Lubrication at the Frontier: The Role of the Interface and Surface Layers in the Thin Film and Boundary Regime,

LUBRICATION AT THE FRONTIER The Role of the Interface and Surface Layers in the Thin Film and Boundary Regime

TRIBOLOGY SERIES, 36 EDITOR: D. DOWSON

LUBRICATION AT THE FRONTIER The Role of the Interface and Surface Layers in the Thin Film and Boundary Regime

edited by

D. DOWSON*, M. PRIEST*, C.M. TAYLOR, P. EHRET, T.H.C. CHILDS; G. DALMAZ, ¥. BERTHIER, L. FLAMAND, J.-M. GEORGES, A.A. LUBRECHT * Principal Editors

Proceedings of the 25th Leeds-Lyon Symposium on Tribology held in the Institut National des Sciences Appliquees de Lyon, Lyon, France, 8th - 1 lth September, 1998.

ELSEVIER Amsterdam • Lausanne • New York • Oxford • Shannon • Singapore ° Tokyo 1999 For the Institute of Tribology, The University of Leeds and Institut National des Sciences Appliquees de Lyon

ELSEVIER SCIENCE B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE A m s t e r d a m , The Netherlands

© 1999 Elsevier Science B.V. All rights reserved.

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First edition 1999

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Proceedings of the 25 th Leeds-Lyon Symposium on Tribology

INTRODUCTION The 25 th Leeds-Lyon Symposium on Tribology was held at the Institut National des Sciences Appliqu6es de Lyon from Tuesday 8 th t o Friday l l th 1998. Its central theme w a s "Lubrication at the frontier The role of the interface and surface layers in the thin film and boundary regime". This topic was chosen because it represents an important evolution of the research field. The Symposium was opened on Tuesday afternoon with a keynote address by Professor P.G. de Gennes, i991 Nobel prize in Physics. In a thought provoking lecture entitled "Role of surface-anchored polymer chains in polymer friction" Professor de Gennes described the processes taking place at the interface between "solid" and "liquid". The keynote address was followed by two invited lectures. The first one given by Dr. S. Korcek entitled "Fuel efficient engine oils, additive interactions, boundary friction and wear" presented the industrial point of view on lubricant formulation and engine testing and its evolution. The second lecture was presented by Professor M. Kaneta entitled "For the establishment of a new EHL theory", who through beautiful and colourful pictures stressed the need to extend the current EHL theory. Initially, a third invited lecture by Professor D. Dowson was scheduled, but due to health reasons, Professor Dowson could not attend the Symposium. His presence and his contribution were sorely missed by everyone at the conference. The Symposium Review board had examined over 140 abstracts of which some 80 were accepted for presentation. In view of the large number of interesting proposals, it was decided to organize a succession of a single and two parallel sessions during the morning and afternoon. Furthermore, up to five papers per session were presented, and due to the animated discussions, more than one chairman had difficulties adhering to the allocated time. The reviewing process, which has proved efficient and stimulating, was extended and formalised. The full manuscript was reviewed anonymously and depending on the comments, corrections were required. The reviewing process has also allowed us to improve the quality of the written English. The organisers would like to thank all authors for supplying their manuscript before the conference, the reviewers for their quick and expert work, and finally the authors for quickly implementing these comments. A complete list of all reviewers appears at the end of the Introduction. The traditional Symposium banquet was held in the "Casino le Lyon Vert". The dinner was prepared by the young, and now established, Chef Philippe Gauvreau. The occasion allowed delegates the opportunity to savour a number of French culinary specialities. The cultural event took place on Thursday evening at the Auditorium of Lyon. The delegates attended a unique presentation of traditional and modern aspects of dance and music rooted in the Mediterranean culture.

vi The usual Friday barbecue party was organised by the laboratory staff The Saturday tour visited the Jura region and included local pipe manufacturing, diamond cutting and stone polishing industries. The waterfall "Chapeau de Gendarme" was fully-flooded and unfortunately the view over lake Geneva only virtual t The organisers would like to thank all the members of the Laboratoire de M6canique des Contacts for participating in the organisation and thereby contributing to the success of the Leeds-Lyon Symposium. They would like to thank in particular Mrs A.-M. Colin for handling the entire administration. The organisers gratefully acknowledge the financial support received from the following companies : SHELL SKF SNR RHODIA CHIMIE

Thornton, UK Nieuwegein, The Netherlands Annecy, France Courbevoie, France

This support allowed us to offer students reduced fees, and we were very pleased to see the large number of students actively contributing to the success of the conference. The Leeds-Lyon Symposia have now covered a wide range of topics, as shown in the following list. The essential aim is to select each year a topic of current interest to tribologists and to contribute to the further advance of knowledge in selected fields.

10 11 12 13 14 15 16 17 18

Cavitation and Related Phenomena in Lubrication Super Laminar Flow in Bearings The Wear of Non-Metallic Materials Surface Roughness Effects in Lubrication Elastohydrodynamics and Related Topics Thermal Effects in Tribology Friction and Traction The Running-in Process in Tribology Tribology of Reciprocating Engines Numerical and Experimental Methods in Tribology Mixed Lubrication and Lubricated Wear Mechanisms and Surface Distress Fluid Film Lubrication- Osborne Reynolds Centenary Interface Dynamics The Tribological Design of Machine Elements Mechanics of Coatings Vehicle Tribology Wear Particles : From the Cradle to the Grave

Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon Leeds Lyon

1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991

vii 19 20 21 22 23 24 25

Thin Films in Tribology Dissipative Processes in Tribology. Lubricants and Lubrication The Third Body Concept : Interpretation of Tribological Phenomena Elastohydrodynamics-'96 : Fundamentals and Applications in In Lubrication and Traction Tribology for Energy Conservation Lubrication at the Frontier : The role of the interface and Surface layers in the thin film and boundary regime

Leeds Lyon Leeds

1992 1993 1994

Lyon

1995

Leeds London

1996 1997

Lyon

1998

We look forward to the 26 th Leeds-Lyon Symposium in Leeds from Tuesday 14th to Friday 17th September 1999 under the title • "Thinning films and tribological interfaces".

Ton Lubrecht

G6rard Dalmaz

List of reviewers Bassani R. Bayada G. Bec S. Belin M. Ben Amotz D. Berthier Y. Bovington C. Brendl6 M. Cann P. Chaomleffel J.-P. Chiu Y.P. Ciulli E. Colin F. Constant B. Coy D.

Dalmaz G. Donnet C. Dubourg M.-C Du Parquet J. Dumont M.-L. Ehret P. Flamand L. Frdne J. Gangopadhyay A. Georges J.-M. Greenwood J. Guangteng G. Heshmat H. Hooke C. Houpert L.

Jacobson B. Kaneta M. Kapsa P. Kennedy F. Kimura Y. Klein J. Korcek S. Larsson R. Lemogne T. Loubet J.-L. Lubrecht T. Mansot J.-L. Mazuyer D. Meurisse M.-H. Mischler S.

Morales Espejel G. Poll G. Roper G. Sainsot P. Sidoroff F. Spikes H. Taylor C.M. Taylor R.I. Tichy J. Tonck A. Torrance A. Vannes B. Venner C. Vergne P. Williams J.

This Page Intentionally Left Blank

ix

CONTENTS INTRODUCTION

SESSION I

Keynote Address Role of Surface-Anchored Polymer Chains in Polymer Friction R. LinGER, H. HERVET and P.G. de GENNES

S E S S I O N II

S E S S I O N III

S E S S I O N IV

Invited S e s s i o n

11

Fuel Efficient Engine Oils, Additive Interactions, Boundary Friction and Wear S. KORCEK, R.K. JENSEN, M.D. JOHNSON and J. SORAB

13

For the Establishment of a New EHL Theory M. KANETA

25

S u r f a c e Force A p p l i c a t i o n s

37

Structure and Mechanical Properties of ZDTP Films in Oil A. TONCK, S. BEC, J.-M. GEORGES, R.C. COY, J.C. BELL and G.W. ROPER

39

The Boundary Lubrication of Glass-Glass Contacts by Mixed Alkyl Alcohol and Cationic Surfactant Systems M.J. ADAMS, B.J. BRISCOE, D.M. GORMAN, F. HOLLWAY and S.A. JOHNSON

49

Mechanism of Friction Across Molecularly Confined Films of Simple Liquids J. KLEIN

59

Asperity Contacts

65

Adhesion at Single Point Contacts J.A. GREENWOOD

67

The Influence of Pressure, Boundary Film Shear Strength and Elasticity on the Friction Between a Hard Asperity and a Deforming Softer Surface J.D. BRESSAN, G. GENIN and J.A. WILLIAMS

79

Effect of Surface Morphology upon Friction of a Metal Substrate Sliding Against Hot Viscous Melt Under Extreme Conditions M. FALIPOU, H. ZAHOUANI and C. DONNET

91

Investigation of Surface Deformation and Friction when a Hard Cylindrical Asperity Slides over a Soft Smooth Surface M. BUSQUET and A.A. TORRANCE

101

SESSION V

SESSION Vl

SESSION VII

Coatings

111

A Tribological Comparison of Some Carbon-Carbon Composites Sliding Against Stainless Steel D.M. ELLIOTT, J. FISHER, S.P. APPLEYARD, E. ZHANG AND B. RAND

113

Low Friction and Low Damage Properties of Diamond with Water Boundary Lubrication S. MIYAKE and A. KINJYO

123

Study on the Friction Characteristics of the Metal with Harder Thin Film A. KOBAYASHI, T. HIRANO and Y. DEGUCHI

133

A Comparative Study of the Tribological Behaviour of TiN and ZrN PVD Coatings F. SILVA, A.T. RIBEIRO and L.A. FERREIRA

141

Roughness and Elastohydrodynamic Lubrication

149

Amplitude Reduction of Non-lsotropic Harmonic Patterns in Circular EHL Contacts, under Pure Rolling C.H. VENNER and A.A. LUBRECHT

151

Thin Film, Time Dependent, Micro-EHL Solutions with Real Surface Roughness C.D. ELCOATE, H.P. EVANS, T.G. HUGHES and R.W. SNIDLE

163

Mapping of Surface Features in the Thin Film Lubrication Regime G. GUANGTENG, P.M. CANN, H.A. SPIKES and A. OLVER

175

The Effects of Transversely Oriented Bump on Point Contact EHL Films in Reciprocating Motion with a Short Length of Stroke M. KANETA and H. NISHIKAWA

185

Surface Roughness Modification in EHL Line Contacts - the Effect of Roughness Wavelength, Orientation and Operating Conditions C.J. HOOKE

193

Stribeck Curves

203

The Importance of the Stribeck Curve in the Minimisation of Engine Friction C. BOVINGTON, S. KORCEK and J. SORAB

205

Theoretical and Experimental Results on Friction for Line Contacts in Mixed and Elastohydrodynamic Lubrication Regimes R. BASSANI, E. CIULLI and B. PICCIGALLO

215

Isoviscous-EHL and Mixed Lubrication Mechanism of Parallel SlideWay with Oil Groove T. NAKAMURA, T. MATSUBARA and F. ITOIGAWA

223

xi

SESSION VIII

SESSION IX

SESSION X

Calculation of a Stribeck Curve of a Journal Bearing D. BARTEL and L. DETERS

231

Real Contact Area, Contact Temperature Rise and Transfer Film Formation Between Original and Worn Surfaces of CFIPEEK Composites Sliding Against Steel K. FRIEDRICH, J FLOCK, K. VARADI and Z. NI~DER

241

Contact Fatigue

253

Shakedown in Dry and Lubricated Surfaces G.E. MORALES-ESPEJEL, A. KAPOOR and S. RODRiGUEZ-SANCHEZ

255

The Fatigue Behaviour of Chamfered Steel Cylinders T.H. KIM and A.V. OLVER

267

The Mechanism of Bearing Surface Fatigue - Effect of Friction and Tensile Hoop Stress on Surface Plasticity and Fatigue Y.P. CHIU

277

Behaviour of Metallic Additive in Composite Metal - Carbon/Steel Brake in Severe Friction Test H. ZAiDI, A. SENOUCI and J. FRI~NE

289

The Influence of Lubricant Type on Rolling Contact Fatigue of Pearlitic Rail Steel D.I. FLETCHER and J.H. BEYNON

299

Boundary and Mixed Lubrication I

311

Low Friction Force of Diamond Sliding on Ag Thin Films Deposited on Si(lll) Plate M. GOTO and F. HONDA

313

Experimental Modelling of Boundary Lubrication Using an Ultra High Vacuum Tribometer M. BOEHM, Th. le MOGNE, J.M. MARTIN, H.M. DUNLOP and G. HAURET

323

Fundamentals on the Friction Mechanism of Diamond-Like Carbon Films C. DONNET, A. GRILL, J. FONTAINE, Th. le MOGNE, F. LEFEBVRE, V. PATEL and C. JAHNES

333

Bench Test Study of Piston Ring Flank and Piston Groove Interaction D.J.W. BARRELL, M. PRIEST and C.M. TAYLOR

343

Roughness

353

The Effect of Roughness Orientation on Mixed Friction T. MAKINO, S. MOROHOSHI and K. SAKI

355

xii

S E S S I O N XI

S E S S I O N XII

A Transient Thermohydrodynamic Analysis of Dynamically Loaded Finite Journal Bearings with Rough Surface Including Mass Conserving Cavitation C. ZHANG, J.X. JIANG and H.S. CHENG

367

The Multi-Scale Mathematical Microscopy of Surface Roughness Incidence in Tribology H. ZAHOUANI, S.-H. LEE, R. VARGIOLU and T.G. MATHIA

379

Sclerotopometric Measurements Assisted by Statistical Methodology for Better Understanding of Abrasion B. BOUALI, V. JARDRET, H. ZAHOUANI, P. LANTERI, B. LAMY and T.G. MATHIA

391

Tribochemistry

403

Transfer Phenomena and Chemical Reactions in MoS= Lubricated Contacts S. DEBAUD, S. MISCHLER and D. LANDOLT

405

Imaging the Chemistry of Transfer Films in AESIXPS Analytical UHV Tribotester Th. le MOGNE, J.-M. MARTIN and C. GROSSIORD

413

The Role of a Reactant Film on Water-Lubricated Si3N41 hBN Surfaces T. SAITO, Y. IMADA and F. HONDA

423

Tribochemical Interactions Between Micellar Calcium Borate and ZDDP : Evidence for Borophosphate Tribofilm by EELS K. VARLOT, J.M. MARTIN, B. VACHER and K. INOUE

433

The Wear Behaviour of a Thin MoS2 Coating, as Studied by Triboscopic Measurements in Friction and Electrical Contact Resistance M. BELIN

439

M o l e c u l a r Modelling

449

Modelling Tribochemical Processes Using a Combined Molecular and Hydrodynamic Approach D. BEN-AMOTZ and I. KUDISH

451

A Molecular-Scale View on Rotary Lip Sealing Phenomena F. SCHULZ, K. WIEHLER, V.M. WOLLESEN and M. VOETTER

457

Hybrid Molecular Dynamics and Continuum Mechanics Analysis of Thin Film Lubrication T.-L. SHAM and J. TICHY

467

A Dynamic Model of the Transfer and Wear Processes Using Soap Bubble Rafts K. HIRATSUKA, Y. ABE and K. FUJISAWA

475

xiii

S E S S I O N XIII

S E S S I O N XIV

SESSION XV

Elastohydrodynamic

Lubrication 1

481

An Analysis of Track Replenishment Mechanisms in the Starved Regime B. JACOD, F. PUBILIER, P.M.E. CANN and A.A. LUBRECHT

483

Shearing of Adsorbed Polymer Layers in an Elastohydrodynamic Contact in Pure Sliding D. MAZUYER, E. VARENNE, A.A. LUBRECHT, J.-M. GEORGES and B. CONSTANS

493

Film Thickness, Pressure Distribution and Traction In Sliding EHL Conjunctions A. JOLKIN and R. LARSSON

505

Elastohydrodynamic Lubrication Characteristics of Electrorheological Fluids A. KORENAGA, T. YOSHIOKA, H. MIZUTANI and K. KIKUCHI

517

Elastohydrodynamic Squeeze of Thin Films for the Sphere-Plane Contact M. TRIFA, F. SIDOROFF and J.-M. GEORGES

523

Solid and P o w d e r Lubrication

535

On the Rheodynamics of Powder Lubricated Journal Bearing : Theory and Experiment H. HESHMAT and C.A. HESHMAT

537

First Steps for a Rheological Model for the Solid Third Body I. IORDANOFF and Y. BERTHIER

551

Third Body Mechanisms in Dry Friction of Carbon-Fibre-Reinforced (SIC) Ceramic Matrix Composites Ph REYNAUD, P. FOURNIER, F. PLATON and J. ABSI

561

The Effect of Hollow Nanoparticles of WS2 on Friction and Wear L. RAPOPORT, Y. FELDMAN, M. HOMYONFER, H. COHEN, S COHEN and R. TENNE

567

Lubricants

575

Choking of Flow Restrictor Caused by Calcium-Detergent in Lubricating Oil A. YANO, S. WATANABE, T. OMURA and K. SAKI

577

IR Spectrocscopic Analysis of Grease Lubricant Films in Rolling Contacts S. HURLEY and P.M. CANN

589

xiv

SESSION XVl

SESSION XVll

Service Life and Lubrication Conditions of Different Grease Types in High-Speed Rolling Bearings E. FRANKE and G. POLL

601

The Inclusion of Lubricant Shear Thinning in Journal Bearing Models R.I. TAYLOR

611

French Contribution to the Study of Lubrication, Oiliness, Molecular Influences. Application to Watch Lubrication J. du PARQUET

621

Friction and Wear

633

Effects of Composition and Surface Finish of Silicon Nitride Tappet Inserts on Valvetrain Friction A. GANGOPADHYAY, D. McWATT, P. WILLERMET, G.M. CROSBIE and R.L. ALLOR

635

Wear Modes in Lubricated Brass-Tungsten Carbide Contact S. HOLLINGER, J.-M. GEORGES, D. MAZUYER, P. BOURi~, S. BEC and G. LORENTZ

645

Influence of Lubricant Properties and Temperature on the Scuffing Failure of FZG Gears J. CASTRO and J SEABRA

655

Surface and Near-Surface Interactions Affecting Friction and Wear R. ROZEANU and F.E. KENNEDY

665

Conception of Numerical and Experimental Tools for Study of the Tribological Transformation of Surface (TTS) A. ELEOD, F. OUCHERIF, J. DEVECZ and Y. BERTHIER

673

Elastohydrodynamic Lubrication 2

683

Thermal Effects in Elliptical Contacts with Spin Conditions P. EHRET. D. DOWSON and C.M. TAYLOR

685

Contact Dynamics in Starved Elastohydrodynamic Lubrication Y.H. WIJNANT and C.H. VENNER

705

New Tools for the Experimental Study of EHD and Limit Lubrications J. MOLIMARD, M. QUERRY and P. VERGNE

717

Lubrication Theory as a Means of Unravelling Flow Structure in Thin Film Roll Coating Systems P.H. GASKELL, J.L. SUMMERS and H.M. THOMPSON

727

Role of Surface Layers of Natural and Artificial Cartilage in Thin Film Lubrication T. MURAKAMI, Y. SAWAE, M. HORIMOTO and M. NODA

737

XV

SESSION XVIII L u b r i c a t i o n a n d F r i c t i o n

749

An Investigation on the Antifriction Performance of Some Organomolybdenum Additives G. TRIPALDI, S. FATTORI, R. NODARI AND A. VETTOR The Behaviour of Molybedenum Modifier Additives J. GRAHAM and H. SPIKES

SESSION XlX

751

Dialkyldithiocarbamate Friction 759

Traction and Film Thickness Characteristics of Traction Fluids in High Speed Elastohydrodynamic Contact J. MAKALA, J.P. CHAOMLEFFEL, B. VILLECHAISE, G. DALMAZ AND K. KARGAR

767

Development of an Apparatus for the Direct Measurement of Traction Coefficients for Lubricants; Preliminary Measurements from a Bouncing Ball Apparatus D. DOWSON, M.F. WORKEL, J. CANELO-QUINTERO and S. MAY

779

Effect of Particles Concentration on Friction M. TOMIMOTO and K. MIZUHARA

789

B o u n d a r y and Mixed Lubrication 2

797

The Effect of Molecular Structure on Boundary and Mixed Lubrication by Synthetic Fluids -An Overview S. BOYDE, S.J. RANDLES and P. GIBB

799

Investigation on Soot Dispersant Properties and Wear Effects in the Boundary Lubrication Regime P. DIATTO, M. AN7_ANI, L. TINUCCI, G. TRIPALDI and A. VETTOR

809

Water in Confined Geometry, an Approach to the Behaviour of Fluids in Boundary Lubrication J. LEPAGE and G. MAURICE

821

Solidified Films and Adsorbed Films in Concentrated Contacts J. SUGIMURA, J. KIM, S.GONDO and Y. YAMOMOTO

829

Written Discussion

839

List of Delegates

877

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SESSION KEYNOTE ADDRESS Chairman •

Professor G. Dalmaz

Paper I (i)

Role of Surface-Anchored Polymer Chains in Polymer Friction

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

Role o f S u r f a c e - A n c h o r e d P o l y m e r Chains in P o l y m e r Friction L. L6ger +, H. Hervet, P.G. de Gennes Laboratoire de Physique de la Matibre Condens6e, URA CNRS 792, Coll~ge de France, 11 Place Marcelin Berthelot, 75231 Paris, Cedex 05, FRANCE The friction coefficient between a flowing polymer melt and a solid surface bearing attached polymer chains has been investigated both experimentally and theoretically. As the shear rate is progressively increased, several friction regimes show up linked to a progressive transition between low and high slip at the wall.

1. INTRODUCTION The question of the boundary condition for the velocity at the wall when polymer melts flow has been widely debated in recent years. An important practical example is that of constant speed extrusion processes where various flow instabilities develop above shear stress thresholds. The origin of these anomalies has long remained poorly understood (lto 16). It is now well admitted that they are related to the appearance of flow with slip at the wall. Indeed, the shear stress at the solid surface is (where rib is the melt

"l;xz=llb(c)V/~Z)z=0

viscosity and (bV/~Z)z=O the shear rate at the interface). If there is a finite slip velocity Vs at the interface, the shear stress at the solid surface can also be evaluated as Zxz =~Vs, where ~ is the friction coefficient between the fluid molecules in contact with the surface and the solid surface (17). Introducing the extrapolation length b of the velocity profile to zero, (see

b=Vs/(~OVfiOZ)z=O

Figurel), one obtains [~=rlb/b. Thus, any determination of b will yield ~, the friction coefficient between the surface and the fluid.

Vt

Figure 1: Schematic of the shear geometry used to characterize the interfacial friction: the lfluid thickness is e, the top plate is translated at the velocity Vt and the bottom plate is immobile. The local velocity of the fluid at the bottom interface is Vs . The shear rate is ~,=(Vt - V s )/e and the velocity profile extrapolates to zero at a distance b below the interface" b =Vs/(8V/8Z)z=O . This friction coefficient is a crucial characteristics of the interface, directly related to the molecular interactions between the fluid and the solid surface. It connects these interactions at the molecular level to the rheological properties of the system.

+ Also University Paris XI and member of Institut Universitaire de France

4

1000 gl

It is worth to notice that measuring the shear stress "Cxz gives only a partial information on the polymer - wall friction, as long as Vs is unknown. Up to 1992, there were no reliable measurements neither of the slip velocity or of the extrapolation length even if direct visualizations of the existence of wall slip had been performed (18). Migler, Hervet and L6ger (19,20) designed an experimental technique which gives a direct access to the velocity of the fluid very locally at the interface, inside a layer with a typical thickness of 70 nm. This spatial resolution is well adapted to the flow of polymer melts, especially when polymer chains are attached to the wall, the range of the interfacial interactions being of the order of the radius of the polymer chains (between 10 and 100 nm). We shall review here the main results of these direct measurements of the interfacial velocity, in the case of PDMS melts flowing on silica surfaces covered with various anchored polymer layers, along with the models which have been developed to describe the different friction regimes identified in these experiments.

100

' ' ' '""1

........

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~" E

I

lO -

11

1

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V*

/

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!

22

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o.1 ~- /..j.~j~.,.,.~ Vs-Vt AI2d 0.01 ~

. . . . . . . . 1

I

,

,

,,

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10

I

. . . . . .

1 O0

,-1 1000

Vt(um/s) 100

~

10 =-

~=1

bo ..~.. " 11¢

H

0.1

1

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1 O0

1000

V s (pm/s)

2. THE THREE FRICTION REGIMES

1000 ¢,= "

The polymer system which has been extensively studied was PDMS flowing (simple shear) on smooth silica surfaces bearing either irreversibly adsorbed or end grafted PDMS chains. In the case of adsorbed layers with low densities, it was necessary to protect the surface in order to avoid any further adsorption during the flow experiment (since the surface was put into contact with a PDMS melt). To do so, the silica surface was previously treated by grafting a monolayer of octadecyltrichlorosilane, the adsorption of PDMS chains taking place in the holes of this protective layer which had an adjusted surface density (21). End grafted layers were produced following the procedure invented by J.P. Folkers and M. Deruelle (22). Over the range of shear rates explored (from 10-2s -] to 100s -] ), and for all the samples investigated, three different regimes have been observed for the evolution of both the slip velocity and the extrapolation length of the velocity profile as shown in figure 2. In figure 2a, the average

........

i

........

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lO

v

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~ ,I

0.1

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10

Figure 2: Typical results obtained at the interface between a PDMS melt (mP = 970 kgmole-~), with the molar mass of the monomer m = 0.074 kg/mole) and a grafted PDMS layer (mN = 96 kgmole 1 and c~ = 0.0055). In figure 2a V~ (measured in a layer from the interface with a thickness 70 nm) is reported as a function of Vt. In figure 2b, b is displayed as a function of Vt, in log scales. In figure 2c, the same data are reported in terms of V~ as a velocity V~, measured in a layer from the interface function of the shear rate experienced by the polymer melt with a thickness 70nm, is displayed as a function of the velocity imposed at the upper

surface of the sample, or shearing velocity, V t . First, wall slip exists at all V t , the measured Vs being always at least ten times larger than the calculated average velocity in the same layer of fluid with zero velocity at the interface (full line in figure 2a). The second clear result is the existence of a transition from low slip to high slip, when the applied shear rate becomes larger than a critical shear rate ~,*. The slip velocity at y* is V*. In figure 2b, the extrapolation length (or slip length) b is reported as a function of the slip velocity Vs . For

the average number of monomers needed to form an entanglement. Thus the surface chains behave independently of each other and are entangled with the melt chains which fully penetrate the surface layer (27). When flowing, the bulk chains exert a friction force on the bound surface chains. If large enough, this friction force can deform the surface chains, which in turn develop a restoring elastic force. In a steady state regime these two forces counterbalance. In the first version of the models, the resulting equilibrium shape of the deformed grafted chains was assumed to be a cylinder with a length 1 and a diameter d, as shown in figure 3.

Vs smaller than V*, b admits a constant value b 0 (of the order of liana): this is a linear friction regime characterized by a friction coefficient independent of

Vs . Between

V*

and

V**,

b

becomes

t

•

proportional to V s , implying a friction coefficient inversely proportional to Vs . This non linear friction regime with a shear stress at the wall not proportional to the slip velocity is called the "marginal regime". Finally, for slip velocities larger than V

m,

, b levels off to a value boo, about twenty

times larger than b 0. In this high slip regime, the friction coefficient between the polymer and the solid is strongly decreased compared to what happens at low velocity, and the polymer melt and the surface are almost de-coupled. In figure 2c, the variations of the slip velocity versus the shear rate close to the surface, ~, , exhibit the same three regimes. The striking feature is that in the whole "marginal regime" ? remains constant and equal to .*

q(. 2. MOLECULAR MODELS

The above described behavior has been interpreted in terms of a molecular model proposed by Brochard and de Gennes (23) and further refined (24,25,26). The first version of these models considers a solid surface bearing a few end grafted polymer chains, with a surface density, c~, below the onset of the mushroom regime (i.e. the surface chains do not overlap and oN < 1, with N the polymerization index of the anchored chains). The melt chains have a polymerization index P . Both N and P are assumed to be much larger than N e ,

Figure 3 Schematic of one grafted chain entangled with melt chains and deformed under the effect of the friction forces. In order to evaluate the friction force, let us consider one surface chain and one bulk chain entangled with it. The process allowing the relative motion of these two chains is schematically depicted in figure 4. To allow the bulk P chain to flow, the entanglement has to be released in a time shorter than the time taken by the P chain to travel parallel to the surface over a distance comparable to the average distance between entanglements, d*_=aNe 1/2 . The velocity of the P chain along its own tube (in the reptation picture, (28))needs thus to be larger than the surface velocity, Vs , by a factor P/N e . Counting the number of entanglements between the two chains, the friction force ff between one surface N chain and one bulk P chain can be evaluated as ff ---a~lbVs.

OeQ, "

; D',

,

(~kT ~(, -=d* a 2 ----lIb

(1)

while b increases with Vs as

k~._

¢

/,L v tub

X\\\\\\\\\\\\\\\\ Figure 4: Schematic of the process allowing one melt chain, P, entangled with one grafted chain N to move parallel to the surface at the velocity Vs . The total friction force between one N chain and the melt is then Ff =_Xft , where X is the number of bulk chains entangled with one surface chain. Ff

llbVs Nel/2a 3 b=_ okT

(2)

The onset of the marginal regime is reached for V~_--V* with: V*_- kT Tib Na2

(3)

When the slip velocity is further increased, the Rouse friction (29) finally becomes dominant, for

increases with Vs , and, consequently, the elongation

Vs>V**o~N -1 . A linear friction regime is then

of the grafted chain increases with Vs . The diameter of the grafted chain is thus a decreasing function of Vs . This description assuming entangled bulk and surface chains, cannot remain valid at large slip velocities: when the diameter of the elongated N

recovered, with a constant extrapolation length, boo,

chains reaches d* (that is for Vs =V* ), one enters into a new friction regime. The cornerstone of the model is that when d reaches d*, the elongation of the surface chain no longer increases with Vs but remains locked to d* over a wide range of Vs values. Indeed, if increasing Vs over V* the diameter of the grafted chain would decrease below d*, the surface and bulk chains would disentangle, and the friction force would decrease. It would then not be able to balance the large elastic force associated with the large elongation of the N chain which would then recoil and re-entangle. This is the "marginal regime" where the progressive transition from low slip to high slip takes place. It is remarkable that the transition is progressive in terms of the evolution of the extrapolation length with the slip velocity (in figure 2 the marginal regime extends over more than one decade in Vs ), while it appears sudden in terms of the evolution of the surface stress as a function of the slip velocity: all along the marginal regime, the surface stress is locked at the value "c :

much larger than b 0 and comparable to what would be observed on an ideal surface without anchored chains (17). The experimental data obtained at low surface densities, for end grafted chains, are in very good agreement with these theoretical predictions, not only for the overall evolution of the slip velocity versus the shear rate or of the slip length versus the slip velocity as shown in figure 2, but also for the molecular weight dependence of the critical velocity V* which follows exactly the laws implied by equation

[3]" V*o~P-3"3N-1

(20,30,31).

The

extension of the non linear friction regime over a wide range of slip velocities and the reproducibility of the location of the onset of the marginal regime can be taken as clear evidences that the deformation of the surface anchored chains under the effect of the friction force exerted on them by the flowing melt is the correct framework to analyze the dynamic de-coupling between the bulk and surface chains. A de-coupling mechanism between the melt and the surface based on the breaking or the desorption of the surface chains (32) would lead to a sudden onset of strong slip, the width of the transition being governed by the polydispersity of the surface anchored chains. It would also lead, because the adsorption process is not a rapid one (33), to an evolution of the parameters of the transition (value of the critical shear rate) with the

time elapsed under shear, evolution which has never been observed for the PDMS - silica system discussed here. 3. MODULATION FRICTION

OF THE INTERFACIAL

interactions between the surface chains, so that they still behave independently of each other (27,36) and the surface stress increases linearly with 6 . At the same time, as shown in figure 6, the extrapolation length at low slip velocity, b 0 , appears to be independent of cy (34).

From the preceding discussion, the friction coefficient ~ is given by okT ~-_-. Nel/2aVs

3

0

versus the grafting density, cy. '

i

,

0.00

i

,

I

6 5

0.00

I

i

I

w

I

i

I

0.01

i

I

0.02

,

I

0.03

(Y Figure 5: Evolution of the critical shear rate j,* at the onset of the marginal regime as a function of the surface density in the grafted surface layer, ~ , for mP =970kgmole -1 , and mN --96kgmole -1 . From ~ = 0.003 to ~ = 0.01

j,* increases linearly

with ~ as predicted by equation 4. This is surprising, because the model has been developed for surface chains well below the overlapping density, c~ > N -1 , while the experiments presented in figure 5 all correspond to surface densities above the overlapping density: N--1000 gives N - l = 0 . 0 0 1 .

0.01

i 0.02

I 0.03

Figure 6 Evolution of the extrapolation length at low slip velocity, b 0 , as a function of the surface density of grafted chains for the experiments reported in figure 5.

7

3

w

2

grafted chains. Figure 5 displays the variation of ~/*

.#.

I

(4)

and can be controlled by modulating cy, the surface density of the surface anchored chains. This has been investigated in detail by Durliat et al. (34,35) for end

O0 v

l

In fact, cy

remains low enough to allow a good penetration of the bulk chains into the surface layer, screening the

The explanation is due to Gay (24,25): the friction between the surface and the melt is fixed by the number of bulk chains entangled with the surface chains. Starting from very low surface densities of grafted chains, and increasing progressively cy, it is natural to think that the number of bulk chains able to entangle with the surface layer first increases linearly with cy. However, the total number of bulk chains trapped by a unit area of the grafted layer cannot increase more than the surface density of bulk chains, With X the number of entanglements between one surface chain and one bulk chain, this means that above the grafting density Cyb = p - l / 2 .

cyc -_-X-1p -1/2 , the surface layer is saturated with bulk chains and the number of entanglements no longer increases when cy increases. The friction coefficient between the surface chains and the fluid is then independent of c~, while the onset of the marginal regime, which corresponds to a given elongation of each surface chain, is characterized by a critical shear rate increasing linearly with cy. For larger ~ values, cy >0.01, in figure 5, ~,* becomes a decreasing function of or. The friction

between the bulk and surface chains is no longer additive as it was at lower surface densities, meaning that a "collective behavior" of the grafted chains shows up. Such a decrease of the critical surface stress for the onset of strong slip means that to disentangle bulk and surface chains at high surface densities is easier than at low ones. This is coherent with the fact that the bulk chains are progressively expelled from the surface layer when is increased (27,36). Additionally, it is also possible that the mechanical response of the dense grafted layer is different from that at low densities. Up to now there is no quantitative model to describe this situation. Similar trends have been observed qualitatively for a melt in contact with irreversibly adsorbed layers. Three friction regimes also show up, with a wide marginal regime in which the extrapolation length b follows a power law dependence versus the slip velocity, Vs a. Quantitatively, the exponent ot of this power law is always smaller than 1 at low grafting density (30, 34) and varies from 0.7 to 1.4 at high grafting densities (34). At the same time, the shear rate is not exactly locked at a constant value inside the marginal regime, but rather follows a S shape curve as a function of the slip velocity, a fact that can be attributed to the polydispersity of the loops and tails forming the surface anchored layer. Besides the essential possibility of controlling the surface friction by changing the surface density of anchored chains all other parameters being kept constant, the value of V* (equation 3) can also be adjusted by changing the molecular weight of the anchored chains (31). The preceding analysis of the progressive decoupling between the surface and bulk chains assumes that the anchored and the bulk chains are entangled, i.e. that N and P are both much larger than N e . What does happen if this is not the case? An interesting situation should be that corresponding to N< Ne, P>> Ne and a high c value. According to references (27) and (36), the bulk chains are then not allowed to penetrate into the dense surface layer of short chains. The surface thus behaves like an ideal one, with a very low friction coefficient, comparable to that observed in the high slip regime previously described, as it has indeed been shown by Durliat et al. (35) with small PDMS grafted chains (Mw=4kgmole 1, Mwe=8kgmole 1)

and long PDMS bulk chains (Mw=970kgmole-~): high slip was always present, even at the lower shear rates experimentally attainable. All the above results dearly show that adsorbing or grafting polymer chains on a solid surface facing a flowing polymer melt can change drastically the friction coefficient and lead to non trivial non linear friction regimes. For the PDMS/silica system, where the surface chains are strongly anchored to the surface, the dynamic de-coupling between the surface and bulk chains occurs through a coil to stretch transition of the surface chains. This leads to a friction governed both by the molecular parameters of the system (surface density of the surface chains, polymerization indices of both the surface and bulk chains) and the level of shear. For weaker anchoring of the surface chains, however, an alternative mechanism of de-coupling is the desorption of these chains, also leading to an onset of strong wall slip above a critical shear stress and to an abrupt transition (32). 4. CONCLUSIONS We have demonstrated that surfaceanchored polymer layers were quite efficient to adjust the friction between a polymer melt and a surface. This friction is governed by the ability of the surface chains to interdigitate into the melt and to entangle with the bulk chains. However, because the surface anchored chains are flexible and deformable objects, they can elongate under the effect of the friction forces, leading to a non trivial friction law when the local velocity at the interface is progressively increased. Indeed, at sufficiently high shear rates, the surface chains become elongated enough so that they disentangle from the bulk chains, leading to an onset of flow with high slip at the wall, i.e. to a dynamic de-coupling between the layer and the bulk polymer. It is possible to account for the different observed friction regimes in terms of a molecular model based on this notion of shear induced disentanglement, thus opening the way to the design of surfaces with adjusted friction properties. Acknowledgements. We are indebted to F. Brochard-Wyart for fruitful discussions, and to J. Folkers and K. Migler for their help in the design of the experiments.

REFERENCES

1. W. ShiQuing , P.A. Drda Macromolecules 29 (1996) 2627. 2. J.J. Benbow, P. Lamb SPE Trans. 3 (1963) 7. 3. de Smet, S. Nam Plastic Rubber Process Appl. 8 (1987) 11. 4. M.M. Denn Annu. Rev. Fluid Mech. 22 (1990) 13. 5. N. E1 Kissi, L. L6ger, J.M. Piau J Non Newtonian Fluid Mech 52 (1994) 249. 6. N. E1 Kissi, J.M. Piau J Non Newtonian Fluid Mecla 37 (1990) 55. 7. S.G. Hatzikiriakos, J.M. Dealy, J Rheol 35 (1991) 497. 8. S.G. Hatzikiriakos, J.M. Dealy J Rheol 36 (1992) 703. 9. S.G. Hatzikiriakos, J.M. Dealy J Rheol 36 (1992) 845. 10. D.S. Kalika, M.M. Denn J Rheol 31 (1987) 815. 11. R.G. Larson Rheol. Acta 31 (1992) 213 12. J.M. Piau, N. E1 Kissi J Non Newtonian Fluid Mech 54 (1994) 121. 13. J.M. Piau, N. E1Kissi J Rheol 38 (1994) 1447. 14. J.M. Piau, N. E1 Kissi, B.J. Tremblay J Non Newtonian Fluid Mech 34 (1990) 145. 15. A.V. Ramamurthy J Rheol 30 (1986) 337. 16. G.V. Vinogradov, V.P. Protasov, V.E. Dreval Rheol Acta 23 (1984) 46. 17. P.G. de Gennes C.R. Acad. Paris 288 (1979) 219. 18. B.T. Atwood, W.R. Schowalter Rheol. Acta 28 (1989) 134. 19. K.B. Migler, H. Hervet, L. L6ger Plays Rev Lett 70(1993)287. 20. L. L6ger, H. Hervet, G. Massey in Rlaeology for Polymer Melt Processing, edited by Piau et al. (Elsevier). (1996) 337. 21. P. Silberzan, L. L6ger, D. Ausserr6, J.J. Benattar Langmuir 7 (1991) 1647. 22. J.P. Folkers, M. Deruelle, E. Durliat, H. Hervet, L. L6ger, submitted to Macromolecules 23. F. Brochard-Wyart, P.G. de Gennes Langmuir 8 (1992) 3033. 24. F. Brochard-Wyart, C. Gay, P.G. de Gennes Macromolecules 29 (1996) 1992. 25. C. Gay (1997) PhD Thesis, University Paris VI (France)

26. A. Ajdari, F. Brochard-Wyart, C. Gay, P.G. de Gennes, J.L. Viovy J. Plays. II France 5 (1995) 491. 27. P.G. de Gennes Macromolecules 13 (1980) 1069. 28. P.G. de Gennes J Chem Plays 55 (1971) 57228. 29. P.E. Rouse J Claem Phys 21 (1953) 1273 30. G. Massey PhD Thesis, University Paris, VI (France) (1996). 31. G. Massey, H. Hervet, L. L6ger, Europhys Lett. 43 (1998) 83.. 32. I. Yongwoo, W. ShiQuing Phys Rev Lett.76 (1996) 467 33. L. L6ger, H. Hervet, Y. Mardano, M. Deruelle, G. Massey Israel J. of Chem. 35 (1995) 65 34. E. Durliat PhD Thesis, University Paris VI (Fance) (1997) 35. E. Durliat, H. Hervet, L. L6ger Europhys Lett 38 (1997) 383. 36. M. Aubouy, E. Raplaa~l Macromolecules 27 (1994) 5182.

This Page Intentionally Left Blank

SESSION II INVITED SESSION

Chsirman •

Professor C.M. Taylor

Paper II (i)

Fuel Efficient Engine Oils, Additive Interactions, Boundary Friction and Wear

Paper II (ii)

For the Establishment of a New EHL Theory

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

13

Fuel Efficient Engine Oils, Additive Interactions, B o u n d a r y Friction, and W e a r Stefan Korcek, Ronald K. Jensen, Milton D. Johnson, and Jagadish Sorab Ford Motor Company, Powertrain and Vehicle Research Laboratory, MD2629/SRL, P. O. Box 2053, Dearborn, Michigan, 48121, U.S.A.

In order to encourage and accelerate development of advanced engine oils which would further contribute to improvement of engine fuel efficiency, Ford developed and made available to the oil industry a new engine test for determination of fuel efficiency of engine oils. This test, called Sequence VIB, was incorporated into the ILSAC GF-3 engine oil standard to be introduced around the year 2000. The main features of this test are increased emphasis on benefits derived under boundary/mixed lubrication conditions and improved retention of fuel efficiency during engine oil use. Friction reducing capabilities under boundary lubrication conditions can be improved through application of effective friction reducing additives, such as molybdenum dialkyldithiocarbamates (MoDTC), which, in combination with zinc dialkyldithiophosphates (ZnDTP) and other antioxidants, must provide good retention of friction reducing capabilities and also adequate antiwear properties. Formulation of such additive systems requires better understanding of various factors affecting performance of MoDTC and their interactions with other additives. From the results of our studies it is clear that ligand exchange reactions between MoDTC and ZnDTP and oxidation and antioxidant reactions involving base oil components, additives, and intermediates derived from them are all important in optimizing the performance and maximizing the benefits derived from these systems. These reactions, although occurring first in the bulk lubricant, also play a very important role in tribochemical conversions in boundary contacts where they are enhanced by more severe conditions. Thus, fundamental understanding of mechanisms and kinetics of these reactions is essential in the process of designing optimized lubrication systems that provide efficient and lasting friction reduction. Along these lines, this paper is intended to review available information, present the most recent data, explain some of the observations, draw some general conclusions, and outline future needs.

1.

INTRODUCTION

At the 24 th Leeds-Lyon Tribology Symposium we discussed the importance of minimizing engine friction through oil reformulation and reviewed engine testing used for evaluation of engine oil fuel efficiency [1]. We also described how the current level of fuel efficiency of engine oils is defined. Finally, we concluded that further improvements in fuel efficiency of engine oils are possible and that such upgrading of engine oils could be encouraged and accelerated if a new engine test would be available to the oil and additive industries for their developmental work.

2. NEW SEQUENCE VIB TEST Our goals in the developmem of the new engine dynamometer test for evaluation of engine oil fuel efficiency, the Sequence VIB test, are listed in Figure 1. Based on our previous work [2] and the work of Japanese researchers [3, 4], improving fuel efficiency must include maximizing the friction reducing effects derived from engine oil additives. Such maximization must involve development of friction reducing additive systems that enable friction reduction to be sustained throughout entire engine oil service intervals. Consequently, the new test must include oil aging represemative of customer service.

14

~velopment Of SequenceVIB for ILSACGF~ GOALS To provide industry with a new tool for evaluation of fuel efficiency of engine oils which would

/

Sequence VIB Protocol • BC oil evaluation - 5 stage fuel economy measurement • Candidate oil evaluation

• Aging 1 : 1 6 hours

• help to maximize engine oil contribution to engine fuel efficiency, • correlate with EPA M/H fuel economy test used for determination of CAFE,

• 5 stage fuel economy measurement • Aging 2 : 8 0 hours • 5 Stage fuel economy measurement • BC oil evaluation - 5 stage fuel economy measurement

• satisfy the lubrication needs of the future engine population, and

BC = Baseline Calibration

• reflect customer vehicle operation.

Figure 1 Goals of the new engine oil fuel efficiency test. We elected to base the development of the new test on the currently used Sequence VIA test [5], as outlined in Figure 2. This allowed accelerated development of the test. The new Sequence VIB test is now completed and will be described in detail at the upcoming 1998 SAE International Fuels and Lubricants Meeting in San Francisco in October [6, 7].

Figure 3 Testing protocol for Sequence VIB. FE Speed stage (rpm)

Developmentof SequenceVIB

"~

APPROACH • Base the development on the Sequence VIA test. • Revise the current Sequence VIA procedure to reflect 4,000 - 6,000 mile (6437 -9674 km) vehicle aging of oil. • Modify fuel economy test conditions to better represent the lubrication needs (boundary/mixed vs. hydrodynamic) of the future engine population.

Figure 2 Approach in development of the Sequence VIB test.

The Sequence VIB test has two oil aging stages. Fuel economy, relative to a base line (BC) oil, is determined after these two aging stages; i.e., after 16 and 96 hours of aging, using five weighted steadystate stages (Figure 3). The test conditions for aging and fuel economy measurement are listed in Figure 4.

(N.m)

(oC)

(oC)

iiiiiii~iii~iiiiii~iii~iiii!iiiii~i~ii~iii!ii!i!~ii~iiiiiii~ii!~!#iii~!~!~!!!!~iii~!~i~iii~iiii~!~iii~iiiiiiii~iiiiiiii~iiiii~i~iiii!iiii~ii~!ii 2

800

26

105

95

I ViA-Stage 1

3 4 5

800 1500 1500

26 98 98

70 70 45

60 60 45

I VIA - Stage2 VIA - Stage4 VIA - Stage 5

Aging S p e e d stage* (rpm)

Torque Oil Temp. CoolantTemp. Comments

(N.m)

(oC)

~',i'~',',~i'~Ti~',',',~',~i~,~i~ii~i~i~i ~,i ,~?,i~',',i'~,'~!~i',~iiii~i.,i~i'~i i~~ *

/~

Torque Oil Temp. CoolantTemp. Comments

Blowby range: 5.3 -

(oC)

ii iiiiiiili!ii i i }i iiiiiiii~iiii}iiiiiiiil ilii#iiiiiiiili~iiiiiiiiiiiiiiil}ii

9.0 (I/m)

Figure 4 Sequence VIB fuel economy measurement and aging conditions. The new Sequence VIB test was shown to correlate with the EPA M/H fuel economy test reflecting customer vehicle operation. The test is now available for development of the next category of fuel efficient engine oils (ILSAC GF-3) which is scheduled for introduction in the year 2000. One of the features of the new Sequence VIB test is the increased emphasis on boundary/mixed friction with the response under such conditions increased to 20-25% (Figure 5). It is expected that application of effective boundary friction reducing additives will be Friction Reduction

Sequence VIA

Sequence VIB ~!i~i~!i~!i~iii~i~i~i~iiiiiiiiii!i~!i~i~iii~i~i~i!i~iiiiiii~iiiiiiiiiiiiiiiiiiiiiii~i::~iii~:=ii!i~iiiii!i!iii!~iiii~i!!

Boundary/Mixed

10 - 1 5 %

Hydrodynamic

85 - 90 %

Figure 5

iliiiiiiiii!iiiT:~:~:~i~%~ iil~::::i!~:' Fsfv). The value of the yield stress depended bottibn the normal load between the surfaces and on the value of n (< nc), and once sliding commenced, it proceeded by a clear stick-slip motion, as indicated schematically in fig. 2. On pulling on the end of the spring in the x-direction the lateral tension Fs increases, as shown schematically in the figure. This is the 'stick' part of the stick-slip cycle. As the

trace - the shear stress across the film reaches the yield value, Fs = Fs(v) = Klx0, and the confined film yields. Soih'e rapid sliding of the top surface relative to the lower one then occurs, for example from point U to point V in the Fs trace in fig. 2 (the 'slip' part of the stick-slip cycle), the tension in the spring relaxes somewhat, and the film then resolidifies abruptly at the point V. As the end of the spring continues to be pulled (at velocity v) the shear stress builds up again in a new 'stick' part of the cycle, 'slip' at a critical value occurs once again, and so on. A better appreciation of the processes occuring in the confined film under shear may be obtained by a more detailed consideration, as illustrated in fig. 3, where a schematic magnification of the gap between the surfaces is indicated. Initially, fig. 3a, the confined liquid film, thickness D, is in a layered state, n layers say, between the confining surfaces (in fig. 3, n = 4). The mean normal pressure on the film is P = F/A, where F is the normal force due to compression of the spring K2 and A is the effective area of the film. When the surfaces are stationary with respect to each other, the normal forces between them are oscillatory due to the layering as illustrated above, and in the unsheared state, for n s no, the confined film is solid-like, as indicated in fig. 3a. The

61

This gives the value of S]tYm)in terms of the structure of the confined and the normal oscillating force profile, and describes rather well the experimentally observed variation of the yield stress with applied pressure P and the number of confined layers n. In what follows we are interested in the processes taking place during the stick-slip cycle itself.

shear force Fs is applied to the top surface as indicated via stretching of the spring, fig. 1, (the corresponding mean shear stress is S Fs/A). At the yield point (e.g. U in fig. 2) the solid-like film abruptly melts. The corresponding critical value of the shear stress at the yield point is Scfy). The issue of shear induced melting was finalysed in detail in ref.[4] using a Lindemann-type criterion.

P II d Fs ~

stick

Ax 6

melt and slip

a

b

~~

Freezeand stick

C

Figure 3

2.1. Yield, liquification and dilatation At the instant of yield and liquification of the confined film, and commencement of slip between the surfaces (as at point U in fig. 2), we expect some dilation of the gap between them. It has long been known that shear of an ordered array of particles can lead to a dilation effect[6] and we believe this occurs also when the confined film undergoes shearinduced melting (when the shear force reaches the yield point Fs(y,)). Computer simulations show precisely sucn a dilation for thin films sheared between two plates[7]. The dilation may also be viewed as resulting from the density difference between the solid and the liquid (typically around 5 - 10% for a range of materials. For example, for bulk OMCTS, the material used in the experiments of ref. [3, 4], the differences are ca. 10%[8, 9]). This dilation must manifest itself in the increased separation of the surfaces, from D to D + 6 say, just as the film melts, as indicated in fig. 3. A 10% density change would

correspond to 6 of order 1 - 2/~ for D around 5 nm. Such a change in D would be difficult to observe from the motion of the optical interference fringes in the surface force balance experiments, and indeed was not observed in the experiments of ref.[4] Immediately following the yield point U the surfaces begin to move relative to each other (slip), since the film separating them is no longer rigid. Motion takes place both laterally, in the x-direction (top surface), driven by the shear force Fs, and, at the same time, normal to the surfaces, in the z-direction (lower surface), driven by the normal force F = PA (fig. 3). In our model, motion continues as long as the confined film remains liquid: when the surfaces have moved together by 6 and the separation between them returns to D, confinement-induced freezing occurs, the film solidifies and the relative motion stops abruptly (point V in fig. 2. The stick-slip cycle then begins anew). The total sliding motion Ax (fig. 3) is of order nanometers to tens of nanometers in the experiments of ref. 4, while the time 6t over which the slip occurs

62

(fig. 2, inset) is around 10 -2 s. The equations describing the motion in the two directions (x and z) during slip have similar forms, consisting of an inertial term, a viscous (friction) term and a term describing the driving force.

2.2 Motion during slip The relative motion of the two surfaces while in the 'slip' regime may be described by two second order differential equations: M(d2q/dt 2) + B(dq/dt) = K(q0- q)

(1)

where q = x o r z ; M = M1 o r M 2 ; a n d K = K a or K2 respectively (see fig. 1). In these equations the term on the RHS of the equation is the force on the surface due to the respective springs. This is balanced on the LHS by the inertial term, and by the friction term B (Bx or Bz) which represents the viscous effects due to the confined liquid in the gap, and are discussed below. The two boundary conditions for this equation are clearly q = (dq/dt) = 0 at t = 0, where t = 0 defines the instant where yield and dilation have just occured (the start of the slip cycle), and q is the displacement during the slip. There are some simplifications in writing the equations in this form, but none of them are important[10]. E l s e w h e r e [ l l , 12] we consider in more detail the solutions to the two equations of motion (1), in particular the viscous term in B. This term can be written in terms of the effective viscosity rleff of the confined liquid during the slip phase, and from the solution to the equations it is possible to evaluate the time fit expected for the slip to occur between the points U and V in fig. 2. By comparing the experimentally observed time (ca. 10 -2 secs from the experimental traces in our experiments[3, 4]) to that predicted from the equations, the value of rleff may be estimated, and is found to have an upper bound of some 30 poise (P). The implications of this result are summarised below: a) The low effective viscosity of the film during the slip part of the stick-slip cycle implies that the molecular mobility within the confined liquid is high, and thus that re-

freezing (point V in fig. 2, and fig. 3c) induced by confinement when the dilation 8 has been eliminated due to approach of the surfaces - can take place very rapidly. The idea of a 'critical shear rate' beyond which stick-slip is suppressed because the molecules cannot rearrange rapidly enough may still be valid, but only at shear rates that exceed the molecular relaxation rate of the liquid in the gap. A rough estimate[13] based on the above results suggests that, for the conditions of the experiments in ref. [4] (for OMCTS and cyclohexane), shear rates of at least 106 s -1 would be required for this to happen. Since the shear rates used in the experiments did not exceed ca. 103 s -1, the observation that stickslip persisted at all shear velocities used is fully consistent with these estimates. b) The dissipation of energy during the stick-slip cycle may be evaluated from the value of heft. We come to the rather surprising conclusion that only a very small fraction (O(1%) at most) of the frictional dissipation is due to this viscous heating. Since there is no energy dissipation during the stick part of the cycle (where purely elastic deformation occurs), the bulk of the dissipation must occur at the point of resolidification (point V in fig. 2). At this point the moving surface stops abruptly, and the impulse imparted to the surfaces generates phonons that are lost as heat in the apparatus. It may be shown explicitly[12] that the frictional work done in sliding the top surface via a stick-slip process past the lower surface is equal to the energy lost at the re-freezing point. These ideas may form the basis of a more general model for static and sliding friction, in particular where a thin liquid layer separates the two surfaces. For the case of friction between two dry solid surfaces in contact (with no extrinsic separating layer), there is a clear analogy in that local shear melting at the interface between them (or at the points where asperities are in contact) may provide such a transient liquid-like film during the slip regime. The situation is illustrated in fig. 4:

63

Figure 4: On shearing an asperity contact, the molecules at the sheared interface (o) are confined between the smooth undistorted lattice plane molecules (o), and on shearing may behave in analogy to the interfacial film indicated in fig. 3 The generality of our model may thus extend beyond the particular model system[3, 4] which motivated it. A c k n o w l e d g e m e n t s " I thank D. Tabor, S. Safran and R. Yerushalmi-Rozen for discussions. Financial support by the Levin Fund, the Israel Academy of Sciences, the Schmidt Minerva Center for Supramolecular Architecture, the US-Israel BSF and the Ministry of Arts and Sciences (Tashtit grant) is acknowledged with thanks. REFERENCES

1. S. Granick, Science, 253 (1991) 1374. 2. R. Horn and J.N. Israelachvili, J. Chem. Phys. 75 (1981) 1400; H. K. Christenson, J. Chem. Phys., 78 (1983) 6906-6913. 3. J. Klein and E. Kumacheva, J. Chem. Phys., 108 (1998) 6996- 7009. 4. E. Kumacheva and J. Klein, J. Chem. Phys., 108 (1998)

5. J. Klein and E. Kumacheva, Science, 269 (1995) 816-9. 6. O. Reynolds, Phil. Mag., 8 (1885) 2 2 53. 7. P. A. Thompson and M. O. Robbins, Science, 250 (1990) 792. 1. S. Granick, Science, 253 (1991) 1374. 2. R. Horn and J.N. Israelachvili, J. Chem. Phys. 75 (1981) 1400; H. K. Christenson, J. Chem. Phys., 78 (1983) 6906-6913. 3. J. Klein and E. Kumacheva, J. Chem. Phys., 108 (1998) 6996- 7009. 4. E. Kumacheva and J. Klein, J. Chem. Phys., 108 (1998) 5. J. Klein and E. Kumacheva, Science, 269 (1995) 816-9. 6. O. Reynolds, Phil. Mag., 8 (1885) 2 2 53. 7. P. A. Thompson and M. O. Robbins, Science, 250 (1990) 792. 1. S. Granick, Science, 253 (1991) 1374. 2. R. Horn and J.N. Israelachvili, J. Chem. Phys. 75 (1981) 1400; H. K. Christenson, J. Chem. Phys., 78 (1983) 6906-6913. 3. J. Klein and E. Kumacheva, J. Chem. Phys., 108 (1998) 6996 - 7009. 4. E. Kumacheva and J. Klein, J. Chem. Phys., 108 (1998) 5. J. Klein and E. Kumacheva, Science, 269 (1995) 816-9. 6. O. Reynolds, Phil. Mag., 8 (1885) 2 2 53. 7. P. A. Thompson and M. O. Robbins, Science, 250 (1990) 792. 8. J. Levien, J. Chem. Thermodynamics, 5 (1973) 679. 9. J. Hunter, J. Amer. Chem. Soc., 68 (1946) 669. 10. For example, the term on the RHS describing the driving force ignores, for the case of the x-motion, the velocity v at which the end of the spring K 1 is stretched; however, as long as the slip velocity (dx/dt) is much larger than v, which can be shown to be the case over most of the slip, this simplification is negligible. Also, for the z-direction motion, z 0 should strictly be (z 0 -5), but since z 0 >> ~5, this makes little difference. 11. J. Klein, J. Non-Crystalline Solids - in press, (1998) 12. J. Klein,- to be published, 13. If we make the usual assumption that the effective viscosity can be equated to the

64

product of a modulus G and a relaxation time x, so that rleff = Gx, then estimating G ( k B T / m o l e c u l a r volume), where k B is Boltzmann's constant, gives x = 10 -6 sec for the upper limit Vleff = 30P. This yields the estimate x -1 = 106 s -1 for the lower limit of the relaxation rate.

S E S S I O N IV ASPERITY CONTACTS

Chairman •

Professor T. Conry

Paper IV (i)

Adhesion at Single Point Contacts

Paper IV (ii)

The Influence of Pressure, Boundary Film Shear Strength and Elasticity on the Friction between a Hard A s p e r i t y a n d a Deforming Softer Surface

Paper IV (iii)

Effect of Surface Morphology upon Friction of a Metal Substrate Sliding Against Hot Viscous Melt Under Extreme Conditions

Paper IV (iv)

Investigation of Surface Deformation and Friction When a Hard Cylindrical Asperity Slides Over a Soft Smooth Surface

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

67

Adhesion at single point contacts. J. A. Greenwood University Engineering Department, Tnm~pington St., Cambridge, CB1 6JX, U.K. With the advent of the Surface Force Apparatus (SFA) in which contact is between atomically smooth cleaved mica, and the Atomic Force Microscope (AFM), where an ultra sharp stylus is loaded against a plane, it is for the first time possible to study the behaviour of a single, well-defined, contact area. But because of the difficulties of the experiments, it is of great importance to study the contact mechanics of adhesive contacts in order to provide the experimenter with a theoretical background to help in interpreting the measurements. For many years the only theory available was the one developed by Johnson, Kendall & Roberts (JKR theory) in studying rubber/glass contacts. This allows for the influence of the surface energy of the solids in increasing the area of contact above the Hertzian value, and good agreement has been found with the observed contact areas. But because it is based on surface energy rather than surface forces, it is unable to deal with surfaces approaching each other, and already experiencing attractive forces while still out of contact: or with the 'jumping-on' of contacts, already observed in the rubber/glass experiments, and an important feature of SFA experiments. Three models based on surface forces are described here. One involves full numerical calculations for a particular law of surface force: the other two are analytical models based on greatly simplified laws of force. The Maugis model takes the surface force to be a constant when the gap between the surfaces is positive but less than a critical value h e , and to be zero for larger gaps: when the gap falls to zero the normal elastic laws apply. An alternative model, based directly on Hertz theory, is introduced here, and the results of all the models compared. 1. I N T R O D U C T I O N It is now well u n d e r s t o o d t h a t the roughness of engineering surfaces acts to hide from us the details of w h a t is taking place at the individual microcontacts: in engineering, the real area of contact will tend to be p r o p o r t i o n a l to t h e load w h a t e v e r t h e area/load relation at a microcontact. This is very convenient - except for the physicist t r y i n g to u n d e r s t a n d the m e c h a n i s m of interaction between solids, and so, indirectly, for us: for we too would like to u n d e r s t a n d what are these basic laws which are being 'averaged out' by the roughness? The first a t t e m p t s to eliminate surface roughness were tried in Bowden's laboratory in the 1950's. Bowden recognised t h a t when mica is cleaved, it produces flakes which are molecularly smooth over areas of m a n y mm 2, and Bailey & Courtney-Pratt (1955) studied

the contact between two flakes bent into cylinders and loaded together at right angles. The contact area is a circle, j u s t as for a Hertzian contact between two solid cylinders, and its size and the shape of the gap around it can be m e a s u r e d interferometrically. The technique became really powerful when Tabor & Winterton (1969) and Israelachvili & Tabor (1972) learnt how to glue the mica onto glass cylinders to obtain something more nearly resembling a Hertzian contact (Fig 1). From the distances at which the mica jumped into contact, it was for the first time possible to determine directly how the forces between solids vary with their distance apart, down to gaps of a few nanometers. Now the [S]urface [F]orce [A]pparatus is a recognised tool used to study normal and tangential forces either between the mica surfaces themselves, or when the surfaces are coated with monolayers of different materials.

68

a) Molecularly smooth mica sheets about 3tun thick are g/tied to cylindrical formers of radius of curvatatrl lcm. = ~ - ~ t m , dm~

mmd~

/ /

/

,I

/

b~ The upper surface h, mapported on a short metal spring. Tim lower m r a m ~ towanis it, first by a ~ w dmmd and tlmn by • p i m m ~ ' w i c transducer ,~t • c:rit~! m l m ~ t k m the t w o mufacu jump ~ .

Fig 1. Early form of the surface force apparatus (Tabor & W'mterton 1969). The S F A is a wonderful device,but it has a drawback: the mechanics of the contact depend on the properties of a) the mica ~ b) the glass substrate and c) t h e glue l a y e r - of u n c e r t a i n m a t e r i a l properties and thickness. The mechanics of adhesion between three-layer solids has been studied by Sridhar, Fleck & Johnson (1997),but the u n c e ~ t y about the properties of the glue layer remains a problem. The alternative way of studying forces between solidshas been betterpublicised,and most engineers know of the A F M and its extension, the [F]riction [F]orce [M]icroscope. Here a n incredibly fine tip mounted on a m i n u t e cantilever is brought near, or into c o n t a c t with, a plane surface, and the deflection of the cantilever measured as the

cantilever is moved normally or tangentially. The difficulties of i n t e r p r e t i n g the m e a s u r e m e n t s are d i s h e a r t e n i n g . A piezoelectric crystal moves the base of the cantilever, and the movement must somehow be calibrated: even the datum from which the separation is, hopeRdly, measured can only be defined by a kink in the force/separation curve: while the forces can only be deduced by measuring, and calibrating, the cantilever deflection. There is nothing comparable with the wavelength of light to set the scale, and there is no direct way of measuring the contact area: the experimenter can try passing a tiny electrical current through the contact and measuring, and interpreting, the c o n d u ~ c e , or can impose tangential vibrations and attempt to deduce, and interpreting, the contact stiffness. But at least the AFM tip is not too far from a Hertzian pamboloid, so that Hertzian contact mechanics, as modified by surface forces, provide a t h e o r e t i c a l background for the i n t e r p r e t a t i o n of the experimental measurements. 2. I. J K R theory. The simplest background was developed by [J]ohnson, [K]endall & [R]oberts (1971) many years ago when Kendall and Roberts in a project on the behaviour of windscreen wipers studied the contact between a rubber sphere and glass, and found the contact areas were considerably larger than predicted by Hertzian theory. They attributed this to the surface energy gained by the formation of a glass/rubber contact, and so available to increase the elastic strain energy. The original analysis used a global minimisation of the total energy (mechanical plus surface) as in Griffith's original analysis of cracks: but tater M a u ~ & Barquins (1978) showed that the standard fracture mechanics ar~,ment gave the same result more quicklyineidentany convincing me for the a r s t time that fraeVare mechanics, with its absurd concept of infinite stresses, was not the complete nonsense it appeared.

69

The Maugis & Barquins argttment is as follows" The H e r t z i a n stresses needed to flatten a sphere of r a d i u s R over a circle r < a are o ( r ) = - 2 E ' ~]a 2 _ r 2 where E' is the plane zR strain modulus [ E / (1 - v 2) ] of the material. For the contact of two bodies with plane strain moduli E~ a n d E~, E' m u s t be replaced by the contact modulus E* where l/E* =l/E~+l/E~, while R becomes the constant in the equation describing the gap b e t w e e n t h e two b o d i e s a t zero l o a d h ( r ) = r 2 / 2R . This can arise in m a n y ways, such as b e t w e e n two spheres provided t h e i r radii satisfy 1 / R = 1 / Ri + 1 / R2 or b e t w e e n two crossed cylinders each of radius R. Thus, the analysis below is general, b u t it is helpful to t h i n k of the contact as occurring between a rigid sphere and an elastic plane. The Boussinesq 'punch' solution w h e n a cylinder of radius a indents a half-space by a d i s t a n c e 6 is t h a t t h e s t r e s s e s a r e E*b 1 o(r) =• so if two bodies are ~a 2 _ r 2 brought into contact and t h e n moved a p a r t by a distance b w i t h o u t c h a n g i n g the size o f the contact circle, the stress distribution will be or(r) = E* z

6 - 2~]a2 -r 2 ~]a 2 _ r 2 R

infinite stresses (!?) a t r = a" E*6 1 1 or(r) . . . . . =

42a

4a-r

with

[or

|

or

t} =_! 2 ~ a E*

Ay

Since the Hertz load is

W = ~3E'a3 / R and

the Boussinesq load is W = - 2 E * a 6 , the load corresponding to a contact of radius a will be W = ~3 E'a3 / R - 2 E ' a _ ! 2~aA7 = E* = ~ E*a3/R

- {8zrE*a3AT} 1/2

This is conveniently w r i t t e n in t e r m s of the fictitious H e r t z i a n load which would give this contact a r e a in the absence of surface energy, W~ = ~3 E*a 3 / R,

w = Wa

-{6RAr- Wa}1/2

The overall approach of the bodies is the H e r t z a p p r o a c h reduced by the Boussinesq q.itt;': 6 = a 2 / R - ~ 2 z a k 7 / E* It win be clear from these t h a t the usual Hertz equations a p p e a r as the high load limit: b u t a t l o w e r loads t h e r e are i m p o r t a n t differences. According to the J K R theory there will be a finite contact a r e a u n d e r zero load: W

= 0 gives

=

{6 Rar

W ~ o = 6 ~ R A 7 and a ~ = ~ R 3W _ O ~ 3W~

N

4a-r

K=~(ZE*Ay)

= 4E'A7

•

},/2

so t h a t

2A7 / E * ;

and there will be a finite pull-off force:

W~-

where N is the 'stress i n t e n s i t y factor'. [The more common notation K includes an additional factor 0.399 whose purpose or point I hope someone will explain to me. ] If the energy needed to create unit area of free surface on both bodies is A y, a n d the process is reversible so t h a t the energy gained by b r i n g i n g two surfaces into contact from infinity is also A~, t h e n b o r r o w i n g Irwin's principle from f r a c t u r e mechanics" t h a t the s t r e s s i n t e n s i t y f a c t o r N is g i v e n b y N=~(E*Ay /z),

E*6

or(r) ~

then

] ,

~ - -3-

W~ =-3 zRA~,, 2

a n d

~RAy with a ~3 - ~ R E A y / E * . 2 J K R found t h a t the complete e x p e r i m e n t a l l o a d / a r e a curves fitted t h e t h e o r y u s i n g a plausible value for the surface energy A y. It is worth noting t h a t the concept of an 'adhesion force' m u s t be t r e a t e d with care" the force of adhesion at p u l l - o f f is 1.5zRAy, b u t it continuosly varies, with the value 6 z2~A7 at zero load. The approximation to the Derjaguin model suggested by Maugis, t h a t the adhesion force should be t a k e n to be a c o n s t a n t , 2 z2~h ~,, has no physical basis.

70

value h,, when they fall abruptly to zero: the 'Dugdale model' of fracture mechanics. Then of course

2.2. The Maugis model. Although the original J K R analysis did not need to adduce the fracture mechanics principle, it does equally imply the existence of infinite stresses: a n d a surface e n e r g y approach cannot avoid this. For a more logical theory we need to abandon the use of surface energy and consider the actual surface forces. C e r t a i n l y we m u s t do this if we wish to analyse the b e h a v i o u r before contact takes place, and both the general theory of solids and the Tabor & Wintert~n experiments show t h a t forces act b e t w e e n solids w h e n t h e y m e r e l y a p p r o a c h each other: c o n t a c t is unnecessary. The surface f o r c e s - we refer to t h e m as 'forces' since they are indeed forces acting between individual atoms, but we shall treat t h e m as s t r e s s e s - are a function of the gap, or separation, between the solids, and we have

Ar = ao'h The Maugis stress distribution, like t h a t in the J K R theory, consists of two parts:

Hertz pressures (~(r) = - 2E* ~/a2 _ r2 zR over r < a, and adhesive stresses, which are equal to o0 over a < r < c (where h ( c ) = h~ ), and the associated internal stresses such t h a t the action of the complete set of adhesive stresses does not u p s e t the f l a t t e n i n g over r < a produced by the Hertzian s t r e s s e s - a r e q u i r e m e n t u n f o r t u n a t e l y overlooked by Derjaguin et al (1975, 1983) in their analysis. Maugis proves t h a t these i n t e r n a l adhesive stresses m u s t be a(r)=

2 ac ° tza n -zl ( ~

a2 -a2)r2

o0

A7 =fh_oo(hldh_ It is not at a]I d e a r t h a t the force between u n i t a r e a of plane solids equals the force between u n i t a r e a of curved solids, or even t h a t b e t w e e n inclined plane solids: t a k i n g t h e m to be e q u a l is t h e ' D e r j a g u i n approximation', a n d it is h a r d to see how progress could be made without it. It m a y be noted, w i t h some relief, t h a t B r a d l e y ' s calculation of the force b e t w e e n two rigid s p h e r e s ( B r a d l e y 1932), not u s i n g t h e Derjaguin a p p r o x i m a t i o n , gives the same answer as is found (very much more readily) by using it: b u t the curvature and inclination in the r e l e v a n t a r e a are in this case both rather small. Realistically we expect ¢l(h) to decrease from some m a x i m u m value Clo a t h = 0,

perhaps like (h + Zo)-3, but while a numerical analysis m a y incorporate such behaviour, the aim here is to provide a simple analytical model, i d e a l l y w i t h e q u a t i o n s no m o r e complex t h a n the J K R equations. Maugis (1992) has provided j u s t such a theory, by postulating t h a t the surface forces retain the value cro u n t i l the gap reaches a critical

Fig 2 compares t h e J K R a n d Maugis stress distributions, for different values of a (7 0

parameter # = (E.2Ay / R) 1/3 • For # ~ 5 the stresses are very close to the JKR stresses,

II jkr iI ii ~ = 3

¢q

zo. But does z > zo imply a gap between the solids? In other words, when have we separated the solids? S t a t e d thus, this is a philosophical question a n d should simply be ignored: though we note t h a t in an ordinary tensile test we should certainly not r e g a r d the tensile specimen as broken when the force/extension curve is still rising. The meaningful question is, how can we best match this model to the ones used in the analytical theories? In the J K R model, the surfaces are in contact over the whole of the stressed region, even though the stresses there reach (tensile) infinity. In both finite stress models, the stress attains its maximum value inside the contact region: it then either remains at a0 or decreases in the 'cracked' region outside the contact. To m a t c h the models, we s h o u l d t a k e t h e gap to be h = z - z03~/6, and write the force law as o0

°=

f _._ ~(h)-= 2

e

h+e

w h e r e we have w r i t t e n

e

h+ e

e - z0 3~/6 =1.2Zo;

then tensile contact stresses will exist as the atomic planes are moved a p a r t from z = z0 to z=l.2z0 [h=-0.167e toh=0.] Then a b e t t e r model of contact between a sphere and a plane is to regard the solids as elastic continua up to the final plane of atoms, and as force fields above this plane; these force fields being such t h a t when the final planes of atoms are a distance Zo apart, no force will act - j u s t as if the prospective surface were merely an internal plane within the solid. The numerical problem is to find a contact stress distribution or(r) which deforms the final planes of atoms, according to the ordinary elastic laws, to leave a gap h(r) such t h a t or(r) ffi f ( h ( r ) ) , where f (h) is the assumed force law. This proves to be straightforward, using the obvious iterative process, for/~ < l, and to be d i s t i n c t l y h a r d w o r k for /~ > l , b u t solutions have been obtained up to tt = 5 (Greenwood 1997). Typical stress distributions and shapes are shown in Fig 6. For the higher values of tt, there is a well-defined 'contact area', in which the gap varies only from h - - O . 0 5 e up to h = 0, while outside this region the gap quickly increases to large values while the force quickly drops to small values - a picture not very different from the analytical models, and which encourages a belief t h a t it would be possible to identify a 'contact area' experimentally. But for small values of tt the picture is quite different: nothing in the shape or the stress distribution points to a contact area or a contact edge. Our definition (" contact is w h e n h < 0") still holds but it is not clear t h a t we should trust it. Over what area of the surface in Fig 6d should we expect friction forces to act opposing motion? Is it possible to define a frictional shear stress when the friction force m u s t be divided by an apparently arbitrary area ? The safer q u a n t i t i e s to examine, and perhaps the more interesting ones, are the load/approach curves. Fig 7 shows the results of the different theories for tt = 1. There is an extensive region in which all four solutions agree well, the curves having similar shapes

74

i

!

.8

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

!

:._-.~-+,

~

i

!

=!2

.... i ....... i.......

~.,,-~./~IF

i

I

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

o.+

o

D

0.6

t3

......

e0.4

, ~._--2!55

0.2

"~

~ -0.5 -1

........ i. ..........

i

0.5

1

1.5 radius r*

2

2.5

3

0

2

(a) Pressure

10

;

6 . . . . . . ~ =0i2 : .........

..... '~i=2 .... i....... i ....... i ....... i~'

8

:

! .............

,,...

/

O N

.......

6

. .......

.......

C2. e"

6

5

o

N

4 radius r*

(c) Pressure

8 N

i ..........

.......

4

.......

:

o~--.2.55].. : i / :

....... ,~., , . ,

:.-I: I /

]

f

./

....

//

N

~=-1

J

Xi=274

:-~_::--.

:

.....

~4

........

o. 3

:

......

..................... j

2

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

0

0.5

1

1.5

radius r*

(b) Shape

2

2.5

]"

l

e¢~

. . . . . . . . . .

. . . . .

,~

0

/

: .~

0

3

:

"

•

:

. . . . . . . . .

: . . . . . . . . . . .

.

.

4

6

!

0

2

radius r* (d) Shape

Fig 6. Typical s t r e s s d i s t r i b u t i o n s (a,c) and s h a p e s (b,d) from the full n u m e r i c a l solution. W h e n a 'neck' exists, as in Fig 6b, a n d t h e 'separation' is a l m o s t c o n s t a n t w i t h i n t h e neck, t h e a r e a over w h i c h friction forces would act opposing m o t i o n seems d e a r . B u t over w h i c h a r e a in Fig 6d should we expect friction forces to act ?

8

75 1

0.9 o.8

iv,

.

.

p=l .

.

.

.

.

.

.

.

.

.

.

. . . . . . . . .

0.7

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

:

. . . . . . . .

i

. . . . . . . .

+ + + Greenwood

I+.z~,.,. ::.' .' .'' "i:, ,.]~Her!z.. +,

.

•. . . . . . . . .

....

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

I~ I: ~

v

. . . . . . . .

.

3h~, where the 3 on the RHS is r a t h e r arbitrary. Setting h~ = A7 / ~1o this gives, approximately,

cro R~ E .2A7

= ~ > 1

At larger loads, a a n d 6 will be l a r g e r , a n d we m i g h t exoect t h e s u r f a c e e n e r g y approach should be valid for smaller values of /~. This does not seem to be the case: for both the Maugis and the Double-Hertz models, the

0 -1

-0.5

0 0.5 load W / 2~:RA7

1

Fig 9 Variation of contact radii with load f o r p ffi 1. The radius in the Lennard-Jones model, defined by the maximum in the force/separation curve, is always close to the JKR radius. Except near pulloff, these lie between the inner and outer radii (a, c) of the Maugis and Double-Hertz models.

77

5. CONCLUSION. The JKR t h e o r y gives a r e m a r k a b l y good description of single-point contact over a wide range of conditions: surface energy is indeed the determining quantity, and the details of the variation of the surface force with the gap are of secondary importance once contact has occurred. But it cannot take into account the very real interactions before contact occurs: and for some m a t e r i a l combinations, and p a r t i c u l a r l y for small contacts, it is very difficult even to define 'contact'.

K. L. Johnson, K. Kendall & A. D. Roberts (1971) Proc. Roy. Soc. London A324 p301-313. Surface energy and the contact of elastic solids. D. Maugis & M. Barquins (1978) J Phys. D: Appl. Phys. 11 p1989- 2023. Fracture mechanics and the adherence of viscoelastic bodies. R. S. Bradley (1932) Phil. Mag. 13 p853-862. The cohesive force between solid surfaces and the surface energy of solids. D. Maugis (1992) J. Colloid and Interface Science 150 p243-269 Adhesion of spheres: the J I ~ - D M T transition using a Dugdale model. B.V.Derjaguin, V.M.Muller and Yu.P.Toporov (1975) J. Colloid Interface Sci 53 p314-326 Effect of contact deformations on the adhesion of particles V. M. Muller, B.V. Derjaguin and Yu. P. Toporov (1983) Colloids and Surfaces 7 p251-259. On two methods of calculation of the force of sticking of an elastic sphere to a rigid plane.

REFERENCES.

A I Bailey & J S Courtney-Pratt (1955) Proc. Roy. Soc A227 p 500The area of real contact and shear strength of monomolecular layers of a boundary lubricant.

J A Greenwood & K L Johnson (1998). To appear in J Phys D: Appl. Phys. (see Cambridge University Engineering Department report CUED/C-Mech/TR-75, March 1998). An alternative to the Maugis theory of adhesion between elastic spheres. D Tabor (1977) J Colloid and Interface Science 58 p2-13 Surface forces and surface interactions.

D Tabor & R H S Winterton (1969) Proc. Roy. Soc A312 p 435The direct measurement of van der Waals ' forces

J A Greenwood (1997) Proc. Roy. Soc. A 453 pp 1277-1297 Adhesion of Elastic Spheres.

J N Israelachvili & D Tabor (1972) Proc. Roy. Soc A S l p 19The measurement of van der Waals ' dispersion forces in the range 1.5 to 130nm.

M A Lantz, J O'Shea, M Welland & K L Johnson (1995) J. Vac. Sci. Technol. B13 p 1945-1953. An atomic force microscope study of contact area and friction on NbSe 2.

I Sridhar, K. L. Johnson and N.A. Fleck (1997) J Phys. D: Appl. Phys. 30p17101719. Adhesion mechanics of the surface force apparatus.

78

A p p e n d i x : S u m m a r y of e q u a t i o n s .

Approach

di = a 2 / R - ,d2~aA7 / E" All 'horizontal' distances are scaled according to *[ R2Ay

afa

l/3 r-r

E*

,

_[

[ R 2 A y ],,3 "g"

or

~"

-

a "2 -

42~a"

~rertical' distances are scaled according to Maugis e q u a t i o n s .

The Tabor p a r a m e t e r is defined as 1/3 /.t

ffi

The surface energy relation becomes ,2 a* = a l~fl(m)+ 4 /z2f2(m)

R

t70

'~2by

where m

c / a,

=

fl (m) ffi ~/m 2 - 1 + (m 2 - 2) * sec -1 m,

JKR equations.

f 2 ( m ) -- ~ m 2 -. 1 * sec cx(r)

=

cr(r) I

% =

E*

[J2=aAy

1

[~ E

2 ~/a2

4aZ_r 2

--R

r2 ] -

and

~.~ ,=-{~.~~ }"~

W= = ~3E'a3 / R:

cx( r)

R~ar = ~

,2

0 gives

s

W,,o =

ao 3 = ~2t t a ~ = ~ R

~r

3

[W=o

=

6zRAy

]

and *

---~

3~ Pull-off force:

and

1

m]

1.

1

-

4a2_r 2

~4m2 - 1 +--a~ 2

2A1,,/E*]

W

OW OW*

-

sec

4a

2 -

r 2

--~

Double-Hertz equations.

Zero load =

2Cro arctan

=

2

+m

a'~

w. . w: _ {~ . w: } ~ W

2 a ,3 - -/~ a .2 [ ~ m 2 _ i l 3~ , ,2 a* 6 -a -2/~ ~m 2

W = W= - { 6~RA ? . W=} '/2

W'~ =- Wa / { 2 zJ~Ay } = 3@e'a~ /

m-m+l.

~l'nen W * ==

-d,[_g__ [ ll-d ~ a"-_-~; - ~~ "/a'~ - r'~ ]

-1

=O=,,W~ =-3~RAy

and

6

,

a

•

--a

--3 ,2

• / 2

qm

+ 1) / [ ( m - 1

+ m + 1)

m-a] +1

1

2

[Wa=3/41

W~f--3:rr~Ay [W'f-3/4]with 2 3 ao = ~tR2Ar 8 /E" a " 3 = ~ t .

(m

~ ---l~a

8

2

2 _-- 3 ( m

or(r) -. where

cro_a-z [ '~c2 - r 2 (-l + k ) ~ l a 2 - r 2 ] k k = ~

/~

2 ,dca _ a ,2

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

79

T h e I n f l u e n c e of P r e s s u r e , B o u n d a r y F i l m S h e a r S t r e n g t h a n d E l a s t i c i t y on the Friction between a Hard Asperity and a Deforming Softer Surface J D Bressan*, G Genin$ and J A Williams$

*Department of Mechanical Engineering, Centro de Cientias Tecnologicas-FEJ/UDESC, 89.223-100 Joinville, SC, Brazil SDepartment of Engineering, Cambridge University, Trumpington Street, Cambridge, CB2 1PZ, UK

When a hard two-dimensional asperity is dragged across a softer surface so that there is significant plastic deformation, the geometry is often idealised as an oblique angled wedge and the boundary lubricated interface as possessing a strength which is equal to some fixed proportion of the flow stress of the adjacent weaker material. Real asperities are, however, more likely to have somewhat rounded summits with radii of curvature which are comparatively large compared to the scale of the deformation taking place. In addition, it is known that the mechanical properties of boundary layers are invariably sensitive to the locally generated pressures. In this contribution we present the slip-line field developed by Challen and Oxley (amonst others) in a form appropriate for locally cylindrical asperities and combine this with an interface between the asperity and the deforming material which exhibits a shear strength which is a known function of the local interfacial pressure. As the attack angle presented by the model asperity reduces to realistic values then so the elastic contribution to deformation becomes increasingly significant and the simplifications inherent in any slip line field solution less realistic. We also examine this factor and indicate how the elastoplastic regime may be mapped out in appropriate co-ordinates.

80

NOTATION L a

N F

asperity wedge or attack angle angle between wave free surface and direction of sliding angle made by slip-lines at "interface with tool surface material yield stress in shear constant or proportionality between normal and shear stress normal load on asperity line contact t a n g e n t i a l or friction load at an asperity line contact

1. I N T R O D U C T I O N

In t h e i r classic w o r k on t h e interaction of sliding metals Bowden and Tabor [1] demonstrated that when two metal surface are loaded together true or intimate contact occurs at a relatively small number of discrete asperity contacts distributed over the geometric or nominal area of contact. The frictional force, i.e. the observed t a n g e n t i a l r e s i s t a n c e to motion, can be associated with two mechanisms operating at these points of contact: these have become k n o w n as e i t h e r t h e ' a d h e s i v e ' and ' a b r a s i v e ' or ' p l o u g h i n g ' t e r m s - or alternatively the 'molecular' and ' d e f o r m a t i o n ' c o n t r i b u t i o n s to friction. Although these relatively simple ideas are q u a l i t a t i v e l y in accord with observation they do not take into account the topography of the surfaces involved and are not fully c o n s i s t e n t w i t h the laws of c o n t i n u u m mechanics. In an a t t e m p t to alleviate these problems, Green [2] and s u b s e q u e n t l y Challen and Oxley [3], Komvopoulos et al [4] and P e t r y k [5] ( a m o n g s t others) have proposed models of surface i n t e r a c t i o n b a s e d on t w o - d i m e n s i o n a l a n a l y s e s in which a rigid asperity with a wedge-shaped profile is drawn across a softer deforming surface. If the softer m a t e r i a l can be idealised as being rigid-perfectly plastic

f R tt Y E

length of line contact perpendicular to sliding direction n o r m a l p r e s s u r e at the a s p e r i t y contact interfacial shear stress friction factor at interface (=v/k) radius of curvature overall coefficient of t r a c t i o n or sliding friction uniaxial yield stress elastic modulus

then its deformation can be examined by the application of the techniques of slip line field analysis. When the included angle of the asperity is large, and so the surface slope or asperity attack angle a in Fig. 1 is no m o r e t h a n a few d e g r e e s (i.e. c h a r a c t e r i s t i c of t h e slopes of m o s t e n g i n e e r i n g surfaces) t h e s t e a d y - s t a t e solution involves no i m m e d i a t e loss of m a t e r i a l from the surface because, by necessity, during the early stages of the relative motion between the two bodies, the apex of the wedge returns to the level of the free surface. In the steady-state the asperity is preceded by a plastic wave of material as illustrated in Fig. l(a) which illustrates the field for an asperity which has a linear profile along the interface DE; the work of friction is partly absorbed by the plastic strain associated with the flow of m a t e r i a l through this wave and partly with shear at the interface between the wave and the wedge asperity. The shape of the slip line field and its associated hodograph, Fig. l(b), is defined by two angles: a which is imposed by the asperity, and 7? which is t h a t made by the free surface of the wave with the direction of the sliding velocity vector. Angle EAB is equal to x/4.

O

81 'k

2a

to the geometry of the field and k the yield stress in shear of the deforming material, viz p

\

~--= I + ~ -2T/+

" .

II1tll

\

D~ deforming maw.hal

2~ - 2a + sin20 = B (say). (3)

E

~ C

B

I1t ~

, , ,

~e

Fig. l(a) Slip line field (region ABCDE) interaction of a soft surface with a moving rigid asperity. Angle a is the effective attack angle. Contact with a cylindrical asperity of radius R can be modelled by replacing the arc of contact along DE by its chord. (b) The corresponding hodograph for this mechanism.

It is easy to show, from the geometry of the slip line field, t h a t sina sinn = ~f-2sinO

(1)

where ~ is the angle at which one family of slip lines m e e t t h e i n t e r f a c e b e t w e e n a s p e r i t y and deforming m a t e r i a l and is related to the friction factor f , i.e. the ratio of interface shear stress to k the flow stress of the adjacent material, by the relation = 0.5arccosf.

(2)

The value of the normal pressure p exhibited at the interface is simply related

Simple resolution of forces y i e l d s expressions for F and N, respectively the t a n g e n t i a l and normal force components on the asperity, as F/L -psina + fkcosa ED N/L = pcosa- fksina ED

(4a) and (4b)

where ED is the contact length at the interface. Thus the overall coefficient of friction /2 for the asperity, i.e. the ratio of the tangential force F to the normal force N, is given by the relation f + Btana # = B - ftana '

(5)

so t h a t when f tends to zero the overall friction coefficient is asymptotic to t a n a . Because the shape of the field is dictated by the angle a and the factor f, the numerical value of /2 is independent of both N, the applied normal force, and k, the value of the m a t e r i a l flow stress. If the normal force applied to the indenter is increased then, although the plastic zone will p e n e t r a t e more deeply into the material of the surface, i n c r e a s i n g the dimension s in Fig. l(a), there is no change in the predicted overall coefficient of friction.

2. EXTENSIONS OF THE S I J P LINE Ft ~:n .D M O D E L

2.1 Asperities w i t h cylindrical p r o f i l e s While the general features of the model described above are compatible with observation, the r e p r e s e n t a t i o n of t h e a s p e r i t y by a simple t w o - d i m e n s i o n a l

82

wedge is clearly a limitation. Asperities on real surfaces are t h r e e - d i m e n s i o n a l and are likely to have slopes which not only vary from one asperity to another but also c h a n g e s a r o u n d the contours of each asperity. It might be argued t h a t most practical production processes, such as g r i n d i n g or f i n i s h m a c h i n i n g , are strongly directional and so will produce roughness asperities with high aspect ratios which are observable in the surface lay. However, these asperities are unlikely to either have initially, or to maintain, the profile of simple wedges. A more realistic approach is to consider their peaks to have rounded or cylindrical profiles in much the s a m e w a y as is conventional in the description of surface topography when m e a s u r e d by s t y l u s or n o n - c o n t a c t instruments. Indeed, in a later paper C h a l l e n and Oxley [6] extended t h e i r original slip line field analysis to cover this situation by approximating the circular profile of the asperity, say of radius R, to a single chord* with one of its ends passing t h r o u g h the lowest point of the arc, as i l l u s t r a t e d by the circular arc between points D and E in Fig. l(a). Now the angle a made by the chord with the direction of sliding is no longer an i n d e p e n d e n t variable but changes if the load on the asperity is varied so that it penetrates more deeply into the surface; such a change will also affect the contact length ED, since from geometry ED = 2Rsin a .

(6)

* Challen and Oxley also investigated a double chord model w h i c h a l t h o u g h d e m o n s t r a t i n g some of t h e f e a t u r e s observed q u a l i t a t i v e l y provided some a n a l y t i c a l d i f f i c u l t i e s : for e x a m p l e , increasing the n o r m a l load N led to a discontinuity in behaviour and a region of the performance p a r a m e t e r space in which n e i t h e r model g e n e r a t e d a theoretically acceptable solution.

Using this relation, t o g e t h e r w i t h equations (3) to (5), we can plot p, the overall coefficient of friction of t h e asperity, as a function of a s u i t a b l y normalised load, say N / L k R , indicating the values of the effective wedge or attack angle a on the plots. Such a set of curves for various values of the friction factor f is shown in Fig. 2 and corresponds to the lower area of Fig. 5 in reference [6].

2.2 Boundary lubricated interfaces One attractive feature of the Challen and Oxley analysis, w h e t h e r applied to angular wedges, or used to approximate the geometry of cylindrical arcs, is the fact t h a t the overall behaviour of the junction can be explicitly evaluated in terms of the input parameters, viz a and f in the wedge case, or R, N / L and f in the case of the singlechord cylindrical approximation. In both cases we assume we know the friction factor f, that is the strength of the interface as a fraction of the deforming material. Unfortunately, this is unlikely to be always the case since the strength of the interface will depend on the nature, both physical and chemical, of the lubricant with which it is supplied. The expectation is t h a t the film will be exceedingly thin so t h a t we are concerned w i t h b o u n d a r y r a t h e r t h a n hydrodynamic conditions and there is a good deal of evidence in the literature t h a t the mechanical properties of b o u n d a r y films, even relatively simple ones such as m u l t i - l a y e r s of f a i r l y s h o r t chain monomers, are influenced by the local conditions especially pressure and temperature. If the strength of the film were to be simply a linear function of the local pressure, i.e. could be described by the characteristic equation "¢ = c . p

then, the friction factor f is given by v p f = k - c . - ~ = c.B. (7)

83

that c is likely to be of the order of 0.1, means that

As has been pointed out by Black et al [7] simply rearranging equation (5), combining with equation (7) and remembering that in practice a < 10 ° and 0.40

...~: f = 0.9 I

i

I~

........" .~

...-""' t

0.30

-

/'1

0.20

.~',,

•

l

~

..","

i/.

"

I

/

I

t ...... "" .... "~"

1

l

$.,-"

.

\

.

.

.

\

..... . ~ ,

1"

. ~

A""

,

/;

" ~ ',

\ .~"/

~ ~ = 0 . 6 ....".'" \ \

\

........

,I

\

.....-"

./

,.

..-""

.

.

.

"'*'"

~

\

~

\

.'~"

.

\

.

.

\

A"" .-- ..... " \

,

............ \

,#"

/'"

...'""" ..'"

f = 0.2

/,""

\ x \

../'" x

\

~.."t"'"

/"

f = 0.4.~ ......

.,,\

(8)

\t

" \

"

,,,." "~"~

\

"'"""

..-.'" 0.I0 Jj,,..../l

".

,..."~"

.......

....

x

~41 ,f

f = 0.8,. / / , .... \

,"

I l

X/-

y" • ~

I

# = t a n a + c.

.

10° ~

...

._

..°~ °°

-'""

//

."/'@

.~

,, /=u

•

...."" 14

o

.9,

,,

.....

. . ".......4"

I ...-"" .... 4""" .4,'"" 2o

0.00

0.0

0.5

1.0 normalised

asperity

1.5 loading

2.0

N/LkR

Fig. 2 Plot of overall coefficient of friction # vs normalised load N / L k R with friction factor f as p a r a m e t e r for the single chord rubbing model used as an approximate solution for a cylindrical asperity of radius R.

The two terms on the RHS of eqn. (8) once again corresponding respectively to the deformation and adhesion c o n t r i b u t i o n s to friction. In such an example, therefore, the g r a p h of overall friction coefficient versus wedge or attack angle a for a boundary lubricated asperity would be s i m p l y t r a n s l a t e d along the friction axis by a constant amount c, when compared to the entirely friction free, i.e. f = 0, situation. However, in the more general case, when the dependence of the shear strength of the b o u n d a r y lubricate interface is a more complex function t h a n the l i n e a r equation (7), the simplification leading to

equation (8) is not possible since interfacial shear strength will depend on the value of the direct stress at the interface (i.e. the value of factor B) which is itself p a r t l y d e t e r m i n e d by the effective local friction factor f . C o n s e q u e n t l y an i t e r a t i v e numerical solution m u s t be employed to reconcile both the local film constitutive relationship and the d e m a n d s of overall equilibrium. Practical frictional m e a s u r e m e n t s on real surfaces covered with thin organic or polymeric films are difficult to translate into m e a s u r e m e n t s of layer shear s t r e n g t h because, although it is relatively easy to m e a s u r e traction forces, there is always

84

u n c e r t a i n t y about the real area of contact over which these act. The most usual e x p e r i m e n t a l a p p r o a c h is to use very smooth and geometrically simple surfaces, e i t h e r a sphere a g a i n s t a flat (or the g e o m e t r i c a l l y similar case of a pair of crossed cylinders) and calculate the area of contact by continuum mechanics. Some of the earliest work of this sort into lubricant rheology was carried out by Bridgman [8] using a flat on flat geometry and later e x t e n d e d by Towle [9] u s i n g polyvinylidene chloride. These studies indicated an essentially steady increase in s h e a r s t r e n g t h with p r e s s u r e and this observation has been corroborated by a number of subsequent studies. For example Amuzu, Briscoe and Tabor [10] found t h a t for a series of methacrylates with varying m o l e c u l a r weights and glass t r a n s i t i o n t e m p e r a t u r e s , i n v e s t i g a t e d up to m e a n pressures of about 300 MPa, there was a linear increase in film s t r e n g t h r with applied pressure p, so that r = r0 +

cp.

maximum values in e x c e s s gigapascal. Fitting the relation

Table I" Va!ue~ of cou~tar~ts in the equation v = Ap n Material anthracene high density polythene mol. mass = 30,000 high-density polythene mol. mass = 10,000 ptfe sebacic acid

a

(10)

r = Ap n

to these data provides the values in Table I. The exponent n is consistently less t h a n unity; the material exhibiting the lowest d e p e n d e n c y on p r e s s u r e was the low friction solid lubricant ptfe. i

I

I

io8

Ill ~.

/

107

.... J

'

A

I 1o 8

I

I 10 9

mm

contact pressure]Pa

(9)

However, w h e n the e x p e r i m e n t a l pressure range is expanded it seems t h a t this region is often part of a more complex dependence. Figure 3, t a k e n from Briscoe, Scrutton and Willis [11] (who used small d i a m e t e r glass spheres loaded against a glass flat carrying films of a range of long c h a i n p o l y m e r s ) shows a power law relation between contact p r e s s u r e p and shear strength v over a range of pressures of more t h a n two orders of magnitude with

of

Fig. 3 Influence of contact pressure on the s h e a r strength of a number of organic materials at 20°C: • anthracene, thick film; o high density polythene, tool mass = 30,000; • high density polythene, mol m a s s = 10,000; h ptfe as a 'rubbed-on' oriented film; • sebacic acid 'rubbed-on' film. The broken line is for calcium stearate layers, taken from Fig. 4.

for ~ number of thin films (from ref. rill) A

n

14.2 14.2 7.58 13.2 7.89

0.78 0.78 0.78 0.67 0.80

85

function of the normalised asperity loading for a cylindrical asperity indenting two different deformable materials with flow stresses of 200 MPa and 800 MPa. In the case of ptfe w h e n (from Table I r = 13.2p 0.67) the effect is small and the

On the other hand, similar work by Timsit and Pelow [12] using multiple stearic acid films on glass surfaces showed a stronger than linear dependence of r on pressure p, best fitted by the parabolic equation r = -0.16 + 0.059p +

1.13 x 10-5 p2

,

The data show that shear strength and its pressure dependence are roughly similar for all the c o m p o u n d s a n d l a r g e l y independent of the experimental method used. The solid curve in the figure is the best fit to a cubic, viz = 1.30 + 0.0104p + 1.46x 10-5 p2

- 1.037× 10-9 p3.

(12)

When the s t r e n g t h of the interface is allowed to be some function of pressure, such as those of equations (10), (11) or (12) and this functional relation is combined with the slip line field model described in section 1 the values of overall coefficient of friction versus wedge angle or asperity load will no longer strictly follow a line of constant friction factor. In addition, values of # will now no longer be i n d e p e n d e n t of the mechanical s t r e n g t h of the m a t e r i a l just beneath the deforming surface since this will affect the absolute values of pressure at the i n t e r f a c e and t h u s , t h r o u g h the a p p r o p r i a t e constitutive law, the s h e a r resistance of the boundary layer. This effect is illustrated in Fig. 5 which shows computed overall friction coefficient # as a

,

i

I

/ 9

(i I)

where both r and p are measured in MPa. Briscoe and Smith [13] bring together data from a n u m b e r of sources u s i n g the t e c h n i q u e s described above for m e t a l s t e a r a t e s and s t e a r i c acid at room temperature and their compilation is shown in Fig. 4.

I

¢S

10a • e I

4 , Q

4 10 6 i 10~

I*

i0 ~

!

10 8

I

i0 ~

prmmlro/Pa

Fig. 4 Pressure dependence of shear strength of stearic acid and certain stearates at 20°C. o calcium strearate as one, three or five monolayers. • comparatively thick films of copper stearate, a calcium stearate-stearic acid composite films. V stearic acid by evaporation, A bulk stearic acid on platinum, V stearic acid as thin film between metal platens, a ferric stearate and sodium stearate as bulk materials. • paraffin wax between glass surfaces. Data from reference [6]. curves for substrates of both hardnesses lie close together (and not far from the line for f = 0.05). However, in the case of the stearate films described by equation (11) there is both a noticeable v a r i a t i o n in g r a d i e n t from the curves for c o n s t a n t values of factor f and a significant spread of values with variation in k. The dotted lines r e p r e s e n t c o n t o u r s of c o n s t a n t effective wedge angles of the values shown.

i0~

86 0.40' ..,....,,,I ' /''°I

-"

So

.i/°

0.30 , t~

,

.f "I 8 o

..- .... 1 0 o . . . . .-

..........

~

.~.:

/:,~/~

0.20 "!

sle~d'~¢ |i ms

0.I0-

..i"

j ~ "

O~..~- ~

- •

.--"'""

..... "" I

......" ~ : " " /

~

J~.':'-':"~

.~-~

p~e n~ps

0.011

0.0

]0

0]5

15

I normalised

asperity loading

I.

2.0

N/LkR

Fig. 5 Variation of the overall coefficient of friction p with the normalised load N / L k R for the rubbing or wave field when the boundary film between a hard asperity and deforming material has shear strength dependent on local pressure. Open symbols for a material of flow stress 200 MPa and closed for one of k = 800 MPa.

2.3 Influence of elastic distortions The smallest value of a shown on Fig. 5 is 1° although there is no difficulty in carrying out the computation to smaller values. However, i n h e r e n t in slip line field methods is a neglect of the elastic compliance of both the i n d e n t e r and the indented surface. When a is large this will be negligibly small but as the effective w e d g e a n g l e gets s m a l l e r (or for a cylindrical a s p e r i t y of a given radius as the n o r m a l load reduces) the contribution from elastic deformation becomes of more significance. Torrance at al. [16-18] have e s t i m a t e d t h a t for typical e n g i n e e r i n g materials for which the ratio of yield stress Y to elastic modulus E lies in the range of O.O025 (GLS). Its principle is based on the evaluation of the energy dissipated in glass cylinder passing through a funnel, by direct measurement of the velocity loss, due to its dynamic contact with the funnel.

92 This study is composed of four parts. The first part presents the GLS apparatus, with some typical experimental results. The second part exposes the experimental method based on the tribological evaluation of several surfaces morphologies, using the GLS apparatus. Results are presented in the third part and analysed with a principle compound analysis method in order to establish a relationship between classical morphology parameters and frictional abilities of the surface. It clearly appears that those parameters are not completely satisfactory to build the relationship. New advanced morphology description methods are proposed and used in the fourth part in order to achieve the connection between friction and surface morphology. 2. E X P E R I M E N T A L A P P A R A T U S

An experimental apparatus called Gob Loading Sensor (G.L.S) has been specifically designed to be the most representative of the tribological conditions encountered in the glass forming process. Those conditions appearing inconceivable to be reproduced at a laboratory scale, it has been decided to take

directly advantage of the industrial forming machine for experiments. The experimental conditions required are the followings (Fig.l) : glass: nature: soda lime weight: 300 g to 600 g. velocity : 6 m/s metal: nature : nickel alloy temperature : 500°C The GLS apparatus, presented on Fig.2, is composed of two flat metallic substrates facing and tilted, in order to create a flat funnel. A glass cylinder usually called "gob" or "parison" crosses the flat substrates so that kinetic energy dissipation occurs with friction and viscous s t r a i n . The temperature, T(°C), of the substrates can be monitored between 20°C and 600°C. The clearance distance 2al between the two substrates and their slope ~ can be handily adjusted. Below the substrates, a velocity sensor (infra-red gates) records the velocity Vout of the gob consecutive to the contact. V0 corresponds to the gob velocity taken at the instant of the first contact with the substrates. Typical results show the relative output velocity as a function of the number of the consecutive gobs. Vi.

~ i v e r y el ao

gob .......................~'X

V

bml velocity sensor

,

~///~ ,~ ,~////x

Fig 1 :forming process scheme

50mm

Fig 2 : schematic view of the GLS apparatus

93

The relative output velocity is the velocity Vou t of the gob after the glass/substrate contact divided by the velocity V0. Two types of curves obtained with two different materials A and B, without any lubrication are shown on Fig.3. The relative steadystate velocity of A is 70% after a running-in period observed during the first five gobs. In contrast, B exhibits a progressive decrease in the relative velocity. 100

~ 90

material B i

0.8 0.6 0.4 0.2 0

c 80

material A

._

I

0

10

~ 70 0 ©

-~ 60 >

I

I

20 30 Consecutive gobs

I

40

50 ~-

Fig 4 • calculated friction coefficient vs consecutive gobs

~5 50 .4--, --3

3. EXPERIMENTAL PROCEDURE

o 40

.>- 30

_

~ 20 rr

3.1.Principle

10 0 0

i

I

i

I

10

20

30

40

Consecutive gobs

50 I~

Fig 3 "experimental graph for two different materials

Moreover, the evolution of the relative velocity related to material B appears to show greater variations than in the case of material A, probably due to higher friction between the surface and the consecutive gobs. A previous work [6] allows the consideration of the GLS apparatus as a real effective instrument for measuring friction between hot viscous glass and metal. The kinetic energy lost during the contact is dissipated by viscous strain and friction. Mechanical modelling allows, on the basis of calculation of the strain dissipation energy induced by the deformation of the glass, and on the basis of a global motion analysis taking into account the dissipation due to friction, to transform a graph showing the relative output velocity (as depicted on Fig.3) into a graph showing a calculated friction coefficient versus the number of consecutive gobs (Fig.4). It must be seen that best reliability of these curves are obtained for friction coefficients ranging between [0.1-0.8]. We shall now use the GLS apparatus for studying the effect of surface morphology of the solid substrate upon friction.

We choose to use a single type of solid substrate for all the experiments, and to produce several surface roughnesses by different machining techniques. The substrate is a nickel base alloy chosen for its wear and corrosion resistance. The method consists in establishing, through a design of experiment test (DOE), a relationship between significant surface morphology parameters and the tribological abilities of the surfaces. A DOE test is composed of several entry parameters ($1, $2 .... Si) all independent and controllable by the user. As a matter of fact, it appears unrealistic to get surfaces showing predefined morphology parameters. Those parameters are the results of a machining operation, which can be executed with different machining parameters. On the basis of classical machining techniques, the experimental method now considered is built on a succession of experimental designs corresponding respectively to different machining techniques. Our objective is to establish a clear relationship between a list of independent morphological parameters and friction, with the help of a Principle Compound Analysis.

3.2.Machining techniques We select different traditional techniques potentially available for processing the mould surfaces.

machining industrially

94

Each sample is characterised by a set of morphological parameters. The following paragraphs present the different machining techniques employed in our study.

3.2.1.hard particle blasting This technique consists in projecting small hard particle onto the surface. The nature of the particles, their average diameters and the air pressure are entry parameters of the following experimental design. Two different material natures for particles are chosen : Alumaglass is the commercial name for glassy material : 53.3% SiO2, 21% A1203, 13% CaO, 9.5% Na20, 2% Fe203 (weight percentages) and Corindon is the commercial name for alumina: 99.7% A1203, 0.12% Na20, others < 0.1% (weight percentages).

3.2.2.superfinishing This technique consists in eroding the surface with spherical ceramic particles (~ = 0.6 mm ). The sample is maintained motionless inside a vibrating chemical container full of those abrasive particles. Nature and size of these particles are process parameters, but of small incidence upon the obtained results. So we chose a unique parameter for this technique : the elapsed time of the bath.

3.2.3.abrasive paper polishing This technique consists in abrading linearly the surface with a grind paper of different size abrasive particles. We chose two parameters for this technique : firstly the grain size of the abrasive particle expressed like P400 (grain size : 3 5 ~tm), P120 (grain size : 106 ~tm), P60 (grain size : 250 ~tm) and secondly the polishing angle versus the trajectory of the glass cylinder (0 °, 45 ° and 90°).

3.2.4.grinding This traditional technique consists in machining the surface with a round grindstone, turning at a co (rad/s) angular velocity and moving at a linear velocity V (m/s). We chose two significant parameters : the linear velocity V (m/s) and the angle versus the trajectory of the glass cylinder (0 °, 45 ° and 90°).

3.2.5.electrical discharge machining This technique consists in reproducing on the surface the shape of a matrix by generating electrical discharge between the surface and the matrix. The only parameter chosen for this technique is the clearance distance between these two surfaces.

3.2.6.electrochemical machining This technique consists in a chemical erosion of the surface. The sample is placed in a chemical bath, and low current is established between the sample and the container. Three parameters are chosen : the bath intensity (8, 12 and 16A), the bath tension (16, 18 and 20V) and the elapsed time (1, 3.5 and 6 min.). In reality tension and intensity are not totally independent.

3.2.7.planing This technique consists in machining scores one by one on the surface with a sharp tool moving linearly. We chose here two parameters : firstly the lateral displacement of the tool inducing different score breadths, and secondly the angle versus the trajectory of the glass cylinder (0 °, 45 ° and 90°). 4. RESULTS The following frictional results are given for the constant following experimental parameters : glass weight of 395g + l g, clearance distance 2al = 24 mm, surface temperature of metallic substrates : 475°C + 25°C, industrial green bottle glass. Friction curves are presented only for the significant cases and not for low performance surfaces. We use a quotation of the surfaces in order to get tangible parameters for the data treatments. This quotation must characterise faithfully the frictional behaviour of the surface. Two parameters are then introduced : a "note" from 1 to 10 corresponding to the number of consecutive gobs gone through the funnel, and an "area" corresponding to the area under the relative output velocity curve. The surfaces showing the best frictional abilities exhibit the highest note and area quotes, as depicted in the following experimental friction graphs (Fig.5).

95

electrical discharge machining

hard particle blasting 1.6

G5 n o t e = 10 } a r e a = 4658 ,~ G9 n o t e =

planing

1 •6 m

9 ; area = 1609

1.4

1.4

............................................................ i .............................................................

1.2

....................................................................................... ~........! ......................

sample

1.6

1 n o t e = 10 ; a r e a = 101

~ " sam.pie 2note

= 7;area

= 675

1.4

t

. il ...............s a m p l e

1 n o t e = 2 - a r e a = 10~Z

: --- s a m p l e

3 note

7

area

;ii;;ii;ii ~1.2

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

._

1

~_

............................................................................................................................. :.---;-.; 1.~-~ .....................................

!!?::iiiiiil ..........

0 o

"d

~ 1.2 .~i.~i~i •~,i'i}!'~i!,'

. . . .

¢9

0.8

~0.6

........................................... ~........ ~ * ; b ~ & ~

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

.............................. :,..........................i.............................................................

g ~~°8

~0.6

~0.6

00.4

00.4

0.2

~dO.8

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

0

:

100

ii

-~0.4

0.2

0.2

o I 50 consecutive gobs

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

19 8

0

,

0

50 consecutive gobs

100

0

50 consecutive gobs

Fig. 5 • example of friction graphs for different surfaces.

All the surfaces processed with superfinishing, grinding and polishing give low performances with note parameter under 2 and area parameter under 100 in all cases. We clearly identify a strong influence of the substrate roughness upon friction. The morphological parameters seem to be good discriminators of the surfaces. A first analysis of the results indicates a significant role of the isotropic nature of the morphology and also indicates that best results are obtained with hard particle blasting surfaces. 5. L I M I T S OF CLASSICAL ROUGHNESS PARAMETERS As mentioned in the introduction part, the objective of this study is to establish a relationship between the morphological parameters and the frictional abilities of the surfaces. The considered method consists in treating the roughness data with a Principle Compound Analysis (P.C.A.). P.C.A. is a descriptive statistical method giving to a data list a representative graphic aspect. This data list is composed of lines with entities and columns with variables. In our cases, surfaces express the entities and the morphological parameters express the variables. P.C.A. can be used for several applications, particularly for getting information about entities' distribution. The first step of a P.C.A. consists in converting the p variables, that can be correlated, into independent

variables called principle compounds. It is then possible to observe graphically the entities presented on planes, whose axes are constituted by the previous principle compounds. Then several planes can be constructed with combinations of the different principle compounds as axes. In reality, only the first two or three planes are sufficient for giving an acceptable representation of the initial array of entities and variables. Indeed, each plane is characterised by an inertia indicator, expressing the percentage of information contained in the graphic representation. Our objective for using a P.C.A. in the present study is to discriminate between the different surfaces using their morphological parameters, and compare the graphic representations on the principle planes with the tribological results. Finally a clear correlation should appear between friction abilities of a surface and its morphological parameters. The previous samples have been surface scanned with a 3D tactile profilometer. The apparatus used is a stylus probe exhibiting the following performances: vertical resolution (nm) lateral resolution

rain. : 5 ; max. : 244 2

(~m) measurable area (ram) tip radius (~m)

max. : 20x20 rain. : 0.5x0.5 5

1 O0

96

F1 = 0.233 (SPt) + 0.493 (Spq) + 0.185 (SPpm) + 0.178 (SPvm) - 0.276 (PSmx) + 0.29 (R) + 0,132 (AR) 0.163 (W)- 0.36 (AW) + 0.216 (AW/W) + 0.164 (AR/R) + 0.447 (Rmoy)

The experimental measuring parameters are the following ones: tip velocity area measured

0.3 mm/s continuous 2.5 mm x 2.5 mm

F2 =-0.382 (SPp) -0.165 (SPpm) + 0.139 (SPvm) + 0.17 (PSmy) -0.171 (taux 5%) + 0.183 (R) + 0.471 (AW) +0.207 (AW/W) + 0.223 (AR/R) - 0.354 (Rmoy) + 0.151 (Rmoy/cy)

.........s t e p (samp!e) .....~..............10~gm ~_~...................................................~....... For each surface, a set of 25 roughness parameters is obtained [7]. A correlation analysis indicates that only 7 parameters from the previous set are uncorrelated or quasi-independant, and then could be sufficient to exactly describe the entities. In fact, each parameter from the complete set gives a particular piece of information, thus we choose to run the P.C.A with 25 parameters. In the other hand we choose to simplify the study by eliminating the anisotropic surface morphologies giving low friction performances. As an example, we expose in Table 1 the roughness data measurements, concerning two hard particle blasted surfaces, and two electrochemical machined surfaces. The planes F1 to F4 give 95.82% of information, mostly contained in the principle plane F1-F2 (87.51%) whose axes are composed as follows : Table 1: roughness parameters for four sample SPt SPa SPq (#m) (jam) (#m) 1.51 blasting 13.07 1.19 G5 2.41 blasting 17.51 1.94 G6 0.70 0.85 electro 4.94 chem.3 0.96 1.21 electro 8.61 chem.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~

z

;

~

;

;

;

;

.......

~-------:

: ....

-

=-----

^:.

:

v--:-----:

..........

different surfaces SPp SPv SPtm SPpm SPvm PSmx (#m) (#m) (#m) (0m) (#m) (#m), 4.80 8.27 6.19 3.04 3.15 86.29 , ..........

-

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

= = -

-:-: ................

~.

.

.

.

.

.

.

.

.

.

a.~---:---

: ................

~:---

......

= - - - - - - - . - - : v - - - - : ~

Spsk Spek

Sdr rate 5% (%) (#m) -0.21 3.29 101.2 2.42

109

99.65

-0.17 2.88 102.1

3.89

9.88

9.44

4.64

1.78

3.17

3.11

1 . 4 1 1.70

92.40

91.58

-0.16 2.35 100.3

0.46

2.83

5.78

5.08

2.24

62.25

56.73

-0.19 3.01 101.4

0.81

,~-"-"~- . . . . .

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

: .............

----

: ..............

4.79

PSmy (jam) 81.41

7.63

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

sample rate 80% (,m) blasting 6.04 G5 blasting 9.73 G6 electro 2.55 chem.3 electro 3.83 chem.8

On the principle plane F1-F2 (Fig.6) we observe rather well separated locations for the superfinished and the electrochemically machined surfaces. The electrical discharge machined surfaces are located on one side of the plane and are not constituting a compact group. The hard particle blasted surfaces are divided into 3 groups located upside the F1 axis, and are respectively constituted by the rough surfaces (6 gm < Spa < 11 gm), the smooth surfaces (0.5 gm < SPa < 2 gm) and the medium surfaces (3 gm < SPa < 5 gm). The smooth surfaces group appears to be located in the same area than the electrochemical machined surfaces. Observations of the F1-F3 and F2-F3 planes allow the following conclusion : The A.C.P analysis appears to be a good method for discriminating the different classes of surfaces.

2.85

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

. .........

x

......

::

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

,.-.--.--~-

.........

: ...........

-

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

:::;;

........

=;::::

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

free vol. 80% R AR W AW AW/W AR/R Rmoy (#m) ~ Rmoy/~ ( , m 3).............. (#m) (,m).(#m)....... (~m) ............................. 9.68E+05 1.74 42.9 2.01 151 75.27 24.60 79.44 154.7 0.513 1.45E+06

2.67

47.4

3.61

183

50.62

17.72

65.46

131.3

0.498

4.73E+05

0.90 44.99 1.02 168.5 165.36 50.04

229.00

453.0

0.505

7.77E+05

1.79 39.85 1.49 140.0

97.06

193.1

0.502

93.96

22.29

97

Unfortunately those two groups of surfaces exhibit opposite frictional abilities. Indeed the two blasted surfaces are the best performing of all, while the electrochemically machined surfaces exhibit very low tribological performances.

o

o ~

•

•

%0

•

•

6. REMARKS -2

-4

-6

i

,

0

L

,

1

5 Axis 1

10

Fig.6 " I hard particle blasting,, A superfinishing, 0 electrochemical machining, 0 electrical discharge machining

From a tribological point of view, the best performing surfaces need to have average roughness amplitude parameters comprised between 1 gm and 2 gm. In a second step it appears that electrochemically machined surfaces (samples 3 and 8) are located very close to blasted surfaces (samples G5 and G6) as shown on the radar graph Fig. 7. SPt 200 T

SPt 200 T Rmoy/s4 .

150

\~°°t

/

2 " Psmx

Rmoy/sx,.

',

sl

',

', Spsk

i l W ~ ~ S p e k

15o t

2"Psmx

\ ~ °\ ~° to ~ ,

~~

'

f

I

AW/W

I Spsk

Spek Sdr

SPt

SPt

200 ]-

Rmoy/sx,.

150t

200

/2"Psmx

100 5O

~

blasted G6

blasted G5 Rmoy/s4`

"~

150

t

i

~/Spek Sdr

electrochem 3

AW

Psmx

100

I

I

I Spsk

~ S p e k Sdr

electrochem 8

Fig7 • radar graph representation of the uncorrelated morphology parameters, for four different surfaces.

The surface morphology parameters neighbouring those representative of the G5 or G6 blasted surfaces, represent a set of conditions absolutely required but not sufficient for predicating a good tribological comportment. Then it appears that one or several significant parameters have not been taken into account in the previous study. We now intent to add new parameters to previous with the help of local description methods, applied to the G5 blasted surface and to the electrochem.8 surface. 7. CONTRIBUTION OF L O C A L ANALYSIS An extended analysis of the friction mechanisms of the glass melt against the substrate clearly demonstrates that the contact does not occur on the whole surface, but only on particular zones called "contact areas". This observation shows the benefit of considering the properties of external shape of the surface, that can be considered as functional surface. One interesting property of the external profile is the distribution of its slopes.

7.1.Slopes distribution of the external profile The external profile of a surface is an imaginary profile obtained by linking together the different vertexes of the original profile. Then the angles between the different segments are depicted on a distribution graph as shown on Fig.8 and Fig.9. This graphic description allows us clearly to distinguish our two surfaces : G5 and electrochem8. The standard deviation of the distributions can also be considered as a good indicator of the external profile morphology. We must notice that this description method depends on the scanning step and on the measurement resolution. Therefore the use of an independent scale analysis, like the fractal analysis, appears more suitable for representing the slopes of the surface.

98

..!:~..

- 1,74

.

".."

.3:~i!~:;:~''.:.~.

H-3.37

i-5.00 l1 -l- 8 ,..... 27

To;osu

~:,

:.~i

.~.~:!~::'~:::!"'.

::.4!! "

15.elfin2x 7.5~m

ii!i!iiiiiiiiiii!::i::!ii::i::i::ii!iii!!iiii!!i::i::!::I

::~:~:~:~:~:

~::~i~ ~i~ ~::~ ~~::~ ~~i~ ~~:::~

ilii iii;

::iii]iiii iii!iii::::

~i i: i

~i~

~ [~i! i::~ ~i

|I

~!~ ~i i.::"~!i

I,,.

iiiiii~iiiiiiii~iiiiiiiiiii iI ~ ~Iiiiiii i ii~,."II liiiiiiiii ii[

~

e

.:~:

:

'

1 1,

ii

i

.... m

1

i! i~ ::~i~i~i ~i i~l

~!i! i!i~i! iii!i~!ii~i~!i~i~ii~ii!i~i~i5i~ii!~i~i~iii;iii~i!~i!~ii~ii~i~~i~ii!~i!i~ii!i~i!ii~i~! !i~~!i!~!i!i~i~!~ii!ii!ii~! !i~!i~i!i~!i!i~! !i!~!i!i~!i!i!~i~i~i~i~!~! i!i!ii!i!i!i~!~i! ~! ! ~!~! ! !I~!~i~! !~~j~ii~i~i~iiiiii~ii~!~i~i~i~ii~ii~i$ji~i!i

0.5 0,

Fig.8 : slopes distribution for sample G5

e

Fig.lO : sample G5 : H = 0.52 2.83

i:;=

N

..... m

'

. . . . .

~-5.~

~i~'

.

.

.

.

.

.

.,,,

1.5

•

Fig.9 : slopes distribution for sample electrochem.8

i~.5

o

Fig.11 : sample electrochem8

:

H = 0.24

7.2.Fractal analysis We choose the Lipschitz-H61der coefficient (H) as the fractal indicator of the surface [8]. H is always ranging between 0 and 1, and indicates a smoother aspect as H rises from 0 to 1. We must notice that this coefficient is well representative of the slopes of the profile independently of the measurement parameters. The H coefficient is extracted for the two surfaces : G5 (Fig.l 0) and electrochem8 (Fig. 11) and appears to be a good discriminator of the two surfaces. We notice that the G5 sample exhibits a smoother surface than the electrochem8 sample. Here again, the slopes of the profile appear to give interesting information about the frictional abilities of the solid surface sliding against hot viscous glass.

8. CONCLUSION The study of the effect of the surface morphology upon the friction of a metal substrate sliding against hot viscous glass allows to point out some major surface parameters governing the sliding phenomenon. The parameters based on the statistical moments of the heights distribution of the profile give necessary but not sufficient conditions for low friction coefficient. For example, the mean value SPa must be contained between 0.95 ~tm and 1.95 ~tm, and the Kurtosis parameter SPek must be contained between 2.29 and 3.92. Then the complete knowledge of the interaction phenomena needs a local description of the surfaces with different methods such as a fractal description of the slopes distribution of the external profile.

99

It appears that local disruptions must be as smooth as possible, so that, from a practical point of view, machining techniques based on plastic deformations are preferred to those based on metal removing. 9. REFERENCES

[1] DoMing W.C., Fairbanks H.V., Koehler W.A. "Study of the effect of lubricants upon the glass-metal sticking phenomena". J. of the Am. Ceram. Soc. Vol. 32, (1950), N°9, p 269-273. [2] Trier W., Hassoun F. "Mechanik des gleitens hei]3en, z/ihfltissigen glases auf metalloberflS.chen". Glastech. Ber. Vol. 45, (1972), N ° 6, p 271-276. [3] Trier W. "Gleitverhalten yon hei]3em z/ihfltissigem glas auf metalloberflS.chen".Glastech. Ber. Vol. 51, (1978), N ° 9, p 240-243. [4] Moalie H., Fizpatrick J.A., Torrance A.A. Proc. I. Mech. E. 201c. (1987), p 321-329. [5] Lacey P., Torrance A.A., Fitpatrick J.A., Trans. ASME J. Trib.III (1989), p 260-264.

[6] Falipou M. Sidoroff F. Donnet Ch. "A new method for measuring friction between hot viscous glass and metal". Glastech.Ber., to be published. [7] Zahouani H., Jardret V., Mathia T.G. "Morphological characterisation of rough material." Surface Modification Technologies, edited by T.S Sudarshan and M. Jeandin, The institute of materials, 1995, p 135-147. [8] Zahouani H., Vargiolu R., Loubet J.L., Kapsa Ph., Mathia T.G. "Effect of lateral resolution on topographical images and 3D functional parameters". Wear, Pub. in progress. 10. ACKNOWLEDGEMENTS

The authors wish to thanks very much Ms S. Mengarduque for her contribution to the design of experiment, Dr B. Bouali for his help in the Principle Compound Analysis and the BSN Company for the authorisation of publishing.

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

101

Investigation o f surface d e f o r m a t i o n and friction w h e n a hard cylindrical asperity slides over a soft s m o o t h surface. M. Busquet and A.A. Torrance Department of Mechanical and Manufacturing Engineering, Trinity College, Dublin 2, Ireland Friction tests were performed where a rigid C.B.N. (Cubic Boron Nitride) cylindrical asperity slides over an aluminium alloy. The results were compared with the friction predictions of the slip-line field proposed by Challen and Oxley [3] for this configuration. Finite element simulations and further experimental tests with cut cylinders showed that both elastic effects and the presence of a third body influence the deformation in the softer material. It was observed also that the more the trailing edge of the cylinder was relieved the better were the friction predictions of the slip-line field theory.

1.

INTRODUCTION

When one metal slides across another one, frictional energy is generally dissipated both by shearing of an interfacial layer, or third body, and by plastic strain in the metal surfaces themselves. In recent years, it has been widely accepted from the examination of worn surfaces and of wear particles that the accumulation of this surface strain is linked to the detachment of wear particles. The task of calculating mechanical wear rates thus requires a model which predicts the extent and rate of strain due to sliding, and the amount of strain needed to produce wear particles. The starting point of such a model must be an idealisation of asperity contacts which allows the calculation of the strains imposed on a wearing surface by an asperity sliding across it. This must be combined with a damage rule so that the rate of debris generation can be found. Finally, a way of characterizing surface texture must be found which allows the result for a single asperity to be extended to a real surface. Over the last few years, two distinct procedures for developing such a wear model have been propose4 and investigated. The first starts from an extension of an elastic asperity contact model into the plastic region [1,2] and is clearly most appropriate at low strain. The second assumes rigid-plastic behaviour of the asperities [3], neglecting elastic effects. Each model of asperity interaction leads to a distinct way

of characterising surfaces, and may also require a distinct damage rule. Recent investigations [4,5] have shown that the rigid-plastic approach can successfully predict friction and wear of some non-ferrous metals. In this work, the hard asperity was simulated with a rigid wedge, which pushed a wave of the soft material ahead of it as it slid across the soft surface. The wave model established by Challen and Oxley [3] then allowed the measured friction and wear coefficients to be related to calculated stresses and strains via a Coffin-Manson low cycle fatigue rule. Although the above results were compatible with experimentally observed phenomena, it is often argued that a hard asperity can be better modelled as a rigid cylinder; but slip-line fields for this type of contact are not so well established. One attempt to provide a simple slip-line field for this configuration is the chord approximation model suggested by Challen and Oxley[6]. In the present work, the friction predicted by the chord approximation model is compared to the results of experiments where a cylindrical C.B.N. (Cubic Boron Nitride) tool slides across an aluminium alloy. The relative importance of elastic effects and the presence of a third body are investigated. Finite element calculations and further tests with cut cylinders are performed to achieve this task.

102

2.

MODEL

2.1. The Chord Approximation Model The model tested in this work is presented in Figure 1. The two-dimensional rigid, circular shaped asperity pushes a plastic wave in the softer material ahead of it. The area of contact between the asperity and the deformed material is approximated by its chord and is assumed to be confined ahead of the lowest point D of the circle. The chord approximation allows the slip-line field and associated hodograph previously established by Challen and Oxley for wedge shaped asperities to be used. [3]. In this last model, the asperity angle a was a constant parameter and only the length of the interface ED and hence the scale of the plastic zone increased with the normal load N. For a circular asperity of radius R, a and ED are now interrelated and depend on the geometrical and loading conditions, introducing this last feature and defining the strength of the interfacial film by the Tresca factor f=- r / k , where r is the shear strength of the film and k is the shear flow stress of the soft material, Challen and Oxley developed the following equations "

from the stress analysis where F and N are the frictional and normal forces per unit width and /t the resulting friction coefficiem. This steady-state field is associated with low load conditions, and hence low angle a of the chord. Some simulations of this so-called rubbing regime are presemed in figure 2, where p is plotted against N/kR (full lines) for differem values of f. It can be seen that for a given f, an increase of the normal load N is predicted to imply an increase in p . For any of these curves, N/kR exhibits a maximum value Nm~x/kR. Two values of /~ are then theoretically possible for a given load, the upper values of ~ corresponding to higher values of a . In terms of energy dissipation, the upper values of a are considered as inapplicable and for higher loads than NmJkR, a double chord model is proposed where a continuous chip formation is considered. [6]. The transition between the single chord model and the double chord model is suggested to occur at the value NmJkR and is associated with a jump of the friction coefficient. The double chord model is not presented here because only the rubbing regime is investigated in the present work.

(sin(a)] r/= asin 4 ( 1 , f i ) ( 1 ) 1a

* =7 DE

R

' = 2sin(a)

(a) (3)

Hard asperity

from the slip-line field geometry analysis, where r/ and • are two angles describing the slip-line field and

F'-F-=2sin(a~c°s(a+2~)+II+2(4+~-rl)lsin(a)} N-~=2sin(a~sin(a+2~)+II+2(4+~-rl)lc°s(a)

soft asperity

flow

(b)

Velocitym directionAE ~ Velocitydiscontinuityalong pole ~ ~ . ~ ~ - i ' U ~ ~ directionED

Figure 1: the singlechordmodel (a) slip'linefield '(b) h . . . . . . . . . .

,

......

aph -

103

P

f-41'4

o.gt

t CHAIAI~Alq30XLEY'S AtC~3X~I~'I(~lVED~- -

0.8

I=02

D.7

~~,~.,

in figure 2 where the dotted lines represent the variations of b/ with N/ld~ for f=0 and various values of B. .... \ ! CENTER

0.6

.

Hard asperi .~

0.5

"

0,4

g

I).3

/"

::

~'l"~m/,~

~1~¢~_

A

0.2 C).1: 0

.,,[

,

......

-, ~ / ~ 0

.

0.5

.:

,i,

1

1.5

,

, i

2

i

25

,

ID

; ! I

soft asl

flow ~

_

i

i

3

3.5

N:=ER

Figure 2: Variation of'b/ WithN/~ for Chall'en and O;dey;s wave model and developed model.

2.2. Development For reasons outlined fimher, the chord approximation model has been developed for the configuration where the lowest point in contact D between the circular asperity and the softer material is not on the centre line of the circle. The parameter B defines the angle between the radius OD and the centre line as shown in figure 3. The hodograph associated with the slip-line field is equivalent to the one associated with Challen and O x l e y ' s model. The new geometrical relation between the chord ED, the radius R of the cylinder and the two angles a and 1~ is as follows :

DE R

= 2

sin(a: - ]7)

Figure 3:the developed single chord model

3.

EXPERIMENTS

t_

~~]~

LOADARM

/ / [ ( ~, IJ

"~,naamwEacE

(3')

~

Equations (1), (2) and (6) can still be used but (4) and (5) become' ._-_-.

-~=2sin(a-fl) c o s ( a + 2 ~ ) +

1+2

+~-

sin(a) (4')

.

.

D~20M-ETER

.

.

.

.

.

.

.

.

.

.

.

.

-

~

.

LATHECROSS-SLIDE

Figure 4i Exp~imental Set-'up

N-~'=2sin(a - fl){sin(a+2(l))+II+2(4+~For a given normal load N, the associated chord angle a is relatively higher for the developed model than for the original one, and hence associated with higher friction coefficients. This change can be seen

The experimental set-up used in this work is shown in figure 4. One end of a 30mm bar of the test material was held in the chuck of a lathe, while the other end was supported on a running centre. The cylindrical C.B.N. (Cubic Boron Nitride) tool

104

was 3.15mm in width and of radius 1.57mm. it was mounted in the loading arm and was held against the bar by tightening the loading bolt. The tool, its holder, and the loading set-up were mounted on a 3 axis Kistler dynamometer fixed to the saddle of the lathe. This allowed the normal and frictional forces N and F to be controlled and recorded during the tests on a chart recorder. The friction coefficient /~ was then calculated from their ratio. Before a test, the lowest line of the cylinder was positioned to contact the bar at its top point, as shown in the figure 4. Lubrication was provided by 1% stearic acid in white medicinal oil. This was fed onto the surface of the bar through a sponge which also served to collect the wear particles. The lathe was set rotating at 35rev.min 1. Specimens were allowed to run in for 10s before every friction recording. Tests ran for about lmin. In order to test the friction predictions of the model against experimental results, tests were performed for a variety of normal loads, N. The material tested was an aluminiummagnesium alloy, 5083-Hl13, whose average shear flow stress k was taken as 232 MPa. This value was estimated from Vickers hardness measurements. The first set, S 1, of tests were performed with a full cylinder. A two-dimensional view of this tool is shown in the photograph of the figure 5a. Then 3 initial cylinders were ground to get the tools for the sets of tests $2, $3 and $4 as shown schematically in figure 6. A photograph of the tool used in the set $4 is shown in figure 5b. The use of these cut cylinders allowed the predictions of the developed model of paragraph 2.2 to be tested for 3 different angles l~. For the sets $3 and $4, this was equivalent to imposing the lowest "physical " point, D, in contact with the remaining circular arc of the tool inclined at an angle fi from the centre line. This relieved contacts between the tool and the deformed material under the trailing half of the cylinder. In order to test quantitatively the predictions of the developed model, the angle ~ had to be estimated accurately. Equipment limitations prevented a reasonable relationship between the ground depth of material and the angle B being developed. Direct measurements on the ground tools with a microscope and successive friction tests with incrementally cut cylinders then gave approximate estimations of the different values of l~ as shown in figure 6.

;i!:))))ii!ili~;i~!:!

m

?ii;:::;!?~;V~i:iii:i?; t:::::: : : : : : : : : : : : : : : : : : : : : : : ;:::::: =======================

iii~i.:~!i!ili:

.:.:...

::::::::::::::::::: ,=.,.... .:-....,.

+-,;..;.;,:,

iiiiiiiiiiiiiiiiii iii.':i:'ii:iii::g!ii!:::gi!

• .-c . . . . . , . , . . . . . , , . .. .. .. .. .. .. .. .. .. .. .. +:.:.:,:.:+:,:.:,:, ..,,,,,.....,......... , ,.-,.,,,..-=.,e.o. ,.,...,.° ,.° ..: ,...., , . . . . . . . . . . . . . . . , °.

i!ii iiii!i i ! : i i i ! !i ! !i i !i' !i!)iii!;ili !;iiiiiiiii:ii'!! ! ii ?!i'/!ii!iili!i /!ii

iiii!iiiiiii,il;ii:

Figure 5 - a" full cylinder. Set S 1 - b" the cut cylinder in the set $4.

........

'SLIDINO DII~ECT!OtN iof the'tool) i Axis

ofthe

cylind~.lr

'

'

!

-

S1;

$2 i ii

i

$3~ i

i

l

$4; .

FignJre 6: The 3 different t~ols used forthe series S1,S2,$31

|

!1

"

The Tresca factor f was estimated using a best fit method. Yang and Torrance [4,5] showed that Challen and Oxley's wave model for wedge shaped asperity successfully predicted experimental friction coefficients when a hard steel wedge slides on the 5083 alloy. Similar friction tests were performed with C.B.N. wedges of various angles a , under the same lubrication conditions as for the cylinder tests. Measured friction coefficients were compared to the wave model, and the chosen value of f was the one which best fit the experimental data. A value of f=-0.05 was obtained this way and used in the present work. A sort of very thin aluminium "coating" was observed on the C.B.N. tools just after their first utilisation. The "coated" areas seemed to remain constant when several tests were performed. Furthermore, the measured friction coefficients were reasonably repeatable for given test conditions. It was then considered that the presence of these areas did not affect the value of the Tresca factor f.

105

4. RESULTS AND DISCUSSION 4.1. Set S1 of experiments with a full cylinder. The friction results of the set S1, where a full cylinder slides under load against a bar, are presented in figure 7. The circles represent the measured friction coefficients, while the full line represents the predictions of the model for f=0.05. It can be seen that the experimental values are lower than those predicted, and that increasing the load does not imply increasing /z . For high values of N/kR where the theory predicts a transition to the double chord model, as mentioned in paragraph 2.1, no change of deformation regime was observed. From the results of figure 7 and the last observations, it can be concluded that the slip-line field theory cannot predict actual measured friction coefficients when the full cylinder slides on the 5083 alloy. There are two possible explanations. Firstly, one potentially serious defect of the slip-line field method is that it takes no account of elasticity. It is often argued that elastic effects cannot be neglected, especially in the case of cylinder/plane sliding contact. If these effects exist, it would be expected that the actual deformation of the softer material will extend further than the rigid-plastic theory predicts, due to elastic expansion. Furthermore, if this elastic deformation not only takes place in the leading part of the tool but also behind its centre line, this could lead to the formation of a trailing interface. The forces then created on this trailing interface will act opposite to the global frictional force, and an associated drop of the friction coefficient would be expected. The quasi-constant friction coefficient, observed over the load range of S1, would suggest that, as the load increases, a trailing angle increase would occur in parallel, and could balance to some extent, the effects of the increase of the attacking chord angle of the tool. As a consequence, the friction coefficient does not increase with the load, as was predicted by the theory. A second reason why the theory fails to predict reality may be the fact that it neglects the influence of the wear particles. In the load range of the tests, wear rates were observed to be quite low but to clearly increase with the load. For the highest loads, a significant amount of particles accumulated, especially in front of the tool but also at the sides

and even slightly behind it. The possibility exists that the wear particles produced influence the contact, acting as a third body. If this happens, sheafing would partly take place in this third body and the overall geometry of the contact would be changed at the same time. The slip-line field theory cannot accommodate a third body and thus cannot accurately model the test conditions. The last two points probably both influence the contact conditions leading to a far less severe regime in terms of plastic deformation and friction than was expected. They can both explain the fact that in the range of the load conditions, no change of regime was observed. In order to investigate these possibilities, an elasto-piastic finite element model was developed and further experimental tests with cut cylinders were performed.

c]4r--~ 335-t Q3-t

tLtL~~ S[$a4II~ERILDlvQZLf4K~ - - - FIN'IE~R,~LY~IS . . . .

325i Q2|

O" 0 .

.

.

.

.

.

.

t ......

f,,

f,

~,

Q5

1

1.5

2

.

.

.

.

i

25 .

i

!

i

i

Figure 7:'Friction results for the S1 configuration.

4.2. Finite element analysis. Finite element models were constructed using commercial software (ANSYS 5.3) to represent a hard cylinder indenting and sliding over 5083 alloy for various depths of penetration (see table1). The model is shown in figure 8. The hard cylinder itself is represented as a perfectly elastic solid with a Young's modulus of 207 GPa. It is supported by a block of low modulus (4GPa) to allow it to ride up to form a stable plastic wave. The 5083 alloy is represented as an linear isotropic hardening solid with a Young's modulus of 70 GPa, a tensile yield strength of 280 lVlPa and a hardening modulus of 4 lVlPa. Four-noded elements were used throughout (Visco 106 for the 5083, Plane 42 for the rest) to allow the contact to be modelled with the software's contact elements(contact 48). The friction

106

at the interface was set to zero. The friction results for the four simulations defined in table 1 are compared with the experimental and slip-line field results in figure 7 where the dashed line represents the finite element results. The deformation pattern obtained for the simulation with a 0.15mm initial depth of penetration is shown in figure 9. A proper quantitative comparison of the finite element analysis and experimental values of g is not possible because no friction is considered at the interface in the finite element analysis. However, if the low friction conditions determined for the test conditions are considered, the finite element results are not expected to significantly change.

As predicted by the slip-line field theory, the deformation pattern of figure 9 shows the presence of a plastically deformed wave pushed ahead of the cylinder in the aluminium alloy. It confirms the presence of a strained layer at and beneath the surface of the softer material. However, the region of contact in the finite element analysis is less concentrated than the region of contact predicted by the rigid-plastic theory. There is a trailing angle behind the centre line of the cylinder. As shown in figure 7, this leads to lower friction coefficients than the slip-line field predicts. Nonetheless, an increase in load is still predicted to cause an increase in friction. This point shows the necessity of including the influence of the third body in order to explain the quasi-constant friction coefficients in the tests with the full cylinder. In light of these findings, when a hard full cylinder slides across the 5083 alloy, it appears that both elastic effects and the presence of the third body influence the results observed. The finite element simulation cannot consider the third body. In order to further investigate these points, experiments using cut cylinders were performed. The friction results from these experiments are presented in the following paragraph.

F i g u r e 8: F i n i t e e l e m e n t m o d e l .

__L__

L___L .......

]

I

I.

I,_ . . . . .

J__A .

.

.

.

I JI I J

I j__i

---,-~-

.....

I I ~ I ~ ' D E ~ 7 - I OFPENETRATION OF THE CYLINDER

.L=_~JI___

~

'

(ram)

0.13 0.09 0.07 0.05

"

fib~

.... r~c'~oN '

LOAD (N)

COEFFICIENT (~)

,

539N 365N . . 268N .... 172N

i

i

0.0944 0.0515 0.0403 0.0210 .....

T A B L E 1" S u m m a r y o f finite e l e m e n t s i m u l a t i o n s .

4.3. Sets $2, $3, $4 of experiments with cut cylinders. --- ....:= Figure

~'- i - - : ........ -,. . . . . . --='---:............ " : . . . . . . . . . . . / .............. -:........ : ..... 9:

penetration.

Finite

element

simulation

for

0.15ram

depth

of

The friction results from the tests using the geometries $2, $3 and $4 as described in paragraph 3 are presented in figures I0, II and 12, respectively.

107

For set $2, the cylinder still contains a trailing part, as was shown in figure 6. The results are shown in figure 10 where the crosses represent the results of $2. It can be seen that an increase in the load now implies an increase in the value of p . However, the values ofp are still lower than those predicted by the slip-line field theory. This suggests that the trailing interface still exists, but that it has been decreased. The lower values of/~ measured for $2 appear to be a result of the effect of the remaining trailing interface. Elastic effects are reduced. It can be noticed also that the friction coefficient vs. load curve in these tests is deafly of similar shape to the one observed in the finite element analysis (whose friction results are represented by the dashed line). One possible explanation is that when the trailing side of the contact is partly removed, a clearance angle is created from which the particles can then escape more easily from the contact. This would mean that the influence of the third body is reduced by the removal of the trailing part of the tool.

ltt 0.5 0.45 0.4 3.35 0.3.

FULL CYLINDER 000 SLIP-LINE FIELD MODEL FINITE ELEMENT MODEL - CUT CYLINDER $2 *****

// //

3.25.

--

0.2:).150.1-

was not accurate enough for small loads, or it might be due to elastic effects [7].

0.6 0.5 0.4

FH~CYL]]q3]~

0.3

0

SLIP-LINEFIELDN/DD~

~

0.2 0.1

'

FINIqEB_Eh/ENr/vDEEL............ CLffCYLI/qgERS3 ii

1i

0 2

1

I I

I

l

3

I

,

~ . , . ~.-~

l~/lflb[ tl

.

|

Figure l 1" Friction results for the S3¢onfiguration

For the set $4, the leading side of the cylinder has been partly removed as shown in figure 6. The results are shown in figure 12 where the triangles represent the results of $4. It can be seen that the friction coefficients are generally higher than in any of the previous sets. This change can be predicted by using the developed slip-line field model, described in paragraph 2.2. For these results, the angle f3 which best fits the data is 5° . Unfortunately, the lack of accuracy of the grinding operation and the practical difficulty in accurately measuring the angle fi on the tool did not allow the confirmation of this value of 5°.

).05-

,,,

0 0

0.5

,.

.,.~

,,

1

1.5

2

,,,

N/Idl

2.5 III

3 |

Ill

.

.

Figure 10: Friction results for the $2 configuration

Of the sets discussed here, $3 is the closest configuration to Challen and Oxley's model. From figure 11 where the squares represent the results of $3, it can be seen that that the slip-line field model gives quite good estimations of the measured friction coefficients. However, some discrepancies are observed for N/kR 1.9. The case of high loads is studied further in this paragraph. For low loads, the measured friction coefficients are higher than the theory predicts. This could be attributed to experimental errors as the set-up used

Ix 0.5

'

J

, ,-,*

0"45" 0.4" 0.35-'

LIP-LINE FIELD MODEL - ' 30~;i

o.2~

~

0.1-

A q d mA"t'A / :" .~'.~

i

~

/ /

~

/

SLIP-LINE FIELD 5degreosMODEL WITH BETA = "'-

CUTC~rND~R s4

~

3.050!'

'

o

I

I

I

I

05

1

1.~

2

,

I'

2.~

3

Figure 12: Friction results for tiae $4 co~lguration.

"lit

~

~

~/!~

'

"ll,'qL

108

However, these results suggest that, as the trailing edge of the cylinder is further relieved (larger 1~), the slip,line field theory predicts friction coefficients more accurately. Compared to the results with the full cylinder (S1), the changes observed in the later tests ($2, $3, $4) can be explained by a reduction of both the elastic effects and the influence of the third body, which is no longer trapped in the contact. Although these tests support the slip-line field theory when the test conditions are controlled, some deviation from the theory has been observed for the change in deformation regime (rubbing to cutting) as the load increases. As mentioned in paragraph 2, Challen and Oxley proposed that the transition to the double chord model would occur at the value Nmx/kR and is associated with a jump in the friction coefficient. In the test conditions of the present work, it would occur at about N/kR-2.5. In any of the three sets, $2, $3 or $4, the transition to a new mode of deformation has been observed at lower loads than the theory predicts. A larger relief in the trailing angle was associated with a lower transition load in the deformation regime. In any of the three sets, as mentioned before, the rubbing regime was associated with a slow accumulation of particles in front of the contact. Beyond the transition load, a continuous formation of "flakes" was observed. Then, as the load increased, the "flakes" disappeared to be replaced by rougher cutting. These last observations shed light on the limitations of the model. Even if the average deformation seems to be well-estimated by the slip-line field theory (as shown by the success of the last friction tests), it does not account for the nuances of the deformation. It also fails in predicting accurately the actual load beyond which cutting occurs. At this stage, it seems that a more refined deformation model would be necessary.

4.

CONCLUSIONS

The results obtained from the tests performed with a full cylinder sliding on the 5083 alloy indicate that the friction appears to be dominated by both elastic effects and the presence of third body. Friction coefficients in this configuration can not well be predicted by the slip-line field theory. When the trailing side of the contact is

removed, the plastic deformation of the first body is concentrated in a smaller zone. Elastic effects become less important. At the same time, the third body might escape more easily from the comact and its influence on the contact be reduced. Furthermore, it was observed that the more the trailing edge of the cylinder is relieved the better were the predictions of the slip-line field theory. It remains to be seen how well these findings apply to other materials. Finally, even if the average deformation seems to be well estimated by the slip-line field theory, some limitations of the model have been shown. One limitation was that the transition to more severe regimes of deformation, observed in the range of the test conditions was not l~redicted. One other was that it does not account for the nuances of the deformation. To account for these phenomena, some more tests need to be performed, finite element analysis needs to be further investigated with friction and a more accurate model in terms of deformation pattern will be necessary.

ACKNOWLEDGMENTS The authors wish to thank Professor Peter Oxley for his interest in the present work and his helpful suggestions, Tom Haveron for his time and his patient technical support during the present experimental work and finally the Marie Curie Research Training grants framework for financial support.

REFERENCES 1. J.E. Merwin and K.L. Johnson, "An analysis of plastic deformation in rolling contact" in Proc. 1. Mech. Eng. (1963) 177, 676-685. 2. K.L. Johnson and J.A. Jefferis, "Plastic flow and residual stress in rolling and sliding contact" in Proc L Mech Eng. Symposium on Fatigue in Rolling Contact (1964) 54-65. 3. J.M. Challen and P.L.B. Oxley, "An explanation of the different regimes of friction and wear using asperity deformation models" in Wear (1978) 53, 229-243.

109 4. Y. Yang and A.A. Torrance, "Wear by plastic ratchetting: an experimental evaluation." in Wear (1996) 196, 147-155. 5. Y. Yang, A.A. Torrance and P.L.B. Oxley, "Modelling mechanical wear processes in metallic sliding friction." in 3'. Phys. D., Appl. Phys. (1996) 29, 600-608. 6. J.M. Challen and P.L.B. Oxley, "Slip-line fields for explaining the mechanics of polishing and related processes" in Int. J. Mech. Sci. (1983) Vol. 26, No. 6-8, pp. 403-418. 7. J. Galligan, "Friction of piston ring - cylinder bores.", Ph.D. thesis submitted to Trinity College Dublin in June 1998.

NOMENCLATURE

A,B,C,D,E f N O,O' R o~#,rl,d~,co 0

Points defining the slip-line field Tresca's friction factor: f = cos2s. Normal load in wear test. Poles of hodograph Radius of the cylinder Angles defined in figure 1. x / 4 - r I.

LIST OF FIGURES

Figure 1: the single chord model (a) slip-line field (b) hodograph Figure 2: Variation of ~ with N/kR for Challen and Oxley's wave model and developed model. Figure 3: the developed single chord model Figure 4: Experimental set-up Figure 5 - a : the full cylinder. Set S1 - b : the ground cylinder in the set $4. Figure 6: The 3 different tools used for the series S1,$2,$3. Figure 7: Friction results for the S 1 configuration. Figure 8: Finite element model. Figure 9: Finite element simulation for 0.15mm depth of penetration. Figure 10: Friction results for the $2 configuration Figure 11: Friction results for the S3configuration Figure 12: Friction results for the $4 configuration. TABLE 1: Summary of finite element simulations.

This Page Intentionally Left Blank

SESSION V COATINGS

Chairman:

Dr. M. Brendle

Paper V (i)

A Tribological Comparison of Some CarbonCarbon Composites Sliding Against Stainless Steel

Paper V (ii)

Low Friction and Low Damage Properties of Diamond with Water Boundary Lubrication

Paper V (iii)

Study on the Friction Characteristics of the Metal with Harder Thin Film

Paper V (iv)

A Comparative Study of the Tribological Behaviour of TiN and ZrN PVD Coatings

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

113

A tribological c o m p a r i s o n of s o m e c a r b o n - c a r b o n c o m p o s i t e s sliding a g a i n s t s t a i n l e s s steel D. M. Elliott and J. Fisher.

School of Mechanical Engineering, University of Leeds, Leeds, LS2 9JT, UK S. P. Appleyard, E. Zhang and B. Rand

Department of Materials, University of Leeds, Leeds, LS2 9JT, UK ABSTRACT The laboratory model used in this present study allowed investigation of the time-dependent variations of dry-sliding friction and wear of some 5 mm diameter carbon-carbon composite pins sliding against disks of 316 stainless steel. The carbon-carbon samples were produced from different pre-cursors and process parameters with the aim of optimising the rate of wear against the steel. These process variables included the carbon fibre type (PAN or pitch based), surface treatment of the fibre, the temperature of graphitization, the origin of the matrix carbon, the fibre orientation and overall structure of the composite. A polycrystalline graphite was used as a control (POCO ZXF-SQ). The surface of each steel disk used was fine ground to an Ra of 0.3 +0.04gm, measured by optical profilometry. The corresponding contacting stylus Ra value was 0.1 +0.01 gm. The pressure on each of the three pins was 1.0 MPa, the disk rotation was 0.17-0.18 ms -1, and the sliding distance was 90 km. Each carbon-carbon sample formed a patchy 0.2-1.0 gm thick lubricating layer of carbon on the disk, and loose wear debris was collected after each 15 km stage for SEM analysis. The variation of the coefficient of friction was similar for each sample as a result of the graphite lubrication, however, the wear rate was seen to depend on the fibre origin, orientation, and the integrity of the matrix. Optimal process parameters produced carbon-carbon which exhibited wear against stainless steel at a fifth the rate of APC2 and lower than PEEK 450G by a factor of 200.

1. I N T R O D U C T I O N Carbon-carbon composites, with their low density, high s t r e n g t h and high melting point, are being used in an ever increasing n u m b e r of tribological applications. It is, therefore, i m p o r t a n t to gain a thorough u n d e r s t a n d i n g of the range of frictional forces and wear m e c h a n i s m s t h a t these composites exhibit. The tribological behaviour of a range of carbon-carbon composites has been investigated and compared with the more widely used P E E K and PEEK-bonded carbon fibre (APC2). Most of the previous tribological studies of carbon-carbon composites have concentrated on their application as a brake material. A comprehensive review of these high energy wear and friction tests, in which oxidative wear predominates, was published by Blanco

et al (1). Low energy friction and wear tests have been carried out by Kim et al (2) using a pin-on-disk both made from the composite. Sliding speeds were from 0.14 to 0.62 ms 1, with the pressure on the pin ranging from 0.5 to 2.0 MPa. They showed t h a t the wear rate of composites with a smooth l a m i n a r structure was higher t h a n those with a matrix of isotropic structure. This suggests t h a t a higher degree of preferred orientation of the matrix leads to weaker interaction between fibre and matrix. J u et al (3) investigated the low-energy wear behaviour of 1D and 2D PAN, fibre-reinforced, pitchmatrix, carbon-carbon composites with a disk-on-disk test configuration. Both disks were made of the composite, the contact pressures were either 1.7 MPa or 2.3 MPa, and the disk rotation was fixed at 60 rpm, giving a relative velocity at the disk edge of

114

0.078 ms -~. They found that initially the 1D composites wore at a greater rate t h a n either the 2D or the bulk graphite samples, but after 10 minutes the wear rates were similar for all materials. The drop in wear rate was seen to coincide with the formation of a smooth a d h e r e n t debris film. The tests were only r u n for 30 minutes. F u r t h e r work by J u and Chen (4), employing the same test method, showed t h a t the initial wear rate of a low density composite was an order of magnitude higher t h a n the other high density composites. The presence of large pores (1.4% vol. more t h a n 100 gm in diameter) would explain the high initial wear, as material could break away easily from the pore edge. The rate at which the debris film formed was seen to differ from one composite to the next. In the present study the counterface to the three composite pins was a fine ground stainless steel disk. Emphasis was placed on measuring the different rates of debris production between the various composites tested, the n a t u r e of this debris (loose or transfer film), and the stability of the lubricating transfer film once established.

2. M A T E R I A L S A N D M E T H O D S

The composites were formed from three sources of carbon: polyacrylonitrile (PAN), pitch, resin and coke. The fibres were either pitch or PAN based. The PAN based fibres were either high modulus u n t r e a t e d (Fibre H T T - 2 2 0 0 °C), or standard modulus surface treated (AS4 Fibre H T T - 1 6 0 0 °C). The surface of the treated fibres was very slightly oxidized. Most of the materials in these tests had matrices formed from resin and coke, with only the matrix of CC6 formed from pitch and coke. Densification, to fill any voids remaining after the initial moulding and carbonization, was carried out using

pitch. The composite t r e a t m e n t t e m p e r a t u r e was either 2,200°C or 1,000°C. A polycrystaline graphite (POCO ZXF-5Q) was chosen as a control sample. It had the highest modulus of elasticity, compressive strength and density of all the grades manufactured by POCO, with a particle size of I gm and 20% porosity of 0.2 gm diameter. Composites with fibres in only one direction were designated "ID". The CC1 2D composite had alternating layers of whole and chopped fibres and the 2D CC7 composite had a woven structure, the resulting ground surface of which had a 1 mm square check pattern. Table 1 shows the various process parameters. The wear test matrix of samples was designed .....so t h a t each "in-house" composite differed from another by only one process parameter. However, as the research time was limited, many parameter permutations remain untested. The 1D composites, CC2-6, were tested with the fibre structure at 90 o to the direction of sliding and the fine grinding scratches across the 316 stainless steel disk lay in one direction. Comparison of CC2 with CC3 showed the effect of t r e a t m e n t t e m p e r a t u r e on the wear rate of these high modulus PAN composites and its variation with time. Comparison of CC7 and CC1 with CC4 showed the effect of fibre orientation on wear rate; although, as there was a lack of available data for the CC1 and CC7 samples, no definite conclusions could be made. Comparison of CC4 with CC3 showed whether high modulus u n t r e a t e d or standard modulus treated fibres perform better. Comparison of CC4 with CC5 showed whether pitch or PAN based fibres are better and comparison of CC5 with CC6 showed the effect of using pitch in the matrix as opposed to resin. In addition to these tests, a series was performed using CC1 against a polished steel counterface and CC4 was also r u n against ground stainless steel with the fibre structure parallel to the direction of sliding.

115

Table 1 Carbon-carbon composite process parameters Sample CC1 CC2 CC3 CC4 CC5 CC6 CC7

Type Industrial HMU-RC HMU-RC AS4-RC P25-RC P25-PC Industrial

Control

ZXF-5Q

Fibre PAN 2D PAN 1D PAN 1D PAN 1D pitch 1D pitch 1D PAN 2D

As the available samples of the various composites were too small to allow sufficient 18mm x 5mm cylindrical wear pins to be cut and turned, a 9mm long, 5mm square block was cut and mounted in a thermo-setting resin. The resulting block was turned down to 9.4 mm diameter, with 2 mm of the composite protruding at one end turned to 5 mm diameter. This process insured that the rather brittle composite would not fracture during machining or subsequent testing and that the fibre structure of the composite was parallel to the wear surface. Four pins were made from each composite, one control and three wear test pins. The three pins were held by collets in a cylindrical block and then "run-in" on a sheet of 1000 grit SiC paper (on a steel flat) by carefully rotating the pin block a few times. The exact orientation of the pins in the block was marked and then each one cleaned with compressed air before removal for weighing. Details of the tri-pinon-disk wear test machine have been published previously (5). Throughout the test series the load on each pin was 2 kg, giving a nominal pressure of 1 MPa, and rotation of the disk produced a sliding speed of 0.17- 0.18 ms -~. The test was stopped at 15 km intervals to weigh the pins, to measure the surface roughness and transfer film across the wear track and to collect the loose carbon debris for SEM

Matrix resin resin resin resin pitch

Densifier

& coke & coke & coke & coke & coke

pitch pitch pitch pitch pitch

Composite HTT 1000°C 2200°C 2200°C 2200°C 2200°C

Poco graphite analysis. Mass changes of the control pin, kept in a metal collet, under the same environment as the wear pins, were used to correct the wear pin mass loss. Any wear debris collected was later dispersed in alcohol and then filtered, drop-wise, on to a 0.1 gm pore-size polycarbonate filter membrane. The centre of these filters, supporting most of the debris, was then cut out and stuck onto an SEM stub using a carbon tab (Agar Scientific). The samples were gold coated and SEM images recorded at 100, 250, 1500 and 5000 X magnification. 3. R E S U L T S A N D D I S C U S S I O N

The results for both coefficient of friction and specific wear rate are presented in four groups: 2D PAN fibre composites; 1D PAN fibre composites; effect of 1D PAN fibre orientation and 1D pitch fibre composites. All the composites were run against fine ground stainless steel disks, but CC1, in the first group, was also run against a polished steel disk. The coefficient of friction results are the average values recorded at the end of each successive 15 km test and the error bars represent the maximum and minimum value recorded. The error bars in the specific wear rate plots are the standard deviation of the average.

116

3.1. T h e c o e f f i c i e n t carbon composites steel

of friction of carbonsliding on stainless

The variation with sliding distance of the coefficient of friction exhibited by the 2D composites is shown, along with the control, in Fig. 1.

km. If this trend were to continue, it would probably develop a slightly lower coefficient of friction than the CC1 composite. 0.35 0.3 -t-

[] CC2

0.25 -

•~

0.4

0.2

0.35

0.15 "-

0.3

• CC3 [] CC4 [] POCO

0.1-

0.25 0.05 -

0.2

~

0.15

I !

0

30

15

~ o.1

! I

I I

I I

45

i I

60

75

90

Sliding Distance (km)

0.05 0

15

30Slidi::Dista:: (km)75

Fig. 1" The coefficient of friction of the 2D PAN composites against 316 steel. [error bars show max. and min. values] The CC1 composite started with a low coefficient of friction of 0.18 compared to 0.25 of the graphite control. The CC1 friction steadily increased throughout the test series as the control decreased. After 75 km they were the same at about 0.22, and after 90 km, the CC1 value had increased to 0.24. Against a polished counterface CC1 started with a higher coefficient of friction than against ground and increased to 0.32 after 45 km. This then dropped to 0.12 after 90 km, but with a large variation of + 0.1. This prominent stick-slip effect was probably caused by the poor adhesion of the carbon debris to the polished steel surface. Most of the small quantity of debris produced was compounded into a patchy film on the pin surface, but this was not able to sustain a constant level of lubrication. About 8% more frictional energy was dissipated throughout the test of CC1 against a polished counterface compared with that against a ground surface. The CC7 composite exhibited a similar coefficient of friction as the control until 45 km and then dropped slightly to 0.19 after 90

Fig. 2: The coefficient of friction of the 1D PAN composites against 316 steel. [error bars show max. and rain. values] Fig. 2 displays the coefficient of friction results from the 1D PAN fibre composite tests. All three composites performed better than the graphite control. However, after 30 km the coefficient of friction of the standard modulus fibres (CC4) remained at about 0.140.15 compared to 0.17-0.2 of the high modulus fibres (CC2 and CC3). CC3, with a higher temperature of graphitization compared to CC2, also had a slightly higher coefficient of friction. 0.35

0.3 -~

m CC4

T

0.25 --

t

t • C C 4 (0)

0.2-[] POCO 0.15 -i 0.10.05 I

0

15

30

im

i

45

60

li

75

90

S l i d i n g D i s t a n c e (kin)

Fig. 3" The coefficient of friction of CC4 with 0 o and 90 ° fibre orientation against 316 steel. [error bars show max. and min. values ]

117

Composite CC4 was r u n in two 90 km tests, one with 900 , and the other 0 ° fibre orientation with respect to the sliding direction (Fig. 3). The 900 fibre orientation produced a reasonably constant coefficient of friction of 0.14 througout the test. In contrast, the 0 ° fibre orientation produced a coefficient of friction that increased from 0.16 after 15 km to 0.22 after 60 km, being slightly higher t h a n that produced by the graphite control. The other composites were all run with 900 fibre orientation. Coefficient of friction results from the pitch fibre composites are shown in Fig. 4. CC6, with a matrix made from pitch and coke, had a similar coefficient of friction to that of the graphite control. CC5, with a matrix made from resin and coke, exhibited the highest coefficient of friction of all the composites tested against fine ground steel disks. It remained at 0.3 for 30 km, then dropped to 0.2 for the next 30 km and then increased again to end the test at about 0.28. o.3s 7

coefficient of friction after 90 km of 0.18. The lowest and most stable coefficient of friction of 0.14 was recorded by the standard modulus PAN fibre with resin and coke matrix composite. CC1 against a polished steel disk had an even lower average coefficient of friction of 0.12 after 90 km, however, there was a large minimum to maximum range of 0.2, and earlier during the test, after 45 km, the coefficient of friction had been much higher at 0.32. 3.2. T h e s p e c i f i c w e a r r a t e o f c a r b o n carbon composites sliding on stainless steel During the first 45 km of sliding the specific wear rate of CC1 was about 50% lower against polished steel compared with that against the fine ground steel. But although the wear rate against ground steel had decreased from 4.2 x 10 .7 mm3/Nm after 15 km to 0.3 x 10 .7 mm3/Nm after 60 km, the wear rate against the polished steel only decreased until 45 km and then increased to 1.5 x 10 .7 mm3/Nm after 60 km (Fig. 5).

!~.

30Shdl: "" tIs" t ~ f ~ i o °efficien

i~

c n 1D p~tch fibre composites against 316 steel. [error bars show max. and min. values] In summary, the majority of the composites tested produced a coefficient of friction after 90 km of about 0.215, the same as the graphite control. However, the pitch fibre with resin and coke matrix composite had a coefficient of friction after 90 km of 0.28 . In contrast, the high modulus PAN fibre with resin and coke matrix composite had a

[]CC7

15

30

45

60

75

SlidingDistance (,l~n)

90

Fig. 5: The specific wear rate of the 2D PAN fibre composites against 316 steel. [error bars show standard deviation from the average] The specific wear rate of CC7 increased from 4.7 x 10 .7 mm3/Nm after 15 km to 6.3. x 10 .7 mm3/Nm after 30 km, but then decreased, until after 90 km, as sufficient carbon debris formed into a film on both the disk and pins, the specific wear rate had become as low as that of CC1 (around 0.3 x 10 .7 mm3/Nm).

118

After 90 km the wear rate of CC1 against the fine ground surface was 77 times lower than the wear rate of the graphite control. Half the surface of the CC7 pins was composed of fibres running parallel to the direction of sliding. As will be discussed later, this tends to increase the wear rate (Fig. 7), and could explain the higher specific wear rate of CC7 compared to CC1 during the initial stages of the test. The specific wear rates of the 1D composites are shown in Fig. 6 and compared with the graphite control in Fig. 6a. A higher specific wear rate was recorded for the standard modulus fibre composite (CC4) after 15 km compared to the two high modulus fibre composites (CC2 and CC3). After 90 km, the specific wear rate of CC4 was still higher than CC2 and CC3, although not significantly so, given the rather large variation between the mass losses of each pin. After 30 km, the specific wear rate of CC2 had increased from 3.5 x 10 .7 mm3/Nm to 5.7 x 10 .7 mm3/Nm, but then steadily decreased to around 2.1 x 10 .7 mm3/Nm after 90 km. CC3 maintained an almost constant specific wear rate throughout the test decreasing slightly from 3.4 x 10 .7 mm3/Nm after 15 km to around 2 x 10 .7 mm3/Nm after 90 km. These results suggest that composites made from high modulus fibres exhibit a lower specific wear rate against fine ground stainless steel compared to those made from standard modulus fibres, particularly during the intitial stages of wear. In addition, it would appear that there is no significant difference in specific wear rate between those high modulus fibre composites graphitized at 1000oC and those graphitized at 2200°C Fig. 7 demonstrates the marked dependence of the specific wear rate of composite CC4 on the orientation of its fibre structure with respect to the direction of sliding. With the fibres at 900 to the direction of sliding, the specific wear rate steadily decreased from about 7 x 10 .7 mm3/Nm after 15 km to about 3 x 10 .7 mm3/Nm after 45 km and the remainder of the test. With the fibres at 0 o to

90

75 45 60 Sliding Distance (km)

15

30

45

60

75

90

Sliding Distance (km)

Fig. 6 and 6a: The specific wear rate of the 1D PAN fibre composites and a Poco graphite control against 316 steel. [error bars show standard deviation from the average] the direction of sliding, the specific wear rate increased from about 1 x 10 .6 mm3/Nm after 15 km to almost 6 x 10 .6 mm3/Nm after 60 km and stayed at that level for the remainder of the test. As there was very little film debris on the wear pin surfaces, the fibre orientation probably affected the lubricity of the transfer film on the disk. Both tests produced a similar film of about 1 pm thickness covering nearly all the wear track area. However, with fibres travelling in the direction of sliding there would be greater penetration of the transfer film, and hence contact with the steel asperities, compared to when they were at 900 to the direction of sliding. SEM observation of the wear debris after 60 km in the two tests revealed a sigificant

119

70

45

60

40 35

~

%

50

[] C C 5

30

40

25

~ 30

20

IN

i

[] C C 6 [] POCO

15

~!~ 20

10 .

10

5

0 -10

0 15

30

45

60

Sliding D i s t a n c e

75

90

I

15

t

30

(km)

Fig. 7: The specific wear rate of CC4 with 0 ° and 90 ° fibre orientation against 316 steel [error bars show standard deviation from the average] number of whole fibres of up to 200 ~tm in length from the composite r u n with 0 ° orientation. This suggests that asperities on the steel surface were able to push out fibre sections and that the fibre to fibre adhesion must be quite low. (Fig. 14) Although this experiment was only performed with one of the composites, it is reasonable to assume that a similar dependence of specific wear rate on fibre orientation exists for other 1D carbon-carbon composites. The specific wear rates of the pitch fibre composites, CC5 and CC6, are presented, along with the graphite control, in Fig. 8. It is clear that these composites exhibited higher wear t h a n the PAN fibre composites and, for most of the test, they lost material at a greater rate t h a n that of the graphite control. Assuming that a stable wear rate had been achieved after 75 km, CC5, with a resin and coke matrix, had a lower specific wear rate than CC6 with a pitch and coke matrix. However, the wear rate of both composites during the first 60 km was quite unstable, particularly that of CC5. The almost two-fold increase in specific wear rate of CC5, between the first and second periods of 30 km, was seen to correspond to a 30% decrease in the coefficient of friction (Fig. 4).

I

45

60

Sliding Distance

I

75

90

(km)

Fig. 8: The specific wear rate of the 1D pitch fibre composites against 316 steel. [error bars show standard deviation from the average] 3.3. A n a l y s i s transfer film

of the

wear

debris

and

Scanning electron microscopy of the carbon wear debris and optical microscopy of the transfer film on the disk showed a great variety between the different composite samples. The Poco graphite control pins formed a transfer film of about 1 ~tm thickness over the whole of the wear track, with evidence of smearing. However, the debris in Fig. 9 shows that a large amount of plate-like particles were also formed.

Fig. 9" Wear debris from POCO graphite after 60 km dry sliding against 316 steel.

120

Fig. 10: Wear debris from CC1 after 60 km of dry sliding against 316 steel.

particles in the centre of the image were not typical of the wear debris produced, there being only about ten such particles per square mm of filter. There were no sharp edged particles as seen with other composites, suggesting t h a t the transfer film was not breaking up, and was similar in appearance to that produced by CC1. However, the clear concentric tracks appeared to coincide with the edge between the adjacent fibre sections in the weave pattern. Despite having almost half of the pin surface composed of fibres at 0 o to the sliding direction, they were not parallel with the wear surface as a result of being woven and thus an increased specific wear rate. as with CC4-0 o was not recorded.

The wear debris from the 2D CC1 composite is shown in Fig.10. The majority of the particles were less t h a n 20 pm in length, and the largest always being a conglomerate of smaller particles. The debris was collected from two 15 km tests which explains why there appears to be more t h a n from CC7 (collected from one 15 km test). The transfer film produced on the disk by CC1 was about 1 ~m thick with a few concentric clear tracks where the pins had scratched the disk. Fig. 12: Wear debris from CC2 after 45 km dry sliding against 316 steel.

Fig. 11: Wear debris from CC7 after 60 km dry sliding against 316 steel. Wear Debris from the 2D CC7 composite is shown in Fig. 11. The two large conglomerate

Figures 12 and 13 show the wear debris from the 1D high modulus fibre composites (CC2 and CC3). The size range and particulate n a t u r e of the debris were similar for both samples. The quantity of debris in each shot was not a measure of the total amount of wear debris produced. The difference in graphitization t e m p e r a t u r e did not have a noticeable effect on the carboncarbon wear debris. The transfer films from these two composites were thinner and less extensive t h a n that from CC1, being 0.2 ~m for CC2 and 0.48 ~m for CC3.

121

Fig. 13: Wear debris from CC3 after 45 km dry sliding against 316 steel.

covering about 80% of the wear track to a thickness of 1 ~m with some isolated streaks of thicker carbon. The wear debris from the pitch fibre composites is shown in Figures. 16 and 17. CC5 (Fig. 16), with a resin and coke matrix, produced a greater quantity of large plate-like particles compared to CC6, with a pitch and coke matrix The transfer film left by CC5 was formed of smeared patches covering about half the wear track area. The transfer film produced on the disk by CC6 developed stress relief in the form 0.1-0.2 mm diameter bubbles of about 6 ~m high. This buckling survived for over 15 km of sliding, sometimes reducing in scale, but eventually fracturing to produce quite large wear particles.

Figures 14 and 15 show the marked difference in wear debris type and size range from two CC4 standard modulus fibre composite samples run with their fibres at 0 o and 900 to the sliding direction respectively. The rod shaped object across the lower right hand corner of Fig. 14 is a 200 ~m long fibre. Debris from CC4-90 o did not contain any particles larger t h a n 25 ~m in diameter. In comparison with the high modulus fibre composites, the standard modulus fibre composites produced larger and more angular wear debris Fig. 15: Wear debris from CC4 (90 °) after 60 km dry sliding on 316 steel

Fig. 14: Wear debris from CC4 (0°)after 60 km dry sliding against 316 steel. The transfer film left on the disk from both tests with CC4 was similar in appearance,

Fig. 16: Wear debris from CC5 after 60 km dry sliding against 316 steel

122

Further analysis of the wear debris and transfer films formed by carbon-carbon composites sliding against fine ground stainless steel will form the basis of a future publication.

Fig. 17: Wear debris from CC6 after 60 km dry sliding against 316 steel.

4. C o n c l u s i o n s This work has shown that the coefficient of friction of carbon-carbon composites against fine ground stainless steel is not greatly affected by the process parameters. The majority of the composites exhibited a coefficient of friction of around 0.2 after 90 km of dry sliding. The standard modulus PAN fibre composite CC4 however had a coefficient of friction of 0.15 and the pitch fibre with resin and coke matrix composite had a coefficient of friction of around 0.3 after 90 km dry sliding. The specific wear rates showed a greater dependence on the process parameters. The lowest stable specific wear rate was recorded by composite CC1 at 3 x 10 s mma/Nm with a similar value for the other 2D composite CC7. The 1D PAN composites were slightly less hard wearing. The high modulus PAN fibre (HTT 2200oC) composite CC3 recorded a specific wear rate after 90 km dry sliding of 1.64 x 10 .7 mma/Nm. The high modulus PAN fibre (HTT 1000 °C) composite CC2 recorded a

specific wear rate after 90 km dry sliding of 2.23 x 10 .7 mma/Nm. The standard modulus PAN fibre composite CC4 recorded a specific wear rate of 2.9 x 10 .7 mma/Nm. There was a 20 fold increase in specific wear rate of CC4 when the fibres were running in the same direction of sliding. Carbon-carbon composites made from pitch based fibres had a specific wear rate greater by a factor of 15 than the best 1D PAN composite. The lowest wear rate recorded by the carboncarbon composites was five times lower t h a n that from similar tests run with APC2 and lower t h a n the specific wear rate of PEEK 450G, against fine ground stainless steel, by a factor of 200. The range of process parameters used in this study was by no means comprehensive and it is likely that other carbon-carbon composites could be produced that would exhibit even lower wear rates. Nevertheless the present work has served as a good basis for further research.. A c k n o wle d g e m e nts The Authors would like to t h a n k the EPSRC for funding this research and Messrs Luciano Bellon and Steven Murgatroyd of the School of Mechanical Engineering, Leeds University for technical support during the wear testing.

REFERENCES 1. C. Blanco, J. Bermejo, H. Marsh and R. Menendez, Wear, 213 (1997) 1-12. 2. D-G. Kim, D-W. Kweon and J-Y. Lee, J. Mater. Sci. Let., 12 (1993) 8-10. 3. C.P. Ju, K.J. Lee, H.D. Wu and C.I Chen, Carbon, 32 No. 5, (1994) 971-977. 4. J.D. Chen and C.P. Ju, Carbon, 33, No. 1, (1995) 57-62. 5. D.M. Elliott, J. Fisher, and D.T. Clark, Wear, 214 (1988).

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

123

Low friction and low damage properties of diamond with water boundary lubrication

S. Miyake and A. Kinjyo Nippon Institute of Technology, Miyashiro, Saitama, Japan Tribological properties of diamond with and without water boundary-lubrication were studied, and the following results were obtained. (1)Friction coefficient of polished diamond film with diamond tip is extremely low as tz = 0.02. This result is deduced to the decreasing of contact area and low shear strength of water absorbed on diamond surfaces. (2)The damage of silicon slid with silicon is very large due to adhesion between similar materials. In contrast, a diamond is used as opposite tip material, the damage can not be observed on the silicon surface both with and without water boundary-lubrication. (3) To clarify the reason why damage free sliding with diamond tip, stress analysis was carried out by the boundary element method. The damage of the silicon slid with diamond tip is very little due to the low shearing stress of surface from which damage seems to be originated.

1. I N T R O D U C T I O N Micro-tribology is a key technology of the advanced industry[ 1]. It is important in micro-machines, medical engineering elements, magnetic recording head-media interfaces, LSI manufacturing systems and mechanisms for use in space. Micro-machines composed of micro-mechanical parts fabricated by LSI silicon processes are being actively studied. Because this is a new field, where micro-tribology is the key technology, micro-motors, micro-sensors, and micro-turbines have only recently been developed. In the equation of motion, the inertia term, which is proportional to mass, decreases as the third power of the scale length. In contrast, the friction force term, such as the molecular interface force or the static electric force, decreases as the second power of the scale length. Consequently, the friction term assumes greater importance in a micro-machine. Moreover, the scale is sufficiently small that micro-wear influences

the machine properties as well. For instance, the frictional torque and wear of a micro-turbine must be reduced. As the most common material used in microfabrication processes is silicon, we need to study the surface modification of a silicon surface and develop new surface materials[2]. In these fields, atomic-scale wear and minute fluctuations in friction degrade equipment performance. The surface material that can reduce atomic-scale wear and friction fluctuations is not the conventional solid lubricant film, but a wear-resistant, low-friction film. Diamond is the hardest material in nature and has been studied with respect to its tribological properties. Diamond has both high wear resistance and low friction. Bowden showed that natural diamond has excellent tribological properties, such as low friction and high wear-resistance[3]. The tribologcal properties of CVD diamond films have been studied by many researchers who pointed out that these films have wear resistance and low friction[4,5].

124

In our previous micro-tribological studies, diamond-like carbon films were deposited[ 1,6]. Those film exhibited microtribologically low friction and wear resistance. Another study investigated the microtribological characteristics of carbon film containing silicon[6]. In still another study, cubic boron nitride film showed wear resistance and low friction[7]. Other studies suggest the effects of ion implantation on the micro wear properties of diamond[8]. Fluorinated diamond films[9] were deposited. Fluorination and ion implantation effects of polished diamond film on reducing the friction coefficient have been evaluated. Polished diamond films show high friction coefficient in vacuum. The effects of N÷-implantation on the tribological properties of diamond films in vacuum have also been investigated, and low friction coefficient in vacuum obtained[ 10]. The amorphous layer formed upon N÷-implantation is thought to reduce the friction coefficient of polished CVD diamond films. However, there has been little of the boundary lubrication properties of diamond films. It is necessary for mechanical parts use in medical or biotechnology applications, to clarify the boundary lubrication properties of water. In this paper, the boundary lubrication properties of diamond and silicon with and without water were studied. 2. EXPERIMENTAL METHODS

(1) Materials Si (100) wafer and diamond film coated silicon nitride substrate were used as plate specimens. Diamond films were deposited on a rectangular silicon nitride substrate (Si3N4) by thermal filament CVD in an atmosphere of 99% hydrogen and 1% methane at 900°C. The diamond surface was then polished to a surface roughness of under 5 nm Rmax as measured by AFM (atomic force microscope). A clear diamond peak is observed in Raman spectroscopy of this film. As opposing tip specimen, S i tip ( R a d i u s" approximatelyl.0 mm) and diamond tip (R= 1.0 mm) were used. (2)Tribological evaluation methods Tribological properties were evaluated with a

reciprocating tribometer as shown in Fig. 1 in air under a humidity of 35-60% and a temperature of 15-20 °C. The plate specimen was moved by a hydraulic actuator. The opposite tip was slid against the plate specimen. Friction forces were measured by strain gauges attached to the plane spring. In order to evaluate boundary lubrication properties with water, sliding tests were performed at low friction velocity as 1.67 mm/s. 1.5 cm3 water is supplied on the surface. The test load was changed from 0.098 N to 1.96 N. 3. E X P E R I M E N T A L DISCUSSIONS

RESULTS

AND

3.1. Frictional properties

Fig. 2(a) shows the friction properties dependence on load with and without water lubrication. The friction coefficient of Si with Si tip shows comparatively high as ~t = 0.56 ---0.98 without water lubrication. This is deduced that same material of Si-Si easily adhered each other. Compared with dry friction, a friction coefficient of Si-Si tip with water lubrication shows slightly lower value as/z =0.18 - 0.50. In contrast, when a diamond is used as opposite tip material, a friction coefficient of Si is low as/z = 0.07 "~0.15 without lubrication. Furthermore with water lubrication, friction coefficient is as low as tz = 0.07. Friction coefficient of polished diamond film with

IZ ~ ~ - - ~

Tip

Sp

~Ty

~

Fig. i. Reciprocating

Specimen holder tribo tester.

125

---0-- Si/Si-tip(No lubricant) A m Si/Diamond-tip(No lubricant) D i a m o n d / D i a m o n d - t i p (No l u b r i c a n t )

10

' '- --

A

r.=l

I0

S i / S i - t i p (Water) S i / D i a m o n d - t i p (Water) D i a m o n d / D i a m o n d - t i p (Water)

10

.

:

[ I

"

!

+.~

1

o

.~-~

.

.

.

.

.

.

i i Hl~--4r "(

.~

O

-

i -4~111

1

) }

-

-

9,--0

-

~

ilr

: •

o

111/

"

~

~i~a~

k

!

=ii

ilC ~--'-

~.

i

i

--D

• 4.9

=

=Dr"

-

"~ O. 1

14P

_

0. I

_

! •

0.1

i~ 1

!

.--

•

i i

•

l

•

0.01

0.01 10 -1

10

Load (N) (a) Load

Fig. 2. F r i c t i o n c o e f f i c i e n t

0.01

_

10

-6

10

Contact area (b) Contact a r e a

-5

(mm2)

I

. . . . . . . 10

0

Hertzian stress

(GPa)

(c) Hertzian stress

dependence on load, c o n t a c t a r e a and H e r t z i a n s t r e s s .

diamond tip is the lowst as ~z = 0.05. The extremely low friction properties of diamond with water was studied [ 11 ] . These low friction properties of diamond seems to be deduced to the decreasing of contact area and low shear strength of water absorbed on diamond surfaces. The friction of diamond in air is generally low. The friction coefficient without water is not constant but decreases as load increases. The friction coefficient of diamond and Si with diamond tip without water shows a tendency to decrease as load increases. These friction coefficient dependences on load can be expressed as ~t = W -a. Generally, the friction coefficient shows a tendency to increase as load decreases. This is interpreted as simply arising from an adhesion mechanism, the area of contact is given by A=K1W 2/3. Assuming, as an upper limit, that the

true area is the same as the geometric, F=sA=sK1W~/3, where s is the specific shear strength of the imerface such that the coefficients of friction are proportional to W-l/3.

With water, the friction coefficient of diamnd and Si with diamond tip is low and nearly constant with load. However, the friction coefficient of Si with Si tip increases and fluctuates with load increase. This is deduced that the direct contact and adhesion increased. In a combination of Si with Si tip, a surface adsorbed layer was excluded by friction and adhesion between S i and S i tip increased. Friction coefficient dependence on contact area of Si with Si tip changes largely as shown in Fig.2(b). Water lubrication slightly decreases the friction coefficient. The friction coefficients of Si and diamond with diamond tip without water decrease with

126

Shear strength s of Si with Si tip with and without water lubrication can express as with s oc k A 0.71, and s oc kA 0.70, respectively. On the other hand, with a combination of Si and diamond tip, shear strength is expressed as s cc kA °2° without water lubrication. The inclination of shear strength of Si-diamond tip increases with water lubrication. By supplying water, the lubrication effect decreases with contact area increase. By using diamond tip, these inclinations of curves corresponded to the power of A with and without water are similar, respectively. The shear strength of Si and diamond tip is smaller than that of diamonddiamond tip both with and without water. The shear strength dependences on Hertzian stress are shown in Fig. 4. The shear strength of Si-Si tip with and without water, is expressed as s o: kP 1.43and s oc kP 140 as shown in Tab.2, respectively. Shear strength of diamond with water shows lower dependence on Hertzian stress than without water. Water lubrication increases the power of E The shear strength dependences of both Si and

contact area increase. While, the friction coefficient of diamond and Si lubricated with water is nearly constant independent of contact area. In contrast, The friction coefficient of Si with Si tip increases and fluctuates with contact area increase. Friction coefficient dependencies on initial Hertzian stress of diamond and silicon are shown in Fig. 2(c). By using diamond, the Hertzian stress increased. The relationship between the friction coefficient and initial Hertzian stress of Si and diamond film without water can be expressed as single straight curves, independent of the specimen material, similarly to the case with water lubrication.

3.2. Shear strength To estimate the boundary lubrication properties, the relation between shear strength and contact area is shown in Fig.3. The specific shear strength s of the interface increases with contact area increase. Shear strength dependences on contact area were evaluated by regression analysis as shown in Tab.1. [~

Si/Si-tip (No lubricant) Si/Diamond(No lubricant) Diamond/Diamond-tip(No lubricant)

- - ~ Si/Si-tip (Water) - - ~ Si/Diamond-tip(Water) . ~ Diamond/Diamond-tip(Water)

] /

~

1011

~ ~

Si/Si-tip (Water) / St/DiMond-tip (Water) Diuond/Viuond-tip(Water)

I

I011 I

0'°

Si/Si-tip (No lubricant) St/Diamond-tip (No lubricant) 1)iMond/Viaaond-tip(So lubricant)

z

1010

!

! _

!

=2

! ,o 9

i

Contact

10 ° i

lO-S

10-s area

I

I

i

i

10 °

Hertzian stress (GPa)

( N / m 2)

Fig. 3. Shear strength on c o n t a c t area.

Fig. 4. Shear strength on Hertzian stress.

Table 1. Shear s t r e n g t h on contact area.

Table 2. Shear strengh on Hertzian stress.

Specimen Si/Si-tip Si/Diamond-tip Diamond/Diamond-tip

iSpecimen Si/Si-tip

Lubricant No l u b r i c a n t Water

S - - 1 . 1 7 x 1011A0"2°

Si/Diamond-tip

No l u b r i c a n t

No l u b r i c a n t

S = l . 5 6 x 1012A°'46 S - - 3 . 4 9 X 1011AO.26

Diamond/Diamond-tip

No l u b r i c a n t

Water

S = 3 . 5 4 x 1012A°" 46

Lubricant No l u b r i c a n t Water No l u b r i c a n t

Experimental formula S-- 1.68 x 1014A°" 70 S--8.28 × 10t3A°'71

Water

Water Water

Experimental formula S----5 . 2 0 x 101°P L 4o S=2.14x S=9.24x S=5.19

101°P 1"43 10 9 p0.39 X

10 9 p0.91 ,

S = 7 . 3 9 × 10 9 p0. 53 S = 4 . 1 5 × 10 9 p0.92

127

(nm) 20

(nm) 20

1000

1000

10

50

10

Low humidity,

50

High humidity,

Load 0 (nN)

Load 0 (nN)

(a) Diamond film

(nm) 0.2

(nm) 2.0 1.00

1.0

1.00

0.1

.75

u./c> Low humidity,

75 )

1.00- t,,,,,)

High humidity,

Load 0 (nN)

Load 0 (nN)

(b) Si

Fig. 5. Surface profile of diamond and Si. diamond with diamond tip express as similar curve independent of the plate specimen materials, with and without water, respectivety. With water, the inclination of curve is larger than that without water lubrication. The effect of water lubrication decreases with a Hertzian stress increase. The lower shear strength of Si with diamond tip than that of diamond-diamond tip is deduced to the shear strength dependence on Hertzian stress. Surface roughness evaluated with AFM decreases with increasing humidity is attributed to the adsorbed water at the diamond film surface. The adsorbed water begins to increase at a humidity of about 50% as shown in Fig.5(a). However, the change of Si surface morphorogy such as roughness can not be observed between low and high humidity conditions as shown in

Fig.5(b). These adhered water on diamond film seems to work as good lubricant. 3.3. Friction coefficient d e p e n d e n c e s on friction n u m b e r of cycles and wear scar

Friction coefficient dependences on friction number of 4-kinds of combinations of Si and diamond are shown in Fig. 6 with and without water lubrication. Friction coefficient of Si-Si tip with and without water lubrication, a friction coefficient show a high value as lz - 0.74 -~ 0.78 and lz = 0.29 - 0.38 respectively. The friction coefficient of Si with diamond tip with and without water is low as 0.1. In the combination of Si and diamond tip, the effect of friction coefficient decreasing with water is larger than that of diamond-Si

128

~

1.0

Si/Si-tip Si/Diamond-tip Diamond/Si-tip Diamond/Diamond-tip

::t 0.8

~

O.20

Si/Si-tip(Water) Si/Diamond(Water) Diamond/Si-tip(Water) Diamond/Diamond-tip(Water)

~

O. 18

Si/Diamond-tip ~ Diamond/Si-tip Diamond/Diamond-tip

Si/Diamond-tip(Water) Diamond/Si-tip(Water) Diamond/Diamond-tip (Water)

O. 16

c

=L

L

L

Jk

or-I

o

.r'-I

q~ ¢D o

o

0.6

00.12

°v--I

q~ 0. I0

o 0 0.08

0.4

,*-* ..=

l| .

.

~ .

.

""

~ .

.

.

. t.

=

0.04

0.2 0

•

.

0.06

0

=-"

~

-,z,~

L

° e...~

0.02 0.0

,

0

I0

20

,

30

.¢

40

,

~

50

,

xw

60

,

x=.

70

,

xu-

80

,

x,..

90

,

O. O0

I00

Sliding cycle

~

0

'

10

'

20

'

30

'

40

'

50

"~

"

#,

70

80

90

i

60

100

Sliding cycle

Fig. 6. F r i c t i o n c o e f f i c i e n t dependences on s l i d i n g cycle. tip. With water lubrication, the friction coefficient of diamond with diamond tip especially decrease to 0.02 after 40 sliding cycles. Friction coefficient of a diamond with diamond show remarkable low friction with water lubrication E11 ]. Water adhered on the diamond surface is thought to decrease the direct contact. A friction coefficient of diamond-diamond tip decreases with a number of friction cycles with water lubrication. It is due to running in effect that lubricating water layer seems to be uniformuly formed on the surface. Sliding surfaces after 100 reciprocating sliding cycles are shown in Fig.7. The wear scar at 0.5 N of Si and diamond slid with Si tip and diamond tip with and without water lubrication. With Si tip, a remarkable damage was formed on the silicon surface, without water lubrication. The damage of Si slid with silicon is very large due to adhesion between similar materials. Further, with water lubrication, wear scar decreases and a plastic deformation was formed on the Si surface at more than 0.5 N load. In contrast, when a diamond is used as opposite tip material, the damage can not be observed on the silicon surface both with and without water. The sliding combination with diamond and silicon, the Hertzian contact stress is larger than that of silicon and silicon combination, however the damage of silicon slid with diamond can not be observed even without water boundary lubrication.

3.4. Contact stress analysis by a boundary element method To clarify the reason why damage free Si sliding with diamond tip, contact stress analysis was carded out by the boundary element method about each sliding combination. Analysis model of contact and analysis conditions were shown in Fig.8 and Tab.3 respectively. Principle stress o 1 o f Si-Si tip without water is shown in Fig. 9(a). Maximum tensile stress and compressive stress show higher value as corresponding to a friction direction. In this case, friction coefficient is as large as # = 0.76. A tensile stress becomes as large as o 1 " - 0.88 GPa. A compressive stress decreases to 0.32 GPa. Fig.9(b) shows principle stress o ~ o f Si-diamond tip( ~ = 0.14). Tensile stress decreases to o ~= 0.32 GPa on the side of a contact area. Shearing stress generally considered as starting point of plastic deformation or destraction was evaluated. In elastic contact of spherical and planar surfaces, the depth of maximum shearing stress is 0.47a, where, a is contact radius. The depth of maximum shear stress decreases by friction. Shearing stress analysis results of Si-Si tip are shown in Fig. 10. In the contact without friction, the depth of shearing stress becomes approximately 8 ~ m and becomes a almost half of a radius 16 ~ m of contact area. With a friction, stress increases, and the depth of maximum shearing stress moves to the

129

201zm ~~

lO0/zm S i / S i - t ip

Diamond/Si-tip

,,

¢',1

Si/Di amond-t ip

v

lO01zm S i/S i - t i p

Si/Di amond- t i p

Diamond/Si-tip

Diamond/Diamond-tip

Diamond/Diamond-tip

(b) Water

(a) No lubricant

Fig. 7. Profile of silicon and diamond sliding surfaces.

Table 3.

Tip

Sliding direct
Ax.

' ' '"1

-

0.6-

Ad/Ai 0.4-

¥. 0.20 0.1

1

•

I

I

I

I

I II1[

I

I

I

I

I II1[

"

,

~ r,q,J

.

.

1 10 100 V2 - ( A / b ) ( M 1 / 2 / L 1/2)

"

"@@~1% i

i

!

!

i!

!

'

'

''"'1

'

'

'

''"'1

0.80.6Ad/Ai

O.4-

%.

O.2O

0.I

I

I

I

I ' ' ''[

i

. . . . . . .

1 V2

-(A/b)(M1/2/L

I

10

,

,

, ~

1/2)

....

J..

100

Ad/Ai as a function of V2 with A Ax. Anisotropic: Ay/l~ - 2 (top), 4 (centre) and transverse (bottom).

Figure 4.

Figure 4 presents the results obtained for Ay/Ax - 2, 4, and for purely transverse, i.e. Ay = c~. For reference the predictions of Eq. (6) are presented. Figure 4 shows that for each ratio Ay/Ax the results fall on the curve obtained for the isotropic case. Deviations occur for smaller wavelengths but they seem to be a second order effect. It thus appears that the main behaviour for Ay > A~ is accurately described by Eq. (6) using A - A~ in V2. This is once more confirmed by Fig. 5 where all results for Ay > Ax are presented in one figure. 5.3. A n i s o t r o p i c : A~ > Ay Figure 6 shows the pressure and film as a function of X and Y for the same case as considered in Fig. 1 but with Ay/b - 0.5Ax/b - 0.25. For this case the value of the reduced amplitude was Ad -- 3.117 10 -3 --0.557Ai. By Eq. (5) the deformed amplitude Ad was defined as half the difference between the maximum value and the minimum value of the film thickness in X - Y - 0 taken over time. This implies that with increasing A~ the required monitoring time increases, i.e. the time before a full period of the oscillation has past. Thus, for the asymptotic case of purely longitudinal waviness (A~ - c~) no result can be obtained. To include this case a generalised definition of Ad is needed. In the

157

high pressure region the Reynolds equation reduces to a transport equation in the X direction. As in this region the film is nominally flat, the deformed amplitude could also be defined as:

0.8

X

i

_

i i

iii

I

i

i

i

i

i ii11

,X~/,Xy - - ( 2 0 ,X~/,Xy - - 2 + --1 . . . .

:~ ~2~.. OO-q-~='.

0.6

(7)

2Ad - max H ( X , O, To) - min H ( X , O, To) X

i

"" : % ; i ' " '

8+'..

Aa/Ai

where the maximum and minimum should be taken over a region of length at least Ax/b entirely in the high viscosity zone, and To is a time taken after which the contact has settled in the steady oscillation.

0.4 0 0.2 -

0 0.1

O

,

,

,

, t , ,,I

i

. . . . . . .

1

"o

I

~4-,'., .... j..

10

100

~2 - - ( ) ~ / b ) ( M 1 / 2 / L 1 / 2 ) 2,00

Figure 7. Ad/Ai as a function of V : with A - Au, for Ay/A~ - 1, 0.5, and longitudinal.

1.0C

Y

O,OO

0.50

-~.o5 ~

-o.so \

-2,

O0

-1.50

g

" -2.50

0,00

For A~/b < 1 (7) and (6) should give the same result, i.e. as long as the value determined by (7) is not influenced by the global changes in X direction of the film. For the isotropic case it was also noticed that the amplitude of the film thickness variations in Y direction at a given instance (taken after the solution has settled) was the same as the amplitude in X direction, as long as the wavelength Ay/b was sufficiently small compared to the size of the contact. Thus it appears that the deformed amplitude could also be taken as:

2Ad -- max H ( X , Y, To) - min H ( X , Y, To) (X,Y)

0.00

i!:i';:!'i;i!!i!::!;iiiiii:.!~i:i!i:!;!i! i:;:ii:!i;i!iii?:?!::'i::'!::':':'..,,--'~ '"

O. 5[J

-0,50 -1.50 -2,00

g

" -2.50

Figure 6. Snapshot of P (top) and H (bottom) as a function of X and Y, under pure rolling Au = b/4, ~ - 2Ay, Ai - 0.2He, M - 1007.6, L = 12.05.

(X,Y)

(8)

with To as before, and the maximum and minimum taken over a sufficiently large region (at least of size £x/b x Ay/b, and well inside the high viscosity region, or more specifically well inside the region in which the film thickness for the steady state is nominally fiat. For £x/b and Ay/b smaller than unity this generalisation remained valid for anisotropic waviness. Consequently, this generalised definition of Ad was used to study the longitudinal waviness A~ = oc, where it reduces to:

2Ad -- m a x H ( X o , Y, To) - m i n H ( X o , Y, To). (9) Y

Y

Figure 7 shows A d / A i as a function of V2 with in U2 taken A - Ay. For clarity, results of

158

only two cases are presented, i.e. Ay/A, = 0.5 and purely longitudinal. For comparison the curve obtained for the isotropic case is also drawn. Figure 7 shows that for each Ay/Ax again a single curve is obtained but it is shifted to the left compared to the isotropic curve. The total shift going from isotropic to longitudinal however is limited and relatively small. It appears that the different results can be scaled onto a single line once again if they are presented as function of f(r)V2 with:

f(r)

-

-

waviness (Ay = oc). For anisotropic waviness with Ax > )ty, once again a reduction to a single curve was obtained when choosing as a dimensionless coordinate the product V2 f(Ax/Ay) using A - Ay in V2. This includes the stationary case of pure longitudinal waviness (A~ = oc) but to include this last case a generalisation of the definition of the deformed amplitude Ad was needed. All cases can be combined in a single equation:

Ad

(10)

e 1--~

1

Ai = 1 + 0.15](r)V2 + 0.015(](r)V2) 2

with r - Ax/Ay. This is shown in Fig. 8. Thus, Eq. (6) accurately describes Ad/Ai if V2 is replaced by f(A,/Ay)V2, and A - Ay is used in V2.

where

f(r) •

•

.i . i

-T-' ' '.'I " ""~" "~I

........

I

........

i

2

0.8 =

1

.

ifr>l otherwise

with

r-Ax/Ay,

.

V2

.

0.6

-

(A/b)(M1/2/L 1/2) with A

-

min(Ax,Ay)

REFERENCES

Ad/Ai 0.4 0.2

el_! 1

and

+ .

(11)

-

0 0.1

-

,

n i i i n ,,i

1

i

i

i i , , ,,i

10

I iq

|i

.

.

100

Ad/Ai as a function of f(Ax/Ay)V2 with A - Ay. Anisotropic: A~ > Ay.

Figure 8.

6. C o n c l u s i o n Based on numerical simulations for many cases a simple relation is derived for the amplitude reduction of anisotropic harmonic surface patterns. For isotropic waviness with A~ - Ay - A all amplitude reduction results fall onto a single curve using the dimensionless coordinate V2 (A/b)(M1/2/L1/2). For anisotropic waviness with Ay > Ax an identical single curve was found when choosing the dimensionless coordinate V2 with A - Ax, including the case of pure transverse

1. Lubrecht, A.A., (1997), "Influence of Local and Global Features in EHL Contacts," Proc. 23rd Leeds-Lyon Symposium on Tribology, Ed. D. Dowson et al., Elseviers Tribology Series, 32. pp. 17-25. 2. Wedeven, L.D., and Cusano, C., 1979, "Elastohydrodynamic Film Thickness Measurements of Artificially Produced Surface Dents and Grooves," ASLE Trans., 22, 369-381. 3. Kaneta, M., and C a m e r o n , A., 1980, "Effects of Asperities in Elastohydrodynamic Lubrication," ASME JOT, 102, 374-379. 4. Kaneta, M., 1992, "Effects of Surface Roughness in Elastohydrodynamic Lubrication," JSME, III, 35, 4, pp. 535-546.

5. Kaneta, M., Sakai, T., and Nishikawa, H., 1992, "Optical Interferometric Observations of the Effects of a Bump on Point Contact EHL," ASME JOT, 114, pp. 779-784. 6. Kaneta, M., Sakai, T., and Nishikawa, H., 1993, "Effects of Surface Roughness on Point Contact EHL," STLE Trib. Trans., 36,4, pp. 605612. 7. Kaneta, J., Kanada, T., and Nishikawa, H., (1997), "Optical Interferometric Observations of

159

the Effects of a Moving Dent on Point Contact EHL," Proc. 23rd Leeds-Lyon Symposium on Tribology, Ed. D. Dowson et al., Elsevier Tribology Series 32, pp. 69-79. 8. Bush, A . W . , a n d Skinner, P.H., (1982), "Surface roughness effects in Point Contact Elastohydrodynamic Lubrication, " WEAR, 83, 285301. 9. Goglia, P.R., Cusano, C., and Conry, T.F., 1984, "The Effects of Surface Irregularities on the Elastohydrodynamic Lubrication of Sliding Line Contacts. Part I - Single Irregularities," ASME JOT, 106, 104-112. 10. Goglia, P.R., Cusano, C., and Conry, T.F., 1984, "The Effects of Surface Irregularities on the Elastohydrodynamic Lubrication of Sliding Line Contacts. Part I I - Wavy Surfaces," ASME JOT, 106, 113-119. 11. Lubrecht, A.A., t e n Napel, W . E . , and B o s m a , R., (1988), "The Influence of Longitudinal and Transverse roughness on the Elastohydrodynamic Lubrication of Circular Contacts," ASME JOT, 110, 421-426. 12. B a r r a g a n de Ling, FdM, Evans, H.P., Snidle, R . W . , 1989, " MicroElastohydrodynamic Lubrication of Circumferentially Finished Rollers: The Influence of Temperature and Roughness," ASME JOT, 111, pp. 730736. 13. Kweh, C.C., Evans, H.P., and Snidle, R . W . , 1989, "Micro-Elastohydrodynamic Lubrication of an Elliptical Contact with Transverse and Three-Dimensional Roughness," ASME JOT, 111, 577-583. 14. Lee, R . T . , a n d H a m r o c k , B.J., 1990, "A circular non-Newtonian Fluid Model: Part I I used in Micro-Elastohydrodynamic Lubrication," ASME JOT, 112, 497-505. 15. Venner, C.H., a n d t e n Napel, W . E . , (1992), "Surface Roughness Effects in an EHL Line Contact," ASME JOT, 114, pp. 616-622. 16. E h r e t , P., Dowson, D., a n d Taylor, C.M., "Waviness Orientation in EHL Point Contact," (1996), Proc. 22nd Leeds-Lyon Symposium on Tribology, Ed. D. Dowson et al., Elsevier Tribology Series 31, pp. 235-244. 17. Chang, L., Cusano, C., and Conry, T.F., 1989, "Effects of Lubrication Rheology and Kinematic Conditions on Micro- Elastohydrodynamic Lubrication," ASME JOT, 111,344-351. 18. Venner, C.H., L u b r e c h t , A.A., and ten Napel, W . E . , (1991), "Numerical Simulation of

the Overrolling of a Surface Feature in an EHL Line Contact," ASME JOT, 113, pp. 777-783. 19. Chang, L., and W e b s t e r , M.N., 1991, "A Study of Elastohydrodynamic Lubrication of Rough Surfaces," ASME JOT, 113, 110-115. 20. Chang, L., 1992, "Traction in Thermal Elastohydrodynamic Lubrication of Rough Surfaces," ASME JOT, 114, 186-191. 21. Osborn, K.F., a n d Sadeghi, F., 1992, "Time Dependent Line EHD Lubrication Using the Multigrid/Multilevel Technique", ASME JOT, 114, 68-74. 22. Ai, X., Cheng, H.S., and Zheng, L., 1993, "A Transient Model for Micro-Elastohydrodynamic Lubrication with Three-Dimensional Irregularities," ASME JOT, 115, pp. 102-110. 23. Ai, X., and Cheng, H.S., 1994, "The Influence of Moving Dent on Point EHL Contacts," STLE Trib. Trans., 37, pp. 323-335. 24. Ai, X., and Cheng, H.S., 1994, "A Transient EHL Analysis for Line Contacts with a Measured Surface Roughness using Multigrid Technique," 25. Ai, X., and Cheng, H.S., 1996 "The Effects of Surface Texture on EHL Point Contacts," ASME JOT, 118, pp. 59-66. 26. Venner, C.H., and Lubrecht, A.A., 1994, "Transient Analysis of Surface Features in an EHL Line Contact in the case of Sliding," ASME JOT, 116, pp. 186-193. 27. Venner, C.H., and Lubrecht, A.A., 1994, "Numerical Simulation of a Transverse Ridge in a Circular EHL Contact, under rolling/sliding", ASME JOT, 116, pp. 751-761. 28. Venner~ C.H., and Lubrecht, A.A., 1994, "Numerical Simulation of Waviness in a Circular EHL Contact, under rolling/sliding", Proc. 20nd Leeds-Lyon Symposium on Tribology, Ed. D. Dowson et al., Elsevier Tribology Series 30, pp. 259-272. 29. Couhier, F., Lubrecht~ A.A., Nelias, D., and F l a m a n d , L., 1996, "Influence of the Sliding Speed on the Elastohydrodynamically Lubricated Film Thickness Shape of Wavy Contacts," Proc. 22nd Leeds-Lyon Symposium on Tribology, Ed. D. Dowson et al., Elsevier Tribology Series 31, pp. 515-526. 30. Venner, C.H., and Lubrecht, A.A., 1996, "Numerical Analysis of the influence of Waviness on the Film Thickness of a Circular EHL Contact", ASME JOT, 118, pp. 153-161. 31. Ehret, P., Dowson, D., and Taylor, C.M. "Time-Dependent Solutions with Waviness and

160

32.

33 ¸.

34.

35.

Asperities in EHL Point Contacts," Proc. 23rd Leeds-Lyon Symposium on Tribology, Ed. D. Dowson et al. Elseviers Tribology Series, 32, pp. 313-324. Lubrecht, A.A., and Venner, C.H., 1992, "Aspects of Two-Sided Surface Waviness in an EHL Line Contact," Proc. 19th Leeds-Lyon Symposium on Tribology, Ed. D. Dowson et al., Elsevier Tribology Series, 25, pp. 205-214. Venner, C.H., and Morales Espejel, G.E., "Amplitude Reduction of Small Amplitude Waviness in EHL Line Contacts", Submitted to ImechE, Part J, Journal of Engineering Tribology. Lubrecht, A.A., 1987, "Numerical Solution of the EHL Line and Point Contact Problem Using Multigrid Techniques," Ph.D. Thesis, University of Twente, Enschede, The Netherlands, ISBN 909001583-3. Lubrecht, A.A., B r e u k i n k , G.A.C., Moes, H., t e n N a p e l , W . E . , a n d Bosma, R., 1987, "Solving Reynolds' equation for EHL Line Contacts by Application of a Multigrid Method," Proc. 13th Leeds Lyon Symposium on Tribology, Elsevier Tribology Series 11, Ed. D. Dowson et al., pp.175-182.

36. Lubrecht, A.A., ten Napel, W.E., and Bosma, R., (1987), "Multigrid, an Alternative Method of Solution for Two-Dimensional Elastohydrodynamically Lubricated Point Contact Calculations," ASME JOT, 109, 437-443. 37. Venner, C.H., 1991, "Multilevel Solution of the EHL Line and Point Contact Problems," Ph.D. Thesis, University of Twente, Enschede, The Netherlands. ISBN 90-9003974-0. 38. Greenwood, J.A., and Johnson, K.L., 1992, "The Behaviour of Transverse Roughness in Sliding Elastohydrodynamically Lubricated Contacts," WEAR, 153, pp. 107-117. 39. Morales Espejel, G.E., 1993, "Elastohydrodynamic lubrication of smooth and rough surfaces," PhD. Thesis, University of Cambridge, Department of engineering. 40. Greenwood, J.A., and Morales Espejel, G.E., 1994, "The Behaviour of Transverse Roughness in EHL Contacts," Proc. IMechE, 208, pp. 121-132. 41. Greenwood, J.A., and Morales-Espejel, G.E., (1997), "The Amplitude of the Complementary Function for Wavy EHL Contacts," Proc. 23rd Leeds-Lyon Symposium on Tribology, Ed. D. Dowson, Elsevier Tribology Series, 32, pp.

307-312. 42. Couhier, F., 1996, "Influence des Rugosites de Surface sur les Mecanismes de Lubrification de Contact Elastohydrodynamique Cylindre-Plan", (in French) Ph.D. Thesis, INSA de Lyon, France. 43. Venner, C.H., Couhier, F., L u b r e c h t , A.A., and Greenwood, J., (1997) "Amplitude Reduction of Waviness in Transient EHL Line Contacts," Proc. 1996 Leeds Lyon Tribology Conference, Elsevier Tribology Series 32, Ed. Dowson et al., pp. 103-112. 44. Lubrecht, A.A., Graille, D., Venner, C.H., and Greenwood, J.A., (1997), "Waviness Amplitude Reduction in EHL Line Contacts under Rolling-Sliding, " ASME JOT, in press. 45. Hooke, C.J., 1997, "Surface Roughness Modification in Elastohydrodynamic Line Contacts operating in the elastic Piezoviscous Regime,", Proc. Inst. Mech. Engrs Part J., V 212, in press 46. Dowson, D., and Higginson, G.R., 1966, "Elastohydrodynamic Lubrication, The Fundamentals of Roller and Gear Lubrication," Pergamon Press, Oxford, Great Britain. 47. Roelands, C.J.A., 1966, "Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils" Ph.D. Thesis, Technical University Delft, Delft, The Netherlands, (V.R.B., Groningen, The Netherlands). 48. Venner, C.H., "Higher Order Multilevel Solvers for the EHL Line and Circular Contact Problem," ASME Journal of Tribology, 116, pp. 741-750. 49. Lubrecht, A.A., and Venner, C.H., 1998, "Elastohydrodynamic Lubrication of Rough Surfaces, " To appear in special issue of ImechE part J, Journal of Engineering Tribology. 50. Private communication/discussion with Drs C.J. Hooke and J.A. Greenwood A. Accuracy For time dependent problems great care must be taken to obtain accurate results. Reynolds' equation in the high viscosity region reduces to an "advection-diffusion" equation: ~

O(fiH)

OX

O(fiH) _ 0

(12)

OT

where $'~ symbolises a differential operator, i.e. in this case the poisseulle terms. The solution in the limit of small ~'~ is fiH ~ ( ~ H ) ( X - T), i.e. variations of (fill) are propagated along the charac-

161

teristic X - T without any change of amplitude. The solution for small ~'~ will show the same behaviour, except that the effect of a small viscous terms is that the amplitude of an oscillatory component in the solution will not be a constant but slowly decay, depending on the (local) value of ~ . It can easily be shown that the solution to the discretised problem up to a higher order terms will satisfy:

$.

cO(fill) OX

O(fiH) ~ TAx,AT = 0 OT

1.2

I

SU2 o NU2 + 0.8 +

Ad/Ai

0.6

(13)

0.4

where wax,AT is the truncation error made in the discretisation. If this error is sufficiently small compared to 9r~ the discrete solution will mimic the physical behaviour of the continuous solution. However, if 9r~ is very small, as is the case in E H L the discrete solution may show viscous effects, e.g. amplitude reduction (or phase shift), caused by the truncation error, which are thus mesh size dependent. Indeed, with decreasing mesh size the truncation error decreases and eventually on very fine grids and using very small time steps one will converge to the right continuous solution, but this only occurs on grids where 9r~ starts to dominate r. In fact, as long as this stage is not reached one simply obtains a solution for a case with much larger viscous effects than should occur for the given operating conditions. This for example shows up as amplitude decay in the solution as a function of space to an extend much larger than the real viscous term could ever account for. These effects will be very strong when a first order discretisation is used, see Venner [37][chapter 8], and [26]. Therefore, generally a second order discretisation should be used. A convenient choice is to separately discretise the wedge and squeeze term with the well known upstream second order discretisation, e.g. see [48, Appendix B], the so-called SU2 scheme (Standard Upstream 2nd Order). In CFD many alternative discretisations for the advective part of (13) can be found. Of particular interest are the so-called narrow schemes. Instead of discretising both terms separately, the combined term (fiH)x + (fiH)T is discretised using a given set of points and demanding a prescribed order of accuracy. Stability of the discretisation

0.2

+

I

0

32

+

I

+

I

64 96 1/Ax

I

128

160

Figure 9. Ad/Ai as a function of the mesh size (timestep) M - 1007.6, L - 12.05, and ) ~ x / b )~y/b- 0.5 ( A x - A y -- AT).

1.2

I

I

I

+ 0.8

Ad/Ai

I

SU2 o NU2 + +

+

0.6 0.4 0.2 o [

0

32

I

I

64 96 1/Ax

I

128

160

Figure 10. Ad/Ai as a function of the mesh size (timestep) M - 1007.6, L - 12.05, and ) ~ x / b )~y/b- 0.25 ( A x - A y - - A T ) .

162

(not amplifying components in the solution) may then require the use of one or more stencils with angles smaller than 90 degrees, together covering all possible directions in the flow each in a manner as narrow as possible. This makes the discretisation formula a bit more complex, but this disadvantage is often outweighted by the gain in accuracy. An example of a second order discretisation thus derived is the narrow upstream scheme "NU2", see [33]. As an example Fig. 9 shows A d / A i as a function of the mesh size obtained with the SU2 and N U 2 schemes for the load case displayed in Fig. 1 with ,,kx/b = Ay/b = 0.5. The figure shows that both schemes converge to the same value for sufficiently fine grids but, even though both schemes are second order, on coarser grids the result obtained with the S U 2 scheme is less accurate. This effect will be stronger if the wavelength is smaller, see Fig. 10, where A d / A i as a function of the mesh size is shown for Ax/b = Ay/b = 0.25. For this case Fig. 11 and 12 show how the differences in accuracy show in the solution, i.e. in the film profile at the line Y - 0 as a function of X. Two effects c a n be observed. Firstly, with decreasing mesh size the level around which the film thickness oscillates converges in the same way as the central film thickness converges for the steady state solution. This behaviour, by definition, is the same for both the N U 2 and S U 2 results. Secondly, the amplitude of the oscillation itself converges. This latter behaviour is governed by the truncation error in the transient equation. Here the difference between the two schemes clearly shows. Even though the SU2 scheme is second order too, and also has a truncation error that vanishes for the characteristic component X = T (for AT -- A x ) , its results, for this high load and small wavelength case, exhibit an almost complete amplitude reduction on the coarsest grids. Only for A x = 1/128 it becomes small. The N U 2 results are much more accurate. Even on the coarsest grids there is no amplitude reduction. However, on these grids there is a slight phase error (related to higher order terms in T). Thus, compared with SU2 already on coarse grids it gives a good approximation to the appropriate "physical" behaviour of the continuous equations.

I

I

0.05

H

.

I

1/16 1/32 . . . . . 1/64 1/128 . . . .

0.03

0.01

.....

-1

----h

I

I

I

-0.5

0 X

0.5

Figure 11. Film thickness at the line Y = 0 as a function of X for M = 1007.6, L = 12.05, and Ax/b = Ay/b = 0.25 obtained using the S U 2 scheme as a function of A x ( A x = A y = A T ) .

0.06

I

I

I

1/16 1/32 . . . . . 1/64 1/128

0.04 H 0.02

-1

-0.5

0 X

0.5

Figure 12. Film thickness at the line Y = 0 as a function of X for M = 1007.6, L = 12.05, and Ax/b = Ay/b = 0.25 obtained using the N U 2 scheme as a function of A x ( A x = A y = A T ) .

1

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

163

Thin film, time dependent, micro-EHL solutions with real surface roughness. C D Elcoate t , H P Evans, T G Hughes and R.W. Snide. School of Engineering, University of Wales Cardiff, Cardiff, CF2 1XH This paper gives results of a time dependent analysis of the elastohydrodynamic (EHL) contact between a smooth disk and a rough one taken from a scutfing experiment. The rough steel surface is finished by transverse grinding and a line contact EHL model is used which can be expected to give a good approximation to conditions on the contact centre-line. A non-Newtonian fluid model is adopted and the EHL equations are solved using a coupled method. Results are obtained for situations where the micro contact film thicknesses are considerably smaller than the typical roughness dimensions. It is found that within the Hertz contact area the local shape of the deformed surfaces is controlled by the direction of relative sliding. Detailed roughness features only influence the hydrodynamic pressures (a) when the contact is in pure rolling, and (b) in the case of sliding when the micro contact film thickness is very thin compared to the roughness. 1. I N T R O D U C T I O N

The mechanism responsible for the protection of the surfaces of heavily loaded rolling/sliding contacts such as those between gear teeth is elastohydrodynamic lubrication (EHL). However, an important feature of gear tooth contacts is that the surfaces produced by present day manufacturing methods have roughness features that are of the same order or even significantly greater than the predicted thickness of the EHL film. Consequently they operate under conditions described as "partial", "mixed" or "micro" EHL. In available theoretical solutions of both the dry contact and micro-EHL problems the presence of significant roughness leads to a severe tippling in the contact pressure distribution with maximum values far in excess of the Hertzian values expected when the surfaces are perfectly smooth. A practical problem which is directly associated with these effects in hardened steel gears is that of "micropitting". This is pitting (rolling contact fatigue) on the scale of the roughness, as opposed to classical pitting which is on the scale of the nominal Hertzian contact. With increased use of hardened gears micropitting has become of widespread concern. The work reported in this paper forms part of an ongoing study of the lubrication of gear tooth t now at Frazer Nash Consultancy Ltd, Bristol.

surfaces with the specific aim of developing a fundamental understanding of the physical mechanisms of micropitting. Factors which affect the formation or otherwise of a lubricant film in such contacts include average and relative surface speeds, load, temperature, lubricant properties and component surface finish. Film-forming conditions in heavily loaded, high temperature gearboxes used in aerospace practice (for example) are often particularly severe because of the need to operate with relatively thin oils. A surface roughness R a value of 0.4 p.m is typical for such gears which must be considered in the context of typical predicted film thickness values in the range 0.05 - 0.5 p.m. If micro-EHL theory is to be of any use in helping to understand problems such as micropitting it must therefore be capable of modelling contacts having ~ ratios of 0.1 or less. Numerical modelling of rough surface EHL contacts has been undertaken by numerous investigators in recent years. Initial efforts involved stationary idealised roughness features Goglia et al. (1984), Lubrecht et al. (1988), Chang et al. (1989) and Kweh et al. (1989). Real roughness features were introduced by Venner and ten Napel (1992) who used a roughness profile with an R~ of 0.04 p.m, and by Kweh et al. (1992) who

164

used a profile with an R a of 0.3 txm that was of the same order as the film thickness. Transient effects have been studied by Chang and Webster (1991), Venner and Lubrecht (1994) and Greenwood and Morales-Espejel (1994) using sinusoidal features or waveforms. Chang Webster and Jackson (1993) and Chang and Zhao (1995) have drawn attention to the difference between Newtonian and non-Newtonian lubricant models in transient micro-EHL. Real roughness was included in a transient line contact by Ai and Cheng (1994). More recently transient point contact analyses have been presented by Venner and Lubrecht (1996) using sinusoidal features and Xu and Sadhegi (1996) using measured roughness data. Where real roughness data has been incorporated in transient solutions it is generally of a relatively low amplitude compared to the film thickness in the numerical solution. This is indicative of the numerical difficulties that occur when the roughness features are large compared to the residual film thickness. The work reported in this paper follows on from an investigation into the benefits of coupling the elasticity and flow equations Elcoate et al (1998). This technique was described by Okamura (1982) who used a fully coupled Newton-Raphson model. This was subsequently extended by Houpert and Hamrock (1986) to enable analysis of heavily loaded, smooth line contacts assuming Newtonian lubricant behaviour. The advantages of coupling the elastic and hydrodynamic equations have not been exploited in the past because of the resulting 'full matrix' problem and the computing resources required to solve it. These difficulties have been largely overcome by the authors (Evans and Hughes, Elcoate et al (a)), so that time dependent models using this technique are now realistic as demonstrated in this paper.

2. NOTATION b

El, E2 E'

Hertzian semi-dimension. Young's moduli of the two surfaces. 2 / E ' = ( 1 - v 2 ) / E l + ( 1 - v2)/E2 .

h hmin

film thickness. minimum film thickness. heffeetiveeffective film thickness. p pressure. R radius of relative curvature. l / R = 1/R 1 + I / R 2. R l, R2 radius of curvature of the surfaces. Ra Roughness average of surface. u elastic deflection. O mean entraining speed = (Ul + U2) / 2. U l, U 2 surface speeds relative to contact. load per unit length. W! co-ordinate in direction of rolling. x pressure viscosity coefficient. o~ parameters in density relationship. )', K heffective/Ra

rl rio p Po 1;0 V 1, V 2

viscosity viscosity at zero pressure density. density at zero pressure. Eyring shear stress. Poisson's ratios of the two surfaces. slide roll ratio = 2(U1- U2)/(U l + U2).

Other symbols are defined in the text. 3. FORMULATION In conventional involute gears the teeth are finished in a direction transverse to that of rolling/sliding and contact is nominally along a line. The results presented in this paper have therefore been obtained with a one dimensional EHL line contact model. Both surfaces are treated as semi-infinite elastic solids so that the displacement normal to the surface is given by:

ux/=- ~E---4I7 p(s) 1

r

ds

--o0

where r is the co-ordinate of the point (usually 2b downstream of the contac0, relative to which the displacement is established. The film thickness is given by: h(x) = q)(x, t) - ~ 4 f°° p(s) I l n[x - : ds + C ~E' -~o r

(1)

where qo(x,0 incorporates both the relative curvature of the two surfaces and the measured

165

roughness of the run-in, ground surface. The constant C is selected to obtain the required load. Isothermal conditions are assumed and the viscosity and density of the lubricant are taken to depend on pressure as follows: 11= rioe l+yp P=Po~ l+Kp The non-Newtonian flow equation adopted is the second order, one dimensional, modified Reynolds equation developed by Conry et al. (1987) to which the appropriate squeeze film term is added to enable time dependence to be considered. ~ph)

t9 (lah 3 o~pS/ - U/9(0h)

(2)

where: S = 3(X cosh X - sinh E) I

E3

1+

1~2(U2 _ U1)2

)-,2

x2h2

sinh 2 5".

and: E= h c3P 2x 0 tgx The representative shear stress, x0, beyond which level the fluid response is non-Newtonian is taken as constant. An implicit formulation for the time dependent term in equation (2) is adopted and each time step

consists of a small number of iterative cycles (typically 4) within which linearised numerical representations of equations (1) and (2) are solved in a coupled scheme as described by Elcoate et al

Co). A finite element method using the weak formulation of the Galerkin weighted residual approach has been adopted to solve equation (1). The domain is discretized using one dimensional quadratic elements and the numerical integration of the resultant equations is carded out on a local elemental level by 3 point Gauss quadrature. 4. ROUGHNESS MODEL

The roughness data used for qo(x,t) is taken from a test disc using a surface profilometer. The ground surface analysed was that from a well run in but unscuffed experimental disc. The disc measured was one used by Patching (1994) in a two disc scuffing rig. The disc was manufactured by transverse grinding to simulate the finish found on gear teeth in aerospace auxiliary gearboxes. The initial distribution of surface heights at manufacture was essentially Gaussian. After running the surface was measured in a circumferential direction along the centre of the running track with heights taken at a spacing of 3.5 ~tm. The resultant profile is shown in Figure 1, where the rounding off of asperity tips caused by the running-in process is apparent. The profile has an R a value of 0.32 ~tm with maximum peak to valley dimensions of

3.0 2.5 '~::L 2.0

"i~

1.5

1.0 0.5 0.0 0

250

500

750

1000

1250

Traverse/Itm

Figure 1. Section of surface profile used in contact (metal above curve) showing extent of running-in.

1500

166

specifies the parameters that remain unchanged in the analysis. The load adopted results in a smooth surface Hertzian contact having b = 0.358 mm and a maximum Hertzian contact stress of 1.07 GPa.

approximately 2 p.m. The resolution adopted for the profilometer gives approximately 200 height measurements over the Hertz contact area. A cubic spline interpolation is used to provide surface heights at intermediate points as required at each timestep in the time dependent solution. In this way the surface is always represented by the same collection of piecewise cubic splines. This approach has been found useful in eliminating spurious squeeze film effects that can be introduced in interpolating between measured height values. The computing nodes are fixed relative to the point of contact so that there is no time dependence of the basic curvature terms of the two surfaces.

Table 1 Conditions assumed for the real rou~:hness analyses R 19.05 mm xo 5.0 MPa w' 600 kN/m rio 0.0048 Pas E 227.3 GPa cz 11.1 GPa "1 The behaviour of the rough surface in this EHL contact can most easily be appreciated by constructing an animated sequence of film and pressure distributions as the time steps progress. The striking feature that becomes apparent in viewing this animation is that the film thickness on an individual micro contact is formed at the inlet to the Hertz area and the deformed shape of the asperity then progresses through the contact in a broadly unaltered way. The pressure distribution associated with the deformed shape keeps pace with the micro contact as it moves. This is in contrast to earlier studies e.g. Venner and Lubrecht (1994)

5. REAL ROUGHNESS RESULTS Results were obtained for a sequence of eleven slide-roll ratios ~ = ± 2, ± 1.2, ± 0.6, ± 0.3, ± 0.15 and 0.0. The convention adopted is that positive values have the rough surface moving faster and case ~ = -2 has a stationary rough surface for which the problem is not time dependent. A range of three entraining velocities was used to simulate different film thickness conditions. Table 1 2.0

10.0

1.5

7.5

1.0

5.0

j

0.5

ft

'%

2.5

0.0

0.0

-2.5

-0.5 -1.5

-1

-0.5

0

0.5

1

1.5

x/b Figure 2. Pressure, film thickness and undeformed roughness profile (thin curve) shown at time step 5000.

167

2.0

10.0

1.5

7.5

//// V

S oo

--~

~"-

J

oo

-0.5

-2.5 -1.5

-1

-0.5

0

0.5

1

1.5

x/b Figure 3. Pressure, film thickness and undeformed roughness profile (thin curve) shown at time step 5500. where film shape disturbances were seen to move through the Hertz contact area at the entrainment velocity.

and film thickness at two such positions for the case of ~ = - 0 . 3 (timestep 5000 and 5500). The entrainment velocity of 25 m/s results in minimum film thicknesses of the order 0.12 ~tm as the different surface roughness features pass through the contact area. This compares with a Dowson and Higginson smooth surface value of 0.43 ~tm.

Figures have been obtained with the rough surface profile in a number of fixed positions which are offset by 0.5b. Figures 2 and 3 show the pressure 2.0

10.0

1.5

I I

7.5

J t~

C,~ 1.0

5.0

g~

0.5

V

"1/

p

r

2.5

0.0

0.0 -1.5

-1

-0.5

0

0.5

1

1.5

Figure 4. Pressure (heavy curve) and film thickness (thin curve) for section of profile at five timesteps during traverse of contact area with { = -0.6. Undeformed roughness profile for section also shown at top left.

168

3 .-¢ 2

0

0.1

0.2

0.3

0.4

0.5

Figure 5. Superimposed film thickness at five positions during traverse of contact area with g = -0.6. entry to the Hertz contact, at three positions within the contact and at the exit to the contact. (The second and third positions correspond to the timesteps illustrated in Figures 2 and 3 for ~ = -0.3) The deformed shape of the micro contact can be seen to be essentially the same within the Hertz contact as it progresses from entry to exit. This is emphasised in Figure 5 where the five timesteps have been aligned with each other and drawn on a larger scale.

Between the two timesteps illustrated the surface features have moved through 0.5 b and can clearly be recognised not only in the undeformed geometry shown offset at the bottom of the figure, but also in the deformed geometry of the contact. A particular length of surface defined by 100 node points and its associated pressure distribution is shown in Figure 4 at five positions during its transit of the contact area with ~= -0.6. It is shown at the 2.0

1.5

10.0

F_ I

7.5

1.0

5.0

0.5

2.5

,.=

g~

0.0

0.0 -1.5

-1

-0.5

0

0.5

1

1.5

x/b Figure 6. Pressure (heavy curve) and film thickness (thin curve) for section of profile at five timesteps during traverse of contact area with ~ = 0.6. Undeformed roughness profile for section also shown at top left.

169

3 :::L 2

0

0.1

0.2

0.3

0.4

0.5

x/b Figure 7. Superimposed film thickness at five positions during traverse of contact area with ~ = 0.6. adjusting to the sense of the relative motion of the surfaces. In Figure 5, the smooth surface is moving faster so that the inlet to the micro contacts is on the left, and the micro contacts align so that they form a converging film in the direction of entrainment relative to the micro contact. When the direction of sliding is reversed then so is the slope tendency of the micro contacts. In Figure 7 the rough surface is moving faster so that relative to

Figures 6 and 7 show the corresponding results when the slide roll ratio has the opposite sign, i.e. = 0.6. Again the deformed shape of the micro contact can be seen to be essentially the same throughout the contact with the pressure form adjusting to produce this shape at the various locations. A comparison of figures 5 and 7 shows that the deformed shape within the contact is 1.5

4

1.0

~

2 0.5 1

0.0

0

-1.5

-1

-0.5

0

0.5

1

x/b Figure 8. Pressure and film thickness at the same profile position with ~ = -1.2, -0.6 and -0.3.

1.5

170 4

1.5

3 1.0

b

i

0.5

0.0

.5

-1

-0.5

0

0.5

1

1.5

x/b Figure 9. Pressure and film thickness at the same profile position with ~ = 1.2, 0.6 and 0.3. the asperity entrainment is from fight to left, i.e. in the opposite sense to the entrainment of the whole contact. Once a micro contact is within the Hertz contact area the deflected shape adjusts so that a converging film is again formed in the direction of entrainment relative to the micro contact. This observation supports the basic assumption made by Evans and Snidle (1996) in proposing a scuffing failure model based on side leakage from deep valley features. The effect of magnitude of sliding speed is also interesting. When cases are compared at the same position of roughness there is considerable similarity between those having the same sign of ~, with the case ~ = 0 emerging as a clearly very special case. Figure 8 compares cases with = -1.2, -0.6 and -0.3 for a particular roughness location. The deflected shape of the micro contacts can be seen to be similar with differences in micro contact film thicknesses in the Hertzian region. At the inlet the smallest film on a micro contact occurs for the case with the highest sliding speed, but the position is reversed for micro contacts in the exit where the smallest film thickness is associated with the lowest sliding speed. The differences in pressure between the three cases follow a

corresponding pattern as can be expected from elasticity considerations. The same conditions but with the rough surface running faster, i.e. ~ = 1.2, 0.6 and 0.3, are shown in Figure 9. In these cases there is less variation between micro contact film thicknesses. Those in the inlet now have smaller films when the sliding velocity is smallest, and this pattern is generally the case for all the micro contacts. Again the differences between the pressure curves correspond with lowest pressure associated with lowest film. For positive slide roll ratio the squeeze film effect will be largest at the highest value of ~, whereas when g is negative the squeeze film effect will be largest at the smallest absolute value of ~. This effect explains the different dependence of micro contact film thickness at the inlet to the Hertzian region.

When the sliding speed is identically zero the result is a special case as illustrated in Figure 10. The fluid in this regime behaves very differently as the square root term in the non-Newtonian factor S becomes identically unity. Consequently the effective viscosity is much higher than in all the other cases considered (where there is sufficient

171 1.5

!

1.0

2

El =L

0.5

/ 0

0.0 .5

-1

-0.5

0

1.5

0.5

x/b

Figure 10. Pressure and film thickness with ~ = O. 2.5

12.5

2.0

10.0

1.5

7.5

Et

5.0 gl,

0.5

2.5

II

0.0

0.0

-o.5

~

1

I

-1.5

-1

-0.5

v

1

1

0

0.5

-

1

-2.5

1.5

x/b Figure 11. Pressure, film thickness and undeformed roughness profile (thin curve) shown at time step 5500 for case with U=5 m/s, ~ =-0.3.

172

sliding to make the t e r m

YI(U2- Ul)

result of the corresponding dry contact analysis (note that in comparison with Figure 11 the pressure scale has been reduced by a factor of two). The maximum pressure in dry contact is about 3.5 GPa and there is a significant increase in the number of individual micro contacts. The subsurface stress field arising from the pressure loadings illustrated in figures 11 and 12 will be very different, as will the number and intensity of the pressure loading cycles experienced as the surfaces move past each other.

significant

"t;oh

compared to confined in through the dictated by features first

unity). As a result the liquid remains the surface features as they pass contact and the pressure response is squeeze film effects as the asperity come into the contact area.

The same pattern is seen to emerge when results are examined at conditions with lower entrainment velocities of 10 m/s and 5 m/s. The minimum film thicknesses on the micro contacts for these cases are of the order 0.04 ~tm and 0.02 }xm respectively to be compared with Dowson and Higginson values of 0.23 txm and 0.14 }xm. At these very thin film values there is less variation possible over the contact area. The waviness in the run-in profile is more completely removed and there is, inevitably, a tad beating e il g tendency to higher pressures on the load i cell p il g asperities. This effect can be seen in comparing latt,~ figure t ue Figure 3 with Figure 11 where the latter nt speed s ~ of ff corresponds to the lowest entrainment IveIt inr this :t is 5 m/s with ~ - -0.3. However , even extremely thin film situation the hydrodynamic Mr¢, I ~ c tttt micro I co pressure remains significant betweent the ied onr the contacts and the load is not carded sla ~ the 1e individual micro contacts. Figure 122 shows 4.0

6. CONCLUSIONS The conclusions that can be drawn at this stage of the investigation based on the analysis of lubricated contacts with a single run-in ground surface are as follows. Film thickness is controlled by micro contact shape rather than by roughness detail. , Inside the Hertzian contact area micro contacts have films that are related to the relative (sliding) velocity of the surfaces. . Pure rolling is a special case where the lubricant pressure is strongly influenced by the roughness detail. • At t, very v,." low ~, values (0.0625 for the case c, ~si ker~, the detailed shape of the asperity lands considered) • 12.5

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173

begins to influence the hydrodynamic pressure distribution. The results also draw attention to the need to consider the actual shape of rough surfaces in any lubrication contact analysis and not the 'as manufactured' ones. To understand the processes at work in the failure of such ground surfaces it is necessary to consider the nmning-in process and how it is related to the loading and kinematic history of the contact. 7. A C K N O W L E D G E M E N T

The work reported in this paper has been supported by EPSRC Grant GR/L90996. REFERENCES

Ai, X and Cheng, H S, 1994, "A transient EHL analysis for line contacts with measured surface roughness using multigrid technique", Trans. ASME, Jn ofTribology, Vol. 116, pp 549-556. Chang, L, Cusano, C and Conry, T F, 1989, "Effects of lubricant rheology and kinematic conditions on micro-elastohydrodynamic lubrication", Trans. ASME, Jn of Tribology, Vol. 111, pp 344-351. Chang, L, and Webster, M. N, 1993, "A study of elastohydrodynamic lubrication of rough surfaces", Trans. ASME, Jn of Tribology, Vol. 113, pp 110115. Chang, L, Webster, M N and Jackson, A, 1993, "On the pressure rippling and roughness deformation in elastohydrodynamic lubrication of rough surfaces", Trans. ASME, Jn of Tribology, Vol. 115, pp 439-444. Chang, L, and Zhao, W, 1995, "Fundamental differences between Newtonian and non-Newtonian micro-EHL results", Trans. ASME, Jn of Tribology, Vol. 117, pp 29-35. Conry, T F, Wang, S and Cusano, C, 1987, "A Reynolds-Eyring equation for elastohydrodynamic lubrication in line contacts", Trans. ASME, Jn of Tribology, Vol. 109, pp 648-654. Elcoate, C.D, Hughes,T.G, and Evans, H.P., (1998), "On the coupling of the elastohydrodynamic problem", Proc Instn Mech Engnrs, Vol 212C, pp 307-318. Elcoate, C.D, Hughes,T.G, and Evans, H.P.(a) "Coupled solution of the Elastohydrodynamic line

contact problem using a differential deflection method" Submitted to Proc. Inst. Mech. Engrs. Elcoate, C.D, Hughes,T.G, Evans, H.P. and Snidle, R.W, (b) "Transient elastohydrodynamic line contact of two rough surfaces using a fully coupled method." Submitted to Proc. Inst. Mech. Engrs. Evans, H.P. and Hughes T.G. "Evaluation of elastic deflection in semi-infinite bodies by a differential method.", Submitted to Proc. Inst. Mech. Engrs. Evans, H P and Snidle, R W, 1996, "A model for elastohydrodynamic film failure in contacts between rough surfaces having transverse finish", Trans. ASME, Jn of Tribology, Vol 118, pp 847-857. Goglia, P R, Cusano, C and Conry, T F, 1984, "The effects of surface irregularities on the elastohydrodynamic lubrication of sliding line contacts. Part I - single irregularities; Part II wavy surfaces", Trans. ASME, Jn of Tribology, Vol. 106, pp 104-112, 113-119. Greenwood, J A and Morales-Espejel, G E, 1994, "The behaviour of transverse roughness in EHL contacts", Proc. Instn Mech Engrs Vol. 208J, pp 121-132. Houpert, L G and Hamrock, B J, 1986, "Fast approach for calculating film thicknesses and pressures in elastohydrodynamically lubricated contacts at high loads", Trans. ASME, Jn of Tribology, Vol. 108, pp 411-420. Kweh, C C, Evans, H P and Snidle, R W, 1989, "Micro-elastohydrodynamic lubrication of an elliptical contact with transverse and threedimensional sinusoidal roughness", Trans. ASME, Jn of Tribology, Vol. 111, pp 577-584. Kweh, C C, Patching, M J, Evans, H P and Snidle, R W, 1992, "Simulation of elastohydrodynamic contacts between rough surfaces", Trans. ASME, Jn of Tribology, Vol. 114, pp 412-419. Lubrecht, A A, Ten Napel, W E and Bosma, R, 1988, "The influence of longitudinal and transverse roughness on the elastohydrodynamic lubrication of circular contacts", Trans. ASME, Jn of Tribology, Vol. 110, pp 421-426. Okamura, H, 1982, "A contribution to the numerical analysis of isothermal elastohydrodynamic lubrication" Proc. of the 9th Leeds-Lyon Symp. on Tribology, in Tribology of Reciprocating engines, Butterworths, London, pp 313-320. Patching, M J, 1994, "The effect of surface roughness on the micro-elastohydrodynamic

174

lubrication and scuffing performance of aerospace gear tooth contacts", Phl) Thesis, University of Wales. Venner, C.H. and ten Napel, W.E, 1992, "Surface roughness effects in an EHL line contact." Trans. ASME, Jn ofTribology, Vol. 114, pp 616-622. Venner, C.H. and Lubrecht, A.A, 1994, "Transient analysis of surface features in an EHL line contact in the case of sliding." Trans. ASME, Jn of

Tribology, Vol. 116, pp 186-193. Venner, C.H. and Lubrecht, A.A, 1996, "Numerical analysis of the influence of waviness on the film thickness of a circular EHL contact." Trans. ASME, Jn of Tribology, Vol. 118, pp 153-161. Xu, G. and Sadeghi, F, 1996, "Thermal EHL analysis of circular contacts with measured surface roughness." Trans. ASME, Jn of Tribology, Vol. 118, pp 473-483.

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

175

Mapping of Surface Features in the Thin Film Lubrication Regime G. Guangteng, P. M. Cann, H. A. Spikes and A. Olver Tribology Section, Imperial College of Science, Technology and Medicine, London, UK

A film image mapping technique, based on ultrathin film interferometry, has been used to study the lubrication of elastohydrodynamic (EHD) contacts with rough surfaces. A very small chromium ridge has been sputtered onto a steel ball and the EHD film thickness mapped for different rolling speeds and orientation of the ridge. The results show that the effect of the ridge on film thickness is local and does not affect other positions in the contact. The ridge showed the effect of increasing the mean EHD film thickness when oriented both transverse and at 60 ° to the rolling direction. Under static loads the ridge is almost completely flattened but as the rolling speed increases the surface tends to lift off and the deformed ridge recovers towards its original form. The deformed ridge height in the contact has been estimated for different operating conditions and compared to existing numerical models.

1. INTRODUCTION As operating conditions become more and more severe, i.e. higher loads, higher temperatures and limited lubricant supply, more machine components are working in the mixed lubrication regime where the lubricant film thickness is comparable with the surface roughness [1]. In such cases, the contact load is partially supported by asperities of the contact surfaces and frequent solid-solid contact is expected. This has practical impact on the performance of machine elements and the design of lubricants to be used in these components. One important issue in EHD is the deformed roughness or the effective roughness in the heavily loaded contact. An early practice in estimating lubricating film thickness in rough surface EHD contact was to calculate the smooth surface film thickness and compared this with the representative, out-of-contact roughness, i.e. measured from stylus instruments. This was perhaps acceptable for cases where the relative magnitude of the surface roughness is small compared to the thicker lubricating films but not for very thin film conditions. It was, however unavoidable when the effect of the surface roughness in the concentrated contact was not well understood.

With recent progress in both computational [2-8] and experimental [9-13] studies, however, this problem has been gradually addressed. Venner et al studied the response of asperity shape in EHD contact using a numerical approach. The change of asperity waviness inside the contact was shown to be a function of a single dimensionless parameter for a line contact [3, 4]. Recently this work has been extended to the circular contact in which the amplitude reduction of an isotropic harmonic pattern was described as a function of a single dimensionless parameter consisting of the dimension of the simulating asperity features and operating conditions. A generalised curve was given for the cases varying from isotropic to transverse, and from isotropic to longitudinal [5]. Experimental study of rough surface EHL has also been carried out by various investigators. The most widely-used and successful technique has been optical interferometry [1]. Most of this experimental work investigated artificially-produced surface features, i.e. dents, grooves, bumps etc. This is because wellcharacterised features are easier to study in experiments and also because it enables the disentanglement of the influence on film thickness of various geometrical features of roughness. Thus it is an appropriate and necessary approach to pave the way leading to better understanding of the rough surface EHL.

176

Kaneta et al described an investigation of the behaviour of a coated transverse ridge in EHD contact [ 11 ], which is relevant to the current study. The ridge was 200 nm high and 50 ~tm wide and its effects on EHD film shape and thickness was investigated using optical interferometry for various orientations of the ridge and slide/roll ratios. They found that the ridge caused mainly local changes in film shape and a film thickness increase occurred at the ridge's leading edge when the ridge was in the inlet region. The film thickness range measured by Kaneta et al was 50 to 500 nm. Thus they were unable to measure the separation at the tip of the ridge, where the film, if any, was too small for the test conditions employed. However their results indicated significant flattening of the ridge in the contact and the presence of separation between the two surfaces at the tip for their test conditions. Recent work by the authors of the current paper on the effects of surface roughness on mean separation in EHD contact showed that the average film thickness was considerably less than that of the smooth surface case in the thin film regime when the lambda ratio (ratio of mean film thickness to out-of-contact composite roughness) was below two [13]. An optically smooth glass disk and steel balls with various isotropic roughnesses was employed and the mean separation measured using ultrathin film interferometry. The advantage of ultrathin film interferometry is its ability to accurately measure mean film thickness in the thin film region [14]. Recently, a spacer layer imaging technique (SLIM) has been developed [15], which can measure film thickness and map the 2D film shape over the whole EHD contact. The method combines the accuracy of the ultrathin film interferometry and the ability of 2D film mapping. This enables the detailed study of rough surface EHL and particularly of micro-EHL behaviour at asperity tips. Similar development using colour imaging technique for relatively thick films can be found in [ 16]. The current paper describes the application of the experimental technique SLIM to investigate the effects of surface roughness on film thickness

and the deformation of asperities in the contact. A single ridge was coated on the steel ball for the experiments. The mean film thickness and the local separation at the tip of the ridge were measured down to a few nanometers, which enables the detailed study of the behaviour of the ridge in the heavily loaded contact. The deformed height of the ridge in the contact has been estimated and compared to existing computational predictions.

2. TEST METHOD

2.1. Test set-up The SLIM method used in the current study is a combination of the ultrathin film interferometry [14] and the colour imaging techniques [15]. The test setup is as shown in Figure 1. A lubricated contact is formed between a steel ball (25.4 mm diameter) and an optically smooth glass disk, between which a lubricant is applied. The underside of the glass disk is coated with a very thin chromium layer, on top of which is deposited a thin, transparent layer of silica, the spacer layer. When a white light source is used, a coloured, interference image is formed of the contact.

Microscope/ video camera

T--~age ~ture

1 K,

Image analysis Steel ball Fi

Contact position

Figure 1. SLIM test set-up.

177

A CCD video camera is then used to detect the interference image which is also frame-grabbed by a PC for image analysis. At each pixel position the colour values (for instance, RGB) are thus known, which are related to the gap between the steel ball and the glass disk at the same location. To convert the colour values into film thickness a calibration is needed.

2.2. Test conditions All the tests were carried out under nominally pure rolling conditions. The lubricant used was a wellcharacterised polyalphaolefin, SHF41. The properties of the lubricant and other test conditions are listed below in Table 1.

Table 1. Test conditions The calibration procedure was as follows. A smooth steel ball was loaded against a glass disk whose spacer layer has varying thickness at different locations. The ultrathin film interferometry technique (which can measure film thickness down to 1 nm) was then used to measure the layer thickness at a fixed disk location. At the same location the colour values were also recorded using the SLIM technique. Thus the layer thickness corresponds to the colour values for this disk position. The procedure was followed for other disk positions. The calibration curve was thus obtained for a wide range of spacer layer thicknesses. For the experiments described in this paper, an artificially roughened surface was produced by sputter-depositing a small ridge, through a mask, on to a steel ball. The test procedures were as follows. The steel ball, glass disk and test chamber were thoroughly cleaned using toluene and then acetone and interference images were then captured using a stationary contact, both with the ridge within and just outside of the contact, to obtain the local spacer layer thickness. The ball and disk were then set in motion and interference images captured for a series of rolling speeds. An angular position encoder, mounted on the shaft of the ball, was used to ensure that the ridge was inside the contact for the captured image. An electric shutter on the camera was set to capture images within a time period of 1/10000 of a second. Over this time interval, at a surface speed of 0.1 m/s, an asperity will travel 10 ~tm. The captured images were later processed based on the calibration to obtain 2D film thickness maps corresponding to each image pattern. For each test, a series of such 2D film thickness maps was produced for the whole rolling speed range.

Lubricant Viscosity Alpha value Test temperature Hertz pressure

SHF41 23.8 cP (25°C) 11.3 GPa 1 (25°C) 24 + 0.5°C 0.45 GPa

The experimental non-dimensional parameters of speed (U), material (G) and load (W) respectively were as follows: U = 1.7 x 10-12 (at a mean rolling speed of 0.1 m/s), G = 1269 and W = 1.0 x 10"6, where these parameters are as defined in Dowson and Higginson [ 19].

3. RESULTS 3.1. Validation of SLIM technique To validate the spacer layer imagining technique, a series of tests were carried out using smooth surface steel balls. The tests were first set up using the ultrathin film technique to measure the mean film thickness in the EHD contact for a range of rolling speeds. The test procedures were as described in [14]. In a separate test, the same cleaning procedure was followed and the spacer layer imaging technique was then employed to measure the mean film thickness with the same lubricant and similar rolling speeds. Figure 2 shows the film thickness results from the two methods in the traditional log(film thickness) versus log(speed) form. It can be seen that the results from the SLIM technique agree well with those from the ultrathin film technique. At very low speed or in the very thin film region, the film thicknesses from SLIM technique were found to be less repeatable ond the technique less accurate for films below about 4 nm thickness. From this study it was established that SLIM can measure film thickness in the 4 to 100 nm range to an accuracy of +5%.

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3.3. Local layer thickness variation with pressure One complication of using a spacer layer in rough surface studies is the effect of pressure at asperity tips. The spacer layer deforms under high contact pressure. This will introduce an error in the measured film thickness at the corresponding positions. Thus it is necessary to correct this error by taking account of the local deformation of the spacer layer.

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3.2. Characterisation of deposited ridges The small ridge deposited on the steel ball has the dimensions of 55 ~tm in width and 160 nm in height. Figure 3 shows a Talysurf trace across the deposited ridge. Using the 3D-Cont numerical analysis procedure [20] the pressure in the stationary contact can be estimated. For the asperity ridge used in the current study, the predicted maximum pressure at the tip was about 1.0 GPa at a load of 18 N.

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179

Figure 4a shows the layer thickness change relative to this reference plotted against the contact pressures. If the layer thickness is backextrapolated to zero pressure, the unloaded layer thickness can be obtained and the layer thickness changes plotted, starting from zero contact pressure, as shown in Figure 4b. It is shown in Figure 4b that at the test contact pressure of 0.45 GPa, the spacer layer is compressed by about 5 nm. At the tip of the coated ridge in the contact the pressure will be considerably higher and the layer further compressed. At a pressure of 0.95 GPa (marked in the figure) for instance, the layer thickness will be reduced by 10 nm; i.e. the local compression of the layer at the tip will be about 5 nm less than that at 0.45 GPa. This shows that there is a decrease in layer thickness of approximately 1 nm for every 0.1 GPa increase in contact pressure due to local layer compression. This 5 nm value was taken into account for measuring the separation of the two surfaces at the tip of the ridge. 3.4. EHD film profiles The SLIM technique maps 2D film over the whole contact, but only the profiles at the midplane are presented here. Typical profiles are presented in figures from 5a to 5f. Figure 5a shows the film profile across the stationary, lubricated contact. The ridge is transverse, i.e. perpendicular to the rolling direction, and lies approximately across the middle of the contact region. The separation baseline used was that of the spacer layer at 0.45 GPa measured in a smooth ball contact. Two features exist around the ridge: (i) slightly negative film at the tip of the ridge, (ii) a positive separation on either side of the tip. The apparently negative film can be explained by allowing for the local layer compression at the tip, where the spacer layer is further compressed by about 5 nm under the higher pressures present at this location. Referring to Figure 5a regarding the positive separation, this corresponds to the valleys in the vicinity of the ridge where the contact pressure is lower. If this lower pressure effect were taken into

account the positive separation region would be decreased slightly. However, the precise extent of the compression or recovery of the layer is difficult to estimate due to lack of information about the actual contact pressure values. Overall the coated ridge is almost completely flattened in the contact. Figures 5b to 5f show film profiles at mid-plane at progressively increasing rolling speeds. In these figures, the inlet is on the right of the figure and the exit on the left and the ridge is transverse to the rolling direction. At very low speed of 0.0068 m/s as shown in Figure 5b, the film at the tip of the ridge is almost unchanged and the average film is only very slightly increased. This shows little change, except near the inlet, compared to the stationary case. It should be mentioned that although images were captured using digital triggers, it was not possible to ensure that the tip was at exactly the same location in every captured frame. As rolling speed increases, as shown in Figure 5c, whilst the overall film thickness increases, the separation around the sides of the ridge also increases. This indicates that asperity deformation is reduced and the height of the ridge starts to recover. This behaviour is predicted by Vcnncr ct al [18]. Another feature is the presence of a thicker oil film region immediately downstream of the asperity ridge. This has been previously observed by Kaneta [11] with much thicker films. It is an inlet-driven phenomenon. When the contact operates in pure rolling, any fluctuations in film thickness produced in the inlet will pass through the contact at the same spe~d as asperity features [ 17]. From Figure 5b through to Figure 5£ two important a ~ t s can be identified: (i) the influence of the ridge on the mean hydrodynamic tiff, i.e. mean film separation, (ii) the formation of film separation at the tip of the ridge. The experimental film thickness results are summarised in Figures 6a and 6b for both the transverse and a 60 ° ridge. Figure 6a shows the results of the mean separation versus the rolling speed and Figure 6b shows the film separation at the tip of

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the ridge. The mean film thickness generally follows the smooth case except for some enhancement over the rolling speed range (0.01 -~ 0.1 m/s). It approaches the smooth surface film value at high rolling speeds where the film thickness reaches approximately the same value as the undeformed ridge height. In their computational work, Zhu et al found that the average rough surface film thickness was slightly higher than that of the average smooth surfaces [8]. 1000 o Smooth • 90 ° ridge • 60° ridge

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From the results shown in Figures 5b to 5£ the general trend of the asperity behaviour is observed. At low speeds the asperity recovers its height, as can be seen in Figures 5b and 5c, compared to that at stationary contact where the ridge is almost flattened. As the rolling speed increases further, the deformation of the asperity is further reduced and the height of the ridge reaches a maximum as shown in Figures 5d and 5e. At still higher rolling speeds the asperity height appears to reduce once more and the film shape becomes smoother in the central contact region. This is shown in Figure 5f. Venner et al provided a generalised curve of amplitude reduction versus operating parameters [5, 18]. Sinusoidal ridges were used in their computational model. A single dimensionless wavelength parameter, A2, was introduced which incorporates characteristics of the ridge, Moes' dimensionless load and material parameters. The equation was given as:

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rolling speed increases further, the results show that the tip of the ridge lifts off, so that it behaves as a local micro-EHD contact. Further details of the film thickness results and analysis are described in [17].

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ridge respectively. A2 is the dimensionless wavelength parameter defined as A 2 - (~b)(M1/2/L 1/6)

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182

Figure 7 shows the experimentally measured asperity heights relative to the initial height as a function of the dimensionless wavelength parameter, compared with the predictions of equation (1). The heights were obtained from profiles such as those in Figures 5b to 5f. In the experiments, L/b = 50/140 (the smoothed, unloaded ridge height of 140 nm is used). For the experimental conditions, the dimensionless wavelength parameter is proportional to the dimensionless speed parameter, U, to the power of -5/12. As the rolling speed increases the dimensionless wavelength parameter reduces, towards the left of the figure.

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reduction of local elastic deformation at the ridge. Although the elastic deformation depends on the whole pressure field, the pressure at or around the tip of the ridge makes the dominant contribution. This implies that the contact pressure at the tip of the asperity is more evenly distributed or less concentrated. The attenuation of the pressure concentration at the ridge has important implications on the fatigue life of the components in practical systems. As the rolling speed further increases however, the deformed ridge height reaches a maximum and starts to reduce, indicating further flattening of the asperity. This phenomenon was predicted by Venner et al [18] for sliding conditions. Although the experiments were carried out under nominally pure rolling, there exists sliding, albeit to a small extent, at least for smooth surfaces. It is therefore not unreasonable to ascribe this reduction of asperity height in part to micro-sliding which was not controlled in the experiments. However, further study is needed to clarify this aspect of the findings.

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Figure 7. Asperity height in EHD contact. 4. Conclusions

In the computational model of Venner et al [5, 18], sinusoidal asperities were studied and Fourier transformation to the asperity heights performed. By contrast, in the current study, a single, quasisinusoidal asperity was used. However, the general trend of the experimental curve will not change, except that a small shift is expected if Fourier transformation were carried out on the single asperity results. As shown in Figure 7, the general experimentally-measured trend follows that of the model. As A2 reduces (at higher rolling speed), the deformed ridge height increases, indicating a

The spacer layer imaging technique SLIM has been used to study the influence of surface features on lubricant film thickness in concentrated contact. It has been shown that the technique is capable of 2D film mapping with good accuracy in the thin film region down to a few nanometres thicknesses. In the presence of an asperity, the film thickness variation is local around the asperity and the mean film thickness is found to be higher than that of the smooth surface case in the medium speed range employed. At high speed the asperity appears to have no effect on the mean separation.

183

The asperity is almost completely flattened in stationary contact, which implies high pressure concentration at the asperity tips. As the rolling speed increases however, the asperity deformation reduces and the asperity height recovers towards its original form. This indicates a spread of contact pressure or less concentrated pressure at the tip of the asperity. The general trend of asperity height in contact has been found t.o agree with the existing computational model at low speeds. However, the asperity height did not recover fully to its original, out-of-contact value under the experimental conditions.

REFERENCES

1. Spikes, H. A. "Mixed lubrication - an overview", Lubrication Science 9 (1997), pp. 221-253. 2. Lubrecht, A. A. "Influence of local and global features in contacts", Proc. 23rd Leeds-Lyon Symp. on Tribology, Sept. 1997, ed. D. Dowson et al, Elsevier Tribology Series, 32, pp 17-25. 3. Venner, C. H. and Lubrecht, A. A. "Transient analysis of surface features in an EHL line contact in the case of sliding and three-dimensional sinusoidal roughness", ASME Trans. J. of Tribology 116, (1994), pp. 186-193. 4. Venner, C. H. and Lubrecht, A. A. "Numerical simulation of a transverse ridge in a circular EHL contact under rolling/sliding", ASME Trans. J. of Tribology I 16, (1994), pp. 751-761. 5. Venner, C. H. and Lubrecht, A. A. "Amplitude reduction of non-isotropic harmonic patterns in circular EHL contacts, under pure rolling", Proc. 25th Leeds-Lyon Symp., Sept. 1998. 6. Kweh, C. C., Evans, H. P. and Snide, R. W "Micro-elastohydrodynamic lubrication of an elliptical contact with transverse and threedimensional roughness", ASME J. of Tribology, 111, (1989), pp. 577-583. 7. Chang, L. and Webster, M. N "A study of elastohydrodynamic lubrication of rough surfaces", ASME J. of Tribology, 113, (1991), pp. 110-115. 8. Zhu, D. and Ai, X. "Point contact EHL based on optically measured three-dimensional roughness surfaces", ASME. J. of Tribology, 96-Trib-24. 9. Kaneta, M. and Cameron, A. "Elastohydrodynamic film thickness measurements

of artificially produced surface dents and grooves", ASME JOLT, 102, (1980), pp. 374-379. 10. Kaneta, M., Sakai, T. and Nishikawa, H. "Effects of surface roughness on point contact EHL", Trib. Trans. 36, (1993), pp. 605-612. 11.Kaneta, M., Sakai, T. and Nishikawa, H. "Optical interferometrical observations of the effects of a bump on point contact EHL", ASME J. of Tribology, 114, (1992), pp. 779-784. 12. Wedeven, L. D. and Cusano, C. "Elastohydrodynamic film thickness measurements of artificially produced surface dents and grooves", ASLE Trans 22, (1979), pp. 369-381. 13.Guangteng, G. and Spikes, H. A. "An experimental study of film thickness in the mixed lubrication regime", Proc. 25th Leeds-Lyon Symp., Sept. 1996, pp. 159-166, ed. D. Dowson et al., publ. Elsevier, Amsterdam 1997. 14. Johnston, G. J., Watye, R. and Spikes, H. A. "The measurement and study of very thin lubricant films in concentrated contacts", Trib. Trans. 34, (1991), pp. 187-194. 15. Calm, P. M., Hutchinson, J. and Spikes, H. A. "The development of a spacer layer imaging method (SLIM) for mapping elastohydrodynamic contacts", Trib. Trans. 39, (1996), pp. 915-921. 16. Gustafsson, L., Hoglund, E. and Marldund, O. "Measuring lubricant film thickness with image analysis ", Proc. I. Mech. E. J208, (1994), pp. 199205. 17. Guangteng, G., Cann, P. M., Olver, A. V. and Spikes, H. A. "An experimental study of film thickness between rough surfaces in EHD contacts", to be presented Austrib, Brisbane, Dec. 1998. 18. Venner, C. H. and Lubrecht, A. A. "Elastohydrodynamic lubrication of rough surfaces", I. Mech. E. Part. J, J. of Eng. Tribology, Special Issue (1998). 19. Dowson, D. and Higginson, G. R.

Elastohydrodynamic Lubrication, $1 Edition, Pergamon Press Ltd, Oxford, 1977. 20. West, M. A~ and Sayles, 1L S., "A 3-dimensional method of studying 3-body contact geometry and stress in real rough surfaces", Proc. 14th LeedsLyon Symp., Sept. 1987, pp. 195-200, ed. D. Dowson et al., publ. Elsevier, Amsterdam 1988.

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185

The Effects of a Transversely Oriented Bump on Point Contact EHL Films in Reciprocating Motion with a Short Length of Stroke M. KANETA and H. NISHIKAWA Department of Mechanical and Control Engineering, Kyushu Institute of Technology, 1 - 1, Sensuicho, Tobata, Kitakyushu 804-8550, Japan Under conditions of a short stroke and a high frequency of reciprocation, a local collapse of EHL films is easily induced, because air bubbles produced in the previous stroke result in oil starvation in the following stroke. Furthermore, thin films produced by a transversely oriented bump entering the EHL conjunction travel through the contact area with approximately the average speed of the contacting surfaces while holding its shape and thickness. In this paper, the effects of above two important phenomena on point contact EHL films and traction forces in reciprocating motion having a relatively short length of stroke are discussed through direct observations using the duochromatic optical interferometry technique. The effects of surface kinematic conditions have also been discussed.

1. INTRODUCTION A c l e a r u n d e r s t a n d i n g of b e h a v i o r of elastohydrodynamic lubrication (EHL) film is very i m p o r t a n t in order to elucidate the working performance and durability of highly stressed nonconformal machine elements. Surfaces of machine elements are never totally smooth and the film thickness in the EHL regime is of the same order of magnitude as the surface roughness. Therefore, a great deal of work on rough surface EHL has been carried out by numerous researchers from different points of view. However, almost all of those investigations are limited to unidirectional and time-independent motion, although there are numerous machine elements which work under reciprocating and oscillating conditions. The authors [1] have pointed out through their experiments that a local collapse of EHL films occurs easily under conditions of a short stroke and a high frequency of reciprocation, because air bubbles produced in the previous stroke result in oil starvation in the following stroke. Furthermore, studies carried out under unidirectional rolling and/or sliding conditions have shown that the effects of a transversely oriented bump on EHL films depend significantly on the surface kinematic conditions [e.g. 2, 3]. When the velocity of a smooth surface is faster than that of a surface having a bump, the bump produces a strong

downstream effect, while in the reverse situation the irregularity produces a strong upstream effect, and the reduced or collapsed film travels through the contact area with approximately the average speed of the contacting surfaces while holding its shape and thickness. The purpose of this investigation is to clarify, through direct observations using the duo-chromatic optical interferometry technique, the effects of transversely oriented bump on EHL films in reciprocating motion having a relatively short length of stroke. 1.1. Nomenclature a = radius of Hertzian circle elastic moduli of steel ball and glass disk E' = reduced elastic modulus, 2{ (1-VD2)/ E D + (1-VB2) / E a }-1 G = materials parameter, txE'

E a, E D =

R = radius of steel ball S B, S o = total amplitudes of steel ball and glass disk surfaces t = time measured from left stroke end T = period of reciprocation uB, u D = surface velocities of steel ball and glass disk U = speed parameter, 1"1(UD+UB) / (2E'R)

186

w = load W = load parameter, w / (E'R 2) position of bump at left stroke end X L = dimensionless position of bump at left XL •

stroke end, x L/a ct = pressure-viscosity coefficient 110 = viscosity at atmospheric pressure l.t = traction coefficient v B, v o = Poisson's ratios of steel ball and glass disk g = slide-to-roll ratio, 2 (%-%) / (%+%)

2. EXPERIMENTAL PROCEDURE 2.1. Apparatus and specimens The duochromatic optical interferometry technique was used to measure the shape and the thickness of the lubricating film in an EHL circular contact. Figure 1 shows a schematic diagram of the experimental apparatus used in this study. The contacting surfaces were composed of a precision 25.4 mm diameter steel ball and a glass disk. The reduced elastic modulus E' was 117 GPa. A long bump having a maximum height of 0.33 ktm

HIGHSPEED I VCR

(see Fig. 2) was produced onto one part of the ball surface by sputter deposition of chromium through a foil mask. The ball was fixed to a shaft so that the orientation of a bump was perpendicular to the direction of ball rotation. In this study, the steel ball and glass disk were driven in-phase (see Fig. 3) by two servo-motors equipped with a function generator through a crank connected with a double eccentric cam, respectively. The oscillatory motions of the ball and disk could be recorded with two sets of proximity detector. The surface speeds of the ball and disk were calculated from the values of stroke lengths and oscillating frequencies measured. The traction force between the ball and disk could be measured by measuring the reaction force on the ball by two pairs of strain gauges stuck on the ball shaft. The interference fringe pattern made with wavelengths of red and green was recorded with a high speed VCR (200 frames per seconds) attached to a microscope. A Xenon flash lamp with a flash duration of 20 Its was used as a light source.

2.2. Experimental conditions The oil used was a mineral bright stock having a kinematic viscosity of 1398 mmE/s at 21.5°C and 393 n l n ' 1 2 / s at 40°C, a specific gravity of 0.878 at 15/4°C,

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187

and a pressure-viscosity coefficient of 22.5 GPa -1 at 21.5°C and 18 GPa -1 at 40°C. The experiments were carried out at a load of 39.2 N, which gave a maximum Hertzian pressure of 0.54 GPa and a Hertzian diameter of 0.37 mm. The oscillating frequency was adjusted so that the dimensionless entrainment or rolling velocity, U, at the center of the stroke became l x l 0 11. The total amplitude of the ball surface was fixed at 0.4 mm which was close to the Hertzian contact diameter. Therefore, the total amplitude ot~the glass disk was 1.2 mm, 0.4 mm and 0.13 mm for the slide-to-roll ratio, Z, 1, 0 and - 1, respectively. The oil temperature in the inlet to the contact was 21.2 + 1°C. These conditions give the dimensionless load parameter W = 2.08x10 -6 and the materials parameter G = 2630. The experiments were conducted by changing the positions of the bump at the stroke ends.

3.

RESULTS AND DISCUSSION

3.1. Effects of slide-to-roll ratio and airbubbles Figure 4 shows series of interferograms, which show variations in film shape during half a cycle,

observed under conditions of Z = 1, 0, and -1 using a smooth surface steel ball. t/T is the dimensionless time, where t is the time measured from the left end of the stroke and T is the period of reciprocation; t/T = 0, 0.25 and 0.5 correspond to the left end, center, and right end of the stroke, respectively. The values in the interferograms indicate film thicknesses in t.tm. In this paper, the terms "right" and "left" strokes are used in describing the direction of motions of the steel ball and glass disk, which are in-phase. The fight stroke means that the steel ball and glass disk move from the left end (t/T = 0) to the fight end (t/T = 0.5). The left stroke means that they move from the right end (t/T = 0.5) to the left end (t/T = 1). It can be seen from Fig. 4 that the oil is entrapped between contacting surfaces at both stroke ends. When the surfaces start to move from the left-hand side to the fight, the entrapped film moves towards the right as if it were frozen, and discharges itself from the EHL conjunction. The oil film is newly produced from the inlet side, i.e., from the left-hand side, after a while when the surfaces start to move. The authors have pointed out in the previous paper [1 ] that when the length of the stroke becomes shorter than a certain critical value, film formation due to the wedge action is inhibited by air bubbles, which are brought about in

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188

the previous stroke, remaining in the inlet of the following stroke. It should be noted that there are air bubbles at the left hand side, which corresponds to the inlet side to the EHL conjunction in the following fight stroke, of each figure corresponding to t/T = 0. Consequently, the film is not formed at the inlet side of the contact at the same time the surfaces start to move. That is, the film formation due to the wedge action is established after the air bubbles left the entrance to the EHL conjunction. The oil between contacting surfaces moves with approximately the average speed of the contacting surfaces since the flow in the EHL conjunction is mainly dominated by shear flow. In this study, the slideto-roll ratio E is changed under conditions where the total amplitude of the ball surface and the entrainment speed at the stroke center are fixed. Furthermore, there is no phase difference between displacements of the steel ball and the glass disk. The traveling distance of the oil, therefore, equals approximately to (SB+SD) / 2, i.e., 0.8 mm, 0.4 mm and 0.27 mm for I3 -1, 0 and -1, respectively. This means that in cases of E = -1 the whole EHL conjunction is never covered with oil films. Furthermore, the value of t/T when the air bubbles existing at the inlet disappear is larger for E - -1 than for E = 1, since the reciprocating period is shorter for I3=-1 than for E = 1 For E - 1, a typical film shape, which has a flat plateau region bounded by a horseshoe shaped constriction, in circular EHL contacts appears after the stroke passes its center. When the stroke passes its center, the wedge action declines according to the decrease in the entrainment speed and at the stroke end the fluid is entrapped between the surfaces. The thickness of oil film entrapped at the end of the stroke is thicker on the outlet side than on the inlet side. This is because local film thicknesses in EHL contacts are established by the fluid moved from the inlet side to their positions; film thicknesses at the inlet side depend on the entrainment speed which decreases as the stroke approaches the end. For E = 0, the fluid which entered the contact area after the disappearance of the air bubbles moves only half of the EHL conjunction. Therefore, the oil is entrapped at the inlet half in the EHL conjunction as shown in Fig. 4B(e). For E = -1, for the reason described above, the traveling distance of the fluid which entered the contact area after the disappearance of the air bubbles is shortest. Consequently, a certain region of the EHL

conjunction contacted directly and the chromium layer sputtered on the glass disk came partly off. 3.2. Effects of a transversely oriented bump Figures 5, 6 and 7 show interferograms observed at various positions when the transversely oriented bump passes through the EHL conjunction under conditions of XL- -1,-1.5 and-2 for E = 1, 0 and-1, respectively. XL=XL/a,where x L is the position of the bump at the left stroke end and "a" is the Hertzian contact radius. Under unidirectional conditions, the very thin film formed on the bump which is entering the EHL conjunction travels through the contact region at the average speed of the surfaces. When the whole of the bump enters the EHL conjunction, the film thickness at the upstream side of the bump recovers to the smooth surface value and the bump itself is flattened out so that the film thickness at the bump equals to that at the upstream side of the bump [2]. The same phenomena also take place under reciprocating conditions. For E = 1, the variation in film profile during the fight stroke under condition of XL= -1 is the same as that during the left stroke, because the movement of the bump is almost symmetric with respect to the center of the EHL contact. Furthermore, the film is hardly influenced by the bump. This is because the effect of the bump is concealed by the oil starvation. In the case of X L • -2, a very thin film formed by the bump entering the contact area in the fight stroke is not discharged from the contact area and remains in the EHL conjunction. Hence, thin films produced by the bump and air bubbles cross over the bump in the following left stroke. Consequently, the film thickness on the bump becomes thinner in the left stroke than in the fight stroke, in particular at both edges where the bump intersects the contact circle and the effect of side leakage is remarkable. In the case of X L- -1.5, since the thin film produced by the bump is discharged from the contact area, only thin film caused by the air bubbles crosses over the bump in the left stroke, although in the left stroke the EHL films are influenced by the air bubbles and the bump. Under pure rolling conditions (E = 0), the influence of the bump is localized to a region around the bump as seen in Figs. 5B to 7B. Furthermore, the vertical deformation of the bump is less than the cases of E = 1 and E = -1, since the film on the bump is not affected by the fluid which exists up- and downstream sides of the bump. It should be noticed from Fig. 7B for X L= -2

189

that a thick film is formed at the leading side of the bump in the right stroke and its configuration is frozen in the contact region even in the left stroke. Such a thick film is produced by the squeeze action that the bump entering the contact area receives. However, we can not observe such a thick film in the case of X L= - 1. This is because the speed of the ball entering the EHL conjunction is faster for XL= -2 than for XL= -1; the leading side of the bump receives stronger squeeze action for XL= -2 than for XL= -1. For Z = -1, as seen in Figs. 5 (a) to 7 (a) the film in the EHL conjunction at the left stroke end is almost completely collapsed, except for the fight hand side of the contact. Furthermore, since there are air bubbles at the entrance to the EHL contact at the beginning of the fight stroke, the formation of thick films at the inlet region of the contact due to wedge action cannot be expected. It should be also noted that for Z < 0 film thicknesses at a certain region upstream of the bump and on the bump are controlled by the fluid existing at the downstream side of the bump. In the case of XL= -1, consequently, films at the neighborhood of up- and downstreams of the bump including the film on the bump are almost completely collapsed during a cycle; the bump itself is almost completely flattened out. For XL= -2, when the bump entered the contact

area, air bubbles almost disappear. As a result, there exists enough fluid outside the contact area to produce thick films. However, the films inside the contact area at this moment are very thin or collapsed. Since the velocity of the ball surface at this moment is faster for XL= -2 than for XL= - 1 and X L= - 1.5, the bump receives stronger squeeze and wedge actions for XL= -2 than for XL= -1 and XL= -1.5. Consequently, in the case of XL= -2 rather thick films are formed near both edges of the bump by the fluid existing at the downstream side of the bump; the film at the central region of the bump remains thin (see Fig. 7C). We can conclude from the above results that the film profile in the reciprocating motion depends on when the bump enters the contact area.

3.3. Effects of a bump on traction force Figures 8 and 9, which correspond to series of interferograms shown in Figs. 4 to 7, show time variation in traction coefficient for E - 1 and Z = -1, respectively. The overall traction force during a cycle is lower for Z = 1 than for Z - -1. This is because the overall film thickness during the reciprocation is thicker for Z= 1 than for Z = - 1. For E = 1, there is no significant difference in the

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192

traction force between the steel balls with and without a bump. It should be however noted that the traction force under the same phase increases slightly with an increase in the area occupied by thin films. For example, the traction force in the case of XL= -2 has two peaks in the right stroke as shown in Fig. 8(d). The first peak is established by the thin film caused by the air bubbles, and the second peak is produced by thin film caused by the bump entering the contact area. The traction coefficient takes the maximum near intermediate time between the right end and the center of the stroke in the left stroke. This is because the area occupied by thin films becomes the maximum at this time due to the combined effect of the thin films induced by the bump and air bubbles. In the case of XL= -1.5 the traction force takes the maximum value immediately before the center of the fight stroke, where the effects of thin films caused by air bubbles and the bump are superposed; in the left stroke, the traction force is not affected by the thin film produced by bump, since the thin film is completely discharged from the contact area. Figure 9 corresponding to E = -1 is noteworthy results. The overall traction force is higher for the smooth ball than for the ball having the bump. The following results may support above phenomenon. In cases where the smooth ball was used the experiments were discontinued in a short time because of the failure of the chromium layer sputtered on the glass plate. However, in cases where the ball having the bump was used it was possible to conduct experiments for rather longer period. At present stage, the authors can not give a clear physical explanation for such a phenomenon. The bump may introduce a very small amount of oil into the EHL conjunction. It would be necessary to increase the accuracy of measurement of film thicknesses.

4. CONCLUSIONS The effects of a transversely oriented moving bump on point contact EHL films in reciprocating motion have been examined by direct observations by means of optical interferometry. The length of the stroke was almost the same as the diameter of the Hertzian contact circle. The entrainment speed at the center of the stroke was fixed at a constant value and there was no phase difference between displacements of contacting

surfaces. The main conclusions are as follows: (1) The film formation in the following stroke is disturbed by the oil starvation due to air bubbles produced during the previous stroke. (2) The area occupied by rather thick films decreases as the slide-to-roll ratio becomes negative from positive depending on the amount of oil drawn into the EHL conjunction. (3) The effects of the bump on EHL films are basically the same as those obtained under unidirectional motion. (4) That is, the EHL film profile is influenced by a local film shape formed when the bump is entering the contact area. The local film shape moves through the contact area towards the downstream side of the bump for each stroke when Z > 0, while in the reverse situation (Z < 0) that moves towards the upstream side of the bump. (5) Therefore, in reciprocating motion having a short length of the stroke, the effects of the bump on EHL films depend on when the bump enters the EHL conjunction. (6) The traction force at the same phase increases with an increase in the area occupied by the thin film; the traction force is larger for Z < 0 than for Z > 0. (7) For Z < 0, the bump reduces the traction force.

ACKNOWLEDGMENTS The authors wish to offer their thanks to Mr. Y. Ohchida for his help for this work. The oil was supplied by Idemitsu Kosan Co., Ltd., and the steel balls were supplied by Nippon Seiko K.K.

REFERENCES 1. H. Nishikawa, K. Handa and M. Kaneta, Behavior of EHL Films in Reciprocating Motion, JSME Int. Journal, C, 38-3 (1995) 558-567. 2. M. Kaneta, T. Sakai, and H. Nishikawa, Optical Interferometric Observations of the Effects of a Bump on Point Contact EHL, J. Tribology, Trans. ASME, 114 (1992) 779-784. 3. C. H. Venner and A. A. Lubrecht, Numerical Simulation of a Transverse Ridge in a Circular EHL Contact under Rolling/Sliding, J. Tribology, Trans. ASME, 116 (1994) 751-761.

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

193

Surface r o u g h n e s s m o d i f i c a t i o n in E H L line contacts - the effect o f r o u g h n e s s w a v e l e n g t h , orientation and o p e r a t i n g c o n d i t i o n s C. J. Hooke School of Manufacturing and Mechanical Engineering The University of Birmingham Edgbaston Birmingham B15 2TT UK Any surface roughness is modified as it passes under an EHL contact with the clearance under the conjunction having an amplitude and spatial distribution that differs from that of the original surface. The essential features of this behaviour can be examined by considering the behaviour of low amplitude surface roughness. Where the amplitude of the roughness is low, the response of the lubrication system is linear and each component of the roughness, defined by its wavelengths in the longitudinal and transverse directions, can be analysed separately. Existing results show, for example, that under pure rolling, transverse roughnesses with wavelengths longer than the entrainment length will be flattened under the conjunction; those with shorter wavelengths will pass through the contact unaltered. The paper shows that the analysis of small amplitude, two dimensional roughness effects in EHL line contacts can always be reduced to the analysis of a linear, steady state system. This applies even when the original lubrication equations incorporate dynamic terms. Results are presented for the effects of transverse, in-line and general roughness in heavily loaded, metallic conjunctions and it is shown that the behaviour depends primarily on the relative velocities of the two surfaces, on the ratio of the roughness wavelengths in the longitudinal and transverse directions to the entrainment length and on a piezoviscous parameter, c. 1. INTROD[JCTION A large number of previous studies, see for example, [1-9] have examined the effect of transverse roughness in line contacts. Some of these [4,5] were concerned with the behaviour of the roughness under the central section of heavily loaded contacts and showed that relative sliding of the surfaces would tend to remove the original roughness profile under the conjunction and replace it by a complementary clearance variation moving at the entrainment velocity. This complementary profile has a spatial distribution that differs from that of the original surface. Those analyses that examined complete conjunctions also showed that the roughness tended to be reduced under the contact. This amplitude reduction depended on the wavelength of the roughness, with long wavelength profiles being

flattened. They also showed that, provided the modified profile was less than about half the film thickness, the system was linear with the amplitude reduction being independent of the amplitude of the original surface profile. These latter results were obtained by solving the dynamic EHL equations for particular surface profiles and great care was required to avoid spurious dynamic effects in the solution. The process is time consuming and generally only transverse roughness profiles have been examined. In [10] the present author developed a method for low amplitude roughness that avoids many of the computational problems and allows low amplitude, two-dimensional roughness to be examined readily. The purpose of this paper is to use the method to examine the behaviour of line contacts operating in the elastic, piezoviscous regime. This includes the majority of metallic, oil lubricated contacts.

194

2. N O T A T I O N

co (8WR'~ °5 = \ hE' J

b

Hertz semi-contact width

c

piezoviscous parameter = 0.9584 pO.25 S

E'

2 1-Vl2 l-v2 2 equivalent elastic modulus ~-7 = El + E2

G h H

= mE' clearance Greenwood clearance = h/R (GU) "2/3

i K0 p P P

modified Bessel function pressure perturbation pressure Greenwood load parameter = c~P.

(WE'

0.5

PH

maximum Hertz pressure = k,2nR'J

r

clearance perturbation

R'

effective radius R ' - R 1 + R"~

R Ro s S t u

undeformed surface roughness amplitude ofundeformed surface roughness s = ~59h + 9r Greenwood speed parameter = G U °'25 time entrainment velocity = (ul + u2)/2

1

1

1

rl0U

U v w x y

= E'R velocity of rough surface perturbation of elastic distortion distance from centre of Hertz contact in direction of entrainment distance along contact

z

=z

Z

= ph3

c~ D,Z q q0 6q q0 9~ 0 p 5t9

12q Barus pressure viscosity coefficient phases of roughness component dynamic viscosity dynamic viscosity at P = 0 viscosity perturbation = vcot roughness wavelength roughness orientation (relative to y axis) fluid density density perturbation

-if+

9

-

q

roughness wave number in the x direction roughness wave number in the y direction

Non-dimensional variables are denoted by an overbar as, for example, ~. Complex variables are denoted by an underbar as, for example, 12. 3. T I t E O R Y Full details of the analysis are given in [ 10] and only a brief summary will be included here. It will be assumed that a solution to the EHL equations for a smooth contact is available in terms of the hydrodynamic pressures, P, and clearances, h. When a low amplitude surface roughness is introduced these pressures and clearances will be modified. Since the response of the EHL contact to small changes in surface profile will be linear, it is possible to replace any roughness profiles on the two surfaces by two-dimensional Fourier integrals and to examine the behaviour of each component separately. The overall behaviour may then be obtained by superposition. We may, thus, consider the effect on the contact of introducing a roughness given by: R = Ro cos(cox- vcot + [3) cos(~y + ~;)

(1)

on one surface only. Ro is the amplitude of the roughness, co and ~ the wave numbers in the x and y directions respectively and v is the velocity of the surface relative to the contact. R is taken as positive where it tends to increase the clearance. The phase angles [3 and ~ will, in general, be non-zero but, because a single waveform is being considered in the analysis, it is possible to set them to zero by selection of the time and y origins. This will be done for convenience. Equation 1 may then be rewritten in complex form as: R = Re[_.R e ,~o]cos(~y)

(2) io)x

where q) = vc0t and _.R= Ro e This roughness will produce a perturbation, p, in the pressure distribution and, because of the linear response of the system to small changes, this will be given by: p = Re[l~ e ,~o]cos(~y)

(3)

These pressure changes will, in tum, produce variations, w, in the surface deformation:

195

w = Re[w e '~] cos(~y)

(4)

and s = 5oh + or

(11)

which will combine with the original surface to produce a final clearance perturbation, r:

Then, noting that neither Z nor P are functions of y, this equation may be rewritten in complex form

r = Re[r e-'~] cos({y)

as"

(5)

Z

where r = R + w

+z--

[3r

-

Zl2=u~-ivc0s

The pressure perturbation varies in both the x and y directions and the elastic distortion may be found from the integral:

w h e r e -z = Z

2 ( ( p ( x ' , y ' ) dy' dx' w(x,y) = hE---7j j ~/(x,_x) 2 + (y,_y)2

3.1 N u m e r i c a l s o l u t i o n

~+

p

-

(12)

lq

and s = 6oh + pr

(6)

6q = Re[ 6he-l~] cos({y)

In order to obtain a numerical solution, the conjunction, from well in front of the contact to the cavitation point, was divided into a number of equal length segments. The pressure perturbation was specified at the segment nodes with an assumed linear variation between them. This enabled the elastic distortions to be determined in terms of the nodal pressures. It was then possible to determine the errors in a finite difference form of equation 12 at each node and this led to a set of simultaneous, linear, complex equations whose solutions gave the complex pressures, 12, at each node. From these the clearance perturbation, r, could be obtained and hence the surface geometry at any time and for any value of y.

where 5t2 =dp12 d9

3.2 V i s c o s i t y a n d d e n s i t y

and 6rl

The formulation given above applies for any variation of viscosity and density with pressure. In order to obtain the specific results presented below a Barus relationship for viscosity:

or, noting the sinusoidal variation of p with y: oo

w(x) = hE--7 4 f

K0[~(s-x)] p(s) ds

(7)

-00

In addition to deforming the surfaces, the pressure perturbation will also change the fluid's density and viscosity and, for a Newtonian fluid, these changes may be written as" 5p = Re[ 5a e

l(p] cos({y)

(8)

and

dq =dpP

The pressure, density, viscosity and clearance perturbations must be compatible with the twodimensional form of Reynolds' equation: 0 [ p h 3 --~1 - + OIph30~] 12rl ~ 12rl

- u Ooh + Oph Ox 0t

(10)

rl =floe

z

z

where Z = ph3 12q z=Z

3r

-if+

6_.R 5__.rt1 p - rl

=uN+

(13)

was assumed while the Dowson-Higginson approximation for density was adopted: 1 + 2.3 x 1 0 9 p

P = P0 1 + 1.7 x 10 -u P

Since the original pressures and clearances satisfy this equation, the perturbations must satisfy:

N

ctP

(14)

3.2 Non-dimensional groups Before carrying out the analysis, a set of nondimensional groups based on the Hertz contact width and Hertz pressure were introduced. These gave: m

x =x/b

y=y/b

t = ut/b

P = P/PH

196

=hR/b 2

W = W/(PH b) = zt/2

n

E=4

ot = OtPH

_ I"IouR2 u = PH b~

1"1= rl/rlo

= P/Po

(15)

v = v/u

2

Provided the obvious changes are made to the expression for density, these non-dimensional groups may be used in place of the dimensional variables in the EHL equations to obtain, first, the smooth contact solution and, second, the effect of the surface roughness using equations 1 to 14. The groups, u and ~ which characterise the nature of the lubrication process may be expressed in terms of the Greenwood load and speed parameters, P and S, as:

_u=~--~l(S)

~=p

4

(16)

while the clearance, h, is related to H by: -

defined by P = 10 and S = 5 with the rough surface sliding under a stationary counterface. The wavelengths in the x and y directions are equal to 1.4 b and the result is for one particular instant of time.

H S 8/3

h = i ~ -ffz-

3

- a ~

I

-3

o

-2

Fig. I Roughness modification,

P= 10, S=5. ~7= 2, kx = ky = 1.4 b. While the flattening of the roughness under the contact is apparent this plot is somewhat difficult to interpret. It is, perhaps, preferable to note that a sinusoidal waveform of wavelength, ~., inclined at an angle, 0, to the y axis can be written as:

(17)

It may be noted that, with this, only the load and speed parameters P and S and the maximum Hertz pressure remain in the non-dimensional equations and that the Hertz pressure affects only the relationship between pressure and density. In order to reduce the number of independent parameters further, it was decided to incorporate the pressure-viscosity coefficient, a, into the expression for density and, taking a typical value of 20x10 -9 m2/N, the non-dimensional equation for density becomes: 0.115 P P P = P0 1 + 0.085 P P

o

1 +

(18)

where P is now the Greenwood load parameter. 4 RESULTS Results were obtained for a wide range of operating conditions, defmed by the load and speed parameters, P and S and for a range of surface velocities and roughness wavelengths. All results were for a unit amplitude of initial roughness, Ro. Fig. 1 shows a typical result for operating conditions

R = Ro cos

(~

2rt 0) x cos 0 - -'~ y sin

(19)

This may be expanded to:

R = Ro cos " ~ x cos

cos " ~ y

sin0)

2zt . 2zt + Ro sin(--~v-x cos 0 ) s m ( - - ~ - y sin0) which simply consists of the superposition of two solutions of the type shown in Fig. 1 with different phasings. Since the original solution can be recovered by superpositioning two sinusoidal waveforms with opposing orientations the two representations are equivalent. The angle 0 thus represents the orientation of a single, sinusoidal roughness or gives the ratio of the wave numbers in the x and y directions. Fig. 2 shows the results for the same operating conditions and wavelengths, replotted in this form, for three cases: a) rough surface stationary, b) pure rolling and c) rough surface sliding.

197

-

pattem at the exit. The effect is thus to change the pattem from one of waves at 45 ° to the y axis outside the contact to a lower amplitude, sinusoidal distribution at 90 ° to the y axis inside the conjunction. With pure rolling any disturbances in the inlet are convected at the entraining velocity - which, in this case, is the same as that of the rough surface and the result is to produce an attenuated clearance variation under the contact with the waves still lying at 45 ° to the y axis. There is, however, a small phase difference between the waves inside the contact and those outside. Finally, where the rough surface is sliding, the roughness reaching the inlet affects the clearances entering the contact. These disturbances are convected at the entraining velocity which is now half that of the rough surface and the effect is to halve the wavelength in the x direction. This results in an attenuated, sinusoidal roughness under the contact with an orientation of 27 ° to the y axis.

2

r'

-2 I

-3

-

2

r

-2 t

a.

--~5

-3

-

4.2 Roughness amplitude Although surface plots of the type shown in Figs 1 and 2 are useful in visualising the way in which the surface is modified, they are of less help when details of the clearance variation under the contact are required. In that case it is more useful to represent the data in terms of a plot of the amplitude of the roughness against x for y = 0 as in Fig. 3.

2

1"

1.0

.

.

.

.

.

.

.

.

•

.

.

.

.

0.5

-2

0.0 a.

-3

--~5

-0.5

-1.0 Fig 2 Sinusoidal roughness modification. P=10, S ......5, k = l , 0 = n / 4 . a) v .....O,b) v = l , c ) V = 2 In all cases the sinusoidal nature of the clearance variation outside the contact is clearly visible and this pattern is altered under the conjunction. Where the rough surface is stationary, the variation in the inlet region is carried into the contact somewhat reduced in amplitude. It is then convected across it, largely unchanged, before merging with the original

-2

0

X

2

Fig. 3 Clearance variation. P = 10, S = 5, 9~= 1, 0 =n/4, ~ = 2 In this figure the full line represents the clearance variation at time t = 0 (the real part of r) while the chain dashed line shows the maximum of this curve as t changes ( the magnitude or r). The features shown in Fig. 2c are clearly visible - the near uniform amplitude of the roughness outside the

198

contact and the attenuation and wavelength halving inside it. However, the graph reveals a little more detail. The amplitude inside the contact is not uniform as might be expected but oscillates slightly with a wave number equal to that of the original roughness. Examination of an equivalent result for an incompressible fluid shows this oscillation to be absent and it appears that fluid compressibility allows some of the original roughness to pass through the contact. Interaction of this with the complementary wave of half the wavelength produces the observed oscillation. This effect is generally of minor importance - except at very low wavelengths - but does make it difficult to define an amplitude of clearance variation under the contact. Finally, the clearance plots show sharp changes in amplitude at the exit and these are thought to arise from slight perturbations in position of the pressure spike as the roughness passes under the conjunction. These changes are critically dependent on the relationship between the convected, complementary wave and the original profile at the exit shown in Fig. 2c and thus change markedly with the roughness wavelength in the x direction. 4.3 Metallic, rolling contacts The complex behaviour shown in Figs 2a and c where there is relative sliding is known [9,10] to be heavily affected by variations in the piezoviscous parameter, c. (This parameter defines the magnitude of the piezoviscous effect and lines of constant c are represented on the P-S chart of Fig. 4 by lines parallel to the EI-EP boundary.) For example, under isoviscous conditions the wavelength halving effect shown in Fig. 2c is entirely absent as is the surface flattening of Fig 2a. This suggests that nonNewtonian effects are likely to be very significant and, for the present, attention will be confined to the case of pure rolling where they are likely to be of less importance. Venner et al. [3] examined this case for a range of metallic contacts with transverse roughness and produced a simple expression for the amplitude reduction. However, their results were restricted to a fairly narrow band of the piezoviscous parameter, c, around c = 25. It was decided, therefore, as an example of the present analysis to examine the full range of operating conditions for metallic contacts and to see how the roughness attenuation varied with operating condition, wavelength and roughness orientation.

:.,4s/.m.y

/!iIIil

,0,_

10 °10 0

lVIll i

."7/o

/o

I

If,'l

o/it

;t' ot/T// 1 01

p

I

III1.,,I

:! 1

Fig. 4 P-S chart for line contacts o EP conditions examined + RP conditions examined Fig. 4 shows a P-S chart for line contacts with lines of constant H drawn. The chain dashed lines define the four regimes of lubrication and are based on a condition that the regime equations define equal values of minimum clearance. The nineteen circles and pluses show the operating conditions for which results were obtained. The plus signs represent conditions where the contact is lightly deformed and the results for these were atypical. They are discussed separately. For each operating condition, the roughness modification was calculated for a wide range of wavelengths and for five values of 0 to obtain as complete a coverage as possible. Fig 5 shows one set of results for S = 5 and for values of P from 2 to 50. The left hand curves show the non-dimensional pressures and clearances for the smooth contact while the right hand curves show the roughness modification, in the form of amplitude plots, for a roughness oriented at 45 ° to the y axis. All results are for rolling contacts and the wavelength was chosen so that )rib pL5 S-2 was equal to 1.26. This group represents the ratio of the wavelength to the length of the inlet pressure sweep in heavily loaded contacts and, as will be seen later, largely controls the roughness modification. It may be seen that the operating conditions cover the region from a nearly rigid, isoviscous contact to a very highly deformed, piezoviscous conjunction with clearances varying by a factor of 1000 from the lightest to the most heavily loaded cases. The pressure spike is relatively small since this is controlled by the speed parameter, S, and low values of S produce small pressure spikes.

199

~)

1.o

10

1.0 r

0.5 ~p

0.5

5

0.0 -0.5

0.0

I

0 -5

b)

0

x

I

yl.O

2

i

-I0

5

1.0

.

.

.

.

.

.

I

i

0

._......

I0

x .

__

.

0.5

# 0.5

-1.0

h 0.0

1

m

-0.5 0.0 ~

_

_

L

-2

0

2

-1.0

0

X

o)

i

i

1

j

1

-5

i

L

I

0

5

x

0.4

1 . 0

m

P

h

0.5

0.2

l.o

....

.\,_.

,

-. . . .

0.5 0.0 -0.5

0.0

-1

0

_

0.0

1

-1.0

d)

1.0

0

-2

X

2

m

x

0.~0

-

~t'O 0.5

0.5

0.05

0.0 -0.5

0.0

0.00 -1

0

~:

-1.0

L

1

-2 _

e)

1.0

0.010

Y 1.0 0.5

0.5

0.005

0.0 -0.5

0.000

-1.0

0.0 -1

0

_ x

1

L

0

x

2

_

f, -

-2

-1

0

Fig. 5 Smooth contact pressures and roughness Inodification v=l 0=45° )~=126bp-15S 2 S=5 a) P - 2 , b) P = 5 , c) P ...... l O, d) P = 2 0 , e) P = 5 0 .

1

;

200

For the three higher loads, cases c, d and e, the roughness amplitude is nearly uniform outside the contact and decreases by around 50% inside it with a near uniform amplitude there. The slight deviations arise from compressibility effects. In all cases there is a sharp reduction in amplitude near the exit. As the value of P is reduced to 5, the extent of the flat under the centre of the contact, under smooth conditions, reduces but even here the roughness amplitude becomes nearly constant over this region with an amplitude ratio, again, of about 50%. In the most lightly loaded conjunction, P = 2, the maximum pressure drops below the Hertz value and, although piezoviscous effects are still present, the characteristic flat of piezoviscous EHL is absent. The shape of the roughness amplitude curve also changes with the region of uniform, reduced amplitude roughness under the centre of the contact being replaced by a narrower, less uniform reduction. This contact lies outside the elastic, piezoviscous (EP) regime. It was noted that all contacts operating inside that regime produced regions of near uniform, reduced amplitude roughness under the contact. Those outside did not.

-

1.0

~

._~.+~~~-+

_+

0.5

c

5

10 -

20

-

.

20

50

-

c,

50-

-

~.

~.. '

JL+

100

limiL a n a l 10-1

1 0 -2

0

=

~!(:~

10

~r

is

10 o

10 1

10

;k/b pS/:z S-2

= ~/4

1.0 o

0=2 cD "el

5

10

0.5

-I- c =

5

* "$" I> 0,0

-

10

20 50

2 - 5

x

4.4 Amplitude reduction For the contacts operating inside the EP regime the amplitude at the centre of the contact was noted and plotted against wavelength for three orientations of the roughness; 0 = O, n / 4 and n/2. The results are shown in Fig. 6. The wavelength is plotted in the form Mb p3/2 S-2 representing the ratio of the wavelength to inlet sweep. This form has been selected since analysis of the inlet of heavily loaded conjunctions [8,9] indicates that it is this ratio that controls the modification of the original roughness. In all cases the amplitude ratio was close to one for short wavelength roughnesses and dropped to zero as the wavelength was increased with the transition occurring through the range ~/b p3/a S-a = 0.1 to 10 although there was considerable variation with operating conditions and roughness orientation. Thus short wavelength roughnesses enter the contact largely unaltered while long wavelength roughnesses are largely flattened. For 0 = 0 (transverse roughness) the amplitude ratio did not vary significantly with operating conditions although there was a slight tendency for more piezoviscous contacts (higher values of c) to have slightly lower amplitude ratios.

5 -

-

.... 0.0

2-

=

x

~

10 20 50 100

-

10 20 50-

-2

10

10 10 ~ / b pSI2 S - 2 0

-1

1

10

=

1.0 o

\J "0 .p=l

5 10

o.s

20 c

x

0.0

c - 2

10 -2

=

2

-

5

I0

5 10 -

20

20

-

50

50

-

100

10

-1

50

o t 10 10 X/b p8/2 8-2

10

Fig. 6 Amplitude ratios For this case the results are compared with the results from the incompressible, limit analysis of [8] for transverse roughness (shown chain dashed in the

201

Figure 6a) and it may be seen that the correlation is reasonably good over the whole range of operating conditions. A separate, detailed comparison, not included in this paper, shows that the results for values of c around 25 agree with those obtained by Venner et al. [3] and also correlate well with the empirical curve given by those authors. However, the curve from the limit analysis seems to give a slightly better fit when the full range of results for all values of c is considered. For the other two orientations shown, operating conditions have more effect with the major influence coming from changes in the piezoviscous parameter, c. A simple curve fitting procedure was carried out for all results to produce an equation for the amplitude ratio: 1 / Amp ratio = 1 + z ( -0.525 + 0.127 cos 0 - 0.084 COS 2 0 ) + z C0.5 ( 0.231 - 0.1607 cos 0 + 0.0536 cos 2 0 ) + 0.4904 z 2 where z = ~,/b p3/2 8-2

(20)

These curves are shown on the figures for the higher values of 0 and, although the fit is not perfect, they do appear to predict the amplitude ratio to within about 5% over the whole of the piezoviscous regime. 4.5 Operation

in the rigid, piezoviscous

regime

Where the operating conditions lay outside the EP regime the behaviour changed and the previous results no longer apply. As an illustration of the change in behaviour, the contact operating with P = 2 and S = 20 will be considered. This contact lies on the boundary between the rigid isoviscous regime and the rigid piezoviscous regime. Under these conditions the smooth film thickness is relatively large compared with the elastic distortions. Fig. 7 shows the amplitude ratio for this contact for a range of roughness orientations. The behaviour when the roughness is in the transverse direction, 0 = 0, is broadly similar to the behaviour of contacts operating in the EP regime, with the amplitude ratio falling from one to zero as the wavelength increases. However, when the roughness lies at an angle to the conjunction the amplitude ratio falls extremely slowly with wavelength. Thus, even for long wavelengths the roughness is only slightly attenuated by the contact. It appears that when the roughness is exactly

transverse to the conjunction, the contact rises and falls as the waves pass under it.

_

!

1.0

0

-I-+

x x +x + + + []i ~-.

A o=.-I

0.5

-+ _

x

,~ -

,~/2

~

~/~o

=

~/200

_ ~- 11 = -

-

.

-~ = , r / z o o o

A

~

o I

0.0 10

-2

=

=

20

-

5

++ +

-X-* -X'-I-

**

[] []

~/2oooo

'~1=0

S P

[]

I I I IIIll

10

I

-1

I I I IIIll

10

I I IPltlIIHI .~,.~I ,-,I I I I III 0 1

10

10

h/b p3/2 8-2 Fig. 7 Amplitude ratio, P = 2, S = 20 Where the roughness is inclined to the y axis the contact is supported at intervals along its length. This prevents any rigid body movement of the contact. Amplitude reduction then depends on the flexibility of the contact support and this flexibility increases with ~,y with a logarithmic relationship between flexibility and wavelength. Because of this, extremely small misalignments between the contact and roughness effectively eliminate the rigid body displacement found at 0 = 0. In practice, therefore, it is, perhaps safer to ignore the amplitude reduction found when there is perfect alignment and to assume that there will be little amplitude reduction when the contact operates in this region. 5. CONCLUSIONS The analysis of two dimensional roughness in line contacts can be reduced to the solution of a steady, one-dimensional equation. This greatly reduces the solution time. The method has been outlined and applied to rolling, metallic contacts. It has been shown that, provided the contact is operating inside the elastic piezoviscous regime, long wavelength roughness components are flattened under the conjunction while short wavelength components pass through the contact virtually unchanged in amplitude. The amplitude reduction depends on the ratio of the roughness wavelength to the length of the inlet

202

pressure sweep, on the orientation of the roughness and on the value of a piezoviscous parameter, c. The magnitude of the surface deformation appears to have little influence. A very large number of cases have been analysed and an approximate equation for the amplitude ratio developed. This is believed to predict the amplitude ratio within 5% over the whole operating range for all wavelengths and all roughness orientations. Outside the elastic, piezoviscous regime the behaviour changes and as the contact becomes less deformed the amplitude reduction at long wavelengths is reduced. REFERENCES 1 Goglia, P. R., Cusano, C. and Conry, T. F., The effects of surface irregularities on the elastohydrodynamic lubrication of sliding line contacts, Part II- wavy surfaces, A.S.M.E., J. of Tribology, 1984, 106, 113-119. 2 Venner, C. H., Multi-level solution of the elastohydrodynamic line and point contact problems, Proefschrift, Universiteit Twente, Netherlands, 1991. 3 Venner, C. H., Couhier, F, Lubrecht, A. A. and Greenwood, J. A., Amplitude reduction of waviness in transient EHL line contacts, Proc. 1996 Leeds-Lyon Symposium on Tribology, Leeds, 1996, 103-112. 4 Greenwood, J. A. and Morales-Espejel, G. E., The amplitude of the complementary function for wavy EHL contacts, Proc. 1996 Leeds-Lyon Symposium on Tribology, Leeds, 1996, 307-312. 5 Greenwood, J. A. and Johnson, K. L., The behaviour of transverse roughness in sliding elastohydrodynamically lubricated contacts, Wear, 1992, 153, 107-117. 6 Lubrecht, A. A. and Venner, C. H., Aspects of two sided surface waviness in an EHL line contact, Proceeding of the 1992 Leeds-Lyon Symposium on Tribology, Leeds, 1992, 205-214. 7 Greenwood, J. A. and Morales-Espejel, G. E., The behaviour of transverse roughness in EHL contacts, Proc. Instn mech. Engrs. J, 1994, 208, 121-132. 8 Hooke, C. J., Surface roughness modification in elastohydrodynamic contacts operating in the elastic piezoviscous regime, Proc. Instn Mech Engrs. J, 1998, 212, 145-162.

9 Hooke, C. J., The behaviour of heavily loaded line contacts with transverse roughness, Proc. Instn Mech Engrs. C, (in preparation). 10 Hooke, C. J., The behaviour of low amplitude surface roughness under line contacts, Proc. Instn Mech Engrs. J, (in preparation).

S E S S I O N VII S T R I B E C K CURVES

Chairman:

Professor R.C. Coy

Paper VII (i)

The Importance of the Stribeck Curve in the Minimisation of Engine Friction

Paper VII (ii)

Theoretical and Experimental Results on Friction for Line Contact in Mixed and Elastohydrodynamic Lubrication Regimes

Paper VII (iii)

Isoviscous-EHL and Mixed Lubrication Mechanism of Parallel Slide-Way with Oil Groove

Paper VII (iv)

Calculation of a Stribeck Curve of a Journal Bearing

Paper VII (v)

Real Contact Area, Contact Temperature Rise and Transfer Film Formation Between Original and Worn surfaces of CF/PEEK Composites Sliding Against Steel

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

205

The importance of the Stribeck curve in the minimisation of engine friction C. Bovington*, S.Korcek** and J. Sorab** * Exxon Chemicals; ** Ford Research

The improvement of engine fuel efficiency through the use of low friction engine oils can make significant contributions to the reduction of gaseous emissions and to the conservation of natural resources. One route to the reduction of friction is the reduction in lubricant viscosity. This, however, may lead to reduced durability because of the consequential reduction of oil film thicknesses. The minimisation of total engine friction requires optimisation of both rheological and surface chemical properties of the lubricant. Solving these problems requires a sophisticated approach because of the wide range of temperatures, pressures and shear stresses experienced by the oil and because of the wide range of surface speeds and contact geometries encountered in an engine. Engine components experience various combinations of hydrodynamic, elasto-hydrodynamic and boundary or mixed lubrication during engine operation. For each of these regimens the factors which control friction can be different. Crankshaft bearings and valve train components are both sensitive to wear and contribute significantly to total engine friction. In this study friction and wear under a range of crankshaft bearing operating conditions has been studied in a bearing simulator rig. The variables were speed, load, temperature and lubricant composition. The Stribeck type curves obtained show clear differences due to rheological properties and also show how the transition from thick film to 'mixed' operation can be influenced. Friction under elastohydrodynamic conditions was studied in a ball on disc traction tester. Traction coefficients of the test oils were measured as a function of slide / roll ratio and of temperature. Stribeck type EHD traction curves were generated showing friction as a function of entrainment speed at the limiting slide / roll ratio. Film thicknesses generated by the test oils, under EHD conditions, were measured as a function of entrainment speed and temperature using an optical film thickness rig. Friction measurements under boundary conditions shows clear differences due to lubricant formulation effects. The resulting 'Total' picture shows that low viscosity oils can be formulated to achieve high levels of friction reduction without risk of reduced durability.

1. I N T R O D U C T I O N A major emphasis in engine lubrication research is the improvement of engine fuel efficiency through the use of advanced low friction engine oils. Friction reduction is achieved by improving the viscometric characteristics of engine oils, as well as by controlling surface chemical interactions between oil-based additives and the lubricated components in the engine. The selection of optimal lubricant rheology and surface chemistry, coupled with component surface geometry to yield high fuel efficiency is a complex problem. This is because friction in an engine originates from several components operating at widely different conditions of temperatures, shear rates, loads, and surface

speeds. All of these factors will impact upon the effective dynamic viscosity of the oil in the various contacts. Some parts of the engine will operate under essentially hydrodynamic conditions and some under essentially elasto-hydrodynamic conditions. The impact of the dynamic viscosity of the oil upon friction is different under HD and EHD conditions. Under both hydrodynamic and elastohydrodynamic conditions, control of the progression from thick film to 'mixed' lubrication is important for the control of both friction and wear The objective of this study was to establish how , by a combination of mechanical design and lubricant formulation, low viscosity oils could be used to give significant energy savings without risk to engine durability.Fundamentally, the aim of this effort may

206

/ H i g h e r viscosity oil ~'

0

~J~- .

ii, / J~

Lower viscosity oil

:' " :~. ~.

Lower power loss in hydrodynamic lubrication

0 •:

,,~ ........................... .........% .......................................................... ~

%'°°°,, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.............•.........................

°°°o°°°

Higher viscosity oil

1¢- .

Lower viscosity oil Lower power loss in hydrodyn.ami...c..1.:..ubri.......ati......0n. c.:

,~..::..:...~

°°°

°°°° . . . . . . . . . . . °'°°° °°°°°°° . . . . . . . . . . . . .

Earlier transition to mixedlubrication: greater powerloss, wear

Latertransitionto mixedlubrication: lowerpowerloss, wearprevention Speed

(a) Effect of reducing oil viscosity

f

Speed

2. E X P E R I M E N T A L

2.1 Bearings Lubricant performance in bearings was evaluated using a static journal bearing test rig [1,2]. Test bearings are housed in a 2.5L V6

f

(b) Effect of reducing oil viscosity with improved EHD, mixed lubrication behavior.

Figure 1" Power loss in different lubrication regimes

be explained graphically using Figure 1. While reducing engine oil viscosity results in lower viscous friction losses in hydrodynamic lubrication, it may move the modes of operation of some components into mixed-boundary regimes at higher speeds and lower loads than with higher viscosity oils. A delayed transition to mixed lubrication (Figure l b) is beneficial to components that operate in these conditions, such as the valvetrain, and the bearings under certain conditions [1,2]. Coupled with low viscosity, this will ensure reduced friction under most conditions of engine operation, while still maintaining protection against wear, which would most likely occur with prolonged surface contact. To achieve this goal, we have been investigating advanced engine oil formulations and their performance under various operating conditions using laboratory bench test rigs. This work complements Ford's efforts to identify component designs that can minimise friction under operating conditions [2, 3].

x.

production connecting rod assembled on the test section of a steel shaft. The shafts are machined from ASTM 1045 steel to simulate the C-38 steel forging used in the Duratec engine, and test sections are finished to the same specifications as those for production crankpins. The test shaft is housed in two heavy duty ball bearing pillow blocks placed symmetrically about the load line, and is driven through a belt drive by an AC motor. Test oil is contained in an externally heated 3 litter tank, and is pumped into the connecting rod diametrically opposite the load line using a 0.4 1/s gear pump. Independent pressure and flow control valves are used to control flow into the bearing; excess oil flows back into the tank. Loads on the bearing are applied by means of a servoactuator comprising of a 6.35 mm diameter hydraulic cylinder coupled to a 3.8 1/s servovalve. A 0.63 1/s hydraulic unit supplies pressurised oil to operate the actuator. A pressure regulator at the outlet of the hydraulic unit controls oil pressures and therefore loads. Measurements include journal speed and torque, connecting rod friction torque, oil inlet pressure and temperature, and bearing wall temperature. A schematic description of these measurements is shown in Figure 2. A typical test starts with the sample oil being heated to its test temperature (IO0°C) while being circulated through the test bearing. When the test temperature has stabilised, a baseline reading is

207

obtained by ramping the joumal speed from 500 rpm to 3000 rpm in 250 rpm increments, and gathering average sensor data at each stage over 5 rotations after a software-determined stabilising period. The baseline friction readings are subtracted from corresponding readings under load to eliminate the friction associated with the pillow blocks and test fixtures from final analyses. At the highest speed used in this test (3000 rpm), the loading mechanism is activated and a 5500N load is applied. The speed is then decremented gradually to 500 rpm and the friction is allowed to stabilise before repeating the data gathering process as speed is ramped up to 3000 rpm. These steps are repeated at l l000N and 22000N load conditions. The

W

nominal oil supply temperature at the bearing was 100°C(+ 2°C), and the nominal supply pressure was 350 kPa ( +5 kPa) for all tests. 2.2 EHD Film Thickness Elastohydrodynamic film forming properties of lubricants were measured in an optical EHD [3] test rig over the temperature range of 40 to 140oC and at speeds of 10-3 to 102 m/s. In this test, a rolling lubricated contact is formed between a reflective, smooth steel ball and a rotating, flat transparent glass disc. This disc is coated with a semi-reflective coating of chromium upon which is deposited a transparent layer of silica.

-applied b a d

15 °

\

___~ FcR• friction fDrc~ on conn ectJng rod

\

T orquem eter

\ \ l

B earing w all te~ perature

\ \ Tj /

•fr/ct/on torque on rotating lburnal

B ]ocJ~s

Inlet oil t ~ perature Inlet oilpressure

Figure 2" Measurements on connecting rod in bearing test

y

! C o n . r o d friction sensor

A pplied b a d

208

The latter acts, in effect, like an oil layer so that the optical interference of the incident light beam occurs even if no oil film is present. As a consequence of this layer, oil films much smaller than the wavelength of light can be measured. A spectrometer and an image analyzer are used to determine the precise wavelength of maximum interference. The combination of spacer layer and spectrometer analysis enables film thicknesses in rolling contact to be measured down to less than 5 nm, with a precision of between 1-2 nm. Figure 3 shows a schematic of the test rig.

Load Beam r

Traction Tmnsd

Ball Motor

Disc

Ball

II J~o

\ ~

//

Load Motor

Di

o

/

I

2.3 EHD Traction Coefficient

Ball Girnbal Mount

Elastohydrodynamic friction or traction properties were using a ball on disc traction rig (Figure 4). Both the ball and disc are driven by separate DC motors, enabling control of the slide/roll ratio. Traction measurements are made between a 19.0 mm diameter AISI 52100 steel ball and the steel disc. The Young's moduli of the two surfaces are both 210 GPa and the applied load was 30N. The behaviour of oils under EHD traction was studied at a range of different slide/roll ratios at a fixed disc speed. Measurements were made at a series of temperatures ranging from 40 to 135 ° C. C~ra~um I Silica

Layer

Glass

I

To SpecCrun~

Figure 4" EHD Traction Rig

2.4 Mixed Lubrication Friction The cam-follower and piston ring-cylinder bore contact operate in mixed lubrication conditions for a significant fraction of time, where contact load is shared between a thin hydrodynamic film and asperity contacts. A measure of lubricant performance under such conditions was obtained in the above rig by maintaining a constant slide/roll ratio (50%) and progressively reducing the rolling speed, and therefore the EHD film thickness. This enables a plot of traction coefficient at various entrainment speeds, similar to the classical Stribeck diagram for hydrodynamic lubrication. 2.5 Boundary Friction Boundary friction coefficients were measured over temperatures from 40 to 140°C using a High Speed Reciprocating Rig (HFRR). The test consisted of a 6 mm AISI 52100 steel ball reciprocating against a similar steel disc at 20 Hz with a stroke of 1 ram. A 1ON load was used in all tests. A summary of the test conditions in all the rigs is outlined in Table 1.

Figure 3: EHD Film Thickness Rig

209 Table 1 Test conditions in various rigs Test rig

Contactpressure GPa

Speed m/s

Shear rate 1/s

Temperature °C

EHD Traction

0.50

0-2

= 10 7

40-140

0.035

BC>M~H

EHD Film

0.34

0-2

= 10 7

40-140

0.015

B~M~H

HFRR

0.35

-- 1 0 7

40-140

0.035

B

Bearing

0.022

2-8

10 6 -

107

100

0.5 - 0.8

MC>H

Bearing

0.011

2-8

10 6 - 10 7

100

0.5 - 0.8

MC>H

Bearing

0.006

2-8

10 6

100

0.5 - 0.8

H

10 7

-

Compositesurface roughness, gm

Lub.regime

Table 2 Test Oils ~ . , . ~ . ~ ; , : ~ . ~ , v , ~ v ~ , ~ . ~ , ~ , ~ , ~ , ~ , ~ . . . . . . . . :

.

.

.

.

.

.

.

Oil code

SAE grade

RO93

5W-30

63.43

RO87

5W-30

RO641

~

=

~

~

~

_

.

-

~

,

~

,

_

-

-

~

.

~

.

Kin. viscosity, mm2/s 40°C 100°C

-

-

~

-

~

-

-

~

_

~

.

~

.

,

~

-

~

-

-

-

~

.

~

.

~

-

~

.

.

~

. ~ . ~ . ~ .

~

HTHS visc. mPa.s.

FM type

ZDDP type

P level

10.78

2.96

-

N/A

0.10

51.65

10.01

2.90

MoDTC

N/A

0.10

5W-20

50.49

8.55

2.69

OFM

Secondary

0.09

RO642

5W-20

50.84

8.56

2.65

OFM

Primary

0.06

RO643

5W-20

52.34

8.69

2.68

MoDTC

Primary

0.09

RO644

5W-20

52.92

8.70

2.67

MoDTC

Secondary

0.06

2.6 Test Oils The test oils used in this study are shown in Table 2. RO641-RO644 are experimental oil formulations developed by Paramins for this study. RO641 and RO642 contain an organic friction reducing additive with differing types and proportions of antiwear additive. RO643 and RO644 contain molybdenum based friction reducing additives, which have been shown in

.

previous studies to deliver lower friction in mixed and boundary lubrication conditions [1,5]. These oils also differ in the amount and type of antiwear additives. For comparison, two oils previously evaluated have been included in this study. 3. R E S U L T S

AND DISCUSSION

Bearing back wall temperatures measured under static load conditions are shown for all the oils in

210

Figure 5. While no significant differences can be observed at the higher speeds, RO93 exhibits a sharp increase in temperature with decreasing speeds. All the other oils also exhibit smaller increases in temperatures, but the transition occurs at lower speeds and with smaller magnitudes of increase. This effect is explained by Figure 6, where the journal friction torque is plotted as a function of speeds.

160 ............................................................................................................................................................

oRO93

.=

• RON1

o C~

n RO542

o 120

• A

• RO643

A 0

0

0

a RO544 • RO87

m I

0

I

1000 2000 SI-Nt speed, rpm

300O

Figure 5" Bearing wall temperature data Data were obtained under steady load of 22000N at 100°C, 345 kPa inlet oil conditions A 5.00

..........................................- ~ " .............................................................................................. /

0

Z 4.00

o RO93

3.00

indicated that oils with effective friction reducing additives, such as MoDTC exhibit a delayed transition to mixed lubrication in this test. This is illustrated in Figure 7, where the Stribeck curve for journal bearings is plotted. The light envelope represents data at several temperatures and load conditions for some nine non-friction modified oils of various viscosity grades. These oils exhibit the sharp increase in friction at low values along the abscissa that is characteristic of mixed lubrication. The dark envelope at the bottom right of the graph contains data from six MoDTC containing oils, that exhibit the delayed transition to mixed lubrication. All the experimental oils in the present study fall in this envelope, despite the fact that two oils (RO641, RO642) contain an organic friction modifier. These oils demonstrate significantly higher friction in a conventional reciprocating boundary friction test (Table 3), suggesting that the delayed transition to mixed lubrication in the bearing test could be due to properties other than friction modification. Only RO93 exhibits the higher friction behaviour typical of non-friction modified oils in both the bearing test and the boundary friction test. Repeatable distinctions are also observed between the pairs of oils containing organic friction modifier (RO641, RO642) and MoDTC (RO642, RO644) in Figure 6. At the lowest speed of the test (500 rpm), which represents the harshest test condition under high load, the oils with MoDTC exhibited slightly higher friction, and correspondingly higher temperature than the oils with organic friction modifier.

u~ 2 • EYa43

0 "~

U.,

0

,1~t7

6

i.

= 1.00 0

0.00 0

Table 3" Friction Coefficients for test oils

•-~ 2.00

I

I

1000

2OOO

3O3O

Figure 6: Journal friction torque measurements Data were obtained under steady load of 22000N at 100°C, 345 kPa inlet oil conditions

Under mixed lubrication conditions, the oils with friction reducing additives exhibit sharply reduced friction relative to RO93.Previous studies [ 1,2] have

...: . . . . . . . . . . . . . . . .

Oil RO93 RO87 RO641 RO642 RO643 RO644

v............. -........:

60°C 0.113 0.045 0.118 0.111 0.06 0.087

~

,

~

:

:

:

:

:

:

100°C 0.138 0.051 0.120 0.118 0.065 0.063

:

~

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

140°C 0.139 0.053 0.122 0.120 0.096 0.078

To better understand the phenomenon of delayed transition observed in Figures 5 and 6, we have investigated the performance of these oils in mixed and EHD lubrication conditions.

211 100 ........................................................................................................................................................................................................................... • RO93 m RO641 • RO642 /x RO643 o RO644 o RO87

r(r/c)

10

•

,0

© f

0.000

0.020

I

0.040

I

0.060 g (N/p)(r/c) 2

I

0.080

I

0.100

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

0.120

Figure 7: Dimensionless analysis of bearing data

3.1 E.H.D. Film Thickness Studies Lubricant film thickness under elastohydrodynamic contact condition varies with entrainment s p e e d , U, dynamic viscosity, rl and with the effective viscosity / pressure coefficient, c~.

hmin oc q 0.67 , U0.67 (3(,0.48

Thus a plot of film thickness v entrainment speed should have a positive slope with a gradient of 0.67. Figure 8 shows film thickness as a function of entrainment speed at 100°C. for all of the test oils. It is significant that, at higher speeds, ( 1 ms-1), the 5W-30 grade oils, RO87 and RO93 did not give thicker films than the lower kV100, 5W -20 grade oils. This suggests that at the shear stresses experienced in EHD contacts, the 5W-30 oils had experienced high levels of shear thinning than had

the 5W-20 oils. These contact conditions are found in Cam / Follower contacts. It is significant that the less viscous oils would, in this case, be expected to give better wear protection than the more viscous ones. The data at lower speeds, ( 0.01ms-1 ) shows clear evidence of a further significant difference between the 5W-30 and 5W-20 oils. All of the 5W20 oils show strong positive deviation from the theoretical slope. All are forming strong, viscous surface films. Such films have been shown to be formed by ZDDP's, friction modifiers and by dispersant VM's. They are associated with good wear protection.[5,6,7]. Neither of the 5W-30 oils tested for comparison showed deviation from the expected straight line. Both Mo and non-Mo oils showed similar behaviour. These trends were also seen at lower temperatures.

212

100

0.035 0.030 0.025

ra~

0.020

O

[--,

• RO641

10

.,...

WRO642

0.010

,:.*,.RO643

J

m

RO641 ....m ......RO642 RO643 --x--- RO644 RO87 + RO93

0.015

0.005

X RO644

.... 0.000

x RO93

0

• RO87

I

I

I

10

20

30

i

40

50

60

Slide/Roll ratio, % 0.01

0.10

1.00

10.00

Speed, m/s

Figure 9: Traction coefficients as a function of slide/roll ratio at 100°C

Figure 8" EHD film thickness as a function of entrainment speed at 100°C. 3.2 Elasto-hydrodynamic Traction Curves: Elasto- hydrodynamic traction curves were generated for all of the test oils. Results obtained at 100 ° C. are shown in Figure 9, below. Traction ( friction ) is measured as a function of slide / roll ratio under EHD conditions. Shear stress, x, increases as the slide / roll ratio increases and the curves generated display three regions. 1/ Newtonian Viscous- a linear region where shear stress, x, is proportional to shear rate, 3,, at the high pressures encountered in EHD contacts, this region is restricted to extremely low sliding speeds, traction is dominated by the non-linear behaviour. 2/ Non-linear region- where shear thinning and viscoelastic response of the lubricant to the high shear stresses is predominant. Here the dependence of shear stress to shear rate is no longer proportional.

3/Plastic Region- At high contact pressures the film of lubricant reaches a limiting plastic yield stress, this stress may fall with increasing shear rate due to the thermal heating in the contact. This heating can cause reduction in viscosity. This region is normally seen at slide to roll ratios of the order of>50 %. We term the traction value at this slide to roll ratio, 50% , the limiting traction coefficient. Low values of limiting traction coefficients are associated with high levels of fuel efficiency. The results obtained on the oils tested show that significantly higher values of limiting traction coefficients were found with the two 5W-30 oils than was found with the 5W-20 oils. These differences would be expected to translate into an advantage in fuel economy performance. Figure 10, below shows values for the limiting traction coefficients for the oils studied.

213 ro o 0.030

0.08

o

• RO641 u RO642 ¢) .1-.q 0

0

o 0

0/)

•,=, - ~ 0.020

x RO641

.,.., o

¢)

o

:~, RO643

0.06

FI, I t

0

~ 0

~ 0

x RO87

ID O

o 0.04 i:~ ° o

• RO93 "

O .,.., ,.J O

X ~ X II'O0

OOe

O0 O0 ,~ O O O

[0.02

I

~ 0

O ~

O

0.00

i

0

Figure 10: Limiting traction coefficients at 100°C

0.5

i

1

i

!

1.5

2

2.5

Speed, m/s

Figure 11" Stribeck-like traction curves at 100°C 3.3 Stribeck Traction Curves: In the 'Stribeck' curves, traction coefficients are measured as a function of entrainment speed. The slide / roll ratio is maintained at 50%. Since film thickness is proportional to entrainment speed, we are effectively measuring friction (traction) as a function of L ratio. Figure 11, below shows curves of traction coefficient as a function of entrainment speed for all of the test oils at 100 o C. At entrainment speeds of 2 ms-l, ~ is typically of the order of 3. Friction under this condition reduces with decreasing values of dynamic viscosity and pressure / viscosity coefficient, a. The value of k decreases to 1 at around 0.5 ms-1 and it is in this region that we see the transition to 'mixed' lubrication with the consequential rise in friction. The values of traction coefficient measured at the slowest speeds approximate to the value of the boundary coefficient of friction. The two 5W-30 oils show inferior performance to the four 5W-20 oils. Under thick film conditions they show high levels of friction, they show transitions to higher friction at high speeds and show higher friction as the boundary lubrication regimen is approached. RO93 is significantly worse than RO87.

It is significant that the oils, RO641 and RO642, formulated without MoDTC performed equally with the MoDTC containing oils. This would not be the case with most other non-Mo 5W-20 oils, the performance seen arises from the use of a particular combination of organic friction modifiers and other additives which have been shown to be especially effective at modifying traction in the 'mixed' regime. Similar behaviour is seen at other temperatures. Figure 12 shows the cumulative area under the Stribeck traction curves. It represents the total frictional losses encountered under all film thickness conditions and low values are a strong indicator of both fuel efficiency performance and of good wear protection. The differences between the 5W-30 and the 5W-20 oils can be clearly seen, with a strong advantage for the 5W-20 oils. Similarly the similarity between the Mo and nonMo oils can be clearly seen.

214

= 1.00 1

The use of high treat rates of Mo additives is not essential to the provision of good wear protection and high levels of energy efficiency. Oils formulated with MoDTC do give lower friction under boundary conditions

100°C "Q 0.80 0.60

REFERENCES

0.40 >

"~ 0.20 0

0

0

0

1.

Sorab, J., Korcek, S., Brower, C.L., and Hammer W. G., 'Friction Reducing Potential of Low Viscosity Engine Oils in Bearings.', SAE 962033, 1996.

2.

Sorab, J., and Korcek, S., 'Engine Oil and Surface Effects in Journal Bearing Lubrication.' SAE 981408, May 1998.

3.

Johnston, G.J., Wayte, R., and Spikes, H.A., 'The Measurement and Study of Very Thin Films in Lubricated Contacts, ' Tribology Trans., 34,pp 187-194,1991.

4.

Johnson, M.D., Jensen, R.K., and Korcek, S., 'Baseoil Effects on Friction Reducing Capabilities of Molybdenum Dialkyldithiocarbamate Containing Engine Oils', SAE 972860, 1997

5.

Tripaldi,G., Vettor A., and Spikes, H. A., 'Friction Behaviour of ZDDP Films in the Mixed, Boundary/EHD Regime.', SAE 962036, 1996

6.

Anghel, V., Bovington, C., and Spikes, H.A., 'Thick Boundary Film Formation by Friction Modifier Additives' Proceedings of the 1 l th Intl. Conf. on Tribology, Esslingen, p 2027, 1998.

7.

Smeeth, M . , Gunsel, S., and Spikes, H.A., 'Friction and Wear Reduction by BoundaryFilm-Forming Viscosity Index Improvers.' SAE 962037, 1996.

~

Figure 12: Cumulative area under traction curves shown in Figure 11.

4. CONCLUSIONS A series of experimental engine oils has been evaluated to assess their friction and film forming properties under boundary, hydrodynamic and elastohydrodynamic, lubrication conditions. Four of these oils were formulated as SAE 5W-20 oils with differing friction modifier and antiwear chemistries. The remaining oils were SAE 5W-30 oils typical of current GF-2 engine lubricants. These oils were formulated with and without MoDTC. Film thickness, friction and temperature measurements in the Bearing rig and traction measurements under EHD conditions show that : 5W-20 oils formulated to expected GF-3 specifications can offer significant reductions in friction related losses in engines. When compared to conventional 5W-30 oils These improvements in performance can be achieved in both thick film and 'mixed' lubrication conditions and under both moderate and high contact pressures.

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

215

Theoretical and experimental results on friction for line contacts in mixed and elastohydrodynamic lubrication regimes R. Bassani a, E. Ciulli a and B. Piccigallo b aDipartimento di Costruzioni Meccaniche e Nucleari, Universith degli Studi di Pisa Via Diotisalvi, 2 - 56126 P i s a - Italy bAccademia Navale Viale Italia- 57100 L i v o r n o - Italy

In this work the typical rectangular conjunction is studied both theoretically and experimentally. Different situations are investigated from mixed to elastohydrodynamic lubrication conditions. Experimental investigation is carried out by means of an apparatus for friction force and film thickness measurements; theoretical study is based on the numerical solution of the thermalelastohydrodynamic lubrication problem for line contacts with a finite element program. The experimental results clearly show the typical transition from mixed to elastohydrodynamic lubrication depending on the surface roughness of the specimens as well as on the lubrication parameters. The numerical program gives results in good agreement with the experimental ones for the EHL regime.

NOMENCLATURE

1. I N T R O D U C T I O N

f F h S St t T

The "Stribeck" curves are used to show the transition between different lubrication regimes, though different curves are obtained for different working conditions of the lubricated contact. The transition between mixed and fullfilm lubrication regimes is also well characterised by the dimensionless film thickness A, defined as

u Ul u2 w

friction coefficient applied load [N] film thickness [m] slide-to-roll ratio, hu/u Stribeck number, ~t0"u/w axial width of the specimens [m] temperature [°C] rolling speed, (Ul+U2)/2 [m/s] surface speed of disc [m/s] surface speed of specimen [m/s] load per unit length, F/t [N/m] = ~(~t/ ~t0)l ~P I(P=°;T = T o)

Au A ~t ~to

[m2/N]

= ~(~t/ ~t0) [1/oc] ~T (p=0;T = T o ) sliding speed, u2-u~ [m/s] dimensionless film parameter lubricant viscosity [Ns/m 2] lubricant viscosity at inlet [Ns/m 2]

n +

where h is a representative value of lubricant film thickness and Rq~ and Rq2are the RMS values of the roughness of the two bodies in contact. As well known, rectangular EHL contacts are widely studied from the theoretical point of view, whereas a r a t h e r smaller n u m b e r of

216

experimental studies are available; some of these are reported for instance in [1]. Studies on rectangular contacts have already been made by the authors [2]. In this work the problem of line contacts is studied from the point of view of friction using some cylindrical specimens in contact with a plane surface of a glass disc in different lubrication conditions. The experimental apparatus, described elsewhere [3], is a typical test rig for film thickness and friction force measurement; different rolling and sliding speeds, load and lubricants can be tested. The specimens are made of different materials and have different surface roughness. The friction coefficient is calculated for each operating condition, in particular varying the rolling and sliding speeds, load and temperature. Results, obtained by variation of the above-mentioned quantities, are grouped together in the form of Stribeck curves.

central zone, framed by the camera used for recording the interference images, without end effects and, in the meantime, to avoid a large variation of speed along the radial direction of the disc. Two specimens are made of steel, one is made of aluminium and the last specimen is a 1.5 mm thick ring of K40 (89% tungsten carbide, 11% cobalt) soldered to a steel core. They are machined in different ways and have therefore a different surface texture.

,!

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

...........

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

i

2. EXPERIMENTAL SETUP AND DATA ACQUISITION

Figure 1. The tested cylindrical specimens.

A data acquisition system has been used with the experimental apparatus. The system is made by a digital acquisition board (100 kS/s, 16 single-ended analog inputs, 2 analog outputs, 8 digital inputs/outputs) connected with a portable modular signal conditioning system which can hold up to 20 modules. In particular, the analog outputs are used for controlling the speed of the electric motors (which drive disc and specimen); the analog input channels are used for recording inlet and outlet lubricant temperature (by means of thermocouples), the speed of disc and specimen (by means of tachometric dynamos) and the traction force on the specimen (by means of a load cell). Four cylindrical specimens, shown in Fig. 1, have been tested. The investigated surface has a diameter of 42 mm and an axial length of 3 mm. The axial length was chosen in order to have a

In Fig. 2 pictures of the specimen surfaces, taken with an optical microscope, are shown together with the traces obtained with a stylus profilometer (due to the light loads used in the tests, the condition of the surfaces remains practically unchanged after the tests). The profilometry traces refer to the roughness measured along the axial direction; roughness in the circumferential direction is generally smaller and with lesser differences among the specimens. Specimens marked with C1 and C3 are both made of steel, but C1 has been ground less than C3 and has been successively polished by hand; consequently, it has a roughness value smaller than C3, though its shape is affected by larger roundness errors and some deeper grooves are present. The specimen indicated with C2 is made of aluminium; though it has been hand polished in a similar way as C1, it

217

presents a very irregular surface caused by the different machinability of the material. Finally, C5 is made by sintered alloy of tungsten carbide and cobalt, very suitable for grinding, and p r e s e n t s the best surface quality. The transparent disc is made of BK7 glass with a 200/~ thick chromium layer, pro-

tected by a 1000 A thick SiO2 coating. Its roughness is Rq=0.015 pm. The lubricant used in all tests is SN600: a paraffinic base mineral oil. The four specimens have been tested for three different loads (F = 20, 30 and 40 N) and two oil temperatures (T = 30 ° and 50°C). The rolling speed u has been varied from 0.05 to 1 m/s and four different values of the slideto-roll ratio S have been used (S = 0, 0.25, 0.5, 1). The tests were carried out in an automatic way with the aid of a numerical program developed using the software LabVIEW. With this program, averaged values of load, friction force, temperature and rolling and sliding speed were stored in files at the end of each run in different conditions.

Figure 3. Detail of the test rig. For tests with very low disc speed an additional oil supply directed towards the specimen has been used together with the one lubricating the surface of the disc (Fig. 3).

3. NUMERICAL SIMULATION

Figure 2. Profilometry traces and magnified views of the surface of the four specimens after the test.

The experimental data collected by means of the aforesaid test rig (especially the coefficient of friction and the shape of the lubricant film) have been compared to similar results obtained by numerical simulation. Calculations have been performed by means of the program MacEHL, which is able to solve a wide range of EHL problems with a complete assessment of the t e m p e r a t u r e field (the algorithms on which it is based are outlined

218

in [4]). An important feature of this program is the inclusion of a flexible lubricant model, t h a t can even emulate roughly the viscoelastic behaviour, which is characteristic of most lubricants in certain operating conditions (far, however, from the conditions experienced in this work). Since M a c E H L was initially developed to study EHL problems characterised by medium and high H e r t z i a n pressure (hardEHL), whereas the contacts considered in the present work show a lubrication regime near the limits of the EHL zone, some minor modifications have been introduced. In particular, a wider integration domain was needed (even more t h a n 60 times the Hertzian half-width). F u r t h e r m o r e , in order to correctly evaluate the friction coefficient it was necessary to assess approximately the tangential force on the rollers in the zone after the outlet point (where relative pressure vanishes), which is usually negligible in case of hard-EHL.

4. R E S U L T S

Both experimental and numerical data are obtained, for each condition of load, temperature and rolling speed, varying the slide-toroll ratio. From the results, it appears clearly that thermal effects are not important in the range of loads, speeds and temperatures used for the tests: the friction coefficient always rises with the slide-to-roll-ratio, S. However, the trends vary for the different specimens and test conditions. As an example, in Fig. 4 the trends recorded for the specimen C1 and C2, in the same experimental conditions, are shown. All curves in these diagrams are assumed to start from zero because, as usually done, friction force in pure rolling conditions is used as a reference value, being negligible in comparison with the friction due to sliding, and therefore set to zero. Comparing the two diagrams, it is to be noted that, while the friction coefficient f increases (for the same S) with the rolling speed for C1, it decreases for C2, clearly indicating a different lubrication regime. In ad-

dition to this, the absolute values of f for C2 are bigger. As better shown later, this can be explained because C1 works in an elastohydrodynamic (or hydrodynamic) lubrication regime, w h e r e a s C2 w o r k s in m i x e d lubrication. 0,008

0,006

-

-

,

u=6.05mSs

-

u=O.O75mls

'

--

u=O.lmSs

- - o - - u=O.2mSs --.i-- u=O.4mfs

0,004

/ f'

0,002

,f

0

0,2

0,4

0,6

0,8

I

s 0,06

-

-- u=13.076mls A u=0.1mls 0,05 - -o-- u=O.2mSs ~u=O.3mSs 0,04 - ~ u = O . 4 m l s

r

,- 0,03-

___----

f/

fJ

0,02 0,01 0

0,2

0,4

0,6

s

0,8

I

b

Figure 4. Friction coefficient as a function of the slide-to-roll ratio S for specimens C1 (a) and C2 (b), in the same test conditions (F = 20 N, T = 30°C). For most tests this kind of diagram shows intersecting lines, clearly indicating transitions between the two lubrication regimes. For a better understanding of the involved phenomena, results are elaborated to be presented in typical Stribeck diagrams, where the friction coefficient is plotted versus the

219

number St. Experimental results for specimen C3, except those obtained for F=30 N, are reported in Fig. 5. In this diagram the typical behaviour of the mixed lubrication (with f decreasing as St increases) is evident for low values of St, whereas for high values of St, f rises with St, as is characteristic of elastohydrodynamic lubrication. The parameter showing the most remarkable effect is clearly the slide to roll ratio S. 0.01

0.008 •

0.006 •

f

y

0.004

0.002

O.OE+O0

4.0 E-06

8.0 E-06

1.2E-05

1.6E-05

St=l.tou/w

Figure 5. Stribeck curves for specimen C3 with different values of slide-to-roll ratio (D, m: S=I; o, .: S=0.5; A, A: S=0.25), load (big symbols: F=40 N; small symbols: F=20 N), and temperature ( i , . , A: T=30°C; D, o, ~: T=50°C). Higher values of f have been obtained for the heavier load (it is not to forget that S is constant for these curves obtained essentially varying u and Au); this effect decreases with S (on the other hand it is well known that in EHL regime f should be almost proportional to S, until thermal or non-Newtonian effects become prevalent). When t e m p e r a t u r e increases the friction coefficient decreases, but, as for the load, the differences in values of f tend to diminish for high values of St. Similar effects of load and temperature have been noted for the other specimens.

Only for C2 the effect of load is inverted: the reason will be clarified later. Since the effect of F and T is small, Stribeck curves can be traced by averaging all the results obtained for each value of S and used for an easier comparison of the experimental behaviour shown by the different specimens (Fig. 6). Results obtained for specimen C1 are not reported because are similar to those of C3 (except for a larger dispersion, d u e in p a r t i c u l a r to the shape errors). The remarkable influence of the surface roughness clearly appears when the diagrams for the three specimens are compared. The specimen C5, with the best surface and shape, does not show evident signs of transition between EHL and mixed lubrication regime, which is still apparent for C3. The curves for C2 are always descending: the decrease of the friction coefficient with St clearly indicates mixed lubrication conditions. A qualitative confirmation of the influence of roughness comes from the different shape of the interference images stored for the same test conditions (note, however, t h a t differences are also due to the different elastic modulus of the specimens). In Fig. 7 an example of interference images, produced using the light of a xenon arc lamp with a yellow interference filter of wavelength 577 nm, is reported (see [5] for details). A more clear indication of the regime transition can be seen by introducing the dimensionless film thickness, A. In this work values of A are calculated using the minimum film thickness obtained by means of the M a c E H L program. Thermal effects have been completely included in these calculations (the program also calculates the temperature profiles within the EHL film, as reported in [4]), though they are almost negligible for the operating conditions experienced in this work. An example of such results is given in Fig. 8. In Fig. 9 the measured values of the friction coefficient for specimens C3 with F=40 N, T=50°C and S=I are plotted as a

220

0.05

C2

0,04

0.03

o

[]

mm

-

f

o~/.~,=~aL - ~. NR m

0.02

Oo

0.01

o

,

1•

o

-

•

~=0.5

*

~ S=0.25

0

O.OE+O0

according to most of the results reported in literature (though for point contacts), as for instance [6]. Two interference images are also reported on the diagram for showing the bhange from elastohydrodynamic to hydrodynamic lubrication, that can be seen analysing the modification of the film profile, in particular in the central zone of the contact.

,

,

4.0E-06

,

8.0E-06

1.2E-05

1.6E-05

St=go.u/w 0.01

C3 0.008

S=1 []

0.006 mm

0.004

•

S=0.5

•

/.

mllmm m

S=0.25 0.002

OI O.OE+O0

,

4.0E-06

,

,

8.0E-06

1.2E-05

1.6E-05

Figure 7. Interferograms of the 4 specimens in the same test conditions (F=40 N, T=50°C, u=0.1 m/s).

St=go.u/w

0.01

C5

0.008

S=1

- 1.5

2O

0.006 ] 0.004

25

1

15

A

/'-"

hm [pm]

10

o

0.5

0.002 1 o o ~,-o,-o •

5 0.0 E+00

4.0E-06

8.0E-06

1.2E-05

1.6 E-05

St-go'u/w

Figure 6. Averaged Stribeck curves drawn from experimental result for the specimens C2, C3, and C5. function of A. It is to be noted that the change of regime appears for values of A of about 3,

0

0

0.25

0.5 0.75 u [m/s]

1

0

Figure 8. Calculated values of minimum film thickness for specimen C3 under pure rolling, for F=20 N, T=30°C (a), F=20 N, T=50°C (b), F=40 N, T=30°C (c), F=40 N, T=50°C (d).

221

tions are summarised in tables 1 and 2; furthermore, a plot of the viscosity-pressuretemperature relationship is given in Fig. 13 (see [4] for details on the viscosity model).

0.01 0.008 0.006

0.008

0.004

0.006

f /Sq'~

f

0.002

o. D

....-. -" "" "" - " > S = 1

9

0.004 o\ 0

2

4

6 A

8

10

12

0.002

"" "" "

~

o ,

~

,

Figure 9. Friction coefficient versus A (specimen C3, F=40 N, T=50°C, S=1). In Fig. 10 the measured values of the friction coefficient for specimens C2 and C3 with F=40 N, T=50°C and S=I are reported for comparison. The different materials could explain the gap between the two curves (but also errors in calculating A or experimental uncertainties should be taken in account). Anyway the indication given by this diagram is clear: C2 has been tested in mixed lubrication conditions.

= .5 = .25

I

2.10 -6

,

,

,

I

4.10 -6

po. U/W

,

,

,

6.10 -6

Figure 11. Experimental (symbols) and calculated (solid lines) values of friction coefficient for specimen C3 and F=40 N, T=50°C. 0.008 lib i\

0.O06

f

... •

,,

•

~

_

- 4 ";

... - t 3 . -

mm"~

~C.

~.

~

~"

""m

.,.,,,~ .,,,,,,"

...,..""""

~

~ i ~ - , -," ~ . -r . ~

aa

0.004

0.05 0.04

•

C3-F=4ON, T=50°C, S=1

•

C2 - F=4ON, T=50°C, S=1

0.002 f 0

0.03 f 0.02 0.01 L

o 0

2

4

6 A

8

10

12

Figure 10. Friction coefficient versus A (specimen C2 and C3, F=40 N, T=50°C, S=1). Some examples of the results obtained by thermal-EHL numerical calculations can be seen in Fig. 11 and Fig. 12, in which they are also compared to the relevant experimental data. The main parameters used in calcula-

i

0

i

i

[

o slo-;

i

i

Po" u/w

i

11'o-

i

' 1.'5.10-5

Figure 12. Experimental (symbols) and calculated (solid lines) values of friction coefficient for specimen C3 for S=I and: F=20 N, T=30°C (o, a), F = 2 0 N , T=50°C (o, b ) , F=40 N, T=30°C (m, c), F=40 N, T=50°C (o, d). Agreement proves to be satisfactory as long as rolling speed is high enough to ensure a full-film lubrication. Since numerical simulation is done assuming perfectly smooth surfaces, no transition to mixed lubrication can be evidenced and, hence, the calculated friction coefficient regularly decreases even at low speed, despite the very low values of film

222

thickness. The gradual transition toward the pure hydrodynamic regime can, instead, be evidenced by inspection of the film profile. Table 1 Main data for lubricant SN600 T=30°C T=50oc Ns/m2 ~to 0.190 0.065 a 21.1.10.9 17.1.10.9 m~/N OC-1 0.061 0.047 Table 2 Main data for specimen C3 Compound elastic modulus E' 124.3 GPa Equivalent radius: R' 21 mm Axial length of contact: t 3 mm Dowson parameters: U = ~ou/(E'R') 1.24 + 7 2 . 7 "10 "12 2 . 1 3 + 2 . 6 2 "103 G = (zE' 2 . 5 5 + 5 . 1 1 "10 -6 W = w/(E'R')

10

3 1

REFERENCES

[Pas]

1. Gohar R., Elastohydrodynamics, Ellis Horwood Limited, Chichester, England, 1988.

0.3 0.1

0

An interferometric survey of the film shape and the simultaneous measurement of the friction force evidenced typical features of different lubrication regimes. Different arrangements of the results have been used for their analysis. In particular, Stribeck curves, as well as diagrams in which friction coefficient is plotted versus the A factor, are useful to evidence the transition from mixed to full-film lubrication. The role of surface roughness in causing the onset of mixed lubrication has been pointed out. On the other hand, it has been verified that when rolling speed is increased a transition occurs from mixed lubrication to full-film elastohydrodynamic lubrication. If speed is increased further, deformation of surfaces becomes less evident, indicating a gradual transition toward a merely hydrodynamic regime. Numerical analysis showed a good agreement with experimental results, as far as full-film lubrication was concerned. Both the mixed and the elastohydrodynamic lubrication regimes will be investigated further.

0

.

0 0.05

3

0.1

~

0.15

p [GPa]

0.2

Figure 13. Viscosity model.

2. R. Bassani, E. Ciulli and P. Forte, Proceedings of the 10th AIMETA Congress, Pisa, 2 (1990) 427. 3. R. Bassani and E. Ciulli, Elastohydrodynamics-'96: f u n d a m e n t a l s and applications in lubrication and traction, Elsevier, Amsterdam, 1997, 81-90. 4. B. Piccigallo, Wear, 193 (1996) 56.

5. C O N C L U S I O N S An experimental work has been carried out on a series of moderately loaded lubricated contacts between a glass disc and four cylindrical specimens of different kinds.

5. R. Bassani, E. Ciulli and B. Piccigallo, to be presented at the 5th AIMETA Tribology Congress, Varenna, Italy, (1998). 6. S. Bair and W.O. Winer, J. of Lubrication Technology, 104 (1982) 382.

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

223

Isoviscous-EHL and mixed lubrication m e c h a n i s m of parallel slide-way with oil groove Y. Nakamura a, T. Matsubara '~ and F. Itoigawa a ~'Nagoya Institute of Technology, Department of Mechanical Engineering, Gokiso-cho, Showa-ku, Nagoya, 466-8555, Japan The pressure generation of a parallel slide-way with an oil groove is examined experimentally and theoretically. In the experiments, the friction force, floating height and oil film pressure are measured with changing sliding speed, groove intervals and lubricants. The experimental results show that the friction property of the parallel slide-way with an oil groove is dominated by a hydrodynamic lubrication mechanism in high sliding speed condition and in mixed lubrication condition. Oil pressure generated at the entrance from the groove to the sliding surface and elastic distortion of the slider are taken into consideration in calculating the oil film pressure generation. The calculated results show that the slider is distorted elastically and forms a micro wedge, and consequently a sufficient load carrying ability is generated. The measured oil pressure distribution resembles the calculated pressure distribution.

1. INTRODUCTION A parallel slide-way has been widely utilized for the guide-way of machine tools. It is well known that the friction force of the parallel slide-way decreases and the slider separates from the guide-way as the sliding speed is increased. Many studies have been carried out to reveal the load carrying ability of the parallel slider ~) 2~. Lebeck reviewed and compared 3) much of the known data on parallel sliding experiments, and evaluated several of the proposed mechanisms for the parallel sliding load support 4) . In his conclusions, he said as follows; 1) The following parallel sliding lubrication mechanisms do not provide sufficient fluid pressure load support to be considered a primary source of beneficial lubrication in parallel sliders: thermal density wedge, viscosity wedge, microasperity with cavitation lubrication, asperity collisions, and squeeze effects.- .... . 2) As is well known, deviations from parallelism (tilt, taper or waviness) cause a strong hydrodynamic load support. When this mechanism is a mixed friction model, it is possible to predict friction versus duty parameter results very much like those of the experiments discussed. However, the results from the self-lapping direction-reversing experiments and the insensitivity of the Kanas experiments to cavitation suppression cast doubt the universality of this mechanism.

In this paper, a new mechanism is proposed from experimental results which were obtained in tests ~) 6) conducted to reveal oil groove effects on the friction property, and oil film pressure is measured.

2. EXPERIMENTS 2.1. APPARATUS AND METHOD In many cases, the slide-way of machine tools moves a finite distance, whereas the friction force and the floating height show transitional behaviour. Cb'v

Speed ControlDC

i i i

,j i

Gear HeadBox Spindle --"\\. To capacitancetester

i

; / / - Load-ApplyingLever

Bearing Surface @ LowerSlider (Stationary)

HoldingChuck

Contact Brush - ~ @ -~.. "c~___t ~) Dynamometerfor L Ceramtc Ball-J~

~ o

Slider Fixture Setting Screw --- UpperSlider (Rotating) t'.' !' ~ D namometorfor Torque

a

~ Base

Fig. 1 Experimental setup

] 5)

224

0.020 rn

!!!!!!!! !!!7! !!! !!!!i!!!! !!!!i!!![............... r:::: ::::r:::: :::: ~:::::::: :::: :::: :: :: ':" ...."

_

O

-

0 1

Sliding direction of upper slider

I ,....:....,.. i.i)i.i.l~!.il,ii i.i.[.i.i.!i.li.i!].ii.i;i;.i.i.}).i.!i.i.ii.i. I ;-i~iliVii!.}.ii.}[email protected].~.).i.).i.i.).i.i.i.

-

'i::'T

(a) Upper slider

()

1

"'""ii:!iiiii

j!'!i!' ]i!:i.... l:::iiiiiil::l[::= l==:i: { :=::![.i:[:':=:i +i~!~~ !!!!!!!!!!!!!!!! !!i!!!!....!!!!!i! iii!i!t~t I iiii !~i-iiiiiii!

~der (Plamtype)

i!ii ilii!ii!::i::,iii .

.

.

.

(c) Lower slider (Narrow-Shallow groove)

ii[::i::i!::!i::

i I ii

5,0;,; i; ii!il }ii;

Fig. 3 Surface profile near the edge of oil groove before test 5~

Table 1 Testing condition

Fig. 2 Configuration of upper and lower sliders 5~ In this study, ring-shaped sliding surfaces are contacting to form a steady-state sliding condition. The testing apparatus is schematically shown in Figure 1. The ring-shaped upper slider is attached to a spindle with three setting screws, and is driven with a wide range of rotating speed. The ring-shaped lower slider (with oil grooves) is supported by a ceramic ball pivot. Contacting load and torque are measured by dynamometers, and electric capacitance between the sliders is measured to estimate the floating height. Configurations of upper and lower sliders are given in Fig. 2. The contacting surfaces are f'mished with 1 gm lapping grain, and an example of the finished surface profile is given in Fig. 3. Testing conditions and lubricants used in this experiments are listed in Table 1 and Table 2, respectively. The lubricant is poured into a recess of the lower slider before the test. At the start of the experiments, the sliders are contacting with a normal load (contact pressure is 0.18 MPa), and the upper slider is rotated with a medium sliding speed (Mixed lubrication condition) to be run in for three hours. During the running-in process, the lubricant is exchanged several times to remove wear debris. 2.2. E X P E R I M E N T A L RESULTS An experimental result of a plain type lower slider (no grooves) is shown in Fig. 4 where the abscissa shows sliding velocity at the centre of contacting width, and the ordinate the coefficient of friction calculated from the measured torque. When the lower slider has no grooves, the coefficient of

Contacting pressure Sliding speed Surface finish Lubrication Temperature

0.18 MPa 0.3 - 400 mm/s Lapping Mineral oil (Multi, Base) 24.0+O.5°(2

Table 2 Lubricants and properties Designation

Types

VG10M VG32M VG32B VG68M

Multi Multi Base Multi

'

¢.~ 0.2

'

'

' "'''1

Viscosity (24.0°C) 0.016 0.062 0.062 0.145

'

' '

'

....

I

[Pa.s]

'

'

'

" "'~1

o

~0.15 0

*-"---o.. " " -0- - 0- -Q- -0" 0-0

• o.1 it:: " 0.05 0

0 --4

1

. . . . . . . .

I

10 -3

. . . . . . . .

I

. . . . . . . .

10 -2

I

10 -1

Sliding Velocity (m/s) Fig. 4 Coefficient of friction as a function of sliding velocity (Lower slider: plain type, Lubricant: VG32M) friction keeps an almost constant value over a wide range of sliding speeds, and the floating can not be observed, i.e. the sliders continue to shortcircuit even at high speed sliding conditions.

•

•

•

'~ ' " q

. . . . . . . .

I

. . . . . . . .

..

I

1NS - e - 2NS

2.5~-

. . . . . . . .

- 1 2

m

ID

I

I

. . . . . . . .

I

. . . . . . . .

2.5E"

I

-

,,,.,, c"

1

2

- o-- VG32

o

- 1 . 5 "~

8NS

-e-

I

VGIO

- e-- 4NS _

....

O

--o- VG68

1.5 "~ +., r"

m"

1

.-~ ¢

-0.5

0

-r-

0.5 0

__o LI_

5' o

E
r r m l ~ ~ RP~ larr~ IP:ion-~ ~ Vl :m.m~on V2:~etion valve V 3 ~ ~ valve V4:leak vatv~ ST.'test stage I--I:t~ld~ E V : ~ FF.-m~ S:shtater HV:high volm~ ~ ree.x~en r e c ~ a ~ LV:lo,v voltage regu]al~ arrta:samka mlplifier t~:qt~rtz crystal r r t x ~ e O:2:c~511m~ ~ FM:frequer~ ~:~ing ~ ctma~ller

2.2. T e s t i n g ~ e n

The Si(lll) wafer was ttsed as an ideal clean with known ~ of Ag on it, as the fia~on of the treating lempetaa~ 5). Staface roughness of the Si plate was 0.68 nrn Rmas by high precision non-contact roughness meastrem~ The diamond pin was also smooth as 9.7 ran, as the result of mechanical polishing at Asahi Diamond Co. Ltd.

315

The Si plate was flashed for cleaning at amtmd 1200 °C before depositing Ag. On the slid diamond pin, XPS meastnement proved no transfer of Ag. To certify the detectable amount of the Wamferred Ag on dimnord, we analyzed the slid pin by restricted-area (about 10 micrometer in diameter) and large spot (0.8 mm in diameter) XPS analyses. Narrow track of slide (28 micrometer-wide by calcaAation) must be included in the spot but no trace of Ag signal was observed by XPS. But still ~ l e amount ofWansferred Ag is probable li~ Ag-Ag contact in the sheafing plane is not denied in the disetmion followed. Within a limit of detection sensitivity, we could not find any coni~rfin~'on atoms or Iramferred Ag on diamond except oxygen and c a ~ The Iransfetred Ag on diamond, if any, may have imlxnmt effect to the sliding characte~'cs that diamond was examined ~ y for Ag. The diamond pin was cleanat by dihaed nitric acid solution after each sliding test on Ag film, to eliminate probable transfer of Ag to diamond. Crystal orientation of the diemaond sliding plane was fixed to (111) and the sliding direction to , which was ascertained by back reflection lane spot.

2.3. Ag film preparation In pteperalion of Ag-deposition-film on Si, the subsa~ was cleaned by iterated flashing trader lff 7 Pa x,~aama, at just taxier the melting ~ of Si, by a direct ~ t through the ~ e r L With the Si ~en, ~ o~dlator was kr, ated side by side to meastne the absolute amount of deposited Ag, and monitored using fimdamental frequency shift of quartz. The sensitivity of fiandamental frequency shill was 7.89 H~monolayer as the results of theoretical calculation atter the ~ eon~orL Evaporation sotar,e of Ag was designed as shown in Fig.3. Thermal electron emitted from ttmgsten filament was accelerated by 1 kV to bombard Ag rod. The flaem~ electron was focttssed to the top of Ag rod and not to heat stm~tmding parts ~ y and minimize the adso~ degassing. The evaporation rate was ar.cesffully controlled by the emission omem and evatx)ration time. The ~ l u t e amount of deposited Ag

was delgnnirgd by the fimdamental frequency shifts, and ascertained by XPS for the commainm~ after the sliding tests. No c o m m a i r ~ were detected by XPS on the Ag/Si plate except 0 and C which have adsodxxt after sliding. By controlling the evaporation time at a constant emisfion c ~ and accelerating voltage, variable thickness of Ag was ~ Our system for sliding tests and Ag delx~tion is separated from XPS and AFM system that exact cleaned state of the substrate were not certified before sliding, But in this work, 0.6 - 2.6 ML Ag layers in average on Si(111) were ~

Oa e l ~ ~ ~ _ ~

~ Fig.3 ~ ~

c

l~lder diagram o f eleem:xa t y ~ evatxralor

2A Results 2.4.1. The sliding test on cleaned surface without Ag Sliding tests on the cleaned Si was started with a friction coefficient 0.7 as shown in FigA. This value is almost equal to the values ~Ix~ted ~. The friction force is defined here as the average of maximum forces in reci~ cyclc~ The three curves of friction force in Fig.4 indicate the tests stm'ted after 13, 103, and 308 minutes after flash cleaning, as a ftmcfion of recipax~

316

cycle numbers. These results indicated the conditions are almost stable at 0.4 and were not affected by time latin after cleaning. These results were co~le to the uncleaned staface which was slid by the

samep~ 1 ~< .................. 0.]

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

=o 0.01 l.w

0.001

•

0

I

!

- - x - - after 13 min.

[

--x-after 103 min. --o.-after 308 min.

I

m,

,,

,,,m

25 50 75 Number of reciprocations

show 0.3 of friction coetticient eventually. It is similar to the restdts of Miyake et al 7). 2.4.2. Sliding on Ag film on denned Si plate The Fig.6 ir~cates the friction coefficients of Ag films on cleaned Si (111) ~ . The thickness of Ag changed as 0, 0.6, 1.0 and 2.6 ML in this figure. An e x t r a - ~ y low friction coefficient (less than 0.01) beyond the reported results for solid/solid sliding codd be observed from the plates with over 1ML of Ag. The lowest value was urfler 0.004 from Ag 1.0 ML fdrrL

I ,

"'X x x ,x .x x x .x ,x ,x ,x x

,

100

0.1

o~,,q

O

Fig.4 Friction coefficients from Si(111), slid after 13, 103, and 308 min. respectively. Surface contamination during this time didn't appeared in the/z.

=o 0.01

- - x - - 0 ML -" 0.6 ML 1.0 ML 2.6 ML

o~,M

0.001 0

100

Fig.6 Friction coefficients fromAg deposited Si(111) cleaned surface. Film thickness dependency was observed.

o

0.1

¢J

25 50 75 Number of reciprocations

0.01

¢J

o

r,.)

,X X X X X'X

0.001 25 50 75 Number of reciprocations

100

Fig.5 Friction coefficient from Si(111) uncleaned surface, with a few nm oxide layers. Figure 5 indicate the tesdt from Si, rinsed ullrasonically but wilimut flashing ptocedt~. A few nanometer thick oxide layer and/or adsorbed atoms on Si affected sensitively on the friction force. The Fig.5 shows oxide layers work to decrease the friction down to 0.02 tnnil it breaks after several tens r e d - - o n , to

0.1 O

8o o=

0.1mm/s

0.01

--x-- 0.2mm/s

"t::

0.4mm/s 0.001 0

Numb-25-er _50 75 orreciprocatlon Fig.7 Friction coefficient of Ag deposited on Si(111) plate, as a function ofthe sliding speed.

100

317

The low friction sliding lasted rather stable for 100 or over this cycles iteration and this sliding was reproducible by repeated mn of tl~ ~ In each run of sliding, friction was ~ gmdmlly with the ~ cycle. The sSding speed affected also to the friction ~ as predicted by theoretical simulations g~. Our results are shown in Fig.7. At the sliding ~ 0.2 and 0.4 mm/s for 1 ML Ag film, low friction as 0.00n level were not observed, but at 0.1 mm/s, the stable and low friction was ~oducible.

had an obvious worn track on it but Ag-deposi~ stefa~ had no clear tracks. The AFM observation indicated the Ra=0.54 nm at the estimated sSd regiorL On the Agdeposited strface, islands of 50 nm in diameter and 6 nm high patches p m ~ l y of Ag were fout~ shown in Fig.10. Except that no ~ were found on the deposited arfa~. The profile of this mound inclt~ AFM probe size that absott~ size is haiti to estimate.

21~.6t

inml

0.1

1

.o= 0.01

,~'\ ta~_~ 1 1 ~

a'0.001 0

25 50 75 100 125 150 Number of resiprocations

tO~3 ./ ~

Z - M ~ 2o3.ol l r m l

O.OO

(a) worn Wackon cleaned Si strface

---o-- cleaned Si (ref.) --o--Ag deposited Si 7.73

iml

Fig.8 Friction coefficient from Ag deposited Si(111) c leaned s urface in UHV, and exposed to N2 atmosphere.

...... i

.;o.~

s.O0 x 5 oo I~ml

To examine about the adsorbed nitrogen gases on the sliding arface, 1 arm of N2 gas was introduced to vacmm~ chamber during sliding at very low friction force. Results are shown in Fig. 8. After a nitrogen gas was inmxtuce~ so high friction over the detection limit was appeared abruptly. Adsothxi nitrogen gas was storied from high purity nitrogen gas cylinder but obviously disarl~ the low friction sliding. For Ag films which the low friction forces were obsewed, this take-off of friction appeared reproductively and the friction imaease ex~ two orders of magnitude.

2.4.3. ~ and X ~ ol~ervatiom The AFM obsen,alion of the Si st~ace gave the image shown in Fig.9. The Si ~ without Ag overlayers

z-4~mt x, r ~ I ~

000

(b) friction smface of Ag 2.6 ML deposited Si anfw.e. Fig,9 AFM image of friction surface on Si

lml

oox t.ool~ Z.Max1~.021nmi

Fig.10 AFM image of Ag 2.6 ML film

000

318

As shown in Fig. 6, very low friction coefficient trader 0.004 was observed from AgMetx~ted surface with over 1 ML of Ag film. With the inereasi~ reeitmx~on up to 100 cycles, friction decreased gradually close to our detection limit. The results of XPS o ~ o n of the Ag-deposited Si sttfface, shown in Fig.11, depicted strong Ag 3d~ u2peaks but no extraneous atoms except O and C, which were adsoflxxt atier the sliding ~ e n t s .

,2°iI

AI

tribologieal proix~es. The lowest friction force on this surface is almost close to the publislxxt results ,0). Atomic scale srnooamess of the polished ( a s - ~ v e d ) s m f ~ and flash-cleaned s t r f ~ may not e x ~ y be equivalent but ll~-eleming t~.l~que is conventional for low etmgy electron ditfaetion (LEED) and scanning amneling microscopy (STM) observation that atomic scale roughness does not extend over which LEED and STM observation are interfered. We have to concltfle the difference of friction between flash-cleaned and oxide covered a r f a ~ of Si is not due to sarface roughness, but relatively soft non-erystalliz~ oxide layer worked as a soM hbricant

8000

4000

"V

.....

0

,

385

I

,,

380

I

375

,,,

='

370

•

365

360

Binding energy(eV) Fig.11 XPS spectra of slid surface, from (a) diamond, (b) Ag deposited Si and (c) cleaned Si, respectively.

(a)

3D-image of oxidized Si surface

3. D I S C U S S I O N !

3.1. Oxide layer on avreeeh, ed Si The oxide layer on as-rec~ved Si(lll) wafer were waflaed by diluted nitric acid and ultrasonically rinsed before setting into the vactma system but was covered by Si oxides of a few nm thick, according to XPS measmenm~ 9). The friction on this aaface is obviously lower than the flash cleaned Si arface, as indicated in Fig.5. The Si oxide layer was smooth, as indicated in Fig.12, and friction coefficient 0.02 was obtained until the oxide film was worn out. The value 0.02 is prol~ly due to adsorbed hydrocarbon and the friction coefficient of 0.3 may be from the friction between the oxide layer and the diamond, although tdbochemically formed oxide layer is not always equivalent to a native oxide layer, in its crystalline ~ and accordingly

/ .....

t J_

--

li,

i I

-IIQ

...

(b) 3D-image of diamond smface Fig.12 31Mmag~ of Slmeimen surfaces Direct cotma of the diamond pin and Si severely high friction comparing Si oxide. Due to the arfac~ roughness on both arfac~, another ~ as contact area and chemical bonding force between C and Si could be considered. By flashing, SiO which has high vapor txemae evatxcates, to exlx~ Si dangling bond to the anfa~ that the activated and tractive bond has higher

319

i n , action force against diarnond ~ . As the results, intrinsic Si stnface ~ s e d to show high friction force. On the other hmfl, oxide covered ~ is saturated with bonded atoms as oxygen. Shear stress between oxygen of Si to C is so low compared with SiC interaction. In this case of sliding, the oxide layer is so thin (a few nm at maximum) that the diamond pin with eurvattre 3 mm in diameter does not indent into the oxide layer, and also Si oxide does not acctmmlate in front of the sliding pin, which make high resistance or high friction foree, if any. AES and XtX3observations of the oxide film prove that the oxide include I-I20, O and probably hydrocarbons which were adsorbed from the atmosphere. Adsorption of these molecules are known to be so low and mostly desodxxt at around 100 °C or a few tens KJ/n~l in vactamL Contribution of the adsoflxxt molecules to the fi'iction force is obviously appeared during sliding~ By exposing to nitrogen gas, abrupt ~ of friction at sliding with low friction appeared, for example. We considered CO-adsorbed molecules disrobe to atmosphere by sliding and rather high friction after sfiding were atln'buted to the adsorbed molecules. E ~ oxide layers has still low friction comparing Si/diamond direct contacts. In this experiment, we conclude low shear resistance material on hanter subsu~ determines the bond to be debonded by sliding and it is the dominant factor of friction source.

3.2. Subnanometer thick Ag films As the result of AFM image of the 2.6ML Agdeposited sazface, islands of 6 nm high and 50 nm wide were observed. The ~ was not ideally tmiform, as the~. At the first stage of sliding on this ~ , tt~ friction coefficient was high, probably ~ these islands of Ag were ~ and expanded into thin layers. With the increasing specific arface area of Ag, the friction decreased to 0.00n range. The average mass ofAg ofthe island almost corresponds to 2.6 ML from the profile size, and XPS m ~ t shows that film thickness fiuaa quartz oscillation measammaent were reasonable estimation, as the average value.

As shown in Fig.7, experiments were carried out at different sliding ~ . Obviously friction depends on the sliding ~ and at high sliding ~ friction could not be ~ as expect~ We increased the sliding from 0.1 to 0.4 mm/s, and at last, retried again at 0.1 mm/s. The retried results at 0.1mm/s is not indicated in Fig.7, but the first results were totally reproduced as 0.1 mm/s results in Fig.7. These experiments coafimxxt the low friction sliding and proved good retxoduefivity. The sliding on the Ag-2.6 ML with low friction is certified by iterated experimems. Theoretical observation m predieted ~ hbricity, if any, speed depetxieaey may be occtare& Presented results can be admitted as matgr lubricity from this point of view. On the other hand, 0.6 ML Ag film showed a high friction of 0.1 that discrete difference occuned between a m t ~ 1 ML. M ~ e n t of film thickmss inclt~ around 10 % of e n ~ but the critical thickness required for high lubricity was arotmd 1 ML. Qualitative explanation for this obsewafion is: Ag works as a lulmc.ant within a thickress range flain enough not to form Ag motmd in front of sliding pin, and thick e n o t ~ to cover Si aafa~. Theseresults may be expressed that low friction is observed on a few Ag atom layer e n o t ~ to cover the Si stwface, to intervene to avoid a direct contact of Si atom to carbon. Shear plane was estimated so far to be in C/Ag and/or Ag/Si.

3.3. Shem"plmle in the eon~et lmin~ On the practically flat ~ , chemical interaction force increase its contribution on friction force u). Theoretical considerations admit that microscopic observation between diverse atoms has its c ~ ' c bonding forces. Stableand strong bond of C-adatom has high friction or high shearing force. The observed results indicate the O-covered and cleaned-Si have charactefi~'c friction force. It sounds reasonable to estimate that chemical interactiom of Ag/C and Ag/Si has very weak bonds in the shearing smfaces. Ag/C and Ag/Si atomic bond energy are dose to van der Ward's force. In this case, danglingbonds of Si are ~ y occupied by Ag but dissociate by sheafing ~ . Ag/Si system is known to form diverse arface 2D slmett~ depending on

320

the temlzraane s. On this state, nitrogen gas was introduced to Mmtb N on Si. On C ard Ag, N is not known to form slmetta~ or strong ~ c a l bonds. The Si matrumeis partially exposed and N can adsorb to form stable SiN lxarts, which restricts Ag movement on contact strfacc. As a model of nitrogen adsorption which interfere Ag-lubrication, we want to present a model here. In estimating the lubricity of Ag-covered stafaces, Hertzian contact area (Arh) is Arh = n(3RP/4E~

inemse with immsing reeiproe ion or ruining dismee. In our remits, rather high friction was observed at initial stage of sliding and decreased with the reciprocation cycle. High hbdcity appem~ at thinner range of Ag. In fact, Ag island have disappeared after sliding, ar~ in&red very low friction force. The mechanisna of sliding may be, ~ f o r e , different and we considered monolayer or thin layer close to 1 monolayer must be examined. Effect of crystal orientation on friction is to be examined, but so far, thickness of Ag was ~ in the following section.

(1) 3.4. Friction decrease with reciprocation cycles

R diamond pin oavattwe, P the load, andE' the Young's m c ~ u s . By using reported tesdts of F .•n ~ = 105 x 104 MPa, ~ = 18.8 x 104MPa and R= 3 x 10.3m, weobtaimdArhis 14 micmmeter in radius. The friction coeflident is defined A f l ~ = ~ z ( 3 R / 4 E ~ p-t~

(2)

We applied P= 025 N ar~ ~ =3.01X 106Xp u3

(3)

which is shear stress of the sliding mafaces. Young's modulus of Ag was 290 MPa and shear sa~gth 20 MPa was used to obtain /z =0.04. This result indicate that one order higher friction is reasonable if Ag/Ag shear is the sliding plane. The ~ e d friction is one order lower lhan estimated or, in o ~ word, the relevant sliding is sheared out by lower sax~. If the shear stmagth ofthe sliding interface c,an be sag~sed 2.1 MPa on the other lmrxi, ,u is c a l ~ out as 0.004+0.001 within the load range 0.25-0.5N. These results suggest friction force is almost constant, and reasonable as is observed within this load range. Donna et al repoted on DLC and s p ~ Mo sultide layers and observed so low friction 0.007 and 0.002 13~4). For layered c o r t ~ u ~ as Mo sulfide, shearing stress can be released by sliding basal plain which is bonded by van der Ward's force. Very low shearing force may suffident by sliding a few layers or multi stacking layers of sulfide. In this case, initial low friction force may be ~ s e d to

As shown in Fig. 6, friction force decreased flom 0.1 which is a reasonable restdts for solid/solid direct contact. This value is a little bit lower, however, than that ot~nved in clean Si/diamond direct contact sliding. We believe the small difference is significant and it is attributed to the locally a~etmmlated Ag layers. With iteaated sliding on a smae track, Ag islmxts diseopeared mad the friction force decreased down to the minirnum tinge. T h e ~ slope is almost extx)mntial in ~ allhough the lowest friction was amimd after 50-90 cycles. In INs stage, Ag islmxt exleaxted to thinner layers close to monoatomic layer in average. Thin layers does not make mounds in front of the sliding plane and kept the contact area conamt as c a l ~ by Hertzian contace 28 micrometer in diameter. Uniformity of the Ag deposition film was hac~mplete probably due to deposition from 60 degree off from rrmml angle. Ag is known not to form island in short diaaw.e under nonml condition but hxx)mplete surface asperity were supposedly made seed to form island and overshadowed zone. The ~ of Ag included in the island is 1.1 × 107 atoms and alnmst coincide with the amount 2.0 × 107 atoms//z m 2, which was c a l ~ 2.6 ML by quartz ~ o n mm.mmnmt. We considered minor kregulmity on arface affected on the u m-size tmem on sliding. We asstmaed the contact of diamond in multi points on Si ~ that Ag-deposited Si ~ also in comaa with diamond by multi-point The experimental ~xtlts ir~cate that direct contact of diamond to Si makes high friction force that Ag islands in contact must be deconstme~ by sliding with a p r e t t y of eomaet, and

321

eventually increase the urfac.e coverage by Ag on Si. After Ag island on sliding track have destructed by repeated sliding, friction reached to the minimum mage as 0.00n. After the low friction has attained Ag is not easily removed from the sliding track due to its extreme low thickness, isotropic and urdocallized bonding force. The Ag atom has one s-orbital electron to make bond with other atoms and has isotropic character in bonding. In fact, low friction sliding lasts at least 40 cycles or over allhough there observed exlxrimental flucttmlion to reach low friction state. With increasing st~ace coverage by Ag, friction decreased. The probability of deslrucfion of Ag island may exponentially increased Ag covered area. Qualitative explanation of Ag island destnLefion is followed. During sliding on a wear track, Ag island c ~ be crushed and extended with some probability to hit with projected points on each sliding aafaces. The number of Ag i s l a n ~ to be extended by pin can be decreased exponerrdally, with a hitting probability( ~ ) and sliding reciprocation cycle(t).

= n • fc~ + 0 (n • fv/P-n • fc~)

=us+

o(u~- u@

=us+

00(1-aexp(-Zt))(u~- it@

(7)

In expression 7, n • fc/P indicate the friction on intrinsic Si and is written /z so and n • fv/P indicate that of Agcovered Si strfa~ and is written It ~ This expression indicate the friction coefficient depend on a Ag coverage expo~y, as is observed. On this model, the calculation results show the same tendency as the e~ental restdts, indicating Fig. 13.

1 :-XX .X X .X X .X X-X X X .X X .X X .X,X.XX °~.~

0.1 0

0 ° ,...¢

- - x - O ML -" 0 . 6 M L 1.0ML - - O - 2.6 ML

0.01

0.001 N=Noexp(- Z 0

(4)

0

25

50

75

100

Number of reciprocations With the decteasi~ N, stafac.e coverage 0 imaease as following

may

0 -- 0 o(1-a N/No)

=0o

{1-a exp(-Z0}

(5)

0 0 denote the maximum coverage, detetmii~ by deposited amount of Ag, and a a factor depending size and height of Ag island( 0 < a < 1). Friction forces are

expressed here F = 0 n • fv+(1- 0)n • fc = n • fc+ 0 (n • f v - n • fc)

(6)

where the friction force is cong~osed of Si-C strong interaction(fc) arfl very weak (van der Waars like) force of Ag-intervened shear plar~fv), n denotes the total number of contact points. /s is defined therefore,

Fig.13 1"he calculated results for ~ decrease.

By the results of these experiments, we want to present a significant proof that ~ topmost atomic species c o n t n ~ to the friction force. The attainable limit of friction coefficient depends on the chemical bond as well as the asperity of sliding materials. Basic concept of matxr lubficity have been dLsctmed but so low friction of thin metal layer is practically un-experienced observation_ ]here is some restriction to observe hibh lubricity as rather high Hertz pressme, high young's mo&dus of pin and plate materials, aptxopri~ amount of metal, which is inactive to bind to both materials. This microscopic consideration appeared a clue to examine macroscopic obsewafion of friction measurements. Ftather ~ o n is required for much ~ r t a n t infonmtion for elucidation of the sliding mechanism.

322

4. CONCLUSIONS

REFERENCE

1) Cleaned Si(111) pla~diamond(111) were slid in ultrahigh vactmm and the very flat strface showed a rather high friction coefficient over 0.4. 2) On oxide-covered Si, tt decreased 0.02 but additional sliding made the fiietion coefficient over 0.1, showing direct contact of Si with diamond. 3) Ag-detx~ted stnfaze on Si(lll) showed extremely low friction 0.004 in high vactarn. Sliding dependency was obviously observed and low friaion at a sliding speed was repnxtudble.

1) DonaldH. B u ~ Proc. ~ Inteml. VaztamaCongr. 1974 J ~ J. Appl. Phys. Sul~l. 2, Pt. 1, 1974. 2) A.I. Sviridenok, A. A. Chizhik and I. E Sveklo, Tribology Intemational, Vol. 29, No.5, (1996) 377384. 3) Kaztthisa MIYOSHI and Donald H. BUCKLEY, Applications of Stnface Seience, 6 (1980) 161-172. 4) K. Shinjo, Surf. Sci.,283 (1993) 473-478. 5) J.E. Demuth, E. J. Von ~ IL M. Tromp, and R. J. Hamers, J. Vac. Sci. Technol. B 6 (1), Jan/Feb 1998 18-25. 6) J. M. Martin and Th. Le Mogne, Surface and Coatings Technology,49 (1991) 427-434. 7) S. Miyake: Surface and Coatings Technology, 554/55 (1992)563. 8) Hisae Yoshizawa, You-Lung Chert and Jacob Israelachivili, Wear, 168 (1993) 161-166. 9) Raider,S. I and Flitsch, R, :IBM J. Rev. Develop., 22, 294(1978). 10) J. M. Martin and Tk Le Mogne, Slrfac.e arid Coatings T~.lmology,49 (1991) 427-434. 11) J. B. Sokoloff, Phys. Rev., B, Vol. 42, No.1 (1990) 760. 12) Y Mori and K Endo, Tribologist, Vol. 37, No. 10 (1992) 806-812. 13) C Donnet, J M Mmfin, Tle Mogne and M Belin, Proceedings of the Imamtional Tribology Conferetr.e, Yokohama (1995) 1153. 14) J. M. Martin, C. Dormet, and Th. Le Mogne, Phys. Rev., Vol. 48, No. 14 (1993) 105

4) Ag-deposited surface was not uniform in Ag thickness, by AFM observation. A sliding model on fftis aaface was ~ for ~ friction e x p o ~ y , by the ~ coverage of Ag. 5) Significant chemical interaction effect on topmost atoms of sliding plane was ~ y presented. Ag was proved as a excellent lubricant in the restriet~ conditions. 5. ACKNOWLEDGEMENTS The autho~ express their acknowledgements to Hino Motors, Ltd. for the financial ~ r t s . ProfessorMohri of Toyota Technological Institute is acknowledged for his cooperation for AFM measurement~ Dr. M. Kokmki of Toyota Cenlral Resea~ and Development Laboratories kindly offered the diamond pins and Dr. Y. Himse was very kind to XPS observation. Mr. M. Ide of Asahi Diamond Co Ltd. was so cooperative to polishing the diamond pin with high accmcy. The atntx~ express sincere gratitude to them.

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

323

Experimental modelling of boundary lubrication using an ultra high vacuum tribometer. M. Boehm a'b, Th. Le Mogne a, J.M. Martin a, H. M. Dunlop b and G. Hauret c Ecole Centrale de Lyon, Laboratoire de Tribologie et Dynamique des Systemes UMR 55 13, BP 63, F-69131 Ecully, France b Pechiney Centre de Recherches de Voreppe, Centr'AIp, BP 27, 38340 Voreppe, France c IRSID, BP30320, 57283 Maizieres-les-Metz, France a

The understanding of boundary additive mechanisms is of primary interest for the development of high-performance lubricants and replacement of environmentally undesirable additives. However, chemical interactions occuring in a boundary lubricated contact under industrial conditions are complex and their study requires a simplified model to boundary lubrication. A new method has been developed, based on in situ friction experiments performed in an analytical ultrahigh vacuum tribometer where the contact is lubricated by low molecular weight molecules which simulate the heavy lubricant components by their chemical function. A study of the evolution of the friction coefficient versus molecular pressure and sample temperature allows a clear differentiation of the different compounds. The in situ analytical tools enable the analysis of sample surfaces before the friction process and the understanding of additive tribochemistry. The friction behaviour and wear track morphologies under gaseous feed can be related to those obtained in classical boundary lubricated contacts. Consequently, this method appears capable of accurately modelling the boundary action of molecules and is likely to be a powerful tool in the prediction and the understanding of the action mechanisms of boundary additives. Keywords: Tribochemistry, additive, boundary lubrication, modelling 1. I N T R O D U C T I O N

Under boundary lubrication conditions, friction coefficients and wear rates can be considerably reduced by chemisorbed or reacted layers (thick films). In particular, chemical interactions between lubricant components and metal surfaces play a major role in tribochemical processes. Hence, studying these interactions is of primary interest for the understanding and the prediction of tribofilm formation in industrial systems. The development of new additives is necessary since many of the empirically developed additives are either toxic or environmentally undesirable and will have to be replaced. Moreover, the development of highperformance additives is both economically

and technologically important for industrial systems. However, the complex phenomena occuring under boundary contact make it a difficult topic to study. First of all, it is very difficult to observe what is happening in the contact and generally tribologists have to deal with 'post experimental data' which may be misleading. Secondly, many compounds are likely to take part in chemical reactions occuring in a boundary contact. In addition to the different oil components used, a wide variety of second generation products are formed in the contact by tribochemistry or in the oil by reaction of lubricant components with oxygen or additives. It is also important to take into account the diversity of activated surfaces present in the contact: hydroxylated; oxidized or metallic surfaces which are likely to have a

324 very different chemical behaviour. Thirdly, tribochemistry between all these compounds involves a considerable set of different physico - chemical interactions: catalytic; thermal; high pressure; oxidation; polymerisation... All these reactions are intricately intertwined, leading to many products and making it almost impossible to determine the reaction pathways. Consequently, the study of the chemical interactions which lead to tribochemical films in boundary contact requires the application of a simplified model approach and the development of new experimental tools. In general, metal surfaces are covered with metal oxides and adsorbed layers. However, during tribological processes the surface layers may be mechanically removed creating nascent metallic surfaces. Such surfaces have been shown to present a high chemical activity enhancing molecular adsorption or decomposition. Morecroft et al. [1] observed that fresh surfaces such as evaporated films decomposed paraffin compounds at ambient temperature. Moreover, it is well known that fresh metallic surfaces generate many chemical reactions in heterogeneous catalysis and this is used industrially [2] S. Mori et al. [3-4] reported that tribological nascent surfaces created by scratching are able to decompose molecules at ambient temperature. Tribological nascent surfaces and more generally tribological surfaces are believed to be far more reactive than, for instance, single crystals, since their reactivity may be enhanced by the presence of many surface defects. Many tribologists have pointed out that due to this high chemical activity, interactions between nascent surfaces and lubricant components may be very important for the formation of tribofilm and therefore for the protection of tribological surfaces in boundary contact. These interactions are vital for processes where large areas of nascent surfaces are likely to be created as in metal forming which is the context of our study. The aim of this paper is to present a new method which attempts to experimentally model boundary lubrication phenomena in

order to obtain a better understanding of the role of additives and in particular of the interactions of these additives with reactive nascent surfaces. In this paper, we focus on the experimental approach which is validated by preliminary results. 2. E X P E R I M E N T A L 2.1. P r i n c i p l e

Surface science analytical techniques are now applied systematically to address problems related to additive chemistry [5] and their use is a prerequisite for further progress in the understanding of boundary lubrication mechanisms. As most of these tools require an ultra-high vacuum chamber which cannot be employed in industrial lubrication conditions, they are generally used for post mortem analysis of boundary films which may significantly alter their chemical nature. In order to avoid these issues in situ analyses have been carried out with an analytical ultra-high vacuum tribometer. In spite of the numerous technological difficulties, this device has many advantages. Firstly, as experiments are run in an UHV chamber, the environment can be precisely controlled or completely suppressed. Secondly, the analytical tools enable an accurate definition of the tribological surface before and after the friction experiment. Moreover, the surface can be generated in situ and friction experiments can be performed on specific oxide, hydroxide, or metallic surfaces. As a result, it is possible to eliminate many of the confusing phenomena which may otherwise modify the reaction pathways of additives. The main issue is to lubricate the contact, that is to say, to introduce the lubricant components inside the UHV chamber during friction. Molecules may be adsorbed on surfaces prior to friction or introduced as a vapour phase. The latter alternative has been chosen since it enables the modification of the ambient pressure and therefore the control of the molecular concentration at the sample surface. However, as the molecules have to be in a gaseous state, only light molecular weight compounds can be considered. The adsorption

325

method may be more appropriate for high weight compounds which are closer to lubricant additives. As a result, we considered low molecular weight molecules which were used to simulate the heavy lubricant components by their chemical functional group. In order to use heavier compounds an introduction system has been designed which enables the introduction of liquids of high vapour pressure. Hence, the experimental modelling of boundary lubrication is based on the introduction of molecules which simulate lubricant components in an analytical UHV tribometer as schematised in Figure 1. The pressure in the chamber can be varied from 10 7 Pa to 103 Pa in order to study the kinetics of tribofilm formation. The evolution of the friction coefficient versus pressure makes it possible to discriminate the different molecules and to appreciate their activity towards the surface (critical pressure) and their lubricating properties (minimum friction coefficient). The temperature was also considered as it plays a major role in boundary lubrication. It can be varied from-160°C up to 600°C. The analytical tools were used to control the surface chemistry and to study the boundary additive mechanisms. Experiments were carried out in a diffusion-pumped UHV chamber equipped with Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), a mass spectrometer and an ion sputtering gun.

Reciprocating Pin-on-Flat Tribometer

.•m

m m m m m m m

0

0

0

Nascentsurfaceor tribochemicalfilm

0

Oxy~elayer

UFuncUonal group

Figure 1: Schematic view of the experimental system for modelling boundary lubrication. The UHV experiments were also compared with classical liquid lubricated friction tests using an atmospheric reciprocating pin-

on-flat tribometer. For these tests we considered the same molecules and the same mechanical conditions. The aim of this comparison was to determine whether these vapour phase experiments can be related to classical contacts. In the preliminary set of experiments we considered the additive alone, excluding the environment and the synergy or competition effects between several additives. We also focus on the interaction between additives and the nascent metallic surfaces which are known to have an important catalytic action for tribofilm formation [3-4].

2.2. Experimental details An analytical ultrahigh vacuum tribometer has been used to investigate reactions between molecules and nascent metallic surfaces. The kinetics of the tribochemical film formation or surface protection were studied as a function of molecule concentration and temperature. Molecules The molecules used were commercial reagent grade organic compounds. Because heavy molecular weight compounds are difficult to introduce into the vacuum chamber, paraffinic and olefinic hydrocarbons (n-hexane and 1-hexene) were used to model the components of base oil. Diallyl disulfide and triethyl phosphate were used as models for extreme pressure additives. Propionic acid and 1-hexanol were used as model compounds for fatty acids and alcohol additives. Oxygen was also studied in order to account for the oxygen gas molecule which is dissolved in lubricants. All organic compounds were degassed by a repeated freeze-thaw technique and the molecules were introduced into the vacuum chamber through a variable leak valve. In this way pressure can be varied from 10 ~ Pa to 1 kPa and therefore the molecular concentration at the sample surface can be controlled. Below 10-~ Pa the system was pumped continuously during introduction of the gazes and the pressure was measured with a Bayard-Alpert ion gauge. At higher pressures the vacuum chamber was isolated from the pumping system and the pressure was measured by a Baratron gauge. The composition of the

326 admitted vapour was controlled by using a mass spectrometer.

Flat and pin

Two different flat samples were considered : one made of Ti-IF steel (cold rolled and annealed) and the other made of an aluminium - magnesium alloy AA 5182 (cold rolled). Prior to friction experiments and in order to completely remove the oxide and contaminant layers, the steel surface was cleaned by several cycles of in situ argon ion bombardment (5 kV, 20 lJA, 40 mn). The cleanliness of the surface was controlled by Auger Spectroscopy (O KLL and C KLL heights were less than 5% of Fe LM~M,, as measured on direct Auger spectra). No sputtering of the aluminium sample surface was made since, for this industrial cold rolled surface, the heterogeneous oxide layer is difficult to remove completely. The oxide layer was only removed from a small area with the focused ion beam (5 kV, 20 IJA, 20 mn). Hence, reactions inside the wear track, on the oxide and on sputtered metallic surfaces can be compared. The pin (AISI 52100 steel) was solvent cleaned and its contamination was also controlled by Auger spectra.

Apparatus

The specificity of this analytical UHV system is the in situ pin-on-flat tribometer which allows surface characterisation of both tribological counterparts [ 6 ] . We used a spherical pin with a radius of 3 mm. All friction experiments were done with a normal load of 0.5 N and a sliding speed of 0.5 mm/s. Severe mechanical conditions were applied (contacts were elasto-plastic for both aluminium and steel at least at the roughness tops) in order to create nascent metallic surfaces. The friction coefficient was recorded for 100 friction cycles. Experiments were performed at different pressures and for two different temperatures (25°C and 200°C). The temperature was applied and controlled on the flat using a standard vacuum manipulator. X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) were performed before and after friction experiments, to investigate the chemical nature

of the surfaces. AES was particularly appropriate for the study of the tribochemical reactions inside the friction scars of both the pin and the flat. All analyses were done in the same vacuum chamber as the friction experiments (eventually after pumping). AES and XPS analyses were performed using a spherical sector analyser (VG 2201). This instrument enables Auger imaging with a maximum resolution of 1 IJm and Auger line scans across the wear tracks. These analyses are particularly useful for spatially localizing the differents elements of the tribochemical films which may be heterogeneous and to compare the reactions occurring inside and outside the wear track. Micro-XPS allows the identification of the chemical nature of the surface with a minimum spot of 50 IJm2 which is close to the size of the wear track. XPS images can also be performed. The XPS measurements were done using an AI Ka X-ray source (1486.6 eV) with a pass energy of 40 eV for chemical bond determination and 100 eV for elemental quantification. Auger analyses were done using a CRR of 4 and a constant primary electron beam current at 5 keV. Auger spectra were quantified by determining peak heights in the direct spectrum mode. Ex situ Small area XPS (20 IJm) profiles were also obtained using a Physical Electronics Quantum instrument. Experiments at ambient pressure under liquid lubrication were performed using a reciprocating pin-on-flat tribometer at ambient temperature under the same mechanical conditions. As a result, for each molecule and for all the different pressures and temperatures considered, we obtained the evolution of the friction coefficient for the first 100 friction cycles. Chemical analyses were performed on the two tribological counterpart surfaces before and after friction, inside and outside the wear track. We also studied the nature of the contact mechanisms by analyzing wear track morphologies.

3. RESULTS Many experimental conditions have been considered but we focus here on two products which only differ by a double bond:

327

hexane and 1-hexene and we consider the experiments run at ambient temperature. Nhexane was used to account for the base oil paraffinic compound. 1-hexene is used as a model compound for molecules having double bonds in the base oil. 3.1 Friction hexene

only a small reduction of the friction coefficient: at 1 kPa a friction of 1.0+0.2 was recorded for steel and 0.6+0.1 for aluminium. In the case of steel and for liquid lubrication with n-hexane, a significant decrease of the friction coefficient is observed. Yet, this value is exactly the same as that obtained for a dry contact in ambient air (0.6+0.1). Consequently, it does not show the ability of n-hexane to lubricate but the incidence of the environment on friction. For aluminium the decrease observed is not significant.

results for n-hexane and 1-

Under a base pressure of 10 .7 Pa the friction behaviour is catastrophic with a very high and perturbed friction coefficient on both steel (1.2+0.2) and aluminium (0.6+0.2) samples (Figure 2). The wear track is marked and is typical of seizure of the two counterparts. The wear scar on the pin is formed by a extensive metallic iron transfer. Nascent metallic surfaces were created on both aluminium and steel surfaces. In view of this disastrous wear and friction behaviour any beneficial effect of introduced molecules should be observable.

For 1-hexene, above 1Pa a significant decrease of the friction coefficient is observed for aluminium : 0.7+0.2 under UHV conditions, 0.2+0.03 at l kPa (Figure 2). At this pressure the friction remains stable at this value for all friction cycles and irrespective of the applied load up to 2N. A protective tribofilm is formed leading to this very low friction. One can note the production of an increasing number of wear particles with increasing pressure. At high pressure, the accumulation of large areas of matter are visible on the pin and on the flat cavities. In the case of steel, we also observed a decrease of the friction coefficient around 10 Pa: 1.2+0.2 under UHV conditions to 0.34+0.02 at 1 kPa.

Figure 2 compares the evolution of the mean friction coefficient with the pressure of nhexane and 1-hexene for steel and aluminium. Clear differences are apparent in the behaviour of n-hexane and 1-hexene. For n-hexane the behaviour observed for the steel and aluminium s a m p l e s is quite similar. This molecule seems to have a very low activity towards the metallic surface. At ambient temperature, the increase in pressure induces 1.2 ,--

E

-*- 1-hexene zx n-hexane

1 ~-

8

,

.

~

-,,- 1-hexene zx n - h e x a n e

1.21

i

~0.8

1.6 1.4

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

.......

....................... t .........

0608

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

0.4

iiiiiiii::::: !

0.4

o.2

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

0 -7

I

I

I

I

I

-6

-5

-4

-3

-2

(a) A l u m i n i u m

I

I

-1 0 Pressure (10 x Pa)

I

I

I

1

2

3

I

111 t

0.2 0

Ail

I

I

I

I

I

-6

-5

-4

-3

-2

I

I

I

-1 0 1 Pressure (10 x Pa)

I

I

2

3

I

I Air

(b) Steel

Figure 2: Evolution of the mean friction coefficient with the pressure of n-hexane and 1-hexene for (a) aluminium and (b) steel. The pressure referenced as 'Air' is related to the experiment performed in a lubricated contact under ambient air.

328

The wear scar becomes very smooth and no wear is detected. Almost no wear particles are produced. The liquid lubricated aluminium contact presents a friction coefficient very close to that observed at 1 kPa. While for steel the friction is somewhat higher and close to that observed for an unlubricated contact under ambient air. This method clearly differentiates the two molecules by their pressure versus friction behaviour. Moreover, this differentiation can be linked to the classical tribological behaviour of these compounds. Contrary to alcane, 1-alcene is known to have very good lubrication properties for aluminium-steel contacts [7-8]

3.2. Analysis The analytical tools enable us to understand more clearly the lubrication mechanisms. Figure 3 shows that a tribofilm has been formed but only in the contact zone of the wear track. So, there is a very Iocalised reaction of 1-hexene with the nascent steel surface on the contact area. Interestingly, 1hexene does not react with the ion sputtered nascent surface. An AES line scan across the

C KLL

SEM iiif::: i~i~ii::i!::!ii!!::i::ii~i~iiliili:::iiiiiiiiiiiiiiiii~i~iiiiW ' ~ .................................. ~ f ~

I N

wear scars confirms that the surface composition of the tribofilm is principally composed of carbon and steel without any oxygen. This clearly demonstrates that contact conditions are required for tribofilm formation and that the nascent ion sputtered surface does not present the same properties compared with a friction activated surface. The particular morphology of the steel wear scar observed on the flat is due to a high initial roughness. Figure 4 compares the Auger spectra performed inside the flat wear scar with 1hexene and n-hexane. The difference in surface composition may explain the friction data. Contrary to 1-hexene, there is no evidence of the formation of a tribofilm on nhexane. In the case of 1-hexene, an e x situ XPS profile obtained inside the flat wear scar on a 20 I~m~ area shows that the tribofilm is very thin, less than 10 nm, and that at higher depths the steel is impregnated with carbon, up to a depth of 50 nm with a carbon atomic percentage of almost 15%.

Fe LMM

i,~. '~:~i.~i~.iiii~.~i~ii~il.i~S-.::.~::i~i¢.~i:iii?~~.~. ~z~ii~ ~ : i ~ : i , ~ > ~ . ~ , ~ i ~ : : ~ ,

~

i';i!i;'.~i~ ......

"

=,,::+i:ii,~iiiiii~iiiiiiiiiiiiiiiiiii!iill~)i ~. iii!!!!!!~iii~i!iiiiiiiiiiiiililiiiiilIII!~I.

ii

50g

F

1

L T

•

~I~

Figure 3: A E S images performed after friction at 1 kPa of l-hexene on steel.

0 KLL

329 ..........-Fiaii-:hexenei--k-F;a

-- Flat n-hexane 1 kPa

particles and sometimes metallic aluminium which respectively account for breakdown of the oxide layer and some severe contact spots which may create nascent surfaces.

............................................................. i.........#e;,~LMMI ............... O KLL ' ~ ' 1

/[/

]

-

-4

200

250 300

350 400 450 500 550 600 650 700 750 Kinetic energy (eV)

Figure 4: Comparison of AES spectra carried out inside the flat wear scar after friction at 1 kPa of 1-hexene and 1 kPa of n-hexane. At a hexane pressure of 1 kPa, approximately one monolayer of hexane is physisorbed, however this layer does not appear to have any incidence on the friction behaviour and it probably does not enter into the contact. As a result, strongly bonded molecules are probably required to have a notable influence in boundary lubrication. Similar analyses were performed in the case of aluminium samples. The AES elementary maps clearly show that there is also formation of a tribofilm inside the wear scar, Iocalised inside the contact area (Figure 5). The images and the Auger line scan indicate that the composition of the film is heterogeneous and composed of oxide

SEM F

L

A

T

C KLL

7(...... •

The XPS analyses realised inside and outside the wear scars permit a clear understanding of the film composition which is summed up in Table 1. The tribofilm is mainly composed of paraffinic chains and the e x situ depth profile shows that the thickness of the tribo film is larger than 100 nm. Consequently, there is extensive catalytic reaction with 1hexene and aluminium during friction. % atomic Inside the wear scar O u t s i d e the wear scar

Flat Pin Flat

II c 64.8

69

27.4

II o

II

MgO

16.5

2

16.6

0

42

12.5

II A~ °

A~O

4.4

8.5

1.6

12.9

6.5

11.5

Table 1 "In situ XPS analysis of aluminium after friction at ambient temperature and at 1 kPa of 1 hexene. Figure 6 explains the difference in friction behaviour observed between n-hexane and 1-hexene. The latter presents an intense carbon peak while the former does not. Consequently, hexane molecules do not seem to form a tribofilm. The high oxygen concentration may be accounted for either by wear debris containing oxide or as a result of contamination by the residua . . . . . . . .ii I[qlllL

0 KLL

!ii!i i!!!!i!i! !i i i!!ii!

iil~'ili~@!iii! iiiii!iiii',~iiiiii~i~ii~~'........ ~ •

J ............ ~;!~;;:iii!!i:illiFi:!i!'.i:!:.i~.:iili;,;i=.:,~;ii;ii!~iiiiiiiii~iii~i!'~!Y ....

~:t

........................ :.~.:.:~:,~.~;;~f~;~ii~ili .:~

.

Figure 5" AES images carried out after friction at 1 kPa of 1-hexene on aluminium.

330

AI KLL

- - n-hexane 1 kPa flat m 1-hexene 1 kPa flat

tJ ,=i// L,

150

250

350

450

.........

, .........

550 650 1100 1200 Kinetic energy (eV)

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

1300

1400

Figure 6: Comparison of AES spectra from inside the flat wear scar on aluminium after friction at 1 kPa of 1-hexene and 1 kPa of nhexane the pumping delay prior to analysis 4. DISCUSSION

The different tested compounds can be clearly distinguished by their friction-induced behaviour (friction versus pressure). Moreover, the results are shown to depend on the nature of the metal substrate. The temperature is also shown to play a significant role. These results can be related to behaviour observed for classical lubricated contacts. They are discussed below in terms of interactions between molecule and the metallic surface. Paraffinic compounds are known to poorly protect tribological surfaces during boundary lubrication [9]. This is confirmed here by the results obtained using n-hexane. Bowden et al. [10] have shown that the protection of tribological surfaces depends of the weight of paraffinic compounds which appears to govern the adhesion strength of these compounds towards the surface. Hence, the weakly adsorbed monolayer which exists at 1 kPa does not seem to modify the behaviour since it does not enter the contact. As a result, only strongly bonded compounds may enter into the contact and modify the friction behaviour. Mori has shown that the small chemisorption activity of n-hexane towards nascent metallic surfaces is not measurable with his experimental apparatus [4]. In

heterogeneous catalysis, paraffinic compounds are known to react with metallic surfaces to form carboxyl species, however, the sticking coefficient is as low as 101° or 1012for methane which only leads to significant reaction products at high pressure [11]. This low sticking coefficient is due to a desorption energy which is lower than the energy barrier for the transition of the physisorbed state to the chemisorbed state. This may explain why the friction behaviour is poorly influenced by the pressure of n-hexane. The carbon double bond present in the olefinic compounds has been shown to enhance their reactivity towards nascent surfaces. Mori reported high chemisorption of 1-hexene and benzene on steel [4]. Hence, the formation of strongly bonded compounds is far more likely to occur for insatured compounds than for saturated ones. This may account for the lower friction observed in the case of the steel. In the case of aluminium, it is well known that olefinic compounds present very good lubrication properties compared to paraffinic compounds [7-8]. However, Mori reported a very low adsorption activity of 1-hexene towards nascent aluminium surface which should lead to poor friction properties. Consequently, these results require further examination to be fully understood. In the case of aluminium-steel contacts lubricated by olefinic compounds, the formation of heavy weight products has been reported [7]. The proposed mechanism is the oxidation of organometallic compounds such as alkyl aluminium by water or oxygen. Despite the absence of water and oxygen, during gaseous lubrication of aluminium by 1-hexene heavy weight compounds are also found inside the plane wear scar. A better understanding of these phenomena may be obtained by considering the organometallic chemistry of compounds formed by reaction of olefins with metallic aluminium surfaces which may lead to many different chemical reactions. In particular, heavy weight products can be formed by simple alcene addition in presence of Triethylaluminium [12]. This reaction is widely used for the production of polyethylene at

331 120°C and 10 MPa. This is a significantly lower pressure than that occuring in the boundary regime. The formation of high weight compounds catalysed by aluminium inside the contact should therefore be considered. Moreover, this may explain why products of reactions with the steel sample are relatively rare. 5. CONCLUSION

We present a new method which attempts to experimentally model boundary lubrication in order to have a better understanding of the role of boundary additives based on in situ friction experiments in an analytical ultra-high vacuum tribometer in which the contact is lubricated by low molecular weight molecules. These molecules are used to simulate the heavy lubricant components by their functional group. This method has been used for different compounds and allows a clear differentiation by their vapour pressure - friction induced behaviour. The results are shown to depend on the sample metal and on the type of molecule. Some molecules are found to efficiently protect the tribological surfaces even at very low pressures, whilst others are inefficient even at 1 kPa. Using this new method, we observe very similar friction behaviour to that obtained for lubricated contacts. Moreover, wear scar morphologies under gaseous feed are very close to those obtained in classical boundary lubricated contacts. Consequently, this method appears to accurately model the boundary action of molecules and is likely to be a powerful tool in the prediction and the understanding of the operating mechanisms of boundary additives Molecules which present almost no activity to the tribological surfaces such as nhexane and are just weakly bonded (physisorbed) do not seem to significantly affect the friction properties. On contrary, strongly bonded molecules such as 1-hexene exhibit good friction properties. The use of the in situ surface analysis is particularly helpful to understand the operating mechanisms of boundary additives.

Future work will entail astudy of mixtures of different products such as two active additives or one active additive and nhexane in order to evaluate the effects of competition and/or synergies between these compounds. Since reactions are Iocalised inside wear scars, the use of model oxide surfaces would clarify whether the nascent metallic surface or the tribo activation of the surface governs tribofilm formation. ACKNOWLEDGMENT:

This work was done with the aid of the Research project contract (C.P.R.)" Mise en forme des materiaux" contact outil-metallubrifiant" between CNRS, Irsid, P~chiney Recherche, ECL (LTDS), INSA de Lyon (LMC), I'ENSMP (CEMEF), INPT (IMF), College de France (PMC), Universite d'Orsay (LMS) et le CNRS (SCA). The authors acknowledge M. Belin for the friction experiments performed at ambient air and R. Frier for the ex situ XPS small area depth profile analyses. REFERENCES

1 D.W. Morecroft, Wear, 18 (1971) 333 2 B.E. Bent, Chem. Rev., 4 (1996) 1361 3 S. Mori and Y. Imaizumi, STLE, Vol. 31, 4 (1988) 449 4 S. Mori, Proce. of Inter. Trib. Conf. Yokohama, (1995) 37 5 C. McFadden, C. Soto and N. D. Spencer, Tribology International, Vol. 30, 12 (1997) 881 6 C. Grossiord, Th. Le Mogne and J. M. Martin, 25 'h Leeds-Lyon (1998) (in press) 7 S. Igari, Y. Takigawa, S. Mori and K. Shimada, Jap. J. of Trib., Vol. 41, 9 (1996) 1035 8 L.E. St. Pierre, R. S. Owens and R. V. Klint, Wear, 9 (1966) 160 9 W. B. Hardy and I. Doubleday, Proc. Roy. Soc., London, Series A, 100 (1921) 550 10 F. P. Bowden and D. Tabor, Oxford university press, 1964 11 F. Zaera, Chem. Rev.,95 (1995) 2651. 12 I. Omae, Application of Organometallic Compounds, John Wiley & sons, New York, (1998) 107

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Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

333

F u n d a m e n t a l s on the friction m e c h a n i s m of diamondlike carbon films C. Donnet a, A. Grill b, J. Fontaine a, T. Le Mogne", F. Lefebvre c, V. Patel b, C. Jahnes b "Laboratoire de Tribologie et Dynamique des Systtmes, UMR 5513, F~cole Centrale de Lyon, B.P. 163 - 69 131 Ecully Cedex, France. bIBM Research Division, T.J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A. cLabomtoire de Chimie Organomttallique de Surface Ecole Suptrieure de Chimie Physique Electmnique de Lyon (CPE) 43, Bd du 11 Novembre 1918 - 69 616 Villeurbanne Cedex, France. The present study proposes to discuss the friction mechanism of DLC films at the molecular scale, as a function of the nature of the films deposited by d.c. plasma enhanced chemical vapor deposition (PECVD). Two films with different hydrogen contents (34 and 42 at.%), relative fractions of hydrogen bounded to carbon (0.57 and 1.00), and ratios of sp2/sp 3 carbon bonds (1.27 and 2.33) have been studied. The film structures and compositions have been investigated by forward recoil elastic scattering (FRES), Fourier transform ilffrared spectroscopy (FTIR), and nuclear magnetic resonance (NMR). Reciprocating pin-on-fiat friction tests have been performed in ultrahigh vacuum, at room temperature and at various mean contact pressures, ranging between 250 and 660 MPa. Chemical analyses have been performed by in situ X-my photoelectron spectroscopy inside the contact tracks. DLC with the highest hydrogen contents exhibit ultralow friction (--- 0.02). DLC with the lowest hydrogen content exhibits high friction (0.5 - 0.7), depending on the contact pressure. These opposite friction behaviors are described in terms of shear strength with two contributions, the first one attributed to the adhesive pressures between the two contacting surfaces, the second one attributed to the applied external pressure. The high shear strength of the DLC film with the highest sp 2 C content is consistent with both extemal and adhesive pressure contributions, the adhesive one being attributed to the predominance of the sp2C re-x* orbital interactions. The weak van der Waals interaction energy of the hydrocarbon polymerlike topcoats is consistent with the ultralow shear strength related to the highly hydrogenated film.

1. INTRODUCTION The deposition, characterization, and applications of diamondlike carbon (DLC) films have been discussed extensively in the literature [1]. As for most of the tribological coatings, DLC films allow heavily-loaded counterfaces to roll or slide over each other with minimum tangential resistance (low friction) and particle detachment (low wear) [2-4]. Improvements in the tribological behavior and expanding the use of DLC films for tribological protection require an enhancement of the understanding of the friction and wear of these films and their dependence on the operating environment and film properties. Indeed DLC films present a wide range of structures and compositions, in terms of hydrogen content, fractions of hydrogen bound and unbound to carbon and sp 2 • sp 3 C hybridization ratio, depending on the deposition conditions. The present paper offers a selection of tribological investigations coupled with analytical characterizations performed on two different hydrogenated DLC films. By coupling a compilation

of previous experimental results [5-6] with complementary new investigations, we propose a model explaining the friction mechanisms of DLC films in UHV conditions, in terms of molecular interactions, using the tribological model proposed previously by Tabor [7] and further developped and discussed by Israelachvili [8] and Georges [91. 2. EXPERIMENTAL Two types of DLC films have been deposited by d.c. plasma enhanced chemical vapor deposition (PECVD) at a substrate temperature of 180°C, one from acetylene C2H2, the other from cyclohexane, C6H12. The substrates were miror polished stainless steel Z100CD17 (440C) for tribological investigations, and silicon wafer and aluminium (for NMR, see below) for analytical investigations. A thin amorphous silicon layer ( 1. However, it is very controversial to apply a flow factor method to the mixed lubrication problem for purely transverse rough surfaces. At a certain value of h/o', the flow factors are indefinable theoretically. Patir and Cheng argued that the flow factors for a transverse roughness become meaningless when h/a" approaches 3. However, strictly speaking, the flow factors in the form of expectation value do not converge for arbitrary h/o" as we mentioned before. In this sense, we couldn't state which value is appropriate for the limiting value of h/o, and it may depend on how many asperities are involved in a control volume or the entire lubricating surface. Hence, we relax this limitation of h/o" and apply the analytical expression of flow factors as,

OpTA - m a x { 1 - 6(h/rr) -2, O}

(7)

CsTA -- min{3(h/o') -1, hT/a'}

(8)

The details and consequences of this assumption are discussed later.

2.2. A s p e r i t y contact force The asperity contact forces Pa are predicted by the Greenwood-Williamson model(G-W model)J4], Pa -

EArlfl o"

(z - h. )3/2 f . (z)dz

(9)

8

where E is an equivalent Young's modulus, A is nominal contact area, fs is the probability density function of summit height distribution and hs is the mean separation with respect to the mean plane of summit height. The input data for the GW model, such as mean asperity radius fl and asperity density ~/, can be found by the random process theory[9]. When the surface roughness has a fully striated pattern, it is difficult to apply the GW model in determining the average contact pressure. This is because the Hertzian contact theory cannot relate the normal approach of two

bodies to the contact pressure, which is necessary to derive an equation like Equation 9. Hence, we take two individual approach to solve this problem. First, we adopt an elliptical anisotropy concept introduced by Sayles and Thomas[10] for the surfaces having 1/9 < 7 < 9. In the elliptical anisotropy concept, an equivalent spectral moment is given by the geometric mean of two individual spectral moments measured along the principal roughness orientations. This method cannot be extended to the fully striated rough surface. It should also be noted that the auto correlation function of linear decay used in Patir and Cheng's flow simulation doesn't exactly correspond to the elliptical anisotropy. Second, for a fully striated rough surface, we approximate the average contact pressure by a 2D stochastic contact model introduced by Aramaki, et all11], which is able to give the relationship between average contact pressure and ideal bearing area explicitly as shown in Equation 10.

Pa/A - V / ~ Eo" ¢2 AA~ 2 - 1.39¢ 2

(10)

where A is the correlation length of rough surface and Ar is the bearing area which is the function of parameter ~. Thus, once the average pressure is specified together with the material constants and the correlation length, we can first solve Equation 10 for ¢. After finding Ar by a simple substitution of ¢ into A,. = func.(¢) (see Reference [l l] ) , we finally arrive at the mean separation using the relationship between A~ and h, which can be written in terms of the error function for Gaussian surfaces. The mixed friction coefficients for totally striated rough surfaces are similar to the results from 7 = 1/9 or 9 cases. However, due to the difference of the contact models, they do not coincide with the asymptotic values intuitively speculated from 1/9 < 7 < 9 results. Therefore, we have to discuss these two cases separately.

2.3. Overall p e r f o r m a n c e Friction force due to asperity contact, Fa, is assumed to be given by the Coulomb's law as Fa = PaPa, where the friction coefficient, pa, is determined by the friction test results at the lowest

358

speed in the experiment. The overall friction coefficient is calculated by/~t = (Fa + F I) / (Pa + Py).

2.4. Numerical procedure Since a relatively small area at the edge of pad might play an important role in fluid pressure generation, unequal discretion in lubricating area is necessary to establish a numerical formulation. To achieve this easily, a finite element method based on the G alerkin method is employed to solve the average Reynolds equation. The half-Sommerfeld cavitation boundary condition is used in case of necessary.

load driving gear linear

oil bath

3. E X P E R I M E N T 3.1. Apparatus An end-face sliding rig shown in Figure 2 was used for friction measurements. The lower specimen, which houses three sector-shaped pads on its upper face, is secured at the bottom of an oil bath. The upper disk specimen, which rotates against the lower specimen, is attached at the bottom end of a rotating shaft. The shaft is supported by a pair of radial bearings located in a bearing housing. The bearing housing is supported by a linear slideway, which enables to transmit a closing force applied on the top end of the housing to contact surfaces between the specimens via. the shaft. Both of the specimens are submerged in the lubricant. The lubricant temperature is maintained at a prescribed value using a recirculation system between the oil bath and a large capacity, constant temperature reservoir. The oil bath is supported by ball bearings, which allow to rotate the oil bath. The rotational motion of the oil bath is restricted by a cantilever and a load cell, by which the frictional force is detected. 3.2. Test specimen The lower specimen is composed of three sector-shaped pads shown in Figure 3. The angular extent of the pad is chosen as 10 degree in order to avoid remaining the waviness on sliding surface. The pads are first prepared to have very sharp edge profiles by machining. The surface roughness of sliding surfaces is controlled to be a prescribed roughness height by an abrasive paper, which has a suitable grain size. Having prepared

housing upper specimen

lower specimen ~ad cell bearings cantilever

Figure 2. Schematics of end-face sliding test rig

0mmI lgm

N ,~

,45turn

Figure 3. Schematics of lower specimen: top view - left, sectional view of a pad - right

359

lower specimen ( stationary )

upper specimen ( rotaional )

Material

JIS $45C

JIS SUJ 2

Hardness

400-500Hv

760-800Hv

211ml~ 0.5ram (1)0.07gmRa with inlet wedge (0)0.02~mRa

Table 1 Roughness Parameters specific load sliding speed lubricant

(MPa) (m/s)

duration

(min)

description 1 0 - 80 0.025, 0 . 1 - 1.0 ISO VG32 mineral oil 30 degC (28-33) 3

Profiles (2)0.3gmRa with inlet wedge

(3)0.61.tmRa with inlet wedge (3')0.6t.tmRa without wedge

Figure 4. Details of test specimens: materials used, hardness, examples of surface profile

a couple of specimens, which have similar roughness structure, the inlet edge is re-shaped by using an abrasive paper on one of the specimens. As the inlet wedge is figured by a hand-lapping, the high accuracy of geometry cannot be achieved. In the experiments, we allowed the wedge depth between 0.5 and 1.5#m (target lpm). The upper specimen is a plain disk finished by lapping. The flatness of the upper specimen is checked by an optical flat and is assured that there is no local waviness whose wavelength is shorter than the size of the pads. The details of the specimens, including materials, hardness and the examples of surface profiles, are given in Figure 4. Hard materials are used to minimize the change of surface profiles during the test. 3.3. Test c o n d i t i o n a n d p r o c e d u r e The operating conditions are summarized in Table 1. A constant l o a d - variable velocity method is employed for the all tests carried out in the paper. Having stabilized the temperature of the lubricant in the oil bath, the sliding speed is set to be 0.025m/s, the minimum sliding speed. The load is then applied to be a specific value. After 3 minutes' run, the sliding speed is stepped

up to 0.1m/s and kept for another 3 minutes. In every 3 minutes, the sliding speed is stepped up in logarithmic order until 1.0m/s. By the primary tests conducted prior to the main test series, the duration of 3 minutes is chosen as a period of which the temperature of lower specimen monitored at l m m beneath the pad surface becomes stable. The oil temperature was able to be maintained between 28 and 33degC while the pad temperature varied from 30 to 60degC. 4. R E S U L T S A N D

DISCUSSIONS

4.1. E x p e r i m e n t a l r e s u l t s Micro inlet wedge Comparison between experimental data and numerical results has been made for a sector pad with isotropic roughness. Since the detailed roughness data for the surfaces actually used in the experiments are not available, we have assumed the spectral moments from several rough surfaces prepared with the same finishing process as was used in the experiments. We have no theoretical background which relates roughness heights to spectral moments. However, we assume that the second and fourth spectral moments as rn2 ~ m0 x 0.187 and rn4 ~ m0 x 0.737, where m0 - a2 in microns. Also, cr ~ 1.2Ra. These relations are not of general validity and are just obtained from roughness measurement for this particular experiment. If the surface is characterized as fractals, m2 and m4 can be written in terms of m0 theoretically. Figure 5 and 6 show the comparison of friction coefficients between experimental results and theoretical prediction. The theoretical curves including micro inlet wedge effects are very close to

360

the experimental results. However, both series of experimental friction coefficients, i.e. the wedged and sharpened pads, are descending as the sliding speed is increasing. As the friction reduction for the wedged pad is obviously greater than that for the sharp edge pad, the difference between these two experimental results seems to represent the role of the micro inlet wedge, which might mainly dominate the capability of fluid pressure generation. Other sources of friction reduction must be addressed due to the fact that the friction coefficient at U = l m / s decreases to 1/2 of that at the lowest speed. However, the degree of friction reduction for two different normal pressures nearly coincides. The velocity roughly contributes the temperature rise of sliding surface to the power of 1/2, while the load does to the power of 1/4. Therefore, one possible reason of the friction reduction might be due to temperature rise at the real contact area. For the micro-wedged cases, the temperature effects might be less significant because the friction itself is low. Nevertheless we do not include the local EHD effects, i.e. the micro-EHD effects, the theoretical results agree well with the experimental results. When the local EHD effects are taken into acfcount, most of real contact area found in the theory has to be replaced with fluid film lubricated area. However, the shear force in such an area is not very different from the boundary friction force assumed in the theory. Furthermore, the area in which the lubricant has much higher viscosity due to piezo-viscus effect might be larger than the real contact area predicted by theory. These effects might help the crude mixed lubrication model to be practically valid.

0.5

experimental (wedge) experimental(sharp) /

:L 0.2 o O o

0.1

0.05

0 o

..... P=

°!,,~

0.02

Ra=0.3~tm 0.01 0.01

Figure 7 shows the fractional hydrodynamic contribution to load support, xf, against various normal pressures. The experimental plots in this figure are calculated by the measured friction forces, the boundary friction force (at lowest speed) and the theoretical friction forces due to fluid film. General agreement is found between the theoretically and experimentally predicted load support contribution. The theoretical

!

0.05

i

!

0.1

i

0.2

i

0.5

1

2

sliding speed U, m/s

Figure 5. Comparison of friction coefficients with theoretical results; normal specific pressure of 20MPa

0.5

experimental (wedge) experimental(sharp) /

o

0.1

° ! o

/

0.05 .....

Q

o o.o2i.... P=40MPa ;~ Ra=0.3gm 0.011

Effect of n o r m a l p r e s s u r e

i

0.02

i

0.01 0.02

~:

/ theoretical i

i

i

0.05 0.1 0.2 0.5 sliding speed U, m/s

i

1

2

Figure 6. Comparison of friction coefficients with theoretical results; normal specific pressure of 40MPa

361

curve can be depicted up to 80MPa because the micro inlet wedge is totally accommodated within the nominal contact area due to elastic deformation for higher specific loads than 8 0 M P a . According to Figure 7, z I is decreasing as the load is increasing and the theoretical curve tends to level off at the higher load region. On the other hand, the experimentally predicted zy rises up slightly at 80MPa load. This means that the friction coefficients is relatively lower than expected. Temperature rise in the contact area may reduce the friction. As the temperature effects haven't been included in the analysis, however, it is uncertain whether the minimum x I exists against the load or not.

U=0.1m/s Ra=0.3l.tm . theoretical

0.5 OO /

experimental

I

50 100 normal pressure P, MPa

Effect of roughness height Figure 8 shows the relationship between z ! and roughness height. Since only three data are available for the roughness effect investigation, it is difficult to reach a comprehensive conclusion. Furthermore, while the repeatability of friction traces are satisfactory in the experiment with rougher surfaces, the data from the smoothest surface of O . 0 7 # m R a are significantly dependent on the flatness of the pad rather than the existence of inlet wedge. Even considering the above notation, it can be said that the agreement in absolute values of z ! between theory and experiment is satisfactory. However, the theoretical curve of z I is descending continuously as the roughness is increasing, while there seems to be a sudden drop of x ! at a certain roughness height in the experimental data.

Figure 7. Hydrodynamic contribution to load support z I for Various loads

Pm=40MPa U=0.1rn/s ©

theoretical ~- 0.5 ~

~

experimental 0

4.2. Roughness orientation As the general validity of the theory is expected to be satisfactory, we investigate the effect of roughness orientation on frictional behaviour in the mixed lubrication region. Results are shown for a circular pin and a square pad with a nominal contact pressure of 2 0 M P a and a sliding speed of O . l m / s (smooth surface moving). Nominal contact geometry is given in Figure 9. The same material constants are used as listed in Figure 4.

~

• 1

0.5 surface roughness, ~mRa

Figure 8. Hydrodynamic contribution to load support z! for various roughnesses

362

¢5mm

o 5mm

1.0 "-" ~ " ~ ~ ", \

0.8 0.5gm

0.5gin

I

---D--- transverse roughness ~ longitudinal roughness " otropic roughness

0.6_

J

0.4_

0.5mm v

r ' ~

0.2- P=2OMPa _

(a) pin

(b) square pad

0.0

"' -,~,,~, " ~

U=0. lm/s B=40mPa.s

0.01

'

I

0.1 roughness height, gmRMS

1

Figure 9. Nominal contact geometry used in the investigation of roughness orientation effect Figure 10. Hydrodynamic contribution to load support of the pin; 3' - 1/9 (transverse), 1 (isotropic), 9 (longitudinal)

elliptical anisotropy The hydrodynamic contribution to load support, z/, is calculated for the pin whose roughness patterns are characterized as 3' = 1/9(transverse), l(isotropic)and 9(longitudinal). The results are shown in Figure 10. Comparing the transverse and longitudinal cases, x I for the longitudinal surfaces is larger than the transverse's one. Obviously the difference of z I gets smaller as the lubrication regime approaches to the boundary or the fluid film lubrication regimes. The direct comparison of the mixed lubrication performance between isotropic and anisotropic surfaces can not be made straightforwardly because of the combined effect of roughness on fluid film pressure and asperity contact force. The mean separation for an isotropic surface tends to be smaller than that for an anisotropic surface when the mean contact pressure is specified, since a single asperity of a specific height for anisotropic rough surfaces has higher load capacity than an isotropic asperity. While the hydrodynamic load capacity for the isotropic surface becomes larger due to the reduction of film thickness or mean separation. Even taking account of the change in fluid film load capacity due to roughness orientation, z/ for the isotropic surface becomes larger than that for the anisotropic surface due to reduced film thickness because the effect of film

thickness on hydrodynamic load capacity is superior than the roughness orientation effect. Figure 11 shows the maximum fluid film pressure. The maximum pressure decreases as the roughness height increase, simply because the mean separation increases. The maximum fluid film pressure for the transverse rough surface is higher than that for the longitudinal rough surface though the overall fluid load capacity is in the opposite order. This implies that there is a localisation of fluid film pressure distribution.

purely striated surfaces Figure 12 shows the fluid pressure distribution on the pin surface with a fully striated roughness of O . 0 7 # m R M S . The sliding direction is along x-axis, from negative to positive. Comparing these two pressure contours, it is found that the maximum pressure for the purely transverse rough surface is three times as high as that for the purely longitudinal roughness. On the longitudinal rough surface pin, the fluid pressure is maintained over the surface while the pressure on the transverse rough surface rapidly decreases and approaches to zero at the centre of the pin. Consequently, the hydrodynamic partial load support of the longitudinal rough surface becomes 15%

363

1000

2-

I.... ~---

]

c~

~

100 -

o

--0.-

X

transverse roughness longitudinal roughness isotropic roughness

2

l

. ._

1

~0-

if0-

-1

-1-

_

,-o -2

10- I

e c~

1

i 0.01

-2-

-2

U=O.lm/s lx=40mPa.s

0 1 2 x, mm (a) longitudinal rough surface

-~'~

0.1

-1

-2

-1

0

1

2

x, nlm

(b) transverse rough surface

1

roughness height, gmRMS

Figure 12. Fluid pressure distribution on the pin surfaces

Figure 11. Maximum fluid film pressure on the pin surface; 7 - 1/9 (transverse), 1 (isotropic), 9 (longitudinal)

5 ,20, 50, 100

~ higher than that of the transverse rough surface. At these conditions, the flow across roughness lays is very restricted, and the pressure contours are parallel to the roughness lay in the parallel film region. Therefore, the pressure field for the transverse rough surface inside the parallel film area might be mainly governed by the film pressure generation at surrounded wedge of the pin. Such behaviours can clearly be seen in the pressure contour on the square pad. Figure 13 shows the fluid pressure distribution with the same roughness configuration as Figure 12. A pressure plateau in y-direction is observed for the longitudinal rough surface (see Figure 13(a)), which is similar to the pressure profiles obtained from a long bearing approximation. The flow restriction along y-axis might results in producing such a flat pressure profile. On the other hand, the fluid film pressure is confined to nearly the wedged area for the transverse roughness case (see Figure 13(b)). The pressure generated at the inlet doesn't spread over the parallel film area. Consequently, the fractional load support by hydrodynamic effect, zy, for the transverse rough surface is only 0.375 while x/ for the longitudinal rough surface is 0.881. The pressure profiles are indeed able to be

3-

.

2-

0

i

~X, m m ~

~

5

(a) longitudinal rough surface

i

0

~

"140MPa

'

I

1

'

I

2

'

I

3

'

I

4

'

X, m m

(b) transverse rough surface

Figure 13. Fluid pressure distribution on the square pad surfaces

found numerically. However, we have to be careful when discussing the hydrodynamic performance of transverse rough surface. Besides the lack of EHD insight into the theory, the assumption of the flow factors for transverse roughness employed in the paper is still not very convincing. Basically, if an asperity contact takes place in a control volume, the flow factors are indefinable for a purely transverse rough surface. Let the size of a control volume be AX and the correlation length be A, the condition that at least one asperity contacts in the control volume is,

AX

f(5)d5 > 1 /o

(11)

364

For instance, substituting typical values such as A X = 100#m and A = lOI.tm into Equation 11, we have h/~r < 1.28. At h/cr < 1.28, the pressure flow factor for a transverse roughness cTp,A -- 0 and the shear flow f a c t o r Cs,AT -- "~T/~r. Namely, the flow across the roughness lay is not permitted. From Equations 7 and 8, we can find that the limiting values of h/cr are 2.45 and 1.72, respectively. Since Equations 7 and 8 were derived by a perturbation technique, it is not very appropriate that we discuss the limiting value of h/~r from these equations. However, these limitations are within a stochastic limitation, i.e. h/~r > 1.28, with practical numerical values. Figure 14 shows the fractional contribution by fluid film to load support, z f, for the purely transverse and longitudinal surfaces. The difference of z! between two types of roughness in the small roughness height region is more remarkable than that is seen in Figure 10. When the roughness height exceeds 0.1#m, z! for the transverse rough surface becomes slightly larger than x I for the longitudinal rough surface. In this region, a strange behaviour is seen in the maximum fluid film pressure as shown in Figure 15. In the region of ~r > 0.1#m, the shear flow term in Equation 1 is nearly zero for the nominally parallel area, i.e. no flow allowed in the parallel region. Strictly speaking, calculations in such a region might be meaningless physically. However, it is practically possible to calculate and the resultant overall performance, such as load capacity, seems to be affected very slightly by this kind of abnormality in fluid pressure generation. In the flow simulation in obtaining the flow factors, one must encounter the similar difficulty of physical accuracy, particularly in considering the no flow boundary condition at the asperity contacts.

A

1.0

5

size of w e d g e

In this section, we have mainly investigated the mixed lubrication performance of a pin which has a wedge of 0.25mm in length. Finally, we briefly mention the effect of the size of wedge on the hydrodynamic contribution to load support, zf. As seen in Figure 16, if a certain size of wedge, say 0.2mm or larger in this case, is formed, zf is

A

-

l---D---transverse roughness I gitudinal roughness]

~',,

0.80 . 6 -

0.40.2- P=20MPa U=0.1m/s la=40mPa.s 0.0

" ~...

0.01

0.1

1

roughness height, grnRMS

Figure 14. hydrodynamic contribution to load support z! of the pin; 7 - 0 (transverse), co (longitudinal)

1000 i P=2OMPa U=O.lm/s ~t=4OmPa.s

Q

t3 - - E l - . G . _G

1o0

1

] 0.01

the

~

"', - ~

"O.

---El--- transverse roughness ---©--- transverse (choked) '

I

0.1

1

roughness height, gmRMS

Figure 15. Maximum fluid film pressure on the pin surface; 7 - 0 (transverse), c¢ (longitudinal)

365

0.6 ! P=2OMPa U--O.lrn/s 0.5 i g=4OmPa.s 04

0.2

...........

//

0.3 !!

[] . . . . . . . . . .

° .................

!

oo//

I ~ ~ - - - -

x/// •

~ longitudinalroughness ~trarisverserougliness ! i - - O transverseroughness (choked) 1

i

0.1 ! 0.0

~.__--------~------&

~

I

0.1

'

!

~

!

0.2 0.3 wedge length, mm

'

T-

0.4

'

0.5

Figure 16. Effects of wedge length on the hydrodynamic contribution to load support

not very much influenced by the wedge size itself. Using even bigger pins up to l Omm in diameter, this trend is the same. What is important to achieve the mild sliding condition in mixed lubrication regime is to provide a micro inlet wedge of 0.2mm or longer. 5. C O N C L U S I O N S The frictional behaviour of nominally flat surfaces in the mixed lubrication regime was investigated. Friction forces were measured for various sliding speeds(0.025- lm/s), nominal contact pressures(20- 80MPa) and roughness heights(0.07- 0.61amRa), using sector shaped steel pads with and without an artificially controlled tiny wedge at the inlet edge. A tiny wedge at the edge of a flat pad enhanced the capability of fluid film formation and the significant decrease of friction. Comparing with the wedged and sharpened pad tests, the principal source of fluid film force has been suggested to be the deviation from parallelism, which supports the conclusion of Lebeck's work[6,7]. The experimental data were reasonably represented by the mixed friction model. The theoretical investigation of the effects of roughness orientation was also performed. An el-

liptical anisotropy is assumed for asperity contacts. Unlike in the fluid film lubrication regime, longitudinal roughness patterns showed a greater performance in terms of film formation than transverse roughness patterns in mixed lubrication. A mixed lubrication model for a fully striated roughness case is also proposed, where the analytical expressions for flow factors derived by Tripp[8] and a stochastic 2D contact model introduced by Aramaki, et al[ll] are exploited. Although the model is not very accurate especially for transverse rough surfaces, the overall performance, such as load capacity, can be predicted and can cope with the elliptical anisotropy model. REFERENCES

1. T. Nakahara, J. of Jap. Soc. of Trib. 39 (1994) 220. 2. N. Patir and H.S. Cheng, Trans. ASME, J. of Lubr. Technol. 100 (1978) 12. 3. N. Patir and H.S. Cheng, Trans. ASME, J. of Lubr. Technol. 101 (1979) 220. 4. J.A. Greenwood and J.B.P. Williamson, Proc. Roy. Soc. Lond. A295 (1966) 300. 5. S. Taniguchi and C. Ettles, ASLE Trans., 18

(1975) 299. 6. A.O. Lebeck, Trans. ASME, J. of Trib. 109 (1987) 189. 7. A.O. Lebeck, Trans. ASME, J. of Trib. 109 (1987) 196. 8. J.H. Tripp, Trans. ASME, J. of Lubr. Technol. 105 (1983) 458. 9. P.R. Nayak, Trans. ASME, J. of Lubr. Technol. 93 (1971) 398. 10. R.S Sayles and T.R. Thomas, Appl. Energy, 2 (1976)249. 11. H. Aramaki, H.S. Cheng and Y.W. Chung, ASME paper, 92-Trib-30(1992).

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

367

A transient thermohydrodynamic analysis of dynamically loaded finite journal bearings with rough surface including mass conserving cavitation Chao Zhang, Jason X. Jiang, and H. S. Cheng Center for Surface Engineering and Tribology Northwestern University 2137 Sheridan Road, 219CC Evanston, IL 60201 U.S.A A transient ISOADI (Isothermal Shaft and Adiabatic bush inner surface) analysis of dynamically loaded joumal bearing in mixed lubrication is presented by solving the average generalized Reynolds equation with the consideration of mass conserving cavitation, 2-D energy equation in the oil, and heat conduction equation in the journal simultaneously. The temperature in the journal is treated as quasi-steady over one loading cycle. A detailed study of the system in term of the minimum nominal film thickness, maximum film pressure, heat flow into the journal, power loss, oil flow rate, and the temperature distribution indicates that the bearing behavior is closely tied to the surface roughness texture, asperity load, bearing geometry, and operating conditions.

B C Cp D E'

NOMENCLATURE t

bearing length nominal radial clearance specific heat bearing diameter equivalent elastic modulus, 1 _ 1 1-u~2 + l_u2 E'

2

E1

T U U, V

Z,0

E2

y, Z

ex, eY journal accelerations in X and Y directions Fo~LX FoilY

FCx, FCy G h ht

CO

film force in X direction

81 , 82

fihTl force in Y direction contact loads in X and Y directions cavitation index nominal film thickness total film thickness

E V 1 , V 2

t~ t~

hmin H ko M P, Pv

minimum nominal film thickness non-dimensional hardness thermal conductivity equivalent journal mass film pressure and cavitation pressure, respectively Pa, Ps atmospheric and oil supply pressures E(Pm~ x ) maximum film pressure pC, p~

non-dimensional

R

2pC)v,/(rtE'~*) radius of bearing

contact

X,Y

pressure,

.

time temperature linear velocity of journal fluid velocities in )~ and y directions coordinates of circumferential direction, O=z/R coordinates in radial and axial directions system coordinates angular velocity of journal roughness heights from mean line of bush and journal surfaces eccentricity Poisson's ratios of the bush and journal standard deviation of roughness height standard deviation of Gauss distribution of combined surfaces density of oil viscosity of oil relative clearance, C/R void fraction in cavitation region, = Vf/V t -1, and dimensionless film pressure in the full [E(P)- Pv ]~2/(g0 o )

pc-K,K

film

region,

=

non-dimensional bearing surface hardness, =

368

~ z

E()

auto-correlation length denotes the expected value

supply oil as well as the reverse flow of the oil are also considered.

1. I N T R O D U C T I O N

2. M A T H E M A T I C A L A N A L Y S I S

The nominal minimum film thickness in dynamically loaded joumal bearings, such as crankshaft bearings, is in the same order of magnitude as the surface roughness. Possible asperity contacts may lead to surface scuffing or seizure. Taking into account of the thermal effects, one can determine the viscosity of oil and the minimum film thickness more accurately, and predict the maximum temperature of bearings, which is important from designers' viewpoint. A transient thermo-hydrodynamic analysis of dynamically loaded journal bearings in mixed lubrication would aid in understanding the bearing behavior deeper and improving the bearing performance. Many endeavors have been made to the study of mixed lubrication (Christensen [1], "In der [2], Patir and Cheng [3]). Boedo and Booker [4] and Ai et al. [5] used 'Average Flow Model' to study the effects of roughness on dynamically loaded journal bearings with Gauss distributed roughness and Newtonian fluid. Zhang et al. [6, 7] employed Christensen's statistic approach [8] to the two-sided running-in roughness and included Non-Newtonian rheologic effects. Paranjpe and Han [9] and Paranjpe [10] made the THD studies of dynamically loaded smooth joumal bearings. For the combination of THD/TEHD and asperity contacts, only steady-state load is considered so far, by Ramesh [11], Shi and Wang [12], and Wang et al. [13]. There is a need to understand the THD with asperity contact interactions in dynamic load cases. In the present work, the ISOADI (Isothermal Shaft and Adiabatic bush inner surface) analysis is presented for dynamically loaded journal bearings with an axial groove in mixed lubrication, with the consideration of mass conserving cavitation. Christensen's stochastic theory is used to model the effect of surface roughness on hydrodynamic lubrication [8] and Lee and Ren' s curve fitting formula [14] is employed to compute asperity contact pressure. The transient two-dimensional energy equation is solved in the center plane of the film thickness, while the temperature in the joumal is treated as quasi-steady state over one loading cycle [9]. The mixing of the recirculating oil and the

In the following analysis, an incompressible Newtonian fluid and Christensen's postulates [8] are employed, and the bush is stationary. 2.1. G e n e r a l i z e d R e y n o l d s e q u a t i o n

The generalized Reynolds equation developed by Dowson [15] can be used in the hydrodynamic area: ~(oF2-~~~] + ~(oF2 ~ ) = U-~-[O( hT - FF--~o ]] +~(phr)

.

(1)

where hT = h - 8 1 - - ~ 2 '

Fo = f T lgd y

F2 = ~T-g y -

dy

yl F1)

F1 = ~ gYdy

Defining 0=Z_- y 2z hx ~ ~1,2 R ' Y=E(hT)' z='-B-' h-~=--C--' 51'2= C ' w

t=to,

g=

g ,

go

=

i'-yd

,

la

-F~=

yd

, Ym=%,

Fo

~22= ~~(y--ym}~y, U=Ro In order to take into account the mass conservation of the flow across the boundaries of film rupture and reformation, a cavitation index G and the void fraction A in the cavitation region are used. In the full film region, A becomes non-dimensional pressure [7]: Full film zone (A > _ O) • Cavitation zone (A < 0)"

A = [E(p)- Pv ~2 gtoCO A = Vf

v,

;G=I

1; G = 0

where Vt and V, are the total clearance volume and the volume occupied by the fluid, respectively. Although the lubricant is considered to be incompressible, this algorithm is same as Elrod algorithm [1 6]. By inserting A and G into the expected value of Eq. (1), one gets:

369 --~[Fc a(o~A)]+ 1

-Yc3LIFD a(GA)] C~ J-" ov {Full + 0 - -

G)A]}

a +--= ~ h~v~1+ (1- G)A]} at where

(2)

flS(g~l) and f2 8~8[)denote the probability density function of ~ and 8--~, respectively. For the full hydrodynamic lubrication, 8'1 = 8Imax and 8'2 = 8: max , while for the mixed lubrication, 8'1 and 5': are obtained according to the elastic modulus ratio of the bush and journal. Expected values Fo and Fu are determined as follows, for longitudinal, isotropic, and transverse textures, respectively: Fc" E(h"-~-3]F2, E(h'--3)F2, T 'F2/E(h--~-3]

Fo"

FE • E(h---~-2)aE~)80, E(~-T2)aE~)ao

(--3), (--3)

EhT F2 EhT F2

l_y m E(h---T-1] f 0 - ym)E(h--T--2/ F-~- E(h-~--3)

E(2hT3) F2

/'2hT19 FF"

gh~T[1-Ym),

g(~-T~l-Ym),

(1- y m)E(h--~--21- E(8-~r -3) E(hT -3) FG "

E(h-~-3), E(h---r-31, CE(hT -3]

FH•

/E(hT-3], E(h--T-3/, E(h--~-3)

film The expected governing equation for dimensional oil temperature can be expressed: pCpoil[dE(T)+ E(u)aE(T)+ E(v)a~T)] = Ot 8z 2.3. The energy equation in the oil

Fu" E(h-~-~X1-Ym),Eh~TXI-Ym), E(h'--~-2)(l - ym)-- E(8-~T -3)

The discretization of the shear flow, pressure induced flow, and time terms in Eq. (2) are same as those in Refs. [6, 7]. The pressure boundary conditions are set to atmospheric pressure on the external boundary, and the supply pressure on the internal boundary of the bearing. Periodicity is also forced in the position where the bearing wraps around.

+ko ~ ~

The components of fluid velocity and flow rate are given by ~o l f f l d~+F E(ff~=d~-y m~ 1 d~/ E=~-~u) g

(3)

E(v) =-E h~T)I°Ic3E(u)~(~--/0E(h-~T)0E(U)]d~

(4)

(7)

where Cpoil and k o are oil specific heat and thermal conductivity, respectively. The nondimensional form of Eq. (7) is" c~ + E(u) a0 + E(h-TT E(v)-E(u~ a =

2.2. The c o m p o n e n t s of velocity and flow rate

two-

[

ALl a2E(T)+ a2g a E(h--T-2) 0 y 2 E(hT ) 8y ]

aE(_T)0y (8)

where

(5)

T=-~T AI=C 2 k o , A2= o g 0 TO ' co pC poil TOpC poillq/2 The thermal boundary condition at the oil-journal interface is given by: [E(T)~__,: Tjourn~ , (9) and adiabatic condition at the oil-bush interface:

(6)

(10)

For longitudinal, isotropic, and transverse surface textures, F~, FF, Fo, and F. read as follows, respectively

Moreover, periodicity is enforced where the bearing wraps around.

O)AF a~

a~ )

-

370

X

2.4. Mixing in the oil groove The groove has a thermal inertia that is roughly of the same order as the oil film thermal inertia. The groove temperature is marched using a real-time transient analysis and is obtained by the overall energy balance on the groove [9]:

Mg~Cp°il dE(Tg~) dt - PQzCpoi,Tm+ PQrecCpoilE(Trec) - p(Qz + Qr~ )CpoilE(Tgr) M~ and E(T~) are the mass

(11) and averaged

temperature, respectively, of the oil in the groove. Q z and Tm are the mass flow rate and the temperature, respectively, of the supply oil. The terms PQr~ and E(Tre¢) represent the mass flow rate and averaged temperature, respectively, of the recirculating oil entering the groove. While P(Qz + Qrec ) is the mass flow rate of the oil leaving the groove and can be solved by:

Qre~ - CpBRm f' E q~x}dz where z, is the nondimensional groove width. 2.5. Heat conduction in journal It is known that the cyclic variation of the journal temperature in the circumferential direction is small so that the journal can be treated as lumped and the temperature in the journal is uniform [17]. In addition, the time that the heat conducts in the journal is several orders of magnitude shorter than the transfer time of the frictional and shearing heating in the oil. The temperature in the journal is expected to be a quasi-steady state over one loading cycle [9], which can be obtained by the following heat balance:

f"{

~-~T)IaE~)I

large time step can be used to achieve the steady state solution [9].

hT(Y'H'P'~)-exp-'T[~"~i][~)(P;)iG , p'~ --16.6pro

90

150

"".

."'"

-24.8 120

->

-. ':.

90

0~, -28.9

->

30

-20.7pro "

..'

60

lY, 2~, -24.8pro

3Y,

Fig. (13) Anisotropy of the texture versus the level of motifs.

VI. Conclusion It is well known that an engineering surface is composed of a large number of length scales of roughness that are superimposed on each other. The multi-scale roughness features are related to different aspects of the processes that the surface has undergone, and influence the functional performance of the workpiece. Conventionally the multi-scale of surface roughness is characterized by parameters ISO, DIN..., these parameters are quantified by determining the reference line after numerical filtering which can separate waviness and roughness by the chosen cut-off. This methodology is adapted to the quality control of manufactured surface, however for some field in tribology such as friction, adherence, adhesion, wettability, lubrication, liquid flow..., it is very important to know the contribution of each scale of roughness component to the macroscopic functionality. As shown in this work, it

390

is clear that wavelet analysis is a valuable signal processing tool for linking the multi-scale features of engineering surfaces with both its manufacturing and functional aspects. In addition to the multi-scale and space frequency localization, this work introduces the use of wavelet transform as a powerfull tool for the characterization of local morphology by localizing the local motif using the modulus and the phase of wavelet transform, so that the roughness and waviness component can be quantified. Extension of this formalism to three dimensional surface analysis opens a new field of the characterization of 3D multi-scale analysis. With this new approach we can take further steps in the multi-scale aspect of the morphological anisotropy, which was up to now limited to a surface texture analysis as opposed to a volume one, thus opening up a new field: dealing with problems related to friction, lubrication, static or dynamic fluid leakage, using new surface parameters showing the geometrical reality of surface roughness.

References

[1].F.HALWATSCH and G.F. BOURDREAUXBARTELS.-" Linear and Quadratic TimeFrequency Signal Representations"- IEEE SP Magazine-Avril. 1992, pp.21-67. [2].Y.MEYER, -"ondelettes et op6rateur.I: Ondelettes. Edition Mermann 1990. [3] I. DAUBECHIES.-" The Wavelet Transform, Time-Frequency Localization and Signal Analysis".-IEEE Transaction on Information Theory, Vol.36, No.5, September 1990.pp.961 - 1005. [4]. A.COHEN, J.KOVACEVIC.-" Wavelets: The Mathematical Background"-Proceeding of the IEEE. Vol. 84, No. 4, April 1996. [5] X.CHEN, J.RAJA, S.SIMANAPALLI-"Multiscale of Engineering Surface"-Int.J.Mach.Tools Manufacts. Vol.35 No.2,pp231-238,1995 [6] D.WOLF, R.HUSSON, -"Application des ondelettes ~ l'analyse de texture et h l'inspection de surface industrielle",- J.Phys. III France, Vol.3, 1993. pp.2133-2148. [7] S . M A L L A T , - " A Theory for Multiresolution Signal Decomposition; The Wavelet Representation",-IEEE Transaction on Pattern

Analysis and Machine Intelligence, Vol. 11, No.7, July 1989. pp.674-693. [8] M. BARRAT, O. LEPETIT.-"Calcul rapide de la transform6e en ondelettes"-Traitement du Signal, Vol. 8, no. 1, Avril. 1990, pp. 43-49. [9] B. TORRESSANI-" Analyse Continue par Ondelettes"-Ed. SAVOIRS ACTUELS, InterEdition/CNRS Editions, 1995, pp 26-28. [10] C. GASQUET, P.WITOMSKI.-"Analyse de Fourier et Applications. Filtrage,Calcul num6rique Ondelettes"-Ed. MASSON, 1990. [11] I. DAUBECHIES.-" The Wavelet Transform, Time-Frequency Localization and Signal Analysis".-IEEE Transaction on Information Theory, Vol.36, No.5, September 1990. pp.9611005. [12] H-S. NICOLAJ, V.W. MILADEN-"Wavelets and Time-Frequency Analysis"- Proceeding of The IEEE, Vol. 84, No. 4, April 1996,pp. 523579. [13] J.F. MUZZY, E. BARCY, A. ARENO. "Wavelets and Multifractals for Singular Signal : Application to Turbulence Data" - Physical Review Letters, Vol. 67, No. 25, 16 December 1991, pp. 3515-3519. [14] M. FARGE, N. KEVLAHAN, V. PERRIER, E. GOIRAND-" Wavelets and Turbulence"Proceedings of the IEEE- Vol. 84, No. 4, April 1996. pp.639-669. [15] S. MALLAT , L. H. WEN -" Singularity Detection and Processing with Wavelets"- IEEE Transactions on Information Theory- Vol. 38, No. 2,March 1992. pp.617-642. [ 16] W. WANG, G. JIN, Y. YAN, M. WU-" Image feature extraction with the Optical Haar wavelets transforms"-Optical Engineering- Vol. 34, No. 4,Avril 1995, pp. 1238-1242. [17] B. TORRESSANI-" Analyse continue par ondelettes"-Ed. SAVOIRS ACTUELS,InterEdition/CNRS Editions, 1995, pp. 26-28. [ 18] Y.THOMAS, -"Signaux et syst6mes lin6aires", Ed. MASSON [19] V.Martin, K.JELENA -" WAVELETS and SUBBAND CODING"-Ed. Prentice Hall, Englewood Cliffs, New Jersey- 1995. [20] C.K.CHE,-"An introduction to Wavelets"Edition. Academic Presse, INC [21] M.VETTERIE, -"Wavelets and filter banks: Theory and Design", IEEE Transaction on Signal Processing. Vol.40,No.9, Septembre 1992

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391

SCLEROTOPOMETRIC MEASUREMENTS ASSISTED BY STATISTICAL METHODOLOGY FOR BETTER UNDERSTANDING OF ABRASION B. B O U A L I * * ; V. J A R D R E T , H. Z A H O U A N I , P. L A N T E R I * * , B. L A M Y * , T.G. MATHIA, Laboratoire de Tribologie et Dynamique des Syst6mes U M R 5513 double site" Ecole Centrale de Lyon & Ecole Nationale d'Ing6nieurs de St. Etienne - Institut Europ6en de Tribologie *Laboratoire M6canique et M a t 6 r i a u x - Ecole Centrale de Nantes **Laboratoire de Chimiom6trie Universit6 Claude B e r n a r d - Ecole Chimie physique Electronique Lyon ABSTRACT Studying different aspects of the abrasion phenomena since more than quarter of the century, the authors will try to demonstrate through illustrative examples that the abrasion as seen both from, a purely physical as well as from a chemical point of view, is very complex irreversible process. This process concerns surface layers not only as negative aspect of the abrasion (such as wear) but also in numerous machining technologies (honing, lapping, grinding, polishing, etc...) as positive aspect. The optimisation of the manufacturing processes and the characterisation of wear of new formulated materials requires the design of the new experimental tools and new research approaches for correctly mastered wear's and the processes kinetics estimation and if possible their prediction. The abrasion process treated in that context requires the introduction of totally modern approaches. The authors experimented and developed during the years new strategies for the optimisation of manufacturing processes as well as of materials properties based on the use of a toposclerometers assisted by experimental design and specific data treatments. The Toposclerometers, which combines instnunental "scratch test" and morphological analysis of removed and displaced material during abrasion, offers the possibility to quantify the corresponding energy. This specific energy of abrasion, as a rheological surface parameter measured on different (heterogeneous, homogeneous) materials and the influence of the environments conditions will be examined in order to optimise engineering materials and manufacturing processes.

1. Introduction 1.1. Technological and scientific context Functional surface properties take a great place in the global performance of most of industrial device. Also we can consider that any technological surface is the result of particular distributions of various scratches, and that the surface morphological properties are determined by the severity and the distribution of the generating scratches. Rheological properties through, residual stresses, hardening, etc.., as well as physical and chemical adsorption of different molecules on different areas contribute to the final definition of surfaces. Therefore, in order

to create specific functions for selected surfaces numerous surface generation techniques appeared this last centre3,. The level of concerned functions in terms of dimensions will involve different rheological, topographical, physicochemical methods of surface characterisations. Even with the recent gain of nano-scratch techniques, the surface characterisation are still very seldom. That on of the reasons of sclerotopometer development corresponding for industrial requirements to improvement the understanding of fundamentals phenomena of abrasive wear and abrasive machining processes.

392

Then surface morphological state is generated by the combination of the elementary abrasive grooves[l].

. . . .

Figure 1 • 3D morphology of polishing oriented scratches In order to understand and predict how surfaces are generated and how they can be worn, the use of a specific device that can create very precise scratches in particular conditions, modelling wide range of industrial surface finishing techniques, assisted by supplementary device giving complete morphological data is necessary. The simultaneous knowledge of rheological properties of materials such as scratch hardness (I-Is) and scratch toughness ( K ) which are respectively intended to measure the resistance to plastic deformation and to fracture seems to be very useful to forecast the abrasive wear as well, to optimise manufacturing abrasive process. Many works on abrasive wear consider that static hardness of a material is the most important parameter determining its abrasion resistance. This assumption is not clearly verified for all dynamic abrasive conditions. In two or three body abrasive wear two modes can be distinguished. "Cutting" is the first one with removed material, and ploughing is the second with no loss of materials but essentially elastoplastic deformation with two or one lateral pilled up pads. The complete understanding of transition from the ploughing to cutting in abrasive wear is of a great help for abrasive process optimisation. From the scientific and technological points of view, the tendency for a surface either ductile or brittle to be deformed by an asperity, a protuberance or a harder particle is very important to understand the phenomenon relative to the wear, friction and adhesion [ 1, 2, 3a, 3b, 3c, 3d, 3e].

It seems necessary to come to a standardisation to evaluate the importance of the parameters concerning the abrasion processes which are known either for their benefical aspects (in manufacturing, gluing, coating, etc...) or for their damaging aspects such as wear. At the origin of the project to built a fully computerised sclero- topo-meter there are two types of motivation which concern: • scientific and technologic aspect, • and economical aspect. The characterisation of new complex materials which, are often heterogeneous and sometimes anisotropic, require the simultaneous measurement of several parameters so that the criteria of abrasion characteristics such as: static and dynamic hardness, toughness. They further allow the determination the brittle index Kc/Hs as well as of the different wear rates.

1.2. Sclerometic characterizations.

approaches

in

material

The German mineralogist Friedrich Mobs developed a scale of hardness in order to assign a definite figure to the values he obtained in determining mineral hardness. Observing the comparative ease or difficulty with which one mineral is scratched by another, he introduced the first scratch-hardness method. The first sclerometer enabling the accurate determination of the scratch-hardness is due to Jagger (4) in 1897. In one of its model, the sample is mounted on a small carriage moving along a track. Upon this is a lever with loaded diamond point which is in contact with the surface to be tested. Weight are then added to a plateau connected via a pulley with the carriage until they are just sufficient to move the carriage and produce a scratch on the sample. In Jagger's sclerometer, scratch hardness is ascertained with any one of the four following variables " r a t e , weight, depth, or duration. Jagger has determined the absolute hardness of some of the minerals in Mobs scale, assuming a value of 1000 for corundum having 9 on Mohs scale and 3300 Vickers hardness number (VHN) to gypsum with value of 0.04 characterized by Mohs with 2 and by 110 with VHN for minerals selected by Molls for his standard of hardness.

393

To simulate the material removal during a scratch test many mechanisms were proposed since the first initiative of Jagger until the recent complete review of scratch test studies performed outside the SEM or in situ SEM by T.H. KOSEL [51. Different sclerometrical approaches have been proposed concerning as well the abrasion of metals especially for manufacturing abrasive process (T.O. MULHEARN and L.E. SAMUEL [6]) as the transition fi'om ductile abrasion to brittle abrasion on brittle materials by pendulum or linear scratch tester(T. G. MATHIA and B. LAMY [31). With the apparition of industrial thin surface coatings it was necessary to develop some specific tests to assess at quick failure mechanism diagnosis by mean of a scratch testing device (J. VON STEBUT [7]).

All these studies and researches carried out by many searchers all over the world have principally a scientific character. Despite the industrial importance of abrasive and wear process the following questions remain still unanswered" 1- how much energy is required to abrade a material? 2- what determines the ductile or brittle abrasion? 3- what governs the "rough" or "smooth" aspect of an abraded material? 4- what is the influence of an anisotropy, heterogeneous or amorphous structure? 5- why do some materials abrade easily while others do not?

1.2. Objectives of a fully computerised selerometer.

The obtainable data from current techniques concerning the characterisation of materials and superficial coatings are not relevant, must be hardly interpreted and consequently cannot be exploited directly, since the abrasive wear is the result of a dynamic phenomenon.

The deformation of a surface induced by a slerometric indentor [6] depends on several parameters such as: • the type of materials, • the shape and the size of the penetrators (axisymetrical :Rockwell, oriented: Vickers, Berkovicks, spherical of various radius of curvature, ); • the force applied on the penetrators, • the trajectories and the speeds, • the environment, • the interface protuberances/surfaces, etc... Because of the multiplicity and the interdependence of the parameters [7] which involved during an abrasive process and in order to make the method easy of handle and universal, it is essential that the operating conditions should be defmed in such a way that they meet the needs of the both scientific and the industrial. The statistical approach through experimental design and principal compound analysis are very helpful and efficient techniques. 2. Experiments and materials 2.1. Instrumental device

The scratch tester is able to perform either constant or variable depth scratches on planar samples. The motion of the indenter is imposed by a continuous current motor in order to obtain a smooth motion along the scratch and avoid the vibrations generally associated with stepping motors. The sample surface is oriented parallel to the indenter motion with the aid of a specific and automatic controlled procedure. The computer then performs the necessary calculations and indicates to the operator how to set the sample holder device before the scratch is performed. The penetration depth is imposed by a Zdisplacement table. The displacement step is of 0.1~tm. The actual penetration of the indenter beneath the surface depends on the machine stiffness and the applied force. The machine stiffness has been carefully calibrated for a wide range of loads, in order to accurately determine the actual penetration depth of the indenter. For the range 0-15 N the machine stiffness in the

394

direction normal to the sample surface is constant and equal to 1.1 N/Ftm. The normal force (Is), tangential force (FT in the scratch direction) and lateral force (FL) are simultaneously recorded by a three dimensional piezo-electric transducer located underneath the sample. The three dimensional scratch morphology was assessed using a conventional 3D SURFASCAN topometer from Somicronic, to quantify the wear parameters of the scratch as explained below. Toposurf 3D, a commercial software package for the treatment of surface morphological images, has been successfully used to estimate the wear scratch parameters (figure2). .....i:~!~i:~.~ ~

ii iii!!iiiiii

Table 2 Some typical parameters of abrasion assessable by Sclero-topometric investil~ations Parameter Relationship Linear abrasion rate Kl=h~ Material removal rate Xv--[At - (B 1+B2)I/At

..~.,:~il.i ~i::;i:~~!!~i)~

I#.IB

iiii: ~

direction of solicitation during their final applications. To understand how these interactions occur, a direct relationship between surface generating processes, their topographies and their applications, must be elaborated. Using 3D tactile profilometer, the ratio of removed material to the displaced volume can be considered. Different criteria of abrasion can be evaluated. The variation of the removed or displaced matter with speed and spatial-temporal gradient of efforts; normal tangential and lateral efforts acting on the penetrator, are characteristic parameters of abrasion. Referring to experimental and theoretical data concerning abrasive processes we are inclined to think that they are a considerable help in characterising some significant parameters, but also they can be very useful to prediction the final topographical parameters which characterising the surfaces issued from such abrasive process.

~ ~,

""i'i~il.

Kv--dv/L Figure 2 : The scratch morphology on alumina assessed by coupled conventional 3D tactile topometer

Volumetric abrasion rate

Weight abrasion rate Table 1 Specifications and explored ranges of the controlled parameters of the scratch tests. Parameter Scratch speed Load Penetration depth

Unit Ftm/s mN ~tm

Range 50 - 20000 1 - 5000 0.1 - 100

Resolution 1 0.1 0.01

2.2. Abrasion parameters

The metrological structure is composed in such manner that it can simultaneously assess a scratch morphology and the scratch arrangement. Most of the wear processes generate oriented anisotropic surfaces which interact with the principal directions of their microstructures and the

- At'(B 1+BE) =xvAt Kp=dG/L=dK v

Abrasion coefficient

Kc---dv/LT=Kv/T A=dv/LN=I~K¢

Specific abrasion energy

Es--TL/LAt=T/At

Energetic abrasion rate

where: L = Length of scratch h = Depth of scratch G = Weight of scratched volume At = Section of material removed and/or displaced B1, B2 = Sections of the 2 flanges of plastically displaced material v = Volume of removed material ~v = Material removal rate N = Normal scratch force T = Tangential scratch force Ft = friction coefficient T/N d = Material density

395

3. Results 3.1. Case of heterogeneous materials (refractor concrete)- Experimental research methodology in abrasion study A common goal of many types of experimentations is to establish the relationship between the response of the tribo-system to a given set of parameters of interest to the tribologist; to understand and to improve the system with which he is working. This is achieved by constructing a model that describes the response over the applicable ranges of the parameter of interest. In many applications the fired model is referred as a response surface because the response can be plotted as a curve in one dimension or a surface in two or more dimensions, respectively as a function of one, two or more parameters. The response surface of the process can be explored to determine important characteristics such as optimum operating conditions.

3.1.1. Experimental design strategy The methodology of the experimentation, i.e. the way the experimental points are chosen in the space of independent variables is called "experimental design". The establishment of the "experimental design" becomes possible only after a model of the phenomenon under study has been postulated. The experiment must be preceded by the model, for example the formalisation of the problem of experimental testing and or the formulation of a material for particular needs. On the one hand optimality criteria are chosen a priori; on the other hand, the model of the phenomenon under study is also chosen a priori, which enables us to relate the concepts of optimum behaviour to the real problem. KIEFER [8] clearly demonstrated that the motivation underlying the theory of optimum design is that experiments should be designed in order to achieve the most statistical inference possible. Essential contribution to the theory has been made by the elaboration of a specific algorithm providing the numerical method for constructing

optimum designs. This by minimising functional of covariance matrices parameters using a design region with a finite number of possible design points, rather than a continuous region with infinite number of many points as pointed out by FEDOROV [9]. The primary reason for limiting the algorithm to finite design spaces is to simplify the task of selecting which point has to be added to an existing design. The contribution of each candidate point can be computed and the best point is then selected. The use of a finite design region is justified even when some of the factors are continuous, quantitative variables because of the limited ability of a given experimenter to exactly fix the levels of quantitative factors. If however, there are many possible settings for each quantitative factor, so that the number of design points, although finite, is quite large, a more efficient strategy may be to consider the design region as if it were continuous. In order to choose the new design point from a continuous region, a functional optimisation algorithm must be implemented and the success of the design algorithm will depend, at least in part, on the ability of the optimisation algorithm to find the best point to add at each iteration. Response surface methodology was developed by BOX [10] and his colleagues to explore relationships such as those between the yield of a chemical process and the pertinent process variables. In its usual form, response surface methodology exploits simple empirical model such as low-degree polynomials to approximate the relationship between a the output variable and a set of input variables over a current region of interest. A key intellectual insight into the development of response surface methodology was the realisation that in chemistry, engineering, and physics, experimental data are often available for analysis much more rapidly than in material science application for tribology. Thus, an efficient way to organise experimental programs in tribology in relation to material formulation and treatment is to adopt a sequential strategy in which the experiment proceeds by stages; selecting significant factors, happens at the beginning of an investigation, settling the effects of known input variables, determining a local approximation of the true response by a polynomial function, with each stage designed i_n the light of results obtained from earlier runs.

396

An experimental design is the protocol to vary all the factors simultaneously, in such a way that from a series of experimental runs, it enables to extract the maximum amount of information with in the presence of "noise". In general, with experimental design, only a small number of experimental runs are needed. Response surface methodology developed by BOX [5] encompass a group of statistical techniques for empirical model building and model exploitation. By careful experimental design and analysis it seeks to relate a response or output variable (y) to the levels of a number of predictors or input variables (Xi) that influence it. Example for 3 variables" y= bo + blxl + b2x2 + b3x3 + bl2XlX2 + bl3xlx3 + b23x2x3 + bllXl 2 + b22x22 + b33x32 (1) coefficients "b" measure the influence of the variables" bixi is a linear term and coefficient bi measures the main effect of variable xi. bij.xixj is a cross-product term and coefficient bij measures the interaction between the variable xi and the variable xj. ba.x~~-is a quadratic term to take curvatures of the response surface into account.

The penetrator used for the tests carried out is a Rockwell C penetrator. However the main difficulties of the test lies in the estimation of the area of the different sections At and T which are not constant during a scratch and are evaluated in different manners depending on the nature of the material and the experimental conditions. This is principally due to: elastic recovering of the materials and brittle fracturation. To calculate the specific abrasion energy Es the loss material volume is derived from 3Dtopographical analysis of the surface aider tests in relation to tangential force recorded T. Expecting only one extreme depending on one variable: speed or depth of penetration one can employ a second degree polynomial model to represent the response in the neighbourhood of technological domains of interest. The minimum location will signify the region of weakness, and the maximum location will indicate the region of highest resistance. In the case of the description of the relationship between the studied sclerometric responses Es (noted Y ) = f(E~0, h, v) and the experimental variables chosen (coded variables noted Xi are used) i.e." _

Y(XI,X2)= ao+ al X1 + azXz + alz XlXz + all X1z +

a22X22.

(2)

3.1.2. Discussions.

The first part of this paper describes some results concerning two families of castables consisting of the same high purity aggregate heat treated at two temperatures (400C ° and 800C °) and of a pure matrix. The aggregate is a pure synthetic polycrystalline material; tabular sintered alumina. In the case of refractors concrete abrasion, it is always useful to estimate characteristics such as: the linear abrasion rate, the material removal rate, the volumetrical abrasion rate, the weight abrasion rate the energetical abrasion rate, the abrasion coefficient and probably most important, the specific abrasion energy. E~= T/At This energy expressed in stress unit determines the energy required to remove elementary volume of abraded material. Expressed in pressure units it can postulated dynamic hardness significant.

With measured values of a~j coefficients of this model it is possible to calculate a Y response surface of the phenomenon. The range of speeds v and depth of penetrations h interesting of practical interest are respectively: 0.2 mm/s >[8], with a sufficiently low activation energy. Before this process takes place in the ZDDP/CB combination, there is a response of the additives like ZDDP alone, whereas after a couple of minutes, the combination gives a lower friction coefficient, similar to CB, because of bond switching in the P-O-B structure. 0.12

O O II II o~P "o~P~,~)O

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

.~ .................

0.10

/

0.08 0., B / O ~ B / O ~ I I 0 0

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

?

--

ZDDP/CB

f

CB O.O6

O O II II O~?~P" O , B/oIP ~'~O.,B.~O I O

ZDDP~

O

Figure 5: typical structures of a) a phosphate, b) a borate and c) a borophosphate glasses (with only BO3 units).

When quantifying the various atomic ratios, phosphorous and boron are found in equal quantity. The borophosphate chain is then assumed to be composed of PO4 and BO3 units linked together through P-O-B chemical bondings, see Figure 5. Only agreement with experimental data is found with a borophosphate of general chemical formula: Ca4Zn3P4B4021. This gives the following ratios: P/B= 1 (experimental value: 1), P/Ca= 1 (experimental value: 1), B/O=0.19 (experimental value 0.12) and Zn/O=0.10 (experimental value

0.14). The formation of a borophosphate glass resulting from the combination of ZDDP and CB under friction could give a good explanation for the

0.04 0.02 0

-.

0

3

I

6

9 Time (min)

.

,

12

15

Figure 6: friction curves for ZDDP, CB and ZDDP/CB. When comparing the three friction curves, it seems that phosphate is first formed in presence of the mixture, then borophosphate appears as the number of cycles increases. Fiction is zero at time zero is an artefact due to the collection system.

The glass transition temperature Tg of borophosphate glasses is not elevated, about 200 ~C [ ]. The possibility of a viscous flow of the molten glass tribofilm [9] in the friction microjunctions can now be envisaged (EHD lubrication by molten glass) in order to explain the anti-wear action of these additives. More work is necessary to verify this assumption, particularly EHD calculations.

438

Conclusion Tribochemical interactions between Zinc Dithiophosphate (ZDDP) and micellar Calcium Borate (CB) in boundary lubrication were investigated by analysing collected wear debris by TEM/EELS. Main conclusions are as follows : 1- CB and ZDDP produce long chain oxide glasses as antiwear tribofilm. The composition of the glasses has been carefully studied by coupling EDX and EELS in the TEM. In the ZDDP case, a zinc polyphosphate is formed with the formula Znl2 P10 O31 whereas a calcium borate Ca9(B7015)2 is obtained in presence of CB alone. The antiwear mechanism of the additives is non sacrificial because practically no iron is detected in the wear debris. The friction coefficient in the steady-state conditions is 0.12 for ZDDP and 0.09 for CB. 2- The combination ZDDP/CB produces a calcium and zinc borophosphate glass tribofilm which could correspond to the chemical formula Ca4Zn3PnB4021 There is evidence for P-O-B bonding in this glass, indicating an atomic scale mixing of the two additives in the tribo contact. No iron is visible in the tribofilm composition. 3- Considering the evolution of friction in the different cases, it seems that ZDDP is first acting in presence of the mixture, then CB becomes active after a few minutes and finally the steady-state behaviour is obtained in presence of borophosphate. 4- It is anticipated that under shear the glasses behave as liquid-like species because the Tg of borophosphates is known to be very low, around 200 °C. A mechanism of viscous flow of the molten glass could explain the protective action in terms of hydrodynamic (or EHD) lubrication by tribochemical products. More work is necessary to verify this assumption.

Acknowledgements. The authors would like to thank the Consortium Lyonnais de Microscopie Electronique (CLYME, INSA-ECL-CNRS) for access to the FEG microscope. References

1 D. Faure et al, Proceedings of the JTC Int. Conf., Nagoya, Japon, (1990) 1043. [5] V. Normand, J.M. Martin and K. Inoue, Trib. Letters, accepted. 2 J.L. Mansot, M. Hallouis, J.M. Martin, Colloids and Surfaces A, 75, (1993) 25. 3K. Inoue, Lub. Eng., 49 4, (1993)263. 4 J.M. Martin, J.L. Lavergne, B. Vacher and K. Inoue, Microsc. Microanal. Microstruct.,6,(1995) 53. 5V. Normand, J.M. Martin L. Ponsonnet and K. Inoue, Trib. Letters, 5 (1998), pp. 235-42. 6 W. Vogel, , Glass chemistry >>, Springer-Verlag (1985), p. 159. 7 R.J. Kirkpatrick, R.K. Brow, Solid State Nuclear magnetic Resonance 5 (1995), pp. 9-21. 8 N.H. Ray, - Inorganic Polymers >>, Academic Press, London (1978), pp. 79-90. 9 0 . L . Warren, J.F. Graham, P.R. Norton, J.E. Houston, T.A.Michalske, Tribology Letters 4 (1998), pp. 189-98.

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

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The wear b e h a v i o r of a thin MoS 2 coating, as studied by triboscopic m e a s u r e m e n t s in friction and electrical contact resistance

M. Belin Laboratoire de Tribologie et Dynamique des Systbmes, UMR 5513, l~cole Centrale de Lyon, B P 163 - 69 131 t~cully Cedex, France.

The wear resistance of thin M o S 2 layers has been extensively studied in the literature. The occurrence of material transfer, mechanical and tribochemical wear has been recently evidenced. Nevertheless, the high durability of this type of solid lubricant is still a matter of controversy. One explanation for this phenomenon is that friction and contact resistance are both controlled by material transfer processes. Then, the in vivo monitoring of the active interface, i. e. during sliding, is found as being a major technical issue. In this paper, we present some results concerning the monitoring of the interface by the means of electrical contact measurements in a reciprocating sphere on plane friction test. Thanks to spatially-resolved mechanical and electrical measurements, we give evidence for debris removal and recirculation through the contact. Based on a simplified model of interface, we correlate the evolution of interfacial thickness and remaining material, as analyzed by EDS. The dependence of the tribological behavior to environmental change is then probed. We precise some limits of this method in the case of moisture.

1•

INTRODUCTION

During the past decades, many papers have been promoting MoS2-type material for the low friction, long wear life and volatile condensible-free nature of these thin films for vacuum (aero-space) applications. The most often used sacrificial solid lubricants have lamellar structure. As shown in a recent review, Gardos [1] has highlighted the link between the atomic-molecular level information on these materials, and practical use of solid lubricants. The layered hexagonal transition metal dichalcogenides (LTMDs) such as MoS2 can be considered lubricating due to their anisotropic structure. Two major properties are here exhibited: low inter-planar attraction, leading to low shear stress cleavage planes, and then low shear stress of the complete film, high-strength intraplanar chemical bonding, leading to a good resistance to asperity penetration occuring in the sliding hertzian contact.

Therefore, different intrinsic physical properties are orientation-dependent in this kind of materials: thermal and electrical conductivity, elastic modulus, critical shear stress and thermal expansion [2]. It is also well known that M o S 2 films are highly environment-sensitive. In the practical case, lamellar lubricants are never in the form of infinitely large, single-crystal sheets. The grains of sputterredpolycrystalline films have a large variety of broken bonds, vacancies. Consequently, environment has a specific effect on these materials. From the technical point of view, high reliability is generally required in the aero-space applications. The behavior of this kind of materials have been widely studied in practical tribo-situations, roller bearings for example. Let us consider the complex assembly of a roller bearing, lubricated by M o S 2. As shown in various studies [3,4], the evolution of the frictional torque is found to remain low and quite stable during a great number of revolutions. Then sudden failure occurs, with a sharp unreversible increase in torque,

440

indicating that the MoS2 film failure occured. At this stage, we can consider that the lifetime of the assembly has been overpassed. No significant variation of the mechanical data is reported to be detectable before breakdown. In order to get more precision on the behavior of the assembly, different additional measurements can be performed. As an example, it is reported in [3] that the bearing outer race temperature and the electrical contact resistance have also been measured on the operating bearings under test. The authors evidenced some drastic variation in these data, synchronized with the mechanical failure. In addition, detection of the outgassing species can be performed, when tests are operated in vacuum. Thank to quadrupole mass spectroscopy, it is possible to follow the evolution of emitted gaseous products. Some specific emissions have been related to the transfer film formation. So, different techniques can be used to get some relevant information from the sliding interface. Some developments have been obtained on more simple situations, like a sliding single hertzian contact. The contact zone is here well defined, and observation of phenomena become easier. In this situation, extensive studies have been performed, concerning friction and wear behavior. It has been found that friction generally remains very stable over a long sliding distance, until a stage at which it increases drastically [3]. Some additional information is obtained by post mortem analysis of the contact [5]. Some in situ visualization has been performed, in order to follow optically the generation, flow and motion of wear debris in the case of thick coatings [6]. Another way to get realtime information in a sliding contact is the use of electrical contact resistance measurements through the operating contact. Some references deal with this subject, in the case of solid lubrication. For example, it is reported that Rc measurements has been used in large plane on plane-type sliding contacts, lubricated by MoS2 [7,8].

2.

A SIMPLIFIED MODEL INTERFACIAL FILM

FOR

THE

In the general case, the actual contact between two solids is achieved by a number of independent junctions (scheme a.). We propose a simplified description of the sliding interface, considering that both friction and electrical interactions are totally controlled by the process occurring at the contact spots.

scheme

a.

In the case of solid lubrication of mirror polished surfaces, thanks to optical observation of both conterfaces at the end of wear tests, we can confirm that the size of the wear scars is consistent with the hertzian zone. Only small agglomerates of debris in the front part of the contact can appear sometimes. We neglect this phenomenon. Therefore, the contact area both submitted to normal pressure, shear and electrical transport is assumed to be the same (scheme b.). Taking into account that a transfer film builds up during the running-in period, steady-state sliding is accomodated between the two counterfaces by interfilm sliding of MoS2-covered smooth surfaces.

£..,

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The goal of this paper is to improve interface monitoring, by means of electrical contact resistance measurements. We will apply this technique to a simplifed situation: a MoS2 lubed hertzian contact, sliding in a reciprocating cyclic motion, in different environments. We will show the capabilities of the method, and some of its intrinsic limits. scheme

b.

,:.,--_,-A.,,-. ;:',4,:..."_,z,L-:.,_,:,

",s

441

Then, we assume that the actual contact is achieved by a single junction, considering that the interfacial material as a thin block of bulk material, homogeneous both in thickness and in lateral size, at the scale of the macro-contact.

2.1.

Mechanical aspect

The actual surface to consider for shearing is assumed to be limited to the hertzian diameter, wich area is called A. If z is the average shear stress of the interface, the friction force F t can be written as: Ft = a . ~ (1) 2.2.

Electrical aspect

We consider that the electrical conduction through the sliding interface is achieved only by the contacting zone. Different asumptions are to be settled: - the zone to be considered is the actual contacting zone. This assumption is supported by optical observations. One restriction is the possible formation of debris accumulation in front the contact, tending to increase the actual contact area; - taking into account the low roughness of the wear scars, we consider that the real contact area is equal to the hertzian contact area A, -electrical resistance is due to the presence of the interfacial material in the contact. In a basic approach, the total electrical contact resistance R c can be written as the sum of two terms: Rc = R1 + R2 (2) Resistance R 1 is due to the ohmic conduction through the interface. If p f is the bulk conductivity of the interfacial film material, thickness t, then: R 1 = Pl " t / a (3) Resistance R 2 , due to the constriction of current lines in the material of the substrates. In the case of a single junction - diameter a, and with Ps the resistivity of the substrate, we can write: R 2 = Ps / 2 . a (4)

2.3.

Electrical

conductivity

Electrical conductivity in LTMDs is determined by their atomic structure, especially the constitutive elements and the type of bonds. This subject is widely described in literature [9,10]. (i) Composition dependence Among the different LTMDs, the nature of the chalcogen atoms causes a large variation of the

electrical properties. As an example, the conductivity is diminishing in the order of: MoTe2 > MoSe2 > MoS2 by roughly two orders of magnitude. Therefore, this point is beneficial for monitoring the presence of a MoS2 layer in a sliding interface, leading to significant values of contact resistance through the interface, even in the case of nanometric thickness layers. (ii)

Structure-dependence

Due to the lamellar structure, the PJ_c volume resistivity of semiconductor MoS2 is reported to be much higher than the PparrC value. As reported in [1 ], the volume resistivity for a single crystal of MoS2 is found to be 12 ~ . c m for P~c and 2.10 3 ~ . c m for PparrC" This effect is expected to be found in polycrystalline ion-beam grown M o S 2 films.

2.4.

Interface monitoring with R c a n d f Therefore, by following the evolution of both the friction force and the contact resistance, we can have some information concerning the evolution of the contact, the actual sheared material and its conducting properties. The friction coefficient is found to vary slightly during a test [10]. We can deduce that the actual area of contact does not vary drastically during the test. Particularly, according to the above section, and assuming that the term of ohmic electrical conduction is predominant on constriction resistance, the dependence of the electrical contact resistance R c is found to be linear with the mean thickness of the interface. Therefore, any change in the interfacial film thickness is expected to have an incidence on the R c value, during a friction test. Contact resistance is measured through a simple electronic apparatus, based on a current generator, by measuring the difference of potential, limited to respectively 1 mA and 1 mV at the contact pair. The dynamic range of measurement is from 0.1 ~ to 10 7 £"~, and the frequency bandwith larger than 100 kHz. The diameter of the hertzian zone is less that 100 gm, and the sliding speed of the order of 1 mm/s. Therefore, based on temporal consideration and according to the data sampling rate, we consider that the lateral resolution of the triboscopic images presented in this paper is close to 2 gm. However, actual spatial resolution is a convolution of the image resolution and the actual contact size.

442

3.

EXPERIMENTAL

life time, as tested in ambient air varies by less than 20 % (on 55 nm thick MoS2 layer).

3.1.

S a m p l e s and tribo-conditions To explore further wear and failure of MoS2, we use spatially-resolved friction f and electrical contact resistance Rc in vivo measurements, coupled with ex situ optical, surface analysis AES, Raman spectroscopy, and EDS [12]. We have performed some wear experiments in reciprocating configuration, on duplex layers of 45, 55 and 170 nm MoS 2, on 35 nm of TiN deposited by ionbeam assisted deposition onto a steel substrate [12]. Experiments have been performed at low speed, high contact pressure: Pmax = 1 Gpa, sphere diameter: 6.35 mm, reciprocating motion of 1 to 3 m m amplitude, in two environments: dry air (RH < 1%) and ambient air (RH = 40%, 60%). 3.2.

Orders of magnitude Let us consider the static contact between a sphere and plane substrate counterface, covered with a thin ion beam deposited MoS 2layer.

Physical data • sphere diameter bulk resistivity Ps • plane substrate bulk resistivity p., • solid l u b r i c a n t thickness bulk resistivity Pr • from [1] Calculations for : hertz diameter max. contact pressure R conduction R constriction Rt

52100 AISI steel 6.35 mm 10 -12 f~.m 52100 AISI steel 10 -12 g2.m sputteredMoS2 45 nm (55, 170) 20 ~2.m *

W = 4.0 N 88 ~tm 1.0 GPa # 40 f~ # 10 -~ ~2 # R conduction

As shown in the example above, we can neglect the constriction resistance compared to the ohmic conduction through the M o S 2 layer.

4.

RESULTS

AND

DISCUSSION

We present below some typical results, obtained on different layers. The repeatabiltiy of results is estimated by running 3 different tests on each layer. It is found that the friction level varies by less than 10% in all cases, the electrical contact resistance repeatability is better than 20%, and the

4.1.

Tests to failure As an example, a friction test is performed in humid air (RH = 60%), on a 55 nm thick MoS2 layer [12]. The motion is reciprocating, amplitude 1.0 mm, and the number of cycles is 2048. In the severe pressure conditions (Pmax = 1.0 Gpa), the test is run to failure. The lifetime is found to be less than 1500 cycles (f < 0.2). During the first stage, the friction coefficient is stable, close to 0.15. We confirm the classical results for the behavior in humid air, i.e. a low life time and moderate friction coefficient (between 0.10 and 0.15). The spatial evolution of data in friction coefficient fix, N) and electrical contact resistance Rc(x, N) are presented as triboscopic images, according to a technique described previously [11]. We show the results obtained in a friction test, as described elsewhere, Fig. 1 from [12]. Briefly, in such conditions, we find: - that friction is very homogeneous and stable, until abrupt breakdown is reached, - conversely, Rc is found to fluctuate, showing some low Rc regions, appearing at a given position, at about cycle 700, and then healing when the test goes on. This type of feature has been attributed to local failure in the MoS 2 layer, recovering thanks to recirculation of debris in the contact.

4.2.

Tests stopped pior to failure Complementary results have been already presented, showing the link between friction, Rc and analytical data on the wear scars. Thanks to EDS analyses performed both on the ball and the plane wear scars, it has been possible to correlate with a good confidence, the value of the measured contact resistance and the actual active thickness of interfacial material, which was found to be the sum of the remaining thickness from the initial layer, added to the thickness of transfer on the counterface [12]. This results confirmed the assumptions related to the electrical model of ohmic conduction through the hertzian contact zone. In this case, the resistivity is found to be 75 ~.m. 4.3.

Environmental sensitivity The effect of moisture is here evidenced with friction tests on thin MoS2 duplex layers, 45 nm thick, as tested in ambient air (RH = 40%), dry air (RH < 1%) and in an environment with varying humidity.

443

(i) Fixed environment The results in friction are quite classical for this kind of environment. The steady-state friction is obtained after a few running-in cycles, during which the transfer film is formed [5]. The friction coefficient value is typically 0.10 in ambient air and 0.02 in dry air, Fig. 2,3. In addition, the durability of the layer is strongly affected by humidity: Catastrophic failure is occurring at N < 1500 cycles in the case where RH > 40%, see Fig. 2. The evolution of Rc in ambient air shows that before failure, Rc value softly increases from 2-5 ~ , up to 10, and back to a value close to 1 f~, Fig. 2. According to section 2.2, a variation by one order of magnitude can be attributed to the build-up of the transfer film, followed by a decrease by one order of magnitude of the active interfacial thickness. In dry air, the Rc value continuously increases by more than 3 orders of magnitude, starting froml ~2 and then reaching 2.103 ~. In this case, this increase can no longer be attributed to an increase of the active thickness by corresponding 3 orders of magnitude. Assuming that the actual contact area A remains constant, it can be attributed to a change in electrical resistivity of the sheared material. In term of bulk resistivity change, two explanations are then possible: tribochemical process and orientation effect. Changing atmosphere can lead to a change in the tribochemical products generated in the contact. According to [13], MoS 2 layers have been found very sensitive to the presence of oxygen, and MoOx products can have very different electrical behavior than MoS2. Nevertheless, only water vapor is different between the two cases under consideration. The hypothesis of a bulk change of composition leading to a change of resistivity is unlikely. From theoretical results, we know that resistivity of MoS2 crystals is orientation-sensitive. Anisotropic ohmic conduction has been reported to increase by 3 orders of magnitude, when the lines of current are perpendicular to the c-axis, compared to parallel direction (i.e. parallel to basal planes compared to perpendicular, see section 2.3.ii). Before friction, the film is fully basally-oriented [14], with the c-axis perpendicular to the surface sample. After friction, it has been evidenced that basal planes are present in the sliding direction, at least in the first atomic layers [16,17]. Therefore, the resistance increase is not likely due to a bulk change in orientation of the film.

(ii) Alternating environment In order to go further in the environment effect, a friction test is run in alternating environment, on a 170 nm thick MoS2 layer. Starting in dry air (RH < 1%), the steady-state behavior is rapidly reached (low friction, Rc increasing), Fig. 4.a,b. At cycle 270, ambient air (RH = 40%) is introduced in the gas chamber. The effect is immediate. In friction, we find that the value reaches 0.10, corresponding to the steady-state friction value in this kind of environment. Simultaneously, Rc is shown to decrease by a factor greater than 10, Fig. 4.b. Then, Rc is found to stay at a stable value, giving no evidence for a significant reduction in thickness over the second stage of the test. Spatially-resolved data maps are presented in Fig. 4.c. Both friction and resistance maps exhibit a very homogeneous value along the wear track. No significant contrast is to be observed, excepted at the environment change. In both atmospheres, data are spatially homogeneous along the track, and the transition is abrupt when changing environment. The images show that the behavior change both in friction and resistance, due to environment change, has a rapid kinetics, compared to the typical 10 -1 s time-scale of the triboscopic images. The assumption of a re-accomodation of the film transfer in its whole volume is then excluded. The environmental stability of LTMDs is inherent with the lamellar structure of their crystal structure. Point-defect-free basal planes are orders-of-magnitude less reactive than edge sites exposed to tribological action. It is reported in [15] that the edge sites of MoS2 are 10 ~1-times more reactive than a defect-free basal plane. These sites can react with environment, since the basal planes remain unchanged. According to theoretical reference [ 1], we attribute variation in electrical contact resistance at the environment change to a surface effect of moisture on the tribosurfaces, by water adsorption. This environment sensivity can be considered as a limitation of the technique of contact monitoring by electrical resistance measurements of the sliding contact. Nevertheless, as far as moisture is high in the tribo-environment, the linear dependence of the electrical resistance on the interfacial thickness can be considered. This work is still in progress, and additional information will be obtained by varying moisture quantity in the tribo-test environment.

444

5.

CONCLUSIONS

In this paper, we present some data concerning the study of the degradation of thin layers of MoS2 solid lubricants, deposited by IBAD on steel substrates. Thanks to experimental work in which friction and electrical contact resistance are both measured during friction, we draw the following conclusions: In the case of the 55 nm MoS2 layers, the electrical contact resistance is very sensitive to incipient failure. It has been shown that major fluctuation in Rc is to be observed, much prior to detectable variation in friction force. In that sense, it can be considered that Rc can provide an "early warning" for mechanical degradation. This result can be extended to practical use for condition based maintenance operation of solid lubricated systems. •

From the interpretation of triboscopic charts, we get evidence for mobility of wear debris, and their recirculation in the contact. We show that some locally severely worn zones on the sample, can recover in the following stage of the test. There is a kind of healing effect of the layer, due to the reservoir effect afforded by the debris surrounding the wear track.

REFERENCE 1

2

3

4

5

6

7 •

Electrical data helps us in monitoring the interface evolution. Settled on a simple ohmic description of electrical conduction, we can affect the variation in contact resistance as being related to variations of effective thickness of material under the contact. A fairly good agreement is found for the results obtained in ambient air. Conversely, in dry air, large variation in resistance is affected to variation in resistivity, much more than variation in thickness. Electrical resistivity is strongly dependent on the presence of moisture. Consequently, the simple dependance of resistance to thickness must be refined, and monitoring of thickness interface is limited to low moisture environments friction experiments.

6.

ACKNOWLEDGEMENTS

The author would like to thank Drs. I.L. Singer and K.J. Wahl, from Naval Research Laboratory, Washington DC, USA - for their help in a fruitful cooperation and precious discussions.

8

9

10

11

12

13

M. Gardos, in New Directions in Tribology, Proceedings of the Plenary and Invited Papers from the First World Tribology Congress, London, 8-12 Sept. 1997, Mechanical Engineering Publications, London, 1997, pp. 229-250. J.A. Wilson and A.D. Yoffe, "The transition metal dichalcogenides - discussion and interpretation of the observed optical, electrical and structural properties", Adavances in Physics, 18 (1969) pp. 193-335. M. Suzuki, M. Nishimura, "Tribological haracteristics of ball bearings lubricated with a sputtered MoS2 film in a vacuum under a high thrust load", Proc. 5th Europeean Space Mechan. Symposium, ESTEC, The Nederlands, 28-30 Oct. 1992. E.W. Roberts, "Ultra-low friction films of MoS2 for space applications", Thin Solid Films, 181 (1989)pp. 461-473. K.J. Wahl and I.S. Singer, "Quantification of a lubricant transfer process that enhances the sliding life of a MoS2 coating" Tribol. Lett. 1 (1995) pp. 59-66. S. Descartes, "Lubrification solide ~ partir d'un rev&ement de MoS2", Ph.D Thesis 97 ISAL 0097, Lyon (1997). C. Gao, L. Bredell, D. Kuhlmann-Wilsdorf and D. Makel, "Micromechanics of MoS2 lubrication" Wear, 1662-164 (1993), pp. 480491. D. Kuhlmann-Wilsdorf, "What role for contact spots and dislocations in friction and wear?", Wear 200 (1996) 8-29. P.D. Fleischauer, "Fundamental aspects of the electronic structure materials properties and lubrication performance of sputtered MoS2 films", Thin Solid Films, 134 (1987) pp. 309322. P.D. Fleischauer, J.R. Lince, P.A. Bertrand and R. Bauer, "Electronic structure and lubrication properties of MoS2: a qualitative molecular orbital approach", Langmuir 1989, 5, pp. 1009-1015. Belin M., "Triboscopy, a new quantitative tool for Microtribology", Wear, 168, 1-2 (1993) pp. 7-12. K.J. Wahl, Belin M. and I.L. Singer, "A triboscopic investigation of the wear and friction of MoS2 in a reciprocating sliding contact", Wear 214 (1998) pp. 212-220. I.L. Singer, Surf. & Coatings technol., 49 (1991) pp. 474.

445

14

15

16

L.E. Seizman, R.N. Bolster, I.L Singer, "Effect of temperature and ion-to-atom ratio on the orientation of IBAD MoS2 films", Surf. Coatings Technol., 46 (1991) pp. 207-216. M.N. Gardos, "The synergistic effect of graphite on the friction and wear of M o S 2 films in air", Tribol. Trans., 1987, 32, pp. 214-227. J.M. Martin, C. Donnet, Th. Le Mogne and Th. Epicier, "Superlubricity of molybdenum

17

disulfide", Phys. Rev. B 48, 14 (1993) pp. 10583-10586. J.L. Grosseau-Poussard, H. Garem and P. Moine, "High-resolution transmission electron microscopy study of quasi-Amorphous MOSx coatings", Surface and Coatings Technology, 78 (1996) pp.19-25.

446

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447

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Friction behavior of a 40 nm thick IBAD MoS21ayer, as tested in ambient air (RH = 40%). Evolution of the average values of the friction coefficient f(N) -left, and the electrical contact resistance Rc(N) -right, in ambient air (RH = 40%). The failure is observed at cycle 1260. The Rc value is found to decrease by a factor of 10. It is interpreted as a reduction of the active thickness of interfacial material.

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F i g. 3 Idem, in dry air (RH < 1%). As expected, the friction value is low, the lifetime is higher. In this case, the Rc value cannot be related to a variation in thickness of interfacial layer.

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F i g. 4 Behavior of a 170 nm thick M o S 2 layer, during an alternate atmosphere friction test: dry air (RH < 1% cycles 1-270), then ambient air (RH = 40%, cycle 271-512). a. Evolution of the average friction coefficient f(N) -left. Once the transfer film is established, we confirm that f value is very moisture-sensitive. b. Idem in electrical contact resistance Rc(N) -right. Notice that the Rc average value is abruptly divided by more than one order of magnitude. c. Composite triboscopic images, showing the spatial evolution f(x, N) and Rc(x, N). In both atmospheres, data are spatially homogeneous along the track. The transition is abrupt when changing environment, suggesting a surface effect due to water adsorption on the wear track.

S E S S I O N XII MOLECULAR MODELLING

Chairman •

Professor J. Klein

Paper XII (i)

Modelling Tribochemical Processes Using a Combined Molecular and Hydrodynamic

Approach Paper XII (ii)

A Molecular-Scale View on Rotary Lip Sealing Phenomena

Paper XII (iii)

Hybrid Molecular Dynamics and Continuum Mechanics Analysis of Thin Film Lubrication

Paper Xll (iv)

A Dynamic Model of the Transfer and Wear Processes Using Soap Bubble Rafts

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

451

Modeling tribochemical processes using a combined molecular and hydrodynamic approach Dor Ben-Amotz a * and Ilya Kudish b ~Purdue University, Department of Chemistry, West Lafayette, IN 47907-1393, USA bKettering University, Flint, MI 48504-4898, USA A recently developed molecular-hydrodynamic approach to modeling tribochemical processes is applied to the prediction of the effects of pressure and temperature on fluid phase dissociation and surface decomposition reactions. The theoretical approach combines molecular statistical thermodynamics and continuum viscoeleastic hydrodynamics. The systems modeled include the dissociation of C12 in the fluid phase, and the decomposition of Cl2 and diphenyldisulfide C6Hs-S-S-C6H5 to form an atomic coating on the metal surface. The lubricated contact is modeled to represent a steel cylinder lubricated with a paraffinic oil with a sliding velocity of 0.01 m/sec to 0.1 m/sec and a load between 0 N/m and 100 N/m. The results indicate that both pressure and temperature may significantly influence chemical reaction thermodynamics in a tribological contact.

1. I N T R O D U C T I O N Any realistic model of chemical processes occurring in lubricated tribological contact must at a minimum include not only the key molecular features of the chemical process of interest but also the significant local variations in pressure and temperature. Here we present new results obtained using a recently developed molecularhydrodynamic approach to modeling tribochemical processes [1]. In particular, we use asymptotic analytical and numerical elasto-hydrodynamic lubrication (EHL) [2-4] results to predict the temperature and pressure in a heavily loaded contact, and perturbed hard fluid (PHF) statistical mechanics [5-7] to model the breaking and reformation of chemical bonds in a tribological contact. In modeling the EHL tribo-contact the lubricant viscosity (and thermal conductivity etc.) is taken to be that of a paraffinic base stock. New results are presented for the effects of both temperature and pressure on the surface decomposition reaction thermodynamics of C12 and diphenlydisulfide (DPDS). These reveal a delicate balance of entropic and enthalpic contributions which often produce opposing temperature and pressure ef*This work was supported by the Office of Naval Research (N00014-95-1-0403).

fects. 2. E L A S T O H Y D R O D Y N A M I C CATION (EHL) MODEL

LUBRI-

The EHL parameters used to model a sliding cylindrical line are similar to those in a standard pin-on-V-block tribo-tester, such as that employed in several previous studies by Kotvis and Tysoe and coworkers at the University of Wisconsin-Milwaukee and Benz Oil [8,9]. In particular, the following cylinder contact and paraffinic lubricant parameters were used [10], pressure-viscosity coefficient Qp = 1.5x10 -8 1/Pa, temperature-viscosity coefficient, Q T - 0.0385 l / K , lubricant and surface inlet temperature To = 38 °C, viscosity at 1 Atm, p0 = 0.4 Pa s, lubricant thermal conductivity X0 = 0.14 W / ( m °C ), Youngs elastic modulus E = 2.12 x 1011 Pa, Poisson's ratio u - 0.3, cylinder radius R = 0.0032 m. The surface velocity of the cylinder is taken to be u - 0.01 m/s, and the load, L, on the line contact is varied from 0-200 N/ram. In a heavily loaded EHL contact the pressure distribution is very close to the Hertzian pressure. Thus the pressure at the contact center, PH , and the corresponding temperature increase in the center of the fluid, AT, may be calcu-

452

lated using the following analytical expressions, appropriate for a heavily loaded sliding contact at shear velocities high enough that the shear friction stress dominates the rolling friction stress [ 1 -

3]. PH

-

IEL rR

(1)

A T - ~TT In [cosh ( B ) ]

(2)

using the PHF model [4,6]. Briefly, The PHF model assumes that the standard Gibbs free energy change for a reaction may be expressed as the sum of the free energy change for the isolated reactants, AG i (in the absence of a lubricant and with no load), and the excess free energy change, AG ~. AG i does not depend on external pressure, and AG x depends primarily on pressure with very little temperature dependence. AG,.,,.,(P,T) = A G i ( T ) + A G * ( P , T )

1 / P o Q T u2 S - 2 sinh- ~/ ~ exp (QppH)

(3)

¥

Figure 1 shows the calculated temperature and pressure at the contact center plotted as a function of load at two sliding velocities. The higher sliding velocity is closer to that used in the pinon-V-block studies [8,9]. Note that the sliding velocity only effects the contact temperature, which approximately doubles when the velocity is increased by a factor of ten.

1.0

p

.... : _

_

• ---- T

fl{53

,, s

S S S

f:L" 0.5

40

20

..... I-lUlO ~

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f = 500 s'l

temperature [°C]

Figure 7. Viscosity/temperature-behaviour of the test fluids. 3.2 Test rig The test rig shown in figure 8 has been designed by Wollesen [6]. It is operated with a 80 mm test shaft which is arranged in horizontal orientation. Fluid is supplied by a circuit providing fluid t e m p e r a t u r e s from 20°C up to 100°C by electrical heating and water cooling. For the tests the fluid is fed on top of the shaft beneath the seal. Special features of the test rig allow frictional torque m e a s u r e m e n t s with the seal mounted in an air bearing and provide, too, capability of t e m p e r a t u r e m e a s u r e m e n t s within the sealing zone. The t e m p e r a t u r e is obtained from a very small thermocouple of 60 pm x 200 pm, thus fitting to the expected sealing zone width of a run-in seal of approximately 200 pm. The thermocouple is glued into the test shaft and after assembly polished together with it. So it fits in flush with the shaft surface with minimum influence on the sealing zone conditions and direct contact to the s e a l i n g fluid. For exact positioning of the thermocouple u n d e r n e a t h the sealing lip the shaft is axially movable on a precision guide way by an electrical actuator.

Figure 8. Test rig 3.3 Shaft and Seal The shaft is fabricated following seal industry recommendations (DIN 3760) out of hardened C45 steel. It is mounted with a dynamic eccentricity of less t h a n 50 pm. Surface orientation is verified. The test seals are of a commercially available type, specification: 80-100-10, material: fluor-elastomer (FKM). The seals have no secondary sealing lip. Four seals were used for the test. Their radial force characteristics were measured with a radiameter according to DIN 3761. The test results of the four seals were averaged arithmetically. 3.4 Test method The tests were as a standard performed at shaft speeds of 200/300/400/500/600/ 1000 min 1. Changes to this test program were only applied in case the supplied fluid could not compensate frictional heating of the fluid within the sealing zone and therefore the intended sealing zone t e m p e r a t u r e s could not be achieved. The sealing zone t e m p e r a t u r e was 100°C resp. 40°C (with fluid A) and was adjusted manually by variing the supplied fluid's temperature at every shaft speed. After a run-in period of 12 h at 1900 min 1 all seals were operated under the following test conditions:

463

Axial movement: The shaft is moved axially (back and forth) over a distance of 5 mm at an axial speed of 1 mm per minute while friction torque is recorded. Pumping: Fluid is supplied manually with syringe in one up to three portions of 0.025 ml to the air side of the seal. The pumping rate is computed by analysis of the friction torque signal (time of attenuation of torque), averaged over three measurements. Pumping rate measurements are made only at one axial position which is the same for all seals. Screening checks are made with reversed shaft speed to exclude the possibility that oriented structures on the shaft surface affect measurements. Every seal is used with both fluids after it is cleaned with ethane. The order of test fluid application is reversed for one seal to check the efficiency of the cleaning method. 4. RESULTS AND DISCUSSION 4.1 Axial movement of the shaft Both test fluids show a significant dependence of the friction torque signal from the axial position of the shaft. Figure 9 shows a representative curve which is qualitatively the same for both fluids. It can be obtained independently from the direction of shaft movement. Comparison of the surface roughness of the shaft with the operational level of torque shows the similarities of both curves. The surface roughness profile was recorded axially at three tracks, distributed around the circumference at a distance of 120 °. It has to be noted that the measured torque results from an integration of roughness effects around the circumference. Even though the roughness is less than two microns, frictional torque varies over a range of 60% for fluid B (at a min. torque level of 0,35 Nm). If fluid is supplied constantly to the air side of the seal during axial m o v e m e n t - more than it could be pumped by the seal - it always runs at the pumping level of friction and is independently of the axial position.

E .-.} ;~

r~ C ¢-

o

/torque

0

-1

0,6 1000 rpm

%,

E zO,5

/

\ vk./

J

operatic nal level

o 0,4 C °0~

.~ 0,3 I,,,.. 0,2

0

0,5 1 1,5 axial position [mm]

2

Figure 9. Torque dependance from the axial position on the shaft related to axial surface roughness (fluid B, 100°C, 1000 minl). The minimum of torque level during axial movement can reach pumping level as some curves show. And if pumping conditions occur without external fluid supply it means that the seal leaks. In fact seals reaching pumping level during axial movement do show a meniscus on the air side. So it has to be concluded that the shaft surface has a significant influence on the seal performance and even though it is manufactured according to seal maker recommendations, it may cause leakage. Moreover it is shown, that a seal is able to run at any torque level between a pumping level and a maximum level during operation. And pumping and operation at maximum level are tribological different states. Whereas in the pumping state there is no influence of the surface texture, the influence is present during normal operation at maximum torqe level.

464

4.2 Pumping By investigating the pumping behaviour the differences between the two test fluids become clearer. Regarding the max. level of torque at a sealing zone temperature of 100°C, it can be seen, that the lower viscosity of fluid A (figure 10) obviously leads to a lower friction torque signal over the whole range of shaft speed.

fluid B, it is less important than normal stress effects which provide better load carrying capacity of this fluid. Figure 11 shows what is observable during pumping. The fluids A40 and B pump on the same torque level and fluid A on a lower one. The pumping rate behaves similarly (figure 12). So fluid A40 and fluid B which run at higher viscosity show better pumping performance. 0,6

0,6

• ,~- • Fluid A (40°C)

o, 1.................................:::::::::::::::::::::::::::::::::::: ..................................... 0,5

E

Z

0,4

(1) :3 ~Q-

o

~ 1, ~

.............................................................. ~.,.~.........:;;:~::.:..,~i........................................................................................................ :!". i, l i ~

~I m i

0,3

.....~.::::~:~::.~.,.•

~ •

ll,,

!, t 4 p i i ........:~:~;:.,.... ....:.::~::~::.:...:::~:: ....... ......:.::::~::"~':.....

~:.,.;~.,.;:-.,.v:~:~:~:::~:::. ::~~:!!:::::' ~ ::::..............................................................................................................................................................

-

m ...............................................................................................................

0,1

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

E z

0,4

E o

0,3

.o

0,2

(D :3

m m t-

.

200

.

.

.

I

400

.

.

.

.

I

'

'

600

I

800

.

.

.

N-----

0,1

Fluid A (100°6)

'

................:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

..................................................................................... ii.;:i::i;i~:;;.:;;....~:.:..,:~:..........................................................................................

._

........... ;~ .........Fluid B (100°C) 0,0

Fluid A ( 1 0 0 ° 0 ) ............. • ............Fluid B (100°C)

0,0

.

'

'

200

1.000

'

'

I

At a shaft speed of 200 min -~ fluid A runs permanently on the pumping level, so that this speed could not be evaluated. Comparison of both fluids operating at the same value of viscosity can be achieved by cooling fluid A down to 40°C (in the following called fluid A40). Because of a relatively high frictional heating of fluid A, this low temperature condition could only be kept up to 600 min 1. In the comparable range A40 has a significantly higher friction torque signal than fluid B. It must be mentioned that we can expect differences in the sealing elastomer behaviour at such different temperatures. But as the elastomeric share of the total radial force is relatively small compared with the share of the garter spring this may not matter. Obviously fluid B provides lower friction in rotary lip sealing if it is compared at the same level of viscosity with fluid B. And even if a viscosity loss occurs in the non Newtonian

'

'

'

I

'

'

'

'

600

I

'

'

800

'

'

1.000

revolutions [min -1]

revolutions [min -1]

Figure 10. Maximum level of frictional torque over shaft speed (non-pumping mode).

'

400

Figure 11. Level of frictional torque during pumping. 1,6

1,4 1 .......I. "~'" e,ui~ A (4ooc) , ~ 1,2 -':I...............I ~

..................................................................... ~;; S'~!'~I

Fluid A (100°C)

............................................. ::;~i:j...f!!Z!:::............................

E

1,0 ----:1

•~

E

o,6 -~ ............................................................. ;:~;~;~; .................~ .:.~:.~..

~

0,4

-

-I ......... ~ ............Fluid B (100°C)

............. ~:"*~"

i

t ............................................................................. iii:ii:ilY;

iiiii iiiiiiiiiiiiiiiiiiii

0,2

0,0

. . . . 200

I 400

. . . .

i

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

. . . .

600

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

I 800

. . . . 1.000

revolutions [min "1]

Figure 12. Pumping rate. So the measurements might be interpreted in this way, that operation at max. level and at pumping level relate to two different friction modes. The friction level of a seal at nonpumping conditions can be lowered using fluid B, containing molecules of higher

465 weight, whereas during pumping viscosity effects prevail over normal stress effects. 5. CONCLUSIONS Shaft surface has an influence on friction torque that cannot be characterized by surface parameters which are nowadays considered to be important for sealing requirements. A tribologically meaningful surface description is needed in rotary lip sealing. Differences in molecular structure show noticeable differences in max. friction torque under n o r m a l - n o n - p u m p i n g operating conditions. An eventual viscosity decrease within the non Newtonian behaving fluid does not exceed a load carrying capacity improvement. The polymeric additive leads to a friction reduction. It may act more locally between single roughness peaks than globally like in a fluid film. During pumping friction torque and pumping rate are independent of shaft surface and strongly affected by fluid viscosity. Pumping and operation at max. level of friction are tribologically different modes.

-

-

-

R

E

F

E

R

E

N

C

E

S

1. E.T. Jagger, Rotary Shaft Seals: The Sealing Mechanism of Synthetic Rubber Seals Running at Atmospheric Pressure, Proc. Conf. Lubric. Wear, Paper 93, 1957, p. 597-616 2. M. Kammueller und H.K. Mueller, Physikalische Ursachen der Dichtwirkung vor Radial-Wellendichtringen, ATZ Automobiltechnische Zeitschrift 88, 1, 1986, p. 3945 3. H.K. Mueller, Concepts of Sealing Mechanism of Rubber Lip Type Rotary Shaft Seals, l l t h International Conference on Fluid Sealing, 8-10 April, Cannes, France, Paper K1, 1987, p. 698-709

4. H . J . v . Leeuwen and M.J.L. Stakenborg, Visco-Elastohydrodynamic (VEHD) Lubrication in Radial Lip Seals: Part 2 - Fluid Film Formation, Journal of Tribology, vol. 112, October, 1990, p. 584-592 5. R.F. Salant, Modelling Rotary Lip Seals, Wear, vol. 207, 1-2, 1997, p. 92-99, 6. V. Wollesen, Temperaturbestimmung in der Dichtzone von Radialwellendichtringen als Randbedingung for die Modellierung des Dichtvorganges, dissertation, Technical University of HamburgHarburg, Arbeitsbereich Konstruktionstechnik 2, 1993 7. L. Horve, The effect of operating parameters upon radial lip sealing performance, SAE Papers 841145, vol. 93, 1985, p. 181187 8. W. Hermann und H.-W. Seffler, Neue Erkenntnisse for den Abdichtmechanismus von Radial-Wellendichtringen, ATZ Automobiltechnische Zeitschrift 87, 9, 1985, p. 475-484 9. A. Gabelli and G. Poll, Formation of Lubricant Film in Rotary Sealing Contacts: : Part II - A New Measuring Principle for Lubricant Film Thickness, Journal of Tribology, vol. 114, April, 1992, p. 290-297 10.R.S. Lenk, Rheologie der Kunststoffe, Carl Hanser Verlag, Mtinchen, Deutschland, 1971 l l.A.O. Lebeck, Parallel Sliding Load Support in the Mixed Friction Regime. Part 2 : Evaluation of the Mechanisms, Journal of Tribology, vol. 109, January, 1987, p. 196205 12.S.J.R. Oliveira, V. Wollesen und M. Voetter, Schmierungs- und Dichtvorg~inge bei Radialwellendichtringen, Tribologie + Schmierungstechnik, 43. Jahrgang, 1/96, 1996, p.35-39 13.K. Kirschke, Documentation and information on rheology : Present state and development in its design and application, Rheologica A c t a , vol.12, 4, 1973, p.432434 14.H.A. Barnes, J.F. Hutton, K. Walters: An introduction to rheology, Elsevier, Amsterdam, 1989

466

15.W.-M. Kulicke (ed.): Das Fliessverhalten von Stoffen und Stoffgemischen, Huetig und Wepf, Basel, Heidelberg, New York, 1986 16.G. BShme: Stroemungsmechanik nichtnewtonscher Fluide, Teubner, Stuttgart, 1981

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

467

Hybrid Molecular Dynamics and Continuum Mechanics Analysis of Thin Film Lubrication Ting-Leung Sham and John Tichy

Department of Mechanical Engineering, Aeronautical Engineering and Mechanics Rensselaer Polytechnic Institute Troy NY 12180-3590 USA

Optimism exists in scientific circles that the mechanisms of friction and boundary lubrication, studied for centuries, can soon be understood and predicted by first principles. However, from the engineering point of view, practical predictive ability seems far away. Toward the eventual goal of applying MD analysis to practical tribological design, we continue our work on a hybrid molecular dynamics - continuum method. Similar approaches have been used in simulating dislocations and other defects in crystalline solids under nanoindenting. Our linkage to MD is established through a variable effective viscosity, which increases near the surfaces due to molecular forces. The classical line contact problem of a rigid cylinder and a sliding plane is addressed. Results are presented showing an increase in pressure due to the presence of nearby surfaces.

I. INTRODUCTION The present paper is a modest extension of an earlier work of ours on this topic [1]. First, we summarize briefly the background and analysis of the previous paper. The reader interested in more detail may consult this work. We devote some attention to new results obtained. Impressive strides have been made in the field of tribology through molecular dynamics (MD) simulations (e.g., [2]-[5]]). Furthermore, there have been many recent advances in experimentation from a pure science perspective -- performing meaningful tests on nanometer-scale films (e.g. [6]-[7]). The convergence of MD and experiment has led to optimism in scientific circles that the mechanisms of friction and boundary lubrication can soon be understood and predicted by first principles. From the engineering point of view, however, practical predictive ability seems far away.

Conditions of MD simulations are highly idealized and the method is computationally intensive. Continuum mechanics based methods are thought to be of little value in describing and predicting boundary lubrication, or lubrication of very thin (nanometer-scale) films. According to Reynolds' theory, only the viscosity of a Newtonian fluid is of importance in determining the behavior of a lubricated contact for a given geometry and kinematics. In boundary lubrication it is well known that many other factors are significant. Reasons cited for the inadequacy of continuum methods applied to boundary lubrication are (1) the problem is too complex, and (2) the film is too thin, such that the assumption that the material is a continuum is not valid. However, Chan and Horn [8] found that the drainage rate of a thin film of fluid between two crossed molecularly smooth mica cylinders is well predicted by the Newtonian Reynolds' equation down to about 30 nanometers. At thinner gaps, good correlation with experiment is

468

obtained by simply adding a fictitious rigid layer to the mica surfaces in the Reynolds' equation model. The apparent viscosity of the thin film can be many orders of magnitude greater than that of the bulk lubricant. An enhanced viscosity liquid regime, and a solid-like regime may exist. Toward the eventual goal of applying MD analysis to practical tribological design, we have discussed a hybrid finite element (FE) - molecular dynamics method [ 1]. We can't claim originality of the concept. Others, such as Tadmor et al. [10] have achieved spectacular results in simulating dislocations and other defects in crystalline solids. The hybrid linking for solids is obtained due to the fact that derivatives of the lattice strain energy density yield Piola Kirchoff stresses which can be used in FEA. Our proposed hybrid method for thin film tribological flows can be summarized sche-matically in Figures 1 and 2. Over most of the region across the surfaces, the gaps are larger than nanometer size (greater than, say, 20 molecules across) and the continuum approach is suitable. At micro-contacts when the film thickness is of molecular scale, simulation occurs in an equivalent MD channel. Elements are arranged across the gap. Linkage to MD is established through an effective viscosity, which increases by an order of magnitude near the surfaces due to molecular forces.

2. ANALYSIS Molecular Dynamics Simulations. Standard methods of MD simulation of liquids are used, as outlined in the text of Allen and Tildesley [ 10]. In the present analysis, described in [1] is similar to those of Thompson and Robbins [2], and Hu et al. [3], using spherical molecules. The force potential used is the standard empirical Lennard-Jones 12-6 potential function. The potential predicts repulsive force between molecules when separated by small distance, and attractive force for larger values. The interaction force tails off rapidly- when distance separating particles is three times the L-J spacing parameter, the force is 1% of the maximum.

surface 2 J micro-contact

surface 1

lubricant ~

~

2

continuum

,,

region

/

h(x) ~ 10 nm

vx

MD region ii

///

i

i ii

i

surface 1

-'~

ii

~ L ~ i txm

i

U

"

r

Figure 1 - Schematic of a microcontact. 0 0 0 0 00012100001]]0 OOOOO 0 O 0 0 [] 121 O [] • •

-._I • h • Ilk- .

• •

• (t) • • "-'~i

•

•

surface2 []

0

n 0 [] 0

0

\

=(z)

.

;/o:o:o" . . -"- .- - "

. ~ _ ~ fromFEM ooooooorOOOO o o ~ ooooooooooo ooooo x

surface 1

dement viscosity l~z =-dv/dz x

)from MI)

Vx(X~)

h(x) [

,

!

II . . . . . . .

"1

Figure 2 - Molecular dynamics and finite element analysis linkage. Two computation saving devices are used to take advantage of this. First, interaction forces are ignored when the separation distance is large. Second, a "neighbor fist" is used. The N molecules

469

are distributed over M cells. The purpose of the cells is to keep track of nearby molecules. When the forces are to be calculated on the ith molecule, only interactions with molecules in the cell where it resides and that cell's immediate neighbors are considered. Most of an MD program "smarts" have to do with these procedures. To keep the number of particles reasonably small, periodic boundary conditions are used. When a particle leaves the domain of interest on, say, the fight side, an image particle enters the picture on the left. In this way, a relatively small number of particles corresponds to a large domain. Parallel sheafing motion (Couette plus Poiseuille flow) is accomplished using a fictitious body force and imposed sheafing motion on each particle. However, sheafing adds energy to the system, which causes a temperature rise. There are many schemes for maintaining isothermal conditions -- we have used the so-called "extended system" method. The fluid exchanges heat with a fictitious reservoir of thermal inertia at the prescribed temperature through an additional degree of freedom, which represents a time transformation. The simulation begins by having particles distributed over a facecentered cubic lattice. The initial particle velocities are randomly selected such that the mean velocity in the three directions is zero, and the magnitudes are such that the temperature is that prescribed. Particle motions are calculated by standard predictor-corrector methods. At each time step, new values of the particle position and its time derivatives are calculated. Our present goal for the MD analysis approach is to find the influence of the nearby wall or surface on the effective viscosity in molecularly thin shearing flow. We assume the following form of the viscosity: I.t = laoklk2 ,

and curve-fit the MD results to these equations. The factors kl and k2 account for the increase in effective viscosity due to the presence of the lower and upper walls, respectively. The parameters ko, 6, and o govern: the amount of the increase, the molecular-scale thickness of the wall effect, and the sharpness of its decay, respectively. Figure 3 shows several types of behavior which could be exhibited by this empirical equation. Of course, many more sophisticated local hybrid MDFE schemes can be envisioned, such as direct calculation of velocity field across the gap for a given sliding speed and pressure gradient (or equivalent body force). 1

6II 0 •2. h tl.15 I =

, ~=

0.6

~

0.4

~

0.2

0

2

4

6

8

10

viscosityratio WI.t°

12

Figure 3 - Viscosity variation across the film, error function model of Eqs. (1)-(3).

Analysis. In the absence of body forces, the inertialess thin film continuity and momentum equations are, Finite Element

OVx bc

OVz . . . . 0, 0z

(4)

(1) -if-

k 1 - 1+ 7 ( 0 - 1) 1-

M-I=0.4, o/h=0.075 ....... ~']: ........ -1

(2)

erf 4"2c/hJJ'

(3) 4

o/h

'

'

Consider a thin domain which is L units in length with a variable height h(x), and reference height H. We normalize the above equations with •

x

L

•

z

h (x) '

h*

h

H'

•

~t

o'

470

•

Vx

Vx=~ U '

Vz

•

vz=

•

, p =

UH/L

(P-Pa)/-/2

(6)

~oUL

Invoking the chain rule of calculus, Eqs. (4) and (5) become,

where Vee are the nodal velocities for elementD~,. The pressure is represented through global shape functions as p

•

(,) ,

m

~Vx

Ox*

1 d h" ,OVx 1 ~ z h* -----wz dr ---+h*cOz* c3z* - 0 ,

h'2~l' I :0'

~"

)~Z*)"

(7)

(8)

v x* = l , v z* = O ;

Z*

(9)

q * = c o n s t = h * ~ *vxdz * .

(10)

We consider a velocity v x - pressure p* formulation of the problem (see Ref. [ 1]) for the implementation of a finite element method based on local/global shape functions. In contrast to many iterative schemes used in the lubrication literature, the present procedure is a direct method in determining the velocity and pressure Finite Element Numerical Procedure. Let the scaled domain be partitioned into rectangular finite

elements {f2~, e = 1,...,E}, where E is the number of elements. The velocity vx is approximated by a standard finite dement method via local shape functions Ne" (.)

x e V~,

•

unknown coefficients and the

Pm~ are global pressure shape functions. From the dimensional considerations of the lubrication problem, a special form for the global pressure shape functions is employed:

Pmn = ~

Integrating Eq. (7) using (9) gives the constant flow rate equation:

•

a~are

h*

h*

~ '

(13)

=1: v x* = O , v z* = O ;

x* : + 1/2" p * : 0

Vx = Z N g

where

n

The

The scaled domain is a unit square. boundary conditions are, z * =0:

(12)

- EEamnpmn x

x e ~neh,

(11)

where x~ is the end point of the film if rupture occurs. The use of a global function to approximate the pressure allows the gradient to be determined more accurately everywhere in the flow field. The global shape functions vanish at the two end points: x = - l / 2 a n d x = x r. Following standard finite element procedure, the shape functions (11)-(13) can be substituted into the integral formulation of the problem (not shown). After imposing the boundary conditions, we arrive at a set of algebraic equations for the nodal velocities and the coefficients. These equations can be decoupled to two sets of algebraic equations from which amn and the nodal velocities can be determined consecutively. The coefficient matrix of the set of algebraic equations for a ~ is in general rank-deficient. The singular value decomposition technique can be employed on this coefficient matrix in order to solve for a ~ . Accurate results were obtained using this procedure for a number of test cases in which exact solutions are known.

3. RESULTS Molecular Dynamics Simulations. In the results presented, we have used a FCC lattice o f N = 1372 molecules. The basic length scaling unit is the Lennard-Jones radius for argon (a nearly spherical

471

molecule) at the triple point T = 131.7 K, for which •LJ = 0.3405 nm. The initial spacing between molecules is 0.5797 nm. The L-J energy parameter e = 1.654 1021 N-m/mol, thus temp-erature T = 1.1 e/kB. At the wall, the L-J energy is ew = 3.5 e. The molecular density i ~ - 0.81/OLj3 ._ 2.052 1028 mol/m 3. The molecular weight of argon is 40 and the mass of a molecule equals 6.628 10 -23 g. The basic time scale x is = 2.155 10"12 s. Several simulations are shown in Figure 4 in the absence of the body force term. Note the flattening of the velocity profile at the near to the surfaces, indicating the increase of apparent viscosity. relative surface velocity

7 t,

........

I

',

i

t

[-~! partic,, velocit~ '~ , ~ 6 T ......... !.......... : ......... i i .,,."- ': . . . . . . .

3

....

3.5

2-*-....~-......-"..... i....?,...i.......... ::.............l .....+ -0.6

-0.4

-0.2 0 0.2 particle velocity v/U x

0.4

0.6

Figure 4 - MD simulations for simple shear flow. Finite

Element

Numerical

Results.

As

a

numerical example, for demonstrative purposes, we consider the flow field in a lubricating film of a plane-cylinder sliding line contact. The film thickness is given by

R

X*=_

~ I . . . . . . .

,7 '

///

H ~- U

Figure 5 - Schematic of cylindrr-plane contact. Parameter values used for the viscosity variation are ko = 10, 61H = 0.2 and 0.4, and o/h(x) = 0.15 and 0.075, from the MD curve-fit Eqs. (1)(3). Thus, the viscosity increases by a factor of ten in surface layers which may comprise 20% or 40% of film at the minimum position. For o/h(x) = O. 15, the high viscosity in the surface layer varies gradually toward the bulk value; for o/h(x) = 0.075 the change is more sudden. We use four-noded rectangular finite elements for the nodal velocities in the FE computations. The finite element grid consists of 20 elements in the zdirection and 150 in the x-direction. We use 5x5 or 25 terms for the unknown pressure coefficients. Figure 6 shows the pressure for the Newtonian case, and several cases in which viscosity increases at the surfaces. Correspondingly, Figures 7-9 depict the velocity profiles, at the inlet, center, and rupture point, respectively. The magnitude of the pressure curves is strongly sensitive to the variable viscosity effect - pressure is increased relative to the purely Newtonian case. However, the rupture point is only slightly affected. T

- xc,,l

!

II

, , o , ~ffI---0.2, oha=0.0751

h*

=

1+ 6 4 x .2 ,

•

g~

X

x = -------842

I ....

(14)

'

r~

...... i ............

0.4 0.3

where R is the effective cylinder radius and H is the minimum film thickness at the center, x = 0. For this nondimensionalization, the film begins at x = 4 ~/2RH

( x* - -1/2 ).

From

the

so-called

Reynolds boundary condition, suitable for this onedimensional contact, the film ends (ruptures) at some unknown x r > 0, where d p * / d x * - O.

0.2 0.1 0 -0.2

-0.15 -0.1 -0.05 0 dimensionless distance x *

0.05

Figure 6 - Pressure distribution for various cases.

472

x:

The velocity curves all indicate the effect of thickened layers at the two surfaces. At rupture, zero pressure gradient, most of the shearing takes place near the film mid-plane.

0.8

"•0.6

"""k~" i"'~,'-'i........i'1

O' 6/I-I-=0.2,¢r/h=O.075

CONCLUSIONS

.,.,,

0.4 0.2 o

0 -0.4

-0.2

0

0.2

0.4

0.6

0.8

1

.

velocity v x

Figure 7 - Inlet velocity profiles for various cases.

~ ~' N

0.8

M-I---0.2,~th=0.15 . o. NH=0.2, ~/h=O.075 -,~., 6/H=0.4, ~/h=0.075

0.6 °,,~

~

0.4

•

0

...... 0

t .... 0.2 0.4

0.6

0.8

1

velocity v x

Figure 8 - Velocity profiles at centerline (x = 0) for various cases.

0.8 b - k - ~ - . - ~ :~- ......... i.... t~ : N

I" ~ . ~ 0.6 t ~

: "~

: ~.:!

/ [

~+.2,o~+.~5

~-" 8/H---0.2, o/h=0.075 ~ : a/H--0.4, ~/h~.075

I

0.4 ~

0.2

A hybrid molecular dynamics-fixate element analysis procedure has been demonstrated which is suitable for molecularly thin film lubrication flows. Over most of the region across the surfaces, the gaps are larger than nanometer size (greater than, say, 20 molecules across) and the continuum FE approach is suitable. When the film thickness is of molecular scale, simulation occurs in an equivalent MD channel with elements being arranged adaptively across the gap. In our preliminary study, linkage to MD is established only through a variable effective viscosity, which increases near the surfaces due to molecular forces. Eventually more complex constitutive relations can define the linkage, or direct iterative simulation of the stresses. Our MD simulations show a flattening of the velocity profile at the near to the surfaces, indicating the increase of apparent viscosity. Our present goal for the MD analysis approach is to find the influence of the nearby wall or surface on the effective viscosity in molecularly thin shearing flow. We assume a form of the effective viscosity using the error function with parameters governing the magnitude of the viscosity increase, the molecularscale thickness of the wall effect, and the sharpness of its decay. The FE analysis assumes a unique global pressure shape function which allows direct solution of the pressure field. For demonstrative purposes we attack the one-dimensional cylinderplane contact and find significantly greater pressure than for the Newtonian case. We conclude that such hybrid methods may hold the key to any practical predictive ability for MD in engineering problems for the near future.

0 0

0.2

0.4

0.6

0.8

1

velocity v

REFERENCES

x

Figure 9 - Velocity profiles at film rupture point for various cases. •

1. 2.

T.-L. Sham and J.A. Tichy, Wear, 207 (1997) 100. P.A. Thompson and M. O. Robbins, Phys. Rev. A, 41 (1990) 6830.

473

3. 4. 5. 6.

7.

°

.

10.

Y.Z. Hu, H. Wang and Y. Guo, Proc. Int. Symp. Trib., Beijing, China (1993) 58. J.A. Harrison and D.W. Brenner, Jour. Am. Chem. Soc., 116 (1994), 10399. U. Landman, W.D. Luedtke, N.A. Burnham, and R.J. Colton, Science, 248 (1990) 454. A. Homola, J. Israelachvili, M. Gee, and P. McGuiggan, ASME Jour. Trib., 111 (1989) 675. M.L. Gee, P.M. McGuiggan, and J. Israelachvili, Jour. Chem. Phys., 93 (1990) 1895. D.Y.C. Chan and G. Horn, Jour. Chem. Phys., 83 (1985) 5311. E.B. Tadmore, M. Ortiz, and R. Phillips, Philos. Mag. A., 73 (1996) 1529. M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids, Oxford U. Press (1987).

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Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

475

A d y n a m i c m o d e l o f the transfer and w e a r p r o c e s s e s u s i n g s o a p b u b b l e rafts

K. Hiratsuka, Y. Abe and K. Fujisawa

Department of Precision Engineering, Chiba Institute of Technology 2-17-1, Tsudanuma, Narashino-shi, Chiba, 275-0016 JAPAN

The tensile and sliding behaviour at the contact junction have been modeled using soap bubble rafts, where the individual bubbles were regarded as atoms. Three types of styrene foams (spheres, large and small disks) were also floated among the group of bubbles. The bubbles with spheres showed higher tensile strength than the bubbles alone. In sliding test, the bubbles were picked up by the moving raft, when the spheres were arranged at the interface of the fixed raft. The increase in tensile strength and transfer is attributed to as the enhanced attractive force between bubbles due to the presence of spheres.

1. Introduction

Bubble raft technique has been used to model

When a pure metal slides against itself, the wear

the mechanical properties of metals such as the in-

mode is classified as adhesive wear, when no abra-

dentation[5] and shear behaviour[6,7]. However the

sives are present at the interface. In the conventional

transfer process associated with sliding has not been

theory of adhesive wear, it is accepted that the shear

modeled using this technique. In this paper, the au-

fracture occurs within the bulk of the softer material

thors demonstrate that the shear and transfer behaviour

leading to transfer and wear[1 ]. However from the

of bubbles are greatly modified by the presence of the

experiments by the authors[2] and others[3], it is

floating spheres and disks at the interface of the rafts

shown that the lower wear is observed for the rubbing

of bubbles. The correlation between the change in

of the self-mated pairs in vacuum. It means that the

the mechanical property and sliding behaviour of the

adhesive wear particles can hardly be produced with-

raft has been discussed.

out atmospheric gases. The author deduced that the shear strength of the interface is enhanced as com-

2. Experimental Procedure

pared to the bulk due to the interaction with the sur-

To get the bubbles of uniform size in a crystal-

rounding environment[4]. This results in the shear

line structure on the liquid surface, three kinds of liq-

fracture within the bulk material rather than the inter-

uids, oleic acid, triethanolamine and glycerine, were

face. This implies that the interaction of the surface

mixed and diluted by water[8]. By blowing the air

with environment is important for material transfer

through the fine nozzle, the bubbles of uniform diam-

and formation of the wear particles.

eter of 2.0mm were floated on water forming a hex-

476

agonal closed packed crystalline structure. These were enclosed by the plastic frame, in which one side was open, so as to maintain the structure. The tensile and sliding characteristics have been studied. The schematic of these two set-ups are shown in Fig.1 and 2, respectively.

Fixed Raft

Moving Raft

Three types of floats were set among bubbles of both moving and fixed rafts as described in Table 1. For tensile tests, the strain gauges were attached to

Fig. 1 Schematic of Tensile Test

the moving raft to measure the forces. In the sliding tests, the moving raft was set in two different orienta-

Slide w

0.2-

Moving Raft Z

E

:.'.'.'.'.'...'.'.'.'.'~ -.,....................:

o.~s-

:......................~ :......................~ .............

Fixed Raft

.i:i.i.[.[yi.i:i:].i:i :......................~ ...................,...~ .............

e-

::i:ii:iiiiiill . ...................... 0,1

(a) Parallel Type Moving Raft

............. :......................~

"

L_

*" V)

::::::::::::::::::::::::I

,::iii:'"'"'"'"'"'": =:.:.:.:.:.:.:.:.:.:.:.~ ,

..,,,.

Slide

"~

0 05

:::::::::::::::::::::::: : :.-.......-............: ..............

,:.:...................+

-:-::::.........:

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

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

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

::.::::::::::: :

tili!iiiiii!iiil ':':':':':':':':':':':'

I--"

+

+

iii+i+iiiii!i!i! ..........

0

°

1:13 v

m

.x

~

Fixed Raft

:i[ii[][iiii[i[iiiiiii[, .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..

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

'

O1

(/~

.-~

--~

(/1

(/)

i:5

i:5

..Q

--

~

:3 1:13

[:: ~ +

t~ _.J +

(/1 L_ e-

(./3

L_

(b) Inclined Type Moving Raft

¢'n

Fig.3 Comparison of the Tensile Strength

Fig.2 Schematic of Sliding Test

Table 1 Experimental Conditions Diameter of Nozzle, mm

0.12

Diameter of Bubble, mm

2.0

Sliding Velocity, mm/s

0.5

Depth of Indentation, mm

1 and 4

Float Types

" .............

Small Disk

Diameter ;3,5 mm,Thickness ;2.0mm

Large Disk

Diameter;6.0mm,Thickness;1.7mm

Sphere

Diameter;6.0mm

,

477

51iiii: !ii!.iill :~!iiiii!:~i ~~ill

i~/~ ii:~ii~ ~ i •

.. @

Movi~ 9

N'!c)v It?ell f{itft

F~xed

R~-~ft

(a) Sliding Distance=0mm

....

Raf~

ixed

Raft-.

(a) Sliding Distance=0mm !~:i,~!~:!~z~,~,~,~:,z~z,z~:................ ,~:~:~: ~ ~ ~ z ~ ~ J ~ : ~ 7 ~ : ~ : ~ ~ ~ : ~ ? ~ : ~

¸

~~ ii"

(b) Sliding Distance=31 mm

(b) Sliding Distance=42mm .... ~i~.-ii!~i!iililili!iliiili!!iiii;ii!iili~!!!;!~!!!!i!iiii~i~ .~

i!

~.................................

.

.....

.

.

.

.

.

.

.

.

.

.

.

.

.

.

•

(c) Sliding Distance= 105mm

(d) Sliding Distance=l 64mm

Fig.4 Consecutive Observation of the Sliding Process (With Spheres in Single Layer, Indentation Depth =1 mm, Parallel Type Moving Raft)

(c) Sliding Distance=101 mm

(d) Sliding Distance=149mm

Fig.5 Consecutive Observation of the Sliding Process (With Spheres in Single Layer, Indentation Depth =4mm, Parallel Type Moving Raft)

478

Fig.3 shows the tensile strength of the bubbles

tions as shown in Fig.2(a) and (b).

and the bubbles with floats listed in Table 1. It is shown that the bubbles have the lowest tensile strength,

3. Results 3-1. Tensile behaviour

Moving Raft Moving Raft !:~i~L..~.

~

Spheres

Spheres Fixed Raft

Fixed Raft

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

[

(a) Sliding Distance=Omm

(a) Sliding Distance--0mm

(b) Sliding Distance=33mm

(b) Sliding Distance=23mm

.... :iiii..... :!

L:ii

,.. . . . . . . • - : . . :

.

-

.

.

(c) Sliding Distance=l 14mm

(d) Sliding Distance=145mm

Fig.6 Consecutive Observation of the Sliding Process (With Spheres in Single Layer, Indentation Depth = 1mm, Inclined Type Moving Raft)

.

.

. ,

. :

.

, .

(c) Sliding Distance=89mm

(d) Sliding Distance=l 36mm

Fig.7 Consecutive Observation of the Sliding Process (With Spheres in Double Layers, Indentation Depth =lmm, Inclined Type Moving Raft))

479

whereas the bubbles with spheres have the highest.

mation of the wear particle. This corresponds to an

Bubbles with disks indicate the lower value than the

adhesive wear process.

bubbles only.

In Fig.5, the moving raft was indented 4mm into the fixed bubbles and was slid parallel to the

3-2. Sliding characteristics

boundary. Some bubbles move over the frame of the

Fig.4 shows the consecutive observations of

moving raft. This process appears to be similar to the

the sliding process of the bubbles with spheres (sur-

abrasion process. However at the back of the moving

rounded by the standard type moving raft) against

raft also, the bubbles exist, which is similar to the case

bubbles with spheres arranged at the sliding interface

of Fig.4. It may be concluded from these observa-

of the fixed raft. It is apparent that the bubbles near

tions that with the deeper indentation of the moving

the interface of the fixed frame transferred to the mov-

raft to the fixed raft, the abrasion process coexists with

ing raft. At stage (d), the transferred bubbles are

adhesion.

pushed behind the moving raft. Stage (a) to (c) can be

In Fig.6, the moving raft is inclined so that the

regarded as the continuous transfer and (d) as the for-

bubbles do not escape easily from the raft. This results in a similar behaviour as shown in Fig.5.

n .Q

m

When the second layer of the spheres were in-

400

troduced inside the fixed raft, the transfer became in-

300

• Bu.,~

i,_ q_. t/1 t-

•

only

With Large Disks

200-

• With Spheres of Single Layer

~- IO0-

[ ] Bubbles Only afer 4ram Indentation 0 With Spheres of Single Layer afer 4ram Indentation

o

E z

hibited as shown in Fig.7. The number of transferred/ploughed bubbles from the fixed raft have been counted in all the four experiments, i.e., bubbles only, bubbles with small disks, large disks, and spheres for increasing sliding

0 0

50

1O0

150

200

distances. These results have been summed up in

Sliding distance, mm

Fig.8. It can be seen that as sliding progresses, the

Fig.8 Number of Bubbles Transferred from Fixed Raft

amount of transfer is increased. It is maximum while

(Parallel Type Moving Raft, Indentation Depth=lor

sliding on the bubbles with spheres.

4mm) ID

The results with the inclined moving raft are shown in Fig.9. Here also it is observed that the

400

bubbles with spheres of single layer transfer more than

C~

m tD q-. 1/1

"

300

•

Bubbles Only

0 With Small Disks

200

.~ lOO

•

With Large Disks

•

With Spheres of Single Layer

0 With Spheres of Double Layers

any other combinations. It is to be noted the spheres of double layers protect the transfer.

4. Discussion From the precise observation, the maximum

z

0

0

50 Sliding

1O0

150

200

Distance,ram

tensile strength was obtained just before the dislocation initiated through the crystal. With spheres, it was observed that the dislocation did not start until the

Fig.9 Number of Bubbles Tranferred from the Fixed Raft (Inclined Type Moving Raft, Indentation Depth=lmm)

higher tensile stress was applied. This means that strong attractive field exists near styrene spheres,

480

which enhances the tensile strength. The mechanism

face, the interface becomes harder as compared to the

of enhancement of attractive force is attributed to the

inside layers. During sliding contact, this harder layer

larger contact of the bubbles with spheres in a three

will pick up / remove bubbles from the inner layers.

dimensional arrangement as shown in Fig.10. When

So it can be summarized that the inclusion of the im-

the styrene spheres are added to the bubbles, bubbles

purities, i.e. the styrene foams improves the tensile

adjacent to the spheres are shifted above the water

strength and results in the enhanced transfer behaviour.

surface level. Then bubbles between the spheres form double or triple layers, as shown in Fig.10(b). This

5. Conclusions

leads to an increase in surface area, which enhances

The bubble rafts with spheres of styrene foam

the tensile strength. The presence of styrene foams in

have higher tensile strength. When the spheres are

the top surface simulate the reaction layer formed at

arranged at the interface between the moving and fixed

the real metallic surface due to interaction with the

raft, the transfer of the bubbles is greater from the fixed

surrounding environment.

to the moving raft than the cases without spheres or

When the spheres are arranged at the top sur-

disks. It is deduced that the enhancement of the tensile strength at the interface helps the transfer process.

Spheres ~(a

Bubbles~ ) TopView

References

1. EP.Bowden and D.Tabor, The Friction and Lubrication of Solids, Oxford Univ. Press (1954)

1

2. K.Hiratsuka, Trib. Intern. 28, 5 (1995) 279 3. N.Soda and T.Sasada, Trans. ASME J. Lubr. Techn., 100, 4 (1978) 492 4. K.Hiratsuka and M.Goto, to be published in Wear

(b) SideView (1) Bubblesalone (2) BubbleswithSpheres

5. J-M Georges, et.al., Nature 320, 27 (1986) 342 6. W.L.Bragg, J. Sci. Instrum. 19 (1942) 148 7. J-M Georges and G. Meille, Proc. JSLE Intern. Trib. Conf. (1985) 885

Fig. 10 Schematics of the Arrangement of Bubbles with and without Floating Spheres

8. W.L.Bragg and J.ENye, Proc. Roy. Soc. London, A 190 (1947) 474

S E S S I O N XlII E L A S T O H Y D R O D Y N A M I C LUBRICATION 1

Chairman •

Professor B.O. Jacobson

Paper XIII (i)

An Analysis of Track Replenishment Mechanisms in the Starved Regime

Paper Xlll (ii)

Shearing of Adsorbed Polymer Layers in an Elastohydrodynamic Contact in Pure Sliding

Paper XIII (iii)

Film Thickness, Pressure Distribution And Traction In Sliding EHL Conjunctions

Paper Xlll (iv)

Elastohydrodynamic Lubrication Characteristics of Electrorheological Fluids

Paper XIII (v)

Elastohydrodynamic Squeeze of Thin Films for the Sphere-Plane Contact

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All fights reserved.

483

An Analysis of Track Replenishment Mechanisms in the Starved Regime

B. Jacod, F. Pubilier a, P.M.E. Cann b, A.A. Lubrecht a aLaboratoire de M~canique des Contacts, UMR

CNRS

5514, INSA de Lyon, France.

bTribology Section, Imperial College of Science, Technology & Medicine, London, UK. In earlier work [4-6] the film thickness reduction due to lubricant starvation was analysed for a circular EHL contact. One conclusion from this work is that without a mechanism to replenish the track with lubricant the process of film thickness reduction would inevitably lead to component failure. Thus in order to explain long term operation, it is essential to include a replenishment mechanism. This paper analyses the replenishment under severely starved conditions. Replenishment is divided into 'out-of-contact' and 'in-contact' reflow. The 'out-ofcontact' reflow occurs in the lubricant track in the time between overrollings. Under severely starved conditions it was found that this mechanism produced negligible reflow into the track. The second reflow mechanism considers flow in the vicinity of the contact due to local capillary forces. In a first approximation the flow around a stationary contact was analysed, and a comparison with experimental observations shows similar flow patterns and similar time scales. An extension of this model to a moving contact was made resulting in a theoretical film thickness versus speed curve.

1. I N T R O D U C T I O N When considering elastohydrodynamic film formation it is usual to assume that there is sufficient lubricant present to form a fully flooded film, however this is not the case in many real life applications [15,16]. Starvation results in operating film thicknesses which can be significantly less than the predicted fully flooded values [4,10]. The onset of starvation can be due to a number of factors: including the operating conditions, lubricant supply and lubricant properties or a combination of these. Starvation is essentially due to the failure of the lubricant to replenish the track after being pushed aside by the passage of the contact. Increasing speed (reduced time between overrollings), high oil viscosity or a limited oil supply (greases, emulsions) will all tend to exacerbate the condition. In simple laboratory experiments the onset of starvation is usually identified by the formation of an air-oil meniscus in the inlet region [14]. The appearance and position of the meniscus relative to the Hertzian zone has proved to be the most easily defined feature relating to starvation [7,13] The meniscus position is however an artifact of the fundamental mechanism controlling starvation which is the amount of lu-

bricant present within the track. When very little lubricant is present the meniscus is no longer visible outside the contact and thus this approach, and the use of meniscus position to predict starvation, is very limited. It is thus more useful to develop models relating starvation to the amount of lubricant present in the track. In more recent studies it has been possible to follow the effect of severe starvation on film thickness. Typically, film thickness is measured with increasing rolling speed in a ball-on-disc device [7,13]. If the supply of lubricant is limited then the contact will pass from fully flooded to starved as the speed is increased. For sufficiently low speeds, the contact operates in the fully flooded regime and follows the theoretical film thickness with speed relation. As the speed increases the contact will move into the starved regime, and the film thickness will fall below the theoretical curve. For even higher speeds the film thickness drops with increasing speeds, and will then stabilise to a constant level [10,11]. This suggests that at some point an equilibrium is reached whereby the lubricant loss from the contact is balanced by replenishment into the track. Obviously it is of great practical importance to be able to predict both the onset and consequences of starvation in

484

real life applications. To do so requires a model which will predict the lubricant level within the track and thus incorporates both the contact loss and replenishment mechanisms. Previous work in this programme has concentrated on developing a starvation model based on the amount and distribution of the lubricant in the inlet and the effect of overrollings on film decay [4-6]. The loss mechanisms have been included but as yet it has not been possible to incorporate replenishment effects into the model. This paper presents new findings whereby a simple model has been developed to describe lubricant replenishment of heavily starved point contacts. Two replenishment mechanisms are considered: 'in-contact' and 'out-of-contact'. The 'out-of-contact' replenishment occurs in the lubricant track after it has emerged from the contact wake. The second mechanism describes lubricant reflow close to the contact. 2. P r e v i o u s s t a r v a t i o n m o d e l s One of the first papers dealing with starvation and lubricant replenishment was published by Chiu in 1974 [7]. The observations and analysis contained in this paper remain the basis for much of our current understanding of starvation. Chiu studied the problem experimentally and theoretically. He noted that the passage of the contact left a depressed track bounded by ridges of displaced lubricant at either side. In Chiu's model starvation was determined by the ability of the lubricant to reflow back into the track, during the time between overrollings. Such reflow is driven by surface tension forces and retarded by the oil viscosity. The high curvature at the side of the track results in a pressure gradient which the surface tension seeks to reduce. Thus oil flows from the ridges into the depleted zone. Chiu's analysis was confined to systems lubricated with a relatively large amount of oil and where starvation was induced by operating at high speeds. Thus his model is valid for relatively thick ambient oil layers (typically 100-500 micron) and is not applicable to situations where there is a very limited amount of oil present on the surfaces. These ideas were developed further by Guangteng [10] who combined both loss and replenishment mech-

anisms in his model to predict starvation in a contact lubricated with a limited amount of oil. In this case oil layers of 10-50 micron thickness were assumed. The analysis accurately predicted film collapse at starvation it did not however explain the levelling-off of the film at high speeds. In a later paper [11] a further development was reported; the inclusion of a disjoining pressure term to explain the equilibrium film observed under severely starved conditions. Good agreement was reported between the experimental measurements and the theoretical predictions. A second explanation for the high speed behaviour was provided by Chevalier [5] who suggested that in the heavily starved regime loss from the track is minimised. Thus the contact becomes increasingly efficient at retaining the lubricant in the track and the film thickness appears to stabilise. There have been several stages in the development of a full starvation model and these perhaps reflect the improvements in the experimental techniques required to study the problem. The work of Chiu and Wedeven [13] was concerned with relatively large amounts of oil and thick lubricant films. As our ability to measure thinner films in the contact improved so it became possible to study starvation under increasingly rigorous conditions. Similarly the models that have been developed have reflected this trend. At present however the models are still confined to relatively thick lubricant layers and cannot be applied to severely starved systems. The aim of this work therefore was to develop these ideas further into the thin film region where the ambient lubricant thickness is less than 10 micron. The second development reported in this paper is the inclusion of an additional replenishment mechanism. Previous workers have confined their models to 'out-of-contact' reflow, however in this case replenishment arising from capillary forces acting on the lubricant reservoir close to the contact are also considered. The role of capillary forces in maintaining a lubricant pool close to the contact has not been considered before in starvation studies. One observation supporting this mechanism comes from optical studies of heavily starved contacts; once rolling has halted, lubricant from the ridges at the side of the track reflows around the

485

contact forming a pool of oil [1,3]. Although this phenomenon is only really observed once the contact has stopped it is likely that it will also operate during motion to provide a small but continuous flow of oil into the track. 3. N O T A T I O N

a A B C

half-width of the circular Hertzian contact Hamacker "constant" ,A - 24~D2o a dimensionless constant, B - ah3tover/3r]a 4 dimensionless constant,

C = Atover/67rhoo~a 2 dh increase of the inlet film thickness during time dt dhoil increase of the inlet film thickness between two overrollings dr relative increase of the inlet film thickness between two overrollings, dr = dhoil/hcp(pH) D diameter of the track Do average equilibrium distance between atoms, Do = O.165nm h film thickness hc film thickness of the track layer heff central film thickness in the fully-flooded case hoil inlet oil film thickness ho~ film thickness of the reservoir H dimensionless film thickness, H = h/a relative central film thickness, H = he~hell He dimensionless film thickness of the central layer He = he / hoo p pressure Rb radius of the ball T~ Central film thickness reduction, Tt = he~hell t time tov~r time between two overrollings of the ball T dimensionless time, T = t/tove~, T = ta/rla U velocity of the ball x position on the profile Xm position of the meniscus X dimensionless position on the profile, X =x/a X m dimensionless position of the meniscus, Xm = x ~ / a viscosity 3' film thickness reduction parameter

a

surface tension

4. O u t of Contact Replenishment The 'out-of-contact' replenishment is considered to take place remote from the contact during the period between two overrollings. Considering a layer of oil on a metal substrate, with a free surface given by a height profile h(x), the pressure p(x) inside this film, due to the surface tension a and the disjoining pressure 1I is given by [8]:

d2h p (x ) - - a -~ffx2 - II(h)

(1)

with the first term representing the YoungLaplace capillary pressure and H(h) the Van der Waals energy (per unit volume of liquid) between liquid and solid. Here we have: A I I ( h ) - 67rh3

(2)

with

A the Hamaker 'constant' [9], A = 247rD2a - 2.1 10-21a. Where Do is the average equilibrium distance between atoms. This distance is remarkably constant and equal to Do = 0.165 n m for most hydrocarbons. Writing the flow equation for thin films (Reynolds) and using equation (1) one obtains:

0 [h30[_ad2h O--'x ~ ~ x dx 2

A

] Oh 67rh 3 ] - 0--t-

(3)

or in the differential form"

a [

3~ 3h2

6~

~7

Oh 03 04h 1 h h3 0x 0x---~ + ~-~ j

~x

h Ox 2

(4)

-

4.1. Dimensionless parameters Using the following set of dimensionless parameters H=

h h~'

z--

x

a~

T=

t

rover

(5)

486

!

where: h ~ is the thickness of the film far away from the track, a is the Hertzian half-width of the contact and rover is the time between two overrollings of the ball, equation 4 becomes:

1.2

!

0.1s ..... O.01s ...... Ii~!a,] geometry ...........

0.8

OH 03H 3H 2 0 X O X 3

-B

1 (OH

2

H3 04H 1 +

1 02H H OX 2

~-~j

A vX "1"

0.6

(6) 0.4

OH OT

0.2 0

where" 3

B - crh°° tover 3r/a 4

c =

Atover 67rrla2hoo

(7)

The value of the disjoining pressure term relative to the capillary pressure term is given by:

B / C - 1.05 1021 h 4

a2

(8)

4.2. R e s u l t s The out-of-contact evolution of the oil film thickness profile h(x, t) is a function of the initial profile, which is defined by two parameters he and ho~. he represents the value of the oil film thickness in the contact track IXI _~ 1, whereas h a is the film thickness far from the contact. In this example he - 10 nm and h a = 1 #m have been chosen. In between these two plateaus the oil film thickness evolves according to the Hertzian shape. Figure 1 shows the initial geometry and the evolution of the geometry with time. The major changes take place around IX] = 2 where the constant layer meets the Hertzian layer. Thus, very little replenishment of the track occurs for these very thin films due to surface tension effects. To study the effect of the disjoining pressure on the replenishment of the central layer independently from the effects of the surface tension, calculations were performed for two values of he: he = 10 nm and he = 5 nm. Once again the evolution of the profile with time is presented (see Figure 2 and 3). The effects are localised around IXI _ 1 where an increase of film thickness can be seen. This increase, however, is very small and very localised. It does not generate any replenishment of the central zone. This effect may become

I

-4

I

-2

/]

I

2

I

4

Figure 1. Evolution of the profile with time. B 2.4 10 -4 C - 1.1 10 -9, h e - 10 nm. very important if hc becomes even thinner, but this would lead to film thickness values which are no longer physically meaningful.

4.3. C o n c l u s i o n From this simple analysis of out-of-contact surface tension and disjoining pressure driven replenishment, we can conclude that for the thin films that are the topic of the current work, these mechanisms do not play a major role. Both only create a slight modification of the oil layer thickness around IXI = 1. This prediction is supported by experimental observations of severely starved contacts. An example is given below in Figure 4 which shows an optical interferometric picture of a heavily starved contact, with minute differences in the oil film thickness in and around the track from the contact exit to the inlet. 5. Close to Contact R e p l e n i s h m e n t 5.1. Stationary 1D G e o m e t r y The previous section has shown that out-ofcontact replenishment seemed to be an unlikely candidate for the track replenishment under very thin film conditions. From the observations of meniscus flow around a halted EHL contact, one can conclude that flow does occur in the vicinity of the contact. Because the Hertzian gap width becomes very small, the radii of curvature become very small, and surface tension effects might cause significant flow. As the geometry of the complete problem is complex, we will start by studying the

487

0.016

i

i

i

i

i

i

i

lOOs lOs . . . . . initial geometry ...... _

0.015

0.014

x I

0.013

0.012

_

~

0.011

0.01

-1.02

I

I

-1.015

-1.01

-1.005

-1 X

-0.995

!

I

-0.99

-0.985

-0.98

Figure 2. E v o l u t i o n o f t h e p r o f i l e w i t h t i m e d u e to t h e d i s j o i n i n g p r e s s u r e . C - 1.1 10 -9, hc 10 n m . 0.011

!

I

!

!

i

i

to inlet.

i

100s lOs . . . . . initial geometry .....

0.01

Figure 4. E v o l u t i o n o f t h e film p r o f i l e f r o m e x i t

z

0.009

x

"1-

0.008

0.007

",~,,,~

0

Figure 5. G e n e r a l g a p g e o m e t r y .

O.006

0.005 -1.02

Xm

-1.015

-1.01

-1.005

-1 X

-0.995

-0.99

-0.985

-0.98

Figure 3. E v o l u t i o n o f t h e p r o f i l e w i t h t i m e d u e to t h e d i s j o i n i n g p r e s s u r e . C - 1.1 10 -9, he - 5 n m . meniscus evolution in a one dimensional gap, as described in Figure 5. The meniscus is considered to be a perfect circle with a film of constant length and thickness supplying the lubricant to the gap. The geometrical assumption may not be too crude as we are only interested in meniscus position close to the Hertzian circle and thus very small gaps. The thickness and length of the conduit have to be chosen arbitrarily. This is not important as we are interested in the qualitative behaviour of the meniscus position Xm as a function of time: Xm = ct ~ where c and fl are constants. For the case of a linear increasing gap height z = c x with x, an analytical solution to the problem can be obtained: Xm = ct 1/3, as is shown

in [12]. In case the gap is parabolically increasing with x, z - k x 2, an analytical solution could not be found and the problem had to be solved numerically. Using curve fitting of the numerical results the following behaviour of the meniscus position was obtained: X m - - c t 1 / 5 . Finally, for a Hertzian gap z - k x 15 the same numerical solution techniques are needed, which after curve fitting give" Xm - ct 1/4. Even though the model has some qualitative interest, it is difficult to generate quantitative data, as the height and length of the supply channel are unknown, and cannot be easily obtained from the full contact problem. Therefore, instead of tackling the supply channel, we will study the two dimensional problem in the next section, which will allow us to clarify the supply channel to some extent.

5.2. Stationary 2D Geometry The severely starved contact can be described by the contact zone, defined by the Hertzian circle,

488

surrounded on both sides by lubricant reservoirs with a central inlet region covered by a layer of lubricant of constant thickness. The initial position of the meniscus in the central inlet region is very close to the Hertzian circle. Once that the ball is stopped, the lubricant flows from the side-reservoirs to the central inlet region under the effect of capillary pressure. This flow can be described by two models: • A radial model: the lubricant is driven from the reservoir by the capillary pressure due to radial radii of curvature. The lubricant comes from the reservoirs either through the conduit formed by the central layer of constant thickness or, laterally, through the already completely filled gap close to the reservoir boundary. • A circumferential model: the capillary pressure driving the lubricant to the central region is due here to circumferential radii of curvature. At a certain radius of the center of the contact, the height of the gap is constant and results in a capillary pressure. The lubricant driven by this capillary pressure is then dispatched towards adjacent parts of the meniscus under the influence of a difference in radii of curvature.

inlet layer to each point of the central region, or, laterally, through already completely filled gap to adjacent ones. Because the meniscus is very close to the contact zone, the initial resistance to flow of the completely filled gap is very high. Thus the flow of lubricant coming laterally from the reservoir is used at first to fill entirely one portion of the gap before flowing into the next. The lubricant brought through the central layer, however, progressively lessens this resistance and the lateral flow is more and more diverted into adjacent portions of the gap thus softening the steep transition between the filled gaps and the other (Figure 6). However, the time scale predicted by the radial model is much too large and this mode of replenishment can be discarded.

5

hc:l. 10-7 h c - ' ~ , IfJ-~' N

These two modes of replenishment are studied separately. The parameters of the problem are given in Table 1.

a Rb a h rl

Table 1 Input parameters.

0.17 0.0127 0.03 0.1 0.807

mm m N/m #m Pa s

5.2.1. R a d i a l M o d e l Driven by the capillary pressure due to radial radius of curvature, the lubricant may flow towards the central inlet region in two ways: either from the reservoir through the conduit formed by the

Figure 6. Meniscus position for hc = 0.1 #m and hc = 0.3 #m, t = 20 s.

5.2.2. C i r c u m f e r e n t i a l M o d e l The lubricant spreads circumferentially from the reservoirs to the central region. To a purely circumferential flow due to the radius of curvature at this distance from the center of the contact, is superposed a transverse flow to the adjacent parts due to the difference in radius of curvature from one position, relatively to the center of the contact, to the next.

489

.

..

.

.

.

.

.

.

.~

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

This model gives a very good approximation of what is observed in reality in terms of time scale and flow pattern. The results obtained are presented in the next section together with experimental observations to facilitate the comparison.

5.2.3. Comparison with experiment Experiments were performed on a ball-on-disc machine to record the evolution of the meniscus when the ball stops. The EHL contact is formed by a rotating ball pressed upon a glass disc. The lubricant used is a high viscosity oil: SHF 401, = 0.807 Pas at 25C and a = 0.03 N / m . The amount of lubricant around the contact is monitored by the size of the side-reservoirs. Here, the reservoirs have a radius close to 6 a. The dimension of the contact and of the ball are those given in the table above. Central film thickness was measured to give an approximation of the central layer film thickness: he = 0.1 pro. The evolution of the meniscus position with time once that the ball was stopped was recorded on video. With a shutter speed of 25 frames per second, it is easy to calculate when the meniscus reaches a certain position. Figures 7 to 11 show a comparison between numerical and experimental results. The numerical calculations were performed to match, in shape, as much as possible the experimental observations. The time for both numerical and experimental results can thus be compared. Figure 9 shows the meniscus position 2 s after the ball is stopped. The predominant motion at this time is still the scissor-like closing motion of the reservoirs. The meniscus in the center of the contact has hardly moved and is still very close to the Hertzian circle. The numerical model gives a very good approximation of this flow pattern, the time scales predicted numerically are however smaller than what is observed in reality but remain of the same order. Experimentally, this situation is observed after 2 s, numerically, it is predicted after 0.61 s only. In all the figures presented here, this behaviour is present: the numerical model gives a very accurate description of the lubricant flow and a not so accurate prediction of time scale while remain-

•:

.~ilili!~iii::i!!ii~ii~!!ii!!!~iiii~ii~i!!:i:: ?::~! ~i~i~iii~!i~i~i~!~ii~ii~i!ii~!~i~i~!iii!ii!~!~i~i~iiii~i~i~i~!~!i~!~.

Figure 7. Meniscus position recorded experimentally, t ~_ 1.4 s.

t=0,4500

s

Figure 8. Meniscus position calculated numerically, t = 0.45 s. ing of the same order. A possible explanation of this difference might come from the contact angle, which was modelled to be zero, see Figure 5. In reality the contact angle is larger than zero, thereby producing a larger radius of curvature of the meniscus. Thus the capillary pressure would be smaller, and the time scale larger. 6. D y n a m i c 2D g e o m e t r y The preceding stationary 2D model enables us to calculate the evolution of the meniscus position with time starting from a known initial geometry.

490 ,.~,

•

:iiiiili)i ,?:i?!:.:)!~:;:~!;:i!~i:~:i):'i,:}'~i~:~:i:;,i!i!'.~ii)i~ ~,~'~.'~i':~i71i '~:i!'~:':{i~':~i~};':i!:i!i

......

.

~ ....,[~:,.~:~~:~j~ +

+

+

+

0

0

0

0

O

0

0

0

0

O

Fig.4 Relation between contact condition and order of interference fringe ( w - 6N, u - 372mm/s )

(a) V=0V -:

:i: :::

:

:

i~i:iziiii!:i::~::i: ;:.!:::,:/:~!~:! ......::::::::::::::::::::::: ......:::::::::::::::::::::::::::::::: .... .:.:.:.:.!:ii!iiiii:i:iiiiiij iii2Zi2!!!!!?!iiiiii:.2?!?!iiiiii2iiiii!!iiiiii :?Siiiiii22 !iiiiiiiiii]iiii!iii:i!i!iii.>.'!;ii:~iil;i[[:iii:"-.x .... ~i::!iiiiii!:iT;i!iiiiiiii!iiiiiiiiiii!ii!!.iii!iii;ii

i!!i~.i;i!i~!i:~i~!~i:'~i:~/:i!~!'?::':::i :.::!'~.!~..ji::ii!!iii~i!:iii?::ii;!iii!iii~iiii:!

!!iiiiii!ii:i!!'ii!ii!ii!!i!:i',iii!iii :!iii:iiii!i!!ii':!:i :i;!?, ili: ii!!ili!ii!iiiiiiiiiiii~i!i ii{g~iiii!i!i;iiiiiiii;i;i;i!iii!ii!i:iii!::iiii!;iii!ii:iLiii!i[ii!iiii!i!iiii!!ii!!iii::!!! "ii::

~.~i~i~!:'..,.!~:!~!.".; :: iii..'~i.' ;!~!::?~!~i:i:~......~:i:,::~:!:;!!'~/i:::?~.:~i:i!i:~:!~!~! : :j:i~:i>.'~i:i:;,. >.!:i:i:i:: ::.i: ::::::::::::::::::::::::::::::::: ":::i:::i:i~'..i:!:i>::i:i:i:i:i:i: ~i:~::: ::i: :!::. ×.!:i:::::i, :::i:~:,::::~:~i:!:~ " .i:i:::: &~:: :i:::i:::::i::: ::: ~-:.~-:~i::::.:::. ,

the region of h ~

was shaped like a horse-shoe.

~2 > ~1-For the LC that we used, the orientation

The shape approached a circle as the voltage w a s

of the molecules was parallel to the direction of the applied electric field for 2kV/mm and ~3 is

521

812 V/mm Steel disk Flow

609

[ Emax=812V/mm I

mmm m,,..2

O

203

Emin=200V/mm] Glass disk

Molecule of Liquid Crystal Type 1

406

Type 2

Type 3 Fig.8 Result of FEM analysis (Electric field strength)

Fig.6 Relation between orientation of molecule and flow direction approximately eight times higher than ~ . However, considering the location of the electrodes, we assumed that the orientation of the molecules would be Type 2. If this assumption was valid, we should not have obtained the results in Fig. 2 because p~ is approximately three times higher than ~ , and the calculated / ~ is twice that in the absence of an applied voltage. To clarify this discrepancy, we did an electric field analysis using finite element method (FEM). Figs.7 and 8 show representative results, which clarify that the steel disk and chromium film on glass disk substituted for the electrodes and that the strongest electric field occurred at the lubrication area (i.e., the center of

........................ ~i~i~ 0, the orientation of the molecules was not influenced by slip ratio, for the conditions studied here.

4.2. Comparison with EHL theory The increase of h ~ was greater for higher rotational speeds of either the steel disk or glass disk. (Fig. 2). This increase can be explained by EHL theory as follows. Fig.9 shows the relation between viscosity and h ~ based on EHL theory. The theoretical hmi~is given by hm~ = 2.69 R G 0.5a U0.67 W-0.0G7(l_e-0.Ta) (2) where R is equivalent radius, G is material

.........•`•.......•............-....`..........`........`•...................

-.-.

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

_1_.

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

.

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

parameter, Uis speed parameter, and W is load parameter.

The

increment

ratio

in

h~

to

viscosity is large when rotational speed is high. Our results coincide with those by EHL theory. Fig.7 Result of FEM analysis

522 ~0.5 # ~ o°'

v0.4 -

...."

u - 377mm/s f "

• f,,-t

.~ e

i~0.3 -

#

.# ##

..'~

###

lubricating film of a few ~tm in thickness if voltage is applied to electrically conducting surfaces directly. The reason why we used such a high voltage is to use a glass disk as a surface to observe the EHL film by interference method.

0# #o

.****u= 252mm/s

5. CONCLUSIONS

0.2Our study focused on the behavior of EHL films 0.1-

of liquid crystal in applied electric field. Under u = 82mm/s

0

0.1 0.2 0.3 Viscosity at ambient pressure, Pas Fig.9 Relation between viscosity and minimum film thickness ( EHL analysis)

4.3. Triboperformance control The change in lubrication conditions seen in this study can be explained as follows. The lubrication conditions shown in Figs. 5a and 5b are typical EHL conditions. Because the viscosity increased as the applied voltage was increased, the lubrication conditions approached that of thick-film lubrication. We assumed that the conditions shown in Fig. 5d were the transition from EHL to thick-film lubrication. All changes in the EHL film thickness and shape measured in this study were rapid and reversible, thereby making it possible to use ER fluids to control the triboperformance of machine elements.

4.4. Strength of applied voltage The voltages applied in our experiments were too high. But the value of applied voltage depends on the location of electrodes. Basically, the electric field of a few kV/mm is necessary to change the viscosity of LC, so it is sufficient by the voltage of a few V to change the thickness of

the EHL conditions studied here, the liquid crystal could change its molecular orientation rapidly and reversibly. The films behaved like a special lubricant whose viscosity at ambient pressure can be controlled. Though many problems remain unsolved in controlling the triboperformance, these results demonstrate the possibility of new lubrication systems and of improving the performance of mechanical systems. ACKNOWLEDGMENT We are indebted to Japan Energy Corporation for providing the liquid crystal.

REFERENCES 1. W.M.Winslow, Journal of Applied Physics, 20 (1949), 1137 2. D.A.Brooks, Proceeding of ERMR'97(1997) ,78 3. J.Furusho and M.Sakaguchi, Proceeding of ERMR'97(1997) ,51 4. A.D.Dimarogonas and A.Kollias,

Tribology

Transactions, 35(1992), 611 5. Y.Kimura, K.Nakano, T.Kato and S.Morishita, Wear 175(1994), 143 6. B.J.Hamrock and D.Dowson, Transactions of the ASME, Journal of Lubrication Technology 99-2(1977), 264

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

Elastohydrodynamic

523

s q u e e z e of t h i n f i l m s for t h e s p h e r e - p l a n e c o n t a c t

M. Trifa, F. Sidoroff and J.M. Georges Laboratoire de Tribologie et Dynamique des Syst~mes, UMR CNRS 5513, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, B.P. 163, F 69131 Ecully Cedex, France

The elastohydrodynamic squeeze of thin films in a sphere-plane contact is analysed under imposed harmonic vertical displacement. A general model is presented taking into account - the viscoelastic rheology of the film, either homogeneous or heterogeneous, - t h e film compressibility, - t h e substrate elasticity. The model case of elasticity then allows the influence of the material properties to be analysed which appears coupled with the thinness ratio D/R. A complete analysis of the case of a viscous compressible fluid is then presented. The solution depends on two adimensional parameters coupling the material properties with the thinness ratio. Three different regimes are identified : hydrodynamic, elastohydrodynamic and mixed. As a conclusion, applications and extensions of these results will be discussed.

1. I N T R O D U C T I O N The nanorheological squeeze of a thin liquid film, as it is for instance realised in surface force apparatus [1-3], is an important experimental method for characterising the structure and properties of lubricants. Analysis of these results, however do require, even in the simplest configurations - sphereplane or crossed cylinders - a precise mechanical analysis of the flow and stress patterns. This is a difficult problem coupling the rheology of the film with the substrate elasticity, thus resulting in a contact behaviour of viscoelastic type. Harmonic characterisation therefore appears natural. In a sphere-plane c o n t a c t - Figure 1 - the typical experiment consists in prescribing a small harmonic displacement around a fixed positive sphere/plane distance D D'(t) = D+SDe ~°~t

(1)

It should be noted that in the frame work, the superimposed harmonic displacement 8/) is supposed to be small enough, so that a linear theory can apply. It follows in particular from this that the pressure amplitude will remain small with respect to the atmospheric pressure, so that no cavitation may occur. The resulting normal force is measured and separated into a static and harmonic part. F'(t) = F~ + F e i'°t

= (k +io~ A)SD

Figure 1. Geometry of the sphere-plane contact

(2)

524

This provides the contact stiffness k and damping A which depend on - t h e geometry of the contact and in particular on the thinness ratio D/R, - the frequency f = o~/2~ of the imposed harmonic motion, - t h e rheological properties of the interfacial layer and the elastic reduced Young's modulus of the substrate E*. The static part Fs may account for capillarity effects, surface forces etc.., but it is not investigated here and we focus on the hydrodynamic force which for D > 0 has no static contribution. The standard thin film sphere-plane geometrical approximation will be used r 2

h(r) = D-~

plane

The purpose of this paper is to investigate the influence of these parameters and in particular the respective film and substrate contribution. This analysis will be based on a combination of the elastic substrate deflection with a thin film model for the viscoelastic harmonic response of the interfacial layer. Compressibility of the film is included and will be shown to play an important part. Special attention will be given to the representative case of a compressible viscous fluid film.

2. VISCOELASTIC SQUEEZE MODEL 2.1. Generalised Reynolds model Assuming a rigid substrate, the harmonic response in linear viscoelasticity can be obtained through the use of complex variables. More precisely the displacement, strain and stress are assumed harmonic, thus

z = 0 • ui = 0

sphere z = h • ~1 = u2 - 0

complex

(3) u3 = W

where W = S D is the imposed vertical displacement, - T h e viscoelastic harmonic isotropic law, relating the complex stress ~ij to the spherical and deviatoric strain e-kk and e~ij ij = K ~kk 5ij + 2 G eij

(4)

(~ij = ~ij(x) eic°t

Xo

The thin film approximation is obtained from the following assumptions a. The vertical stress ~ = ~33 does not depend on z. b. The terms 3ua/~z (a = 1,2) are prevailing in eaz. c. The horizontal strain ea~ are small with respect to ezz which are a natural extension of the classical lubrication theory [4]. This leads to the following generalisation of Reynolds equations [5, 6] @ ~ - div (~1 grad ~) = "vV

displacement

the case of an homogeneous film (K and G do not depend on x, which will be assumed in the most part of this paper) h(xa)

ui(x)

) •

and

stress ~ij(x) are solutions of the boundary value problem combining

(5)

where @ and ~t are two quantities which in

45(

The

(quasi-static

where K(co) and G(co) are the complex compression and shear moduli depending on co and, in the case of a heterogeneous film, on

2R

u i = ui(x) e ic°t

- the equilibrium equation approximation), - t h e boundary condition

h3(xa) K(co) - 2 G(co) ~ = ~ 12 G(co) K(CO)+ ~5(co)

(6)

525

With respect to the standard Reynolds formalism [4, 7] this equation includes -viscoelasticity through the use of complex quantities, -compressibility through the term in ~. This term in fact introduces a complete modification of the problem and plays, as will be seen later, an important role. For an axisymmetric problem, such as the sphere-plane problem, this equation reads h(r)

~(r)

r

r dr

~

w(r) = -

1

d~)/K(co)-~G(¢o) ) ,

~

12 G(¢o) dr

dr

~

(7)

E*-

2.2. Elastic substrate deflection The elastic deflection of the substrate is obtained from the general relation [8]

~E

ff

o

o ( r 1) r1 dr1 dO r12 + r 2 - 2 r 1 rcos0

/ 1 -Vp + l _ V s2/-1 2

Ep

where r~ is the outer radius of the film which in the classical lubrication model can be taken as co. This equation can be solved numerically with standard techniques.

contribution

(s)

- 2~

K(oo) + ~ G(¢o)

c=O

can also be

w(r)-Wp(r) + Ws(r )

--W

~(r~) = 0

w(x) = - 1 - v 2

~/r12 + r 2 _ 2 r1 r cos 0

for a thin film ( r ~ - ~ - R D )

with the following boundary condition =o

p(rx) r1 dr 1 dO

A similar relation holds for the sphere which

~:E* d~

fl

-

considered as a plane. Finally the total substrate will be taken as

~(~)+45(~)

l d(ha(r)

For an axisymmetric distribution this relation becomes (Figure 2)

Es

It should also be noted t h a t this approach neglects the deflection resulting from the shear stress ~rz, ; this appears to be a reasonable assumption. Again this deflection can be computed numerically from the normal stress distribution a(r).

2.3. The c o m p l e t e c o n t a c t p r o b l e m The imposed displacement 5D at each point can be decomposed into two parts

p(x') dS' Ix-x' I

providing the vertical elastic displacement at the surface of an elastic half space resulting from a pressure distribution p on the surface.

P(rl)

5D = ~(r) + W(r)

(9)

where the substrate contribution ~(r) is obtained from the elastic relation (8) which is directly extended to harmonic viscoelasticity while the film squeeze W(r) is governed by the generalised Reynolds model of section 2.1

i

~

r

x

Figure 2. Integration of the displacement.

and therefore by (7) where W(r) now is no longer 5D but only the film contribution. The complete contact problem now requires the solution of the coupled equations (7), (8) and (9).

526

This is achieved practically by an iterative procedure. Starting from a given distribution ~(i)(r) the normal stress distribution ~(i+l)is obtained from the viscoelastic squeeze model.

(]~~(i+l) _ div(~1grad ~(i+l)= w(i+l) = 5D .~(i) -

transforms this equation into

lx xX ,//12 3,xx :l I010 x Xl Xl Xld0 x~ 2x

1 +x

The substrate computed by

deflection

~(i+l)

is

then where the two adimensional parameters ¢z and ~ are

_l__.~fi:I'2n

~(i+l)

- 2 x x lcos0

~(i+l)(rl)rldrldO

E*

0 ~rl 2 + r 2 - 2 r l r c o s 0

K-

This procedure usually converges in a few iterations.

E* K-

a

Solution of this equation is z = Z(x;a,~)

3. THE E L A S T I C CASE 3.1. A d i m e n s i o n a l a n a l y s i s Let us now consider as a first example the case of an elastic film. This is an academic problem but it will provide a significant physical insight into the problem and in particular about the respective influence of the material parameters. The problem here depends on three material constants: the elastic equivalent modulus of the substrate E* and the shear and bulk modulus G and K of the film. The equation to be solved then is

-----~o-h(r)K - § G I K+~G

K+~G

d(rh3(r) do I=

r dr

12G dr

.i [ r~[2n ~ (rl)rldr1d0 nE 5----¢0 ----D¢0 ~rl2 + r2 - 2 r1rcos0 The followingreducedvariables 5D

Ii-

r

x = ~

K + 4G U=SD~--- o K -2G

F= 6nGR2U~ D

GRU Z ~ =------D2

x2 h=l+~ h(x) = ~ 2

(i0)

so that finally F = 6 n G R 2 K + ~ G f(a,~) 5D D K --~G

(12)

3.2. D i s c u s s i o n The contact force in (12) has been normalised from the Chan-Horn solution i.e. from the incompressible case with rigid substrate, a = 13= 0, f(0,0) = 1. The function f(a,~) therefore appears as a "correction" accounting for the film compressibility and the substrate elasticity. This correction is represented in Figure 3. The fundamental result is that this correction strongly depends on the thinness ratio D/R. Considering for instance a, relation (11) shows that even for a weakly compressible material G/K 1.2 MW/m2. 5. CONCLUSION

Figure 7. C-SiC composites" lower first body surface after friction transition. The third hypothesis concerns mechanical damages of first body surfaces. S.E.M first body surface observations (Fig. 7), after elimination of third body particles, show the microcracking of the

C-SiC composites are self-lubricating materials with low p.v values. When p.v > 1.2 M W / m 2 friction transition appears before the expected test duration. During the low friction phase, the lameUar graphite, in the periphery of the fibres, allows natural fltird body films to be formed. Velocity accoaunodation occurs mainly by shearing in the thickness of the third body layers (VAM $3M3). After friction transition, the third body is mainly formed of finely ground matrix particles and fragments of fibres. The compaction of the

566

powdery third body results in velocity accommodation mechanism by shearing through its

thickness (VAI~ 83M3). Static SEM observations and dynamic observations with a linear alternative motion tribometer, have been very useful to apprehend formation mechanisms of the third body and velocity accommodation mechanisms within the contact. The serf-lubricating effect is due to tile nature of the fibres. All the fibres do not produce lamellar graplfite. The use of C-SiC composites can be limited for friction applications at high temperatures. The increase of temperature leads to premature friction transition. REFERENCES

1. Y. Berthier, Tribologie, Science Carrefour, journ6es Europ6ennes du Freinage, JEF 92, GFC 92, Lille, 1992. 2. F. Platon, G. Kapelski, P. Boch, M. Godet, Y. Berthier, "Le frottement h haute temp6rature des c6ramiques" lubrification solide. " M6canique Mat6riaux Electricit6, Revue du GAMI, 439, 1991, 27-33 3. F. Platon, Y. Berthier, "Etude du comportement tribologique de couple c6ramiques SiC et Si3N4 en fonction de la temp6rature • la r6alit6. "Proc. Internat. Symp. "Advanced materials for lightweight structures", ESTEC, Noordwijk, The Netherlands, 25-27 march 1992 (ESA SP-336, October 1992) 4. H. E. Sliney, "Solid lubricant materials for high temperatures - a review."Trib. Int. 5, 1982, 303-314. 5. B. Prakash, "Frictions and wear caracteristics of advanced ceramic composite materials ", Advances in Composite Tribology - Composite Materials Series, Vol. 8, p. 405, Volume Editor" K. Friedrich - Series Editor" R. B. Pipes, Elsevier Science Publishers, 1993 6. Z. Lu, "Tribological properties of unidirectionally oriented carbon fiber reinforced glass matrix composites" Advances in Composite Tribology - Composite Materials Series, Vol. 8, pp. 367-403, Volume Editor: K.

Friedrich - Series Editor" R. B. Pipes, Elsevier Science Publishers, 1993 7. Z. Lu, K. Friedrich, W. Pannhorst, J. Heinz, "Sliding wear of unidirectional carbon-fibre reinforced glass composite against steel.",J. Mater. Sci. Lett., 12, 1993, 173 8. O. Jacobs, "Scanning electron microscopy observation of file mechanical decomposition of carbon fibres under wear loading ", J. Mater. Sci. Lett., 10, 1993, 838 9. N. Alexeyev, S. Jahanmir, "Mechanics of friction in self-lubricating composite materials. I: Mechanics of second phase deformation and motion ; II : Deformation of the interfacial film" Wear, 166, 1993, 41-54 I0. F. Platon, P. BocK, "Stand,'trd Tribological Tests for Engineering Ceramics ", Ceramic Materials and Components for Engines, D. Keram. Ges. Publi., 1986, 735-757. 11. H. Czichos, S. Becker, J. Lexow, "Multilaboratory tribotesting : results from the Versailles advanced materials and standards programme on wear test methods" Wear, 114, 1987, 109-130. 12.R.A.J. Sambell, D. C. Phillips, D. H. Bowen, "The technology of carbon fibre reinforced glasses ,and ceramics ", Carbon fibres, their place in modem technology, Proc. lnt. Conf., 1974, Plastics Institute, London 13.O. Dalverny, "Vie tribologique b. chaud et temp&ature interfaciale darts des contacts c6ralniques", Ph. D. Thesis, Bordeaux University, France, 1998. 14. P. Taravel, I. Akl, M. Bouvier, Y. Berthier, M. Godet, "Simulation induite en petits ddbattements", 8~m° Congr~s de M6canique, Nantes, 1987, p. 85. ACKNOWLEDGEMENTS Tile authors ,are very grateful to their industrial partner (Cdramiques et Composites, F 65300 Bazet) for his financial support and for tile supply of the samples. They also gratefully acknowledge the assistance of Dr. Y. BERTHIER (Laboratoire de M6canique des Contacts, INSA Lyon) in his dynamic observations of the third body and in his valuable discussions of tiffs work.

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

THE EFFECT

OF HOLLOW ON FRICTION

567

NANOPARTICLES

OF WS2

AND WEAR

L. Rapoport a, Y. Feldman b, M. Homyonfer, b H. Cohen, CS. Cohen c, R. Tenne b a. Department of Science, Center for Technological Education Holon, Israel b. Department of Materials and Interfaces, Weizmann Institute, Rehovot 76100, Israel c. Chemical Services Unit, Weizmann Institute, Rehovot 76100, Israel Abstract Friction and wear behavior of new nanomaterial - inorganic fullerene-like (IF) WS 2 supramolecules has been compared with layered solid lubricants MoS2 and WS2. Lubrication mechanism of IF nanoparticles and tribochemistry of contact have been studied. The main advantages of IF nanoparticles lies in their round shape and the absence of dangling bonds. Velocity accommodation modes under friction with solid lubricant powders were considered. The main lubrication mechanism of contact with IF nanoparticles appears to be rolling friction.

1 . Introduction Layered materials such as graphite, MoS 2 and WS 2 (platelets of the 2H polytype) are used both as solid lubricants [1-2] and as additives in liquid lubricants [3-4]. The layers can slide over one another thus providing low friction. Minimum tangential resistance is commonly associated with easy interplanar shearing due to the weak van der Waals (vdW) bonds in these materials [5,6]. Unfortunately, the 2H platelets tend to stick to the mating metal interfaces through the reactive dangling bonds on their prismatic edges (0110), which results in their rapid annihilation through burnishing and oxidation. Recently, the tribological properties of C60 and C70 fullerenes were elucidated [7, 8]. It was speculated that C60 molecules in sliding contact may roll like tiny ball bearings [8]. In fact, the fullerene powders tended to clump and compress into a high shear strength layer resulting in a high friction coefficient [9]. For practical surfaces, the fullerene molecules are too small to separate between asperities of the mating metal surfaces and therefore they tend to enter into crevices or valleys. Within the past few years, inorganic fullerene-like (IF) supramolecules of metal dichalcogenide MX 2 (M=Mo,W, etc.;X=S,Se), materials with structures closely related to (nested) carbon fullerenes and nanotubes have been synthesized [ 10,11]. Recent experiments show that IF possess superior lubricating properties over 2H

platelets in a wide range of operating conditions, for example with respect to their concentration and also the load/speed ratio (see Table 1 in Ref. 12). We attribute the recently reported outstanding tribological behavior of IF-WS 2 to its chemical inertness and to the hollow cage structure, which leads to high elasticity and allows the particles to roll rather than to slide (rolling friction) in a specific loading range. One of the important problems in the friction and wear behavior of IF nanoparticles is the evaluation of the lubrication mechanism. Effect of lubrication is discussed here on the basis of the velocity accommodation concept in third-body contact [13-15]. Third body includes a "bulk" and two "screens". The size of screens in third body varies at around 10.9 m, while the third -body bulk varies at around 106m. The velocity is accommodated in the oil film through shear. The velocity is accommodated by two modes: shear and roll formation. The shear mode is determined by plastic and viscous shear. In this work the authors propose a lubrication mechanism of IF-WS 2 nanoparticles based on friction and wear data and the analysis of tribochemistry of contact. The results are compared with 2H-WS 2 and MoS 2 platelets. 2.

Experimental procedure The IF-WS 2 nanoparticles used in the

present study were synthesized by a solid-gas reaction between WO3 and H2S in a reducing

568

atmosphere [ 16]. The size and shape distributions of the nanoparticles were studied by transmission electron microscopy (TEM). The average size of the IF-WS2 particles was 120 nm, while that of 2H-WS2 and 2H-MoS2 was 4 gm. Samples of the 2H-WS2 and 2H-MoS2 powder were milled for 24 hours, leading to platelets with an average size of 0.5 ~tm.

The chemical reactivity of the different powders in oxygenated atmosphere was verified by heating the powders in ambient atmosphere. The friction experiments were performed in laboratory atmosphere (humidity _050 %) using a reciprocating ball-flat tribometer and a ring-block tester (more details in [ 12]). Ball-flat test was performed at sliding velocity of 2xl 0 -4 ms -1 with load of 1.5 N during 4 hours. Ring-block experiment was performed at sliding velocities V=0.22-0.44 m/s and loads of 150-1200 N during 8-16 hours. The friction coefficient, the wear loss and temperature of the block were measured. The wear loss results are presented as the wear coefficient Kw [ 17]. The limited amount of the available IF-WS2 material restricted the number of measurements that could be carried out. Single-crystal LiF was used for determination of the dislocation density induced by a top sliding surface. In the present experiment LiF crystals were immersed in mixture containing 5% of the solid lubricants for 5 min and then used as the flat surface in the tribometer. In another kind of experiment, the dry solid lubricants (SL) were deposited as a dense film (0.2 mm thick) from an alcoholic suspension onto a glass. The films were covered with a top glass, so that a glass/SL/glass sandwich was obtained. This pair was subjected to friction measurement. Prior to tribological testing, the specimens were ground and polished to a surface roughness of Ra-0.15 ~tm. To simulate typical industrial conditions, most experiments were carried out with 5 wt % of solid lubricants dispersed in a commercial oil "Delmol" ( kinematic viscosity of 32 cSt at 40 ° C). Moreover, the effect of concentration (5-60 wt %) was considered. The lubricating dispersions were stirred throughout the testing period. After wear testing, the particles were extracted from the lubricant, purified and studied by different techniques. The surface topography of the disk and block was evaluated before and after testing. A

portable profilometer, connected to a personal computer, was used for surface roughness measurements. Complementary information on the state of wear of the powders in the lubricating fluid and on the metal surfaces of the specimens was obtained using a combination of TEM; scanning electron microscopy (SEM); X-ray photoelectron spectroscopy (XPS) and energy dispersive X-ray spectroscopy (EDS). Nanotribological evaluation was performed on a Topometrix TMX2010 Discoverer scanning force microscope (SFM) equipped with microfabricated cantilevers with integrated Si tips (Nanoprobe, Singlefen, Germany). All SFM measurements were carried out in ambient conditions at 25°C and ca. 60% humidity.

3. Results 3.1 Analysis of tribological parameters The size and shape distributions of the nanoparticles were studied by transmission electron microscopy (TEM). Although most if not all of the nanoparticles were closed and hollow, their shape was found to be very irregular with a small fraction of the particles ( 300 N, part of the particles (ca. 50%) were deformed and frequently observed to be compressed into ovoid shapes, Fig. 4 a. Than the radius of curvature was decreased, Fig. 4b. Force vs. Distance

2O ~" lO

-10 -20 -30

i

1

51

,

101

i

1

151

201

Distance (nm)

Fig. 3" Force-distance curves for Si tip on wear tracks from experiments with (1) IF (upper curve) and (2) platelet (lower curve). Note the large

]|)

llnl

Fig. 4 IF-WS2 particles after wear. P-300 N. 3.2 Tribochemistry of contact XPS analysis of the wear tracks revealed a strong carbon Cls peak (284.8 eV), which was not removed upon careful cleaning prior to the analysis. Therefore, the carbon feature could be attributed to partial polymerization of the lubrication fluid at the elevated temperatures which develop during the wear tests. The quantity of oxide is substantially higher on the surface of the wear track in contact with 2H-WS2 platelets, Table 2. The relative intensities (RI) of WS2 to WO3.x, were found to be 5:3 in the contact with IF nanoparticles and 1:13 for the platelets. Deconvolution of the W(4f), Mo(3d) and the S(2p) spectra permitted an estimation of the fraction of WS2 : WO3.x, in the platelets and hollow nanoparticles after wear test. It was found the appreciably larger oxidation for the 2H platelets (1:1) than for the IF nanoparticles (1:11). For Mo this ratio was 1:6. For S the ratio was 1:32, 2:3 and 1:3.8 for IF-WS2, 2H-WS2, and 2H-MoS2, respectively. The ratio of S/W intensities for the wear track in contact with IF was 2:1 while in contact with 2H-WS2 platelets that ratio was lesser. Thus it is seen that lesser than 10% of IF are oxidized in the bath comparing to 50% of 2H-WS2.

571

uncertainty due to the deconvolution procedure was estimated to be 10%. Table 2 XPS analysis of Wear Tracks and Lubricants IF-WS2

Solid 1 Lubric Wear Track

2i Wear Track

2H-WS2

WS2:WO3.x from W(4f) 11:1 1:1

5:3

1:13

S(2p) : W(4f) Scone. Scone. (WS2+FeS2) (WS2+FeS2) - 2 Weone < 2Wcone (WS2+WO3) (WS2nt-WO3)

4. Discussion 4.1. Mechanism of lubrication by IF nanoparticles One of the main questions in the study of friction behavior of materials is "Where" and "How" contacting materials accommodate relative motion. This problem has been recently discussed by Godet and colleagues [ 13-15]. Two modes of accommodation will be considered here: shear and roll formation modes. For friction with lubricants including layered solid lubricant powder, velocity accommodation occurs due to the weak van der Waals forces operating between layers, which leads to easy shear of the films in the "third body". The accommodation of friction pair with solid lubricant can occur due to intrafilm flow, interface or interfilm sliding [6]. Sliding tests between a steel ball and an MoS2 - coated steel flat showed that some MoS2 are transferred to the steel ball [6]. The transfer of materials was also observed both on the surface of the flat and the ball in contact with WS2 platelet powder. Thus the transfer of "third body" material alludes to the fact that interfilm sliding between the adhered films is the dominant mechanism of accommodation of relative motion. Low friction is determined by low interplanar shear strength of platelet solid lubricants. It is reasonable to suppose that the tribological properties of IF- WS2 powder can not be controlled by easy shear of the atomic layers as are attributed to

MoS2 and WS2 platelets [ 11-12]. The tribological benefits of the IFs can be probably assigned to a number of factors. The particle size of the IFs, typically > 100 nm, is sufficient to prevent asperity contact between the mating surfaces. This, taken together with their round shape, opens the possibility for rolling friction, so that rolling is a significant mode of lubrication with IF. It may be the other friction mechanisms participate also in the contact with IF. We have not the straight confirmations of rolling friction. Although indirect, the following evidence of rolling mechanism points to this conclusion: 1. The friction coefficient in contact with round IF nanoparticles is lower than with platelets. 2. The round shape of the nanoparticles is preserved after the wear tests in a definite load range. 3. No material transfer to the mating surfaces is observed in contact with IF. 4. Lowered adhesion between the SFM tip and the surface with IF nanoparticles is observed. Ideally, the spherical shape of IF opens the possibility for an effective rolling friction mechanism. The hollow cage structure of the IF imparts a high elasticity which augments their resilience over a wide loading range. However the discommensurations between the regions of good lattice match observed in friction experiments with IF, decrease resilience and lead to plastic deformation (an ovoid shape) and finally to their destruction. It is expected that smaller (ca. 30 nm) and more spherical IF nanoparticles will exhibit superior rolling. In this case mainly a roll mode will provide velocity accommodation. Absence of transfer as is typically observed with platelets confirms the dominant roll mode in contact with IF. No clumping and compression of IF in the wear track attests to their lower tendency to stick to the substrate, or to one another due to the absence of dangling bonds (edge effects), decrease the adhesion and thus facilitates the rolling effect. Different lubrication mechanisms may be obtained under friction in a wide range of loads and sliding velocities. Boundary lubrication is of great interest in engineering practice. Surfaces lubricated with boundary films have friction coefficients in the range 0.05-0.15 [ 1]. One may speculate that in our case, when the friction coefficient is 0.03-0.08 with appreciable wear of the contacting surfaces, the

572

dominant mechanism of lubrication is boundary lubrication. The thickness of the lubricant film usually varies from about 0.01 ~tm up to the size of the surface asperities at heavy loads (0.5 ~tm in our case, for example). Thus boundary lubrication can be obtained by rolling of one layer of nanoparticles or due to internal friction between rolled nanoparticles. Plowing tracks on the surface of flat in contact with WS2 platelets, (Fig. 2) indicates thicker lubricant film in comparing to contact with IF nanoparticles. Thus in the case of contact with IF nanoparticles, the velocity accommodates only by the rolling mode in third body. In this case, the third -body bulk varies at less than 10-7m, and the low friction will be obtained by high resilience and chemical stability of IF. The mechanisms of velocity accommodation were developed for dry friction and for thick film (hydrodynamic) lubrication (TFL). The roll mode was found during dry friction with diameter of the order of 30~tm. Friction with IF occurs on other scale level when "third body" is the thickness of boundary lubrication. Concerning the IF nanoparticles rolling mode determine friction and wear in the contact. 4.2 Tribochemistry of contact. Low friction Chemical effects play also an important role in wear protection by solid lubricants. The chemical reactions that are relevant to wear of platelet materials occur predominantly at the prismatic edges (llc), where reactive dangling bonds exist. The presence of unsaturated or dangling bonds in metal dichalcogenides leads to oxidation of the surface in the surrounding environment, especially at elevated temperatures which may occur as a result of friction. For instance, a switch from an environment of dry nitrogen to humid air led to an increase of the friction coefficient for 2H-WS2 from 0.03-0.04 to 0.15-0.20 and a decrease in its endurance against oxidation by several orders of magnitude [ 18]. The present XPS analysis confirms the slow oxidation of IF powder and the wear track as opposed to the relatively fast oxidation when 2H platelets were used. The absence of dangling bonds, leading to low adhesion, may therefore be one of the prime advantages of IF nanoparticles over the crystalline platelet (2H) particles for reduction of friction and wear. It is to be noted that as the 2H platelets are burnished and ground during the wear tests, their diminished sizes lead to higher reactivity and

appreciably lower oxidation temperatures. Conversely, the chemical stability and rolling friction of IF will provide low friction and high longevity of the new nanolubricant. Conclusions 1. IF-WS2 nanoparticles appear to have excellent tribological properties in comparison to typical MoS2 and WS2 platelets. Deformation and destruction of IF nanoparticles were significantly lower than for the platelets. The main advantages of IF nanoparticles lies in their round shape and the absence of dangling bonds. 2. No transfer, clumping and compression of IF particles was observed at the mating surfaces. Oxidation of the IF particles and wear track size were much less than with solid lubricants made of platelets of the same chemical compound (WS2). 3. Velocity accommodation modes under friction with solid lubricant powders were considered. 4. The main lubricant mechanism in contact with IF nanoparticles is apparently rolling friction. At the third-body contact with IF nanoparticles, the velocity accommodates due to rolling of IF nanoparticles. Acknowledgment This research was partially supported by the UK-Israel Binational S&T Foundation and ACSPRF (USA). References 1. 1. F.P. Bowden, and D. Tabor, The Friction and Lubrication of Solids, Parts I, II. Oxford University Press, London, 1964. 2. B.Bushan, and B. K. Gupta, Handbook of Tribology, McGraw Hill, Inc., New York, 1991. 3. A.L. Black, R.W. Dunster, and J.V. Sanders, Wear, 13 (1969) 119. 4. J. Gansheimerand and R. Holinsky, Wear, 19(1972)439. 5. F.P. Bowden and D. Tabor, Friction: An Introduction to Tribology 91, Anchor, Garden City, New York, 1973. 6. I.L. Singer, in I.L Singer, and. H.M. Polock (eds.), Fundamentals of Friction : Macroscopic and Microscopic Processes, Kluwer, Dordrecht, 1992.

573

7.

B. Bhushan, B.K. Gupta, G.W.Van Cleef, C. Capp, and J.V. Coe, Appl. Phys. Lett., 62 (1993) 3253. 8. S.E. Campbell, G. Luengo, V.I. Srdanov, F. Wudi and J.N. Israelashvili, Nature, 382 (1996) 520. 9. P.J. Blau and C.E. Haberlin, Thin Solid Films, 219 (1992) 129. 10. R. Tenne, L Margulis, M. Genut, and G.Hodes, Nature, 360 (1992) 444. 11. Y. Feldman, E. Waserman, D.J. Srolovitz, and R. Tenne, Science, 267 (1995) 222. 12. L. Rapoport, Yu Bilik, M. Homyonfer, S.R. Cohen, and R. Tenne, Nature, 387 (1997) 791. 13. M. Godet, Wear, 100 (1984) 437. 14. Y. Berthier, M. Brendl6 and M. Godet, STLE Tribol. Trans., 32 (1989)490. 15. Y. Berthier, L. Vincent and M. Godet, Wear, 125 (1988) 25. 16. Y. Feldman, G.L. Frey, M. Homyonfer, V. Lyakhovitskaya, L. Margulis, H. Cohen, G. Hodes, J.L. Hutchinson, and R. Tenne, J. Am. Chem. Soc., 117 (1996) 5362. 17. E. Rabinovicz,, Product Eng., 19 (1958) 31. 18. S.V. Prasad, and J.S. Zabinski, J. Mater. Sci. Lett., 11 (1993) 1413.

This Page Intentionally Left Blank

SESSION XV LUBRICANTS

Chairman •

Professor H.A. Spikes

Paper XV (i)

Choking of Flow Restrictor Caused by CalciumDetergent in Lubricating Oil

Paper XV (ii)

IR Spectrocscopic Analysis of Grease Lubricant Films in Rolling Contacts

Paper XV (iii)

Service Life and Lubrication Conditions of Different Grease Types in High-Speed Rolling Bearings

Paper XV (iv)

The Inclusion of Lubricant Shear Thinning in Journal Bearing Models

Paper XV (v)

French Contribution to the Study of Lubrication, Oiliness, Molecular Influences. Application to Watch Lubrication

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

577

C h o k i n g of F l o w R e s t r i c t o r C a u s e d b y C a l c i u m - D e t e r g e n t

i n L u b r i c a t i n g Oil.

A. Y a n o , S. W a t a n a b e a, T. O m u r a b a n d K. S a k i c a Nagasaki Research & Development Center, Mitsubishi Heavy Industries, Ltd., 5-717-1, Fukahori-machi, Nagasaki 851-0392, Japan b Nagasaki Shipyard & Machinery Works, Mitsubishi Heavy Industries, Ltd., 1-1, Akunoura-machi, Nagasaki 850-0063, J a p a n c Department of Mechanical Engineering, Kyusyu Kyoritsu University, 1-8, Jiyugaoka, Yahatanishi-ku, Kitakyusyu-shi, Fukuoka 807-0867, Japan Under a lubricating oil flow with an average velocity 15~ 50m/s in flow restrictors in hydrostatic bearings, we found out a phenomenon that 1 ~ 5 ,u m particles of calcium carbonate are deposited on the inside of the restrictor. The effects of calcium-detergent and water in oil on this phenomenon were examined. The relationship between the flow velocity and the position of deposition was also examined. The process of this phenomenon could be explained experimentally as being closely related to the streaming electrification which occurs at the interface between lubricating oil and the restrictor.

1. I N T R O D U C T I O N

in Figure 1 (b) does not occur. The choking shown in Figures 1 (a)and(b)

Flow restrictors in hydrostatic bearings are occasionally choked with c o n t a m i n a n t solid

occurs mechanically at the inlet of the flow restrictor. However, we found out a phenom-

particles in lubricating oil. Both larger and s m a l l e r particles t h a n the d i a m e t e r of the

enon that 1 ~--5/~ m particles are deposited on the inside of the restrictor under a lubricating

restrictor can cause choking as shown in Figures 1 (a)and(b). The choking shown in Figure

oil flow with an average velocity 15 ~ 50m/s.

1 (a) is quite obvious. The other case with the smaller solid particles, as shown in Figure 1

The size ratio of the particles to a diameter of the restrictor was considerably low, about 1/200 1/1000.

(b) has been discussed by Hwang et al [1-4].

The deposited solid particles consisted of cal-

They have proposed a choking process that con-

cium carbonate originating from calcium-deter-

t a m i n a n t solid particles become larger due to

gent used as a lubricant additive, but was de-

contact and cohesion with each other while

graded by the addition of water. The degrada-

passing through the flow restrictor, and they

tion of calcium-detergent caused by water, and

reported an experimental result that if the solid

the choking of a suction filter, have been re-

particles are under three-hundredths of the size of the restrictor diameter, the choking shown

ported by Tamura et al. [5], Sugiura et al. [6], Overton et al. [7], Isobe [8], Hikosaka [9], Inoue

578

Table 1

FIo

Typical characteristics of test oils A and B

mm2/s

(a) Mechanical choking(Dp>D)

Flow

A

B

103 11.4

93.4 11.0

15 -6,100

0.23 9

Oil kinematic viscosity,

4o°C lo0oc

TBN, mgKOH/g TAN, mgKOH/g Ca conc., ppm

and B were used as well as oils C and D, which contain 30wt% w a t e r in oils A and B, respec(b) Mechanical choking(Dp< D)

tively. To prepare oils C and D, thorough stirring was carried out at a t e m p e r a t u r e of 60°C.

Flow

2.2. S h a p e of flow r e s t r i c t o r s Figure 2 illustrates shapes and sizes of the (c) Deposit along the inside surface(Dp




! r

. .' . .ii .

\

L_

4. S T R E A M I N G E L E C T R I F I C A T I O N MEA.

!

O9

/

I:

:

:

,3.75 I

:

,/

I L4()

//~

Both inlet and inside --H FF! Inlet only I I -Fill F'] No deposition @ -1--I ( • Velocity measurement) ]

,Ill

1 Oil supply pressure,

1

I

MPa

J I lllJI

10

particles to move them towards the metal sur-

Figure 9. Plots of the positions deposited rela-

face in fluid, such as van der Waals force, elec-

tive to oil supply p r e s s u r e vs. average flow

trostatic force, magnetic force, thermal migra-

velocity. ~L0.5, 3.75, 40' Length of restrictor~

582

Therefore, it can be reasonable to infer that the

can be expressed by:

deposition phenomenon is closely related to the s t r e a m i n g electrification which occurs at the interface between oil and the restrictor, and t h a t particles of calcium carbonate adhere to the inside surface of the restrictor by electrostatic attraction. The experimental results of s t r e a m i n g electrification at the flow restrictor

V = V0 exp(-t / CR)

(1)

where V: terminal potential (V), Vo: initial terminal potential (V), t: time (s), C: capacitance (F) and R: resistance ( f2 ). If V o is known, the quantity of electricity Q (C) can be found from: Q = c y0

(2)

are given in the following sections.

v 0 was obtained by solving the simultaneous

4.1. M e t h o d o f m e a s u r e m e n t

Magnitude of s t r e a m i n g electrification was

equations with Eq.(1) from two point data on the discharge curve, and f u r t h e r m o r e , calibrated by a calibration curve which was ob-

m e a s u r e d for fluxed oil t h r o u g h t h e flow restrictor, b e c a u s e its m e a s u r e m e n t at the restrictor metal could be impaired by neutralization of electrical charges due to particle depo-

tained by giving a known quantity of electricity to the condenser. The electrostatic capacity of the oil vessel was ignored because it was too small.

sition. The electrical circuit is schematically shown in Figure 10. First after discharges from a condenser and an oil vessel, a certain amount of fluxed oil is placed into the oil vessel with switch S1 closed and switch $2 opened. Subsequently, w h e n switch $2 is closed w i t h S1 opened, charges stored in the condenser are released. Electrical potential change during this discharge was recorded with a recorder. The change of the terminal potential with time

4.2. R e s u l t s o f m e a s u r e m e n t

Firstly in turbine oil(40°C, 30mmVs) without any additives, the relationship between the average velocity and the quantity of electricity in fluxed oil is shown in Figure 11. This fluxed oil was positively electrified and its quantity of electricity tended to increase with increasing velocity. This tendency d o e s n o t contradict a

0.10

•- ~ u.u~,, ,,,, f:

LFIow .~A

restrictor

._o

_.e ~E

Oil f f _ A9.2MQ ~/~ I

J Amplifier J Recorder

S1 T 0.25,uF

E

,~o

Figure 10. Electric circuit for s t r e a m i n g electrification m e a s u r e m e n t .

//

0.06

0

.~'~~.~ 0.04-

0

i

y

i

20

i

I

40

i

Averageflowvelocity. m807s I

7~T

_

I

I

60 I

I

I

100

I

0.20.5 1 2 3 4 5 6 Oil supply pressure, MPa Figure 11. Relation between average flow velocity and quantity of electricity in fluxed oil.

583

previous knowledge that the streaming electrification increases exponentially with velocity [20]. Subsequently, m e a s u r e m e n t was conducted on oil sample C which poses the problem of deposition, to measure the quantity of electricity in its fluxed oil due to changes of the average velocity, under test condition undeposited immediately after the test r u n and the condition deposited all over the inside of the restrictor after 5-hour r u n at 2MPa.

The r e s u l t s are

shown in Figure 12. Change of the quantity of

0.05 ," .m

I

0.04

'-....

._O,E~ 0.03

I

Oil sample A

~

Oil sample C

0

"~ O

0.02

.~"6

=x

O=

\ r-'-""-

.-

0.01

=

~ P

0 -0.01

- ~""-,.~ L ,

0

,F

';

,

1

2

3 Time,

,

,

4 hour

|

5

|

6

Figure 13. Plots of q u a n t i t y of electricity in fluxed oil vs. operation time.

electricity in fluxed oil under undeposited condition showed a drooping curve, differing from the case of the nonadditive turbine oil. Simi-

sample A showed a n e a r l y constant value of

larly, a drooping curve was obtained in the case

positive e l e c t r i f i c a t i o n w h e r e a s s a m p l e C

of deposited condition, but as opposed to the

showed shifting from positive to negative elec-

positive charges at all times under undeposited

trification with time passage; a constant value

condition, the fluxed oil under deposited condi-

of negative electrification after 5 hours.

tion showed a unique characteristic that it was charged negatively in a region of average ve-

5. D I S C U S S I O N

locities 15 ~- 45m/s. ity in fluxed oils from oil samples A and C sub-

5.1. D e g r a d a t i o n of c a l c i u m - d e t e r g e n t d u e to w a t e r in oil

jected to 6-hour testing at the oil supply pres-

The deposition test results as listed in Table

s u r e of 2 M P a are s h o w n in F i g u r e 13. Oil

2 to examine the effects of calcium-detergent

Changes with time of the quantity of electric-

and water in oil have already shown t h a t cal0.14 E >.,

0.12

°{ •.E= 0

_.e o

~E

"5

i

- ~

\

0.08

i

i

• " Under undeposit - - • " Under deposit

1

_.

0.10

I

cium-detergent and water are necessary for the

0.06

1

x,.

T.V. Liston [21] has reported that the calcium-

/

\

. 0.04

deposition to occur. detergent consists of super fine particles, having a micelle structure as shown in Figure 14

-.-I"

in its sulfonate system. This means t h a t par-

c "~ 0.02

-.~

=x

O=

ticles of calcium carbonate are stably dispersed

0 -0.02

.

0 i

i

00.2

in oil, surrounded by alkylbenzene sulfonic acid.

. . . . . . 10 20 30 40 50 60 70 Average flow velocity, m / s 01.5 Oil

j

i

I

1 2 3 supply pressure,

J

4 MPa

80 I

5

On the other hand, calcium carbonate particles cohere together and become larger to several microns when w a t e r is contaminated into lu-

Figure 12. Relation between q u a n t i t y of elec-

bricating oil containing calcium-detergent. This

tricity in fluxed oil and average flow velocity.

phenomenon has already been reported in many

584

+ @--,. ® + nCaCO3-MSO3R H20

nCaCO 3 H20-MSO3R ......

(1)

......

(2)

A , d l L

nCaCO 3

www~z~-

SO3 (CAC03)150 03S-,~,~v~,~,~v

sS,cP cPeo,s

j Figure 14. Schematic micelle structure of calcium sulfonates Reprinted from:T. V. Liston, STLE lubrication engineering, 5(1992)389.

publications [5-12]. In this study, we confirmed presence of degraded particles of calcium carbonate, approximately 0.1 - 2/~ m as shown in Figure 5, by separating oil centrifugally. Regarding the degradation mechanism of calcium carbonate, it is inferred that alkylbenzene sulfonic acid is consumed to form water in oil emulsion as shown in Figure 15, causing particles of calcium carbonate to expose themselves, which in turn, causes those particles to co-agglomerate and degrade. From the inside of the flow restrictor as shown in Figure 7, calcium carbonate particles measuring about 1-~ 5/1 m were observed and their particle sizes are very similar to those of degraded particles of calcium carbonate obtained from the centrifugal separation of oil contaminated with water in Figure 5. It is, therefore, reasonable to infer that if oil containing calcium-detergent is contaminated with

nCaCO 3

mCaCO 3

Figure 15. Degradation process of calcium-detergent.

water, degraded particles of calcium carbonate are formed in oil and that such degraded particles are deposited on the inside of the flow restrictor, eventually leading to its choking thereby.

5.2. Streaming electrification and choking process The results of the measured electrifications as shown in Chapter 4 have already shown that fluxed oil passed through a flow restrictor has been electrified. According to the law of electrical neutralization, it should be thought that the flow restrictor must be electrified to an opposite charge in the same quantity of electricity, compared with those of the fluxed oil. Regarding deposition of calcium carbonate, it is, therefore, hypothesized that degraded particles of calcium carbonate which have grown in oil adhere electrically to the flow restrictor charged with streaming electrification. According to this hypothesis, the process explanation of choking of the flow restrictor and why the deposition to the inside of the flow restrictor should be limited to a velocity range of the average velocity 15 ~ 50m/s will be discussed in the following section.

585

As shown in Figure 13 for oil sample C, elec-

tively electrified, whereas after 5-hour test run

trification of its fluxed oil shifted from the positive to the negative charge with time passage,

where the overall inside of the flow restrictor has been covered with calcium carbonate, oil

showing a constant value of negative electrifi-

negatively electrified flows out and thereby,

cation after 5 hours. F u r t h e r m o r e , as shown

calcium carbonate deposited over the internal

in F i g u r e 6, t h e overall inside of t h e flow restrictor was covered with calcium carbonate

surface of the restrictor has been positively electrified.

after 5 hours. These facts signify t h a t the re-

In Figure 13, electrification indicated zero

lationship between deposition of calcium car-

after 3 hours, and it is inferred t h a t it was

bonate and electrification of the fluxed oil fol-

caused by co-existence in the interface of the

lows a process as shown in Figure 16; i.e. in an

metal surface and the surface of calcium car-

initial stage with no deposition of calcium carbonate, oil positively electrified flows out and

bonate. Although s t r e a m i n g electrifications showing opposite charges may be occurring in

thereby, the metal of the flow restrictor is nega-

respective interfaces as viewed microscopically, it is inferred macroscopically that electrical neutralization can take place with the fluxed oil not electrified. Situation where the metal sur-

~"

~~van derWaalsforce Fluxedoil#@ Positivelycharged "~:i:"

"::i::'

:':':':':':':'::

":i::'

':i::"

":i::"

"i::'

":

face and the surface of calcium carbonate coexist in the interface can be recognized in the observation results of an initial period of the deposition as shown in Figure 8.

:":':':':':':':':':':':':':':':':':':':';';'~'r;';';';'r~';';';'i:

Next, average velocities 15 - 50m/s where deposition of calcium carbonate occurs on the

![iiii::i!iiiiiiiiiiiiiiiiiiiii !i:iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiji ii Fluxedoil -~Uncharged iiiiiiiiNiHi!!iiii!iiiiiiiiilQi !iiiiiiiiii!i!iii!iiiiiiii }!!i!iiii!!i•!H!iii•i!ii•!i!!!!!Hii!ii!i!!!!i!i!!!•iiiii•!}!!!i!!i•i•i•i!!!!!!!!H!}

inside of the flow restrictor as shown in Figure 9, nearly correspond to average velocities 1 5 -

45m/s which show negative electrification in

Figure 12 in relation to changes of streaming electrification by change of the oil supply pressure under the test condition of deposited cal-

cium carbonate. If it is considered in addition that electrification of the fluxed oil shifts from

•~l--lwl~ Ii1i1!i•i•i•!•i•!ii•i!iiifii:!JiiiiFluxed ijJi!l•Iioili1i!(~~ iii•i•i•!•iIii•iiiii••!i•ii!i!iii•

the positive to the negative charge, accompa-

~

~

~'~rElectrostaticforce 1- -

i ~--------:~--.', = ' ,

~

"-

liii!iiiii!iii!ii!iii!ili!iiiili!iiiii!iiiiiii[iiii!iJiiiiiiNegatively iJiiii charged Figure 16.

The relationship between deposi-

tion of calcium carbonate and electrification of fluxed oil.

nied with progress of deposition of calcium carbonate, as shown in Figure 13, it should be

thought t h a t the surface of calcium carbonate must be positively electrified for its deposition to progress. In the present stage, it still remains unknown w h e t h e r colloidal particles of calcium carbonate are electrified positively or negatively, but

586

if it is assumed t h a t they are negatively elec-

6. C O N C L U S I O N S

trified, progress of their deposition can be explained by a s s u m i n g t h a t such colloidal par-

We found out a phenomenon that 1 ~ 5 , u m

ticles adhere to the surface of deposited calcium

particles of calcium carbonate are deposited on

carbonate positively electrified, caused by the

the inside of flow restrictors under a lubricat-

electrostatic attraction. However, because the

ing oil flow with an average velocity 1 5 - 5 0 m /

metal of the flow restrictor is negatively elec-

s in flow restrictors in hydrostatic bearings. In

trified in the initial stage of its operation, the following inference can be given for the reason why calcium carbonate particles assumed for

this work, the effects of calcium-detergent and water in oil on this phenomenon were examined and the relationship between the flow ve-

its negative electrification can first adhere to

locity and the position of deposition was illus-

this negatively charged metal surface. That is,

trated. Furthermore, we discussed the chok-

when one checks electrification of the fluxed oil

ing process which could be explained experi-

under undeposited calcium carbonate as shown

mentally as being closely related to the stream-

in Figure 12, it is known that its electrification

ing electrification which occurs at the interface

takes a m i n i m u m value in the range of aver-

between oil and the restrictor. From the fore-

age velocities 15 --- 50m/s where calcium car-

going results, the following conclusions could

bonate starts to be deposited on the inside of smallest value of the streaming electrification

be drawn. (1) The deposited substance is calcium carbonate, and degraded particles of calcium carbon-

in the flow restrictor metal. It is, therefore,

ate produced by contaminating a lubricant oil

inferred t h a t the electrostatic repulsion be-

containing calcium-detergent with water are re-

comes small in this velocity range, whereas the

lated to their deposition.

the flow restrictor, which corresponds to the

van der Waals attraction can govern more domi-

(2) Deposition of calcium carbonate particles on

n a n t l y t h a n the electrostatic repulsion, lead-

the inside of the restrictor occurs in a range of

ing to a first deposition of calcium carbonate

the average velocities approximately

thereon. It is, however, inferred t h a t inhibi-

50m/s. (3) It is inferred t h a t the initial deposition of

tion of its deposition can work due to rapid flow

15-

at velocities exceeding 50m/s. New particles tend to be preferentially depos-

calcium carbonate particles on the restrictor is

ited onto a nucleus of an initial deposition al-

new deposition on the deposited calcium car-

ready pointed out as the feature of an initial

bonate grows due to the electrostatic attraction

deposition state and this is probably because

caused by streaming electrification.

caused by the van der Waals attraction whereas

the electrostatic attraction acting between flowing calcium carbonate particles and deposited

REFERENCES

calcium carbonate particles can be stronger

1.T.Y.Hwang and A.Yamaguchi, J. of the Japan

t h a n the van der Waals attraction acting be-

Hydraulics and Pneumatics

tween the calcium carbonate particles and the

22,3(1991)348.

restrictor metal.

Society,

2.T.Y.Hwang and A.Yamaguchi, ibid., 24,

1(1993)138.

587

3.T.Y.Hwang and A.Yamaguchi, ibid., 24, 6(1993)716. 4.A.Yamaguchi and T.Y.Hwang, ibid., 27, 3(1996)410. 5.K.Tamura, S.Hatami, K.Ishii, J. Japan Soc. Lubr. Eng., 27, 5(1982)308. 6.K.Sugiura, N.Isobe, T.Mito, Nisseki Technical Rev., 26, 5( 1984)310. 7.R.Overton and W.N.Rogers, SAE Paper 840344(1984). 8.N.Isobe, Nisseki Technical Rev., 27, 6(1985)332. 9.S.Hikosaka, J. Japan Soc. Lubr. Eng., 32, 11(1987)797. 10.K.Inoue and Y.Nose, STLE Trans., 31, 1(1988)76. 11.K.Inoue, T.Mito and K.Yumoto, 33th Proc. Japan Soc. of Lubr. Eng.(1989)69. 12.H.Imamura, Marine Diesel Lubrication, Sankaido(1995)165.

13.Ed. by The Japan Petroleum Institute, Handbook of Electric I n s u l a t i n g Oil, Kodansha(1987)93. 14.Ed. by The Society of Polymer Science Japan, Handbook of Static Electrification, Chijinshokan Co.(1971)86. 15.A.Kitahara and A.Watanabe, Kaimen Denki Gensho, Kyoritsu Shuppan co.(1972)117. 16.K.Asano, Proceedings of the Institute of Electrostatics Japan, 2, 3(1978)150. 17.M.Honda, M.Ikeda and H.Okubo, ibid., 3, 5(1979)258. 18.S.Watanabe, A.Ohashi and M.Ito, ibid., 4, 2(1980)109. 19.H.Suga, T.Isii, T.Miyamoto and N.Yamada, Nisseki Technical Rev., 23, 2(1981)73. 20.S.Watanabe, Proceedings of the Institute of Electrostatics Japan, 10, 6( 1986)401. 21.T.V.Liston, STLE Lubrication Engineering, May(1992)389.

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

589

IR Spectroscopic Analysis of Grease Lubricant Films in Rolling Contacts S. Hurley and P.M. Cann Tribology Section, Department of Mechanical Engineering Imperial College of Science, Technology & Medicine London SW7 2BX

Abstract

In this paper, the composition of grease lubricant films formed in rolling contacts has been studied using IR reflection spectroscopy. A simple ball-on-fiat test arrangement has been used. Greases are two-phase lubricants composed, primarily, of a thickener dispersed in a basestock. The lubricant film in the contact region however, does not necessarily reflect the bulk composition, but will depend critically on the mechanism of lubricant supply to the contact. If flow of bulk grease into the contact occurs then both thickener and base oil will be present. The grease structure however will be heavily degraded by the very high local shear stresses as it passes through the contact. If the contact is starved of bulk flow then film generation is due to local base oil flow from the grease reservoir. In this case, the separating film is primarily base oil. Thus the composition of the film depends on the lubricant supply and is likely to change with operating condition and time. In this work, the composition of grease films under both fully flooded and starved conditions has been studied using IR reflectance spectroscopy. This technique provides information on the concentration and distribution of the grease components both within the track and in the reservoir at the sides. Under fully flooded conditions both thickener and base oil are present in the inlet, although the thickener concentration varies depending on speed and proximity to the Hertzian zone. Under starved conditions there is an initial deposition of bulk grease in the track as fresh grease is overrolled at the start of the experiment. As the test continues however, the grease structure is broken down and base oil is expelled from the track. There is also evidence of shear degradation and oxidation of the thickener within the track. The condition of the grease close to the track also changes as the test proceeds and there are local thickener concentration changes in this region. These findings are discussed in the light of current theories of grease lubrication. 1. GREASE LUBRICANT FILMS IN ROLLING CONTACTS

Lubrication performance is essentially determined by the properties of the film formed in the contact region. The physical properties, chemical composition and thickness will determine the levels of friction and wear, and ultimately component life. In this paper the composition of lubricating films formed by greases in rolling contacts is examined. Although there have been many studies devoted to the analysis of films formed by liquid lubricant and additive systems, there is very little work in the literature where film formation by greases is considered.

Grease is a two-phase lubricant comprised primarily of a thickener physically and chemically dispersed in a basestock. However, the lubricant film in the contact region will not necessarily reflect the bulk composition but will depend critically on the mechanism of lubricant supply to the contact. Two supply regimes are identified in this work: fully flooded and starved. In the fully flooded condition the inlet is considered completely filled with lubricant. In the starved regime there is a limited amount of lubricant present and the inlet meniscus is close to, or at, the Hertzian circle. Under fully flooded conditions if flow of bulk grease into the inlet occurs then both thickener and base oil will be present. The grease structure

590

however will be heavily degraded by passage through the contact and it is likely that some deposition of thickener occurs in the rolled track. For the fully flooded condition film thickness will scale with the usual EHL criteria of inlet viscosity and rolling speed (1). If inlet flow is not maintained then the rules governing film formation are different. Under starved conditions base oil is thought to bleed out of the grease reservoir at the side of the track, replenishing the contact (2). This model implies that the film is composed of base oil alone. However, recent work has shown that the film composition is more complex and that both thickener and base oil are present (3). The thickener forms a thin (~5-10 nm) residual film on the metal surface which is augmented by a hydrodynamically-generated film (3). The operating requirements for bearing greases are low friction with a relatively long lubrication life. The ideal condition is therefore semi-starved as the friction losses and thermal effects are minimised. The lubricant film however must be sufficient to prevent surface damage and thus in this regime the thin film properties will be increasingly important in determining performance. Deposition of the thickener to form thin residual films which act as antiwear or boundary layers is one possible mechanism (4) and this has been observed with urea greases (5). An alternative mechanism is the formation of high viscosity layers (6) at the surface. Optimisation of the local rheology at the surface might have beneficial effects, particularly in the prevention of damage due to component vibration. The possibility of controlling grease formulation so as to optimise the surface film properties has not been explored as yet. Most of the research into grease has been concerned with their bulk rheologieal behaviour. There is very little published work concerning the properties of the grease lubricant films formed under different contact conditions. Therefore, the aims of the study were: • to develop techniques to characterise grease lubricating films • to apply these techniques to establish the chemical composition and physical properties of grease films / • to study film composition under fully flooded and starved conditions.

IR reflectance spectroscopy has been used to charactefise the grease films both in and out of contact. IR spectroscopy is ideally suited to the examination of greases as it can distinguish between the thickener and base oil phases and identify new organic species. IR transmission spectroscopy is routinely used to examine grease during manufacture and as samples from failed beatings. There is thus a large reference body of literature for comparison of results. This technique is also useful for providing information on structural changes such as alignment or destruction of soap thickener fibres (7). 2. EXPERIMENTAL PROGRAMME 2.1. Film thickness in rolling contacts

The first requirement was measure film thickness under both fully flooded and starved conditions. Once the lubrication behaviour had been established then IR analysis of the lubricant films could be carried out. In this study, grease film formation in a rolling point contact was measured for a ball on flat configuration using a high-resolution optical imerferometry technique (1)(8). The contact is formed by a loaded steel ball (diameter 19ram) rolling against a silica-coated glass disc. The thin film interferometry technique gives improved thickness resolution (1 nm) and minimum film thickness detection (1 rim) compared to the conventional methods. Two film thickness test procedures were used. All tests were carried out at 25°C: (i) Fully flooded - film thickness was measured with increasing speed, a small channelling device was used to push the overrolled grease back into the track. (ii) Starved - film thickness change with time was measured at constant speed. A single charge of grease was injected into the rolling track at the start of the test. 2.2 Characterisation of grease films in and out of contact

Film thickness measurements were carried out on the greases under fully flooded and starved conditions. In a corresponding series of tests the composition of the films formed under similar conditions was analysed by IR spectroscopy. IR

591

reflection-absorption techniques were used to analyse grease films both in and out of contact. Specular reflectance micro-spectroscopy was used to determine the composition and distribution of the grease components in the rolled track on a steel surface. A second method whereby IR reflection spectra were taken directly from the rolling contact was also developed to study the composition of the inlet and Hertzian region. These techniques are described in more detail below.

2.2.1 Out-of-contact analysis In a separate series of tests rolled grease fdms were prepared on polished steel discs and then analysed by IR reflectance spectroscopy. An IR microscope (Spectratech) coupled to a FTIR spectrometer (Perkin Elmer 1740) was used to take single reflection spectra from small areas (- 150 l.tm diameter) of the grease film from in and around the rolled track. A simplified diagram of this technique is shown in Figure 1. Spectra were taken with 200 scans at a resolution of 8cm 1

spectrometer

I

rolled grease track

Figure 1 IR reflectance sampling from rolled track The grease films were prepared on the rolling contact rig but in this case the glass disc was replaced by a polished steel disc. The working tests were carried out at constant rolling speeds, typically 0.1ms 1 and 1.0ms "1. At the start of each test approximately 1 ml grease was injected as an even layer around the rolling track. The ball and disc motors were then set to the desired speed and a load of 20N applied. Previous film thickness tests (see Figure 4) have shown that under these conditions, the film thickness will decrease with time The tests were stopped at intervals, the disc removed for analysis and then replaced, with the grease film

undisturbed, allowing the test to be continued. The width of the track was approximately 280 lain. Spectra were taken at various positions: in the track, at the edge of the track and increasingly further away (see Figure 5 below).

2.2.2 In-contact analysis A second technique whereby IR spectra are taken directly from the operating EHL contact was also used (7). In this case an 1R transparent window was used instead of the glass disc. The FTIR microscope was used to take spectra from small areas in and around the contact. In earlier work the technique was limited to sliding contacts and a diamond window (3mm diameter) was used as the (stationary) counterface to the steel ball. In this study the technique has been applied for the first time to rolling contacts and a new test rig has been developed. One of the problems with this configuration is that a large IR transparent rotating disc is required and in this case a 10cm diameter CaF2 window was used. A diagram of the technique is shown in Figure 2. This approach means that it is now possible to monitor grease lubricant composition both in the starved and fully flooded regimes. In the fully flooded regime, the film composition in the contact and inlet regions has been studied. In the starved regime the film thickness in the contact is generally too low to be detected and there is little lubricant in the inlet. However it has been observed that once rolling has been halted lubricant flows out from the grease reservoir and forms a meniscus around the stationary Hertzian contact. It is likely that this reflow also occurs during rolling and thus provides a continual flow of lubricant into the track. By stopping the test rig and taking spectra from the reformed meniscus it is possible to analyse the composition of the lubricant replenishing the track under starved conditions. 2.3. Test Greases A set of four simple additive-flee model greases were used. These were lithium hydroxystearate: (CH3 (CH2)5 CHOH(CH2)10COOLi) and a tetraurea (general formula R1-NHCONH-R-NHCONH-R2NHCONH-R-NHCONH-R3 where R is an alkyl group), both containing 7 and 14 % w/w thickener. These greases had the same mineral base oil (viscosity @ 40°C 200cSt.)

592

,/sample areas sample area for results in Figure 9

optical view

FTIR ' ] microscope

IR transparent wi,~A . . . .

,,

, ,,,,,,,

, ,

,,

,

,

,

,

it

,,

,

,

,,

IR spectrum from sample area ste~

at film

Figure 2 IR spectroscopy sampling from the contact region

3. RESULTS AND DISCUSSION 3.1 Film thickness results

Representative, fully flooded results are plotted as log film thickness against log rolling speed in Figure 3 for the 14% lithium hydroxystearate and tetraurea greases at 25°C. For both greases, the overall film thickness is higher than that of the base oil. However, two distinct speed regimes are observed: low speed region where the film thickness is unstable and tends to fluctuate wildly higher speed regime where the film steadily increases, with a log-log film thickness/speed exponent close to 0.7. The instability at low speed is due to the intermittent passage of thickener lumps through the contact distorting the EHL film. Such behaviour is probably one of the origins of grease 'noise' in beatings.

As the rolling speed increases this behaviour lessens and the film in the contact assumes the usual EHL shape. At higher speeds the film increase with increasing speed follows the usual EHL considerations, suggesting that the inlet rheology is essentially Newtonian. This implies that the grease structure has been fully degraded by the greater inlet shear stresses experienced at these speeds and that the grease has effectively reached a constant apparent viscosity. A typical starved test is shown in Figure 4 for the 14 % lithium hydroxystearate grease at 25°C and 0. lms "~. In this case film thickness is plotted against disc revolution (time). At this temperature the inlet is severely starved and film thickness decays steadily throughout the test giving a final thickness which is considerably less than the fully flooded case.

593

uneven residual film (typically 2-60 nm thick) is seen. On either side of the track, the bulk grease reservoir sits with a series of corrugations or 'fingers' reaching towards the rolled track; these are formed by the film cavitating in the exit region. The composition of the track (sample position 1) and at the edge (sample position 2) have been examined later in this paper.

1000

.. ~ ~ W ~ b a s e•.......... 100

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

o,_

,.~ 0

o°j:

O/

........

i//"

oil i ................... ,

lithium hydroxystearate

0

"' .......

0.00

'

'

.

.

.

.

.

.

"

0.01

I"

'

'

0.10

1.00

Rolling speed (ms-l)

Figure 3 Fully flooded film thickness results for the 14% lithium hydroxystearate (open symbol) and tetraurea (closed symbol) greases at. 25°C. Base oil result shown as solid line.

160

Figure 5 Phase contrast microscopy photograph of a rolled grease track. The rolling direction is from fight to left. The rolled track corresponds to the Hertzian width of 280 ~tm.

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

140 ,D D.......................................................... 120 - j ......................................................... o

3.2. IR Spectroscopy Results

~.~ 100 ..............................................................

t 80 .......................................................... ~2 6o ~ 40

3.2.1. Transmission spectra of fresh samples IR transmission spectra (limited wavelength range) are shown for two grease types (7% tetraurea and lithium hydroxystearate) in Figure 6 For the lithium hydroxystearate grease: the absorbances at 1580 and 1560cm "~ arise from the soap thickener. The characteristic double band corresponds to the asymmetric stretching of the carboxyl group (9). Peaks at 2955, 2925, 2850, 1463, 1377 and 720cm "1 are primarily due to the paraffinic base oil, arising from the CH2 and CH3 groups. However, it must be remembered that the hydrocarbon portion of the hydroxystearate thickener will also contribute to these peaks. The CH2 deformation for the pure soap occurs at 1453 cm "~. These assignments are summarised in Table 1 below.

t:K ::i:i:iii:i:ii iii:iiii:iiiiiiiiii i !

0

. . . . . . .

i

.

500 1000 Disc revolution

.

.

.

.

1500

Figure 4 Starved film thickness decay for 14% lithium hydroxystearate grease at 25°C, 0.1 ms "1.

At the end of the test, the rolled grease track can be examined by a low power optical microscope and a photograph of this is shown in Figure 5. Several features should be noted as these are examined in the IR work. In the centre is the rolled track, where an

594

Polyurea thickeners give several characteristic absorption bands and those for the tetraurea are listed in Table 2. Urea thickeners have C=O, NH2 and NH bands similar to those of amides. The C-H bands are similar to those reported above for the lithium hydroxystearate grease. Transmission spectra can be compared directly to those from the reflection and in-contact studies.

Table 1 IR peak listing for lithium hydroxystearate thickener and base oil. Peak position cm

Structure

-1

2955

C-H asymmetric stretch (CH3)

2925

C-H asymmetric stretch (CH2)

2850

C-H symmetric stretch (CH2)

1580

COO asymmetric stretch

1560

COO asymmetric stretch

1463

CH deformation (CH2)

1402

COO symmetric stretch

1377

CH deformation (CH3)

Table 2 lit peak listing for tetraurea thickener. Peak position cm-1 3360-3260

Amide I band (C=O)

1565

.~maide II (C-N and N-H) Amide III (N-C=O & N-H) doublet

CH2 twist and rock in phase (CH2), rocking

720

2

1463 / ~

CH2 ~I C arboxylate CO0- 1578

Amide I

C=O A

Strong N-H stretching

1631

1233 &1302 1310-1175

Structure

1632

1377

~! i i~~~ ~ii~i':~!:~'~ ~!~)~

Amide II ~ C-N N-H '

1650

~i~

1600

1567

1550

1500

1450

A

1400

1350

Figure 6 IR spectra for fresh greases: 7% lithium hydroxystearate (solid) and 7% tetraurea.

em "1 1300

595

3.2.2. In-contact analysis In this study IR spectra were taken from a rolling contact for fully flooded operation. The intemion was to determine the composition of the lubricant erecting the contact under differem speed conditions. Typical spectra are shown for a lithium hydroxystearate (14%) grease in Figure 7. Two speed levels were chosen corresponding to the 'noisy' (low speed) and 'EHL' (high speed) regimes noted in the film thickness work. The thickener content at low speeds is very high, in some cases it is higher than the average value recorded for the bulk grease. This suggests that in this region there is entrainmem of concentrated thickener bundles into the inlet. At higher speeds the concentration of thickener in the inlet region decreases to less than that of the bulk grease, although variations are also observed depending on the distance from the comact. Typically the thickener concentration decreases close to the contact both in the inlet and at the sides. An example of this for a tetraurea grease (7%) is shown in Figure 8. In this case, all the spectra have been normalised to the same value of the 1460 cm "1 band. The urea absorbance increases with distance from the Hertzian contact both in the inlet and at the side of the contact.

t

.

Under heavily starved conditions there is very little lubricant in the inlet so this precludes IR analysis during rolling. The film in the comact was also generally too thin to be detected by this technique. However one observation from the starved studies is that once rolling has been halted lubricant flows from the grease reservoir to reform a meniscus around the contact. This process is due to capillary forces close to the contact and does not occur in the rolled track 'out-of-contact'. It is likely that this process operates during running to provide a local supply of lubricant to the contact. In-contact IR spectra have been taken from the meniscus to identify the composition of this lubricant and an example is shown in Figure 9. Spectra were taken at increasing distances from the stationary contact (this corresponds to increasing reflow time). The lubricant which reflows first is essentially base oil containing very little thickener. This free base oil has been released from the grease close to the track probably through the shear degradation of the thickener structure. With increasing time however, higher viscosity material containing some thickener returns to the track. This behaviour obviously provides a mechanism whereby flee oil and bulk grease can return to the track during periods when a beating is not in operation.

" 1580 i

j

1460

1562 t

¢

• t

1650

1600

1550

1500

1450

cm -1

Figure 7 IR spectra from inlet region for a fully flooded rolling contact at two speeds, ---0.011 ms1, - - - 0.08 ms 1. A spectrum of the bulk grease (14% lithium hydroxystearate) is also shown (solid colour ).

1400

596

Normalised CH: peak

~.~:.~;:~'..~i~;~:.~.-,~ ~!~ ~:i~.:~,~:~!:~ ; ...~ ~:-;~:~i~:.:~i~ ~

A

~|

1650

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

i

. . . .

1600

1550

1500

cm -1

|

.

.

.

.

.

.

'~

.' . . . . .

1450

I'

i

1400

Figure 8 IR spectra taken from the inlet region for tetraurea grease (7%) at 0.1 ms "1. For positions 1 (-~2801xrn) and 2 (--560~tm) from the centre of the contact, above. The bulk transmission spectrum is also shown ( .... ).

1460._

close to contact

"I

A from' Contact' '[

much"further from contact

1581

1377

no thickener present essentially base oil

thickener band at 1581 cm "1 appears

more thickener is present although still less than for the bulk grease

cm

Figure 9 IR spectra from lubricant reflowing into the track once rolling has been stopped. The distance from the contact reflects the length of time it takes for that material to reflow.

597

structure. In this case, thickener-rich particles were deposited in the track during the first few minutes of operation. These were clearly visible in the rolled track using an optical microscope. In Figure 10 spectra are shown of a deposited thickener particle and from the surrounding film. The increased concentration of urea thickener is seen by the intense absorption bands at 1636- 1515 and 1305-1234 cm "1 compared to the 'CH' bands at 1460 and 1377 cm1. The shift of the CH2 band to 1465 cm "1in the particle spectra is also indicative of almost pure urea. The thickener lumps gradually fragment with overrolling, and eventually break down to give a more uniform film. Cavitation patterns, seen within the track area, signify that the film is highly viscous rather than simply a solid layer. The 'high viscosity layer' mechanism for starved grease lubrication was suggested by Scarlett (6) and this result shows that it can be a viable mechanism.

3.2.3. IR reflection spectra from rolled grease films 'out-of-contact' The starved rolling tests show that the grease film decays very rapidly in the first few minutes of running. In a separate series of tests, the glass disc was replaced by a polished steel disc so that IR reflection-absorption spectra could be taken from the rolled track. The test was run in the usual way except the steel disc was removed periodically for analysis. IR spectra were taken from small areas (-150 lxm diameter) from within the rolled track and the 'fingers' at the side (sample positions 1 and 2 in Figure 5). Tests were run at two speed levels: 0.1 and 1.0 m/s. Initially, flesh grease is overrolled in the track. As the test proceeds, the film breaks down and base oil is released. At the lower speed the urea and high concentration lithium hydroxystearate greases were able to maintain a thick film in the track for very long periods. This was particularly seen with the high concentration urea greases which had a very lumpy

1636

1564

1515

1234

A 'thickener bundle' 1465

1305 1459 1410 1377

"1

1700

I

1600

I

1500

I

1400

1183

I

1300

|

1200

1110 "

-

-

cm -~

Figure 10 IR reflectance spectra taken from a 14% tetraurea grease thickener particle deposited in the track ( - ) and the usual film within the track (- - -) 1.0 m/s after 20 seconds running.

598

The lower concentration lithium hydroxystearates tended to decay very quickly giving much thinner residual films. There was also evidence of thickener structure breakdown giving physically or chemically transformed layers. This occurred both within the track and in the grease at the side. Figure 11 shows a series of spectra that have been taken at different times from the track (position 1 in Figure 5). Results showed broadening of the asymmetric carboxyl band at 1580cm1 and gradual disappearance of the corresponding one at 1560cm1 as rolling proceeded. The absorbance of the carboxylate band also increased relative to the CH2 band suggesting that as the grease breaks down in the track, a thickener rich layer is left and base oil is expelled. This free base oil is thus available for reflow, as seen in Figure 9 above, and the formation of a hydrodynamic film during rolling. The CH2 absorption at 1463 cm~ also appears to resolve into two peaks at 1460 and 1465cm"x. One possible explanation for this is that the soap or base oil has been chemically transformed within the track. In this case mechanical degradation of the soap fibres, followed by chemical reaction of the reactive molecular fragments is a more likely option. The 'scissoring' frequency of CH2 groups is very sensitive to the molecular environment. When a CH2 group is adjacent to oxygen atoms this frequency decreases and there is also an increase in intensity (9). Thus one interpretation of the decrease in the deformation frequency observed in the spectra of the rolled track is that oxidation has occurred and acidic products are beginning to form. Alternatively, the second peak may be another CH2 deformation at a decreased frequency from a new chemical species with a shorter hydrocarbon chain. The CH3 absorption at 1378cm"~ decreased in height and gradually increased in frequency, becoming a shoulder of a new peak arising at 1411cm~. This latter peak is due to the CH2 deformation frequency of short chain carboxylic acids such as ethanoic acid (9). This again would suggest that the soap thickener is being physically degraded by the high shear stresses in the contact and that new shorter chain or oxidised species are being formed. The condition of the grease at the side of the track will have an influence on replenishment and IR spectra have been taken from the grease 'fingers' (position 2 in Figure 5) to study thickener

concentration and breakdown (see Figure 12 below). Increasing the speed from 0.1 to 1.0ms"1 increased the rate of track depletion. Initially base oil is expelled from the track but at a later stage thickener is also lost. Thus at the edges of the track the (relative) soap absorbance increased slightly with extended running time. This was also seen in the characteristic shift of the CH2 deformation peak towards the lower frequency of 1453 cml; which is characteristic of the soap. These spectra also exhibited further evidence of chemical degradation. All spectra taken from the edge of the track showed an increase in the absorbance band at 1410cm1 which is associated with short chain acidic species (9) and is taken as an indication of oxidation. There is also further evidence of this: in some of the spectra taken in the high speed tests, a series of overlapping absorption bands appeared between 1630 and 1800cm 1. These are due to C=O stretching of acidic species, particularly ketones (~1700crn"1) aldehydes (-~1710cm"l) and carboxylic acids (>1720cmI). All these effects were only observed in spectra taken in, or close to, the track. In IR spectra taken well away from the edge of the track, the soap ratio decreased and the degradation bands were not present. The lit results from the out-of-contact analysis show that deposition of grease occurs in the track. forming a thickener-rich film. The stability and adherence of such a film could have significant implications for the continued operation of beatings under conditions where a hydrodynamic film is not formed. For instance: when severely starved, during start-up or at low speeds. Thickener films might also help to prevent surface damage through damping of transient effects, for example the low load vibrations that result in false brinelling. IR spectra taken from the films after extended running under starved conditions have shown that degradation of the grease film occurs. Evidence of structural breakdown, concentration changes and oxidation to form acidic species has been found. In the starved regime the conditions within the contact are very severe; in this case films below 20 nm have been measured. It is likely therefore, that the combination of high local shear stresses, thermal effects and the proximity of the steel surface will contribute to the breakdown of the thickener to form oxidised, possibly acidic species. This has implications for oxidative wear of the metal surface.

599

1581

1460

o

t:" I tl |

1465 s

"

I

.

t

•

•

; L.

: -

-1 I-

-

'

."

1561

',

I

/ I :

!

!.';:~

!::"

:

.

"

.

:,

.

.',

•

,-/:-",

.

-/ii _i~ •' / ! ' i

i

1600

\

1550

I

.

i

\

" -

\

l

".

-

:.

:

•

\

:

:

:.

,.. :,... :

I

1500

1450

''"

: ,

:

'/ii !i ki~ i

30 m i n u t e s

1377 i

i

\,,

i

",

:

;

:1 i

...............~

1411

,

.

:-

•

I

.

l'i

:.ll

!'.

I

",.

~

:1:

.,-,

-

•

"

.

;/!

i

/!!'L:..;.

i

,!°

"!"',

k

i

,: .:

:

•

//i

.-

,

.1

,,

•

,,.:

I

1400

7 minutes

X ::

j~

-

."

•

.

45 seconds

.

.

.

5 s e c.o n. d. s.

-

-

I

I

1350

-1

cm

Figure 11 IR spectra from rolled grease track, position 1 in p h o t o g r a p h in Figure 5, 14% lithium hydroxystearate, 25°C, 0.4 m/s.

"

start

......... 1581

30 minutes

, ,/1450

1460 ,'1 i

t

A t

,

1561 it ~

1411

i I • .

~,m

i

s

w 1

• ~ , , P/" ~ •

B

,t

-, ,. ~ .P

'i

. . . . . . . .

1600

i

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

1550

I

.

1500

.

.

.

.

.

.

i. . . . . . . . . . . .

1450

t .......

1400

Figure 12 R e f l e c t a n c e s p e c t r u m 14% lithium hydroxystearate g r e a s e e d g e o f track 1 . 0 m s "l

s

B

I

1350

---

.........

o

t

cm "1

600

4. CONCLUSIONS

ACKNOWLEDGMENTS

The findings from this study are summarised below:

The authors would like to thank the EPSRC and the NLGI Fundamental Research Committee for financial support of this study.

Development of IR analysis methods: - The in-contact IR technique has been extended to rolling contacts and has been. applied to the study of grease film composition both in the contact and inlet regions. Grease EHL film thickness: - Fully flooded: two distinct speed regimes, low speed 'noisy' regime where thickener lumps survive passage through the inlet and enter the contact. At higher speeds, film thickness increases according to usual EHL rules. - Starved: at ambient temperatures film thickness decays rapidly to a lower value than the fully flooded level. Analysis of grease lubricant film composition: - Fully flooded: at low speeds, much higher thickener concentrations are obtained in the inlet region confirming the presence of local thickener 'bundles' although this is an intermittent occurrence. At higher speeds, the inlet thickener concentration drops close to the contact and this has important implications for the development of inlet rheological and film thickness prediction models. - Starved: a thick grease film is deposited in the initial stages which breaks down releasing base oil and leaving a thickener rich layer. Concentration changes are seen in the 'finger' region at the side of track. - There are indications of a breakdown in the thickener chemical structure forming oxidised, acidic hydrocarbon species. - Lubricant that reflows around the stationary contact is flee base oil released from grease close to the track. This mechanism could provide continual replenishment during running. The work has shown that the Scarlett (6) model of a high viscosity deposited layer is valid although the life is limited unless it is renewed. Such films might offer very different surface protection properties to the conventional fluid EHL film and it should be possible to optimise grease composition to exploit these properties for particular applications.

REFERENCES

1. "Starved Grease Lubrication of Rolling Contacts," P.M. Cann, accepted for publication STLE Trans. 2. "Minimum Oil Requirements of Ball Bearings," E.R., Booser and D.F Wilcock, Lub Eng., 9, 140 (1953). 3. "Understanding Grease Lubrication," P.M. Cann, Proceedings 22na Leeds-Lyon Symp. on Trib., (1996). 4. "Friction of Grease and Grease Components during Boundary Lubrication," D.J. Godfrey, Lub. ASLE Trans., 7, 24, (1964). 5. "Recent Developments in Diurea Greases," T. Endo, NLGI Spokesman, 5_7.7,532, (1993). 6. "Use of Grease in Rolling Bearings," N.A.Scarlett, Proc. IMecE. Part 3A, 182, 585, (1967). 7. "In Lubro Studies of Lubricants in EHL Contacts Using FTIR Absorption Spectroscopy," P.M. Cann and H.A. Spikes, Trib. Trans. 34, 248, (1991). 8. "The Measurement and Study of Very Thin Lubricant Films in Concentrated Contacts," G.J Johnston, R.W. Wayte and H.A. Spikes, Trib. Trans., 34,187, (1991). 9. "The Handbook of Infrared and Raman Characteristic Frequencies of Organic Molecules," D. Lin-Vien, N.B. Colthup, W.G. Fately and J.G Grasselli, Academic Press, (1991).

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

601

Service life and lubrication conditions of different grease types in high-speed rolling bearings E. Franke and G. Poll University of Hannover, Institute of Machine Elements, Engineering Design and Tribology, Welfengarten 1A, 30167 Hannover, Germany This paper deals with the influence of lubricating grease composition on grease service life and tribological performance characteristics in high-speed rolling bearings. First of all the test rig including the measuring system used to determine the lubricant film thickness in operation as well as the greases used in the study will be explained. Experimental results will then be used to analyse the influence of thickener type and content, base oil type and viscosity and anti-oxidants on grease service life, lubricant film thickness, bearing temperature and friction torque. 2"10'

1. INTRODUCTION The overwhelming majority of rolling bearings are lubricated with grease, since this type of lubrication offers a range of advantages over oil lubrication with regard to the design and maintenance effort involved. That is why grease lubrication is penetrating into areas of application which had previously been reserved for oil lubrication. Attempts are being made not only to further extend the permissible temperature range but also to increase the limiting speed for grease lubrication [4]. Greases of different structure show considerable differences in their functional properties [1], [3]. These become particularly apparent when rolling bearings are operated at high speeds. Traditionally, selection criteria for the use of greases are based on practical experience, and also partly on estimates or extrapolations of known results. In order to determine the high speed suitability of lubricating greases, the diagram from the GtT 1worksheet 3, "Rolling bearing lubrication" (,,Arbeitsblatt 3, W/ilzlagerschmierung") can be used [9]. It indicates the limiting characteristic speed n.dm for lubricating greases as a function of the base oil viscosity vs0, albeit within fairly large confidence limits.

1 GfT: Gesellschaft ftir Tribologie e. V. (German Tribological Society)

~,.~:~

min 1- mm

l

i

I

~

,

7"10~ 5"106

¢::

i

-----t bearing temperature: 50 ... 70 °C ~-

"~ ~ w z ~ l l i i

~J~m,~

3.10 s 1.10 5

10

50

- "~liim 100

~tmM Mmii~3 150 mm=.s ' 250 base oil viscosity v . =

Figure 1. Limiting characteristic speed n'dm for grease lubricated ball bearings [9]. The diagram was created by evaluating observations of proven cases in practical use over the years. It is mainly based on non-critical operating conditions in standard rolling-bearing applications. The diagram does not include the influence of base oil type, thickener type and content and additives, which are all supposed to have a decisive influence on the high speed suitability of a lubricating grease. Also missing is precise differentiation with regard to important boundary conditions and operating parameters such as the bearing operating temperature and load. That is why the diagram is only of limited use for the estimation of the actual speed limit of a specific grease. The mechanisms of grease lubrication are still not fully understood. Sound scientific knowledge concerning the effects and the mutual influence of the various lubricating grease components is lacking.

602

Thus in DGMK2-Project 379 / 379-01 the impact of these components on the grease service life and the tribological operating characteristics in highspeed rolling bearings was experimentally analysed at the Institute of Machine Elements, Engineering Design and Tribology of the University of Hannover. As there is no generally recognised testing procedure for determining the limiting characteristic speed n. dm of lubricating greases in rolling bearings a testing system for lubricating grease investigations in continuous operation at speeds of up to 24,000 min -~ corresponding to a characteristic speed of n. dm = 1.3" 106 minl.mm was developed as part of the project, as well. In addition to measuring speed, temperature and friction torque, the lubrication conditions in the test bearings are determined with the aid of a capacitance measuring system [2], [7], [8]. I.I. Notation A Hertz C

dm F~x Fs0h

h

I0 kc

kh MR n t T u

U Z eo er V

Hertzian contact surface (1 mm 2)

electrical capacitance (1 F) mean bearing diameter (1 mm) axial load (1 N) grease service life (1 h) film thickness (1 larn) charging current (1 A) capacitance factor ratio of film thickness friction torque (1 Nmm) rotational speed (1 min -~) time (1 s) comparator signal hydrodynamic velocity (1 mm/s) voltage (1 V) number of balls electrical field constant (1 F/(Vm)) relative dielectric constant bearing temperature (1 °C) kinematic viscosity (1 mm2/s)

2. EXPERIMENTAL 2.1. Test Rig

A three-phase asynchronous motor drives an intermediate spindle via a flat-belt drive. The intermediate spindle absorbs vibrations originating from the drive and transmits the driving torque to the test spindle via a multiple-disc clutch free of additional forces. The test speed is measured using a toothed disc with a Hall probe, Figure 2.

Figure 2. General view of a test rig. The test spindle has a housing suspended in two deep groove ball bearings. Thus, the friction torque can be measured by means of a bending beam. The bearing temperature at the outer ring is also measured, Figure 3. If the friction torque or the temperature in the test bearings increase beyond freely definable limits as a result of a change in lubrication conditions, the test rig is automatically switched off. As test bearings, size 7008 angular contact ball bearings are used. They are loaded purely axially with the aid of an adjustable compression spring, creating equal stresses in all rolling contacts. capacitance measurement thermo couples

2 DGMK: Deutsche Wissenschaftliche Gesellschaft

for Erd/51, Erdgas und Kohle e. V. (German Scientific Society for Mineral Oil, Natural Gas and Coal)

friction torque measurement Figure 3. Test spindle.

carbon brushes

603

2.2.

Measurement thickness

and

computation

of

film

The procedure for the determination of the operational grease film thickness hmeas from the measured total electrical capacitance, Figure 4, is based on the EHD theory after Dowson/Higginson and Wilson [5], [6], [10], [11], [12]. This theory allows to compute the minimum EHD lubricant film thicknesses hmin, thermal at the inner and outer race for non-isothermal conditions. Thereby, the differing pressure angles and loads as a result of the high speeds are taken into account, but the high spin on the inner race is ignored. The computations are based on the viscosity-temperature and viscositypressure relationships of the base oils as well as on the measured bearing temperatures.

To determine the total capacitance CK of a single contact, the following simplifying assumptions are made: • the inlet region of the contact zone is continually filled with lubricant; • the Hertzian contact region is assigned a constant lubricant film thickness; the narrowing towards the outlet is neglected; • in the outlet region the lubricant divides into two equal partial flows which adhere to the two contact partners.

! contact region

Hertzian

inlet region

outlet region

ho hm,n I I.....'-capac . ita'n:ce~'~':"Oi"~:"":'~'~ 2 spindle bearings

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

r..o

===================!==~::. =i===~==:~:~:~. ====reu. ~====~=:.==.:=:;~:~-~% =r==ii==iili! iill!ii!!iliii!i~iiiiii!iiii! =====ii===~=== ::::::!iiii::iiiiiiii::ii::::ii:~ ........

i1i~:~!~!i;iiiiii~i!ii!~ii~:i~::~::~::~:~:~i!i~:i~!~!~i :!i~i~i:~:~':i~!~i~!~i~!i~:i.~!:,:~:~ii~i~!i:!~i.:ii~:i~:ii~:iii~i~:!i!!!i~:iiil

~r

relative dielectric constant

~r,O,grease

i iiiii!!ii!i!i!uii~i~!~i!~iiii!ii!~!!!!~ii

_

2b

:!!ii l;:ii i i;~ii:::::~ r,O,a i r

...~;..:.~:i !i:!!i:!ii;;iii:iii::~o iiii ,.,..

=

1 kinetic analysis computation of film thickness using EHD theory

I

A.... z size of Hertzian contact surface kh ratioof film thickness k. = ho/h i

kc

! C,.,.,

! C,,..,.

! Cou,,.,

capacitance factor

kc = CK / C.==

,l

film thickness

Figure 4. Diagram of film thickness measurement. The surfaces in rolling contact are treated as the plates of a capacitor, the lubricant between them as a dielectric and the lubricant film thickness as the distance between the capacitor plates. An EHD rolling contact zone is divided into three sections, inlet region, Hertzian contact region and outlet region (Figure 5). The total electrical capacitance of a contact (inner race/ball or ball/outer race) is determined by the electrical capacitance of these regions [2], [8].

T h I > A..r=

CK -

kc- So. Sr"

A Hertz

Figure 5. Capacitance model of an EHD contact. The lubrication gap capacitance can then be treated as plate capacitors connected in parallel, the formation of inhomogeneous fields being ignored. The following relation applies: C K -- Cinle t Jr CHert z Jr Coutlet

(1)

size of the Hertzian contact region is for the geometry of the whole contact zone. thus make the simplifying assumption that contact capacitance CK is a function of the capacitance CHertz of the Hertzian contact surfaces, which can be determined with sufficient accuracy: The decisive We can the total

604

CK=f(fHertz)=kc .CHertz

(2)

The conversion factor kc is a function of operating conditions, bearing type, lubricant, running time as well as other difficult to determine factors and is in a range of kc = 3...4. The capacitance CHertz c a n be considered as that of a plate capacitor and as a good approximation be described by the following equation:

CHertz "-£O "Er AHertz

(3)

h

In the present experimental set-up, the capacitance is measured via the two test bearings connected in parallel. The test bearings in turn consist of a parallel arrangement of Z series connections of contact capacitances Cr,i and Cx,o at the inner and outer race. The following relation thus applies:

Ct°tal

Z

CK, i .CK, °

=2"Cbearin=2"Z g 0 CK,i +'C--KKo ,

(4)

The equal axial loading of the angular contact ball bearings leads us to assume that the contact capacitances CK,i at the inner race and Cx,o at the outer race are the same for both bearings. Using the factor kh, which describes the ratio of the grease film thicknesses at the inner and outer race based on the computed minimum thermal EHD lubricant film thicknesses hmin ' thermal, h°

hmeas'°

hmin' thermal'°

(5)

contacts at the inner and outer race forms a dielectric layer and the capacitance stays constant during the charging phase, the voltage increases linearly with time. The required capacitance is directly proportional to the charging time tload, which the capacitor needs to reach a predetermined voltage Umaxwith constant-current charge: Ctotal= Umax I° • tload

(6)

In order to avoid any errors when determining the charging time, a breakdown detector is built into the measuring system. Due to partial or mixed lubrication there may be metallic contacts of surface roughnesses in the rolling contacts, and the electric charges may drain through those local short circuits. These momentary discharges result in a voltage drop, so that the reference value Umax is not reached without renewed charging. Without the detection system there will be errors, because it appears to the measuring system that a longer period of time elapses until the reference voltage Umaxis reached.

1 0 gram

1

I

_ r

U,,=p

~

' i

t

film breakdown

kh ="~i = hmeas, i = hmin, thermal, i we can derive the lubricant film thicknesses hmeas,i and hmeas,o from the measured total capacitance Ctoua, since all the rolling contacts at the inner as well as at the outer race are uniform in shape as a result of the purely axial load. Were there combined axial and radial loads, the non-uniform distribution of the rolling body load would have to be taken into account. The inner rings are connected to the measuring circuit via two carbon brushes which slide along a copper ring on the test shaft, and the outer rings are connected to it via the housing. The measurement system uses the principle of constant-current charge. A previously discharged capacitor, in this case the test spindle with the rolling contacts, is charged with a constant current I0. If the grease film in the rolling

', t 1

'

0

t

1 04 1 0

-

v

Figure 6. Diagram of capacitance measurement (film breakdown).

605

Figure 6 shows in simplified form the principle of obtaining measurement data and how lubricant film breakdowns are detected. The output pulse Uout is formed by an AND operation on the comparator signals Ton and Toee, which themselves are derived from the comparison of the measured voltage Uramp and the voltage levels Umin and Umax. The duration of the output pulse Uout results from the time the signal Uramp needs to rise linearly from voltage level Umin to voltage level Umax. The dielectric properties of the greases were determined experimentally in a separate set-up consisting of a plate capacitor with exactly known geometry. Prior to this, the grease samples used for these measurements were subjected to shear stresses in a roller bearing until the dielectric properties reached a stable level.

2.3. Test parameters The lubricating grease long-time tests were carried out using the following parameters: • spindle bearings: B 7008 C.TPA.P4.UL, • a minimum of four pairs of bearings tested with each grease type, • grease quantity: 30% of the free bearing space, • rotating speed: n = 24,000 min -1, • characteristic speed: n.dm = 1.3.10 6 min-l.mm, • axial load: Fax = 160 N, • constant cooling by means of a fan except for three test series without cooling; the bearing temperature was not controlled but allowed to arise freely, based on the heat balance resulting from the actual friction losses in the bearings. Before the start of each long-time test, there was a grease distribution run which resulted in steadystate temperature with constant friction torque. Each test was continued until the end of the grease service life. In the investigation we assumed that the end of the grease service life was reached when as a result of a change in grease condition in the contact zone the bearing friction torque for both bearings rose above 400 Nmm or when the bearing temperature exceeded 100°C.

[8], which is fully supplied with additives. The grease parameters varied in the investigation were • base oil type • base oil viscosity • thickener type and • thickener content. In additional tests, an anti-oxidant was added to two model greases, so that a total of ten test greases were available. Table 1. Composition of the greases investigated. type

viscmity v4o

content additive

~

varied

in %

in mm2/s Lithium I

MPA

22.0

Li-12-OH

10

Lithium H

MPA

220.0

Li-12-OH

10

-

Lithium lII

PAO

22.0

Li-12-OH

10

-

Lithium IV

ESTER

19.6

Li-12-OH

I0

-

Lithium V

MPA

22.0

Li-12-OH

16

Lithium VI

MPA

22.0

Li- 12-OH

!0

=ntiox.

Lithium VII

MPA

22.0

Li-12-OH

16

antiox, thickene~ contmt/additive

C~cium I

MPA

22.0

Ca- 12-OH

!0

-

Calcium II

MPA

22.0

Ca-Complex

!7

-

ESTER, MPA

23.0

Ba-Complex

35

EP

NBU 15

-

imc dl vt~o=ty

b ~ c oil type

-

thicimmr

content

additive

thickener type thickener t y p e / c o n t e n t commercial grease

MPA: lm~tffinicmineral oil PAO: polyalplmol©fine

4. RESULTS The experimental investigations showed that base oil viscosity, base oil type, thickener type and content and addition of an anti-oxidant exert a strong influence on grease service life, lubricant film structure, bearing temperature and friction behaviour. 4,000 &

mathematical model: 8REF- 8 L

P x

h -~ ~

3,000 !-~>3"~0h :

Fsoh(.9.)= 2

2,000

mathematical

= 500 "

Figure

• Fsoh (9.EF)

[] expedment

1,000

40

[ ] LithiumI • LithiumII

8.EF = 70 *C Fs0h (SREF)= 500 h (experimental)

ti

0

TM

I lithium grease:

U. 2,500

3. GREASES INVESTIGATED The investigations focussed on seven model greases which contained no additives (five with lithium and two with calcium based thickeners) and the commercially available standard grease NBU 15

thickener

oil

type

.~.

I

!~I + antioxJdant=

• Uth,umm

• LithiumIV 1~ LithiumV [ ] LithiumVl ~ LithiumVII • r..,~um I X GtgclumII 4" NBU 15

tern wah mod~Dd

* ~

cooling conditions

"~

50 60 8~a=70 mean bearing t e m p e r a t u r e ~L

80 =--

*C

90

7. Grease service life vs. mean bearing temperature.

Comparison of the non-additive-treated lithium greases shows that the service life decreases with

606

increasing operating friction torque and increasing bearing temperature. Thus for example lithium grease III, which has the longest service life of these greases and has a PAO base oil, has the lowest operating temperature and the lowest friction torque. By contrast lithium grease II with a mineral base oil of high viscosity (220 mm2/s) has the shortest service life, the highest friction torque and the highest temperature. Thus, with non-additive-treated greases of the same thickener type, the mean operating temperature that ensues correlates with the service life of a grease and can thus be used as a criterion for the assessment of its service life. For greases with a lithium soap base, there was a relationship between the service life and the bearing temperature in line with the well known Arrhenius' law. This means that in a temperature range from approx. 45°C to 85 ° there was a drop in service life by 50% for each temperature increase by 15°C, see Figure 7. At temperatures below 45°C, the experimentally determined service lives are above the values which would result according to the model. This temperature can hence be viewed as a limit below which this relationship between bearing temperature and lubricating grease no longer exists. So far, the temperature limit has been commonly assumed to be between 70 °C and 80 ° C. This relationship could only be proved for nonadditive-treated greases up to now. If a lubricating grease has suitable additives (e.g. for the formation of boundary layers) which only become effective when a minimum temperature is exceeded, a longer service life may certainly be reached in spite of a higher operating temperature. Using anti-oxidants alone, the service life in the entire temperature range under consideration can be considerably increased. At the same time the friction torque and the operating temperature fall, so that the results can be fitted into the general relationship between bearing temperature and service life. The functioning mechanisms of the anti-oxidants are accordingly more complex than expected, as obviously they do not simply increase the aging resistance at a given temperature level. The mean friction torque can also, just like the bearing temperature, be used as a criterion for lubricating grease suitability. However, since the dissipatable heat output by the bearing has a direct influence on the relationship between friction torque,

temperature and hence service life, this criterion would only apply to systems with sufficiently similar heat transfer characteristics. Further consideration of the experimental results shows that lithium grease VII (PAO base oil with a viscosity of 22 mm2/s at 40 °C) with an Fs0h of 3,649 h has the longest service life. Calcium grease I with an Fs0h of 289 h has the lowest service life of all the model greases in spite of a low operating temperature, lying outside the trend of the lithium greases below the values of the worst lithium grease (II) with an MPA base oil of 220 mm2/s at 40 °C and a service life of 738 h. The test results for NBU 15 only allowed an estimate of the lower limit for the service life Fs0, of 3,500 h, since only one failure was registered until the test was suspended. This commercial grease, which has been fully additive treated, thus reaches at least the service life of the model grease with the longest life and does not follow the trend of the lithium greases either. Figure 8 is a chart of the service life Fs0h, the measured mean grease film thickness hmeas, the bearing temperature 0~ and the friction torque MR for some selected test greases.

10,000 1,000 100

[hi 10

n]

lu

-z,

16 % thickener content

Figure 8. Test results for some selected greases. A comparison between the measured minimum thermal EHD film thickness and that computed according to Dowson and Higginson while taking into account the measured bearing temperature and the lubricant temperature rise in the rolling contact according to Wilson is shown in Figure 9 [5], [12]. Lithium grease II, in contrast to the theoretical predictions, has the lowest film thickness in spite of

607

the highest base oil viscosity at reference temperature; its operating temperature is the highest and its life the shortest of all lithium greases. The PAO base oil of lithium grease III, on the other hand, causes a thicker lubricant film than the mineral oil of lithium grease III, although the base oil viscosity and the thickener content are the same. Lithium grease V with a thickener content of 16% has the greatest lubricant film thickness, a lower operating temperature than the other MPA-based variants and accordingly the longest service life of these. Thus, thickener content in addition to base oil is an important influence on the film thickness and service life. .

I (MPA,10 %th., v,o = 22 mm'/s) ~ Uthiumgrease

I

0.096 ~ ~

="omm'i,;o.o ,,) 8

II (MPA, 10 % t h . ,

Lithiumgrease

Lithiumgrease,,, (PAO,10 %th., v'°=22mm'/s' ~ V (MPA,16%th., ~ v,, = 22 mm'/s) Uthiumgrease

~

.

range of speeds. It can be seen that the range of assumed starved lubrication in comparison to complete lubrication with oil starts even at a relatively low speed of 2,000 min-l; the values from then on are considerably smaller than according to Harris. The causes of this may have to do with the neglect of the high proportion of spin at the inner race contact, a subsequent underestimation of the contact temperature and overestimation of the effective viscosity as well as with the fact that Harris's starvation factor was developed for a line contact. The measured grease film thickness falls continuously starting from this speed and from a speed of 17,000 min -1 on reaches a stationary value.

l 0.8

[] h m . , [pm]

~

~ ~ i

~.~,~

I

0.283 0~154 ~ ~

o....,,,--- ~

w 0.4

0.57

_.E

p 0.545 i J~':~~

l

pm *-

I ~ ~ i ,. II0"1~1B ~

.

[] hm, / hmi,.therm,l [] hm=,t~rml [IJm]

~ 0.483

0.099

.

Higginson and Wilson and starvation according to Dowson, Higginson, Wilson and Harris over a wide

Figure 9. Measured and computed mean film thickness for some selected greases. The minimum grease film thicknesses computed with the aid of the thermal EHD theory for the base oil in each case are greater than the measured film thicknesses for all greases. Under the operating conditions under consideration, therefore, this may be attributed to starved lubrication, most notably, for lithium grease II: with lithium grease I I in distinction to the other greases - we get a clearly larger deviation between the computed and the measured film thickness, since the high base oil viscosity on the one hand results in a high theoretical film thickness and on the other hand it can be assumed that less base oil continues to flow into the rolling contact in comparison to lithium grease I, for example, thereby causing the low measured film thickness mentioned before. In Figure 10, the measured grease film thickness and bearing temperature of lithium grease I is compared with the computed minimum thermal film thicknesses for full lubrication according to Dowson

0.2

~=

0.0~

~

60

~

-i"

~

hm,., ~m-,, s=~==l~""~

~

Q.

' E

I

~

r-

o

hm., 5,000

1o,ooo 15,000 speed n

oC

i~~

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

L,~

/ / ~

~

min 1

25,000

_ ~ ~

20 ~

~

~'----

index:

i : Innerdng

f

o: outer ring

0

Figure 10. Measured and computed film thickness vs. bearing speed for lithium grease I. The long-time tests also revealed that the grease film thickness exhibits relatively constant behaviour and does not decrease with time, see Figure 11.

l°°e:

pm "=: 0.4

¢/J (-,3¢

~ ~

0.3

~ , ~ , ~ , , ~ ,,~mJ =,====m,..~,.._.~ =m=~= -

I hmIn. ~ , , ~ . ==v,=o~

o 0.2 e-

E 0.1 :.-= 0.0 o

"~ ° c ~ •

E =

20 0

'

hrnelB

100

200

300 400 running time t

500

A

600 h 700

I

"

experimental grease f service life: 673 h I

I

Figure 11. Measured and computed film thickness vs. running time for lithium grease I.

608

No relationship between the behaviour of the film thickness over time during a long-time test and the running time reached could be shown, as with the behaviour over time of temperature and friction torque. It is only towards the end of the experiment that the measured lubricant film thickness decreases abruptly, and at the same time there is a sudden jump in temperature and friction torque. Further investigations have shown that, under the operating conditions we considered, the oil separation of the lubricating greases under static and dynamic conditions and the unworked and worked penetration cannot be used as characteristics for the estimation of service life, as no relationship between these factors and service life could be found. 5. CONCLUSIONS 1. The lubricating grease service life can be increased by using a PAO or ESTER base oil instead of a comparable mineral oil, by increasing the thickener content or by adding an anti-oxidant. Operating temperature and friction torque are lowered. High base oil viscosity results in high friction, high operating temperature and thus in shorter lubricating grease service life. 2. Lithium soap greases (Li-12-OH) have a longer service life than comparable calcium soap greases (Ca-12-OH) in spite of having a higher operating temperature. 3. With non-additive-treated greases of the same thickener type, a variation in the grease parameters which causes a fall in bearing temperature leads to an increase in grease service life. The stationary bearing temperature can be used here as a criterion for the assessment of grease service life, since the service life decreases with increasing operating temperature. 4. The effects caused by the anti-oxidants are more complex than expected, as they influence friction torque and operating temperature as well. 5. For non-additive-treated greases on the basis of lithium soap, there is a relationship in a temperature range from about 45°C to 85°C between service life and bearing life according to Arrhenius' law. The service life decreases by 50% for each temperature increase by 15°C. 6. The measured grease film thicknesses show that above a speed of 2,000 l/min there may be starved lubrication, since the measured film

thickness is lower than the computed thermal EHD grease film thickness. 7. The grease film thickness is raised by increasing the thickener content with the same base oil or by using a PAO base oil instead of a mineral oil; it is reduced by a high base oil viscosity. 8. It is not possible to predict the failure time from the behaviour over time of the quantities measured for bearing temperature, friction torque and grease film thickness during a long-time test. ACKNOWLEDGMENTS

The authors wish to thank the German Scientific Association for Mineral Oil, Natural Gas and Coal (DGMK), the German Organisation of Industrial Research Associations (AiF) and the Department of Trade of the German Government (BMWi) for initiating and supporting this project. REFERENCES

H. Astr6m, Grease in Elastohydrodynamic Lubrication, ISSN 0348-8373, Doctoral Thesis 1993, Lule~t University of Technology. Barz, Die Schmierfilmbildung in [21 M. fettgeschmierten schnellaufenden Spindellagern, Dissertation 1996, Universit~it Hannover, Fakult~it fiir Maschinenwesen. [3] P. M. Cann, Starvation and Reflow in a Grease-Lubricated Elastohydrodynamic Contact, Tribology Transactions, Volume 39 (1996), 3,698-704 P. M. Cann, B. P. Williamson; R. C. Coy and [4] H. A. Spikes, The Behaviour of Greases in Elastohydrodynamic Contacts, Journal of Physics D: Applied Physics, Band 25 (1992), Heft 1A, S. 124-132. [5] D. Dowson and G. R. Higginson, ElastoHydrodynamic Lubrication, 2. Auflage 1977, Pergamon Press LTD, Oxford. [6] D. Dowson, C. Taylor and H. Xhu, Elastohydrodynamic Lubrication of Elliptical Contacts with Spin and Rolling, Proceedings of the Institution of Mechanical Engineers: Part C, Band 205 (1991), S. 165-174. [7] E. Franke, Ermittlung von SchmierfettKennwerten zum Reibungsverhalten und zur Schmierwirkungsdauer in schnellaufenden W~ilzlagern, Reibung, Schmierung und [1]

609

VerschleiS, Tribologie-Fachtagung G6ttingen 1997. [8] E. Franke, E.-G. Paland and G. Poll, Ermittlung von Schmierfett-Kennwerten zum Reibungsverhalten und zur Schmierwirkungsdauer in schnellaufenden W~ilzlagern, DGMK Bericht 379-1, Hamburg, 1997. [9] Gesellschaft ftir Tribologie (GfT), GfTArbeitsblatt 3: W~ilzlagerschmierung, Mai 1993. [10] R. Gohar, Elastohydrodynamics, 1988, Ellis Horwood LTD, John Wiley & Sons Inc., New York. [11] B. Hamrock and D. Dowson, Ball Bearing Lubrication, 1981, John Wiley & Sons Inc., New York. [12] T. A. Harris, Rolling Bearing Analysis, 3. Auflage 1991, John Wiley & Sons Inc., New York.

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

611

The Inclusion of Lubricant Shear Thinning in Journal Bearing Models R.I. Taylor Shell Research & Technology Centre, Thornton, P.O. Box 1, Chester, CH1 3SH, UK The Short Bearing Approximation is often used in the preliminary design stages of automotive engine bearings. However, amongst its many limitations, the assumption is made that the lubricant is Newtonian. Modern automotive lubricants are multigrade oils containing polymeric additives at treat rates of several percent. This results in the lubricant viscosity having a significant dependence on shear rate (temporary shear thinning). This paper extends the Short Bearing Model to allow for lubricant shear thinning, as described by the Cross model. The modified model has been applied to a modern automotive con-rod bearing for various automotive multigrade lubricants. 1. I N T R O D U C T I O N

For short, plain, journal bearings (typically where L/D < 0,.5, where L is the length and D is the diameter of the bearing), such as those used in modern automotive engines, the Short Bearing Approximationl,2 is an attractive, fast, preliminary design tool. Essentially, the approximation is made that the pressure variation across the width of the bearing is far greater than that around the circumference of the bearing. With this assumption, it is possible to greatly simplify the solution of Reynolds' equation 3, and an analytic expression for the pressure variation around the bearing can be developed. Integration of the pressure around the bearing leads to a relationship between the load applied to the bearing, W, and the eccentricity ratio, ~, induced in the bearing. However, one of the limitations of the model is that it assumes that the lubricant is Newtonian. Most modern automotive lubricants are multigrade oils, containing polymeric additives at treat rates of up to 20%. Such oils exhibit temporary shear thinning, whereby the lubricant viscosity can decrease significantly with applied shear rate. In this paper, the standard Short Bearing Model has been modified to allow for

lubricant shear thinning. The variation of lubricant viscosity with shear rate is assumed to be as described by the Cross equation 4, which has previously been shown to give a good fit to measured multigrade lubricant flow curves~,6, 7. In the following Sections, a description of the analysis is given, together with results obtained when the model was applied to a modern automotive bearing. Note that we have not taken into account the effects of pressure on lubricant viscosity, but as the model gives an estimate of peak pressures, we can test whether the operating conditions are such that this effect can be neglected. 2. THE I N C L U S I O N OF L U B R I C A N T S H E A R T H I N N I N G IN T H E S H O R T BEARING APPROXIMATION

The following is effectively the textbook derivation of the Short Bearing Approximation, as described in respected textbooks (e.g. Stachowiak et al 1, and Frene et al2). Reynolds' equation can be written as :

...(1)

612

where, for simplicity the squeeze term has been neglected. In equation (1), y is the coordinate across the length of the bearing, and x is the coordinate along the circumference of the bearing. P is the pressure in the lubricant at the point (x,y). ;7 is the lubricant viscosity, U is the relative sliding speed of the bounding surfaces, h is the oil film thickness at point (x,y). The Short Bearing Approximation basically assumes t h a t the pressure variation across the y direction is far greater than across the x direction. It is known to be good ~ for bearings whose L/D ratio is less t h a n 0.5, where L is the bearing length, and D is the diameter. Using the Short Bearing Approximation, equation (1) simplifies to become :

p __

2)

3 , sinO Rc 2 (1 + e cosO) 3

--Y

...(5) So far, no assumption has been made about how the lubricant viscosity varies around the circumference, 0 of the bearing. In the standard Short Bearing Approximation, it is assumed that the lubricant is Newtonian, so that the viscosity is constant. However, we now assume that the viscosity is dependent upon shear rate, y, as described by the Cross equation 4.

r / - rLo +

I+L ...(6)

c~

12r/

2 dx ...(2)

It is convenient, for a journal bearing, to use cylindrical polar coordinates rather than cartesian coordinates, so the following substitution is made "

x-RO

In the above equation, rio is the zero shear rate viscosity (mPa.s), r]~ is the viscosity (mPa.s) at infinitely high shear rate, y is the shear rate (s -1) and yc is the shear rate (s -1) at which the lubricant viscosity lies exactly halfway between rio and ri~. We couple the use of the above equation to the shear rate by assuming that the shear rate, at any position (y, ~ in the bearing is given by:

...(3)

U where 0 is the circumferential (angular) position on the bearing, and R is the radius of the journal bearing. In addition, oil film thickness, h, is given by •

y

h(y,O) ...(7)

If we define Po(y, ~ as"

2)

3UGc sin O (@

h - c(1 + ~ c o s O)

...(4) where c is the radial clearance of the bearing, and c is the eccentricity ratio. Since the viscosity of the lubricant, 7?, does not vary with y (since it is assumed that the bearing is rigid), it is possible to integrate equation (2), to obtain:

R c 2 (1 + c c o s O ) 3

- y ...(8)

Then the pressure in the bearing, P, may be written as"

613

1-- /7oo ~7o

v- e,

lyl

r/°

l+--

Yc ...(9) To obtain the load acting on the bearing, the above pressure must be integrated across the bearing. To solve for the bearing eccentricity ratio, the load acting on the bearing must be equal to the load generated by the lubricant. Therefore, W is known, and ~, the eccentricity ratio, can be determined. Full details are given in a previous paper s. Once ~ is known, other bearing p a r a m e t e r s such as the attitude angle, the friction torque etc., may be calculated. The friction torque, F, may be calculated. To a first approximation, F is given by :

F-

2LR3( c

rL°

41-

+

,/(1 + A) -

t ...(10)

where all p a r a m e t e r s have been defined before, apart from co, which is the angular velocity (rad/s) and A, which is defined as :

A-

IuI Zc c

...(11) As before, this expression reduces to the standard expression for a Newtonian lubricant in the appropriate limits 1. It should be noted t h a t evaluating the friction torque in the Short Bearing Approximation requires some thought. In the Short Bearing Approximation, the bearing is assumed to be full of oil, but only the oil in the converging part of the bearing is assumed to contribute to the load bearing capacity. However, oil in

the diverging part, whilst not contributing to load bearing capacity, certainly contributes to friction losses. We take the pragmatic view, as do the standard textbooks1, 2, t h a t it is more accurate to include friction from the diverging part of the bearing t h a n it is to ignore it. This also ensures that there are no discrepancies when ~=0, since we know then that the friction torque should be the same as that given by the Petrov equation 9. It is important to realise that, in this simple model, the viscosity varies around the bearing due to the changing oil film thickness around the bearing. At any position, (y, 0), the model will predict an oil film thickness, h, which can then be used to calculate the shear rate, y, which can be used to calculate the lubricant viscosity from the Cross equation (equation (6)). It should be pointed out that there are still deficits in the model. Firstly, the model assumes a rigid bearing, and effects due to the variation of viscosity with pressure have been neglected. A further deficit of the model is that the short bearing approximation is known to break down as the eccentricity ratio approaches 1. However, the model is still useful as a first step for a bearing designer. In addition, for our purposes, the model is to be used to study the lubricant sensitivity of load bearing capacity and friction torque for a given bearing. For these purposes, the modified short bearing approximation is adequate 3. A P P L I C A T I O N OF M O D I F I E D S H O R T BEARING APPROXIMATION TO A MODERN AUTOMOTIVE CON-ROD BEARING

The modified short bearing model described in Section 2 has been applied to study the load-eccentricity relationship, and friction characteristics of a modern automotive conrod bearing (from a Mercedes Benz M l l l 2.0 litre gasoline engine). The load-crank angle data used for this con-rod bearing is shown in Figure 1. Table 1 gives some geometrical details of the con-rod bearing.

614

exp(

20000 T

t~2 + ...(22)

e~

where K (mPa.s), 01 (°C) and 02 (°C) are constants for a given lubricant. For simplicity, 7/oois assumed to have the same temperature dependence. Therefore :

!

°

r,,,)

-10000 -360

-180

1 0

180

360

C r a n k angle (degrees)

-r

~7o ...(23)

F i g u r e 1 • C o n - r o d l o a d c u r v e u s e d in b e a r i n g oil f i l m t h i c k n e s s c a l c u l a t i o n

where r is a constant, assumed to be independent of temperature, whose value will generally be in the range 0.5-1.0.

Stroke (mm)

78.7

Con-Rod Length (ram)

154.0

Bore Diameter (mm)

89.9

Engine Speed (rpm)

2500

...(24)

Engine Load (Nm)

95.4

Bearing Diameter (mm)

47.96

Bearing Length (mm)

21.70

Values for the Vogel p a r a m e t e r s for the SAE15W/40, SAE-0W/40 and SAE-5W/20 oils are given in Table 2. Values for the Cross equation parameters for the oils are given in Table 3.

Radial Clearance (gm)

30.0

The temperature dependence of the "critical" shear rate is assumed to be given by •

log lo (7"c) - A + B- T

K (mPa.s)

01(°C)

02(°C)

SAE15W/40

0.0292

1424.3

137.2

SAE0W/40

0.0114

1986.4

189.7

SAE5W/20

0.0389

1224.0

134.1

N u m b e r of Bearings Table 1 • Geometrical details of con-rod bearings

Results from the modified short bearing approximation model have been obtained for three oils, an SAE-15W/40, an SAE-0W/40 and an SAE-5W/20. The lubricant viscosity varies strongly with temperature, and it is assumed that this variation is well described by the Vogel equation:

T a b l e 2 • V o g e l p a r a m e t e r s for t h e t h r e e oils c o n s i d e r e d in t h e b e a r i n g simulations

615

SAE15W/40

0.79

SAE0W/40

0.67

SAE5W/20

0.94

A

B(°C-1)

2.5

0.026

100 ,~ 7

5

~

5o

2.5

0.026

~ SAE.-15W/40 ~ SAE-0W/40 -×- SAE-5W/20 I ~

25

2.5

0

0.029

I.E+00

1.E+02

1.E+04

I

I

I

1.E+06

1.E+08

1.E+10

Shear Rate (1/s)

Table 3 Cross e q u a t i o n p a r a m e t e r s The shear flow curves corresponding to these three oils, at 40°C, 100°C and 150°C are shown in Figure 2.

12 10 8

Using these predicted flow curves, the modified short bearing approximation has been used to predict oil film thickness and friction torque values for the con-rod bearing. Figure 3 shows the predicted oil film thickness values at the three different temperatures, and Figure 4 shows the predicted friction torques at the three different temperatures.

x--x--x--x--x--x--×--x--x~x--x~x_x~x_x__x_x__x__x__x_

6~-

4_

+s 15w ° 1,

2 -

~ SA1L-0W/40 i

1.E+00

1.E+02

1E + 0 4

I

I

I

I.E+06

1.E+08

1.E+10

Shear Rate

Minimum predicted oil film thicknesses and predicted average torque values are summarised in Tables 4 and 5.

(l/s)

5 ~

•

x

150C

2

0 -1.E+00

1.E+02

1.E+04

1.E+06

Shear Rate

1E+08

1.E+I 0

(l/s)

F i g u r e 2 : S h e a r f l o w c u r v e s for SAE15W/40, SAE-0W/40 a n d SAE-5W/20 o i l s at different temperatures

616

•

30.00 -

1.50 ~-

40 C

g ~

.2

10.00

0.50

x SAE-5W/20 ~ SAE-0W/40 = SAE-15W/40

,m

0

~' I

t

0.00

,

I

-180 0 180 C r a n k angle (degrees)

-360

"7.

a SAE-0W/40 o SAE-15W/40 I

I

I

360

-360

-180

0.00

15.00

0.30 - \ 100 C

•"~

a SAE-0W/40

O

n SAE-15W/40 I

t

-360

-180

j

5.00

I

360

100 C

×

•,~,. •7.

x ,~.~¢

0.00

V

I

I

I

360

-360

-180

I

0 180 Crank angle (degrees)

~

I

0 180 Crank angle (degrees)

x SAE-5W/20 A SAE-0W/40 [] SAE-15W/40

0.00

r

0

.... I

180

360

Crank angle (degrees)

0.150

10.00 150 C

~

"7

××××500

-

x

a SAE-0W/40 [] SAE-15W/40 I

I

-360

-180

2.50

0.00

0

"~

x SAE.SW/20

"7.

~ SAE-0W/40 D SAE-15W/40

I

I

I

,,

180

360

-360

-180

Crank angle (degrees)

F i g u r e 3 • P r e d i c t e d b e a r i n g oil film t h i c k n e s s e s for t h e t h r e e oils at different temperatures

0.000

0

V

I

I

180

360

Crank angle (degrees)

Figure 4 • Predicted bearing friction t o r q u e (Nm) for t h e t h r e e oils at t h e three different temperatures

617

Min OFT (gm) at 40°C

Min OFT (gm) at 100°C

Min OFT (gm) at 150oC

SAE15W/40

8.17

3.12

1.98

SAE0W/40

6.48

2.78

1.87

SAE5W/20

6.31

2.65

1.72

T a b l e 4 • P r e d i c t e d m i n i m u m oil f i l m t h i c k n e s s for t h e t h r e e d i f f e r e n t oils at different temperatures

(Nm) at 40°C

(Nm) at 100°C

(Nm) at 150°C

SAE15W/40

1.031

0.1863

0.08818

SAE0W/40

0.6571

0.1591

0.08319

SAE5W/20

0.6236

0.1379

0.06764

Table 5 :Predicted average friction t o r q u e s for a s i n g l e c o n - r o d b e a r i n g for t h e t h r e e d i f f e r e n t oils at d i f f e r e n t temperatures

Figures 2, 3 and 4, together with Tables 4 and 5 provide a wealth of data which is discussed in more detail in the next Section. 4. D I S C U S S I O N Figure 2 shows the shear flow curves for the SAE-15W/40, SAE-0W/40 and SAE-5W/20 oils. At all three temperatures (40°C, 100 °C and 150°C) the SAE-15W/40 oil has the highest viscosity. The SAE-0W/40 oil is a relatively wide span multigrade oil, and so has to contain a relatively high level of Viscosity Index Improver (VII). This explains why the SAE-0W/40 oil exhibits a relatively high level of temporary shear thinning.

Therefore, at high shear rates, the SAE0W/40 and SAE-5W/20 oils have very similar viscosities, but at lower shear rates, the SAE5W/20 oil has the lower viscosity. The concept underlying the SAE-5W/20 was that the oil should have a low viscosity at low shear rates (to give lower friction), whereas at high shear rates, the viscosity should stay approximately the same (to ensure durability). This means, of course, that the oil has hardly any shear thinning. The high temperature high shear viscosity (HTHSV, as measured at 150°C and a shear rate of 10 ~ s 1) of the SAE-5W/20 oil was targeted to be 2.9 mPa.s, whereas the HTHS viscosity of the SAE-0W/40 oil was targeted at 3.5 mPa.s. One further point to note is that at the three different temperatures, the viscosity scales on the graphs in Figure 2 are quite different. At 40°C, the viscosity of the oils lies between 50 and 90 mPa.s, whereas at 100°C, the viscosity of the oils is between 7 and 12 mPa.s, and at 150°C the viscosity of the oils lies between 2.6 and 4.0 mPa.s. This temperature variation of viscosity is by far the dominant effect when considering the oil film thickness and friction torques at different temperatures. The shear flow curves of Figure 2 help to explain the oil film thickness results shown in Figure 3, and the predicted friction torque results shown in Figure 4. At all three temperatures, the predicted oil film thickness ranked in the same order : SAE-15W/40 was greatest, then the SAE-0W/40, and the SAE5W/20 had the lowest oil film thickness. However, differences in the minimum oil film thickness (which occurs close to top dead centre (TDC) firing) are quite small, compared to differences away from TDC firing. At 40°C, the SAE-0W/40 and SAE5W/20 oils have a very similar oil film thickness, whereas at 150°C the SAE-0W/40 predicted oil film thickness is more similar to that for the SAE-15W/40 oil. If the simulations had been performed at very low temperatures (e.g. -30°C), it would be expected that the SAE-0W/40 would have the lowest oil film thickness (since at those

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temperatures viscosity).

it

would

have

the

lowest

The predicted friction torques show a similar trend to t h a t for the oil film thickness, in t h a t at 40°C, the predicted friction torques of the SAE-0W/40 and SAE-5W/20 oils are almost identical, whereas the predicted friction torque for the SAE- 15W/40 oil is approximately 60% higher. At 100°C the predicted friction torque for the SAE-5W/20 oil is lowest, and the SAE-0W/40 oil has a predicted friction torque t h a t is 15% higher, and the SAE-15W/40 has a friction torque t h a t is 35% higher. At 150°C, again the SAE5W/20 oil has the lowest friction torque, whereas the SAE-0W/40 has a predicted torque t h a t is 23% higher, and the SAE15W/40 has a predicted friction torque t h a t is 30% higher. Tables 4 and 5 summarise the data shown in Figures 3 and 4. Basically, the tables show t h a t relatively large differences in friction torque can occur between the three multigrade oils, whereas the differences in the m i n i m u m oil film thickness is much less. Table 4, containing the oil film thickness data, enables an estimate of the shear rate to be made. For the SAE-5W/20 oil, the shear rate in the bearing at 40°C varies between 0.2 x 106 s -1 and 1.0 x 106 s I, whereas at 100°C, the shear rate varies between 0.2 x 10~ s "~ and 2.4 x 106 s "1, and at 150°C, the values lie between 0.2 x 106 s -1 and 3.6 x 106 s -1. Under these conditions, the SAE5W/20 oil has a lower viscosity t h a n the SAE0W/40 oil which is why the m i n i m u m oil film thickness of the SAE-5W/20 oil is lowest. If the shear rate exceeds 2.9 x 107 s -~, then the SAE-0W/40 has a lower viscosity than the SAE-5W/20 oil. In summary, both the SAE-5W/20 and the SAE-0W/40 oils considered here show considerable con-rod bearing frictional benefits when compared to a "conventional" SAE-15W/40 oil. The SAE-0W/40 oil is expected to be have lower friction t h a n the SAE-5W/20 oil at extremely low

temperatures (100°C). With judicious design of the shear flow curves, both the SAE-5W/20 and the SAE-0W/40 options could be used to develop fuel efficient automotive lubricants. Of course, other SAE grades could also be considered, e.g. SAE-0W/30. 5. C O N C L U S I O N S In this paper the Short Bearing Approximation has been modified to allow for lubricant shear thinning effects in a fairly simple and realistic manner. The model has been used to consider options for developing fuel efficient lubricants, and it was shown t h a t there is considerable scope to decrease friction in automotive con-rod bearings by moving from a relatively high viscosity "conventional" SAE-15W/40 multigrade oil, to lower viscosity oils, such as an SAE-5W/20 oil. There is also scope for obtaining benefits from wide span multigrade oils, such as SAE-0W/40 grades, which, because of the relatively high level of Viscosity Index Improver contained in the oil rapidly shear thin to give relatively low viscosities in the bearing. Note t h a t the lower viscosities t h a t have been discussed in the paper are not too low to impair engine durability. 6. R E F E R E N C E S

1. G.W. Stachowiak & A.W. Batchelor, "Engineering Tribology", (Tribology Series, 24, published by Elsevier, 1993) 2. J. Frene, D. Nicolas, B. Degueurce, D. Berthe & M. Godet, "Hydrodynamic Lubrication Bearings and Thrust Bearings" (TriboIogy Series, 33, published by Elsevier, 1997) 3. A. Cameron, "The Principles of Lubrication" (Longmans Green and Co. Ltd., 1966)

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4. M.M. Cross, "Rheology of Non-Newtonian Fluids : A New Flow Equation for Pseudo Plastic Systems", J. Colloid Sci., 20, p 417, 1965 5. R.I. Taylor, T. Kitahara, T. Saito & R.C. Coy, "Piston Assembly Friction & Wear : The Influence of Lubricant Viscometry", Proceedings of the International Tribology Conference, Yokohama, 1995 6. J. Sorab, H.A. Holdeman & G.K. Chui, "Viscosity Prediction for Multigrade Oils", SAE 932833 7. B. Wright, N.M. van Os & J.A. Lyons, "European Activity Concerning Engine Oil Viscosity Classification- Part I V - The Effects of Shear Rate and Temperature on the Viscosity of Multigrade Oils", SAE 830027 8. R.I. Taylor, "The Inclusion of Lubricant Shear Thinning in the Short Bearing Approximation", accepted for publication in the Proceedings of the Institution of Mechanical Engineers Part J, Journal of Engineering Tribology. 9. J.A. Williams, "Engineering Tribology", page 273 (Oxford University Press, 1994)

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Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

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French contribution to the study of lubrication Oiliness, molecular influences Application to watch lubrication J. du Parquet Total - C.E.R.T. BP 27, F76700 Harfleur Little is known about the French contribution to the study of oiliness and adsorbed monomolecule layers. The work of Langmuir, Hardy, Doubleday, Rayleigh and others was known to French scientists. G. Friedel, F. Grandjean, even Jean Perrin and Louis de Broglie studied these layers of fatty acids or soaps. The French "Academie des Sciences" was regularly informed of the new results by Marcel Brillouin. As early as 1925, the X Ray experiments of J.J. Trillat showed that lubricating greases and fatty acids did form stratified layers on surfaces. Since 1926, Paul Woog's theory of "molecule trapping" met with less success than the commercial application of his "surface neutralization" process. Thanks to his cooperation with a well known watchmaker, Paul Ditisheim, and a French oil company his range of products allowed a real technical leap in the lubrication of clocks and watches. The range of temperature operation and the reliability of horological production were considerably increased. The modem tribological concept of barrier films, additive competition and oil formulation were already identified by Paul Woog. They led to further developments when new chemicals like silicones and perfluorinated polymers became available.

1. I N T R O D U C T I O N Tribology is considered to be an interdisciplinary science. This is particularly true where a thin oil film separates surfaces in a rubbing contact. Therefore it is not surprising that the understanding of boundary lubrication eventually emerged from studies related to the physical state and flow behaviour of liquids in the vicinity of solids, to their thermodynamic properties and generally speaking to bulk and surface chemistry. The first purpose of this paper is to identify different French contributions to this scientific puzzle in order to fit them into the general picture of boundary lubrication. The second objective is to show how the perfect understanding of the latest scientific discoveries

enabled Professor Paul Woog to solve the ancient problem of watch lubrication.

2. BASIC RESEARCH 2.1. Early optical studies on molecular orientation As early as 1890 a German specialist in crystals O. Lehmann (1) had noticed the birefringence of certain liquids in contact with solid. He made a distinction between viscous flowing crystals and thin flowing crystals. The physical state of these materials attracted the attention of French physicists. From 1910 to 1922 Georges Friedel and Frangois Grandjean (2), Charles Mauguin (3), and even Jean Perrin (4), studied these materials. A review of the work done during this

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period was published by Georges Friedel in 1922 (5). He rejected the expression "liquid crystal" as being incorrect and misleading. He felt necessary to introduce new expressions such as "mesamorphous materials" which were to be divided in two groups : - the first group, corresponding to the "viscous flowing crystals" of Lehmann was originally called "liquids with conic focal" (from their optical properties). But he subsequently suggested a neologism which has been universally adopted: "smectic liquids" (from the Greek word for soap)". - the second group, corresponding to the thin flowing crystals of Lehmann, was first called "liquids with threads". He then suggested that they should be called "nematic fluids" (from the Greek word for thread). In his review, Georges Friedel mentioned the work of Jean Perrin (4) and Philip Varnum Wells (6) who had studied the stratified structure of thin layers of soap. He was also able to show that the structure with equidistant planes, described by Francois Grandjean (7) for cholesteric fluids, belonged to the nematic structure, with the threads having a high rotational power. 2.2. Application of X-Ray diffraction It seems that the first application of X-Ray techniques to the study of surface films was published in 1923 by A. Maller and C. Shearer in the United States (8), and by S.H. Piper and E.N. Grindley in Great Britain (9). It is less known that during the same year, Maurice de Broglie, associated with Edmond Friedel (10), applied the technique to soap layers. They demonstrated that the layers studied by Jean Perrin were not amorphous but had a smectic structure. The techniques of X-Ray diffraction were further developped by Jean Jacques Trillat (11) who applied them to lubricating greases. He greatly improved the quality of the spectra by first dissolving fatty acids in a solvant and by letting it evaporate. Louis de Broglie himself helped Jean-Jacques Trillat in the interpretation of these spectra (12). Thus they complemented the explanations of W. Bragg and showed that the molecules of fatty acids were bound at their ends by the terminal groups CH3. 2.3. Surface film properties and lubrication The pioneering work of Agnes Pockels and Lord Rayleigh on thin films spread on liquid surfaces,

reported in 1891 (13) and 1899, was well known in France. Just before the first world war, W.B. Hardy (14) mentioned the changes in surface energy introduced by polar molecules. During the 1914-1918 period, it is not surprising that important publications on the subject were to be found only in American Journals. I. Langmuir in 1916 (15) (16) and in 1917 (17). W.D. Harkins et al in 1917 (18) developed Hardy's views. But immediately after the first world war, the increase in related publications was spectacular, especially in Great Britain. Lord Rayleigh described the lubricating properties of thin oily films in 1918 (19). During the same year, A.E. Duston and F.B. Thole on one hand (20) and R.M. Deeley on the other hand (21) emphasized the importance of unsaturated molecules. Then in 1919, W.B. Hardy (22) released his first publication on friction and lubrication and drew attention to the adsorption of colloids on surfaces. In France, Marcel Brillouin tried to provide an explanation of oiliness properties. In 1920 (23) he suggested that lubricants were concentrated solutions of anisotropic crystals in a small quantity of viscous isotropic fluid. This concept was compatible with the anisotropic fluids studied by Lehmann and G. Friedel. It implied a viscous behaviour in the flow direction and an elastic behaviour in the transverse direction. But the theory did not account for the oiliness of "normal" fluids. Consequently, Marcel Brillouin initiated research work on oiliness and entrusted Paul Woog with this subject for his thesis at the University of Paris (figure 1). 2.4. Research work of Paul Woog As early as 1921, Marcel Brillouin presented two communications from Paul Woog to the French Academy of Sciences. The first one was the entitled "On the oiliness of fatty materials" (24) and the second "On the dimensions of the molecules of fatty oils and on some phenomena of molecular dissolution" (25). In 19:22 a new communication was presented on "The spreading speed of thin layers of oils on a water surface" (26). In 1925, it was followed by "The measurement of onctuous friction" (27) and by "On the spreading of lubricants on metallic surfaces" (28). Paul Woog's thesis "Contribution to the study of lubrication - oiliness - molecular influences" was

623

defended in Paris on the 17th of July 1926, with Professor Cotton as President of the jury. It was published the same year by the Librairie Delagrave (29). But it was also the basis for an extensive book which was published under the same title by the same editor (30). The oiliness of oils was explained by the socalled theory of "molecule trapping". The first form of trapping is purely steric and similar to the behaviour of granular materials. The second form of trapping accounts not only for the dimensions of the molecules but also for their shape, orientation, adhesion, elasticity and viscosity. The lateral compressional forces, tangent to the surfaces are responsible for the disturbance of the flow. The molecule trapping is said to divide, to distribute, to reduce the disturbance and hence the friction. In addition, the book includes a last chapter of 41 pages "Conclusions - Applications" (Choosing lubricants - Improving lubricants - Artificial lubricants) with one page devoted to watch lubrication and to the special process of surface neutralization. More research work was carried out by Doctor Paul Woog after he graduated. In 1928, he received the arreas of the Foundation Cldment Felix of the French Academy of Sciences, in order to "carry on his work on oiliness" (31). The members of the Committee who showed their interest in the study of oiliness had names as famous as : Joseph Boussinesq, Emile Picard, Paul Villard, Edouard Branly, Paul Janet, Jean Perrin, Aim6 Cotton, Edouard Fabry and Marcel Brillouin.

3. APPLICATION TO INDUSTRIAL LUBRICATION 3.1. Connection between academical work and petroleum industry In 1920, Professor George Friedel was appointed Director of the newly created Institute of geological sciences at the University of Strasbourg, close to the French oil field of Pechelbronn. When the Institute of Petroleum was created in 1922, Paul Woog was requested to read courses on viscosity and lubrication. He retained the same responsibilities at the Ecole Nationale Sup6rieure du Pdtrole et des Combustibles founded in 1924.

As soon as it was created in 1929, the Compagnie Frangaise de Raffinage decided to have the best possible research laboratory. In 1931, the new buildings of the Laboratoire Central in Paris were inaugurated, with Doctor Paul Woog as Director. His terms of reference were "the study of processes related to petroleum industry and the control of quality products". From the very beginning, the Laboratoire Central included a Department for watch lubrication and this needs some preliminary explanations. 3.2. The watch lubrication problem Since Huygens had invented the first pendulum clock in 1657 and the balance-wheel watch in 1675, the oil problem was considered as a nightmare by all clock makers. Friction and wear problems were described in 1714 by the French clock maker Henry Sully (32) : "Friction is almost the only obstacle to the perfecting of mechanics... Oil is absolutely necessary to prevent wear of constantly rubbing metals, even if the value of friction changes as a consequence of the drying or evaporation of the oil". During the same year 1714, the Longitude Act was passed by the British Parliament with a prize of £20,000 to reward any accurate and practical solution to the determination of longitude at sea. The carpenters' clocks (Harrison 1,2 and 3) were built by John Harrison from Yorkshire with self lubricating tropical hardwood and selected oakwood for the rubbing parts. They almost solved the problem of lubrication, wear and corrosion. But the fourth instrument H4 built by John Harrison in his competition for the Parliament Prize was in fact a watch, not a marine clock. Harrison used diamonds and rubies to reduce friction and wear, but he was unable to miniaturize the anti-friction wheels (and caged ball bearing of H3) so that he had to come back to lubrication. In 1762, H4 successfully passed the trial imposed by the Board of Longitude (five seconds lost after the 81 days voyage from Portsmouth to Jamaica, i.e. one minute and fifteen seconds in longitude against a requirement of 30 minutes). Paradoxically, the marine clocks H1, H2, H3 are still working in the National Maritime Museum in Greenwich, while the lubricated watch H4 would require such repairs that it was preferred to keep intact this historical piece of horology with all its original components. Obviously, lubrication at the time was not a long term solution.

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The fascinating book "Longitude" by Dava Sobel (33) does justice to the contribution of John Harrison to the quest for the Longitude, but the demand for the perfect oil had still to wait an answer for nearly two centuries... According to a tradition reported by Paul Chamberlain (34), the following dialogue took place between Napoleon and Abraham Louis Breguet, a French watchmaker, a native of Neuchatel : "Give me a perfect oil and I will give you a perfect watch" said Breguet to Napoleon. Napoleon had in a manner dared Breguet to make a clock for him which would wind the watch at midnight, set it to the exact time and move the regulator if necessary". In 1869, Henry Robert, a famous watchmaker appointed by the French State Navy found it necessary to publish again his "Summary on practical considerations on oils used in watch making" (35). The first paragraph reads as follows: "There is no perfect oil. Nothing is more frequent than hearing watch makers complain about the bad quality of the oil used to ease the friction between clock parts. Several of them have made great efforts to find methods which would give a constantly good oil. Celebrated chemists tackled the problem and nevertheless, all the work done up to now has produced nothing which could be considered as perfect, in all the force of that word".

3.3. Cooperation between watch makers and Paul Woog Charles Edouard Guillaume, Director of the Bureau Intemational des Poids et Mesures was very much involved in time control. He received the Nobel prize in 1920. He was the inventor of the alloys Invar and Elinvar. His spiral spring made of Elinvar which had an elasticity independent of temperature was further improved in 1922 by a famous watch maker of Neuchfitel, living in Paris, Paul Ditisheim. About 1925, at the request of the British Aviation Ministry, the British Engineering Standard Association established a test programme for watches and chronometers designed for aviation purpose between-60 and +60°C (an interval later moved to -20 to +100°C) instead of the usual interval +4 to +32°C. It was Doctor Guillaume who introduced Paul Ditisheim to Doctor Paul Woog whose patented process of neutralizing surface force fields

prevented the mineral oils from spreading out over metallic surfaces (36). The technical success of their cooperation was immediate. The watches lubricated with mineral oils passed the most severe tests of the National Physical Laboratory at Teddington in the best possible conditions. The results were similar in Neuchfitel and Besam;on (37) (38). An official presentation was made in London at the Exhibition of chronometers and watches organized by the Physical Society in 1926. As can be seen in figures (2) and (3) the technical press was as enthousiastic as the newpapers : "remarkable achievement", "genius of Mr Woog from Paris". The first version of the neutralization process, called Sigma and the first oils of Paul Ditisheim were further improved by the Laboratoire Central of the Compagnie Fram;aise de Raffinage.

4. THE EPILAME PROCESS

4.1. Original presentation of the Epilame process (figure 4a) The first patent on the method of "neutralizing metallic surfaces" was granted to Paul Woog's first employer George Wisner in Paris on the 1 l th of June 1925 under the title : "Improvement of the lubrication of mechanical components" (39). It refers especially to small mechanisms such as clock mechanisms. The patent starts from the fact that fatty oils currently used resist the attraction field of the metal but are too viscous at low temperature and unstable at high temperature. On the contrary, mineral oils may be both fluid at low temperature and stable at high temperature, but they spread out on metallic surfaces because of the attraction of the metal. The patent claims an improvement "consisting in the preliminary neutralization of the attraction field of the surfaces by depositing a layer of neutralizing substances, fatty acid or similar, in order to subsequently allow the lubrication of these components with liquids having liquid cohesion such as mineral oil, without any risk of spreading of the said liquids onto surrounding surfaces. In the communication to the French Academy of Sciences which followed on the 23rd of November 1925 (28), Paul Woog explains that "on the surface of a solid.., when a ring of oriented molecules is formed on the edges of the drop, this kind of barrier

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anchored on the solid modifies completely the appearance of the phenomenon. The active centers here mainly act by mutual attraction which is no longer counterbalanced by the attraction of the surface, the latter being neutralized by the fringe of oriented molecules. Thus a better apparent cohesion of the active molecules is to be found". Fifty two years before the concept of barrier films was described in the standard MIL-STD-1334 in 1977, Paul Woog described the barrier effect of the oriented molecules. He named the neutralizing layer Epilamen. The original process Sigma was later improved and renamed Epilame. The original patent received two additions. The first one in 1929 (40) claims that the invention is also valid for blends of mineral oils with fatty oils. The second addition in 1931 (41) combines the neutralizing effect with the anticorrosion properties of a varnish (figure 4b). In 1951, a US patent (42) was granted to a further improvement of the Epilame. The stearic acid was replaced by a baryum stearate which resisted abrasion better and remained effective from -60 to +IO0°C. Several processes called "epilamages" using silicones and derivatives as well as perfluorated polymers have been developed following the success of the Epilame (43) (44) (45) (46) (47). 4.2. The theories

Epilame process

in the light of modern

The work of Marcel Brillouin and Paul Woog is well known from Russian scientists and often quoted by A.S. Akhmatov (48). In 1964, M. K. Bernett and W.A. Zisman (49) provided the fundamental explanation of the Epilame process : "Essentially, the Epilame is a modification of surface substrate. A close-packed adsorbed monolayer of higher fatty acid, such as stearic acid, has a 7c value of 24 dynes par cm. Any oil and other liquid having a surface tension 7Lvo, at 20°C, greater than 24 dynes per cm would therefore be nonspreading on such a monolayer, and the equilibrium contact angle would be greater the larger the difference from liquid surface tension to critical surface tension". In the literature review presented at the same Symposium (50), Zisman provides a possible explanation for the fact that Paul Woog systematically avoid any reference to the contact angles which had been defined by Thomas Young as early as 1805. Until 1936, when R. Wenzel

developed a relation between macroscopic roughness of a solid surface and the contact angle, the measurements of contact angles were not considered as reliable by scientific authorities because they were not reproducible. The main criticism formulated by Zisman about the Epilame process were : a / a new treatment was necessary after solvent cleaning (is it a handicap in the case of watches ?) and b/the process itself would promote oxidation (or corrosion ? the varnish Epilame was designed to overcome this problem).

5. F O R M U L A T I O N OF LUBRICATING OILS FOR W A T C H M A K I N G Whereas Europe still used neat's foot oil or sheep's foot oil and the United States prefered oil from the head of the porpoise, Paul Woog developed pure mineral oils sometimes blended with animal oils. These oils were specially treated to improve their purity and low temperature behaviour. They were also treated with anti oxidant additives. 5.1. Stabilization against oxidation - Compatibility of additives

Paul Woog (51) knew very well the work done by the French chemists Charles Mouren and Charles Dufraine on the inhibition of acrolein by the socalled "antioxygene agents" such as phenols, diphenylamins naphtylamins... He used them in order to stabilize the commercial oil Chronax (figures 4c and d). But he also observed that some of these chemicals formed a surface layer of their own which reduced the lubricating efficiency. Hence Paul Woog's idea to add to these antioxygene agents, introduced to protect the bulk oil, some molecules of a chemical product which could show "a greater affinity for the solid surfaces" and would deplace the antioxygene molecules already adsorbed". This mechanism of additive competitivity was fully described in the French patent "Improvement in lubricants" granted in Paris on the 13th of March 1926 (52) and its addition of 1927 (53). The phenomena became even more important with the introduction of new additives in oil formulation (54) (55) (56) (57) (58).

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5.2. Stabilization against light The French patent "Means of protection of lubricants against the action of light" was granted in Paris on the 2nd of December 1929 (59). It describes the use of yellow or red opaque dyes as built-in filters of UV Rays. For the stabilized oil Chronax red dye was preferred as it recalled the colour of the ruby stones used in clocks and watches.

6. CONCLUSION There is not enough room here to describe all the innovations introduced by Professor Paul Woog in the field of watch lubrication and industrial lubrication. Some of them are to be found in reference (60). It is hoped that the examples given in this paper will increase the international recognition of the French contribution to lubrication problems in the twenties. It might be adequate to quote the last words of Paul Woog's book published in 1926 (30) : "ART OF OILING, SCIENCE OF LUBRICATION Now that we have reached the end of the programme we set ourselves, we feel better than ever how justified is the title of our work : Contribution to the study of lubrication. As has been seen, the question of oiling is most complex, and only a deep scientific study will allow it to be mastered : but on the basis of such a study, whose mathematical analysis has already enlightened some fields, we are convinced that the Art of Oiling, based on passed experience, will evolve to a Science of Lubrication, henceforth permitting a better efficiency of the forces used by human beings". If the concept of Tribology emerged only forty years later, it is certain that it was already conceived and evoked by Paul Woog in 1926.

REFERENCES 1. 2. 3. 4. 5.

Lehmann O., Ann. der Phys., t.XL, 1890, p.401 ; t.41, 1890, p.525 Friedel G. and Grandjean F., Bull. Soc. Min., t.33, 1910, p.192 Mauguin h., Bull. Soc. Min., t.34, 1911, p.71 Perrin J., Ann. Phys., i-9, t. 10, 1918, p. 160 Friedel G., Ann. Phys. s-9, t. 18, 1922, p.273

6. 7.

Wells Ph-V, Ann. Phys. s.9, t. 10, 1918, p. 160 Grandjean F., Bull. Soc. Min., t.xxxiv, 1916, p.164 8. Mt~ller A., and Shearer, G., J. Chem. Soc., vol. 123, 1923, p.2083, 3152 9. Piper S.H. and Grindley, E.N., Proc. Phys. Soc., t.35, 1923, p.269 10. de Broglie M. and Friedel, E., C.R. Ac. Sc., t.176, 1923, p.738 11. Trillat J.J., C.R. Ac. Sc., t.180, 1925, p.280, 1838 12. de Broglie L. and Trillat, J.J., C.R. Ac. Sc., t.180, 1925, p.1485 13 Rayleigh J.W.S., Nature, 02.03.1891 and 12.03.1891 14. Hardy W.B., Proc. Roy. Soc., s.A., t.88, 1913, p.303 15. Langmuir I., Chem. Mct. Eng., t. 15, 1916, p.468 16. Langmuir I., J. Am. Chem. Soc., t.38, 1916, p.2221 17 Langmuir I., J. Am. Chem. Soc., t.39, 1917, p.1848 18. Harkins W.D., Davies and Clark, J. Am. Chem. Soc., t.39, 1917, p.1848 19. Rayleigh J.W.S., Phil. Mag. t.35, 1918, p.157 20. Dunstan A.E. and Thole, F.B., J. Petr. Tech., t.4, June 1918, p. 191,205,206 21. Deeley R.M., Proc. Phys. Soc., t.32, part II, 1920, p.15 22. Hardy W.B. and Hardy J.K. Phil. Mag., $6, 38, 1919, p.32 23. Brillouin M., J. Phys. et Rad., t. 1, 1920, p.33 24. Woog P., C.R. Ac. Sc., t.173, 1921, p.303 25. Woog P., C.R. Ac. Sc., t.173, 1921, p.387 26. Woog P., C.R. Ac. Sc, t. 174, 1922, p. 162 27. Woog P., C.R. Ac. Sc., t.180, 1925, p.1284 28. Woog P., C.R. Ac. Sc., t. 181, 1925, p.772 29. Woog P., "Contribution ~ l'6tude du graissage, oncuosit6, influences mol6culaires"- th6ses pr6sent6es h l'Acad6mie des Sciences, Paris, Delagrave, 1926 30. Woog P., "Contribution h l'6tude du graissage, onctuosit6, influences mol6culaires" Paris, Delagrave, 1926 31. C.R. Ac. Sc., t.187, 1928, p.1208 32. Sully H., "R6gle artificielle du temps, trait6 de la division naturelle et artificielle du temps, des horloges et des montres de diff6rentes constructions,...", Paris, G. Dupuis, 1737, p.206

627

33. Sobel, D. "Longitude", Fourth Estate Ltd., London 1996, ISBN 1-85702-571-7. 34. Chamberlain P.M., "Laboratory Research and the Solution of the Watch lubrication problem", The Horological Journal, March 1936 35. Robert H., "Abr6g6 de consid6rations pratiques sur l'huile employ6e en horlogerie", Paris, 1869 36. Ditisheim P., "Sur l'emploi des huiles d'horlogerie naturelles et artificielles", Revue Opt. Theor. Instrum, 1939 37. Ditisheim P., "Etat actuel de la question du graissage en horlogerie" Ann Franc. Chronometrie, N°2, 1931 38 Ditisheim P. "Bull. Ann. Sce et LSRH, Berne, 1932, p.27-29 39. Wisner G. Brevet Fr., Gr., C1.3, N ° 612.077, 11.06.1925 40. Idem, Add. 1, N ° 37667, 1929 41. Idem, Add. 2, N ° 40504, 1931 42. Woog P. and CFR, US Pat. N°2, 673, 818, 1951 43. Brilli6 H., "Influence de l'6tat de Surface sur les Ph6nom6nes de Lubrification", Compagnie G6n6rale Transatlantique, 3 Journ6es Int. Chrono. & M6trologie, 1937, Paris, p.590-618 44. Dinichert P., Renauld J., "Etats de Surface et Etalement des Huiles d'horlogerie", Laboratoire Suisse de Recherche Horlog6re, 31 Bulletin Annuel de la SSC & LSRH, 1956, Neuchfitel, p.681-696 45. Massin M., "Epilames et Lubrifiants Associds /~ Haute Stabilit6 - Rdsultats en Horlogerie", CETEHOR- Centre Technique de l'Industrie Horlog6re, Bulletin Annuel de la SSC & LSRH, 1970, Lucerne, p.93-98 46. Renaud J.P., Renfer A., "M6thodes de Nettoyage et Comportement des Huiles d'horlogerie sur les Rubis, LSRH Laboratoire Suisse de Recherche Horlog6re, 06 Congr6s Int. de Chrono., 1959, Munich, p.779-788 47. Renaud J.P., Renfer A., "Contr61e de l'6tat de Propret6 des Surfaces par des Mesures d'6talement d'huile", LSRH - Laboratoire Suisse de Recherche Horlog6re, 48 Bulletin Annuel de la SSC & LSRH, 1973, Lausanne, p.447-453

48. Akhmatov A.S., "Molecular Physics of Boundary Friction", Israel Program for Scientific Translations, Jerusalem, 1966, p.217-218, 308-309, 317, 322-323,328 49. Bemett M.K., and Zisman W.A., "Prevention of Liquid Spreading or creeping", in Contact Angle, wettability and adhesion, Advances in Chemistry series 43, ACS, 1964, p.232-340 50. Zisman W.A., "Relation of the Equilibrium Contact Angle to Liquid and Solid Constitution", Advances in Chemistry Series, ACS, 1964, p. 1-51 51. Woog P., "Etude sur la Stabilisation des Huiles pour l'horlogerie", Annales Fran~:aises de Chronom6trie, N°2, 1931 52. Wisner G., Brevet Fr., Gr. 14 - C1.4, N ° 646.756, 1926 53. Idem, Add. 1, N ° 36.428, 1927 54. Dtirr F., "Une contribution au sujet des Tests M6caniques Dynamiques des Lubrifiants", Universitt Stuttgart, 08 Congr6s Int. de Chrono., (C) 1969, Paris, p.C32001/1-23, Allemand 55. Renaud J.P., Renfer A., "Essais d'usure sur la Machine /l Quatre Billes, Applications aux Lubrifiants utilis6s en Horlogerie et en Microm6canique", LSRH - Laboratoire Suisse de Recherche Horlog6re, 09 Congr6s Int. de Chrono., (D), 1974, Stuttgart, p.D3.10 56. Renaud J.P., "Expos6 de Synth6se ; Frottement, Usure, Lubrification", LSRH Laboratoire Suisse de Recherche Horlog6re, 49 Bulletin Annuel de la SSC & LSRH, 1974, Gen6ve, p. 715-720 57. Renaud J.P., Renfer A., "Essais d'usure sur la Machine /t Quatre Billes. Applications aux Lubrifiants utilis6s en Horlogerie et en Micromdcanique", LSRH 6 Laboratoire Suisse de Recherche Horlog~re, 49 Bulletin Annuel de la SSC & LSRH, 1974, Gen6ve, p.741-748 58. Maillat M., "Am61iorations apport6es aux huiles d'horlogerie en relation avec des mesures de frottement et d'amplitude - Lien entre le frottement et l'amplitude" - LSRH Laboratoire Suisse de Recherche Horlog6re, 10 Congr6s Int. de Chrono (3), 1979, (54 CSC), Gen6ve, p.401-412 59. C.F.R., Brevet, Fr., Gr. 14 - C1. 4, N°701.522, 1929

628

60. du Parquet J., "Horlogerie m6canique et tribologie" - Actes des Joum6es Intemationales Francophones de Tribologie 1997, SIRPE, Paris, 1998.

M. W ~ Directeur des Laboratoires de la Compagnie Francaise de Ra~inage.

Figure 1

629

TIlE WATCHblAI(ER, JEWELER

SII.VERSblITII AND OPTICIAN NEW

WATCH

for E X T R E M E

TEMPERATURES',

Amollg t lie exhibits at. tim Pilysica.l Society's Exhibition were a number of cllronomelers and watches by Paul Ditisheim, of Ln Chaux-de-Fonds, Switzerland. This manufaclurer llol(Is tile best reconls sil~ce 1905 ill t.lm Kew Trials. One o[ the watches shown havillg obtained 97 marks in the 1924 tests attracted considerable attention whilsg another piece was exl~ibited witl~ its curl'iculum vit,-e in the shape of five different certificates: Record at Geneva Observatory, NeuchMel Observatory, Besan~;on Observatory, besides having reached 96.5 marks at Kew. This timekeeper obtained 892 marks at Geneva Observatory, the previous best. result being 879 only. Tl~e high degree o[ accuracy reached is due partly to simplicity and robustness of design, but, largely to the scientific t r e a t m e n t of the compensation problem. Paul Ditisheim uses balance springs made o[ Guillaume's Elinvar alloy, which does not vary in elasticity v,"~ temperature and is, in addition, non-magnetic an(i inoxydizable. The balance is a simple, solid wheel, rendered adjustable by two bimetallic " affixes." This combination gives the most accurate compensation at all temperatures, and is being used in a new, machine-made pocket watch wl~iel~ has recently been tested at NeuchStel Observatory between - 6 ° Fahr. and + 119 ° Fahr. ('that~ is to say, beLween arctic and tropical extremes). Over that~ unprecedently wide ravage it shows only m i n u t e cl~anges ill rate; a remarkable achievement, duo to the use o[ a special lubricat, ing oil developed by M. P a u l Ditisheim in conjunction with M. Paul Wo££ga o[ Paris. Tile lubricanL r e m a i n s fluid within the temperature range indicated, and in order that~ it; shall be retained in the bearings to wl~ich it is applied, the metal is " neutralized " b y dipping in a preparation which prevents the oil spreading. In exploration work and on aeroplanes this invention should prove invaluable.

THE

CLOCKMAKERS'

COMPANY.

At the Christmas Quarter Court,. held on J a n u a r y l l t h , Ernest Edward Finch, Esquire, Chie[ Engineer to the Corporation o[ the City o[ London, was admitted to the Freedom and elected to the Livery. In addition to t,ho usual subscriptions to cra.[[ charities, the Company made tile undermenlioned donations : - Clerkenwell Maternity I n s t i t u t i o n , £5 5s. Clel'kellwell Police Court., £5 5s. City of London Pension Society, £5 5s. Police Courl~ Mission, £5 5s. Hoxton Market Mission, £5 5s. The Court decided to accept, an invitation, received from the President of t h e Board o[ Education through the Victoria and hlbert~ Museum, to loan their Collection o[ Clocks to the Exhibition to be held at South Kensington next Summer.

Figure 2

tfie~:hd0pt'roli of a slyle-:--a l:ath.ol.ic style, I ..... if you'iwill--wli.i'cll Ihe oouturicrs v,ould I'P.res IJe.,'-~l)l'[ged to f o l l o w . ~ e can never l °lsn -l"AVh'eri .,Cat,ho~i(~ ,France ~nows l.ne-r~ .~. wa.~. in/~al:s.'fl/Cld~for modest.y, Catholic , " •

do

WATCH AND THE CHRONOMETER. .

/t/

STUDY ....

•

IN

MECHANICAL

INTELLIGENCE.

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"Dally Express" Speolai ..Representative. I went to see an exhibition of chronometers and WatChes at the llbyal Instil u t i 0 n in Albenmrle.street and came away chastened. These instruments are not watches in tl~e p o p u l a r sense ot t h e w o r d . "131iey are i n h u m a n l y accurale. Ti~ey gain or lose a second or two a day--the best watch does this; but you c a n .rely on them to gain or lose constantly. They never vary. " T h e i r virtue lies in thetr balance springs, made of an alloy--Elinvar-I h a t never varies in elasticity, despite '~changing t e ~ p e r a l u r e s . Chronometers have, too, a superior system of lubrication'. They enjoy the benefit of t h e . g e n i u s of Mr .Woog, of Paris, who discovered d~ow to prevent mineral, oils spreading by coatlng, the mechanism witl~ an acid .preparation. Mineral oils are really better than the less spreading sheep's foot and fishoils used i n ordinary xVatches: I took o u t . m y watch in the presence of the demonstrator to compare It with the c h r o n o m e t e r s : it had stopped. As an example of supreme tact I think this would be l~ard to beat. .

Figure 3

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E P 1L A M E PROCESS THE EPILAME BATH EFFECTIVELY PREVENTS M I N E R A L A N D O T H E R OILS F R O M S P R E A D I N G A N D = IS S P E C I A L L Y S U I T A B L E F O R W A T C H E S , CLOCKS AND SM:ALL MECHANISMS.

A.

S P R E A D S S 'U R F A C E ~1S U S E D

B.

$ H O W ' I N G E F F E C T OF' T R E A T I N G S U R F A C E 'WI;TPI EPIL, AME SOLUTION, THE OIL FORMS A GLOBULE ~D DOES N O T S P R E A D

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Figure 4 a

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DI~PA, R T E M E : N T HUIL:ES D'HORLOGERIE Dt~LI~:GATION G~_N~RALE • P A U L D I T I S H E I M

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631

VERNIS Ilrc~~.l("

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Les vernis habituels employ6s dans les fabriques de r6veils, eompteurs, etc., sont efficaces pour prot~ger la surface des platines de laiton eontre l'oxTdation, mais ces v e m i s p r o v o q u e n t la disparition p r e s q u e i m m e d i a t e des huiles. Le ~t:,t~ \ I~ E P I L A M E assure, au contraire, le m a i n t i e n du graissage. II p r u r i e n t l ' d t a l e m e n t des huiles et joint a u x qualit~s de I ' E P I L A M E ses propri~t~s de V E R N I S p r o t e c t e u r des surfaces (consul-

ter le Mode d' Emploi). Le t t!III~N I~ E P I L A M E s'obtient sous la forme repr~sent~e page 4, en bidons de 1 litre et en bidons de 5 litres.

Figure 4 b

H UILES

CHRONAX

STABILISEES

Ces huiles de colrleur rouge-rubis, poss~dent une stabilit6 remarquable et assurent un graissage de choix p e n d a n t une dur6e considdrable. Les qualit6s sp6ciales des H U I L E S CHRf~X=~X ST ABIIII~ISEES rdsultent d ' u n t r a i t e m e n t fait au m o y e n de certaines substances Antioxygbnes qui prdvient leur ddcomposition : s i m u l t a n ~ m e n t , des corps a b s o r b a n t les rayons, actiniques e m p ~ c h e n t les alterations ddtermindes par l'action de la lumibre. Les Huiles C H R O N A X ~.T ~ B ILI S t!!~E ~ sont livrdes c o m m e suit au m~me t a r i f que les Huiles C H R O N A X normales, qu'elles sont appeldes h remplacer : Flacons 5 gr. Flacons 15 gr. Type ES en ~tui Flacons 30 gr. Type FS aluminium Type industriel Types AS .... Flacons 125 gr. BS ....CS .....DS Types A I S - BIS ..... CIS - FIS

Figure 4 c

632

TABLEAU DES VISCOSITES Waleur~ des, ,eoelli(.',ients

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S E S S I O N XVI FRICTION A N D W E A R

Chairman •

Dr. G.W. Roper

Paper XVI (i)

Effects of Composition and Surface Finish of Silicon Nitride Tappet Inserts on Valvetrain Friction

Paper XVI (ii)

Wear Modes in Lubricated Brass-Tungsten Carbide Contact

Paper XVI (iii)

Influence of Lubricant Properties and Temperature on the Scuffing Failure of FZG Gears

Paper XVI (iv)

Surface and Near-Surface Interactions Affecting Friction and Wear

Paper XVI (v)

Conception of Numerical and Experimental Tools for Study of the Tribological Transformation of Surface (TTS)

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

635

Effects of Composition and Surface Finish of Silicon Nitride Tappet Inserts on Valvetrain Friction

A m p Gangopadhyay, Douglas McWatt, Pierre Willermet, Gary M. Crosbie, and Richard L. Allor Ford M o t o r Company, Dearborn, MI 48121, U S A

In order to build more fuel efficient engines, new materials and lubricant formulations are being sought to reduce frictional losses. The valvetrain contributes about 6-10% of the total frictional losses in an engine. To reduce valvetrain frictional losses, polished silicon nitride tappet inserts were evaluated for their friction reduction potential. Silicon nitrides obtained from three sources were polished using three different processes: the supplier's conventional diamond polishing technique and two non-diamond polishing techniques -"Ford Finish" and chemo-mechanical polishing. The valvetrain friction torque was measured in a laboratory apparatus using a single cam lobe rotating against a direct acting mechanical bucket tappet with production engine hardware. The friction torque values obtained with surfaces prepared by all three processes differed significantly although their initial centerline average surface roughnesses were similar. All three silicon nitride surfaces prepared by "Ford Finish" showed lower friction torque than the production steel surface when an engine oil containing no friction modifier was used. With a low friction oil containing a friction reducing additive, friction torque values were significantly lower and polished silicon nitride surfaces did not offer additional friction reduction benefit relative to the production steel surface. A simple calculation showed a maximum of about 0.5 % fuel economy benefit can be gained clue to polishing with the engine oil without friction modifier but very little, if any, with low friction oil. However, silicon nit.ride inserts may be useful for weight reduction and increased durability.

1. I N T R O D U C T I O N In order to build to more fuel efficient engines, new materials and lubricant formulations are being sought to reduce frictional losses in engines. The valvetrain, piston ring/cylinder bore and bearings are the three major component systems which contribute greatly to frictional losses in engines. The valvetrain contributes about 6-10 % of the total frictional losses, depending on design (1). Valvetrain frictional losses have been reduced in the past through better design, i.e., use of roller followers, lower spring loads, lower reciprocating mass by using lightweight material, etc., (2). However, some of Ford engines use slider cam followers, e.g., direct acting bucket tappets. Although a sliding contact is generally expected to produce higher friction than a roller follower, a bucket tappet design is favored for

its simplicity, cost and packaging. In the mechanical bucket tappet design, a removable steel insert is used as the cam contacting element. The direct acting mechanical bucket tappet typically operates under boundary and mixed (boundary plus hydrodynamic) lubrication regimes." This offers an opportunity to reduce frictional losses in this contact with improved surface finish on the insert and cam lobe, new insert materials and lubricants containing effective friction reducing additives. Masuda et al. (3) and Katoh and Yasuda (4) showed that a significant reduction in valvetrain friction torque can be obtained if surface roughnesses of both camshaft and inserts are reduced. It has been reported that silicon nitride inserts with mirror-finish surfaces (R~ - 0.02 ~m) reduced valvetrain friction by about 20 - 25 % in a motored

636

test which translated into 2-3% improvement in fuel economy in a Japanese driving cycle (5). The use of silicon nitride inserts appears additionally attractive because of its rigidity, light weight and higher wear resistance. Masuda et al. also showed that deposition of a TiN coating on a mirror-polished (R, - 0.02 ram) steel reduced cam lobe surface roughness to 0.02 ram R, in a short time. The low surface roughness of both the contacting surfaces achieved a 40 % reduction in friction torque compared to a conventionally finished insert. The objective of t h e present investigation was to evaluate the effect of polished silicon nitride inserts, prepared by various techniques including one inexpensive non-diamond process, on the valvetrain friction torque. Another objective was to evaluate the friction reduction potential previously claimed by other researchers in a Ford valvetrain design.

2. EXPERIMENTAL 2.1 Test Apparatus The cam/tappet apparatus was described in detail elsewhere (6). It essentially consists of a single cam lobe from a production engine which is driven by a 2 horsepower motor against a direct acting mechanical bucket tappet with a removable insert as shown in Figure 1. A steel valve having a mass equivalent to a production valve was used with a production valve spring. The tappet reciprocated in an aluminum bore made out of a production cylinder head. The center of the cam lobe was at an offset from the center of the tappet insert to allow tappet rotation and reduce friction torque (7, 8). The cam lobe/insert contact area is lubricated by a jet of lubricant at 100°C at 30 psi. The friction torque is measured by a transducer mounted in line with the drive shaft. This particular cam lobe had been used in past testing for several hundred hours and therefore, it was considered already ran-in. A new production bucket tappet and a new aluminum bore were used for all the tests. Only the tappet insert was changed for each test.

2.3 Materials Silicon nitride inserts obtained from three sources represent a range of microstructures, compositions, and mechanical properties as shown in Table I and Figure 2. All three materials contain needles of beta silicon nitride with an amorphous grain boundary phase. The needle dimensions varied from the coarsest in the SN-U 1 material to the finest in the SN-J material. Each silicon nitride included yttria as a sintering additive. The back scattered scanning electron micrographs in Figure 2 accentuate the distribution of yttria, which appears as light areas. The uniformity of the yttria distribution follows the needle sizes. Other constituents in the materials are alumina and magnesia. Alumina is present in all materials but the highest amount is in the SN-U material, where there is more alumina than yttria.

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F i g u r e

2.2 Lubricants The lubricants used were (a) 5W30 factory fill oil (Oil A) containing no friction modifier and (b) a low friction 5W30 European factory fill oil (oil B) containing about 700 ppm molybdenum dithiocarbamate (MoDTC) as a friction modifier.

Magnesia appears only in the SN-J material and the amount of magnesia is about the same level as that of

1 Ceradyne grade 147-3

637

(a) alumina. The SN-E: silicon nitride contains tungsten carbide presumably from contamination in milling the starting silicon nitride powder The mechanical properties of the SN-U and SN-J materials were determined at Ford, but the reported values for SN-E were obtained from the supplier's literature. The finer grain size of the SN-J material leads to exceptionally high strength, at 1450 MPa in a 4 point bend test. The SN-U material showed the highest measured fracture toughness at 6.4 MPa.m in. The Weibull modulus of all silicon nitrides is in the range 15 to 20. All the silicon nitride inserts were highly polished when received and hereafter referred to as "As received". In addition, a slightly oversized blanks were also obtained for finishing by other techniques for comparison. These were an inexpensive nondiamond polishing technique referred to as "Ford Finish" and a chemo-mechanical polishing (CMP) technique referred to as "CMP Finish". In "CMP Finish" the inserts were lightly pressed against a slowly rotating cast iron wheel in the presence of an oxidizer. Also evaluated were (a) a production steel insert with a 4-8 l~m thick manganese phosphate coating, (b) a polished production insert after removing the phosphate coating, and (c) a diamond ground SN-U insert. The polished steel was evaluated to examine whether the friction reduction was due to surface finish only. The ground SN-U insert was evaluated to determine the friction reduction potential of polished surfaces.

2.4 Surface Roughness Characterization The surface roughnesses of all inserts were measured in two orthogonal directions before and after test using a stylus profilometer to monitor changes in surface roughness. The surface roughness of the inserts prior to testing is shown in Table II. The back side of each insert was marked prior to test to ensure roughness measurements were done in the same general area after test for a meaningful comparison. The surface roughness of the cam lobe was not monitored.

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The inserts were also weighed before and after test for wear estimation.

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2.6 Test Procedure

Any previous lubricant remaining in the test apparatus was first flushed and only then the apparatus was filled with the desired lubricant. The lubricant temperature was raised to the set level and then the lubricant was circulated through the apparatus. The measurements were started after the lubricant was circulated for about half an hour to allow for temperature equilibrium in the system. The friction torque data were averaged over 17 cycles. The average friction torques were collected at 500, 750, 1000, 1250 and 1500 RPM cam lobe speeds. The initial run-in was performed with a production steel insert and friction torque measurements were recorded at 15 minutes intervals. The friction torque value continued to drop for about 30 hours due to run-in between the cam lobe and the new insert and also between the steel tappet and the new aluminum

recorded for two SN-E inserts with Ford Finish in the presence of oil B. The results in Figure 4 show good repeatability supporting that "Ford Finish" is reproducible. The repeatability of friction torque measurements across the test period was also 0.2 0.18 0.16 0.14 A 5107-148-6

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5

Test D u r a t i o n , h o u r s

Figure 3. A typical friction torque curve obtained with oil B for SN-J /Ford Finish. bore. A shorter run-in period (about 5 hours) was observed with a new insert. At any cam lobe speed, friction torque data were recorded until a steady state value was maintained for about an hour as shown in Figure 3. Only then was the cain lobe speed increased to the next level.

3. R E S U L T S

AND

DISCUSSION

In order to check the sample to sample repeatability of measurements, friction torques were

confirmed which will be shown later. The friction torques obtained with various insert materials finished by different techniques are shown in Figure 5 using oil A. In general, friction torque decreased with increasing speed due the change of lubrication regime from more boundary to mixed. Both the production and polished steel showed similar friction torques although the initial surface roughness levels in these inserts were different. In the case of SN-U inserts, all finishes showed lower friction torque compared to the production steel insert with the exception of the ground insert which showed higher friction torque. In the case of SN-E, both "As received" and "CMP Finish" inserts showed higher friction torques than that of the production steel insert. Only the SNE "Ford Finish" insert exhibited lower friction torque than the production steel insert. Interestingly, the SN-E "CMP Finish" insert with the lowest initial Ra value exhibited the highest friction torque The SN-J insert with "As received" exhibited higher friction torque compared to that of the production steel insert in spite of lower initial Ra value. The SN-J "Ford Finish" insert exhibited lower friction torque compared to the SN-J "As received" but "CMP Finish" exhibited much higher friction

640

0.3 0.28 0.26 0.24 0.22 0.2 0.18 I

~7

0.16

Ill

@

0.14 0.12 0.1 Polished steel + Polished steel X Production steel [] SN-E / As received • SN-E / Ford Finish O SN-U / As received • SN-U / Ford Finish SN-U / CMP Finish A SN-J / As received A SN -J / Ford Finish SN-E / CMP Finish & SN-J / CMP Finish - SN-U / Ground Finish

0.08 0.06 0.04 0.02

I

0

250

500

750

I

I

f

1000

1250

1500

1750

Camshaft RPM

Figure 5. Friction torques obtained with oil A . torque, although " CMP Finish" had the lowest initial R~ value among the three finishes. All three silicon nitrides with "Ford Finish" showed lower friction torque than that of the production steel as shown in Figure 6. (These results although included in Figure 5, are shown separately for clarity). The lower friction torque is conjectured to be related to possible transfer layer formation on on silicon nitride surface from the grinding wheel. The production steel and the ground SN-U inserts had comparable initial Ra value yet, the latter exhibited higher friction torque. However, there may be cam durability issue with ground insert which has not been addressed here. The production steel became

smoother (Ra - 0.09 gin compared to 0.28 gin) at the end of test whereas the surface roughness of the ground SN-U insert remained almost the same. The surface roughness of other silicon nitride inserts also did not change significantly at the end of test with the exception of the SN-J insert with "CMP Finish" which showed a slight increase of Ra value (0.04 gin compared to 0.02 gm) due to the formation of thick lubricant derived surface film as discussed later. The wear of the inserts was too small to be measured because the observed weight change was very small and it was within the accuracy of the scale.

641

It was observed that inserts also rotated independently of the tappet. Therefore, the relative motion between the insert and the tappet could contribute to the measured friction value. The surface roughnesses on the back side of the inserts were measured to ensure that differences in surface

.~

smooth whereas the SN-J insert appeared somewhat rough in a submicron scale. But the surface roughness values, measured by a stylus, were similar on both inserts. It is possible that stylus measurements are not sensitive enough to capture submicron level features. Examination of worn surfaces (with oil A) did not show any obvious (a)

0.3 0.275 0.25 0.225 0.2 0.175 0.15 0.125 0.1 0.075 0.05 0.025 0

X Production • SN-E •

:.. ~ i ~ =--~:'~ ;~ '.i:~ " : •

&eel

""

.'?.~:~ :~i:"

~.i~-" ~i~. . . . . .! '

. ii!

SN-J

::i:i;...... i'i. ': ....i: ~.x~..N . ..'..~:

'

• SN-U

i r

250

500

~~--~.~--

X

'

i

i

1000

1250

1500

1

750

l

Camshaft

l

l

1750

RPM

Figure 7. Friction torques obtained with "Ford Finish" with oil A. roughness on the back side of the inserts did not influence friction torque measurements. It was observed that SN-U "as received" and "Ford Finish" inserts have similar R~ values on the polished side but significantly different Ra values on the back side, yet both inserts exhibited similar friction torque. Similar observations were made for SN-J "As received" and "Ford Finish" inserts. It was, therefore, concluded that the finish on the back side of the insert contributed very little to the measured friction torque values. In order to understand the possible cause for higher friction torque observed with "CMP Finish" on the SN-J insert compared to that on the SN-U insert, the two unworn inserts were examined under a scanning electron microscope attached with a x-ray energy dispersive spectroscope. "CMP Finish" used an oxidizer during polishing. It was postulated that during polishing the oxidizer may attack the MgO and Y203 rich grain boundary phase which would result in weakening of bonds between grains. During friction testing, the grains would pull-out which would result in higher friction torque. Examination of the unworn surfaces of SN-J and SN-U inserts at high magnification under the scanning electron microscope (Figure 7a and 7b respectively) showed different microstructures. The SN-U insert appeared quite

(b) "" [$'.'i!~ •' ~"i~'~ .~,~ii.:'

•

'

~.

"

"

:

i~

-

........ ~

~

~

.'

Figure 6 Secondary electron micrographs of unworn surfaces of (a) SN-J and (b) SN-U silicon nitride inserts following CMP Finish. evidence of grain pull out. Therefore, the reason for higher friction torque observed with SN-J insert is not fully understood. The sliding areas on both inserts however, contained thin films which were believed to have formed due to interactions between lubricant additives and surfaces. The films on the SN-U insert appeared to be distributed more evenly than those on the SN-J insert as shown in Figure 8. The elemental analysis from a spot on the films on the SN-J insert

642

:,~r~:,~.,.,'.!i~.:,::~:'.~,

(a)

,.: .~::...:+:::., ~ .... ,:::.. : x~:"::~:!:i;!:":~," ....

. .. ~ : . . . . .~,~.~':': " ...." ~ .- ..... ~ -~7 ~~;.. ......

. .

~ ~ . . . : ..... ......:. .~.~x.. ~:!:~~~i!~~ :::% ' ':'"'!"~::: "- ~,.x% ':: ;~.~ ~;

0.2 0.18 0.16

B Run # 1 .~Run # 2 IRun # 3

0.14 0.12 0.1

I R

0.08 0.06 •~

0.04 0.02

........ :...

:

'.,.,~4 •:,',,~.~.

,~ ~

'"':~

~

(b)

...........

..........

.,

"

-z~. . . . . . - .. ~

~

:

~

Imm

~ ~

~ ~. -

,~.,'

.! i~$:~

,

.. . ~ ~

"

•:i& :,.."~

..:~ Ii~i1

"il !!i~

1~!i7 lii::. ..~:" :~:~'

.:~~

:~ii~ ~"

•:& "-i~::

I

1000

1250

1500

Camshaft

1750

RPM

Figure10. Friction torque data for SN-E obtained with oil A. .

~

750

I

": ...,,, : ~..... t.~'.~.::::::::!:::i~;~

. --oB V~B

ii i

iliiii!ii!jilil

i [ iiti !ii: iii!i:i:iii.i:ii::i!iiiii;ii:iii;;iiii !

i li: : ~i I ~ ii

\~ J !~ii~ ~i[:! li ~i ii!/! ~ ~ I : ..- ~ii:i!ii!ii!iiiiiiiiiii!!i::~:~ii:i~:iil ~ .... : : .........:.: .:-.. ~! :iiili I.........ei~!68 ~ .l ~iii : 1 ' .

I :

i i J

I!

C

ii~i

0: :5:::~:::. ::q::..::::-:.::. i0 :::::::::::::::::::::: 15 :::::::::::::::::::::::::::::: .! ! : : • .........:. vs,!(n~sii)!ii:::::!::.:::i: :i: :i ::-::..

(4)

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

Figure 1 - Curves Pl+°14vl-°14=Const.

,

.::::

,

,

i

658

..... :C~i;~i s.o,~i

.................. i..... i.... i..... !.................. i i

i ! !i}

ii

! ;i

i

!i !::

ii • ii

:!:ili:i::li it I I : .......... o 0 ............. 2o: .............. 40 ............... ~0 ............... s.0 ...............

!ii iiiiiiiiiiiii!iliiii!iiiii)il iiii~'iilTis!iil ii iili iiiiiiiiiiiiiiiiiiiiiiiiii!i)ii!iiii Figure 2 - Representation of pl'14V°'86 =C Vo (9o'9R). Table 2 Traction coefficient and FPI criteria Test N °

~MIC

IXlSO

~c,~c

g~cPV

glsoPV

gc~cPV

1

0.038

0.057

0.174

0.100

0.151

0460

2

0.049

0.084

0.085

0.259

0.443

0 447

3

0.057

0.116

0.054

0.455

0.922

0.430

4

0.062

0.126

0.140

0.206

0.417

0.463

5

0.044

0.073

0.118

0.176

0.290

0.469

6

0.029

0.040

0.097

0.116

0.158

0.386

7

0 066

0.138

0.106

0.262

0.546

0.422

8

0 046

0.076

0.090

0.215

0.350

0.414

9

0.032

0.044

0.075

0.171

0.233

0.397

10

0.042

0.071

0 042

0.445

0.746

0.444

11

0.051

0.091

0 079

0.306

0.543

0.467

0.246

0.436

0.436

Mean values (GPa.ms")

It is possible to observe in figure 3 and in table 2 that traction coefficients ~so and ~cale are normally higher than ~t~c. Figure 4 clearly shows that FPI criteria using ~qso and g~c traction coefficients, produce quite random values, not in agreement with the criteria. On the

opposite, the FPI criteria with the tXcal¢ traction coefficient produces almost constant values. Figure 5, shows the relation between laca~ctraction coefficient and the specific lubricant film thickness in scuffing conditions. In general, high traction coefficients are related to low specific lubricant film thickness, which is typical for mixed lubrication

659

[

iiiiii~P...V..~3Ptt~.i:iiiiiiii!ii!!iii!iii!i~!iiiiiii!iiiiiiiiiiii!!iiiiiii!iiiiiiiiii

0.14

i ::

i]?

i:

:.

]

i: ::!!iiiii (?:.iii:.i~~~/i!.!~)~~-::i~:::~::!:!i:

~:i:!::!!i

: : o.o2 I i .......

I i

2 ..... 3 .... 4 ..... 5 ...... 6 .... 7 ..... 8 ..... 9 ..... i0

11',:,

. i i ..................

~teil nb

Figure 4 - FPI criteria. Expressions (6) and (7) are plotted in figure 6 in function of temperature and for each lubricant. The intersections between those curves, for each oil, represent the calculated value of the scuffing load stage. The experimental results plotted are very close to the predicted values.

:::::::::.:::::::::::::::::::::::::::::::::::::::::::::::::::::::.:::::::::::::::::::::::::::::::::::::::::

o:'t I: i!::0.2!

" " '0.3

,!ii!ii!iiiiili i iiiiiiiiii

i~ii~!ii~i~i~:~ii!~i~!i~i~ii!~i~ii~t!ie!~iii~i~i~iii~i~i!i!~!i ii!i!iiiiii!iiii!!iiiii

Figure 3 - Traction coefficients. regime [17]. Another interesting result, is that for a similar specific lubricant fihn thickness, the "thinner" oil, with smaller viscosity and specific mass, produces higher traction coefficients.

0.1

!i

I o ........

0i4 ........

0i5

::::::::: :::::::::::::::: ::::: ::ii i3 i ! ii iii ii! iiiiii i i i iii iiii i i! iiiiii i ii!i~ iiiiii!i iii i i iiiiiii!ii2iii! iii

i;t 1~ ~ I I ISiii/ ll::iii2:~o~ ~il~l~ilNI t~l I I flit li[ ~io~i',',i,~[ .

.

.

.

.

.

......

"

i::!il!::~i80i!::i~::::i00 iiliOiii-~.?::i30iilN::::fSO!if.~::!fTOii::ilili!ili::ii::!i!::i!!ii!iiii

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

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

Figure 5 - Relation L - ~calc.

Figure 6 - Application to standard tests.

3.1. Application to standard tests In standard tests (DIN 51354), the oil bath temperature increases linearly with the applied load. Such evolution is represented by the following expression:

3.2. Critical temperatures If bath oil temperature reaches such a value that the oil specific mass is similar to reference value (PR), than traction coefficient ~toalo attains values typical of metal-to-metal contact, meaning that lubricant film breakdown has occured. The bath oil temperatures for which the lubricant reaches the reference specific mass (pR=Po) can be called critical scuffing temperatures (Tcr). Table 3 presents the critical temperatures for each oil above which scuffing can occur in any conditions.

To = 72 + 6k

(6)

Considering expression (5) at the sliding speed of standard tests and relating the Hertzian Pressure to the FZG load stage, the follow expression is obtained: k = [0.08 Vo(9o-826)] 0/114)

(7)

660 Table 4 Factors for ~,cr Oil 68 220 680

Table 3 Critical temperatures Oil Wcr(°C) ISO VG 68 118 ISO VG 220 138 ISO VG 680 173

3.3. Specific lubricant film thickness at critical temperatures The lubricant film thickness (for linear contacts) is defined according to Dowson expression [18] for the centre film thickness (ho) and is corrected because of the lubricant piezo-viscous shear heating in the inlet of the EHD contact [19] (see appendix

1). The specific lubricant film thickness (k) is determined as the ratio between the corrected film thickness (hoc) and the composit roughness of the contact surfaces. For FZG type A gears, and for point B of gear contact path, L is defined by, FZG A _ B

1.54xl 0 6 (TIoO¢) 0"727 %/0"727D-0" 1 sB8 2.toB " ( 131.1° )0.64

1+ 1 . 8 3 5 / ~ /

t,K,ub )

(8) xzl.28 *sB

The specific fihn thickness calculated for each oil at critical bath oil temperature and for a low load (first FZG load stage), represents the minimum specific film thickness (or the critical specific film thickness for scuffing conditions, LcR ). In those conditions, the lubricant film thickness is calculated by: ~'cR =

2.28x 106 tqOt)M [ \0.727 V$13727 ,,

\0.64

I+1.835[ 13rl /

l, I~luu)M

C~ 0.093 0.117 0.106

C÷ 0.0164 0.0197 0.0170

In figure 7, the specific lubricant film thickness at critical temperatures (critical specific lubricant film thickness, L~) are plotted for each oil, against the sliding speed. Figure 7 shows there is a strong agreement, between critical specific lubricant film thickness curves and specific lubricant film thickness in scuffing conditions calculated for each test conditions. The critical specific lubricant film thickness, ~,~, seams to be an interesting parameter, which can be used as supplementary information to the classic scuffing criteria. It may represent the lubricant film breakdown, or a necessary condition for scuffing to start and develop, as suggested by Foussat [3]. The extrapolation of these results to other type of gears is not yet possible. The FZG type A gears, have a very special geometry, with a maximum slide to roll ratio along the contact path of 75%, and a very good surface finishing of the tooth flanks (R, = 0.35 gm) [1, 12]. They are made of a well defined steel, and the scuffing behaviour depends on the gear material. On the other hand, the experimental results used in this analysis are only concerned with base oils, and gear lubricant additives introduce very

iiiiiliiiiiii:qii!il

(9)

\,1.28

i

VsB

iiiiiii;i:iiiii :ii

i

and for each oil the expression can be resumed by, %10.727

kca

C~. *sB 1 + C¢ v~:s, ~3

(10)

where Cx and C, values for each oil are given in table 4.

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Figure 7 - ~c1~curves.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

i!i}?ii?)i??i?i ? .

.

.

.

.

.

.

.

.

.

.

.

.

.

..

.

.

.

.

.

.

.

.

.

.

.

.

.

661

significant modifications to the scuffing characteristics of the gear/lubricant mechanism. The roughness and other contact parameters (like local temperature and local lubricant film thickness) are treated globally, because this work relates global scuffing with generic lubricant properties (at bath oil temperature) and contact conditions. A solution considering local roughness, lubricant rheology and local temperatures is important to give a more comprehensive scuffing mechanism. 4. C O N C L U S I O N Both experimental and analytical results, suggest that scuffing is related to a critical value of friction power dissipation above which scuffing occurs. The influence of bath oil viscosity in scuffing is greater than predict by FPI criteria calculated with colnlnon expressions for the traction coefficient. Considering the influence of oil specific mass in traction coefficient, it is possible to correlate all the experimental scuffing results, obtaining a more general expression for the FPI criteria. The definition of the traction coefficient proposed, allowed the evaluation of critical scuffing temperatures for each base oil considered. The calculation of specific lubricant fihn thickness at those critical temperatures, for a low load or low pressure, produce critical specific film thickness values, below which scuffing occurs. These critical values depend on gear pitch line velocity and depend on base oil viscosity. Symbols (SI units) gi - material parameter. ho - lubricant fihn thickness. hoc - corrected lubricant film thickness. k - FZG load stage. ui - speed parameter. wi - load parameter. E - Young's module. E* - equivalent Young's module. Fni - normal contact point load.

Klub "lubricant thermal conductivity. L - lubricant thermal parameter. Po - Hertz maximum pressure (GPa). Reqi - equivalent radius of curvature in contact point. R a - roughness parameter (~tm). So - Roelands exponent. To- bath oil temperature (°C). TM - mass temperature (°C). Ve - sliding rate. Vi- contact point speed. Vroli- contact point rolling speed. W - W point of the path of contact (transition point from 1 to two gear tooth pairs in contact). o~ - piezo-viscosity coefficient. 13 - thermal-viscosity coefficient. #PT - thermal correction factor. rio - dynamic viscosity. L - lubricant specific fihn thickness. ~ti - friction coefficient in contact point. v - Poisson' s coefficient. Vo - kinematic viscosity (cSt). V4o - kinematic viscosity at 40 °C (cSt). p - oil specific mass. 9~ - reference specific mass. cy - equivalent roughness (RMS) (cr~4s ~ 1.11 Ra). subscripts i - generic point of gear line of action. o - bath oil temperature conditions. ref- reference value. s - sliding. B - B point of the path of contact (pinion tip - wheel foot). C R - scuffing conditions. References

1. Winter, H. and Michaelis, K.: Scoring Load Capacity of Gears Lubricated with EP-oils. AGMA, Fall Technical MeetingMontreal, Canada, October, 1983. 2. Henriot, G.: La Lubrification Industriele - La Lubrification de Engrenages Tome 1 Transmissions, Compresseurs, Turbines. Publications de l'Institute Fran~ais du Pdtrole. t~ditions Technip, 1984, 297 - 385.

662

3. Foussat, E.: Approche d'un critere de grippage au travers de la rupture du film elastohydrodinamique. These pour obtenir le grade de Docteur, pr6sent6e devant 1' Institut National des Sciences Appliquees de Lyon. Mai 1994. 4. Dyson, A.: Scuffing - a review. Tribology International. June, 1975, pg. 77 - 87. 5. Ku, P. M.: Gear Failure Modes - hnportance of Lubrication and Mechanics. ASLE Transactions 19.3,239 - 249. 6. Winer, W. O. and Cheng, H. S.: Film Thickness, Contact Stress and Surface Temperatures. Wear Control Handbook, 81-141. 7. Castro, J. and Seabra, J.: Scuffing FZG Gears Lubricated with base Oils. 10th International Colloquium in Tribology - Solving Friction and Wear problems. Vol. III. Pg. 2047-2061 Wilfread J. bartz. - Ostfildem: TAE. 09-11 January 1996. 8. J. Castro and J. Seabra. New PV Scuffing Criteria considering Lubricant film Breakdown for FZG Gears Proceedings of the llth International Colloquium Tribology: "Industrial.and Automotive Lubrication ". Technische Academie Esslingen, Ostfildern, Germany, 13 to 15 January 1998. Vol I, 409418. 9. J. Castro and J. Seabra. Scuffing and Lubricant fihn Breakdown in FZG Gears - Part I. Analytical and Experimental Approach. WEAR 215 (1998) 104-113. 10. J. Castro and J. Seabra. Scuffing and Lubricant film Breakdown in FZG Gears - Part II. New PV scuffing criteria lubricant and temperature dependent. WEAR 215 (1998) 114-122. 11. J. Castro, S. Gonqalves and J. Seabra. InfluSncia da Espessura de Fihne Lubrificante na Gripagem de Engrenagens FZG. Proceedings of 6as Jornadas Portuguesas de Tribologia. Universidade de Coimbra, Portugal, Junho de 1998. 12. Winter, H.; Michaelis, K.: Scoring Tests of Aircraft Transmission Lubricants at High Speeds and High Temperatures. Journal of Synthetic Lubrication, 3 (1986) 2, 121 - 135. 13. Winter, H.; Michaelis, K.: FZG Gear Test Rig Description and Test Possibilities. Co-ordinate European Council Second International

Symposium on The Performance Evaluation of Automotive Fuels and Lubricants. Wolfsburg, West Germany, June 5-7, 1985. 14. Norm DIN 51354 part 2:FZG - Zahnrad Verspannags - Prufmashine Prufverfahren AJ8.3/90 fur Schmierole, April, 1990. 15. Michaelis, K.: Testing Procedures for Gear Lubricants With the FZG Test Rig. Industrial Lubrication and Tribology, May- June, 1974. 16. Jackson, A. and Enthoven, J. C. "The Effect of Lubricant Traction on Scuffing". S T L E Tribology Transactions. Volume 37 (1994), 2, 387 - 395. 17. Hamrock, B. and Dowson, D.: Ball Beating L u b r i c a t i o n - The Elastohydrodynamic of Elliptical Contacts. A W i l e y - Interscience Publication; John Wiley and Sons. U.S. ISBN 0471-03553-X, 1981 18. Dowson, D. and Higginson, G. R.: Elastohydrodynamic Lubrication. S. I. Edition, Pergamon Press Ltd, Oxford, 1977. 19. Gohar, R.: Elastohidrodynamics. Ellis Horwood series in Mechanical Engineering, 1988.

APPENDIX 1. LUBRICANT FILM THICKNESS At any point along the gear line of action the film thickness will be defined according to Dowson's expression [18] for the centre film thickness (ho), which for a line contact is given by:

0.727 _ 0.727 ~-0.091 hoi - 0.975 eeq i u i gi w

(A1)

The speed (ui), material (gi) and load (wi) parameters are given by:

Wroli U i - TIo 2 R e q i E , ; g i -

Wi

2orE*;

Li ReqiE*g"

This isothermal centre fihn thickness (A1) must be corrected because of the lubricant piezo-viscous shear heating in the inlet of the EHD contact. The corrected lubricant fihn thickness (hoc) is defined as [191:

663

which depends on the operating conditions (load and rolling speed) and lubricant properties. This expression might be rewritten in terms of maximum hertzian pressure PoB and sliding speed

h oci -- h oi(l)Ti with,

~)Ti - [ 1

+ 0.1(1 +14.8

Ve~"83)L~64 ]

(A2)

The sliding rate is given by"

[Vsi[ Vei - Vroli

Since PoB --

]Vii -V2il VI i + V2 i

K lub

A specific lubricant fihn thickness can also be determined as the ratio between the corrected film thickness and the equivalent roughness of the contacting surfaces, that is: h ~i - ooi (A3), O

~]lO

0

_

2 1 +02

2 ,

and c;~= 1.11Ral; eye= 1.11Ra2 For FZG type A gears, the minimum value of occurs in point B of gear line of action (pinion tip wheel foot) and the parameters needed to calculate specific fihn thickness at this point are:

Introducing these relations in expression (4) gives,

FZG A hB

=

34"170 (rio°t) 0"727Xr0"727Po°182 *sB (A5) 1 + 1.835 ( 13rl° ) °'64 viii8

K lub

The piezoviscosity parameter (o0 is given by: c~ - (or, + c~ 2 - ot 3)xl 0 -8 [A1]

c~ 1 - 1 . 2 1 6 + 4 . 1 4 3 [ L o g ( v

rio VroiB u B - 2.33x109

g B=2"26x1011°~

Using the equations and numerical values given, the lubricant fihn thickness can be defined as:

(

)0.727 xr 0.727 Fng.091 *rolB

1 + 1.260 ( ]3rl° ) 064 xr 1.28

Klub

o

106)] 3.0627

ot 2 - 2 . 8 4 2 x 1 0 -4 n519°[gog(v ° 106)] 15976

FnB 23.3 5X106 ' o=0"512x10-6m; VeB=0"745

FZGA 1.311 1"1oot hB =

VrolB

with

E*=113GPa; R~qB=0.0103m; Za =0.020m;

W~

WsB - ~V, eB thus VsB=0.745 VrolB --

The relation between sliding speed (at B point) and pitch line velocity, is: V,B - 0 . 6 7 1 v t

/

with

2 FnB E* = 18.69xl 06 ~-F, B , rtg Roq B

thus, FnB - 2.863xl 0 -~5 Po2 and

The lubricant thermal parameter is defined as: Li -

V~B:

( ~ 2 - 3.999[Log(Vo 106)]30975(19o 10-3)°1162 The lubricant thermal conductivity: 1 _ 5x10-4 To Klub _ 0.12

(A4)

Po 10-3

3

[A2]

The thermal-viscosity parameter is given by:

Vr°lB

13-So

L n ( r l o ) + 9.67 TO +135

664

with,

Ln

LnI'°°1 '1"]40

+1

So ~-

Ln( 40+135~

i b+i35) The dynamic viscosity is calculated according to ASTM D341 equation: ~ l o - P o 1 0 - 6 [ 10(~°.... ,ogTo)__C] The specific mass depends on temperature according to [6]" Po - P r e f -

0.6[To - Tref]

References (appendix) A I. FrSne, J., Nicolas, D., Degueurce, B., Berthe, D., Godet, M.: Lubrification Hydrodynamique: Paliers et Butdes - Cap. 2 - Les Huiles lubrifiantes. Direction des/~tudes et Recherches d'I~lectricit6 de France. Editions Eyrolles, 1990. A2. Cameron, A.: Basic Lubrication Theory - Cap 2 - Viscosity. Ellis Horwood Series in Engineering Science - 3rd edition.

Table A1 Base Oil characteristics Cinematic viscosity (cSt) ISO VG 100°C 40°C 68 8.3 72.8 220 18.52 236.8 680 37.7 680

Specific mass Kg/m 3 (15 °C) 888 900 921

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

665

Surface and Near-Surface Interactions Affecting Friction and Wear L. Rozeanu a and F.E. Kennedy b aDepartment of Materials Engineering, Technion - Israel Institute of Technology, Haifa, Israel bThayer School of Engineering, Dartmouth College, Hanover, NH, USA

Interactions between contacting surfaces in boundary or mixed lubrication, as well as those in dry sliding, can lead to wear of surfaces and can contribute significantly to friction. This paper discusses some of these interactions and some ways to limit their effects. The first interaction discussed in the paper is that between contacting asperities, resulting in wear of one or both of the asperities. This is discussed as a function of apex angle and surface strength (hardness) ratio. The second interaction is the surface temperature resulting from frictional heating. The effects of temperature are discussed in terms of both temperature magnitude and temperature gradients. Examples of each of these interactions are presented. 1. I N T R O D U C T I O N It has long been known that interactions between contacting solid surfaces are responsible for friction and wear of both dry and boundary lubricated surfaces. Real engineering surfaces are rough, and contact between the surfaces occurs first and foremost at the highest asperities of the contacting surfaces. Plowing of a softer surface by asperities on a harder surface can be a major contributor to friction in both dry [1-3] and boundary-lubricated sliding [3, 4]. Such plowing is also responsible for much two-body abrasion of soft surfaces [1-3]. Yet, when a hard surface is in contact with a softer surface, there is usually some wear of the harder surface as well as the soft one [5]. Although asperity deformation models have been used to model friction and wear [2, 3, 6], they have not usually considered deformation or wear of the harder surface. One objective of this work is to develop a model of asperity contact that accounts for and can explain the wear of hard surface asperities. A second objective is to describe factors influencing sliding surface temperatures and their effect on friction and wear. The inelastic deformation which occurs when asperities on sliding surfaces contact each other is one of the primary ways that

frictional energy is dissipated. This deformation occurs within the real area of contact and in the nearsurface layer (mechanically affected layer) directly beneath the contact surface. The transformation of frictional energy to heat in that region is responsible for temperatures that can have a major influence on the tribological behavior of the sliding system, especially when the sliding velocity is high [7]. The magnitudes of sliding surface temperature are known to be affected by sliding conditions, particularly velocity, as well as by the properties of the sliding bodies. Other factors which have an important influence on contact temperature, and therefore on friction and wear, are the thermal boundary conditions seen by the contacting bodies. This paper will show that changes in the temperature of the non-contacting surfaces of the sliding bodies can have an important influence on friction and can be beneficial in some cases. The effect of sudden cooling of the sliding surface will also be discussed, and it will be shown that it can have deleterious effects. 2. SURFACE ROUGHNESS REVISITED The roughness of contacting surfaces may be characterized by the heights of the surface asperities,

666

and when two surfaces come into contact the highest of the asperities are the ones which contact each other. When two asperities come into sliding contact, a substantial shear stress may be developed in each asperity at the contact site. Although others have modeled the plastic deformation that occurs in asperity contact [2, 3, 6, 8], we will assume that an elastic stress analysis can provide sufficient information about the contact stress situation to serve our purposes. We will assume that an asperity will shear, or wear will occur, if the maximum shear stress exceeds the material's shear strength. In the case shown in Figure 1, in which the two contacting asperities have the same apex angle ~, the maximum shear stress in the two contacting asperities is equal. If the contacting materials have different hardness or shear strength ratio, the weaker of the two asperities will shear first. The shear strength ratio ® can be defined as: ® = shear strength of material A / shear strength of material B.

(1)

In general, we could also say that ® = hardness of material A / hardness of material B. For the case of equal apex angles shown in Fig. 1, asperity A will shear first if ® < 1, while asperity B will shear first i f ® > 1. If the two contacting asperities have different apex angle, the shear stress will be different in the two asperities. This is illustrated in Figure 2. The tangential contact force F H is concentrated at the tip of the sharper asperity, but is distributed over a wider area of the asperity with the larger apex angle. Therefore the shear stress will be much higher at the tip of the sharper asperity A. The stress in ridge-like asperities in 'head-on collision' (as in Figure 2) can be determined by an analysis based on the theory of elasticity using Airy stress functions. The solution for the m a x i m u m shear stress for this twodimensional case (line contact of symmetrical ridge-

like asperities) is given by the following expression [5]" (2)

~Xymax = (2 F H / r ) G (~) where

(3)

G (o0 = [cos (o0 sin 2(00] / [2o~- sin (2c~)] for o~ < n/4 G (~) = 0.35/[2~ - sin (2~)] for ~ > n/4 F H = tangential force acting between the two asperities r = depth of contact on the contacting asperity = r A for asperity A = rB for asperity B c~ = apex half-angle for given asperity = C~Afor asperity A = O~B for asperity B

Values for G (c~) are given in Figure 3 for various apex angles. If the two asperities shown in Figure 2 have the same hardness (O = 1), the sharper asperity will shear first. For the general case when the contacting asperities have both different apex angle and different strength, asperity A will shear first if (~maxA / strength of A) > (~maxB ] strength of B) or using (1) and (3), asperity B will shear asperity A if ® < G(O~A) / G (O~B)

(4)

Surface A

r ( = r B)

.FN Surface B Figure 1. Contact between two asperities with the same apex angle.

667

in question. F H

Surface A

material are found in the right tail of the apex angle distribution curve (noted by A in Figure 4), whilst the asperities of a harder material that are most likely to be worn are those beneath the left tail of the distribution curve (B in Figure 4).

rB

I

Surface B Figure 2. Contact between two asperities with different apex angles. 10

.

,

0 . . . . . . . . . . . . . . . . . . . . . . . .

(I3 r"

~.

~m,

.

,

i •

,

!

,

.

i

8

•

:

•

..........................-*.......................... ~.........................

6

Therefore, the asperities of a softer

material which are most likely to wear a harder

-3b-t m -20"x [ -ICx I0" 27°

.

I

o_

Xff

60 ° t

80= 1

......a ................ .j,.......................... ~.........................

4

Figure 4. Distribution of apex angles. ...............

n

'

0

,

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

i .........................

; ° ° ° 9 ° e n m ~ m o

30

Alpha

60

90

Figure 3. Values of function G(o0 for different apex angles (o0. For example, assume material B is l0 times harder than material A; then ® = 0.1. If C~A = 80°(or 20~A = 160°), then from Figure 3, G(O~A)= 0.14. From equation (4), we find that the harder material B will shear the softer material A as long as G(C~B) is less than 1.4, or (from Figure 3) as long as (XB > 28 ° (or 2(~B > 56°). If O~B is less than 28 °, however, the softer asperity A will shear the harder but sharper asperity B. In general, apex angles are not constant on a surface, but vary according to some statistical distribution, such as a Gaussian distribution. The probability of encountering an asperity with an apex angle greater than (or smaller than) a given angle can be determined by finding the area beneath the distribution curve to the right of (or left of) the angle

If it is assumed that the distributions of apex angles for both surfaces are Gaussian, then the areas under the distribution curves can be determined by integration. Thus, the probability that an asperity on surface A will shear an asperity on surface B is found to be [5]:

P(B ---> A ) =

I(XAmax(F(~A)I(~BminT1;[2F(o~ B )d(~ B )d(~A O~A:O

(5)

50/2 r(o~ A )do~ a Io/2 r(~ B)d(~B where F(o0 are the apex angle distribution functions for the two surfaces. The integrals in (5) have been determined for several different apex angle distribution functions of the following form. F(o0 = exp {-S (o~- 71;/4)2 }

(6)

where S is a scale factor which represents the magnitude of apex angle variation on the surface. The results are shown in Table 1 (adapted from [5]).

668

Table 1 Probability of failure of the stronger material for a distribution function F(c~) o,, exp{-S(o~- ~/4) 2 } ®

Scale S

Probability of failure in shear

5 10 20

0.50 0.50 0.50

0.8

5 10 20

0.43 0.40 0.37

0.5

5 10 20

0.28 0.22 0.14

0.2

5 10 20

0.07 0.031 0.0042

5 10 20

0.027 0.0042 0.0001

5 10 20

0.0083 0.0007 ':'ii ~?I "~i ~ 1. This is evident because then, at some stage, the load is negative and should be compensated by tensile stresses at the contacting surfaces. These tensile stresses contradict the Hertzian assumptions. Figure 1 shows A(T) for A = 1, 0.5 and 0.1. It clearly illustrates the non-linearity in Hertzian contacts; the solution is a-symmetric around the nominal approach A = 1. We may thus conclude that the solution is governed by the parameter A only. The frequency w maps onto 27r and drops from the set of independent variables. This latter conclusion will proof

- -

708

to be quite useful in the discussion of the lubricated problem. Note that, evidently, dissipation is absent in the dry contact case, as only elastic deformation is taken into account. 3.2. L u b r i c a t e d c o n t a c t For lubricated contacts, the modified Reynolds equation governs the flow in the gap between the two contacting solids, see Bayada [1] and Chevalier [2]. In terms of the dimensionless variables, given in the nomenclature, the modified Reynolds equation reads:

The dimensionless film thickness H(X, IT, T) is given by: X2

y2

H(X, Y, T) - - A ( T ) + --~ + 2 2 ff + -~-ff

P (X',Y') dX'dY'

JL v/(x-

x,) + (Y-

Finally, the force balance equation, which determines the value of A, reads:

3 / f s P(X, Y, T)dXdY - 1 + A sin(gteT)

27r

OX

OA OX

+'g-Y OA OY OOpH OOpH OX OT = 0.

(3)

In this equation, 0 denotes the fractional film content, defined as the ratio between the (dimensionless) height of the lubricant layer, Ht(X,Y,T), and the total gap, H(X, Y, T), at that location:

O(X, Y, T) - HI (X, Y, T) H(X,Y,T) "

(4)

For brevity, Ht will be referred to as the lubricant layer. Hence, 0 < 0 < 1, if the lubricant only partly fills the gap, whereas if it completely fills the gap, 0 = 1. To obtain a unique solution, Equation 3 is subjected to the complementarity condition:

P(X, IT, T) (1 - O(X, Y, T)) = 0, with P(X, IT, T) >_0 and 0 < O(X, Y, T) ___ 1.

(5)

That is to say, 0 and P are treated as two separate variables and either P > 0 and 0 = 1 or 0 < 1 and P = 0 . The boundary condition for 0, on the inlet of the computational domain, is derived from the lubricant layer at the inlet, Hl(Xa, Y, T). For simplicity, Hl(Xa, Y, T) = Hoil is assumed to be constant and independent of the spatial coordinates and time. The boundary condition for 0 thus becomes:

Hoil

O(Xa, Y, T) - H(X~, IT, T) ' see also [2].

(6)

(7)

(8)

where 9t~ = 2aw/u8 is the dimensionless excitation frequency. Roelands' relation [8] for constant temperature, has been used to account for the increase of the visosity with pressure and the relation proposed by Dowson and Higginson [3] was used to account for the increase of the density with pressure. 3.3. J F O r e l a t i o n On the free boundary between the starved and pressurized region, the solution should satisfy the JFO relation, see [7,5]. For steady state conditions, this relation states that a discontinuity or jump in the fractional film content exists, if the component of the flow due to entraining motion, in the direction normal to the meniscus, is negative. (The normal direction is chosen to point into the starved region.) The jump, which directly relates to a discontinuity in the derivative of the pressure at that location, thus only exists at the inlet. At the outlet, the relation reduces to the Reynolds condition, stating that the fractional film content is continuous and the pressure gradient vanishes. For transient problems however, the J F O relation reads:

h 2 (OPn~

,l

Op \

+N nu)

+ 6u8(1 - Oc)nx

+12(1-Oc)nt = 0 ,

(9)

where Oc is the value of 0 which is in the starved region but closest to the boundary, n denotes the unit normal vector on the meniscus in the three dimensional (x, y, t)-space (pointing towards the

709

starved region), nx is its component in the xdirection, n y is its component in the y-direction and n t in the t-direction, see Appendix A. From this relation, it can be inferred that the existence of a jump in 0, and the associated discontinuity in the pressure gradient, in addition, depend on the normal velocity of the meniscus. It states mathematically that, if, relative to the meniscus, lubricant enters the pressurized region, a jump in 0 occurs, whereas, if lubricant leaves the pressurized region, no such discontinuity is observed. In fact, similar to the steady situation, the discontinuity thus occurs at the inlet and disappears at the outlet. The numerical solutions, presented in Section 5, will indeed show these phenomena.

Figure 2. Steady state pressure distribution.

4. N u m e r i c a l s o l u t i o n The equations, given in Section 3.2, were discretized by a second order discretization. Specifically, narrow upstream discretization was used for the wedge and squeeze term, see Venner and Lubrecht [13]. The discrete equations were subsequently solved, in principle, using Elrod's algorithm [4]. The actual algorithm is similar to the one described by Chevalier [2]. Improvements such as second order discretization and line relaxation and details related to time-dependency will be reported elsewhere, see [11]. Multilevel techniques were used to accelerate convergence and for the fast evaluation of the elastic deformation integral, see, e.g., Venner [12]. The presented results have been obtained using a mesh of 257x257 points. The size of the domain, and as a result the meshsize, were choosen such that the pressurized region is within the computational domain at all times. The timestep h T -- h x

Figure 3. Steady state fractional film content.

= hy.

5. R e s u l t s 5.1. S t e a d y s t a t e As a reference, Figure 2 shows the steady state pressure distribution for M = 100, L -- 5 and Hoil = 0.0978. Figure 3 shows the associated fractional film content.

Figure 4. Steady state lubricant layer.

710

In Figure 4 the lubricant layer or lubricant profile Ill -- OH is shown. This may seem a peculiar quantity to depict, but, as will be shown, it is very useful to explain phenomena in starved contacts. In the starved region, Ht represents the amount of oil in the gap, as if it were adhered onto a single surface (as may indeed be true in the inlet). In the pressurized region, it is simply the film thickness. For clarity reasons, the various variables on the centerline Y - 0, are shown in Figure 5

1

"'

o.s I[-

/

"...] \

::1

o.6r

p,

0.4 b-

i',

//

P --~\

;

H ........ ', \ -

/

/

-2

\ -

---"

,

~

I ), ', I 0 2 I-_._/.: ,,; O ~

\

\..t

!

X

', .. ,,

K

.

-1

if'_ _ .

0

Figure 4 shows what would actually be observed in experiments; a 'bow-wave' forms on the inlet meniscus. In addition, it clearly shows the wake, as well as the lubricant "ridges," formed on the sides of the contact and extending downstream. These ridges contain the lubricant that has been pushed aside and separate the wake from the starved region with lubricant, unaffected by the passage of the rolling element. The figure, in addition, shows the well-known plateau of constant film thickness and horse-shoe shaped constriction near the outlet. However, with respect to the film thickness, we will restrict ourselves to the remark that, as was pointed out in [2], starved lubricated contacts are very efficient. They are efficient, in a sense that side leakage reduces as starvation increases. At values of Hoil below, approximately, 0.5Hell, virtually all lubricant available at the inlet, enters the high pressure zone and is used to separate the surfaces.

1

X

Figure 5. O(X, 0), P(X, 0), Ht(X, 0) and H(X, 0).

The specific value of Hoil equals the central film thickness in the fully flooded situation, denoted by Hell. For this particular value, starvation is significant, however it is not severe or so-called parched, see [2]. As in fully flooded conditions, the pressure distribution observed in Figure 2, closely resembles the Hertzian pressure distribution, including the Petrusevich like spikes. Contrary to fully flooded conditions however, a discontinuity in the pressure gradient at the inlet meniscus occurs. Figures 3 and 5 clearly show that the jump in 0 occurs only at the inlet meniscus. Figures 2 and 3, as well as Figure 5, confirm the complementarity condition, i.e., the region at which 0 = 1, coincides with the region at which P > 0.

5.2. T r a n s i e n t The transient simulation starts at the steady state solution, given in the previous section. Subsequently, the pressure and film thickness as well as the fractional film content and lubricant distribution are monitored, as the force oscillates sinusoidally. As it is believed to be the most revealing, Figure 6 shows interference plots of the lubricant distribution Hi at different times in the simulation. The meniscus is indicated by means of the solid line. This line thus encloses the pressurized region. This is also the region in which the figure shows the usual interference pattern of the film thickness. Outside the region, it shows the lubricant layer. Figure 7 shows the associated pressure, film thickness and lubricant layer on the centerline (Y = 0). As a result of the large stiffness, the central film thickness hardly reduces in the initial stages of the simulation, despite the increase in the load. Hence, to compensate for the increased load, the contact area expands. The resulting squeeze motion near and outside the Hertzian contact circle, induces pressures, which cause the film thickness reduction to be less compared to the steady state film thickness (associated with the increased load). Therefore, as for fully flooded conditions,

711

Figure 6" Snapshots of the lubricant layer distribution H1 at different times in the simulation (left to right, top to bottom). The timeincrement between consecutive frames is 0.25. Lubricant flow is from left to right. The dimensionless wavelength is A - 0.06.

712

!._

1.2 1 0.8 0.6 0.4 0.2 0

I

I

I

0.3 0.2 0.1 0

_

1.2 1 0.8 0.6 0.4 0.2 0

0.3 0.2 0.1 0

0.2 0.1 0 -2

-1

0

1

0.1 0 -1

0.3

0

1

2 0.3 0.2 0.1

-1

0

1

0 2. 0.3

0.2 0.1 0 -1

0

1

1 . 2 [ -__. - - /I' 1

'

''

'' ] /'

2 "-!0.3

-

-2

-1

0

1

F i g u r e 7: P r e s s u r e ness

H(X) ( r i g h t

2

0.4

0

0.~

u

I[

_ 0.3

_

O. 0.6 0.4 02 "0 -2

- 0.2 - 0.1 0 2

-1

0

1

1.2 [-" / i

l

U / - 0.3

0.8 0.6 0.4 02 "0 -2

- 0.2 - 0.1 0 -1

0

1

1.2 ~- / u

I

I[

1

-2

0.1

1.2 ~- / I

.L

1.2 1 0.8 0.6 0.4 0.2 0

2

1.2 1 0.8 0.6 0.4 0.2 0

0.3

0.2

-2 0.3

I

1.2 1 0.8 0.6 0.4 0.2 0

-1

1.2 1 0.8 0.6 0.4 0.2 0

I

1

-2

_

-2

I

1.2 1 0.8 0.6 0.4 0.2 0

0.2 0.1 0

-2

P(X) (left

-1

0

1

labels) on the centerline Y -

-

-1

0

1

- 0.2 - 0.1 0 2

1.~ ~

/'

'

']

_-0.3 - 0.2

0.8 0.6 0.4 0.2 0

0.1 0 -2

layer O.

_ 0.3

0. 0.6 0.4 02 "0 -2

2

labels), lubricant

2

-1

0

Hi(X) a n d

1

2

film thick-

713

described in [10], film thickness modulations are induced in the inlet of the contact, which subsequently propagate downstream at the dimensionless speed of unity, see below. The wavelength of the film thickness modulations is easily derived from the relation between the "Hertzian" timescale T, introduced in Section 3.1, and the timescale T used in the simulation. (Note the similarity between the present derivation and the derivation of the wavelength for film thickness modulations induced by inertia in [10].) It is easily verified that T is related to T as:

T = acT.

(10)

Since the period of oscillation in terms of T, was shown to map onto 27r, the period of oscillation, in terms of T is 27r/Fte. Because the velocity at which the film thickness modulations propagate is unity, the wavelength of the modulations is thus 142 = 27r/Fte. Hence, for the values used in the simulation W = 1. The pressurized region expands as a result of the increased load. Because the flow induced by squeeze motion and the lubricant fraction present near to the meniscus, are now enough to fill the gap, the meniscus shifts into the (initially) starved region. The figures show that lubricant has been squeezed out of the pressurized region as a result of the approaching velocity at T = 0 (as can be concluded from the uprising in the lubricant layer seen at T = 0.25). This lubricant is subsequently transported downstream. In the same manner as the propagation of the film thickness modulations, lubricant layer modulations, formed at the outlet of the contact, propagate at the dimensionless speed of unity. This follows directly from the assumption that lubricant in the starved region is transported by means of Couette flow only. That is to say, in the starved region, the modified Reynolds equation reduces to -OOH/OX - OOH/OT = 0. Consequently, Ht = OH = O H ( X - T) and, indeed, the lubricant layer in the starved region propagates at a dimensionless velocity of 1. It is noted that the transportation of lubricant inside the wake and, in fact, in the entire starved region is governed by the same mecha-

nism, as by which lubricant is transported within the high pressure zone. Inside the high pressure zone, Poiseuille flow is virtually absent and the Reynolds equation reduces to - O f H / O X OfH/OT = 0. Hence, fSH = f H ( X - T) which, by neglecting the effect of pressure on ~, validates the given statement. With respect to the JFO relation, from Figure 7, it can be inferred that the lubricant layer modulation, induced at T = 0, was transported downstream at a higher velocity than the maximal velocity of the outlet meniscus. That is, if the velocity of the meniscus would have been larger, a bow-wave would have formed at the outlet, which would thus have shown in the lubricant layer profile. (The uprising is formed at the instant at which squeeze motion is maximal and not, as one might believe, at the point of maximal load.) Near the two lubricant ridges however, the normal velocity of the meniscus has exceeded the normal component of the outflow velocity. This can be concluded from the solution in Figure 6 at T = 0.25, by the somewhat ragged circular arc, showing the discontinuity or bow-wave. At T = 0.25, the load has reached its maximum and squeeze motion becomes zero. Note that if the load becomes smaller, especially near the sides of the contact, the inlet meniscus ceases to be concentric to the Hertzian contact circle. At this location, no lubricant is available; it was squeezed out previously. It is shown most clearly in the interference plot at T = 0.75, that the lubricant profile, which forms in the wake, resembles a "foot-print" of the film thickness at the maximal load. Obviously, it only changes its shape due to the Poisseuille term near the outlet. Since Poisseuille flow is virtually absent in the high pressure zone and is absent, by definition, in the starved region, it is evident that only a very small "boundary layer" exists, for the Poisseuille term is of any influence. Remarkable is also the lubricant layer distribution, in the wake, at times T > 1.75. From this time on, the film thickness modulations, which were induced at the start of the simulation, significantly start to effect the lubricant profile at the outlet. Obviously, at locations where the film thickness is larger, the outflow is larger and subse-

714

quently, so is the uprising of the lubricant profile. Hence, also the cresently shaped film thickness modulations appear in the lubricant layer profile in the wake. At T -- 2.75, one clearly observes the particular lubricant profile, one would see periodically at all later times.

0.5

1 "

I

0.45 I/

0.4 p 0.35

L

'il,l

I

'it q

i lIll , ,l', ~l :'lil

0.25

I"

I,'

l li

2.00 . . . . /,, .

.

.

.

-

.

la v, /,,.: V,I,.:'";

0.2 -2

-

I -1

I 0

I 1

-

the relation of A ~ versus the load parameter M, the stiffness following by inversion. (The subscript c~ has been added to denote equilibrium.) To show how starvation influences the flexibility of the contact, the mutual approach A ~ is shown in Figure 9 versus the ratio Hoit/Hcff, for M - 100 and L - 5. The figure shows that, for values of Hoit significantly larger than Hell, A ~ is close to the fully flooded approach ( A ~ = 0.897). With decreasing values of Hoit, it is observed that A ~ increases slowly. Effects of starvation are only significant at values of Hoil less than, approximately, Hell. For values below Hell, A ~ steeply increases, in a virtually straight line, upto the Hertzian value A ~ = 1. It may thus be concluded that starvation only significantly affects the flexibility for values below Hell.

2

X 1< 0.98 - Figure 8. and 2.25.

HI(X, 0) and H(X, 0) for T - 1.75, 2 g

~ 80 aCal.

~ 60

@

~ 40 20

I 200

I 400

I 600

I 800

Thickness (nm) Figure 2. Comparison of thickness-intensity relationships.

white balance). Furthermore, it is hard to calculate h for a given intensity, because the relationship is strongly non-linear. Finally, calibration is easier to carry out and has been chosen in this work. It only needs to verify the Hertzian theory assumptions, which seem to be valid in our case, even in the small thickness domain (below 100 nm).

3.2Image Analysis light interferometry

method

for

white

The intensity/thickness relationship is not a bijection: one single intensity is not enough to calculate thickness. Consequently, the right fringe order is usually chosen arbitrarily. In our approach, the thickness is determined considering different wavelengths: a colour video camera measures light intensity through three different filters (Red, Green and Blue). This gives a triplet of intensities (R0, Go, B0). All the solutions of each wavelength are calculated. They are then crossed together to find out the right thickness.

3.3 C o l o u r i m a g e r e p r e s e n t a t i o n For a given hue, the h u m a n eye can not differentiate between a monochromatic colour and a mix of three fundamental ones. Each point in the colour image is represented by three variables. Opticians tried to find a representation of colour t h a t corresponds to what the h u m a n eye sees r a t h e r t h a n a direct measurement. Different colour models have been studied for calibration purposes. The RGB model stems from direct coloured light measurement: the others are based on this model. The L*a*b* model defines two chromatic p a r a m e t e r s (a* and b*) which are colour coordinates of redness-greenness and yellowness-blueness. Finally, the HSI model describes hue by only one p a r a m e t e r (H).

721

Three different light b r e a k d o w n s were m a d e from the same image for each colour model (Figure 3). Results clearly show t h a t the L*a*b* model (Figure 3a) and the HSI model (Figure 3b) are very suitable above 100 n m because the p a r a m e t e r s H(h), a*(h) and b*(h) have a steep gradient. Unfortunately, these p a r a m e t e r s t e n d to be constant below 100 n m (H and a*) and below 40 n m (b*). No d e t e r m i n a t i o n can be m a d e from H, a* or b*. 300

a)

200 •or) ~ 100 0

-~~

l~'\

~ ~

200 \3?0

100

-100 ~(

40(k/500

In this range, film thickness m e a s u r e m e n t becomes impossible. In the RGB system (Figure 3c) intensities are never constant. It can be used for any thicknesses w i t h o u t a low limit. F u r t h e r m o r e , it p e r m i t s the use of three v a r y i n g signals which allow us to improve the accuracy of the thickness m e a s u r e m e n t by crossing three sets of solutions. This is especially true in the small thickness domain (below 100 nm). By this technique, the m e a s u r e m e n t s in this r a n g e are m a d e in acceptable conditions, compared to other image processing techniques [9,12,14]. Finally, we consider t h a t the RGB system is the most appropriate to r e p r e s e n t physical m e a s u r e m e n t s (video).

x a* 600

700 800

3.4 U n i c i t y -200

I

-

600

Thickness (nm)

300

b)

H

200 l .~..~

It is f u n d a m e n t a l to verify t h a t only one thickness h o corresponds to a given experimental triplet (Ro, Go, Bo). The calibration curve can be d r a w n in the RGB space (Figure 4). This 3D curve never crosses itself. This m e a n s the relationship is a bijection.

(D

i00

/-: o

i

i

i

i

200

400

600

800

/~:~

I~~i

~ ~ ..... ~'I"~'~"I. ~

I............... !................... ~" ~[I

Thickness (nm) "

1~t0

200

c) ~150 100

:\

4-)

•' '~

50

~

'

4

'

"

\

' ,'

.~...~

""

B

200

400

600

800

Thickness (nm) Figure 3 a, b, c. Comparison between the different colour models.

!I ......

~L ......... ii...~i~.::;:~.::~'~~:~:~~ I ~ii ~y ........ :7:>": .~..::.~::::".~..~...~::L..-. ./.~ ~~-.-~,~ i;'.~.~.~.~i >.~~ ~-~..-~: ~':>:: :~

...'............. .::: < ............ ,.: !"

~..~.~_.i.:>~..............">; ,e)

0

1

,®L-~""~ .~, ....... ti,...:?",!"ii../l ....i'~..>Y"X...... ...... ,......... ,~.... I t.....-"~ ....... ~....k~i~.ii....~,i"~. _~~~i .............. iX~l .......... ....... ~......... ...........

121F-~.,._~

0

'~

-..

-~,,~-~

Figure 4. Calibration curve in RGB space.

722

3.5 R e f r a c t i v e pressure

correction

with

Calibration is performed under pressure even though in the EHD m e a s u r e m e n t is carried out under pressures. The fluid refractive index with pressure. In order to take into this variable, the Lorentz-Lorentz perfect fluids has been used:

ambient contact, varying changes account law on

l.

D

n 2

-1

n 2 +2

1

---*

Po

index

2 -1

no

- Rs

(4)

n2 +2

Density variation under pressure is estimated by the Dowson and Higginson law [16]" P=Po

1+

0"6" 10-9p / 1+1.7.10-9p

(5)

Minimum film thicknesses with both processings are smaller t h a n the value calculated with the Hamrock and Dowson relationship. This was already noted by Hartl [15]. ...........................................................................................................................................................................................................................

Consequently, the refractive index of the fluid u n d e r pressure can be written as: l1 + 2 p . R s

The central and the m i n i m u m film thicknesses are measured. Comparisons between these latter, the Hartl results and the Hamrock and Dowson predictions are presented in Table 3. Unfortunately, the load in the Hartl static experiments is unknown. In this special case, we had to evaluate it from the contact diameter, which is a less precise method t h a n our (see §3.1). At this level, a deviation of one pixel generates several nanometers variation in film thickness. This certainly explains the few differences between the results.

no

n : ~" -1--_-p-~s . It gives: htrue : hread*--n

-.

Central film thickness Experimental Hartl LMC

233 nm 222 nm 232 n m

Hamrock & Dowson Minimum film thickness Experimental Hartl 100 nm LMC 96 nm Hamrock & Dowson 134 nm

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

: .........................................................

-.

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

The pressure is not known experimentally. The correction at any point inside the contact is made with the assumption t h a t the dynamic pressure is close to the Hertzian one.

4. V A L I D A T I O N 4.1 V a l i d a t i o n o n i m a g e a n a l y s i s

A static and a dynamic picture provided by Dr. Hartl are used to validate our image processing. These pictures were analysed in a previous work [15]. The dynamic picture was taken under the following conditions: U=l.03 10 11, G=3760, W=1.53 10 8, where U, W, and G are the classical dimensionless p a r a m e t e r s [2].

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

Table 3. Comparison between two image processings and the Hamrock and Dowson results.

4.2 S t a t i c c o n t a c t s t u d i e s

Pictures of static (Hertzian) contacts were taken for different loads with the materials described in Table 6. Film thicknesses were measured using the same calibration curves deduced from another static image. In each case, a profile beginning at the centre of the contact is compared to the profile calculated with the Hertzian theory (continuous lines, Figure 5). The m a x i m u m difference between experimental and theoretical profiles is 20 nm for all the different loads of this study. This deviation is mainly due to surface

723

defects" it roughness.

is

close

to

the

ball

600 -

surface

Z~

500 -

0 X

400 -

4.3 C o m p a r i s o n model

with

a complete

EHD

or]

300--

Comparisons with the EHD model developed in the l a b o r a t o r y [17] h a v e been carried out. C o n t a c t conditions are r e p o r t e d in Table 4. F i g u r e s 6a a n d 6b p r e s e n t t h e o r e t i c a l a n d e x p e r i m e n t a l contact profiles in the two m a i n directions. The m a x i m u m deviation is less t h a n 10 nm. All the r e s u l t s p r e s e n t e d in this v a l i d a t i o n show t h a t the image processing gives film t h i c k n e s s e s in both static a n d d y n a m i c (EHD) cases w i t h acceptable precision. This first s t u d y confirms t h a t i m a g e recording, calibration process, t h i c k n e s s a n d fringe o r d e r d e t e r m i n a t i o n , and finally, r e s u l t processing are validated.

•~ 200-100 -0

--t 0

50

100 150 Radius (lZn)

200

250

Figure 5. C o m p a r i s o n b e t w e e n t h e o r e t i c a l and e x p e r i m e n t a l profiles.

400l !i Experimental profile ~o[ lil ............... Numericalprofile j//;/

"50

Central film thickness

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

U=1.24 10 -11, Experimental G-3760, Model W=1.53 10 .6 Hamrock & Dowson '-ii U=1.3 10 , Expertmental G=4842, Model W=0.89 1 0 s Hamrock & Dowson Minimum film thickness U=1.24 1 0-11 , Experimental G=3760, Model W=1.53 10 -~ Hamrock & Dowson '-ii U=1.3 10 , Expertmental G=4842, Model W=0.89 10 .8 Hamrock & Dowson

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

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

.

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

222 230 232 256 256 266

nm nm nm nm nm nm

30

"'

100 -200

-150

-1O0

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

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

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

.

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

96nm 110 n m 134 n m 150 n m 156 n m 154 n m

-5O

0

50

1O0

I 15O

20(

150

200

a) Transverse position (pm)

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

:

350 r/2

300-

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

t

i Numerical profle ~ i i " "'"...... Experimental profile

o,-q

Table 4. C o m p a r i s o n w i t h a complete E H D model.

,--..0

200

-200

-150

- 100

-50

0

50

100

b) Longitudinal position (pm) F i g u r e 6 a, b. C o m p a r i s o n b e t w e e n e x p e r i m e n t a l a n d t h e o r e t i c a l profiles.

724

5. R E F E R E N C E F L U I D T E S T S The whole approach developed above has been applied to di-(2-ethylhexyl)phtalate (DOP) which can be considered as a reference fluid. Its central film thickness is well described by the H a m r o c k and Dowson relationship down to 10 n m [18, 19]. Tests are conducted u n d e r pure rolling conditions. O t h e r e x p e r i m e n t a l and m a t e r i a l conditions are listed respectively in Tables 5 and 6. M e a s u r e m e n t s are made for a wide speed range. The thickness range lies from the first to the fourth fringe order. A 3D e l a s t o h y d r o d y n a m i c m a p is presented in Figure 7 as an illustration of our results. E x p e r i m e n t a l central film thicknesses are compared to the H a m r o c k and Dowson results (Figure 8). A good correlation from 0.45 ms -1 to 5.12 ms is observed. Differences a p p e a r u n d e r 0.45 m. S-1. They can be justified from surface r o u g h n e s s conditions. The polishing m e t h o d gives a longitudinal r o u g h n e s s of 30 n m (Ra). Roughness -1

__._. . / . ~ ~ ~ -

"~"'~~

Onm 1

influence on film thickness is t a k e n into account according to the J o h n s o n and Greenwood model [20]. The results are reported in the dashed line, Figure 8. For these conditions, the rough film thickness becomes smaller t h a n the smooth equivalent one. Calculated and e x p e r i m e n t a l film thicknesses are in good agreement, even if the roughness size is close to the film thickness. The results are quite dispersed u n d e r 20 nm. This was previously observed in the literature [17]: this critical thickness corresponds to limit lubrication. In this condition, central and minimum film thicknesses are difficult to distinguish.

: ........................................................................................................................

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

Hertzian pressure Temperature

482 M P a 40 °C

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

i

~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

-.~. . . . . . . . . . . . . . . . . . . . . .

....S p . e e d .

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

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

Table 5. E x p e r i m e n t a l conditions.

1000 "1

ilOO,I •

Hc expe. Hc H&D + J&G Hc H&D

800 nm i 1001

0,1 Speed (m/s)

Figure 7.3D shape of an EHD lubricated contact.

Figure 8. Central film thickness(nm) versus speed (ms-1).

10

725

Ball

E v E v

France (PMC), ECL (LTDS), INSA de Lyon (LMC), INPT (IMF), ENSMP (Cemef), CNRS

210 GPa 0.3 68 GPa 0.203 1.4792 0.97 kg/1 25.93 mPa.s

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

Disk

(SCA).

....................................................................................................................................... : ........................................................................................

Fluid (at 40 °C)

no Po Viscosity .

............................................................ P

.

ez.o:V/s.co.s.,t

.

.

.

..........

1

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

Table 6. Material parameters.

6. C O N C L U S I O N S A new original method supported by a new experimental apparatus has been developed. It has been validated under EHL and limit lubrication conditions. This work shows that both apparatus and processing run in a thickness range from 20 to 600 nm. The method is based on the analysis of RGB colour images. The first step establishes an intensity-thickness relationship with a calibration made on a static contact. Then image processing leads to film thickness without any assumption on fringe order. Latterly, the results are corrected because of the refractive index variation with pressure. This method eliminates manual calibration and visual comparison of hues, which are difficult and sometimes hazardous tasks.

Aknowledgements The authors would like to thank Georges ROCHE (LMC) for his technical support, Fabrice PUBILIER (LMC) for the theoretical calculations, and Dr. Martin HARTL (Univ. of Brnb, Czech Republic)) for providing images and results for comparisons.

This work was carried out under the CPR "Mise en forme des mat~riaux" Contact m~tal-outil-lubrifiant" supported by CNRS, IRSID (Usinor), Pechiney Recherche, involving Paris Sud Univ. (LMS), Coll~ge de

Symbols incident light wavelength Absorption coefficient in the fluid Phase shift between two successive beams Metallic phase shift Fluid density (running pressure) P Fluid density (normal pressure) Po Metallic absorption coefficient (ball) A a Contact size (radius) E* Reduced Young's modulus Dimensionless material parameter G Lubricant film thickness h Light intensity I Refractive index (running pressure) n Refractive index (normal pressure) no Running pressure P P0 Hertzian pressure Radius from contact centre r Ball radius R Rs Specific Refraction Transmission coefficient at disk/oil T interface Dimensionless speed parameter U (Ro, Red, Green, Blue intensities triplet. Go, Bo) Dimensionless load parameter. W (~0

References 1.

Gohar R., Cameron A., The mapping of elastohydrodynamic contacts; ASLE Transactions 10, 215-225, 1967.

2.

Hamrock B.J., Dowson D., Isothermal elastohydrodynamic lubrication of point contact: Part III-Fully flooded results, Journal of Lubrication Technology, Vol. 99, 264-276, April 1977

3.

Zhu D., Bireshaw G., Clark S.J., Kasun T.J., Elastohydrodynamic lubrication with W/O emulsions, Transactions of

726

ASME, Vol. 116, 310-320, April 1994. .

.

.

.

o

.

1995.

Westlake F.J., Cameron A., A study of ultra-thin lubricant films using an optical technique, Proc Instn Mech Engrs1967-1968, Vol 182 Pt3G, 75-78, 1968.

12.

Gustafsson L., Hoglund E., Marklund O., Measuring lubricant film thickness with image analysis, Proc Instn Mech Engrs Part. J, Vol. 208, pp 199-205, 1994.

Israelichvili J.N., Thin film studies using multiple beam interferometry, Journal of Colloid and Interface Science, Vol. 44, No. 2, August 1973.

13.

Hoglund E., EHL and the use of image analysis, Wear Vol. 179, 49-56, 1994.

14.

Cann P.M., Spikes H.A., Hutchinson J., The development of a spacer layer imaging method (SLIM) for mapping elastohydrodynamic contacts, Tribology Transactions, Vol. 39, 915-921, 1996.

15.

Krupta I., Hartl M., Cermak J., Liska M., Elastohydrodynamic lubricant film shape comparison between experimental and theoretical results, Tribology for Energy Concervation, Proceeding of the 24 th Leeds-Lyon Symposium on Tribology, D. Dowson et al (editors), 221-232, Elsevier Science B.V., 1998.

16.

Dowson D., Higginson G.R., Elastohydrodynamic lubrication SI Edition, Pergamon Press, 1977.

17.

Chevalier F., Lubrecht A.A., Cann P.M., Colin F. and Dalmaz G., Film Thickness in Starved EHL Point Contacts, Journal of Tribology, vol. 120, 126-133, 1998.

18.

Guangteng G. and Spikes H.A., Boundary film formation by lubricant base fluids, Tribology Transactions, Vol. 39, 2, 448-454, 1996.

19.

Cooper D., Moore A.J., Application of the ultra-thin elastohydrodynamic oil film thickness technique to the study of automative engine oils, Wear Vol 175, 93-105, 1994.

20.

Johnson K.L., J.A. Greenwood, Poon S.Y., A simple theory of asperity contact in elastohydrodynamic lubrication, Wear vol. 19, 91-108, 1972.

Johnston G.J., Wayte R., Spikes H., The measurement and study of very thin lubricant films in concentrated contacts, Tribology Transactions, Vol 34, 2, 187-194, 1991. Perry D.M., Robinson G.M., Measurement of surface topography of magnetic recording materials through computer analysed microscopic interferometry, IEEE Transactions on Magnetics, Vol. MAG-19, No 5, September 1983. Cline H.E., Holik A.S., Lorensen, W.E., Computer aided surface reconstruction of interference contours, Applied Optics, Vol. 21, No 24, 15 December 1982. Bassani R., Cuilli E., Lubricant film thickness and shape using interferometry and image processing, Elastohydrodynamics '96, Proceeding of the 2 2 th Leeds-Lyon Symposium on Tribology, D. Dowson et al.(editors), 8190, Elsevier Science B.V., 1997.

10.

Luo J., Wen S., Huang P., Thin film lubrication part I: Study on transition between EHL and thin film lubrication using a relative optical interference intensity technique, Wear Vol. 194, 107-115, 1996

11.

Wahl M.H., Casmer S. and Talke F.E., Multi-wavelength intensity-based interferometry for flexible head/medium interfaces, Tribology Transactions, Vol. 38, No. 3, 533-540,

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

727

Lubrication theory as a means of unravelling flow structure in thin film roll coating systems P.H. Gaskell, J.L. Summers and H.M. Thompson Fluid Mechanics Research, School of Mechanical Engineering, University of Leeds, UK. The aim of this paper is to demonstrate that lubrication theory provides a simple, yet powerful, means for understanding a wide variety of complex flow phenomena inside the bead of roll coating systems. Attention is focussed on the forward regime, with rollers moving in the same direction through the nip, and analytical predictions are obtained over a wide range of low flux (meniscus roll coating) situations. Although the full flow field within the coating bead is often quite complex due to the existence of eddies and transfer-jets, it is shown that the structure can be classified analytically according to the nature of the stagnation points within the flow. The analytical predictions are compared with those from a full numerical solution of the flow field, which incorporates the effects of the upstream and downstream free surfaces. The agreement between the analytical and numerical results is extremely good in all instances, a fact which clearly demonstrates that much of this complex flow behaviour can be well understood without having to resort to complex numerical solutions.

1. I N T R O D U C T I O N Roll coating is an industrial process whereby two rotating rolls, separated by a very small gap, are used to lay down a thin film of liquid onto a moving substrate. The fluid is brought into the gap, the minimum part of which is called the nip, by the action of viscous lifting by the lower roll and two films are formed downstream of the nip, attached to the upper and lower rolls, see Figure 1. A number of workers have analysed, both theoretically and experimentally, the structure of the flow within the fluid bead in a forward roll coating system. The flow domain in the bead is bounded by two free surfaces, the roll surfaces and has an extra feature of a dynamic contact line where the incoming fluid meets the upper roll surface. This flow domain presents a considerable challenge to theoreticians, which led them to exploit Taylor's [1] observation that flow in the nip region is quasi-one-dimensional and can therefore, be described by the equations of lubrication theory. Consequently the pressure field in the nip region is described by the one-dimensional Reynolds' equation and several works have pro-

posed a range of boundary conditions which are needed in order to determine the velocity and pressure fields. Dowson and Taylor [2], for example, showed that the condition of vanishing pressure and pressure gradient are more suitable to situations where the film splits by cavitation within the fluid whereas in forward roll coating the film splits by a smoother separation mechanism. This insight led to a number of different separation-based boundary conditions (Savage [3], Greener and Middleman [4] and Coyle et al [5]) which enabled both the flux and film thicknesses on the rolls in forward roll coating to be predicted to a reasonable accuracy. All previous workers assumed t h a t the inlet was supplied with sufficient fluid in order for it to become "flooded" the inlet. However, for precision ultra-thin coatings it is sometimes preferable to operate the coater with a substantially reduced flux - the meniscus roll coating regime. Malone's [6] experimental study of meniscus roll coating revealed that the flow field is quite different in the meniscus regime from the flooded regime, the former being typified by the existence of large recirculations, spanning the entire width of the bead, and sub-ambient pressure fields domin-

728

ated by surface tension effects at the free surfaces. Gaskell et al [7] obtained a lubrication model for the flow in a meniscus roll coating bead, together with finite element solutions of the full two dimensional flow problem which incorporated both free surfaces. In the present paper the lubrication theory as presented in Gaskell et al [7] is further exploited to identify the paths and strengths of transfer jets in meniscus forward roll coating by classifying the stagnation points within the nip region. Due to the geometry, namely a converging and diverging gap the stagnation points reside at the nip provided the flow rate is less than some critical value. This approach is used to map o u t , analytically, the regions within the bead where the transfer jets occur and the lubrication calculations are compared with numerical solutions of the full flow problem. The agreement between lubrication and numerical solutions is exceptionally good.

the flow is then described by Stokes' equations; 0P

_ .v_:u,

OX O

(1)

OP OZ

__.

ttV2W"

H

!

X

2H

t4 H • l

\

R

H

F i g u r e 2 Cross section of the roll coating head showing orientation o/ the axes and the fluid domain. F i g u r e 1 Schematic o/ a roll coating head operating in forward mode. Figure 2 identifies the domain of interest and the important dimensional quantities.

2. T H E B A S I C

LUBRICATION

MODEL

Based on the assumptions that the fluid is Newtonian with constant density and viscosity, steady with no axial velocity, fluid inertia or body forces,

The variable S is introduced as the speed ratio of the two rolls given by S - g-~ u2, while the rolls have radius, R. Assuming lubrication theory to be valid (where the flow is effectively one-dimensional; w < < 1

729

and o Op

.

i

, j

°.%.'oo

o.io"

o.lo

o.3o ....

0.40

Inlet f l u x = q / 2

evaluated and is given by, q

=

4 3

4v~ 3(1+s)

(10)

7 Comparison of lubrication theory with

Figure

numerical solutions for jet strengths as a function of inlet flux with speed ratio 1.0

The boundary labelled V I V 2 was first evaluated using lubrication theory by Gaskell et al [7] and is given by the following expression, q

1.0 • F l u x transferred to top r o l l o P r i m a r y jet to top r o l l • Secondary jet to top r o l l , A s y m m e t r i c jet to top r o l l , Odd jet to top r o l l

0.8 I

0 6

J,."

04t

/~/"

~2 ( 3 + 2 S - v / S

2 + 3S)

( 11)

The boundary was later experimentally validated by Gaskell et al [12] and results are shown in Figure (9) for a speed ratio range of 0 to 2. The

. ; •; • • / ,,--;;• ~".~

~zCf~

=

i

i

J s ~ ~'

%.oo

'

0.10

0.20

0.30 . . . . . .

6.40

Inlet f l u x = q / 2 "--.... o ....... e ......................

F i g u r e 8 Comparison of lubrication theory with numerical solutions for jet strengths as a function of inlet flux with speed ratios 2.0 0

0

i

i

i

i

i

i

i

i

i

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

S

the conditions for each of the possible boundaries. In addition to those boundaries listed above, one also occurs when the two nip stagnation points coalesce, that is when the expression under the square root in equation (7) vanishes. This can be

F i g u r e 9 The flow transformation boundary given by equation (11) (---), and by experimental data (o)

734 1.5

1.5

No solution - stagnation points no longer in vertical alignment.

No solutions - stagnation • vertical points no longer in vertic~ afignment.

[~

lk

1.0

0.5

V2

0.5 V2

O.Oo!

.

o,2

,

o,4

.

o, 6

Speed ratio (S)

0.8

1.0

Figure 10 The flow transformation boundaries ] o r O < S ~IO -1

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

3. RESULTS AND DISCUSSIONS

3.1. Friction tests of natural articular cartilage Figure 5 shows the changes in the frictional behaviours in sliding pairs of natural articular cartilage and glass plate with the sliding distances under unlubricated and saline lubricated conditions. For both conditions the friction was increased with the sliding distance. However, under not a lubricated but an unlubricated conditions, the lower friction was maintained. Particularly, at the initial stage very low friction was observed. Figures 6 and 7 show the changes in frictional behaviours with the definite sliding distances under unlubricated and saline lubricated conditions, respectively. It is noticed that the value of the

........

!

.......

:

!..................

................ "................... i

n

2.3. Force-distance curve measurement of articular cartilage To examine the changes in mechanical properties such as viscoelasticity and adhesiveness of cartilage surfaces with rubbing, the force curve measurements were conducted by the contact mode in fluid. The stiffness of the cantilever with Si3N4 tip was 0.58 N/m. The measured data were depicted as the force- distance curves.

0.3wt%HA 0.5wt%HA 1.0wt%HA

:

• :..~..j..,..

10

i

SPM systems (Nanoscope III, Digital Instruments, USA). By this non-contact method immersed in liquid, the influence of capillary force between the tip and the observed surface was diminished and the rubbing action by the tip was minimized. The scanning speed is 1 to 2 lines/s. The articular cartilage specimens were cut as 2 mm thickness and adhered to PMMA flat plate by the cyanoacrylate adhesive to fasten the specimen in the AFM stage. Careful setting to keep the surface untouched was conducted.

mm-.i l i i I l i l

"'A,AAAAAA ill

iN.Hill-

-. . . . . . . mllli

i. . . . . . . . . . . . .

] mnUN ................ :................. :................. :......",..,.O..'..':.,...o...

:

o .co 10- 2 >

:.

;

o OOI!OOOOOOOIto.-._

.

:

10 -s

........

10

1

i

10

:

........

:|

101

:

........

'l

102

....

.... i

103

....

104

Shear rate 1/s

Figure 4. Viscosity of HA solutions

0.3 ,e..I 0

,~ 0.2 o t-

•O-~ 0.1 ,I

o

2.2. Observation of articular surfaces by AFM To investigate the changes in surface morphology with repetition of rubbing, the articular cartilage surfaces were observed in saline by AFM as fluid tapping mode using scanning probe microscopy

o

0

2

4 6 Sliding distance, m

8

10

Figure 5 Comparison of frictional behaviour of natural articular cartilage against glass plate under unlubricated and lubricated conditions

741

0.15 tO

0.10

o

"6

4--' t"

.--

I.o_ :1= o 0

0.05

iAisi! [g]

[C] Slidingdistance=9m Slidingdistance=6m

2

0

4

6

Sliding distance, m

8

10

Figure 6. Frictional behaviour of natutal articular cartilage under unlubricated conditions 0.3

[F] Slidingd ' i ~

:

t-

Figure 8 AFM image of intact surface of natural articular cartilage (fluid tapping mode in saline)

O ,B O .m

o

0.2 -[D] Slidingdistance=0.35m~ .... - .................

t'I1)

/

0

~0.1

~

[El Slid:ngdistai:e=:m

o O

0

2

4 6 Sliding distance, m

8

10

Figure 7. Frictional behaviour of natural articular cartilage under lubricated conditions (saline)

ordinate axis in Fig.6 is two times higher than that in Fig.7. In friction tests under unlubricated conditions, the lubricant was not supplied. Therefore, the role of surface layer of the lubricating adsorbed films and/or gel films was expected to be emphasized, although some contribution of exudated fluid to lubrication was anticipated. To examine the friction mechanism in these transient rubbing process, the articular surfaces were observed by the fluid tapping mode AFM. 3.2. AFM images of natural articualar cartilage surfaces Figure 8 shows the AFM images of an intact articular cartilage surface, which has considerably smooth morphology with maximum height of 1 to 2 gm. Figures 9 and 10 show the AFM images of articular cartilage surfaces at definite sliding distances shown in Figs. 6 and 7 under unlubricated and lubricated conditions, respectively.

3.2.1. Unlubricated conditions At short sliding distance of 0.35 m [A] under unlubricated condition whose coefficient of friction is less than 0.01, the cartilage surface was slightly rubbed resulting in the smaller roughness. With proceeding of rubbing, the friction gradually increased at 6 mm sliding [B]. On the cartilage surface, the transversal ridges were observed. With further rubbing, the fibrous tissues appeared at 9 m sliding [C], where coefficient of friction is about 0.1. Therefore, it is considered that the acellular and non-fibrous surface layer has been rubbed off at this stage. Next, in order to examine the role of counterface, the rubbed surfaces of glass plate at stroke centre was observed by the fluid tapping AFM. At short sliding distance [A] showing low friction, there are little materials on glass surface as shown in Fig.11 (a). This suggested that the low friction was maintained mainly by the cartilage surface containing the lubricating molecules. At 6 m sliding [B], plenty of materials composed of small granules of 150 to 300 nm and larger aggregate were observed in Fig. 11 (b). These are transfer materials or wear debris from articular cartilage and might raise friction. At 9 m sliding [C], the morphology of transferred materials was varied as shown in Fig.ll (c), probably due to higher shearing force. 3.2.2. Saline Lubrication Even at short sliding distances [D], the rubbed surface was roughened as shown in Fig.10 (a) than

742 Sliding directions

Figure 9. AFM images of cartilage surfaces at definite sliding distance in reciorocating tests under unlubricated conditions

Figure 10. AFM images of cartilage surfaces at definite sliding distances in reciprocating tests under lubricated conditions with saline

743

Sliding directions

unlubricated condition in Fig.9 (a). Further rubbing promoted the roughening of cartilage surfaces. The AFM images at F (Fig.10 (c)) appears to correspond to deeper zone than at C (Fig.9(c)). Under lubricated conditions with low viscosity saline, the easy removal of lubricating molecules or surface layers from cartilage surface during rubbing process seems to be responsible for a rise in friction. The time-dependent frictional behaviour with running time may be simulated with the similar method to the theoretical formulation based on the biphasic model for boundary friction in articular cartilage proposed by Ateshian [39]. In contrast, under unlubricated conditions lower friction was preserved at the initial stage. This fact suggests that low friction is ascribed to the surviving of adsorbed molecules and/or gel film. Therefore, the force curves for the corresponding surfaces were measured to investigate the forcedistance properties. 3.3. Force-distance articular cartilage

Figure 11. AFM images of counterface glass plate after reciprocating tests under unlubricated conditions

curve

measurement

of

Figure 12 shows the force-distance curves corresponding to the cartilage surfaces observed by AFM. In this force curve measurement, the force begins to rise when the tip of cantilever contacts the cartilage surface. As the cantilever is indented along z-axis (vertical to surface) at the constant speed driven by the piezo-actuator, the compressive force increases. The gradient of force-distance curve is equivalent to the stiffness of testing material surface. At the reversing process as the unloading, the compressive force is lower than the corresponding penetrating process. This hysteresis phenomena as shown by grayed zone in Fig.12 reflect the viscoelastic properties of cartilage surfaces. As the unloading process proceeds near the initial contact position, the force in opposite direction appears. This tension force appears to be caused by the adhesive and sticky surface films. For the intact natural articular cartilage with an amorphous surface layer, the position of the occurrence of contact is not obvious and the gradient of the force curve or the stiffness is low. In the reversing unloading process, the remarkable hysteresis and the occurrence of tension force before the detachment of the tip from cartilage surface are noticed. For rubbed cartilage surfaces, the stiffness

744

lubricated with Saline

unlubricated

..=

.....

~ = = ,,-ir~-.... = ,, = -~-~_ _ 2 " 2 " =

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

o i,..,.

0 Ii

......... : . . . . . . . . . . . . . . . . . .

. . ~ . . . 4 .......... a

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

.............. :.;....- ~ .

intact

lOnN [

200nm

Z displacement Figure 12. Force-distance curve for natural articular cartilage at definite sliding distances

gradually increased, particularly under lubricated conditions. The hysteresis was reduced with sliding distances under unlubricated conditions. At sliding distance of 9 m under unlubricated condition where the clear fibrous surfaces was observed, the hysteresis effect was diminished, because of removal of viscoelastic amorphous materials. At shorter sliding distances (A and D) for both unlubricated and lubricated conditions, the adhesion and/or sticky forces before detachment were increased due to raising of resistance of disarranged surface layer

3.4. Comparison of frictional behaviour between natural and artificial cartilage The frictional behaviours of natural articular cartilage and PVA hydrogel against TZP are shown for three kinds of operating conditions in Fig. 13. Under slow speed and low viscosity condition in Fig. 13 (a), friction for both materials increased with running time. It is noticed that the low friction was observed for natural articular cartilage at the initial stage. In contrast, the significant high friction was

observed for PVA even at shorter sliding time. In the saline solution of sodium hyaluronate, little adsorbed films are expected to be formed. This fact suggests the natural cartilage has a lubricating surface layer as described above, but PVA hydrogel surface has little boundary lubricating ability under thin film condition. Furthermore, PVA hydrogel surface appears to have some irregularities as shown by AFM images in Fig.14, while natural articular cartilage has smoother surface (Fig. 8). The increasing of sliding speed from 5 mm/s to 20 mm/s slightly improved the frictional behaviour for natural cartilage. Furthermore, the addition of 7globulin could reduce the friction of natural cartilage, although it raised friction for PVA hydrogel as shown in Fig. 13 (b). Next, the increasing of lubricant viscosity enhanced fluid film formation resulting in reduction of friction for both materials. Furthermore, the addition of proteins at this condition improved the friction of PVA, which is steady and low or similar compared with natural cartilage.

745

c

.uo

0.5

...........PvA ..........i......................................................................i

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

q.-

o

0.3

e-

0.2

4.a

52 u

~-- 0.1 o O

0

0.5

1.0

1.5

2.0

Running time, h (a) v = 5 mm/s, 0.3 wt% HA ._o .__t2 0 . 4 o

0.3

t-

0.2

(.,)

o.1

~ 0

0

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

............. Natural cartilage ~

0

Fig.14 AFM images of PVA hydrogel surface by fluid tapping mode ......................... i..................................

t

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

0.5

1.0

1.5

2.0

R u n n i n g time, h (b) v = 20 mm/s, 0.3 w t % H A + 1.0 w t % T-globulin

,-- 0.5

~'

0

._o 0.4 t__ O

0.3

..................................................................... i................................... i................................ ....................................................................~...................................~.................................

~A, P V A

._~ = 0.2

.............................. ~..................................~ A Natural cartilage -

=

0.~

...................................i...................................i...................................)-...................................

0

0

0.5

1.0

1.5

2.0

R u n n i n g time, h

(c) v = 20 mm/s, 0.5 wt% HA + 1.0 wt% ]'-globulin Figure 13. Frictional behaviours of natural and artificial cartilage against ceramic plate These results indicate that natural cartilage has low friction property particularly at short sliding distance, but PVA has little boundary lubricating ability at severe mixed lubrication regime. However, PVA hydrogel exhibited superiority in frictional property with the aid of protein in mild mixed lubrication regime. 4.

DISCUSSIONS

ON

ROLE

OF SURFACE

LAYER IN THE THIN F I L M LUBRICATION

4.1. R o l e o f s u r f a c e l a y e r o f n a t u r a l cartilage

articular

In this paper, the authors focused the role of surface layer in thin film mixed and boundary lubrication regime. As indicated by MacConaill [40] as lamina splendens observed using a phase contrast microscope, the lubricating surface layer appears to present, although the detailed structure of acellular and non-collagenous tissue has not yet been clarified. The surface amorphous layer of 2 to 200 lim thickness observed in cryo-SEM by Kobayashi et al. [23, 24] may include the considerable part of molecules originated from hyaluronate in synovial fluid. In the present study, the changes in the articular cartilage surface morphology in the thin surface layer with rubbing process were successfully imaged by AFM fluid tapping mode. As discussed in the authors' previous paper on the pendulum tests of pig shoulder joints lubricated with sodium hyaluronate solutions of different viscosity [11], the removal of protective adsorbed film had little effect on frictional behaviours under fluid film lubrication mode such as the swinging motion immediately after loading at high load., o~- low load with highly viscous lubricants. In mixed lubrication mode under low load lubricated with iow ~iscosity lubricants, the removal of adsorbed film significantly raised friction. In these mixed lubrication regime, the addition of phospholipid as liposome of L~-DPPC of physiological concentration and 7-globulin of higher concentration

746

was effective in improvement of friction. In this paper, the natural articular cartilage was rubbed against glass plate under severer rubbing condition such as unlubricated and lubricated with very low viscosity lubricant (saline). Consequently, it was expected that not only adsorbed film but underlying gel film can contribute to maintain low friction and protect the rubbing surfaces. At shorter sliding distance, very low friction was preserved particularly under unlubricated conditions. This indicates that the surface layer consisting of adsorbed film and gel film can play the lubricating role in thin film lubrication with some direct contacts. The changes in surface morphology with rubbing process imaged by the fluid tapping mode AFM and the corresponding force-distance curves suggest that the lubricating viscoelastic surface layer was worn with the progress of severe rubbing. When this non-fibrous surface layer had been removed, the underlying collagenous layer with higher stiffness showed the higher shearing resistance. As described in this paper, the natural synovial joint has the splendid hierarchic lubrication and protective system as the adaptive multimode lubrication. In healthy synovial joints, the adsorbed films and/or gel films are likely to play the lubricating and protective roles even under extremely thin film conditions in various daily activities by replenishing of the adsorbed and gel films with the aid of the self-organization mechanism in unloading period. 4.2. The role of surface layer in artificial cartilage As shown in Fig.13, PVA hydrogel layer as an artificial cartilage showed the inferior frictional behaviour to natural articular cartilage in low viscosity conditions. The increasing viscosity of lubricants improved the frictional behaviour of PVA by thickening of fluid film based on the soft-EHL effect, and the addition of serum protein was effective in reduction of friction. Similar phenomena were found in simulator tests of knee prostheses with PVA layer [10, 11]. The addition of La-DPPC was not so effective for PVA, but the repetition of rubbing gradually reduced friction [10]. As indicated by AFM images of PVA surface (Fig. 14), the surface morphology has some irregularities. To improve the lubrication property of PVA hydrogel as artificial cartilage, the surface

modification with lubricating adsorbed films and gelled film [8] and appropriate surface morphology is expected to be effective. 5. CONCLUSIONS The role of surface layers of natural articular cartilage and PVA hydrogel as artificial cartilage in thin film lubrication has been examined in reciprocating friction tests. The changes in rubbing surface morphology and mechanical properties of natural articular cartilage were examined by AFM. Furthermore, the frictional behaviour of PVA hydrogel was compared with that of natural cartilage. The experimental observation for natural articular cartilage showed that the low friction was maintained for a considerable period at the initial rubbing stage in not a lubricated but an unlubricated condition. This fact suggests that the lubricating surface layer probably composed of adsorbed molecules and gel films existed in the rubbing surfaces. With repetition of rubbing, the friction gradually increased from the initial low value. AFM images of the intact articular cartilage and the rubbed cartilage surfaces at def'mite sliding distances indicated that the smooth surfaces were preserved for the low friction stage, and the underlying fibrous structure was visible as a result of removal of nonfibrous viscoelastic surface layer for the higher friction stage. In friction test, PVA hydrogel showed higher friction than natural articular cartilage even at the short sliding distance under thin film condition. This discrepancy might be derived from the deficiency of lubricating surface layer. ACKNOWLEDGMENTS The authors thank Mr. K. Nakashima, graduate student of Kyushu University for his cooperation for AFM measurement for PVA specimen. Most of measurements by AFM were conducted using AFM at the Center of Advanced Instrumental Analysis, Kyushu University. Kyocera Corporation provided ceramic specimens. Financial support was given by the Grant-in-Aid for Scientific Research of The Ministry of Education, Science, Sports and Culture, Japan ((B) No.9480254, International Scientific Research (Joint Research) No. 1004165).

747

REFERENCES

1. D. Dowson and Z.M. Jin, Engng. Med., 15 (1986) 65. 2. D. Dowson and Z.M. Jin, Fluid Film Lubrication - Osborne Reynolds Centenary, ed. by D.Dowson, et al, Elsevier Sci. Pub.,(1987) 375. 3. D.Dowson, Proc. Instn. Mech. Engrs., 181, Pt 3J, (1966-67) 45. 4. A. Unsworth, D. Dowson and V. Wright, Ann. Rheum. Dis., 34 (1975) 277. 5. T. Sasada, J. Jpn. Soc. Lubr. Eng., (in Japanese), 23, 2 (1978) 79. 6. T. Murakami, JSME International Journal, Series III, 33, 4 (1990) 465. 7. K. Ikeuchi, Lubricants and Lubrication, ed. by D. Dowson et al., Elsevier (1995) 655. 8. T. Murakami, N. Ohtsuki and H. Higaki, Thin Films in Tribology, ed. by D. Dowson et al. Elsevier (1993) 673. 9. T. Murakami, N. Ohtsuki and H. Higaki, Proc. Int. Tribol. Conf. Yokohama 1995, (1996) 1981. 10. Murakami, T., Sawae,Y., Higaki, H., Ohtsuki, N. and Moriyama, S., Elastohydrodynamics-'96 :Fundamentals and Applications in Lubrication and Traction, ed. by D. Dowson et al., Elsevier (1997) .372. 11. T. Murakami, H. Higaki, Y. Sawae, N. Ohtsuki, S. Moriyama and Y. Nakanishi, Proc. Instn. Mech. Engrs.,212, Part H (1998 )23. 12. B. A. Hills, J. Rheumatol., 16 (1989) 82. 13. H. Higaki, T. Murakami, Y. Nakanishi, T. Katagiri, H. Miura and T. Mawatari, Trans. Jpn. Soc. Mech. Eng.(in Japanese), 63-605, (1997) 549. 14. H. Higaki, T. Murakami, Y. Nakanishi, H. Miura, T. Mawatari and Y. Iwamoto, to be published in Proc. Instn. Mech. Engrs., Part H. 15. D.A. Swann, The joints and synovial fluids, Academic Press (1978) 374. 16. W.H. Davis, Jr.,S.L. Lee and L. Sokoloff, Trans ASME, J. Biomech. Engng,. 101 (1979) 185. 17. G.D. Jay, Conn. Tiss. Res., 28 (1992) 71. 18. H. Higaki and T. Murakami, Proc. Int. Tribol. Conf.Yokohama 1995, (1996) 1982. 19. H. Higaki, T. Murakami and Y. Nakanishi, JSME International Journal, C, 40-4 (1997) 776. 20. K. Ikeuchi, K., and M. Oka, Thin Films in Tribology (Eds. Dowson, D. et al.), Elsevier (1993)513,. 21. G.W. Stachowiak, A.W. Batchelor and L.J. Griffiths, Wear, 171 (1994) 135.

22. Kirk, T.B., Wilson, A.S. and Stachowiak, G.W., J. Orthop. Rheum., 6 (1993) 218. 23. S. Kobayashi, S. Yonekubo and Y. Kurogouchi, J. Anat., 187 (1995) 429. 24. S. Kobayashi, S. Yonekubo and Y. Kurogouchi, J. Jpn. Soc. Clin. Biomech. and Rel. Res., 16 (1995) 337. 25. H. Higaki and T. Murakami, Japanese J. Tribology, 39-7 (1994) 859. 26. T. Murakami, Y. Hayakawa, H. Higaki and Y. Sawae, Proc. JSME Intern. Conf. on New Frontiers in Biomech. Engng., (1997).233. 27. J.R. Jurvelin, D.J. Muller, M. Wong, D. Studer, A. Engel and E.B. Hunziker, J. Struc. Biol., 117 (1996) 44. 28. T. Sasada, M. Takahashi, M. Watakabe, K.Mabuchi, Y. Tsukamoto and M. Nanbu, J. Jpn. Soc. Biomaterials (in Japanese), 3, 3, (1985) 151. 29. T. Murakami and N. Ohtsuki, Fluid Film Lubrication - Osborne Reynolds Centenary, ed. by D. Dowson et al., Elsevier, (1987) 387. 30. A. Unsworth, M.J. Pearcy, E.F.T. White and G. White, Proc. Inst. Mech. Eng., C219/87 (1987) 715. 31. M. Oka, T. Noguchi, P. Kumar, K. Ikeuchi, T. Yamamuro, S.H. Hyon and Y. Ikada, Clin. Mater., 6 (1990) 361. 32. D.D. Auger, J.B .Medley, J. Fisher and D. Dowson, Mechanics of Coatings, ed. by D. Dowson, et al., Elsevier (1990)264. 33. D. Dowson, J. Fisher, Z.M. Jin, D.D. Auger and B.Jobbins, Proc. Instn. Mech. Engrs., 205, Part H, (1991) 59. 34. L. Caravia, D.Dowson, J. Fisher, P.H. Corkhill and B.J. Tighe, J. Mater. Sci., Mater. in Medicine, 4 (1993) 515. 35. D.D.Auger, D.Dowson and J. Fisher, Proc. Instn.Mech. Engrs., 209, Part H (1995) 73. 36. D.D.Auger, D.Dowson and J. Fisher, Proc. Instn.Mech. Engrs., 209, Part H (1995) 83. 37. Y. Sawae, T. Murakami, H. Higaki and S. Moriyama, JSME International Journal, Ser. C, 39, 2 (1996) 356. 38. Y. Sawae, T. Murakami, H. Higaki, Proc. Int. Tribol. Conf.Yokohama 1995 (1996) 1969. 39. G.A. Ateshian, Trans. ASME, J. Biomech. Engng., 119 (1997) 81. 40. M.A. MacConaill, J. Bone Joint. Surg., 33B (1951) 251.

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S E S S I O N XVIII L U B R I C A T I O N A N D FRICTION Chairman •

Professor F.E. Kennedy

Paper XVIII (i)

An Investigation on the Antifriction Performance of Some Organomolybdenum Additives

Paper XVIII (ii)

The Behaviour of Molybedenum Dialkyldithiocarbonate Friction Modifier Additives

Paper XVIII (iii)

Traction and Film Thickness Characteristics of Traction Fluids in High Speed Elastohydrodynamic Contact

Paper XVIII (iv)

Development of an Apparatus for the Direct Measurement of Traction Coefficients for Lubricants; Preliminary Measurements from a Bouncing Ball Apparatus

Paper XVIII (v)

Effect of Particles Concentration on Friction

This Page Intentionally Left Blank

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

751

An Investigation on the Antifriction Performance of some Organomolybdenum Additives Giuseppe Tripaldi 3, Silvano Fattori t,, Riccardo Nodari a, Antonio Vettor a

aEniTecnologie SpA, Via Maritano 26, 20097- ,San Donato Milanese (MI) bEuron/AgipPetroli SpA, Via Maritano 26, 20097- San Donato Milanese (MI)

ABSTRACT Molybdenum dithiophosphate (MoDTP) and molybdenum dithiocarbamate (MoDTC) additives are added to automotive and industry, lubricants for their performance as friction modifiers and antiwear agents. In recent years an increasing attention has being paid to these additives, because they can improve energy saving. However their effectiveness may be strongly affected by synergistic or antagonistic effects of additive packages. The aim of the present work is to investigate the antifriction performance of MoDTC and MoDTP in the presence of two alkyl (secondary and primary) ZnDTPs, the main antiwear agents currently used worldwide. Rolling-sliding tribometry has been extensively used to chart Stribeck-like friction curves in the elastohydrodynamic, mixed and boundary lubrication regimes. Results show that at 135 °C, typical temperature for a fully warmed-up engine, in the mixed and boundary regimes, the chosen MoDTC and MoDTP give no friction reduction when added alone to the base oil. But in the presence of both the two ZnDTPs, added at .typical concentrations of full-formulated engine oils, a strong synergism generates a drastic friction coefficient reduction~ resulting in Stribeck-like curves flattened at level of about 0.05 in the mixed/boundary regimes. However, such antifriction properties of organomolybdenum compounds are overcome by higher concentrations of ZnDTPs. Tests carried out in dry conditions on reacted layer previously obtained from effective antifriction blends, confirm the presence of a stable film, probably rich of MoS2, as frequently suggested in literature.

I. I N T R O D U C T I O N

In order to reduce CO2 emissions and to improve resource saving, in recent years an increasing attention has being paid to automotive engine fuel economy [1-5]. The lubricant plays an important role to improve fuel economy through friction reduction under hydrodynamic regimes (using low viscosity oils) and boundary/mixed regimes (adding friction modifiers additives). Molybdenum dithiophosphate (MoDTP) and molybdenum dithiocarbamate (MoDTC) are oil-soluble organomolybdenum commonly used as

friction modifiers (Mo-FMs), but their effectiveness is strongly influenced by synergism and antagonism with the other additives [6-9]. The present paper deals with a study on the interactions of Mo-FMs and with some zincdithiophosphates (ZnDTPs), well known antiwear and antioxidant agents. Examples of formula are illustrated in figure 1; depending on the alcohol/alkylphenol mixture used in the synthesis, the alkyl or aryl groups R~ to IL can be the same or differ, both within a

752

R1N

O

N-c- 1G/s \

(a) R

(b)

0 II

S

NS,/

o-S- c- N II

S

N R4

R10 Oil S O ° OR3 \ p_ S_.Mo/ \ _ S_p / " \S / ~ \ OR4 R20/ l lS

R,O \ / / S

(c)

/R3

Zn S % p / O R 3

R o/P s / \ s / \OR,

Figure 1. Examples of chemical structure of MoDTC (a), MoDTP (b) and ZnDTP (c).

molecule or between molecules in an additive sample. Although the mechanism of action is still debated, it is generally believed that the Mo-FMs, after adsorption, react on the rubbing surfaces and form a protective layer mainly containing MoS2, whose lamellar structure can be sheared easily [ 10]. It has been also suggested that the presence of MoS2 gives a better control of the wear and smoothing of tracks could contribute to lower the friction. But the presence of MoS2 in the boundary layers is questionable; according to some authors, Mo-FMs can reduce friction forming surface coatings not containing MoS= [7]. Concerning the interactions between Mo-FMs and ZnDTPs, different mechanisms are suggested in literature. ZnDTPs, or other sulphur base additives, promote the formation of MoS2 [cited in 4]. XPS studies indicate that iron phoshate, which has high hardness and a marked wear resistance, is formed in advance or simultaneously to MoS2 [11], and probably act in a way similar to the binders for solid lubricant applications. Also, the role of ligand exchange between MoDTCs and ZnDTPs has been extensively studied [ 1]. Starting from this basis, the present study has the following three aims: 1) to investigate the interactions of some Mo-FMs and ZnDTPs, that we commonly use to formulate engine oils,

2) to assess the optimum balance for candidates to "fuel economy" engine tests 3) to improve our knowledge on the film properties and mechanisms of the interactions between MoFMs and ZnDTPs. A recently developed rolling-sliding ball-on-disk tribometer was used to plot the Stribeck-like curves (traction coefficient against speed) that allow exploration of the performance of tested lubricants in the full range of lubrication regimes, from elastohydrodynamic, through mixed, to boundary. Also, a classical sliding machine was used mainly to study the wear behaviour.

2. EXPERIMENTAL

2.1 Test methods The test rigs used for the friction measurements were the EHL apparatus [12] developed at the Tribology Section of Mech. Eng. Deptm. of the Imperial College and commercially available by PCS Ltd. (London) and the high temperature pinon-disk tribometer by CSEM (Nefichatel, Switzerland). In the EHL rig (figure 2) the contact is formed between a steel ball (19.5 mm diameter) and a steel disk. The friction is measured inserting a torque transducer on the ball drive motor.

Ball Drive

Steel Disc

ShaPe

Strain

Gauge

StrainGauge /

Output

-~

Disc Drive

Shah

Figure 2. Rolling/sliding friction set-up [13].

753

Time min 30 60 10 60 10 60 10 60 10 60 10

Working Cond. m/s % N °C 0.5 0 0 135 0.1 50 30 135 - 50 30 135 0.1 50 30 135 - 50 30 135 0.1 50 30 135 - 50 30 135 0.1 50 30 135 - 50 30 135 0.1 50 30 135 - 50 30 135

heating up to form the film 1st measurement pause 2ndmeasurement pause 3rdmeasurement pause 4th measurement pause 5th measurement

Table 1 - Experimental protocol for Stribeck-like curves. Working cond.: Speed, SRR, Load, Temp.

The experimental protocol, reported in table 1, consists of a running-in stage to get a reacted layer and five measuring stages to evaluate kinetic effects. Before each test, new specimens and equipment were cleaned with toluene and hexane. Figure 2 shows the schematic set-up of the CSEM pin-on-disk tribometer, in which a stationary ball is loaded against a rotating disk. The rig was used to chart the friction coefficient against running time under pure sliding conditions at the chosen temperature, at 1 N load (corresponding to a maximum hertzian pressure of 0.6 GPa), and 0.11 m/s speed. In all the tests performed, after a short transient, the friction coefficient signal reach an almost constant level; its average value in the last 5 minutes will be used in the following sections.

135 / ,~~---. lvdt

load

0.5 w% MoDTC

ball holder 3.~

0.31 w% MoDTP

Figure 3. Three-factors design. Figure 2. CSEM pin-on-disk set-up.

The rig was used to chart the Stribeck-like curves (traction coefficient against entrainment speed) under rolling-sliding conditions at the chosen temperature, at 30 N load (corresponding to a maximum hertzian pressure of 0.9 GPa), and at 50% SRR. In this study the roll-slide ratio is defined as: SRR (%) =

sliding speed = 200 Ub~l - U~iS°1% mean rolling speed Uball + Udise

Base oil ZnDTP1 ZnDTP2 MoDTP MoDTC EHL rig ball EHL rig disk PoD ball PoD disk

Main Properties 29.99 cSt @40 °C, 5.24 cSt @ 100 °C C4 primary, 8.2 w% P, 8.5 w% Zn C4-6, secondary, 8.1 w% P, 8.5w% Zn 8 w% M o, 5.5 w% P, 12.3 w% S 4.9 w% Mo AISI 52100, Ra - 10 nm AI SI 52100, Ra -___25 nm X100Cr6, Ra _---25 nm, 63-66 HRC X100Cr6, Rz 450+650 n m , - 60 HRC

Table 2. Fluids and specimens used

754

At the end of each test, the wear was evaluated measuring on the ball, by means of an optical microscope, the average scar diameter. All the specimens and the holders were cleaned in ultrasound with toluene and acetone before use.

2.2 Materials and experimental design Two commercial ZnDTP and two commercial MoFMs were used. Blends were made in a 150 SN mineral base oil according to the experimental design illustrated in fig. 3. The two level of MoFMs were chosen as follow: the MoDTC was used at the maximum concentration suggested by the supplier, and the MoDTP keeping the same level of Mo in the oil (about 250 ppm). All the tests at 135 °C were run at least twice, but to be more confident in repeatabili.ty sometimes even four and five times; the tests at 40 °C were run for a less extent because no significant changes due to additive blend were detected. A total number of 51 tests were carried out; only 4 showed an unexpected behaviour; they were considered experimental outliers and then rejected. Further details on products and specimens are reported in table 2.

3. RESULTS

3.1 Stribeck-like curves Measurements at 40 °C. Typical results at 40 °C are shown in figures 4 to 6, each including all the five Stribeck-like curves of the protocol described in Table 1. Repeated tests on 150 SN + 0.31% MoDTP and on 150SN + 0.31% MoDTP + 1.3% ZnDTP2 showed an overall good repeatability. All the results indicate that at speed down to 0.1 m/s an elastohydrodynamic film is formed between the two rubbing surfaces and the friction is controlled by the bulk properties of the mineral base oil. At speeds below 0.1 m/s, in the mixed/boundary regimes, the friction behaviour is almost similar to that measured in a previous works [13]. At 40 °C, in the working conditions indicated, the Mo-FMs and the ZnDTPs studied give small friction reduction. Measurements at 135 °C. Figure 7 to 9 show the results of three repeated tests on 150SN + 0.5% MoDTC + 1.3% ZnDTP2. The repetitions of the 1st

Stribeck-like curves gave very different traction coefficient in the mixed/boundary regime; the differences tend to disappear, improving the repeatability of the measurements, at the 5th curves. In the following, all the results will be plotted in term of 5th stage measurement curve (mean value and standard deviation on repeated tests). In figure 9 the traction coefficient at speeds above about 0.1 m/s is higher than at lower speeds. One possible reason is that a viscous layer, probably from ZnDTPs decomposition, is formed above an inner layer containing the anti-friction agents. The friction behaviours of additive-free base oil and mixtures only containing MoDTP or MoDTC are compared in figure 10. The reduction of traction coefficient to values about 0.05, typical of the effectiveness of the two additives, were not observed in the mixed and boundary regimes. Also, the MoDTC gives higher friction than MoDTP. This behaviour could be related to a better antiwear performance of the latter resulting in a smoother surface finish, and consequently the contact operates in an improved lubrication state. In a previous work [13] on friction and film forming properties of ZnDTPs we observed, in quite similar working condition, that some secondary ZnDTPs gave higher friction than primary ones. In order to verify, if similar effects can be ascribed to the MoFMs organic radicals, deeper analytical studies have been planned to elucidate their structure. Figure 11 to 14 illustrate the effects of ZnDTPs on the friction performance. At concentrations of 1.3 w% and 1.9 w%, due to the synergism between MoFMs and ZnDTPs, all the mixture give low friction all over the speed range. At higher concentrations the pro-friction effect of ZnDTP tend to overcome the performance of the friction modifiers. State of the film. In figure 15 is illustrated the behaviour of a 150SN + 0.31% MoDTP + 1.3% ZnDTP2 blend at 40 °C, carried out on the same wear tracks of a test previously performed at 135 °C. It clearly shows that the previous surface modifications are still effective at low temperature. It was also verified that, even after drained out the lubricant and cleaned the specimens with toluene and hexane, the films were still effective for a short time.

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757

3.2 Pure sliding friction and wear Figure from 16 and to 18 show typical results at 135 °C obtained under pure sliding conditions. These results agree with the ones obtained in rolling-sliding conditions. The friction bars (light) in figure 16, confirm the synergism between ZnDTP1 and MoDTP and an optimum concentration of ZnDTP1 about 1 w%. Wear results (dark bars) indicate that MoDTP alone is effective to reduce wear (typical wear scars for 150 SN are about 0.2 mm) and the wear scar diameter tend to level at about 0.13 mm increasing the ZnDTP1 content. In figure 17 and 18 are respectively compared friction and wear for blends at concentrations similar to the applications. The combination of ZnDTP2 and MoDTP gives higher friction than the other blends; under rolling-sliding conditions was observed a similar trend but the difference is not so marked. As regards the wear, no differences were measured.

4. DISCUSSION The obtained results show that under the chosen working conditions, the investigated Mo-FMs are not effective if added alone to a mineral base oil. The anti-friction effectiveness of the organomolybdenum compounds can be controlled by synergism with ZnDTPs in a wide range of concentrations. At very high concentrations, ZnDTPs pro-friction behaviour overcomes the Mo-FMs performance, that is probably due to the increased polyphosphates film thickness from the ZnDTPs decomposition. The low traction coefficient measured at low temperature and in dry contact on the same wear tracks previously obtained in effective conditions, indicate that the anti-friction reacted layer is coated on the surfaces but it can be easily removed by rubbing; in relation to the mechanisms reported in literature, it seems realistic to think that the friction reduction is more likely due to the presence of MoS2 than to a smoothing of surface roughness. In order to reduce the mixed/boundary friction of motor oils as candidates for fuel economy engine

tests, the results indicate that, at Mo/Zn ratio about 0.22: 1) all the blends of studied MoDTP, MoDTC and ZnDTPs give good anti-friction performance 2) the friction reduction is not significantly affected by ZnDTP orgamc radicals structure 3) MoDTC and MoDTP give the same behaviour 4) no detrimental effects on the wear have been observed. • Then, the selection of the studied additive can be driven by the following criteria: optimise the ZnDTPs secondary/primary mixture looking to the wear performance, and prefer the MoDTC in order to minimise the phosphorus content in the oil, taking into account also the effects of the remaining additives.

5. CONCLUSIONS Effects of the interactions between ZnDTPs and anti-friction oil-soluble organomolybdenum compounds were investigated under rolling-sliding and pure sliding conditions. A clear synergism between the studied additives results in a significant friction reduction in the mixed/boundary regimes. The performance of the MoDTP and MoDTC is related to a surface reacted layer "solid-like" rather than "viscous-like" that is formed at high temperature (in our tests 135 °C) and is still effective at lower temperature (in our tests 40 °C). Future works will concern studies on the effects of different base stocks and synergism/antagonism in mixture containing other package additives.

ACKNOWLEDGEMENTS The authors wish to thank Salvatore D'Ambrosio for his helpful contribution in everyday lab activities.

758

REFERENCES

1. S. Korceck, M. D. Johnson, R. K. Jensen, C. McCollum, Retention of Fuel Efficiency of Engine Oils, Proc. of the l lth Int. Colloquium Technische Akademie Esslingen (1998), pp. 1281-1287. 2. W. J. Bartz, Fuel Economy Improvement by Engine and Gear Oils, in Dowson: Tribology for Energy Conservation, Elsevier 1998, Proceedings of 24th Leeds-Lyon Symposium on Tribology, pp. 13-24. 3. M. Yamada, Fuel Economy Engine Oils: Present and Future, Jpn. J. of Trib., Volume 41 (1996), pp. 783-791. 4. A. Yaguchi, K. Inoue, Development and Field Test Performance of Fuel Efficient SAE 514/-20 Oils, SAlE Paper 952341. 5. B. R. Dohner, M. A. Wilk, Formulating for ILSA C GF-2: Obtaining Fuel Economy Enhancement .from a Motor Oil in a Modern Low Friction Engine, SAE Paper 952343. 6. R. Sarin, D. K. Tuli, A. S. Verma, M.M. Rai, A. K. Bhatnagar, Additive-additive Interactions: Search for Synergistic FM-EP-A W Composition, Wear, 174 (1994) 93-102. 7. D. Wei, H. Song, R. Wang, An Investigation of the Effects of Some Motor Oil Additives on the Friction and Wear Behaviour of Oil-soluble Organomolybdenum Compounds, Lub. Science, 1991, pp. 51-72. 8. F. Rounds, Effects of Organic Molybdenum Compounds on the Friction and Wear Observed with ZDP-Containing Lubricant Blends, Trib. Trans., Volume (1990), 3, 345-354. 9. Y. Lin, Antifriction and Antiwear Characteristics of Molybdenum Dithiophosphate in Engine Oils, Lubr. Eng., Vol 51 (1995) pp. 855-860. 10. Y. Yamamoto, S. Gondo, Environmental Effects on the Composition of Surface Films Produced by an Organo-Molybdenum Compound, Trib. Trans., Vol. 37 (1994), pp 182-188. l l.Y. Yamamoto, S. Gondo, T. Kamakura, N. Tanaka, Frictional Characteristics of Molybdenum Dithiophosphates, Wear, 112 (1986) 79-87. 12. G. J. Johnston, R. Wayte, H. A. Spikes, The Measurement and Study of Very Thin Lubricant

Films in Concentrated Contacts, STLE Trans 34 (1991), pp 187-194. 13. G. Tripaldi, A. Vettor, H. A. Spikes, Friction behaviour of ZDDP Films in the Mixed Boundary/EHD Regime, SAE Paper 962036.

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Figure 18. Wear for 250 ppm Mo and 1.3 w% ZnDTP blends (135 °C).

Lubrication at the Frontier / D. Dowson et al. (Editors) 1999 Elsevier Science B.V.

759

The Behaviour of Molybdenum Dialkyldithiocarbamate Friction Modifier Additives Jocelyn Graham & Hugh Spikes Tribology Section, Imperial College, London SW7 2BX, United Kingdom

In recent years there has been growing concern to produce energy-efficient lubricated components and modem engine oil specifications require lubricants to demonstrate fuel efficiency in standardised engine tests. One important method of producing low friction and thus fuel-efficient lubricants is to use oil-soluble, molybdenum-containing, friction modifier additives. In optimal conditions these additives are able to produce very low friction coefficients, down to values in the range 0.06 to 0.075 in boundary lubrication conditions. This paper describes work to investigate the reaction and friction reduction mechanisms of molybdenum dialkyldithiocarbamate solutions in mineral oil. It is shown that this additive is able to produce friction reduction in the absence of other additives but that the range of conditions within which it works is strongly dependent upon temperature and additive concentration. This range of conditions can be influenced by the method of solution preparation and by the presence of other additives in the lubricant.

1.

BACKGROUND

Soluble molybdenum compounds were first identified as potential lubricant additives in the 1950s (1) but began to be seriously considered as friction-reducing and thus energy-saving additives only in the late 1970s (2)(3). In 1978 it was suggested; 1fit were possible economically to produce soluble antiwear compounds based on molybdenum then they would certainly have a place in transport lubrication (4).

Since that date, such additives have become one of the most important classes of friction-modifier agents and in recent years the requirement for low friction, fuel-efficient engine oils has served to greatly enhance this importance. Over the last thirty years, considerable research has been carried out to investigate the mechanism by which soluble molybdenum additives function. It has been shown, using electron diffraction (5)(6) and later X-ray techniques such as XPS (7) and XANES (8), that they form MoS2 on immersed and rubbed surfaces. This has led to the general presumption that the additives reduce friction by forming a reaction film containing MoS2 which, because of its

layer lattice structure, has inherently low boundary friction. Recent work has, however, shown that the presence of soluble molybdenum additives also leads to smoothing of rubbed surfaces, which may produce a reduction of friction by promoting hydrodynamic or elastohydrodynamic films at the expense of boundary lubrication (9). Very little is known about the chemical pathways by which soluble molybdenum additives react with rubbing surfaces. One complicating factor is that many studies have suggested that a significant friction reduction is only reliably observed when molybdenum additives are used in combination with other additives, such as zinc dialkyldithiophosphates (10) or other sulphurcontaining species (2). In part, this is because a large proportion of work has focussed, for practical reasons, on the influence of molybdenum additives in fully-formulated oils, but it has been also observed in much simpler formulations, especially when using molybdenum dialkyldithiocarbamates. It has been variously suggested that (i) sulphur-containing additives are needed to promote MoS2 formation (2); (ii) antioxidants are required to prevent molybdenum additives from behaving as peroxide-decomposers and thereby being consumed (11)(12); (iii) ligand exchange between the dialkyldithiocarbamate moiety and the dialkylthiophosphate in zinc

760

dialkyldithiophosphate is an importam stage in the friction-modifying reaction of molybdenum dialkyldithiocarbamate (13); (iv) antiwear additives promote the formation of MoS2 films by reducing the rate of their removal by wear (10). It should be noted, however, that a recent study has shown that molybdenum dialkyldithiophosphates were able to reduce friction effectively in mineral oil in the absence of other additives (14). At the end of 1997, a research programme was initiated in the Tribology Section at Imperial College to study the behaviour of soluble, molybdenumcontaining, friction modifier additives. The main objectives of the work are to identify the chemical pathways by which these additives form films on rubbing metal surfaces and to investigate the way that the films formed reduce friction. The first stage of this work, which is described in this paper has three aims; to develop friction tests able to reliably produce friction reduction using molybdenum additive solutions; (ii) to clarify whether such friction reduction can be produced in the absence of other lubricant additives; (iii) to explore the influence of temperature and concentration on friction-modifying behaviour.

and frequency that can be set by the user. A comrol circuit maintains constant stroke length regardless of the friction value. Friction between the ball and fiat is measured using a load cell attached to the lower specimen holder. Electomagnetic Vibrator

Ball Flat

Flexible Supports

Force Transducer /

\

Figure 1. Schematic of HFRR Test Rig

(i)

2.

Table 1 lists the main test conditions used in this study. Tests generally lasted 60 minutes and were carried out at a fixed temperature in the range 50 to 200°C. A new ball and fiat, cleaned successively in Analytical Reagent Grade toluene and Analar acetone in an ultrasonic bath, were used for each test.

TEST METHODS

2.1 High Frequency Reciprocating Rig OtFRR) Pure sliding friction tests were carried out in a high frequency reciprocating (HFRR) rig. This is commonly used to measure the wear properties of fuels and the friction properties of engine oils (15)(16). The test rig is shown in figure 1. A 6.0 mm diameter steel ball is held in a chuck and loaded downwards on the fiat face of a 10.0 mm diameter steel disc. The disc is held in a bath which contains test lubricant so that the contact between the ball and fiat is fully immersed. The bath has heaters and a control system so that the temperature can be set at any required value between room temperature and 200°C. During a test, an electrical vibrator is employed to oscillate the ball backwards and forwards in contact with the fiat at a stroke length

Table 1. Main HFRR test conditions used in this study Test Duration 60 minutes Stroke length 1000 ~m 20 Hz Stroke frequency 3.9N, (1.03 GPa max. Hertz) Load Temperature 50°C to 200°C Ball properties AISI 52100, 800 VPN Disc properties AISI 52100, 750 VPN

2.2

Mini-Traction Rig (MTM)

As well as pure sliding conditions it was also considered important to measure the friction behaviour of molybdenum additives in mixed sliding-rolling conditions such as are present in c a m and gear-type contacts. In pure sliding conditions,

761

one surface remains in contact continuously, which produces a very differem contact environmem from that where both surfaces move with respect to the contact. For mixed sliding-rolling tests, a minitraction or MTM rig was employed. This is a ball on disc set-up as shown in figure 2

A new steel ball and disc were used for each test and these were cleaned in Analar toluene and Analar acetone in an ultrasonic bath before testing.

3.

TEST MATERIALS

In this paper, results using one base fluid and one soluble molybdenum additive are reported. The base oil was a solvent-refined mineral oil, SN150 of viscosity 31 cSt at 40°C and 5.28 cSt at 100°C. The friction modifier additive used was molybdenum diethylhexyl-dithiocarbamate (MoDTC). It was provided in the form of a yellow powder and had the structure shown below.

R

Figure 2. Schematic test set up of MTM rig A 19.5 mm diameter steel ball is loaded against the flat surface of a steel disc. Ball and disc are driven independently by separate motors to obtain any required combination of entrainment speed U = (U1+U2)/2 and slide-roll ratio SRR. The SRR is defined in this study as;

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Table 3. Commercial antioxidams used

U 2 +U 1 The ball shaft is angled with respect to the disc to minimise spin. Friction force measuremems are made by means of a very stiff force transducer mounted perpendicular to, and in contact with, the ball shaft. The test conditions used in this study are listed in table 2.

Abbreviation

Description

DPA PSE

Alkylsubstituted diphenylamine Hindered phenolic substituted ester Hindered phenolic substituted ester disulphide

PSEDS

4.

H F R R TEST RESULTS

Table 2. Main MTM test conditions used in this

st.+ Entrainment speed Slide roll ratio Load Temperature Ball properties Disc properties

0.003 to 3 m/s 50% 42 N (1.05 GPa max. Hertz ) 40°C to 140°C AISI 52100, 800 VPN, 12-15 ~tm rms. AISI 52100, 750 VPN, 7 ~tm rms.

4.1 Influence of Additive Concentration and Temperature Figures 3a to 3c show typical friction trace results using the HFRR test for three fluids at the same temperature of 100°C; (a) the mineral base oil alone; (b) a 0.05% wt. solution of MoDTC and (c) a 0.18% wt. solution of MoDTC. The mineral oil alone shows high friction throughout the test with an average friction coefficient during the last 30 minutes of 0.166.

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molybdenum friction modifier additives which have the ability to produce remarkably low friction coefficients of 0.05 to 0.08 in boundary lubrication conditions, considerably lower than those normally seen with surfactant-type friction modifiers. This type of behaviour, i.e. the ability to produce a sudden and dramatic reduction in friction coefficient from values well above 0.1 to values below 0.08 within the test time of 60 minutes is taken, in the current study, to represent an effective MoDTC friction modifier response in the HFRR test. It is noteworthy that this was obtained with a simple MoDTC/mineral oil combination without other additives being present. Tests were carried out at a range of additive concentrations and temperatures to explore the conditions in which the MoDTC additive system worked. The results of this are summarised in figure 4. The darkly shaded area on this chart represents the conditions under which MoDTC reduced friction coefficient below 0.075 within the HFRR test. The dashed line on the chart shows the solubility line for the MoDTC in the mineral oil used. This was determined using optical transmission measurements with a HeNe laser. Above this line the additive was fully soluble in the base fluid. It was possible to obtain solid additive-free solutions below this line but these represent super-saturated solutions.

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HFRR friction traces for three test fluids at 100°C

The dilute MoDTC solution shows reduced friction but still with a coefficiem value of 0.152. The more concentrated solution exhibits a two-stage response, with initially quite high friction followed, after 1.5 minutes, by a rapid drop in friction to a low value. Immediately after the drop, the friction coeffcieint reached 0.063, but it then rose slightly to stabilise at 0.075 over the last 30 minutes of the test. The latter value is characteristic of the behaviour of oil-soluble

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Figure 4. Zone of activity of MoDTC

763

It can be seen that at concentrations below 0.09% wt. (180 ppm Mo), the additive failed to reduce friction at any temperature. At concentrations above 0.2% wt., the additive reduced friction very effectively at all temperatures between 70°C and the maximum temperature tested of 200°C. Below 70°C, friction reduction became less and less effective, especially at high additive concentrations but some additive response was still seen. Solution concentrations above 0.5% wt. were not tested. In the concentration range between 0.09% and 0.2% wt. friction reduction took place only within a limited temperature range, with a lower cutin temperature of 50-70°C and an upper cut-off temperature whose value rose linearly with additive concentration. This upper temperature limit was remarkably repeatable in tests on a given solution, with behaviour switching from effective friction reduction to no friction reduction over less than 1°C. The time for the sudden onset of friction reduction to occur was only moderately repeatable. It generally took place about 10 to 40 minutes after starting a test at low additive concentrations, reducing to less than 10 minutes into a test at additive concentrations above 0.15% wt.

4.2

Influence of Solution Preparation Method In the initial stages of this study, the MoDTC solutions tested showed no friction-reducing response in the HFRR test. Further work indicated that this was due to the method of solution preparation. All the test results shown in figure 4 are for solutions prepared by gently heating the MoDTC solid with mineral oil in a water bath at 80°C whilst stirring. In initial work,, however, solutions were prepared by heating solutions in a beaker on a stirrer hot-plate at a nominal temperature of 85°C and it is believed that this subjected the solution and undissolved solid to considerably higher temperatures. The consequent solutions gave much poorer friction-reducing response. This is shown in figure 5, which compares the temperature range of effective response of solutions prepared using direct and water-bath heating at two different concentrations. It can be seen that direct heating greatly narrows the temperature range over which the solution can reduce friction.

200

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500.155% wt.

0.18% wt.

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Dissolved using water bath Dissolved using hot plate Figure 5. Influence of solution preparation method on MoDTC performance

Influence of an Antioxidant It has been reported in the literature that some amioxidants are able to enhance the frictionreducing properties of soluble molybdenumcontaining additives (12)(13). Tests were carried out to see whether added antioxidants influenced the response of the MoDTC additive used in the current study. A Mo additive concentration of 0.085% wt. was employed, this being in the range whether the additive showed no friction reduction at any temperature between 50 and 200°C. Three antioxidants were employed, as indicated in table 4. They were all used at a concentration of 5% wt.. It was found that the two antioxidants DPA and PSE had no effect on promoting friction reduction by MoDTC under these conditions. However the addition of PSEDS to MoDTC resulted in rapid reduction in friction at all temperatures tested up to 200°C. 4.3

5.

M T M TEST RESULTS

The MTM test rig can be programmed to carry out tests automatically over any sequence of operations, including the programmed control of temperature, applied load and motion. Considerable

764

experimentation was required to develop optimum test conditions for testing molybdenum friction modifiers. The sequence finally adopted is shown in table 4.

oil. Friction coefficient also falls progressively with test stage, stabilising at about 0.095 after seven eight stages. 0.2

Table 4. Main MTM test sequence used in

study Step 1 Step 2 Step3 Step 4

Subsequent stages

. Temperature raised to set value 30 minutes pure rolling at 0.5 m/s entrainment speed, no load 10 minutes, 50% SRR, 1 m/s entrainment speed, 42 N load Measure friction coefficient variation with entrainment speed at 50% SRR, 42 N load Repeat steps 3 and 4 (typically 9 times)

As will be seen below, this type of repeated stage testing enabled the development of frictionreducing behaviour to be observed with MoDTC solutions. Because the MTM tester was able to control the speed of both ball and disc independently, it was possible to measure friction coefficient as a function of varying entrainment speed whilst maintaining a constant slide roll ratio. Since elastohydrodynamic film thickness varies with entrainment speed but not significantly with the proportion of sliding (17), such results effectively show how friction coefficient varies with film thickness, passing from EHD film friction at high entrainment speeds, through mixed lubrication into full boundary lubrication at very slow speeds. Figure 6 compares a plot of friction coefficient versus entrainment speed for the additivefree base oil with a sequence of plots corresponding to stages in a test with 0.18% wt. MoDTC solution. (The last number in each data set legend is the test stage number). At high entrainment speeds, the additive-free plot is very similar to the MoDTCcontaining ones, indicating, as might be expected, that the Mo-additive makes no contribution to friction in full film EHD conditions. At slow speeds, in the near or full boundary lubrication regime, however, the MoDTC friction values are considerably lower than those for the additive-free

"~ 0.15 .~_

&SNIO02 &SNIO04 X MoDTC 2 m MoDTC 4 0 MoDTC 6 • MoDTC8 • MoDTC 10

~ L

o

o= 0, ~. 0.05

w

10

100

1000

10000

Entrainment Speed mm/s Figure 6. Friction versus entrainment speed plots

6,

DISCUSSION

From the above results it can be seen that molybdenum dialkyldithiocarbamate is able to reduce friction effectively in the absence of other additives. The range of conditions over which it works is, however, quite limited and can be considerably extended by the presence of other additives. Thus a sulphur-containing antioxidant enables friction reduction to occur at lower additive concentrations than would otherwise be the case. It is also likely that the extent of friction reduction may be increased by the presence of other additives such as ZDDPs. From the MTM results in this paper, it appears that MoDTC only reduces friction to boundary values of around 0.095. (This is quite compatible with the friction levels observed in the HFRR test if it is noted that the mean entrainment velocity in the HFRR is around 0.02 m/s. This lies in the mixed lubrication regime, where, according to the MTM results, friction coefficient should be around 0.075.) However recent work using a similar test apparatus to the HFRR shows that mixtures of MoDTC and ZDDP can give much lower boundary friction values, below 0.04 even at very low speeds (18).

765

It is interesting to note that the method of solution preparation can also have a marked influence on whether an MoDTC solution can reduce friction. The reasons for this sensitivity have not yet been established but are being investigated. However it might also have led to a failure in some earlier work to obtain a friction-reducing response in the absence of other additives.

7.

CONCLUSIONS

Friction tests have been carried out in pure sliding and in mixed sliding-rolling conditions using solutions of a molybdenum dialkyldithiocarbamate in mineral oil. Friction reductions have been observed over a range of additive concentrations and temperatures. There appears to be a threshold concentration below which the additive only responds within a limited temperature range. It has been found that the method of solution preparation is quite critical in determining additive friction reducing response. Samples prepared on a hot plate under relatively severe heating conditions gave more limited response than those prepared in water bath at lower temperature. An antioxidant additive was found to considerably broaden the range of conditions over which the MoDTC functioned.

8.

ACKNOWLEDGEMENTS

The authors wish to thank Ford Motor Company, Dearborn for a grant which enabled this work to be carried out and also Enitecnologie, Milan for useful discussions.

REFERENCES

1.

2.

Spengler, G. and Weber, A., "On the Lubricating Performance of Organic Molybdenum Compounds", Chem. Ber. 92, (1939), pp. 2163-2171. (In German). Mitchell, P.S. "Oil-Soluble Mo-S Compounds as Lubricant Additives", Wear 100, (1984), pp. 281-300.

3.

Greene, A.B. and Risden, T.J. "Effect of MoContaining Oil Soluble Friction Modifiers on Engine Fuel Economy and Gear Oil Efficiency", SAE Tech. Paper 811187, (1981). 4. Braithwaite, E.R. and Greene, A.B., "A Critical Analysis of the Performance of Molybdenum, Wear 46, (1978), pp. 405-43. 5. I-Ming Feng, Perilstein, W.L. and Adams, M.R. "Solid Film Deposition and NonSacrificial Boundary Lubrication", ASLE Trans. _6, (1963), pp. 60-66. 6. Isoyama, H. and Sakurai, T. "The Lubricating Mechanism of Di- jx-thio-dithio-bis (diethyldithiocarbamate) Dimolybdenum During Extreme Pressure Lubrication", Trib. Intern. 7, (1974), pp. 151-160. 7. Gondo, S. and Konishi, M. "Organoamine and Organophosphate Molybdenum Complexes as Lubricant Additives", Wear 120, (1987), pp. 51-60. 8. Kasrai, M., Cutler, J.N., Gore, K., Canning, G. and Bancroft, G.M. "The Chemistry of Antiwear Films Generated by the Combination of ZDDP and MoDTC Examined by X-Ray Absorption Spectroscopy", Trib. Trans. 41, (1998), pp. 69-77. 9. Tohyama, M., Ohmori, T., Shimura, Y., Akiyama, K., Ahida, T. and Kojima, N. "Mechanism of Friction Reduction with Organo-Molybdenum Type Additives", Proc. Intern. Trib. Conf. Yokohama 1995, pp. 739744, publ. JST, Tokyo, 1996. 10. Murald, M., Yanagi, Y. and Sakaguchi, K. "Synergistic Effect on Frictional Characteristics Under Rolling-Sliding Conditions due to a Combination of Molybdenum Dialkyldithiocarbamate and Zinc Dithiophosphate", Trib. Intern. 30, (1997), pp. 69-75. 11. Arai, K., Yamada, M., Asano, S, Yoshizawa, S, Ohira, H., Hoshino, K, Ueda, F. and Akiyama, K., "Lubricant Technology to Enhance the Durability of Low Friction Performance of Gasoline Engine Oils", SAE Tech. Paper 952533, (1995). 12. Korcek, S., Jensen, R., Johnson, M. and Clausing, E. "Antioxidant Reactions of Engine Oil Additive Systems Containing Friction Modifiers", Proc. Intern. Trib. Conf.

766

Yokohama 1995, pp. 733-737, publ. JST, Tokyo, 1996. 13. Johnson, M.D., Jensen, R.K. and Korcek, S., "Base Oil Effects on Friction Reducing Capabilities of Molybdenum Dialkyldithiocarbamate Containing Engine Oils", SAE Tech. Paper 972860, (1997). 14. Satin, R., Tuli, D.K., Sureshbabu, A.V., Misra, A.K., Rai, M.M. and Bhatnagar, A.K., "Molybdenum Dialkylphosphorodithioates: Synthesis and Performance Evaluation as Multifunctional Additives for Lubricants", Trib. Intern. 27, (1994), pp. 379-386. 15. Spikes, H.A., Bovington, C., Caprotti, R., Meyer, K. and Kreiger, K. "Development of a Laboratory Test to Predict Lubricity Properties of Diesel Fuels and its Application to the Development of Highly Refined Diesel Fuels." Tribotest 2, (1995), pp. 93-112.

16. ASTM-D6079, "Standard Test Method for Evaluating Lubricity of Diesel Fuels by the High Frequency Reciprocating Rig (HFRR), 1997, ASTM Philadelphia. 17. Ball Bearing Lubrication: The Elastohydrodynamics of Elliptical Contacts, Hamrock, B.T. and Dowson, D., publ. J. Wiley & Sons, New York, 1981 18. Tripaldi, G., Fattori, S., Nodari, R. and Vettor, A. "An Investigation on the Antifriction Performance of Some Organomolybdenum Additives", paper to be presented at Leexts/Lyon Symposium, Lyon, Sept. 1998.

Lubrication at the Frontier / D. Dowson et al. (Editors) © 1999 Elsevier Science B.V. All rights reserved.

767

Traction and film thickness characteristics of traction fluids in high speed elastohydrodynamic contact. By J. M a k a l a **, J.P. Chaomleffel ~ , B. Villechaise *, G. D a l m a z ~ , K. K a r g a r * * Laboratoire de M6canique des Solides - Universit6 de Poitiers * Laboratoire de M6canique des Contacts - Insa de Lyon # Renault - Direction de la Recherche - Technocentre Renault - Guyancourt

The performances of continuously variable transmission have been investigated experimentally. The aim of this approach was to determine simultaneously traction and film thickness under isothermal elastohydrodynamic conditions. The experiments have been carried out with four traction fluids under various ranges of pressure (0.5 - 2 GPa) and speed (0.5 - 12 m/s). The profile of lubricant and film thickness separating the surfaces between a steel ball and a sapphire plate was determined by the use of a well-known interferometry technique. For high rolling speed and high pressure, the modification of the usual optical arrangement with a new system allows the observation of the interference pattern and thus the measurement of oil film thickness with a good quality.

1. I N T R O D U C T I O N Continuously variable automatic transmission for automotive use have been the focus of considerable research and development efforts in recent years. CVT can bring improved fuel economy benefits under good speed ratio changes for automobile propulsion systems in which engines can produce their power under optimum conditions. Today there are two types of Toroidal drives for automobile CVTs. One is Half Toroidal, Fig. 1, and the other is Full Toroidal, Fig. 2. Toroidal drive consists of an input and an output disks, and power rollers which transmit engine power to the output shaft by the shear force of the elastohydrodynamic

film existing elements.

between

the

pair

\\\ ~ m

r, -(

\

-

/

I

/

/

/

Fig. 1 : H a l f toroidal drive

of

rolling

768 \\ \\\

/

/

"'I

/ / / /

Fig. 2 : Full toroidal drive Half toroidal traction drive has been studied for a long time by Kraus [1], Machida [2] or Tanaka [3] and Hewko [4] or Patterson [5] for the Full conception. The state of art of CVTs has been made by several authors as Machida [6] or Loewenthal [7]. For the traction drive CVT in an automotive power transmission, a specific fluid with high traction coefficient and high viscosity is required also at high temperature. Traction lubricants also need good film formation qualities for lubrication of ordinary bearings in drive assembly. The performance of traction drives depends on a large extent on the rheological properties of the fluid in the EHL contact as mentioned by Johnson and Tevaarwerk [8]. The traction coefficient is def'med as the ratio of the traction force to the applied load. This parameter seems certainly to depend on the molecular structure of the lubricant as mentioned by Tsubouchi and Hata [9] or Muraki [10]. Traction fluid was developed in 1968's by Monsanto and received a patent on Santotrac, a synthetic hydrocarbon lubricant with a tested traction coefficient of 0.1. This well-known lubricant has an increase in viscosity with pressure that is 20 percent higher than petroleum oil. Traction fluid has been improved

considerably over the last ten years. Recent developments in oil producing techniques bring about traction oils with high traction coefficients. The speeA and torque efficiency models require the knowledge of traction fluid, local contact phenomena and a shear model of EHL contact. In order to explain the characteristic behavior of oils in EHL contact, a number of rheological models have been proposed in which oils are assumed to behave as non-Newtonian viscous fluid, elastic or plastic solids. At high pressure and speeA, typical of traction drives contacts, it has been generally accepted that oils with high viscosity behave as an elastic solid at moderate temperature and low shear rates. At high shear rate, the fluid behave as a plastic solid, there is a limiting stress at which shear stress becomes independent of the shear rate. Since 1960's numerous papers have been presented on the prediction of traction in EHL contacts. A comprehensive traction contact model is proposed by Johnson and Tevaarwerk [11]. This model covers the full range of viscous, elastic and plastic behaviour of the EHL film. Bair and Winer [12] have also suggested a non-linear rheological model with a limiting shear stress in which they assume that the fluid behaves as a visco-elastic-plastic solid. To be able to apply the Johnson and Tevaarwerk model, fundamental fluid properties must be known under required operating pressure, speed and temperature. These properties are the shear modulus and the limiting yield shear stress of the lubricant. As mentioned by Bair and Winer [13] or Kato [14], the limiting shear stress seems to be the material property which determines the maximum shear stress that can be transmitted in an EHL contact and therefore in a traction drive. Because of the difficulty of simulating the highly transient nature of an actual traction contact, the most reliable basic fluid property data have been traditionally deduced from initial slope and maximum traction coefficient of experimental

769

traction curves. There are several methods of measuring the rheological properties of traction lubricant; they are divided into "steady state" methods and "transient" methods. Evans and Johnson [15] used this principal and wellknown method for measuring rheological properties of Santotrac50. They obtain their experimental data with a disc machine which is used as a high-pressure viscometer. Jacobson [16] has developed a device in which a steel ball makes an oblique impact with a lubricated, hard steel surface. The mean shear stress in lubricant film is deduced from the rotation given to the ball. This device can operate under conditions of high pressure and shear rate in which the fluid reaches its limiting shear stress. Bair and Winer [17] evaluated the limiting shear stress and shear modulus of the same lubricant by the steady state methods using a stress-strain high pressure apparatus. This technique has the avantage to provide data which are independent of the EHL process as the rollers compliance effects but their apparatus is limited in pressure. In order to evaluate the relationship between limiting shear strength and pressure for lubricants, a high pressure chamber was built by H6glund and Jacobson [18], at Lulea. It was possible to measure the pressure, the shear strength of the solidified oil, the increase in shear strength of the oil for an increase in pressure and to measure the compression of the oil with very high precision. In elastic-plastic regime, Loewenthal and Rohn [19] give for Santotrac50, correlation equations to predict rheological properties of traction fluid from traction disc machine experiments. It is very difficult to know the behavior of fluid according to the different operating conditions. Evans and Johnson [20] etablished, from the rheological properties of Santotrac50, a map in which different areas correspond to different regimes of behavior. Given the load, speed and temperature, the operating conditions can be located as a point in the map.

The purpose of this paper is to evaluate the performance of four traction fluids. This experimental study was initiated using an experiment initially designed by Dalmaz [21]. The apparatus has been greatly modified for the observation of elastohydrodynamic contacts at high speeds and pressures. Traction data and film thickness are determined for elastohydrodynamic point contact, in isothermal conditions. To compare traction fluids in term of friction at high speed, in the same conditions of load and viscosity, the oil feed conditions must be controled. Film thickness are compared with the EHL Hamrock and Dowson theory. The experimental data are compared and discussed in order to select the traction fluid with the highest traction coefficient and oil film thickness. The rhe01ogical properties obtained with this technique are compared with independent measurements. The interest in both film thickness and traction data for EHL point contacts is due to the difficulty encountered in effectively lubricating mechanical elements such as ball bearings, gears and in the selection of operating fluids for traction power transmissions. The centre film thickness has received the most attention in this study and from the stand point of wear protection, the minimum film thickness has also been determined. This investigation allows a better characterization of the experimental data compared to those obtained on disc machine where the interaction of asperities seems to influence the traction. In this study the thermal exchanges and oil feed conditions are, however, different from traction drive.

2. EXPERIMENTAL TECHNIQUE AND EQUIPMENT The apparatus, as shown in Fig. 3 and Fig. 4, allows the simultaneous measurement of normal load, angular speeds of plate and steel ball,

770

traction force in rolling direction, lateral traction force and film thickness. As shown in Fig. 3, the tangential force is measured on the surface of the ball, in the rolling direction ~, by a sensor on the axis of hydrostatic bearing. Tests have been performed at room temperature between 25°C and 27°C in lubricated rolling-sliding hertzian point contacts under fully flooded conditions. The inlet oil temperature are controled with a good accuracy by thermocouples located near the surfaces of the ball and of the disc. The profile of lubricant and film thickness separating the surface between a sapphire plate (E~=370 GPa and ~ - 0 . 3 4 ) and a steel ball (E2-210 GPa and 1,2 =0.29) were determined by the use of the well-known interferometry technique. To properly observed the properties of the film, it is necessary that the roughness of the element surfaces is significantly less than the thickness of the film. The surface roughness is approximately 0.005 lam for sapphire plate and 0.01 iam for steel balls.

The mechanical and thermo-mechanical properties of the sapphire disc are different from those of steel but it has been shown that the effects of the material properties (Young modulus and Poisson coefficient) upon the film thickness in elastohydrodynamic point contact are negligible [22] and [23]. ::~~ ..... . _i2

...... .::~!ii

..... :........ ~.....~'!.......,..........

.~.~...~ii~i~i~i~ii~i~.~:~i~!~!!!!!~!!!~ii~ii~i~ii

~ - .

~~i! ~

,.-

:~i~.........._,__:~i.~"~;?:..~i:

~:ii~liiiiii~iiiiiiiiiii::iiiiiii::i::i::ii!ii~iii::i::i::i::~::~!:!!:::::i::!::!i ::i~

!~:~.....

Y~%..

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

.

"'-

..

~~~:.:::::!.:!!!!i!i::

:::,:ii ~...... :':~ i::~,!~:iii~i~:~~,','::'e~.:...

~ii'~iii'~

Fig. 4 : view of sapphire plate and steel ball

The simultaneous measurement of traction force in rolling direction, central and minimum film thickness were carried out with two different steel balls under the following running conditions:

1 Microscope

Light Source

~o~on - , , , , , .

? t ............. l l ~ n

0.): / Axisof Sphere SapphirePlate ~,,,,,~ ~ ~ --, Rotation =============================================================================== , Y / ......:::.... i " -:i:::.. " / OilFeedSy. . . . ~ I:1 ~ (o: a er

ac :o

rce y

~

Motor j

S ~ i

- - - ~

Dynamometer TractionForce Dynamometer

-~

y

'~ Axisof Hydrostatic Bearing

Fig. 3 : schematic diagram of the experimental equipment

Small steel b a l l : The contact is formed by a steel ball whose principal radii of curvature are Rx=Ry=4.95 mm. * the applied load varies from 6 to 50 N with a maximum Hertzian pressures up 2 GPa * speed U~x+U2xvaries from 0.5 to 4 m/s * rolling-sliding ratio (Ulx-U2x / Ulx+U2x) varies from -0.2 to 0.2 Big

steel

ball"

The contact is formed by a bigger steel ball whose principal radii of curvature are Rx=Ry= 14.95 mm. * the applied load varies from 8 to 110 N giving maximum hertzian pressures up 1.3 GPa * speed U~x+U2xvaries from 0.5 to 12 m/s * rolling-sliding ratio (Ulx-U2x / Ulx+U2x) varies from -0.08 to 0.08

771

The smaller ball allows high pressure while the bigger one allows high speed. The contact location and the position of the axis of sphere rotation compared to the axis of plate rotation are chosen to allow experimental kinematics conditions without spin and no lateral sliding, Fig. 3. In this study Santotrac50 is used as a reference fluid, it is well-known and have been studied by numerous authors. The measured viscosity characteristics of the traction fluids selected for this study are listed in Table 1. Pressure-viscosity were determined with a falling body viscometer for pressure varying from 0.1 MPa to 0.1 GPa. The results obtained showed that the variation of viscosity with pressure is approximately exponential. This group of special fluids have a high viscosity and a high pressure-viscosity exponent at ambient temperature and atmospheric pressure. High viscosity is required to prevent metal-to-metal contact by a sufficient film thickness between rolling elements. High pressure-viscosity coefficient shows an ability of lubricant to support a higher normal load. Fluid Viscosity at 0.1 MPa fm.Pa.s~

ot (GPa)-~

25°C 40 °C

Santotrac50 56.0 23.4

25 °C 40 °C

13 (°C)-' Table

HTF A 84.0 49.0

HTF B 77.0 24.3

36.0 26.0

32.0 26.7

28.0 22.7

0.029

0.034

0.031

HTF (~ 67.5

0.028

1 " viscosity characteristics

At high speed, the information of friction force can be interpreted if film thickness are known and if oil feed conditions are controled. For high rolling speed and high pressure, the modifications of the oil feed system and the usual optical arrangement were necessary. For a speeA of 0.5 m/s, a color photography was taken in 0.5 ms with a film of 6400 AS A and continuous light lamp of 150 W. At higher speed the observation of contact phenomena requires an exposure time of 10 las for a speed of 10 m/s and a length of contact of 100 lam. The xenon white light lamp was replaced by a high power

flash. The technological limits allow the use of flash with an exposure time of 40 p s and a film of 400 AS A. In fully flooded conditions, the use of the flash enables the observation of the interference patterns with an exposure time of 40 las rather than 4 ms for the old system. This technique does not modify temperature and local phenomena in the elastohydrodynamic contact. To control oil feed conditions at high speed, an oil feed system has been added on the steel ball.

3. RESULTS

Experimental traction forces, minimum and central film thickness are obtained versus slideroll ratio (U1-U2)/ (U~+U2), for no spin and no lateral sliding conditions, at room temperature. 3.1. Film Thickness

With the old system at high speexl, the observation of the contact is poor, as shown Fig. 5. For a speed above 2 m/s, oil feed conditions become difficult, the inlet meniscus is near the edge of contact. The combination of high speed with sliding speed leads to the contact to be starved. The resulting decrease in film thickness can be the cause of a possible change in lubrication regime. The interpretation and comparison of traction force between fluids are difficult in these conditions because oil feed conditions and film thickness are not controled. Fig. 6 depicts typical elastohydrodynamic film shapes given by the interferometric technique obtained for high speeds. The modification of the usual optical arrangement and the oil feed system allow the observation of local phenomena. The conditions are fully flooded, the inlet meniscus distance is three or four times greater than the semi-length of Hertzian area. The minimum and central film thickness can be extracted with a good accuracy. Fig. 7 is a view of contact at high speed.

772

:::::::: .... ::::::::::::::-::~:::.:~.~,:~:.~:.,,,:~:'.,'~:~:::'. .... :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ..........:::::::::::::::::::::::::::::::::::::::::::::::::

~~~:~:~~.,..,,~.,.:..:..., ................................. ~\,,~-..~.,:.-~~~,~::::..'.~.:~:0.1 ).

Paper IV (iii) "Effect of Surface MorpholoRv Upon Friction of a Metal Substrate Slidinv Al~ainst Hot Viscous Melt Under Extreme Conditions", by Dr. M. Falipou (BSN Givors, France), Professor H. Zahouani and Dr. Ch. Donnet (Ecole Centrale de Lyon, LTDS, France). Dr. J. Sul~imura ( Kyushu University, Fukuoka, Japan). Assuming sliding surfaces as fractal implies that you assume the surfaces to have a selfsimilar, or self-affine, structure in the statistical sense, with asperities of various scales. Do you think there is any relation between such fractal structure and the friction behaviour you observed? If there is, can you describe how the coefficient of friction is affected by the fractal dimension? Reoly by the Authors. Yes, the problem of variations in slopes is very connected to the fractal aspect. As we have shown in our study, the distribution of the scales of slopes affects the friction

848

Professor M.J. Adams (Unilever Research, Port Sunlight, Wirral, U.K.). For a viscous melt it is appropriate to have a kinematic wall boundary condition such as "no-slip" on the Navier. In this context, what is your definition of friction coefficient?

Dr.J.A.Williams (The University of Cambridge, U.K.). Your experiments clearly show that the presence of local wear debris produces levels of overall coefficient of friction lower than those expected from the application of slip line field treatment. Do you have an explanation for this behaviour? If the particles are removed (is this possible?) is there some recovery in the value of the observed friction force?

Reply by the Authors. The definition of the friction coefficient used in our study is based on the global energy balance of the tribo-system. Indeed, the kinetic energy lost by the viscous glass cylinder during the contact is dissipated by viscous strain and friction, as we assume no thermal and no rheological variation of the glass in the contact. So we do not define this coefficient in a kinematic wall boundary context.

Reply by the Authors. If wear particles lodge beneath the slider, they will almost certainly alter the surface deformation field. We speculate that less frictional energy will then be dissipated in shearing the surface, and more in shearing the layer of debris so that the latter process comes to control the friction. So far, attempts to remove the particles have failed, and we have no experimental justification for our hypothesis.

Paper IV (iv) "Investigation of Surface Deformation and Friction when a Hard Cylindrical Asperity Slides Over a Soft Smooth Surface", by Melle M. Busquet and Dr. A.A. Torrance (Trinity College, Dublin, Ireland).

Professor F.E. Kennedy (Dartmouth College, Hanover, NH, U.S.A.). It appears that both elastic deformation and 3rd. body particles influence friction in the system studied by the authors. It would be interesting to study the relative importance of the two factors. One possible way to do this in the experiments would be to advance the hard cylinder along the soft counterface, as on a lathe for example, so that a helical wear path would be produced; 3rd. body effects should be less important in such a test because the wear track would be passed over only once.

behaviour, and the fractal aspect has a clear consequence in friction variations.

Dr. J.A. Greenwood (University of Cambridge, U.K.). (See also the discussion on Paper IV(ii)). The original Courtel "bourrelet frontal" and the Oxley 'wave' as studied by Williams and Busquet were both 'steady state' mechanisms: the 'bourrelet' never became any larger. In contrast, the 'prows' observed and studied by Cocks and by Antler appeared to grow continuously until at some point the slider jumped over the prow leaving it as a relatively large, enormously hard, transfer particle. My recollection is that all the experiments were under lubricated conditions. What determines which sort ofbehaviour occurs?

Reply by the Authors. One way of determining whether a steady wave or a prow is formed by a slider was given by Oxley. He suggested that if c~ > s then the slip-line field for the steady wave is no longer valid. Then, if the friction is enough, a prow will form. The effect will be more pronounced with materials which work-harden. Otherwise the slider will cut a chip. The general outline of this prediction was confirmed experimentally by Kato and Kokkirigawa and published in Eurotrib in 1985.

Another possible study would be to extend the finite element elasto-plastic analysis to the cut-away cylinder case. Such an analysis would clarify the role of elastic deformation, particularly in the trailing part of the contact.

Reply by the Authors. Since the Symposium, we have tried Professor Kennedy's suggestion of getting the slider to follow a helical path, but so far, this does not alter the friction; nor does blasting the slider with compressed air, though some of the debris is removed from its sides. We are currently improving the finite element models we are using, and hope that these may throw more light on the process.

849

SESSION

V- COATINGS

Paper V (i) "A Tribological Comparison of Some Carbon-Carbon Composites Sliding Against Stainless Steel", by Dr. D.M. Elliott and Professor J. Fisher (School of Mechanical Engineering, The University of Leeds, U.K.) Dr. S.P. Appleyard, Dr. E. Zhang and Professor B. Rand (School of Materials, The University of Leeds, U.K.).

Dr. A. Y A. Gangooadhv (Ford Scientific Research Laboratory, Dearborn, MI, U.S.A.). What is the difference between PAN and PITCH type fibres? The specific wear rates of different materials varied with sliding distance. In the conclusions, when the wear rates are compared, what sliding distance was selected?

Reply by the Authors. The main difference between these two types of fibres lies in the structure and form of the carbon therein. Carbon derived from polyacrylonitrile has a turbostratic structure which does not develop into a three-dimensional graphiticlike carbon, even upon heating to temperatures above 2000°C. Conversely, carbon derived from carbonaceous mesophase pitch will readily develop three-dimensional crystallinity at such temperatures. In general, so-called 'non-graphitic' and 'graphitic' carbons may exhibit very different properties, differing in, for example, elasticity, hardness, thermal and electrical conductivity. The specific wear rates compared in the conclusions were the steady-state specific wear rates. The materials tested had usually reached a steady state of wear after 60 km sliding distance and in all cases after 90 km

Dr. A. O. Mian (Federal Mogul Technology, Cawston, U.K.). The authors have presented some very interesting findings for specific wear rates at specific loads of 1 MPa. For typical engineering applications, however, specific loads of 20-30 MPa are not unusual. Could the authors speculate on the effect of higher specific loads on the current conclusions?

Reply by the Authors. The work concluded that the majority of the carbon-carbon composites had lower wear rates than PEEK and PEEK-bonded carbon fibre. This would probably continue to be

true at higher pressures and concomitant higher temperatures, as the carbon-carbon composites do not contain a polymer. The low wear rates of the carbon-carbon composites were achieved with the aid of a lubricating transfer film on the steel disks. At pressures of 20-30 MPa this film should continue to form, the ground surface of the steel entrapping the carbon wear debris on which more would then attach. However, the 5 mm diameter pins used in our tests might not withstand the increase in friction force and would most probably start to fracture at the perimeter. Larger blocks of the composite, with a more favourable contact geometry, should exhibit low wear rates at these higher pressures, and certainly out-perform dry-sliding metal components.

Paper V (ii) "Low Friction and Low Damal~e Properties of Diamond with Water Boundary Lubrication", by Professor S. Miyake and Mr. A. Kinjyo (Nippon Institute of Technology, Saitama, Japan).

Dr. A Y A Gangopadhy (Ford Scientific Research Laboratory, Dearborn, MI, U.S.A.). The morphology of diamond film was rough at low humidity but smooth at high humidity. What do you mean by that?

Reply by the Authors. Surface morphology change of diamond film is shown in order to clarify microscopic surface wettability with water. Surface roughness decrease with increasing humidity is attributed to the adsorbed water on the diamond film. The adsorbed water covered and smoothed the rough diamond surface at higher humidity condition of about 50% as shown in Figure 5(a). This good wettability seems to produce good boundary lubrication properties of diamond films with water.

Paper V (iv) "A Comparative Study of the Tribological Behaviour of TiN and ZrN PVD Coatings", by Dr. F. Silva, Professor A.T. Ribeiro and Professor. UA. Porto, Portugal).

Ferreira

(DEMEGI/FEUP,

Dr. L. Rapoport ( C.T.E.H., Holon, Israel). You have different roughnesses for TiN and ZrN coatings. What is it that determines more friction and wear behaviour -the roughness structure? Reolv by the Authors. The authors wish to thank Dr. L. Rapoport for his interest in our work.

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The surface roughnesses obtained for the coated blocks and rings, were as the following table, as a media. The difference between the surface roughness of the TiN and ZrN specimens does not seem large enough to explain the wear rates obtained in the experiments.

Coating TiN Ra = 3.73 ~tm

ZrN Ra = 3.28~tm

Rz = 17.03 ~tm Ra = 0.663 ~tm

Rz = 15.76 ~tm Ra = 0.733 ~tm

Rz = 6.19 ~tm

Rz = 7.70 ~tm

Rings

As stated in the text, the more globular topography of the ZrN coating and its worse adhesion to the substrate can explain the higher wear measured with this coating when compared to TiN coatings.

AND

Paper VI (i) "Amplitude Reduction of NonIsotropic Harmonic Surface Patterns in Circular EHL Contacts under Pure RollinR", by Dr. C.H. Venner, (University of Twente, Enschede, The Netherlands) and Professor A.A. Lubrecht (INSA, LMC, France).

Dr. R.I. Taylor (Shell Research Limited, Chester, U.K.). Some engineering surfaces exhibit the phenomenon of "Correlated Surfaces", where each surface has a relatively high surface roughness, but the surfaces "fit together" so that the combined surface roughness is very small. How does your model cope with such a situation? Surface 1

as depicted by the discusser this implies that there is no relative motion, i.e. pure rolling, and thus if the undeformed film thickness is known, the deformed film thickness can directly be obtained from the formula presented in the paper. In fact, for pure rolling it is irrelevant which surface carries which part of the waviness.

Dr. L. Houpert. ( Timken France, Colmar, France). Did you calculate the elastic deformation

Blocks

SESSION Vl - ROUGHNESS ELASTO-HYDRODYNAMIC LUBRICATION

Reply by the Authors. If the surfaces fit together

for transverse roughness and, if so, could you please comment on the results?. The amplitude of roughness height was limited to the film thickness height. Could you consider the inclusion in your study of valley depth of the roughness, or scratches, to 15 times the depth of the film thickness? For engineering purposes, could you please show pressure fluctuations associated with roughness dimensions (amplitude and wavelength) as a function of the operating side lobes (contact dimensions, contact pressure, ......... )?.

Reply by the Authors. The elastic deformation of transverse roughness is given in figure 4 of the paper. With the algorithm in its present form, surface features can be considered as long as local cavitation does not occur, e.g. at the location of the valleys. For deep scratches cavitation will surely occur. Such a situation requires an extended algorithm where pressure built-up is controlled by mass-balance in the cavitated region, see Chevalier et al. and Wijnant and Venner. However, if the main interest is to determine the magnitude of the pressure oscillations caused by the feature this may be done in a simpler way. In EHL contacts, the elastic deformation is generally much larger than the film thickness. Thus, a good estimate of the pressure profile can already be obtained from the dry contact problem, see for instance Lubrecht and Ioannides. In general, the pressure fluctuations can be directly obtained from the deformed waviness using the equations given by K.L. Johnson. Additional References" Chevalier, F., Lubrecht, A A, Cann, P M E, Colin, F. and Dalmaz, G. (1998), "Film Thickness in Starved

Surface 2

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EHL Point Contacts", ASME, Jnl. of Trib.,120, pp 126-133. Wijnant, Y.H. and Venner, C.H., (1999), " Contact Dynamics in Starved Elastohydrodynamic Lubrication", Presented at the 1998 Leeds-Lyon Conference. Lubrecht, A.A. and Ioannides, E. (1991), '~4 Fast Solution to the Dry Contact Problem and the Associate Sub-Surface Stress Field, using Multilevel Techniques", ASME, Jnl. ofTrib., 113, pp 128-133. Johnson, K.L., (1985), "Contact Mechanics", Cambridge University Press.

within the Hertz contact area when subject to pressure gradients. This has a significant effect on the way in which the surfaces are required to deform in order to satisfy the elastic and hydrodynamic equations in comparison to that which is seen when Newtonian lubricant models are used.

Paper VI (ii) "Thin Film~ Time Dependent~ Micro-EHL Solutions with Real Surface Roughness", by Dr. C.D. Elcoate, Dr. H.P. Evans, Dr. T.G. Hughes and Professor R.W. Snidle (University of Wales, Cardiff, U.K.).

Reply by the Authors. The results presented are preliminary and friction coefficients have not been evaluated. Smooth surface modelling of the meshing cycle of superfinished gears in a gear friction rig give a good fit to experimentally measured friction values with the fluid model adopted and Xo values in the range 3MPa to 5MPa. The effect of surface finish and Xo values on the predicted friction coefficient could certainly be investigated but such results may well benefit from the inclusion of a thermal model which is currently under development.

Mr.F.H. Bucher (TU Berlin, Berlin, Germany). Looking upon the deformed profile and comparing it with the undeformed profile, one could get the impression that due to the fact that every asperityvalley-sequence is modelled by only a very few nodal points, the local deformation of the asperities tends to be zero. Has any research been made with respect to mesh-refinement to make every asperity "softer"?. I would expect the deformations at points of local pressure-peaks to be much larger than shown. Reolv by the Authors. The results presented in the paper have been obtained at a resolution of 200 mesh points to the Hertz semi-contact dimension, (b). This means that the profile section considered at five different locations within the contact in Figures 4 and 6, for example, is defined by 100 mesh points. The elastic deflection equation is well able to deform the individual asperity features in different ways at this resolution as can be seen by comparing the deflected asperity shapes in the two figures (whose operating conditions differ only in the direction of sliding). When examined at a resolution of 400 mesh points in dimension (b) the results are effectively unchanged. At thinner micro-asperity film values some minor differences are seen in the deformed shape of asperity tips, but there is no significant change in the film thickness level or in the pressure response to the roughness profile. The non-Newtonian fluid model adopted in the analysis has the effect of allowing the fluid to flow

Dr. R.I. Taylor (Shell Research Limited, Chester, U.K.). What range of values of friction coefficient are predicted by your EHL model?. Can the effects of surface roughness and the fluid model, on friction coefficient be seen?.

Dr. Venner C.H. (University of Twente, Enschede, The Netherlands). Can you provide clarification of the interpolation procedure for the surface profile and the time step adopted for calculation? ReDly by the Authors. A cubic spline interpolation is used in order to ensure that the surface height profile and its first spatial derivative are continuous functions. If the surface height profile of Figure 1 is denoted by Q then as it moves through the contact with speed U~ it makes a contribution to the evaluation of the squeeze film term 0h/~ given by the expression U1 dQ/dx. If Q is to be determined by interpolation then it is clearly advantageous to do this in a way that ensures that the resulting expression for dQ/dx is continuous. If linear interpolation is used, for example, the animated sequence of pressure distributions is seen to have small pulsing oscillatory components. These can be established as being directly related to the time step as a result of the interpolation and the consequent inconsistencies from one time step to the next in the terms dQ/dx as evaluated at the fixed spatial mesh points. The cubic spline interpolation adopted

852

removes this component.

spurious

small pulsing pressure

SESSION VII - STRIBECK

CURVES

The time step adopted for the calculation is At=-Ax/(4U1) where U 1 is the speed of the rough surface or the speed of the fastest moving rough surface when two rough surfaces are used. This value has been found to be sufficiently small to ensure that further reduction in the time step makes no discernible difference to the results.

Paper VII (i) "The Importance of the Stribeck Curve in the Minimisation of Engine Friction", by Dr.C.H. Bovington (PARAMINS Exxon Chemical, Abingdon, U.K.) DR. S. Korcek (Ford Motor Company, Dearborn, MI, U.S.A.) and Dr. J. Sorab (Ford Motor Company, U.K.).

Paper VI (v) "Surface Roughness Modification in EHL Line Contacts-the Effect of Roughness Wavelength~ Orientation and Operatin~ Conditions", by Dr. C. J. Hooke (University of Birmingham, Birmingham, U.K.).

Professor J.-M. Georl~es (Ecole Centrale de Lyon, LTDS, France). You find that friction is sometimes independent of the speed- you are in the EHD regime. Can you say more about the shear strength of the fluid?

Mr.F.H. Bucher (TU Berlin, Berlin, Germany). You were talking about a line contact, which is twodimensional, with three-dimensional surface roughness. What is there to say about the boundary conditions in the y-direction, especially with respect to the mass-flux in the y-direction ?

Reply by the Authors. We considered two possible explanations of the observed limiting values of the traction coefficients. These were:-

Reply by the Author. The analysis in the paper was of a line contact with a surface roughness that was assumed to be small relative to the film thickness. (In practical terms this appears to mean that the residual roughness, after any attenuation by the contact, should be less than 50% of the clearance). Because of the low amplitude, the response of the contact to the roughness could be assumed linear and it was possible to express any roughness as a Fourier integral and examine each component separately. Thus the paper was concerned with components of roughness that varied sinusoidally in both the x (in-line) and y (transverse) directions. Because of the sinusoidal variation in the y-direction the roughness pattern produces variations in pressure, clearance, density and viscosity that also vary sinusoidally. With this it was possible to include the transverse pressure gradients and the transverse mass-flux into the analysis with no approximations (apart, of course, from the initial assumption that the amplitude of the roughness was low). Again, because the roughness repeats continuously in the y-direction there were no boundary conditions to be considered in the ydirection.

(a) that we had reached the limiting shear stress of the fluid in the contact. (b) that we were observing shear thinning of the fluid. Work presented by LaFontaine, A., Spikes, H. and Johnston, J. at the STLE Conference in Detroit in May 1998, to be published, supports strongly explanation (b).

Dr. R.I. Taylor. (Shell Research Limited, Chester, U.K.). Is the increase in bearing friction torque at low speeds due to a transition to the mixed regime, or simply due to higher eccentricities overcoming the speed reduction? Reply by the Authors. Yes, the increase in friction observed at low speeds in the bearing friction rig, is due to a transition into the mixed regime. Calculations show that at the transition point in the friction/speed curve, the oil film thicknesses under these load / speed conditions are of the same order as the effective surface roughnesses. Paper VII (ii) "Theoretical and Experimental Results on Friction for Line Contacts in Mixed and Elastohydrodynamic Lubrication Regimes", by Professor R. Bassani, Professor E. Ciulli (Universita Degli Studi di Pisa, Pisa, Italy) and Professor B. Piccigallo (Academia Navale, Livorno, Italy).

853

Professor R.C.Coy (Shell Research Ltd., Shell Research and Technology Centre-Thornton, Chester, U.K.). Did the authors take into account spin effects due to the width of the roller against the rotating disc? Reply by the Authors. The width of the roller was optimised for having a contact zone, framed by the video camera, big enough to avoid the presence of end effects and in the meantime small enough to have negligible variation of speed along the radial direction. Dr. A. Dratva (CIBA Speciality Chemicals Inc., Basel, Switzerland). Four test specimens of various surface roughnesses and various surface compositions were used. Were the specimens of equal hardness? Is that of importance for comparison of the results presented? Reply by the Authors. There were specimens of equal and different hardness. The effect of different hardness should be of secondary importance in comparison with the effects of other quantities that we investigated (like speed and roughness). Anyway, it is our intention to investigate also the influence of the different materials in the future. Unfortunately it is not easy to find workshops able to realize specimens with well defined roughness for different materials!

Paper VII (iii) " Isoviscous-EHL and Mixed Lubrication Mechanism of Parallel Slide-way with Oil Groove", by Dr. T. Nakamura, Professor T. Matsubara and Dr. F. Itoigawa ( Nagoya Institute of Technology, Nagoya, Japan).

In this paper, the contacting pressure in the runningin was equal to the condition in the friction test. The micro-slant edges could not be detected because the size is too small to distinguish from the surface roughness. In the isoviscous-EHL calculation (Figure 13) the height of micro-slant edge Tsl was postulated as 0.01 pm, and the calculated result showed a sufficient load carrying ability.

Paper VII (iv) "Calculation of a Stribeck Curve of a Journal Bearing", by Mr. D. Bartel and Professor L. Deters (Otto-von-Guericke Universitat Magdeburg, Magdeburg, Germany). Professor Dr.-Ing. G.W.G. Poll~ (University of Hannover, Hannover, Germany). The authors attribute the friction contribution of the asperity contacts to energy losses during asperity deformation. On the other hand, they assume the presence of a very thin film of lubricant at the asperity contacts (except when a critical temperature is exceeded). Why do they not consider the friction to be due to shearing of these thin films? Reply by the Authors. In the calculation presented, fluid friction is determined by using the Newtonian shear stress model for a smooth surface. Presently, a rough surface is not considered since this would require an analysis of each lubricating film contraction and opening resulting from the asperities of shaft and bearing. Hence, calculations would lead to unjustified time consumption.

Dr. C.J. Hooke University of Birmingham, Birmingham, U.K.). The authors assume a profile on the surface of the slider to account for the generation of hydrodynamic pressures in the bearing. This was not visible on their profile of the original surface. Did they measure the profile after nmning?

When assuming that the Newtonian shear stress model is also applicable to the asperity contacts, this would suggest that very high shear stresses occur in the lubricant in the very small lubricating films in these asperity contacts. This does not seem very likely. We should rather assume that the Newtonian shear stress model is not applicable here. A solution to this problem could be non-Newtonian fluid rheology models (e.g. of Eyring, Hamrock, Winer), molecular-dynamic approaches (e.g. quantummechanical solutions) or the investigation of the lubricant as a "third body".

ReDly by the Authors. The surface profiles after running-in were measured as shown in Figure 9. The micro-slant edges (about 0.1 gm) could be observed when the contacting pressure in the running-in was three times as large as this experimental condition.

The authors are of the opinion that the friction at the asperity contacts resulting from the lubricant does not exert any major influence on the integral fluid friction. Considering the real-to-nominal contact area ratio, it rums out that this ratio is very small. In

854

the case that higher friction occurs in the lubricant at isolated asperity contacts, this friction would probably exert only little influence on the integral fluid friction of the bearing.

SESSION

VIII-

CONTACT

FATIGUE

Paper VIII (ii) "The Fatigue Behaviour of Chamfered Steel Cylinders", by Mr. T.H. Kim Dr. A.V. Olver (Imperial College, London, U.K.). Dr. J.A. Williams (The University of Cambridge, U.K.). Other speakers have referred to the phenomenon of shakedown which, through both the generation of residual stresses and changes in surface profiles, can lead to increases in the load carrying capacity of components. Does your analysis take these effects into account? Reply by the Authors. The shakedown phenomenon was not taken directly into account in the analysis, however, the steady state topography of chamfered cylinders was assumed in the analysis by using measured comer profiles of the run specimens. It was found from this that the Von Mises equivalent stresses were just below the yield stress at the edges for both chamfer angles at the contact pressure of 2.0 GPa, suggesting an elastic shakedown has occurred. However, for the contact pressure of 2.4 GPa the comer values were still just above the yield stress for both chamfer angles. The stress components Xyz at the edges were also examined and they were found to be almost identical for both chamfer angles at both loads, suggesting further signs of shakedown. As for the residual stresses, only the nominal values of the residual stresses due to surface engineering processes were used to investigate their influence on fatigue life and no change or generation of residual stresses due to shakedown was included. A significant improvement in the fatigue performance of a nitrided specimen, which has substantial compressive residual stresses in the near surface region, suggests that any generation of residual stresses from shakedown could contribute further in improving the load carrying capacity. However, since no accurate measurements of residual stress generation or relief has been carried out to confirm

the phenomenon, the analysis assumed the nominal values to persist throughout the contact.

Dr. C.F. Kernizan (The Lubrizol Co.). How did you measure or calculate the residual stresses on the steel components? Were there changes in the steel crystal structure, hardness, residual stress after the test? Reply by the Authors. The residual stress values of M50NiL through hardened steels were measured using the X-ray diffraction technique. As for the 16NCD13 steel, no measurements were available and an expected residual stress distribution of a carburised steel was used instead. This was generated from an empirical equation which just requires a surface residual stress value and the case depth of the carburised steel. No post-test examination of the steel crystal structure, hardness and residual stress was carried out in the current study.

Paper VIII (iii) "The Mechanism of Bearing Surface Fatigue-Effect of Friction and Tensile Hoop Stress on Surface Plasticity and Fatigue", by Dr. Y.P. Chiu, (Advanced Technology Centre, Torrington, CT., U.S.A.). Dr. C.F. Kernizan (The Lubrizol Corporation, Wickliffe, OH, U.S.A.). Did you calculate or measure (XRD) the residual stress? How do the calculated and measured residual stresses, compare to one another? Do you then generate wear debris or at what point in the fatigue --->micro-pitting stage do you create wear debris? Reply by the Author. The results of residual stress given in this paper are based on a numerical elastoplastic calculation for a work-hardening material, applicable to hard bearing steels. Micro-pitting can generate small size debris. The occurrence of micro-pitting is considered to be a fatigue process, i.e. requiring many stress cycles (or revolutions) for micro-crack generation and growth under the repeated action of a high magnitude of compression and a smaller magnitude of (residual) tension.

855

Hardness plays an important role on micro-pitting. First, it affects the plastic deformation and the residual tensile stress. Secondly, the number of stress cycles to generate the micro-pit for a given (residual) tensile stress again depends on the hardness and the material cleanliness. The micropitting life is thus a function of a number of variables, consisting of hardness, asperity pressure, contact size and steel cleanliness.

Paper VIII (iv) "Behaviour of Metallic Additive in Composite Metal-Carbon/Steel Brake in Severe Friction Test", by Professor H. Zaidi, Mr. A. Senouci and Professor J.Fr~ne (Universite de Poitiers, LMS, Poitiers, France). Dr. J.A. Williams (The University of Cambridge, U.K.). You speak of the transfer of iron to the surface of the carbon composite. Is there transfer the other way? Many carbon / metal contacts operate satisfactorily because of the formation of a stable carbonaceous transfer layer on the metal counterface-in reality they are running as carbon-oncarbon. Reply by the Authors. The transfer in carbon/metal contacts depends on the hardness of metal and on that of the carbon. The Young's modulus of carbon varies from 36 GPa to 1000 GPa according to the graphite orientation. We can obtain a stable carbonaceous layer on the metal as we can obtain the transfer of metal on the surface of carbon. Professor F.E. Kennedy (Dartmouth College, Hannover, NH., U.S.A.). Under what conditions was melting of brake components observed? What melted? Was it only the brass that melted? Was there more transfer noted when melting occurred? Reolv by the Authors. The brake components were melted under a severe friction test. The melted component was the brass and no more transfer was obtained. Paper VIII (v) "The Influence of Lubricant Type on Rolling Contact Fatigue of Pearlitic Rail Steel", by Mr. D.I. Fletcher and Professor J.H. Benyon, (University of Sheffield, U.K.). Professor J. Klein (Weizmann Institute of Science, Rehovot, Israel). Has there been work done on incorporating surface active species-that

would act as lubricants-into the steel of the rails or wheels? Reply by the Authors. There has been no work carried out at the University of Sheffield on the incorporation of lubricants into the rail or wheel steels. Elsewhere work has taken place on coating steels with layers of lubricants such as molybdenum disulphide (Cunningham et al. (1994)). The rail is currently viewed as a consumable item in railway operation, and in many countries the rail surfaces are regularly ground to maintain the rail head profile and to remove small surface defects before they grow to form potentially dangerous rolling contact fatigue cracks. Any coating or other surface based lubricant would therefore be removed, unless grinding was made unnecessary by the use of a coating which would successfully prevent damage-an unlikely prospect. Additional difficulties would exist in the economical production of a lubricant coating over the rail gauge face or wheel flange while avoiding the rail head or wheel tread, where good traction is essential. The combination of these problems has, to the best of our knowledge, prevented the incorporation of lubricants into the rail or wheel materials. Additional References Cunningham, J.M., Ford, I.J., Ogilvy, J.A. and Roberts, E.W. (1994), " Interpretation of Friction

and Wear Properties of MoS2 Coated Steel Substrates", WEAR, 177, 93-101.

SESSION IX- BOUNDARY MIXED LUBRICATION I

AND

Paper IX (iii) "Fundamentals of the Friction Mechanism of Diamondlike Carbon Films", by Dr. C. Donnet, (Ecole Centrale de Lyon, LTDS, France), A. Grill (IBM Research Division, NY, U.S.A.), J. Fontaine, T. Le Mogne, (Ecole Centrale de Lyon, LTDS, France), F. Lefebvre (Laboratoire de Chimie Organom6tallique de Surface, CPE, Lyon, France), V. Patel and C. Jahnes Grill (IBM Research Division, NY, U.S.A.). Professor H. Zaidi ( Universite de Poitiers, Laboratoire de M~canique des Solides, France).

856

(1) Can you measure the desorbed hydrogen during friction?. (2) What is the friction behaviour of diamond coating deposited from carbon only? (3) What is the influence of low traces of humidity on the friction behaviour of hydrogenated diamond coating in U.H.V.?

Reply by the Authors. (1) Yes. The UHV tribometer is now equipped with a mass spectrometer allowing the partial pressures of the gases surrounding the contact to be measured. It has been upgraded recently and was not used in the present set of experiments. (2) In UHV, the friction behaviour of unhydrogenated DLC is similar to the friction behaviour of DLC containing less than 34 wt.% of H, meaning high steady-state values (> 0.5). (3) In a recent paper (Tribology Letters, (1998),4, 259-265), we have presented experiments with continuous increases or decreases of the partial pressure of water vapor during friction, from UHV up to RH=100% . We have also performed tests at various static partial pressures of water vapor. The transition between ultra-low friction ( 106s-l). Since no hydrodynamic pressure due to wedges is expected, the fluid film thickness will become very small, leading to an increase of the shear rate under the seal lip at constant pressure. Hence viscoelastic properties will develop in the fluid and a fluid film with load carrying capability is created. There is the possibility that not the whole fluid film is actually contributing to this feature. This capacity could be caused locally, e.g. surface roughness peaks.

Prof. G.W.G. Poll (University of Hannover, Germany). The paper shows clearly that under normal operating conditions, the sealing contact is partially pumped dry. Therefore, one should expect the friction torque to be composed of a boundary portion and a portion due to shear in the lubricant in the still lubricated part of the contact. From the measurement results we can see clearly that the friction increases linearly with speed and that the slope is a function of viscosity. More specifically, it is the same when the apparent viscosity is the same. However, there is an offset which can be altered, e.g. by adding polymer, that cannot just be attributed to the fact that there is a boundary layer formed by the polymer, the shearing of which gives the friction contribution of the non-lubricated part of the contact area? Is it not by definition that such boundary layers have non-Newtonian properties? Is it then justified to consider the lubricant as a whole to be non-Newtonian? Reolv by the Authors. Taking the extreme sealing zone conditions, it seems unlikely that different layers with varying molecular structure build up (scale: fluid film thickness / roughness). In order to investigate the existence of functional layers on the shaft surface, we utilised SEM (Scanning Electron Microscopy) including energy dispersive X-ray spectroscopy, and have not found a polymeric boundary layer that might alter the conditions in the sealing zone of radial lip seals.

Paper XII (iii) "Hybrid Molecular Dynamics and Continuum Mechnaics Analysis of Thin Film Lubrication", by T-L Sham and Prof. J.A. Tichy (Renssealer Polytechnic Institute, Troy, U.S.A.). Prof. R.C. Coy (Shell Research Ltd., Chester, U.K.). One advantage of molecular dynamic simulations is that they give physical insight into the processes taking place. Your Hybrid system

862

introduces a Ko factor which adjusts the viscosity response. What is the physical significance of this Ko factor? Reply by the Author. Certainly a major motivation for many molecular dynamic simulations is to gain physical insight into the lubrication process as noted by Prof. Coy. Such efforts are largely the domain of the physicists and physical chemists who have applied their skills to tribological problems. Our motivation is simply to apply the existing methodology to obtain engineering results. We believe, for the foreseeable future, molecular dynamics will only be useful in engineering through the development of constitutive equations or by hybrid methods such as those discussed. Specifically, the Ko factor is simply a curve fitting parameter linking the molecular scale to the continuum scale. The parameter specifies the relative strength of viscosity of the surface layer to that of the bulk fluid.

Paper XII (iv) "A Dynamic Model of the Transfer and Wear Processes using Soap Bubble Rafts", by Prof. K. Hiratsuka, Ms. Y. Abe and Mr. F. Fujisawa (Chiba Institute of Technology, China). Prof. J.M. Georges (Ecole Centrale de Lyon LTDS, France). I agree with you that a soap model can give information about the formation of transformed layers in the case of dry contact. In order to improve your simulation, I suggest that you take into account the diameter of the soap bubble, because the local force distance law between two bubbles is dependent on the bubble diameter (S. Argon). Reply by the Authors. Prof. Georges' suggestion to take into account the diameter of soap bubble is well taken and it will be incorporated in our future studies. Prof. F. Sidoroff (Ecole Centrale de Lyon LTDS, France). I wonder if the greater transfer observed with the large spheres cannot be more simply explained by the disorder induced in the crystalline bubble structure by the spheres? Reply by the Authors. We have used the spheres and disks of the same diameter, so that the extent of the induced disorder is the same. Bubbles that contact the spheres become double layers, whereas

those that contact the disks remain single. So the main cause for the transfer is attributed not to disordering in the bubble structure but to the enhanced attractive force between spheres and bubbles due to the larger contact area.

SESSION XIII - ELASTOHYDRODYNAMIC LUBRICATION I

Paper XIII (ii) "Shearing of Adsorbed Polymer Layers in an Elastohydrodynamic Contact in Pure Sliding", by Dr. D. Mazuyer, Mr. E. Varenne (Ecole Centrale de Lyon LTDS, France), Prof. A.A. Lubrecht (LMC, INSA de Lyon, France), Prof. J.M. Georges (Ecole Centrale de Lyon LTDS, France) and Mr. B. Constans (Elf Solaize, France). Prof. D. Ben-Amotz (Purdue University, U.S.A.). The earlier paper by Spikes and co-workers suggested that strain induced chemical degradation of polymers in the contact may be important. Do have any evidence of such degradation? Reply by the Authors. The only observation we made is that the application of high shear strain leads to decohesion of the boundary polymer layers. Their shearing is dependent on their interactions with the wall. However, we have not made any in-situ chemical characterisation to control a possible degradation of the polymer. Therefore, under pure sliding, we have no evidence of such phenomenon but it may occur nevertheless.

Paper XIII (iii) "Film Thickness, Pressure Distribution and Traction in Sliding EHL Contacts", by Mr. A. Jolkin and Dr. R. Larsson (Lule~ University of Technology, Sweden). Dr. G.E. Morales-EsDeiel (ITESM, Mexico). I would like to congratulate the authors for such nice work. However, I would like to come back to the question about the error in the film thickness measurements. Is it possible for you to give us a number: 5%, 2%, 20%? How can one determine it? Reply by the Authors. In reply to Dr. MoralesEspejel the authors cannot give any exact answer. The error in the film thickness measurement is affected by different sources, study of which is yet to

863

come. One of the sources is the phase change that occurs upon reflection. If the phase change differs from the assumed value by 25% the absolute error in film thickness will be approximately 5% for a film of 200 nm. Such a large error as 25% is, however, not expected and the absolute error should be much less than 5%. Another error source is refractive index and its dependence on pressure and temperature is briefly discussed in the paper. However, the relative errors in the film thickness measurements are small, probably less then 5% at films of about 200 nm.

Dr. G. Guanteng (Imperial College, London, U.K.). There are several factors that may affect the accuracy of determining pressure from measured 3D film maps. One important factor is the error in determining the elastic deformation. Could the authors explain how they determine the geometrical centre of contact based on their 3D film thickness measurements, and the effect of the errors on the calculated pressure distribution?

Prof. H. Spikes (Imperial College, London, U.K.). The authors note small pressure fluctuations which they attribute to surface features/particles. Could these fluctuations arise from small offsets in the real location of the contact centre, compared to the position presumed? Reolv by the Authors. In reply to Prof. Spikes and Dr. Guanteng the authors would like to say the following. The present paper describes a method of measuring film thickness and reconstructing the corresponding pressure distribution. The film thickness and pressure distribution are coupled parameters that are determined by the lubricant flow in an EHL conjunction. Changes in lubricant flow as the sliding occurs should be reflected in both film thickness and pressure distribution. Obvious changes in film thickness were detected under sliding conditions. Measurements of the film thickness do not require finding the contact centre. The measurements and calculations were carried out for approximately 18 slide/roll ratios in the range 200% to ÷200% for each of the tested lubricants. The observed effects of sliding on the film thickness are detected at moderate and high degrees of sliding. The only results for three extreme conditions, slide/roll r a t i o - 2 0 0 % , 0% and +200%, were presented. Changes observed in pressure distributions are mostly related to the changed shape

of the film thickness profiles. However, as the special numerical routine was employed to find the centre of contacts, certain error might insinuate into the calculations. The task of finding the centre of the EHL conjunction has great importance in calculating pressure and is a very difficult technical problem. Unfortunately, the limited size of the present paper does not allow a description of the employed method, neither carry out a detailed analysis of eventual error. In a simplified form, the method of finding the EHL contact centre is based on fitting the ellipses to the contour segments similar to those seen in Figures 2(a) and 3(a), and analysing the origins, the radii etc. of these fitted ellipses. This error is believed to be very small. The effects of possible centring error were studied by Ostensen et.al. [ 17]. The authors are very grateful to delegates who have taken part in the discussion for their valuable points that will certainly be considered in future investigations.

Paper XIII (iv) "Elastohydrodynamic Lubrication Characteristics of Electrrheological Fluid", by Mr. A. Korenaga, Dr. T. Yoshioka, Mr. H. Mizutani and Mr. K. Kikuchi (Mechanical Engineering Laboratory, MITI, Japan). Prof. F. Sidoroff (Ecole Centrale de Lyon LTDS, France). I guess that the viscosity induced by an electric field is strongly anisotropic. Did you investigate this, for instance, by applying the electric field in different directions? Reolv by the Authors. We have not investigated the difference of tribological behavior with direction of electric field yet. However, our opinion is that the viscosity of the liquid crystal depends on the relation between the orientation of the molecules and the direction of the flow, as shown Figure 6 in our paper, basically. So when we apply the voltage in different direction, we will get results following the principle mentioned above.

Prof. R.C. Coy (Shell Research Ltd., Chester, U.K.). Did you measure the friction force in the experiments and the electrical energy dissipation? Hence can you say anything about the overall efficiency of the system?

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Reply by the Authors. We have not measured both of them yet. We have a plan to measure the friction force when the voltage was applied. As for the energy dissipation, we think it is a very important indication, it may be less than O.1W because the order of the electric current was microampere. Dr. J.A. Greenwood (University of Cambridge, U.K.). Can you tell us anything about the change in viscosity with field strength: is there a continuous increase, or is the field a kind of switch where an increase occurs at a critical field strength? Reply by the Authors. The relation between electric field strength and viscosity is shown in figure below. Fundamentally, the change in viscosity increases continuously with electric field strength while the molecular orientation changes from type 1 to type 3 (see Figure 6 in our paper). When the molecular orientation becomes type 3, the viscosity will not increase any more even if the voltage increases.

Electric fxel'~t strength

Prof. B.O. Jacobs0 n (Lund Institute of Technology, Sweden). The experiments were performed with one electrically conducting and one insulating surface. Can you describe how this phenomenon could be used for normally heavily loaded contacts like gears and rolling bearings? Reply by the Authors. In our experiments, both surfaces are conductors, because the glass disk was coated by chromium. Of course, the electrical resistance of the thin chromium film is high, however, the basic phenomenon is the same. Considering the electrical resistance, this system will suit gears and bearings more than our experimental apparatus because electrical losses will be small.

SESSION X I V - SOLID AND POWDER LUBRICATION Paper XIV (i) "On the Rheodynamics of Powder Lubricated Journal Bearing: Theory and Experiment", by Dr. H. Heshmat and Ms. C. Heshmat (Mohawk Innovation Technology Inc., Albany, U.S.A.). Prof. M.J. Adams (Unilever Research, Port Sunlight, U.K.). How were the constitutive relationships and wall boundary conditions measured? Does the sliding velocity dependence arise from an entrainment effect into the contact region? Reply by the Authors. In a separate technical paper we have shown pressure dependent properties of various powders (see Reference 9). A short shear cell type experimental device was designed to measure these properties. With regard to wall boundary conditions, theoretical predictions are made based on the third body's theological properties, which have been measured. However, further work remains to be conducted to delineate the effect of 1st bodies on the pressure dependent properties of the 3rd body. With regard to the Prof. Adams' last question, we would like to state powder lubrication is an altemative method of addressing the role of the third body in the contact region. Thus the velocity accommodation across the film that we have shown could be interpreted and extended to address entrainment of the third body. Not all the particles leave the contact region, and we believe that under certain circumstances end flow may reenter the contact region; hence this may alter velocity accommodation along and across the third body. Paper XIV (iii) "Third Body Mechanisms in Dry Friction of Carbon-Fibre-Reinforced (SIC) Ceramic Matrix Composites", by Dr. P. Reynaud (IUT Limoges, France), Dr. P. Fournier and Prof. F. Platon (ENSCI, Limoges, France) and J. Absi (IUT Limoges, France). Dr. G. Liraut (Renault, Boulogne-Billancourt, France). Do you have any industrial applications in mind for such a material?

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Reply by the Authors. The materials Carbon-FibreReinforced (SIC) Matrix Composites have been elaborated only for this study. The aim of the research program was to compare the tribological behaviour of the composites with monolithic SiC ceramic. No industrial developments of these composites have been made after this study.

SESSION XV-

LUBRICANTS

Paper XV (i) "Chokin~ of Flow Restrictor Caused by Calcium-Detergent in Lubricatin~ Oil", by Mr. A. Yano, Mr. S. Watanabe, Mr. T. Omura (Mitsubishi Heavy Industries Ltd., Nagasaki, Japan) and Mr. K. Saki (Kyusyu Kyoritsu University, Kitakyushu, Japan). Prof. B.O. Jacobson (Lund Institute of Technology, Sweden). Have you tested if the depositions occur also at lower water concentrations than 3 0%? Reoly by the Authors. We conducted another test under 3wt% water concentration, but the deposition did not occur. Prof. H. Spikes (Imperial College, London, U.K.). Does streaming electrification depend on flow velocity or velocity gradient? If the latter, do you think that it may occur in lubricated shearing contacts?

Reolv by the Authors. Streaming electrification depends on velocity gradient. This phenomenon signifies that small solid particles (colloidal particles) in lubricating oil tend to deposit on a metallic surface by electrostatic attraction due to the streaming electrification. Besides the calcium carbonate deposition reported in this paper, we experienced some other deposition with high speed sliding bearings, for example, ZnDTP, copper sulfate and degraded amine compound from the oxidation inhibitor. These deposits were composed of small solid particles (colloidal sizes), so it is inferred that the depositions could be also closely related to the streaming electrification which occurs at the interface between lubricating oil and the bearing surface.

Dr. S. Korcek (Ford Motor Co., Dearborn, USA). Why do you need an overbased detergent in your equipment? Did you test other detergents? Reply by the Authors. The use of detergent oil as hydraulic oil is unusual but in the special case of marine diesel equipment, we occasionally apply this type of oil as hydraulic oil. We did not test other detergents except calcium sulfonates. Paper XV (ii) "IR Spectroscopic Analysis of Grease Lubricant Films in Rolling Contacts", by Ms. S. Hurley and Dr. P.M. Calm (Imperial College, London, U.K.). Prof. R.C. Coy (Shell Research Ltd., Chester, U.K.). Do you believe the experiments you describe have measured films that have reached steady equilibrium conditions? For example, in the figure on starved lubrication the film thickness was still declining at the end of the test. Are your results thus representative of real operating conditions where bearings run for many tens, hundreds or even thousands of hours? Reolv by the Authors. The authors recognise that the timescale of these experiments really only represents the first few seconds of operation of a bearing and it is likely that an equilibrium film thickness condition has not been attained. However in tests lasting up to eight hours it was found that the film thickness generally stabilised within the first hour of running and that little change was observed after this. Similarly the chemical and physical degradation of the grease will continue and become more severe as the test continues. However this paper was mainly concerned with developing the analytical techniques and the approach to the problem and as such only represents the first stage of the work. The study is continuing and tests are currently being run under increasingly rigorous conditions (higher speeds and temperatures) and for longer times thus providing a better simulation of that experienced by the grease in real life. It is hoped that bulk grease from actual used bearings can be acquired and compared with these test results. However, it is not possible to disassemble a bearing, leaving the rolled track undisturbed, for local IR examination.

Prof. A.A. Lubrecht (LMC, INSA de Lyon, France). Could the authors explain why there

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seems to be more thickness in front of the contact (position 2) compared to the position close to the inlet and outside the back (positions 1 and 3)? Reply by the Authors. At present, we do not understand the origins of the thickener concentration changes around the contact. This behaviour was most marked with the urea greases but was also observed with the Lithium hydroxystearate grease. The inlet theology and flow pattern of the grease in the inlet will be very complex and it is possible that local 'dead' flow or recirculation zones exist. We are currently examining this phenomenon for a wider range of greases and contact conditions.

Paper XV (iii) "Service Life and Lubrication Conditions of Different Grease Tvoes in HighSpeed Rolling Bearings", by Dipl.-Ing. E. Franke and Prof. Dr.-Ing. G.W.G. Poll (University of Hannover, Germany). Dr. J.A. Greenwood (University of Cambridge, U.K.). You report that failure occurs with no warning. As you explain, you are measuring a racerace capacitance, so the measured value represents n capacitances in parallel, each of which is two contact capacitances in series. I know from experience how large the background capacitance is" given that, would you expect the shorting a single contact capacitance to be detectable? Reply by the Authors. Dr. Greenwood's remark points indeed to a problem that should have been addressed in the paper. Obviously, a metal to metal contact would not be detected as a breakdown of lubricant film if it occurred in one raceway only. However, the total capacity and hence the charging time would change, e.g. by a factor of two if the capacitance of the inner and outer race contacts were equal under fully lubricated conditions. Therefore, if lubrication deteriorated over time for one contact only, it should still be noticeable. Also, if short-time breakdowns occurred that were not detectable as such, they would still increase the charging time the more frequently they happened. Therefore, there should still be a declining tendency in the measured overall capacitance.

Paper XV (iv) "The Inclusion of Lubricant Shear Thinning in Journal Bearing Models", by Dr. R.I. Taylor (Shell Research Ltd., Chester, U.K.).

Prof. J. Frene (Universit6 de Poitiers, France). The results presented in the paper are obtained using the steady state simplified Reynolds equation without squeeze effects but the application concems the connecting rod bearing. In that case the squeeze effects are very important and largely modify the bearing behaviour. Could the author comment on that point and explain why he thinks that the results could be used. Reply by the Author. Prof. Frene makes the valid point that the model we have presented does not include the squeeze effect. However, the way in which we have put lubricant shear thinning into the Reynolds' equation is general and the squeeze term could be retained if necessary, the only problem being that analytical results would not be obtained. The aim of the paper was to extend the standard Short Bearing Approximation to allow for lubricant shear thinning effects, so that differences in the oil film thickness and friction could be quantified for different viscosity grades. With hindsight, it may have been better to apply the models to a main bearing rather than a connecting rod bearing, although we did not have access to the main bearing load curves when we did the work. I am confident that the ranking of oils achieved with this model would still hold if squeeze effects were included.

Prof. C.M. Taylor (University of Leeds, U.K.). Whilst the condition that the length to diameter ratio of a joumal bearing be less than about 0.5 for the short journal bearing approximation is a necessary one, it is not sufficient. At high eccentricity ratios the approximation is very poor and the bearing you have considered will operate at high eccentricity ratios. This means that your predictions of film thickness are highly inaccurate. In this context, what is the implication for shear thinning assessment/benchmarking, which will be based on potential poor estimations of shear rate? Reply by the Author. Prof. Taylor rightly points out that the Short Bearing Approximation is poor at very high eccentricity ratios. As mentioned in the reply to Prof. Frene, one of the main purposes of this work was to have a simple tool capable of simply ranking multigrade oils, rather than have a tool that is highly accurate. At high eccentricity ratios, the assumption of a rigid bearing also comes into question, and it may be necessary to allow for the increase of viscosity with pressure. There are many

867

uncertainties, but we believe the simple model is robust if we simply make relative comparisons between oils.

Dr. C.J. Hooke (University of Birmingham, U.K.). The Cross and other equations for shear thinning are essentially one-dimensional. When used in situations where the shear strain in the circumferential direction is greater than in the axial direction, there is a difference between the effective viscosities in the circumferential and axial directions. Was this considered? Reolv by the Author. Many thanks to Dr. Hooke for his interesting question. We have not considered the possibility that the viscosity is different in the circumferential and axial directions in this model. It would be an interesting area of future work to develop a simple model that took this effect into account.

SESSION XVIWEAR

FRICTION

AND

Paper XVI (i) "Effects of Composition and Surface Finish of Silicon Nitride Tappet Inserts on Valvetrain Friction", by Dr. A.K. Gangopadhyay, Mr. D.G. McWatt, Dr. P.A. Willermet, Dr. G.M. Crosbie and Mr. R.L. Allor (Ford Motor Co., Dearborn, USA). Dr. M. Priest (University of Leeds, U.K.). The experiments presented used the same cam for all the tests after an initial running-in period. Bearing in mind that the running-in of the cam surface will be affected by the physical nature of the insert counterface and the chemical activity at the surfaces, a realistic assessment of the insert materials and surface finishes should use a new cam for each new insert. Differences in running-in will most likely influence the long term friction behaviour. The authors' comments on this point would be appreciated. Reoly by A. Gangopadhyay. I agree with your comment that running-in of the cam surface will be affected by the physical and chemical nature of the insert material. Keeping this in mind we allowed

nmning-in for about 530 hours with each new insert until we observed a steady friction torque and we did that for every speed. Of course, the ideal situation would have been to use a new cam lobe with each new insert. The drawback is that it becomes quite time-consuming.

Dr. C.F. Kernizan (The Lubrizol Corporation, U.S.A.). Is there significant chemical reactivity between the lubricant additives and the steel and Si3N4 material? If so, does this reactivity affect the formation of the boundary layer and the reduction of friction? Reoly b v A. Gan~ooadhvav. We did see chemical interaction between lubricant additives and all silicon nitride materials. The micrographs in Figure 8 show the formation of lubricant derived films on silicon nitride materials. These films are also thick at some places. Whether these films reduce friction coefficient would depend also on the lubricant formulation. For example, with oil B, which contains MoDTC, a reduction in friction was observed with silicon nitride. With steel inserts, the reduction in friction with MoDTC containing oil has been attributed by several researchers to the formation of a thin MoS2 layer. With silicon nitride the reduction in friction may be due to the formation of MoS2 layer although we did not demonstrate that.

Dr. A.A. Torrance (Trinity College, Dublin, Ireland). The friction coefficient of boundary lubricated contacts can be related to asperity shape as measured by slope or curvature. Very smooth asperities can sometimes give anomalously high friction (A.A. Torrance, J. Galligan and G. Liraut, "A model of a smooth hard surface sliding over a softer one", Wear 212 (1997), pp.213-220). Did you consider this as a possible explanation for the high friction obtained with the smoothest inserts? Reolv by A. Gangopadhyay. We tried to correlate measured friction torques at 500 rpm, in the boundary regime, with various roughness parameters including del Q, which is asperity slope, as measured by a 3D optical profilometer. The correlation coefficient was only 0.03.

Dr. G. Liraut (Renault, Boulogne-Billancourt, France). Could you, please, give us some more information about the "Ford Finish" process or is it too secret?

868

Reolv by A. Gangopadhyay. It is our proprietary process but we may be able to discuss it further once we have obtained intellectual property rights.

Dr. T.G. Mathia (ECL-ENISE-CNRS, France). Did the inserts move during the tests or were they fixed relative to the anisotropic morphology of the ground surface of the cam? Have you observed any correlation between 3D topographic parameters, machining process and friction torque? Reply by A. Gan~opadhyay. The cemer of the cam lobe was at an offset from the center of the insert. Therefore, the inserts were always rotating. We measured surface roughness parameters with a 3D optical profilometer and attempted to correlate friction torque with the centerline average roughness, r.m.s, roughness, asperity slope, lubricant volume and several other parameters but did not observe any correlation.

Paper XVI (ii) "Wear Modes in Lubricated Brass-Tungsten Carbide Contact", by Mr. S. Hollinger, Prof. J.M. Georges, Dr. D. Mazuyer, Mr. P. Bour6, Dr. S. Bec (Ecole Centrale de Lyon LTDS, France) and Dr. G. Lorentz (Rhodia Research, Aubervilliers, France). Dr. S. Mischler (EPFL, Lausanne, Switzerland). What is the thickness and structure of the copper layer? What is the mechanism leading to the formation of this layer? Reply by the Authors. The "copper" layer, which is in fact, a copper enrichment zone of the bulk brass at the interface was shown to be between 0.2 and 2 micrometers thick. The formation of this layer might be due to, at least, two mechanisms: diffusion of copper, because of thermal gradient, between the surface and the pin core; zinc consumption due to reaction with lubricant components. The structure of the "copper" layer is an ongoing subject of study. Indentation tests have shown a very hard layer at the surface, probably due to work hardening of the copper. The surface temperature should not be very high because of good cooling properties of the lubricant, for this reasons we think that the layer should be amorphous. Dr. G.W. Roper (Shell Research and Technology Centre, Chester, U.K.). What sort of lubricant

chemistry should be considered for the particular material combination of brass/tungsten carbide?

Reply by the Authors. The emulsion lubricant is clearly designed for a contact including brass. The lubricant contains soaps and phosphorated anti-wear additives, which create protective layers during the process. As for wire drawing, the lubricant ability improves with running time, this is correlated with the presence in the bath of copper and zinc ions. The chemical reactions occurring in the contact are probably of different kinds as the lubrication conditions are unsteady in the contact. Paper XVI (iv) "Surface and Near-Surface Interactions Affectinl~ Friction and Wear", by Prof. L. Rozeanu (Technion- Israel Institute of Technology, Haifa, Israel) and Prof. F.E. Kennedy (Dartmouth College, Hanover, U.S.A.). Dr. A.A. Torrance (Trinity College, Dublin, Ireland). Was the function G(a) calculated from a stress function? Would the plastic model of asperity contact proposed by Kopalinsky in 1982, which allows for the effects of frictional heating and strain rate on flow stress, be a useful adjunct to your model? Reply by the Authors. The function G(a) was calculated using an Airy stress function from the theory of elasticity. It is therefore subject to the assumption that all deformation is elastic. Kopalinsky used her plastic model (1982) to study material removal, heat generation and rubbing interactions during grinding of a deformable solid by hard grits. Later, Kopalinsky and others (references [3] and [8]) used similar models to study frictional interactions between sliding asperities. In all of those studies, however, it was deformation of the softer material that was of interest. In this work, the stresses in both harder and softer materials were studied; instead of modeling the deformation after yielding, we were most interested in the shearing of either asperity. Certainly future extensions of this work could benefit from the use of plastic models of asperity deformation like those of Kopalinsky and others.

Prof. J.M. Georl~es (Ecole Centrale de Lyon LTDS, France). In the case of two asperities in

869 sliding, can you estimate the initial wear rate of the material? Reply by the Authors. It is difficult to estimate a wear rate of a material based on a model of a single asperity contact. Each contacting surface consists of a distribution of asperity heights and asperity apex angles. Models such as this one can be used to predict the failure (or wear) of one contacting pair of asperities, but the total wear rate is determined by failures of a multitude of contacting asperities, each with their own height and apex angle. Perhaps a stochastic approach could be used to estimate an initial wear rate, but that estimate would have to be modified after initial wear owing to the changes in asperity height and apex angle distributions that result from wear.

Paper XVI (v) "Conception of Numerical and Experimental Tools for Study of the Tribological Transformation of Surfaces (TTS)", by Prof. A. Eleod (Technical University of Budapest, Hungary), Mr. F. Oucherif (LMC, INSA de Lyon, France), Mr. J. Devecz (Technical University of Budapest, Hungary) and Prof. Y. Berthier (LMC, INSA de Lyon, France).

Dr. P. Kapsa (Ecole Centrale de Lyon LTDS, France). You have shown that when observing a wear scar with scanning acoustic microscopy, the contrast observed can be associated with plastic deformation, which can be theoretically predicted. It is well known that the scanning acoustic image of a surface is strongly dependent on the surface geometry and that a scratch can create a contrast on the image. How can you separate the contrast which is due to the geometry from the one due to plastic deformation? Furthermore, how can you explain a contrast due to plastic deformation? Reply by the Authors. We made only a semi-cycle, one amplitude, of the oscillatory sliding. The surface topography of the specimens was measured before and after the sliding test and we could not detect any scratch on the surface. However, we could detect the contrast even at a depth of 30 pm under the surface. Generally a contrast observed by acoustical microscopy may be due to a geometrical or constitutional change of the material. In our case the surface topography did not change, so the contrast indicates a constitutional change, which is a result of a local plastic deformation, i.e. of the TTS.

SESSION XVII - ELASTOHYDRODYNAMIC LUBRICATION 2

Paper XVII (i) "Thermal Effects in Elliptical Contacts with Spin Conditions", by Dr. P. Ehret, Prof. D. Dowson and Prof. C.M. Taylor (University o f Leeds, U.K.).

Prof. R.C. Coy (Shell Research Ltd., Chester, U.K.). What thermal properties did you use for the two solids and how sensitive are your results to these properties, e.g. if one was steel and the other ceramic? Reply by the Authors. Both bounding surfaces were considered to be steel. We have not investigated cases where the material of the two solids is different. Considering the example suggested of a contact between steel and ceramic surfaces, a rapid estimate of the changes in temperature compared to a steel/steel contact can be obtained by calculating the changes in the coefficient of the surface energy equations (Equation 11, and 12). If we take for example Silicon Nitride (Si3N4), the density of the material is about 3180 kg/m 3 compared to 7800 kg/m3 for steel. The conductivity is 30 W/mK instead of 42 W/mK. The heat capacity corresponds to 710 J/kg°C, which is to be compared to 460 J/kg°C for steel. This results in the coefficient of the surface energy equations of the ceramic surface being 1.49 times larger than its steel counterpart for the same surface velocity. It is reasonable to consider that the temperature of the ceramic surface should therefore increase by the same proportion compared to the steel one.

Dr. L. Houpert (Timken France, France). At high entrainment speed, negative flow can occur in the inlet zone. How are convection effects considered when negative flow occurs? The parabolic temperature distribution through the film is only valid at low/moderate shear rate in a Hertzian contact. A triangular temperature distribution should be used at high shear rate, leading to smooth temperature increase (2 times smaller). Should you not account for a displacement of the contact centre relative to the pole of spinning, especially at high speed? This causes the sliding distribution through the elliptical contact to be non-syngnetrical.

870

Reply by the Authors.

The full details of the reverse flows are not taken into account with the present formulation since it is based upon an average of the energy equation across the film. Some numerical difficulties are encountered at high reverse flows. This is essentially caused by the incompatibilities of fixing a priori the temperatures at the inlet when these depend upon the energy transported by fluid particles as they reverse back to the entrance of the contact. We agree with the concems regarding the choice of a parabolic approximation for the temperature. Even if a range of full simulations for point contact tends to confirm that such a condition is valid for a Newtonian fluid, there are no clear indication whether such an approximation is still consistent with real situations where non-Newtonian effects OCCur.

The influence of the location of the pole of spinning can be analysed by varying in an arbitrary fashion the ratio of the slide to roll ratio over the spin parameter ~. At the present time, the calculation only takes into account the balance of the normal forces which act on the contact. This does not allow us to investigate the influence of the displacement of the contact centre compared to the position of the spinning pole.

Paper XVII (ii) "Contact Dynamics in Starved Elastohydrodynamic Lubrication", Mr. Y.H. Wijnant and by Dr. C.H. Venner (University of Twente, The Netherlands).

Prof. F. Sidoroff (Ecole Centrale de Lyon LTDS, France). I am surprised that the stiffness reduction of the fully flooded case is so small compared to the Hertzian contact. I would have expected a much stronger reduction?

Reply by the Authors.

In the present paper the authors have not made statements about the stiffness of the contact. Fig 9 shows the mutual approach as a function of the inlet oil film thickness. The figure shows that for the conditions considered the mutual approach for the fully flooded contact differs by only 10 percent from the mutual approach in the Hertzian contact. This indicates that the elastic deformation of the surfaces is large compared to the lubricant film thickness, and as starvation decreases the film

thickness, a decreasing layer thickness in the inlet, leads to a mutual approach going to unity, as for the Hertzian contact. To determine the stiffness of the contact, the variation of A~o with the load must be known. Subsequently the stiffness of the contact can be determined by inverting this relation and differentiation. For a fully flooded contact this approach is documented in detail in chapter 5 of Wijnant (1998), with an example of stiffness versus approach plot given in Fig. 5.7. It is shown that the stiffness of the lubricated contact approaches the Hertzian stiffness for large 6, whereas for small 6 it is significantly different. A large 6 implies a small film, and thus a high load. As the viscosity of the lubricant in the film will be very high in fact the lubricant film will be stiffer than the elastic surfaces, and thus the stiffness approaches the stiffness of the Hertzian contact. The results presented in this paper show that for the range Hoil/aeff> 1 the value of Aoo does not differ much from the value for fully flooded conditions. Thus under these conditions the stiffness will be close to the stiffness of the fully flooded contact. Now if under the fully lubricated conditions the film thickness is small compared to the elastic deformation the stiffness will be close to the stifness of the Hertzian contact. On the other hand, if the film thickness under fully flooded conditions is large the stiffness will deviate significantly from the Hertzian stiffness. In both cases the effect of starvation will be that with a decreasing thickness of the layer of oil in the inlet, the film thickness will decrease and the stiffness will gradually approach the Hertzian stiffness.

Dr. C.J. Hooke (University of Birmingham, U.K.). Your dynamic results show a film thickness variation on the track behind the ball that varies with time. Clearly this will reenter one of the conjunctions in the bearing. Have you any information on the importance of this?

Reply by the Authors.

To be precise, the results show a variation of the "'lubricant layer" thickness on the track behind the ball, where "'lubricant layer" refers to the amount of lubricant present at the location presented as if it were a single layer on one of the surfaces. However, strictly spoken in the

871

outlet region one does not have a single layer, but a mixture of vapour/air and oil. Nevertheless, for a next contact this will imply a variation of the inlet fractional film content 0 with time. The exact implications of this phenomenon have not yet been investigated, but it does seem to indicate that resonance phenomena could occur under certain circumstances, i.e. if the frequency of the oscillation coincides with the natural frequency of the contact. However, such phenomena can only be observed if the acceleration terms of the equation of motion are included. Even then it will probably also depend on the thickness of the remaining layer, and the degree to which the contact is starved. For example, some preliminary calculations were performed where the outlet film layer thickness was used as input condition for the contact. For the specific conditions considered in the paper no resonance effects were observed.

Paper XVII (iii) "New Tools for Experimental Study of EHD and Limit Lubrications", by Mr. J. Molimard, Dr. M. Querry and Dr. P. Vergne (LMC, INSA de Lyon, France).

leads us to choose the experimental calibration. During the calibration process, intensities are averaged over concentric circles and consequently over a large number of pixels. The contribution of the roughness influence on the calibration curves is thus reduced and becomes almost negligible for thicknesses lower than the ball roughness. On the other hand, Greenwood et al [Additional Reference 1] defined a dimensionless roughness parameter c~: (yR a

2

where cy is the combined r.m.s, surface roughness, R the ball radius, and a the contact radius. According to our experimental conditions, used to establish the calibration curves, c~ is equal to 0.02. In that case, the difference between the real contact radius and the radius given by the Hertzian theory varies from 1% to 3 % following the Greenwood et al [ 1] work. Additional References:

Prof. H. Spikes (Imperial College, London, U.K.). You indicate that the ball surface roughness is approximately 30 nm and use this to explain the deviation from normal EHD behaviour of your film thickness results. How did you manage to calibrate down to less than 30 nm using a ball with roughness of this order?

Reply by the Authors. As is pointed out by Prof. Spikes, experimental calibration is the most important phase in our image analysis process. The answer to Prof. Spikes' question may be supported by experimental and analytical considerations. The first one concerns the process used to build up a calibration curve. The second one deals with the roughness influence on the contact radius, which is implicitly taken into account during the calibration process. We tried to do without experimental calibration as it is shown in Figure 2. We compared the experimental calibration to a multi-reflection model: in the low thickness domain, the difference between the two approaches is within 3%. However, the optical model requires a large number of parameters, both those of the fluid and those of surfaces, and this

1. Greenwood J.A., Johnson K.L., Matsubara E., A surface roughness parameter in Hertz contact, Wear, Vol. 100, 47-57, 1984.

Paper XVII (iv) "Lubrication Theory as a Means of Unravelling Flow Structure in Thin Film Roll Coatin~ Systems", by Prof. P.H. Gaskell, Dr. J.L. Summers and Dr. H.M. Thompson (University of Leeds, U.K.).

Mr. F.H. Bucher (TU Berlin, Germany). In your mechanical model, the substrate (paper, foil, etc.) seems to be directly connected to the upper steel roller. Should you not pay more attention to modelling that fourth body and take into account the low elasticity and fluid adsorbing properties of the substrate?

Reolv by Dr. J.L. Summers. Yes it is true that the property of the substrate is important in roller coating processes. In the paper the flow between the two rollers was studied and it was assumed that the substrate was wrapped around the upper roller and in effect became the upper moving boundary for the problem. In analysing the small scale flow (approximately 5 mm by 200 ~tm) the adsorption or

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elastic properties of the substrate are secondary to its wetting characteristics which is a research area in its own right. The way that this problem was tackled from a simple modeling point of view was to impose a dynamic contact angle and slip length at the wetting line.

Additional References: 1. T. Murakami, H. Higaki, Y. Sawae, N. Ohtsuki, S. Moriyama and Y. Nakanishi, Adaptive multimode lubrication in natural synovial joints and artificial joints, Proc. Instn. Mech. Engrs., Part H, Vol. 212, 23-35 (1998).

Paper XVII (v) "Role of Surface Layers of Natural and Artificial Cartilage in Thin Film Lubrication", by Prof. T. Murakami, Dr. Y. Sawae (Kyushu University, Fukuoka, Japan), Mr. H. Morimoto (Sumitomo Metal Industries, Japan) and Mr. M. Noda (Mitsubishi Heavy Industries Ltd., Japan).

SESSION XVIII - LUBRICATION FRICTION

Dr. L.K.Y. Li (City University of Hong Kong, Hong Kong). Why use glass as the lower specimen when testing natural cartilage? Would natural cartilage not be more appropriate? Please comment on why TZP was used for the artificial cartilage tests?

Paper XVIII (i) "An Investigation on the Antifriction Performance of Some Organomolybdenum Additives", by Dott. G. Tripaldi (EniTechnologie SpA, San Donato Milanese, Italy), Dott. S. Fattori (Euron/AgipPetroli SpA, San Donato Milanese, Italy), P. Ch. R. Nodari and Dott. A. Vettor (EniTechnologie SpA, San Donato Milanese, Italy).

Reply by Prof. T. Murakami. In this paper, the glass plate was used as the reciprocating lower specimen as a counterface of natural articular cartilage to clarify the lubricating role of the surface layer of natural cartilage. The frictional behaviour of natural articular cartilage against itself depends on the joint geometry and motion conditions. The friction characteristics in pig shoulder joints (as a rubbing pair of natural cartilage against itself) were evaluated by the pendulum tests as reported in the authors' previous paper [Additional Reference 1]. Furthermore, the preparation of a flat specimen of intact articular cartilage from animal joints is very difficult. Therefore, the glass flat plate with a hydrophilic and smooth surface was used as the lower specimen. From the AFM observation of glass plates after rubbing tests, it was found that the transferred materials from the surface layer of natural articular cartilage changed depending on the friction level in rubbing process. The main reason why the zirconia ceramic TZP was used for the artificial cartilage is that the authors intended to evaluate the frictional behaviour in artificial joints composed of biocompatible prosthetic joint materials.

AND

Dr. S. Korcek (Ford Motor Co., Dearborn, USA). In the investigation of friction reduction by MoDTC, there are two important factors to be considered: the rate of formation of the low friction layer and level of friction reduction. MoDTC concentration and temperature significantly affect the formation rate. This could explain the lack of friction reduction by MoDTC under your experimental conditions? Reply by the Authors. The chosen combinations of Mo friction modifiers and ZnDTPs give low friction coefficient at 135°C with solutions containing 1.3%wt of ZnDTPs. The lack of friction reduction at higher concentrations of ZnDTPs could be related to the low level of Mo friction modifiers; it reasonably affects the rate of growth of MoS2 inside the higher friction phosphate-rich film derived from the ZnDTPs. On the other hand, the lack of friction reduction at 40°C could be explained through the effect of temperature on the layer formation rate: it would be interesting to clarify the influence of the lubrication regime (at lower temperatures the Stribeck curves span more of the EHD regime than the mixed/boundary).

Prof. H. Spikes (Imperial College, London, U.K.). Did you test the effect on molybdenum additive performance of ZDDP concentrations below 1.3%? If so, did they work?

873

ReDly by the Authors. Yes, we obtained results under pure sliding conditions using a pin-on-disk tribometer. At 135°C, the solutions containing 0.31% MoDTP + 0.7% ZnDTP, primary and secondary, gave a friction coefficient 0.04 + 0.01.

Dr. T.G. Mathia (ECL-ENISE-CNRS, France). Listening to your presentation, it seems that you do not use an experimental design strategy. Is that so? Reply by the Authors. As better reported in the paper, we planned the present study using two different 3-factors experimental designs: one for each kind of ZnDTPs (primary or secondary). The chosen factors were the temperature, the friction modifier addition and the ZnDTP concentration. The ZnDTPs were tested at more than two levels: mainly at a typical value for applications, its double and triple. A complete statistical data analysis is not presented in the paper because the results of some treatments are not yet reliable enough. Paper XVIII (ii) "The Behaviour of Molybdenum Dialkyldithiocarbamate Friction Modifier Additives", by Ms. J.C.H. Graham and Prof. H. Spikes (Imperial College, London, U.K.) Dr. G.W. Roper (Shell Research and Technology Centre, Chester, U.K.). Is the zone of MoDTC effectiveness (i.e. concentration versus temperature) affected by other tribological factors such as contact pressure? Reolv by the Authors. Load and contact pressure are areas that we hope to thoroughly investigate in future work. So far we have established that a considerable friction reduction is observed using the additive in conditions of pure sliding. Under conditions where there is a mixture of sliding and rolling, there is a much less marked difference between the additive solution and the pure base oil.

Dr. A. Gangopadhyay (Ford Motor Co., Dearborn, USA). In the HFRR experiments, additions of antioxidants (3.5 - 5%) increased the upper end of the temperature range in which friction reductions were observed from 80°C to 200°C. What about increasing the temperature range towards lower temperatures, say 40°C? At lower temperature, say 40°C, the solubility of MoDTC in

the base oil was very low. was difficult to achieve.

Therefore low friction

Reolv by the Authors. At lower temperatures, say 40°C, the solubility of MoDTC in the base oil was very low. Therefore low friction was difficult to achieve. Even using solutions where the MoDTC had been completely dissolved at 80°C it was found when the solution was cooled, that the sample was not completely dissolved at 40°C. Although this was not visible to the naked eye, optical techniques revealed the presence of particulate debris in the solution.

Dr. S. Korcek (Ford Motor Co., Dearborn, USA). Based on our results, as well as your own, oxidation is an important process in mechanisms of friction reduction by systems containing MoDTC. I encourage further investigation of these effects. Reoly by the Authors. Two different MoDTC additives have now displayed the phenomenon at higher temperatures and low concentrations, of no longer producing friction reduction. This result indicates that oxidation has an important effect on the additive which is why oxidation processes are the subject of further work in this study of MoDTC oil-soluble additives. Paper XVIII (iii) "Traction and Film Thickness Characteristics of Traction Fluids in High Speed Elastohydrodynamic Contact", by Mr. J. Makala (Universit6 de Poitiers, France), Mr. J.P. Chaomleffel (LMC, INSA de Lyon, France), Prof. B. Villechaise (Universit6 de Poitiers, France), Prof. G. Dalmaz (LMC, INSA de Lyon, France) and Mr. K. Kargar (Renault, France). Dr. L. Houpert (Timken France, France). I would suggest the inclusion of the temperature increase in the film and on the surface for defining the fluid operating temperature and the use of the latter when plotting the limiting shear stress versus temperature, not the initial oil inlet temperature. ReDly by Mr. J. Makala and Professor G. Dalmaz. The authors would like to thank Dr. L. Houpert for his useful remark about the fluid operating temperature and the limiting shear stress values. In traction drives, the maximum traction coefficient will be obtained with the limiting shear

874

stress of the lubricant. The limiting shear stress has been found to increase with pressure at constant temperature. It is well known that the rise of temperature will decrease the limiting shear stress but, as mentioned by Loewenthal and Rohn [Additional Reference 1], the inlet fluid temperature seems to have a small effect on limiting shear stress. However, as shown by Tevaarwerk [Additional Reference 2], the limiting shear stress is more influenced by shear heating in the Hertzian area. In the linear region of the traction curve, only partial dissipative behaviour takes place by the shearing of an elastic/plastic material, while in the high strain rate regime, only dissipative behaviour occurs. The shearing of a plastic material has a thermal influence on the shear stress of the material. At the larger values of sliding speed and spin, the elastic effects in the fluid are negligible and the shearing is purely dissipative in nature. In our experiments, the limiting shear stress of fluid has been extracted from the traction curve, at a slide-roll ratio of 2.3 percent. At this value thermal effects are not yet significant. The limiting shear stresses have been calculated at a mean inlet temperature of the fluid and rolling elements which varied in a range of 25°C + 2°C. It is possible to estimate the mean value of fluid temperature, in the contact, from the expression reported by Tevaarwerk [Additional Reference 2] using the shear plane hypothesis. The mean temperature increase, due to the sliding speed, is approximately 10°C for a speed U~+U2 = 4 m/s, Pmax = 2 GPa, with a contact formed by a steel ball on sapphire plate and lubricated by Santotrac50. This result appears to agree with independent experiments obtained by Dow et al [Additional Reference 3]. With the same fluid and similar operating conditions, the increase of film temperature is approximately 15°C for a slide-roll ratio of 2 percent and inlet temperature of 20°C. Note that, at higher sliding speed, Dow has observed a fast increase of peak surface temperature which can reach 50°C at 5.5 percent slide-roll ratio. Additional References: 1. Lowenthal S.H. , Rohn D.A, "Elastic Model of the Traction Behavior of Two Traction Lubricants", Trans. ASLE, Vol 27, No. 2; (1983), p. 129-137.

2. Tevaarwerk, J.L., "Thermal Influence on the Traction Behavior and Elastic/Plastic Model", Proc.of the 7th Leeds-Lyon 1980, P302. 3. Dow T.A., Stockwell R.D., Kannel J.W., "Thermal Effects in Rolling / Sliding EHD Contacts :Part 1 - Experimental Measurements of Surface Pressure and Temperature", Journal of Tribology, 109, July 1987, p 503-511.

Paper XVIII (iv) "Development of an Apparatus for the Direct Measurement of Traction Coefficients for Lubricants~ Preliminary Measurements from a Bouncing Ball Apparatus", by Prof. D. Dowson, Mr. M.F. Workel, Mr. J. Canelo-Quintero and Mr. S. May (University of Leeds, U.K.). Dr. L. Houpert (Timken France, France). Could the authors comment on the friction coefficient decrease versus pressure? Could it be a temperature/squeeze effect that is responsible for this decrease? Dr. G.W. Roper (Shell Research and Technology Centre, Chester, U.K.). Could the reduction of traction with increasing pressure be associated with thermal effects? Reply by the Authors. We thank Dr Houpert and Dr. Roper for their similar suggestions and questions. We have always associated the decline in traction with increasing pressure with thermal effects. There are two sources of the temperature rise; adiabatic compression and viscous dissipation during the sliding phase of the motion of the ball over the plate. It may be necessary to take both into account under some conditions and this will form the subject of a further study. Prof. B.O. Jacobson (Lund Institute of Technology, Sweden). Figure 4 shows mechanical coupling between normal and tangential forces with a time delay of the same order as the impact time. That means that only information on the total momentum transferred can be determined from the measurements not the instantaneous forces. That is the same as in the experiments of Jacobson and H/Sglund but have you any ideas about how to measure the local stresses in the oil? Can you also

875

explain the strange friction behaviour for Santotrac at high contact pressures in Figure 9?

Reolv by the Authors. The main objective of this new approach to measurements in the bouncing ball project originally introduced by Professor Jacobson was to attempt to measure both normal and tangential impact forces simultaneously. The present design of apparatus clearly demonstrates the phase shift problem between the two force components, but we find that this is strongly dependent upon the design and hence the dynamics of the apparatus. We believe it to be worthwhile to continue the development of the apparatus in order to approach the situation in which the two force components can be measured directly and reliably, since this will reveal the variation in the traction coefficient throughout the impact and such information cannot be extracted from overall momentum considerations. Neither approach, however, will reveal 'local' stresses in the lubricant. The decrease in traction coefficient with increasing pressure shown in Figure 9 appears to occur with four fluids and not just Santotrac. A similar trend has been reported by H6glund (see reference 18).

Prof. G.W.G. Poll (University of Hannover, Germany). Is there a reason to believe that the limiting shear stress continuously rises with increasing pressure? Is it not possible that there is a ceiling value, as is true with pastes? Reo!v by the Authors. The expression "~L --TO +'}tp

has been shown to be quite a good representation of the behaviour of the limiting shear stress by a number of authors (see for example references 6, 7 and H6glund, E. and Jacobson, B.O., (1986), Trans. ASME, Journal of Tribology, Volume 108, pp571578).

SESSION X I X - B O U N D A R Y AND MIXED L U B R I C A T I O N 2 Paper XIX (i) "The Effect of Molecular Structure on Boundary and Mixed Lubrication by

Synthetic Fluids- An Overview", by Dr. S. Boyde, Dr. S.J. Randles and Dr. P. Gibb (ICI Synthetic Lubricants, Wilton, U.K.). Mr. A. LaFountain (Imperial College, London, U.K.). You showed a wide variety of chemicals which might be used in modem applications. It seems that in your overview, a combination of methods and purpose of analyses would have better integrated the audience's understanding of your long term goals and paths toward your goals. Please comment. Reply by the Authors. Synthetic lubricating fluids are used in a wide variety of applications, for diverse reasons. Each application has its own performance requirements, and its own preferred tests to characterise lubricant performance. These tests are chosen for practical relevance and may often be difficult to interpret in terms of the underlying tribology. However, as the vast majority of the available data are based on such application-specific test methods, we opted to base the presentation on this available data, aiming to draw general conclusions where appropriate. Paper XIX (iii) "Water in Confined Geometry, an Approach to the Behaviour of Fluids in Boundary Lubrication", by Mr. J. Lepage and Mr. G. Maurice (LSGS UMR CNRS, Nancy, France). Dr. E. Rosset (EPFL-DMX-Tribology, Switzerland). In this study, it is assumed that pores in the bulk materials may represent "tribological" pores, i.e. spaces between the asperities of the mating surfaces. Is it possible to comment on the differences in morphology of pores between the different materials under study as well as the "pores" between tribologically exposed surfaces? Reolv by the Authors. In the author's mind, the pores of large porous media are not representative of the voids between the mating surfaces of a tribological contact, but of the inner surfaces of the third body layer. It is well known that materials entrapped in the contact are finely ground and have a high surface/volume ratio. We think that fluids adsorbed at these surfaces behave as fluids entrapped in the poral space of macroscopic porous samples. In this case the parameter of interest is the specific surface area As. Of course, mechanical

876

models involving for instance the compliance of the surfaces would require assumptions concerning geometry of the contact, and then of the porous media, according to Reference [10] for instance.

Paper XIX (iv) "Solidified Films and Adsorbed Films in Concentrated Contacts", by Dr. J. Sugimura, Mr. J. Kim, Mr. S. Gondo and Prof. Y. Yamamoto (Kyushu University, Fukuoka, Japan). Prof. J.M. Georges (Ecole Centrale de Lyon LTDS, France). TCP is very sensitive to hydrolysis. Did you take this into account in your experiment? ReDly by the Authors. We would like to thank Prof. Georges for his question. We did not consider details about the ways in which TCP decomposes and reacts with sliding surfaces, because the aim of looking at phosphorus concentration was simply to compare the effect of chemical structures of the base oils on adsorption or reaction of polar agents. The phosphorus concentration shown in Figure 10 should be taken as results of all possible processes of reaction and decomposition involved, although there should have been little or a very small amount of decomposed agents such as phosphate acids because TCP used in the tests was highly purified one. Nevertheless, we think that effect of the base oil structures on each of these elementary processes will be another interesting point to be investigated.

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2 5 th

LEEDS-LYON SYMPOSIUM ON TRIBOLOGY

LUBRICATION AT THE FRONTIER : The role of the interface ,and surface layers in the thin fihn ,and boundary regime S e p t e m b e r 8th - 1 l t h 1998

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Prof

KIMURA Y.

KAGAWA UNIVERSITY Faculty of Engineering 1-1 Saiwai-cho TAKAMATSU 7608526 JAPAN

Prof

KLEIN J.

WEIZMANN INSTITUTE OF SCIENCE Department of Materials REHOVOT 76100 ISRAEL

Prof

KOBAYASHI A.

MEIJO UNIVERSITY Department of Mechanical Engineering, Faculty of Science and Technology 1-501 Shiogamaguchi, Tenpaku-ku NAGOYA 4688502 JAPAN

Dr

KOENEN A.

VALEO SYSTEME D'ESSUYAGE 44, rue Louis Lormand LA VERRJERE 78321 FRANCE

Mr

KONDO S.

IMPERIAL COLLEGE Dept. of Mechanical Engineering, Tribology Section Exhbition Road LONDON SW7 2BX UK

Prof

Dr

K A N E T A M.

KAPSA P.

KYUSHU INSTITUTE OF TECHNOLOGY Departement of Mechanical and Control Engineering 1-1, Sensui-cho, Tobata, KITAKYUSHU 8048550 JAPAN ECOLE CENTRALE DE LYON LTDS B.P. 163 ECULLY cedex 69131 FRANCE

Prof

KENNEDY F.

DARMOUTH COLLEGE Thayer School of Engineering HANOVER, NH 03755 USA

Mr

KERNIZAN C.F.

THE LUBRIZOL CORPORATION 29400 Lakeland Boulevard WICKLIFFE, OH 44092-2298 USA

Mr

K E R O U A N I Y.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

887

Title

Name

Affiliation

Title

Name

Affiliation

Dr

K O R C E K S.

FORD MOTOR COMPANY Research Laboratory, MD 2629/SRL PO Box 2053 DEARBORN, MI 48121-2053 USA

Mr

LE MOGNE T.

ECOLE CENTRALE DE LYON LTDS BP 131 ECULLY cedex 69131 FRANCE

Mr

LEPAGE J

ECOLE DES MINES Parc de Saurupt NANCY cedex 54042 France

Mr

LESIGNE F.

SNR ROULEMENTS 1, rue des Usines, BP 2017 ANNECY 74010 FRANCE

Mr

LETALLEUR N.

INSA LYON Laboratoire de Mdcanique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Dr

LI L.K.Y.

IMPERIAL COLLEGE 3, Mablethorpe rd. LONDON SW6 6AQ UK

CITY UNIVERSITY OF HONG KONG Depamnent of MEEM, Tat Chee Avenue KOWLOON HONG KONG

Dr

LIRAUT G.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

RENAULT Service 60152, DIMAT, TPZ OOA 337 860 Quai de Stalingrad BOULOGNEBILLANCOURT 92109 FRANCE

Dr

LORENTZ G.

RHODIA Centre de Recherche d'Aubervilliers 52 rue de la Haie Coq AUBERVILLIERS 93308 FRANCE

Prof

LOUBET J.-L.

ECOLE CENTRALE DE LYON LTDS BP 163 ECULLY 69131 FRANCE

Mr

Dr

Mr

Ms

K O R E N A G A A.

KRUPKA I.

LAFOUNTAIN A.

L A H M A R F.

MECHANICAL ENGINEERING LABORATORY, MITI Machine Elements Division Namiki 1-2, Tsukuba IBARAKI 305-8564 JAPAN TECHNICAL UNIVERSITY OF BRNO Faculty of Mechanical Engieering, Institute of Design Technicka 2 BRNO 616 69 THE CZECH REPUBLIC

Mr

LAMARE A.

SNFA Z.I. n 2 Rouvignies VALENCIENNES 59309 FRANCE

Dr

LARSSON R.

LULEA UNIVERSITY OF TECHNOLOGY Division of Machine Elements LULEA SE-971 87 SWEDEN

888

Title

Name

Affiliation

Prof

L U B R E C H T T.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Dr

M A G N Y C.

SOCIETE SOLLAC LEDEPP 17, avenue des Tilleuls, BP 70011 FLORANGE cedex 57191 FRANCE

Mr

Dr

Mr

Prof

Mr

M A H E L.

M A K A L A J.

M A K I N O T.

M A N S O T J.-L.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE DIRECTION DE LA RECHERCHE RENAULT Technocentre RenaultSce 0076 1, avenue du Golf GUYANCOURT 78288 France IMPERIAL COLLEGE Dept. of Mechanical Engineering, Tribology Section Exhibition Road LONDON SW7 2BX UK UNIVERSITE DES ANTILLES ET DE LA GUYANE Facult6 des Sciences, Campus Fouillole POINTE A PITRE cedex 97159 GUADELOUPE

M A R C H E T T I M. INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Title

Name

Affiliation

Prof

MARTIN J.-M.

ECOLE CENTRALE DE LYON LTDS BP 163 ECULLY cedex 69131 FRANCE

Dr

MATHIA T.G.

ECL - ENISE - CNRS 41 Allde des Chines MARCY L'ETOILE 69280 FRANCE

Dr

M A Z U Y E R D.

ECOLE CENTRALE DE LYON LTDS BP 163 ECULLY cedex 69131 FRANCE

Mr

MESSE S.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Dr

MEURISSE M.-H.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Dr

MIAN A.O.

FEDERAL MOGUL TECHNOLOGY Engine Systems Cawston House, Cawston Lane CAWSTON CV22 7SA UK

Dr

MISCHLER S.

EPFL DMX - LMCH LAUSANNE CH-1015 SWITZERLAND

Prof

MIYAKE S.

NIPPON INSTITUTE OF TECHNOLOGY 4-1 Gakuenndai Miyashiro

Min,-unisaitama SAITAMA 345850l JAPAN

889

Title

Name

Affiliation

Title Name

Affiliation

Dr

MIZUHARA K.

NIHON PALL Ltd. SLS Div. 46 Kasuminosato Aanimachi IBARAKI JAPAN

Mr

NEDER Z.

TECHNICAL UNIVERSITY OF BUDAPEST Miiegyetem rkp 3. BUDAPEST H-1111 HUNGARY

Mr

MOLIMARD J.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Mr

NICCOLINI E.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Mrs

MOORE S.

THE UNIVERSITY OF LEEDS Department of Mech,-mical Engineering LEEDS LS2 9JT UK

Mr

ODONIL.

ECOLE CENTRALE DE LYON LTDS BP 163 ECULLY 69131 FRANCE

Dr

MORALESESPEJEL G.E.

ITESM Campus Querdtaro, Dept. de Ing. Mecanica e Industrial Jesus Oviedo A. N 10, Parques Industriales QUERETARO 76130 QRO MEXICO

Mr

OUCHERIF F.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbamle cedex 69621 FRANCE

Dr

PASQUIER V.

EXXON RESEARCH & ENGINEERING Co. Clinton Township Route 22 East, Room LF 380 ANNADALE, NJ 08801 USA

Prof

PLATON F.

E.N.S.C.I. Laboratoire Mat6riaux C6ramiques 47, avenue Albert Thomas LIMOGES cedex 87065 FRANCE

Prof

POLL G.W.G.

UNIVERSITY OF HANNOVER Institute ~ r Maschinen elemente, Konstntktionstechnik und Trilogolie Welfengarten 1A HANNOVER 30167 GERMANY

Prof

Mr

Dr

MURAKAMI T.

NAGANUMA N.

NAKAMURA T.

KYUSHU UNIVERSITY Dept. of Intelligence Machinery & Systems, Faculty of Engineering 6-10-1 Hakozaki, Higashi-ku FUKUOKA 812-8581 JAPAN ELF SOLAIZE CRES BP 22 - Chemin du Canal SOLAIZE 69360 FRANCE NAGOYA INSTITUTE OF TECHNOLOGY Dept. of Mechanical Engineering Gokiso-cho, Showa-ku NAGOYA 466-8555 JAPAN

890

Title Name

Affiliation

Title Name

Affiliation

Dr

PRIEST M.

THE UNIVERSITY OF LEEDS Department of Mechanical Engineering LEEDS LS2 9JT UK

Mrs

RIOLLET A.-M.

Mr

PUBILIER F.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

SNCF Direction de l'Infrastructure, Subdivision des Rails IV MR2 17, rue d'Amsterdam PARIS 75008 FRANCE

Dr

ROBBE VALLOIRE F.

ISMCM 3, rue Fernard Hainaut SAINT OUEN cedex 93407 France

Dr

QUERRY M.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Dr

ROMANA L.J.

UNIVERSITE DES ANTILLES ET DE LA GUYANNE Campus de Fouillole POINTE A PITRE 97159 GUADELOUPE

Dr

R A P O P O R T L.

C.T.E.H. Departement of Science PO Box 305 HOLON 58102 ISRAEL

Dr

ROPER G.W.

Dr

RATOI M.

IMPERIAL COLLEGE Mechanical Engineering Dept, Tribology Section Exhibition Road LONDON SW7 2BX UK

SHELL RESEARCH AND TECHNOLOGY CENTRE Thornton PO Box 1 CHESTER CH1 3SH UK

Dr

ROSSET E.

EPFL DMX-Tribologie LAUSANNE 1015 SWITZERLAND

Mr

REVIRON O.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Prof

ROZEANU L.

TECHNION -ISRAEL INSTITUTE OF TECHNOLOGY Department of Materials Engineering HAIFA 32100 ISRAEL

Dr

REYNAUD P.

IUT LIMOGES D6partement G6nie Industriel et Maintenance Place Albert Faucher TULLE 19000 FRANCE

Dr

SAINSOT P.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

891

Title

Name

Affiliation

Title Name

Affiliation

Mr

SCHULZ F.

TECHNICAL UNIVERSITY OF HAMBURGHARBURG Section of Engineering Design II AB 5-03 HAMBURG D-21071 GERMANY

Dr

SUMMERS J.

THE UNIVERSITY OF LEEDS Department of Mechanical Engineering LEEDS LS2 9JT UK

Mr

TASCHE T.

SHELL RESEARCH & TECHNOLOGY CENTRE Thornton CHESTER CH1 3SH UK

Dr

TAYLOR R.I.

SHELL RESEARCH Ltd. AND TECHNOLOGY CENTRE Thornton PO Box 1 CHESTER CH1 3SH UK

Ms

TAYLOR L.J.

IMPERIAL COLLEGE Mechanical Engineering Department, Tribology Section Exhibition Road LONDON SW7 2BX UK

Prof

TAYLOR C.M.

THE UNIVERSITY OF LEEDS Department of Mechanical Engineering LEEDS LS2 9JT UK

Prof

TICHY J. A.

RENSSELAER POLYTECHNIC INSTITUTE Dept. of Mechanical Engineering, Aeronautical Engineering and Mechanics TROY, NY 12180-3590 USA

Mr

TOMIMOTO M.

NIHON PALL Ltd. SLS Div. 46 Kasuminosato Amimachi IBARAKI JAPAN

Prof

Mr

Prof

Mr

Dr

SIDOROFF F.

SIX M.-F.

SPIKES H.

STAHL J. L.

SUGIMURA J.

ECOLE CENTRALE DE LYON LTDS BP 163 ECULLY cedex 69131 FRANCE INSA LYON Laboratoire de Mdcanique des Contacts 20 Ave A. Einstein Villeurbatme cedex 69621 FRANCE IMPERIAL COLLEGE Department of Mechanical Engineering, Tribology Section Exhibition Road LONDON SW7 2BX UK LUND INSTITUTE OF TECHNOLOGY Division of Machine Elements Box 118 LUND SE-22100 SWEDEN KYUSHU UNIVERSITY Department of Energy and Mechanical Engineering 6-10-1 Hakozaki, Higashi-ku FUKUOKA 812-8581 JAPAN

892

Title

Name

Affiliation

Title

Name

Affiliation

Dr

T O N C K A.T.

ECOLE CENTRALE DE LYON LTDS BP 163 ECULLY cedex 69131 FRANCE

Prof

VARADI K.

Dr

TORRANCE A.A.

TRINITY COLLEGE Parsons Building DUBLIN 2 IRELAND

TECHNICAL UNIVERSITY OF BUDAPEST B.M.E. Miiegyetem rkp.3 BUDAPEST H-1111 HUNGARY

Ms

VARLOT K.

TRIFA M.

ECOLE CENTRALE DE LYON LTDS BP 163 ECULLY 69131 FRANCE

ECOLE CENTRALE DE LYON LTDS BP 163 ECULLY cedex 69131 FRANCE

Prof

VELEX P .

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Dr

VENNER C.H.

UNIVERSITY OF TWENTE Faculty of Mechanical Engineering PO Box 217 ENSCHEDE 7500 AE THE NETHERLANDS

Dr

VERGNE P.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Mr

VILLE F.

INSA LYON Laboratoire de M6canique des Contacts 20 Ave A. Einstein Villeurbanne cedex 69621 FRANCE

Prof

VINCENT L.

ECOLE CENTRALE DE LYON BP 163 ECULLY cedex 69131 FRANCE

Mr

Mr

TRIPALDI G.

ENITECNOLOGIE Via Martano 26, SAN DONATO, Milanese 20097 ITALY

Dr

T R U O N G DINH N.

CONDAT Avenue Fr6ddric Mistral, BP 16 CHASSE SUR RHONE 38670 FRANCE

Mr

URBANIAK J.-lVL

SNFA Z.I. n 2 - Rouvignies VALENCIENNES 59309 FRANCE

Mr

VAN ODIJCK D.

UNIVERSITY OF TWENTE Faculty of Mechanical Engineering, Laboratory for Applied Mechanics & Tribology PO Box 217 ENSCHEDE 7500 AE THE NETHERLANDS

Prof

VANNES A.-B.

ECOLE CENTRALE DE LYON LTDS BP 163 ECULLY 69131 FRANCE

893

Title Name

Affiliation

Title Name

Affiliation

Mr

WIJNANT Y.H.

UNIVERSITY OF TWENTE Faculty of Mechanical Engineering, Laboratory for Applied Mechanics & Tribology PO Box 217 ENSCHEDE 7500 AE THE NETHERLANDS

Prof

UNIVERSITE DE POITIERS Laboratoire de M6canique des Solides, S.P.2M.I BP 179 FUTUROSCOPE cedex 86960 FRANCE

Dr

WILLIAMS J.A.

CAMBRIDGE UNIVERSITY Engineering Departement Trumpington Street CAMBRIDGE CB2 1PZ UK

Mr

WORKEL M.F.

THE UNIVERSITY OF LEEDS Department of Mechanical Engineering LEEDS LS2 9JT UK

Dr

XU H.

FEDERAL MOGUL TECHNOLOGY Cawston House RUGBY CV22 7SA UK

Mr

YANO A.

MITSUBISHI INDUSTRIES Ltd. Nagasaki Research & Development Center 5-717-1, Fukahorimachi NAGASAKI 851-0392 JAPAN

Mr

YOKOYAMA F.

IMPERIAL COLLEGE Department of Mechanical Engineering, Tribology Section Exhibition Road LONDON SW7 2BX UK

Dr

ZAHOUANI H.

ECOLE CENTRALE DE LYON LTDS BP 163 ECULLY cedex 69131 FRANCE

ZAIDI H.

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