour. The results for the wavy PMMA disc are presented in Figure 8 and show that the coefficient of friction, which was initially as high as 0.14, decreased and became less than 0.03 after 2 x lo4 s, consecutively the cartilage

10 15 Time ( s )

0.6

-E2

0.3

0.4

-4

w

4J

2 & 0

w

0

0.2

a, Q

0

0 5

10

15

w

Time ( s )

Figure 8. Deformation and coefficient of friction for the cartilage-wavy disc combination.

0

'8

20 X ~ O

25 1

4.DISCUSSION

Figure 9 shows the results for cartilage vs. porous metal. The porous metal was made of bronze balls 50pm in diameter. The coefficient of friction decreased continuously over 2 x lo4 s. However, the coefficient of friction and the rate of deformation were much higher than that for the cartilage-wavy disc combination. We believe that though a great deal of fluid weeps from the cartilage into the gap, it leaks through the porous metal immediately without generating any effective hydrodynamic pressure. Figure 10 shows the results for the cartilagecartilage combination. The coefficient of friction decreased form 0.028 to 0.016 in 60 s, and thereafter, was constant. Deformation continued for a long time. The initial decrease in friction was probably due to flattening of the surface, because flow exudation is more active at any raised point on the cartilage surface. Figure 11 compares the deformation under static and dynamic conditions. The deformation rate for the rotating case was about 64% of static case. If we assume that the deformation rate is proportional to the contact pressure, then in the rotating case approximately 36% of the applied load is supported hydrodynamically, while the remaining 64% is supported by contact pressure. This ratio is not probable in a human joint. A model analysis estimates that about 97% of the total load is supported by fluid pressure in a normal joint [17]. 0.3

0.6

It has been generally believed that cartilage behaves like an elastic solid under full fluid film lubrication, but experimental verification has not been reported previously.

+J

. u

-4

Li

0.2

w W

0 Q

c

0.1

.:

U

-rl

o 0.5

1.0

1.5

a

2.0 x10

w w

r

'8

Time ( s )

Figure 10. Deformation and coefficient of friction for the cartilage-cartilage combination.

e.

0

.4

Q U

E

.ri

u

Y

g

0.2

0.4

w

..-i

0

+J

m

E0

w a,

0.1

0.2

c, e.

,: U .4

a

w

w

o a , 0

5

10

15

20

0

x10 3 0.5

1.0

1.5

2.0

Time ( s )

x103,0

Time ( s )

Figure 9. Deformation and coefficient of friction for the cartilage-porous disc combination.

Figure 11.Effect of sliding on the deformation for the cartilage-cartilage combination.

252

The present experimental results confirm clearly that creep deformation due to interstitial flow does not substantially arise if full fluid lubrication conditions are maintained. As creep deformation only occurred with contact and it is directly related to the contact pressure, it is a good index of the contact and lubrication conditions While most of the load in the joint is supported by fluid pressure, direct contact occurs between the cartilage surfaces. The water exuded from the cartilage near the contact location temporarily lubricates the surface until the joint recovers its optimal lubrication conditions. However, if the contact conditions are too severe and direct contact continues too long, the water beneath the surface may be exhausted such that the exudation stops and the cartilage surface may become damaged. However, such an extreme situation seems improbable under normal physiological conditions. Thus, it is probable that cartilage may be damaged only when the multi-mode lubrication mechanism does not function well. This suggests that the tribological considerations are indispensable in elucidating and finding cures for joint diseases involving cartilage wear. 5. CONCLUSION The experimental results obtained in the present study confirm the following: (1) If full fluid lubrication conditions are maintained, no substantial creep deformation occurs in the cartilage. (2) Fluid exudes from cartilage corresponding to the contact pressure and temporarily lubricates the cartilage surface. (3) As the deformation rate of cartilage also corresponds to the contact pressure, it is a good index of the lubrication condition.

REFERENCES 1. D. Dowson, Proc. Instn. Mech. Engrs., 181, 35 (1967) 45. 2. J. B. Medley and D. Dowson, ASLE Trans., 27, 3 (1984) 243. 3. J. B. Medley, D. Dowson and V. Wright, Engng. in Med., 13,3 (1984) 137. 4. K. Ikeuchi et al., Bull. JSME, 27,226 (1984) 809. 5. K. Ikeuchi and H. Mori, Bull. JSME, 27, 231 (1984) 2024. 6. K. Ikeuchi and H. Mori, Bull. JSME, 27, 231 (1984) 2030. 7. D. Dowson and Z. M. Jin, Proc. Instn. Mech. Engrs., 206 (1992) 185. 8. V. C. Mow, Et al., J. Biomech. Engng., Trans. ASME, 102 (1980) 73. 9. C. G. Armstrong and V. C. Mow, J. Bone and Joint Surgery, 64-A, 1 (1982) 88. 10 P. A. Torzilli, D. A. Dethmers and D. E. Rose, J. Biomech, 16,3 (1983) 169. 11. R. Y.Hori and L. F. Mockros, J. Biomech., 9 (1976) 259. 12. R.Parsons and J. Black, J. Biomech., 10 (1977) 21. 13. R. L. Spilker, J-K. Suh and V. C. Mow, J. Biomech. Engng., Trans. ASME, 112 (1990) 138. 14. Z. M. Jin, D. Dowson and J. Fisher, Proc. Instn. Mech. Engrs., 206 (1992) 117. 15. J. M. Mansour and V. C. Mow, J. Lub. Techno]., Trans. ASME, 99 (1977) 163. 16. M. Watakabe, K. Mabuchi and T. Sasada, J. LSLE,International Ed., 9 (1988) 139. 17. K. Ikeuchi and M. Oka, Proc. 19 LeedsLyon Symp. on Trib., (1993) 513. 18. T. Murakami, JSME International J., 33, 4 (1990) 465. 19. C. W. McCutchen, Nature, 184 (1959) 1284. 20. C. W. McCutchen, Proc. Instn. Mech. Engrs., 181, 35 (1967) 55. 21. F. Guilak, et al., 1988 Advances in Bioengineering, ASME (1988) 183.

Dissipative Processes in Tribology / I>. Dowson ct al. (Editors) 0 1994 Elscvicr Scicncc I3.V. All rights rcscrvcd.

253

Characteristics of Friction in Small Contact Surface By Yasuhisa ANDO, Hirofumi OGAWA and Yuichi lSHlKAWA

Mechanical Engineering Laboratory, AIST, MlTl Namiki 1-2, Tsukuba, lbaraki 305 Japan

To determine the friction characteristics of small contact surfaces, the friction coefficient between steel balls of 0.5 to 5 mm radii and block gauges were measured while varying the friction speed, normal load, sliding distance etc. A high friction coefficient was found under a low normal load such as 1 mN, particularly for larger steel balls. However, the friction coefficient under a low normal load increased with sliding distance. Observations by AFM (Atomic Force Microscope) showed that deposited material thought to be wear particles accumulated on the steel ball with sliding distance. The adhesion force between a steel ball of 2 mm radii and a block gauge waq measured under friction in order to quantify the adhesion force which affects the friction force under low normal load. The results show that the adhesion force varies greatly, and is sufficiently large to influence the friction coefficient under low normal load.

1. INTRODUCTION Many studies on the manufacture of micro machines which are one tenth to one hundredth as small as present machines have been conducted recently. For micro machines, as the dimensions of components decrease, the surface area decreases in proportion to the square of the linear decrease while the volume decreases in proportion to the cube power of the linear decrease. Therefore, the influence of the surface increases dramatically, and the problem of tribology becomes more important. The friction coefficient is independent of the contact surface area and the friction force is proportional to the normal load as stated in the Coulomb's law. But in the case of a small contact area and an extremely low normal load found in micro machines, i t is not obvious whether Coulomb's law is still applies due to the effect of the adhesion force between the surfaces. Although some studies are revealing the tribological characteristics on a nanometer scale using AFM (Atomic Force Microscope), STM (Scanning Tunneling Microscope) etc. Il,2], it is difficult for such studies to explain the tribological phenomenon on an ordinary scale. Therefore, it is essential to investigate the tribological characteristics on the pm scale, not only

in order to construct micro machines, but also to help establish the connection between nanometer tribology and ordinary scale tribology. However, there are very few reports regarding measuring the effect of a normal load and the contact area on the friction coefficient, and experimental conditions are limited in such reports. Thus, in order to understand the tribological characteristics of the contact area in micro machines, the friction coefficients between smooth block gauges and smooth steel balls of 0.5 to 5 mm radii were measured while varying the radii of the steel balls, normal load, sliding speed, sliding distance, etc. Furthermore, the adhesion force under friction was measured and the friction surface was observed by AFM, then influences of the adhesion force and conditions of the friction surface on the friction coefficient were examined.

2. EXPERIMENTAL METHOD 2.1. Measurement of friction characteristic of small contact surface The experimental apparatus shown in Figure 1 was used to measure the friction coefficient. This apparatus consists of a X table and a Y table, and each one moves perpendicularly to each other.

254

The X table is driven by a speed control motor and the Y table moves when the micrometer head is turned by hand. A block gauge is installed on the X table and is parallel to its traveling direction. There are two parallel leaf spring units, which displace perpendicularly to each other, and a steel ball of the other test piece faces the block gauge and is fixed on the head of the spring units. The whole apparatus is placed on an air spring vibration isolator.

Effect of load Steel ball

Test pieces R= 0.5 mm

Roughness : 7. I 1 nm

Steel ball

R= 1 mni

Roughness : 6.74 nm

Steel ball

R= 2 mm

Roughness : X.20 nm

Steel ball R= 5 mm block gauge

Roughness : 10.1 nm Roughness : 6.20 nm

Conditions Load Sliding speed Sliding distance of a stroke

-

0.62 25.6 mN 0.16 mm/s 58.8 mm

Roughness : Surface Roughness, RMS

Effect of sliding distance Test pieces Steel ball R= 1 mm block gauge Conditions

Fig. 1. Schematic of exp rim ntal apparatus to measure friction force When the steel ball is pressed against the block gauge under a suitable load and the X table moves, friction occurs. The displacements of the spring in the X and Y directions are measured with two laser sensors, and the outputs of the sensors through DC amplifiers and low pass filters are recorded on a pen recorder. The friction force and the normal load can then be calculated. Table 1 Experimental conditions to measure friction coefficient

-

1.46 1.77 mN Load Sliding speed 0. I6 mm/s Sliding distance of a stroke 58.8 mm Roughness : Surface Roughness, RMS

The radii of the steel balls, normal load, sliding distance and sliding speed were selected as experiment parameters, and the influences of these values on the Friction coefficient were examined. The experimental conditions are shown in Table 1 . All the test pieces were cleaned with ethanol before the measurements, and the measurements were canied out in air of relative humidity 45.7 to 65.3 % anda temperature of 25.7 to 3 1.1 "C. 2.2. Measurement of adhesion force of a small contact surface

Effect of sliding weed Test pieces Steel ball R= 1 mm block gauge

Roughness : 7.64 nm Roughness : 6.20 nm

Roughness : 5.38 nm Roughness : 4.46 nm

Conditions Load Sliding speed

0.65 -1.0mN

Sliding distance of a stroke

1.2-58.6 mm

0.0043- 1.83 mnds

Roughness : Surface Roughness, RMS

Figure 2 shows the apparatus used to measure the adhesion force. A steel ball is installed on the X-Y table which is driven by a stepping motor, and a block gauge of 1 mm thickness is fixed on the leaf spring and faces the steel ball. The displacement of the leaf spring is measured by a capacitance sensor. After the normal load was set and the adhesion force was measured using the Y table and a PZT actuator, friction occurred by driving the

255

X table. The whole apparatus was also placed on an air spring vibration isolator. block gauge PZT actuator

\

n

leaf spring

Fig. 2. Schematic of experimental apparatus to measure adhesion force Table 2 Experimental conditions to measure adhesion force

3. EXPERIMENTAL DISCUSSIONS

RESULTS

3.1. Friction characteristics contact surfaces

of

AND small

Figure 3 shows an example of measuring the friction coefficient. The figure shows the displacement of the steel ball in the friction direction measured by the sensor when the block gauge moves back and forth in a stroke of 29.4 mm. When the friction direction is reversed, the friction force is also reversed from plus to minus. The friction forces on the plus and minus side are read on a graph recorded at each stroke, and the difference in the forces divided by two gives the average friction force. The fnction coefficient is obtained by dividing the average friction force by the normal load.

Test nieces

Steel ball R= 2 mm Block gauge

Roughness : 6.51 nm Roughness : 10.7 nm

Conditions 1.2 mN Load while friction Sliding speed 0.025 mm/s Sliding distance between 10.0 to 100 mm measurements Roughness : Surface Roughness, RMS

Measurements were made i n the following way. The test pieces were set and the adhesion force measured in the initial state. Then the steel ball was pressed against the block gauge and rubbed back and forth against it. After a suitable distance of friction, the X table was stopped and the adhesion force measured. The adhesion force was measured in the following way. When the steel ball is pressed on the block gauge, it is moved backward by the PZT actuator, and the leaf spring with the block gauge also moves with it. If there is any adhesion force between the steel ball and the block gauge, the steel ball pulls the leaf spring and displaces it from its neutral position. When the force required to restore the leaf spring just exceeds the adhesion force, the leaf spring moves back to its neutral position with damped oscillation. The adhesion force between the steel ball and block gauge can be obtained by measuring the maximum displacement of the leaf spring using a capacitance sensor.

Fig. 3. Changes of friction force during friction

3.1.1. Influence o f sliding speed on friction coefficient Figure 4 shows the relationship between the friction coefficient and sliding speed. Measurement starts at a sliding speed of 0.23 mm/s and the speed was decreased step by step down to 0.0043 mm/s, then up to 1.83 mm/s, and finally down to 0.024 mm/s again. In this experiment, measurements were made at the lowest possible normal load in order to minimize changes of the surface condition through wear. Although the friction coefficients are scattered in the speed range of 0.1 to 1 mm/s, they are considered to be independent of sliding speed across the whole speed range used.

256

c c

o 0.6 ...........

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

5

15

10

25

20

30

Load, mN 0.01

0.1

(b)R=l mrn

Sliding speed, mm/s Fig. 4.Relationship between friction coefficient and sliding speed

.......

c c

0

3.1.2. Influence of normal load on friction coefficient The influence of normal load on the friction coefficient was examined by varying the radii of the steel ball. Measurements were made at a normal load of about 0.6 mN at first, then the normal load was increased step by step to about 25 m N then decreased to 0.6 mN, and the friction coefficients were measured at each load. This procedure was repeated once more. Figures 5 (a)-(d) show the relationship between the friction coefficient and normal load a$ measured above. Figure 6 shows the relationship between the friction coefficient and the maximum contact pressure assuming Hertz's contact.

. . .

-5

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

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

g

.,g .c .c

0

I

0.6c-

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

1.20

1.0

0.8

;

. . . <. . .

i

.; .

.;

..

I

.

.

j

0.64.......... i.............. 0

0.4

:

-. y " i +,.,.............

0 0.2-.

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

30

25

1.4-

0

;..............

20

(c) R=2 mrn

5

.-.-,-

15

10

Load, mN

.-5 0 1.0

....

5

0

+

g

0.8

L

.

.

.

:

1...............

i

i

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

,. ........................................................ ~

- 1 . . . .1j

I

....

I

: 0. j I .................

I

I

.i

0;. 1

Load, mN 0

I

0

(d) R=5 mm I

1

I

1

I

5

10

15

20

25

30

Load, mN (a) R=OS rnm Fig. 5. Relationship between friction coefficient and normal load

Fig. 5. Relationship between friction coefficient and normal load

These figures indicate that the friction coefficient increases at a lower normal load,

257

particularly for a larger steel ball. Figure 6 shows that the friction coefficient increases with a lower maximum contact pressure. The normal load measured by the sensor is an external force which is applied to the contact surface by the leaf spring. If there is not only an applied normal load but also an adhesion force proportional to the contact area between the test pieces, then when the normal load is small, the adhesion force is not negligible compared to the applied load. The adhesion force acts as a hidden normal load, so the friction coefficient increases. For the same reason, the bigger the steel ball with its larger apparent contact area, the higher the friction coefficient at a low normal load.

Sliding distance , mm Fig. 7. Effect of sliding distance on friction coefficient using a steel ball of 2 mm radii

14 1.2-

I

0

R=l R=2

..

1.01

1

I . .

..........

I

0

I 1

I 2

I 3

1

4

I 5

I

6

7

Maximum contact pressure, x l O6 Pa Fig. 6 . Relationship between friction cocfficient and maximum contact pressure

3.1.3. Influence of sliding distance on friction coefficient The data in Figure 5(c) is arranged in Figure 7, which shows the changes of normal load and friction coefficient at each measurement versus sliding distance. Although the changes of friction coefficient at higher normal loads are very small, at lower normal loads, the friction coefficients increase with longer sliding distance. I n order to determine the relationship between the increase of friction with sliding distance and the surface conditions, the surface of the steel ball was observed by AFM and the coefficient of friction was measured during friction at a constant normal load.

0

200

400

600

800- 1000

~

1200

Sliding distance , mm Fig. 8. Effect of sliding distance on friction coefficient when normal load was constant

Figure 8 shows the friction coefficient versus sliding distance measured for a steel ball of 1 mm radii. At the numberedpoint in Figure 8, the steel ball was removed from the apparatus and its contact area was observed by AFM. Although there are some fluctuations, the friction coefficient generally increases with longer sliding distance as shown in Figure 8. Observations by AFM showed that material, thought to be wear particles, accumulated on the surface as the sliding distance increased. Figure 9 shows some of the observations made by AFM.

258

(a) After friction of 58.8 mm ( [ I ] in Fig. 8 )

was removed with ethanol, the surface of the steel ball was worn and flat (Figure S(c)). This material was observed on all steel balls used in all the experiments. Figure 10 shows the results of EPMA analysis of the steel ball used in the experiment shown in Figure 4. Although it is impossible to confirm that wear particles from the block gauge transferred to the steel ball due to friction between similar materials, if this material is wear particles, then the iron would oxidize and the material should contain oxygen atoms. If the material is contamination from the block gauge, then carbon atoms should be present since such contamination usually contains a lot of hydrocarbons. If we examine the distribution of Fe, 0 and C in this figure, then oxygen atoms are much more common in the deposited material than in other areas. This fact suggests that the deposited material is wear particles of iron oxide.

(b) After friction of 882 mm ( [ S ] in Fig. 8)

Fig. 10. Distribution of Fe, 0 and C on friction Surface 3.2. Adhesion surfaces

(c) Deposited material was removed after friction Fig. 9. Change of surface topography during friction

In Figure 9(a) and (b), both surfaces of the deposited material are smooth. In Figure 9(b), deposited material are observed on another material which pressed and spread widely. After this material

force

of

small

contact

Figure 1 I shows an example of the measurement. The vertical axis represents the displacement of the leaf spring vertical to the test piece surfaces. In this example, the block gauge which adhered to the steel ball detached suddenly from the steel ball at about 8 sec. and stopped at its neutral position after vibrating for about 2 sec. The adhesion force can be calculated From the maximum displacement of the spring. Figure 12 shows the

259

relationship between the adhesion force and sliding distance measured as shown in Figure 1 1.

Fig. 1 1. Example of measuring adhesion force

The adhesion force was about 0.3 mN before sliding, and this increased to between 0.6 to 0.8 m N by friction. After a sliding distance of 500 mm, the force varied greatly. Observation by AFM after the test shows dispersed, deposited material over a small area (Figure 13), as observed in the friction force measurement. Changes in the adhesion force due to friction are thought to be greatly influenced by wear and wear particles deposited on the surface of the steel ball. For example, if there is a big wear particle between the two surfaces as shown in Figure 14(b), the distance between the test pieces is greater and the adhesion force is smaller. If such wear particles disappear or are flattened and the surface of the steel ball gets flatter by wear, then the adhesion force works over a larger area than between a simple round ball and flat surface, hence increasing the adhesion force (Figure 14(c)).

(a) Before friction (medium adhesion force)

0

200 400 600 800 Sliding distance , mm

1000

Fig. 12. Changes of adhesion force during friction

W 11111

(b) Distance between the surfaces is increased by wear particles (small adhesion force)

(c) The surface is worn and wear particles are spread widely (large adhesion force) Fig. 14. Effect of wear particles on adhesion force

Fig. 13. Surface of steel ball used in the measurement of adhesion force

3.3. Relationship between adhesion force and friction coefficient Although the adhesion force probably

260

increases the friction coefficient at a low load. it is not clear whether the adhesion force measured in 3.2 quantitatively increased the friction coefficient in 3.1. The maximum adhesion force in 3.2 was about 1.1 mN (Figure 12). This force was added to the normal load i n the experiment using R = 2 of 3.1.2 (Figure S(c) ) and the friction coefficients were recalculated. The result is shown i n Figure IS. The mark represents the friction coefficient calculated from the normal load and adhesion force.

-

0 LoadtAdhesion Force

1.0

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

.....

1

0

5

1 10

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

I

15

I 20

.........

I

25

30

Load, mN

Fig. IS. Relationship between friction coefficient between normal load using steel ball of 2 mm radii when considering adhesion force.

If we compare with the case neglecting the adhesion force, the friction coefficients regarding an adhesion force of 1.1 mN are almoqt same in whole region of load. This indicates that the adhesion force works between the surfaces of the test pieces, acting as an extra normal load and increasing the fTiction coefficient at low loads. The friction coefficients described in 3.1 are stable while the adhesion force in Figure 12 varied greatly. This is because measurements of the friction

coefficient are not sensitive to the adhesion force since the average dynamic friction coefficient is detected during friction, while the adhesion force is determined for a specific transient friction surface.

4. CONCLUSION The influences of steel ball radii (0.5-5 mm). sliding speed (0.0043-1 3.3 mm/s), sliding distance, and normal load (0.62-25.6 m N ) on the friction coefficient for a small contact surface were measured. The findings are as follows: (1) The sliding speed had no effect on the friction Coefficient. (2) The friction coefficient tended to increase with lower normal load, particularly for larger steel balls. (3) The friction coefficient at a low normal load increased with sliding distance. Observations by AFM showed that deposited material, thought to be wear particles, accumulated on the steel ball with sliding distance. The adhesion force between a steel ball of 2 mm radii and a block gauge was measured during friction. The findings are as follows: (4) The adhesion force varied greatly with friction. The maximum adhesion force measured is sufficiently large to influence the friction coefficient at low normal loads.

REFERENCES I . Weissenhorn, A, L., Hansma, P. K., Albrecht, T. R.,and Quate, C . F., Appl Phys Lett. Vol. 56, NO. 26, pp. 2651-2653, 1989 2. Kaneko, R., Proceedings IEEE Micro Electro Mechanical Systems, pp. 1-8, 1991

Dissipative Processcs in Tribology / D. Ihwson ct a]. (Editors) 0 1994 Elscvicr Sciencc U.V. All rights rcservcd.

26 1

Sliding friction in porous and non-porous elastic layers : The effect of translation of the contact zone over the porous material L. Caraviaa, D. Dowsona, J. Fishc13, P.H. Corkhillb and B.J. Tigheb

a Department of Mechanical Engineering, University of Leeds, Leeds, LS2 9JT,UK. Department of Chemical Engineering and Applied Chemistry, Aston University, Birmingham B4 7ET, UK. Measurements of sliding friction under a mised lubrication regime have been carried out to determine the effect of translation of the contact zone over porous and non porous elastic layers. For non porous polyurethane layers, there was little difference in the friction when the contact zone remained fixed on a polyurethane slider, and when there was translation of the contact zone ovcr a polyurethane layer. However, with a porous hydrogel layer and translation of the contact zone over the fully hydrated material the coefficient of friction was significantly lower than when the contact zone was fixed on a porous hydrogel slider. In the latter configuration, the watcr was squcezcd out of the hydrogcl matcrial under load, and the entraining action appeared insdlicient to cflcctively lubricate thc contact. 1. INTRODUCTION

The use of compliant layers in cushion form bearings for total artificial joints is currently generating considerable interest in a numbcr of centres (1,2,3,4). In our centre (4.5) cushion form bearings have been manufactured from thin layers of polyurethane material 2 to 4 mm thick which are integrally bonded to a rigid polymcr substrate. Under conditions of continuous cyclic loading and motion as found in the walking cycle, fluid film lubrication and extremely low values of friction (less than 0.01) can be achieved (5,6). Fluid films of the order of 300 to 500 nm thick can be preserved by microelastohydrodynamic lubrication (4,5,6) in polyurethane materials with an elastic modulus as high as 20 MPa. In a knce joint simulator test, with the simulated walking cycle conditions, thc cushion form bearing has been tested to 5 million cycles without evidence of the gcncration of wear dcbris (7), A cushion form bearing, which can articulate with full fluid film lubrication during the normal walking cycle, has considcrable potcntial to reducc wear and wear dcbris in total artificial joints. However, total artificial joints are only under continuous cyclic motion, as in the walking cycle, for about five percent of the time. For the remainder of the time, there is little or no cntraining action in the joint, and for some periods of timc, such as during standing, the joint is also hcavily

loaded. Under these conditions the lubricating film and thickness is reduced to much less than 100 nm and the fluid film breaks down. High levels of start up friction can occur under these conditions with polyurethane cushion form bearings (8). It has been shown that the high levels of start up friction of grcatcr than one which are found with polyurethane layers, are reduced to less than 0.5 when porous hydrogel materials are used (9). In addition, under conditions of constant load and low velocity sliding, which produced a film thickness of less than 60 nm and a mised lubrication regime, the hydrogel materials produced consistently lower friction than the polyurethane materials (10). These studies indicatcd that the porous hydrogel materials can have considerable frictional advantages over the non-porous polyurethane materials in cushion form bearings, when operating in the mised lubrication regime. In the design of the cushion form bearing with a porous hydrogel material, it is important to select carefully the bearing surface which incorporates the hydrogel layer. If the hydrogel layer is applied to the tibia1 surface in the knee or the acetabular cup in the hip, where there is little movement of the contact zone when the femur rotates, the contact zone is essentially fixed in one position on the porous hydrogel layer. In contrast, if the porous hydrogcl layer is applied to the femoral component in the hip or knee. rotation of the fcmur produces

262

translation of the contact zone over the porous hydrogel layer. In the former case, with a fixed contact zone, the hydrogel material in the contact is continuously under load and water is forced out of the porous elastic material. In contrast, in the latter case with translation of the contact zone, fully hydrated hydrogel material is continuously being moved into the contact zone. The purpose of this study was to investigate the effect on the friction of translation of the contact zone over the porouselastic hydrogel material when sliding in a mixed lubrication regime.

containing NVP, methylmethacrylate (MMA), cellulose acetate butyrate (CAB) and an aliphatic polyetherurethane. The three materials had an elastic modulus of between 20 and 23 MPa (9). The materials were produced in layers 0.8 mm thick, by either injection moulding (polyurethane) or polymerisation (hydrogels). The layers were bonded to a rigid substrate. Each of the compliant layers was slid on a smooth metal and a glass surface with a counterface roughness R, of 0.01 p m with the contact lubricated with deionised water. 2.2 Methods

2. MATERIALS AND METHODS 2.1 Materials Three compliant materials were used in the study. A non porous aliphatic medical grade polyurethane (Tecoflex 93A); a terpolymer hydrogel (ASTI) containing N-vinyl pyrrolidone (NVP) cyclohexyl methacrylate (CHex MA), hexyl methacrylate (Hex MA) and a semiinterpenetrating network hydrogel (PC114)

Compliant Slider

The test configurations used to simulate a fixed contact zone and translation of the contact zone are shown in Figures l a and l b respectively. For a fixed contact zone the compliant material was attached to a spherical slider which was loaded and slid over a hard flat counterface Figure la. Translation of the contact zone over the compliant layer was achieved with a hard spherical indentor, sliding on a flat compliant layer Figure lb.

Compliant Layer

w

I

I

1

I Fixed Contact Zone Figure 1. The experimental design (a) a compliant slider with a fixcd contact zone.

Translation of Contact Zone (b) a compliant layer with translation of the contact zone

263

The contact was designed such that an average normal stress of 2MPa was achieved for all the material combinations. Sliding was carried out at 8 mm s-l. The predicted elastohydrodynamic film thickness was 52 nm, ensuring the contact slid in a mixed lubrication regime (9,lO). Under these conditions, the lubricating film was not suflicient to separate the surface asperities and direct contact between the materials was expected. The apparatus used to measure friction has been described in detail previously (8,9,10). The slider, or indentor, was held at one end of a pivoted arm and loaded on to the flat counterface. The arm was pivoted with an air bearing, and the rotation of the arm resisted by a piezo-electric force transducer which measured the friction force. A constant sliding spced in one direction was achieved with a variable spccd motor and the displacement monitored with a linear variable differential transducer (LVDT). Both the signals of friction force and displacement were collected and analysed with Unkelscope software on a micro-computer. One set of tests was carried out for each material combination for each configuration. In each set of tests the slider was loaded for a period of time of between 5 and 400 seconds prior to the initiation of sliding. Seven differcnt test runs were carried out to establish a mean and standard deviation. In each case, the steady state sliding friction was measured after the start up period during constant velocity sliding. Results were compared for the test configurations which gave a fised contact zone and translation of the contact zone for each of the compliant materials using a one way analysis of variance and Students' T test.

3. RESULTS AND DISCUSSION

3.1Polyuret hane Figure 2 shows the mean cocficicnt of friction during sliding in the mixed lubrication regime for the polyurethane slider with a fised contact zone and the polyurethane layer with translation of the contact zone, for periods of loading prior to sliding ranging from 5 to 400 seconds. In both configurations the coefficient of friction was essentially independent of the period of loading

prior to sliding. The differences were not statistically significant. The levels of friction during steady state sliding in this mixed regime (approximately 0.05) were much less than those found at start up of motion (8) under the same loading conditions (up to 0.8). This indicated that although the elastohydrodynamic action was not sunicient to generate a full fluid film, it dramatically reduced friction in the mixed lubrication regime with polyurethane. 20MPa Polyurethane

c0

068eEI layer

slider

0.40

0.30 Ll

0

u

2

0.00 ~ 1 , , , , , , , , , , , , , , , , , , ( , , , , , , , , , ( , , , , , , , , , , 0 100 200 300 400

Loading Time (s)

Figure 2. The coefficient of friction plotted against time of loading prior to sliding for the polyurethane layer and polyurethane slider. 3.2ASTI Hydrogel Figure 3 shows the coefficient of friction during steady state sliding for the ASTI layer and ASTI hydrogel slider for periods of loading prior to sliding of between 50 and 400 seconds. For the compliant layer configurations, where there was translation of a hard indentor and contact zone over the hydrogel layer, the friction was very low (0.01 to 0.02) and independent of the loading time prior to sliding. In this configuration with translation of the contact the hard indentor moved over the hydrogel layer that had not been previously loaded, and was therefore fully hydrated. In this case, the friction was lower than in the non-porous polyurethane.

264

This was consistent with our previous studies. The friction during sliding was also much lower than that found at start up of motion with the same materials (lo), which also indicated that the entraining action was effective in rcducing friction in this mixed lubrication regime with the ASTI hydrogel layer. In contrast, with the hydrogel slidcr configuration, where the area of the contact was fixed on the porous slider during sliding, the levels of friction were much higher 0.18 to 0.35, and they increased as the period of loading prior to sliding increased. The loading of the porous slider in this configuration squeezed out water from the hydrogel, and the amount of water lost was dependent on the duration of loading prior to sliding. The rcduction in water content of thc loadcd hydrogcl niatcrial in the contact increased the lcvcl of friction. The levels of steady state friction for the ASTI slider which increased with loading time prior to sliding, were similar to the levels found at start up of motion (10). It would appear that the entraining action had very little effect on reducing friction with the compliant slider whcn the hydrogcl inaterial was depleted of water by loading prior to sliding. 0.50

ASTl l laper

C

slider

F:

0

-&

a

0.40 4

0

2 0.20

.r(

k

k

Figure 4 shows that differences in the coefficient of friction for the PC114 hydrogel layer and hydrogcl slider were similar to those found with the ASTI hydrogel. The friction for the hydrogel layer when there was translation of the contact over the fully hydrated hydrogel material was much lower than for the slider, and was independent of the loading time prior to sliding. The friction was much greater for the loaded compliant slider and increased with the period of loading time prior to sliding. The values of friction for the PC114 hydrogel were slightly greater than for the ASTI hydrogel, indicating a difference in chemical composition and surface energy. There was little difference in the friction values for polyurethane or hydrogel material when sliding on glass or metal countcrfaces of similar roughness. The same diffcrences between the slider and layer configuration occurred for both counterface materials.

:2c

0.30

c

4

P)

0

u0 0.10

"fk

.A

Q)

0.00

1 l0 , , , a , a , , ,, ,, 3~200 , a~ 100

, , , , , ~ ~ " " , , , ~ 300

Loading Time ( s )

0.10

400

V 0

0.00

, I

0

z

' , ' , , , , , 1 , 1 , , , , , , , , , , , , , , , , , 1 , , " , ~ , , , ,

100

200

300

400

Loading Time (s) Figure 3. The coefficient of friction plotted against time of loading prior to sliding for the ASTI hydrogel layer and slidcr. 3.3 PC114 Hydrogel

Figure 3. The coefficient of friction for the PC114 hydrogel layer and slider as a function of loading time prior to sliding. Figure 5 shows the coefkient of friction plotted against sliding distance for the PCll4 hydrogel slider with 80 seconds of loading prior to sliding. This graph shows that there was only a small

265

reduction in the friction for the slider during steady state sliding compared to the start-up value (0.35 compared to 0.39). This confirmed that the friction of the hydrogel slider (which was depleted of water) was not reduced much by the entraining action of the lubricant, This was in contrast to the PC114 layer and where the material in the contact was fully hydrated where the steady state sliding friction was reduced to less than 0.08 by entrainment. 0.50 2

PCl14

n

E E

W

0.10

F: 0 .rl

4

td

PC114

0.00

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

0 3

s

0.20

.r(

Is

rc

0,

% 0 0 0.10

100

200

300

400

Time (s)

t.

Figure 6 . Deformation of the PC114 hydrogel with time

3

4. CONCLUSIONS

0.00 4l 0 . 0 0 " " " " " " 10.00 ""'

20.00 I '

"

' 30.00 I t '

'

40.00

" I '

Sliding Distance ( m m )

Figure 5. The coemcicnt of friction plotted against sliding distance for a single test on the PC114 hydrogel slider. Measurement of the deformation of the hydrogel during indentation helped to confirm the hypothesis that the loss of water from the hydrogel slider was an important determinant of the coefficient of friction. Figure 6 shows the variation with time of the indentation of the hydrogel by a small spherical ball. After the initial elastic deformation of 80 micrometres, the hydrogel deformed a further 20 micrometres over a period of 300 seconds as fluid was squeezed out of the contact. and then the deformation stabilised at between 300 and 400 seconds. This can be compared with the rise in friction with the loading time prior to sliding in the PC114 slider in Figure 4.

The results show that for non-porous polyurethane, the configuration of the compliant layer did not have a significant effect on the friction during steady state sliding. The level of friction was however reduced significantly by the entraining action in the mixed lubrication regime, compared to the high levels measured at start up (8). In both hydrogel materials, the configuration of the test had a marked effect on the friction during steady state sliding. For the hydrogel slider, where the contact zone was fixed on the slider, the friction was high between (0.15 to 0.4) and increased with the period of loading prior to sliding, as water was squeezed out of the hydrogel in the contact. These values of friction approached those found at start up, and the entraining action was not effective at reducing friction when the hydrogel in the contact was depleted of water by the applied load. In contrast, with the porous hydrogel layer and translation of the contact, the friction values were much lower (0.01 to 0.05), as the contact area was always fully hydrated during steady state

266

sliding. In this configuration the friction was always much lower than found at start up and was independent of the loading time (9,lO). The results show that, if minimum friction is requircd with hydrogel porous layers, they should be used on the femoral surface in artificial hips and knee joints in order to try and obtain translation of the contact zone over the porous layer. There may, of course, be other design considerations which preclude this configuration. In this configuration, both lower start up friction and low sliding friction may be achieved with hydrogel material. 5. ACKNOWLEDGEMENT

This work was supportcd by the Wellcome Trust and the SERC.

REFERENCES 1. J.B. Medley, R.M. Pilliar, E.W. Wong, A.B. Strong. Eng. in Med. (1980), 9, 59-65. 2. A. Unsworth, M.J. Pearcy, E.F.T. White, G. White. Eng. inMed. (1988), 17, 101-104. 3. M. Oka, T. Noguchi, P. Kumar, K. Ikeuchi, T. Yamamuro, S.H. Hydon, Y. Ikada. Clinical Materials (1990), 6, 361-381. 4. D. Dowson, J. Fisher, Z.M. Jin, D.D. Augcr, B. Jobbins. J. Eng. Med. (1991) (205H) 59-63. 5 . D.D. Auger, D. Dowson, J. Fishcr, Z.M. Jin. J. Eng. Med. (1992) 206H, 25-33. 6. D.D. Auger, D. Dowson, J. Fisher . In "Thin Films in Tribology", Tribology Serics 25, 1993, Elseveir, Amsterdam, 683-692. 7. D.D. Auger, D. Dowson, J. Fisher. Proc. 8th Meeting of the European Socicty of Biomechanics (1992), 115. 8. L. Caravia, D. Dowson, J. Fisher, WEAR (1993), 160, 191-199. 9. L. Caravia, D. Dowson, J. Fisher, P.H. Corkhill, B.J. Tighe. J. Mat. Sci. Mat. in Mcd. (1993), 4, 515-520. 10.L. Caravia, D. Dowson, J. Fisher, P.H. Corkhill, B.J. Tighe. In "Thin Films in Tribology", Tribology Series, 25, Elsevier, Amsterdam, pp 529-534.

Dissipative Processes in Tribology / D. Dowson ct al. (Editors) 0 1994 Elsevier Science B.V. AU rights rescrvcd.

267

The effect of additive of silane coupling agent to water for the lubrication of ceramics K. Matsubara'.

S. Sasanuma- and K. Nagamorib

"Department of Production Mechanical Engineering, Tokai University 1112, K i takaname H i ratsuka-shi Kanagawa 259-12 Japan 3hinagawa Refractories Co. Ltd. 707 Ibe Bizen-shi Okayama 705 Japan In t h i s study, concentrations of silane coupling agent t o water have taken i n a range of 0.01 t o 1 mole including d i s t i l l e d water. Using the Westover testing apparatus it i s found that the wear of ceramics decreases w i t h increasing q N/P and becomes zero a t a l i m i t i n g value. The wear of ceramics occurs based on removal o f some parts of the contact surfaces by repeating slidings. At the same time the surface asperities of ceramics continue t o cut the mated surface of stainless steel. Then, the detached o r the wear particles of the stainless steel adhere t o i n the surface defects o f ceramics such as voids of the alumina or scratched marks of the si I icon n i t r i d e examined by SEM and EPMA.

1. INTRODUCT ION The t r i b o l o g i c a l studies of ceramics have been done enormously a l l over the world. I n t h i s f i e l d ceramics are intere s t i n g i n performance under the worse s l i d i n g o r r o l l i n g c o n d i t i o n such as d r y . h i g h t e m p e r a t u r e s and bad lubricants. Water lubrication may be included i n these categories. Among them Hibi and EnomotoCll have s t u d i e d e f f e c t s o f s i l a n e coupling agent i n water on the f r i c t i o n a l f o r c e and wear o f ceramics. They have found t h a t f o r b o t h f r i c t i o n and wear o f S i 3 0 4 the aqueous s o l u t i o n s i n a range o f 0.001 t o 0.1 mole are e f f e c t i v e . F o r S I C and A l o 0 3 , l o w e r l u b r i c a t i v e e f f e c t s are noted i n the s i lane solutions. I n t h i s study, the concentrations of s i lane coup1 i n g agent t o water have taken i n the expanded a range t o 1 mole including d i s t i I led water. The aqueous

solutions made i n t h i s study shov that a r e l a t i o n between the coefficient of v i s cosity and the concentration o f s i lane i s expressed as a 1 inear relationship. The tests were done a t a s l i d i n g speed of 2.5 m/s on a load of 60 g with the apparatus used by Westover e t alC21. The surface configurations o f the ceramics a f t e r the experiments were examined by SEM and the transferred materials on the surfaces by EPMA. 2. TESTING APPARATUS AND PROCEDURES 2.1 Testing apparatus A testing apparatus used i n t h i s study has been reported by Westover e t alC21 t h a t i s established as a standard by 4STMC31. The schematically drawing i s shown i n Fig. 1. The apparatus i s consisted of a rotating d i s k 0 1 o f 100 mm i n diameter made of a stainless steel on which a testing saaple(B) of a r i n g form i s ridden.

268

4

d imens iona I adjustab 1 e pos i t ion i ng stand ( S ) on which a plastic f o a d P ) was a t tached. The plastic foam connecting with a p l a s t i c p i p e ( L ) can c o n t a i n the aqueous solution and supply i t t o the disk. The s u i t a b l e contact p o s i t i o n between the foam and the d i s k can be controlled with the aid of the stand(S). The aqueous solution through the pipe(L) i s supplied constantly during s l i d i n g by a pump.

,Spring

Fig. 1 Testing ,Apparatus

The v e l o c i t y of disk can be changed from nominal 0 t o 2.5 m/s with an inf i n i t e l y variable motor. In t h i s study, a sliding speed of 2.5 m/s was chosen. The f r ic t ion between the spec iRen and disk i s measured by a pendulum(E) as shown i n Fig. 1. The pendulum can turn on an a x i s w i t h small f r i c t i o n o f a r o l l ing bearing mounted on the axis. The center of the axis i s in common with the axis of the disk. When rotate the disk anticlockwise by the motor the pendulum w i l l s h i f t f o r the l e f t - h a n d s i d e according t o the frictional force under the testing conditions. The angle of s h i f t can indicate a measure of f r i c t i o n a l force. Here. items t h a t signs of the parts and distances show as f o l l o w s ; the radius(D) o f disk(A), f r i c t i o n a l force (F), actual distance (C) and v e r t i c a l distance(1) between the centers of disk and gravity of the pendulum system and weight(W) of the penduludE). Du r i ng s 1 i d i ng the balance of moment of the system w i l l be as follows: DF=WI =WC*sin8

(1)

2.3 Aqueous solution of s i lane coupl ing agent The silane coupling agent i s supplied by Shinetsu Chemical Co. The chemical formula i s as follows: CH2NC2HNHC3 He S i ( OHC3 1 I (Cata I ogue No. KBM 603). In t h i s study, the concentrations of s i lane coupl ing agent t o water have been taken i n a range of 0.01 t o 1 mole and including d i s t i I led water. The coeff i cient of viscosity of the aqueous soluti ons increases I inear 1 y w it h increas ing the concentration as shown i n Fig.2.

2.4 Samples A r o t a t i n g d i s k ( A ) o f 100 mm i n diameter was made of stainless steel -3

x 10-

I

‘P 0

2.2 Method f o r lubrication The method f o r l u b r i c a t i o n i s a l s o shown i n Fig. 1. There i s a t h r e e -

11111 11111 11 0.5 1.0 Concentration o f s i l a n e C [mol/ll

Fig. 2 Relation between con-

centration and Viscosity

269

Tab1e 1 Propert i es o f samples

3.1 kear

3.1.1 Wear rate against s l i d i n g distance

Sanpl e

The wear r a t e f o r each specimen decreases w i t h i ncreas i ng the s I i d i ng distance. As an example the wear r a t e f o r the coefficient of viscosity of 0.01 mol ( l.lX10-3 Pa*s ) s o l u t i o n i s shown as Fig. 3. According t o a law of adhesive wear under keeping the same physical p r o p e r t i e s during experiments the wear r a t e should be kept. constant, f o r the load and the s l i d i n g distance. However. t h e wear r a t e c l e a r l y decreases w i t h increasing the sl i d i n g distance. I t w i l l be considered t h a t ceramics have very high hardness. so the surface asperities of ceramic may act as c u t t i n g edges of abrasive wheels f o r the mated specimen of stainless steel. A t the beginning of s l i d i n g distance the efficiency of grinding operation o f ceramics may be h i g h f o r t h e mated specimen. Then around t h e s u r f a c e asperities of ceramics are covered with the ground p a r t i c l e s that w i l l make the t r a n s f e r f i l m on it. .As a r e s u l t s the a b i l i t y of grinding action i s lost gradually with increasing s l i d i n g d i s tance. As the wear rate was changed by the loading of surface asperities of ce-

Oensi tr W C i ' )

1

Young' modu I us Hardness

(Hv) F r a c t u r e toughness

Klc,(MNm'3'2) Roughness (Ra) ( p i )

I 1 1 I :: I 1600

1100

3.0

7.5

0.55

0.25

---

1600

(SUS 304. surface roughness Ra = 0.12 0 m. hardness Hv = 270). 4 testing sample (B) o f r i n g form o f 20 mm i n diameter and 6 mm i n thickness was made. Three kinds o f ceramics of AlnOa, Z r O p and S i a l o n and a r e f e r e n c e sample of PTFE were chosen. Properties of these samples are shown i n Table 1.

3. EXPERIMENT.AL RESULTS FOR WEAR AND FRICTION The experimental data f o r wear and f r i c t i o n of the samples were examined by both the coefficient of viscosity and the nondimensional factor of g N/P.

XlO'll

A

"'"I/4

5t

3 0

-0-AltOs -0-2rOt -A- Si a I on

-0-PITE

0 0

I

1

5

10

15

I

I

20

25

I

3 XIO-'

Slidini Distme [Kal Fig. 3

Wear Rate and Sliding Distance f o r a 0.01 mol Solution

Coef, of Viscosity [Pats] Fig. 4

Wear Rate and Viscosity

270

ramics during s l i d i n g , the mean values f o r each sl iding distance are calculated and shown on the wear curves i n Fig. 3. 3.1.2 The e f f e c t of viscosity The e f f e c t o f v i s c o s i t y of the s o l u t i o n s on the wear r a t e s are shown i n Fig. 4. Each v a l u e on t h e graph i s the mean values f o r each s l i d i n g distances as marked i n F i g . 3. For the d i s t i l l e d water and the thinnest s o l u t i o n o f the c w f f icient of viscosity of 0.9 and 1.1 Pa*s, the wear rates show high values, but the higher viscosity the wear rate the lower, and the wear rate approaches t o z e r o except PTFE. As a g e n e r a l opinion on t h i s phenomenon i t may be accepted t h a t the wear r a t e o f ceramics depends on the viscosity. 3.1.3 The wear rate f o r nondirensional To examine the tranfactor of 7N/P s i t i o n from t h e boundary t o f l u i d l u b r i c a t i o n t h e wear r a t e t r i e d t o express f o r 7 N / P as shown i n Fig. 5 . Here, N (Hz) i s the speed of revolution o f the r o t a t i n g disk and P i s the contact pressure between the rotating disk and the samples. By the principle o f journal bearing the speed of revolution N i s the journal i tse If based on a conformal contact.

I

0sI B0

\

6

\

Coef, of Viscosity n Fig. 6 The Relation between the Coefficients of F r i c t i o n and Viscosity [Pals]

However, i n t h i s case, as the counterformal contact i s formed, a discrepancy between them may be shown as the equivalent r a d i i and the conformities. I n the actual contact condition i n t h i s experiment these configurations keep constants during t h e experiments. Conveniently, the behaviours of the counterformal cont a c t assumed t o hold the same as the conformal contact, and t r i e d t o calculate them as the speed of revolution of the conformal contact. The wear r a t e s o f ceramics decrease exponentially with increasing qN/P and becomes zero a t a l i m i t i n g value as shown i n Fig. 5 . These r e l a t i o n s are expressed i n a curve. PTFE i s shown ana-

‘00,

-0- ZrO 2

\

-A- S i a I on

O\ c 0 L

-0- PTFE

1

O% \

--10-I

c Lr. 0

O\ 0

-0

I

\

\‘O

c aJ 0

U

10-21

1 0-lo

Fig. 5 Relation between Wear Rate and

1NIP

I

I

I

I

I

1 0 - s2 3

0-9

v N/P

Fig. 7 Relation between the Coefficient o f F r i c t i o n and qN/p

27 1

other exponential curve. Among them the wear rate of PTFE occurs obviously a t the lowest. one. 3.2 The coefficient, of f r i c t i o n 3.2.1 The e f f e c t o f v i s c o s i t y The c o e f f i c i e n t o f f r i c t i o n f o r the v i s cosity i s shown i n Fig. 6. The f r i c t i o n decreases w i t h i ncreas i ng v iscos i t y and reaches a t own constants. 3.2.2 The expression on the vN/P The c o e f f i c i e n t o f f r i c t i o n f o r vN/P i s expressed i n a log-log scale as shown i n Fig. 7. The f r i c t i o n o f ceramics and PTFE decreases exponentially w i t h i n creasing vN/P. The slopes o f ceramics and PTFE may be the same but an i n t e r cept. of vertical axis of the coefficient, of f r i c t i o n of PTFE a t an axis of of q N / P i s about 40 times higher than that, of ceramics r e s u l t i n g from t h e lower surface energy of PTFE than that of ceramics. From both data of the wear r a t e and the c o e f f i c i e n t s o f f r i c t i o n t h e m a t t e r s t o be discussed a r e a s follows: The wear behaviours are c l e a r e r than t h e f r i c t i o n a l ones a s a g e n e r a l knowledge. The tribological behaviours of ceramics are governed by the lubricat i o n theory under the condition that the values of vN/P e x i s t i n the boundary lubrication.

t o be examined by EPMA. The analyzed p a t t e r n s o f the actual three elements show a simi l a r tendency among them. so that Cr was chosen as an example. Traces of C r are presented i n black appearances i n each photographs. The experiments were done under a sl i d i ng speed of 2.5 m/s on a load of 60 g f o r a suitable s l i d i n g distance.

4. OBSERlATlONS AND ANALYSES ON THE CERAMICS WORN SURFACE BY SEM 4ND EPM4

4.1 The surface of A 1 203 Fig. 8 (1) and (2) are showing the surface of A 1 2 0 3 observed by SEM. Some regions on the photograph look I ike transfer traces of the mated sample of stainless steel. Fig. 8 (2) shows the s l i d i n g surface enlarged by the high 5000 m a g n i f i c a t i o n . and can see t h e grain sizes of A120a. Fig. 8 (3) shows the distributions of Cr as black appearances. and Fig. 8(4) a large black one taken by EPMA. From the transferred traces i t i s conf i rmed that the stainless steel e x i s t s on the s u r face of AlnOa. The transferred stainless steel were d i s t r i b u t e d a t random over the whole p o r t i o n s o f the actual s l i d i n g on the surface of AloOs. They seem t o adhere t o choose preferred voids o r portions o f the boundary o f grains. k c o r d i n g to the high magn if icat i on the transferred mater i a l s seem t o occupy many grains t o make a film. The s i z e s o f the t r a n s f e r r e d m a t e r i a l s a r e l e s s than 0.05 mm i n d iameter

4 f t e r the experiments done the s u r faces of ceramics were observed by SEM and t r a n s f e r r e d m a t e r i a l s on t h e c e r a m i c s a l s o examined by EPMA. Photographs of SEM f o r each ceramic were taken i n magnifications of 400 and 5000. Microanalysis o f the transferred material on ceramics was done f o r the same target taken by SEM. For the stainless s t e e l o f mated specimen which may be t r a n s f e r r e d t o on ceramics. t h e transferred elements o f N i , Cr and Fe as the essential constituents expected

4.2 The surface o f Z r O z Figs. 9 (1) and (2) show a surface configuration and the signs of transfer o f s t a i n l e s s s t e e l on the surface o f ZrOz. Comparing w i t h the d i s t r i b u t e d particles of stainless steel on A 1 2 0 3 as shown i n Fig. 8 (3) and (4), t h e t r a n s f e r s o f s t a i n l e s s s t e e l on t h e surface o f Z r O z form the networks as shown i n Fig. 9 (1). Then. Fig. 9 (2) and(3) o f the magnification 5000 shows t h a t t r a n s f e r r e d materials made a film and covered a group of grain.

.

212

Fig. 8

SEM(lI(2) and EPMA(3)(4)

The each transferred portions consist of very small points o f d i s t r i b u t e d elements of about 1 t o 0.5 ~ n n ni n diameter seen i n the real photograph as we1 I as alumina observed by the high magnification 5000. 4.3

The surface of Sialon

on Surface o f AlaOa Fig.10 (1) i s showing the surface asperites o f sialon are flattened by f r i c t i o n , these areas are distributed over the whole sl iding track. The transferred material cover the fattened portions as shown i n F i g . 10 (3) and the enlarged p i c t u r e o f Fig. 10 ( 4 ) . The covered f i l m s a r e u n i f o r m l y adhering on the flattened portion examined by EPMA.

273

Fig. 9

SEM(1)(2)

and EPM.4(3)(4)

5. WE4R MECHAN ISM OF CERAM ICS

The actual contact area o f ceramics may be a few percent of an apparent area of contact due t o i t s very hard surface. Under the s l i d i n g conditions the surface a s p e r i t i e s may a c t as an a b r a s i v e machining f o r the mated contact surface

on Surface o f ZrOa of stainless steel f o r as well as cutt i n g edges o f abrasive wheel. During sliding. a t the same time the wear o f ceramics may occur based on the detachment o f s u r f a c e a s p e r i t i e s due t o shearing, transfer, b r i t t l e fracture o r f a t i g u e o f the surface a s p e r i t i e s by the repeating sl iding.

274

Fig. 10

SEM(1)(2)

and EPMA(3)(4)

4s the experimental results the wear a r t i c l e s or the cutting chips of stainless steel have been observed t o adhere t o i n the voids ( A 1 , 0 3 ) . scratches (ZrO,) and j u s t sl i d i n g p o r t i o n s (Sialon) the s u r f a c e o f ceramics as shown i n the photographs of SEM. The wear curves f o r the s l i d i n g d i s tance show that the wear rate decreases

on Surface o f Sialon

with increasing the s l i d i n g distance. I t may be based on that as the c u t t i n g chips of stainless steel get i n the Kay of c u t t i n g edge. the c u t t i n g a b i l i t y of the a s p e r i t i e s does deteriorate during sliding. The experimental r e s u l t s analyzed by SEM and EPMA a r e explained i n d e t a i l . The discrepancies among them are noted

215

as described above. However. taking a wide view of things. such discrepancies does n o t s i g n i f i c a n t l y e f f e c t t h e general s i t u a t i o n i n the t r i b o l o g i c a l behav iou rs of ceram ics

.

6. CONCLUS IONS The experimental studies have been done under the aims t o examine the e f f e c t o f additive o f s i lane eeupl i n s agent t o water f o r l u b r i c a t i o n o f ceramics and t h e c o n c l u s i o n s a r e a s f o l lows: (1) The wear of ceramics i s governed independently of the kinds of ceramics by the nondimensional factor of S N I P , that is, the wear decreases with increasing 1 NIP. (2) The t r i b o l o g i c a l behaviours o f ceramics are shown by the boundary l u b r i c a t i o n theory under the condition of water and s i lane aqueous solutions. (3) The wear o f ceramics occurs t o be based on remova I o f surface asperities due t o one or more factors o f shearing, transfer, b r i t t l e fracture o r fatigue by the repeating sliding. (4) The surface asperities continue t o cut the mated surface. and the detached p a r t i c l e s adhere t o i n the voids o r scratched on the surfaces o f ceramics. ACKNOWLEDGMENTS The authors would I ike t o thank Mr. Y. Miyamoto f o r taking p i c t u r e o f SEM and EPMA, and Mrs. Y. Yoshizawa and N. Onuma f o r arrangement of graphs. REFERENCES 1. Y. Hibi and Y. Enornoto, Proc. Japan Int. Tribology Conf. Nagoya 1990, P .451-456. 2. R.F. Westover and W.I. Vroom, ASTM Paper, 62-WA-321,(1962), 1. 3. ASTM , D3028- 1972.

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Dissipativc I'roccsscs in Tribology / D. I>owson et al. (Edimrs) 1994 Elscvicr Scicncc B.V. All rights reservcd.

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The origin of super-low friction coefficient of MoS2 coatings in various environments C. Donnet, J.M. Martin, Th. Le Mogne, M. Beiin

&ole Centrale de Lyon. Laboratoire de Tribologie et Dynamique des Systemes, URA CNRS 855, Npartement de Technologie des Surfaces, B.P. 163 - 6913 1 &ully Cedex - France.

The ultra-low friction coefficient (typically range) of MoS2-based coatings is generally associated with friction-induced orientation of "easy-shear" planes of the lamellar structure parallel to the sliding direction, particularly in the absence of environmental reactive gases and with moderate normal loads. We used a AESlXPS ultra-high vacuum tribometer coupled to a preparation chamber, thus allowing to elaborate oxygen-free MoS2 PVD coatings and to perform friction tests in various controlled atmospheres. Friction of oxygen-free stoichiometric MoS2 coatings deposited on AISI 52100 steel has been studied in ultra-high vacuum (UHV, 5.10Pa), high vacuum (HV, Pa), dry nitrogen (16Pa) and ambient air ( 1 6 Pa). "Super-low" friction coefficients below 0.004 were recorded in UHV and dry nitrogen, corresponding to calculated interfacial shear strength in the range of 1 MPa, about ten times lower than standart coatings. Ultra-low friction coefficient of about 0.013-0.015 were recorded in HV, with interfacial shear strength in the range of 5 h4Pa. Friction in ambient air leads to higher friction coefficients in the range of 0.2. Surface analysis performed inside the wear scars by Auger Electron Spectroscopy show no trace of contaminant, except after friction in ambient air where oxygen and carbon contaminants are observed. In the light of already published results, the "super-low" friction behavior range) can be attributed to a particular case of superlubricity, e.g. a combination of crystallographic orientations, surface chemistry and absence of contaminant allowing a strong decrease of the interfacial shear strength. 1. INTRODUCTION

Molybdenum disulphide (MoS2) is a wellknown lamellar solid lubricant with a hexagonal structure. Extensive survey dealing with the tribological behavior of sputter-deposited MoS2 coatings exists in the literature [l-41. Ultra-low friction of MoS2 coatings has been identified when running friction tests in the absence of oxygen andlor water vapour. In such conditions and depending on normal load in the sliding contact, friction coefficients values between 0.01 and 0.05 have been measured, which already represents uncommon values in solid film lubrication. The mechanisms of ultra-low friction of MoS2 (typically observed in dry nitrogen or in high vacuum) can be summarized with the three following conditions [2] : a. built-in of a MoS2 transfer film on the frictional counterface. This transfer film is

formed thanks to a good adhesion of MoS2 to the antagonist material. b. friction-induced orientation of the (0001) basal planes of the MoS2 grains in the interface products, parallel to the sliding direction (in the transfer film. the film itself and eventually the third body in general). It is anticipated that friction-induced basal plane orientation occurs very early at the beginning of sliding, by a simultaneous orientation-switching of all the individual nanometer-scale MoS2 grains in the interface. c. absence of contaminants. C a r b o n and oxygen are well-known contaminants of MoS2, coming from the residual gas during the sputtering process or from the MoS2 target. A special attention must be paid to the effect of water vapour coming from the ambient air or from a humid environment during storage, for example. It has been suggested

278

that liquid water could be formed by capillary condensation in the defects of the MoS2 crystal structure and that water could then modify the easy shear between basal planes [5]. Recently, using a dedicated ultra-high vacuum analytical tribotester, a "super-low" friction behavior was identified (average friction coefficient in the range) when testing in an ultra-high vacuum a sputtered MoS2 coating exempt of impurities such as carbon, oxygen and water vapour. In some cases, the recorded tangential force was hardly detected as if the friction force completely vanished. Although the as-sputtered grain size was not modified by the tribological process, frictioninduced orientation of the MoS2 grains in the contact interface was clearly demonstrated by electron diffraction and high resolution TFM studies, canied out on selected wear debris collected at the end of the friction test [6,7]. Consequently the three conditions exposed above are verified and thus are not sufficient to explain the origin of the "super-low" friction behavior. The Bowden and Tabor model of friction provides a good starting point for understanding how thin solid film can reduce friction [8].The friction coefficient is assumed to depend on the normal load W, the real area of contact A and the shear strength S of the interface film as :

The shear strength S of solids at high pressure has been observed to have a pressure dependence, approximated by 191 :

According to the hertzian theory, the friction coefficient in the sphere-on-plane configuration below the elastic limit depends on three variables [lo]as :

p = S O . J C . ( ~ . F U ~ . +E a )~~~.W ( 3-) ~ ~ ~ where E is the composite elastic modulus of the contacting materials, R is the radius of the ball. This model assumes that the real contact area corresponds to the herztian zone, as calculated in

equ.(3). This assumption is justified by the soft behaviour of MoS2 film and debris in the contact. It has been proven to be valid for thin MoS2 coatings [lo].Therefore, friction measurements can be used to determine So and a values : friction of MoS2 in dry air leads to So=25 MPa and a=0.001 [lo], friction in vacuum leads to Sp7 MF'a and a=O.OOl 11 11.

From these data, it appears that MoS2 coatings have So values which depend on the atmosphere during friction, since the presence of oxygen (in dry air) increases the shear strength of the film. These results suggest that surface chemistry due to atmospheric conditions during friction processes are of great importance on the tribologcal performances and mechanical characteristics of M o S 2 thin films. Taking into account this approach, different questions are raised, in order to go further in the understanding of the friction mechanism of these coatings : 1 . How do different kinds of atmosphere (Ultra-high vacuum, poor vacuum, nitrogen, air) alter the friction behavior of MoS2 for a given structure and film composition ? 2. According to equ. (1).what are the respective contributions of the shear strength S and the real area of contact A in the different levels of friction observed in various atmospheres ? In particular, is a "super-low" friction behavior due to a low value of the shear strength S or to a reduction of the real contact area A ? Wheeler [20]recently suggested that a partial pressure of pure oxygen reduces the friction by influencing the transfer of interfacial material to the pin in such a way as to reduce the area of contact. As an attempt to progress in this field, we performed tribological tests (pin-on-disc configuration) on pure and stoichometric sputterdeposited MoS2 coatings in various controlled atmospheres, at a given contact pressure. Experiments were canied out using a ultra-hgh vacuum analytical tribometer coupled with a preparation chamber, which has been already described in detail [13].With this apparatus, sputterdeposited MoS2 thin films were obtained on steel and analyzed by X-ray Photoelectron Spectroscopy (XPS) and Auger Electron Spectroscopy (AES).

279

Chemical analyses were performed by AES inside and outside the wear tracks, after each tribotest carried out in the different atmospheres. Optical micrographs gave an estimation of the real areas of contact in the sliding contact, thus allowing the determination of the shear strength S, depending on the atmosphere during friction. I n tlie following experiments, the normal load, the pin curvature radius and then the contact pressure were not changed, because of techcal difficulties in the UHV tribometer. Consequently, the computed values of So, S and a will be determined with a quite poor precision.

hemispherical pin (4 mm radius curvature) as a hard material, and several identical MoS2-on-steel coatings, we performed 100-cycle tests with a normal load of 1.0 N, corresponding to a mean contact pressure of 0.37 GPa, a linear sliding speed of 0.5 mmls and a 3 mm wear track length. Tribotests were performed in various kinds of controlled atmosphere :

2. FRICTION MEASUREMENTS VARIOUS ATMOSPHERES

2.3. Effect of the atmosphere on the friction coefficient We show the typical evolution of the average friction coefficient, as a function of the number of cycles in UHV. in HV and in d-N2 (Fig.1). In both UHV and d-N2 conditions, the friction coefficient begins at 0.01 but i t drastically decreases to 0.001-0.003 a few cycles later. In the case of the UHV test, negative values arise from the calculation indicating that, in this case, the noise can be larger than the signal from the transducer. In UHV, we practically observe a vanishing of the friction force, which has never been observed before. In HV conditions, the friction coefficient remains stable between 0.015 and 0.018 over the hundred cycles. The tribotests performed in at-Air (RH=40%) gave an average friction coefficient between 0.15 and 0.20 (not shown), as already published [16]. AES spectra performed inside the wear tracks are presented in Fig.Z(b-d). The AES spectrum of the initial film is presented in Fig.Z(a). No oxygen and carbon were detected inside the wear track performed in UHV and HV. No nitrogen was detected inside the wear track performed in d-N2. Oxygen and carbon were detected inside and outside the wear track performed in at-Air. These results show that friction in UHV, HV and d-N2 does not induce any chemical reaction in the sliding contact. Moreover AES confirms the absence of iron signals in all cases, thus indicating that the MoS2 layers in the wear tracks were not taken away after the 100

IN

2.1. Elaboration and characterization of MoS2 coatings Radio-frequency (RF)magnetron sputtering of MoS2 was performed on a cleaned bearing steel (AISI 52 100) surface at room temperature, using a previously degassed MoS2 target. A 120 nm thick film was obtained by sputtering MoS2 at 7.4 Wlcm2 with a current intensity of 300 mA. An insitu analysis of the coating was performed by X-ray Photoelectron Spectroscopy [7]. The Mo3d512 and S2p3l2 signals were respectively centred at 228.8 2 0.2 eV and 162.0 r ~ :0.2 e V , in agreement with already published values corresponding to MoS2 [14]. The chemical composition of the film was calculated using the Mo3d and S2p peak intensities and sensitivity factors published by Briggs et a1 [15]. The experimental S:Mo ratio was 2.04, thus suggesting the film to be nearly stoichiometric. Auger Electron Spectroscopy analyses did not show any trace of contamination element such as carbon or oxygen, within the detection limits of the technique. The TEM analysis of the coating has been already published [6].

2.2. Tribological conditions The friction measurements were carried out using a reciprocating pin-on-flat tribometer. The tribological parameters of the reciprocating pin-onflat machine were the following : using a steel

- ultra-high vacuum - high vacuum

05.10-8 Pa,

10-3 Pa, (d-N2) lo5 Pa, (at-Air) 105 Pa, (relative humidity RH=40%). (HV)

- dry nitrogen - ambient air

280

cycle tests. On another hand, no iron was transferred from the pin. 2.4. Estimation of the shear strength values of the MoS2 film From the hertzian theory, we can deduce the theoretical diameter of the contact zone D ~ ~ = pm 58 in our experimental conditions. This calculated value can be compared to experimental ones deduced from the optical micrographs, as shown in Fig.3. Whatever the nature of the atmosphere during friction, the diameter of the contact zones Dexp has values between 60 and 70 pm. Although the precise measurement of the track width is not easy due to blurred edges as seen with the optical contrast, the experimental values Dexp are all of the same order of magnitude than the theoretical one From these results and according to equ.(1). one can deduce that the friction coefficient of MoS2coated steel under elastic conditions is controlled by the shear strength S of the interfacial film, which directly depends on the nature of the atmosphere during friction. Table 1 gives the shear strength values S of the interfacial film, calculated from equ.(l) using a contact width of 58 pm. From equ.(2), the pressure-independent So value is less than the S values. However, assuming a=0.001 whatever the atmosphere during friction, as already mentioned in the literature [3], So is in the same range as S. As to conclude, the super-low regime is characterized by an interface shear strength of the order of 1 MPa.

3. THE ORIGIN OF FRICTION IN UHV NITROGEN

SUPER-LOW AND DRY

As mentioned in the introduction, the ultralow friction of MoS2 in high vacuum is generally attributed to friction-induced basal plane orientation. Friction coefficients in the range correspond to interface film shear strength values in the range of 10 MPa (assuming a=O.OOl, see equ. (2)). Superlow friction of pure and stoichiometric MoS2 reaches the range and w e have shown that this effect can be explained by a decrease of the interface

shear strength S to approximately 1 MPa. with no change of the contact area. The decrease of the shear strength has been correlated to a superlubricating state during friction. Superlubricity is the state in which two contacting surfaces exhibit no resistance to sliding. Shinjo el al. [17] have shown that superlubricity is related to the atomistic origin of friction and that the phenomenon appears when the sum of the force acting on each moving atom against the entire system vanishes. A specific case of superlubricating situation is frictional anisotropy [ 181 when incommensurate contacting surfaces are sliding on each other, which can be the case of two contacting crystal lattices at a certain misfit angle. The existence of superlubricity has been recently suggested for a hexagonal symmetry of the crystal: experiments were carried out by measuring friction between two contacting surfaces of cleaved mica, when changing the lattice misfit angle [19]. The friction force can be lowered by one order of magnitude. No frictional anisotropy could be seen in ambient atmosphere, showing that the absence of surface contaminants is a determinant factor to reach the superlubricating state. However, no direct experimental evidence for this mechanism has been given by the authors. In our opinion the results depicted in the present paper and in Ref. 7 give strong evidence for superlubricity of MoS2 coatings by frictional anisotropy in UHV or in d-N2. Considering these data, the effect of the atmosphere during friction can play a role at two levels : (i) change in the nature of the MoS2 crystal by chemical reaction (oxidation, atomic substitution) modifying both the basal plane orientation and the rotational disorder between grains. It has been suggested that the substitution of sulphur by oxygen atoms could be at the origin of an increase of the basal plane distance and could explain a decrease of the shear strength [20]. Alternatively, the formation of bulk oxides makes friction to drastically increase by eliminating "easy shear" basal planes. (ii) contamination or adsorption of the gas species onto the sulphur-rich basal planes, eliminating the frictional anisotropy effect by

28 1

-

masking the atomic lattice. This effect has been shown by Shinjo et al, using freshly cleaved mica surfaces [171. We observed that nitrogen did not modify the UHV super-low friction behavior of MoS2 and this is in agreement with previous work in the ultralow friction regime, indicating that no reaction takes place between the gas and the solid in the working conditions (as confirmed by AES investigations). An introduction of a low partial pressure of humid air has an effect very similar to the presence of impurities in the coating material. The friction mechanisms seems to be deeply affected by the presence of oxygen or water vapour. As no chemical reaction between these two impurities and MoS2 occurred, only physical processes have to be taken into account, such as liquid water condensation in crystal defects. More work is necessary to clarify if the crystal orientation is only affected or if the contamination is only involved in the processes

the width of the contact zones is very close to the theoretical width calculated from the hertzian theory. Consequently, the experimental values of the average friction coefficients are correlated to values of the shear strength of the interfacial film : 0.7-1.1 MPa in UHV or d-N2, 4.9 MPa in HV, and 56 MPa in at-Air, - in UHV, the vanishing of the friction force is attributed to a superlubricating state, by frictional anisotropy of basal plane oriented MoS2 grains. In dry nitrogen, it seems that the situation is hardly affected and that no vibochemical reaction exists between MoS2 and nitrogen, - in a partial pressure of water vapour, the increase of the shear strength cannot be attributed to a chemical interaction. It seems that physical processes such as liquid water condensation have to be involved in the mechanisms.

WI.

REFERENCES

4. CONCLUSION

We have studied the tribological properties of RF-magnetron sputtered MoS2 coatings deposited on cleaned bearing steel surfaces, in different environments. Using a Ultra-High Vacuum (UHV) analytical tribometer, with a sphere on plane reciprocating contact. Great care was taken to measure very low friction coefficients accurately,by optimizing the data processing and the calibration procedure of the friction force. - The friction coefficient exhibited by the MoS2 coating in UHV (5.10-8 Pa) and in dry nitrogen (lo3 Pa) was extraordinary low. The calculated average value on each cycle was below 0.003 and in some cases, the tangential force was hardly detected as if the friction force completely vanished, - the friction coefficient in HV (10-3 Pa) remains stable between 0.015 and 0.018 during the friction process, whereas the friction coefficient in ambient air (RH=40%) is comprised between 0.15 and 0.20,

T. Spalvins, J. of Vacuum Science and Technology, A5(2) (1987) 212. E.W. Roberts. Tribology International, 23(2) (1990) 95. I.L. Singer, "Fundamental in Friction: macroscopic and microscopic processes", I.L. Singer and H.M. Pollock (eds.), Kluwer Academic Publishers, (1992) 237. P.D. Fleischauer, R. Bauer, Tribology Transactions, 31(2) (1988) 239. M. Uemura, K. Saito, K. Nakao, Tribology Transactions, 33(4) (1990) 551. C. Donnet, T. Le Mogne, J.M. Martin, International Conference on the Metallurgical Coatings and Thin Films, April 19-23, 1993 San Diego (USA). To be published in Surface and Coatings Technology. J.M. Martin, C. Donnet, Th. Le Mogne, Th. Epicier, To be published in Physical Review B. F.P. Bowden, D. Tabor, The Friction and Lubrication of Solids (Clarendon Press, Oxford, 1964), Part 1 (pp. 110-121). Part 2 (pp. 158-185).

P.W. Bridgeman, Proc. Am. Acad. Arts Sci., 71 (1936) 387. I.L. Singer, R.N. Bolster, J. Wegand, S. Fayeulle, R.C. Stupp, Appl. Phys. Lett., 57 (1990) 995. E.W. Roberts, Proceedings of the Institute of Mechanical Engineering Tribology. "Friction, Lubrification and Wear, fifty years on", Institute MechanicalEngineering, London (1987) 503. D.R. Wheeler, Thin Solid Films, 223 (1993) 78. J.M. Martin, T. Le Mogne, Surface and Coatings Technology, 49 (1991) 427. T.B. Stewart, P.D. Fleischauer, Inorganic Chemistry, 21 (1982) 2426.

D. Briggs, M.P. Seah, "Practical Surface Analysis by Auger and X-Ray Electron Spectroscopies", Wiley Science, New -York, 1985. J. Moser, F. Levy. J. Mat. Res., 8(1) (1993) 206. K. Shinjo, M. firano, Surface Science, 283 (1993) 473. J.B. Sokoloff, Phys. Rev., B42 (1990) 760. M. Hirano, K. Shinjo. R. Kaneko, Y. Murato, Physical Rewier Letters, 67(19) (1991) 2642. J.R. Lince, M.R. H i l t o n , A.S. Bommannavar, Surface and Coatings Technology, 43/44 (1990) 640. M. Uemura, K. Saito, K. Nakao, Tribology Transactions. 33(4) (1990) 551.

Table 1. Average friction coefficient of a MoS2 coating against a steel pin at cycle N=100 and corresponding shear strength S of the interfacial film in various atmospheres during friction. See text for calculation procedure of s. Atmosphere during friction

UHV

Hv d-N2 at-Air

Average friction coefficient at cycle N=100

Calculated shear strength S (ma)

0.002 0.013 0.003 0.150

0.7 4.9 1.1 56.0

283

0*020

F

Number of cycles, N

Figure 1. Average friction coefficient versus number of cycles of a MoS2 coating tested in ultra-high vacuum (UHV: 5.10-8 Pa), high vacuum (HV: Pa) and dry nitrogen (d-N2: 1 6 Pa). Normal load: 1.0 N, mean contact pressure: 0.37 GPa. (3

IS

AIR

I

DO

a00

,

I

aoo

TOO

’

100

300

Energy (eV)

SO0

700

Figure 2. Auger sp ctra carried out on the MoS2 surface. outside the wear track (a), inside the wear tracks performed: (b) in UHV (5.10-* Pa), (c) in HV ( Pa), (d) in ambient air (lo5 Pa, RH=40%). (e) in dry nitrogen (10sPa). Primary electron energy: 5 keV.

284

b

Figure 3. Optical micrograph of wear scars on: (a) the steel pin and (b) MoS2 thm coated steel plane. Surrounding the Herztian mne (dotted line) we can observe a small amount of wear fragments.

SESSION VII COATINGS AND THIN FILMS Chairman:

Professor W 0 Winer

Paper VII (i)

Characterisation of Elastic-Plastic Behaviour for Contact Purposes on Surface Hardened Materials

Paper VII (ii)

On the Cognitive Approach Toward Classification of Dry Triboparticulates

Paper VII (iii)

Surface Chemistry Effects on Friction of Ni-P/PTFE Composite Coatings

Paper VII (iv)

Transfer Layers in Tribological Contacts with Diamond-like Coatings

Paper VII (v)

Surface Breaking Crack Influence on Contact Conditions. Role of Interfacial Crack Friction. Theoretical and Experimental Analysis

This Page Intentionally Left Blank

Dissipative Processes in Tribology / D. Dowson el al. (Editors) 0 1994 Elscvier Scicncc I3.V. All rights reserved.

287

Characterisation of elastic-plastic behaviour for contact purposes on surface hardened materials Ph. Virmoux, G. Inglebert and R. Gras L.I.S.M.M.A. Groupe Tribologie I.S.M.C.M. 3, rue Fernand Hainaut, 93407 Saint-Ouen Cedex, France

When one examines parts having worked under strongly loaded contact situations, irreversible marks can be seen; they are the results of a dissipative process: contact plasticity. Residual stresses measurements can confirm this plastic evolution. Often, for hard materials having a quite brittle response, tensile tests classically used to identify the characteristics for plastic behaviour give very uncertain results. Contact tests, such as indentations, coupled with a numerical model, allow a much better knowledge of this plastic behaviour using an inverse method. For components on which a thermo-mechanical treatment has been performed, such as carburizing or induction quenching, the surface layers have quite distinct elastic-plastic properties compared with the bulk material, and d o not exist freely. From our indentation test and associated code, the behaviour of these surface layers can be determined. The knowledge of the surface layers' behaviour will then allow the prediction of the evolution of treated industrial components. It will be quite appropriate especially for contact purposes such as those which are encountered in rolling bearings or gears. 1.INTRODUCTION

evolution under service of the whole treated part.

1.1.Contact plasticity

Mechanical parts, such as rolling bearings or gears, are subjected in motion to high contact loads which lead to an important gradient of stresses generating a phenomenon of contact plasticity [l] [2]. The appearance of plastic deformations and residual stresses in the material characterises this phenomenon (cf. Figure 1). Irreversible prejudicial marks can also be seen at the surface of parts having worked under strongly loaded contact situations. For a component on which a heat treatment (superficial induction quenching ...) or a thermo-mechanical treatment (nitriding, carburizing ...) has been performed, the surface layers have quite distinct elastic-plastic properties compared to the bulk material. The knowledge of the surface layers' behaviour is important, because it allows one to predict the

I

I

Depth below the surface (mm)

. a

I

Initial state Pmax = 4000 MPa

Pmax = 6000 MPa

Figure 1 . Evolution of nonnal residual stresses us maximal contact pressure (from 131)

This work has been done thanks to ROLLIX and P.S.A. societies.

288

1.2. Elastic-plastic behaviour A definition of a material elastic-plastic

behaviour requires the knowledge of an elasticity field and a hardening law which characterises this field evolution vs plastic strain. Tensile or compressive tests on ductile metals show the existence of a yield beyond which irreversible strains (plastic strains) appear, and of a yield variation in translation (kinematic hardening) or/and in dilatation (isotropic hardening). These yield variations are known as "Bauschinger effects". Superficial hardened steels have a martensitic or ferritic basis structure. Microscopically, these two structures have close crystallographic lattices (*), type BCC, for which easy sliding systems are quite distinct, and deviated sliding systems are rare [4]. This type of crystallographic structure easily explains that, macroscopically, elastic-plastic tensile curves of hard steels are quite bilinear. Kinematic hardening phenomena are then more important than isotropic hardening phenomena.

(a) Evolution ofglobal strain with stress

(b) Evolution of plastic straiii with stress

Figure 2. Linear kinematic hardening law 1.3. Classical tensile test

Hard materials have a quite brittle tensile behaviour, and so the initial yield strength ay and linear kinematic hardening modulus h cannot be precisely determined from a classical tensile test. Moreover tensile fracture limit and yield limit are rather close (cf. Figure 3).

A linear kinematic hardening law is

thus sufficient to describe the elastic-plastic behaviour of metals closely approximating reality (cf. Figure 2). With such a law only two constants can characterise the plastic behaviour: - the initial yield strength ay - the linear kinematic hardening modulus h The modulus h allows one to link the elastic Young's modulus E and the plastic tangent modulus ET through the formula: 1 = -1+ - 1 E, E h (*) Martensite is an

interstitial compound of carbon in a tetragonal iron lattice similar to ferritic BCC lattice.

I

&

Figure 3. E.ryeriinenta1 tensile curve ofa hard inaterial

Besides, the surface layer of a treated component does not exist freely, so determining its elastic-plastic characteristics from a classical tensile test on an homogeneous specimen is not possible. That is why a new method, which allows the determination of the treated surface layer elastic-plastic characteristics, has been devised.

289

2. ELASTIC-PLASTIC ANALYSIS METHOD

2.1. General principles

The elastic-plastic analysis is explained in Figure 4. It combines contact tests and a numerical simulation:

- Experimentally, indentation tests performed for many normal loads allow a determination of the material strain evolution from the measurement of residual indentations radius and depth.

- Numerically, an axi-symmetric model of the indentation is conducted using a 2D finite element code. Purely elastic analysis is based on Hertz theory. Elastic-plastic analysis supposes a material behaviour having a linear kinematic hardening law.

EXPERIENCE Indentation tests

for many contact pressiires

NUMERICAL MODEL Model of the contact

Finite elnrzent method

Elast ic-plnst ic calciilation program

J Experimental

Numerical

indentation profile

indentation profile

MECHANICAL CHARACTERISTICS OF THE SURFACE LAYER ELASTIC-PLASTICEVOLUTION STRESS & STRAIN DISTRIBUTION

Figure 4. Diagram of the elastic-plastic analysis principl

Surface l a y e r e l a s t i c - p l a s t i c characteristics can be obtained from a comparison between the experimental indentation profiles (characterised b y indentation radius and depth) and profiles obtained using the finite element model. For a multilayer material, bulk and each layer characteristics are successively determined. This method is derived from the method performed for homogeneous materials in the research group about cryotechnical bearings (GDR 0916 CNRS-CNES-SEP) [2] [3] 151 PI. 2.2. Indentation tests

For hard materials, plasticity phenomena can b e easily observed in sufficiently loaded contact tests. Analysing these contact tests is often difficult, because of the stress heterogeneity they entail. However, induced hydrostatic pressures are very high, a fact which explains the preponderance of plasticity phenomena over fracture phenomena. So the results given by this method enable a reliable and precise determination of the treated surface layer elastic-plastic characteristics. In order to avoid singularities and to have an easily modelled contact, we chose a spherical indentation. Contact tests are performed for maximal pressures at the contact centre ranging between 2000 and 8000 MPa in order to describe the whole elastic-plastic field of the material. Maximal pressures are calculated using Hertz theory taking into account normal loads applied on the ball by a contact test machine. From each test, experimental residual indentation radius and depth are determined from an indentation profile measured on a Talysurf 5 profilometer. The experimental process is shown in

Figure 5.

290

Pmax

-

(a) INDENTATION TESTS for many contact pressures

The contact test is modelled on the finite element code in axi-symmetry (cf. Figure 6 4 ) ) . We suppose the part consists of two different materials: one for the bulk material and another one for the treated surface layer. This hypothesis is reliable in our experimental tests taking into account the hardness profiles in surface treated parts (cf. Figure 6.(b)). Particular attention is given to the mesh size in the contact zone (cf. Figure 6.(c)). Perfect adherence is assumed to exist between the lavers.

RADIUS

hed zone (a) MODELLED ZONE

Hardness

(b) INDENTATION PROFILE Qire 5. Experimnitnl process

F 7

2.3. Numerical model 2.3.1. Presentation

(b) MATERIALS

The elastic-plastic calculation program has been performed on a P.C. from the finite element code ACORD2D, using the simplified analysis of inelastic structures developed by J. Zarka and G. Inglebert [7] [8]. This method is based on:

- an analytic calculation of contact stresses in elasticity calculated from Hertz theory at each mesh point, - a n estimation of elastic-plastic evolution only using purely elastic calculations and local projections.

(c) MESH 3gnre 6. Contact test model

29 1

From contact parameters (geometry, maximal contact pressure ...) a hertzian elastic calculation program enables the numerical evaluation of stresses at each mesh point, supposing a purely elastic behaviour of all the layers. It is a classical calculation of hertzian stresses created by a normal concentrated load on a plane surface and determined using Belayev's results. An elastic-plastic calculation program enables the evaluation of residual stresses after the contact. From it, all elastic-plastic data (strains, stresses ...) can be determined. The principle of the program is explained here after (Q 2.3.2.). When the elastic-plastic calculation is performed, having a graphical visualisation of the residual deform of the structure on the finite element code is easy. We can then evaluate indentation radius and depth due to the loading (cf. Figure 7). Numerical values of uy and h for the surface layer are progressively adjusted until experimental radius and depth and calculated solutions are sufficiently close.

2.3.2. Elastic-plas tic calculation program

To obtain the limiting state, two conjugate effects are involved: the local behaviour of the materials and the structural effects depending on the shape of the structure and the loading path.

Material behaviour The fundamental volume of material is considered as a microstructure made of inelastic mechanisms linked together through an elastic matrix. The local deformations of the inelastic mechanisms are taken as internal variables. A s we suppose a linear kinematic hardening law, the elasticity field of the two materials can be described through a Prager yield criterion (generalised Von Mises yield criterion using the Hill-Mandel principle):

Classical Von Mises yield criterion

d" 2

11

9

s uy

Prager yield criterion This work is performed from each contact test, which allows one to know the elastic-plastic behaviour evolution of the surface layer. If possible, a single value for each constant is searched for in order to describe the whole elastic-plastic field of the surface layer.

z.

-

(3)

where uii : stress tensor 1 S ~ = u ~3- - ( u l , + u 2 ~ + u 3 3 ) d i j

RADIUS

E;

stress tensor deviator : plastic strain tensor

The evolution laws for each mechanism are:

I

F i p r e 7 . Nuineriuzl indentntion

(4)

292

f(up)) is the convex function defining the

Consequently the global residual stresses p j

local yield surface:

and the global inelastic strain tensor solutions of the homogeneous problem:

S j\ S (p m - uy (5)

f(UF') =

la' are

pii Statically Adinissible with 0 in V and 0 on S,

E?

Kinematically Admissible with 0 on S,

Structure

So the global residual stresses pij are linearly

The quasi-static evolution of the structure can be obtained by solving a linear elastic problem with initial strains E P for the given loading, F d body forces in the volume V, T d surface forces on a given part S, of the boundary of the structure, and U d given displacements on the complementary part Su of the boundary

dependant on the global plastic strain

uijStatically Admissible with Fdin V , TdonS, Kinematically Admissible with U don S,

gii

Real stresses aij can be written as a sum of elastic stresses

&I;.

lntroduction of transformed variables The transformed variables Y are defined by:

If we introduce them in the expression of the local stresses on the elementary mechanisms, we obtain:

and residual stresses pij :

The same decomposition can be done for strains: So, the Prager yield criterion can be written:

So, the global inelastic strain tensor expressed by:

E;"

can be

Jc's;

-Yij)(Sf

2

-YJ

say

I n the space of the transformed variables Yq, the elastic field appears like a sphere centred on elastic stresses, whose radius is uy. For cyclic loading in the elastic shakedown regime, the final value of Y q can be estimated by a local projection. So, the whole elastic-plastic calculation can only use elastic

293

calculations and local projections: as soon as the evolution of the purely elastic solution 0: is known, the evolution of the yield surface vs loading path is completely known. The yield surface is deduced from the initial surface through a translation of vector s$. The way back from the transformed variables to the classical ones - global residual stresses p i j , plastic strain E$ - can be achieved quite simply through elastic calculations.

3. RESULTS

The method presented here above allows us to have a quite complete knowledge of the elastic-plastic behaviour of surface hardened materials and to determine the relative influence of the surface layer and the bulk material in this behaviour. So the following results are obtained:

A diagram of this elastic-plastic :alculation method is in Figure 8.

- Elastic-plastic characteristics From each contact test, values of the yield strength oy and the linear kinematic hardening modulus h of the surface layer are determined using- the numerical model (cf. Q 2.3.1.).

I lnitialconditions:

(7

0

E l

I Hertzian elastic calcul on each element

I

=+ uc'

Ed

I

i" iteration + Pmjection on the elastic space defined by PRAGER criterion f(UO,&~)SO 3 ui

Transformed parameters Y (New mechanical characteristics) =+ E' II

I

Elastic calculation: - Combination of the rigidity matrix [K] - Triangularisation of the matrix - Resolution of the linear system [u] - Calculation of deformation [ E ] - Calculation of stresses la] I

Figure 8. Diagram of the elastic-plastic calculation

Ei

I I

i = 1 No residual stresses i * 1 Residual stresses

evaluated by the method proposed by J. ZARKA mid G. 1NGLEBERT

294

Remark: the elastic-plastic characteristics of the bulk material are assumed to be well known. If such is not the case, the method presented here can be first applied to this bulk homogeneous material.

- Stress and strain distribution Global stress and strain tensors, elastic stress and strain tensors, plastic stress and strain tensors, residual stress and strain tensors are calculated for each element of the axisymmetric model. They all can be visualised on the finite element code, either through amplitude values at each mesh point or through curves of isovalues (visualised stresses are equivalent to Von Mises stresses).

J. Zarka and G. lnglebert and experimental residual stress distribution measured by X Ray diffraction.

Measurement of residual stresses Residual stresses are measured in different specimens at the surface and in the volume [9]. Measurements are realised on a SET X apparatus equipped with a linear detector and a computer for the automatic piloting of the goniometer and the estimation of stresses. This estimation on the surface of a polycrystalline material is obtained by X-Ray diffraction on the steel part under various angles corresponding to diffraction angles verifying Bragg's law (cf. Figure 9 ).

- Elastic-plastic evolution The evolution of indentation radius and depth vs maximal contact pressure can be determined from the indentation tests. This allows one to characterise the "indentation capacity" of the surface hardened material. Moreover the model of the contact allows one to visualise the state of the part after the contact for any contact pressure, and also to determine:

- the pressure of first plastification and the localisation of first plastified zones,

- the evolution of plastified zones in the surface layer and in the bulk material, - the relative influence of the surface layer and the bulk material in the elastic-plastic compressive evolution.

The axes system of the measurement is defined in Figure 10. In this system, we have:

4. VALIDATION

Obtained results are validated through a c o m p a r i s o n between residual stress distribution calculated b y the method of

This method enables one to determine residual stresses at the irradiated surface.

295

Knowing residual stresses in the volume is possible by removing inner layers by electrolytic polishing and by making measurements at the selected depth.

5. APPLICATION

We will now see the application of the method presented here before to a classical hardened bearings steel and explain the results it allows one to obtain. Parts of these results were shown at Congds Francpis d e la MCcanique [lo]. 5.1. Studied material

The studied specimen is a surface carbonitrided 27MC5 steel. The hardened layer is less than 0.5 mm thick and has a martensitic structure with a high rate of residual austenite (almost 30%) which can be characterised by X-Ray diffraction using a Manganese anticathode. With this anticathode, only the austenite peek on (3 1 1) plane appears in the window of the linear detector used for X-Ray measurement (cf. Figure 11).

Theoretical values of residual stresses The method of J. Zarka and G. Inglebert allows one to calculate for each element the residual stress tensor. A t a given depth, we can then know the values of oR(r)and a @ ( r )for any point placed at a distance r from the contact centre. The mean value of residual stresses which can be compared to the experimental value at the same depth is given by:

z=-I a2

1''

(o,+a,)rJr

The obtained superficial hardness is around 900 Hv whereas the bulk hardness is around 500 Hv.

800

600 400

200

(13)

0

where a is the radius of the irradiated zone.

0

UI

140

Remark: Taking into account initial residual stresses is necessary to be able to compare experimental and theoretical profiles of residual stresses in the surface hardened material.

145

I

I

I

150 155 160 20 (degrees)

1

165

b

170 I

296

carbonitrided layer elastic-plastic behaviour does not really follow a linear kinematic hardening law. This phenomenon is probably linked with the high rate of residual austenite in the surface layer.

5.2. Mechanical characteristics

Indentation tests have been done on carbonitrided 27MC5 steel for maximal contact pressures between 4000 MPa (pressure from which an irreversible mark can be seen on the specimen) and 8000 MPa using an alumina ball the diameter of which is 4 = 12.7 mm. The axi-symmetric model on the 2D finite element code ACORD2D is a square 4 x 4 mm .The carbonitrided layer is assumed to be 0.4 mm thick. The mesh is done of 2000 triangular elements with a high density in the contact zone.

- The yield strength uy determined here is lower than the one calculated using empiric laws linking this strength with superficial hardness. In fact the value of uy usually used to characterise a material is the value for 0.2% strain. Here this value is:

Combination of contact tests and numerical models enables to obtain mechanical characteristics of the carbonitrided layer. These results are consigned in Table 1. Many results are interesting:

- The linear kinematic hardening modulus h is really high for low stresses beyond the yield strength. The plastic tangent modulus E, is then close to the elastic modulus E. So detection of plastic strains for low contact pressures is difficult. This result enables to explain observations made on industrial parts which were plastified in motion.

- Only one value for yield strength uy has been obtained for all contact tests, whereas different values for linear kinematic hardening modulus h have been obtained. That means the

Natural state steel Young's modulus E (MPa)

200 OOO

205 OOO

0.3

0.3

1100

1450

Poisson's ratio v Yield strength q (MPa)

Carbonitrided layer

Pinax (MPa)

Linear kinematic hardening modulus h (MPa)

t

I

150 OOO

Table 1. Mtrhnwixl clznracteristics of the cnrbonitrided 27MC5 steel

4000 4500 5000 5500 6OOD 6500 7000 7500 7800

......

1500000

......

800 000 475000 325 000 250 OOO 160000 120 000 85 000 70 000

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

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

297

5.3. Evaluation of the tensile curve of the carbonitrided layer

Considering that the treated layer of the carbonitrided 27MC5 steel does not follow a linear kinematic hardening law, plotting from precedent results the elastic-plastic behaviour of this layer on one curve is interesting. "Rebuilding" the response of the surface layer to a tensile test is possible, considering that the maximal equivalent stress (calculated from Von Mises yield criterion) applied in the contact volume is equivalent to the stress applied in a section during a simple tensile test.

From each contact test, we determined one couple a y , h . Each couple is corresponding to one tensile behaviour secant model. Finding the point of the modelled tensile curve which is corresponding to the studied contact test is immediate using the hypothesis about stresses explained here above.

I }

The obtained curve which is modelling the elastic-plastic behaviour of the carbonitrided 27MC5 steel is in Figure 12. We can there easily see that the hardening law is more complex than the modelled one. However we can remark that complex results close to the reality have been obtained from simple hypothesis about material and hardening law.

5000 4500

4000

3500

7 300@

3 i!

2500

Gi 2000 1500 1000

I

500 U

l

0

1

2

3

4

Strain (7%)

'igure 12. Evaluatioii ofthe tensile curue ofthe treated layer of carbonitnded 27MC5 steel

5

6

298

5.4. Elastic-plastic evolution

are both determined using the numerical model).

Once the model of the carbonitrided part is done on the 2D finite element code and the mechanical characteristics of the bulk material and the surface layer are well known, studying the elastic-plastic evolution of the part vs maximal contact pressure is easy. It allows one to obtain results which cannot be reached using contact tests alone. 5.4.1. Beginning of ylastification

Contact tests have been done for maximal contact pressures superior to 4000MPa. Indeed this pressure is the one under which n o indentation can be experimentally detected. But this fact does not mean that there is no plastification in the material for lower pressures. Because of the surface rugosity of the specimen, determining the beginning of plastification is often hard. The numerical model for this contact allows one to evaluate the beginning of plastification by doing calculations for low contact pressures. The study of carbonitrided 27MC5 steel shows that plastification begins for a maximal contact pressure equal to 2400 MPa. For this pressure, the maximal equivalent stress in the volume (calculated from Von Mises yield criterion) is localised in the carbonitrided layer and is equal to ay=1450 MPa, so that plastified elements appear. 5.4.2. Evolution of indentation radius

Contact tests allow one to determine the evolution of indentation radius vs maximal contact pressure. We can verify in Figure 13 that this evolution is quite bilinear. This result can be explained if we compare the evolution of indentation radius vs evolution of plastified zones at the surface and in the sub-layer (they

0 1000 2000 3000 4000 5000 6000 7000 800( Maximal contact pressurr (MPa)

Indentation radius

Indentation radius

Radius of the surface Radius of the sublayer plastified zone plastified zone

Figure 13. Evolution of indentation radius

- First, for maximal contact pressures inferior to 6000 MPa, the indentation radius is evolving like the radius of the plastified zone at the surface. For low pressures, the sub-layer does not play an important part in contact. But, when the contact pressure increases, the sublayer plastification is evolving quite faster than the surface plastification.

- Secondly, for high contact pressures, the sub-layer plastification is so important that the indentation radius is evolving like the sublayer plastified zones. The carbonitrided layer has here a secondary part in the contact.

299

5.4.5. Residual stresses

5.4.3. Evolutwn of indentation depth

Contact tests and numerical models allow as well to know the evolution of the indentation depth vs maximal contact pressure and to compare it with the evolution of the sublayer sinking (cf. Figure 14).

Validation of previous results has been done by comparison between experimental and numerical profiles of residual stresses at the surface and in the volume (cf. Q 4). Experimental parameters for X-Ray diffraction measurements are in Table 2. Results for the indentation obtained for a maximal contact pressure equal to 8000 MPa are in Figure 16. These results confirm that our numerical model allows u s to predict a material elastic-plastic behaviour close to the real one.

0 1000 2000 3000 4000 5000 6000 7000 8001 Maximal contact pressure (MPa)

0

Sinking of the sublayer Indentation depth

3 p r e 14. Evolution of indentation depth

The indentation depth is evolving more and more quickly when the contact pressure increases. Two phenomena can explain this fact. First, the sub-layer plays a part more and more important in the contact and its sinking becomes high for high pressures. Secondly it has been shown that the indentation depth is linked with the kinematic hardening modulus h. As h is decreasing for high pressures, the indentation depth is evolving fast. 5.4.4. Material behaviour

Figure 15 is an abstract of the elasticplastic evolution of the carbonitrided 27MC5 steel. I t describes the beginning of plastification, and the evolution of indentation radius and depth, of plastified zones, of global stresses and of residual stresses in the material.

Apparatus

SET X

Anode Diffraction line radiation

K a Cr(211)

Cr

Numberof tp angles Numberof ly angles

2

Acquisition time

120 s

Surface of irradiation

9 2mm

11

-

Table 2. X-Ray diffraction parameters

I

I

I

Depth below the surface (mm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-500

I

I

I

I

I

X-ray diffraction

Pmax = 8000 M p a

Figure 16.Residual stresses

I

300

1

Pmax = 2400 MPa c ~ > 1450 , MPa ~ in~ the ~carbonitrided ~ ~ layer

Beginning of plastification in the carbonitrided layer. Indentation and residual stresses appear.

Pmax = 3000 MPa

The plastified zone is reaching the surface. The indentation radius is about equal to the radius of the surface plastified zone. Beginning of surface plastification

Pmax = 3500 MPa oMisrs> 1100 MPu in the bulk material

Beginning of plastification in the bulk material.

I

I

Pmax = 7000 MPa

Plastification is proceeding quite faster in the bulk material than in the carbonitrided layer. The indentation radius is nearly equal to the radius of the sub-layer plastified zone.

? p r e 15: h4atenhl elastic-plastic mollition

30 1

6. CONCLUSION

An inverse method, coupling numerical and experimental results, has been derived to approach the plastic behaviour of surface hardened materials. Only the used normal load and geometrical data are sufficient to derive this behaviour law. Results obtained on the carbonitrided 27MC5 steel emphasise the interest and potential efficiency of the method even for a complex hardening law of the studied layer. Tests on other materials are planed thanks to our sponsors to confirm these results. NOMENCLATURE Young's modulus Plastic tangent modulus

E ET

f(of9))Local yield condition 'I

Body forces Linear kinematic hardening modulus Elastic compliance Maximal con tact pressure Stress tensor deviator Part of the boundary of the structure where surface forces are given Part of the boundary of the structure where displacements are given Given surface forces Given displacements Local transformed parameters Global strain tensor Purely elastic strain tensor Inelastic strain tensor Global plastic strain tensor Initial plastic strain Poisson's ratio Residual stress tensor Mean stress value

aq

Initial stress Radial stress Tangential stress Global stress tensor

aet

Purely elastic stress tensor

ay

Initial yield strength X-Ray diffraction angles

a, OR 00

'I

q, J/I

REFERENCES K.L. Johnson, Contact Mechanics, Cambridge University Press 2. G. Inglebert & al., Fatigue dans les roulements, MCcanique MatCriaux ElectricitC, Revue du G.A.M.I. No441 pp 11-13 (1991) 3. V. Audrain, Fatigue de contact d'un acier B roulement B tempirature ambiante et cryotechnique. Etude expirimentale et modklisation, Thesis E.N.S.A.M. Paris (1992) 4. R. Bensimon, Les Aciers (tome I), PYCEditions (1971) 5. G. Inglebert & al., Residual stresses induced by contact fatigue. Experimental and modelling study, Residual stresses, Francfort, pp 655-662 (1992) 6. V. Audrain & al., Characterisation of elastoplastic behaviour applied to the contact, Eurotrib'93, Budapest, Vol. 5 pp 272-277 (1993) 7. G. Inglebert & al., Structures under cyclic loading, Arch rech., Varsaw, 37 4-5 pp 365-382 (1985) 8. G. Inglebert, Quick analysis of inelastic structures using a simplified method, Nuclear Engineering and Design No 116 pp 281-291 (1989) 9. L. Castex & al., Publication E.N.S.A.M. No22 (1986) 10. Ph. Virmoux & al., Acier 27MC5 CarbonitrurC. Caractirisation micanique de la couche traitde A partir d'essais d e contact, Actes du llkme Congrks Franqais de MCcanique, Vol. 4, pp 85-88 (1993) 1.

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Dissipative Processes in 'I'ribology / D. Dowson ct al. (Editors) 0 1994 Elsevier Science U.V. AU rights reserved.

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On the Cognitive Approach Toward Classification of Dry Triboparticulates Hooshang Heshmat" and David E. Breweb "Technology Group, Mechanical Technology Incorporated, 968 Albany-Shaker Road, Latham, New York 12110, USA bU.S. Army, ARL, NASA-Lewis Research Center, Cleveland, Ohio 44135, USA

To relate wear debris to a wear mechanism is a challenging task since one must describe the particle shape. Here, the "cognitive approach" is adapted to classify particles of powder, wear debris, and hiboparticulate matter in general. This method is considered to be not only convenient, but also the best method that the state of the art can provide over other known mathematical models, when complex particles are the subject of study. This paper describes a procedure used to select suitable experiments to develop a fundamental understanding of packdsheared dry particulate samples. As part of the triboparticulatecharacterization,packed samples of ten various dry powders were prepared for investigation. Each pressed sample was then fractured diagonally and three sites (fractured, pressed and sheared) were examined. This paper presents scanning electron photomicrographs (SEPs) of a particle ensemble from each site, along with a quantitative image analysis (QIA)of the individual particles, and the relationship between the powder property and average particle size. It has been postulated that solid particulates in an interface gap, when sheared, exhibit a molecular-like motion in liquid lubrication. It is a widely accepted assumption, however, that these molecules, under mild shear slress, remain unbroken and unworn. Fine solid triboparticulates, on the other hand, even under mild stress, undergo tribocomminution, i.e., they deform, fracture, wear, agglomerate, and alter their physical and chemical states. In other words, they do not remain in the precise condition, like molecules, in which they first began to exist or entered into the interface gap. Since utilizing the cognitive approach to describe the shape of a particle itself is a matter of subjectivity rather than collectivity in terms of a scientific approach, this paper discusses some of the pros and cons relevant to application of the cognitive approach toward classification of particulates in tribology.

INTRODUCTION

Recent works have demonstratedthat solid particles can form load-carrying lubricant films and that triboparticulate films exhibit a quasicontinuum behavior resembling that of fluid fdms. Given the proper particulate size and appropriate tribosurface geometry, the particles exhibit a layer-like shearing reminiscent of genuine fluids. Dry triboparticulates can flow like liquids. But, unlike liquids, they can, to a certain degree, withstand imposed shear forces without deforming or flowing. Thus, a lubricant consisting of a fine debris or dry powder inserted either deliberately or generated by wear of the mating surfaces constitutes a viable lubricant that generates the required flows and

presslires to prevent contact between surfaces. A mechanism of hiboparticulate flow that possesses some of the basic features of the hydrodynamic lubrication regime holds only for a certain range of particle sizes with respect to the nature of mating materials. A h y p thetical curve for wear of a particular material combination versus particle size is shown in Figure 1. When the particles are large, their behavior is primarily one of an in-situ elastic body; when they are very small, they compact to form a nearly solid body. Between the two regimes, there is another regime where the particles exhibit a layer-like shearing, reminiscent of fluids. The latter is deemed responsible for the drop of wear in the regime [1-4].

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For the purposes of this discussion, the terms "lubricant" and "triboparticulates" are defined as follows: Lubricant: any substance (gaseous, liquid, wear debris, powdered, or solid) located in the clearance that is not integral with either surface. Triboparticulates: any ensemble of particles that vary in size and shape, are in a solid form, and have tribological properties with respect to a particular tribosystem (wear debris and dry powder). The tribological process is dynamic in nature, and released wear debris is always present in the interface gap. Any wear particles produced by the sliding process thus should be considered a lubricant, and, since wear accompanies all dry sliding, there is lubricant present in all tribological processes. To quantitatively evaluate the performance of triboparticulatefilms, an equivalent rheological model that describes lubricant behavior in terms of its relevant physical properties and characteristicsis required. This paper reviews the classification of triboparticulates, addressing the main characteristics of particle size, particle geometry, and powder density (solid fraction). The paper also attempts to highlight their salient features, and, most importantly, their interrelationship with respect to their roles in triboparticulate rheology. To relate wear debris to a wear mechanism is a challenging task since one must describe the particle shape. Here, the "cognitive approach" is adapted to c l a s s 9 particles of powder, lubricant, and triboparticulate matter. This method is considered to be not only convenient, but also the best known method to study complex particles. Cognitive science stems from a recognition process. In this context, "recognition"means the continual adaptive matching or fitting of elements in one physical domain to the novelty occurring in elements of another more or less independent physical domaina matching that occurs without prior instruction [ 5 ] . All the laws of physics nevertheless apply to systems derived by the recognition process. However, the cognitive approach has its own drawbacks. To illustrate this point consider popcorn as an ensemble of matter that has similar shapes. One might compare the shape of some unknown particle or matter to the shape of popcorn. However, this very familiar item, popcorn, has no definitive describable shape, nor could one find two popcorn shapes exactly alike in a

ton. The similarity of one popcorn to another is deceiving to the observer's eye, stemming from their color, density, average size, their common peculiar irregular shapes, etc. On the other hand, it is widely believed that the approach toward the classification of triboparticulates ought to be scientific. The parts of this approach must be testable, and it must help to organize most, if not all, of the known facts about triboparticulates and their formation. To accomplish this means sifting through several layers of triboparticulates in a tribosystem. However, to relate wear debris to a particular wear mechanism is analogous to stating: "If one could show us the footprints of a dragon, then we could state whether or not the dragon was here!" Although it is perhaps the smallest and most superficial characteristic, geometrical (shape) description of triboparticulates has become the chief determinant of the boundary and property of particles. Thus, using a cognitive approach to describe particle shape is a matter of subjectivity rather than collectivity in terms of a scientifk approach. Therefore,we propose that the cognitive approach should be emphasized and the appre priate logic, such as rule-based logic ("fuzzy logic"), should be used toward its relevant tribological role. BACKGROUND

The constitution of a particle assembly is a major factor in determining the tribological behavior of triboparticulates. Size is a relative term and in using terms such as coarse, big, small, fine, etc., to describe particles in an interface gap, the size of the particles must be related to the gap (film) dimensions and classified with respect to their use or relationship with particular tribomaterials. Particles can be classified as primary or secondary based on their nature rather than their shape or size. Primary particles stand alone and do not associate with other particles. Secondary particles may join together to form agglomerates that move like a single body (Figure 2). Powders that consist mainly of primary particles are free flowing; there is no cohesion of particles and the force of gravity predominates. This type of powder is usually coarse and does not have good tribological properties. Powders with good tribological properties are generally fine and are a mixture of primary and secondary particles.

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In this type of triboparticulates, surface forces, van der Walls adhesion forces, electromagnetic, electrostatic, molecular, and valence forces play a more significant role. In a tribological system, particles may undergo a tribocomminution process in which their geometries change and become more complex even if their initial geometries were simple. Furthermore, in this system, particles are produced (such as wear debris), altered, destroyed by diffusion, absorption, and thermochemical reactions. In addition, the density of triboparticulates is a strong function of the degree of packing or compaction, and this affects the way the powder behaves in a film. The mass of the particles is also important because it influences the interactions between particles and their surroundings. Tnboparticulateensembles can be categorized into a combination of the physical dimensions of mass, volume, and time. The interrelationship of mass and volume (or density) and the determination of this basic property is essential to understanding the film behavior of triboparticulates. In the relationship of mass-tc-mass, the phenomena of particle-particle or particleenvironment/particle interaction is important. Finally, the volume-to-volumerelationship influences the degree to which the particles are packed together during the tribochemical process that occurs with compaction. Mass, volume, and time play important roles in categorizing powder behavior as shown in Table 1. The mass-time and volume-time relationships are very significant in powder lubrication, because these relate to flow of the powder. Powder density and the ability of a powder to flow can be enormously influenced by the size, distribution, and shape of the particles; their surface and physical properties; and the properties of the associated environment. The above discussion only briefly mentions the role and effect of solid bodies intended to impose shear onto triboparticulates film in tribosystems. The interaction between a solid body surface and triboparticulates should be considered in a class by itself (boundary conditions) and dealt with separately. PARTICLE SHAPE AND SIZE

Over the years, many studies have been conducted on the packing of particles [6, 71, and it has been found that one of the most important factors is

the distribution of the size of the particles. The tensile strengths of fine powder depend on their packing fraction [3], particle size and shape [8, 91, chemical nature, and other factors. It has also been postulated that the formation of a quasi-hydrodynamic powder film is limited to a certain range of particle size [3]. Outside this size range, the presence of particles will result in wear of the tribosurfaces. The random form of the particles in a particle ensemble means that the properties of a triboparticulate film can only be described in stochastic terms. Nevertheless, in recent years, a number of mathematical models have been proposed to predict some properties such as porosity and flow for simple particle geometries. The size of simple geometric forms such as a sphere, cuboid, or rod shape can be defined in terms of a small number of dimensions. Unfortunately, triboparticulates rarely have simple shapes, and analyses so far have been based on recognizable shapes as shown in Figure 3. The tribological significance of some of these shapes is discussed below. Figures 4a and 4b show optical micrographs of spheroidal nickel powder, while Figure 5 shows a scanning electron microscope (SEM) photograph of the nickel oxide on the surface of one of the particle spheroids shown in Figure 4b. Figure 6 shows a light micrograph of a packed, nickel oxide powder in which the particles have spherical or irregular shapes. These shapes could become far more complex if the powder was subjected to a tribological process (tribocomminution). Figure 7 shows a light micrograph of a rutile form of titanium dioxide powder that had been isostatically pressed at 10,OOO psi. The powder particles do not conform to any particular geometric form. As shown in Figure 8, boron nitride powder contains particles of irregular polyhedric, isometric, and nonisometric shapes combined with particles with flake (plate-like) shapes. The flakes are 1- to 2-pm thick and 10 to 20 pm in diameter. Figure 9 shows an example of mixed powders of rhenium oxide and copper oxide. It is much more difficult to identify particle shapes in these mixtures. There are highly porous regions, which are groups of primary particles, held together by agglomerates and aggregates (secondary particles). One must note that even a high resolution micrograph provides only some

306

two-dimensional information on the particles' surface image, which is far removed from their total form. Equivalent Particle Diameter In order to characterize the size of irregularly shaped powder particles, it is convenient to use the concept of an equivalent spherical diameter. Definitions for the equivalent particle diameter (D,) vary, depending on the particular powder properties being addressed. Some examples of these are: Equivalent volume diameter: D, = d, = ( 6 f l ) ' ' Equivalent surface diameter: D,, = d, = ( S / X ) ' ~ Equivalent surface-volume diameter: D, = ds, = 6V/S Equivalent projected area diameter: D, = da = ( 4 A l ~ ) ' ~ Equivalent perimeter diameter: D, = dp = P/z Martin diameter: D, = dM = (LX + d,,,,,,)/2 Sieve diameter: D, = dSi where V is particle volume, S is particle surface area, A is projected area of particle, P is perimeter of particle, is maximum particle diameter, and d,,,,n is minimum particle diameter. It should be kept in mind that the surface density of a particle is minimized when the equivalent spherical shape is considered relative to any other possible particle geometry (surface density is the ratio of surface area to its volume). As reported in Reference 3, when particles become other than spherical, the solid fraction and the number of contact points rise and can increase by as much as 50%. Therefore, the equivalent particle diameter is a convenient parameter only for characterization of particle size and should be treated in conjunction with other parameters. One always begins with the simple, then moves to the complex, and, through desperation or the urge for elegance, one often reverts to the simple in the end. Such is the course of the state of the art in defining particle size. It is tempting to try to impose unity on disparate blocks of knowledge, and the state of the art in presenting equivalent particle size may

seem a case in point. However, it is not the urge for elegance that motivates the present practice of assigning a common equivalent spheroidal diameter to all sorts of particle shapes. Rather, it is desperation that constitutes the driving force behind this overly simplified assignment of equivalent diameter to the various unrecognizable particle shapes. Particle Shape Index There are several approaches used to characterize particle shape. One of these, the geometric signature approach, has been used to characterize the shapes of primary particles. This approach is based on a Shape Index, which is a nondimensional function of two or more equivalent diameters. Many fonns of the Shape Index have been used. One widely used example is the Wadell Index, @, which is defined as follows: @ = [dJd,]' @ is therefore a function of the ratio of the diameter of

a sphere having the same volume as the particle and the diameter of a sphere with the same surface area as the particle. Since a sphere has the smallest surface area for a given volume, the maximum value for @ is 1. For a cube, equals 0.806, and round sand particles have a value of @ in the range of 0.8 to 0.9. One of the shortcomings of the widely used Wadell Index is that the value of @ is not unique; an infinite number of shapes could have the same value of @. One modem technique for characterizing the shapes of fine particles is the geometric signature waveform [lo], which is applied to a projected profile (image) of the particle. A reference point is chosen within the profile, usually the centroid of the profile, and a vector is drawn from this point to the periphery. The vector is then rotated in equal increments, and the length of the vector is recorded. An example of the construction and appearance of a geometric signature waveform is shown in Figure 10 [l 11. The waveform can be subjected to Fourier analysis, and the harmonic spectrum can then be used to characterize the particle shape. This technique is a powerful method of describing a particle shape as long as the profile is not too complex or irregular. For very irregular profiles where the vector may intersect the profile periphery at a number of points, there are uncertainties associated with this technique. Further, it cannot be used

307

to characterize very rugged profiles such as those of carbon-black agglomerates. Here, the first difficulty is locating the centroid, which sometimes lies outside the profile. The second difficulty involves establishing the vector R, which is drawn from the centroid to the boundary. It is especially challenging if the vector R crosses the boundary several times, making it difficult to know which value of R to use to set up the geometric signature waveform of the profile. There are other approaches to particle shape characterization besides geometric signature. Kaye [ 111 claims that the fractal dimension (a measure of the ruggedness of the two-dimensional profile of a particle) provides a better description of particles. Another approach involves image analysisbased on morphology [ 121. The theory of morphology enables the observer to measure specific features of an image or surface following rigorously defmed procedures. At present, morphological analyses are limited to the analysis of surfaces [13] and cannot be applied to threedimensional bodies. COMPACT BULK DENSITY OF TRIBOPARTICULATES AND POWDER CHARACTERIZATION From a rheological standpoint, bulk density is an important parameter that affects the yield behavior, the equivalent viscosity, compressibility, flow rate, and heat transfer properties of a triboparticulate system [14-191. The bulk density of a powder does not have a specific value such as it would have for a solid. It is a complex property that is a function of the shape and size of the particles, the degree of compaction, and the conditions to which the triboparticulate ensemble is exposed. Compaction has a profound effect on the physical properties of a triboparticulate ensemble such as density, elasticity, plasticity, deformation rate, fragmentation, coherency, strength, and so forth. The compressibility of the triboparticulate ensemble is considered to be an effective parameter for quantifying the uniformity of particle size, shape, hardness, moisture content, shear strength, and cohesiveness of particles. Therefore, compressibility may be a useful tool in selecting triboparticulates and assessing their rheology. This unique property of the wear debris particles and, in general, triboparticulates, may be

utilized as a cognitive means to characterize a dry particulate ensemble. To clarify this phenomenon and develop an understanding of packedsheared triboparticulates, experiments were conducted on more than ten dry triboparticulates samples. These powders were selected based on their tribological and rheological characteristics as discussed in References [ 181 and [20]. Seven different powder compositions were selected for investigation: titanium dioxide (TiO,) consisting of three powders, the first two with the same crystal form (futile) and the third one in anatase form; two different average particle sizes of molybdenum disulfide (MoS,), cerium trifluoride (CeF,), zinc oxythiomolybdate (ZnMo0,SJ. carbon graphite, fire-dry fumed silica (SiO,), and nickel oxide (NiO). Experimental Setup and Powder Characterization Procedure Accurate measurement of density variations in packed bulk powders are quite difficult. However, qualitative assessments of the density variations were made using the following technique. Designed and fabricated to act as a consolodometer, the test fixture shown in Figure 11 consists of a cylindrical container and a piston made of porous nickel base alloy. The piston and cylinder porous media (0.5 micrograde) allow fluids (gasiliquids) to escape from the compressed samples. Each test was initiated by pouring and tapping the powder sample simultaneously into the porous cylinder until the powder amount was leveled flat with the top of the cylinder. The sample powder to be tested was then weighed and placed under the press in the test rig. The tapped powder mass-tocylinder volume ratio was considered to be the reference powder density (pJ The test was continued by applying a steady load to the piston in small increments. At each load increment, piston displacement was measured. Piston displacement versus load was converted to a change in volume, which, in turn, was used to calculate the change in bulk density as a function of pressure (oYy). Pressed sample powders were then extruded from the test cylinder to characterize the triboparticulates. Light micrographs were taken and QIA performed. Each pressed sample was fractured diagonally, and a total of three sites (Figure 11) were examined

308

thoroughly: the compressed face, the fractured face, and the boundary layer face. Figure 12 presents a photograph of a prepared powder sample. The latter was considered a boundary layer face since a thin layer of fine powder adhered to the inner surface of the tube under the action of shearing and sliding during removal of the pressed sample from the test fixture (akin to the extrusion process). Examination of the adhered layer of the sample powders on the inner surface of the test cylinder revealed a noticeable resemblance to the surface appearance of the pressed sample's wall (Figure 11, boundary layer face). The cylindrical surface of the pressed powder sample is designated by the boundary layer surface in Figure 11. This surface appearance provides insight into the nature, orientation, and condition of triboparticulates in a boundary plane between the intermediate film and core powder lubricant. Appearance and Characterization of Pressed Powders

The following paragraphs review the appearance and characterization of the selected test samples. Information relevant to powder properties is presented such as 50% accumulative particle size range (<), purity level, thermal properties, SEPs, results of qualitative image analysis, and powder density. To conserve space, sample powders TiO,, MoS,, and ZnMoO,S, are discussed (see Reference 3 for further details). Powders TiO, (Rutile Form) Titanium dioxide in a rutile form is considered to be a lubricous material. The tribological properties of the bulk solid rutile form and its relevant hypothesis explaining its lubricious nature were proposed and reported recently by Gardos et al. [21 and 221. Friction, traction, and wear tests with powder rutile (TiO,) were reportedly indicative of promising results [23 and 241. Titanium dioxide powder (TiO,, rutile form) has a boiling point of 2480 to 3000°C, a melting point of 3300 to 3330'C, and a molecular weight and density of 79.9 and 4.26 g/cc, respectively. Particulate size analyses of the powders are based on a 50% accumulative particle size distribution of 2 pm for Sample Powder A and 5.95 microns for Sample Powder B, and these were 99.5% pure. Impurities found in Powders A and B included A1 - 0.04%, Ca - 0.05%,

-

Cr - 0.1%, Cu - 0.001%, Fe - 0.02%, Mg - 0.04%, and Si - 0.04%. SEPs of pressed Powders A and B are presented in Figures 13 and 14, respectively. Each figure consists of SEPs of three sites: compressed, fractured, and sheared (boundary layer). The common feature among SEPs of Figures 13 and 14 is the appearance of the sheared faces (boundary layer face). Close examination of these sites indicated that the particulates have a tendency to be densely packed and also that their size appears to be smaller than the other sites (i.e., compressed and fractured sites). However, the compressed and fractured sites of Powder B show some indication of fractured and crushed particles as a result of compressive stress. The fracture marks are more pronounced on those particles that are relatively large in size. Furthermore, Powder B exhibited a high level of porosity relative to Powder A. Powder C, TiO, (Anatase Form) This material is typically used in the sandpaper industry because of its abrasiveness, and it is also used widely to produce oil base white paint because of its stable chemical composition and thus its color. Titanium dioxide white crystalline powder, anatase form, has a boiling point of 2500" to 3000°C, a melting point of 1830' to 185OoC, and a molecular weight and density of 19.9 and 3.84 glcc, respectively. Analysis of Powder C showed it to have a 50% accumulative particle size distribution of 0.4 pm. Spectrographic analysis indicated it to be 99.9% pure with impurities including A1 cO.Ol%, Co ~0.01%.Mg cO.Ol%, and Si ~0.02%. SEPs of the compressed and fractured faces of the sample pellet are shown in Figure 15. As shown, particulates in this powder maintained a spheroidal shape and some formed agglomerates. Powders D and E, MoS, (Lubricating Grade) Lubricant-grade molybdenum disulfide (MoS,) is used alone as a lubricant and as a lubricant additive to reduce friction and wear. MoS, was obtained in two grades, suspension grade (Powder D) and technical grade (Powder E). which are essentially the same except for average particle size. The 50% accumulative particle size distribution was 1 to 2 pm for Powder D and 12 pm for Powder E. With coarser particles, Powder E readily formed agglomerates when poured out of its container. When the finer size particles were pressed, Powder D formed an aggregate volume of discrete particles. Powder E

-

-

309

also showed an aggregation after being pressed. However, during the extrusion process, the edges of the test sample pellets fractured off, producing crumpled fragments with various sizes of aggregates. SEPs of pressed Powders D and E are presented in Figures 16 and 17, respectively. Fractured and compressed sites of both samples indicated that the particles consist of irregularly shaped platelets with a large diameter-to-thickness ratio. A comparison between these SEPs of compressed and fractured faces to the particles of unpressed MoS, powders revealed no significant differences, except the change in porosity levels. The most significant observation here is the generation of a distinct pattern occumng on the sheared face of both powders. The sheared faces of pressed Powders D and E were photographed with extra magnification to bring out this feature as depicted in the bottom of Figures 16 and 17. The form that they assume is of particular interest from a tribological point of view. Packed particles at this site form dense clusters reminiscent of the surface pattern of cauliflower tops. The surface topographies of various sputterdeposited MoS, films are shown by Fleischauer et al. [25] and Pierce et al. [26]. In these papers, the different surface topographies were produced as a result of differences in the growth pattern of the films. The shape of the MoS, particles, like domeshaped "cauliflower tops" was produced via sputter deposits at the lowest temperature (24" to 70°C). Although the process of producing similar morphological patterns with MoS, is completely different here (shearing packed powder versus sputterdeposited film), the relevant tribological characteristics of the "cauliflower pattern" is an intriguing subject. The cauliflower pattern induced by shearing of the packed powder (yielding), considered to be a boundary layer face most likely separating the intermediate film from core powder, is a reproducible process and independent of the MoS, particle size. This interesting phenomenon should be investigatedthoroughly beyond the scope of the present work since it is believed to contribute immensely to the slippery nature of the MoS, powder film and thus its rheological nature. The aforementioned observation with MoS, powder vindicates the earlier argument regarding the

particulate shape description. By comparing the boundary layer face with the other two sites, one can see clearly the difficulty associated with relating shape and size of wear debris to a wear mechanism in a tribosystem. In Figures 16 and 17, the sheared face patterns indicate a simple tribocomminution process that plays a major role in the formation of particulate patterns regardless of particle average size and shape (pressed or unpressed). Powder G, ZnMoO,S, Zinc dithiomolybdate, with a chemical name of "zinc oxythiomolybdate," was studied because of its high-temperature lubrication property and complex particulate and chemical nature [24, 271. The reaction temperature, reported also by Sutor [28], was that ZnMoO,S, lubricant began oxidation (decomposition)at moderate temperatures (approximately 260°C) in air. It was suggested that the major oxidation product of Powder G is zinc molybdate, ZnMoO,, which is expected to be a lubricating species in ZnMoO,S, at high temperatures. Melting temperature is reported at 1049°C in air. Powder G appeared orange, consisting of some dark brown particles with a specific gravity of 3.17 g/cc and a calculated molecular weight of 473.94. The powder as received contained some moisture, mainly water, and it was quite difficult to distinguish the primary from secondary particles due to a strong bond among the particulates. The average particle size reportedly was about 5 pm [29]. The pressed powder sample shown earlier in Figure 12 consisted of the compressed, sheared, and fractured faces. The sample was fractured in the direction orthogonal to the applied normal load (W, = 5,000 lb, 6, 12.5 ksi). Figure 18 presents photographs of all three sites. Note especially the boundary layer site. Close examination of the fractured and compressed faces showed slight differences in the arrangement of the powder ensembles in terms of the level of interparticleporosities. However, the sheared face was different from other sites, as is evident from the SEPs of these sites given in Figure 18. Sheared face particles appeared to be an aggregate massed into a dense cluster, analogous to a smeared colored chalk. Also, the sheared face appeared light orange to yellow (discoloration). Similar surface patterns could be found on the inner surface of a test cylinder.

-

-

310

Solid Fraction and Density of Powder

Following the experimental procedure and powder characterization, the solid fraction and density of the powders was determined. The solid fraction, C, is the ratio of powder density to solid phase density, C =pip,. In the plots shown in Figures 19 through 21, the data are extrapolated linearly up to C = 1. With the solid fraction greater than 1 (C ) l), they can no longer be categorized as a "powder." Consolidated powders with C approaching unity could be considered a solid material analogous to those materials deduced by powder metallurgy techniques. Figures 19 and 20 show composite plots of the powder solid fraction, C, as a function of compression, b,,, for two groups of powders. The first group consisted of powders TiO, and ZnMoO,S, (Figure 19). The second group consisted of powders NiO, MoS,, and CeF, (Figure 20). Figure 2 1 presents the composite plots of bulk powder density pp as a function of byyfor the TiO, powders. These figures show qualitatively the two behavioral regimes of the compact density of powder: primary and secondary consolidation regimes. At low values of compression (owup to about 35 MPa), the bulk solid fraction and density of powder is strongly affected by applied pressure. As the compression increases, a transition occurs (26 < bYy< 50 MPa), and, with a further increase in oyy, the powder masses consolidate into the secondary regime where the packed powder stiffness increases linearly and progressively. Sample composite plots for the group of TiO, powders (A, B, and C) are presented in Figure 21. Their similar behavior (p, versus by,)is an anomaly for some powders so different in particulate shape, size, and crystal form. Interestingly, a similar statement can be made by grouping Powders D and E or others based on the slope of the curve, dpdda,,. Quantitative Image Analysis

The sample powders were also subjected to QIA. The QIA technique is similar to that of the geometric signature waveform analytical method, which utilizes an SEM inline with a computer. The periphery of each individually designated particle in the sample was first outlined, then the image was analyzed. QIA was performed on the individual particles from each site (compressed, fractured, and sheared), and sample

populations of 164 to 187 particles per site were investigated. Tabulated data for a powder sample of TiO, (anatase form) is presented in Table 2. Table 2 also provides comparative statistical data (morphological) consisting of equivalent particulate diameter (p), perimeter projected area, and shape factor. The TiO, (anatase form) powder sample was selected for this analysis based on its recognizable particulate shape (spheroidal). Based on sample statistical morphological data (Table 2 and Reference 3) the following observation is made: Average particulate size for the sheared face (boundary layer face, Figure 11) is slightly smaller relative to the other two sites. Sheared and fractured faces appeared to be more densely packed than the compressed face (based on particle's perimeter and area). Shape factor is highest for the sheared face and smallest for the fractured face. (The higher the shape factor, the greater the sphericity.) COGNITIVE APPROACH

This paper demonstrates that all attempts to describe particulates have been directed toward expressing a particle's shape as a simple spheroidal shape by providing equivalent diameters. Thus, any cognitive approach applied to date has been based on a set of unproven assumptions. Classical attempts to categorize particle shapes have been based on twodimensional images and the perception that all particle shapes fit into the parameters defined by a solid rigid sphere. This situation may have arisen from the complexity associated with the shape and the nature of triboparticulates, where simple concepts are more apt to be crisp and complex ones vague. The dynamic behavior of triboparticulates and agglomerates cannot be predicted from their static properties. In order to attempt to characterize the behavior of a particle ensemble, a distribution of the collective particle properties is required. In properties and phenomena associated with a particle ensemble, we encounter structure, configuration, and certain constraints, some known and many unknown. Much of this uncertainty actually contains useful information, albeit of a fuzzy type but information nevertheless. This uncertainty appears in the form of imprecision, vagueness, and ill

31 1

defined, inseparable, and doubtful data. From this uncertainty, or fuzzy information, we undertake to understand the dynamics of triboparticulates in a tribosystem under study. The subject of approximate reasoning, information processing, and decision analysis - especially using data arising from the cognition process - has occupied a prominent place in the information processing literature since the introduction of fuzzy set theory in 1965. The role of fuzziness in managing complexity is implicit in Zadehs paper [30]. The cornerstone was his law of incompatibility: "As complexity rises, precise statements lose meaning and meaningful statements lose precision." [3 11 To address the vagueness of the shapes of various particles we may define them in terms of fuzzy set theory. A set could have members who belonged to it partly, in degrees. For example, if NiO particles assume a spheroidal shape, the fuzzy set asks, "How spherical is the NiO particle?" The answer is a partial membership in the fuzzy set, such as 0.8, which gives the NiO particle a value of 0.8 spherical and so on. Likewise, the set of particles can be crisp or fuzzy as shown in Table 3. To study this situation level by level, the shape may be decomposed at each level into the maximum subrelations of similitude used in cognition and presented in a fuzzy set (Table 3). It can be concluded that these triboparticulates are similar but that the resemblances are not necessarily transitive. Note that crisp values for these examples are zero based on a logical system of true or false. Therefore, we propose to build better models from the fuzzy and subjective data that are available, combined with strong statistical data from a tribosystedtriboparticulates. Since fuzzy logic provides a useful tool to utilize a cognitive description of particulates, fuzzy numbers (fuzzy arithmetic) [32] could be used to address the role of triboparticulates and identify wear problems in tribology. Transverse and Longitudinal Variation in Solid Fraction, C The variation of C in bulk powder was qualitatively established as varying in the direction x (motion) due to variation in the local film pressure and across the film, y. A schematic interpretation of

this phenomenon in a core triboparticulates film is depicted in Figure 22. Hence:

Although the variation in C in the x direction is pressure dependent:

c (x) = c @) + c ( 0 ) Based on experimental data trends, an empirical relationship can be shown in the following form:

c (x) = c (0) [l-P/K, + ...I where C ( 0 ) is a reference solid fraction, P is local pressure, and K, is a solid fraction-pressure coefficient for given triboparticulates.

The variation of C across the film, y, may be simulated mathematically where C is a solid fraction of powder, C, is the solid fraction of powder near the wall (near mating surfaces), C, is the maximum bulk solid fraction (approximately = 1) of the material, and p is the constant to be determined empirically. It is believed that p would be a strong function of local film pressure and the nature of triboparticulate material. Indeed, we are showing the variation in a continuum fashion despite fact that the particulate arrangements were observed to be vaguely and discretely graded. However, it is agreeable statement that vagueness stems from a continuum and it has degrees. In fact, a continuum need not actually be continuous. It can be discrete, and, if the intervals are small enough, it will then escape notice. CONCLUSIONS

An investigation was made of the dynamic properties of a medium consisting of fine triboparticulates using various dry powders. This investigation has demonstrated that, even under minute stress, fine

312

solid triboparticulates undergo tribocomminution and consequently undergo a morphological change. In most cases, ideal rigid spheroidal particles have been used to build fundamental descriptions and categorize particulate shape and size. This paper has attempted to explore the inadequacy of state-of-the-art techniques as well as elucidate the interrelationship between particulate size, shape, and powder density. The variation of the powder solid fraction as a function of particulate size distribution, compaction level, and nature of the hiboparticulate was also discussed. The investigation shows that the solid fraction of a particular powder was very sensitive to changes in compression and also sensitive to some degree to a change in the average particulate size distribution for a given powder material. It also appeared that particles under high pressure reorder themselves so that there is a higher concentration of finer particles and a low level of interparticle porosities toward the center of the bulk packed powder. The sheared face particles appeared to be finer and denser. The variations of the shape and size of a particulate ensemble in a compressed sample at various sites were examined, and findings were documented. Results of QIA and SEPs of a particulate ensemble at compressed, fractured, and sheared sites led us to explore the variation of solid fraction in triboparticulate lubrication. Triboparticulatecharacterizationin terms of shape and relevant theories is still in the embryonic stage. This study intended to represent a step toward development of a viable model and parameterization of tribopatticulates. Caution must be exercised in relating a particular wear debris shape to a wear mechanism. ACKNOWLEDGMENTS

This program was jointly sponsored by the Propulsion Directorate, U.S. Army Vehicle Propulsion Directorate, and Mechanical Technology Incorporated. The authors wish to thank Dr. R.C. Bill of ARL for his support. The authors also acknowledge the support of Mr. T.K.Hare for providing the sample analyses using SEWQIA techniques.

NOMENCLATURE

Projected area of particle Solid fraction of powder Reference solid fraction Solid fraction of powder near wall Maximum solid fraction of powder (- 1) Equivalent particle diameter (pm) Envelope volume Solid fraction-pressure coefficient Mass Perimeter, Pressure ZMEV Particulate average size (Pd) Reference direction Surface area of particle Scanning Electron Microscope Scanning Electron Photomicrograph Surface velocity Volume of particle Load Specific wear Equivalent projected area diameter Maximum particle diameter or major diameter Minimum particle diameter or minor diameter Martin diameter 50% accumulative particle size distribution Equivalent surface diameter Sieve diameter Equivalent surface-volume diameter Equivalent volume diameter (pm) Film thickness Position coordinate Position coordinate Constant of density distribution across the film Reference powder density Bulk density of powder as a function of compaction Solid bulk density of material Applied stress to a plane in direction perpendicular to y-axis Wadell Index (particle shape index)

313

13. Luerkens,

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4, Particle." NO. 4, (1986): 371-78. Yu, A.B. and Standish, N. "An Analytical-Parametric Theory of the Random Packing of Particles." Powder Technoloev, 55, (1988): 171-86. Stanley-Wood, N. "The Bulk Properties of Powders." W.S. Notes, Powder and Bulk Solids Conference, (1989): 4-1 1. Heshmat, H. "The Quasi-Hydrodynamic Mechanism of Powder Lubrication -- Part I: Lubricant Flow Visualization." Paper 9 1-AM-4D-1, Journal of STLE,48, No. 2 (February 1992): 96104. Heshmat, H. "The Quasi-Hydrodynamic Mechanism of Powder Lubrication: Part 11: Lubricant Film Pressure Profile." Journal of STLE, 48, NO. 5 (1992): 373-83. Heshmat, H., and Brewe, D.W. "On Some Experimental Rheological Aspects of Triboparticulates." 'WEAR PARTICLES: From the Cradle to the Grave,' Ed. D.D. Dowson, C.M. Taylor, T.H.C. Childs, M. Godet, and G. Dalmaz, Elsevier Tribology Series 2 1, Amsterdam, ( 1992): I

1.

Oike, M., Emori, N., and Sasada, T. "Effect of Fine Ceramic Particles Interposed Between Sliding Surfaces on Wear of Metals." Proceedings of the JSLE International Tribology Conference

15.

(1985). 2.

3.

4.

14.

Nikolakakis, I. and Pilpel, N. "Effects of Particle Shape and Size on the Tensile Strengths of Powder." Journal of Powder Technology, 56, NO. 2, (1988): 95-103. Heshmat, H. "The Rheology and Hydrodynamics of Dry Powder Lubrication." STLE Tribology Transactions, 34, No. 3, (1991): 433-39. Heshmat, H., Pinkus, O., and Godet, M. "On a Common Tribological Mechanism Between Interacting Surfaces." Trana i ,

16.

17.

32, (1989): 32-41.

5.

6.

7. 8.

9.

Edelman, G.M. Brbht Air Brilliant Fire - On the Matter of the Mind. Basic Books, a Division of Harper Collins Publishers, (1992): 74. Haughey, D.P. and Beveridge, G.S.G. "On the Packing of Solid Particles." Canadian Journal of Chemical Engineering, 47, No. 130 (1969). Gray, W.A. The Packing of Solid Particles, Chapman and Hall, London (1968). Farley, R., and Valentin, F.H.H. "Effects of Particle Shape on the Powder Strength." Journal of Powder Technoloev, 1, No. 3, (1968): 344-49. Nikolakakis, I. and Pilpel, N. "Effects of Particle Shape and Size on the Tensile Strengths of Powder." Journal of Powder Technology 56, NO. 2, (1988): 95-103. Kaye, B.H. "The Interrelationship of Geometric Signature Waveforms and Fractal Dimension Description of Fine Particle Structure and Texture." Proceedings of the 14th Annual Powder and Bulk Solids Conference (1989).11. Kaye, B.H. "Lecture Note on Fourier Analysis and Fractal Dimension of Fine Particle Profile." Sudbury, Ontario: Laurentian University (1985). Luerkens, D. W. Theorv and Application of Momholopical Analvsis: Fine Particles and Surfaces, CRC Series on Fine Particle Science and Technology, Editor-in-Chief, John Keith Beddow, Book No. 0-8493-6777-8, by CRC Press,Inc., (1991) 7

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12.

18.

357-367. 19. Heshmat,

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21.

22.

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24.

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314

of Powder Lubricated Ceramics at HighTemperature and Speed." 47th Annual STLE Meeting, Philadelphia, PA, May 1992; to be published by STLE Lub. Eng. (1993). 25. Flischauer, P.D., Milton, M.R., and Bauer, R. "Effects of Microstructure and Adhesion on Performance of Sputter-Deposited MoS, Solid Lubricant Coatings." Paper V(i), Tribology Series, 17, Mechanics of Coatings, (Leeds-Lyon), Elsevier, (1990): 121-28. 26. Pierce, D.E., Dauplaise, H.M., and Mizerka, L.J. "Thermal Desorption Spectroscopy of Sputtered MoS, Films." STLE Transach'ons, 34, No. 22 (April 1991): 205-14.27. 27. Heshmat, H. "High-TemperatureSolid-Lubricated Bearing Development: Dry-Powder-Lubricated Traction Testing." W S A E / A S M E 26th Joint Propulsion Conference,Paper 90-2047(July 1990), J O U mal of Promlsion and Power, 7, No. 5 (1991): 8 14-20. 28. Sutor, P.A., Sr. "High Temperature Lubricant Characterization." Final Report for Period August 1987 - April 1990, prepared for U.S. Air Force, Wright Research and Development Center, No. WRDC-TR-90-2069 (December 1990). 29. King, J.P. and Amerson, Y. "Solid Lubricants for Improved Wear Resistance." Final Report for Period 1, April 1979 - 30 September 1981, Office of Naval Research Contracts NOOO14-79C-0305 (July 1982). 30. Zadeh, L. "Fuzzy Sets." Information and Control 3, (June 1965): 338-53. 31. McNeill, D. and Freiberger, P. Fuzzv Logic. Simon and Schuster, New York, (1993): 43. 32. Kaufmann, A. and Gupta, M.M. Jntroduction to Fuzzv Arithmetic - Theory and ADglicatiQg VanNostrand Reinhold, New York (1991).

315

-5

-20 Particulate Average Size (P,), pm

Figure 1.

095V

Generic Curve for Wear Using Abrasive Powder Materials for a Set of Tribological Combinations

Open Pore

ill ?P =

Porosity J b) Primary and Secondary Partlcle 93061

Figure 2.

Primary and Secondary Particles

316

Table 1 . Powder Behavior Properties Categorized by Mass, Volume, and Time

Dimenslonal Groups

Bulk Powder Properties

Vo1ume:Volume (Solid Fraction)

Packing

Mass:Volume (Mass Density)

Single Particle Ensemble of Particles

Mass:Mass (Interaction)

Particle-Particle

Particle-Fluid

Mass:Time (Flow Rate)

Particle-Particle

Volume: Time Particle-Fluid (Transportation)

Densification Porous Nonporous Compressed Sheared Aerated Vibrated CohesivenesdTensile Strength Densification Expansion Fluidization Pneumatic Transport Fluidization Catalytic Agglomeration Flowability Floodability Gaseous Liquid

317

Spherical Rounded Isometric Rounded Nonisometric

Modular

Regular Polyhedral (Isometric)

Irregular Polyhedral (Angular, Sharp Edges)

Isometric (Granular) Nonisometric

Nonisometric

Flakey (Plate-Like)

Fibrous (Thread-Like)

Nonisornetric

Acicular (Needle-Like) Dentritic (Branched)

93059

Figure 3.

Recognizable Particle Shapes

318

b) After Exposure at 1500°F

a) Prior to Exposure at 1500°F

Figure 4.

Figure 5.

Pure Nickel Particles

Nickel Particle Surface After Exposure at 1500°F (SEM Photograph)

Figure 6.

Compressed NiO Particles: Fractured Face Diagonal to Compressed Face (Light Micrograph; 300-psi Isostatic Pressure)

319

TiO,

x300 Compressed Face

Figure 8. v93-178(L)

Figure 7.

Compressed T i 0 Particles (Rutile Form; Light Micrograph; 10,OOO-psi Isostatic Pressure)

Figure 9.

Re,O, and CuO Powder Mixture After Exposure at 1500°F

Boron Nitride Powder

OZE 0'L 8'0

9'0 "H P'O

Figure 1 1 . Test Fixture Used for Powder Compaction; Pressed Sample Sites Also Shown

Figure 12. Isostatically Compressed Then Extruded Powder Sample; Fractured in a Plane Diagonal to Pressed Direction

32 1

Ti02 (Rutile Form), P d = 2 pm; [A]

Figure 13. Scanning Electron Photomicrographs of Powder A

Ti02 (Rutile Form); Pd = 6 pm; [B]

Figure 14. Scanning Electron Photomicrographs of Powder B

322

Ti02 (Anatase Form); p, < 0.4 pm; [C]

MoS2 (Finer Size Particles); pd < 2 pm; [D]

Figure 15. Scanning Electron Photomicrographs of Powder C

Figure 16. Scanning Electron Photomicrographs of Powder D

323

MoS2 (Moderate Size); Pd

-,12

pm;[El

Figure 17. Scanning Electron Photomicrographs of Powder E

ZnMo02S2, 'iS;d = 5 pm; [GI

Figure 18. Scanning Electron Photomicrographs of Powder G

324

No. Ref. dp- (urn) 0 1'

I

I

I

290

-10

I

1

1

590

I

890

I

1

1190

1490

oyy (MP4

1.o

83580

Figure 19. Solid Fraction versus Compression: TiO, and ZnMoO,S, (Extrapolated for aw > 350 MPa)

Y

3

m

0.2 -

No. Ref. dp 0' -1 0

I

I

170

I

I

I

I

530

350

I

- (wrn)

I

710

oyy ( M W

Figure 20. Solid Fraction Venus Compression: MoS,, CeF,, NiO (Extrapolated for uyy> 350 MPa)

I

890 93581

325 3.0

2.4

TiO, c 0.4 (Anatose) 1.8

1.2

.6

No. Ref. d, 0 -10

62

278

- (urn) 350 93579

Figure 21. Bulk Density versus Compression: TiO,

326 Table 2. QIA of Particulate Ensemble of TiO, (Anatase Form)

Statistical Parameter

Compressed Face

Fractured Face

Sheared Face

0.36 0.008 0.092 0.128to 0.735

0.34 0.008 0.089 0.164to 0.59

Equivalent Diameter (pm)

Mean Value Variance Standard Deviation Limits

Mean Value Variance Standard Deviation Limits

I

0.33 0.010 0.101 0.167to 0.78

1.22 0.235 0.485 0.527to 3.85

I

I

1.33 0.103 0.322 0.575to 2.59

1.17 0.083 0.289 0.571 to 1.90

0.016 0.126

0.79 0.009 0.096 0.528to 0.987

Shape Factor

Mean Value Variance 0.027 Standard Deviation 0.164 Limits

P447

327

wn

I

t

-U

89579-1

Figure 22. Transverse and Longitudinal Variation in Density with Powder Lubrication

5c

5

10

h h

x

‘K

3

0.6

C

.-c. 0 0

e

un 0

0.4

a

0.2 U

Dh = 0.5 I

-0

0.2

I

I

0.4

I

I

I

0.6

I

0.8

Normalized Film Thickness (y/h)

Figure 23. Proposed Mathematical Model for Variation of Solid Fraction Across Powder Film

1.o 93582

328

Table 3.

Fuzzy Subset Values: Triboparticulate Shape Memberships

I

BN

MoS,

0.4

0.2

0.3

:nMoOzSz

%

cz3 6)@

a /

&

I

Triboparticulates Co losition

0.7

0.6

0.3

0.3

0.5

O3

0.8

0.8

0.5

0.3

0.05

0.1

0.3

0.9

0.8

0.05

0.2

0.4

0.05

0.4

0.05

0.2

0.3

0.05

0.05

0.1

0.6

0.6

935790

Dissipative Processes in l’ribology / D. Dowson et al. (Editors) 1994 Elsevier Science R.V.

329

Surface Chemistry Effects on Friction of Ni-P/PTFE Composite Coatings E.A. Rosset, S. Mischler, D. Landolt Materials Department, Ecole Polytechnique F6dCrale de Lausanne, 1015 Lausanne, Switzlerland Electroless and galvanic deposition are inexpensive and flexible methods for the fabrication of functional metal films on a wide range of substrates. These techniques are also suitable to produce metal matrix composite coatings such as self-lubricating coatingscontainingPTFEspheres in a metallic matrix. In the present work the tribological behaviour of electroless Ni-P/P”FE metal matrix composite coatings has been studied in air and in pure nitrogen by using a reciprocating motion test rig. The chemical state of the surface was characterised by Auger Electron Spectroscopy. Results are interpreted by considering the third body concept proposed by Godet and co-workers.

1. INTRODUCTION Despite the wide application range of self lubricating Ni-P/lTFEcompositecoatings[1,2,3], the friction and wear mechanisms of this class of materials is only partially understood [4,5]. In the literatureit is generally assumed that PTFEalone is responsible for the self lubricating properties of the composite even if surface oxides should, in principle, play a role in the tribological phenomena. The aim of the present paper is to investigate the influence of the surface composition on the dry sliding behaviour of an electrolessNi-P/PTFE Composite coating. For this friction and wear tests are performed in air and, in order to avoid surfaceoxidation, in a pure nitrogen atmosphere using a reciprocating motion wear test rig. Frictional coefficients and wear rates are measured and the surface composition and morphology of the wear scar are determined by Auger Electron Spectroscopy (AES)and ScanningElectronMicroscopy(SEM), respectively. For comparison the tribological behaviour of a Ni-P coating was investigated in air under the same conditions.

2. EXPERIMENTAL

Sliding friction conditions were established by rubbing a 1 0 0 0 6 steel ball (lOmm diameter) against a Ni-P/PTFE or a Ni-P coating plated on aluminium. The Ni-P coating was 10 pm thick and smooth (Ra0.05, cut off length 0.8 mm) The composite coating exhibited a rough surface (Ra 0.8 1, cut off length 0.8 mm) and the average film thickness was 9 pm. The PTFE content of the compositecoating was 30% PTFEby volume and the averagediameter of the PTFE spheres was 0.4 pm. Thephosphorus content of the matrix was 9% for both coatings. No heat treatment was performed on the coated sample. The hardness of the Nip coating was about 500HV corresponding to an approximate yield strength of 1200 MPa. Frictional tests were carried out in the reciprocating ball-on-plate rig described in more details elsewhere [6]. During the test the frictional and the normal force as well as the horizontal and vertical displacement of the rubbing interface were monitored using a Macintosh IIfx computer (Labview2 software from National Instruments). The coefficient of friction was determined by dividing the frictional and thenormal forcesmeas-

330

ured when the pin was in the middle of the wear scar. The ball was oscillating at a frequency of 5 Hz. The stroke length of 4 mm corresponded to an averagesliding velocity of 0.040 m/s. The applied normal load was of 0.6 N. Prior to the test the samples were cleaned in an ultrasonic ethanol bath, rinsed with fresh ethanol and dried using an argon jet. After the friction test the samples were transferred to the AES analysis system for chemical characterisation. Subsequently their morphology was studied using SEM and stylus profilometry. Some tests were carried out in a glove box allowing for working in a nitrogen atmosphere (measured oxygen level below 5 ppm). The transfer of the samples after the wear test to the AES system was carried out in the laboratory atmosphere. Each experiment was repeated three times in order to check for reproducibility. The surface compositionwas determined in a Perkin Elmer 660 Scanning Auger Microscope using a lOkeV (50nA)electron beam. Surface analysis was carried out by focusing the electron beam (beam diameter of 1pm) on selected points of the sample surface.

Depth profile acquisition was performed by rasteringa2keVAr-tbeamoveranareaof 1.5x1.5 mm. Under these conditions the sputter rate of Ta205 was 0.5 nm/min. The surface morphology was observed with a Cambridge Stereoscan 650 SEM or a JEOL 6300 F SEM. Wear track profiles were measured using a Taylor-Hobson Talysurf 10 profilometer.

3 RESULTS Ni-P in air: Generally the coefficients of friction were found not to depend significantlyon sliding distance and therefore the average p values listed in Tab.1 for each experiment can be used to characterisethe frictional behaviour of the systems studied here. The values of Tab. 1 were determined by calculating the average and the standard deviation of the coefficients of friction measured every 20s during sliding. The frictional behaviour of the Ni-P coating is characterisedby a coefficient of friction of 0.36 (average of three experiments) and a standard deviation of about 30% due to important oscillations in the p values during sliding. Such oscillations are usually observed on this rig when a significant amount of wear particles is present in the contact. ~~

Table 1 Averaged coeilkients &friction Sample Atmosphere

p: average

p:standarddeviation

Ni-P

air

0.38 0.34 0.35

0.12 0.09 0.09

Ni-PPTFE

air

0.12 0.11 0.14

0.03 0.03

0.17 0.18

0.03 0.04

0.16

0.04

Ni-P/PTFE

N2

0.05

33 1

----

The wear behadour of Ni-P was characterised by relative littledamage to the coated surface as shownbytheweartrackprofile(Fig. 1).Important wear of the steel ball and some material transfer from the coating to the steel was observed N P In Alr. 18'0ooStmb8 N P +TFE in Ah, 18'Ooo slrobs

induces shadowing effects of the ion beam used for sputtering. If locally the oxide film is not

N M InAlr, 11QOOO Irokcls

Figure 1. Wear track profiles (Talysurf). by SEM (Fig.2~). Wear particles were found aggregating at the end of the wear track (Fig. 2a). The size distribution was not uniform ranging from a maximum of 1 pm down to less than 0.1 pm with an aspect ratio near to the unity. Ploughinginducedridges and alarge number of cracks were observed using SEM on the Ni-P wear track (Fig.2b). This indicates that delamination by subsurface crack propagation was the dominant wear mechanism. The thickness of the delaminated sheets was about 1 p. Cracks were also observed on the steel ball. A typical Auger profile measured on the NiP wear track is shown in Fig.3a. It indicates the presence on the metal surface of a thin oxide film (about 2 nm thick). Carbon is present as a surface contamination only. ?his is suggested by the fact the carbon signal goes to zero at a depth of 0.3 nm. No iron was found on the wear track surfaceon the coating. Theoxygenprofiledoes not show asharp interface possibly because the surface roughness

Figure 2. NiP in air, 18'000 strokes. a) wear track b) detail of wear track c) steel ball

332

a

substrate contact as consequence of wear of the coating. The SEM investigation and the wear track profiles recorded at different sliding times indi-

I NIP In Air

-------.------------0

2

4

6

8

lo

Approx. Depth [nm] Figure 3. Auger depth profiles measured on wear tracks. removed by sputteringit contributesto the overall Auger signal even at large sputter times. Because of this effect no quantification of the profile of Fig. 3a was carried out. Surface analysis could not be performed on the wear debris and on the worn surface of the ball because of charging due probably to an important surface oxidation. Ni-PPTFE in air:The frictional behaviour (Tab. 1) of the composite coating sliding against a 100Cr6 ball was characterised by a relatively constant coefficient of friction of 0.12 (average value of 3 experiments, standard deviation 8 96). Oscillations and an average increase in p were observed only after about 18oooO strokes and were attributed to the beginning of the ball-

Figure 4. Ni-P / PTFE in air a) wear track, 1'800 strokes b) wear track (endon theright), 11O'OOOstrokes c) steel ball, 11O'OOOstrokes. Light grey zone correspondsto the material transferredfrom the coating

333

cates that asperity deformation (Fig. 4a) was followed after about 18'000 strokes by general plastic flow of the compositecoating (Fig. 4b). Some laminated sheet separating from the substrate are also observed by SEM (Fig.4b) on the wear track . Their thickness is about 0.1 pm, significantly lower than in the case of Ni-P coatings (Fig.2b).Important material transfer was observed on the ball (Fig.&) while wear debris generation was negligible. An Auger depth profile measured on a deformed surface similar to that pictured in Fig. 4a is reported in Fig. 3b. Again no iron was found here. Similar profile were obtained at different slidingdistances (1800,18000and 1loo00 strokes) on deformed zones of the coating and on the transferred layer on the ball. The simultaneouspresence of Carbon,Fluorine and Oxygen together with Nickel and Phosphorous observed by AES indicates the presence of thin surface films of P E E and a NickelPhosphorous oxide. The thickness of the oxide layer correspond to about 2 nm, i.e. in the same order of magnitude as the value observed on the Ni-P coating. The apparent thickness of thePTFE determined in Fig. 4b is about 1 nm, but is believed to be higher since the sputter rate of polymers is about 2-3 time higher than that for oxides. From the measured profile it is not possible to determine if the oxide and the PTFE layers coexist on the surface as islands or if the one layer is covered by the other. Scanning Auger mapping results obtained with a lateral resolution of 50 nm and not presented here show however a homogeneous surface distribution of the elements. This and the well known trend of PTFE to form thin interfacial films under tribological conditions [7] suggest the presence of a PTFE film covering the oxidised surface of deformed asperities. Further experimental evidence is needed to confirm this hypothesis.

N i - P m F E in N,: Rubbing the steel ball against the composite coating in absence of oxygen lead to an average coefficient of friction of 0.17 as shown in Tab.1. The wear rate in nitrogen is much higher than in air as seen in Fig. 1 a n d 5 The profilometry shows that the wear scar after 1800 strokes in nitrogen is nearly six microns deep. In comparison more than 1loo00 strokes are needed to wear off 5 pm in air. The important difference in wear

Figure 5. Ni-P / PTFE, N,, wear track, 1'800 strokes rate is evident when comparing the surface morphology after the same number of strokes: after 1800 strokes in air only some asperities have interactedwith the ball (Fig. 4a) whilst in nitrogen generalisedplasticdeformationhas occurzed (Fig. 5). The wear morphology in nitrogen does not differ significantly from the one observed in air flow on the wear track. This indicates that the presence of oxygen in the atmosphere influences the wear rate but not the wear mechanism. Surface analysis indicates that the Ni-PI PTFE wear track surface is covered with a few nm thick PTFE film (Fig. 3c). Because of its high surface reactivity, the metallic nickel is expected to oxidise during the transfer of the sample from the glove box to the Auger analysis system. However no oxygen was found by AES. This indicates

334

that PTFE film forms an adherent and compact layer on the metal surface acting as barrier against oxidation. Very thin PTFE films formed during sliding of PTFE containing polymer composites have been observed recently by Fletcher et a1 using imaging XPS [S]. DISCUSSION The obtained results show that the tribological behaviour of the analysed coatings depends critically on the presence of PTFE in the material and on the test atmosphere. In order to understand the mechanismsinvolvedit is convenient to make use of the concept of third body presented i.e. by Godet et al. [9] The simple three body contact model proposed by these authors includes two first bodies (in our case the coated sample and the steel ball), the third body and the two third-body/ first body interfaces also called screens. By separating the two first bodies the third body transmits the load from one first body to the other and accommodates by dissipation most of the velocity difference between the first bodies. A list of the nature of third bodies and screens possibly present under the present test conditionsisproposedinTab.2. Itis assumedthat the transfer layer observed on the ball as well as the plastic deformed zone on the coatings are part of the first bodies. The experimental results obtained here can be explained by considering the effect of the presence of screens and different

third bodies in the tribological systems investigated. Third bodies: During rubbing of the Ni-P coating against the steel ball particles are generated by delamination of the two first bodies. Once detached and before being ejected from the wear scar the particles form a powder bed (the third body) separating the two first bodies. Due to the inhomogeneous nature of the powder bed the load is not distributed uniformly in the contact so that locally the contact pressure may reach the critical stress required for subsurface crack nucleation and propagation in the first bodies. Under the assumption that the stress required for crack nucleation in delamination corresponds approximately to four times the shear yield strength of the deposit [ 101 one obtains a critical stress of about 2400 MPa (the shear yield strength is assumed to correspond to half the yield strength). The fact that this value is well above the nominal contact stress calculated according to the Hertzian formalism (400 m a ) support the hypothesis of the inhomogeneous load carrying behaviour of the particles bed. The third body formed during rubbing of the compositecoating consists in a low shear strength PTFE film formed by plastic deformation during the contact of the PTFE spheres present at the coating surface.This PTFE film can be assimilated to athin lubricant film and as such it reduces friction and distributes the load homogeneously in the contact so that the probability to reach the critical stress for subsurface cracking is much lower than in the case of Ni-P. According to the

Table 2

Summary of results and proposed mechanisms Sample Atmosphere p 1 Wear Wear mechanism NiP

Air

NiP-PTFE Air NiP-PTFE N2

0.36 0.12 0.17

1) Average of three experiments

low low severe

Delamination Asperity Deformation Asperity Deformation

Thirdbody

Screen

Weardebris P"FEfilm PTFEfilm

Oxide Oxide None

335

delamination theory of wear [ 101the thickness of the delaminatedsheets correspondsto the depth of crack nucleation which is proportional to the friction force and the local normal stress. This explains the formation of thinner sheets on the composite coating than on the Ni-P coating. Due to the different nature of the third body only little wear by delamination occurs during sliding of the composite coating, however. The damage is limited to the surface where asperity deform and a adhesive wear take place. Screens: The thin lubricating PTFE film can break down locally when first body asperities interact strongly or as a consequence of scuffing phenomena (thermally induced film breaking or insufficient film-substrate adhesion). In such an event metal-metal contact and adhesion may occur leading to the observed transfer of material to the ball and to the wear of the coating. The oxide screen can prevent metal-metal contact thus limiting the extent of adhesive wear. During rubbing in nitrogen no oxide screen is formed. This may explain the higher wear rate. Another application of this is that the presence of the oxide may improve the adhesion of the PTFE film, thus reducing the possibility of scuffing phenomena. Therefore, altough the wear mechanism of Ni-P / PTFE in air and in nitrogen is conditioned by the nature of the third body, the wear rate is governed by the presence or not of oxide screens. The oxide screen also plays a similar antiadhesive function during rubbing of the Ni-P coating in air. This explains why no significant material transfer was observed in air. The third body / screen approach allows one to explain the mechanismsleading to the observed sliding behaviour of Ni-P and Ni-P/PTFE coatings. However further experimentalwork is needed in order to better understand the role of intrinsic material properties, surfacecomposition and third

bodies for the tribological behaviour of these materials. CONCLUSION Under the present experimental conditions the wear and frictional behaviour of self lubricating Ni -P/PTFE compositecoatings aredetermined by the formation of very thin surface layers of PTFE or Ni-P oxide. The observed differences in tribological behaviour of Ni-P/PTFE coatings in air and nitrogen stress the important role of surface oxidation for friction and wear.

Acknowledgement This work was financially supported by the CERS (Bern). The coatings were manufactured by Steiger SA (Vevey). The authors thank M. P. Mettraux for the SEM analysis. REFERENCES 1. R.N. Duncan Hardness and wear resistance of electroless Nickel-Teflon composite coatings Metal Finishing, 9 (1987), 33-34 2. P.R. Ebdon Composite electroless NickeVPTFE coatings Surface Engineering, 3 (1987), 114-116 3. E. Steiger Nickelage chimique avec incorporation de FTFE Oberflkhe-Surface, 10 (1990), 19-22 4. K.Matsukawa,A. IchikawaandM. Kobayashi Effects of Heat treatment on tribological properties of electroless Nickel- P h o s p h o r o u s coated steel Proc. Japan International Tribology Conference, Nagoya (1990), 7-12 5. T. Sakamoto, M. Abo, 0. Takano and M. Nishira Friction and wear of electroless Nickel-PTFE composite coating

336

Roc. Japan International Tribology Conference, Nagoya (1990), 31-36 6. E.A. Rosset, S. Mischler and D. Landolt Wear and Friction Behaviour of Ni-Sic Composite Coatings in Thin Films in Tribology (Leeds-Lyon 19) D. Dowson et al (Editors), Elsevier Science Publishers B.V .(1993), 101- 108 7. S.K. Biswas and K.Vijayan Friction and wear of PTFE - a review Wear, 158 (1992), 193-211 8. I.W. Fletcher, M.Davies and D. Briggs Surface modifications introduced to a Pol ytetrafluorethylene-filled Polycarbonate compound by dry sliding against steel as revealed by imaging X P S Surface and Interface Analysis, 18 (1992), 303-305 9. M.Godet, Y.Berthier and J. Lancaster Wear modelling: using fundamental understanding or practical experience Wear, 149 (1991), 325-340 1O.N.P. Suh Tribophysics Prentice-Hall Inc., Englewood Cliffs, New Jersey (1986)

Dissipative Processes in 'I'ribology / 1994 Elsevier Science B.V.

D.Dowson et a]. (Editors)

337

Transfer layers in tribological contacts with diamond-like coatings J. Vihersaloa,H. Ronkainena,S . Varjusa,J. Likonenband J. Koskinenc "Technical Research Centre of Finland (VlT) , Laboratory of Production Engineering, P.O.Box 1 1 1, FIN-0215 1 Espoo, Finland bTechnical Research Centre of Finland (VTT), Reactor Laboratory, P.O.Box 200, FIN-02151 Espoo, Finland "Technical Research Centre of Finland (V'IT), Metallurgy Laboratory, P.O.Box 113, FIN-02151 Espoo, Finland

The tribological properties of amorphous hydrogenated carbon (a-C:H) films deposited on steel AISI 440 B in a radio frequency (RF) assisted plasma were studied. The films were studied using a pin-on-disc machine with steel AISI 52100 and alumina as the counterface materials. The sliding velocities varied from 0.1 to 3.0 m / s and the normal forces from 5 to 40 N. The tests were carried out unlubricated in room air at 22k2 "Ctemperature and with 50*5 % relative humidity. Tribofilms formed on the pin and coating wear surfaces were studied by secondary ion mass spectrometry (SIMS). The coefficient of friction strongly depended on both the sliding velocity and the load. For the steel pin sliding against coating the coefficient of friction varied from p=0.42 to p=O.l and for the alumina pin sliding against coating the coefficient of friction varied from p 4 . 1 3 to p=0.02. The formation of a tribofilm on the pin had a significant effect on both the friction and the wear properties of the coating.

1. INTRODUCTION

2. EXPERIMENTAL PROCEDURE

Diamond-like carbon films have favourable tribological properties, which make them good candidates for many tribological applications. The tribological performance of diamond-like carbon coatings can be affected by e.g. the deposition method [ 11. The environment has proved to have a considerable effect on the friction and wear properties of diamond-like carbon coatings [2-41. The tribological tests have typically been carried out with low sliding velocities and moderate normal loads. Only in a few studies have higher loads and velocities been applied.

2.1. Coating deposition

In previous studies we have evaluated the performance of hydrogen free carbon coatings[5,6]. In the present study the authors have evaluated the hydrogenated carbon coatings deposited in a RF plasma. In order to study the effect of the frictional power input and the tribofilm formation on the tribological performance of these diamond-like carbon coatings, the pin-on-disc tests were carried out in a wide range of sliding velocities and normal loads. The wear surfaces were characterized and analysed by SIMS.

The amorphous hydrogenated carbon films (a-C:H) were deposited in a RF-plasma using methane (CH,) as the process gas. In the deposition chamber the substrates were placed directly on a water-cooled cathode. The deposition parameters were kept constant during the a-C:H film deposition. The pressure during the deposition was 5.5 Pa and the bias voltage was -550 V. The deposition temperature was close to 100 "C. Prior to deposition all substrates were cleaned by ultrasonic washing in 1,1,2-trichloro-1,2,2-trifluoroethane followed by rinsing in ethanol and drying in hot air. Finally the substrates were sputter cleaned in argon atmosphere for 5 minutes at a bias voltage of -300 V and a pressure of 0.7 Pa. For improving the adhesion of the coating to the substrate, a titanium carbide (Tic) layer was applied as an intermediate layer.The Tic layer was deposited

338

discharge using methane as the process gas. During the Tic deposition the bias voltage was -680 V and the pressure was 0.8 Pa.

d -

E

@b

30-

'u

it P

-&

d

20-

10-

d d

d

b

Sliding velocity v [mh]

Figure 2. Experimental parameters in pin-on-disc tests.

Figure 1. The principle of the deposition chamber Stainless steel AISI 440B (DIN X 90 CrMoV 18) was applied as the substrate. The hardness of the substrate material was 620 HV,,, and the surface roughness (R,) after the deposition was 0.03 pm. The total thickness of the coating was about 1.O pm. The Tic-layer was up to 0.5 m thick and the a-C:H-film on the top was about 0.5 pm thick. 2.2. Tribological experiments

The tribological experiments were carried out as pinon-disc tests in order to evaluate the effect of the load and the sliding velocity on the tribological behaviour of the a-C:H coatings. Polished 10 mm balls manufactured from steel AISI 52100 (100Cr6) and alumina (-A1203)were used as pins. The tests were performed unlubricated in room air at 2222 "C temperature and 50*5 % relative humidity. The sliding distance in the tests was 2000 m. Both the normal force and the sliding velocity were vaned within a wide range. The parameters were chosen for evaluating the effect of the normal force and the sliding velocity separately and as a combination of both. The normal force varied in the range 5 to 40 N and the sliding velocity in the range 0.1 to 3.0 m/s.

The friction force was measured during the tests. The pin wear rates were calculated from ball wear scar diameters, which were determined by optical microscopy. The disc wear rates were calculated as an average value from four profilograms taken across the disc wear track. All the presented values are mean values of two tests at a specific test parameter combination. The film composition was determined by Rutherford backscattering spectroscopy (RBS). The hydrogen content of the sample was measured using standard forward recoil spectroscopy (FRES). The wear surfaces of the pins and the coated discs were analyzed by optical microscopy and SIMS. The SIMSanalyses were carried out using a VG IX 70s doublefocusing magnetic sector instrument. Ga ions with energies of 10 keV in depth profiling and 22 keV in elemental imaging were used as primary ions.The primary ion current was typically 10 - 15 nA during depth profiling and 1 nA in the elemental imaging. To achieve uniform bombardment, the focused ion beam was raster-scanned over an area of 140 x 175 pm2in depth profiling. The alumina pins were analyzed with optical microscopy only.

339

3. RESULTS 3.1. Tribological evaluation The coefficient of friction showed a strong dependence on both the normal force and sliding velocity. The highest values of the coefficient of friction were measured when a low load and a low sliding velocity were applied. An increase in load and/or sliding velocity caused a decrease in the coefficient of friction. In Fig. 3 the coefficient of friction for a steel pin sliding against the coating is presented. The highest value of the coefficient of friction (p=0.42) was achieved at a normal load of 5 N and a sliding velocity of 0.1 m/s. The lowest value of the coefficient of friction (p = 0.10) was achieved when a high load (FN=35N)and a high sliding velocity (v=2.6m/s)were applied.

Figure 4. The coefficient of friction at the end of the pin-on-disc tests with alumina pin against a-C:Hcoatings. The specific wear rate (later wear rate) i.e. the wear volume divided by the load and the sliding distance decreased slightly when the load and sliding velocity were increased separately. An increase in both the sliding velocity and the normal load led to a strong reduction in the wear rate of the pin (Fig. 5). The wear volume of the pin remained almost constant when both the load and the sliding velocity were increased simultaneously, but increased when the load was increased at a low sliding velocity.

Figure 3. The coefficient of friction at the end of the pin-on-disc tests with steel pins against a-C:H - coatings. Fig. 4 presents the coefficient of friction when the coatings were tested against aluminapins. The highest value, p = 0.13, was achieved when the normal load was 5 Nand sliding velocity 0.1 m/s. The lowest value, p = 0.02, was achieved when a load 22 N and a sliding velocity of 1.5 m / s were applied.

Figure 5. The Wear rate Of pins in the pin-on-disc tests with steel pins against a-C:H coating.

340

The wear rate of the coated disc when sliding against a steel pin exhibited a systematic behaviour when either the sliding velocity or the load or both were increased, being highest when a low sliding velocity and a low normal force were applied and lowest when a high sliding velocity and a high load were applied (Fig. 6).

Figure 6. The wear rate of the disc in the pin-on-disc tests with steel pins against a-C:H coatings. For aluminapins sliding against a-C:H coateddiscs no systematic wear behaviour was observed in terms of the wear rate. An increase in the normal load from 5 Nto22 Nledtoalowerwearrateofthepin, butwhen a 40 N normal load was applied the wear rate was increased but was still lower than at the 5 N normal load (Fig. 7).

The disc wear rate when sliding against alumina pins also behaved systematically when both the sliding velocity or the load or both were increased. The highest wear rate was observed when a low sliding velocity and a low normal force were applied, and the lowest wear rate was observed when a high sliding velocity and a high normal force were applied (Fig. 8).

Figure 8. The wear rate of the disc in pin-on-disc tests with alumina pins against a-C:H coatings.

3.2. Coating characterization According to the FRES analysis the coatings contained about 26 at.-% hydrogen. The RBS analysis showed that the intermediate layer beneath the a-C:Hfilm consisted of a Titanium layer and a Tio,z8Co,,z layer, approximately 100 nm and 400 nm thick, respectively.

3.3. Characterization of the wear surfaces The SIMS elemental imaging revealed that elements (Fe,Cr) from the steel pin were transferred onto the aC:H coated disc. A higher wear volume of the steel pin correlated with increased concentrations of iron and chromium in the wear track. The thickness of the layer, which contained material from the pin, was typically about 10 nm and it seemed to be independent of the sliding velocity and the load used in the pinon-disc tests (see Fig. 9). Figure 7. The wear rate of the pin in pin-on-disc tests with alumina pins against a-C:H

34 1

The formation of a tribofilm on the steel pins was observed with all test parameter combinations. At higher sliding velocities the appearance of the tribofilm was more evident. The thickness of the film was not constant across the contact area (Fig. 1 1..14).

10

-

10

u)

n 0

Y

T, l o 3 E

m .u)

10

10'

t

i

10 O

0

150

100

50

200

Depth [nm]

Figure 9. A S M S depth profile of a disc wear track from a test with steel against an a-C:H coating at 5 N load and 0.1 m / s sliding velocity.

Figure 11. A micrograph showing a steel pin surface (5N,0.1 ds).

0

10

20

30

Time [min]

Figure 10. A SIMS depth profile of a pin wear track from a test with steel against and a-C:H coating at 35 N load and 2.6 m / s sliding velocity. Accordingto~SIMS~p~p-ofilesthetin~ pin weartracks showedchromiumdepletionandiron enrichment.Furthertothis,thetribofilmcontainedhydrogenandoxygen.Thetriboslmspmbablyconsistedof amixture of iron oxide and chromium oxide. SIMS resultsindicatedthatthemtion layercontainedasurFigure 12. A micrograph showing a steel pin surface prisinglylowamountofcarbon.(Fig. 10). (40 N, 0.1 d s ) .

342

tracks after tests against steel. Different features of formed layers on the alumina pin surfaces are presented in figures15 ...18.

Figure 13. A micrograph showing a steel pin surface (5 N. 3.0 d s ) .

Figure 15. A micrograph showing an alumina pin surface ( 5 N, 0.1 d s ) .

Figure 14. A micrograph showing a steel pin surface (35 N, 2.6 d s ) .

When the alumina pin was sliding against the hydrogenated a-C:H coating, aluminium was transferred onto the disc wear track. The tribofilm formed on the pin wear track was transparent. As the worn volume of the alumina pin was lower the amount of aluminium in the disc wear track was smaller than the amount of iron and chromium in the a-C:H wear

Figure 16. A micrograph showing an alumina pin surface (40 N, 0.1 d s ) .

343

When investigating the pin wear surfaces, the formation of tribofilm seems to be more evident at higher loads and sliding velocities. The tribofilm covered more when the frictional power input in the contact was higher and when a higher contact pressure was applied.

The tribofilm has a strong influence on the tribological behaviour of the a-C:H-film. The thickness of the film on the pin was not constant across the contact area. When the tribofilm was thin the adhesive contacts between the transferred material in the disc wear track and pin possibly caused a high coefficient of friction. A thicker tribofilm on the pin acted as an protective layer decreasing the pin wear. Figure 17. A micrograph showing an alumina pin surface ( 5 N, 3.0 d s ) .

Based on the friction results and pin wear surface morphology the properties of the tribofilm governed the frictional behaviour. According to the SIMS analyses the tribofilmon the steel pin contains mainly iron, chromium, oxygen and hydrogen, but carbon content was surprisinglylow. The oxygen was probably bonded to the iron and chromium. A formation of a graphite layer on the steel pin has been reported as an explanation for the low coefficient of friction with a-C:H-films [ 5 ] . However, in the present study the formed layer contaned mainly iron, chromium, oxygen and hydrogen, which indicates that the role of the graphite leading to a low coefficient of friction is not so obvious.

CONCLUSIONS

Figure 18. A micrograph showing an alumina pin surface (35 N, 2.6 d s ) .

DISCUSSION The coefficient of friction showed a significant decrease when the sliding velocity and the load were increased. For the steel pin sliding against the coating the coefficient of friction varied from p=0.42to p=O. 1 and for the alumina pin sliding against coating the coefficient of friction varied from p=O. 13 to p=0.02.

Tribofilm formation governed the tribological properties of a-C:H films. The formation of protective tribofilm reduced the pin wear and the coefficient of friction with steel pins. The coating wear volume generally increased, whereas coating wear rate decreased with higher loads. When higher sliding velocities were used the coating wear volume slightly decreased. The tribofilms formed on the steel pin wear surfaces consisted of iron and chromium oxides, carbon and hydrogen.

344

REFERENCES 1. A. Grill and V. Patel, Diamond and related mate rials, 2 (1993) 597.

2 K.Enke, H. Dimigen and H. Hubsch, Appl. Phys. Lett. 36 (4), 1980 29 1. 3. K. Miyoshi, P. Pouch and S.A. Alterovitz, NASA TM 102379 (1989) 4. D.S. Kim, T. E. Fischer and B. Gallois, Surface

and Coatings Technology, 49 (1991) 537. 5 . H. Ronkainen, J. Koskinen, A. Anttila, K. Holmberg and J.-P. Hirvonen, Diamond and related Materials, 1 (1992) 639.

6. H. Ronkainen, J. Likonen, J. Koskinen, Surface and Coatings technology, 54/55 (1992) 570.

Dissipative Processes in Tribology / D. Dowson et al. (Editors) 0 1994 Elsevier Science B.V. All rights reserved.

345

SURFACE BREAKING CRACK INFLUENCE ON CONTACT CONDITIONS. ROLE OF INTERFACIAL CRACK FRICTION. THEORETICAL AND EXPERIMENTAL ANALYSIS M.C. DUBOURG" ,T. ZEGHLOUL"" ,B. VILLECHAISE""

* Laboratoire de MCcanique des Contacts, UR4 CNRS 856, INSA, 20 Av. A. Einstein, Bdt. 113, 69621 Villeurbanne Cedex, France. ** Laboratoire de Mecanique des Solides, URA CNRS 861, UniversitC de Poitiers, 861 Av. du Recteur Pineau, 86022 Poitiers Ctdex, France Abstract Numerous studies are devoted to the determination of two body contact conditions, i.e the contact area, the stick and slip zone repartition, the normal and tangential pressure distributions. Interfacial roughness, friction, worn profiles for instance are taking into account as they disturb the hertzian stress field, but no specific attention is paid to the influence of surface breaking cracks. The mutual influence of surface breaking cracks on two body rolling contact conditions was studied theoreticalyy in a previous paper by Dubourg and Kalker [l]. Significative overpressure relatively to the classical maximum hertzian pressure and split up of the contact area were obtained numerically. An original experimental simulation is undertaken to validate these results. The theoretical model is the combination of a two body rolling contact model and a fatigue crack model. The steady rolling contact between the wheel and the rail is solved as a unilateral contact problem with friction. Displacement and stress expressions derive from Boussinesq and Cermti potentials. The fatigue crack model is based on distributions of dislocations for crack modelling and unilateral contact analysis with friction for the contact solution between crack faces. These two problems are solved in turn as displacements generated by cracks modify the two body surface geometry. This process goes on until convergence is reached, i.e when the two body contact coqditions are stabilised from one iteration to the next. The experimental work is based on photoelastic technique. Birefringent slabs for both wheel and the cracked rail are employed. Isochromatic fields, normal and tangential loads and global displacements are recorded continuously during the loading. Visualization and calculation of pressure peaks in the wheel and extent of the contact area are performed. 1. INTRODUCTION

In a previous theoretical study [I] the mutual influence of surface breaking cracks on the wheel-rail contact conditions was investigated. Modifications of the traction distributions with and without split up of the contact area were determined, depending on the relative position of the wheel with respect to the cracks. This paper is concerned with the experimental validation of these results. The experimental part includes the simulation of the contacting movement of the wheel relatively to the cracked rail with vizualisation through photoelasticity technique of the

isochromatic fields in both contacting bodies. Theoretical simulation of this experiment will be conducted simultaneously. 2. THEORETICAL APPROACH A steady contact model and a fatigue crack model including frictional locking at crack interface are combined. Connection between the two problems is introduced through surface geometry modification caused by displacements generated by cracks. Both models are half analytical and numerical that imply inexpensive computer time and great accuracy.

346

d

2.1 Two-body contact

Steady state normal contact of a cylinder (the wheel) over an elastic half-plane (the rail) is considered. Perfectly elastic conditions are considered, the solids are homogeneous and isotropic. A theory of contact is required to predict the shape of the area of contact, the slip and stick zone repartition, the magnitude and distributions of surface tractions, normal and possibly tangential, transmitted accross the interface (cf. figure 1).

way that satisfies the boundary conditions along the faces of the presumed cracks.

-P

J

p ------0

/-i Figure 2 : Fatigue crack model I

h

slip zone

stick zone

Figure 1 : WheeYrail contact model This contact problem is solved as a unilateral contact problem following the method developed by Carneiro Esteves at al. [2]. As semi-infinite bodies are considered, Boussinesq and Cemti potentials are used. Relations between displacements and stresses are obtained. The potential area of contact is discretized into segments on wich stresses are assumed constant. 2.2 Crack model

These boundary conditions (cf. figure 3) are expressed as in a : contact zone

-

k=0,

4,( 0

(1)

d = O ,

&,)O

(2)

- open zone:

- backward slip zone: - 4=f.4, ~ , * a J t ) 0 - forward slip zone d=-f*d 4*dt)0 9

I

(d

(4)

-stick zone &t

A theoretical two-dimensional linear elastic model of multiple fatigue cracks was developed [3,4] to determine the stress and displacement fields in cracked solids and the stress intensity factors (SIFs) at crack tips. Multiple interactive cracks, straight or kinked, surface breaking or not, taking into account frictional locking and situated in an isotropic medium can be modelled (cf. figure 2). The model rests on the continuous dislocation theory, pionnered by Keer and Bryant [5,6] and on the unilateral contact theory developed by Kalker [7]. Resultant stress and displacement fields ,FU , FV ) are given by superposing the uncracked solid ( $"" ) and the crack ( d,6u, Fv) responses to the load in such a

(3 )

=0

I

ldtl(f

openzone I

stick zone backwardslipzone

----

Figure 3 : Boundary conditions at crack interface

(5)

347

The continuum stress f l C in the uncracked solid may be obtained numerically (finite element analysis for instance) or analytically in the case of a halfplane. The crack response corresponds to displacement discontinuities along its faces, opening and slip, that generate stresses. These displacement zones are modelled with continuous distributions of dislocations bx and by. Single distributions of dislocations bx and by are considered along each crack. It is assumed that by and bx are square root singular at crack tips, and at crack mouths for embedded cracks, bounded elsewhere. The correct behaviour of the stress field along cracks is thus guarantee. The strength of these singularities is then driven numerically to zero in the case of a contact zone or a stick zone at crack tip [3]. Consistent equations come from corresponding boundary conditions (6u, = 0, 6u, = 0). This method gives single stress and displacement expressions for the whole crack, independent from the final contact division:

g([ w w ~ . Y " . a

&+

or=9 &)

jb,(S)K,:(x.yq.Rd5 rl

i j = x,y

I

(6)

r;

hn= jbIJOd5

(8)

r;

where p is the shear modulus, k=3-4v for plane strain or (3-v)/(1+v) for plane stress, v the Poisson's ratio, Kvx,K; the stress kernels expressed in [3], crack 1 profile, m the number of cracks. Stress expressions are singular integral equations, solved following Erdogan et a1 [S]. Discretized stress and displacement expressions are obtained. The 2NI unknown are the bx and by values at the discretisation points, where NI is defined by

r,

rn

NI = c p i , p, the number of discretisation points i=I

for crack i. The contact problem solution between crack faces as a unilateral contact problem with friction gives automatically the contact area division, slip, stick and open zones, and the suitable distributions of dislocations. Load cycles are

described with an incremental description which takes into account the load history as hysteresis is generated by friction at crack interface. This model was used to determine the stress intensity factors experienced at crack tips under various loading conditions, sliding or rolling contact conditions, bulk tractions ... 2.3 Crack influence on two-body conditions

contact

Conditions at interface between the wheel and the rail influence significantly contact stresses. Surface roughness, interfacial friction, worn profiles are taken into account. No specific attention is paid to crack influence. For convenience of data treatement, the global problem is split into two parts, the two-body contact and the crack problems, which are solved independantly in turn. Connection between the two problems is introduced through surface geometly modification caused by displacements generated by cracks. Note that the displacement field generated by cracks is continuous except along the crack where displacement discontinuities correspond to slip or opening. The normal displacement at the smooth half-plane surface Vsurf is calculated at the discretization points of the contact area 2a from bx and by. Iterations on crack influence are organized in the following manner (cf. figure 4): First iteration: the surface geometry considered H(y) corresponds to a cylinder over a smooth half-plane. The contact problem is solved as exposed in the section 11.1. The contact area 2a and the normal traction p(y) are determined. The crack behaviour is then determined. Surface displacement V,,rf is calculated. H(y) is modified, h'(y) = H(y) + relax* V_ surf. Next iteration: h'(y) is considered as the new profile. The two-body contact is solved again. Continuuum stress field at iteration j is the resultant stress field calculated at the (i-1) iteration. Variations in normal tractions 6p cause variations in distributions dislocations 6bx and 6by. Slip and opening along crack faces are modified and SIFs too. Surface displacement Vsurf induces by theses variations is determined agam and added to the geometry. This

348

process goes on until1 convergence is reached, i.e normal tractions exerted on the half-plane surface are stabilized from one iteration to the next. For the next load step, the geometry is reinitiated to Hb) GIVEN LOAD STEP

iterafion n"l :

hertzian analysis fatigue crack model

-

2a, P,9 Vsud

iferation ny :

2a', p', q'

-

6p = p' - p 6q = q* - 4

bodies are presented on figure 5 . The loading frame is placed in an optical system of photoelasticity. Photoelastic picture acquisition is realised by the use of a CCD camera for numerical treatement. Both wheel and rail scale models are made in polyurethane PSMl of 9.6 mm width, a birefringent material sold by the Vishay-Micromesures society. The loading frame was realised to ensure the plane stress assumption. The apparatus is made of two parts where the two contacting bodies are fixed. These two parts can move in two perpendicular directions corresponding to normal and tangential loadings. The horizontal guide is realised through two ball columns. The vertical displacement compresses the force sensor N providing the wheel normal loading. The wheelrail sytem is based on a gas slider. The cracked rail scale model is realised from two trapezoi'd reamed parts. These two parts are partially sticked together along their inclined face, forming thus a parallepiped. The unsticked remaining surface corresponds to the crack. The stiffness of the glue, once dry, is identical to those of the polyurethane. This technique guarantees a good geometric definition of the crack.

--

E-2400MPa

Figure 4: Crack influence on wheelhail contact conditions.

v

3. EXPEFUMENTAL APPROACH

t-10rnrn b - 15 mm

C

R

The contact formation and behaviour and particularly in the case of frictional contact is still not yet understood in some cases. A formal definition of the problem particularly in terms of boundary conditions for theoretical modelling is difficult. Understanding frictional phenomena and interactive mechanisms between two body contact and surface breaking cracks on one hand and determing the key parameters on the other hand require an experimental analysis of the contact evolution. The work presented here is concerned with normal contact of a wheel over a cracked rail, and more precisely with the study of the influence of cracks on the contact conditions. 3.1 Loading frame

The experimental set-up and both the geometrical and mechanical characteristics of the two contacting

038

3.5 N/mmiFna~c 1000 mm

rl

h

Figure 5 : Experimental set-up 3.2 Tests

The main goal of the tests realised during this study is to show the influence of a crack on the contact conditions at the wheelhail interface, i.e changes in the contact conditions during the passage of the wheel over the cracked rail. In this first approach the rotating movement of the wheel is not realised

349

experimentally. Only the normal loading is performed. A load step consists in normal loading, unloading and wheel displacement. The running conditions are a normal load of 290 N, a wheel radius of 1 m that correspond to a contact area 2a of 10,5 mm. The crack length b is equal to 15 mm and its inclination is 8 = -40'. The position of the wheel is defined with respect of the trailing edge of the loading zone yt. yt varies from -27 mm to 11 mm with a 2 mm displacement increment. 19 load steps are thus realised. The isochromatic field is numerized for each wheel position.

model describes in that case both the overpressure and the split up effects. These phenomena are due to the location of the crack mouth inside the contact area.

Step 4: yt 2 5 m m The wheel moves away from the cracked region which therefore influences no more the wheel-rail contact. The behaviour observed is similar to those described in step 1: 4. NUMERICAL SIMULATION

3.3 Analysis of the isochromatic field evolution A phenomenological analysis of the tests was conducted. At yt = -10mm the leading edge of the contact area moves over the crack mouth and at yt = 0 mm the trailing edge moves away from crack mouth. Depending on the wheel position several steps were observed:

Step 1: yt I

- 25 m m

The normal loading is imposed by a vertical displacement of the wheel. The isochromatic field changes continuously and is slightly disymmetric. This disymmetry is due to a torque associated to macrogeometric difects created at the manufacturing stage of the wheel scale model. During this step, the the wheel is far from the crack and no interacting effect between them is observed.

Step 2:

- 23 m m

I yt I -11 m m

The wheel rolls nearer the crack; from yt = 9.64mm the wheels is above the crack tip. Crack faces are pressed together and sheared. Further stress concentration at crack tip is observed, corresponding to the slip of the left part of the rail. This stress concentration increases when the wheel comes nearer.

Step 3: - 9 m m I yt I 3 m m The surface breaking crack modifies the contact conditions at the rail surface. The pressure distribution along the contact area is modified locally with split up of the contact area in two parts without modification of its extent Accordingly the numerical

Concerning the two-body contact simulation, a potential contact area of 12 mm discretized with 121 points is considered. The maximum hertzian pressure Po is equal to 3.67 MPa and the contact area is 10,47 mm width. The origin of the reference axis is placed at the crack mouth. 30 discretization points are distributed along the crack. Different friction coefficient values were tested, ranging from 0.1 to 0.3. The best match between theoretical and experimental stress field is obtained for a friction coefficient equal to 0.1.The relaxation coefficient relax is equal to 0.3. For all the load steps the crack behaviour is determined (slip, stick and open zone distribution), the stress intensity factors are calculated (figure ) and the stress fields computed over an area of width 45 mm along oy and of length 17 mm over ox. The width is centered with respect to y = -7.5 mm. The mutual influence of crack on the contact conditions generates: stress intensity factor variations, pressure distribution modifications with local overpressures, contact area width changes, - split up of the contact area.

-

Step 1: No significative influence: yt I - 11 mm

No significative mutual influence between crack and the two-body contact is noticed as long as the wheel is not situated over the crack mouth, i.e yt less than -1 1 mm. At the load step 1, the the crack is partially open at its mouth, then a forward slip zone holds and the crack tip is sticking. KII is very small 55 Padm. The state of the crack changes at load step 2: from crack

350

Figure 6 a) : l o a d s t e p 6

yT =

-

1 7 mm

35 1

F i g u r e 6 b) : load step 9

yT =

-

11 mm

352

-2.0

-7.0

-12.0

-17.0

F i g u r e 6 c : l o a d s t e p 10

YT -

5 t h coupling i t e r a t i o n

-

9mm

353

Figure 6 d) : load s t e p 12 yT 4th coupling i t e r a t i o n

-

-

5

m

354

-R.S -10.2 -11.9

-13.6

-15.3 -17.C

-16.5

yT 4 t h coupling i t e r a t i o n

F i g u r e 6 e ) : load s t e p 14

-

1mm

355

-1.7

-

-3.4

-

-5.1

-

-6.8

-

-8.5

-

0.0

-1u.2-11.9-

F i g u r e 6 f) : l o a d s t e p 16

yT = 3 mm

356

tip to crack mouth a bakward slip zone, a stick zone, a forward slip zone and finally an open zone are distributed. This state doesn't change up to load step 9 included.

A qualitative comparison is performed between the experimental and the theoretical results. It is based on

- mainly on informations concerning the two-body

Step 2 : Influence: -9 mm I yt I-1 mm 4 to 5 iterations are needed to converge. Different

mechanisms are observed: -load step 10: yt = -9 mm: the leading edge of the contact area is situated over the crack mouth. A global backward slip zone holds along the crack. Coupling leads firstly to split up of the contact area in two parts situated on each side of the crack faces with local overpressures up to 6.8 MPa and increase in KII from 11250 to 113 10 Padm. But at the next iteration the contact area is again in one part, the pressure distribution is very similar to the initial one, and the stress intensity factors too. -load steps 11 and 12: yt = -7 mm and yt = 5mm: A particular distribution of displacement zones is observed: the crack is open at crack tip, and a backward slip zone spreads from it up to crack mouth. The compressive action of the two-body loading closes obviously the crack faces at crack mouth. Further the crack tip is situated outside of the compressive zone and therefore an open zone holds there. Coupling leads for load step 11 to overpressure up to 4.49 MPa, i.e a 22% increasing without modification of the contact area width. For the load step 12, overpressure up to 4.7 MPa, i.e a 28 % increasing is noted. For both load steps, MI variations are very small, less than 1%. -load step 13: coupling is negligible -load step 14: yt = -1 mm A global forward slip zone holds along the crack. A sligth increasing in the maximum pressure is noted, from 3,67 to 3,69 MPa. But split up of the contact area in two parts is obtained: from -1 to to 0.05 mm and from 0.15 to 9.7 mm.

-

Step 3: No more influence: yt 2 1 mm An open zone spreads out from the crack mouth, then a forward slip zone at crack tip. 5. COMPARISON

-

contact conditions and their modifications due to the crack influence. Split up of the contact area is observed for yt varying from -9 to 3 mm. This behaviour is numerically obtained for yt = lmm. experimental and theoretical isochromatic fields, presented for load steps 6, 9, 10, 12, 14, 16 (cf. figure 6). They are very much alike.

CONCLUSION

The influence of surface breaking cracks on two-body rolling contact conditions was previously studied theoretically by one of the authors. Significative overpressure relatively to the maximum hertzian pressure and slip up of the contact area were obtained numerically. An original experimental simulation was undertaken to validate these results. This experimental work is based on the photoelastic technique. Comparison between isochromatic fields and computed stress fields, experimental and theretical two-body contact behaviour (slip up of the contact area) confirms the previous results. REFERENCES

M.C. Dubourg, J.J. Kalker. Crack behaviour under rolling contact fatigue. In "Rail quality and maintenance for modern railway operation". Proceedings of the International Conference on "Rail quality and maintenance for modem railway operation", Delft (NL), June 1992, Ed. by J.J Kalker, D.F. Cannon, 0. Orringer, Kluwer Academic Publishers, p. 373-384, 1993. A. Carneiro Esteves, J. Seabra, D. Berthe. Roughness frequency analysis and particle depth. In Interface dynamics, Proceedings of the 14eme Leeds-Lyon Symposium, 8-1 1 Sept. 1987. Ed. by D. Downson, C.M. Taylor, M. Godet, D. Berthe. Amsterdam: Elsevier, p 209213, 1988.

M.C. Dubourg, B. Villechaise. Analysis of multiple fatigue cracks Part I: theory. ASME,

-

357

Journal of Tribology, Vol 114, pp. 455-461, 1992. 4

M.C. Dubourg, B. Villechaise, M. Godet. Analysis of multiple fatigue cracks - Part 11: results. ASME, Journal of Tribology, Vol 114, pp. 462-468, 1992.

5

L.M. Keer, M.D. Bryant and Hiratos G.K. Subsurface and surface cracking due to hertzian contact. ASME, Journal of lubrication technology, Vol. 104,, pp. 347-351, 1982.

6

L.M. Keer and M.D. Bryant. A pitting model for rolling contact fatigue. ASME, Journal of lubrication technology, Vol. 105, , pp. 198-205, 1983.

7

J.J. Kalker. Three-dimensional elastic bodies in rolling contact. Kluwer Academic Publishers, 1990,3 14 p.

8

F. Erdogan, G.D. Gupta and T.S. Cook. Numerical solution of a singular integral equation. In Method analysis and solution of crack problems. Ed. by Sih, Leyden, Nordhoff International Publishing, p. 368-425, 1973.

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SESSION VIII MACROSCOPIC ASPECTS, FRICTION MECHANISMS Chairman:

Professor K L Johnson

Paper Vlll (i)

The Generation by Friction and Deformation of the Restraining Characteristics of Drawbeads in Sheet Metal Forming Theoretical and Experimental Approach.

-

Paper Vlll (ii)

A Model for the Estimation of Damping in Helical Strand Under Bending Vibration.

Paper Vlll (iii)

Energy Dissipation and Crack Initiation in Fretting Fatigue.

This Page Intentionally Left Blank

Dissipative Processes in Tribology / D. Dowson ct al. (Editors) 0 1994 Elsevier Science B.V. AU rights reserved.

36 1

The generation by friction and plastic deformation of the restraining characteristics of drawbeads in sheet metal forming - Theoretical and experimental approach E. Felder and V. Samper Groupe Surfaces et Tribologie - Ecole des Mines de Paris CEMEF - URA CNRS 1374 BP 207 , F 06904 Sophia-Antipolis Cedex, France During its drawing through the drawbead, the sheet undergoes successive bending cycles and friction along the surface of the shoulders and the bead. Starting from the work of Stoughton (1988) and Marciniak & Duncan (1989), we develop a simple theoretical model for describing the behaviour of an anisotropic sheet material whose flow stress is a power function of strain 00 = K en; an energy balance provides the contribution of plastic deformation to drawing load; then the holding force is deduced from a stress balance; the analysis of stress and strain increment distributions accross the sheet thickness provides the thickness reduction. The reliability of the rheological assumptions for steel and aluminium sheets is discussed by comparison with experiments performed between rollers by Nine (negligible friction) at the maximal depth of bead penetration. Then we study theoretically the influence of the depth of bead penetration and friction on the loads for strips holded by rollers in the original plane of entry (case 1) or sliding on blankholder (case 2) Reliability of the model is discussed by comparison with experiments published by Stoughton (case 1) or performed on a super formative sheet SPC 3C and a Zn-Ni coated sheet HPC 35 (case 2). Endly we study experimentally the restraining characteristics on the sheet HPC 35 of single and multiple drawbeads; they can be described by a single apparent friction law; the geometry of the drawbeads defines the range of accessible holding forces, but an increase in the number of drawbeads produces a significant decrease in the efficiency of the system and a significant increase in the thickness reduction of the strip. which is a power function of the drawing load. 1 .INTRODUCTION

Sheet metal forming for manufacturing autobody parts involves various plastic deformation modes, particularly drawing or simple sliding between die and blankholder; the stress balance induces at the boundary between these both modes marked shear and ultimately rupture of the blank. So drawbeads are implemented along the sliding parts of the workpiece in order to homogenize the metal flow towards the punch; but a good design of the operation, especially by numerical simulation (1-4) requires the knowledge of their restraining characteristics, namely the evolution with the depth of bead penetration 6 of the holding H and drawing F forces. Despite the previous work performed by Nine (8,9), Stoughton (11) and Yellup & Coll. (12,13) among others, the influence of the sheet rheology, friction, the sheet clamping system or number of drawbeads cannot be predicted easily. We aim to provide such information by theoretical and/or experimental work. Before any calculation, we can remark that

drawbead induces plane strain of the sheet; so forces increase in direct relation with the strip width w and are characterized by their value by unit width and the apparent friction coefficient pa :

For theoretical calculations, we assume that the strip is rigid- plastic and yields according to the Hill's quadratic plastic criterion; so its behaviour is characterized by the normal anisotropy factor r and the evolution of the effective stress 00 versus the effective strain E; we assume monotonic strain hardening Hollomon law:

Hill's plasticity criterion implies that any plane principal strain increment dep induces an effective strain increment de (11) :

362

work required for performing such strain increment for an unit length of strip; so 2. Forces generated by deformation

In this part, we assume that the friction of the strip on tools is negliaible; so forces depend only on the rheologicarpropertiesof the strip. 2.1 Theoretical model We assume that in the drawbead the shape of the mid-surface of the strip consists of three circular arcs with the radius Rb (angle 244 in the central part and R, in the lateral parts (angle @) (figure la). According to the elementary theory of the bending of thin strips (7),the effective strain increases in direct relation with the distance to the mid-surface y (figure 1c) and has the value at the limit between the two first circle arcs (with t the strip thickness):

t/2 AEl(Y) f d l ) = 2 jdy

End&

0 Kt (a)ltfl fdl)= (l+n)(2+n) R,

where the variation of the strip thickness for the moment is assumed negligibleSimilarly, we obtain (cf figure 1b) Kt

f ~ ( 2 ) = (1+n)(2+n)

1

1

( a t (-+-))'+" R, Rb

2 1 Kt (at(-+-))l+n fo = fo(3) = (l+n)(2+n) Rs Rb

(6)

(7)

The force balance of the central part of the strip and the bead provides the related holding load The related drawing force f o ( l ) is the plastic

ho(2)=( fo(l)+-fo(2)) sin (I

(8)

Figure 1: Analysis of the strip deformation in the drawbead a) Assumed geometry of the mid-surface b) Force balance on the bead c) stress and strain increment across the strip thickness

363

As demonstrated by previous calculations, the bending cycles are induced by increasing axial stress ox = Wt;. by an analysis of the stress and strain increment distribution across the strip thickness (cf figure l c ) Duncan & Marciniak (7) have demonstrated that any increase in the tensile bending strain (d&M)/a induces the thickness variation:

0.2. Kt

Steel sheets

0.18.

/

/'

/'

I

aoo

,/*

oo is some mean effective stress across the strip thicknes and is equal to a first approximation i I

IKEndde= K(AEM)" l+n

%=AEM

so as X'

0,

Aluminium sheets n 0.25-0.29

I+r

v

AEM

n=

-

0.14.

1F x -_d _ - -dEM t

Theory

fo

A

1

0.08

b

I

0.09

t

G%G ., 1

0.1

.

0.11

0

--_

K(A&M)~+~d AEM =(l+n)(2+n) t - a(2+n) 'EM I

and by integration, we obtain the final strip thickness: (AE3M)2

1

In(-)= t 2a(2+n) = 2a(2+n) (

2

1

~ ( G + )*G(9))

2.2 Comparison with experiments Nine (8,9) has performed measuments of drawing and holding loads for drawing two aluminium and steel sheets (0,761110.99mm) between rollers of radius p = 5.5 and 4.75 mm at the maximal depth of bead penetration 6 ~ ; for his experimental conditions where the clearance is very small (LdP+t&M) (ci fig lb)

Conditions of strip clamping imply that ho(2) is equal to the the total holding force (cf 9 3), so formula (7) and (8) imply that

In order to compare the behaviour of the various alloys, we have reported with logarithmic scale on fig. 2 the reduced drawing force fo/Kt versus the increase in effective strain induced by one bending Ae3~/6.

Figure 2: Comparison between the theoretical drawing force and the experimental one (8,9) for negligible friction and maximal depth of bead penetration (drawing speed V=85 mmls) In such representation, the theoretical values are located on a straight line which depends only on the value of the strain-hardening exponent n. Notice that the rheological data are related to classical uniaxial tensile testing performed at very low strain rate 10-3 s-l in the range of strain ~ ~ 0whereas . 2 drawing through the drawbead at the velocity V induces cyclic hardening at high strain rate = V/R 520 s-' and an effective strain EI 0.6. Nevertheless we observe a good agreement between theory and experiments for the steel sheets, but theory overestimates the drawing forces of aluminium sheets from about 20 %. Such conclusions have been previously drawn by Nine (8,9) ; the probable explanation is that the hardening effect of high strain rate present in steel (cf 94) is cancelled by the lesser hardening produced by cyclic straining, whereas the absence of strain rate effects in aluminium sheets produces the gap between theory and experiments. Theory predicts that the apparent friction coefficient depends only on n and increases slightly with it (formula (10);

364

we observe some scatter in the experimental values, but the mean values increase with n and generally are slightly higher than the theoretical ones (figure 2), again the gap is maximal for aluminium sheets but is lesser than 6 Oh. The drawing of the 0.97 mm A.K. steel between rollers p= 5.5 mm, produces a 8.7 O h reduction in thickness (8); formula (9) predicts a good order of magnitude: 6.5 'lo. So the theory can be considered as providing easily satisfactory results when the strip shape in the drawbead is known. 3. Influence of the bead depth and friction for strip clamped by rollers

3.1 Theoretical model For such clamping, the maximal strip deflection is equal to the bead depth 6 ; so the figure 3 summarizes the main assumptions on the strip shape: it is tangent to the plane part of the shoulders and the bead at its deeper point: elementary geometrical analysis provides the basic relations:

the shoulders radius p s ; for small bead depths where R according to the relation (13) is greater than pb+t/2, we assume that Rb=Rs=R; for 6>SC we assume: t L R (14) 2 S-sin$ Rb For analysing the effect of friction, we adopt the same assumptions as Nine (8,9): Coulomb friction between tool and strip and the contact traction uniformlv distributed along the circular parts of the strip: So stress and energy balance in the first part provide the relations:

&,=Po+-

h(1) = f ( l ) sin@=p i Rs sin$ (1 + p tan($/2)) f(1) = fo(1) + @ Rs PP1

so

f(1) = f o ( l ) +

f(1) 1+ptan($/2)

Similarly, we obtain : h = h(2) = ( f ( l ) + f(2) ) sin

= 2 sin4

Rb p2

',.

Two cases are currently met: -The radius of the shoulders and the bead are equal; we assume that the radius of the strip mid-surface is uniform R = Rb = R s and according to the relations (11) has the value

L R= 2sind1 -the bead radius pb for example is greater than

rollers

I

''

f(2)=fo(2)+ cl4 ( 1+pt;($,2)

\

+f(l)+f(2)) (16)

h(3) = f(3) sin@=p3 Rs sin$ (1 - p tan($/2) ) f = f(3) = fO(3) + $p(Rs p1 + 2 Rb P2 + Rs P3)

Elimination of the mean contact pressures p i , p2 and p3 in the last equation by using the previous stress balance equations provides

sheet

Figure 3: Assumed geometry of the strip and distribution of contact traction for a strip clamped on the shoulders by rollers

365

h 100-

Theory 11 = 0

- - - 0.163 d r aw be ad,

\

<

.o-

rollers

a 0

Q5

i

Figure 4: Comparison between theory and experiments (11) for the influence of the bead depth 6for drawing a strip holded by rollers - A.K. steel (cf fig2) ps =pb = 4.76 mm t = 0.737 mm

3.2 Comparison with experiments

the drawing force as:

So by neglecting in first approximation the last term, we obtain a relation which generalizes the relation obtained by Nine for

Q= n/2: 2+ sin$ f-fo f=fo +(-) ph or p=(-) (7) (17) sin+

20

By expressing f(l)+f(2) with the equations (15) and (16), we obtain a rather complex

expression for the holding force h:

The formula (17) and (18) demonstrate that the both forces f and h increase with friction, as expected.

Stoughton (1 1) has published some results related to the influence of the bead depth for drawing aluminium killed steel sheet between rollers (p=O) and through a drawbead with a mill oil as lubricant ; geometry of tools was as described in 8 2.2; we compare on fig. 4 the theoretical values with the experiments ones: -for the drawing between rollers (p=O),we observe a good agreement between theory and experiments, especially as the bead depth 6 is greater than 6 ~ / 2for ; smaller bead depth& the theory overestimates the drawing force and particularly underestimates the holding force. So we can conclude that the relations (12) and (13) furnish a rather good description of the strip geometry for estimating forces fo and ho with relations (5) to (8) for 6 2 8 ~ 1 2 . - for the drawing through the drawbead with a mill oil, we have deduced the value of the friction coefficient by applying the relation (17) to experimental values of lo, f and h for the maximal bead depth; so p 0 . 1 6 3 ; with this value, the relations (17) and (18) (+( 5) to

366

((8)) furnish values of forces again in good agreement with experimental ones for 6 2

6&.

Notice that the relation (17) applied to the experimental values of fo, f and h provide a rather constant value for the friction coefficient for the various bead depths. So we can conclude that despite the doubtful assumptions on the contact traction distribution the theoretical equations provide reliable values of forces and the shape of a strip clamped by rollers. 4. Influence of the bead depth and friction for striD clamped by blankholder 4.1 Theoretical model Here the maximal strip deflection remains always equal to the maximal bead depth 6 ~ ; so the figure 5 summarizes the main assumptions on the strip shape: it is tangent to the blankholder, to the shoulders at the points where the change in curvature occurs and the bead at its deeper point; elementary geometrical analysis provides that again tha arc angle $ verifies the relation (12); but we have now:

L

(8) supplies only the contribution of the bead to the holding force; additional holding forces Ah1 and Ah3 are supplied by the blankholder in order to induce in first approximation the curvature Rs to the lateral parts of the strip; consider for example the entry arc; its bending moment M i is:

tl2

We assume that M i is equal to the mean moment of the force Ah1 along the entry arc;

so

Similarly we obtain (equation (22) ):

t

FB=,ing -Ps-s R --- a' Rb s- 1-COS@

and we assume that the total holding force under negligible friction is:

Under negligible friction, relation (7) provides the drawing force, but the relation

sheet' should er

shoulder

Figure 5:Assumed geometry of the strip for a strip clamped by the blankholder

367 4.2 Experimental study

increase linearly with

We have performed experiments on a super formative sheet SPC 3C and a Zn-Ni coated HPC 35 sheet; the table 6 summarrizes their rheological and friction properties: notice three facts - The sheets have the same thickness: 0.7 mm and almost the same roughness =1pm - According to uniaxial tensile testings performed between and 4 s - l the SPC 3C sheet has lower effective stress than the sheet HPC 35; the both shets are strain and strain rate sensitive: as the strain rate increases from to 1. 4 s 1 (=V/R) the consistance K of the SPC 3C (HPC 35) increases from Ko=548 (623) to Kd=570 (658) MPa whereas its strain hardening coefficient n decreases from n,=0.318 (0.217) to nd=0.258 (0.19) - On the contrary, according to friction testings performed between flat tools (2-30 MPa) with the protective oil as lubricant, friction of SPC 3C sheet is higher (0.2) than friction of the HPC 35 sheet (0.13). Drawbead testings were performed at 10 mm/s for bead depths ranging from 60 oo/ and 95 o/o the maximal value 6 mm; the dimensions of the tool (ground cast iron) are stated precisely on figure 7 and for the maximal bead depth induce an arc angle $M = ld3 and a strip curvature radius Rz6.4 mm Beside testings performed with the protective oil as lubricant, we performed testings on the SPC 3C sheet with teflon coating stuck on the two sides of the sheet and castor oil as lubricant in order to minimize friction. From the results summarized on figure 7 we can draw the following conclusions: - For the both sheets drawn with the protective oil the drawing force and the holding force for a given value of the bead depth 6 have almost the same value f=h which does not depend on the sheet material and in first approximation they

increases steeply with

Materials KO MPd no SPC3C 548 0.318 HPC35 623 0.217

Eo o/o .517 .29

a .0053 .0074

limited: 4 o/o for 6

6; thickness reduction

6, but

remains

~ .

- For the SPC 3C sheet the use of teflon coating produces a significant decrease of the drawing force, but the decrease of the holding load is much smaller. For the rheological data of the SPC 3C sheet related to the strain rate induced by drawbead testing (1.4 s-l), the theoretical value of fo and ho (relation (23) ) are in good agreement with the experimental values of the forces for testings performed with teflon coating whereas the rheological data related to very low stain rate underestimate drawing and holding load. This suggests that for the SPC 3C sheet the high strain rate rheological data are the pertinent ones. On the contrary for the HPC 35 the theoretical drawing forces deduced from the high strain rate rheological data are almost the values obtained under experimental conditions where friction is surely not negligible; so for HPC 35 sheet the low strain rate rheological data are the most pertinent ones as for the steel sheets tested by Nine ( cf. 9 2.2). So it suggests that the cyclic hardening of the SPC 3C sheet is almost the same as its monotonic hardening. - This interpretation is confirmed by the values of the friction coefficient related to experiments performed with the protective oil; they are deduced tentatively from the relation (17) starting from the experimental values of f and h and the theoretical values of fo related to the pertinent rheological data as defined above; they are almost constant and a little smaller than the values related to tribological experiments: for SPC 3C 0.17 against 0.2 and for HPC 35 0.1 against 0.13. - The relation (9) provides values of the thickness reduction in good agreement with the experimental ones related to drawing of SPC 3C sheet with teflon coating. So we can conclude that the relations (12), b .2326 .06

C

.0284 .018

r 2.36 1.33

Ra P ~1 =1 0.2 0.9 0.13

Table 6: Properties of the 0.7 mm studied sheets -Plastic behaviour described by (4) o ~ = KE( + E ) ~ K = K ~ ( E / E ~E ) ~= E ~ ( E / E n=no(E/Eo)-C ~)~ ~ ~ = 1 0s-1 -3

368

rn

.

Sheeet SPC 3C + teflon

1

0

0

..u

:

i

Sheet HPC 35 + protective oil Sheeet SPC 3C + teflon or protective oil or 14 s-l Theoretical curve for p = 0 for rheology at 1O 3 Figure 7: Comparison between theory and experiments for the influence of the bead depth 6 for drawing a strip (t = 0.7 mm) holded by blankholder Ps=Pb=6 mrn L=10.83 mm 6 ~ =mm 6 (19) and (20) provide a description of the shape of a strip clamped by the blankholder satisfactory for estimating forces under negligible friction. In addition, it appears that in first approximation the relation (17) can be used to estimate the contribution of friction to the drawing force for the two strip clamping systems studied here and that the

influence of friction on holding force seems lower for blankhoder clamping than for roller clampinc. But the pertinent rheological data depend on the sheet material and uniaxial tensile testings performed at very low strain rate can underestimate the forces for some steel sheet ( here the SPC 3C).

369

5. Experimental study of the drawing through multiple drawbeads

5.2 Results We can draw from the experimental results summarized on figure 8 the following conclusions - As expected, the forces increase with the bead depth for each system - For the step bead (SB) they are of the same order of magnitude as for the drawbead tested previously. - Each addition of a drawbead produces a marked increase in force: for 6= 3.4 mm for example, we observe an increase in a ratio 2 about from SB to SB+DB and from SB+DB to SB+2DB for drawing force and in a ratio of about 2.5 for the holding load. The figure 9 describes the evolution of the drawing force versus the holding force; we can notice that this evolution can be described in first approximation by a single apparent friction law; the geometry of the

5.1 Experimental conditions Testings were performed on the HPC 35 sheet under conditions similar to those described previously: 10 mm/s and the protective oil as lubricant: Three tool geometries were used (cf. figure 8): - A step bead (SB) with radii ps=2.5 mm and pb=3.5 mm and a distance between the circle axes L=6.65 mm. - A tool (SB+DB) with the previous step bead and a drawbead with following dimensions: ps=2.5 mm pb=4 mm and L=6.8 mm. - A tool (SB+2DB)with step bead and twofold the previous drawbead. 4 The maximal bead depth is 6 ~ = mrn.

1

0 T7 f

SB

SB + DB

SB + 2 DB

400,

&I-

I (.se+zosl I

4

SB+DB

__

I

SB+2DB

1

0.5

,'

/ -

0.5

zoo{'

_.

0.5

0.75

Figure 8: Geometry of the multiple drawbead systems and forces induced on the HPC 35 sheet

370

L

0.3 kN

mm

.

FDB.

0.2

%-

20 - Atlt a.

.*

10 -

c'

5':

0,l f I 'n

f

C

I

.

10

20

L

r

,

/ /, ,

50

. , . I

100

f 200 N h m

Firrure 9: Apparent friction law of HPC 35 sheet for drawing through multiple drawbead systems and rerated thickness reduction drawbead system defines the range of accessible holding forces, but an increase in the number of drawbeads produces a significant decrease in the efficiency of the system: pa decreases from 1. to 0.6 about. - An increase in the number of drawbeads produces a significant increase in the thickness reduction of the strip. which is a power function of the drawing load (figure 9). We have not developped a theory for describing the sheet behaviour in multiple drawbead system, but we can notice thet such results are in agreement with extrapolation of the theory of 9 2.1. - For the thickness reduction we can deduce from relations (7) and (9):

The related theoretical curve is located below the experimental one, which demonstrates that the theory underestimates the thickness reduction, as

expected, and, as the two curves are parallel; in a constant ratio equal about to 2 - Similarly from the relation (10) and its generalization we deduce the apparent friction coefficient under negligible friction (n=0.2; I$= d 3 ) : Single drawbead

Double drawbead 61 + n pa =1.18 ( 1+21+n,ql+n+gl+n ) = 0.65

So theory predicts the decrease of the apparent friction coefficient observed experimentally, apparently it overestimates this decrease. A possible explanation is that in experiments friction increases with the number of contact with the tool; so the decrease in the plastic contribution could be partly cancelled by an increase in friction contribution.

37 1

6. Conclusions

We can conclude that our theoretical approach provides easily an estimation of the holding and drawing forces required for drawing a strip through a drawbead and some simple relations for describing the restraining characteristicsof multiple drawbeads systems. A very useful result from a practical point of view has been obtained: for the two strip clamping systems drawbeads work in first approximation as if the friction coefficient is constant and according to the generalized Nine's equations:

20 ph f=fo +(-) sin$

sin$ f-fo

cL=(---)

24)

where fo is the drawing force for zero friction and the angle can be deduced easily in the both cases from the bead depth 6 and the distance L betwen the axes of the bead and a shoulder:

+

But some additional work is required in order to state more precisely the influence of some factors which have been taken into account only with some approximation: cyclic strain hardening, strip shape, distribution of contact traction... Experiments and numerical simulation could certainly provide very useful contributions for performing such improvements. Acknowledgments This work was supported by Engineering Systems International. Helpful discussion of experimental results with Dr L. Pknazzi are gratefully acknowledged. References (1) Aita S., Di Pasquale E.& Haugh E., "Sheet Metal Forming Simulation and Process Optimization Methodology", Actes du Seminaire International ESI "PAM 91", Paris, 7-8 novembre 1991 (2) Aita S., El Khaldi F., Fontaine L., Tamada T..& Tamura E., "Numerical Simulation of a Stretch Drawn Autobody - Part 1: Assesment

of Simulation Methodology and Modelling of Stamping Components - Part 2: Validation versus Experiments for various Holding and Drawbead Conditions", 1992 SAE International Congress & Exposition, Cob0 Center, Detroit, Michigan (USA", 24-28 February 1992(3) Chenot J.L., Wood R.D. & Zienkiewicz O.C.(Ed.), "Numerical Methods in Industrial Forming Processes: NUMIFORM 92", A.A. Balkema Brookfield, 1992 (4) EL Khaldi F., Aita S., Penazzi L., Tamada T;, Ogawa T., Tasaka S. & Horie O., "Industrial Validation of CAE Finite Element Simulation of a Stretch-Drawn Autobody Part (Front Fender Case)", Proc. 17th Bienn. Congr. IDDRG Shenyang , China, 11-13 June1992 (5) Felder E. & Samper V.,"Anisotropic friction laws", Final Report , BriteIEuram Contract 0062C (CD) BE-3486-89 - 1993 (6) Levaillant C., Felder E.& Penazzi L., "Rheological and Tribological Effects for Automotive Stamping Applications", Actes du Seminaire International ESI "PAM 91", Paris, 7-8 Novembre 1991 (7) Marciniak Z.& Duncan J.L., "Sheet Metal Forming Developments", in "Plasticity and Modern Metal Forming Technology", Blazinsky T.Z. (Ed.), Elsevier, Londres, 1989, 359 p. (8) Nine E H.D., "Drawbead Forces in Sheet Metal Forming", in "Mechanics of Sheet Metal Forming", Koistinen D.P. and Wang N.M. (Ed;) , Plenum Press, pp. 179-211, 1978 (9) Nine H.D., "The Applicability of Coulombs Friction law to Drawbeads in Sheet Metal Forming", J. Applied Metal Working, 2, No 3, pp. 200-210, 1982 (10) Samper V., "Etude Thkorique et Experimentale du Frottement et des Forces de Retenue en Emboutissage de T6les d'Acier doux Nues et RevBtues", These de Doctorat de I'Ecole des Mines de Paris, Juin 1993 (11) Stoughton T.B., "Model of Drawbead forces in Sheet Metal Forming", Proc. 15 th Bienn. Congr. on IDDRG, Deadborn, 1988 (12) Yellup J.M. & Painter M.J.,"The prediction of Strip Shape and Restraining Force for Shallow Drawbead Systems", J. Applied Metal Working, 4, No 1, pp.30-38, July 1985 (13- Yellup J.M.,"Modelling of Sheet Metal Proc. 13th Flow Through a Drawbead Bienn. Congr. on IDDRG, pp. 166-177, 1984 'I,

This Page Intentionally Left Blank

Dissipative Processes in Tribology / D.Dowson et al. (Editors) 0 1994 Elsevier Science B.V. All rinhts resewed.

373

A model for the estimation of damping in helical strand under

bending vibration. A. Hadj- Mimoune* and A. Cardou"

* Graduate student, Department of Mechanical Engineering, Laval University Ste-Foy, Que., Canada G 1K 7P4 ** Professor, Department of Mechanical Engineering, Lava1 University Ste-Foy, Que., Canada GlK 7P4 A semi-continuous model previously developed for quasi-static bending of helical strands away from terminations is used to study vibratory behaviour of strand close to terminations. Internal contact parameters such as contact forces, relative displacements, sliding and non-sliding zones are determined and used to estimate energy dissipation, damping factor and bending stiffness for one-layer helical strands. Damping measurements are made and compared with predicted values.

1. INTRODUCTION Relatively low bending stiffness is typical of helical strands (cables, overhead electrical conductors). This is due to the relative sliding motion that may take place between constituent wires. In turn, such motion induces energy loss as well as wear, fretting fatigue etc [l]. These processes are related to the contact conditions within the strand, which depend on its structure and on the applied load. Mathematical models have been developed recently to understand how the various parameters are related. The classical approach is to consider each wire individually and use curved rod equations with various hypotheses on contact conditions. It has been applied to energy loss evaluation in bending by LeClair [2], Vinogradov [31, Sathikh [41 and Hardy [51. When constituent wires are small compared with strand diameter, another approach has been proposed by Hobbs and Raoof [6]. It consists on replacing each layer in the strand by an equivalent orthotropic sheet, with axes of orthotropy locally parallel and perpendicular to a wire axis. Curved rod constitutive equations are then replaced by standard plane elasticity equations. The model works well for axisymmetric loads (tension and torsion). It has been extended by Raoof at al. [7,8] to the bending case. Here, however, difficulties arise from the nonuniform contact conditions between the layers. Indeed, as the strand curvature increases, some local

slip occurs between wires and between layers. Recently Raoof and Huang [9] have obtained a solution for constant radius bending and they applied it to structural damping calculation in the lateral vibrations of steel cables [lo]. In a previous paper [ 111, the present authors have studied the same problem using Hobbs and Raoof's orthotropic sheet model with a different approach for the inter-layer contact conditions. There, helical line contacts are used, and the usual Coulomb's friction law is applied along those helical lines, yielding one-dimentional stick-slip zones, to be detcrmined along each line of contact. It is, in effect, a mixed model, since it uses continuous layers and discrete contact lines. However, energy dissipation under constant radius bending does not lend itself easily to experimental verification. This is generally done through dynamic response under impulsive (logarithmic decrement) or, as in this work, harmonic excitation. Thus, in the present work, the model is extended to the study of bending near clamped sections, with a sinusoidal variation of strand center-line curvature. Theoretical results are then compared with experimental results. 2.

THEORETICAL BACKGROUND

The present study is a continuation of earlier works (Hobbs and Raoof [6] and Hadj-Mimoune at a]. [ I 11) where the same hypotheses are considered

374

again and the layers are regarded as a system of orthotropic concentric sheets. The basis of the theory already established is extended here for vibratory loadings. However, only the necessary equations are repeated due to space limitation. Consider a strand specimen comprising a cylindrical core surrounded by single layer counting N wires. The specimen has both ends fixed against rotation and all its components lay well on each other in undeformed state. The specimen initially under tension is subjected to steady state vibrations. Strain tensor is determined for each component of load and the resultant is deduced by superposition. With respect to axes of orthotropy parallel and perpendicular to wire cross section, the constitutive equations are:

adhered regions, we assume that cross sections remain plane and normal to the deformed axis. Furthermore, we use an approximation of the first mode rather than the exact mode shape which involves hyperbolic functions. If the cable undergoes a mode shape of the form

1

y(x) = - Y cos ( a x ) - 1 2l [ L

a fibre at the central axis of the wire elongates by the following amount: &lb

= r cos2a cos (0 + 00) d2Y

(3)

dx with

eo=(I -

N

; I = 1, ..., N

and

where

d2y = - 2(E)2Y cos (a x) dx2

1

s11

s12

0

1

0

0

S66

1

Axial strain due to vibration is determined later in this paper. Radial and tangential strains arc calculated after mechanical contact theory as developed by Mindlin [12,13] and Dcresiewicz [ 14,151. Contact theory concerning such application is fully detailed by Hermann [ 161 Johnson [ 171 and later by Hobbs and Raoof [6]. Since layers are assumed to be orthotropic, usual formula from continuum mechanics can be used to derive axial, radial and tangential stresses. Nevertheless, kinematic formulations established by Hobbs and Raoof [6] are used Lo maintain compatibility in wire displacements along the cable. This leads to a nonlinear system of equations to bc solved iteratively.

L

L

(4)

8 0 is the angular position of a wire at the constrained end (Fig. l), 8 is the angular position of any wire cross-section in the layer, Y is the magnitude of vibration, L is the cable length, r is the helix radius and E i b is the axial strain in the wire due to bending. According to Fig. 1, one can write the following relation

r

x=-

0

tan ci

Letting

k= 2

Ycos2a (LS

and A,= 2

IF.

L tan rx

axial strain in wire “I” becomes 3. S T U D Y VIBRATION

OF

STRAND

UNDER

Consider an helical strand clamped at both ends and subjected simultaneously to tension and transverse vibration. At small amplitude and in

Relative displacements are governed by contact forces. As shown in Fig. 2, there are normal contact forces per unit length p and p+dp for wire-

wire contact and q for wire-core contact. Tangential forces are assumed to be parallel to wire axis: fw and fw+dfwfor wire-wire contact and fc for wire-core. The only wire internal force being considered is axial force T.

4

x2

e

dx

r d0

Fig. 1: Illustration of wires disposition at the termination and stick-slip zones. For a given wire element ds, axial and radial equilibrium equations are (neglecting second order terms):

x

(10)

whcre X is the radial resultant on clcment ds stemming from tension T. For a perfectly flexible wire,

With friction coefficicnt p, the no-slip condition is

4

Fig. 2: Equilibrium of wire element.

from Eqs. 5,9 and 10

Els

E

q + 2 p cosp =

I

q

Tension T is given by

T = To+ES

(14)

To being the average component from axial loading and E l b the axial strain in the wire given by Eq. 8. Combination of Eqs. 8, 13 and 14 leads to the final non-slip conditions

376

[=Lq

and G(B,-cp)>- K

sin a

de

dT< 0

if

d0

wire-wire normal contact force is obtained from Eqs.

whcre

10 and 11. Depending on the sign of

de'

Eq. 23

becomes (18)

tan cp = p sin a

E=JL[TSLCL de sin a r

1

2

and

aui .-

G(8, +_ 9)= h, sin hc8 cos (8 + 00) t

a= -L [ de sin a

- 2pcosp ifdT>O

(24)

a<0

(25)

d8

I

cos hcO sin (0 + 00k cp) cos cp

(19)

Study of slip and non-slip conditions shows that angle cp is small for practical helix angles (a=20" and p= 0.35, cp= 6 . 8 O ) . Then, it can be neglected comparatively to 8 + 80 at the onset of sliding (G(0, k cp) = G(0))where maximum of IW)( is equal to K (K >O). This is obtained when the first -derivative of G(0) with respect to 8 is zero. This leads to tan hcO tan (8 + 00) =

1 + h,2cos cp L (1 + cos cp)

(20)

T

h r

- 2 p cos p] if

d0

Axial force T (Eq. 14) is a function of EI b which can be written in terms of displacement. E l b = d u - sin a du ds r d0 Subtituting Eq. 26 into Eqs 24 and 25 to obtain differential equations governing wire displacement in sliding zones

and &+(psina$=-~ de d€?

If solutions of this equation are 0= ern,(0 l 0 , I 2n), one must have

if dT -SO d0

(27)

where A=

Neglecting vibration effect on normal contact forces (p = PO)and substituting Eqs. 8 and 17 into Eq. 21, we obtain the amplitude of vibration, Yo, which corresponds to the limiting case

K= 2

r

r

E S sin a

[psin a TO - 2-cos CLpr sin rx

p]

First integration of these equations gives

E S H cos a sin a (L

3.1 Relative displacement in sliding zones

Sliding occurs when tangential force fc is equal to the frictional limit p q. Then Eq. 12 becomes

Constants C and C' are determined by using boundary conditions. Finally, one can deduce axial strain in wires in sliding zones due to vibration

377

(36)

Letting the sliding zone in its general form [0i , displacement of a section in that region is

&I, with

Y'3sin (hnO+ 00) + Y'40 On the other hand, the displacement of the corresponding fiber on the core surface is obtained from

+ Y's

if

d xI 0 d0

(38)

with yl1= -c' , yt2 = k R2 , psin a 2hmsin a

y3=kR2 , 2hnsin a

where

Xc=2 R R ~

L tan a

Letting X,,,= ht, - 1 and hn= h', + 1 and integrating Eq. 34 with 0i as reference point

6, is the maximum relative displacement corresponding to the onset of sliding

k R2 ~ 4 8- )uc(0i) = - 2 sin a sin (hmO- 00)- sin (Lei - 00)

+

L sin (hn0 + 00) - sin (hn0i + 00) hn Thus, relative displacement is

Boundary conditions At the non-sliding zone borders, micro-slip reaches a maximum and transforms gradually to gross-slip. Boundary conditions are

3.2

(35)

(39)

378

(40) Conditions 39 and 40 introduced into Eqs. 37 and 38 yield

C=

- p sin a

( ~ [sin z (Xmer - eo) &sin a)&.. e@sina)&

sin (hm8- 00)

+

sin ( L e i - ~ 0 ) ] + ~ 3 [ s(hef i n + eo)-sin (Lei + 00)]+

sin (knO+ 00) hn

(47)

At the fixed ends

8 = 0 and S(e=O) = O yielding

c1=

(49)

Finally, micro-slip in h e adhered region is

S(0) = - k ( f 2 - R 2 ) 2 sin a sin (Arne-0o)+ sin 00 sin ,

3.3 Relative displacement in non-sliding zones In these regions, strand plane sections are assumed to remain plane after loading. Displacements in wire and core are respectively governed by de

=

-krz cos Le cos (e + eo) sin a

(43)

I

+

( L O + 00)- sin 00 hn

1

(50)

Maximum relative displacements 6i and 6r are obtained by substituting 0i and 0r in Eq. 50.

& = - k(?- R2) 2 sin

*.

and sin (Lei- 0o)+ sin 00

+

sin

1

(Lei+ 00)- sin 00 An

(51)

and where

& = - k(?-R2) 2 sin a sin (L0f0o)+ sin 00

Ratios 1and R are slightly different from each L L other since r and R are almost equal and division by length L renders this difference negligible. Hence, one can approximate hc= Calling S(0) that micro-slip, Alc.

+

sin (An&+ 00)- sin 00 Xn

1

(52)

At an intcrmcdiate position, 0, in the stick regions, maximum relative displacement, 6Imax , is obtained by introducing YOgiven by Eq. 22 in Eq.50

379

61max =

- ko(?-R2) 2 sin

sin (LO+00)- sin 00

+

sin ( L O + 00)- sin 8 0

A, with

4.

ds=kxde= L x d 0 de sin a thus

01

1

(53)

(57)

(54)

Since parameters q, & and 61max are functions of angular position, Eq. 57 is evaluated numerically. Near strand termination, relative displacements and, consequently, energy dissipation may differ from one wire to another. For a complete cycle of vibration, we have

ENERGY DISSIPATION

Apart from internal material damping, three energy dissipation mechanisms have to be considered: - Coulomb friction dissipation due to gross sliding between wires and core - Micro-slip dissipation between adjacent wires - Micro-slip dissipation between wires and core In this model, we assume that gross sliding may occur in the layer-core interface only. Within the layer itself, wires are assumed to slick together and only micro-slip is allowed. In this case, it is assumed that slip does not propagate along entire line of contact, otherwise gross motion would violate the orrhotropic sheet awmption. Coulomb friction dissipation Energy dissipated by Coulomb friction is the integral of the products of net relative displacement and frictional force taken along the sliding regions. Net relative displacements are obtained by substracting maximum relative displacement, 6lmax , at the onset of gross sliding, from wire-core grosssliding, &. Wire-core normal contact forces, q, are assumed to be large enough to maintain contact. The friction coefficient is assumed to be constant over the practical range of frequencies and independent of contact forces. No distinction is made between static and kinetic coefficient of friction. 4.1

Energy dissipation by Coulomb friction along arc “ds” in sliding region [€I, €If] is: dW,r = -

d lq - 61maxI ds

(55)

Element ds can readily be expressed in tcrms of angular position 8.

I=1

Index “I” refers to wire “I” and N is the numbcr of wires in the layer. Layer micro-slip dissipation Micro-slip energy dissipation for two contacting cylinders has been determined by Deresiewicz [ 151. It involves a dimensionless factor 4) depending on contact parameters. 4.2

5

AE = ,

(.r

6PP

10G 1 + (1

-;I]

l\l

f, T

PP

4)

(59)

This formula is based on relative displacement 61 between two contacting non-spherical bodies in the tangential direction. For incipient gross sliding, maximum relative displacement 61max may be expressed in terms of 4). This assumption is reasonable since cylinders (wires) are long enough to consider that contact is linear.

Combination of Eqs. 59 and 60 yields

380

where micro-slips 6lrnax and 61 are

what follows, strain energy stored in one pitch length of the cable is determined by using strain energy density, UO,defined as

and where p is the normal contact force between adjacent wires, &6 is the resultant shear strain in the wire and szz is the normal compliance (Eq. 4). Micro-slip energy dissipation in the layer is then determined by introducing appropriate parameters (p, 61 and 6lmax) into Eq. 61 and integrating over one pitch length of the helix,

In this case, Eq. 67 takes the following development

and 6 ' 6 b are strains and stresses in the layer due to vibration. They are calculated through usual transformation from orthotropy axes (Eq. 1) to principal strand axes. Introducing Eq. 69 into 6 and integrating over one pitch length to obtain

d l b , d a b , ~ ' 6 b b, ' l b , b ' 2 b N

ra

Core-layer micro-slip dissipation In core-layer non-sliding regions, we assume that displacements occur along initial line of contact with the core. Micro-slip energy dissipation can then be calculated according to Eq. 61

4.3

Index "I" refers to the wire I, (I= 1. N). Eq. 71 has to be integrated numerically. On the other hand, the core stores also some strain energy which may be calculated as follow: here q is the wire-core normal contact force. Relative displacements 61 and 61max are given respcctively by Eqs.50 and 53. At the micro-slip limit, 61 = Slmax , energy dissipation becomes Similarly, one can find strain energy stored in wires bent about their own axis as Again, Eq. 64 is used to calculate resultant corelayer micro-slip dissipation over one pitch length from termination. Finally, total energy dissipation in the cable over one pitch length from the attachment is

Strain energy In the case at hand, strain energy is calculatcd taking account of sliding and non-sliding zones. In

4.4

U,=

I"[ ?&)I

K E N rD4cos2O! 2y K+ sin 4h, 8(2+ sin2 a r t a n a [(I-)

(73) Finally, we obtain the total strain energy stored in a portion of cable having a length corresponding to one pitch lcngth of the helix away from tcmination:

381

5.

BENDING STIFFNESS

In service, bending stiffness may vary between theoretical lower and upper bounds. The lower bound B, corresponds to the rigidity of a slack cable where each element responds individually to the excitation, while the upper bound Bmax represents the flexural rigidity when a complete interlinkage between elements is obtained and the cable behaves as a solid body. This variation is mainly associated with relative displacements caused by sliding friction forces. In the experimental set up, strands are made of a cylinder wrappcd with one layer of helical wires. Thus, the theoretical bounds arc

B, = K D4N cos a 32 (2 + sin2 a) Finally, we obtain the global strand bending stiffness over one pitch length from termination B, =B1+ B,

6.

+ B,

(82)

DAMPING FACTOR

The damping factor is defined as in reference [18]

wd where is the energy dissipated per cycle (Eq. 2 K 67) and u h is the strain energy stored in the strand (Eq.74).

An equivalent layer bending stiffness BI is defincd here based on the strain energy stored over one pitch length from the fixed end. For the equivalent solid beam,

(77) Substituting Eqs. 4 and 5 into Eq. 77 and integrating over one pitch lcngth to obtain

1

7.

EXPERIMENTAL WORK

Theoretical application and experimental tests are performed on two generic one-layer strands made of ~ v= 0.33). They aluminium (E= 7 . 0 5 ~ 1 0N.mm2, consist of a cylindncal tube surrounded by N helical wires, Detailed description for both specimens is given in the table below. Each specimen is mounted with clamped-clamped ends and is excilcd at its mid-span by a cyclic force of constant amplitude.

(78)

.c

Equating it to that given by Eq. 78 yields

external internal wire wire helical diameter diameter number diameter angle (mm) (mm) (mm) (degre)

1

6.40

4.55

9

3.17

4.50

2

7.925

5.33

11

3.17

6.05

On the other hand, bending stiffness of the core is B, =

E d:xt

-

&ni

64 Moreover, helical wires bending stiffness is

(80)

The response is collected with the analyser as a function of the frequency of the driving force. Since it is convenient that resonance be as pure as possible, the specimen must be sufficiently axially

382

preloaded so as to exhibit resolved resonance peaks. For very high magnitudes of vibration, measurements become difficult since resonance peaks are not pure. In this case, the operator may adjust conveniently the amplifier to avoid any source of noise. Furthermore, one should mention that this technique uses low amplitude tests and applies only to linear samples having low loss and sufficiently high rigidity such that they exhibit resolved resonance peaks. It can be accurately applied for determining damping factor from fundamental resonance peaks up to 0.4. Application is made for a wide range of axial preloadings converted into axial strain and for various amplitudes of vibration. The coefficient of friction is considered to be contact forces and velocity independent. An average of 0.35 is used in all the calculations. The dynamic bending stiffness testing is based on the vibrational mode shape function and resonant frequency of a clamped-clamped strand specimen under axial load which is assumed to behave as a solid beam with equivalent bending stiffness B,. After measuring the lowest resonant frequency of the given specimen, one can proceed by iteration to determine the dynamic bending stiffness from the characteristic equation by varying B, from Bm,,,toBmrx. The selected solution has to correspond to the first mode of the equivalent beam. The damping factor is determined by using the half-power bandwidth technique based on the following equation

where q is the damping factor and f, is the first resonant frequency. At or near the natural frequency of the vibration the displacement amplitude is maximum. The two frequencies on either side of resonance, f l and f2, where the displacement amplitude is 0.707 time the displacement amplitude at resonance are the half-power points (see Fig. 3). It is assumed that all elements of the strand vibrate in phase and the strain energy may not fluctuate markedly throughout each pitch of the cable and each cycle of vibration.

Fig. 3: Bandwidth representation Contact parameters are predicted owing to the present model and used to determine energy dissipation, bending stiffness and damping factor. Total energy dissipation for specimen no 1 is displayed in Fig. 4. As expected, energy dissipation increases either with magnitude of vibration and axial preloading. This indicates that higher tractions raises the contact forces whereas increased magnitude of vibration accentuates wires mobility.

Measured and predicted bending stiffnesses for specimens no 1 and 2 are shown in Figs 5 and 6 respectively. Experimental results approach those determined theoretically at low amplitude (Y=4 mm for specimen no 2). For small axial strain lo3). bending stiffness shows small dependency on vibration magnitude and tends towards 40% of the theoretical upper bound (L). However, when axial load on specimens is sufficient and vibration amplitude is relatively small, equivalent bending stiffness tends towards 85% of the theoretical upper bound (b). Alternatively, when comparing Fig. 4 to Fig. 5 , one can see that, for a given axial strain, bending stiffness decreases when energy dissipation increases. Indeed, this suggests that relative displacements and contact forces are of importance in the bending stiffness pmdction.

383

wd

+el

= 103

+€'I

= 2 x lo-' =3 103 =4 103

+el +Ell

Fig. 4: Total energy dissipation in specimen no 1

7.00+07

+- Y = 4 m m +Y = 6 +Y = 8

vl

2 4.00+07

% . d

vl

0.

1

I

I

1

1.00-03

2 -00-09

9.00-03

4 .00-09

axial strain Fig. 5: Bending stiffness of specimen no. 1

m m

384

1 *10*07

0. 0.

1 .oo-os

o .oo-0s axidsnrrin

a .oo-oa

4 .oo-oa

Fig. 6: Bending stiffness of specimen no. 2

Experimental and theoretical values of damping factor for each specimen are shown in Figs 7 and 8. Also shown are constant radius curves (HadjMimoune at al. [l 11) for mid-span bending curvature corresponding to 2 , 4 and 6 mm maximum vibration amplitude (Eq. 4). They follow he same pattern, with respect to axial load effect, as do the clamping zone curves. However, curvature varies continuously between both inflexion points (first mode shape) and it is not clear if and how constant

radius solution can be extended to variable radius case. On the other hand, it is interesting to note that experimental damping factor fits fairly well with theoretical values based on clamping zone calculation. This tends to show that, for short specimens, damping is mostly controlled by such regions. It is indeed well known that free field damping must be obtained from very long specimens.

385

4 .oo-02

= wd(2 ub) +Y=2mm y=4mm +Y=6mm p=68m

3 .so-02

*

h h 0

2

3 .oo-02

-,,

c!

2

2 .so-02

-o p = 3 4 m

II

p=27m

-0

5 2 .oo-02

8

0

flcxp.

cr 0 1.60-02

rrD

."C

8

1 .oo-02

n

6 -00-09 0.

I

1

I

I

10-4

I

I l l 1

I

I

I

1

I

I I I I

10-2

10-3

Fig. 7: Damping factor for specimen no. 1

4 .oo-02

2

3 rn EO-02

D

3 .oo-02

c!

2

2.60-02

I1

5 2.00-02 8

-1 -

E 1.60-02M C

.I

f 1 .oo-02 -

a

6 .00-03 0.

I

I

I

1

1 I " I

1

I

I

I

Fig. 8: Damping factor for specimen no. 2

I

r r c l

386

8.

CONCLUSION

For helical strand lateral vibration, inter-layer relative motion plays a prime role. In parallel with the orthotropic sheet model, a new stick-slip mechanism has been proposed and applied to clamping zone behaviour of a single layer strand. Experimental data from first mode damping behaviour of clamped-clamped specimens compare reasonably well with theoretical predictions. More complex situations (higher modes, multi-layer strands etc.) are currently under study. ACKNOWLEDGEMENTS

wire and much ATSOC. con8 on offshore applications, Proc. 3rd Int. Conf., Behaviour of offshore structures, Chryssostomidis and J.J. Connor eds., Hemisphere PublishingMcGraw-Hill, New-York, N.Y., pp.77-99. 7. Raoof, M. and Huang, Y. P. (1991). “Upperbound prediction of cable damping under cyclic bending.” A X E J. of the Engineering Mechanics, vol. 117, No 12, Dec., pp. 2729-2747.

8. Raoof, M. and Huang, Y. P. (1992). “Free bending characteristics of axially preloaded spiral strands.” Proc. Instn Civ. Engrs Strucs & Bldgs, Nov., VOI. 94, pp. 469-484.

Financial support from the Natural Sciences and Engineering Research Council of Canada, Grant No. A8905, is gratefully acknowledged.

Y. P. (1992). “Simple methods for estimating various sheathed spiral strand bending characteristics.” Proc. Instn Civ. Engrs Strucs & Bldgs, Nov., vol. 94, pp. 485-500.

REFERENCES

10. Raoof, M. and Huang, Y. P. (1993). “Lateral vibrations of steel cables including structural damping.” Proc. Instn Civ. Engrs Strucs & Bldgs, Nov., VOI.99, pp. 123-133.

1. Cardou, A., Leblond, A., Goudreau, S. and Cloutier, L. (1993). “Electrical conductor bending fatigue at suspension clamp: a fretting fatigue problem“ Intl Conf. on Fretting Fatigue, Sheffield, U. K., april 19-22.

2. LeClair, R. A. (1989). “Upper bound to mcchanical power transmission losses in wire rope.” ASCE J. of Engineering Mechanics, Vol. 115, No. 9, Scpt, pp. 201 1-2019. Vinogradov, 0.G. and Atatekin, J. S. (1986).”Intemal friction due to wire twist in bent cable.” ASCE J. of Eng. Mech., vol. 102, pp. 859-

9. Raoof, M. and Huang.

11. Hadj Mimoune, A. , Cardou, A. and El Chebair, A. (1993). “Free constant curvature bending of axially preloaded strands.“ To appear in CSME Trans., vol. 17, no 3.

12. Mindlin, R. D. (1949). “Compliance of elastic bodies in contact.” ASME J. of Applied Mechanics, V O ~16, . pp. 259-268.

3.

873.

13. Mindlin, R. D. and Deresiewicz, H. (1953). “Elastic spheres in contact under varying oblique forces.” ASME J. of Applied Mechanics, Vol. 20, pp. 327-344.

4. Sathikh, S. (1989). “Effect of interwire friction

on transverse vibration of helically stranded cable.” Proc. of the ASME Des. Tech. Conf..:Sept. 17-21, 1989; Montreal: ASME, DE-Vol. 18-4, pp. 147-

14. Deresiewicz, H. (1957). “ Oblique contact of non-spherical bodies.” ASME J. of Applied Mechanics, Vol. 24, pp. 623-624.

153.

5. Hardy, C. (1990). “Analysis of self damping characteristics of stranded cable in transverse vibrations.” CSME Mechanical Engineering ,forum 1990, June 7, Toronto. 6. Hobbs, R. E. and Raoof, M. (1982). “Prediction

of elastic properties of large strands and cables.” Int.

15. Deresiewicz, H. (1974). “ Bodies in contact with application to granular media.” in R . D. Mindlin and Applied mechanics, G . Herrmann, ed. Pergamon Press Inc., pp. 105-147. 16. Herrmann, G . (editor) (1974). “R. D. Mindlin and applied mechanics.” Pergamon Press Inc.

387

17. Johnson, K. L. (1985). “Contact mechanics.” Cambridge Universiry Press.

18. Lazan, B. J. (1968). “Damping of materials and members in structural mechanics.” Pergamon Press Inc.

NOMENCLATURE Equivalent bending stiffness of the cable Bending stiffness lower bound of the cable Bmax Bending stiffness upper bound of the cable D Wire diameter E Young’s modulus fc Wire-core tangential force pcr unit length fw Wire-wire tangential force per unit length f l , f2 Half-power frequencies fr Resonant frequency G Shear modulus N Number of wires in the layer p Resultant wire-wire normal contact force per unit length po Initial wire-wire normal contact force per unit lengh q Wire-core normal contact force per unit length r Radius of the hclix R Wire radius S Cross-sectionalarea of the wire Sij Compliances of the wire in the layer T Axial force in the wire B,

Bmin

u Axial displacement of a point along the helix Total strain energy stored in cable one pitch length longer uc Axial displacement of a point on the core surface W,-,,WRs Micro-slip and gross-sliding energy dissipation Wij, Wr Gross-sliding energy dissipation Wd Total energy dissipation in cable one pitch length longer X wire-core contact force Y Magnitude of vibration a Lay angle 6,61ij,61 Relative displacements 61i,61max Maximum relative displacements & I , EZ, &6 Axial, radial and tangential strains with respect to wire axis &‘I, E‘z, &‘6 Axial, radial and tangential stresses with respect to cable axis E I b Axial strain in the wire due to bending Angle dimensionless factor Coefficient of friction Damping factor Poisson’ratio Angular position 8& Angular position for incipient gross sliding 61, 6 2 , 0 6 Axial, radial and tangential stresses in the wire 0’1, 0 ’ 2 , 0 ’ 6 Axial, radial and tangential stresses in the layer Ub

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Dissipative Processes in 'rribology / D. Dowson e l al. (Editors) 0 1994 Elsevier Science B.V. AU rights reserved.

389

Energy dissipation and crack initiation in fretting fatigue D. Nowell, D.A. Hills, and D.N. Dai

a

aDepartment of Engineering Science, University of Oxford, Parks Road, OXFORD, OX1 3PJ, U.K. This paper considers two possible approaches to the analysis of crack initiation in fretting fatigue. A macroscopic analysis, based on bulk properties derived from a smooth contact model is presented first. In particular, the use of the distribution of dissipated frictional energy as a guide to the probability of crack initiation is discussed. An alternative microscopic approach considers the contact on an asperity scale and considers crack initiation under the influence of stresses caused by a sliding asperity. A model for the initiation process, based on accumulation of slip along parallel slip bands, is presented and some sample results are given.

1. INTRODUCTION Fretting fatigue is an important phenomenon which can occur whenever an assembly of engineering components is subjected to cyclic loading or vibration. The prediction of fatigue lives under fretting conditions is of particular importance in safety-critical applications such as those found in the nuclear or aerospace industries. In comparison with plain fatigue, however, fretting is much less well understood. This lack of understanding is due to the large number of variables present in fretting problems and the complexity of the stress fields under which crack initiation and propagation takes place. It is well known that fretting can affect both the initiation and propagation phases of crack life although the division of crack life into these two periods is to some extent artificial, and from an experimental standpoint the boundary depends on the resolution of the equipment used to observe embryo cracks. Initiation is usually taken to refer to processes occurring before a crack is observed, whereas propagation denotes that part of crack life which may be observed and monitored. It should be noted that crack initiation should be considered as a process rather than an event - some authors prefer the term nucleation on semantic grounds but we shall retain the commonly accepted terminology here. From an applied mechanics standpoint the division of crack life into initiation and propagation phases may be undertaken on a different basis. Propagation is taken as the period during which crack growth is amenable to analysis by fracture

mechanics methods. This means that the material through which the crack is growing must be treated as a continuum and that the crack must be significantly larger than any microstructural features present. The term initiation is then used to refer to that period of component life which occurs before the propagation phase and for which few mechanics models are available. In fretting fatigue, the propagation phase requires careful analysis because the cracks invariably exist in a complex and rapidly-varying stress field and are subjected to compressive loading over a t least part of the loading cycle, leading t o full or partial closure. In addition, near-surface residual stresses frequently exist, resulting from either the manufacturing process or from surface treatments (e.g. shot peening or ion implantation) which are designed to increase component life. Nevertheless propagation should be amenable t o treatment by fracture mechanics techniques provided that these complications are recognised and addressed. Powerful techniques involving modelling the crack as an array of distributed dislocations (see, e.g. [l]) are capable of representing fretting fatigue cracks with the required degree of sophistication and can incorporate crack closure [2], and residual stresses [3]. It is also possible to analyse kinked cracks [4] and multiple arrays of cracks [5]. All of these features are frequently observed in fretting fatigue. Analysis of the initiation phase of fretting fatigue is far more challenging than that of propagation. Such analysis is, however, extremely important. In many applications (e.g. civil aircraft)

390

Wear ( r n 3 ~ r n )

Life (cycles) 1.0E+8

7

Partial slip

Sliding L

i

i-

l.OE+’

1.OE+6

d

1 -

1.OE+5

1.OE-14

ative displacements. This type of analysis is relatively straightforward to perform and is likely to yield some useful information but cannot model the nature of the initiation process itself. Alternatively, a local or microscopic approach may be adopted where a model of the initiation process is established. We shall proceed to examine the application of each of these methodologies for the case of cracks initiated by fretting contact.

1.OE-15 /---

I I I 111111

2. A MACROSCOPIC MODEL

I

11111111

I I

11111r-

1.OE-16

Figure 1. Variation of fretting fatigue life and wear rate with slip amplitude (after Waterhouse

components are removed from service as soon as a detectable crack is observed and therefore initiation consumes the majority of useful component life. It is well known that slip amplitude plays a crucial r61e in fretting fatigue (see, e.g. [ S ] ) . Figure 1 depicts the variation of fretting fatigue life with amplitude of slip. The propagation phase of crack life cannot be directly affected by slip amplitude since the crack can only respond to conditions in the process zone (as characterised by the stress intensity factor); variations in slip amplitude will have no effect here. Thus, we must conclude that the primary influence of slip amplitude must be on crack initiation. Crack initiation in fretting fatigue is much more predictable than that in plain fatigue. Initiation takes place on the surface and a t repeatable locations within the contact. Fretting fatigue therefore provides an excellent opportunity to study and model crack initiation in a more general sense. Modelling of crack initiation can be approached from two standpoints. A global approach can be adopted which seeks to characterise the conditions under which initiation takes place in terms of macroscopic variables such as stresses and rel-

INITIATION

Development of a macroscopic initiation model can be commenced by observing that initiation is a process involving plastic deformation which is driven by the interaction of the contacting surfaces. This plastic deformation process absorbs energy as the material is deformed and we would therefore expect initiation to occur preferentiaIly at locations where large amounts of energy are available to drive the deformation process. Let us consider a pair of surface particles in a fretting contact which undergo slip during a t least part of the loading cycle. If the local shear traction, q , is plotted against the relative slip between the particles, g, during one complete cycle a rectangular hysteresis curve of the form shown in fig. 2 is obtained. During forward slip the shear stress is constant at a value given by = 7 3 fIP(.>l (1) where f is the coefficient of friction and p ( x ) the normal pressure. When the maximum overall load is reached (point A in fig. 2) the relative displacement will have attained its maximum value, 6. The load now starts to decrease and no further slip takes place until a local shear traction q = -f lp(z)l is reached. Reverse slip now occurs until the overall load starts to increase once more. The area enclosed by the loop is the frictional energy dissipated (per unit area of contact surface) during one complete fretting cycle, e , and it is immediately apparent that, for the fully-reversing loading shown in fig. 2, e is proportional to the product of maximum relative displacement and maximum shear traction i.e. e

a 76

(2)

39 1

‘:IT

Shear traction

,

,,,A

\I

6 displacement Relative

] Figure 2. Variation of shear traction q with relative displacement g for a pair of particles undergoing fully reversing cyclic loading.

The value of e varies from point t o point throughout the contact; figure 3 shows a typical distribution for the contact of cylinders under a cyclic tangential force Q = Qmaxsin(wt). Cracks are found to initiate experimentally close to the edges of the contact and it is in precisely these regions that the dissipated energy reaches a maximum. Unfortunately locations of crack initiation and maximum energy dissipation do not coincide for all configurations. Experiments involving a spherical fretting pad on a flat surface were carried out by Kuno e t al. [8]. In this case the dissipation of frictional energy may be calculated from the results of Mindlin [9] and Poritsky [lo]. A contour plot of the variation of energy density over the contact patch is given in fig. 4 . An axi-symmetric distribution is revealed since both the shear tractions and I-direction displacements are functions of radius alone. Kuno et al. found that the fretting damage w a s distributed approximately evenly around the contact but that cracks initiated in approximately the positions shown in fig. 4. It is well known that Mindlin’s analysis is not quite correct for materials which exhibit a Poisson effect since the shear tractions do not precisely oppose the relative displacement of the surfaces. A more accurate analysis, using a nu-

-1.0

-0.5

0.0

0.5

1.0

Position (da)

Figure 3. Variation of dissipated frictional energy r.6 and Ruiz’s initiation parameter a.r.6 for a cylindrical fretting contact: QmaZ/fP= 0.8, f = 0.8, no bulk stress. p is the modulus of rigidity , Y Poisson’s ratio, and a the semi-width of contact.

merical technique has recently been undertaken by Munisamy et al. [ l l ] . This reveals a different distribution of energy, as shown in fig. 5 . Here the areas of maximum energy dissipation lie to either side of the contact and do not coincide with the locations of crack initiation. In a study of fretting fatigue in dovetail roots of turbine blades Ruiz and Chen [12] experienced similar difficulties in reconciling the locations of initiated cracks with positions of maximum energy dissipation. It was found that, whilst r.6 was a good measure of the amount of fretting damage it did not provide a reliable means of estimating crack initiation. Ruiz argued that, in addition t o fretting damage, it was necessary to have a tensile in-plane stress in order that the damage could take the form of propagating cracks; if fretting damage occurred in a region of compressive in-plane stress then wear w a s the most likely result. Ruiz therefore proposed an initiation parameter u.r.6, obtained by multiplying the local value of r.6 by the maximum in-plane

392

Approsimalc crack sites

Figure 4. Contour plot of the variation of frictional energy dissipation, ~ . 6 pf 2/ a p o 2 over the contact patch for fretting contact of spheres: Qma,/fP = 0.9, v = 0.5 (Mindlin solution).

Figure 5. Contour plot of the variation of frictional energy dissipation, r . 6 p / f 2 a p o 2 over the contact patch for fretting contact of spheres: Q m a s / f P = 0.99, v = 0.5 (Munisamy et al. [ll]).

3. A

MICROSCOPIC MODEL

stress experienced at the surface of the fretted component during the fretting cycle. The combination of the two requirements by multiplication is, of course, purely arbitrary but good agreement w a s found between the locations of crack initiation and maximum values of a.r.6 in the turbine blade problem. Similar agreement has been found in other geometries, including contacting cylinders [13] (see fig. 3) and spheres [8] (fig. 6) .. A similar parameter has been used to characterise fretting fatigue between strands in wire ropes by Rmof [14] an provides good estimates of the fatigue life. Thus, predictions of the probability of crack initiation based on macroscopic parameters such as the stresses and displacements obtained from smooth contact models. However, these models have severe limitations and empirical combinations of parameters, which are difficult to justify from a theoretical standpoint, are required to give good results.

INITIATION

To make further progress towards a reliable method for predicting the locations of crack initiation and the likely fatigue life it is necessary to attempt to understand and model the initiation process itself. This process takes place at a microscopic scale and it is therefore necessary to examine the contact at this scale. All contacts are microscopically rough and most engineering contacts are composed of areas of high pressure, corresponding to asperity contact, separated by areas where no contact occurs. In analysing the propagation of cracks which are long with respect to a typical asperity contact dimension it is not necessary to consider the individual asperity contacts and the crack may be considered as propelled under stresses found from an equivalent smooth contact model [15]. At shorter crack lengths it may be necessary to consider individual asperity effects [16] and it is certainly necessary to do so in establishing a model of crack initiation. If

393

Shear stress (dp ) 0

1

4

I -2

Figure 6. Contour plot of the variation of / U ~ the ~ ~ Ruiz's initiation parameter, C Y . T . ~ ~ over contact patch for fretting contact of spheres: QmaZ/fP = 0.9, v = 0.5, f = 1.0 (Mindlin solution).

the asperities are widely-spaced, crack initiation can be thought of as taking place under the influence of a single asperity contact, together with any bulk stresses present. Since the surfaces experience relative slip which is much greater than may be accommodated in the intrinsic compliance of a single asperity it is likely that most asperities in the slip zone will slide during part of the loading cycle. We shall start, therefore, by examining the stresses induced by a sliding asperity. Figure 7 shows the shear stress history experienced by a particle a t the surface of body due to an asperity sliding backwards and forwards across the surface. We have chosen to plot shear stress since initiation is acknowledged to be driven by shear stresses'. In the example shown the asperity pressure distribution is modelled as Hertzian and acts over a circular contact patch. If there is significant plasticity the appropriate pressure distribution may be closer to that of uniform pres'Figure 7 shows shear stresses occurring on a plane at 4 5 O to the surface as this is the approximate orientation of initiated cracks observed in practice.

1

I

I

I I I -1 0 1 Asperity position (s/a')

I

I 2

Figure 7. Shear stresses beneath a sliding asperity (modelled as a circular Hertzian contact). T h e stresses plotted are those experienced by a point on the surface coincident with the centreline of the asperity and are those occurring on a plane at 45" to the free surface. Here po is the peak pressure under the asperity, f = 0.75, and v = 0.3.

sure [17] but the resulting shear stress history differs only in detail. In fig. 7 the amplitude of sliding is twice the asperity contact radius, u'. It is clear that the stresses induced decay rapidly once the asperity has passed over the point on the surface and stresses experienced once the asperity centreline is further than 2a' from the surface point rapidly become negligible. Consider a point located on the surface of the fretted body immediately beneath the centre of the asperity. If the amplitude of asperity sliding, 6, is less than u' the amplitude of shear stress experienced will be directly proportional to the amplitude of sliding. This gives a possible explanation for the variation of fatigue life with slip amplitude observed experimentally. Points beneath asperities will experience a larger amplitude of shear stress as the slip amplitude is increased and hence will accumulate damage more rapidly. Once the slip am-

394

plitude exceeds the asperity contact radius the amplitude of shear stress will be independent of slip amplitude as the maximum values are experienced when the edge of the asperity passes over the point in question. Much larger slip amplitudes may cause multiple asperity passes so that points experience more than one asperity stress cycle in an overall fretting cycle. This mechanism would also result in a reduction of fatigue life with slip amplitude but a t such large amounts of slip it is likely that wear will become significant. An increase in the wear rate is thought to be the cause of the increased fatigue life observed at large slip amplitudes (fig. 1) [7]. It is now appropriate to examine in more detail how cracks might initiate under such stress fields. It is widely acknowledged that in plain fatigue initiation takes place by accumulation of slip on parallel slip bands [18]. The resulting extrusion or intrusion evolves into an embryo crack. Mura and ceworkers [19, 201 have recently produced a model of this process. The slip bands are modelled by two parallel arrays of dislocations (fig. Sa). Movement of the dislocations under the applied stress is opposed by a friction stress, ~ jso, that the equilibrium equation for the dislocations can be written

+ Td = f r f

Initiated crack Figure 8. Mura model for crack initiation (a) an extrusion formed by slip on parallel slip bands, and (b) an initiated crack formed when the accumulated slip is released.

(3)

where T, is the applied shear stress, Td the stress produced by the dislocation arrays themselves, the sign applies on one slip band and the sign on the other. When subjected to a cyclic load above a certain amplitude slip accumulates on alternate slip bands so that an extrusion forms (fig. 8a). The strain energy stored in this configuration may be compared with that for a state where the slip has been released and a crack formed (fig. 8b). At a particular number of cycles it is found to be energetically favourable for the second configuration to be adopted and initiation takes place. Using this technique S-N curves for the number of cycles to initiation in plane fatigue may be generated and an example is shown in fig. 9. The basic model can now be applied to the fretting case where initiation takes place under the influence of a sliding asperity. We suppose that the slip bands exist under the centre of an

+

Slip band

asperity and that extruded material is smeared out by the asperity as it is produced. Since the amplitude of the stress cycle experienced varies with slip amplitude it is possible to predict the number of cycles to crack initiation under asperity sliding and a sample curve is shown in fig. 10. It will be seen that the initiation time decreases as slip amplitude is increased until a limit is reached where the asperity is sliding completely over the slip bands. No further decrease in initiation cycles takes place until slip amplitude increases to such an extent that a second asperity starts to influence conditions in the slip bands. The Mura initiation model is still in an early stage of development, particularly when applied to fretting fatigue. In a real situation there will be a bulk stress present as well as stresses due to one or more sliding asperities. However, the model does offer considerable promise. Already

395

Slip amplitude (s/a')

Bulk stress range (a/rr) loo

1 Slip band length (b/a')

n in

10

100

1000

10000

100000

0.4

1

0.2 0.1

10

Figure 9. Typical S-N curve for crack initiation in plane fatigue produced by the Mura model.

it has enabled the identification of a number of salient length scales viz. the asperity contact radius, the amplitude of sliding, and the length of the slip bands2. The full effects of varying the relative magnitudes of these quantities remain to be investigated, both theoretically and experimentally but it might be hoped that control of some of these parameters would lead to enhanced component performance in fretting fatigue. 4. CONCLUSIONS

This paper has reviewed two possible approaches to the characterisation of crack initiation in fretting fatigue. A macroscopic approach, based on the distribution of frictional energy can be shown to characterise the fretting damage experienced but is a poor predictor of the location and probability of crack initiation since other factors including the in-plane stress are involved in the initiation process. The limitations of this approach can be overcome to some extent by the use of empirical combinations of parameters. Whilst these are of some use in assessing the severity of ~

2hpractice it is likely that slip will accumulate against some obstacle such as an inclusion or a grain boundary. In many casea it might be reasonable to equate the length of the slip bands with the grain size or some other sutiable microstructural dimension.

100

1000

Cycles to initiation

Cycles to initiation

Figure 10. Typical variation of initation life with asperity slip amplitude as predicted by the Mura model.

any particular problem they are difficult to justify from an theoretical standpoint and offer little understanding of the process of initiation. A micromechanics approach seeks to model the actual initiation process in some detail. In fretting fatigue this necessitates considering the contact on an asperity scale. Recent work on the development of initiation models in plane fatigue may also be applied to fretting and goes some way towards explaining the variation of fatigue life with slip amplitude observed in practice. Both approaches have their merits. A macroscopic approach can be employed to give a rapid assessment of the severity of a fretting problem encountered in practice whereas a micromechanics approach should prove a useful research technique leading to a greater understanding of the fretting process and, ultimately to improved methods of predicting and enhancing fretting performance. 5. ACKNOWLEDGEMENT D.N. Dai would like to acknowledge the support of the SERC under contract number GR/G57536.

REFERENCES 1. Nowell, D., and Hills, D.A., 'Open cracks at

396

or near free edges’, Jnl. Strain Analysis, 22, 3, 177-186, 1987. 2. Hills, D.A., and Nowell, D. ’Stress intensity calibrations for closed cracks’, Jnl. Strain. Analysis, 24, 1, 37-43, 1989. 3. Wilks, M.D.B., Nowell, D., and Hills, D.A. ’The evaluation of stress intensity factors for plane cracks in residual stress fields’ Jnl. Strain Anal., 28, 3, 145-152, 1993. 4. Hills, D.A., and Nowell. D. ’Kinked cracks: finding stress intensity factors’, pp 36-50 of ’Applied Stress Analysis’, Ed. T.H. Hyde and E. Ollerton, Proc. Conf. on Applied Stress Analysis, University of Nottingham, 30-31 August 1990, Elsevier, 1990. 5. Dubourg, M.C., and Villechaise, B. ’Analysis of multiple fatigue cracks - partl: theory’, Jnl. Appl. Mech. 114, 455-461, 1992. 6. Nishioka, K., and Hirakawa, K., ’Fundamental investigations of fretting fatigue (part 2)’ Bull. JSME, 12 , 50, 180-187, 1969. 7. Waterhouse, R.B. ’Fretting fatigue’, Int. Materials Reviews, 37, 2, 77-97, 1992. 8. Kuno, M., Waterhouse, R.B., Nowell, D., and Hills, D.A., ’Initiation and growth of fretting fatigue cracks in the partial slip regime’, Fatigue and Fracture of Eng. Mats. and Structures, 12, 5, 387-398, 1989. 9. Mindlin, R.D., ’Compliance of elastic bodies in contact’ Jnl. Appl. Mech., 16 , 259-268, 1949. 10. Poritsky, H., ’Stresses and deflections of cylindrical bodies in contact with application to contact of gears and of locomotive wheels’ Jnl. Appl. Mech., 72, 191-201, 1950. 11. Munisamy, R.L., Hills, D.A., and Nowell, D. ’Contact of similar and dissimilar elastic spheres under tangential loading’, pp 447461 of Proc. Contact Mechanics International Symposium, Lausanne, Oct 1992, Ed A. Curnier, Presses Polytechniques et Universitaires Romandes, 1992. 12. Ruiz, C., and Chen, K.C., 1986 ’Life assessment of dovetail joints between blades and discs in aereengines’ Proc. Int. Conf. Fatigue, I Mech E, Sheffield, 1986. 13. Nowell, D., and Hills, D.A. ’Crack initiation criteria in fretting fatigue’, Wear, 136, 329-

343, 1990. 14. Raoof, M., ’Free-bending fatigue prediction of steel cables with the effect of interwire fretting taken into account’ Proc. International Conf. on Fretting Fatigue, Sheffield, April 1993, I.Mech.E., London, 1993. 15. Nowell, D., ’An analysis of fretting fatigue’, D.Phi1. Thesis, University of Oxford, 1988. 16. Miller, G.R., Keer, L.M. and Cheng, H.S., ’On the mechanics of fatigue crack growth due to contact loading’ Proc. Roy. SOC.London, A397, 197-209, 1985. 17. Hardy, C., Baronet, C.N., and Tordion, G.V., ’Elastoplastic indentation of a half space by a rigid sphere’, Jnl. Num. Methods in Engineering, 3, 451, 1971. 18. Suresh, S., ’Fatigue of materials’, Cambridge University Press, Cambridge, 1991. 19. Mura, T., and Nakasone, Y., ’A theory of fatigue crack initiation in solids’, Jnl. App. Mech., 57, 1-6, 1990. 20. Venkataraman, G., Chung, Y-W., Nakasone, Y., and Mura, T. ’Free energy formulation of fatigue crack initiation along persistent slip bands: calculation of S-N curves and crack depths’, Acta metall. mater., 38, 1, 31-40, 1990.

SESSION IX ENERGY AND FRICTION: THEORETICAL AND NUMERICAL ASPECTS Chairman:

Professor B J Hamrock

Paper IX (i)

Friction in Partially Lubricated Conjunctions

Paper IX (ii)

Third Body Theoretical and Numerical Behaviour by Asymptotic Method.

Paper IX (iii)

Thermomechanical State Near Rolling Contact Area.

This Page Intentionally Left Blank

Dissipative Processes in 'I'ribology / I). Dowson et al. (Editors) 0 1994 Elsevier Science I3.V. All rights rcscrvcd.

399

Friction in Partially Lubricated Conjunctions 1.1. Kudisha and B.J. Hamrockb

aDepartmat of Physics, University of Scranton, Scranton, PA 18510-4642, USA bRobinson Laboratory, The Ohio State University, 206 West 18th Avenue, Columbus, OH 43210-1107, USA The problem formulation of the partially lubricated conjunction is formulated by assuming that two moving (rolling) bodies with smooth surfaces made of the same elastic material are lubricated by a Rivlin type of incompressible, nonNewtonian viscous fluid under isothermal conditions. The fluid film thickness is considered to be several orders smaller than the contact size and the geometry of the solid surfaces. The slippage and adhesion mechanisms of friction are taken into account in direct contacts. The solid surfaces are assumed to experience an external compressive. Under these assumptions the solid surfaces can be replaced by two contacting elastic halfspaces. The problem is reduced to a system of alternating nonlinear integral-differential Reynolds and integral (describing contact interactions between elastic bodies) equations and of inequalities valid in the conjunction. The inlet boundary is considered to be known and located near the boundary of the Hertzian contact zone. The location of the exit boundary must be determined during the problem solution, as well as the number of internal contact boundaries separating the dry and lubricated subregions of the conjunction. Continuity conditions for friction (dry and fluid) stresses on the internal boundaries are formulated. The theoretical analysis of a partially lubricated contact is given for the case where side leakage is small relative to flow in the direction of motion. With this assumption, asymptotic methods can be successfully applied. The specific features of the friction in partially lubricated conjunctions (i.e., the location and magnitude of dry and lubricated regions, slippage, friction stresses, and pressure) are found to be mainly dependent on the boundary configuration of the conjunction inlet. The average influence of regions of the conjunction separated by fluid film and experiencing direct contact is described by a statistical approach. Specific requirements for lubricant viscosity behavior in very thin films and near conjunction boundaries are formulated.

400

It is shown that for starved lubrication and mixed friction conditions the film thickness is directly proportional to a positive power of the distance between the inlet point and the input Hertzian boundary of a dry contact. It is also shown that the friction force is greater under partial lubrication than under fluid film lubrication and becomes greater as the dry friction region enlarges. 1. INTRODUCTION

If the pressures and running speeds in elastohydrodynamically lubricated machine elements, such as rollingelement bearings or gears, are too high, an instability of oil supply may result. Some contact will take place between the asperities, and partial lubrication (sometimes referred to as "mixed lubricationtt)will occur. The behavior of the conjunction in a partially lubricated regime is governed by a combination of boundary and fluid film effects. Interactions take place between one or more molecular layers of boundary lubricating films. A partial fluid film lubricating action develops in the bulk of space between the solids. A good indication of when partial lubrication is occurring might be gained from knowing how much of the fluid is locally moving through the conjunction. In practice - for a variety of reasons (such as starvation, surface topography, lubricant flow instability, influence of lubricant surface tension, etc.) the inlet oil meniscus is sometimes close to the Hertzian contact region.

Moreover, the meniscus often changes its location and configuration with time. Usually, this is reflected in graphs of frictional stresses versus time. The oscillations of friction stress in such situations may be dramatically large. Interference methods allow one to observe the film thickness through the conjunction and to indicate the location of the stagnation curve. The stagnation curve indicates that backflow occurs to the left and flowthrough occurs to the right. The inlet oil meniscus is thus the region where backflow takes place. From the experiments it is observed that film thickness is ample as long as the stagnation curve is sufficiently far from the Hertzian contact region. In a cylindrical roller bearing, as the film becomes thin, one can observe the existence of alternating lubricated and nonlubricated stripes in the direction of motion. The objective of this paper is to provide a mathematical formulation of partial lubrication taking into account the existence of zones with different (dry or lubricated) mechanisms of

40 1

friction. The approach used is to model. the event occurring in partial lubrication rather than dealing with the physical phenomena (such as starvation, amount of side leakage, surface toPograPhYl and lubricant flow instability) that cause partial lubrication to occur. Side leakage and a non-Newtonian fluid model are present in the formulation. Smooth surfaces are assumed. In this paper the focus will be on the modeling, and in later publication results from the theory will be presented. 2

PROBLEM FORMULATION

The formulation of the problem will assume that two moving (rolling) bodies with smooth surfaces made of the same elastic material are lubricated by a Rivlin type of incompressible, nonNewtonian viscous fluid under isothermal conditions. Consideration of non-Newtonian fluid properties is essential because it is necessary to take into account transition from liquid to dry friction mechanisms. The lubrication layer is considered to be small related to the characteristic contact area and the size of the bodies. The bodies are in concentrated (local) contact, and they experience an external compressive force (Fig. 1) Under these assumptions the bodies can be replaced by two contacting elastic half-spaces.

Separate sections will describe the relevant equations relating to fluid film lubrication and direct elastic interaction. The method used describe the combined effect is given in the section Partia 1 Lubrication"

.

Lubricantus R h e o l o g y Fluid film lubrication occurs when opposing surfaces are completely separated by a lubricant film. The applied load is carried by the pressure generated within the fluid, and frictional resistance to motion arises entirely from shearing of the viscous fluid. Let us introduce a moving coordinate system: the z-axis passes through the bodies centers of curvature, and the xy-plane is equidistant from the bodies. It is assumed that the bodies' motion is slow and occurs with linear velocities u,7(ul,vl) and u2=(U2,vt). The sliding velocity is assumed to be small relative to the rolling velocity 0.5 (u,+u,) The inertial forces in the lubrication layer are considered to be sma11 relative to the viscous forces Under these assumptions the tangential stress vector ~(x,y) in the lubrication layer is proportional to the gradient of lubricant linear velocity aU(x,y) / a z 2.1.

.

.

402

where 1-1 is the lubricant viscosity, F and CEi are given inverse monotonic smooth functions describing the lubricant rheology, F(O)=CEi(O)=O, and E is a twoby-two unit matrix.

'I

determined by the properties of the solids. The regions of a dry contact are represented by the adhesion and slippage zones in which the relative bodies' sliding velocities s(x,y) are zero and different from zero, respectively. Moreover, the frictional stress and sliding velocity satisfy Coulomb's law,

where p(x,y) is the contact pressure distribution, and f(p,lsl) is the coefficient of dry friction. 3. FLUID FILM LUBRICATION

Let us consider the equations governing the process in the lubricated regions. Under conditions of a thin lubricant layer and slow motion the equations of fluid motion are [l] Figure 1. A general view of contacting bodies. Boundary Friction Rheology The boundary lubrication fluid effects are negligible and there is considerable asperity contact. The contact lubrication mechanism is governed by the physical and chemical properties of thin surface films of molecular proportions. The frictional haracteristics are primarily

aP

r--Vp, --0, aZ (V,w) -0.

(3)

2.2.

The latter leads to the equation p=p ( x , y) Assuming that Vh [where h(x,y) is the gap between contacting bodies] and that s/(u,+uZ) are small the components of the liquid particle velocity w=(u,v,w) at the contacting surfaces are

.

u - u ~ ,w - -1- ( u ~ , V for ~ ) z---h 2

2'

403

where the fluid flux components can be calculated from h/2

Integrating the continuity equation ( V , w ) = O with respect to z from -h/2 to h/2 and using the boundary conditions ( 4 ) we obtain (where Q, and Q, are the x- and y-components of the fluid flux)

Integrating the first equation in (1) with boundary conditions from ( 4 ) we find

’1

Q-hu,+l

dz

-h/2

Z

1FE(g+sVp)ds. -h/2

(9)

Obviously, Eqs. ( 7 ) to (9) hold only in the lubricated regions. Now, let us consider the difference in elastic displacements AW=(AU,AV,AW) of the surface points of the two (upper and lower) contacting bodies. The well-known formulas give [ 2 ]

A U-

u-u,+

AV=

where g=(gx,gy) is the pure sliding frictional stress the components of which satisfy the equations h/2

AW-

for h(x,y)> o .

1-2v 4xG

Finally, by using Eqs. (5) and ( 6 ) we derive the analog of Reynolds’ equation, h/2

( V , L1 dz 1 FE(g+tVp)dt)+

’

-h/2

(u,,Vh)-0

2

-h/2

for h(x,y)> O , (8)

,

sine (T;,t2,,) R

1 &&+

404

sine-- Y-9 R t

cose--

non-compressible material of the bodies for which ~ 0 . 5 and

X-2 R '

where fl is the contact area, G and v are the shear elastic modulus and Poisson's ratio of the bodies material , 7+= (4 and 7 - = ( 7xz',T ~ ~ are The tangential stresses acting on the surfaces of the upper and lower bodies which for dry contact regions satisfy conditions ( 2 ) and for lubricated regions are determined by the equations (see Eqs. (11, ( 6 1 , and ( 7 ) ) +,

T*'rg--Vpr h 2

(11)

Using well-known considerations applied to contact problems of elasticity and the expression for difference in vertical displacements AW we get the relation for the gap h between the contacting bodies 2Rx

2R,

2xG,

2R,

2R,

4xG,

R

- )

4.

BOUNDARY FRICTION

The solution of the problem for boundary lubrication involves determination of the pressure P(XtY) and gap h(X1Y) distributions (normal problem) and the frictional stress 7 and sliding velocity s distributions (tangential problem). Consider the normal problem. In the dry regions the gap between the contacting bodies is zero

R

for h ( x , y )- 0 . (14)

where h, is an unknown constant, R, and are the effective radii surface curvature for the contacting bodies in the directions of the Xand yaxes respectively. Eq. (12) can be simplified for the case of a

,"r

I

Under the conditions of a slow stationary motion and small slippage the equation for the sliding velocity s can be obtained by applying the differential operator 0.5(u,+u2,V) to both sides of the first two equations in ( 1 2 ) (It means differentiating with respect

40 5

to time.) This equation can be expressed in the form s--B(r)

+v, V = ~ - U 1 ,

behavior of the conjunction in a partial lubrication regime is governed by the combination of boundary friction and fluid film effects. Everywhere within the partially lubricated conjunction the pressure p(x,y) is assumed to be nonnegative, P ( X 1 Y ) 20.

case (3~sin~0-1) Dx11--

Dx22-

-

Several additional conditions must be imposed on the derived equations. One of them is the static condition

I

XGR~

(16)

co s0 ( v - 1.- 3 v sin28 I

XGR~

where P is the external force sin0 ( ~ - 1 - 3 ~ ~ 0 ~ ~ 0 ) applied to the bodies. Dy11Everywhere at the contact XGR~ boundary r vcos0 (1-3sin20) Dy12 -Dy21- pl r-0 I XGR~ I

I

Dy22-

-

s i n 0 ( 3vcos20-1) XGR~ (15)

Here 7 is the sliding frictional stress, which coincides with the frictional stress in the dry regions and is equal to g in the lubricated regions. 5. PARTIAL LUBRICATION

When some contact takes place between the asperities, partial lubrication (sometimes referred to as “mixed lubricationw1)will occur. The

r-

unknown if d r-0.

(Is)

Note that boundary condition (19) is the local one. Therefore, some pieces of the contact boundary r are known and some are unknown. Also, the problem solution must satisfy the boundary conditions for p, different at different parts of the contact region boundary, whether belonging to dry or lubricated regions, to the inlet or exit zones of the contact. Suppose that ri and re are the inlet and exit parts of the contact area boundary, which are given and unknown in advance,

406

respectively, r=riUre. The boundary condition for the dry contact region boundary is given in (18). Let us consider the lubricated contact regions. This case requires different boundary conditions. Here is the precise meaning of this assumption: r i - g i v e n if h lrl>O A ( 9 , d 1,/0;

(11)). The boundary conditions will be based on the requirement of the frictional stress continuity on the internal boundaries. Suppose li and ni are the i-th internal boundary and a unit normal vector to it, respectively. Therefore, the continuity condition can be expressed in the form: lime+ [ T ( x-enx,y-en,) -

eu

T (x+en,,y+eny)1 -0

f o r ( x , y )Eli.

The indicated boundary conditions (18) and (19) must be combined with conditions (16) and (17). Besides, the frictional stress 7 must vanish at the contact region boundary

TI ,-Om

(20)

The formulation of the boundary conditions imposed on the external boundaries of the contact is completed. In the case of mixed friction conditions the contact area may contain some internal boundaries between dry and lubricated regions that, apparently coincide with flow lines of the lubricant. Now, it is necessary to formulate the boundary conditions that must be held on the possible internal boundaries. A s we know, the frictional stresses for lubricated and dry conditions are described by Eqs. (1) and (2) (see also

Let us consider the physical nature of the transition from liquid to dry friction. A fundamental experimental study [ 3 ] shows that a continuous transition of the frictional stress from liquid friction to dry friction occurs in a small number of molecular liquid layers on a solid surface (Fig. 2). The specific features of this transition have been studied to a small extent and depend on the adsorption properties of the lubricantsolid surface interface. Let us consider the internal boundary between lubricated and dry regions on which slippage occurs i.e., la1>0. Then by using Eq. (21) together with (2), and (11), we obtain limh,os(p,h , p I I d

-

407

Owing to adsorption effects, the lubricant boundary layers show the properties of structural anisotropic fluids, and p=p(p,h, Is[). For a particular case of Newtonian fluid with F(x)=x, Eq. (22) becomes more transparent,

for Id>0.

':Boundary : rPartial rElastohydrodynmic

II 11 1

I

I I

1

1

I--

-

a :

c-c

.$ .0 p \

--

0

Hydrodynamic

I

5

10

15

I

20

Figure 2. Variation of friction coefficient with film parameter c43

(8),(7),(11) for the fluid film lubrication regions, and by equations (2),(14), and (15) for the dry regions together with additional conditions (16)-(21). In addition to these equations and inequalities the relations for functions F(@), p , f, and ri must be given. The problem solution consists of the functions p(x,y), h(x,y), r(x,y), and s(x,y), the exit boundary re, some parts of the inlet boundary ri that represent the boundaries of the dry regions, the internal boundaries li between the lubricated and dry contact regions, and the constant h,. In the case of contacting bodies made of the same material and small influence of elastic deformations on slippage the normal and tangential problems can be solved separately. It means that in this case s=uzu,+o ( I uz-u, I ) and the normal problem becomes independent of the tangential problem. Thus, first the normal problem must be solved for p(x,y) and h(x,y), and after that the tangential problem must be solved for r(x,y) and a(x,y).

A=PISI/P. 6.

It can be shown that (22) can be condition satisfied if the fluid viscosity approaches zero as the pressure approaches zero (see Eq. (36)). It is obvious from Eq. (23). Finally, the considered problem is completely described by equations

STATISTICAL APPROACH

A s already mentioned the shape of the inlet meniscus depends on many different factors that currently cannot be registered. Therefore, it is appropriate to treat the shape of the inlet meniscus ri as a random function depending on several

408

p a r a m e t e r s e.g. 7 . NARROW CONTACT UNDER PARTIAL LUBRICATION ri ( a1 / a2/ / an) Then the problem solution depends on the values of this set of Let us consider the case parameters [i.e. , p= p(x,y, of an incompressible elastic (-0.5) and a al/az, tan) / h=h(~/~/al/a2/material long in the direction *.*/an) ~ = ~ ( ~ , ~ / a l / a 2 , * * . / acontact n) .]. of the y-axis and narrow in s=s(x,y,al,a2,. ,an), In most practical cases it the direction of the x-axis. is important to know the This condition is equivalent average values of such to the inequality R,/%<
..

/

..

..

. ..

..

(a/. . .[f a, (

4

.

I

2 - -X1 I

...

I

a,) da, . . . da,x

aH

y-& aH

Z 2--# he

409

for H o - 0 ,

(where pH is the maximum Hertzian (dry) pressure, 27rpHa,bu=3P, po is the fluid viscosity for p=O, and he is the film thickness at the exit point for the fixed y) and asymptotic expansions [ 5 ] for the integrals involved in the problem equations, the normal problem for principal asymptotic terms can be found in the form

ah --0

(l-% 2

ax

for H,>O,

H, (h-1)-x2-c;+ C"

Here [ay(Y),cy(Y)l is the contact region for the fixed y, ay and cy are the inlet and exit points, and P,(y) is the unknown maximum pressure over the segment P(X,Y) [a rCy1* Note that in Eqs. the dimensional (2%)-(31) constant h, is replaced by a function h,=h,(y) in such a way that h=h, for (x,y)Ere, and the lubricant film thickness H,=H, (y) Besides , in the case 6<<1 the conditions h(x,y)>O ( = O ) can be replaced by H,>O (=O). In a similar way, for &<
.

for H,>O, c..

410

tx-gx

for H o > O ,

(32)

the line y=y is lubricated (i.e., H,>O) ' By introducing the following transformation of variables :

.

(x,a,,,c,,)- 0 k1,a, c) P - P O ~ ~ , I

It J d f p f o r IsJ-o ,

Therefore, the problem for mixed friction is reduced to a family of plane problems for lubricated and dry conditions. Here it is important to mention that if H,(y.)>O, the whole segment [a,(y ) ,c,(y ) J is lubricated, and 'if H,'(y')=O, the whole segment [a,(Y*) ,C,(Y') 1 is dry. This follows from the fact that the lubricant volume flow rate is constant in the plane case. For 6<<1 the systems of Eqs. (25)-(31) and (32)-(34) hold outside of small vicinities, of order 6 , of the points y=-d, and y=d, and the points where the radius ri is of of inlet boundary order 6. In the case considered the contact area is represented by alternating strips (bounded by straight lines, y=const) in which liquid or dry friction occurs. In general the systems of Eqs. (25)-(31) and (32)-(34) must be solved simultaneously. Let us analyze the normal problem first. Suppose that

Ho-HooHl, V-VoV,,

po-b (POD)

Eqs. (25), (26), (28)-(31) can be reduced to the equations of a plane elastohydrodynamic lubrication problem in generally accepted form [6-81. The solutions of this problem for different lubricant rheologies obtained by numerical and asymptotic methods [6-101 are well known. Some analytical asymptotic results for this problem (formulas for film thickness and friction force) are found for the cases of lightly (V,>>l) and heavily (V,<
.

41 1

contact elasticity problem [2]. The solution of this problem is the Hertzian pressure p (x,y)= (1-XZ)1'2, c (y)=-a (y)=l. This analysis of the normal problem shows that for starved (limited) lubrication and mixed friction conditions the behavior of the lubricant film thickness H resembles the behavior of tie distance I ay(Y1 -a,(Y) I between the corresponding points of the input oil meniscus and the input Hertzian boundary of a dry contact. In particular, it can be shown that H =A(V)B(ao(Y)-a,(Y)) I where tie specific form of functions A and B depends on details of the lubrication regime, and that ~ ( x-B(M) ) for X>O, B ( x ) -0 for xso. The solution of the normal problem will be completed by determining the function P,(y). By using asymptotic expansions of integrals [ 51 it can be shown that out of the vicinities of the vertices located approximately at y=f6-' the function Po(y) satisfies the following equations:

CV

d"

where -d, and d, are the lower and upper boundaries of the contact area, d ld,=0(6~1)~ In several speciai cases the solution of Eqs. (36) can be obtained asymptotically in an analytical form. Let us consider the tangential problem [Eqs. (32)(34)]. Suppose that at the chosen segment y=y. the lubricant is present (i.e., H>O). It can be shown that sliding velocity s, is unbounded at x=a and x=cy if the sliding frickonal stress g, does not vanishes at these points. The only way to make s, bounded everywhere is to accept the fact that limpop(p,h,ld)-0. (37) This condition is in a perfect agreement with the conclusion obtained from Eq. (22) (see also (23)) and the frictional stress continuity condition Eq. (21). Under this condition the regular solution of the problem Eqs. (32)-(34) can be found numerically or asymptotically for the case r l < < l . Suppose that the line y=y is not lubricated (i.e.,* H,=O) In this case the analytical solution of the problem is well known [ Z ] . It depends on the value of /78f

.

412

and may contain segments of relative slippage and adhesion. In the particular case of a Newtonian lubricant the normal problem [Eqs. ( 2 5 ) (31)1 can be solved separately from the tangential problem [Eqs. (32)-(34)]. The reason is that all integrations in Eqs. (7)- (9) can be performed analytically and

This is true for the original (non-simplified) problem as well. under equal Usually , conditions dry frictional stress is greater than liquid frictional stress. Therefore, the friction force is higher for mixed friction than for a purely liquid regime. The increase in friction force depends on the relative portion of the contact area occupied by dry friction regions. Figure 3 illustrates the type of pressure, film shape and boundary that can be expected in a partially lubricated conjunction. The top view of the conjunction [Fig. 3 (a)] shows the dry and lubricated regions as well as the Hertzian contact zone. Figure 3(b) shows a threedimensional view of the pressure within the conjunction. Note that in the dry region the pressure profiles are Hertzian but in the lubricated regions a

pressure spike exists. Figure 3(c) gives the film shape and boundary in a two-dimensional view along the y-axis. CONCLUSIONS

The work presented in this paper is only a beginning in understanding the major mechanisms governing mixed friction. A mathematical formulation of the contact problem with mixed friction is given. The problem is reduced to a system of mechanisms governing mixed friction A mathematical formulation of the contact prdblem with mixed friction is given. The problem is reduced to a system of alternating nonlinear

.

Figure 3 (a). Two-dimensional view of conjunction.

41 3

.

Figure 3 (b) Three-dimensional view of pressure profile.

equations and inequalities with some unknown external and internal boundaries. A statistical approach to the problem of mixed friction is proposed. The necessity of taking into account structural non-Newtonian lubricant behavior in thin films and the approach of the lubricant viscosity to zero as contact pressure vanishes is shown. The asymptotical analysis of the problem is conducted for the case of a contact stretched in the direction perpendicular to the lubricant flow. It is shown that for starved (limited) lubrication and mixed friction conditions the behavior of the lubricant film thickness resembles the behavior of the distance between the corresponding points of the input oil meniscus and the input Hertzian boundary of a dry contact. It is also shown that the friction force is higher under mixed friction conditions than for purely liquid friction and becomes greater as the dry friction region in the contact area enlarges. ACKNOWLEDGMENTS

.

Figure 3 (c)

Two-dimensional view of film thickness and boundary along the y-axis while setting X=O.

The authors wish to thank SKF Engineering and Research Centre (The Netherlands) for its support of this effort. The first author wishes also to thank the College of Arts and Sciences of the University of Scranton for supporting research and financial assistance.

414

REFERENCE8 1. 2.

3.

4.

5.

H. Schlichting, Boundary Layer Theory. McGrawHill, New York, 1960. L.A. Galin, Contact Problems of Elasticity a n d V i s c o elasticity. Nauka, Moscow, 1980 (in Russian). A.S. Akhmatov, Molecular Physics of Boundary Friction. Fizmatgiz, 1963 (in Moscow, Russian). B.J. Hamrock, B.J., and D. Dowson, Ball Bearing The Lubrication Elastohydrodynamics of Elliptical Contacts. Wily-Interscience, New York, 1981. J.J. Kalker, On Elastic Line Contact. ASME Trans., Ser. E, J. Appl. Mech., Vol. 39, No. 2,

9.

10.

11.

1972. 6.

7.

8.

Dowson and G.R. Higginson, Elastohydrodynamic Lubrication, The Fundamentals of Roller and Gear Lubrication. Pergamon, Oxford, 1966. B.J. Hamrock and B.O. Jacobson, Elastohydrodynamic Lubrication of Line Contacts. ASLE Trans., Vol. 24, No. 4, D.

1984. 1.1. Kudish, Asymptotic

Methods of Investigating

12.

Plane Problems of Elastohydrodynamic Theory of Lubrication Under Heavy Loading Conditions. Part 1. Isothermal Problem. Izvestija Akademii Nauk Armjanskoj SSR, Mekhanika, Vol. 35, N0.5, 1982 (in Russian). L.G. Houpert and B.J. Hamrock, Fast Approach for Calculating Film Thickness and Pressures in Elastohydrodynamically Lubricated Contacts at High Loads. J. Tribology, Vol. 108, No. 3, 1986. V.M. Aleksandrov and 1.1. Kudish, Problem of Contact-Hydrodynamic Theory of Lubrication for a Viscous Fluid with Complex Rheology. Mechanics of Solids, Vol. 15, No. 4, 1980. 1.1. Kudish, Some Problems of Elastohydrodynamic Theory of Lubrication for a Lightly Loaded Contact. Mechanics of Solids, Vol. 16, No. 3, 1981. 1.1. Kudish,

Extremely Heavy Loaded Lubricated Contact and Critical Analysis of Some Approximate Analytical Theories. Proceedings of the 6th Intern. Congr. o n T r i b o l o g y EUROTRIB I 9 3 'I, Budapest, Hungary, 1993.

Dissipative Processes in Tribology / D. Dowson et al. (Editors) 0 1994 Elsevier Science B.V. All rights reserved.

41 5

Third body theoretical and numerical behavior by asymptotic method G.Bayadaab , M.Chambatb , K.Lhalouanib and C.Licht“

“Mecanique de Contacts CNRS URA 856 Institut National des sciences Appliquees 113, 69621 Villeurbanne Cedex France bLab.Analyse Numerique, CNRS URA 740,Universite Claude Bernard, 69622 Villeurbanne Cedex France ‘L.M.G.C, CNRS, Universite Sciences Techniques du Languedoc, 34095 Montpellier Cedex France We consider the behavior of a device with a thin soft layer between a rigid support and an elastic first body. We show how the expression of the interface law depends on the relative asymptotic behaviors of the parameters of thickness, stiffness and dissipation.

1. INTRODUCTION A trend in the study of friction between two bodies involves introducing a very thin third body between them. Sticking two elastic bodies also implicates a third thin material with a rather different mechanical behavior. It is then of interest to study the asymptotic behavior of a thin layer between a rigid body and an elastic one. A major assumption in this paper is that the third body is softer than the first body. A lot of papers have been devoted to such study with various geometries, behavior laws and more or less rigorous approach. In [l] closed analytical form solution with Bessel series are gained. In [2] the asymptotic method has already been used for a particular value of Lami coefficients with respect of the thin height E of the joint. A lot of related references are discussed in this paper. Preliminary results concerning our approach can be found in [3],[4]and [5]. The thin layer is stuck to the rigid body while various boundary conditions are considered between the thin body and the elastic one

as well as various relationship between stress and displacement for the thin body. The second section is devoted to a basic linear problem with perfect adhesion boundary condition. The problem is similar to an adhesively bonded joint. A rescaling of the coordinate through the joint is performed. An identification of the leading terms for displacement and stresses after asymptotic expansion allows us to obtain new boundary conditions at the interface between first body and the rigid support. In the third section, numerical results using finite element codes are given and compared with the theoritical preceeding results. To gain more realistic model of a third body, we replace in the fourth section the perfect adhesion condition by a Tresca’s boundary condition, acting on the tangential part of displacement and stresses vector. The asymptotic study leads to a similar behavior as in the second section, with the exeption of a new boundary condition occuring for a peculiar value of the stiffness Lame coefficient of the joint. The last section involves an evolution equation with dissipative generalized stan-

416

dard material whose caracteristics relie on E . Whether the ratio between the dissipative part and the purely elastic one is big or not, the range of the assymptotic boundary conditions goes from a sticking behavior to a slipping one.

strain.

The interface is located at x3 = 0 (see fig 1) while the joint lies between 23 = 0 and x3

This section is concerned with a model of soft joint of thickness e bounded by an elastic solid with perfect adhesion condition and a rigid body with zero-displacement condition (see figl).

2.1. Equations

So that equilibrium equations are

+ fi = o

aj.5'

+ fi

a+' 'I

= Ae,+Jij

i

= 1,2,3

x3 = --E

,4

I

in the joint

(1)

in the first body

(2)

Fig 1 : the Basic device

=0

= Xsae;k6ij

=0

:

2.2.

With the stress-displacement relation : 0:' IJ

and adhesion at the bottom implies U;

Various conditions cau be introduced (imposed displacement, external forces). Being applied to the first body, they don't modify the present asymptotic study. Let (A, p ) be the Lame coefficients of the first body and A', p c those of the joint. As the joint is assumed to be softer than the first body, we are led to introduce a and 4 such that :

a .Ju - c11

= --b.

At the interface, perfect adhesion boundary condition are :

BASIC PROBLEM

2.

= 1 if i = j and zero if i # j .

6ij

+ P&

e;

(3)

+2pet

(4)

Where ut (resp. u') and u+ (resp.)'u are stress and displacement in fitst body (resp. in the joint) and = i(6'i.j'- 6'ju;-) the

et-

+

Rescaling and Asymptotic Expansion

As a first step towards obtaining an approximate solution of problem (1). . . (7), we define an equivalent problem posed over a domain that does not depend on E by way of the rescaling :

417

Tentatively, we assume that a solution ( u , u) can be written in the following form :

By inserting (9) in (10) and identifying the leading terms, we obtain :

By inserting (9)-(10) in (2), we have to examine various situations.

we use equation (11) for i = id we have to discuss the leading terms witu respect of cr and p for the equation :

The same arguments as for the tangential problem can be used and we obtain the following table 1 which summarizes the various boundary counditions for z = 0 so obtained. u;=o u;=o

u; = x u ,0 u+o

=0 '1. i,j = 1,2 UP.

If ,f3 > 1,leading term is uGO= 0 and taking (6) into account we gain : uTfo = O

z =O

for

(12)

If ,f3 < 1, leading term is &(ti;') = 0 and taking (5) and (7) into account, we deduce Table 1 : Asymptotic boundary condition at the bottom of the first body (pure adhesion condition)

If p = 1, equation (2) reduces to /&(u;O)

= us;0

a2 aZu-0

and from (14) and ( l l ) , we get that all = 0 in the joint so that the following relation holds for L = 0 UT-0

By inserting (9) (10) in (2)-(4) we find that the classical linear elasticity equations are fulfilled by (u+',uf0) as E infers neither in the change of variable in the first body nor in the coefficients, so :

=jlu;o

and condition (5)-(6) allows us to carry on these condition from the joint to the first body:

To get information about the normal displacement and normal stress on the interface

Equations (15) (16) together with boundary condition of table 1 at the bottom 1 3 = 0 give a closed system which can be solved without any reference to the third body. So the asymptotic behavior of the device is well known by solving this system.

418

3

COMPARISON BETWEEN NUMERICAL AND THEORICAL RESULTS

a = p = 1 and UT and un for 0 < LY < 1 and p = 1. The results in the table 2 shows that the convergence of the characteristic ratio q - / q and Un/Un is very fast for the inner points of the interface. For E = 0.01, the convergence towards the asymptotic value is obtained within 1%. However, strange results appear a t the corner points (tl = 0.33 and 1 1 = 9.33) for which no convergence seems to occur. This is the consequence of boundary layer phenornena near the corner (see [3]). The asyrnptotic method gives average convergence and not a point- wise convergence. In other words, only the overall elastic energy of the system is proved to be converging. In the table 3, overall view of the convergence is shown for various values of a and p . The recorded values have been computed at an inner point of the interface to avoid boundary layer problem. The good convergence of the process is confirmed for all values of Q and p. To be noticed also is that results appearing in the columns E = 0.0005 and E = 0.0001 are comd e t e h different. This is caracteristic of an other difficulty for computing directly such

The previous asymptotic analysis is valid for

‘‘ small values of E. ”

To gain quantitative informations on the precise values of E for which the theoritical study is applicable, we perform some numerical computation for the initial problem with two different codes : Systus and Modulef. Both give the same results. The device is a square first body of length L = 10. A tangential displacement of L/lo is imposed at the upper surface while lateral sides are free. The corresponding Lame coefficients are A = 1,15 10l1 and p = 0 , 7 l o l l . At the bottom, there is an horizontal thin layer of thickness stucked to a rigid support, Regular finite elements discretization has needed 3000 triangles in the first body and 700 in the joint. We compute for various value of E = Q and /3 the displacement and stress in the whole device and retain the value related to the asymptotic theoritical behavior for five points on the interface . For example, we retain uT/uT and Un/Un for

4,

= 0.05 I 0.585E + 11 I 0.781E + 11 0.779E + 11 0.781E + 11 0.5856 + 11 0.2416 + 12 0.2736 + 12 0.2716 + 12 0.271E + 12 0.241E + 12

E

= 0.01 1 0.541E+ 11 I 0.775E + 11 0.773E + 11 0.776E + 11 0.541E + 11 0.1936 + 12 0.271E + 12 0.270E + 12 0.270E + 12 0.193E + 12

e

e=0.005

I ~=0.001 I 0.342E+ 11 I

0.491E+ 11 I 0.771E + 11 0.770E + 11 0.771E + 11 0.491E + 11 0.174E + 12 0.270E + 12 0.269E + 12 0.270E + 12 0.174E 12

+

+ +

0.7686 11 0.7696 11 0.7686 + 11 0.3426 + 11 0.135E + 12 0.2696 + 12 0.269E + 12 0.2686 + 12 0.135E 12

theoretical values

0.769E

+ 11

0.2696 + 12

+

Table 2 : numerical values obtained at the interface using MODULEF code for various x and

Q=p=l

E

for

419

E

(Y = 1 /3= 1 (Y = 2 P=1

I

= 0.2

I 0.9456 + 12 % -

1

I

1

.. I

0.3216+12 0 . 4 3 3 6 11 0.8796 12

+ +

E

= 0.01

+ 11

0.7736 0.2706+ 0.7656 0.155E

+ +

12 11 12

E

= 0.005

E

+

0 . 7 7 0 6 11 0.2696+12 0.767E 11 0 . 1 5 4 6 12

+ I + I

= 0.001

+

0 . 7 6 9 6 11 0.2696+12 0.769B 11 0 . 1 5 4 6 12

theorie

e = 0.0001

I 0 . 5 7 4 6 + 08 I 0 . 7 6 9 6 + 11

1

0.119E+09

I

0.2696+12

+ I 0 . 4 3 5 6 + 08 I 0 . 7 6 9 6 + 11 + 1 0.155E + 09 I 0 . 1 5 3 6 + 12

4 = 0.5 I U T I 0 . 5 6 8 6 - 05 I 0.181E - 10 I 0 . 1 4 6 6 - 10 1 0 . 1 3 2 6 - 10 I 0 . 1 1 2 6 - 06 I Table 3 : comparison between theory and numerical results for various a and /3

0

~~~

device : the locking phenomena, well known for plates, which prevents the right calculation for devices with thin layer using classical codes. This emphasis the interest of the theoritical study.

4 . THIRD BODY LAYER As a tentative to model the thin layer as a third body, we replace the boundary conditions (5) (6) by the Tresca condition, allowing a possible jump of the tangential displacement uf and u7 i = 1 , 2 at the interface. Let g a given upper bound for the tangentical stress modulus, the Tresca conditions are

[ut] denoting the jump of the tangential displacement at the interface. Clearly, this condition is nothing else than a Coulomb like condition with a fixed upper bound for bt in (18). Equations (1)-(4) and (17)-(20) together with loading conditions define a well posed problem which is a non linear one due to (18)-( 19), so that the formal identification procedure as in section 2 is no longer valid. However, mathematical analysis approach [6] allows us to obtain the asymptotic behavior of the device. New asymptotic boundary conditions associated to the equations (15)-( 16) are shown in table 4. By comparing table 1 and table 4, differences only appear for ,f? = 1. In that case the boundary condition .to = p u t o is replaced by a Tresca’s like condition. An important feature is that in the case ,f3 = 1, it is not possible to solve the asymptotic problem without taking the joint into account and we must add to (15)-(16) the asymptotic elasticity equations in the joint :

420

P>1

u;

=0 =0

uo

=0

UT 0

u: = xu; u; = 0

UQ.

i,j

=0 = 1,2

uo = 0

uo

=0

J.

p=1

05p<1

O
a=l

( Y > l

Table 4 : Asymptotic boundary condition at the bottom of the first body (Tresca's adhesion condition) 0-

up-13 = ? a z!L uii 0-

= 0,

u;; =a:;,

"30;

i = 1,2,3

(23)

= p&(u!-)

ifa

>1

=0

if a

<1

za( u : - )

I

a,(u8iC) + f , ( r , t )= 0

+

in the joint

13j(utc) f i ( z , t )= 0 in the 1" body

(24)

As this overall system of equations is defined in the rescaled domain, which is not a thin one, and as E does not appear in the coefficients, this system is not a stiff one as the initial one. Moreover, it can be posed as a variational problem, allowing a finite element solution [ S ] .

5 . JOINT WITH DISSIPA-

TIVE MATERIAL In this section, we consider a quasistatic behavior of the device by introducing time t and a dissipative law for the joint. New equations are (. denoting the derivative with respect of time) :

(26) (27)

and

equation(4) and boundary conditions ( 5 ) ( 6 ) ( 7 ) being the same. We assume that the parameter p involved in the definition of the dissipative part is such that 1 5 p 5 2 while, for sake of simplifaty, we also assumed & = /3 in the elastic part. The asymptotic limit boundary condition for the first body is given in the table 5 . A full range of behavior, for a dissipative one to a pure elastic appears. This table make evidence that disipative effect are not present if y > p - 1 or if a < 1. In these cases, the results of table 1 and 5 are the same (remember that Q = p). A critical value Q = 1 and 7 = p- 1 allows both elastic and dissipative effects to appear

42 1

Table 5 : Asymptotic boundary condition at the bottom of the first body (dissipative problem) simultaneously at the limit. That means they have the order of magnitude with respect to E . The function g1 and 92 could be precisely defined (see [5]). The dissipative effects appears only for a >_ 1 and y 5 p - 1. In that case the coefficient ca in front of the elastic part is sufficiently small so that the elastic effect vanishs at the limit.

6. CONCLUSION It has been evidence that the asymptotic approach is valid for the study of non linear boundary conditions or non linear behavior law for the study of devices with a thin inclusion. We obtain the qualitative behavior of the device and gain information on the influence of E on this behavior without any calculation.

REFERENCES 1. T.Sawa,

K.Temma and H.Ishikawa, J.Adhesion, 3 1 (1989) 33. 2. A.Klarbring, 1nt.J.Engng. Sci, 29 (1991) 493. 3. A.Ait Moussa, C.Licht and P.Suquet, Acte du gkme Congrb FranGais de Mecanique, Metz (1989) 258.

4. G.Bayada, M.Chambat, K.Lhalouani and

C.Licht, reprint, Lab0 Meca.Contact, INSA (1993). 5. C.Licht, C.R.Acad. Sci. Paris t.317, Series 1, (1993). 6. K.Lhalouani, Preprint Lab.Anal.Num, Lyon, (1993)

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Dissipative Processes in Tribology / D. Dowson et al. (Editors) Q 1994 Elsevier Science B.V. All rights resewed.

42 3

Thermomechanical st ate near rolling contact area K. Dang Van and M.H. Maitournam Laboratoire de Mkcanique des Solides, CNRS URA 317, Ecole Polytechnique, 91128 Palaiseau, cedex, France A numerical investigation of the temperature rise in the vicinity of a moving contact area is performed. A steady-state motion is assumed. A coupled thermomechanical algorithm is used. The coupling is realised : i) in the thermal equations by volumic heat sources (intrinsic dissipation (u- c P ): ip,reversible heat source p o i ) and by interfacial dissipation; ii) in the mechanical equations, by thermal expansion. Numerical calculations are carried out to evaluate separately the parts of the temperature rise due to volumic and interfacial dissipations.

1. INTRODUCTION

Metallurgical transformations are often observed near the contact area of two metallic solids. For instance micrographic sectionning of high speed lines rails shows transformed metal in a white layer of less than 200 pm depth. This phenomenon is also observed in rolling bearing and in components subjected to fretting fatigue. Although great efforts have been to understand phenomena arising near the contact area of two rolling and sliding solids, the real cause of these metallurgical transformations is not identified : are they driven by high contact temperature or by high contact pressure? Probably by both! This work is an attempt to numerically evaluate the temperature rise in a moving contact. In fact, taking account of thermal state could have a real importance in the study of the origin of wear and damage (like pitting, frosting, shelling, ect) by changing the stress and strain fields. And uncoupled elastic computations, which are most of the time carried out, poorly evaluated these quantities. Recently a new approach in inelastic repeated rolling contact was proposed [l-41. It is based on stationary elastoplastic algorithm. This method is detailed in [l]. Steady-state assumption was used to analyse mechanical problems involving moving loads. Uniqueness theorem was proved in the case of elastoplastic behaviour. Two numerical procedures were proposed : the pass-bypass stationary method (PPSM) which rigorously treats the case of a single load pass, and the direct stationary method going straight to the steady

state in the case of repeatedly moving load. These procedures were applied to forward motion and t o forward and backward motion [2]. Discussions of shakedown limits for line contact were done. In this paper, these procedures are extended in the case of thermomechanical coupling realised by the presence of thermal expansion in the mechanical problem and of heat sources (due to inelastic deformation, thermoelastic coupling and interfacial dissipation mechanism like friction and micro-slip) in the thermal problem. Our aim is to evaluate the temperature field in the vicinity of the contact area. After recalling the general equations governing the coupled thermomechanical problem, we derive the steady-state equations in the reference frame of the moving contact. The case of a line contact, with the mechanical and geometrical characteristic of a rail-wheel contact is traited. The temperature rises due to volumic (intrinsic dissipation and thermoelastic coupling) and interfacial (friction and micro-slip) heat sources are computed separately in order to evaluate their respective contributions. Influences of the normal load, the tangential load and the friction coefficient on the heat generated are discussed. 2. GENERAL FORMULATION 2.1. Governing equations The equations governing the thermomechanical problem for one the contacting bodies are the following : -balance of energy

divq

+ pBs = r + V,

(1)

424

Vi is the irreversible heat source corresponding to the intrinsic mechanical dissipation, p86 the reversible heat source corresponding to the themoelastic coupling, r a volumic heat source and q the heat flow vector; -equations of motion diva = pii

(2)

-constitutive laws u =L : E

= (8

-

(yer)+ go

(3)

+ EP)

E

T

af

= -.(grad 1 u

2

div(-k. grad 8) - pcVB,, =

(4)

= Af 5 0 , A 2 0 , Af = 0 do -equation of compatibility ip

2.2. Steady-state e q u a t i o n s We assume first that the contact is moving with a velocity V = V e,, and second that there is a steady-state in a reference moving with the contact. The above governing equations are rewritten in a frame of this reference and in the case of an elastoplastic linear kinematic hardening Von mises material. The equations in which time explicitely intervenes are -balance of energy

(5)

- V ( u - CEP) : €P,, +Va&r(u),,

-equations of motion diva = pV2u,,,

+ tgrad u )

(14)

(15)

-constitutive laws

-thermal conduction law q = -k grad 8

(7)

with the following boundary and initial conditions : u.n = F

u = ud €P(X,

on d V f ( t ) on aVu(t)

(9)

0 ) = €P(X)

8 =ed

f(U,€P)

= /;(u - C E P ) : (u- CEP) - UY

(19)

(10)

on d b ( t )

-q.n = -csu.n.[lvl]on

(8)

(11)

dV,(t)

(12)

[IvI]is the discontinuity of the velocity in the contact reference, c, a coefficient of sharing of the interfacial generated heat. In fact, equation (12) the discontinuity equation corresponding to the application of the first principle of thermodynamics (energy balance) on both the contracting bodies. It is rigorously given by

with c=1

f=O if f
if

(=O

(13)

For the sake of simplicity, the mechanical and thermal parameters have been assumed temperature independent.

[Iq.nl] is the heat generated at the interface of the two bodies. Its distribution between the two bodies depends on the their conduction properties. The second law of thermodynamics ensures that it is positive [5]. In the case of two similar bodies c, equal 0.5.

2.3. Numerical solution The numerical analysis is performed by a finite element method taking account of the steady state assumption. The thermomechanical solution procedure is iterative, and has the two following main steps:

[Is.nll = ff.n.[lvll

425

- solution of a steady-state mechanical problem with a given initial temperature field; the method used is given in [ l , 41 ; - solution of the thermal problem with a given mechanical state, obtained by using a streamline upwind Petrov-Galerkin formulation. These steps are alternatively performed until convergence is achieved. 3. NUMERICAL RESULTS 3.1. Characteristics used The characteristics of the considered material are : E = 210 GPa, u = 0.3, uy = 237 MPa, C = 32 GPa, a = 1.5 10-5(0C)-1, p = 7800 kg/m3, c = 449 J/kg/OC, k = 48 W/m/OC. E is the Young's Modulus, v the Poisson's ratio, uy the initial shear yield stress, C the hardening modulus, a the coefficient of thermal expansion, k the thermal conductivity, c the specific heat, p the density. A line contact is considered moving with a velocity V = 100 km/h. Its characteristics are : a = 8.75 mm the contact width; POthe maximum Hertz pressure, and p the friction coefficient. A parametric study is carried out with various contact loads and friction coefficients. The condition of no exchanged heat with environment is assumed.

-1y -50

0

C], P& = 3.75 P&=S.

,

,

P

1

2

,

,

5

6

E7.5

3

4

Temperature rise (C)

Figure 1. Variation of temperature in depth at the center of the contact for various normal loads.

where the plastic dissipation is maximum. The effect of the contact velocity is clearly seen in this figure. The heating appearing ahead of the contact (even for large Peclet numbers), is due to thermoelastic coupling.

6.0

. .

,

.

,

,

.

.

.

,

.

.

,

.

.

3.2. Temperature rise due to volumic sources In this section, our objective is to evaluate the temperature rise generated by the volumic heat sources, and also to quantify the effect of the normal load and the friction coefficient on the distribution of this temperature. This evaluation is performed only for the first pass of the load. 3.2.1. Effect of the normal load The friction coefficient is assumed equal to zero. The load parameter P0/uy is varying and takes three values (3.75, 5. and 7.). Fig.1 shows the variation in depth of the temperature rise at the center of the moving contact. Fig.2 shows the variation of the surface temperature. The elevation of temperature is in this case not important (maximum = 6.4OC on Fig.A). For high pressure (Poloy = 7.5), it can be seen in Fig.A that the maximum temperature rise is reached in depth,

Figure 2. Variation of surface temperature for various normal loads.

3.2.2. Effect of the friction Coefficient Figures 3 and 4 show for Polo, = 3.75, the distributions of temperature in depth at the center

426

i

i

Figure A. Temperature rise due to volumic dissipation in the first pass of a frictionless rolling contact. The width of the figure is about 7a.( Po/a, = 7.5; uy = 237 MPa; V=100km/h )

0

15.0

I

"

'

.

,

-

I

-5

-B

~

.I0

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

v

E

.I5 -20

-25

-30

Figure 3. Variation of temperature in depth for different friction coefficients.

-100

-so 50 Distance from the contact center (mm)

n

Figure 4. Variation of surface temperature for different friction coefficients.

421

-0.8

.1.0

f 1 n

100 200

300 400

500

MX)

700

800

900

1000

Temperature (C)

Figure 5. Variation of temperature due to friction in depth in the case of sliding line contact.

of the moving contact and at the surface obtained for p = O., 0.5,0.8 and 1. One can notice that the elevation of temperature is not important (maximum = 8.5OC ). The cooling (negative temperature variation) is due to thermoelastic coupling. 3.3. Temperature rise due to interfacial sources In this section, our objective is to evaluate the temperature rise generated by the interfacial dissipation (essentially friction and micro-slip). A Great number of studies are devoted to moving heat source. Solutions of contact temperature rises in thermoelasticity are available [6].The interfacial dissipation Psis due to friction and slip or micro-slip. It is given by :

Ds =I

(.)t.

I

-,-;.1

____r_r____-

-I00

-80

i 1

,

,

,

,

-m 0 m 40 (10 Distance fmm the contact center (mm)

-60

40

,

, 80

I00

Figure 6. Variation of surface temperature due to friction in the case of sliding line contact.

IS0

-

(22)

where T ( Z ) is the tangential stress, and vt the sliding velocity. In the case of two sliding solids, the heat generated is elliptical :

--q.n = qoJ1 40 = ,PPoVt

-100

(23)

(24)

In this paper, the considered values of qo are 1, 10,100 and 200 (106W/m/s) for wt = 30 m/s. Because of this high sliding velocity, The very high temperature can be obtained (Figs.5, 6).

-80

-40 -20 n M 40 60 Distance fkom the contact center (mm)

-60

80

IM

Figure 7. Variation of surface temperature due to micro-slip in the case of tractive rolling.

428

But a more realistic case is given by the tractive rolling. In this case, the contact area is divided into slip and slick zones. Dissipative processes take place only in slip zone due to micro-slip. The temperature rise is calculated for P0/oy = 4.75, V=100 km/h, p =O (Fig.7). The ratio (T/N) of the normal and the tangential load is varying from zero to p. The maximum temperature rise obtained in this case is higher than the one due to volumic dissipation, but the sum of both heat generated is not enough to explain metallurgical transformations. 4. CONCLUSION

A steady-state method for the numerical analysis of dissipation in moving rolling-sliding contacts has been presented. As an illustration, the example of rail/wheel contact has been treated as a line contact. The calculated heat generated by both volumic and interfacial dissipation does not explain the experimentally observed metallurgical transformations. Only the first pass of the loading was analysed. It is well known that it gives more important plastic deformation than the stabilized state (for repeated rolling-sling contact). In this last case, the contribution of the volumic heat sources will be negligible in practical railwheel contact. This study is a first step of the thermomechanical analysis of rolling-sliding contact. Nevertheless, the formulation used is sufficiently general for taking into account more sophisticated interfacial dissipation mechanisms, temperaturedependent parameters and heat transfert between the contacting bodies and the environment. And then, the realistic prediction of the temperature rise and its influence to fatigue failure will be achieved. REFERENCES 1. K. Dang Van and M.H. Maitournam, Steady-

State Flow in Classical Elastoplasticity: Application to Repeated Rolling and Sliding Contact, J. Mech. Phy. Solids, (1993) to be published.

2. K. Dang Van and M.H. Maitournam, Elastoplastic Calculations of the Mechanical State in Alternative Moving Contacts: Application to Fretting Fatigue, International Conference on FRETTING FATIGUE, Sheffield, (1993). 3. K. Dang Van, G. Inglebert and J.M. Proix, Sur un nouvel algorithme de calcul de structure Qlastoplastique en rQgime stationnaire, 3Qmecolloque ” Tendances actuelles en calcul de structures”, Bastia (1985), Ed. Pluralis, Paris. 4. M.H. Maitournam, Formulation et Resolution NumQrique des Probkmes Thermoviscoplastiques en RQgime Permanent. Thkse ENPC, Paris, (1989). 5. P. Germain, M6canique (tome I), Ed. Ellipses, Paris, (1986). 6. K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, (1985).

SESSION X THERMAL POWER DISSIPATION IN MACHINES Chairman:

Dr Philippa Cann

Paper X (i)

Thermal Dissipation in Elliptical Bore Bearings

Paper X (ii)

Material Dissipative Processes in Automotive Engine Exhaust Valve-Seat Wear

Paper X (iii)

Thermal Matching of Tribological Systems

Paper X (iv)

Power Loss Prediction in High-speed Roller Bearings

Paper X (v)

Power Dissipation in Elastohydrodynamic Traction Drives

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Dissipative Processes in Tribology / D. Dowson ei al. (Editors) 0 1994 Elsevier Science B.V. All rights resewed.

43 1

Thermal Dissipation in Elliptical Bore Bearings M-T Ma* and C M Taylor# *Department ?f Engineering and Product Design, University of Central Lancashire, Preston, Lancashire P R l 2 H E . U.K. %epartment of Mechanical Engineering, University of Leeds, Leeds, Yorkshire LS2 9JT, U.K.

In this study, a comprehensive thermohydrodynamic analysis has been developed to predict the detailed and global thermal performance of profile bore bearings. The effects of reverse flow and oil groove mixing were taken into account. With considerations of the effect of oil back flow from grooves, temperatures in the cavitation region were evaluated by an elemental heat balance method established by the authors. Experiments have been carried out for a 110 mm diameter elliptical bearing with specific loads up to 4 MPa and rotational frequencies up to 120 Hz. Power loss, flow rate and detailed temperature profiles were measured under steadily loaded conditions. Comparison between the predictionsof theory and experiment has shown an excellent agreement. NOTATION A symbol with an overbar represents a nondimensionalquantity. oil dependent constants =Rb-R, bearing radial clearance =RL-R, lobe radial clearance =O 1 , empirical coefficient lubricant specific heat journal diameter horizontal fluid film force vertical fluid film force local film thickness lubricant thermal conductivity bush thermal conductivity bearing width axial groove length =l-Cb/CL, preload ratio rotational frequency local film pressure oil feed pressure specific load volumetric flow rate journal radius radius of inscribed circle (see Fig. 1)

-

radius of lobe (see Fig. 1) outer radius of bush preload local film temperature ambient temperature local bush temperature lubricant feed temperature shaft surface temperature journal surface velocity velocity components in x,y direction respectively applied or external load Cartesian co-ordinates polar CO-Ordinates angular extent of groove lubricant dynamic viscosity lubricant kinematic viscosity groove wall heat transfer coefficient outer bush surface heat transfer coefficient circumferential co-ordinate measured from middle of upper lobe lubricant mass density =cb/R, CltXtEinCe ratio

432

Subscripts

in C

f g p r t

inlet cavitation feed groove lobe or groove number reverse flow trailing edge

1. INTRODUCTION

Hydrodynamic journal bearings are important elements in high speed rotating machinery and widely used in industry. Thermal effects in these bearings have been recognised and studied for several decades. Much valuable work has been done both theoretically and experimentally by many researchers. A large volume of research papers and reports can be found in academic and technical journals and books [l-101.A review of the literature was reported by Pinkus and Wilcock [ l l ] in 1979. More recently, a comprehensive literature survey was presented by Khonsari [12] (1987).A review of the literature reveals that almost all the previous work on thermal effects in journal bearings pertains to circular type. Fixed profile bore or non-circular bearings, which are extensively used in turbomachine9 due to their excellent stability characteristics, have been scarcely studied from a thermal perspective. There is a lack of both theoretical predictions and reliable experimental data of the thermal performanceof these bearing types. Elliptical (or lemon-bore) bearings, due to their manufacturing simplicity, are commonly used to overcome self-excited vibrations in rotor dynamic systems. In this study, a detailed numerical model has been developed to predict the temperature dishbution and global static performance characteristics of fixed profile bore bearings. Experiments have been undertaken for an elliptical bearing and measurements carried out for power loss, flow rate and temperatures in the bearing. Some

experimental and theoretical data for the bearing will be presented and compared with each other in this paper. Before doing so, it is appropriate to review briefly the literature on thermal effects in noncircular bearings. Singh et a1 (1989) carried out an elastothermohydrodynamicanalysis of flexible shell elliptical bearings, considering principally the effects of bearing liner elastic deformation on the static and dynamic bearing performance characteristics [133. An experimental investigation into the thermal behaviour of a 500 mm journal diameter elliptical bearing under transitional conditions was reported by Hopf and Schuler 1141 (1989). They found that under laminar flow conditions, the circumferential temperature excursions and the temperature differences across the film could be very significant, and a transition to turbulence would cause an improved heat exchange across the film and, accordingly, a reduction of the bush inner surface temperatures. A comprehensive model was developed by Mittwollen and Glienicke [15](1990)to predict the thermohydrodynamic behaviour of profile bore bearings. Sample calculations for an elliptical bearing were carried out and the results were compared with Hopf and Schuler's experimental data and agreement was good. An adiabatic thermohydrodynamic solution of an elliptical bearing was obtained by Croby [16](1991).In this procedure, the separation cavitation boundary conditions were adopted for the generalised Reynolds equation and reverse flow in the inlet region was considered in the solution of the energy equation. Some valuable work on the thermal performance of three-lobe bearings were carried out both theoretically and experimentally by Gethin and his co-workers (1990 -1991)[17-191.In their work, both simple and rigorous approaches were adopted and the effect of loading direction was stressed.

2. MATHEMATICAL FORMULATION

The detailed analysis can be found in reference [20]. In this section, only an outline of the model is presented. Figure 1 shows the nomenclature and geometry for an elliptical bearing. The co-ordinates for the mathematical model are illustrated in Figure 2.

433

Bush

(a) Dimensional

I

Shaft

Figure 1 Nomenclature for an elliptical bearing

2.1. Governing Equations Bush

The governing equations are subject to the following normal assumptions: 1.

2.

3. 4. 5.

6.

7.

Steady-stateconditions. The lubricant is an incompressible Newtonian fluid. Flow in the bearing is considered as laminar. Axial variation of temperature is negligible. The bearing is well aligned. The bearing is fully flooded with lubricant. Viscosity is a function only of temperature.

(a) Non-dimensional Figure 2 Co-ordinate systems for the analysis

hdy

Fo

=JOT =

The film pressure field was obtained by solving the generalised Reynolds equation which can be written as follows,

rhb

JOT-'

%)&

F, = johL(,, T

From assumptions 4 and 5, the simplified energy equation can be written as,

pc, (u where,

g+ 2) Y

+

= KOay" a2T rl(

$) 2

(2)

434

According to McCallion et a1 [l] (1970), for a journal bearing the velocity component in the y direction can be approximately evaluated by the following expression,

(7) At the two sides,

vzu--Y dh

hdx

Substituting this approximation into equation (2), we have,

23.2. Temperature Boundary Conditions

At the interface between the fluid film and the bush the heat flux continuity condition was used,

To predict the temperature distribution in the pressure region of the film, equation (3) was solved on the centre plane of the bearing.

At the interface between the shaft and the fluid film

In this study, the Laplace equation was used to establish the temperature field in the bush. In polar co-ordinates,it can be written as,

Jo2*~o

a2Tb aTb azTb rz-+r-+-=O ar2 ar aez

(4)

The Walther equation was used to relate lubricant viscosity to temperature with the v in CS and the T in Celsius, Ig[lg(v + 0.811= A, + By lg(T + 273)

the temperature was assumed to be constant and the no-net-heat flow condition was applied, aT aY

-dx

= 0 , and TIy=,,= T, = constant

(10)

The oil temperature at the inlet of a lobe was considered to be constant and determined by a new oil groove mixing model, which was detailed in reference [21]. The mathematical expression can be written as follows,

(5)

where, A, and B, are lubricant dependent constants. 2.2. Boundary Conditions

The above governing equations are subject to a set of boundary conditions, which can be described as follows: 22.1. Pressure Boundary Condltions

The free convection hypothesis 0.e.. natural heat transfer without forced cooling) was applied to the outside surface of the bearing and its related interfaces in the groove regions. The outside surface of the bearing was considered to be exposed to ambient conditions, thus the temperature on this surface can be determined by the following expression,

For the fluid film the classical Reynolds boundary conditions were applied, i.e., PI,‘,

=0, and

*I

=O

ax x-zw

At the inlet and outlet of a lobe the pressures were equal to the oil feed pressure over the full groove

width,

Two walls adjacent to a groove were exposed to the fresh feed oil in the groove. The temperatures on the walls were calculated respectively from the following equations:

On the inlet wall of lobe p,

435

K F j ax

x-x-

= h,(%-xw

-d

(13)

On the outlet wall of lobe p. (14)

2.3. Prediction of Temperatures in the Cavitation Region

It has been shown that the thermal behaviour of lubricant in the cavitation region is some what different from that in the pressure region of journal bearings. It has been postulated by some researchers [2] that the energy equation for the pressure region of the film is also applicable to the cavitation region if oil streamlets are considered as an effective full fdm in an accumulative width along the axial direction. However the bush inner surface temperatures predicted by solving the usual energy equation are contrary to the experimental observations in the cavitation region. The conventional thermohydrodynamic analyses predict more or less rising temperatures in the cavitation region, while the experimental evidence shows a significant drop in bush temperature, namely the temperature fade. In order to investigate this contradiction between

negligible in the cavitation regions. This postulation and explanation were detailed later by Heshmat [241 (1991) with three cavitation models. Knight et a1 [25] (1990) developed a new film rupture model called the Gas Bubble (GB) Model in order to cope with the temperature fade. It was found that much better agreement was achieved between the predictions of the GB model and the experimental data in the cavitation region. In fact, this model also implied the reduction of energy dissipation in the cavitation region. According to the authors' experience, with the consideration of heat transfer and diminution of energy dissipation in the cavitation region the predicted temperatures do decrease gradually from the rupture cavitation boundary to the outlet of a bearing lobe. However, it is not adequate and the predicted temperatures are still considerably higher than the measured results, especially for non-circuIar bearings. The authors believe that the discrepancy is mainly due to the effect of the cold oil back flow from the associated downstream oil groove. In order to cope with this discrepancy, an approximate but effective method was created by the authors to calculate temperatures in the cavitation region. This method was based upon the elemental heat balance with considerations of the mixing between the upstream hot oil and the oil back flow from the associated downstream groove. The modelling details can be found in reference [20] and will be available in due course in the learned society literature 1261.

theory and experiment, Booser and Wilcock [22]

2.4. Global Solution Procedure

(1987) examined the significance of several factors which may be involved in the temperature fa& by a simple energy rate accounting procedure. They found that three factors were principally responsible for the temperature fade: First, the recuperator role of the shaft in removing heat from hot film areas and adding an equivalent amount to cool film areas; second, the allowance for a reduction of viscous heat generation in the cavitation zone beyond that resulting from the reduced area of the streamlets; and third, heat removal via heat conduction through the bearing, The reason for the reduction of energy dissipation in cavitation regions was explained by Heshmat and Pinkus [23] (1986). They postulated that in the cavitation region most of the oil moved with a velocity very near journal speed U. Thus the principal strain occurring near the stationary surface was insignificant. Hence the power loss would be

The governing equations were nonnalised and discretized using the finite difference method. The discretized Reynolds equation was solved iteratively with the Successive-Over-Relaxation scheme. The so-called Sweep method (i.e., a modified Gaussian elimination technique) was adopted to solve the energy and heat conduction equations. In order to handle reverse flow situations, the energy equation and the heat conduction equation were solved separately with the imposition of the heat flux continuity condition at the interface. To speed up the temperature iteration process, the under-relaxation technique was employed to establish the nodal film temperature values for the next iteration cycle. For a defined external load case, the global solution procedure can be summarised as follows:

436

1. Set up the initial values and guess an

eccentricityratio and attitude angle. 2.

Calculate film thicknesses and solve Reynolds equation. With the established pressure field, the components (Fp F’) of the resultant fluid film force are computed and, if necessary, the attitude angle is updated and then the process is repeated until the following criterion has been fulfilled,

3. Solve the energy and heat conduction equations. As soon as the whole temperature field has been obtained, the shaft and mixing inlet temperatures are calculated and with these new values the solution procedure for the temperature field will be repeated until the convergence is obtained. 4.

With the current temperature values, the pressure field is updated and the entire cycle is repeated until both the pressure and temperature fields converge.

5. The vertical load support is checked against the given external load. If the relative difference between the computed load support and the given external load is greater than the assumed tolerance (0.0005), the eccentricity ratio is modified and the whole computation procedure will be repeated starting from step 2 until converged. 3. EXPERIMENTAL WORK

The experimental apparatus used in this work has been described in reference [21]. Figure 3 illustrates a schematic arrangement of the apparatus. A shaft supported on two oil lubricated rolling ball bearings was driven by a variable speed motor through a toothed drive belt. The test bearing, having two spherical seats, was seated on and in the housing. They were rested on four linear roller bearing assemblies and loaded against the journal by four hydraulic cylinders. Filtered, recirculating and

temperature and pressure maintained oil was fed to the bearing via two oil galleries located on the bearing seats of the bottom half, each connected to both grooves through two slots. The applied load was measured by monitoring the hydraulic fluid pressure to the cylinders with a pressure gauge. The rotational speed and torque were measured by transducers inserted into the drive shaft using a pair of couplings. The readings of the rotational speed, torque and power loss could be directly obtained from the associated electronic indicator. The lubricant flow was measured by collecting the drain oil with a bucket and a stop watch was used to determine the rate. The temperatures were measured by Iron-Constantan thermocouples.Those located in the whitemetal were 0.5 to 1.0 mm from the lubricant interface. Figure 4 illustrates the thermocouple locations in the bush and grooves. Most of the thermocouples was mounted on the centre plane of the bearing. A number of thermocouples were fitted in the bush along four axial lines in order to obtain the temperature variation in the axial direction and to check the alignment of the bearing. The detailed temperature information was acquired by ADCs on a VAX 8600 computer through a multiplexer unit. An elliptical (or lemon-bore) bearing has been tested. Its dimensions and the test conditions are listed in Tables 1 and 2 respectively.

Table 1: Dimensions of the bearing considered

Nominal journal diameter : Bearing length : Outer radius of bush : Angular groove extent : Average axial groove length : Clearance ratio : Preload ratio :

d=llO mm L=80 mm R2=100 mm 4=55 degrees ~ + j o mm pO.00188 m=0.5 15

4. RESULTS AND DISCUSSION

In this section, some of the theoretical and experimental results are presented and compared

431

Oiliank

He\ater

Figure 3 Schematic arrangement of the experimental apparatus

I Lower Half

Figure 4 Thermocouple locations in the bushes and grooves

438

against each other. The thermophysical properties adopted for the calculationsare given in Table 3.

Table 2: Test conditions Oil feed pressures : Oil feed temperature : Lubricant : Specific loads :

67 kN/m2 (10 psi), 48 "C I S 0 VG 32 0.2, 1.0. 2.0, 3.0, 4.0

MPa Shaft rotational frequencies :

1000,2500,4000, 5500,7000 rpm

I Table 3: Thermophysicalproperties adopted

KO=0.13 (W/m "C) h, = 100 (w/m2"C) p = 850 (ks/m3) A,= 9.455

KB=52 (W/m "C)

A,, = 55 (w/m2"c) Cp = 2ooo (J/kg "C) = -3.176

Bv

4.1. Temperature Profiles

Figure 5 (a) and (b) shows the circumferential temperature variations on the bearing centre plane for a light load of 1.694 kN @,=0.2 MPa) and with the rotational speeds of 2500 and 4OOO rpm respectively. Good agreement between the predicted and measured bush inner surface temperatures can be clearly seen. The temperature excursions in the two lobes are quite similar and small. This arises from the significant effect of hot oil carryover and the comparatively uniform film. It is noteworthy that the temperature could be maximised in the upper lobe for the light load, as shown in Figure 5 (b). At the light load, the elliptical bearing could operate with a small eccentricity and large attitude angle over 90 degrees. Thus the minimum film thickness would occur in the upper lobe and the effect of hot oil carryover become even more significant for this lobe.

Consequently, the maximum temperature occurred in the unloaded half of the bearing. Figures 6 and 7 show the centre plane bush temperature profiles respectively for a moderate load of 16.94 kN (pS=2.0MPa) and a heavy load of 33.88 kN @,=4.0 MPa) at the same speeds as presented in Figure 5. Excellent agreement between the predicted and measured results can be noted, especially in the upper lobe. Compared with those in the loaded lobe, the temperature excursions in the unloaded lobe are negligible. For these higher loads, the film might be cavitated over the whole upper lobe, thus only a small amount of heat was generated and this was almost completely removed by heat conduction. Hence the temperature remained nearly constant in this unloaded part. Moreover, unlike Figure 5 in which the inlet bush temperatures of the downstream lobe are similar to the outlet ones of the upstream lobe, Figures 6 and 7 illustrate that the bush temperatures at the inlet of the upper lobe are considerably lower than those at the outlet of the bottom lobe and very close to the feed temperature. This is because the cold supply oil dominated in the oil groove mixing. It is particularly noteworthy that a very significant temperature fade exists in the outlet region of the bottom lobe and the temperatures at the outlet of the lobe are even lower than those at the inlet for W=33.88 kN. The former may be principally caused by cold oil back flow from the downstream groove. The latter might be due to reverse flow in the vicinity of inlet. Since under the heavily loaded conditions reverse flow usually occurs in the vicinity of inlet, particularly for an elliptical bearing, this can result in a considerably higher temperature of the bush surface than that of the inlet film. Clearly, the predicted temperatures are in close agreement with the measurements not only in the inlet region but also in the outlet region of the loaded half of the bearing. In other words, the current detailed model is very effective and satisfactory in coping with the temperature fade phenomenon in the exit region. Figure 8 (a) and (b) shows the circumferential bush surface temperature distributions for the highest test speed of 7000 rpm at the light and moderate loads of 1.694 kN and 16.94 kN respectively. Obviously agreement between the theory and experiment is still fairly good.

70.0

-

Elliptical Bearing

80.0

* G 80.0 -

50.0

-

i

ki

;i"

8

40.0

r*

f

-

n X

A

.' .

30.0 80

,

I

,

I

,

'.

210

150

I

,'

.

,

270

Measured Predicted ,

330

I

,

1 .i

I.

30.0: 450

380

Circumferential coordinate (Deg.)

v

-

PI

e 50.0 I.8

6a E!

F 40.0

I

-

90

2

I

, I ,

270

I

,

I

380

450

Predicted Measured

H

B-

e 60.0

e

1' n

b

Measured Predicted

40.0

I I

330

,

&

60.0

+ I

5

270

,

A x

1

- - I !

I 210

I

Elliptical Bearing

V

A

. .

,

150

.

v

I3 ,

210

'.I

70.0

I

I

,

I

h

X

30.0:

,

Figure 6 (a) Comparison of the predicted and measured centre plane temperatures W=16.84 (kN). N=2600 (rprn), pl-67 (We). Tf=M ('C) 60.0

y

,

I

Circumferential coordinate (Deg.)

W=1.884 (W). N=2600 (rprn), pl=67 (Wa), Tf=M ('C)

. 70'01

,

150

90

Figure 5 (a) Comparison of the predicted and measured centre plane temperatures

8 00.0

1

4 */-y

v

t

Predicted

.

"

'

990

'

l

.

.

I

I

380

Circumferential coordinate (Dee.)

Figure 5 (b) Comparison of the predicted and measured centre plane temperatures W-1.684 (W). N=4000 (rpm).pl=87 (Wa). Tf=M ('C)

I

30.0

460

80

160

210

270

330

380

4

I0

Circumferential coordinate (Deg.) Figure 6 (b) Comparison of the predicted and measured centre plane temperatures W = l 6 . 8 4 (W), N=4000 (rpm), p,-67 (Wa). Tf=M ('C)

P

W

\o

P P

0

-

80.0

u

A

-

x Measured

-

E

s;80.0 ;

V

-70.0

a

-8

I

50.0

-

40.0

-

al

iI

(1

al

c.

80.0 -

Predicted

b

150

80

210

270

X

Measured

A

Predicted 4sa

380

330

Circumferential coordinate (Dee.) Figure 8 (a) Comparison of the predicted and measured centre plane temperatures

Figure 7 (a} Comparison of the predicted and measured centre plane temperatures

W=1.694 (W). N=7000 (rpm). p,=67 (Wa), T,=M CC)

W=33.88 (H),W-2M10 (rpm). p,=67 (Wa). T,-M (T) 90.0

-

80.0

V

-70.0

z

2c.

60.0

.

Elliptical Bearing

-

al

a

E 50.0 P)

L

30.0 *-O 80

150

210

b

40.0

270

330

-

30.0:

380

450

80

. ’ .

. .

I

150

I

210

.

. I .

270

I

1

I

390

I

. ,

, I .

380

Circumferential coordinate (Deg.)

Circumferential coordinate (Deg.)

Figure 7 (b) Comparison of the predicted and measured centre plane temperatures W=33.88 (W), N-4000 (rpm). ~ = 6 (kPa), 7 T,=M CC)

Figure 8 (b) Comparison of the predicted and measured centre plane temperatures H=16.94 (kN), N=7000 (rpm). p,=67 (kPa). T,=M CC)

450

44 1

4.2. Global Performance Characteristics

Figures 9 illustrates the variation of the elliptical bearing performance with specific load for a fixed speed of 4000 rpm. It can be seen that all the predicted performance characteristics presented are in good agreementwith the experiments. As might be expected, the maximum bush temperature and power loss increase moderately with increase in specific load. The variation of flow rate is interesting. For lower specific loads, the flow rate increases considerably, then decreases gradually with specific load. This is not difficult to understand, since in the lower range of loads, the film temperature rises fast with increase in load and film pressurisation exists in both lobes, consequently the flow rate will increase with load. With continuous increase in load, on one hand, the film temperature and the axial pressure gradients at the ends of the bearing still increase gradually. On the other hand, the film extent reduces very significantlysince cavitation may occur over the whole upper lobe. Hence the combined effect is that the total flow rate decreases smoothly in the higher load range. Figure 10 indicates comparison of the bearing performance over a range of speeds up to 7000 rpm for a fixed load of 16.94 kN. Again the performance trends agree well between theory and experiment though some discrepancies exist at the extreme speeds. For much higher speeds, the model predicts modestly higher maximum temperatures than the experiments. The discrepancies may result from the thermal distortion of the bush and the cooling effect of the supply oil on the outer surface of the bearing. It can be also seen that the calculated power losses are lower than the experimental data at high speeds and the discrepancies increase with increase in speed. This may be mainly due to the surface drag loss in the region of oil feed grooves. This was not taken into account in the model. Since the feeding oil contacts the rotating shaft in the groove area there will be a frictional drag and this will consume a certain amount of power, especially for the present test bearing which had a large angular groove extent (4=55 OC). According to Booser and Missana [27] (1990). the surface drag loss is proportional to the surface speed cubed. This is why the discrepancies increase with rotational speed.

Due to the higher operating temperatures predicted at the extreme speeds, the calculated flow rates are higher than the measured at the same speeds. It is clear that the maximum temperature, power loss and flow rate increase very significantly with increase in operating speed. 5. CONCLUSIONS A theoretical and experimental study of thermal effects in an elliptical bearing subjected to steadily loaded conditions has been carried out. Some of the predicted and measured results have been presented and discussed. From this work, the following important points can be obtained:

The circumferential temperature excursions in the elliptical bearing were significant and should be considered in the bearing performanceanalysis and design. The experimental evidence indicated that the axial temperature variation was small with the bush temperatures on the centre plane being slightly higher, but by not more than 4 OC, than those at the bearing edges. The experimental results showed a very significant temperature fade in the cavitation region of the loaded lobe and the numerical predictions were in good agreement with the measurements. This indicates that unlike the conventional thermal analyses, the present model can provide an effective and satisfactory tool for predicting the temperature fade in the cavitation region. This is important if thermal analysis is to be effective. The bearing performance characteristics, including the maximum bush temperature, power loss and flow rate, were affected very significantly by rotational speed and increased markedly with speed. The maximum temperature and power loss were moderately influenced by load and increased with specific load. For lower specific loads (about less than 1.5 m a ) , the

7

h

Y

100.0

v

2.5

f!

h

6.0 A

Predicted

x Yr~~ured

X

h

l=

W

-g a

2

m

70.0

h

L

0)

g 1.0

0)

a A

Predicted

0.0

1.0

2.0

3.0

g 2.0

n 80.0

a

0.0

,”

Y

1.5

4.0

0.0

Specific load (MPa)

1.0

2.0

3.0

Specific load

(a) Maximum temperature

4.0

g

50.0

=

40.0

0.0 1 .o

(ma)

(b) Power loss

Uaanved

00.0

4

% 2.0

I

A Predicted

(a) Maximum temperature

(b) Power loss

100.0 >

180’0

7

240.0

3 220.0 \

-g

200.0

v

T

$:

180.0

180.0

0 4

140.0

g

120.0

E

100.0

80.0 0.0 -

0.0

1.0

2.0

3.0

4.0

. 0.0

80.0 1.0

20

3.0

4.0

Specific load (ma)

Specific load (ma)

(c) Total flow rate

(d) Film thickness

0.0

2.0

4.0

6.0

8.0

0.0

2.0

4.0

6.0

Speed x 1000 (rpm)

Speed x 1000 (rpm)

(c) Total flow rate

(d) Film thickness

t

Figure 9 Comparison of performance characteristics of t h e elliptical bearing for different specific loads

Figure 10 Comparison of performance characteristics of t h e elliptical bearing for different shaft speeds

N=4000 (rpm), @=0.00186, pf=67 (Wa), T,=48 (‘C)

W=16.94 (kN). $=0.00188. pf=87 (Wa), Tt=48 (‘C)

P P h)

443

flow rate increased noticeably and then decreased slightly with in the higher range of specific loads.

Theory", Trans. ASME, J. Trib., Vol.106, 1984, p.228-236. [4] Gethin, D.T. and El-Deihi, M., "Thermal

The frictional power loss due to surface drag in the groove area should be taken into account in the thermal analysis.

behaviour of a twin axial groove bearing under varying loading direction", Proc. I. Mech. E., Part C, Vo1.204, 1990, p.77.

Comparison between the theory and experiment has shown an excellent agreement under all circumstances. Thus the present model has been verified and validated and can be used in the thermal performance analysis and design of elliptical bearings.

[5] Boncompain, R., Fillon, M. and Frene, J., "Analysis of thermal effects in hydrodynamic bearings", Trans. ASME, J. Trib., Vol.108, 1986, p.219-224.

ACKNOWLEDGEMENTS The research work presented in this paper was part of a co-operative project with Michell Bearings Vickers plc and the support of Mr S. Advani and some helpful discussions with Dr D. Horner are acknowledged with thanks. One of the authors (MTM) was holding a Sino-British Friendship Scholarship Scheme (SBFSS) award. The work was carried out in the Department of Mechanical Engineering of Leeds University and during the tests much help was given by Mr R. T. Harding, Mr L. Bellon, Mr A. Heald and other colleagues. All these are gratefully acknowledged.

REFERENCES [ll McCallion, H., Yousif, F. and Lloyd, T., "The analysis of thermal effects in a full joumal bearing", Trans. ASME, J. Lub. Tech., Vo1.92, 1970,p.578-587. 121 Ott, H. H. and Paradissiadis, G., "Thermohydrodynamic analysis ofjournal bearings considering cavitation and reverse flow", Trans. ASME, J. Trib., Vo1.110, 1988,p.439-447.

131 Lund, J. W. and Hansen, P. K., "An approximate analysis of the temperature conditions in a journal bearing. Part 1:

[6] Mitsui, J., Hori, Y. and Tanaka, M., "Thermohydrodynamic analysis of cooling effect of supply oil in circular journal bearing", Trans. ASME, J. Lub. Tech., Vo1.105, 1983, p.414-421.

[7] Khonsari, K. K. and Wang S. H., "On the maximum temperature in double-layed journal bearings", Trans. ASME, J. Trib., Vo1.113, 1991, p.464. [S] Tonneson, J. and Hansen, P. K., "Some

experiments on the steady state characteristics of a cylindrical fluid-film bearing considering thermal effects", Trans. ASME, J. Lub. Tech., Vo1.103, 1981, p.107.

[9] Gethin, D. T. and Medwell, J. O., "An experimental investigation into the thermohydrodynamic behavior of a high speed cylindrical bore journal bearing", Trans. ASME, J. Trib., Vo1.107, 1985, p.538-543.

[lo] Pinkus, O., "Thermal Aspects of fluid film tribology", ASME Press, 1990.

[ l l ] Pinkus, 0. and Wilcock, D. F., "Thermal effects in fluid film bearings", Proc. of the 6th Leeds-Lyon symposium on tribology Thermal Effects in Tribology, ELSEVIER, 1979, p.3. [12] Khonsari, M. M., "A review of thermal effects in hydrodynamic bearings. Part I1 : Journal bearings", Trans. ASLE, Vo1.30, 1987,p.26.

444

1131 Singh, D. V., Sinhasan, R. and Prabhakaran Nair, K., "Elastothermohydrodynamic effects in elliptical bearings", Trib. lnt., V01.22, 1989, p.43-49.

[22] Booser, E. R. and Wilcock, D. F., "Temperature fade in journal bearing exit regions", STLE, Trib. Trans., Vo1.31, 1988, p.405-4 10.

[14]Hopf, G. and Schuler, D., "Investigations on large turbine bearings working under transitional conditions between laminar and turbulent flow", Trans. ASME, J . Trib., Vol.111, 1989, p.628.

[23]Heshmat, H. and Pinkus, O., "Mixing inlet temperatures in hydrodynamic bearings", Trans. ASME, J. Trib., Vo1.108, 1986, p.23 1.

[U]Mittwollen, N. and Glienicke, J., Wperating conditions of multi-lobe journal bearings under high thermal loads", Trans. ASME, J . Trib., V01.112, 1990, p.330. [ 161

Crosby, W. A., "A thermohydrodynamic solution of the two-lobe bearing considering reverse flow at the leading and trailing edges", Wear, Vo1.143, 1991, p.159.

[17]Gethin, D. T., "Predictive models for the design of profile bore bearings", Trans. ASME, J. Trib., Vol.112, 1990, p.156. 1181 Gethin, D. T., Basri, S. B. and Mahdar, M., "Loading direction effects in a three lobe journal bearing", Proceedings of Tribology Group Meeting on Developments in Plain Bearings for ~ O S ,I. Mech. E., London, 1990, p.33. [191Cethin, D. T. and Basri, S. B., "An experimental and numerical investigation into the thermal behaviour of a three-lobe profile bore bearing", Proc. I. Mech. E., Part C,Vo1.205, 1991, p.251. [20]Ma, M-T, "Thermal Effects in Circular and Non-Circular Plain Journal Bearings", Phil Mechanical thesis, Department of Engineering, University of Leeds, 1992. [21]Ma, M-T and Taylor, C. M., "A theoretical and experimental study of thermal effects in a plain circular steadily loaded journal bearing", Proceedings of 1.Mech.E. Seminar on Plain Bearings Energy Efficiency and Design, I. Mech. E., London, 1992,p.31

"The mechanism of [24]Heshmat, H., cavitation in hydrodynamic lubrication", STLE, Trib. Trans,, Vo1.34, 1991, p.177.

[25]Knight, J. D. and Niewiarowski, A. J., "Effects of two film rupture models on the thermal analysis of a journal bearing", Trans. ASME, J . Trib., Vol.112, 1990, p.183. [26]Ma, M-T and Taylor, C. M., "Prediction of temperature fade in the cavitation region of two-lobe journal bearings", To be published in Proc. I.Mech.E., Part J, Journal of Engineering Tribology, 1994. [27]Booser, E. R. and Missana, A., "Parasitic power losses in turbine bearings", STLE, Trib. Trans., Vo1.33, 1990, p.157.

Dissipative Processes in Tribology / D. Dowson et al. (Editors) 0 1994 Elsevier Science B.V. All rights reservcd.

445

Material dissipative processes in automotive engine exhaust valve- seat wear Zuomin Liua and T.H.C.Childsb a

b

Institute of Tribology, Wuhan Institute of Technology, P.O.Box 117, Wuhan 430070, P.RChina Department of Mechanical Engineering, University of Leeds, L.eeds LS2 9JT. U.K.

A dissipative process diagram for automotive engine exhaust valve-seat wear has been developed in terms of theoretical analysis, experimental results and micro-structure observations. The diagram describes interconnection of effect of elevated temperature, impact contact stress and exhaust gas corrosion on valve-seat wear. High temperature decreases yield strength of materials , repeated cycle impact contact results in deformation and fatigue of materials, exhaust gas corrosion speeds up the extension of fatigue cracks and produces abrasive wear products. Of these, plastic fatigue damage is a main factor. In the paper, the wear law of the valve-seat is also probed in terms of a simulation wear test.

1. INTRODUCTION The exhaust valve is one of the important components in an automotive engine. Seal properties of the valve-seat directly affect the dynamic behaviour of the engine and economy of fuel consumption. However, the valve-seat operates in hard conditions. While the valve is opening, exhaust gas in the cylinder escapes by the gap between the valve-seat and seat-insert. The exhaust gas temperature is usually about 600-900 "C [l]. While the valve is closing, the valve-seat impacts its seat-insert at a high impact loading P (some researches show that P = 2 2 . 5 ~ 1 0N~for an automobile engine [2] )which is determined by the profile curve of its driving cam , and at the initial instant of the impact, a relative sliding between the valve-seat and its seat-insert occurs due to the spinning of the valve-seat spring. Under these conditions, wear and failure of the valve-seat frequently occurs. To improve service life of the exhaust valve, previous researches have mainly focused on either materials' selection or dynamics of the exhaust valve [2-51. There has been little study of dissipative process of the exhaustvalve wear. In fact, the combination of rigorous

-

a

conditions of the exhaust valve can give rise to different wear dissipative processes, such as fatigue wear or failure, or corrosion, abrasion and other mechanisms, For improving service life and developing new exhaust valve materials, it is important to appraise which are significant. In this paper, three main factors are considered for their effect on wear of the valve-seat: (1) fatigue process of the valve-seat materials under elevated temperature and high contact stress, (2) effect of exhaust gas corrosion on wear of the valve-seat and (3) effects of abrasion on wear. A dissipative process diagram to describe the interrelation of several kinds of mechanisms of valve-seat wear has been developed. Because these discussions are in terms of simulation tests and an actual engine test, the research result is beneficial for the design of valve-seat material in engineering practice.

2. EXPERIMENTS 2.1 Experiments in the laboratory The laboratory tests were carried out in a simulation wear tester. The operating principle of

Visiting scholar of Dept. of Mechanical Engineering in University of Leeds (U.K.)

446 the tester is shown in Fig.1. A driving shaft(1 1)drives the exhaust valve motion by means of cam (12), follower(l0) and tappet(9). The exhaust valve-sea (2) and its insert (3) may be heated from ambient to 800°C by the furnace (1). A strain gauge(4) on the valve stem (6) is used to measure actual loading of the valve seat force P. The valve seat force P consists of two parts. Firstly a part F, is due to the static spring loading kx, where k is the spring constant of the valve spring(5) and x,, is its precompression that can be varied by adjusting the height of the cushion(7). Secondly a dynamic part has a maximum value 8 equal to kx where X is the maximum lift of the exhaust valve and can be controlled by the driving cam (12). While the valve is being set up, the clearance 6 between the valve stem and tappet is adjusted by the tappet adjusting nuts@)between 0.4 to 0.8 mm.

Chemical compositions of the valve-seat test materials are listed in Table 1. Table 1 also records the composition of the seat-insert material. The shape of the specimens tested is the same as used in an actual automotive engine. Surface roughness of the specimens R = 0.241m, hardness HRc = 38. The wear loss is expressed by measuring the normal displacement amount Ah of the worn valve-seat relative to a standard seat-insert. Two series of tests have been performed on the simulation rig. In one, end of test wear depth after 6x105 impacts was measured over the temperature rang 100°C to 800°C, to obtain an overview of wear rate. In the other, more detailed tests were performed at 800°C. Each test was repeated three times and the mean value was taken as the final test result. After testing, the micro-structure of the subsurface of a worn specimen was analysed with S.E.M.

2.2 Experiment in an engine A group of Stellite 12 valves were set in an automobile engine for purposes of the test. After the automobile was driven about 100 thousand kilometres, the specimens tested were cut along their transverse section and their subsurface micro-structure was checked with S.E.M.The end of test wear depth was also measured.

3, TEST RESULTS AND ANALYSES 3.1 Simulation test results

Fig. 1 Schematic diagram of valve-seat simulation wear tester 1, Hot furnace. 2, Exhaust valve-seat. 3, Valve-seat insert. 4, Stmin gauge. 5, Seat spring. 6. Valve stem. 7, A&usable cushion. 8, Tappet a4usting nuts,9, Tappet. 10, Follower. 11. Shaj. 12, Cam

3.1.1 Wear law of the valve-seat Fig.2 shows an example of progression of the normal wear depth Ah of valve-seat vs. numbers of impacts N. The test were at 8OO"C, to represent a high engine temperature. Impact loads of 2010N and 2520N were chosen , also to present high engine conditions, as discussed further later. The number of impacts of 6 x los took 8 hours to perform but was still only a small fraction of the

447

estimated lo6 impacts over a typical engine life, and the high load conditions were chosen possibly to accelerate wear. Analysing the curves, it can be observed that they consist of two parts: running-in stage(1) and stable wear stage(2). In the running-in stage, wear rate is high and decreases with number of impacts. After the wear process enters the secondary stage, the wear rate keeps constant for a relatively long period which depends on operating conditions of the valve-seat. Therefore, by analysing the wear process in the stable wear stage 2, dissipative mechanisms of the valve-seat wear can be effectively discussed.

0.0

1.0

2.0

S.0

4.0

6.0

8.0

IMPACT NUMBER ( X losN)

Fig.2 Wear process curves of valve-seat (Materials: Stellite 12. Service conditions: Impact frequencyf = 201s. operating temperature 800 T)

subsurface after 6 x los impacts at 8OOOC. Because the contact stress is impulsively exerted on the contact surface, a high strain rate in the contact region occurs. Higher strain rate will result in serious plastic damage of materials, even intense slipbands occur [7]. Fig.4 shows a micrograph of valve-seat wear. Cross slip bands in the micrograph indicate that the impulse force causes fully plastic conditions on the contact surface (although the depth of the plastic zone is only about 30 pm). As a result of this plastic flow, grain boundary energy may be increased, to favour precipitation of elements there.

3

-

0

100 200 $00 400 6 0 0 600 700 800 000

-

> TEST TEMPERATURE ("C) Fig.3. Curves of wear rate vs. operating temperature (Test conditions: Loading P = 2520N, Number of impacts 6 x I @ . Impactfrequencyf = 20h)

3.1.2 Effect of temperature and material strength on wear The effect of temperature on wear is shown in Fig.3, in which the end-point wear after 6 x lo5 impacts is recorded from 100°C to 800OC. Data is shown for the tool steel 2 1-4N material (curve B) as well as Stellite 12 (curve A). It can be seen that Stellite 12 wears less. Curves C and D are respectively the 0.2% yield strength curves of 214N and Stellite 12 [6]. Observing figure 3, it is evident that there is an inverse relation between wear rate and yield stress. 3.1.3 Dissipativeprocess of the valve-seat wear

Scanning electron microscope metallographic studies have been made of the Stellite 12 valve-seat

Fig.4 Micrograph cross-slip deformation of subsurface of contact zone Material: Stellite 12.) (Test conditions: Number of impacts 6 x 10'. Loading P=201 ON,

Impactjrequency f = 20h)

448

On the other hand, high temperature also changes the stability of the micro-structure. In particular, during its manufacture, the exhaust valve is heattreated, to enhance wear and corrosion resistance, to create uniform and fine carbides (e.g. Cr2C3 and Cr& ) in micro-structure. Under high temperature and high contact stress, these microparticles can diffuse again toward these high energy interfaces. Figure 5 shows the distribution of carbon along a line-scan through a slip-band region. Peaks in figure 5 are a result of dissolution of fine carbides in the microstructure and their precipitation again to form larger carbides. Figure 6 is a magnified view of part of figure 5 , focusing on a region of carbon peaks. It shows examples of such precipitated carbides. Obviously this change of microstructure will reduce wear resistance.

crystal boundaries. This would speed up the fatigue process of deformed material. Because the corrosion process needs a relatively longer period than wear, it is not easy to assess its effect in a simulation test in the laboratory. However, observation of the micro-structure of a worn section of a valve-seat from an actual engine test shows the effects of exhaust-gas are great. Fig.7 is a section through the subsurface of a valve-seat. It can be observed that grains in the micro-structure have plastically deformed and the deformed degree gradually become weaker from the surface toward substrate, and that microcracks exist along boundaries of these grains, and that some fatigue wear particles exist in the path of the cracks.

Fig.6. Carbides separated out in slipdeformation process (Test conditions are the same as in Fig..?) Fig.5. Carbon wavelength spectrum analysis of the deformed section (Test conditions are the same as in Fig.4)

3.2 Real engine test results 3.2.1 End-point wear depth After lOO,OOOkm, Stellitel2 valves were removed from an engine. Their wear depth was measured to be between 0.5 and 0.65mm. 3.2.2 Metallographic studies While an automotive engine is operating, exhaust gas passes through the gap between the valve-seat and its seat-insert. Some unburned matter in the exhaust gas will deposit on the contact surface of the valve-seat, elements such as Pb and C1 have a strong activity. They would penetrate any surface film, and migrate to the surfaces of deformed

Fig.7 Micrograph of fatigue cracks of worn subsurface of exhaust valve-seat in an actual engine (Material: Stellite 12. Opemting distance 100,000 hl).

449

Fig.8 Energy spectrum elements of wear micro-particle of exhaust valve-seat in an actual engine (Material: Stellite 12. Opemting distance 100,000 km.)

Obviously, the topography reflects both dissipative processes of corrosion and fatigue wear of the exhaust valve-seat. If we analyse these wear products (as shown Fig 8), it is found that in these products there are high concentrations of C1 and Pb which originally exist in petrol , as well as Cr and Co which originally exist in grain structure of the material. It is evident that entering of these corrosive materials into the fatigue cracks accelerates the wear process of the valve-seat material. Table2. Elemental compositions of a fatigue

Abrasion of the frictional surface between the valve-seat and its insert may also result. It could occur in two ways: from unburned matters in petrolldiesel and fatigue wear debris of material of the valve-seat or its insert. The latter plays a very important part in acceleratingthe valve-seat wear.

Generally, the fatigue wear debris from alloy materials contains some alloy elements such as Co and Cr. Table 2 is the elemental composition of micro-wear particles in Fig.8a. We can see that in these particles the amount of elements Co , Cr ,Pb and C1 is higher, and that the shape of the particle is a ball. This shows that forming of the abrasion is a result of a combination action of fatigue and corrosion. It is possible that, after these fatigue wear particles enter the frictional surface and being further oxidised at high temperature, the particles will become hard and abrasive and contribute to wear of the valve-seat. This also shows that the abrasion accelerating the valve-seat wear partly comes from fatigue wear debris of the material of the valve-seat.

4. DISCUSSION 4.1 Wear rate and contact stresses The wear depth from the engine test after 100,OOkm

450

was from 0.5 to 0.65mm, that from the simulation test at a load of 20210N was 0.085mm after 6 x lo5 impacts. Extrapolation of the linear wear rate in the simulation test to lo8impacts(the estimated number in the engine test) gives a wear depth of 5 to 6 nun, some ten times greater than observed. The simulation test, at two loads, however, shows the wear rate to be sensitive to load raised to a power greater than one. Part of the greater wear depth in the simulation than the engine test is a result of greater loading in the simulation test.

have produced a much lower wear rate, and further work is planned at lower loads. In terms of its geometry of contact between the valve-seat and its seat-inserts, the force P can be resolved into two components: normal N and tangential T (as shown in Fig.9). Because the seat-insert is fixed into the top of the cylinder, it has no normal displacement. If elastic deformation of the valve stem is ignored, the effect of the T force on wear of the valve-seat can be ignored. Therefore, only the normal component N of the P force is considered as causing a contact pressure stress resulting in wear of the valve-seat. If we consider the contact region and ignore the change of the contact width B during wear, the normal contact stress a,,canbe written: K d .P c o s a a, = (2) An

Fig.9 Contact state between valve-seat and seatinsert. While the exhaust-valve is closing, the valve-seat impacts its seat-insert with an impulse seat force P, The force theoretically consists of a static spring force F, (=kq)and a dynamic spring force Po . However, P changes with the increase of the valve clearance 6 which will increase with wear between the valve stem-top and tappet-top. Therefore, a dynamic loading factor I& should be introduced: p~~vol = Kd * (1) A test result shows that at a running speed of 1200 r.p.m, when the valve clearance 6 is 0.4 mm, a dynamic load set is P = 2010N. However, when 6 is adjusted to 0.8mm, the dynamic load set is increased between 1.8 and 2.2 times (up to between 3620N and 4400N, i.e. I(d = 1.8 2.2, Pac&d= (1.8 2.2) x 2010N). The values of I(d in simulation test, in fact, is approximately consistent with measurement value in actual engine[2]. At the same time, variation of 6 through the life of the engine would have caused to vary between 800 lOOON(6 = 0.4mm) and 2000 - 2500N(6 =0.8mm). The load in the simulation test may have been up to 2 times as high as that in actual engine. Inspection of figure 2 suggests a lower load would

-

-

-

where An = Id)B--- normal contact area, D is the diameter of the valve head and a is the taper angle of the valve seat. For the present test, D = 38mm, B = 1.5mm and a = 45". Taking P = 2010N and Kd = 2 gives a,,= 16I"a. The yield stress of Stellite 12 at 800°C is 280MPa (figure 3). It is therefore clear that the plasticity observed in figure 5 is associated with real contact area, asperity, stresses and not with bulk overloading. This is consistent with the depth of the plastic zone, 30pm, in figure 2. It is therefore strange that wear rates in the simulation tests (figure 2) are loaddependent to a power greater than one, as contact statistics[7] would suggest that wear be proportional to load. The results indicate that the running-in process is important in conditioning the surface state of the valve seat, and that is another reason for further work at lower loads.

4.2 Microstructural observations However, the simulation tests do compare with the real engine tests in showing precipitation of carbides in slip-bands .They focus attention on the interaction of high contact stress and temperature in causing element solution and precipitation to change the microstructure, and hence to influence wear resistance through reduced yield strength and changed fatigue wear resistance . The engine test in addition focuses attention on the role of exhaust gases in causing corrosion and further changing the composition of the micro-structure.

45 1

Fig. 10 Dissipative diagram in automotive engine valve-seat

4.3 A dissipative process diagram On basis of the discussion above, it is evident that high temperature reduces yield strength of the valve-seat materials so that plastic deformation occurs at the surface or subsurface of the contact zone under high contact stress, and that corrosion accelerates the fatigue process of the deformed material and that hard particles of the fatigue wear debris provide abrasion of the frictional surface. Thus, we can deduce a dissipative process diagram of the valve-seat wear. By the diagram(as shown in Figlo), a mutual connection among various mechanisms in exhaust valve-seat wear can be seen to exist. Their relative importance and interactions are the subject of continuing study.

5. CONCLUSIONS 1. A dissipative process diagram in automotive engine valve-seat wear has been developed on the basis of simulation wear tests and analysis. The diagram effectively describes the effect of contact stress, elevated temperature and exhaust gas on dissipative processes of the valve-seat wear. 2.High temperature decreases yield strength of valve-seat materials so that the wear rate of the valve-seat decreases with increase of the temperature. 3.During the dissipative processes in the valve-seat wear, deformation fatigue is a main factor. High

temperature and corrosion of the exhaust gas accelerate the fatigue process of materials. The fatigue wear debris provides abrasion for the contact surface between the valve-seat and its insert.

REFERENCES 1. C.F.Taylor, Internal combustion design" 1977 V01.2 $521-575. 2. K. Akiba and T. Kakiuchi "A dynamic study of engine valve mechanisms: Determination of the impulse force acting on the valve" SAE 88 0389. 3. T. Kurisu, K. Hatamura and H. Omoti "A study of jump and bound in a valve train" SAE 91 0426. 4. C.B. Allen. J.L. Sullivan and T.F.J.Quinn,"The wear of valve-seat materials at elevated temperatures" Tribology of reciprocating engines 1982 ~279-284 5. Y. Hagiwara, M. Ishida and T. Oh, "Development of Nickel-base super alloy for exhaust valves" SAE 91 0429. 6. American Society of Metals, 'I Metals Handbook" 8th edition 1961 Vol. 1 p666 7. S.P. Bhat and C. Laird, I' Cyclic stress-strain response and damage mechanism at high temperature" ASTM Stp 675 1979 p592-623 8. J. F. Archard, "Theory and mechanism of wear" Wear control handbook 1980 p35.

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Dissipative Processes in 'l'ribology / D.Ilowson et al. (Editors) 1994 Elsevier Science I3.V.

453

Thermal Matching of Tribological Systems by A. V. Olver Department of Mechanical Engineering, Imperial College

When there is si@cant sliding or other dissipative processes present, simplistic application of the elastohydrodynamic film thickness regression equations can be highly misleading. This paper describes a simple model which seeks to predict and account for the consequent temperature rises. The case of a twin-disc machine and that of a high-speed spur gearbox are examined and the results compared with earlier measurements. 1. Introduction: Macrotribology

It is rare for the mechanical conditions in a rubbing contact to be independent of its environment. More commonly there is a dynamic interaction such that the conditions within the contact affect those in its surroundings and vice versa. Examples of this interaction may be found in such diverse phenomena as lubricant supply, debris transport and heat flow and often have the capability to alter radically the practical outcome. This can lead, for example. to a poor agreement between simple test machines and real equipment. In the present paper. the thermal behaviour of some elastohydronamic systems is modelled and the results compared with earlier experiments. 2. Thermal Model

It is, of course widely recognised that elastohydronamic lubrication is highly sensitive to temperature. Film thickness, for example, depends on inlet viscosity which depends on surface temperature. However, film thickness itself affects friction which affects heat generation, bulk temperature and hence inlet viscosity. The contact cannot be considered in isolation; a thermal model of the whole system is necessary. Such a model is presented here and has the following components:

- a conventional ehl model based on disc or gear kinematics and an appropriate

film thickness regression equation, - a traction model based on measurements carried out in a controlled test. - a partition theorem which allows the calculation of heat input to each component in the set notwithstanding its (different) bulk temperature, a conduction and convection model of heat transfer, - a simple treatment of windage and friction - an iterative solution method which allows compatible values of traction, temperature and film thickness to be found.

-

This model is identical to that presented in (1) except that here we introduce the traction model of Bair and Winer (2) in order to predict the coefficient of sliding friction. Details of this and some other aspects of the model are given in appendix 1. The key concept is that the heat partition, determined from Jaeger's theory of moving heat sources is applied, not just to the determination of the flash temperature, as by Blok (3), but also to the steady state heating of the body. T h s enables the calculation of the surface temperature of the disc or gear tooth under the (realistic) circumstances of sigrufcant frictional heating. In order to apply the method to gear pairs, some additional steps are necessary. Firstly the excess of the ambient temperature, T,, over the oil supply temperature, To,,. is calculated from the theories of windage (4) and churning (5,6) and knowledge of the oil flow rate and heat capacity.

454

Figure 1. Comparison of the predictions of bulk temperature TB of rubbing discs with the measurements of reference 7.

Heat generated by other sources, for example bearings is neglected; this is considered justifiable on the grounds that tooth temperature is not greatly affected by heat from the bearings (or vice versa) but again some caution may be advisable if, for example, hot oil from a bearing installation can impinge upon the gearset. Next, the parWion of heat between the two gears is found using the modified Jaeger method. Because the contact between the gears involves a cyclic meshing action, it is necessary first to find an average heat partition coefficient,a,, for the whole cycle. This is used to find a mean tooth temperature, TB, and contact temperature, Tc, the latter varying throughout the mesh. At each stage, the necessary iteration to find the local friction coefficient is carried out, noting that this is itself a function of the mean contact temperature. Details of the method are given in appendix 2. 3. Results: Disc Machines

Some predictions of the model are now given and compared with temperatures measured in earlier experiments. Because the novel part of the calculation is that associated with prediction of the inlet (or 'skin') temperature,TB, we shall first concentrate on measurements of this quantity. Paliwal and Snidle (7)have made extensive measurements on their disc machine using embedded thermocouples.

Figure 1 shows an example of their results together with the predictions of the present model. The operating parameters and the assumed material and lubricant parameters are given in the tables in appendix 3. It is noted that the faster disc of the two is the hotter because it absorbs a larger proportion of the frictional heat, this effect being greater than that of its higher convective heat transfer coefficient. Overall, the measured temperature rise is within about 10Y0 of the predicted value, the main error being in the prediction of the friction coefficient, which nevertheless shows a similar qualitative trend with applied load. Predictions of the behaviour of a smaller, higher speed, disc machine are shown in figure2 which shows the contact, and skin temperatures, film thickness and friction coefficient as a function of applied load. The discs are rotating at a speed of 10000 and 20000rev/min respectively and the other parameters are given in appendix 3. Increasing the load beyond a critical value c a w s the friction coefficient and temperatures to rise sharply, while the film thickness declines to a low value. This occurs because the declining film thickness causes an increase in the friction which in turn increases the inlet temperature causing the film to become yet thinner. An instability results which in its main features (temperature and friction rise and loss of film)bears a striking resemblence to the phenomenon of scuffing.

455

1800 IWJ

14m 1ZUI lm,

800 Bm Qo

am 0 0

91)

lm,

l r n a m a a s x a Mill

Figure 2. Predictions of maximum contact (T(C)) and skin (T(B)) temperature, Jilm thickness (expressed as a lambda value), and friction coeflcient (Mul for a small (19 mm diameter) disc machine For details see appendix 3.

Figure 3. Predictions of temperature, Jilm thickness (expressed as a lambda value), and friction coeflcient for the disc machine ofJigure 2, but running at higher speeds (see tex?).

Figure 3 shows the same prediction with the speeds increased to 15 0oO and 30 OOO rev/min. In this case the instability is still present but of lower severity. This is because the the rate of change of viscosity with temperature is lower at the higher temperature and the higher speed makes continuing elastohydrodynarmcsupport easier. Photographs of discs run under these conditions are shown in figures 4 and 5.

The higher speed test does indeed result in a less severe failure; because of the absence of a marked friction increase, the test was continued resulting in wear rather than d n g as was the case at the lower speed. The predictions of failure load are quite inaccurate but this is not unexpected as the model in its present form does not recognise the possibility of boundary lubrication.

456

Figure 4. Photograph of discs run under the conditions offlgure 2.

Figure 5. Photograph of discs run under the conditions ofjigure 3. 4. Results: Gears

Next, the temperature predictions of the model are compared with measurements taken with thermocouples embedded in high speed spur gear teeth. The results of Mizutani, Isikawa and Townsend (8) were used for the comparison and are distinguished for being unusually thorough in their provision of the background data needed for the modelling. Figures 6(a) to (d) show the effects of operating (pinion) speed and (wheel) torque on temperatures, mean friction coefficient and minimum lubricant film thickness (expressed as a lambda value) in the high speed spur gearbox of Mizutani & al. Throughout the useM operating range of the gearbox the film

thickness is highly sensitive to torque but relatively little affected by speed. This again is because of the thermal effect on the contact inlet. The temperature increase diminishes the beneficial effect of speed and greatly adds to the detrimental effect of torque. The tooth temperatures are compared with the experimental results in figures 7 and 8. The closeness of the agreement is almost certainly fortuitous in view of the uncertainties in the analysis. The predicted friction coefficients (figure 6d) differ somewhat from those given by Mizutani & al. but these are believed to be unrealistically low, having been derived by an indirect method.

457

Figures 6a and 6b. Predictions of maximum contact temperature (top) and pinion tooth temperature in the gearbox of reference (8).

458

Figures 6c & 6d. Predictions ofpiction coeflcient (top) and lambda value in the gearbox of reference (8).

459

55

-

50

Pinion

45

---- wheel

0

P

U \

2 40 a E 35

Oil

1.1.1.-

CI

L! f

Pinion

*

30

I-

25

I

20 4 2000

55 6o

d,

U \

x a, L

Wheel

Oil ,

4000

I

I

6000 8000 Speed I rpm

10000

12000

T

9.66

---- 19.32

501

-.--..28.98

45

- - - - -38.64

(D L

E

48.3

,!! 30 20 25

48.3

i 35

A

0

2000

4Ooo

6oOo

8Ooo

loo00

12000

O

2

Speed I rpm Figures 7 & 8. Comparison of the predicted temperatures in a test gearbox with the measurements of reference (8). figure 7 (above)shows the pinion, wheel and oil temperatures as a function of speed at a wheel torque of 196 Nm and an oilflow of 35 ml/s. Figure 8 (below)shows the eflect of varying the oilflow rate. The line plots are the theoreticalpredictions and the discrete points the measurements; the units of oil flow rate are ml/s.

2

460

5. Discussion and Conclusion

Useful application of ehl in situations such as those encountered in gearboxes. where significant dissipation occurs requires a unified thermal model of the type presented.

of Concentrated Contacts'. National Aeronautics and Space Administration. Wa~hington.D. C.. U. S. A.. 1970. 153-248. 4. P. H. Dawson. Windage Loss in Larger.

High Speed Cears. Proc. lnstn. Mech. Engineers London, 198 (1984) part A No.1

Results show that a simplistic application of the ehl regression equation can be misleading; for example the film thickness is seen to be highly dependent upon load (torque in the gearbox model). In addition a wide range of Merent thermal characteristics exist, some situations involving a rapid increase of skin temperature with load (e.g. the discs of figures 2-6) whde others show high contact severity (high T(:) with little bulk heating. The presence of the singularity, which is a consequence of rapid bulk heating and specific traction behaviour, suggests that some smaller test machines could fail in ways that larger equipment might not. Some of the well known discrepancies between different lubricant test methods - many of which are dependent on small and hence rapidly heating test components - might be related to this. The analysis presented here enables tests to be thermally as well as kinetically matched to the application they are intended to simulate. RReferences. 1. A. V. Olver. Testing Transmission Lubricants - the Importance of Thermal Response. Proc. Instn. Mech. Engineers London, 205 part G (1991) 35-44.

2. S . Bair and W. 0. Winer, Regimes of Traction in Concentrated Contact Lubrication, Trans. Am. SOC. Mech. Engineers, J. Lub. Technol. 104 (1982) 382-391. 3. H Blok, The Constancy of Scoring Temperature. in P. M. Ku (ed.) 'Interdisciplinary Approach to the Lubrication

51-59. 5. R. I. Boness. Churning Losses of Discs and

Gears Running Partly Submerged in Oil. Proceedings of thc 1989 International Power Transmission and Gearing Conference. Chigago, U. S . A.. Am. Soc.Mech. Engineers (1989). 355-365. 6. N. E. Anderson and S. H. Lowenthal, Design of Spur Gears for Improved Efficiency, Am. Soc. Mech. Engineers. I. Mech. Design, 108 (1986) 767-774. 7. M. C. Paliwal and R. W. Snide. Runninginand Scuffing Failure of Marine Gears, University College, Cardiff, Report for Ministry of Defence, Contract No. D/ER1/912072/045. (1987). 8. H. Mizutani, Y. lsikawa and D. P. Townsend, Effects of Lubrication on the Performance of High Speed Spur Gears, Proceedings of the 1989 International Power Transmission and Gearing Conference. Chigago, U. S. A., Am. Soc.Mech. Engineers (1989), 327-334.

9. D. Dowson. G. R. Hiwnson, J. F. Archard. and A. W. Crook. Elastohydronamic Lubrication, Pergamon, 1966. 10. Anon.. ASTM Standard D341, Appenlx X1, American Society for Testing and Materials (1977). 11. R C. Gunther, Lubrication, Bailey Brothers and S W e n (1971) 141-142.

46 1

Appendix 1

friction and u the s p e d of the surface mlative to the contact.

(a)Heat Transfer The contact temperature is given (1) as:

Expressions used for M here are now given. For results in figure 1 the 'radial' approximation was used:

= TA+ A T , +AT,

1/ M = l/MWd+l/Mdiscwhere where, for body 1 of a pair:

(AT,), =aQ(l.GOB,) and

M,, = (27dUh)-'and MhC= (8.88(hk)112 I 112R x I, (nR)/ I,,(nR)]-'

where the frictional heat generated, Q, is given by:

a is the proportion of heat going into body 1 and is given by:

where R is the radius. f the track width, I . and I, are the appropriate Bessel functions and n = (2h/ kf)'" For the results relating to figures 2-6, where the geometry is shaft-like as opposed to discl i e , the 'axial' approximation (1) is used:

a=(l.06B2+ M 2 )

+ {1.06(B,+ B , ) + ( M , +M2)) Here, the quantitiesB and M are the transient and steady state thermal compliances of the two bodies where:

Mhc = (4.44(hk)"2R3I2 x (tanhmL, + tanhmL,))-' where m = (2h/ kR)'".

B = (11 A k ) ( X b l U )

h, the convective heat transfer coefficient, was

and M, defined for the two bodies by:

b) Film thickness

must be calculated for each body from a suitable steady-state heat transfer model. x is the diffusivity, k the conductivity and b and A the contact area and width respective1y.W is the total load, and p the coefficient of slidmg

found by the method given in (1).

The Dowson-Higginson film thickness equation (9) was used together with the ASTM kinematic viscoSity relation (10) and an empirical relation (11) for the variation of density with temperature. c) Traction The fiiction coefficient, following Bair and Winer (2) is given by

462

where ,fqis the friction at 0 OC,A is the ratio of film thickness to composite (rms)roughness and Tea"is thc mean contact temperature. The constant C1 is taken, using the data of (2) for esters as unity and is given in appendix

c2

3.

d) Solution An iterative solution method was used to obtain consistent values of friction coefficient, temperatures and film thickness. The iteration was terminated when successive values of p Wered by less then .0005.

Appendix 2 Application of the model to gear pairs. The average heat parbtion coefficient, Orav is first found by stepping through the entire mesh, and applying the method of appendix 1. The local heat partition is now found by the following which accounts for the mean tooth temperature being held constant:

a=I%f4-am(4+M2) + 1.06B,} / 1.06(B,+ B, ) where &is the ratio of average, to instantaneous, heat generation. The radial approximation (appendix 1) was used to find the M's, the value of hfpd being modified for the increased peripheral area due to the teeth. In order to estimate the local ambient temperature relevant to the gears, the assumption is made that half the windage and churning energy and all that due to friction, is trwsfqqed to the oil prior to lubricating the gqq. Jp practice, it is accepted that th~smay yqy pn$jderably.

463

Appendix 3. Data for disc machines; Figure 1:top;Figures 2-6: bottom

Speed of Slow disc , rev/min, ratio of disc speeds Oil supply temperature, deg C Radii of slow, Pst, disc,m Shaft lengths, m Track width, m Plane Strain Elastic Constants JY(1 4 ) : fast, slow disc Pa Thermal Conductivity of fast, slow disc, W m-1 K-1 Thermal Diffisivity of fast, slow disc, m2 s-l ASTM viscosity constants of oil: A, 8,Density at 60 deg F, g cm-3 Alpha value at 0, 100 deg C, GPa-1 Composite RMS Roughness, m. Friction coefficient at 0 deg C, rate of change with film temperature, deg C-1 Specific heat capacity of lubricant, J K-1 kg-1 Thermal conductivity of lubricant, W m-1 K-1 Speed of Slow disc, revhin, ratio of disc speeds Oil supply temperature, deg C Radii of slow, fast, disc,m Shaft lengths, m Track width, m Plane Strain Elastic Constants E/(l-vz): fast, slow disc Pa Thermal Conductivity of fast, slow disc, W m-1 K-1 Thermal Difisivity of fast, slow disc, m2 s-1 ASTM viscosity constants of oil: A, B, Density at 60 deg F, g cm-3 Alpha value at 0, 100 deg C, GPa-1 Composite R M S Roughness, m. Friction coefficient at 0 deg C, rate of change with film temperature, deg C-1 Specific heat capacity of lubricant, J K-1 kg-1, Thermal conductivity of lubricant, W m-I KI

485.1. 3.0 45 0.038125,0.038125

(radial approximation used) 0.0047625 2.2X10~~,2.2XlO~~ 35.4, 35.4 8.56x104, 8.56~1 0" 24.661, -4.0313, 0.895 20, 14.6 0.925~10~ 0.06, 0.00010 2040, 0.138 10 000,2.0 75 0.0095, 0.0095 0.046, 0.046, 0.042, 0.042 0.00I 87s 2.2X10~~,2.2XlO" 35.4, 35.4 8 . 5 6 lOd.8.56x10-6 ~ 22.525, -3.6425, 0.995 14.9, 10.9 0.925~10" 0.025,0.00020 2040 0.138

Appendix 3 continued: Data for gearbox

Tooth numbers: Pinion, wheel Oil supply temperature, deg C Centre distance (C. D.), m, Tip Radi2C.D.: pinion,wheel. Root Radi2C.D: pinion, whee Nominal Pitch Radius/C.D., Effective Facewidth/C.D., Nominal Pressure angle (deg) Plane Strain Elastic Constants E/( I-v2): pinion, wheel, Pa Thermal Conductivity of pinion, wheel, W m-I K-1 Thermal Diffisivity of pinion, wheel, tn2 s-1 ASTM viscosity constants of oil: A, B, Density at 60 deg F, g cm-3 Alpha value at 0, 100 deg C, GPa-1 Composite R M S Roughness, m. Friction coefficient at 0 deg C, rate of change with film temperature, deg C-1 Specific heat capacity of lubricant, J K-I kg-1, Oil jet flow rate, m3 s-1 Thermal conductivity of lubricant, W m-1 KI Wheel Torque ,Nm, Pinion Speed,rev/min

40,77 28 0.1753, 0.36337. 0.67992 10.3171I , 0.65476 0.3423,O.14261, 20 2.2x1011,2.2x1011 35.4, 35.4 856x10". 8.56~10" 26.3883, -4.3756, 0.895 20, 14.6 5x 10" 0.06, 0.00010 2040,0.0000483 0.138 500, 12000

This Page Intentionally Left Blank

Dissipative Processes in Tribology / D. Dowson et al. (Editors) 0 1994 Elsevier Science B.V. AU rights rescrved.

465

POWER LOSS PREDICTION IN HIGH-SPEED ROLLER BEARINGS D. NELIAS*, J. SEABRA**, L. FL,AMAND* and G. DALMAZ*

*

**

-

INSA de Lyon - Labratoire de M M q u e des Contacts CNRS URA 856 - BAt.113, 20 Av. A. Einstein, 6962 1 Villeurbanne Cedex, France CETRIB Departamento de Engenharia Mecanica e Gestao Industrial - Faculdade de Engenharia da Universidade do Porto, 4099 Porto Codex, Portugal

-

ABSTRACT

Friction between the various elements in a rolling bearing results in power loss and heat generation. Therefore, an estimation of the rolling bearing power losses is necessary to refine lubrication techniques and to optimize machine component design. A new model which predicts and locates power losses in a high-speed cylindrical roller bearing, operating under purely radial load, is presented. Its new features come from the consideration of both cage action and the effect of lubricant film thickness in the computation of bearing kinematics at equilibrium. Lubricant rheological properties are used in order to calculate hydrodynamic and elastohydrodynamic forces in each lubricated contact. This model considers cage and roller kinematics to be unknown. These are obtained by solving the equations of motion for each bearing element. The computation and the location of power losses are given by the friction forces and the sliding speeds among the various bearing elements, i.e., contact between roller and inner or outer ring, roller edge-raceflange, roller-cage pocket and cage-ring pilot surface. The authors compare first the values of the calculated power loss with experimental data to assess the program's predictive capability. AJenvards the model is used to estimate and locate power losses in a welllubricated high-speed roller bearing. Results show that the total power loss varies strongly with the rotational speed, the lubricant inlet temperature and the oil flow through the bearing. Nevertheless, it is less sensitive to radial load Power loss results are also given as a function of the bearing internal geometry. NOMENCLATURE CC Friction torque between roller ends and cage pocket CE Friction torque between roller ends and race flanges DM Bearing pitch diameter DR Roller diameter Ei.2 Elastic modulus F Traction force between roller and raceway FC Centrifugal force acting on the rollers X I ,Traction Z force at the roller-cage pocket contact E?? Traction force between roller ends and race flanges FOL Oleo dynamic drag force acting on the rollers FR Applied radial load h Elastohydrodynamiclubricant film thickness at the roller-ring raceway contact H J , ~Roller position in the cage pocket JCC Roller to cage pocket circumferential clearance JD Bearing diametral clearance I Contact length Q Normal load between roller and raceway

QC Hydrodynamic normal load at the cage-ring contact QCJ,ZNO load ~ at the roller-cage pocket contact x Angular direction of the normal load at the cagering contact E Cageeccentricity S Roller-raceway contact deformation Sr Radial deflection of the bearing # Cage attitude angle (short journal bearing effect) v1.2 Poisson's ratio w Rotationalspeed wc Cage rotational speed wr Roller rotational speed 5 Angular location of the cage center (gq+@ ty Roller angular location

Subscripts Referstoherring Refers to outer ring Refers to roller number j

,-

,

466

1.

INTRODUCTION

It is commonly known that lubrication in rolling bearings prevents metallic contact, reduces friction and wear of interacting elements, and serves as a coolant by evacuating heat dissipated inside the bearing. Lubricant film thicknesses which separate friction surfaces range usually from micrometer up to tenth of millimeter. That means that the amount of oil addressed to a bearing mainly has a cooling function. Over recent years the operating environment in engines has become increasingly severe. The lubricant supply has therefore become increasingly important for its cooling function. Oil flow rates need to be high to achieve the desired temperatures and thus lead to excessive parasitic thrashing and churning of the oil before it is scavenged from the chamber. Furthermore, the oil flow to the bearing which was adequate when the emphasis was on provision of lubricant, is not at all appropriate when the cooling aspect becomes so important. Simple empirical expressions have been developed in order to give the overall bearing heat generation in terms of load, speed, lubricant supply, etc. However they do not identifj the distribution of heat generated among the various dissipative mechanisms as the parasitic churning and the contact between roller and raceway, roller-cage pocket and cage-ring pilot surface. Experience has also shown that such empirical rules cannot be applied to applications that require extrapolation sigmfkantly beyond the boundaries of the actual test data. The present, unsophisticated method of throwing more lubricant at the bearing to achieve a few degrees temperature reduction increases oil heating and leads to oversized and overpriced engine oil systems (oil mass, oil tank, exchangers, filters, pumps). It is clear from this analysis that it is advantageous to reduce the oil flow to the bearings, with associated benefits on oil system components. Most bearing users and manufacturers still estimate rolling bearing performance from 1960's and 1970's approaches, based on Harris' work [l], without taking into account kinematic effects of force balance in the bearing or recent progress in hydrodynamic or elastohydrodynamic lubrication.

These ball and roller bearing calculation methods remain helpful to establish general trends in a parametric design study, but do not accurately predict or locate the power losses of a welllubricated high-speed rolling element bearing. Since 1970, a few attempts have been carried out in order to evaluate the internal kinematics [24] or the heat generation (7-121 in oil lubricated roller bearings. In this field, the studies based on computer programs, such as Cybean [6], Shaberth [8] or Adore [ l l ] can be noted. They point out that the energy dissipated depends clearly on the lubricant drag forces and churning moments due to the substantial quantity of oil present in the bearing cavity. Shaberth software is capable of steady state and transient thermal analysis of shaft and rolling element bearing systems whereas Adore deals with the dynamics of rolling elements. However, the lack of knowledge about the equivalent density of the oilair mixture present in the bearing, implies that only a first approximation to the actual losses can be made. More recently, Chittenden [13] and Ndlias [14,15] have shown the internal bearing kinematic effects on the estimated power loss and its location for ball bearings. Furthermore, since the internal kinematics depends on the amount of lubricant in the bearing, it is not correct to separately study bearing cage slip and heat generation. We present here a new roller bearing model, including hydrodynamic and elastohydrodynamic lubrication analyses. It predicts and locates power losses in a high-speed cylindrical roller bearing, operating under purely radial load and oil lubricated. Rheological properties of the MIL-L23699 type lubricant are given by Houpert [16], Gupta et al. [17] and Ndlias et al. [IS]. An empirical model for the windage torque acting on the rotating element, constituted by both the cage and the rollers, is proposed. Other sources of energy dissipation are evaluated and located from the friction forces and the sliding speeds between the various bearing elements, including roller-raceway, roller-cage and cage-ring contacts. 2.

ROLLER BEARING MODEL

A comprehensive quasi-static model which provides a simulation of the heat generation in a

467

roller bearing is reported here. More details are given in reference [19]. The quasi-static model basically consists of the formulation of the geometrical relations and the equilibrium equations for the various roller bearing elements. The different assumptions are presented and the contact loads are identified. The force and moment equilibrium equations for each bearing element and the geometrical relations are presented. Finally, the algorithm developed to simultaneously solve the equilibrium and geometrical equations is discussed. 2.1. Rheological Behaviour of Non-Newtonian Fluids Traction studies in lubricated Hertzian contacts (E.H.D.) have shown that lubricant behaviour cannot be described by a simple Newtonian model. More complex rheological models have been suggested and have relied on transient viscosity and viscoelasticity to explain discrepancies between classical theory and experiments. Gupta and Forster et al. [20,2l]have shown that a simple non-linear viscoelastic model can be used to predict with good accuracy traction results obtained on a twodisc machine. The lubricant behaviour is represented by three parameters, which are considered to vary with pressure and temperature:

- the dynamic viscosity - the shear modulus - and a critical shear stress

p@,0,

G@*7')s roe,7').

The linear viscous law is written as:

where y is the shear strain rate, r the shear stress and p the viscosity. According to the Ree-Eyring theory [22],nonlinear viscous behaviour can be expected at high shear stress. That behaviour is described by a hyperbolic sine function. To take into account the transient effect, a transient viscosity concept can be introduced.

where ro is a critical shear stress which must be defined. A viscouselasto-plastic behaviour of the fluid is also considered. The model used is similar to that presented by Johnson and Tevaarwerk [23], and combines an elastic and a viscous shear rate. It reads: 1 dr y=--+F(r) G dt

I dr ro =--+-&G dt

p

r ro

(3)

where G is the shear modulus and where F(7) takes the Ree-Eyring form. 2.2. Roller Bearing Element Interactions The existing hydrodynamic and elastohydrodynamic models are used to determine the normal and traction forces corresponding to the geometrical interactions between the different elements of a roller bearing. This part of the paper is limited to the discussion of the models and formulations used in the computer program presented here. Solving bearing equilibrium requires a few simplifying assumptions. As it is a quasi-static analysis, inertial effects except centrifugal forces are neglected in this model. The geometry is assumed to be perfect, i.e., rings, cage and rollers are cylindrical. As it is a plane model, ring misalignment and roller skewing are not considered. The outer ring is stationary. Though, it is possible to take into account; an outer or innerring guided cage, an outer or inner-ring guided roller, and race flanges, which are guiding rollers, with or without flange angle. The basic geometry of a roller bearing is presented in figure 1. The different formulations relating cage-ring pilot surface forces and moments to the cage rotational speed and eccentricity; tangential and normal cage forces to the roller position in the cage pocket; and those defining traction forces at the roller-raceway interactions are summarized in table 1. From most of the available literature, it can be established that contact forces resulting from rollercage pocket and cage-ring pilot surface contacts are small in comparison to the forces at the roller-raceway contacts. Furthermore, due to a lubricant film at the interfaces, hydmdymmic models can be considered, and elastic

468

deformations are neglected in steady-state operating conditions. The computer program shows that rollers moving through the loaded zone, are located in the front of the cage pocket and consequently are driving the cage. While the opposite rollers, in the unloaded zone, are located at the rear of the cage pocket and act on the cage as a braking system. The interaction between cage and outer or inner ring pilot surface is assumed to be purely hydrodynamic, and no elastic deformations resulting from the hydrodynamic forces are considered. In a rolling bearing, the ratio of pilot surface width to cage diameter is always lower than

CONTACTS

0 WINDAGE

a CAGE I RING

ASSUMPTIONS

1/6. So the hydrodynamic of the cagehace contact is simply modelled by the well-known "short journal bearing" solution [24] in laminar or in turbulent flow. In this model, the attitude angle of the cage denotes the angle between the center line direction and the external load direction. Resulting from a lubricant film at the interface, low load and conform surfaces, the interaction between roller and cage pocket is considered being purely hydrodynamic. This contact is very simply simulated by the well-known "long journal bearing" solution [24], using the analytical solution of Martin for isoviscous fluid.

1

MODELS

RESULTS

Bearing Tests

Air-oil mixture generates oleodynamic drag

- light load

- experimental results

- windage torque

Hyddpamic

- load - torque - attitude angle

- "shortjournal bearing"

- rigid surfaces - laminar or turbulent flow

as h c t i o n of the eccentricity Elastohydrodyamic

- lubricant film thickness - Cheng theory - Gupta, Cheng et al. factor - thermal reduction factor

- from none up to heavy load ROLLER I RING

( h e r ring) I

Elastohydr+amic

RACEWAY

- elastic deformations

- rolling and sliding speeds @ ROLLER / CAGE POCKET

0 ROLLER EDGESlPOCKET EDGES

GI ROLLER EDGES/RING RIDING

- light load - rigid surfaces - no load - no skewing

- no load - no skewing - with race flange angle

- Johnson and Tevaarwerk theory Hydrodynamic

- Martin theory

- hction force - normal load - friction force as h c t i o n of the roller position

- couette flow

- hction force

Hydrodynamic

- couette flow

Table 1 - Roller bearing element interactions

- friction force - hction torque

469

Where c c c c

N*

I' 2'

S P @i @C

Qh

and

d,,,

are appropriate coefficients, is the number of rollers, is the roller frontal area, is the lubricant viscosity, is the inner ring speed, is the cage speed, is the lubricant flow, is the bearing pitch diameter.

With g=O for a lubrication by an external jet and g=l for a lubrication through the inner ring. The last term in equation (4) quantifies the lubricant drive effect when oil is provided through the inner ring, assuming that all the rotational energy of the lubricant is absorbed by the cage. Fig. 1- Roller bearing element interactions

2.3. Basic Eauations Concerning the roller endcage pocket edge interaction, assuming there is no roller skewing in the cage pocket and no normal load between roller ends and cage pocket edges, the model is similar to the hydrodynamic solution of couette flow [191. The roller-ring raceway contact is described by Cheng 1251 for the lubricant film thickness in an E.H.D. line contact, including a thermal corrector factor given by Gupta, Cheng et al. [20], and by Johnson and Tevaanverk for the traction force [23]. We assume that, at the roller end-race flange interaction, which can include a race flange angle, there is no normal load and that the roller is rolling centred between the two guiding shoulders without skew angle. Then we can use the well-known couette flow model [191. The empirical model for the windage torque acting on cage and roller elements, which is proposed, comes from several experimental studies of power loss in high-speed roller bearings, for different bearing geometries (35 to 142 mm pitch diameter) and different lubrication types (by jet and through the inner ring). Experimental results have been reduced to a simple model, with appropriate coefficients derived by curve-fitting the drive torque measured to the operating conditions and bearing geometries. From reference [26], the windage torque acting on the cage is predicted as follows:

Equilibrium equations In this model, the kinematics of the cage and of each roller are unknown. They are determined by the force and moment balance of the different bearing elements. Figure 2 shows the interactions around a roller, with an outer ring guided roller. These interactions may be represented by traction forces and moments, as shown in figure 3. So, equilibrium equations for the rollers are defined as follows:

-

0 = Qij Qoj - FClj + FC2j + FC

(5)

Fij-FOJ.-QClj+QC2j + FEij + FEoj - FOL

(6)

O=

0 = (-Fij - Foj + FClj + FC2j).DW2

+ CEij + CEOJ. + CCj

(7)

The cage equilibrium equations (Fig.4), along the horizontal and the vertical axes are written as: N O = Cl(eC2j-eClj).cos~jl+(eCi + eCo).sin(~I j=l (s)

470

N 0 = / y [ - ( F c 2 j -Fclj).COSylj J + ( Q c i + Q c , ) . C O . ( ~ ) j =I

(9) and the moment equilibrium equation is given by:

The outer ring is stati0~1-y and mounted in its housing. The mounting forces ensure the outer ring equilibrium without influencing the bearing behaviour.

N 0 = z [ ( Q c l j -Qc2j).DM / 2 - ( F C l j + F c 2 j ) . D R / 2 j=l -CCj J + CCi CCo

-

(1 0)

If

rotating inner nn9

Fig. 4- Cage balance, forces and moments

Fig. 2- Roller balance, geometrical interactions

Fig. 3- Roller balance, forces and moments The quasi-static equilibrium of the inner ring (Fig.5) can be reduced to one equation defined as follows:

0

=

N z[Q,ij.co~vj J - FR j =I

(11)

if the hydrodynamic load QCi at the cage-inner ring contact is neglected compared to the normal loads Qg at the roller-raceway interface and the applied radial load FR.

Fig. 5- Inner ring balance, forces and moments Geometrical relations When the roller moves through the loaded zone, its circumferential position in the pocket is modified. In this model this position is an unknown. From figure 2 a geometrical relation is given by:

0

=

Hl.+H2j-JCC J

(12)

47 1

For a line contact, according to Palmgren [27], the normal load Q is related to the normal contact deformation 6 as follows:

S = 0.39 [4(1-~12)/E1+4(1~22)/E2]0.9 .(Q.9 / Cds)

(13)

where vl. E l , v2 and E2 are the Poisson's ratio and the elastic modulus of the two interacting bodies, and 4 is the contact length. From figure 6, the knowledge of the load deflections and lubricant film thicknesses at the inner and outer ring contacts, for one roller, allows to determine the total elastic deflection for other rollers. Contact exists only for a positive value of S, and the contact load is determined by equation (13). As shown in figure 6, the inner race deflection is given by Cforj =I ) : 4 . = J D / 2 + 8'I. . + 8OJ. - h '.I. - hOJ.

An algorithm has been developed to solve simultaneously the non-linear equilibrium and geometrical equations set out above. This set of (4Nf3) equations, related to (4N+3) unknowns, is solved using the Newton-Raphson iterative method. The (4N+3) unknowns are the cage eccentricity, E, and its angular location, 6, the rotational speed of the cage, a+, and for each roller; its location in the cage pocket, HI, the inner and outer normal load, Qi and Qo, and the rotational speed of the roller about its own axis w,.. One of the most important advantages of this procedure is the small number of iterations required to obtain convergence. Convergence is reached within a maximum relative error of 10-6 after 20 to 80 steps, depending on the number of rollers, the initial conditions and the relaxation coefficient.

(14)

Then, for a prescribed roller azimuth rvj, i.e. for j = 2 to N, the geometrical relation is written as: O=(JD/2+ 6..+6 ~ - h . . - h o , ) - 8 r C O S ~ 'I OJ 'I

2.4. Numerical Procedure

(15)

3.

RESULTS

3.1. Data

The specifications of the bearing example are listed in table 2. Both cage and rollers are guided by the inner-ring. The lubricant is a tetra ester, qualified to the MIL-L-23699 specification. Lubrication is provided under the inner race, therefore, the whole input flow rate goes through the bearing. The range of operating conditions is described in table 3. 3.2. Test-Model Correlation

Fig. 6- Inner ring radial deflection The set of equations (5)-(1 I) and (15) describes the roller bearing balance.

The authors first compared the values of calculated drive power with experimental results. It must be noted that the drive power is equal to the total power loss. The experimental work used to validate the computer program has been performed on several high-speed roller bearing test rigs. The test-model correlation was originally reported in [26]. The predicted bearing heat generation agreed very well with the experimental data obtained from different sizes of roller bearings (35 to 142 mm pitch diameter), for a lubricant provided by jet or through the inner ring and over a speed range from 0.3 up to 3 million DN. The appropriate coefficients derived to estimate the windage torque appear to be valid over the range of shaft speeds, lubricant flow

412

rates, lubricant inlet temperatures and radial loads for the four bearing geometries investigated. ROLLER BEARING SPECIFICATIONS External geometry (ID,OD,width),mm Pitch diameter, mm Number of rollers Roller diameter, nun Roller length, mm Bearing diametral clearance, pm

3.3. Total Power Loss Prediction Vs. Operating

19x164~40 142 30 12 14 30

Cage guidance type

inner ring

Cage diametral guiding clearance, pn

480

Roller guidance type

Roller axial guiding clearance, pn Race flange angle, degree

inner ring 30 0.375

Race and ball material

AISI M-50

Table 2 - Roller bearing specifications

I

RANGE OF OPERATING CONDlTlONS ShaA speed, rpm Radial load, daN Lubricant flow, l/h Lubricant inlet temperature, "C Lubricant speciJication

Typical results of power dissipated versus lubricant flow rate are shown in figure 7, for the 142 m m pitch diameter bearing described in table 2.

I

0 to 20000 0 to 5 000 0 to 300 60 to 200 MIL-L-23699

Conditions Figure 8 shows the total power loss prediction versus the shaft speed for several radial loads varying between 500 and 4000 daN, a lubricant flow of 150 Uh and a lubricant inlet temperature of 100 "C. Heat generation increases greatly with the shafl speed, whereas it seems independent of radial load (all plots seem as one). In fact, a decrease in power loss can be observed for radial loads lower than 200 daN, as shown in figure 12. It must be emphasized that, as earlier noted for ball bearings [15], power loss prediction and location depend strongly on the roller bearing internal geometry, and more specifically on cage and roller guidance type, i.e. guided by inner- or outer-ring. For example with this specific internal geometry, where both cage and rollers are guided by the inner ring, a small cage slip occurs for radial load lower than 200 daN. This phenomenon is important because changes in cage speed produce a strong variation in windage loss, according to equation (4).

Table 3 - Range of operating conditions

-

0

5

3000-

8

2000-

,c

e

=

500 daN

N I = 2500 rpm 4

0

4000

8000

12000

I6000

20000

INNER RING SPEED (rpm)

/

0

0

FR

50

100

I50

200

1 250 MO

LUBRICAN1 FLOW (I/h)

Fig. 7- Predicted and experimental total power loss vs. lubricant flow and inner ring speed. Lubricant inlet temperature, 100°C; radial load, 2500 daN. (Symbols for tests; and line for model)

Fig. 8- Predicted total power loss vs. inner ring speed and radial load. Lubricant flow, 150 lh;lubricant inlet temperature, 100°C.

Figure 9 shows the total power loss prediction versus the lubricant inlet temperature varying from 6OoC up to 2OO0C, over a speed range from 2500 to 14000 rpm, with a lubricant flow of 150 Uh and a radial load of 2500 daN. It can be noted that the

473

decrease in total power loss with increased lubricant inlet temperature is very marked. The predicted trends of increased heat generation with increased shaft speed, increased lubricant flow rate and decreased lubricant inlet temperature were verified by the experimental data. 10000

+ 8000

g

6000

\+

+

N i = 14000 rpm

A

N i = 10500 rpm

7000 rpm N i = 4500 rpm N i = 2500 rprn

m Ni =

\

v 0

3.5. Power Loss Location Vs. Internal Geometry

v

[L W

3 a

0

4000

2000

0

300

350

400

4 50

500

LUBRICANT INLET TEMPERATURE ( K )

Fig. 9- Predicted total power loss vs. lubricant inlet temperature and inner ring speed. Radial load 2500 daN; lubricant flow, 150 Vh.

Loss Location Vs. Operating Conditions Figures 10, 1 1 and 12 present the estimated distribution of the heat dissipated in the bearing, versus the lubricant flow rate (Fig. lo), the inner ring speed (Fig. 11) and the radial load (Fig. 12). The cage contribution to the total power loss is important, mainly due to the fluid windage, and also due to the short journal dissipation at the cageinner ring pilot surfaces and to the power dissipated at the rollercage pocket interfaces. The decrease of the total power loss with decreased lubricant flow rate is mainly due to the windage loss reduction, as shown in figure 10. Predicted power loss location shows that cagering pilot surface contribution to the total energy dissipated can be more important than the windage contribution at very high speeds (Fig. 11). A shaft speed of 20000 rpm for a 142 mm pitch diameter bearing corresponds to 2.84million DN. As it was mentioned above, figure 12 presents some interesting results on power loss distribution 3.4. Power

under light radial load, typically for radial loads lower than 200 daN. The cage slip which produces a decrease in windage and total power losses also strongly modifies the power loss distribution. Then, dissipation can reach 300 W at the roller-race flange interface and 150 W by sliding at the rollerinner ring raceway contact. Note that both cage slip phenomenon and power loss distribution are strongly dependent on the roller bearing internal geometries, and then results for other geometries can be completely Werent. A parametric study was conducted in order to evaluate the effects of bearing internal clearances on power loss prediction and location. Power loss versus the bearing diametral clearance, the cage diametral guiding clearance, the roller axial guiding clearance and the race flange angle value are presented respectively in figure 13, 14, 15 and 16. The basic roller bearing geometry is presented in table 2. Operating conditions are the following; an inner ring speed of 10500 rpm, a radial load of 2500 daN, a lubricant flow of 150 l/h and a lubricant inlet temperature of 100OC. Figure 13 shows that no important change can be observed in the distribution of heat generated in the bearing versus the diametral clearance, as far as this clearance remains positive. Increase of the total power loss with decreased cage diametral guiding clearance is mostly due to the cage-ring pilot surface contribution, as shown in figure 14. Local effects of roller-race flange geometry are presented in figures 15 and 16. Decreasing both roller axial guiding clearance and race flange angle value increases power loss generated at this interface, without significant effects on the total power loss. 4.

CONCLUSION

The authors have presented a new roller bearing model based on cage and roller kinematics. This model includes both hydrodynamic and elastohydrodynamic analyses to describe interactions among the various rolling bearing elements, and an empirical windage torque model.

474

Experimental results were compared to computer predictions.

permission to publish this work, and to Gerard Paty of Turbomdca and Guy Dusserre-Telmon of SNECMA for their assistance.

The following major results were obtained:

REFERENCES 1. Although it is a quasi-static model, a good correlation between theory and experiment was obtained on power loss. 2. The contribution to the total energy dissipated of each lubricated contact is established, i.e., interface between roller and raceway, roller and race flange, roller and cage pocket, cage and ring pilot surface, etc. 3. Results show that parameters af€ecting the power loss may be classified in descending order as follows: - for operating conditions; the rotational speed, the lubricant inlet temperature and the lubricant flow, whereas the radial load effect is considered to be less important. - for internal geometry; the cage guiding clearance and its location on inner- or outerring, the roller guiding clearance, its location and the value of its race flange angle. The influence of the bearing diametral clearance can be considered as negligible. Finally, the authors point out that the knowledge of internal kinematics and contact loads in high-speed roller bearings is of great interest on heat generation, since power losses are related to sliding velocities and friction forces.

ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support given under a BRITE-EURAM contract number AER04007-C(A) (proposal number PL1103), by the Commission of the European Communities (CEC-DGXII). This work was also jointly sponsored by Turbomdca, SNECMA, Hispano-Suiza, GLCS and MSA in France, Rolls-Royce and Leeds University in England, BMW-RR and MTU in Germany and FEW at Port0 University in Portugal. The authors wish to express their thanks to the SNECMA and Turbomica Companies for performing the roller bearing tests and their

Harris T.A., Rolling Bearing Analysis, Wiley Intersciences, New York (1966). Boness R.J., #*TheEffect of Oil Supply on Cage and Roller Motion in a Lubricated Roller Bearing," A W E Jour. of Lubr. Tech., Paper 69-LUB 8-73, pp.39-53 (1970). Poplawski J.V., "Slip and Cage Forces in a High-speed Roller Bearing," A W E Jour. of Lub. Tech., Paper 71-LUB-17, pp.143-152 (1972). Rumbarger J.H., Filetti E.G. and Gubernick D., "Gas Turbine Engine Mainshaft Roller Bearing-System Analysis," A W E Jour. of Lub. Tech., 95, pp.401-416 (1973). Berthe D. and Flamand L., "Skidding in Roller Bearings, Effect of Lubricant," Proc. AGARD Symp., 323, Problems in Bearing Lubrication, Ottawa (1982). Kleckner R.J., Pirvics J. and Castelli V., "High-Speed Cylindrical Rolling Element Bearing Analysis "CYBEAN" - Analyt~c Formulation," A W E Jour. of Lubr. Tech., 102, 3, pp.380-388, discussion, pp.388-390 (1980). Coe H.H. and Schuller F.T., "Comparison of Predicted and Experimental Performance of Large-Bore Roller Bearings Operating to 3.0 Million DN," NASA, Washington, D.C. NASA Technical Paper 1599, 18p. (1980). Hadden G.B., Kleckner R.J., Regan M.A. and Sheynin, L., "Research Report - User's Manual for Computer Program AT81YOO3 Shaberth. Steady State and Transient Thermal Analysis of a Shaft Bearing System Including Ball, Cylindrical and Tapered Roller Bearings," NASA, Washington, D.C. NASA CR 165365 (1981). Coe H.H., "Predicted and Experimental Performance of Large-Bore High-speed Ball and Roller Bearings," NASA Conference Publication 2210, Advanced Power Transmission Technol., pp.203-220 (1983).

475

i 400

- Total Power Loss 0

-3

m

3000 2500

350

Windage

300

Cage-Ring

2000

T

Roller-Outer Ring

A

Roller-inner Ring

+

Roller-Ring Riding

*

Roller-Cage

I

Roller Edges-Pocket

m

2 50

0

1500

2

:: 1000

200 150 100

we-------*

1

500

LUBRICANT FLOW (I/h)

LUBRICANT FLOW (I/h)

Fig. 10-Power loss location vs. lubricant flow. h e r ringspeed, 10500 rpm; radial load, 2500 daN,lubricant inlet temperature, 100°C. 1000

8000

- Total

Power Loss

m

Windage Cage-Ring

v

3

v

Roller-Outer Ring

m

A

Roller-lnner Ring

9

0

6000

5

,-, 8

'z

800

600

-1

4000

Roller-Ring Riding

+

[L W

Roller-Cage a

400

a

Roller Edpes-Pocket

2000

0

-

0

5000

15000

10000

20000 INNER RLNG SPEED (rprn)

INNER RING SPEED ( r p m )

Fig. 11- Power loss location vs. inner ring speed. Radial load, 2500 daN, lubricant flow, 150 vh, lubricant inlet temperature, 100°C.

,

3000

2500

z-

- Total

-

1

Power Loss

-

-

-

-

a

*

-

-

--.---.-

,

Cage-Ring

Roller-Inner Ring

1500

+

I

Roller-Outer Ring

,------.

m

3oo

a Windage

-

2000

u,

9

1

s

2oo

W (L

3

2

1000

500

0

0' 0

10000 20000 30000 40000 50000 RADIAL LOAD (N)

0

10000 20000

30000

40000

50000

RADIAL LOAD (N)

Fig. 12- Power loss location vs. radial load. Inner ring speed, 10500 rpm; lubricant flow, 150 vh, lubricant inlet temperature, 100°C.

476

100

- Total Power Loss

E v

t1

2500 2000

Windage h

cn cn

5

80

Cage-Ring

1500

v

Roller-Outer Ring

A

Roller-Inner Ring

+

Roller-Ring Riding

*

Roller-Cage

1

Roller Edges-Pocket

5 R 53 LL

W L11

?

g

1000

5n

6o 40

20

n 50

0

100

200

150

BEARING DIAMETRAL CLEARANCE ( 1

0

.e-6*m)

50

100

150

200

BEARING DIAMETRAL CLEARANCE ( 1 e-6.m)

(regular view on the left; zoom 011 the right) Fig. 13- Power loss location vs. bearing diametral clearance.. Inner ring speed, 10500 rpm; radial load, 2500 daN; lubricant flow, 150 fi;lubricant inlet temperature, 100°C. - Total Power Loss

--

0

100

200

300

400

500

Roller-Outer Ring Roller-Inner Ring

+

Roller-Ring Riding

.

t

Cage-Ring

A

-

0

loo

Windage

Roller-Cage Roller Edges-Pocket

600

CAGE DlAMElRAL GUIDING CLEARANCE (1.e-6.m)

LL

E

40

0

0

100

200

300

400

500

600

CAGE DIAMETRAL GUIDING CLEARANCE ( 1 .e- 6.m)

(regular view on the lett; zoom on the right) Fig. 14- Power loss location vs. cage diametral guiding clearance. Inner ring speed, 10500 rpm; radial load, 2500 daN; lubricant flow, 150 yh; lubricant inlet temperature, 100°C.

[lo] Pirvics J. and Kleckner R.J., "Prediction of Ball and Roller Bearing Thermal and Kinematic Performance by Computer Analysis," NASA Conference Publication 2210, Advanced Power Transmission Technol., pp. 185-202 (1983). [ l l ] Gupta P.K., Advanced Dynamics of Rolling Elements, Springer-Verlag, New-York, 295p. (1 984). [I21 Schrader, S.M., "Performance of a Hybrid Cylindrical Roller Bearing," Lubr. Eng., 48, 8, pp.665-672 (1992).

[I31 Chittenden R.J., Dowson D. and Taylor C.M., "Power Loss Prediction in Ball Bearing," Proc. of the 15th Leeds-Lyon Symp. on Trib., pp.277-286 (1989). [14] NClias, D., "Skidding in High-speed Aircraft Turbine Engine Ball Bearings: Effects of Lubricant Contamination," Doctoral Thesis, INSA Lyon, 292p. (1989). I151 Nelias D., Sainsot P. and Flamand L., "Power Loss of Gearbox Ball Bearing Under Axial and Radial Loads," Presented at the 48th STLE Annual Meeting in Calgary, Alberta, Canada, May 17-20, 1993, Preprint 93-AM-4C-3.

477

100.

3000

- Total 2500

1

I

I

10

20

30

I

I

50

60

Power Loss

Windage

80 :

Cage-Ring

y

2000

w

Roller-Outer Ring

A

Roller-Inner Ring

v

ul

9

c

5 VI

SOL

i

VI

4

1500

1

*'

W Lz

b

a

1000

500

0

10

0

20

30

40

50

0

60

40

ROLLER AXIAL GUlOlNG CLEARANCE (1 .e-6+rn)

ROLLER AXIAL GUIDING CLEARANCE (1 .e-6-m)

Fig. 15- Power loss location vs. roller axial guiding clearance. (regular view on the left; zoom on the right) Inner ring speed, 10500 rpm; radial load, 2500 daN; lubricant flow, 150 yh; lubricant inlet temperature, 100OC. 3000

- Total

Power Loss

Windage

80 :

Cage-Ring

ul

9

1500

w

a 1000

E I 500

0

1 I- -*.I

i 1

3

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 RACE FLANGE ANGLE (degres)

Fig. 16- Power loss location vs. race flange angle.

.

.. . . .

^--^

. .-. . .

[I61 Houpert L., "A Contribuhon to the Study ot

Friction in E.H.D. Contacts," Doctoral Thesis, INSA Lyon, 265 p. (1980). [ 171 Gupta P.K., Flamand L., Berthe D. and Godet M., "On the Traction Behaviour of Several Lubricants," ASME Jour. of Lubr. Tech., 103, 1, pp.55-64 (1981). [18] Nelias D., Dalmaz G. and Flamand L., "Roller Bearings, Part 111: Traction Behaviour of a MIL-L-23699 Type Lubricant," Brite-Euram Contract, Aero-0007-C(A), Bearing with Minimum Lubrication, LMC INSA Lyon, 3 lp. (1992).

.

-

(regular view on the left; zoom on the right)

---.". . .

L l Y ] Nelias D.,

.

.

...

.

.^^^^

Dalmaz ti. and Flamand L., "Roller Bearings, Part I: Quasi Static Analysis of Lubricated Roller Bearings," Brite-Euram Contract, Aero-0007-C(A), Bearing with Minimum Lubrication, LMC INSA Lyon, 7 lp. (1993). [20] Gupta P.K., Cheng H.S., Zhu D., Forster N.H. and Schrand J.B., "Viscoelastic Effects in I: MIL-L-7808-Type Lubricant, Part Analytical Formulation," Trib. Truns., 35, 2, pp.269-274 (1992). [21] Forster N.H., Schrand J.B. and Gupta P.K., "Viscoelastic Effects in MIL-L-7808-Type

478 Lubricant, Part 11: Experimental Data Correlations," Trib. Trans., 35, 2, pp.275-280 (1992). [22] Ree T. and Eyring H., "Theory of NonNewtonian Flow. Part I- Solid Plastic System, and Part II- Solution System of High Polymers," Jour. of Appl. Phys., 26, pp.793800 (Part I), pp.800-809 (Part 11) (1955). [23] Johnson K.L. and Tevaarwerk J.L., "Shear Behaviour of Elastohydrodynamic Oil Films," Proc. Roy. SOC. Lond., A356, pp.2 15-236 (1977). [24] F r h e J., Nicolas D., Degueurce B., Berthe D. and W e t M., Hydrodynamic Lubrication, Journal and Thrust Bearings, Eyrolles, Paris, 488p. (1990). [25] Cheng H.S.,"A Numerical Solution of the Elastohydrodynamic Film Thickness in an Elliptical Contact," ASME Jour. of Lubr. Tech., 92, F, pp. 155-162 (1970). [26] Nelias D., Dalmaz G.and Flamand L., "Roller Bearings, Part V: Experimental Validation and Typical Results of the Computer Program QUASAR," Brite-Euram Contract, Aero-0007C(A), Bearing with Minimum Lubrication, LMC INSA Lyon, (1993). [27] Palmgren A., Ball and Roller Bearing Engineering, 3rd Edition, SKF Industries Inc., Burbank, (1959).

DissipativeProcesses in Tribology / D. Dowson et al. (Editors)

479

Q 1994 Elsevier Science B.V. All rights resewed.

POWER DISSIPATION IN ELASTOHYDRODYNAMIC TRACTION DRIVES I.M.CIORNEI", E.N.DIACONESCU", V.N.CONSTANTINESCUb and G.DALMA2'. "University of Suceava, 58OO,Suceava, Romania bPolytehnic Institute of Bucharest, Romania "Laboratoire de Mecanique des Contacts, INSA Lyon,69621, Villeurbanne, France SUMMARY The paper presents an analysis of friction power losses in elastohydrodynamic traction drives and underlines the possibilities of optimisation of these transmissions. Finally, several high performance traction drives are described. INTRODUCTION Elastohydrodynamic traction drives represent one of the few fields in which the fluid friction is an useful phenomenon. Mechanical power is transmitted between the active elements of these drives by shear of elastohydrodynamic oil films. A part of the input power is dissipated in the film by parasitic shears. The remaining part represents the useful, transmitted power. In order to optimise the efficiency of elastohydrodynamic traction drives, the parasitic shears must be minimised. Traction drives conceived to this end are finally described in the paper. FRICTION SOURCES IN ELASTOHYDRODYNAMIC TRACTION DRIVES The fluid friction in EHD traction drives depends on many physical factors, of which the most important are macro and microgeometry of contacting elements, contact deformations as functions of material properties, lubricant nature and lubrication procedure, [l]. Nowadays it is convenient to measure global power losses in an EHD traction drive and to assess theoretically the components of friction. Consequently, the possibilities of optimisation of traction drives are severe limited,

[1,17,19,20]. As a general view, the power losses in a traction drive are composed of: - friction in kinematic pairs; - friction between moving elements and lubricating medium; - friction in sealing elements; - air ventilation for cooling the drive. As shown in figure 1, each of these components is a sum of several sources and can be identified finally as a part of global friction torque of the drive. Losses by elastic hysteresis. During rolling, the inlet zone of the contact is subjected to loading, whereas the output is unloaded. The loading and unloading loaddeformation curves do not coincide and the area limited by them is a measure of the energy loss by elastic hysteresis per cycle. This l o s s depends, [1,2,6,18], on: - elastic properties of contacting materials: as the material behaves more elastic, the energy losses decrease whereas a viscous behaviour increases the power dissipation; - contact stresses: at low levels of contact stresses the material behaves more linearly and the hysteresis decreases; - stressed volume. Hysteresis losses are small in comparison to other losses. For instance, Drutowski, [6], attributes

P W

0

I

DISTRIBUTION OVER CONTACT AREA

FRICTION IN EHD TRACTION DRIVES

FUNCTIONAL

PARASITIC (LACK OF SYNCHRONISATION)

I

WITH FLUID ENVIRONMENT

WITH POSITIONING AND SUPPORTING ELEMENTS

1

LIMITING FRICTION WITH HOUSING MATERIAL

Figure 1. Power disipation in EHD t r a c t i o n d r i v e s

48 1

a friction coefficient of to hysteresis losses. Although small, these losses increase as the transverse reduced radius of curvature of the raceways increases, as a result of increasing stressed volume. Losses by nonuniform pressure distribution over the contact area. The hydrodynamic pressure generated in an EHD oil film yields a resultant force which is displaced towards the entry zone into the contact. It is assumed that this effect is responsible for the major part of rolling friction, [3]. Losses by microslip inside the contact. Two loaded active elements of a traction drive make contact over a finite area. Only a small fraction of the points placed in this area belong to the axoydes of motion. In the remaining points microslip occurs. This determines a local microshear of the oil film and consequently, shear stresses opposing the relative displacement. The resultant tangential force generates power dissipation, which increases with normal load nad contact ellipticity, [ E l . Losses by lonqitudinal slidinq. Longitudinal sliding occurs in an EHD contact either as an useful result of the operating process or due to parasitic shear produced by lack of synchronisation between parallel intermediate elements. This sliding is the result of shear behaviour of the oil film and is characterised by the traction [ 14 1. Specific coefficient, measures, such as the use of special lubricants, small rolling speeds or low temperatures are required to reduce the longitudinal sliding. Diminution of this sliding also requires a better synchonisation of multiple intermediate elements of the drive, [ 4 ] , figure 2 . Losses by spin. The spin motion is a result of contact kinematics. Experimental and theoretical investigations,[1,5,7,13,15,19],

indicate that spin greatly affects the traction curves.

Figure 2 . Lack of sincronisation due to Losses by side slip. Side slip occurs in a contact when the axes of the contacting elements are crossed. It reduces the traction capacity of the contact, as the spin does, [ 1 4 ] . Losses in main bearinqs. Usually, the rotating elements are supported in traction drives by rolling element bearings. These are heavily loaded by the normal load applied to the contact. As a result the friction in bearings is high and it dissipates an important part of the drive input power, [ll]. Losses in auxilliary bearinqs. Friction pairs are formed between active elements and their housing. The sliding friction in these pairs can be high, especially when lubrication is poor. Auxilliary, lightly loaded bearings are used to support and position the assembly of intermediate elements. The friction in these bearings is usually small. Losses by churninq become important when the surface of moving elements is large and the oil level is high. These can be reduced by using an incorporated pump to lubricate the drive and a low oil level. Losses in sealinq elements cannot be eliminated due to the design of the drives. Sealing elements having low power losses are therefore required.

482

Losses by air ventilation occur because the drive case must be cooled by means of a fan placed on the input shaft. A low temperature is required by a correct opperation of the drive.

v= 6,5 m/s

POSSIBILIES OF FRICTION DIMINUTION IN EHD TRACTION DRIVES The major part of power losses in a traction drive are caused by rolling, longitudinal sliding, spin, side slip, churning and ventilation, [ 91. The other power losses, shown in figure 1, are of secondary importance. The negative effect of spin upon power losses into an EHD contact is well known, [1,5,7,9,13,15,16]. It consist of a reduction of the slope of traction curves and of an increase of longitudinal sliding. This effect increases with rolling speed and it depends essentially on the rheological behaviour of the lubricant, [14]. The spin also reduces the maximum value of the traction coefficient, as shown in figure 3 . At small values of spinroll ratio this effect is unimportant, but it increases drastically above o limiting treshold of about (2-3)%, [ l ] . The influence of spin upon maximum traction coefficient, at various rolling speeds, is shown in figure 4.

Relations to estimate the spinroll ration in a point contact, as deduced by authors, are given in Table 1. Some of these are experimentally verified, as seen in figures 5 and 6 for, respectively, a ball on disc and a kopp B traction drives. Side slip occurs in a contact due to cross missalignment of the element axes. The negative effect of this parasitic shear is comparableto that of spin, [6]. High precision machining and mounting are required to reduce the side slip.

0.01

1

I I I

I

I I

I

1

I

0

2

1

3

L pivotement

Figure 3.Effect of spin upon maximum traction coefficient for oil T90EP2

Ci, = 3GPa

I

2

t

6

8

c

so vfdd

Figure 4.Effect of rolling speed upon maximum traction coefficient.

483 Table 1. Equations of spin calculation for point-contact traction drives Nr.crt.

1

Versiod

PERBURY

3

KOPP B

Ball on disc

Diagramma

I R

Input contact

x-

[R,+RcosaI s i n a - [ R , t g ( a - p ) + R s l n a ]c o s a - + R s i n a ]cos ( a -p) - [R,+Rcosa] s i n ( a -p ) Y= Rcosa [ s i n a - c o s a t g ( a - p ) I [R, t g ( a -P) * R s l n a ]cos ( a -p) - [R,+Rcosa] s i n ( a -p ) [ R ,t g ( a

output contact

T.= X ' s i n ( a + p )- Z ' c o s ( a + p ) X'=Z'=-

Observations

S-

nondirnensional longitudinal sliding

X'sina -2'cosa RI +Rcosa sina-cosatg(a+p) R s l n a +R,t g (a +p ) sina-cosa t g ( a t P )

Contact ball-retaining ring

o,*=o,xsinp-

w,R,S

(l+;)Rcosp

Ysinp

Figure 7 indicates the values of the cross angle as function of maximum Hertz pressure which reduce the transmitting capacity of the contact by 10% and 20%. It is advisable to keep this angle below 50'.

Figure 5.Variation of maximum traction coefficient and of efficiency with nondimensional spin for ball on disc traction drive.

Figure 6.Spin in Kopp B traction drive

Figure 7.Limiting values ior crossangle: a)for 10% diminuation of transmitting capacity; b)for 20% diminuation of transmitting capacity; When thermal conductivity is predominant, the energy balance equation yields relationships for the ratio of traction force under spin and side slip to the traction force when no parasitic shears act, [lo]. These can be written as:

where S'=o,,/o,under spin and S'=Av/v under side slip. In these relations p is the thermo-viscous coefficient, i l c the viscosity inside the contact, u the rolling speed and K, the thermal conductivity. Two possibilities exist to reduce the parasitic longitudinal sliding caused by lack of synchronisation between multiple intermediate elements of a traction drive. The first consists in rising the precision of the drive but it rises the price of the transmission. The second relies on supplimentary mechanisms to allow the selfpositioning of the intermediate elements. It seems to be more efficient than the former. As shown above, the friction in the main bearings of the drive can

485

be comparable to the traction transmitted through the active contacts. As a result, if traction oils are unavailable, it is of utmost importance to unload the main bearings, [ 1 ] The reduction of churning and ventilation losses requires lubrication of the drive by oil circulation. To this end a small incorporated oil pump can be used.

performances of this ball on disc traction drive are high. A different version of this design is shown in figure 13.

.

VARIABLE RATIO, HIGH PERFORMANCE TRACTION DRIVES As stated above, the reduction of spin-roll ratio in the active contacts is a very efficient solution to decrease the power losses in a traction drive. This ideea led to two new designs of traction drives, namely an improved Perbury drive, shown in figure 8, and a reduced spin torical drive, illustrated in figure 9, [ 11. These use double rollers that lead to a decreased spin-roll ratio, a higher contact fatigue life and improved conditions of lubrication of both contacts. The corresponding analytical relationship are given in [7] and shown in figure 10.

Figure 9.Traction drive with reduced spin.

'1

Figure 10.Spin-roll ratio in Perbury traction drives CI classical version; 0 improved Perbury drive; A reduced spin drive; Figure 8.Improved Perbury traction drive. Another efficient solution consists in an internal design of the drive based on unloaded main rolling bearings and on an incorporated oil pump for lubrication, [12]. Such a traction drive is shown in figure 11,[11). As indicated in figure 12, the

CONCLUSIONS The following conclusions can be drawn as a result of the analysis performed above: - improved performances of EHD traction drives require reduction of functional longitudinal sliding by use of special lubricants, of

486

adequate cooling of the drive and a low treshold rolling speed just able to form a fluid film;

Figure 11.Ball on disc traction drive with unloaded rolling bearings

"1

G:ZPGPa

-

higher performances of EHD traction drives are obtained if the spin-roll ratio in the active contacts of the drive is reduced by an adequate geometrical design of these components; - a high precision machining and mounting is necessary to produce a high performance traction drive; - when multiple parallel intermediate elements are used, these must be synchronised by carefully conceived mechanisms; - normal contact load must be applied directly to the active elements in such a way that the main rolling bearings remain unloaded; - an internal oil pump to assure a correct lubricant flow through the contacts is essential for a high efficiency transmission; - examples of improved versions of traction drives which incorporate these principles can be seen in this paper. REFERENCES l.I.M.Ciornei, Ph.D.Thesis, Polytechnic Institute of Bucharest (1986) (in Romania) 2.D.R.Adam and W.Mirst, Frictional Traction in EHD Lubrication, Proc. Roy.Soc.Lond.(l973),332.

3.B.I.Klem2,R.Gohar and A.Cameron, Photoelastic Studies of Lubrication Line Contact,Proc. Inst.Mech.Engs.(l971). 4.0.S.Crefu,Ph.D.ThesisIPolytechnic Institute of Iassy, (198l),(in Romania). 5.E.N.Diaconescu,Ph.D.Thesisl

University of London,(1975). G.R.C.Drutovsk1,Energy Bases of Balls Roeling an Plotes',ASME, Series D,Journal of Basic Engineering,81,(1959). 7.I.M.CiorneiIThe Optimisation of Perbury Traction Drive by Spin Reduction,Proc.of the 5-th Europeean Trib.Congress,Eurotrib '89,~O~.5,~.100-105,(1989).

Figure 12.Perforrnances of ball on disc traction drive with unloaded rolling bearings.

8.A.V.Sprisevschi,Rolling Bearings, Masinostroenia,Moskval(1969),(in Russian).

487

Figure 13.High efficiency ball on disc traction drive S.W.Wenitz,Friction at Hertzian Contact with Combined Roll and Twist. 10.V.N.Constantinescu and 1.M.Cionei On the Evaluation of Traction in Concentrated Contacts, Acta Tribologyca,vol.I,1,(1992),p.21-31 ll.E.N.Diaconescu,O.S.Crefu and

I.M.Ciornei,Traction Drives,Proc. of the Seminar on Present and Future Trends in Research of Rolling Contact,Suceava,(l985), p.42-701(in Romanian). 12.E.N.Diaconescu and A.G.Graur, Effect of Bath Oil Level Upon Performances of an EHD Traction Drive,VAREHD 2,SuceavaI(1982), p.249-257,(in Romanian).

l3.I.L.TevaarwerktA Simple Thermal Correction for Large Spin Traction Curves,ASME,vol.l02,(1989),p.440-

446. 14.I.L.Tevaarwerk and K.L.Johnson, The Influence of Fluid Rheology on the Performance of Traction Drive, ASME,Jour.of Lubrication Tech., ~01.101,(1979),~.266-274.

lS.I.M.Ciornei,The Implication of Spin of EHD Traction Drives, International Scientific Conference in Traction,Wear and Lubricants,Taskent,URSS,(1985),

p.22-28. 16.E.N.Diaconescu and I.M.Ciornei, Traction EHD,TCMMl,Editura Tehnica Bucharest,(l987),p.l58-165,(in

Romanian).

17.K.Okamura,Mechanisrn and Performance of Traction Drives, Japanese Journal of Tribology, vo1.35,no.1,(1990),p.23-33. 18.I.Koizmui and O.Kuroda,Analysis of Damped Vibration of a System with Rolling Friction,Japanese Journal of Tribology,vol.35,no.6, (1990),P.733-739.

19.M.PattersonITraction Drive Contact Optimisation,Proceedings of the 17-th Leeds,Lyon,Symposium in Tribology held at the Institute of Tribology,(l99l),p:295-300. 20.A.IshibashiIS.Hoyashita and H. Takedomi,Evolution of Efficiencies and Speed Ratios of CVT's with Planetary Cones,Proceedings of the 17-th Leeds,Lyon,Symposium on Tribology held at the Institute of TribologyI(l99l),p.277-294.

SESSION XI GENERAL ASPECTS OF FRICTION Chairman:

Professor F Kennedy

Paper XI (i)

Frictional Heating of Elliptic Contacts

Paper XI (ii)

Soil-Structure Interface Friction in Reinforced Soils

Paper XI (iii)

Diagrams for Estimation of the Solidified Film Thicknesses at High Pressure EHD Contacts

This Page Intentionally Left Blank

Dissipative Processes in Tribology I D. Dowson et al. (Editors) 1994 Elsevier Science B.V.

49 1

FRICTIONAL HEATING OF ELLIPTIC CONTACTS J. Bos and H. Moes University of Twente, Dept. of Mechanical Engineering, Tribology Group,

P.O. Box 217, 7500 AE Enschede, The Netherlands Wherever friction occurs mechanical energy is transformed into heat. The maximum surface temperature associated with this heat generation can have an important influence on the tribological behaviour of the mating components. For band contacts and circular contacts this temperature has already been studied extensively. However for elliptic contacts only approximate solutions exist. In this work a fast numerical algorithm is presented to calculate the steady state solution for the flash temperature for elliptic contacts with arbitrary entrainment angle. The heat generation may be due to either a uniform or a semi-ellipsoidal shaped heat source distribution, more or less representing EHL conditions and dry or boundary lubrication conditions, respectively. The asymptotic solutions for large and small PCclet numbers and numerical solutions will be presented. Function fits for the flash temperature will be proposed that are more reliable than the function fits in current use, even for circular contacts. Aspect ratios of the contact ellipse in the range of 0.20 - 5.0 are covered. Within this range the fits were found to be accurate within 5%.

1

Introduction

The publication by Blok (1937a) of a model for the surface temperature rise due to friction stimulated a series of studies about frictional heating and flash temperatures. For simplicity reasons most of the attention was directed to the contact temperature under steady state conditions between two semi-infinite solids, for either a band shaped contact or a circular contact. The work of Jaeger (1943) and of Carslaw and Jaeger (1959) [§10.7] extended Blok’s model to a band shaped contact with limited PCclet numbers. These were all band shaped contacts, though, whereas in practice elliptical contacts are much more common. Therefore Jaeger’s (1943) solution for rectangular contacts has generally been used as an approximation to the elliptic contact problem. For circular contact areas Archard (1959) introduced an approximate solution on the basis of Jaeger’s work together with a simple rule of thumb for the partitioning problem, a solution that meanwhile has proven to be quite useful. By introducing curve fit solutions Kuhlmann-

Wilsdorf (1986, 1987) introduced solutions for elliptic contacts that are quite generally applicable but differ slightly from Archard’s solutions. For a comprehensive review of the literature on flash temperatures see Kennedy (1984). Unfortunately most of these results are restricted to approximate solutions of the average contact temperature. Accurate flash temperature calculations, i.e. of maximum contact temperatures, that apply t o the general elliptic Hertzian contact are still lacking. The authors will try to fill up this omission as a first step in the implementation of a theory in which the tribological contact is part of a thermal network, as proposed by Blok (1989).

It has been a handicap that according to Carslaw and Jaeger’s theory heat exchange through a band shaped contact and a noninsulated stationary solid are incompatible. This incompatibility has been confirmed by calculations conducted by Allen (1962). In order to overcome the problems involved, Cameron, e.a. (1965) even assumed infinitely low temperatures distant from the heat source. This was dropped later (Cameron, 1966).

492

According to De Winter (1967) for a band shaped contact and a stationary solid a logarithmic singularity occurs. Therefore the introduction of an insulated stationary solid is essential when calculating the flash temperature. Fortunately, though, this singularity occurs only for band shaped contacts. Calculation of the heat exchange through an elliptical contact for a noninsulated, stationary solid is feasible. This singularity is the main reason why the solutions for band shaped contacts have not been incorporated in the present work. It would have led to unnecessary complications.

important role. Therefore keep in mind that it has been defined as

In order to present solutions that are generally applicable, function fits will be introduced, fitted to the numerical results obtained with the presented algorithm. The introduction of the function fits is based on the following three principles:

In the literature a uniform heat source has generally been assumed. This seems to be a fair approximation if full film lubrication conditions prevail, i.e. in EHL. For dry contact and boundary lubrication conditions, though, a semielliptic heat source distribution, due to an elastic (Hertzian) contact pressure distribution, seems more t o the point. Therefore in the present work both heat source distributions will be considered.

First, in the function fits a minimumnumber of similarity parameters should be figuring. Therefore the method of optimum similarity analysis introduced by Moes, (1992) has been applied. Second, the function fits should be based on simple algebraic relations only, i.e. additions, substractions, powers, exponential functions and logarithms. This facilitates reproduction and prevents self-deceit with erroneous data or inaccurate asymptotic solutions. Third, all the asymptotic solutions should be taken into account. Therefore they will be the building blocks of these function fits and may be distinguished at the first glance. Unfortunately, there is some confusion about the correct definition of the Pdclet number, i.e. the ratio between the bulk heat transfer and the conductive heat transfer. In the ensuing paper the characteristic length figuring in the PCclet number is the length of the heat source. However, this is four times the dimensionless group that has been applied by Carslaw and Jaeger (1959), Archard (1959) and Archard and Rowntree (1988) and eight times the dimensionless group that has been applied by Blok (1937b). Anyhow, in the derivations to follow, the Pkclet number of the solid in contact plays an

2aU K

where tc is the diffusivity and U is the velocity relative to the heat source. Whereas the characteristic source length a is half the maximum length of the heat source in the direction of the velocity.

Nomenclature a,, b, a b C

F Ir' P

Q U

2

Y

a

e 29

6J IC

P

40

4

- semi-axes of the heat source ellipse, . L velocity related heat source length, L velocity related heat source width, L - specific heat, L 2 / T 2 0 - rate of heat supply, FL/T - conductivity, F/TO - (2aU/n) Pdclet number - heat supplied per unit area, F/TL - velocity, L/T - coordinate in the direction of the velocity, L - coordinate perpendicular to the velocity, L - entrainment angle relative to a-axis - flash temperature number - temperature, 0 - flash temperature, 0 - ( K / p c ) diffusivity, L2/T - density, FT2/L4 - (b,/a,) aspect ratio of the heat source - (b/a) velocity related aspect ratio -

493

Asymptotic solutions

2 2.1

Y

Large P6clet numbers

An asymptotic solution for large PCclet numbers that applies to a band shaped heat source with a uniform distribution has been derived by Jaeger (1943). The authors will extend this solution to elliptic contacts with either a uniform or a semiellipsoidal heat source; the latter in correspondence with Hertz’ (1881) contact theory and a uniform coefficient of friction. For a uniform heat source distribution over an elliptic area the heat generation per unit area is given by

1F

Q ( ~ , Y= ) -ir ab

(1. - ~ Y I<

~:S(Y)

9

IYI < b )

.

Whereas for an elliptic contact with a semiellipsoidal source of heat follows

Q(x,y) =

+L/l-

(+)2

(5)

-

2

2ir ab

Figure 1: Geometrical relations for an inclined ellipse. The corresponding asymptotic solution for the surface temperature at large PCclet numbers may be solved by calculating

The x, applied is defined by

Whereas k follows from

(1) In this equation the integration boundaries are defined by

(b: - a:) tan(&) k= a; tan2(a) ’

db:+

with a representing the entrainment angle relative to the a,-axis direction; see figure 1. The velocity related heat source length a applied represents half the maximum length of the heat source in the direction of the velocity and the velocity related heat source width b represents half the overall width of the heat source. They follow from

.l(Y)

= ICY - .S(Y)

1

4 Y ) = kY

+ XS(Y)

.

Actually the model that has been presented is analogous with the temperature variation with time in a rod; see Carslaw and Jaeger (1959). The flash temperature follows from the maximum for the contact temperature and reads

1

+

b = b , d b : cos2(a) a? sin2(a)

In this relation 6+ = 2 f i / . l r f i = 0.507949.. for a uniform heat source (Jaeger, 1943) and 8+ = 0.589487.. for a semi-ellipsoidal heat source (De Winter, 1967).

494

Less interesting, although more generally applied, is the average temperature of the contact area that, for a uniform heat source distribution, reads

e+

=

32J2r (a) = 0.309955. 5~2r

(a)

From this it follows that Archard's (1957) approximate solution of the average temperature, i.e. 8, = 0.31, is quite to the point. Also quite to the point is the maximum temperature according to Archard and Rowntree (1988)' viz. 1.64 times the average temperature. The solution according to Kuhlmann-Wilsdorf (1986) though, viz. 8, = 9/32 M 0.281, underestimates the average temperature by about 10 percent. For the sake of completeness the average temperature of the contact area for a semi-ellipsoidal heat source distribution has been calculated as 0, = 0.322991.. . This differs only 7% from the average temperature for a uniform distribution. For general applications, though, the maximum temperature is of more importance. In fact the solution that has been presented is an obvious generalization to elliptic contacts for the asymptotic solution that applies to a band shaped heat source. Please notice though, that the actual flash temperature for an elliptic contact is much larger than the average temperature over the contact area, that in accordance with the experience with band contacts, has quite generally been used as an approximation. This applies to uniform heat sources as well as to semiellipsoidal distributions. Therefore, in the forthcoming sections the authors will emphasize the maximum temperature since this seems more to the point.

2.2

Stationary solids

The asymptotic solution for small PCclet numbers is the solution for a stationary solid. For a stationary solid the flash temperature can be defined

For a circular contact area and a uniform heat source distribution the maximum dimensionless contact temperature in a stationary solid is 8, = 1 / = ~ 0.318310.. (Blok, 1937b). The average dimensionless contact temperature is 0, = 8/37? = 0.270190.. (Carslaw and Jaeger'1959). The solution for the actual temperature distribution has been presented by Carslaw and Jeager (1959) in terms of Bessel functions; see appendix A. For a circular contact area and a semiellipsoidal heat source distribution the maximum dimensionless contact temperature is given by 8, = 318 = 0.375 and the average dimensionless contact temperature is 8, = 9/32 = 0.28125. This follows from the analogy with the theory for concentrated elastic contacts (Hertz, 1881), with Q representing the contact pressure, 19 representing the indentation and I< representing the elasticity parameter E / 4 ( 1 - v2);see appendix A. It is clear that transforming the shape of the heat source has an effect on the resulting temperature distribution, even if the rate of heat supply and the heat source area remain unaltered. For an elliptic contact area and either a uniform or a semi-ellipsoidal heat source distribution the dimensionless contact temperature can be calculated by applying the shape factor:

where K(k) represents the complete elliptic integral of the first kind; see Abramowitz, e.a. (1965). Please note that this exact solution for S ( & ) applies t o the maximum contact temperature only. Fortunately, for the average contact temperature S ( & ) happens to represent a very good approximation. For a fair approximate solution of the elliptic integral see appendix B. In figure 2 S(40) is shown for 40 E [0.1,10] using the approximate solution for the elliptic integral of appendix B.

3 Where the shape factor S(#,,), with 4o bolao, accounts for the ellipticity effect. For a circular contact area S(l) = 1.

Numerical Approach

Throughout this paper the dimensionless temperature and the dimensionless heat supply per unit

495

and

1.10 I

I

I

0.85 0.80 0.75

L -

40

x-&zzzz

By approximating the heat source by a piecewise - constant function with the value Q k , l = &(&, B I ) in the region {(<,7) E R21
+4

I 10

I

1

+

+

4 <

+

Figure 2: The shape factor S(q5,,). area, defined by

where the coefficients Kht!h are given by

6 ab and Q i Q F F respectively, and two dimensionless coordinates, defined by -

79=29-

-

K

X E -

X

a

and J E -Y

a

,

are applied. The steady state surface temperature of a semi-infinite solid, due to a moving heat source with an arbitrary heat distribution, written in these dimensionless variables reads (Carslaw and Jaeger 1959):

with S, the region over which the heat source extends, and

RG

&(E,r])

or

d(5- <)2 + (jj - v ) ~ . 2

= &dl- (L1<')2- I

(*)

H

depending on whether the heat source is semi ellipsoidal or uniform. For <,r] @ S, Q(<,r])

= 0

where sina

cosa

with

(5)

To the authors' knowledge a closed-form solution for this integral does not exist. Carslaw and Jaeger (1959) found an analytical expression for this surface integral which reduces it to a line integral. This expression, however, contains infinite integrals, which makes it less suitable for numerical evaluation. The authors applied the following, more useful, exact reduction to a line integral which consists of, apart from exponential integrals, finite integrals only. Polynomial as well as rational approximations do exist for the exponential integral (Abramowitz and Stegun, 1965). Appendix C lists the ones used in the present work.

496

-l:d

e - 4l

+1:d-

P ( ~ ~ 2 + z m ~ - vz2m )

w(

d m - x m )

e- j P ( d F + z p )

dv

v2

(d--xp)

dv

(7)

All numerical results presented in this paper are obtained by applying this Multilevel Multiintegration algorithm to equation (6). This resulted in a reduction of computing time from some 90 minutes to less than 5 minutes on a HP 9000/720 machine for (1+256)x( 1+256) nodes. This number of nodes has been applied for each temperature distribution calculation.

Where El is the exponential integral, defined by El(x)

J,"

- dt e;t

(X

>0) .

The line integral of the equation (7) has been solved numerically using the doubly-adaptive algorithm of Oliver (1972). Equation (6) in itself represents a straightforward way of calculating the surface temperatures. It is generally referred to as a multi integration or multi summation. From a computational point of view, straightforward evaluation of equation (6) ) N is inefficient since it costs O ( N ~operations, being the number of nodes on the grid. So, if this equation has to be evaluated frequently, like for instance in an iterative scheme t o solve the energy equation for the thermal EHL-problem, it will dominate the computation time. Brandt and Lubrecht (1990) presented an algorithm called Multilevel Multi integration which can evaluate multi integration type expressions in only O ( N log N ) operations, provided the matrix li' meets some smoothness requirements. Basically application of the algorithm consists of four steps: Restrict equation (6) to a grid consisting of fi nodal points by adjoint interpolation. Perform the summation on this grid. This will take O ( N ) operations. Interpolate the solution to the fine grid (again O ( N ) operations). If necessary, make local corrections. These corrections take only O(1og N ) operations for each point if the smoothness properties of Ii', as stated in Brandt and Lubrecht (1990), are met. So the total complexity is reduced to O ( N log N ) .

4

Results and Discussion

Figure 3 shows the isotherms of the surface temperature, in the neighbourhood of the heat source, for increasing Pkclet numbers, and a semi infinite body moving from right to left, along a uniform circular heat source. This figure clearly demonstrates the influence of the Pkclet number on the temperature distribution. The first plot of this figure shows the temperature distribution for a stationary solid, where as the last plot already shows the characteristics of the asymptotic solution for large PCclet numbers. The flash temperatures in the transition zone between small and large PCclet numbers, of which plots 2 and 3 of figure 3 are examples, have been calculated numerically. Based on these solutions and the asymptotic solutions, the equations (2) and (3), the flash temperature for an arbitrary Pkclet number may be estimated by applying the function fit

where 8, and 8, represent the dimensionless flash temperature solutions for small and large PCclet numbers respectively, with S(40) according to equation (4), and

s

= 0.5 * exp

(10) The values of 0, and ,8 depend slightly on the shape of the heat source distribution and on the kind of flash temperature concerned, i.e. the maximum or the average. The various values for 80 and ,8 are listed in table 1.

497

percent. Figures 5 and 6 show results with zero entrainment angle for semi ellipsoidal and uniform heat sources respectively. Both average and maximum temperatures are shown. The same small differences between numerically computed results and function fit values occur. Calculations for entrainment angles in between OOand 45'demonstrated a similar accuracy. 1

\

2

I

I

3

4

Figure 3: Temperature distribution due to a uniform circular heat source, 1: P = 0, 2: P = 1, 3: P = 10 and 4: P = 100.

The first term of this formula is the asymptotic solution for stationary solids. Naturally its contribution to the temperature should be independent of the entrainment angle, therefore, 40 is figuring instead of 4. With respect to this the formula is consistent. The second term represents the assymptotic solution for large PCclet numbers. This term becomes dominant for high PCclet numbers as it should. Note that in this term 4 is figuring not 40. It can easily be verified that the formula is consistent; an entrainment angle of 90'has the same effect as taking the reciproke of 40 and an entrainment angle of 0'. The physical background of the formula is the idea that, for large PCclet numbers, the temperature distribution due to an elliptical heat source with a certain entrainment angle can well be approximated by the temperature distribution due to an elliptical heat source with an aspect ratio 4

,

em

I

00

&a

0.318310 I 0.507949 0.270190 I 0.309955 semi ellipsoidal average maximum I

I

60

em

00

0.375

0.589487

0.28125

I

I &e I 0.322991

Table 1: Survey of the flash tempeperature numbers

5

Conclusions

Based on numerical calculatons and asymptotic solutions for large and small Pkclet numbers, an equation has been derived that approximates the flash temperature for an arbitrary PCclet number and an arbitrary entrainment angle with an error less than 5 percent; see equations (8, 9 and 10). This function fit equation contains the analytical asymptotic solutions for small and large Pkclet numbers and circular heat sources as basic components. Both uniform and semi ellipsoidal distributions are covered. Ellipticity of the heat source is accounted for by means of the shape factor of equation (4). By the way, Archard's rule of thumb may be applied as a fair approximation for the flash temperature between two sliding solids, reading -

and entrainment angle of 0'. Figure 4, in which both the numerically calculated temperatures and the function fits for an entrainment angle of 45' are plotted, shows that this approximation results in errors less than 5

-

average

maximum 00

1

N

291

-

_

1

61

1 +-; 292

where 291 and 292 are the flash temperatures that follow from the assumption that all the heat is supplied to either solid 1 or solid 2.

498

+ Maximum Dimensionless Temperature

0.40

I

O.'8.b1

'

' '*'

I

I

0*1° O.O8.bi

I

1 10 PCclet Number

Average Dimensionless Temperature

- --

100

I

'

0.1

'

I

I

1 10 PCclet Number

I

T

100

Maximum Dimensionless Temperature

Figure 4: Maximum temperature, uniform heat source, entrainment angle = 45'. Markers denote numerically calculated values. The lines represent the curve fit function. 0 : 4 = 1, : 4 = 3, 0 : 4=5.

+

Acknowledgement I

O.O8.lOl

The authors gratefully acknowledge the support of the Technology Foundation STW.

'

0.1 '

'

I

1 10 PCclet Number

, 100

References Abramowitz, M., and Stegun, LA., 1965 (eds), Handbook of Mathematical Functions, New York. Allen, D.N. de G., 1962, A suggested approach t o finite-difference representation of differential equations, with an application t o determine temperature-distribution near a sliding contact, Quart. J. Mech. and Applied Math., Vol. 15, pp. 11-33.

Figure 5: Average- and maximum temperature , semi ellipsoidal shaped heat source, a = 0. Markers denote numerically calculated values. The line represent the curve fit function. : 4 = 1/5, 0 : 4 = 1/3, 0 : 4 = 1, A : 4 = 3 , j, : 4 = 5 .

+

Archard, J.F., 1959, The temperature of rubbing surfaces, Wear, Vol. 2, pp. 438-455.

Blok, H., 1937b, Theoretical study of temperature rise at surface of actual contact under oiliness lubricating conditions, Instn. Mech. Engrs., Proceedings of general discussion on lubrication and lubricants, Vol. 2, pp. 222-235.

Archard, J.F., and Rowntree, R.A., 1988, The temperature of rubbing bodies; part 2, the distribution of temperafures,Wear, vol. 128, pp. 117.

Blok, H., 1989, Adaptation of the Bash temperature theory t o thermal-network applications f o r band shaped contact areas in machinery, Technical University of Delft.

Blok, H., 1937a, The surface temperatures under extreme pressure lubricating conditions, Contributions by the Delft laboratory of the Royal Dutch/Shell t o the 2nd World Petroleum Congress, Paris 1937, the Hague 1939, pp. 151182.

Brandt, A. and Lubrecht, A.A., 1990, Multilevel matrix multiplication and fast solution of integral equations, J. of Comp. Phys., Vol. 90, NO. 2, pp. 348-370. Cameron, A,, Gordon, A.N., and Symm, G.T., 1965, Contact temperatures in slid-

499

0.30 I

Average Dimensionless Temperature 4

I

I

I

I

Kennedy, F.E.,1984,Thermal and thermomechanical effects in dry sliding, Wear, Vol. 100, pp. 453-467. Kuhlmann-Wilsdorf, D., 1986,Sample calculations of flash temperatures at a silver-graphite electric contact sliding over copper , Wear, Vol. 107, pp. 71-90.

Maximum Dimensionless Temperature 0.40

~

Kuhlmann-Wilsdorf, D., 1987, Temperatures at interfacial contact spots: dependence on velocity and on role reversal of two materials in sliding contact, J. of Tribology, Vol. 109, pp. 321-329. Moes, H., 1992, Optimum similarity analysis with applications t o EHL, Wear, Vol. 159, pp. 57-66.

Oliver, J., 1972, A doubly-adaptive ClenshawCurtis quadrature method, Computer Journal, Vol. 15, pp. 141-147. Winter, A. de, 1967, De berekening van de flitstemperatuurverdelingen in en aan weerstijden van een bandvormig contactvlak (tevens warmtebron) tussen twee over elkaar glijdende loopvlakken, Masters Thesis (in Dutch), Technical University of Delft. Figure 6: Average- and maximum temperature, uniform heat source, CY = 0. Markers denote numerically calculated values. The lines represent the curvefit function. : 4 = 1/5, : 4 = 1/3, 0 : 4 = 1, A : 4=3, * : 4=5.

+

ing/rolling surfaces, Proc. Roy. SOC. A, Vol. 286, pp. 45-61. Cameron, A., 1966,Principles of lubrication, London. Carslaw, H. S., and Jaeger, J.C., 1959,Conduction of heat in solids, 2nd ed., Oxford.

Appendices A

Surface temperature distributions

For a uniform and a semi-ellipsoidal heat source the asymptotic contact temperature for large Pkclet numbers has been solved by Jaeger (1943) and De Winter (1967), respectively. In the presentation of these solutions the following new variables will be used

Heijningen, G.J.J. van, 1990,Memorandum, Technical University of Delft. Hertz, H., 1881, Uber die Berihrung fester elastischer Korper, Journal fur die reine und angewandte Mathematik, Vol. 92, pp. 156-171. Jaeger, J.C., 1943,Moving sources of heat, J . and Proc. Roy. SOC.N.S.W., Vol. 76, pp. 203224.

Thus for a uniform heat source the solution reads

500

B

with

F(g)=a

;

(O
F(a)=a-@T

(U?

1) .

Whereas for a semi-ellipsoidal heat source the solution reads

Function fits for elliptic integrals

The complete elliptic integrals of the first and second kind, K(k) (equation (4)) and E(k) (Appendix A), may be approximated by

{

K(k) = 1Tk12 1 2

+ k21n(4/k') rrk,2 2

0.251nk'} with F ( u )= (1 - a2)K(a)- (1 - 2g2)E(u) ;

(0 5 fJ 5 1) F ( u ) = 0{2(1 - u2)K(1/g) - (1 - 2u2)E(1/c7)}

In these equations K ( k ) and E(k) represent the complete elliptic integrals of the first and second kind, respectively; see Abrarnowitz and Stegun (1965). Useful approximate solutions for these elliptic integrals will be presented in the appendix B. For a uniform heat source at circular contact the asymptotic contact temperature for small Pkclet numbers has been solved by Carslaw and Jaeger (1959) as

'1

00

3=

lr

with k' d m . The error is less than 0.5 percent. Whereas Kuhlrnann- Wilsdorf (1987) introduced the following function fit for the shape factor of equation 4 4 S(4) = J(3 4314) (3 4-314)

+

(. 2 1).

du Jo(UR)J1(C7)U

( P = 0) ;

=

with R & and JO and J1 representing Bessel functions. For a semi-ellipsoidal source of heat at a circular contact the asymptotic contact temperature for small Pkclet numbers may be solved by applying the thermo-elastic analogue to Hertz (188l), leading to

( P = 0)

with H representing the Heaviside step function. The solutions for elliptical contacts are too complicated to be of any use.

+

The error is less than 3 percent.

C

Flash temperature calculations

Abramowitz and Stegun (1965), presented, among others, the following approximations for the exponential integral function:

+

~ l ( x ) Inx with lc(x)I

=

+

a0

+ u1x + a2x2 + a3x3 + a4x4

a5z5+c(x)

<2.

(0

< 2 5 1) ,

for

a0 = -0.57721566 , a1 = 0.99999193 , = -0.24991055 ,

a3 = 0.05519968 , a4 = -0.00976004 , a5 = 0.00107857 ;

whereas xe"El(x)

with Ic(x)I

(2 - R 2 )tan-' d m } H ( R- l)]

;

+ u 3 x 3 + u2x2 + a1x + a0 + b 3 t 3 + b2x2 + biz + bo

=

x4 x4

+

42)

< 2 . lo-*

(. 2 1)

7

for

uo = 0.2677737343 , bo = 3.9584969228 , a1 = 8.6347608925 , b l = 21.0996530827 , = 18.0590169730 , b2 = 25.6329561486 , a3 = 8.5733287401 , b l = 9.5733223454 .

Dissipative Processes in Tribology / D. Dowson et a]. (Editors) 0 1994 Elsevier Scicnce B.V. AU rights rcserved.

Soil

50 1

- Structure interface friction in reinforced soils

F. Bahloula, Y. Bourdeaub and V. Ogunrob alUT Bourges 63 Avenue Delattre de Tassigny, 18018 Bourges Cbdex, France bGeotechnical Laboratory, bat. 304, INSA of Lyon, 20 Avenue Albert Einstein, 69621 Villeurbanne Cedex, France

ABSTRACT The interfacial friction behaviour along soil-metallic inclusions were investigated both in modified shear box and pull-out tests. Two dense Hostun sands were used in the shear box in contact with steel plates of different degrees of roughness. The effects of steel roughness on the interfacial friction are presented as the ratio of the interfacial friction angles to the respective internal angle of the sands. Two different shapes of steel of different lengths were used in combinaison with one of the sands to perform pull-out tests in both small and large scale models. Influence of the shape, the length and the placement method of the inclusion on the interfacial friction behaviour were also examined. It was found that the apparent friction coefficient used here to show the effect of soil dilatancy on the test results decreases and tends towards an asymtotic value (the value of the friction coefficient of the smooth plate measured in the shear box and defined as tg Osa) as the applied vertical stress or confining stress increases. 1. INTRODUCTION

Soil, a highly economical natural construction material, having relatively good compressive and shear resistance, is known for its weakness in resisting tensile stresses. To eliminate this deficiency and thus improve the mechanical properties of soils (especially weak soils) for construction purposes, the technique of introducing tensile resisting inclusions in soils was developed and has for some recent years witnessed a great scientific success. This technique is referred to in general as soil reinforcement. When linear, horizontal, passive metallic inclusions are used in this technique to build an embankment from borrows we talk of "reinforced earth", while it is "soil nailing" if the reinforcements are introduced into in-place soil especially into excavated slopes of an embankment [l, 21. The principle of the last technique is represented in figure 1.

POTENTIAL FAILURE SURFACE

REINFORCEYENlB (METALLIC BARB)

1

Figure 1. Schema of the principle of soil nailing

502

For these types of applications, the inclusions carry the tensile forces prompting soil-inclusion interfacial friction to be mobilised, both in the active and the passive zones. Consequently, the taking into consideration of this phenomenon constitutes a fundamental element of soil reinforcement designing. From numerous experimentally based results (both from in-situ pullout tests and shear box friction tests), it became an established fact that, for tests performed on rigid inclusions, friction is a local and tridimensionnal phenomena, where the interacting soil dilatancy for granular soils plays a dominating role [3]. Furthermore, it was also discovered that soilinclusion friction is mobilised at relative slips of the order of millimetres for smooth inclusions, while for rough inclusions they are between a few millimetres and a few centimetres. Nevertheless, no conclusive study had earlier been conducted to determine these phenomena for the same soil-inclusion interface subjected to different variable conditions. Such a study was performed in Geotechnical laboratory of INSA in Lyon using Hostun sand and metallic shapes commonly used in Civil works. Direct shear and pullout tests were performed both in small scale (reduced model) and large scale models [4].

2. PLANE FRICTION APPROACH

mm dimension steel plates used in this study.

20\

I -'4J

RT RA

= 20.205mlcronr = 3.390mlcronm

RMS = 4.206 mlcronm

Figure 2. Profile of the smooth plate surface

Furthermore, tests were carried out on grooved surfaced steels with the aim of highlighting the influence of the state of the surface on friction mobilisation [S]. This type of artificial roughness is presented in figure 3 and table 1.

EXPERIMENTAL

2.1. Introduction Using the direct shear box or the simple shear box, friction tests can be carried out either under constant vertically imposed stress path or under imposed constant volume or even under an imposed stiffness. In the cases whereby the two latter conditions are adopted the soil is consequently prevented from dilating. In order to establish a pullout reference test for which the effect of dilatancy is dominant, friction tests under imposed constant normal stresses were performed on smooth steel plate placed in the lower box. Presented in figure 2 is a typical roughness profile of a 100 mm by 100

Figure 3. (a) Direct shear box test - (b) Detail profile of the surface of the steel plates

503

Table 1 Influence of Osa versus plate roughness (a x b) with "sand 2" in dense state (00= 39'8)

1

plate roughness (mm)! friction angle

0 2 2 2 1,5 3

1

1

23'3 25'6 26'4 28'1 39'7 39'7

I

Table 2 Influence of [asa versus plate roughness (a x b) with "sand 1" in dense state (00= 35'8)

I

0,59 0,64 0,66 0'71 1 1

Two types of Hostun sand both in densed state were used for this study: a fine sand (referred to in this publication as "sand 1") and a coarse sand (represented as "sand 2"). The respective maximum sizes of these crushed sands are 1 mm and 3 rnm, which are in fact equivalent to the most important dimension of the artificial roughness. It should be noted however that these tests were conducted for a maximum vertical stress of 200 kPa corresponding of course to an overburden load of a 12 m high earth fill. 2.2. Analysis of test results Tests results analysis is based essentially on the comparison between the sand-plate interfacial friction angle, referred to as Osa ,and the soil internal friction angle, referred to as eb

Tables 1 & 2 show the evolution of 0 ,,

the dilatancy effect.

with

plate roughness. We can notice also, that the ratio 'dsa / 0,, close to 0.6 for smooth plates, tends towards 1 once the grooves' s size approaches that of grains. This phenomenon may be explained by the fact that a better penetration of grains into the ribs induces rupture by soil shear to the detriment of soil-plate interface friction failure. From which resulted a rise in the volume of displaced grains, and thereby led to growth of

I

plate roughness (rnm) friction angle

I

3. THE EFFECT OF DILATANCY ON PULLOUT TESTS 3.1. Introduction Pullout tests were performed using fine dense "sand l", and two different types of steel shape: steel angles of 50 mm x 50 mm x 5 mm and 30 mrn x 30 mm x 3 rnrn laid in a box of 0.6 rn long. Two placement methods were utilised for these inclusions: by laying in place in or by driving into the soil. cylindrical steel bars of 8 mrn diameter laid in a small box (of 0.12 m long) and in two large test tanks of 2.4 rn and 4.9 rn long respectively. For the small scale models, the applied vertical charges varied between 10 and 250 kPa; while for the large scale models the heights of the overburden soil mass varied between 0.2 and 2.5 m.

-

-

3.2. Influence of test conditions and

Shape effect The comparison of the evolution of the average skin friction with respect to relative slip for the tests performed under a vertical stress of 100 kPa in the small scale models is presented in figure 4.

504

Experimental curves of the cylindrical inclusion present a peak softening behaviour contrary to those of other tests. This typical behaviour is observed both in the small scale models (figure 4) and in the large scale models (figure 5) where the confining stress is however much smaller.

100

+\

80

short bar 'laid"

n (0

4

steel angle "driven"

60

._E0

,

steel angle "laid"

.-0

+,

-f

60

r L

40

smooth plate

CI

(P

test conditions:

20

- small scale models

- dense line sand -0, = 700kPa I

4

0

I

0

1

2 3 slip U (mm)

4

5

f

I -

test conditions: cylindrical bars dense fine sand - a, = 79 kPa

-

Figure 4. Relationship between the skin friction and the relative slip for small models The reference curve, relating to the plane friction test performed with a smooth surfaced steel, permits us to show that the effect of dilation in the case of placed steels is a lot more pronounced for round bars than for the angle types. A possible explanation is the relatively elevated value of the blade dimension to grain ratio which might account for the softening of the tridimensionnal effect. Unlike the above, the repulsion and the densification of the sand as a result of the driving of the same angle steel is translated into an effect equivalent to that of dilation. The required slip to mobilise friction under this test condition (of the order of 10 mm) is however highly superior to those measured for the other types of tests (of the order of 1 mm).

I

O&

0

20

40

60

80

slip U (mm) Figure 5. Relationship between the skin friction and the relative slip. Comparaison between small and large scale models

3.3 Behavioural law governing t h e interfacial bond stress response of sand-steel Analytical or numerical modelling of the interfacial behaviour of cylindrical bars pullout response leads to taking into consideration of strain softening in the interfacial behaviour of sand-steel (figure 6).

505

Figure 7 shows the variation of p* with 0,for all the tests performed using dense "sand 1" and the steel inclusions. From this figure we notice that the effect of soil dilatancy becomes more and more obvious as the applied vertical stress becomes smaller, which may in some cases lead to values of p* greater than 1. It can be observed that for high values of 0, the experimental points tend towards a value corresponding to that of plane friction, given here as 0,416 (value defined by tg Osa). Furthemore, through the cluster of experimental points, we can notice a more or less pronounced effect of placement method and that of the shape of the inclusion.

local slip U (mm)

Figure 6. Relation between the skin friction and the local relative slip This type of governing behavioural law explains why friction is more rapidly mobilised in short bars (considered rigid) than in long ones (considered more flexible). Friction is progressively mobilised throughout the length of a long inclusion starting from a extreme zone no matter how small it may be. 3.4 Coefficient of apparent friction To evaluate the friction resistance of soilinclusion interface, certain codes of practise for reinforced soils resort to the local interfacial law concept usually of the elasto-plasticity or of FRANCK-ZHAOtype [6]. It is also possible however to adopt the notion of the apparent friction coefficient between the soil and the reinforcement. As a result of the difficulties in determining the stress field around the inclusion, this friction coefficient ( p * ) was consequently defined as the ratio of the maximum average frictional ("pullout") stress to the initial vertical or confining stress 0".

confining stress 0, (kPa)

Figure 7. Relationship between the apparent friction coefficient and the confining stress for dense fine sand

506

CONCLUSION

As a result of numerous researches undertaken on the field, the friction mobilised by a metallic section in contact with a dense sand susceptible to dilatancy remains a highly complex phenomenon to analyse. We noticed in particular that the shape, the length, the state of the surface and the placement method of an inclusion influenced its bond behaviour. Moreover, the respective influence of these different parameters can also depend on the confining stress REFERENCES

1. SCHLOSSER, F. "Analogies et differences dans le comportement des ouvrages en terre armbe el par clouage du sol". Annales de I'lnstitut Technique du Bgtiment el des Travaux Publics, 1983, no 418, pp. 8-26.

2. GUILLOUX, A. SCHLOSSER, F. "Soil nailing: practical applications". Proc. Symp. on Soil and Rock Improvements Technique including Geotextiles, Reinforced Earth and Modern Piling Techniques. Bangkok, 1984, vol. 1, pp. 237-252. 3. SCHLOSSER, F. GUILLOUX, A. "Le frottement dans le renforcement des sols". Revue Francaise de Geotechnique, 1981, no 16, pp. 65-77. 4. BOURDEAU, Y. LAREAL, P. BAHLOUL, F. "Frottement d'interface sol - metal: synthese d'experiences d'extraction". Sbminaire National du GRECO GBomateriaux, 1990, pp. 267-271. 5. BAHLOUL, F. "Etude experimentale de I'interaction sable structure et comportement en extraction d'inclusions m6talliques". These de Doctorat, INSA de Lyon, Sept. 1990. 6. FRANCK, R. MAO, S.K. "Estimation par des parametres pressiometriques de I'enfoncement sous charge axiale de pieux for& dans des sols fins". Bulletin de Liaison P. et CH., 1982, no 119, pp. 17-24.

-

Dissipative Processes in Tribology / D. Dowson et al. (Editors) 0 1994 Elsevier Science B.V. All rights rcserved.

507

D i a g r a m s for Estimation of the Solidified F i l m Thickness at High Pressure EHD contacts

N. Ohnoa, N. Kuwanoa and F. Hiranob

%epartment of Mechanical Engineering, Saga University, 1, Honjyo, Saga, 840, JAPAN, bProfessor Emeritus of Kyushu University, Visiting Professor of Oita University, 4-10-12, Takamiya, Minamiku, Fukuoka, 815, JAPAN,

This paper deals with diagrams for estimation of the film thickness at point contacts based upon observation by means of optical interference at pressures, sufficiently high to cause solidification of lubricants. The observed minimum film thickness at rollin contact is plotted here in the form the Greenwood's parameter HKmin - hmin/(arn0u) ?/3R1/3. This serves to estimate the minimum thickness with sufficient accuracy under wide conditions of circular and elliptic contacts. It is noted that in the solidification ranges VE (viscoelastic) and EP ( elastic-plastic) larger thickness is formed. The upper parts of these thickness curves are limited by the boundary of the PR (piezoviscous-rigid) range defined by Houpert. Notation

semi-width of contact ellipse in a y direction semi-width of contact ellipse in b x direction E' effective elastic modulus 2 2 [ 2/E'= (l-vl )/El+ (l-v2 /E21 G material parameter, aE' HK dimensionless film thickness, h/ (arlnu)W R 1 / 3 h film thickness k ellipticity parameter, a/b K modulus - bulk p average contact pressure pmax maximum Hertzian pressure R effective radius of curvature of contact, [2/R=l/s+l/%I radius of curvature in x direction radius of curvature in y direction % S shape parameter after Chiu and Sibley u speed parameter, q0u/E's u mean entrainment velocity 01 pressure-viscosity coefficient

?lo viscosity at atmospheric pressure

p

lubricant density

IE IR PE PR

isoviscous-elastic isoviscous-rigid piezoviscous-elastic piezoviscous-rigid

L

liquid viscoelasitc solid elastic-plastic solid

VE

EP

1. lIaxDumIoN

Since the establishment of the EHL theory in 1960s (1) a variety of theoretical and experimental investigations have been presented to solve practical problems concerning lubrication of machine elements and to apply to their design. For these purposes correct estimation of the EHL film thickness has been

always needed as t h e p r i n c i p a l s u b j e c t , : T h e o r e t i c a l l y , Hamrock and Dowson (2) p u b l i s h e d a series of t h e formulae f o r Hertzian contacts with general e l l i p t i c i t y corresponding t o t h e 4 r e p r e s e n t a t i v e regions : isoviscous-rigid IR, p i e z o v i s c o u s - r i g i d PR, i s o v i s c o u s - e l a s t i c I E , and p i e z o v i s c o u s - e l a s t i c PE. F u r t h e r d e t a i l e d d i s t r i b u t i o n of t h e EHL f i l m t h i c k n e s s and pressure were developed w i t h t h e a i d o f t h e m u l t i g r i d method a l s o a p p l i c a b l e t o c o n t a c t s between s u r f a c e s w i t h complicated f o r m s (3). I n spite of remarkable p r o g r e s s o f the theoretical treatment there is s t i l l a g r e a t gap between r e s u l t s and a c t u a l EHL phenomena, i n p a r t i c u l a r , i n high p r e s s u r e c o n t a c t s , where d e v i a t i o n from t h e g e n e r a l l y a s s u m e d pressured e n s i t y r e l a t i o n , e.g. by Dowson's formula ( 4 ) . I n f a c t , under u s u a l o p e r a t i n g cond i t i o n s of machine e l e m e n t s c o n t a c t pressures reach t o l e v e l s s u f f i c i e n t l y high not o n l y t o cause marked d e v i a t i o n from t h e DOwSOn'S d e n s i t y formula, b u t a l s o t o s o l i d i f y as showing v i s c o e l a s t i c or e l a s t i c - p l a s t i c behaviour ( 5 ) ( 6 ) . A t t h e p r e s e n t stage it i s e x t r e m e l y d i f f e r e n t t o t a k e t h e s e real phenomena i n t o c o n s i d e r a t i o n t h e o r e t i c a l l y . Hence, w e s h o u l d attempt f i r s t t o r e a r r a n g e e x p e r i m e n t a l r e s u l t s so f a r reported by a number o f a u t h o r s , where t h e h i g h pressure c o n d i t i o n s were considered whether c o n s c i o u s l y or not. Foord, Wedeven, Westlake and Cameron (7) observed i n t e r f e r e n c e EHL p a t t e r n s u s i n g t h e t y p i c a l t r a c t i o n o i l 5P4E. Chiu and S i b l e y (8) reported v a r i a t i o n o f t h e EHL p a t t e r n s i n c i r c u l a r contacts under r o l l i n g / s l i d i n g c o n d i t i o n s and demonstrated t h e r e s u l t s w i t h t h e a i d o f t h e s h a p e p a r a m e t e r , i.e. t h e r a t i o of t h e maximum hydrodynamic press u r e t o t h e maximum H e r t z i a n p r e s s u r e . The EHL p a t t e r n s i n a n e l l i p t i c

c o n t a c t were o b s e r v e d by T h o r p a n d Gohar (9) a n d Dalmaz (10). Koye a n d W i n e r (11) i n v e s t i g a t e d t h e e l l i p t i c p a t t e r n s w i t h a v a r i e t y of e l l i p t i c i t y . Recently, Kaneta e t al. (12) i n v e s t i g a t e d t h e effect o f t h e d i f f e r e n c e o f elastic moduli of c o n t a c t i n g s u r f a c e s on t h e i n t e r f e r e n c e p a t t e r n s c o n s i d e r i n g s o l i d i f i c a t i o n of l u b r i c a n t s . Here, i t is considered t o be s i g n i f i c a n t for r e a r r a n g e m e n t o f experiment a l r e s u l t s t o select t h e a p p r o p r i a t e graphical representation. The a u t h o r s (13) reached t h e conclus i o n t h a t t h e diagrammatic r e p r e s e n t a t i o n proposed by Greenwood (14) i s t h e most s u i t a b l e o n e , i.e. p l o t t i n g t h e EHL f i l m t h i c k n e s s by u s i n g t h e dimens i o n l e s s parameters G u l l 4 a n d apmax (cf. t h e list o f Notation). Greenwood u t i l i z e d t h i s r e p r e s e n t a t i o n t o show t h a t t h e r a t i o o f t h e M L f i l m t h i c k n e s s h (minimum or central) t o (arlou) 2/3R1/3 is limited within a c o m p a r a t i v e l y narrow range. The main r e a s o n t o u s e t h i s diagram f o r t h e authors' purpose l i e s i n t h e f a c t t h e s o l i d i f i c a t i o n b e h a v i o u r as w e l l as t h e d e n s i t y - p r e s s u r e r e l a t i o n is governed by t h e p r o d u c t of t h e press u r e - v i s c o s i t y c o e f f i c i e n t a and t h e a v e r a g e H e r t z i a n p r e s s u r e H as Greenwood proposed : upma = (3/2)ap. The a u t h o r s ' o b s e r v a t i o n was extended t o t h e s o l i d i f i c a t i o n r a n g e s ap > 1 3 ( v i s c o e l a s t i c range) and ap > 25 (elast i c - p l a s t i c r a n g e ) . The G r e e n w o o d ' s r e p r e s e n t a t i o n w a s used l a t e r by Hooke (15) a n d S u t c l i f f e (16) f o r d r a w i n g contour l i n e s of t h e c o e f f i c i e n t HKmln o r HKCen f o r t h e c e n t r a l f i l m t h i c k ness. A s a r e s u l t of o b s e r v a t i o n u s i n g a variety of lubricants d i f f e r e n t i n the p r e s s u r e - v i s c o s i t y c o e f f i c i e n t s dependi n g on t h e i r molecular s t r u c t u r e s , and optical f l a t s o f pyrex g l a s s and sapp h i r e , t h e a u t h o r s o b t a i n e d systema-

509

tically wide variation of the EHL film thickness and patterns. The representation is shown in the form of a group of contour lines together with the interference patterns. In particular, in the case of rolling accompanying sliding the differences due to the solidification ranges become quite significant.

Synthetic hydrocarbon oil HC40 Synthetic traction oil SNlOO Beside these oils in pure rolling contacts, other lubricants were used for rolling / sliding experiments : Hydrogenated tar naphthenic oil TN220 5 ring polyphenyl ether 5P4E Their physical and chemical properties are listed in Table 1.

2. ExP-AL-

The apparatuses used in the present investigation for measuring basic properties of lubricants are the viscometer of a falling ball type, the high pressure cylinder for the density measurement at pressures up to 1.2 GPa and at temperatures from o to 100 OC as described in the authors' previous reports in detail (13)(17). Hence, the general views of these apparatuses are omitted here. For observation of EHL patterns by means of the usual interferometic method a rolling/sliding apparatus was composed of a pyrex glass or sapphire optical flat, a rolling ball of bearing steel, 23.8 mm in diameter or a barrel shaped roller, 23.6 mm in max. outer diameter and 84 mm in radius of curvature in the meridian plane. The experimental conditions in the EHL experiments are as follows : Rolling speed 30 - 600 mm/s Contact load 22 - 119 N Mean Hertzian contact pressure in circular contact with pyrex glass 0.29 - 0.50 GPa with sapphire 0.57 - 1.00 GPa in elliptic contact with pyrex glass 0.16 - 0.29 GPa with sapphire 0.33 - 0.58 GPa Temperature room temperature The experimented lubricants are : Paraffinic mineral oil, superheated steam cylinder oil sco

3.1 Density measurements An example of the density measurements is shown in Fig. 1 for the traction oil SN100. Here, it is noted that remarkable deviation from the Dowson's formula generally assumed in theoretical investigations of EHL is observed at high pressures, and that the density - pressure curve approaches a linear relation. The bulk modulus is estimated from the density - pressure curve by differentiating as K = p(dp/dp). Fig. 2 shows plots of the bulk moduli of the experimented oils SCO and S N l O O against the product of the pressure-viscosity coefficient c1 and pressure p, a single relation is obtained irrespective of temperatures and the difference of oils. Furthermore, there are two characteristic points up = 13 and 25 corresponding to transition from liquids to viscoelastic solids and that from viscoelastic to elastic-plastic solids, respectively. Beyond the elastic-plastic transition points the bulk moduli attain constant values. From results of density measurements of a number of paraffinic, naphthenic mineral oils and synthetic traction oils, the general feature is confirmed to be little influenced by the difference of oils. However, the constant values of K in the elastic-plastic range are different

510

depending on molecular structures of oils. 3.2 EHL patterns Examples of interferometric patterns in the circular and elliptic contacts are shown in Fig. 3 and Fig. 4. The fringes represent contour lines corresponding to the difference of height 0.2 pm. The regular variation of the EHL patterns will be explained in relation to the diagrammatic representation in the next paragraph.

As briefly mentioned in the Introduction, the authors attempted to construct diagrams for estimation of the EHL film thickness based upon the observed results, referring to the Greenwood's representation, where the product of the pressure-viscosity coefficient ct and the maximum Hertzian pressure pm, as the abscissa and the dimensionless parameter GU1/4 as the ordinate are used. Here, however, considering the facility to correlate with the measurements of the high pressure viscosity and density under static conditions, the maximum Hertzian pressure pm, was replaced by the average contact pressure = (2/3)pmax. The dimensionless parameters G and U were calculated under the experimental conditions by the usual means as listed in the Notation. Thus, the dimensionless coefficient HKmln according to Greenwood was estimated by counting the order of interference fringes corresponding to the minimum film thickness at the bottom of the horse shoe. Here, the abscissa ap was changed under 18 different experimental conditions with combination of 3 kinds of oils different in a, 3 different aver-

age pressures, and 2 kinds of the optical flats, i.e. pyrex glass and sapphire different in the elastic modulus El. On the other hand, the speed parameter U was changed continuously in the range shown in the paragraph 2. Thus, the diagram shown in Fig. 3 covers a quite wide range of practical significance. The contour lines ,corresponding to the values of HK min are drawn based upon plenty of experimental points. These are also evidenced by regular variation of the EHL patterns, in particular, that of the horse shoes being influenced b the dimesionless parameters ctF and GU5 4. First, it is pointed that the group of the contour lines is characterized by a ridge running in the parallel direction to the border line between the isoviscous-rigid region IR and the piezoviscous-rigid region PR. The summit of the ridge is suggested to appear in the solidified range as the elasticplastic solids. As evidenced by the concentric fringes, the zone near to the border line of IR is considered to be occupied by the PR region modified by Houpert (18). The peculiar patterns with sharp notches appearing near the border line between PR and PE regions, i.e. according to Houpert the physical EHD zone were also observed by Foord et al. ( 7 ) using 5P4E. Fig. 4 shows the contour lines and the interference patterns for elliptic contact with an ellipticity parameter k = 3:6. The presence of the ridge of HKmln is also clearly recognized here, but the general feature is slightly different from the circular contact. The concentric patterns are also observed in the PR region. Comparing with the diagram for the,circular contact, the values of HKmln for the elliptic contact are higher, as theoretically suggested by the Hamrock-Dowson's formulae (2) in the form:

511

{l-exp(-0.68k) }.

5 . DISCUSSIm

owing to a variety of combination of the experimental conditions, the diagrams for estimation of the film thickness by the authors are characterized by a much wider range compared with those reported so far, as depicted in Fig. 5. The plotted points in the Greenwood's diagram are theoretically calculated results by several authors in the majority, expect a few points experimentally observed by Koye and Winer (ll), which show a good coincidence with the results in Fig. 3. Though their experimenta1 ranges were limited to narrow one, the presence of the peak in the vicinity of @ = 20 and GU1/4 = 20 noted here. other experimental work was carried out by Chiu and Sibley (8). They demonstrated the regular variation of the EHL patterns in relation to the shape parameter s as the ratio of the maximum hydrodynamic pressure to the maximum Hertzian pressure. The fact according to them that the transition from the EHL patterns to the concentric ones appears under the condition of S = 1 coincides with the treatment by Houpert (18) and also with the authors' result shown in Fig. 3. Concerning the regular variation of the interference patterns, similarity is first recognized in the direction parallel to the ridge of the contour lines. On the other hand, in the transverse direction marked transition in the shape of horse shoes takes place quite regularly. According to Chiu and Sibley (8)the location coordinate of the pressure spikes estimated by the ratia of the distance between the beginning of the

constriction in the film shape to the contact centre increases with an increase in the shape parameter. The lines of constant values of the shape parameter are also shown in Fig. 5 , running in the direction parallel to the ridge. This coincides with the authors' results in Fig. 3, which suggest another remarkable change in the width of the horse shoe. With a decrease in or an increase in the shape parameter its width in the direction of motion decreases and beyond the ridge line the location of the minimum film thickness becomes to appear on both sides of the horse shoe, as shown by the patterns corresponding to HK = 0.8. Next, Fig. 4 for the elliptic contacts shows the similar trend of the interference patterns, though the variation in the location of the minimum film thickness is not always clear. In fig. 3 and Fig. 4 the solidified regions L to VE and VE to EP are indicated by vertical lines corresponding to the condition ap = 13 and 25 as shown in Fig. 2. under the pure rolling condition the effect of the solidification of oils hardly recognized explicitly. Under the rolling/sliding condition the indirect evidence is considered to be given by the range of occurrence of dimples which is limited to a comparatively narrow range under the solidified region (12). As shown in Fig. 6, there is a marked change in the EHL patterns caused by the slide/roll ratio C : Fig. 6 a) observed with a lower ratio shows little deviation from the pattern in pure rolling. In contrast to this, in Fig. 6 b) the film profile exhibits no parallel film, but remarkable inclination develops on the the inlet side corresponding to a higher slide/roll ratio . In Fig. 6 c) more deviation is noted in front of the inlet. The abrupt changes of the pat-

6di4

512

terns are observed under the transition conditions VE/L and EP/VE, as shown in Fig. 7. Here, qualitative estimation of the minimum film thickness is omitted and will be reported in the near future. The changes caused by the solidification of oils occurring predominantly on the inlet side of the contact are considered to be responsible for emphasizing its effect. Throughout the present investigation the product of the pressure-viscosity coefficient and the average pressure is used as the characteristic parameter concerning the aggregation states of lubricants depending on pressures, temperatures, and molecular structures. However, it should be further discussed considering that the pressure-viscosity coefficient is only applicable to liquid states of oils. The authors are investigating the free volume of lubricant, which can be estimated from the results of density-pressure curves as shown in Fig. 1 using the lines of constant bulk moduli in the range of elastic-plastic solidification as a reference condition. It is confirmed that thus estimated free volumes is closely related with the product ap in spite of the discrepancy pointed above. Hence, finally the apparent pressureviscosity coefficient should be replaced by the free volume.

6. coNcIuslONS

The authors carried out a series of systematic experiments on EHL film patterns, under wide conditions varying pressures, temperatures, and lubricants with different molecular structures. The most suited representation for the results of observation is concluded to use the diagrams developed by Greenwood with the coordinate system ap and

GU1/4 as defined in the text. For circular contacts and also elliptic contacts the dimensionless parameter to estimate the minimum film thickness is plotted in the Greenwood's representation. The contour lines of this parameter are characterized by the presence of the ridges running in the parallel direction to the border lines between the isoviscous-rigid and piezov ' Scous-rigid regions. The general € tures are evidenced by the regular Ige in the interference patterns.

ie authors wish to express their <s to Mr. Y. Nakahara, Saga univer-

, for his efforts in preparing the rimental apparatuses; and also to jrs. I. Komori and K. Tanimoto for r cooperation. The oils were sup2d by Idemitsu Kosan Co., Ltd and pon Steel Chemical Co., Ltd. The sent research was supported by a nt-in-Aid for Scientific Research 1. 03650131) from Japanese Ministry . Education. IFERENCES 1. D.Dowson and G.R.Higginson(eds.) , Elasto-Hydrodynamic Lubrication, Pergaman, Oxford, 1966. 2. B.J.Hamrock and D.Dawson(eds.), Ball Bearing Lubrication, John Wiley 6i Sons, New York, 1981. 3. A.A.Lubrecht, W.E.ten Napel and A.V. Bosma, T r a n s ASME, JOT, 109, 3 (1987) 437. 4. D.Dowson, G.Higginson and A.V.Whitaker, J.Mech.Eng.Sci. , 4, 2 (1962) 121. 5 . B.Jacobson, ASLE Trans, 17, 4 (1974) 290. 5. M.Alsaad, S.Bair, D.M.Sanborn and W.O.Winer, Trans ASME, JOLT, 100, 3

513

(1978) 404. 7. C.A.Foord, L.D.Wedeven, F.J.Westlake

and A.Cameron, Proc. Instn. Mech. Engrs, 184, Pt.1 (1969-70) 487. 8. Y.P.Chiu and L.B.Sibley, Lubrication Engineering, J.ASLE, 28 (1972) 48. 9. N.Thorp and R.Gohar, Trans ASME, JOLT, 94, 3 (1972) 199. 10. G.Dalmaz, Proc. of the 5th LeedsLyon Symposium on Tribology, (1978)

14. J.A.Greenwocd, Proc. Instn. Mech. Engrs, 202, C 1 (1988) 11. 15. C.J.Hooke, Proc. Instn. Mech. Engrs, 204, C3 (1990) 199. 16. M.P.Sutcliffe, Proc. Instn. Mech. Engrs, 204, C4 (1990) 273. 17. F-Hirano,N.Kuwano and N.Ohno, PrOC. of the JSLE International Tribology Conference Tokyo, (1985) 841.

18. L-Houpert, Trans ASME, JOT, 106, 3

71.

11. K.A.Koye and W.O.Winer,Trans ASME, 103, 2 (1981) 284. 1 2 . M-Kaneta,H.Nishikawa, K-Kameishi, T.Sakai and N.Ohno, Trans ASME, JOT, 114, 1 (1992) 75. 13. F.Hirano, N.Kuwano and N.Ohno,

(1984) 375. 19. A-Vakilzadeh and R.Gohar, Journal

Mechanical Engineering Science, 19, 1 (1977) 22.

Proc. of the Japan International Tribology Conference Nagoya, (1990) 1629.

Table 1 Properties of oils

Atomospheric viscosity

Oi1

(m2/s) 4OoC 100°C ~

sco

597 409 99.5 203 326

HC40

SNlOO TN220 5P4E

SCO HC40 SNlOO

:

: :

TN220 :

5P4E

:

~~

35.3 40.3 7.94 8.28 11.9

Density (g/mu

l5OC

Pressure-viscosity coefficient

Refractive index 20

(GPa-') 4OoC 100°C

~~~~~~~~~

"D ~

0.9030 0.8300 0.9289 1.0029 1.2088

21.0 15.7 40.0 60.4 37.3

11.5 9.0 16.9 23.9 10.9

paraffinic mineral oil, superheated steam cylinder oil synthetic hydrocarbon oil synthetic traction oil hydrogenated tar naphthenic oil 5 ring polyphenyl ether

1.4969 1.4665 1.5010 1.5337 1.6329

514

t

Fig. 1 Density

0

1

-

p r e s s u r e c u r v e of t r a c t i o n o i l SNlOO

2o

ap

40

60

F i g . 2 B u l k m o d u l i of SCO a n d SNlOO o i l s p l o t t e d a g a i n s t ap 01 : P r e s s u r e - v i s c o s i t y c o e f f i . c i e n t

515

Fig. 3

Contour lines of dimensionless minimum film thickness parameter HFin = h,in / (allou)2/3R1/3 €or circular contact P : pyrex glass S : sapphire W : load parameter w/E'RX2 w : load

516

Fig. 4

Contour lines of dimensionless minimum film thickness parameter HEin = hmin / (ar)o~)2/3R1/3 for elliptic contact k=3.6 P : pyrex glass S : sapphire W : load parameter w / E @ R , ~ w : load

517

50 -

I

I

I

I

I

I

I l l

-

-

x3 --

Kaneta,Nishi kawq

0

Foord,Wedeven, WestIake & Cameron

-

Ohno,Kuwano & Hirano

Fig. 5

Comparison of experimental ranges S : shape parameter defined by Chiu and Sibley

a) TN220-S, s : = 1 4 % Up=42, GU'/~=~I Fig. 6

b ) TN220-S, &=112%

C@=43,

GU1/*=57

C) 5P4E-S, t = 5 0 % 0$=30, GU1/4=34

EHL patterns in rolling/sliding contact t : sliding/rolling ratio (u1-u2)/{(ul+u2)/23 ul: ball speed u2: optical flat speed P : pyrex glass S : sapphire

518

Fig. 7

Changes of EHL patterns and film profiles at transitions from liquid (ap13) and from viscoelastic ( a p ( 2 5 ) to elastic-plastic state (ap)25) S : sapphire r : sliding/rolling ratio

SESSION XI1 FATIGUE AND DAMAGE Chairman:

Professor K Ludema

Paper XI1 (i)

Fracture Modes in Wear Particle Formation

Paper XI1 (ii)

The Influence of Lubricant Degradation on Friction in the Piston Ring Pack

Paper XI1 (iii)

High Speed Damage Under Transient Conditions

Paper XI1 (iv)

Incipient Sliding Analysis Between Two Contacting Bodies. Critical Analysis of Friction Law

This Page Intentionally Left Blank

Dissipative Processes in 'l'ribology / I). Dowson e l al. (Editors) 1994 Elsevicr Scicncc R.V.

52 1

Fracture modes in wear particle formation. A.A.Torrance"and Zhou F.b a

Department of Mechanical and Manufacturing Engineering, Trinity College, Dublin 2, Ireland. Department of Mechanical Engineering, Beijing Civil Engineering Institute, P.R.China.

One way of studying the way wear particles are produced is to slide a hard wedge against a soft metal and to observe what happens. The stresses and strains can be calculated simply in the plastically deforming region from a slip-line field as an aid to interpreting the results. This paper reviews recent work in this field, then describes some experiments which show the complete fracture process leading to wear particle formation. Two distinct particle shapes may be produced, depending on wedge angle and coefficient of friction: "blocky" at low fixtion and "flaky" at higher friction. This cannot be explained purely on the basis of stresses in the plastic region. However, calculation of the stresses just behind the plastic contact using a stress function allows crack propagation directions and wear particle morphology to be predicted satisfactorarily. 1. INTRODUCTION

n \ Hard Wedge

From the earliest days, the plasticity which occurs at the contact between rough surfaces has dominated the study of wear. It is an important feature of abrasive ( I ) and adhesive (2) wear, and in the more recent theory of delamination wear (3). This has naturally led to attempts to understand hction and wear by analyzing the stresses at asperity contacts using the theory of plasticity. Early work (4)assumed flat asperity contacts and led to the theory of junction growth which was successful in explaining many frictional phenomena. Subsequently, more refined contact models, based on slip-line fields have been developed (5,6). These allow a calculation of asperity stress which explains the effects of roughness on friction coefficient (7,8). Calculations of the plastic strain caused by the passage of an asperity can be used as the basis for predictions of wear coefficients (9- 1 1). More recent work (12), in which the asperity contact is modelled by using a hard steel wedge sliding against an aluminium alloy has confirmed by visioplasticity the main features of the strains predicted from slip-line fields. It has also been possible (10,12) to observe the progressive development of cracks after repeated passage of the wedge over the aluminium.

---

% <7-----

Sofl Material

Range of stress plots. (figs 12 - 14) Elastic/Plastic Boundary

Figure 1. Slipline field for asperity contact with angles used for elasto-plastic calculations. The essential features of the deformation field are shown in figure 1. Close to the wedge is a region of high plastic strain represented by the slip-line field ABCDE. This is surrounded by a region of "contained plasticity" where the plastic strains are low even though the stresses are above yield. The elastic/plastic boundary at the rear of the contact is straight close to the surface to which it makes an angle Kopalinsky (10,12) found that the front surface of the wave (AE) was not flat. Local variations in deformation caused it to become

w.

522

Figure 2. Bowden-Leben machine. Section through hard slider shown in inset. wrinkled. When the wrinkles passed through the contact (ED), they were folded over and ironed out into small crack-like defects roughly parallel to the surface. Once they had formed, these defects could develop into cracks which propagated down into the soft metal at angles of between 10' and 20' to the surface in the opposite direction to the motion of the wedge. The length of these cracks increased progressively with the number of passes of the wedge and with the strain induced by each pass. However, when the wave started to break up, the experiments were discontinued, so it was not possible to observe the complete cycle of crack nucleation and propagation leading to the formation of a wear particle. As for the initial direction of crack propagation, it corresponds very roughly to the direction of maximum shear stress at the front of the wave, given by the slipline AB in fig.1. However, over the range of conditions studied by Kopalinsky (10,12), the angle which AB makes to the surface varies between 39' and 14', which hardly corresponds exactly to the observed direction of the cracks. This could be partly due to the cracks rotating out of their original positions as they pass through the wave, but calculations of the expected rotation show that this cannot be the complete explanation. Since the work of Kopalinsky verifies many of the predictions of Challen and Oxley's wave theory of fhction and wear (5,6) and gives

much usehl information on the genesis of cracks which must lead to wear particles, it seemed worth pursuing it further. Therefore, in this paper we describe some experiments where wear particles were actually produced, and some where crack development and propagation were studied. As it had not been possible to find agreement between crack propagation directions and the calculated plastic stress field, calculations were also made of the elastic stress field to the rear of the contact using an approximate stress function solution given by Olver and Johnson (13) which allowed the observed crack directions to be better explained. 2. EXPERIMENTAL

In the fist series of experiments the Bowden-Leben machine shown in figure 2 was used. The hard wedge (1) was produced by turning a 12.5 mm diameter bar of AISI 52100 to the shape shown in the inset. It was then hardened to 800 Hv and ground. A square sided block of H321 aluminium alloy (90 Hv) (2) was loaded against it. The steel bar was moved beneath the soft slider at a speed of 0.33 mm/s with a leadscrew (7) driven by a stepper motor (8). A known load is placed in (3) and the frictional force recorded by monitoring with the transducer (6) the displacement of the bar (4) which is attached to the slider and restrained by the cantilever (5). The system was calibrated with deadweights. A load of 50N was applied at (3).

523

The attack angle of the wedge was altered between 5' and 15' by placing packing pieces under either end of the AISI 52100 bar. No lubricant was used. For each attack angle, several tests were run, with the number of strokes increasing from 5 to 20. The coefficient of friction was recorded continuously with a chart recorder. After each test, the aluminium slider was sectioned along the centre line of the wear track, parallel to the direction of motion, and examined in a Hitachi S520 S.E.M. for surface and subsurface cracks. While this first test was suitable for investigating the initial stages of the wear process: crack nucleation and propagation, it was not suitable for generating wear debris and studying its shape. A second test was developed for this purpose using the apparatus shown in figure 3.

7

throughout a test on a chart recorder. Grooves were machined in the bar to allow the wearing surface to dip into an oil bath mounted on the trunnions. Lubrication was provided by engine oil (Elf 15W/40 competition S). The wearing surface was 10 mm in width - significantly wider than the wedge. Tests were run with a variety of attack angles between 2.5' and 10'. 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 test was allowed to run for 10 minutes, giving 350 passes of the wedge over each point of the bar's surface. Normal loads of 400N, 500N and 600N were used for each wedge angle. After each test, the oil was diluted with solvent and filtered to collect the debris. The volume of wear ddbris produced in each test was calculated from measurements of the diameter of the aluminium bar before and after each test. Unfortunately, due to the small number of specimens available, the aluminium had to be re-used for different wedge angles. Therefore it was not possible to obtain micrographs of crack propagation from these tests. However, as described below, it was possible to obtain useful information on the shape of wear debris.

3. RESULTS. DYNAMOMETER

3.1 Microscopy The initial examination of specimens worn in the Bowden-Leben machine confirmed the observations of other workers (10,12). Cracks started from surface wrinkles and propagated down into the aluminium at relatively shallow angles against the direction of motion of the wedge. Figure 4 shows an example of such a crack. It is at a well developed stage, having started to turn up towards the surface at its tip. It may easily be supposed that one further pass of the wedge would lead to detachment of a flaky wear particle. This particular crack was observed after 15 passes at an attack angle of 8'. Its total length is around 50 pn and its maximum depth around 8 p.For most of its length it runs at an angle of about 12' to the surface. Whatever attack angle was used, the crack orientation was generally much the Same in these

1 LATHE SADDLE Figure 3. Wedge wear test on lathe. One end of an aluminium bar (9= 34 mm, Hv45) 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 to a blunt wedge of the desired attack angle. It was 6.5 mm in width and was mounted in the loading arm,held against the bar by tightening the loading bolt. Alignment with the axis of the bar is ensured by mounting the loading assembly on trunnions. These in turn are mounted on a 3-axis Kistler dynamometer fixed to the saddle of the lathe which allows normal and tangential forces to be recorded

524

Figure 4. Crack in section. a=8’, 15 passes. Motion of wedge: -p tests. However, in some cases, mainly at lower attack angles and smaller numbers of cycles, it was possible to observe pairs of cracks, more steeply inclined to the surface as shown in figure 5. Here, if the cracks were to join, a more equiaxed, blocky wear particle might be expected to result. If the test is continued to higher numbers of passes, it is possible to observe the sites from which wear particles have become detached. A typical example is shown in figure 6 . The crack has evidently started by propagating down from the surface at a shallow angle against the direction of motion of the wedge (lefi hand side of figure) as observed by Kopalinsky (IO,l2). It has then run roughly parallel to the surface until a secondary fracture has occurred perpendicular to the surface (right hand side of figure) allowing a flake of metal to detach itself. A similar fracture, viewed from a different angle is shown in figure 7. The metal surface beneath the site of the wear particle is heavily scored in the direction of motion of the wedge. This is consistent with the crack having propagated under shear stress combined with hydrostatic pressure, as might be expected in an asperity contact. The average length of the plastic wave formed by the wedge in these experiments was about 120 p.The length of the cracks leading to

-

Figure 5 . Pair of cracks. 0(=8”, 10 passes. Motion of wedge:

Figure 6. Site of particle detachment. a=7’, 20 passes. Motion of wedge: 4 wear was around 1/3 of this, whlst their depth was only 1/20 of this. Therefore, it is the stresses close to the surface which must be responsible for the process. As explained above. it was necessary to use the lathe test to generate sufficient debris to

525

Figure 7. Surface after wear. a=8" , 15 passes. Motion of wedge:

Figure 8. Wear particles from high angle test. a = 8 O , p = 0.16.

study the nature of the wear particles produced by sliding the wedge . over the aluminium. At higher friction and attack angles (a > 5 O , p > 0.15) the flaky wear particles which might be expected from the cracks seen in the previous micrographs were observed. A typical sample is shown in figure 8. Rather surprisingly though, a completely hfferent shape of particle was observed at lower attack angles. An example is shown in figure 9. The particles are blocky and resemble irregular pyramids. This suggests that there must be a change in the stress field responsible for producing the wear debris at low attack angles.

3.2 Friction and wear The friction and wear results from these tests are presented in figure 10. Wear results from the lathe test are presented in non-dimensional form as Archard's wear coefficient defined in (2). The friction results are consistent with the predictions of the slip-line field of figure 1. For the lathe tests, which were lubricated, the ratio of interfacial shear strength to the shear strength of the aluminium is in the range 0.25-0.3, whereas for the unlubricated Bowden-Leben tests it is within the range 0.6-0.7. It would be possible to use these results as a test of some of the theories of friction and wear mentioned in the introduction. However, this is not

Figure 9. Wear particles from low angle test. a=2.5', p=0.13

our purpose here. It is rather to explain the way in which cracks propagate to form wear particles. Furthermore, to test properly these theories, a more comprehensive set of results would be needed which must await the completion of further experiments.

526

( 5

0.7 I

3,

I

11 4

0' 0

5

10

' 0 15

Attack angle

Figure 10. Friction (jt) and wear (k) coefficients. l:p, Bowden-Leben. 2: p, Lathe. 3: k, Lathe.

4. DISCUSSION.

Using the slip-line field of figure 1 alone, it is difficult to explain completely the crack directions and the form of the wear particles described in the previous section. As we have pointed out elsewhere (14), the most favourable place for cracks to propagate within the field is at the front of the wave, along AB, where the hydrostatic pressure is at a minimum. However, if the crack were to follow this slip-line, we would expect large, blocky particles to be produced in every case. Moreover, their thickness and length would be similar to those of the wave, whereas they are actually shorter and, in most cases, much thinner than this. Also, it would be very difficult for cracks to propagate within the region ECD where the hydrostatic pressure may be up to four times the shear yield strength. It is possible that easier crack propagation could take place immediately behind the wave, in region of contained plasticity or in the elastically stressed region. An approximate method of calculating the stresses here using a stress function has recently been developed (15) from an earlier indentation model of Olver and Johnson (13). A brief description is given in the appendix.

b) Q = 8O, p = 0.215, f = 0.3. Figure 11. Principal stresses behind wave. Scale of distance shown at top right. Scale of stress at bottom right.

This method was used to generate the diagrams shown in figure 11. The stress calculations have been restricted to a narrow region, 0 . 2 behind ~ the tip of the wedge and O.la beneath it, where 2a is the length of the wave (AD). Previous work (15) indicates that the magnitude of the stresses falls quite rapidly at greater distances from the wedge tip. The stresses at greater depths are probably not significant since it has already been shown that the cracks leading to wear occur within 0 . 1 ~of the surface. Restricting the stress calculation to this narrow region has the added advantage that it is here where it should be the most accurate, its basic assumption of the elastic region acting as a wedge loaded along one face with a

527

Figure 12. Hydrostatic pressure and shear stress at a depthofO.la. cx=2.5',p=0.109,f=0.3. 60

rIydrostatic pressurc

.

40

I

20 0

T i b 5 0

6

-20

Shear stress

-40

-60 -0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

xla

Figure 14. Hydrostatic pressure and shear stress at a depthofO.1u. a = 10',p=00.254,f=0.3. shear stress and a hydrostatic pressure being close to reality. The two loading conditions in figure 1 1 have been chosen to illustrate how the stresses change as the friction rises from a lower level, where blocky wear particles are produced (1 la) to a slightly higher value where flaky particles result ( 1 lb). Arrows point outwards for tensile stress and inwards for compressive stress. It can be seen at once from this figure that the stresses are almost everywhere compressive at p = 0.144, whereas at

Figure 13. Hydrostatic pressure and shear stress at a depth of O.la. a = 5 O , p = 0.144, f = 0.25. p = 0.215 there are significant tensile stresses close to the surface. Below the surface, the most compressive principal stress is more steeply inclined to the horizontal when the hction is higher. The magnitude and direction of the shear stresses which probably control most of the crack propagation are less obvious from this figure. It can be better seen in figures 12-14, which show plots of hydrostatic pressure, and shear stress magnitude and inclination against position at a depth of 0. la. Choosing a smaller depth would give the same form of plot, since the stresses in the elastic zone (HDI) are a function only of 8; but the stresses and inclination would change more rapidly with x. The origin of these plots is beneath the point D in fig. I . The positive direction of x is towards the right, i.e., behind the contact, and the range over which they have been made is indicated in fig. 1 by the mowed line. The inclination of the shear stress is taken as negative when it is against the direction of motion of the wedge. Thus the slip-line AB has a negative inclination whilst the slip-line CD has a positive inclination. Ease of shear crack propagation at any particular point can be judged relative to the conditions along AB (fig. l), where the hydrostatic pressure and the shear stress are both equal to K. A lower pressure or a higher shear stress will give easier crack propagation. Thus when a = 2.5' and

528

0.8

1.5

0.7

0.6

1

0.5

e

$

B

3.-

(c.

0

0.5

0.4

b

v)

0.3

0.2

0

3

‘E k u8

0.1

0

-0.5

5

0

15

10

20

25

Attack angle (degrees)

Figure 15. Maximum surface stress (upper curve) and coefficient of friction (lower curve) vs. a. when a = 5’, the hydrostatic pressure at the origin is around 1.6K, so crack propagation at this point will be more difficult than at the front of the wave even though the shear stress is the same. Further back from the origin, the hydrostatic pressure falls faster than the shear stress, and they both become equal to 0.8K at xla 0.05. In both cases, the inclination of the shear stress to the surface is positive here (10’ - 15”).Shear cracks will therefore propagate more easily at the front of the wave, against the motion of the wedge (negative inclination). An example is the right-hand crack in fig. 5 . At the rear, they may also propagate, but more slowly and with positive inclination. At no point will propagation parallel to the surface be favourable. The result of this would be to generate pairs of cracks like those shown in fig. 5 . If they join, a blocky wear fragment will leave the surface, but in the test of fig. 5, flakes form more quickly. At higher attack angles the hydrostatic pressure falls more rapidly behind the deformation region. Thus at a = 10’ both shear stress and hydrostatic pressure are equal to -K at the origin. However the inclination of the shear stress is now slightly negative (--8”), becoming parallel to the surface at x/a -0.1. Conditions will now be more favourable for crack propagation nearly parallel to the surface, which should favour the formation of flaky wear particles.

-

-

Another factor which may influence crack propagation paths and the shape of wear particles is the size of the surface stress. The way this changes with attack angle and friction coefficient is shown in figure 15. Below 01 = 4’ (p = 0.14) it is compressive, so there is no possibility of tensile cracks forming perpendicular to the surface to finish the process of detaching a flake. At higher values of OL and p the surface stress becomes steadily more tensile, whilst the depth of the shear zone becomes steadily smaller, increasing the tendency for flakes to form. Using these arguments, it is possible to explain the shapes of the wear particles observed and why there should be a change in particle morphology at low attack angles. The changeover between the two shapes, blocky and flaky, occurs when the maximum surface stress becomes tensile. This coincides with a reduced hydrostatic pressure behind the contact and a change in the orientation of the shear stress which together favour the formation of flakes. However, the exact inclination of the cracks to the surface is not easy to predict from the stress field. There are perhaps two reasons for this. Firstly, each crack, as it passes through the contact, is subject to a stress field which varies greatly in intensity and inclination. Thus the propagation direction may vary as the position of the crack changes. Secondly, the material passing through the high deformation zone (ABCDE in fig. 1) suffers considerable strain, especially at high friction, and this will be sufficient to rotate cracks out of their original orientations as Kopalinsky has already pointed out (10,12).

5. CONCLUSIONS. 1. The orientation of cracks formed in aluminium surfaces by the repeated passage of a blunt hard wedge has been found to be as described by previous workers. 2. Prolonged sliding of the wedge produces debris which is blocky at low friction and flaky at high fnction. 3. The morphology of the debris, and to some extent, the orientation of the cracks can be explained using stress fields calculated from an approximate elastoplastic analytical model.

529

REFERENCES. 1. R.C.D.Richardson, The wear of metals by hard abrasives, Wear, I0 (1 967) 29 1. 2. J.F.Archard and W.Hirst, The wear of materials under unlubricated conditions, Proc. Roy. SOC. London Ser. A , 236, (1956) 397. 3. N.P.Suh, The delamination theory of wear, Wear, 25 (1973) 11 1. 4. F.P.Bowden and D.Tabor, The Friction and Lubrication of Solids Vol 11, Oxford 1964. 5. J.M.Challen and P.L.B. Oxley, An explanation of the different regimes of friction and wear using asperity deformation models, Wear, 53 (1979) 229-243. 6. J.M.Challen, L.J.McLean and P.L.B.Oxley, Plastic deformation of a metal surface in sliding contact with a hard wedge, Proc. Roy. Soc. London Ser. A , 394 (1984) 161-181. 7. H.Moalic, J.A.Fitzpatrick and A.A.Torrance, The correlation of the characteristics of rough surfaces with their friction coefficients, Proc. I. Mech. E., 201 (1987) 321-329. 8. P.Lacey, A.A.Torrance and J.A.Fitzpatrick, The relation between the friction of lubricated surfaces and apparent normal pressure, Trans ASME, J. Trib., 1I I (1989) 260-264. 9. J.M.Challen, E.M.Kopalinsky and P.L.B.Oxley, An asperity deformation model for relating the coefficients of hction and wear in sliding metal friction, in Tribology - Friction, Lubrication and Wear fifty years on, Vol II. I.Mech E., London (1987) Paper C156/87. 10. B.S.Hockenhul1, E.M. Kopalinsky and P.L.B.Oxley, An investigation of the role of low cycle fatigue in producing surface damage in sliding metallic fnction, Wear 148 (1991) 135-46. 11. P.Lacey and A.A.Torrance, The calculation of wear coefficients for plastic contacts, Wear 145 (1991) 367-383. 12. E.M.Kopalinsky Investigation of surface deformation when a hard wedge slides over a soft surface. Trans ASME, J.Trib, 114 (1992) 100-105. 13. A.V.Olver, H.A.Spikes, A.F.Bower and K.L.Johnson, The residual stress distribution in a plastically deformed model asperity, Wear, 107 (1986) 151-174.

14. Zhou, F., S.Leavy and A.A.Torrance, The plastic deformation influence on the formation of wear particles under sliding conditions. Proc. Irish Advanced Manufacturing Technology Conference, Dublin City University (1993). 15. A.A.Torrance, The calculation of residual stresses in worn surfaces . Submitted to Proc I. Mech E. (Zond.) Ser. J, (1994).

NOMENCLATURE. ABCDEFGHI A’

a

f H J k

K P

PI 4 S

r

Points in stress field (see fig. 1). %W4+&-a-q. Half width of wave (a = %AD). Tresca’s factor (f= cos2~). Coefficient in stress function. Coefficient in stress function. Archard’s wear coefficient. Shear yield strength of Al. Hydrostatic pressure on CD. Hydrostatic pressure on DH. Pressure normal to a surface. Shear stress parallel to a surface. Radial distance from D.

c1

P E

Angles defined in figure 1.

11

e

0

P

Stress function Coefficient of friction.

6, 6 8

‘TI3

Q w

Elastic stress components. w4 + E-Ct-11. Angle between surface and boundary of plastic zone (HDI).

5 30

APPENDIX

Stresses hehind the wave. The starting point for the analysis is shown in figure A l A rigid wedge traverses an elastoplastic material pushing a plastic wave ahead of it, which is modelled by the slip-line field ABCDE. Below ABCD there is a region of contained plasticity, which is bounded near the surface at the rear of the field by the line AH. The passage of the wave leaves behind it a highly strained layer of depth FG below DI, as verified experimentally by Kopalinsky (12). Within the slip-line tield (ABCDE) the stresses may be found from Hencky’s equations as described in reference ( 5 ) . Outside this region, they may be found using the method of reference ( 13) as follows. In the region CDE, there is a hydrostatic pressure, p and a shear stress K where:

“461

,

Therefore, by Hencky’s theorem, there is a hydrostatic pressure p’ along DH where :

The stresses under load can now be calculated using the above equations [A3-A6] in the elastic zone (DHI) and Hencky’s equations in the plastic region, (CDH and ABCDE). Hard Wedge

Elastic/Plastic Boundary

Figure Al . Field used to calculate stresses. The region DHI may be treated as a semi-infinite wedge with a pressure y ‘ and a shear stress -k along DH. It can then be shown (13) that the following stress function satisfies the boundary conditions:

where K H = -2 sin(2yr)

and

.I

-Kco~wco~(~w)

0 is measured clockwise from DH, and r is the radial distance from D. The stresses can then be found from the usual relationships:

Dissipative Processes in Tribology / I). Dowson e l al. (Editors) 1994 Elsevier Science R.V.

531

The Influence of Lubricant Degradation on Friction in the Piston Ring Pack R.I. Taylor and J.C. Bell Shell Research Ltd., Thornton Research Centre, P.O. Box 1, Chester, CH13SH, UK

An improved understanding of lubrication within the piston ring pack is expected to contribute to

efforts aimed at improving the fuel economy of automotive engines. However, most studies of frictional losses within the piston ring-pack use viscometric data for 'fresh' lubricants. T h e changes that occur to the viscometric properties of the lubricant in a working engine are not generally taken into account. The lubricant in an engine is subjected to a harsh physical environment, and the aggressive chemistry t h a t takes place in the vicinity of the top piston ring causes lubricant degradation by both evaporation of the lower boiling point components and by oxidation. Top ring zone oil sampling studies show that this degradation changes the viscometric properties of t h e lubricant. Measured viscometric data have been used in a piston ring pack model to estimate t h e effects of oil degradation on frictional power losses within the ring pack. In a n extreme case, degradation increased these losses by up to 40%.

1. INTRODUCTION

The desire to improve the fuel economy of diesel and gasoline engines h a s focussed attention on frictional energy losses in the piston assembly. As the lubricant in an engine is subjected to a n increasingly harsh physical and chemical environment in the vicinity of the piston rings, due to changing engine design, the influence of oil degradation (either by evaporation of lower boiling point compounds or oxidation), and the resulting changes that occur in the frictional force between ring and cylinder, are of increasing importance. The changes in viscosity and composition of the lubricant in the region of the piston ring pack were monitored by the use of a top ring zone (TRZ) sampling technique'. Oil samples were obtained through an orifice in the top ring groove of a Caterpillar 1Y73 single cylinder diesel engine. A substantial increase in the viscosity of these samples was observed within the first ten hours of engine operation,

although the oil in the crankcase had shown no detectable change'. More recently, TRZ samples were collected at higher power outputs of 10 a n d 14 bar brake mean effective pressure (BMEP)~,using a very high quality SAE 10W/30 multigrade diesel engine lubricant. The viscosities of at these samples were measured temperatures between 40 a n d 150°C, using special viscometric techniques for very small oil samples. These data were input to a piston ring pack oil film thickness model to compare the frictional power losses with those of t h e fresh SAE 10W/30 multigrade oil and a n SAE 30 single grade oil. In this particular study, t h e degradation process resulted in substantially thickened oils. A simplification used here was t h a t t h e degraded lubricant lubricated t h e whole of the piston ring pack. In reality, although the oil in the vicinity of top dead centre would have the same viscometric properties as the TRZ samples, lubricant lower down the cylinder

532

would more closely resemble ‘fresh’ oil. In this sense, the study presented here represents a ‘worst-case’ scenario. Average power losses for the piston ring-pack were calculated for both ‘fresh’ and ‘used’ oils, and increases of up to 40% were found for the ring-pack power loss when ‘degraded’ oil viscometric properties were used in place of ‘fresh’ oil viscometric properties. For the top ring, the power losses were similar for both sets of oil, except that the proportion of hydrodynamic to boundary friction power loss decreased substantially for the ‘degraded’ lubricant. 2. PISTON RING-PACK LUBRICATION MODEL

The piston ring-pack lubrication model used a robust non-linear algebraic equation solver to solve for the minimum film thickness, and inlet and outlet positions on the piston ring for each ring in the ring-pack3. Reynolds’ equation was used, although the (very small) squeeze term was neglected, and a separation boundary condition was used a t the outlet position, whereby the lubricant pressure was constrained to equal the gas pressure on the outlet side of the ring, and the pressure gradient was taken to be zero4. The viscositytemperature variation of the lubricant was taken into account by using Vogel’s equation5.

In the above equation, K , h and 8 are Vogel parameters. T ( x ) is the liner temperature a t position x , assumed to be the same as the (x) is the lubricant temperature, and lubricant’s dynamic viscosity. Bottom dead centre and top dead centre cylinder temperatures were specified, and a linear variation of temperature was assumed inbetween. At any piston position, the lubricant temperature, and hence the viscosity, could be

determined. Changes in the viscometric properties of the lubricant were represented by changing the Vogel parameters. Vogel parameters for various ‘fresh’ and ‘degraded‘ lubricants a r e given in Table 1. Figure 1 shows the dynamic viscosities, of the ‘fresh’ and ‘used’ oils. The BDC temperature was taken to be 100°C, and the TDC temperature was 15OOC. T h e ‘degraded’ SAE 10W/30 oils h a d dynamic viscosities approximately 2-3 times greater than t h a t of the ‘fresh’ oils. The oil sampled at the higher power output was more heavily degraded and suffered a greater viscosity increase. In the model, the variation of viscosity with pressure was neglected, since t h e pressures were not expected to be high enough to cause more than a 10% increase in viscosity. The variation of viscosity with shear rate was also neglected. This was a more severe shortcoming for multigrade oils, since maximum shear rates of 3 x lo7 s-l were computed for the top ring a n d at these shear rates the multigrade lubricant would exhibit shear thinning. The ring pack h a s four piston rings ; a n oil control ring ; two identical tapered rings ; and one barrel shaped top compression ring. Talysurf profilometer traces of both “new” and “worn” piston rings for t h e Caterpillar 1Y73 single cylinder diesel engine were obtained and it was clear t h a t after t h e initial runningin period t h e “worn” ring profiles differed markedly from the “new” profiles. The profiles of t h e “worn” set of rings were used as inputs to t h e model. The oil control ring was assumed fully flooded during the downstroke, but the limited oil film left behind on the liner caused the higher rings to be starved of oil. On the upstroke, t h e rings ran on the oil film left on the liner from the downstroke. For each crank angle in the engine cycle t h e oil film thickness for each of the four rings was calculated. Also, the viscosity for each of t h e four ring positions a t each crank angle was known. T h e frictional

533

Table 1: Viscometric properties of ‘fresh’SAE 30, SAE 1OWl30. and ‘degraded’ SAE 10Wl30 lubricants

Fresh’ SAE3O ‘Fresh’ SAElOWl30

I I

2.275 x 13.64~ loT2

I I

1361.0

123.3

849.8

99.9

‘Degraded’ SAE 10W/30 (10 BMEP)

12.71 x

954.0

96.4

‘Degraded’ SAElOWl30 (14 BMEP)

6.361 x

1395.5

133.6

1000

100

10

1

0

50

100

150

200

Temperature (C) Figure 1 : The temperature dependence of the dynamic viscosity of the four different lubricants

534

force acting between ring and liner could thus be calculated. Multiplying the frictional force by the piston velocity gave the instantaneous power loss, and this was averaged over the engine cycle t o give the average power loss. If the film thickness fell below a certain value, taken t o be 0.25pm, typical of the r.m.s roughness of cylinder liner and piston surfaces, boundary lubrication w a s assumed to occur, and the frictional force was calculated using an appropriate friction coefficient (a value of 0.08 was used).

3. RESULTS The average power losses calculated for the oils described in Table 1are given in F i y r e 2. Viscous power losses were found to be higher when the ‘degraded’ viscometric properties were used, simply because the viscosity was higher. As a consequence, oil film thicknesses were found t o be larger so that boundary

friction for the top ring was reduced. The contribution of boundary friction to the power losses of the other rings was insignificant. The ring-pack average power loss was approximately 16% higher for the 10 bar BMEP ‘degraded’ oil, and approximately 40% higher when it was lubricated with oil having the 14 bar BMEP ‘degraded‘ viscometric lubricant properties compared with an oil having the ‘fresh’ viscometric properties, as shown in F i y r e 3. The results for average power losses mask large variations between the individual rings, as can be seen in Figure 2. For the top ring, in particular, the average power loss is roughly the same with both ‘fresh’ and ‘degraded’ oil properties, since the reduction in boundary lubricated power losses for the ‘degraded’ oils was compensated for by an increase in hydrodynamic power losses.

It must be stressed, however, that the calculation presented here represents a ‘worst-case’ scenario, in which the viscometric

Average power loss (Watts) Figure 2 : Ring pack power losses for each ring in the piston ring-pack for each of the four lubricants considered in this study

535

% cd

a en C

2 Figure 3 :

Lubricant type ring-pack power losses for each of the four oils considered here

properties of oil sampled from the top ring zone were assumed to hold for the whole ring pack. In addition to a gradation in temperature from BDC to TDC, a gradation in Vogel parameters should also be expected, since the lubricant near BDC is relatively ‘fresh’, whereas that near TDC would be expected t o exhibit the viscometric properties of the TRZ samples. Either way, an increase in the total average power loss is still expected, and since friction in the piston ring area is thought to contribute approximately 20-30O/o6 of total engine friction, the error incurred in using ‘fresh’ oil viscometric properties a s opposed to ‘degraded‘ oil viscometric properties is likely to be significant. In order to get information on the appropriate gradation in Vogel parameters, samples of oil from the lower rings need to be collected, and such a n exercise is now beginning. The results of these calculations show that short term lubricant degradation can significantly affect power losses in the piston ring assembly, and thereby overall engine fuel economy. I t follows t h a t to enable accurate estimates of engine power losses the viscometric properties of representative degraded oils must be used.

ACKNOWLEDGEMENTS The authors would like to thank the following colleagues at Thornton Reseach Centre, B. Bull, Dr. P.J. Burnett, Dr. R.C. Coy, D.J. Evans, Dr. L.E. Scales a n d R.J. Wetton together with M. Priest from Leeds University. The authors would also like to thank Shell Research Ltd. for permission to publish this work.

REFERENCES 1. M. Thompson, S.B. Saville, “The Use of Top Ring Zone Sampling and Analysis to Investigate Oil Consumption Mechanisms”, I. Mech. E. Conference on “Automotive Power Systems - Environment and Conservation”, Chester College, 10-12 Sept 1990 2. P.J. Burnett, B. Bull, R.J. Wetton, “Characterisation of the Ring Pack Lubricant and its Environment”, I. Mech. E. Conference on “Experimental and Predictive Methods in Engine Research and Environment”, Birmingham University, 17-18 Nov 1993

536

3. Y-R.Jeng, “Theoretical analysis of pistonring lubrication part I1 - starved lubrication and its application t o a complete ring pack”, Trib. Trans., 35, (19921, 707-714

4. D.E. Richardson and G.L. Barman, “Theoretical and experimental investigations of oil films for application to piston ring lubrication”, SAE92234 1

5. A. Cameron, “Basic lubrication theory”, Third Edition (published by Ellis Horwood Ltd., 1983)

6. P.K. Goenka, R.S. Paranjpe and Y-R. Jeng, “FLARE : An integrated software package f i r friction and lubrication analysis for automotive engines - part I : overview and applications”, SAE920487

Dissipative Proccsscs in 'I'ribology / D. Dowson ct al. (Editors) 1994 Elscvicr Science 13.V.

537

HIGH SPEED DAMAGE UNDER TRANSIENT CONDITIONS 0.LESQUOIS~.J.J. SERRA~,P. KAPSAC. s. SEFU~OR~

aDGA/ETCA/CREA/PS40,Arcueil, France bGA/ETCA/CREA/CEOFont Romeu, France Qcole Centrale de Lyon, LTDS. URA CNRS 855 Ecully. France ABSTRACT:

The ETCA high speed tribometer is a facility able to achieve tests involving sliding speeds up to 350 m/s and loads up to 5000 N. The moving part is a 360 mm diameter stainless steel cylinder and the slider is a 5 mm side parallelepiped pin. The test duration does not exceed a few seconds. Several measurements have been carried out during the tests: - the evolution of the load and the friction forces by a piezoelectric triaxial sensor, - the evolution of the pin length loss by a capacitive sensor and of the pin weight loss during the test. - the evolution of the temperatures at different depths in the pin, using fast response intrinsic thermocouples. From this data, we can compute: the evolution of the friction coefficient, of the linear wear speed and of some thermal results. In addition. a high speed video camera (1000 picturedsecond) has been used to point out the different phases of the wear process. During the tests. competitive process between two types of physical phenomena appears: mechanical ones coming from the friction itself and thermal ones coming from the energy generated by the friction. When the pressure*velocity product (homogeneous to a heat flow) is low, mechanical phenomena are governing the processes. Thermal effects become more and more important when the PV product increases. and for very high values the pin frictional surface is partially molten. In such conditions, the incoming heat flux and surface temperature are important parameters for the understandng of pin wear process. These two parameters can be calculated from thermocouple measurements, using a space marching inverse conduction algorithm taking into account the free boundary. The obtained results show heat flux evolution curves versus time involving instability phases. These instabilities are due to metal particles transferred from the pin to the cylinder, which form rough asperities pushmg away the pin for a certain time. This aspect has been confirmed by the high speed film recorded during the tests. NOMENCLATURE -WR : wear rate, -f : friction coefficient, -V : slidingspeed. -P : contact pressure. -N : normal loa4 -Z : melted zone limit. -H heatflux -p : volumetric mass, -L : latent heat of fusion.

-T, : melting temperature, -To : room temperature, -T : temperature. -x : space, -t : time, -F : non Qmentional number, Fourier modulus type?

-C :speclfi~heat, -K q -Q,

: thermal conductivity, : interface heat flux, : heat flux used by melting.

538

1. LNTRODUCTION

High speed friction corresponds to situations where superficial melting of at least one of the two slidmg materials happens in the contact. This phenomenon generally occurs for high contact pressures (a few MPa or more) and for high slidmg speeds (several 10 m/s and more). High speed friction is. for example. observed for brakmg systems. rotating electrical contacts and friction between a projectile and a gun tube. The first important works on hgh speed friction are duc to Montgomery ( I ] during the fifties (and published in 1975). These stubcs have been made for the US Army aiming to reduce the wear of weapon's tubes. Several conclusions have been pointed out. the amount of heat which is received by a projectile dunng a shot is due to three phenomena: the friction, the deformation of the belt and the creation of heat by the propellant. Then the fomiation of a liquid metal film at the surface of the belt is observed earlier in real cases than in laboratory tests where we haven't the propellant effect. high friction coefficients and fluctuations have been recorded for low value of the PV product (pressure * speed). For values hgher than 6000 Mpa.m/s. the friction coefficient is low. stable and decreases slowly when the PV product increases. the wear rate is related to the speed of heat production. and then to the friction coefficient, the slidlng speed and the contact pressure:

where k is a constant. The product fPV is used because it is homogencous to a power per unit surface equal to a heat flux. It corresponds to the heat flux generated at the interface. the evolution of wear rate (weight loss divided by thc distance of sliding) versus the inverse of the melting temperature of sliding materials, on semi-log coordmates. is a straight line nith a positive slop indicating that high melting temperature materials are more resistant to wear. the results of these stuQes have shown that the w a r mechanism for high speed fnction is

superficial melting followed by an eliniination of a part of the melted layer. The surfaces are not in dlrect contact but are separated by a liquid layer. Then the wear speed is only a function of the melting temperature. The other material parameters. such as the thermal conductivity, the materials compatibility. the crystalline structure, the hardness. ... are of secondary importance or even negligble. However, if the slidmg duration is not sufficient to produce a total melting. these factors can become important. There is also important plastic defornmtions of the pin. Sternlicht and Apkarian 121 have modified the Montgomery friction machine to make experiments with a contact subjected to an electrical current. They have then observed a decrease of the friction force due to an increase of the energy dissipated in the contact by Joule's effect. Williams and G a e n 131 pointed out that the increase of the material temperature produces a decrease in the shearing force of the interface. The friction coefficient is then reduced. The friction coefficient is related to the sliding speed and the normal load (k is a constant):

High speed fnction situations are characterised by melting phenomena due to the energ?. dssipation in the slidmg interface. To have a better understanding of these situations. some authors have studed the propagation speed of the melted zone limit in the pin. One can notice in particular the works of Landau [7] used by Serra [S] who exhibited the important thermomechanical parameters. The dlsplacement speed of the melted zone limit can be evpressed by: (3)

The aim of the present work is Lo understand and modelize the phenomena governing the friction between two metals. at high speed and in a transient regme. The thermal exchanges in the contact have been considered in order to determine the thermal distribution coefficient

539

between the hvo slidlng W e s . This study have used a high speed friction machine developed at ETCA.

load is applied with an arm and dead load. The test duration is controlled by two pneumatic jacks which move the pin. T h s duration ranges from 0.2 to several minutes. Most of the tests were done for a rotational speed of 1500 rpm and a 1 s contact time.

2. EXPERIMENTATION 2.1. Friction machine

The whole pin support can be moved horizontally to change the wear track in the cylinder. Around 30 various tests can be perfornied on the same cylinder.

The high speed pin on cylinder tribometer is presented figure 1. The sliding speed ranges from 5 to 350 d s . correspondmg to a rotation speed up to 18 000 rpm. An orignality of this device is the use of active magnetic bearings (S2M) to support the cylinder which have a mass of around 3000 N. The axle and the cylinder are rotating around their inertia axis reducing $he vibrations. The stainless steel (Z6CN17 4 1 ) cylinder is of 360 nun diameter and was used for all the tests. The axle is horizontal and the pin, with a 5 x 5 mm square section and a 22 nun length. is underneath the cylinder. The cylinder is polished with abrasive papers to a 0.15 Ra value.

2.2. Measurements A triaxle piezo-electric transducer is used to measure the normal load and the friction force. A capacitive transducer is used to follow the evolution of the pin position during the test. indcating then the pin length worn. A tachometer gives the rotating speed of the cylinder.

The pins are weighed before and after the tests. The mass loss can be then compared to the indication of the position transducer. The data are collected during the test by a PC computer, then stored and processed after the tests.

For the pin. the tested materials yere iron, 100C6' (AISI 52100) steel. 35NCD16 , copper, aluminium. zinc, chromium, tungsten and lead and have been chosen for their known thermomechanical properties. All materials. except steel, are pure. For this paper, only the cases of pure iron and steels are considered.

CYLINDER

CYLINDER \MAGNETIC BEARINGS

n

I

I

L p

Figure 1: the friction machine.

For the set of test whch is studled here, the range of the normal load was 10 to 500 N. This

* AFNOR standard

I

Figure 2: Position of thermocouples on the pin. From some authors [1.2]. the pin surface is melted when the PV product (contact pressure x speed) is high. Then it has been interesting to perform thermal measurements of the surface temperature and the heat flux entering in the pin during the tests to validate this assumption. It seems diffkult to measure directly these values during the test. but it is possible to use thermocouples on the surface of the side of the pin at three different depths. As the pin is in iron or

540

steel. we can use an intrinsic thermocouple method using an iron wirc as a common reference and three aluniel wires which were welded by capacitive discharges at 1.5, 2.5, 3.5 mm from the contact surface (Figure 2). The main advantage of this intrinsic method, which is very important for such short tests. is to have a quicker response than with the classical two wires thermocouple method. 3. RESULTS

same wear, but the iron wear is much more important. At the beginning of the test, there is a competition between the wear and the linear expansion caused by the increase of the pin temperature. This competition causes low apparent wear which could be either positive or negative depending of the dominating phenomenon. If the contact time is long enough. a phase of rapid wear of a few mm/s occurs when the temperature of the surface of the pin is high enough.

3.1. Tribological results

Iron and steel pins create on the cylinder an irregular layer of transferred material composed of important rough deposits which can go up to a few tenth of millimetre high. The cylinder does not appear to be worn. However, an Electron Probe Mmoanalysis (EPMA) of the pins reveals sometimes some chronuum or nickel traces coming from the cylinder in the bulk. Figure 3 shows for three tests with same parameters (normal load 150 N. sliQng speed 28 d s . contact time 1 s) the evolution of the normal load and of the friction force. The n o d load decreases during the test when the linear wear is important because the mechanical system need to follow the wear. and its response is not instantaneous. The swingng that appear during the first 1/10 s come from the shock at the beginning of the test.

Figure 3: evolution during the test of normal load and friction force for iron and both steels. The curves in figure 4 are for the same tests as thc ones in figure 3. Both steels have about the

Figure 4:evolution during the lest of the linear wear. 3.1.1. Computation of tribological results

From the results of the measurements. we can compute the evolution of the friction force and the linear wear speed. Figure 5 shows these results for the same three tests.

Figure 5: evolution during the test of the friction coefficient and of the linear wear speed.

For iron. a friction coefficient of about 0.3 is

54 1

measured at the begmning of the test. Then. it increases up to a maximum and decrease to finish in the range of the initial values. The initial growth comes from the bad tribological behaviour of iron when the temperature increases. However when the temperature is hgh enough, iron in plastic flowing offers a lower resistance, and the contact is partially lubricated by melting iron. So the coefficient of friction decreases. The friction coefficients of both steels have the same behaviour of the iron ones. but the value obtained are lower. and may sometimes be less than 0.1 at the end of the test.

">,

1

I"

3l"

MEI\NNORMALLOADl NL

IRON

3.1.2. Comparaison criteria In order to compare the different tests. some criteria have been chosen to characterise friction and wear.

1OOC6

JSNC1)L

Figure 6: mean friction coefficient as a function of the mean normal load.

The three criteria which have been chosen for the friction coefficient were: - the initial fnction coefficient. - the mean value of the friction coefficient during the whole test, - the final fnction coefficient. For the wear, the criteria were: -the linear wear. - the bulk wear. - the linear wear speed at 0.5 nun and at 1 mm of wear. - the time to obtain 0.1 mm of linear wear which characterises the time to obtain the h g h wear phase.

"

.

IOU

.

li 0

20"

MEkrlNORMALLOADIM

RON

1OOC6

a JSNCDL

Figure 7: linear wear as a function of normal load.

c

I

I

1

All the three fnction coefficient criteria are proportional with the mean normal load; there is on some curves an evolution which may be either positive or negative. and some time no evolution. In figure 6. one can see that the mean value of the fnction coefficient as a function of the mean normal load decrease for 100C6 steel and is approximately constant for iron and 35NCD16.

The linear wear. the bulk wear and the linear wear speed increased proportionally with the normal load as it can be seen on figure 7 and 8. However. if the load is not hgh enough. there is a bend on the curve because the lines don't pass by 0. or with a load of 0 there must be a wear of 0.

Figure 8: linear wear speed as a function of normal load.

As it can be seen on figure 9. the time to obtain 0.1 mm of wear decreases exponentially with the mean normal load. One can observe that the beginning of the high wear began more

542

qwckly with iron at low load but at high load it is with the steels that the high wear began first. The explication is in a fnction coefficient effect, because if we plot the time to obtain 0.1 mm of wear against the mean friction force in spite of the mean normal load, both the steels began their hgh speed phase before iron for all the loads. We can assume that since the steel has a greater hardness than iron. the abrasion is more important in steel than in iron at the beginning of the test. II 8

,

I

Figure 10: contact between the cylinder and the pin.

Figure 9: time to obtain 0.1 mm of wear as a function of normal load. 3.2. Visualisation of the contact A high speed video system (60 to 1000 pictureds) was used to observe the behaviour of the pin during the test. There is a tranfer of the material of the pin on the cylinder and this transferred material temperature is quite low. because it has time to cool between two contact periods. Each time that this transfer pass in the contact, it plough the pin whch skip. Thus. we observe on the video film that from time to time. the pin is skipping, so the contact is periodically broken. With the increase of the temperature, the surface of the pin has a low hardness. and the transferred material produces sparks in relatively large area which are the real contact area. An hydrodynamic model has been developed for these important flash temperature areas. T h s model will be the subject of an other paper. The video film shows also the formation of the bulk. the occurrence of sparks and, at the back of the contact, the ejection of clouds of very small pamcles whch are droplets of molten metal or oxide dust.

Figure 11: break of the contact. Figure 10 and 11 are pictures coming from the video recording. The pin is at the bottom of the picture and the pad can be easily seen. Thc cylinder is at the top of the picture. and one can see the reflection of the pin in it. In t h s picture we have the contact at the left of the pin by a rough asperities stuck on the cylinder. This contact corresponds to the 1 cm length zone of the interface where there is a supplement of light. The figure 11 comes from the same test. but a few thousandth of second after. and the contact is broken because of the push caused by the passage of the tranferred material of figure 10. 3.3. Thermal results 3.3.1. Thermocouples results

Three temperatures are relavent to these

543

experiments: ambient temperature. global temperature of the contact surface and flash temperature whch are ephemeral and localised around the real contact zones, usually very small in dimension. The flash temperature can reach very high values even in low sliding speed ( [ 5 , 111). From the thermocouple data, we can compute to obtain thc temperature at the surface and the flux of heat entering into the pin with the method described below. Figure 12 a and b show the thermocouples results for two tests. one in iron and one in 35NCD16 steel respectively. In both cases, the linear wear is about 1 mm. The temperature increases more quickly on the iron pin than that on the steel, but it reaches a lower maximum temperature as compared to steel.

flux coming into the pin can be obtained in solving a one-dimensional inverse heat conduction problem with a moving boundary. This problem, called Stefan's problem. is not analytically solvable, and numerous authors have proposed numerical solutions. However, a method recently developedby Raynaud and Bransier can be used to take this conditions into account [9, lo]. So a code adapted to the high speed tribometer using this method has been developed. 3.3.2. Principle of thermograms interpretation Let us consider a one-dimensional heat conduction in the pin. initially at an uniform temperature To. At time t = 0. the contact surface of the sample, noted x = 0 in our problem, is subject to a frictional thermal flux. The objective is to estimate the interface heat flux q(0,t) at x = 0 (node I), given the inner temperatures at x = xj and x = Xk. The problem is solved using the space-marching finiteditTerence algorithm developed by Raynaud & Bransier [9, lo].

n+2 n+l n

Figure 12 a: evolution of wear and the 3 thermocouples measurementson an iron test (23 m / s , 75 N, 1 s).

n-1 n-2

1

2

3

i-1 abscissa

101

i

i+l

.

100

Figure 13 : principle of the space-marching finitedifference algorithm. Figure 12 b: evolution of wear and the 3 thermocouples measurementson a steel test (35NCD16.28 m / s . 230 N, 1 s). The temperature of contact and the thermal

The temperature field in the direct region x. < J: x I Xk can be calculated with a pure implicit scheme because the boundary conditions of the first kind in xj and Xk are known. Similarly, in the

544

inverse regon (0 I x 2 x.), J we note Tin the temperature at time nAt and at depth iAx. In this regon, the authors demonstrate that the temperature Ti-1". at point (i-1)Ax and time nAt, can be calculated as a function of the temperatures Tin. Tin-1 and T.+ln-l (past temperatures), Tin+1 and T ~ + I " +(future ~ temperatures). The relation obtained is:

last half (Ax1/2 width) control volume using an explicit formulation.

n+2 n+l n

n-I n-2

Where the quantities F1, F2 and F3 (non drmensional numbers. Fourier modulus type) are given by : 1+1

j-1

i-I

I

1+1

abscissa

Where C is the volumetric specific heat and k the thermal conductivity. The interface heat flux qln is calculated from an energv balance on the half (Ad2 width) control volume on the right of the node 1. q.AY q; =-[(2.F,4.At

l ) . z y +(2.F, +l)&-+l -2.4. - 2. F;.? + I ]

(6)

When the pin abrades (by melting, wear or any other way) the contact surface moves about the temperature sensors. The surface displacement is continuously measured using a capacitive sensor, so its abscissa s(t) is known at any time. The iterative calculation - equation (4) - giving the space forward temperature at a given time is repeated until the next node is over the ablation front location. Then, the calculation cell size is reduced in order to place the forward temperature on the contact surface and the backward temperatures symmetrically compared with the last calculated position (fig.14). These temperatures are interpolated between the known valucs Tinf1 and Ti+lM1, and the Ti,ln temperature is given by the relation (1) in with Ax is replaced by Ax' = iAx - s(t). The interface heat flux is calculated from an energy balance on the

Figure 14: arrival at the surface when using the space-marchingfiniteaerence algorithm. If the pin is worn by melting. the frictional heat flux involves an additional part which is used by the melting front displacement : As At

Q, = p.L.-

(7)

3.3.3. Thermal calculation results

In the present case, after the calculations (At = 0.004 s, Ax = 0.001 mm) we can see that the

global temperature of the surface reaches a maximum value of 120OOC (fig.15 a and b). The three curves of the figures correspond to the calculated values of the surface temperature using respectwely thermocouples 1 and 2, 1 and 3 and 2 and 3 as boundary conditions. TI-2 and Ti-3 results are in good agreement, but T2-3 is, mainly in the beginning of the curve, different. A numerical explanation is that the calculation by the inverse method begins at the thermocouple 1 in the case 1-2 and 1-3 and at thermocouple 2 in the case 2-3, and the distance from the surface to the thermocouple 2 is too large for the space marching algorithm. What is more, in the case 23, more errors appears mainly at the beginning of

545

the test where the thermal gradient is the highest and where the thermocouple 2 is farthest from the contact. We have a first phase corresponding to the low wear phase where the temperature increased very quickly. Then began the high wear phase where a part of the heat is used to melt the material which is going to leave the contact. In iron, the surface temperature increased more quickly than in steel, but iron has a temperature decrease during the high wear phase. Th~scan be explained by a vibrational problem on the tribometer. We saw with the hgh speed video camera that there is an adhesive transfer from the pin to the cylinder, and that the transfers are plouglung the pin at each rotation of the cylinder which cause the pin to skip. This phenomenon causes the real contact time to be much lower than the apparent one. The reduction in the real contact time leads to a reduction in the heat flux coming into the pin. This reduction in heat flux can cause the mean surface temperature to decrease.

The heat flux evolution curves versus time are presented in figure 16 a and b. In this curve, we observe instabilities in the form of abrupt falls. the biggest one which reaches zero a little bit before 0.9 s on the iron curve. This phenomenon can be explained by the break of the contact observed on the video recording. The important breaks of the curves comes from the great ruptures of the contact, but the video shows that there is also a lot of little breaks of a few thousandth of second. The existence of these little breaks can explain the little peaks in the incoming flux curves. They do not go down to zero because the acquisition frequency is actually only 250 Hertz, so it is difficult to see completely such fast phenomena. I

00

1

I,

0.

06

08

I 0

TQlD(S1

Figure 16 a: heat flux and heat dissipation coefficient on iron (23 m/s; 75 N, 1 s).

Figure 15 a: calculated surface temperatures on iron (23 m/s; 75 N, 1 s). 1500

1

1 I

"

00

01

6

o*

I 0

Tha (5)

OI

Figure 16 b: heat flux and heat dissipation coefficient on 35NCD16 (28 ds, 230 N, 1 s). The curve of the heat dissipation coefficient, which is calculated as the ratio of the heat flux coming into the pin versus the heat flux produced by the friction, follows approximately the variations of the heat flux. The values obtained are between 0.1 and 0.5.

Figure 15 b: calculated surface temperatures on steel (35NCD16, 28 m/s, 230 N, 1 s).

546

3.3.4. Metallographic observations

Figure 17: Metallographic cut, slidng direction from the left to the right (Magnification *20).

Figure 18: Metallographic cut, perpendicular to sliding direction from in front of to behmd (Magnification *20)

Some of the used pins have been cut, polished and observed with a microscope after etclung. Figure 17 and 18 show the pin of a steel test (100C6, 350 N, 28 m/s, 1 s). The cut was made in the direction of the sliding in figure 17. and in the other drection in figure 18. The contact surface is at the top of the figures. The contact surface is very irregular in figure 18 because of the rough transfers on the cylinder which plough the pin. One can see on the pin an important bulk coming from the plastic deformation at the end of

the contact, smaller ones on the sides, and a much smaller one at the beginning of the contact. There is also an important martensitic transformation area (in white) which take the all back bulk. But the most interesting comes from the fact that we can see the fibres of the pin. and these fibres are convolving on the bulks when they are near the end of the contact, but stop at the contact surface when they are too far away from the end of the contact. We can deduce from this observations that during the beginning of the test, the temperature of a part of the pin which is in the contact increases. When the temperature is lugh

541

enough. the material began to deform plastically and move to the end of the contact, and during this movement. the temperature continues to increase. If the distance to the end of the contact is small enough, the material is out of the contact before its temperature reaches the melting point. and the material form a bulk. If the distance to the end of the contact is large, the material is melted in the contact; it is then ejected in the form of droplet of molten material or in oxide dust. 4. CONCLUSIONS

A test machine was used to characterise tribological phenomena in high load and high speed conditions. Three thermocouples give thermal measurements in addition to tribological ones. The evolution of the normal load the friction force and the linear wear are computer recorded during the test. From this data, the evolution of the friction coefficient and of the linear wear speed are computed. Some criteria have been chosen to compare the various tests. The thermal measurements are treated by a code using the Raynaud and Bransier's space marching inverse conduction algorithm, which takes into account the free boundary. The results are accurate enough to show the skipping of the pin which is confirmed by the observation made on a high speed video recording. More tests with Merent materials and a better speed of acquisition are expected in the future.

REFERENCES 1 R.S.MONTGOMERY; Friction and wear at high sliding speeds; Wear, vol. 36, n03 pp 275278, Mars 1976. 2 B.STERNLICHT et HAPWAN: Investigation of melt lubrication; A.S.L.E. Trans. 2,248 (1956). 3 K.WLLLIAMS et E.GIFFEN; Friction between unlubricated steel surface at sliding speeds up to 750 feet per second; Roc. Inst. Mech. Engr 178,24 (1963/4). 4 F.P.BOWDEN, F.R.S. et E.H.FREITAG; The friction of solids at very high speed 1. metal on metal; 2. metal on diamond; Proc. Roy. Soc., Ser. A 248, 350 (1958). 5 S.C.LIM et M.F.ASHl3Y; Wear-mechsm maps; Acta metall., vol. 35. nO1, ppl-24 (1987). 6 H.S.CARSLAW & J.C.JAEGER; Conduction of heat in solids; 2nd ed.oxford: Clarendon Press (1959). 7 H.G. LANDAU; Heat conduction in a melting solid; Quart. Appl. Math. 8(1): 81-94 (1951). 8 J.J. SERRA et P RIBERTY; Analyse thermique de l'usure par ablation de metal fondu en frottement A grande vitesse.: Rapport ETCA NO89 R 139. 9 M.RAYNAUD et J.BRANSIER; A new finitedifference method for the nonlinear inverse heat conduction problem ? Numerical heat transfert, vol9, NO1,p27 a 42, 1986. 10 M.RAYNAUD et J.BRANSIER; Evaluation au moyen dune mdthode inverse. du partage du flux gentirk par frottement entre deux solides en mowement relatif; Soci6te Franpise des thermiciens,journke d'etude du 8 mars 1989. 11 T.F.J. QUINN and W.O. WINER; Wear 102, 67 (1985).

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Dissipative Processes in Tribology / I). Dow'son et al. (Editors) 0 1994 Elsevicr Science R.V. AU rights reserved.

549

INCIPIENT SLIDING ANALYSIS BETWEEN TWO CONTACTING BODIES. CRITICAL ANALYSIS OF FRICTION LAW.

T. ZEGHLOUL", M.C.DUBOURG"", B. V I L L E C M E "

* UniversitC de Poitiers, Laboratoire de Mtcanique des Solides, URA CNRS 861, Av. Du Recteur Pineau, 86022 Poitiers Cedex, France. ** INSA, Laboratoire de Mecanique des Contacts CNRS URA 856, B3t. 113, 20 Av. A. Einstein, 69621 Villeurbanne CCdex. France. Two non-conforming bodies are brought into contact. They touch over a plane surface of extent size compared with the dimensions of the solids. Then they are subjected to a tangential force until gross sliding is observed at the contact interface. Under certain circumstances, this phenomemom is preceeded by local slidings over part of the contact area, named as "sliding waves". They are similar to the Schallamach waves. Relations between these instabilities and the stick limit and the friction conditions on one hand and with the body compliance on the other hand must be investigated as they generate vibratory phenomena like for instance judder. Progri et al. [l] have identified the experimental conditions for reproducing these phenomena. A two-body contact is established between a rectangular polyurethane slab (L = 80mm, 1 = lOmm, h = 40mm, Young modulus E = 7 MPa, Poissonk ratio v=0.48) and an araldite flat, considered as rigid comparatively. Phenomenological description of these phenomena was performed. Mouwakeh et al [2] performed a quantitative analysis and show that the energy dissipated during sliding was comparable with the energy associated with the propagation of a shearing mode interface crack. Numerical simulations based on variational formulations were proposed by numerous authors, and more particularly by Raous [3]. The friction law used is the Coulomb's law. Sliding waves are observed experimentally at one edge of the contact area, sweep through it first partially, then entirely and lead finally to gross sliding. Correct modelling of all stages of the sliding evolution from rest up to gross sliding is still not performed: a central slip zone is predicted, based on the assumption of a friction coefficient equal to the ratio of the tangential load corresponding to the gross sliding over the normal load. This study deals with these differences. Thus: - modelling of interface behaviours based on the Coulomb's law were listed. The numerical model is based on a combination of the finite element technique, the interfacial crack theory and the unilateral contact analysis with friction. Geometrical dimensions of the slab and the friction coefficient value have a great influence on the way the sliding stages progress. - tests were realised to give an accurate phenomenological description of the sliding waves. The influence of both the geometrical dimensions of the slab and the friction coefficient value have been verified. Further both load and displacement variations when the sliding waves sweep through the contact area, partially or totally, were performed. Particularly, informations on the influence of the loading speed on sliding were obtained. For the configuration studied, incipient slidings are highly dependent on the parameters mentionned above. These results can't be extrapolated directly to industrial configurations due to the difference in material, a very compliant one in tests, rigid ones in industry. But this device is of a great help for local frictional behaviour analysis. Comparisons between experimental and theoretical results and the behaviours noted from the parametric study lead to the conclusion that a parameter adjustement will allow to model sliding stages with a Coulomb law type.

550

tangential load leading to gross sliding over the normal load- defines the shear stress onti = fd

1. INTRODUCTION

A theoretical approach of friction and sliding phenomena between two frictional contacting bodies is presented in this paper. Progri et a1 [ l ] and Mouwakeh et a1 [2] have previously studied experimentally these phenomena and identified conditions leading to "sliding waves" resembling "Schallamach waves" [4] between two contacting bodies. A two-body contact is formed between a rectangular polyurethane slab and an araldite rigid flat (cf. figure 1). The slab is first pressed against the flat, then a tangential load is imposed until gross sliding is detected. Sliding is due to successive pertubations or waves located at the interface and wich travel through it. These pertubations are associated to the propagation of a shearing mode interface crack, as the energy dissipated during sliding and the energy dissipated during the propagation of an interface crack are comparable 121. Numerical simulations of these experiment based on variational formulations were proposed by Fbous [3] (finite element method) and Deshoullieres [ 51 (boundary integral equations). These simulations are based on the Coulomb's law with static and dynamic friction coefficients: a static coefficient of friction fs defines the "stick limit", ( < fs *

I

* Onn( ). The stick and slip zone evolutions in the contact are modelled. But the evolution of the state of the contact is still different numerically from the one observed experimentally [ 1,2]. Further a stress field singularity associated to the sliding zone extension is numerically obtained, but less marked than in the experimental case. The Coulomb's friction law and the experimental observations of the contact phenomena disagree. This study aims at : listing the different behaviours described by the Coulomb's law. The influence of the coefficient of friction and the slab dimensions will be studied with a parametric study. Location of initial slidings and the direction of extension of the sliding zones will be particularly observed. - an accurate experimental observation of "the sliding wave" phenomenom. This model combines numerical and analytical methods. The stress and displacement fields are calculated and the stick, slip and open zones at the contact interface are determined. Further the different behaviours at the contact interface depending on the Coulomb's law are identified and listed. This theoretical study is undertaken jointly with an experimental one. A loading frame was developed which allows us to perform accurate

-

1 anti

1

(I

annl ), a dynamic coefficient of friction fd equal to the ratio of the limiting value of the

t

L DT

-r3(

'

PolyurCthane E,= 7 MPn

h

H

Ve= 0.48

DD

V--T

L=80mm Araldite

EA2500MPa

A

A

'

5 niin

1

H

vA=0.38

A

A: comoressed air supply GasPad x Figure 1 : Experimental device. Mechanical Properties and geometrical dimensions of the contacting bodies

I

Y

55 1

analysis of the contact evolution during a load cycle. Both loads and displacements are measured continuously and their variations are studied in relation with sliding wave travelling. 2. MODELLING

The simplicity of the geometrical shapes of the solids, of their law of behaviour, of the cinematic conditions characterise the experimental configuration. Therefore the following simplifling assumptions are retained for the theoretical modelling:

displacements, and respects the interface equilibrium. The finite element method is used to calculate this field. The crack field (oF), corresponding to displacement discontinuities like slip and opening at the contact interface is a corrector field, added when the boundary conditions are no more respected. The resultant field (0) satisfies the boundary conditions listed underneath (7-10). Analytical expressions for the crack field exist in the literature [8]. The coordinate system (o,x,y) is introduced. x is the inner normal at the body 1 contacting interface, y is the tangential component (cf. fig. 1).

- steady-state sliding as -

the sliding speeds are small, elastic linearity : the deformable material of the slab behaves homogeneously and isotropically according to Hooke's law, two-dimensional and particularly plane strain: the specimens are assumed to be of infinite width compared with the contact dimensions, displacements are allowed accross the boundary of the two specimens.

The two-body sliding contact behaviour is particularly difficult to model. A gross sliding event is often preceeded by partial slips over part of the contact surface, causing: tangential displacement discontinuities within slip zones, - normal and tangential displacement discontinuities within open zones, - continuous normal and tangential displacements within stick zones. The slip and open zone distribution (number and location) is unknown at priori and changes during loading. This model uses the previous works of Comninou [6] and Dubourg [7]. It is based on the method of continuous distributions of dislocations for modelling the displacement discontinuities at the contact interface and the contact solution for determining the slip and open zone distribution as a unilateral contact problem with friction. The resultant stress and displacement fields are obtained by superposing the continuous and the crack responses to the load. The continuous field ( oc ) corresponds to sticking at the contact interface, i.e continuity of the normal and tangential

k, ( l - A ) + l - B 4 (k, + 1)

L

bx(q)dr

(3)

-

with A = - 1-r l+Tk,

B = k, - T k , k, + r

ki=3-4vi k.1 = (3 - vi) / (1 + vi)

r =P 2 PI

plane deformation plane stress

where the indices 1 and 2 correspond respectively to the flat and the slab, L is the contact width, bx and by are the Burgers vectors corresponding to open

552

and slip. Integration and observation points ri and s, are given by:

(::1:pj

ri =cos -

i=l,n

3. NUMERICAL RESULTS

j=l,n s, = cos- 2 j p 2n+l where n is the number of discretisation points. Stress and displacement expressions are determined from Airy stress functions, and satisfy therefore automatically to the compatibility and equilibrium equations. Further the stress field singularity at crack tip is correctly taken into account. The contact interface state is determined numerically by solving the unilateral contact analysis with friction. The boundary conditions for a model using the Coulomb's friction law are the following : Normal or opening problem (N) Contact zone onnI 0 Au = 0 AU = u 1412 Open zone an, = 0 A u > 0

reached, i.e when the distribution of open, stick and slip zones is stabilized from one iteration to the next.

(7) (8)

Tangential problem (T)

The starting point for studying the contact interface behaviour is to know the location of the first sliding, as this event is determinant for the interface behaviour. Location of the first sliding is predicted in previous studies [ I l l by the Coulomb's law depending on a stick threshold and slab dimensions WL. A normal displacement is first imposed. It corresponds to a normal load of about 76 N. Then a tangential displacement from the left to the right is applied. The terms "left" and the "right" corrcspond to the left and right of the reader. This convention is used in the remainder of the paper. The increment of the tangential load is constant and equal to 2N whatever the ratio WL is. The sliding zone evolutions were analysed for numerous contact configurations. The variation range of the parameters considered is : - friction coefficient: from 0.1 to 1.4, step 0.01 - ratio WL from 0.1 to 1, step 0.1 ratioH/L= 1.2 and 1.5

-

f

1.4

L: Location of the first opening at thc right edge of the contact

1.3

1.2

A v = v , -v, Slipzone lontl
1.1

1.0 0.9

where onnis the normal stress, antthe tangential stress, Au the opening, Av the slip and fs and fd the static and dynamic friction coefficients. The algorithm for the contact problem solution follows the method developed by kalker 191 for twobody in rolling contact and Dubourg 171 for the interfacial crack contact. The contact problem is split in two parts, the normal or opening problem (N) and the tangential one (T). In the normal problem, the contact and open zone distribution along the interface is determined. The stick and slip zone distribution along the contact zone is then determined by the tangential contact solution. (N) and (T) are solved in turn until convergence is

0.8

0.7 0.G 0.5 0.4

0.3 0.2 0. I

B/L

0.0

c

1

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Figure 2 : Contact interface behaviour from numerical simulation based on Coulomb's friction law.

553

,mi)

to the right. This latter point was described in previous numerical studies [4,5]. It comes out from this parametric study that the Coulomb's law covers a wide range of sliding phenomena that depend strongly on parameters non directly linked with the interface. The numerical ZD behaviour seems to correspond to the experimental one on the basis of the analogy between the numerical sliding zones and the experimental sliding waves. It seems therefore possible to reproduce the sliding wave phenomenom by fitting the Coulomb's law.

U; BEIIAYIOUR

A+-=$ SL OP

4. EXPERIMENTAL PROCEDURE

An accurate experimental study is neccessary to understand friction and sliding phenomena. Numerical modelling requires a good knowledge of mechanisms, displacement evolution, contact forces and generalized forces. The photoelastic bench includes 4 functional groups, (cf. Figure 4) - 1: the loading frame, is formed of two parts holding the test specimens. Displacements in two perpendicular directions are feasible. The horizontal guide is performed by two ball columns, the horizontal one by a gas slider. The araldite counterface is mounted on a car differential screw. A sensor force T which controls the tangential force imposes this displacement. - 2: the optical photoelastic device, allows the continuous observation of the isochromatic field.

LEGEND ST:SnCli

SL: SLIP

O P OPEMNC

Figure 3 : ZD and ZG behaviours Eight zones of behaviour, labelled C1 to C8, are obtained from this wide parametric study (1572 cases) (fig. 2). Each zone corresponds to a typical behaviour of the interface during the loading, i.e identical succession of events (sliding, sticking and opening) takes place at the interface. The ZD and ZG behaviour.are presented in detail in Figure 3. The other ones are described in [12]. ZD is related to a sliding zone sweeping through the interface from the right to the left, and ZG is related to a sliding zone starting at the middle of the interface and sweeping through it I

a

I

A

Figure 4 : Photoelastic bench

4

554

T(N)

'lo 1od

0 , -10 -20 -30 -40 -50

/

40

80

120

160

200

240

280

40

80

120

160

200

240

280

-60 -70

-80 -90 -

d

100 1 IC

1

40

80

120

160 200

80

120

160 200 240 280

240

280

-2

-1

0

40

0

Figure 5: 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

H/L = 0.5 V = 4.8. N d = - 85 N

mm/s

555

- 3:

load and displacement measurement system, containing - sensors for normal (N)and tangential (T) load measurements, - sensors for flat travel @T) (sliding and slab deflection), for the left edge @G) and right edge @D) slab sliding measurements - 4: measured parameters acquisition and treatement: all signals are recorded and monitored during tests on an informatic system The picture acquisition for numerical treatement or continuous recording on video tape is performed with the CCD camera. 4.1 Analysis of a typical test

Recordings of the normal and tangential loads, the lateral edge displacements DG and DD of the slab and the counterface displacement DT are presented figure 5 . Several steps are noted during this test:

- Step 1: loading to 5 t I t,. The normal load increases from zero to Nd= 85 N. The tangential load is nil and the tangential 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 displacement sensors are situated 5 mm above the contact surface. The isochromatic field changes continuously and is symmetric.

-

- Step 3: opening sliding t, I t St,. An open zone is situated at the right edge of the slab. At t=t2 , a sliding wave starts at the right side of the slab and sweeps entirely through the contact (cf. figure 6). Tangential load drop is measured as the sliding 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 sliding wave from one side of the contact to the other is in the opposit direction to those of the imposed tangential displacement. After this event, the interface is again fully adherent. The tangential displacement and therefore the tangential load continue to increase. Three other sweeps are recorded that correspond also to gross slidings. Resulting tangential unloadings and displacement DD and DG variations increase with the number of sweeps. The normal load evolution is similar to those of the tangential load.

-

- Step 2:

complete sticking t, I t St,. 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. The tangential load increases progressively and continuously. The interface is still sticking. The flat shift causes defections of the lateral edges of the slab. Theses deflections modify the displacements DD and DG. Continuous evolution of the isochromatic field through the whole slab is observed, due to shearing.

Figure 6 : Sliding wave

-

Step 4: partial sliding t, I t St,: At t = t4, a sliding 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 up to the end of the test. The maximum tangential load does not vary any more. The tangential load over normal load ratio corresponding to the gross slidings is roughly constant and equal to 1.

556

The interface contact behaviour is summarized in three steps: the stick step: during normal loading and for small tangential loads, the interface is completely sticking. There is no energy dissipation and no hysteresis.

within the paraffin layer and not at the interface parflidpol yurethane.

-

5. COMPARISON. CONCLUSION

- the partial slip and stick step: increasing the tangential load causes sliding waves or Schallamach waves at the contact interface. No gross slidings are observed. This transient step is the connection between the stick step, corresponding to a bulk deformation, and the next step, corresponding to shearing at the interface. Energy is dissipated during this step, which is irreversible.

The contact evolution during cyclic loading was analysed accurately. The interface behaviour depends on numerous parameters. Their importance and role are sometimes still misunderstood. Two kinds of contact evolution, characterized by the location and the travelling direction of the sliding waves, are highlighted in this study. Numerical results show that the contact interface behaves differently depending on parameters non directly linked to the interface. Nevertheless an analogy is noted between the experimental sliding waves and the theoretical slip zones. Numerical modelling of these phenomena requires important fitting of the parameters that justify modifications of the Coulomb's friction law.

- the gross sliding step: the sliding 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 in the slab is different before and after this event. 4.2 Influence of the flat nature

The sticking conditions and friction at the interface, characterized by a mean friction coefficient, are changed here. Therefore physical and microgeometrical parameters thought influent have been modified. This control is obviously not very accurate as this tribological problem is very complex [ lo]. Different manufacturings of the surface conditions of the rigid flat were realised. The contact evolution is similar to those described above. The influence of the surface conditions is therefore small on the T/N ratio. Then different coatings or lubricants were employed to modify the sticking and frictional proporties o the counterface. For instance the flat was coated with paraffin. This third body changes completely the beheviour observed during previous tests. No travel of sliding waves is observed at the contact interface. The speed accomodation was performed

REFERENCES Progri R., Villechaise B., Godet M. "Fracture mechanics and initial displacements", Mechanisms and surface distress, D. Dowson, C.M. Taylor, M. Godet, D. Berthe Eds., Butterworth London, pp. 47-54, 1986. Mouwakeh M., Villechaise B., Godet M. 'I Quantitative study of interface sliding phenomena in a two-body contact", Eur. Jnl. Mech., NSolids, 10, n05, pp. 545-555, 1991. Raous M., Chabrand P., Lebon F. "Numerical method for fiictionnal contact problems and applications", Journ. Mec. theo. et applic., Special issue, sup. nO1to vol. 7, 1988, p. 1 I1128. Schallamach A. "How does rubber slide", Wear, 1971, v. 17, p. 301-312. Deshoullieres B. "Contact avec frottement sec entre deux solides. Resolution pour la loi de Coulomb et des lois non-classiques par la mtthode des equations intdgrales de frontitres", Thtse de Doctorat de I'Univ. de Poitiers, 1990, 116 p. Comninou M. "The interface crack with friction in the contact zone", Journ. Appl. Mech., 1977, vol. 44, p. 780-781.

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Dubourg M. C. "Le contact unilateral avec frottement le long des fissures de fatigue dans les liaisons mkcaniques", These de Doctorat, INSA de Lyon, 1989,253 p. 8 Dundurs J., Mura T. "Interaction between an edge dislocation and a circular inclusion", Journ. Mech. Phys. Solids, 1964, vol. 12, p. 177-189. 9 Kalker J. J. "TWOalgorithms for the contact problem in elastostatics", Report of the Department of Mathematics and informatics, 1982, Delf, no 82-26, 8 p. 10 Godet M. "Aspects mecaniques de la tribologie", 6eme Congrks franqais de la Mkcanique, Lyon, Sept. 5-9, 1983. Paris A.U.M., p. 1.1 - 1.24. 11 Zeghloul T., Villechaise B. "Phenomenes de glissements partiels decoulant de I'usage de la loi de Coulomb dans un contact non lubrifie" Materiaux et Techniques, Special Tribologie, dCc. 1991, p. 10-14. 12 Zeghloul T. "Etude des phenomenes d'adherences et de glissements dans un contact entre solides: Approche experimentale et modelisation", These de Doctorat de I'Univ. de Poitiers, 1992, 188 p.

7

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559

@) You stated that if you stopped feeding powder

-

Written Discussion Contributions DISCUSSION SessionII

- LIQUID

AND LUBRICATION

POWDER

Rheological Basis for Paper II(i). 'A Concentrated Contact Friction' by S Bair and W 0 Winer (Georgia Institute of Technology, USA).

to the bearing the temperature went up. How much of the cooling was a result of the air used to feed the powder to the bearing? (c) In our paper we argue that liquids behave like solids (shear bands). In your paper you argue that solid powders behave like liquids. Did you see shear bands in the solid powders?

ReDlV bv Dr H Heshmat (Mechanical Technology Inc., Latham, USA).

(a) The development of a recessed piston, capable Dr J A Greenwood (Cambridge University, UK). The strain birefringence patterns you show indicated a varying stress-field; but when you go on to your Mohr-Coulomb analysis you assume a uniform field. Can you say a little more on this? Replv bv Dr S Bair and Professor W 0 Winer (Georgia Institute of Technology, USA). We measure shear band angles at a location far enough from either the inlet or exit that the stress-field is uniform as indicated by the birefringence patterns. Dr R C Coy (Shell Research Limited, Chester, U K). Molecular dynamics simulations suggest the orientation of the molecules takes place when nonlinear effects are observed. Have you any evidence for molecular orientation in your experiments? Replv bv Dr S Bair and Professor W 0 Winer (Georgia Institute of Technology, USA). Flow birefringence has been ascribed to molecular orientation and is observed even for linear response. Paper INii). 'On the Theorv of QuasiHvdrodvnamic Lubrication with Drv Powder: Apdication to Development of Hiph Speed Journal Bearing for Hostile Environments' by H Heshmat (Mechanical Engineering Inc. Latham, USA). Professor W 0 Winer (Georgia Institute of Technology, USA). (a) How did you measure pressure as you showed in an earlier viewgraph?

of recording continuously and simultaneously the quasi-hydrodynamic normal load, tangential friction forces, and the generation of pressure profiles generated by the dry TiO, powder is given in Ref. [5]. Briefly, a pressure transducer was mounted in the test runner supported a properly recessed piston, 3.2 mm in diameter by 5.1 mm in height. The location of the recessed piston, that is the pressure sensor, with respect to the slider pad was at the mid-span of the test slider. The pressure sensor was to sweep approximately through the center of powder film pressure. (b) In this test setup the powder discharge flow rate could be adjusted via a powder supply control system independent of dry air flow which was supplied to the unit. Therefore starvation test was achieved by reducing powder flow while maintaining air flow constant. The heat removal capability of the carrier dry air at max operating condition was calculated to be about 0.01 Hp. The experimentally measured powder lubricated journal bearing power loss at the same condition was about 2.5 Hp, thus dry air contribution to the cooling of the bearing would amount to some 0.4%.

(c) In a previous powder publication experiment (Lubricant Flow Visualization) "shear bands" or slip at the boundary have been observed and documented [4].

560

Professor T H C Childs (University of Leeds, UK). Does the powder particle shape and size influence the lubrication? and if so, what shapes and sizes did you use and what was their influence? ReDlv bv Dr H Heshmat (Mechanical Engineering Inc., Latham, USA). Professor Childs has touched upon a rather complex issue! A companion paper in this proceedings [lA] and pertinent cited references there may elucidate the relevance of particulate shape, size, and other properties on the rheology of the triboparticulates. Although it is perhaps the smallest and most superficial characteristic, geometrical (shape) description of triboparticulates has become the chief determinant of the boundary and property of particles. Yet particle size, nature, powder density, powder limiting, and yield shear strengths and their salient features, and, most importantly, their interrelationship with respect to their roles in triboparticulate rheology ought to be sought. Furthermore, it appears to be particle size with respect to a particular set of tribomaterial combinations influences the lubrication regime than particle shape.

starvation. During the experiment, recorded frictional forces as well as bearing surface temperature both were greatly influenced by the degree of starvation (reduction in powder flow rate). (b) With respect to the second comment, the mode

and nature of quasi-hydrodynamic powder lubrication is deemed responsible for the drop of coefficient of friction, thus heat generation. The heat is generated within the film, and heat transfer mode is so called convection rather than conduction, thus heat capacity of the particles play a weak role. Professor K L Johnson (Cambridge University, UK). If the powder behaviour is viscous in nature, what is the mechanism of the rate effect? ReDlv bv Dr H Heshmat (Mechanical Engineering Inc., Latham, USA). It was stated that the region of quasi-hydrodynamic lubrication should be treated as a single continuum, analogous to fluid. The flow behaviour of liquids whose viscosity obeys

Professor F E Kennedv (Thayer School of Engineering, Dartmouth College, NH,USA). (a) You mentioned that the measured surface temperatures were much lower than theoretical maxima, presumably due to heat being carried away by side flow of particles. Did you note a temperature change as powder supply rate was changed? (b) Was the heat capacity of the side flow particles (theoretical) sufficient to be responsible for the low pad surface temperature?

are frequently called Newtonian. Note that the designation Newtonian refers to flow behaviour and not to a generic type of liquid. However, powders that are made to flow through a thin gap under the action of sliding or rolling exhibit modes of flow behaviour that are non-Newtonian. Rheological models of triboparticulate film and the rate effect and so on are thoroughly discussed in Ref. [2,6 and 2A]. Additional References

ReDlv bv Dr H Heshmat (Mechanical Technology Inc., Latham, USA). (a) With regard to the first comment of Professor Kennedy, referring to Figure 1, bearing side leakage provides a significant mechanism for heat dissipation, and bearing side flow is a function of operating condition and level of

(1A) Heshmat, H and Brewe, D E.

"On the Cognitive Approach Toward Classification of Dry Triboparticulates", Presentation at 'The 20th Leeds-Lyon Symposium on Dissipative Processes in Tribology', Lyon, France, (7-10 September 1993), Will be

56 1

published by Elsevier Science Publishers, Tribology Series 23, (1994). Heshmat, A. "Solid Lubrication Roller Bearing Development: Static and Dynamic Characterization of High-Temperature, Powder-Lubricated Materials". Technical Report MTI 92TR191,prepared for US Air Force Report No. Contract No. F33615-87C-2707 for period 1987 to 1990, Wright Lab. Wright-Patterson A x Force Base, Ohio, (30 November 1992). PaDer II(iii) 'The Influence of Base Oil Rheology on the Behaviour of V1 Polymers in Concentrated Contacts' by P M Cann and H A Spikes (Imperial College of Science, Technology and Medicine, UK). Mr D Brewe (NASA Lewis Research Center, Cleveland, Ohio, USA). What was the size of the long chain polymers relative to the film gap? We have performed hydrodynamic analysis using a micropolar theory (Khonsari & Brewe) for particles embedded in a fluid. These 'particles' were small compared to the film gap and could be conceivably made up of long chain polymer additives. Our calculations indicated that load capacity was increased as a result of adding particles to the fluid. Our reasoning for this was that the particles acted as flow restrictors within the film gap thereby increasing the pressure build-up. I suspect that the mechanism at work for our hydrodynamic films could not work for the EHD film thicknesses in your investigation because of the relative size of the polymer chain to film gap. Have you plans to do any further investigations for thicker (hydrodynamic) films? It would be interesting to see if the effects of shear thinning in the inlet would dominate the effects of 'particle flow restriction' for thicker films. Redv bv Dr P M Cann and Dr H A SDikes (Imperial College of Science, Technology and Medicine, London, UK). An interesting point certainly at low rolling speeds the gap size in the Hertzian region is comparable to polymer coil size (< 10 nm). The adsorbed polymer layers are not visualised as smooth surfaces rather as lumps with hydrodynamic thickness determined by the polymer

tails. It is conceivable that such structures could restrict lubricant flow although how this would happen under the high pressure, thin film conditions of the Hertzian contact is difficult to envisage. It might be that such films help to entrain lubricant and aid pressure build-up in the inlet region thus contributing to the enhanced (additional to the boundary layer) film thicknesses observed when they are present. Such an effect would be reduced as the rolling speed and hence gap size increase. Dr I L Sinper (US Naval Research Laboratories, Washington, DC, USA). Please tell us the friction coefficient of the three fluids. ReDlv by Dr P M Cann and Dr H A SDikes (Imperial College, London, UK). The friction data for the three fluids used in this work can be seen in Table 1. The value reported in this table is the average friction coefficient at the last load stage. In the experiment with hexadecane + 1.0 wt% DBDS the friction coefficient varied by k 10% while at this load. Load, N

friction coefficient

hexadecane

250

0.030

hexadecane + 1.0 wt% DBDS

450

0.049

hexadecane + 0.1 wt% stearic acid

500

0.040

Table 1

Friction data for the three fluids

Dr J Greenwood (University of Cambridge, UK). It would be greedy to ask if you could tell us about film thickness as well as surface temperatures. Answer 1: Yes it would be greedy. Answer 2: The film thickness can be calculated using the Hamrock and Dowson film thickness equation and the lubricant information from Table 2.

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Temperature

Viscosity

"C

CP

Pressure viscosity coefficient. 1/GPa

(i) What are the sizes of the scanning spot and the EHD contact?

20

3.2 2.3 1.6 1.2 0.9 0.6 0.3

12.6 11.2 9.79 9.25 9.02 8.85 8.75

(ii) Are you scanning in the direction of sliding?

40 60

80 100 120 150

Table 2

If so, is it possible that you are missing some high temperature regions in the contact where you are not scanning? (iii) Is it possible that you are (before scuffing) seeing a spot on the ball surface with a different emissivity synchronously being sampled by your scanner?

Viscosity and pressure-viscosity data for hexadecane [ 101

For a sliding speed of 1.99 d s and a contact load of 300N the film thickness was calculated. The results can be seen in Table 3. Inlet Temperature

"C

Film thickness urn

Lambda ratio

80 100 120 150

0.016 0.012 0.009 0.006

0.93 0.74 0.56 0.35

Table 3

Film thickness and lambda ratio for hexadecane

The polished balls used in the experiments had a surface roughness of 0.016 pm RMS. The surface roughness of the sapphire flat was 0.005 pm RMS. All roughnesses were measured using a Form Talysurf. The composite RMS roughness of the two surfaces is thus 0.017 pm. Using this information and the film thickness values, the lambda ratio was calculated. The results can be seen in the same table. [lo] Johnston, G J, PhD thesis, Imperial College, University of London, 1990.

Professor W 0 Winer (Georgia Institute of Technology, USA).

ReDlv bv Dr P M Cann and D r H A SDikes (Imperial College, London). (i) The size of the scanning spot is 36 pm. The diameters of the EHD contact at a contact load of 250,450 and 500 N are 501,609 and 63 1 pm respectively. (ii) The temperature profiles were taken in the direction of sliding through the centre of the contact area. It is possible that we are missing a high temperature region in the contact where we are not scanning. (iii) The authors assume this question refers to the behaviour seen with hexadecane + stearic acid as seen in Figure 10. The ball rotates at 1500 rpm, which means the ball rotates with a frequency of 25 Hz. The scanning frequency is 16.7 Hz. This means that the effect seen in Figure 10 cannot be due to a spot on the ball. Confirmation of this is that the temperature rise is only seen in the area of the maximum Hertzian contact pressure. M r P Chu (London, UK). Is your flash temperature higher compared with steel-steel? I have similar experience of better scuffing load with stearic acid-hexadecane. ReDlv bv Dr P M Cann and Dr H A SDikes (Imperial College, London). No experiments were carried out using steel-steel, so no frictional data is available, so no flash temperatures can be calculated or have been measured.

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Paper IUv) 'Comwtational Fluid Dynamics /CFD) Analvsis of Stream Functions in Lubrication' by D Dowson and T David (University of Leeds, UK). Professor J J Kalker @em University of Technology, The Netherlands). What is the connection between Airy Stress Function, and the Stream Function? Can this relation, mutalis, be extended to 3D? Reulv by Professor D Dowson and Dr T David (The University of Leeds, UK). Both Airy Stress functions and stream functions are limited to 2D, although streamlines may be easily defined for 3D. This, however is where the similarity ends since Airy functions x are based on the assumption of body forces having a potential form and that the stress zxy is proportional to the second cross derivative of x. The stream function on the contrary is defined independently of but does comply with the continuity of mass and therefore has no restrictions laid upon it. Under certain conditions both x and cp (the stream function) may be solutions of the bi-harmonic equation V44 = 0. In the case of fluid flow modelling this is equivalent to that of zero Reynolds number flow. Dr H Heshmat (Mechanical Engineering Inc., Latham, USA). How would one handle the moving boundaries with the CFD method, such as the situation which occurs in compliant bearings? Reply by Professor D Dowson and Dr T David (The University of Leeds, UK). FIDAP certainly does have a moving boundary capability. But the method of solution depends on the boundary conditions imposed and whether certain approximations concerning the physics at the surface may be tolerated. The most general way would be to use a quasi-steady state approach in which the fluid vector of unknowns (u, v, w and p) is calculated, the boundary face moved locally according to the local prescribed boundary conditions and the fluid domain remeshed. This new domain is then used as a starting point for the next solution of u, v, w and p.

However it should be stressed that for accurate predictions the boundary interface should be part of the implicit solution process.

PaDer IIcvi) 'Shear Properties of Molecular Liauids at High Pressures - a Phvsical Point of View' by Professor E Diaconescu (INSA, Villeurbanne, France). Dr R C Coy (Shell Research Limited, UK). You have assumed quasiequilibrium conditions in your analysis explain these high deformation conditions? Reply by Professor E Diaconescu (INSA, Villeurbanne, France). The performed analysis indicates that, at high pressures, two types of molecular displacements, namely viscous and solid like, take place in a sheared liquid, as implied by a Maxwell rheological model. The viscous displacements are accomplished by molecular jumps and increase with time. If the shear stress is smaller than the limiting shear stress of the liquid, the solid like deformations consist of slight displacements of the equilibrium positions of the molecules and do not depend on time. During a practical observation time, which is several orders of magnitude larger than the period of molecular jumps, the solid like deformation is overwhelmed by viscous displacements and it cannot be observed. Although unnoticeable, this small deformation is responsible for the solid like behaviour of the fluid. As the fraction of molecules performing a jump at a given instant is extremely small, the solid like properties can be assessed by disregarding these jumps i.e. the viscous deformation, and by considering the instantaneous liquid lattice as being "frozen". The solid like shear properties are derived for this lattice by using a solid state, quasiequilibrium type of approach in which, for the sake of simplicity, the molecular vibration motions are neglected. Nevertheless, allowance is made in the paper for a possible effect of these vibrations upon the stress-strain curves. Obviously, more work is needed in order to precisely take account of this effect. It can be concluded that the large nonequilibrium deformations take place either by viscous flow which is governed by non-Newtonian

564

viscosity of the liquid or by a solid like shear breakdown of the fluid, once the limiting shear stress is reached. A simple quasi-equilibrium approach is used to derive the stress-strain curve for the liquid in the range of small solid like deformations.

Professor L Rozeanu (Technion, I.I.T., Haifa, Israel). I assume your fluid is a single species system. What happens if you add in your reasoning the pressure of another non-soluble (dispersed) molecule? Renlv bv Professor E Diaconescu (INSA, Villeurbanne, France). As already mcntioned, the investigation is based on several simplifying assumptions in order to obtain a physical understanding of basic mechanisms of liquid flow at high pressures. According to one of these assumptions, the investigated liquid is made of identical molecules. No attempt was yet made to extend this analysis to a mixture of molecules. Nevertheless, such an extension will complicate considerably the analysis by introducing new mechanisms of molecular displacements and several interaction potentials. SESSTONIII SURFACE DAMAGE AND (Oral presentations associated with WEAR posters). Paper III(iv) 'Effects of Surface Tonowaphv and Hardness Combination unon Friction and Distress of RollindSliding Contact Surfaces', by A Nakajima and T Mawatari (Saga University, Japan). Mr J Lundberg (Lulea University of Technology, or R, ?) is the Sweden). Which parameter hax best in order to describe the influence of surface topography? R e d s bv Professor A Nakaiima (Saga University, Japan). The reduction in the height of surface profiles or roughness curves in the running-in process is caused by plastic deformation and wear of the higher parts of asperities on the surface. Therefore, in order to grasp roughly the overall displacement of asperities, we may read the height change of the total roughness depth or the peak-tovalley height Q,,, and that is effective as far as

the deepest valley remains undeformed. That is the reason why the authors adopted the parameter hax instead of R, (center-line average roughness) or (root mean square roughness). However, as shown in the paper, the frictional force or the state of oil film formation could change significantly while the magnitude of roughness was hardly changed. Considering from such a viewpoint, neither haX nor R, is a satisfactory parameter, and it is necessary to take into account the microgeometry and its microscopic change of asperities which engage in contact actually, including the effect of surface pattern (i.e. the directional properties of roughness).

Paner IlT(v) 'Anti-Wear Performance of New Svnthetic Lubricants for Refrigeration Svstems with New HFC Refriperants' by T Katafuchi, M Kaneko and M Iino (Idemitu Kosan Co. Ltd, Japan). Mr R J Smalley (SKF-ERC,Nieuwegein, The Netherlands). (a) Is there evidence of Oxide formation with the two lubricants? (b) How are the "wear" results modified by the presence of refrigerant?

Renlv bv Dr T Katafuchi (Idemitu Kosan Co. Ltd, Japan). (a) No, there is no evidence of Oxide formation with the two lubricants. The reason is that gaseous HFC134a is supplied to the test lubricant at 5Phr for 30 minutes before the start of the wear test in order to remove oxygen dissolved in the test lubricant. Therefore, there is no significant difference in cps of OKa by EPMA between rubbing surface and nonrubbing surface of test specimens. (b) When the wear test had been conducted using the test lubricants without the HFC refrigerant under the operating conditions described in this paper, the wear was not observed. The reason why the HFC refrigerant adversely affects the wear is considered to be the

565

decrease of the lubricant viscosity by the dilution with the refrigerant.

Professor L Rozeanu (Technion, I.I.T. Haifa, Israel). Please explain how you get leakage of energy to appear as dissipation (friction).

SESSION IV MICROSCOPIC ASPECTS PaDer IV(ii)_ 'A Molecularlv-Based Model of Sliding Friction' by J L Streator (Georgia Institute of Technology, USA). Professor J J Kalker (Delft University of Technology, The Netherlands). I have two questions; (1) Why have you not put dashpots in your model? (2) Why do you not use one of the older models, e.g. Frankel-Kontorova?

ReDlv bv Dr J L Streator (Georgia Institute of Technology, USA). Regarding your first question, our emphasis here was to investigate whether or not and to what extent - energy propagation influenced the friction force. We did not include dashpots in the model because we wished to study a system for whch the total energy was conserved as in a real system. If dashpots were present, then the total energy of the system would not be conserved and the effect of energy propagation on the friction force would be obscured.

-

On the second question, our model is, in part, a combination of the Independent Oscillator (10) model and the Frenkel-Kontorova (FK) model. Neither of the older models, alone, is as well equipped to study the role of energy propagation on the friction force. First, for the I 0 model (Fig. la), each mass acts independently, so that there is no energy propagation whatever from one mass to the next. Secondly, for the FK model (Fig. lb) resistance to the displacement of the masses comes via the constraint imposed at the boundaries. Modeling a surface of infinite extent (i.e. one for which energy continually propagates outward without returning) would require that there be no interaction with the boundaries. This condition results in arbitrarily large displacements of the masses in the contact region which is not physically realistic.

ReDllv bv Dr J L Streator (Georgia Institute of Technology, U.S.A.). We simply integrate the equations of motion for each mass and calculate the friction force. Our results show that the development of a large dissipative component is associated with the leakage of energy. Dr A Kanoor (Cambridge University, U.K.). What happens to friction forces if separation of atoms in the hard asperity is different from that in the adsorbed film? Renlv bv Dr J L Streator (Georgia Institute of Technology, U.S.A.). We have investigated the case where ah = 1/&. In this case, since the molecules do not move in phase, the friction forces are reduced in magnitude. However, the same trends are found with respect to surface extent and contact length: the more readily energy propagates away from the contact, the greater the dissipative component of the frictional stress. Professor K L Johnson (Cambridge University, UK). Are you able to make order of magnitude estimates of frictional energy dissipation by this mechanism? ReDlv bv Dr J L Streator (Georgia Institute of Technology, USA). Within the context of our model, Fig. 9 suggests that about 80% of the energy dissipated occurs by energy propagation. Paner IV(iii) 'Friction of Dielectric Materials: How is Enernv Dissinated' by B Vallayer, J Biyarre, A Berroug, S Fayeulle, D Treheux, C Le Gressus and G Blaise (ECL, CEA-DAM and Universite Paris Sud, France). Professor G Inplebert (I.S.M.C.M., St Ouen, France). To understand the coupling between friction zones and others, had you looked at special continuum mechanics for materials capable of torque at the elementary volume element level (2nd gradient and related theories)?

566

ReDlv bv Mr S Faveulle, (Ecole Centrale de Lyon, Ecully, France). No, we have not looked at this kind of theory. We have mainly focalised on the many-body universal model of dielectric relaxation as developed by Dissado et al. This model describes the relaxation of energy through several kinds of processes (large and small transitions) among which some allow the redistribution of energy. For example, the so-called flip-flop transitions cause a redistribution of energy between different points of the system without coupling to the thermal bath before transfer to phonons (the flip-flop transitions represent a tunneling mode for electronics between different configurations in a double-well potential). This kind of mechanism could help to understand the distribution of energy in the whole sample after a friction test. SESSION V - POLYMERS PaDer V(ii) 'Effect of Thickness on the Friction of Aculon - A Problem of Constrained DissiDation', by L Rozeanu, S Dirnfeld and J Yahalom (Technion, Haifa, Israel). Dr I L Sinper (US Naval Research Laboratories, Washington, DC, USA). Referring to the "anomalously low" hardness at 1.2 mm, why is the hardness lower? - could it be an error? ReDlv bv Professor L Rozeanu Technion, Haifa, Israel). It cannot be an error because it is the initial point of a curve representing the hardness function of specimens thickness in the 1.2 9 mm range. The shape of the curve could be approximated in this interval by an appropriate function so that a similar low value would have been obtained by extrapolation of the points for higher tluckness values. By comparison with the performance of tyres, soft tyres give high friction. The low friction of the very thin specimen associated with higher hardness is due to the "wall constraint" and is similar to a hard tyre performance.

-

567

XXth SYMPOSIUM LEEDS-LYON ON TRIBOLOGY

'DissipativeProcesses I n Tribology'

-

Lyon 7th-10th September 1993 List of Delegates

Title Name

Miliation

Title Name

Affiliation

Ms ADERINM.

IMPERIAL COLLEGE Tribology Section Dept. of Mechanical Engineering Exhibition Road LONDON SW72BX U.K.

Dr

INSA Laboratoire de Mkanique des Contacts - B i t I13 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

Prof A K A Y k

CARNEGIE MELLON U N N E R S m Mechanical Engineering Department PIlTSBURGH. PA 15213 U.S.A.

Dr BIGNONC.

MECHANICALENGINEERING LAB. Namiki 1-2, Tsukuba m w 30s

Mr BOSJ.

UNIVERSlTYOFTWENTE Department of Mechanical Engineering PO Box 217 ENSCHEDE 7500 AE THENETHERLANDS

AEROSPATIALE Direction des offaires techniques et industrielles 37, Boulevard de Montmorency Paris Cedex 16 75781 FRANCE

Dr

INSA

GEORGIA INSTITUTE OF TECHNOLOGY School of Mechanical Engineering ATLANTA, GA 30332-0405 U.S.A.

Dr

INSA Labratoire de Mkanique des Contacts - Bit I 13 20 Ave A. Einstein VILLEURBANNE Cedex 6962 I FRANCE

Mr BRAULTG.

Mr ANDOY.

BERTHIERY.

-

JAPAN MI

Dr

ARMBRUSTERM.

BAIRS.

Prof BAYADA G.

INSA Labratoire de M h i q u e des Contacts B i t 113 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

BOU-SAIDB.

Labratoire de Mkcanique des Contacts - Bit I I3 20 Ave A. Einstein VILLEURBANNE Cedex 69621 FRANCE BOURDEAUY.

INSA Labratoire Ghtechnique, GCU Bitiment 304 20 Avenue Albert Einstein VILLEURBANNE cedex 69621 FRANCE DRET Service des Recherches Groupe 8 ARMEES 00460 FRANCE

568

Title Name

AfIiliation

Title Name

Affiliation

Dr

BRENDLEM.

CNRS Centre de Recherches PhysicoChimie des Surfaces Solides 24 Av. du President Kennedy MULHOUSE 68200 FRANCE

Mr CAR0NJ.-M

Societk DELTALAB Essai des materiaux VOREPPE 38340 FRANCE

Mr

BREWED.

NASA LEWIS RESEARCH CENTER MS 23-2, US Army VPD 2 1000 Brookpark Rd CLEVELAND, OH. 44135 U.S.A.

Mr CARTON J.F.

EPFL MXG-3 18 Ecublens LAUSANNE CH 1015 SUISSE

Prof BRISCOE B.

IMPERIALCOLLEGE Dept of Chemical Engrg & Particule Technology LONDON SW72BY U.K.

Dt

CHANDRASEKARS.

PURDUEUNNERSITY School of Industrial Engineering 1287 Grissom Hall W. LAFAYETTE, IN 47907 U.S.A.

Mr

UNnrERSllY OF SUCFAVA SUCEAVA 5800 ROUMANIA

Dr

CHAOMLEFFEL J.-P. INSA Laboratoire de Mkcanique des Contacts BEt I13 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

TRANSROL CHAMBERY cedex 73024 FRANCE

Mr CHATEAUMINOIS

Mr

BUTNARUN.

BUVRIL G.JJ

-

Prof CAMERONA

Mr ANGLIA POLYTECHNIC UNIVERSlTY Victoria Road South CHELMSFORD, Essex CMI ILL U.K.

Dr

IMPERIALCOLLEGE

CANNP.

CHENY.M.

Prof CHILDS T.H.C.

Tribology Section. Dept. of Mechanical Engineering Exhibition Road LONDON SW72BX U.K. Prof CARDOUA.

Mr CHUP. UNIVERSlTY LAVAL Dtpartement de Genie Mkanique CitC Universitaire QUEBEC GIK7P4 CANADA

ECOLE CENTRALE DE LYON Dept. M.M.P. BP 163 ECULLY 69 I3 1 FRANCE CETIM 52 Ave Felix Louat SENLIS 60304 FRANCE

UNIVERSlTY OF LEEDS Department of Mechanical Engineering LEEDS LS29JT U.K. 45 Monk'sDrive LONDON W 3 0 C B U.K.

569

Title Name

Affiliation

Title Name

Affiliation

Dr

COLINF.

INSA Laboratoire de Mkcanique des Contacts - Bit 1 13 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

Mr DEYBERP.

BP FRANCE BP 100 GENNEVILLIERS 92232 FRANCE

Mr

CONSTANSB.

ELF ANTAR FRANCE Centre de Recherche Elf de Solaize ST SYMPHORIEN DOZON 69360 FRANCE

Prof DIACONESCU E.

INSA Laboratoire de Mecanique des Contacts - Batiment 113 20. Ave A. Einstein VILLEURBANNE Cedex 69621 FRANCE

Dr

CONTEM.

INSA Laboratoire de Mecanique des Contacts - Bbt 113 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

Dr DONNETC.

ECOLE CENTRALE DE LYON LTDS 36 Avenue Guy de Collongue B.P 163 ECLJLLY 69 I3 1 FRANCE

Dr

COYRC.

SHELL RESEARCH LTD Thornton Research Centre PoBox 1 CHESTER CHI 3SH U.K.

Mr DORIERC

EDF-DER Deartement Machines 6 quai Waitier CHATOU 78401 FRANCE

INSA Laboratoire de Mecanique des Contacts - Bit I 13 20 Ave A. Einstein VILLEURBANNE Cedex 6962 I FRANCE

Prof DOWSOND.

UNIVERSITY OF LEEDS Departernent of Mechanical Engineering LEEDS LS29JT U.K.

Prof DALMAZ G.

Mr

DARBEIDA AD.

ECOLE DES MINES Laboratoire de Science et G h i e des Surfaces Parc de Saurupt NANCY 54042 FRANCE

Dr DUBOURGM-C.

INSA Lnboratoire de Mkcanique des Contacts - Bdt I 13 20 Ave A. Einstein VILLEURBANNE Cedex 6962 I FRANCE

Dr

DENEUVILLE P.

PECHINEY CRV BP 27 VOREPPE 38340 FRANCE

Mr EASTBURYD.

BUTIERWORTH HEINEMANN Linacre House, Jordan Hill OXFORD OX28DP U.K.

LABORATOIRE SEP

Mr

IMPERIAL COLLEGE Tribology Section, Dept of Machine Engineering Exhibition Roadx LONDON SW72BX U.K.

Mr D E W F J . F .

B.P. 802

VERNON 27207 FRANCE

ENTHOVENJ.

570

Title Name

Aftiliation

Title Name

Affiliation

Mr

LULEA UNIVERSITY OF TECHNOLOGY Division of Machine Element LULEA S-97187 SWEDEN

Prof GEORGES J.M.

ECOLE CENIRALE DE LYON LTDS 36 Avenue Guy de Collongue B.P 163 ECULLY 69 I3 1 FRANCE

INSA Laboratoire de Mecanique des Contacts BPt I 1 3 20 Ave A. Einstein VILLEURBANNE Cedex 69621 FRANCE

Dr GIUDICELLIB.

ECOLE CENTRALE DE LYON Dept. MMP 36 Avenue Guy de Collongue BP 163 ECULLY 69 13 1 FRANCE

Prof GODETM.

Dr

ERMSSONP.

FANTINOB.

-

-

-

Mr FAYEULLES.

INSA Lnboratoire de Mecanique des Contacts BPt 113 20 Ave A. Einstein VILLEURBANNE Cedex 69621 FRANCE INSA Laboratoire de Mecanique des Contacts BPt 113 20 Ave A. Einstein VILLEURBANNE Cedex 6962 I FRANCE

-

-

Dr

FELDERE.

C.E.M.E.F Ecole des Mines de Paris B.P 207 SOPHIA-ANTIPOLIS 06904 FRANCE

Dr

Dr

FISHERJ.

UNIVERSITY OF LEEDS Departement of Mechanical Engineering LEEDS LS29JT U.K.

Prof HAMROCKB.

INSA Loboratoire de MCcanique des Contacts BPt 113 20 Ave A. Einstein VILLEURBANNE Cedex 69621 FRANCE

Mr HARDINGRT.

UNIVERSITY OF LEEDS Department of Mechanical Engineering LEEDS LS29JT U.K.

JRSID

Mr HERSANTD.

EDF MTC Route de sens Ecuelles MORET-SUR-LONG 77250 FRANCE

Dr HESHMAT H.

MECHANICAL ENGINEERING

Prof FLAMAND L

GREENWOOD J.A.

FOURNELB.

34, rue de la Croix de Fer STGERMAINENLAYE 78105 FRANCE

Mr

FOUVRY

OHIO STATE UNIVERSITY 206 West 18th Ave. COLUMBUS, OH 43210-1 107 U.S.A.

-

Dr

CAMBRIDGE UNIVERSITY University Engineering Department Trumpington Street CAMBRIDGE C52 IPZ U.K.

ECOLE CENTRALE DE LYON Dept. MMP 36 Avenue Guy de Collongue BP 163 ECULLY 69131 FRANCE

-

-

InC.

968 Albany Shaker Rd LATHAM. N.Y. 121 10 U.S.A.

57 1

Title Name

Afliliation

Title Name

Affiliation

Dr

HOOKE C.J.

THEUNIVERSITYOF BIRMINGHAM School of Manuf. & Mech. Engrg. Edgbaston BIRMINGHAM B15 2TT U.K.

Prof JOHNSON KL

CAMBRIDGEUNIVERSITY 1, New Square CAMBRIDGE CBI 1 EY U.K.

Dr

HOUPERTL

TJMKEN France 2 Rue T d e n - B.P 89 COLMAR 68002 FRANCE

Mr JONES D.A.

UNIVERSITYOFLEEDS Department of Mechanical Engineering LEEDS LS2 9JT U.K.

KYOTO UNIVERSITY Res. Centre for Biomed. Eng 53 Kawaharaxho, Shogoin, silky*ku KYOTO 606-01 JAPAN

Prof KALKER J.J.

DEUTUNIVERSITYOF

3 Wingate Ave. HAIFA 33724 ISRAEL

Dr

Prof INGLEBERT G

ISMCM Laboratoire de Tribologie 3 rue Fernand Hainaut STOUEN 93407 FRANCE

Dr KAPSAP.

ECOLE CENTRALE DE LYON LTDS 36 Avenue Guy de Collongue - BP 163 ECULLY 69131 ERANCE

Dr

UNIVERSITY OF CAMBRIDGE

Dr KATAFUCHI T

I D E m KOSAN Co. Lubricants Research Laboratory Anegasaki-Kaigan Ichihara Chiba 299-01 JAPAN

Prof KENNEDY F.

THAYER SCHOOL OF ENGINEERING Dartmouth College HANOVER,N.H. 03755 U.S.A.

Prof IKEUCHI K

Mr

ILANI (Baum) S.

IZUMIN.

TECHNOLOGY Mekelweg 4 DELFT 2628CD THENETHERLANDS KAPOORA

Dept. of Materials Science & Metallurgy Pembroke Street CAMBRIDGE CB23QZ U.K. Dr

JAKOBSENJ.

THE TECHNICAL W.OF DENMAUK Dept. of Machine Elements Building 403 LYNGBY 2800 DENMARK

Mr JOBBINSB.

UNIVERSITY OF LEEDS Department of Mechanical Engineering LEEDS LS29JT U.K.

Dr

KUDISHLI

CAMBRIDGELJNIVERSITY Engineering Department Trumpington Street CAMBRIDGE CB2 IPZ U.K.

UNIVERSITY OF S C M O N Departement of physics SCRANTON, PA 185104642 U.S.A.

572

Title Name

Affiliation

Title Nnme

Affiliation

Dr

LANGLADEC.

ECOLE CENTRALE DE LYON Dept. M M P 36 Avenue Guy de Collongue - BP 163 ECULLY 69 131 FRANCE

Dr

ECOLE CENTRALE DE LYON LTDS 36 Avenue Guy de Collongue - BP 163 E C U U Y 6913 1 FRANCE

Dr

LARACINEM.

INSA Laboratoire de M e q u e des Contacts Bat 113 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

Prof LUBRECHT T.

INSA Laboratoire de Mecanique des Contacts - Biit 113 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

DGA E T C N C W S 16 Bis Avenue Prieur de la CBte d'Or ARCUEIL cedex 94114 FRANCE

Prof LUDEMAK.

UNIVERSITY OF MICHIGAN MEAM Dept. ANNARBOR&II 48109-2125 U.S.A.

INRETS - MMA

Mr

LUNDBERGJ.

LULEA UNNERsIlY OF TECHNOLOGY Division of Machine Elements LULEA S-97187 SWEDEN

DGA - E T C N C W S 10 16 Bis Avenue Prieur la CBte #Or ARCUEIL 941 14 FRANCE

Dr

MAM-T.

UNIVERSlTY OF CENTRAL LANCASHIRE Dept of Engrg. & Product Design PRESTON PRI 2HE U.K.

EXXON RESEARCH & ENGINEERING Co. 79 Rt. 22 East-Clinton Township ANNANDALE, N.J.08801 U.S.A.

Dr

MAEKAWAK.

mmuuuNIvERsm Dept.of Meclianical Engineering 4- 12-1 Nnkanarusawa HlTACHI 316

LOUBET J.-L

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Mr LEDERERG.

Dr

LELONGJ

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109, avenue Salvador Allende Case 24 BRON cedex 69675 FRANCE Mr

LESQUOISO.

Dr

LETAD.P.

JAPAN

Mr

L1GIERJ.L

GLACIER SIC Recherche et Developpement B.P. 2073 ANNECY Cedex 74008 FRANCE

Dr MAHMOODS.

Mr

LIUZ-M.

UNIVERSITY OF LEEDS

Dr

Departement of Mechanical Engineering LEEDS LS29JT U.K.

UNIVERSITY OF LEEDS Department of Mechanical Engineering LEEDS LS29JT U.K.

MAITOURNAM M.H. ECOLE POLYTECHNIQUE Laboratoire de Mecanique des Solides PALAISEAU cedex 91 128 FRANCE

573

Title Name

Aililiation

Title Name

Afiliation

Ms MARTINB.

ECOLE CENTRALE DE LYON Dept. MMP 36 Avenue Guy de Collongue BP 163 ECULLY 69 131 FRANCE

Mr MOES H.

UNIVERSKYOFTWENTE Departement of Mechanical Engineering PO Box 217 ENSCHEDE 7500 AE THENETHERLANDS

ECOLE CENTRALE DE LYON

Mrs MOORE S.

UNIVERSITY OF LEEDS Deportement of Mechanical Engineering LEEDS LS29JT U.K.

SNCF Direction de la Recherche, Departement RP 45 Rue de Londres PARIS 75379 FRANCE

Prof MOREAU J.J.

UNIVERSlTEMONTPJiLLERII Laboratoirc de MeCanique et Genie Civil, Case Counier 048. MONTPELLIER 34095 FRANCE

Prof MATSUBARAK

TOKAIUNIVERSITY Kitnkaname Hiratsuka-shi KANAGAWA 259-12 JAPAN

Prof NAKAJIMAA

SAGA UNIVERSITY Dept. of Mech. Engineering. Faculty of Science and Eng. I Honjo-machi, Saga-shi SAGA 840 JAPAN

Dr

INSA Laboratoire de Mkanique des Contacts Bit I 13 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

Dr NELIASD.

INSA Laboratoire de Mtcanique des Contacts Bat 113 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

ROBERT BOSCH GinbH Postfach 106050 D-STUlTGART 70049 GERMANY

Dr

-

Prof MARTIN J.M.

LTDS

-

36 Avenue Guy de Collongue BP 163 ECULLY 69 131 FRANCE Dr

MASMOUDIW.

hfEURISSEM.-K

-

-

Mr

MEYERK.

-

-

NICHOLSF.

ARGONNE NATIONAL LAB ETl2 12 9700 S. Cass Avenue ARG0"E.IL 60439 U.S.A.

Dr

MISCHLERS.

EPFL DMX LMCH Tribology Group LAUSANNE CH 1015 SUISSE

Mr N0AKESD.E.

ANGLIA POLYTECHNIC UNIVERSITY Victoria Road South CHELMSFORD, Essex CMI ILL U.K.

Mr

MITSUIK

IMPERIAL COLLEGE Tribology Section Dept. of Mechanical Engineering Exhibition Road LONDON SW72BX U.K.

Dr NOWELLD.

UNIVERSITY OF OXFORD Department of Engineering Science Parks Road OXFORD OX1 3PJ U.K.

574

Title Name

Affiliation

Title Name

Affiliation

Dr

SAGA UNIVERSITY Faculty of Science and Engineering I, Honjyo SAGA 840 JAPAN

Dr SAINSOTP.

INSA Labontoire de M k m i q u e des Contacts Bat 1 13 20 Ave A. Einstein VILLEURBANNECedex 6962 1 FRANCE

IMPERIAL COLLEGE

Mr SAUCER

Dr

OHNON.

OLVERAV.

-

Tribology Section, Dept. of Mechanical Engineering

ECOLE CENTRALE DE LYON Dept. MMP 36 Avenue Guy de Collongue BP 163 ECULLY 69 I3 1 FRANCE

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Exhibition Road LONDON SW72BX U.K. Mr PEZDIRNMJ.

UNIVERSlTY OF LJUBLJANA Faculty of Mechanical Engineering Askerceva 6 LJUBLJANA 61000 SLOVENIA

Dr SEABRAJ.

DEMEGI Faculdade de Engenharia Rua dos Bragas PORT0 4099 PORTUGAL

Dr

INSA hboratoire de Mkanique des Contacts - Bat 1 13 20 Ave A. Einstein VIUEURBANNE Cedex 6962 I FRANCE

Dr

ATR Optical Radio Communications Research Laboratories 2-2 Hikmdai Seika-cho S o d - -

PILLONG.

SHINJOK.

gun

KYOTO 619-02 JAPAN US NAVAL RESEARCH Lab Code 6170 WASHINGTON DC 20375 USA.

Dr

QUERRY M.

INSA Labontoire de M h i q u e des Contacts - Btit 1 13 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

Dr

Dr

R0PERG.W.

SHELL RESEARCH LTD Thornton Research Centre P.0 Box 1 CHESTER CHI 3SH U.K.

Mr SMALLEY RJ.

EPFL - DMX - LMCH Tribology Group LAUSANNE CH 1015 SUISSE

Dr

STREATOR J.L

G.W. WOODRUFF SCHOOL OF MECHANICAL ENG. Georgia Institute of Technology ATLANTA, GA 30332-0405 U.S.A.

TECHNION, LLT. Depnrtement of Materials Engineering HAIFA 32000 ISRAEL

Dr

SUCIMURAJ.

K W S H U UNIVERSITY Department of Mechanical Engineering 6-10-1 Hnk0zaki.HiHigashi-h FUKUOKA 812 JAPAN

Dr

R0SSETE.A.

Prof ROZEANUL

SINGERLL

SKF-ERC Postbus 2350 NIEUWEGEIN 3430DT

THENETHERLANDS

575

Title Name

Afliliation

Title Namc

Affiliation

Prof SZUDER A.

ECOLE CENTRALE DE LYON Department MMP ECULLY Cedex 69 I3 1 FRANCE

Dr

INSA Labomtoire de Mtcanique des Contacts - Bit I13 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

Mr TANIGUCHIM.

UNIVERSITY OF LEEDS

Dr VERGNEP.

INSA Labratoire de Mkanique des Contacts - Bit I13 20 Ave A. Einstein VILLEURBANNE Cedex 6962 1 FRANCE

VELEXP.

Department of Mechanical Engineering LEEDS LS29JT U.K. Prof TAYLOR C.M.

UMVERSKY OF LEEDS Department of Mechanical Engineering LEEDS Ls29JT U.K.

Mr MIERSAL0J.T.

TECHNICAL. RESEARCH VlT CENTRE OF FI"D. Engineering Laboratory of M. P.0 Box 11 1 ESPOO 02151 FINLAND

Dr

TAYLORRL

SHELL RESEARCH LTD. Thornton Research Centre PobxI CHESTER CHI 3SH U.K.

Prof VINCENTL

ECOLE CENTRAL.E DE LYON Dept. MMP 36 Avenue Guy de Collongue - BP 163 ECULLY 69 I3 I FRANCE

Dr

TORRANCEA.

TRlNlTY COLLEGE Parsons Building DUBLIN 2

Dr VON STEBUT J.

ECOLE DES MINES Labratoire de Science et Gtnie des Surfaces Parc de Saurupt NANCY 54042 FRANCE

Prof WINER W.O.

WOODRUFF SCHOOL OF MECHANICAL ENGINEERING GA TECH ATLANTA, GA 30332-0405 U.S.A.

Prof YAMAMOTO Y.

KYUSHUUNIVERSKY Dept. of Mechanical Engineering, Facul. of Engineering 6- 10- 1 Hakozaki, HigaShi-kU FUKUOKA 812

IRELAND

Prof TRIPP J.H.

SKF-ENGINEERING AND RESEARCH CENTRE PO Box 2350 NIEUWEGEIN 3430DT

THENETHERLANDS Dr

VAN DER HOEK B.

Prof VANNES B.

ELSEVIER SCIENCE PUBLISHERS B.V. Engineering & Tech. Department P.O.Box 1991 AMSTERDAM IOOOBZ THENEmRLANDs ECOLE CENTRALE DE LYON Dept. MMP 36 Avenue Guy de Collongue - BP 163 ECULLY 69 I3 I FRANCE

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