Mechanics and Chemistry in Lubrication (Tribology Series)

MECHANICS AND CHEMISTRY IN LUBRICATION

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

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

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

TRIBOLOGY SERIES, 9

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

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

ELSEVIER Amsterdam

- Oxford - New York - Tokyo

1985

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

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

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

~21.0'9

I.

Ludem,

K.

C

85-6885

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

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

V

PREFACE

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

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

VI

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

treat-

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

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

DORINSON

K. C LUDEMA

This Page Intentionally Left Blank

IX

ACKNOWLEDGEMENTS

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

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

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

XI

CONTENTS 1

2

.

.

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

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

. . . . . .

. . . . .

Simple in Two 2.1. 2.2.

. . . . .

. . . .

. . . . . .

. . . .

. . . . .

.

. . . . . .

. . . . . .

. . . . . .

. . . . . .

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

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

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

3

. . . . .

Some 3.1.

3.2. 3.3. 3.4. 3.5.

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

. . . . .

. . . . .

4.4. 4.5. 4.6. 4.7. 4.8.

1

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

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

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

1

. . . . . . . .

.

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

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

79 80

.. . .. .. .

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

. . . . . . . . . . .

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

. . . .. .

. . .. .. . .

.. . .. .. .

. .

XI1

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

. . . . . . . . . .

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

5

.

. . . .

. . . . . . Lubricating Fluids .

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

. . . . . . .

6

.

. . . . . . . . . .

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

83 87 92 99 100 102 102 103 106 108

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

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

7

.

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

. . . . .

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

. . . . . .

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

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

. . . .

. .

. . . .

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

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

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

.

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

. . . . . . . . . . .

Simple Absorbed Films Chemisorbed Films

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

XI11

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

. . . . . . . . . .

. . . . . . . . . . .

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

. . . .

. . . .

. *

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

. . . . .. . .

. . . . .

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

. . . . . . . . . .

. .

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

.

Wear: 13.1. 13.2.

13.3.

255 255

276

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

13

231 235 236 238 241 250 252

. . . . . . . . .

. . .

.

226

.

. .

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

.

224

261 261 268 272 274

.

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

12

219 219

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

. . . .

...

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

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

XIV

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

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

. . . . . . . . . . .

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

. . . . . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . .

. . . . . . . . .

. . . .

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

16

.

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

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

.

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

. . . . . .. .

472 472 476 480

. . .

480

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

484 487 488

. . . .

491

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

17

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

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

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

. . . . . . . .

495 499 501 50 1 507

xv

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

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

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

581 589 594 610

Author Index

615

19.2.

. . . . . . . . . . .

Subject Index

. .

552 566 572 577

. . . . . . . . .

579

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

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

. . . . .

. . . . .

. . . . .

. . . . . . . .

621

This Page Intentionally Left Blank

1

Chapter 1 INTRODUCTION

1.1.

WHAT IS LUBRICATION?

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

...

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

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

2

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

FRICTION AND WEAR

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

3

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

1 .3.

TRI BOLOGY

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

view

into

broad

language,

we

say

that

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

SOME FURTHER STATEMENTS hBOUT LUBRICATION

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

5

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

-.

----.

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

6

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

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

r3cthe the en-

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

.

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

7

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

practical

lubrication

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

2.

3.

4.

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

8

Chapter 2

SIMPLE HYDRODYNAMIC THEORY: THE REYNOLDS EQUATION IN TWO DIMENSIONS

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

2.1.

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

9

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

Figure 2-1.

Beauchamp Tower's experimental bearing.

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

distribu-

10

I

I

I

I

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

Figure 2-2.

C i rcumferent i a

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

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

is

propor-

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

( 3 ) The weight of the fluid is negligible.

11

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

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

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

(8) There

is

no

slip

between the lubricant and the bounding sur-

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

that

the

( 1 0 ) The

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

(11)

The two bounding surfaces are not parallel.

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

U-

Figure 2-3. surfaces.

Analysis of the hydrodynamic film between

converging

plane

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

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

12

aTX

i X d x d z and

( T ~+

- dy ay

)

dxdz

on the top and bottom faces.

(

pdydz +

a-r,

T~

+

- dy ay

)

dxdz

-

Neglecting inertial forces, for equilibrium

(

p

+

dydz ax

-

1,dxdz

= 0

(2-1)

which reduces to ap

-

31,

ax

ay

From

the

(2-2)

definition

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

get au l X = T I -

ay

On introducing this value for

(2-3) T~

into Eqn 2-2

(2-4)

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

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

=

h

are

in-

which reduces to

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

13

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

udydz + v d x d z

+

wdxdy

=

(u

+

- dx ax

)

dydz

+

av

(,v

+

- dy ay

)

dxdz

whence au

av

aw

ax

ay

az

- + - + - =

0 (2-9)

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

fluid

of

mechanics.

aw

- =

0

az so that

av

au

aY

ax

- = - _

(2-10)

On introducing u from Eqn 2 - 8 ,

with the restrictions imposed there,

(2-1 1 )

Since

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

-

hy)

+

A

or

B, the integral of

U ( v ) ] d g

= 0

(2-12)

is a

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

4(x)

1 f(x,y)dy ax

=

a $(X) -j ax

funct on

f(x,y)dy

-

$ 1

x;

of

l x i f [X,$IXl]

4(x)

In our case 41x1 = 0 ,

JI'lxi

$lxl = h,

ah

=

-,

+"x)

= 0

ax

and since u = 0 when y = h

hence

flx,yl

=

u

+

the

following

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

14

Therefore

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

(2-13)

or

ah ax

(2-14)

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

% ( h3 s)

= 6Tlu

is constant

dh

az

(2-15)

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

THE REYNOLDS EQUATION IN USE: THE PLANE SLIDER BEARING

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

Figure 2-4

Diagram of plane slider bearing with fixed shoe.

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

15

the film thickness are greatly exaggerated. 2.3.1.

Integration of the Reynolds Equation

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

(2-

16a)

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

Since h = ax

( 2 - 16b)

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

2

=

-

(7 1

6qU

+

of

3)

(2- 17a)

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

(’

T + -

a x

k3 32+k4) 2cr x

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

2hlh2 fig=--

hl

+

h2

1

(2-20)

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

16

60

I

0

0.2

I

0.4

I

0.6

I

0.8

1.0

X/B

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

Load Capacity of the Plane Slider Bearing

2.3.2.

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

W

=

of

the

integrated

i Jh l pdx h2

An equivalent expression is

(2-21 b)

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

is

hl xdx

(2-22 ) Then by using the relation

h2(a h = c u x =

-

1) X

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

(2-23)

and then to

(2-24a)

17

An equiva ent expression in which

w=

01

is retained is

6qUL

2

(2-24b)

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

ENERGY LOSSES IN THE HYDRODYNAMIC LUBRICATION OF BEARINGS

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

Using this result in Eqn 2-3 gives TX =

2 (y - $

-

T1

+)

(2-26)

The total frictional force is

(2-27)

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

fh,o = L J h l h2

(2 $

+

i)dx

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

18

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

w 2

VULU

+

-

(2-30)

ci

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

2.5.

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

THE PIVOTED SLIDER BEARING:

DESIGN VARIABLES

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

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

19

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

xw

=

Jh' pxdx (2-31)

h2

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

8

ad

- 1

-

2a e n a

-

( a 2 - 1 ) en a

2[

a2 - 1

2a

-

( a 2 - 1 ) en a

2(a

2a en

-

-

1)

2

a

2(a -1) 21

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

(2-32)

(2-33)

x

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

THE FULL JOURNAL BEARING

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

20

Figure 2 - 7 .

The full journal bearing.

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

Application of the Reynolds Equation to the Full Journal Bearing

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

c =

O'A

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

e

=

00'

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

= c +

e cod e

(2-34)

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

( +1

E

can

e)

2-35)

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

we

change

from

21

Cartesian to polar coordinates as follows: x = he

(2-36a)

d x = ad8

(2-36b)

whereupon Eqn 2 - 1 5 becomes (2-37

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

where k,

is a constant of integration.

Evaluation from Eqn 2 - 3 5 gives

(2-39)

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

(2-40)

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

Friction in the Full Journal Bearing

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

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

22

(2-42)

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

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

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

(2-44)

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

=

J

2n

Lap s i n

8

de (4-45)

0

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

The integration can be

(2-46)

By our assumption, $ = n / 2 ;

hence

E

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

(2-47)

The ratio F . / W consequently reduces to j

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

2-47

can be transformed to

(2-49)

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

p=-

journal

in

units

consistent

W 2hL

(2-50)

23

and substituting into Eqn 2 -49 ,

($; =

(2

+

E

2

)

(1 -

12n

2

E

we get

2 1/2 )

(2-51)

E

The dimensionless quantity

(2-52)

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

As

is evident from Eqn 2-51, it is a

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

(2-53)

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

0

0.10

0.20

0.30

0.40

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

friction

curves

24

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

0.0024 c

0

.- 0.0016

t u0

c

c

.~0.0008 .. uc 0)

0

0

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

0

2

4

-

Figure 2-9.

the

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

25

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

2. 3.

4.

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

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

26

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

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

Lon-

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

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

21

Chapter 3

SOME ADVANCED ASPECTS OF HYDRODYNAMIC LUBRICATION

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

THE CLASSICAL FLUID

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

Stress Analysis of a Fluid

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

28

Figure 3-1.

Stress components in the body of a fluid.

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

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

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

(3-2a)

(3-2b)

29

a#

6lLj

- bx ax

=

+

a 11;

a U'

ay

az

- 6y + - 6z

(3-2c)

When we use the following notation: a = -

aw

au

c = -

az

ax aw

aw

ay

az

bl=--+-

au

aw

az

ax

d2=-+-

aw aw 51=--ay az

aw au 6 3 = -ax+ - ay

av au 5 3 = -ax- - ay

Eqns 3-2 become

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

Lh,

6y

=

mn,

Figure 3-2.

6z

= nh

Orientation of the flow vectors in a fluid.

30

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

au

6X

+

-

6y

+

(

av

6g

+

+

-

av

6X

+

ax

- 6z az

ag

- 6g a9

+

-

62

az

aw

(3-4)

2Z

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

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

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

k2

=

ax 2

+

by2

+

cz

2 +

dlgz

+

d2xz

+

d3xg

(3-6)

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

2

+

by2

+

cz

2

(3-7)

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

31

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

Y

By the familiar transformations of vector analysis

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

b

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

c

=

2 n,a'

+

2 n2b'

+

2 n3c'

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

+ 6' +

c'

(3-9)

Expressions of the form aui

avi

awi

axi

ayi

azi

- + - + -

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

32

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

On carrying the complete transformation through we get

h2 d3

3- 10a)

+

m2n2b'

+

m3n3c')

(

= 2(Llnln' +

L2n2b'

+

L3n3c')

(3-lob)

2(Llmla'

L2m2b'

+

L3m3c')

(3-10~)

/J1 = S ( m l n l a '

=

+

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

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

ox =

o l e2l 2

Oy = o , m l

2 aZ = o l n l

2

+

+

a2L2

2

+

03L3

+

03m3

+

+

03n3

2 02n2

(3-1 la)

2

2 02m2

On ap-

(3-llb)

2

(3-llc)

and from the properties of direction cosines we get ax

ay

+

+

oz

=

al

+

o2

+

a3

(3-12)

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

YZ

T~~

=

almlnl

+

02m2n2

+

03m3n3

(3-13a)

=

olL,nl

+

02L2n2

+

a3L3n3

(3-13b)

33 T XY

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

=

+

a3L3m3

(3-1 3c)

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

The Simple Viscous Fluid

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

.

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

ox

=

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

(3-14a)

0

=

-p + i ( a + b + c )

(3-14b)

Y

o Z = -p

+

xta

+

b

+ c)

+ 2qb +

2qc

(3-14c)

TZX = 62

(3- 14e)

T x y = 63

(3-14f)

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

+ 2q =

0

in

Eqns

3-14a

to

(3-15)

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

34

ox

0

Y

0,

T YZ

=

-p -

= -p

=

av aw ;, i” + -+ \ax ay az

2 - 7,

- p - 7,

=,I-+-

ay

ag

az

au av - + - + ax ay

aw

az

(3- 16a)

ax av

(-+-+‘ax

aL:

azl

(3-16b)

aw

+ 2 n -

az

ZY

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

,

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

35

3.2.

THE NAVIER-STOKES EQUATIONS

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

p

Dt

Dv

= px

aoX + -+ ax aT

p-=py+-+-+-

Dt

Dw p - =

Dt

XY

ax a1xz pz + - + - + ax

aTXY

a1xz

ay

az

-+ aay ay a1

YZ

ay

aT

( 3 - 17a)

YZ

az

(3-17b)

aoZ

az

(3- 1 7 ~ )

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

(3-18a)

36

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

a(pu

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

au ax

;jv

aw

ay

az

+ - + - = o (3-20)

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

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

2.

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

3.

The flow is laminar; there anywhere within the film.

4.

No external forces act on the film, so that X

5.

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

6.

There is no slip at the bearing surface.

7.

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

is

no

the

thickness

of

the

vortex flow or turbulence

=

Y

=

Z = 0.

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

(3-21a)

37

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

be found in a specialized monograph on

ThE GENERALIZED REYNOLDS EQUATION

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

aTz

( T +~ - __ d x ’i d y d z ax

aTz

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

+

(3-22b) which simplifies to

aTx

ap

- + - = ay az

ax

ZT,

aTz

- + - = ay ax

( 3-23a )

ap

az

(3-2333)

By introducing the relations for Newtonian viscosity du T

x

=

n

G

dw T z = q Z j

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

we obtain

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

from

38

Figure 3-3.

‘oLu

aLu

ap

- + - = - -

ay2 ayaz 2 2 aMi aLo -++ay2 axag

Forces acting on an element of fluid.

ax

TI

1 az

( 3-25a )

(3-25b)

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

U2 at y

=

h

we get

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

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

39

a(pu) --

a(pw)

- = -

a(pw)

ax

ay

az

(3-28)

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

a

h - g

ax

( 3-29)

Integrating with respect to g, with w gives

U at y

=

=

0 and v = 0 at

g

=

h,

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

a (ph)

U2) ax

(U, -

+

(3-3l a )

which rearranges to

+ 6ph - ( U ,

+

U2)

+

12pV

ax

(3-31b)

It can be demonstrated by an analysis of

the

journal

bearing

[71

that

h

0

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

ax

2

12p -

V

+ 12pV

R

where R i s the radius of the journal.

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

40

a

6pk - ( U , +

U2)

+

12pV

(3-32b)

ax

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

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

Tl

a2

/

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

12pv

2X

(3-33 1

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

(3-34)

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

(3-35)

SQUEEZE FILMS

3.4.

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

lh3 d p

1 2 v R d6

(3-36)

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

Q

=

v

L R nin 6

Combining these two equations and integrating we get

(3-37)

41

Figure 3-4.

Geometry of squeeze film in journal bearing.

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

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

12nnLR

El

(3-40)

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

Figure 3-5.

Cylindrical coordinate notation for squeeze film geometry.

(3-4la)

(3-41 b) dropping written as

the

by

inertial

force terms.

The equation of continuity was

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

w=--

2h3

dt

where d h / d t 3.5.

13-43) =

V.

ELASTOXYDRODYNAMIC LUBRICATION

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

43

are the two most important examples technology.

of

counterformal

configuration

in

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

Elastohydrodynamic Theory

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

- (- GI d

h 3 dp

dx

TI

TI =

f ( p )

=

6 udhz (3-44)

(3-45) 2

h = h o + - + 2R

4J

(3-46)

44

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

1

(3-47)

R2

R1

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

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

C a pdP -

=

6n0u

iz - h m ( 7)

dx

(3-49)

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

(3-50)

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

Since 4:

=

0 when p

=

0,

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

aE'

4,

(x -

4)2dn

+

conntant (3-52)

45 where

E'

2

\

El

E2

'

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

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

II

Figure 3-6.

I .

Elastic deformation of boundary and thickness of oil film.

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

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

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

(3-55)

46

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

2

P

dP

B

dx

(3-56)

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

1

dp

- =

--

ay

2 n dx

1

(2y - h )

+

- ( U2 h

-

Ul)

(3-57)

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

T

(3-58)

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

PC A ' + - + - -

3.5.2.

-

function [ 1 3 1 by

T o dp

pCg

po

quantities

no,

1 +

where the tions.

7

varia-

dT po

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

Some Elastohydrodynamic Solutions:

Line Contact

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

47

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

Figure 3-7.

Elastohydrodynamic pressure and film profile.

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

Pressure Y P Cornputing Hydrodynamic Elastic

(A)

Film Thickness

A’

(a) Low Load

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

and

48

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

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

Location on Surface, m m

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

49

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

h,

=

2.65

&0.54 Ro.34

(ll0

E'o.03 w,o.13

(3-60)

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

ess the rst the

50

7--..-.

-_

\-

Hertzian Pressure

'

\

\

\

\

\

I

1

I

0.2

0.4

0.6

0.8

1.0

Surface Location, x / x ,

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

0.125 po =

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

I

1

-2.0 -1.5

I

1

1

I

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

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

51

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

Q

6 1.0

1

I

I

I

I

1

1

-

M 0

-2.0 -1.5

-1.0 -0.5

0

1.0

0.5

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

3.5.3.

Elastohydrodynamic Solutions for Point Contact

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

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

at

(3-61)

where " = - Wl

+

"2

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

52

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

w'

R

= f(k,,

o', W',

G)

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

It

can be readily seen that

R m is less for a circular contact area

1 ) than for "line" contact between

values of ti', G and

cylinders

with

the

same

(he = effective

W'.

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

53

(b) k, = 1.25

(a 1 k, = 8

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

.

L+

lu

2 2.0 d

2ox10-6

C

;1.2 ul

$ 0.8

8

t

.%0.4 4

E o

.-

n

-2.4 -1.6-0.8 0 0.8

2

-

0

-

-2.4 -1.6-0.8 X

0

0.8

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

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

54

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

al

0.2 ; 01 1 - 1

11

-0.4-0.2

I

1

0

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

0.2

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

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

55

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

(a) In the direction of rolling

(b) Transverse to roiling direction

200

100 0 100 200 z,km

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

(3-63)

56

TABLE 3-1.

CONSTANTS FOR EQUATION 3-63

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

K

M

N

3 1.4 1.69 1.73

1 0.74 0.725 0.714

-0.33 -0.074 -0,058 -0.048

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

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

51

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

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

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

28.

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

58

29. 33. 31.

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

D. M.

59

Chapter 4 THE NATURE AND PROPERTIES OF LIQUIDS

4.1.

PROPERTIES OF LIQUIDS AND LUBRICATION

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

60

VISCOSITY AND VISCOMETRY 4.2.

NEWTONIAN AND NON-NEWTONIAN VISCOSITY

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

v

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

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

ST;^/&;

Lj

planes

in

the

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

61

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

q = 7= constant Y

i.

=

o

when

T.. =

(4-2)

o

xj

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

t

i c 0 0 c 0

a

Shearing Stress-

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

CAP1 LLARY V I SCOMETRY

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

62

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

f

i

a

l7

Flow direction)

Figure 4-3. lary.

\

. \

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

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

AP(iTh2 )

(4-3a)

APn T = - Z

(4-3b)

4.3.1.

Newtonian Flow through a Capillary

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

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

63

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

h

and using the boundary condition

0

=

M)

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

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

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

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

Bi

of

the

(4-10)

(a)

k -

Velocity-

0

R

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

relation

(b)

64

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

Non-Newtonian Capillary Flow

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

j,

= f(T) =

(1/cl)Tn

(4- 1 )

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

(4-12) where T7? =

AP z

(4-13)

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

Sub-

(4-14) When n = 1 ,

Eqn

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

n.

Velocity

Reduced Distance from Center , r / R

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

puted

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

65

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

4-14 into logarithmic form:

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

The quantity using Eqns 4-4 and

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

c, 4-11

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

Sources of Error in Capillary Viscometry

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

(1)

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

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

( 3 ) Heat effects: conversion of energy

arising

from

pressure

and

shear into heat energy. The next t icular :

four

sources

of error apply to capillary viscometers in par-

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

End

effects:

energy

losses

due to viscous o r elastic effects

66

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

liquid

adhering

to

the

leav-

walls of the reservoir and

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

one

liquid

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

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

for

certain polyphase and Bingham fluids. (10)

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

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

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

4.4. CAPILLARY VISCOMETERS

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

.

67

The Cannon-Fenske Viscometer

4.4.1.

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

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

dV =

dt

~

(4-17)

811.e

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

t

TI=-

8LW

(4-18)

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

(4-19)

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

T!

=

€LA-

no poto

(4-20)

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

(4-21)

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

68

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

Li=voG

vis-

(4-22)

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

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

69

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

cs/s

Viscosity range

Capillary diameter

llrn2s - 1

mm

(centistokes) 3 5 10 30 100 300

500 1000 3000 5000 10000 (a)

0.003 0.005 0.01

0.6-3 1-5

2-10

0.03 0.1 0.3 0.5 1 3 5

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

10 (a)

2000-10,000

6-30

20- 100

0.31 0.42 0.63 0.78 1.02 1.26 1.48 1.88

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

f f 2.20 f 3.10 f 4.0

0.02 0.02 0.05 0.05

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

.

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

Capillary Viscometry under Pressure

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

70

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

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

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

71

-546.8 -463.4 -403.4

cn

*

.In

e

327.5

-257.2 0.10

.>

-

-

203.4

-

129.6 69.0 2

0.01

.

i

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

10 t

3

’

0.01 10

lo2

lo3

lo4

lo5

lo6

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

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

72

4.5. ROTATIONAL VISCOMETRY AND VISCOMETERS

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

A

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

4.5.1.

The Couette Viscometer

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

13

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

(4-23)

or alternatively

(4-24)

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

+

At) (4-25)

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

see

that

4nl

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

[ 2

may

be

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

14

A1

I

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

(4-26)

and its average value by

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

very thin films I n such case it is easy to show that liquid; i . e . (R2 - R,)/R, > x; hence the behavior of the interface between the rubbing track and the rider will be dominated by the behavior of the lubricated asperities. As is seen in Fig. 8 - 1 2 , the displacement of surfaces lubricated with lauric acid in cetane goes over to sliding at levels of the coefficient of traction significantly lower than is observed for unlubricated surfaces. To explain why no stick is observed prior to macroscopic sliding in the boundary-lubricated case, it is postulated that shear of the lubricated asperity junctions occurs without the lag characteristic of junction growth of unlubricated asperities; i.e., in the case of adequate lubrication the contribution of the first term of Eqn 8 - 3 3 is insignificant. Hence there is no stickslip in boundary-lubricated sliding.

cs 0 .-

f : "

.-

'

0.14- Louric Acid 0.020 molol

ic Acid 0.0037 molol

60.04

1

1

1

1

1

1

1

1

1

.

Rubbing Speed, cm /s

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

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

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

SLIDING SPEED AND FRICTION

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

Since

M,

g and

K

are not zero, it follows that

pA

is

indistinguishable

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

** In

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

173

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

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

'dt2

+

dY 1-

dt

+ KY

[

= ffl5 urn +

&

(. -31

(8-35)

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

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

func-

(8-36b) m

being the maximum amplitude of vibration.

It can be shown that

VAY

(8-37

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

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

(8-38)

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

174

0.08

1

1

I

I

0.04

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

0

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

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

+

KY

=

F

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

175

0.08C

8-

0.06-

6-

c

c

c

5 4-

E 5- 0.04 -

;2-

%S 0.02 -

0.

E&

I

0

I

I

I

I

2

%?*

, D

0

0

4

2

4

Sliding Velocity v - j , cm/s

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

in

a

single

stick-slip

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

NON-ADHESIONAL MECHANISMS FOR FRICTION

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

F

&

-,

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

The plowing mechanism in friction.

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

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

176

W

A = P

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

S

=

Ah

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

F

+-

= S +

d3

P' 12h

(8-39)

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

F

=

p =

d3

- p' 12h

(8-40)

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

177

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

178

Chapter 9 LUBRICATED FRICTION

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

9.1.

THE CONTACT AND FRICTION OF CLEAN SURFACES

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

179

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

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

Adhesion coefficient before sliding

Coefficient of friction during sliding

Adhesion coefficient after sliding

Single-crystal, matched (100) planes

1.02

40

Single-crystal, matched (110) planes

0.61

40

50.0

Single-crystal, matched ( 1 1 1 ) planes

0.30

21.0

10.5

Polycrystalline

1 .oo

40

130

100

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

180

TABLE 9-2.

COEFFICIENTS OF FRICTION IN VACUUM

Rider

Platen or disk

Iron (a)

Iron

2.2

-_---

Nickel (b)

Nickel

0.5-4

1.33 x

Platinum (b)

Plat i num

0.6-4

1.33 x

Silver (b)

Silver

0.4-3.5

1.33 x

Copper (c)

Copper

3.0

Copper (c)

Copper

4.0-5

Copper (c)

Copper

Copper (d)

Nickel

4.0

1.33

Copper (d)

Cobalt

2.00

1.33

Copper (d)

Tungsten

1.40

1.33

Cobalt (d)

Cobalt

0.35

1.33

Co-50/Fe alloy (e)

Co-50/Fe

1.2-1.3

1.33

Co-25/Mo-lO/Cr

Co-25/Mo-lO/Cr

0.25

1.33

(e)

Coefficient of friction

15

Vacuum, Pa

399 665-1330 x lo-’ 795-1330 x

lo-’

IO-’

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

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

181

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

Adhesion coefficient before sliding

Coefficient of friction during sliding

Adhesion coefficient after sliding

Copper (111) on copper (111)

0.30

21 .o

10.5

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

0.25

4.0

2.0

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

0.10

2.0

0.5

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

4 ) , the thermocouple must be located precisely because of the magnitude of the temperatures as well as the steepness of the gradient. The temperature gradient with a stationary source is not linear either, as inspection of Eqn 15-10 indicates.

441

Dimensionless Distance Z

Figure 1 5 - 1 0 . Penetration of heat from the interfacial rubbing into the moving body as calculated from the temperature analysis. by J. C. Jaeger 1 2 1

area Data

M. Furey 1 1 6 1 carried out a direct experimental comparison of the temperatures measured by the dynamic thermocouple technique with the temperatures indicated by an embedded thermocouple located 0 . 0 2 5 cm from the rubbing interface of a constantan ball sliding on a rotating steel ring. The temperatures sensed by the dynamic thermocouple were higher than those of the embedded thermocouple; as the dynamically measured temperature increased, the proportionate lag in the temperature by the embedded thermocouple became greater. A. Cameron and his co-workers studied the use of embedded thermocouples in the determination of the temperature in an oil film between two disks rotating with different peripheral velocities. The theory of a moving heat source was adapted to the analysis of this particular problem [18]; the experimental work is described by O'Donoghue and Cameron 1 1 9 1 and by O'Donoghue, Manton and Cameron [ 2 0 ] . The problem is a difficult one and the degree of confidence in the results has considerable bearing on understanding the effect of temperature on fluid film failure in the lubrication of gears. The reader can consult the original work f o r deta i 1s.

15.2.3.

The Strip Thermistor

Strip thermistors are used to scan the temperature profile of an elastohydrodynamic contact in a fashion analogous to the scanning of a The early pressure profile as described in Chapter 3 , Section 3 . 5 . 4 . ones were adaptions of platinum resistance thermometers made by painting a thin, narrow strip of platinum powder suspended in a carrier across the width of a glass disk and then firing in a furnace to burn off the

448

vehicle. Characteristic dimensions are 35-37 pm wide and 0 . 1 vm thick [211. The thermistor, of course, requires an electrically insulated backing: hence the glass disk. Hamilton and Moore [22] used nickel a s the thermistor element. Kannel and Dow employed titanium on quartz and also described a method for sandwiching the thermistor between two insulating layers of silica or alumina for use on a steel disk 1231. A bisignal transducer on a steel disk for the simultaneous measurement of temperature and pressure is described by Kannel, Zugaro and Dow [24]. The signal issuing from the thermistor is amplified and displayed on an oscilloscope whose sweep time is synchronized with the passage of the strip through the conjunction between the disks. The results’ obtained by Kannel, Zugaro and Dow for the temperature profile with the bisignal transducer [ 2 4 1 show good parallelism with the pressure profile, the temperature peak being very close to the pressure peak. Cheng and Orcutt [21] reported that the temperature rise they observed was only about a third of the value calculated by elastohydrodynamic theory and that there were also differences between the shape of the experimental and the calculated temperature profile. In view of the work of Kannel e t u L . 1241, it seems likely that measurements with improved modern techniques will agree better with calculations from theory. However, the thickness and width of the thermistor relative to the thickness of the lubricant film and the dimensions of the conjunction constitute a fundamental uncertainty in the measuring system. 15.2.4.

Emission of Infrared Radiation

I t is a familiar fact that the radiation emitted by heated bodies characteristically lies in the infrared region of the spectrum. The ideal emissive behavior of a radiating source is that of the theoretical black body. By the Stefan-Boltzmann law the emissive power, i . e . the rate at which energy is radiated per unit area of radiating surface, is proportional to the fourth power of the absolute temperature of the radiating source. The emissive power of a real body is a constant fraction of the emissive power of the black body at the corresponding temperature, the constant of proportionality being characteristic of the particular substance. Details of the theory of the emission of infrared radiation can be found in the standard physics texts and in specialized monographs 125, 261.

If the infrared radiation from an emitting body can be captured and transduced into a usable signal, it can be made the basis for measuring the temperature of the emitting surface. Such a method is particularly attractive for the measurement of the temperature at a rubbing interface, since it does not require the insertion of a probe which might introduce a major perturbation into the system. However the method does require that the behavior of the system obeys the Stefan-Boltzmann relation

449

within the limits of experimental error, since calibration is carried out by comparison with an emitting surface at a known temperature. There are also ccmplications of technique, in particular knowledge of the cmissivity of every surface that contributes to the radiant energy received by the instrument and access of the instrument to the rubbing interface.

Photoconductive materials such a s lead sulfide, lead selenide or indium antimonide, which respond to incident infrared radiation by changing their electrical resistance, are used as the sensing elements in instrumentation for radiometric measurement of temperature. Bowden and Thomas [ 2 7 ] measured t h e temperature of "hot spots" in the sliding of a metal rider against a glass disk with a lead sulfide cell in the arrangeA glass disk was used because the ment illustrated in Fig. 15-17.

Figure 15-11. Measurement of "hot spot" temperatures at the rubbing surface with a lead sulfide photocell. A : Glass disk. B: Metal slider. C: PbS photocell. D: Brass shield. E: Chopper. After Bowden and Thomas [271.

countersurface must be transparent to the radiation generated at the interface. Caiibration is effected by means of a fixed filter; another technique is to use a chopper in conjunction with selectively placed filters. Bowden and Thomas studied the rubbing of sliders of steel, constantan and invar. Maximum hot spot t mperatures ranged from 773 to 1323 K (500-1050 C). The temperatures obse ved for a gold-aluminum alloy with a bulk melting point of 643 K (570 C did not exceed 873 K (600 C ) even at the highest loads and speeds, which was taken to be an indication of the reliability of the method. Some individualistic characteristics of the dry rubbing of metals on glass have been reported by Heighway and Taylor 1 2 8 1 . The temperature at the rubbing interface of two opaque solids can be measured by the use of a "peep hole" through which the detector sights on the rubbing surface. This technique was employed by Reichenbach [ 2 9 ] to measure the shear-plane temperature in orthogonal metal cutting (planing) and by Chao, Li and Trigger I301 for the flank temperature in orthogonal turning, using a lead sulfide detector. Deyber and Godet [31] described r h e measurement of the interfacial temperature generated by the lubri-

450

Running Time, minutes

Figure 15-12. Temperatures at the rubbing interface by infrared emission viewed through a peep hole. T : Contact temperature at interface by infrared emission. u: Coefficient of friction. Thermocouple temperatures: T B , block; T R , ring; T F , , oil film impinging on ring; T F 2 , oil film near conjunction; T F , bulk temperature of the oil stream. After Deyber and Godet 1 3 7 1 . cated rubbing of a block against a rotating ring with a lead sulfide cell which viewed the rubbing interface and a reference surface alternately through a peep hole in the ring. Figure 15-12 shows the results they obtained. The close parallelism between the coefficient of friction and the surface temperature indicates that the source of the temperature was the rubbing. Other temperatures, measured by thermocouples, were substantially lower and were much less sensitive indicators of the action of friction in generating temperature. The elegance and power of the infrared emission method is exemplified by the work of W. 0. Winer and his collaborators on surface temperatures in elastohydrodynamic lubrication. The techniques are described by Turchina, Sanborn and Winer [ 3 2 ] and Ausherman, Nagaraj, Sanborn and Winer 1331. The oil film was generated by rotating a steel ball under load against a flat, polished sapphire plate. The geometry of the interface and the oil film was monitored by optical interferometry essentially as described in Chapter 6, Section 6 . 2 . The radiation collected by the objective of the microscope viewing the interface was split between an eyepiece for the visible wavelengths sent to the interferometer and an indium antimonide detector cooled by liquid nitrogen for the infrared emission, thus enabling the temperature data to be oriented with respect to location in the interface. The infrared radiation comes from four sources: I,, the intensity due to reflected background radiation; I,, due to emission from the sapphire; 'I,,, due to emission from the ball; and 1 6 , due to emission from the lubricant film. Attenuation factors y reduce the intensity actually incident on the objective of the microscope, as shown in the diagram of Fig. 15-13. With suitable calibration and techniques the system can be

451

Figure 1 5 - 1 3 . Sources of infrared radiation emitted from a system posed of an oil film between a sapphire plate and a steel ball.

com-

0.20 E E- 0.15

tJ E 0.10

c

0 c

g

0.05

c

s 0.00 c

al

2

0.10

0 c

8

0.15

0.20

BALL OIL FILM Figure 1 5 - 1 4 . Temperature field on the ball surface and in the oil film as measured by the emitted infrared radiation. After Ausherman, Nagaraj, Sanborn and Winer 1 3 3 1 .

operated to yield separate data for the temperature of the oil film and the average temperature of the ball surface. Figure 1 5 - 1 4 shows typical plots of the temperature field on the ball surface and in the lubricant film. The isotherms for the ball surface are systematically spaced; those for the lubricant film are somewhat irregular and exhibit localized hot spots, particularly at locations where the optical interferograms indicate a thinning of the lubricant film. The resolving power of the detector is an area 38 um in diameter, as shown in the diagrams. Figure 1 5 - 1 5 shows the temperature profiles of the ball surface along the center line in the direction of sliding. The temperature in the film and on the ball surface is generated by the compression and the viscous shear of the lubricant as it passes through the conjunction gap. Ball surface temperatures were found to increase systematically with in-

452

180 160

@ I00 3

E 80

4-

60

I I

I-

.-E

I

40

LL

I )

0.2

0.1 0.0 0.1 Distance from Center,mm

0.2

Figure 1 5 - 1 5 . Temperature profiles on the ball surface and in the oil film along the center line in the direction of sliding by infrared emission. After Ausherman, Nagaraj, Sanborn and Winer [331.

2oo

f

I

I

k

0 Average -Calculated

I

1

I

I

I

I A

175

4 150 -

25 5 0 75 100 125 150 175 200 Calculated Temperature, degrees C Figure 1 5 - 1 6 . Comparison of calculated lubricant temperatures with experimental values obtained by infrared emission. Data by Nagaraj, Sanborn and Winer [ 3 4 1 .

453

crease of load or rubbing speed: a similar general trend was observed for Interfatemperatures in the lubricant film, with some irregularities. cial temperatures tended to rise with increased surface roughness, particularly i f some of the asperities penetrated the oil film and caused even the slightest wear [341. The interfacial temperatures were at a minimum for pure rolling of the ball against the sapphire plate and rose sharply with increasing ratio of sliding to rolling, with maxima for pure sliding [35]. The temperatures in the high-slip domain with the ball as the stationary surface were higher than those with the ball as the moving surface. The work of Winer e t aL. with smooth steel balls and sapphire flats is probably the best experimentation available to date for testing the applicability of continuum heat conduction theory to a tribological situation. The interface between the heat source in the lubricant film and the contact area on the ball is as close to an ideal interface as one can reasonably expect to achieve. Figure 15-16 shows the comparison Nagara), Sanborn and Winer 1341 made between experimentally measured temperatures and those calculated by Archard's adaption [ 3 1 of Jaeger's treatment [Z]. The agreement of the average measured temperatures with the average calculated temperature is quite good, especially at the higher pressures. Measured peak temperatures are higher than the, calculated ones. The use of the infrared emission method in the far from ideal circumstances prevailing in an operating spiral bevel gear set is described by Wymer and Macpherson 1361. The highest temperature rise of the tooth surface above that of the bulk oil ( 8 0 - 9 0 C) was found to be 50 C. 15.3.

AMBIENT TEMPERATURE EFFECTS

The implicit assumption in the tribological temperature calculations discussed in Section 15.1 is that the initial temperature of the rubbing interface is arbitrarily selected as zero. But in practice the rubbing interface has a real, finite value to which the tribologically generated temperature is added as an increment. Furthermore, there is an ambient environment with which the rubbing system interacts and temperature is one of the components of the environment that participates in the interaction. Therefore an examination of the mutual influences of the ambient environment and the rubbing interface is manifestly in order. I n controlled experimentation the temperature of the environment can be manipulated externally so that its influence dominates what is observed macroscopically. Thus in an experimental study of oil film thickness between two rolling/sliding bodies, the bulk oil temperature can be fixed by thermostatic means, and i f the bodies are immersed in the oil, their bulk temperature will be fixed also. The temperature field in the oil film as it passes through the conjunction and the surface temperature

454

of the disks will be the resultant of the various dynamic actions we have studied. To control a given experiment we could, for instance, establish an empirical relation between the minimum oil film thickness in the conjunction and the bulk temperature of the oil and vary that temperature to suit our requirements. This is the thinking that governs many of the experiments on the response of friction to temperature in the presence of "boundary" lubricants. Usually the slider is a body of small mass and restricted conjunction area, while the counterbody has a large mass and surface area. The lubricant layer is very thin, often only a monomolecular film, s o that effectively the temperature of the experiment is that of the counterbody. Cases arise in which the thermal contribution of the rubbing action to the bulk temperature of the ambient lubricant is significant. In many such instances temperature probes in the bulk oil or in the mass of the rubbing specimens indicate a steady-state condition when operating parameters such load or speed are held fixed. The macroscopic temperature behavior of the system is the balanced resultant of heat input from the rubbing interface and heat loss to the surrounding atmosphere and to the mass of those parts of the experimental device which, although not considered part of the ambient environment, are not part of the rubbing system either. An example of such a situation is the four-ball lubricant test, where the volume of oil is small relative to the mass of the four rubbing specimens. Such systems are very sensitive to thermal upset by scuffing, incipient seizure, or an increase of wear rate. Figure 15-17 illustrates diagrammatically the complexities of heat flow and temperature differences in a gear system as typically encountered in technological practice. The sources of heat that can raise the temperature of the bulk lubricant in the gear case are the following: ( A ) shear of the oil film at the gear tooth contact; ( B ) churning of the bulk oil in the gear case; ( C ) shearing and churning of the oil in the bearings; (D) heating of the oil film at the seals; ( E ) miscellaneous external sources. There are fifteen pathways by which heat can be transmitted from one part of the system to another. Not all of them may be operative in a particular case: there must be a temperature difference for heat to flow, and whether such a difference exists for two given locations depends on the individual circumstances. For example, i f the main source of heat to the bulk oil in the gear case comes from friction at tooth contacts, then part of the temperature rise in the bulk oil will be by pathway F (direct mass transport) and part by pathways G and H (conduction into the bulk of the gear, conduction out of the gear and mass transport by stirring of the oil). Whether a steady-state equilibrium is established in the bulk oil depends on the magnitude of the heat losses out of the oil and the gear case by the other pathways shown

455

Drive 4 R

C

I

dJ

4~

-

d S

Casing

Air and near-

by surfaces t

I

I1

l--l

0 Mounting

Figure 1 5 - 1 7 . Block diagram of the thermal flow in a lubricated gear and bearing system. Heat sources.-A: oil film at tooth contact; B: churning of bulk oil; C : oil film in bearings and bulk churning; D: oil film at seals; E: external sources. Heat transmission.-F: m; G: c; H: c , m; I: c; J: f; K: m; L: f; M: f; N: m; P: f; Q: c , f , r; R: c; S : n, f , r; T: c. c = conduction; f = forced convection; m = mass transport: n = natural convection; r = radiation. TABLE 15-4.

DISTRIBUTION OF HEAT LOSSES IN OPERATING GEAR UNITS

Type of gear unit

%

of heat generated

Tooth losses

Bearing losses

Seal

losses

Lubricant churning

Oil dip-lubricated, single-reduction worm gear, 1 5 0 0 rpm input

78

17

5

6

Oil dip-lubricated, double-reduction spur gear, 1 5 0 0 rpm input

29

13

0

50

Spray-lubricated, single-reduction helical gear (plain bearings), 1 5 0 0 rpm input

18

69

0

13

Spray-lubricated, single-reduction helical gear (tapered roller bearings, 1 5 0 0 rpm input

56

31

0

15

From data by Bathgate, Kendall and Moorhouse 1371.

in Fig. 15-17. Table 15-4 summarizes some estimates of the sources of heat flow For a into the bulk oil supply of operating reduction gear units [ 3 7 1 . worm gear unit the major contribution is from tooth rubbing, a s would be expected from the intrinsic nature of worm gear action, and hence in assessing sources of temperature which might influence lubrication failure, greater weight would be given to the direct action of heat generated at tooth contact than to the other contributions to the bulk temperature of the lubricant. But in the case of a spur gear unit, 71% of the heat input into the system comes from bearings, seals and churning. In a helical gear unit the major source of heat loss is shifted from the bearings to tooth contact by changing from plain bearings to rolling element bearings. It is not uncommon for external sources to furnish the major heat input to a lubricated system. For example, an oil sump may be exposed to the natural temperature of a hot environment such as a furnace room or the conducted heat of an internal combustion engine. I n the design of a lubricant system subjected to such influences, usually provision is made f o r forced cooling. But often the cooling facilities are limited by circumstances, and the lubricant perforce must function in a hightemperature environment. The study of lubrication in the ambient environment of high temperature may have as its direct objective whether o r not the lubricant will perform satisfactorily in this environment. However, the imposition of high-temperature environmental conditions is frequently used in bench testing to induce a transition from satisfactory performance to lubrication failure (scuffing, seizure, high wear, high friction, etc.). The critical imposed environmental temperature is reported a s the transition temperature for lubricant failure. The reader should be aware of potential complications in such an interpretation. The thermal influences of significance for lubricant failure operate at the rubbing interface, whereas temperature increases supplied externally are superposed grossly on the ambient temperature of the rubbing parts. Fast thermal feedback from the tribological events at the rubbing interface into the bulk of the lubricant will result in a different macroscopic temperature than i f the feedback is sluggish.

15.4.

EFFECTS OF TEMPERATURE ON FRICTION AND WEAR

A large proportion of the observations on the effect of temperature on friction and wear is empirical, and though the results may be of practical utility they afford n o insight into the basic reasons for this behavior. On the other hand, data such a s are seen in Fig. 15-18 [ 3 8 ] not only show observed behavior a s a response to temperature but have inter-

457

2.2

I

i

i

2 “0 1.8 1.6 C

2

1.4

0

5

1.2

0

E0, 1.0 .-

0

5 0.6

0”

0.6

0.4 0.2

0 300

400 500 600 Temperature, degrees K

Figure 15-18. Response of friction to ambient temperature. (a) Silver on silver, dry. (b) Silver on silver, lubricated by white o i l . (c) SAE 5 2 1 0 0 steel on SAE 4140 steel, dry. (d) SAE 5 2 1 0 0 steel on SAE 4 1 4 0 steel, lubricated by white oil. (el SAE 5 2 1 0 0 steel on silver, dry. (f) SAE 5 2 1 0 0 steel on silver, lubricated by white oil. From data by D. Godfrey 1381.

C

I-

Friction----

-------

r” 10-3

1.0

0

0.6 E 0.4 0.2 E 0.1

.Q

300 400 500 600 700 800 90C 000 Temperature, degrees K

Figure 1 5 - 1 9 . Effect of external ambient temperature friction of 6 0 / 4 0 brass sliding against tool steel. Lancaster [391.

a, 0

V

on the wear and From data by J. K.

458

pretations in terms of mechanisms as well. The strong upturn in the dry friction of silver against silver can be attributed to temperaturepromoted adhesion, and the strong thermal influence on lubricated friction can be ascribed to film breakdown. The much lower friction when hardened steel slides on silver is associated with a decrease in adhesion; the minimum at c a . 573 K (300 C) represents a balance between the The counteracting influence of temperature on plowing and on adhesion. influence of lubrication is not prominent in this case but becomes more pronounced when hard steel slides on hard steel. The sharp drop in the coefficient of friction for lubricated silver on silver and for lubricated steel on steel at the high-temperature end of the diagram could be the consequence of chemical action involving the lubricant. Chemical activity is the explanation for the wear and friction behavior shown in Fig. 15-19 [391. The data were obtained by the low-speed sliding of brass against tool steel ( 1 . 1 cm/s) so that the temperature of the rubbing interface was dominated by external ambient heating and the contribution from frictional heating was relatively minor. The wear rate of the brass rider decreased by two orders of magnitude a s the ambient temperature increased from 573 K (300 C) to 673 K (400 C); at 673 K the This behavior was coefficient of friction showed a sharp upward jump. correlated with the rate of oxidation of the film of brass.which was transferred to the tool steel ring in the wear process. If the rate of transfer is not inhibited by oxidation, then the wear particles are mostly metallic and the rate of wear is high. Oxidation of the transferred film changes the wear debris to small, unagglomerated particles of oxide and the wear rate decreases. The role of temperature in the process is obvious. However, when loads and rubbing speeds are high, the situation hecomes more complicated, although basically the effect of temperature on oxidation remains the same [401. The influence of temperature is especially significant in lubricaI n the tion, particularly i n the breakdown of lubricating action. descriptive literature the overt behavior associated with lubrication failure is usually designated as "scuffing." The difficulty of assigning a single-valued meaning to the term ACU66,inCj was discussed in Chapter 13, Sections 13.4 and 13.6, and this difficulty ccmplicates the study of temperature effects, which are strongly conditioned by the experimenter's criteria for scuffing. For example, H. Blok, a pioneer in the development of a quantitative temperature theory of lubricant failure [41], used the behavior of steel specimens in the I. A . E. spur gear rig a s the basis of his postulate Of a constant temperature of incipient scuffing [421. However, the concept is claimed to be valid only for lubrication by uncompounded mineral oils. The critical scuffing temperature was found to be responsive to the viscosity of the lubricant: 403-433 K (130-160 C ) for an oil of 7 cs at 60 C , 493-573 K (220-300 C) for an oil

459

of 1 5 0 cs at 60 C [ 4 2 1 . The basic mechanism of the critical temperature concept

is

simple.

Lubrication failure is envisioned a s occurring at the conjunction of the rubbing surfaces, and it is the critical temperature at this conjunction that controls the lubricating action. This temperature, T c , is made up of T,, the bulk temperature of the macroscopic rubbing specimens, and T 6' the added "flash" temperature generated by rubbing, which can be calculated by methods such as are presented in Section 1 5 . 1 . 2 ( e . g . Eqns 1 5 - 2 7 and 1 5 - 2 8 ) : Tc = T,

+ T6

(15-43)

Operating parameters such as load and rubbing speed, which according to theory systematically influence the frictionally generated flash temperaBut the ture, affect scuffing through the difference between T c and T,. analysis of real-life cases is more complex than this, and observed behavior is complicated further by the introduction of factors such as temperature-influenced changes in the properties of materials, surface contact conditions, etc. Hence, though the critical temperature concept seems valid in principle, a s of now it has not been tested enough to assess its practical utility thoroughly. Leach and Kelley 1 4 3 1 carried out an extensive test of the Blok hypothesis with an apparatus whose rubbing specimens were differentially rotating disks in contact on their cylindrical surfaces. The reading of a small thermocouple riding on the oil film at the inlet of the conjunction was taken as the value of T c ; the value of T d was calculated from the relation v;'5)

(15-44)

where u is the coefficient of friction at the conjunction, is the load in lbs force per inch of contact conjunction width, V 1 and V 2 are the peripheral velocities of the disks in inches per second, and 1 . 3 0 is a constant determined from the physical and thermal characteristics of the disk material and disk geometry. Scuffing (which Leach and Kelley called "scoring") was determined by the condition of the disks a s observed at the end of the test and by the sudden loss of electrical resistance across the conjunction. The latter observation leads to the conclusion that scuffing under these circumstances is the consequence of the breakdown of the oil film. Broadly, Leach and Kelley found the Blok critical temperature hypothesis to hold for three uncompounded mineral oils with viscosities ranging from 4.80 to 1 5 . 0 0 c p at 3 7 2 . 0 K ( 2 1 0 F ) and a compounded engine oil, 4 . 6 0 c p at 3 7 2 . 0 K; the average critical temperature for scuffing was 6 3 9 K ( 3 3 6 F), with an average deviation of 2 3 3 degrees K ( C 6 0 degrees F). This much deviation is a serious disadvantage for the

460

practicai utility of the critical temperature criterion, but it is not large enough to invalidate the differences Leach and Kelley found between Tc as calculated by Eqns 15-43 and 15-44 and and the measured values of T..) over the range of their experimental conditions. contradistinction to the viscosity effect reported by Blok [421, Leach and Kelley's critical temperature was not influenced by the viscosity of the lubricant; however, the range of viscosity for Leach and Kelley's oils was smaller than that of Blok's. A comparison of the two sets of results with respect to the range of experimental uncertainty is given in a discussion by Blok appended to Leach and Kelley's publication In

[431.

The constant critical scuffing temperature observed by Leach and Kelley may be the fortuitous consequence of a limited range of operating parameters in testing. Working with a similar two-disk machine, R. S . Fein [441 found the critical scuffing temperature to be affected by experimental details such as the break-in procedure, the magnitude of the load steps in the testing sequence, the spindle velocity of the machine, and the rubbing ratio of the specimens. Selected data are shown in Table 15-5 for squalane (2,6,10,15,19,23-hexamethyltetracosane), viscosity 4.19 cs at 2 1 0 F , and in Table 15-6 for a solvent-refined mineral oil, viscosity 5.09 cs at 2 1 0 F. Influences that prolong the duration of the test allow the base temperature of the disks to increase; among such influences are the break-in procedure, which conditions the surfaces of the disks, the load increments and the rubbing speed. The higher the scuffing load, the greater the frictional energy generated at lubricant failure and the greater the increment contributed to the conjunction temperature by the flash temperature. The conjunction temperature was computed by the formula (15-45)

where N is the spindle speed in rpm, W is the applied load in lbs force and v is the rubbing ratio of the two specimen disks. This is Blok's flash temperature equation adapted to these particular experimental conditions; the numerical coefficient 9.5 takes care of the material properties, geometry of the specimens, etc. Fein's evidence shows that the condition of the rubbing surfaces has a crucial effect on the scuffing load and the associated critical scuffing temperature, which accounts for the influence of the break-in procedure and the duration of the test proper. The observed cases of constant critical scuffing temperature for certain types of lubricants implies a rigorously standardized break-in and testing procedure. Niemann and Lechner 1451 investigated surface temperatures of gear teeth with respect to scuffing. This problem is complicated by the

461

T?.BLE 1 5 - 5 . CRITICAL SCUFFING TEMPERATURES FOR ROLLINGSLIDING STEEL DISKS LUBRICATED WITH SQUALANE Run-in Spindle Load Scuff Disk temperConjunction procedure speed in increment, load, lbs ature at scuff, temperature at test, rpm lbs deg. F scuff, deg. F A B None A B (a) A (b) B

425 425 850 850 850 850 1280 1280 1280

65 26 65 65 65 65 65 26 26

1080 2210 300 620 690 1210 360 600 880

129 182 92 114 109 163 102 114 103

402 590 313 320 323 552 307 372 37 1

Test r u n s : 2 minutes at each load increment. Bulk oil temperature held at 6 5 ? 5 F. Run-in procedure: rubbing ratio/rpm/minutes at l b s load. A: 1 . 5 0 / 8 5 0 / 1 0 @ 1 1 4 3 , 5 min 0 1 7 9 3 , 1 5 min 4 2 4 4 3 . B: 1 . 5 0 / 4 2 5 / 1 0 @ 1 1 4 3 , 5 min 4 1 7 9 3 , 1 5 min @ 2 4 4 3 ; then 2 . 6 0 / 4 2 5 / 5 @ 2 3 3 , 5 min @ 6 2 3 , 5 min @ 7 5 3 , 10 min 4 8 1 8 . (a) 1 . 5 0 / 4 2 5 / 1 0 @ 1143, 5 min @ 1 7 9 3 , 15 min 4 2 4 4 3 ; then 2 . 6 0 / 4 2 5 / 5 @ 2 2 3 , 5 min @ 4 9 3 , 5 min @ 6 2 3 , 5 min 4 7 5 3 , 4 0 min @ 818.

(b) 1 . 5 0 / 4 2 5 / 1 0 4 1 1 4 3 , 5 min 4 1 7 9 3 , 1 5 min 4 2 4 4 3 ; each 4 2 4 4 3 1 b s / 6 4 0 , - 8 8 0 , - 1 2 8 0 rpm. From data by R. S. Fein [ 4 4 1 .

then,

5 -min

TABLE 1 5 - 6 . CRITICAL SCUFFING TEMPERATURE FOR ROLLINGSLIDING STEEL DISKS LUBRICATED WITH MINERAL OIL Run-in Spindle Load Scuff procedure speed in increment, load, lbs test, rpm lbs C

425

65

B

425

65

B

425

26

C

1280

65

C

1280 1280 1280 1280

26 65 65 26

1210 1340 1530 1660 > 2 5 10

Conjunction Disk temperature at scuff, temperature at deg. F scuff, deg. F 114 136 151 153 >175

322 432 500 473 >499

67 89 102 94 170 >236

273 293 326 322 603 >776

(no scuff)

C' B B

230 360 360 430 1340 21420

( n o scuff) Test runs: 2 minutes at each load increment. Bulk oil temperature held at 6 5 ? 5 F . Run-in procedure: rubbing ratio/rpm/minutes at lbs load: 4 1 1 4 3 , 5 min 4 1 7 9 3 , 15 min @ 2 4 4 3 ; then B: 1 . 5 0 / 4 2 5 / 1 0 2.60/425/5/ 0 2 3 3 , 5 min 4 6 2 3 , 5 min 4 7 5 3 , 10 min 4 8 1 8 . C: 2 . 6 0 / 4 2 5 / 1 0 4 7 4 , 5 min 4 2 3 3 . C': 2 . 6 0 / 4 2 5 / 1 0 @ 7 4 , 20 min 4 2 3 3 . From data by R. S . Fein [ 4 4 ] .

462

functional relation of velocity to the location of contact on the tooth profile and by the division of contact between two adjacent pairs of teeth when the rubbing velocity at one pair is higher. Two material combinations of alloy steel lubricated with a formulated gear oil were Cr, VHN tested for scuffing. For one combination (1.25% Mn:1.15% 718-803, against 12% Cr:13% Ni, VHN 196) the measured surface temperature at incipient scuffing was 451 K (178 C ) as against 499 K (226 C) computed from flash temperature theory. With a harder combination (1.25% Mn:1.15% Cr against 1.1% Cr:4.5% Ni, VHN 5851, the measured critical surface calculated 718 K (445 C ) . Ishikawa, temperature was 623 K (350 C ) , Hayashi and Yokoyama 1461 carried out similar tests on spur gears of chrome-molybdenum steel, VHN 642-657, lubricated with uncompounded mineral oil. Scuffing temperatures were found to lie in the range 623-673 K (350-400 C). Using a slow-speed technique (0.04 cm/s) with the four-ball machine, Matveevsky [471 observed a critical seizure temperature of 423 K (150 C ) for the pure sliding of hardened alloy steel on hardened alloy steel. Due to the extremely slow sliding speed, the contribution from interfacial rubbing was negligible so that the effective temperature was that of the bulk oil. Hydrodynamic effects were eliminated from consideration at such slow sliding speed and the the onset of scuffing was governed principally by temperature. For softer metals, where plastic deformation can be an important influence on the true contact area, the critical temperature was found to fall off at higher loads. Bailey and Cameron [481, using the slow-speed technique with a modified four-ball apparatus and stainless steel specimens, observed a 423 K (150 C) scuffing temperature with white oil as the lubricant. With hardened AISI 52100 steel rubbing on stainless steel lubricated with white oil at the higher speed of 185 cm/s, a conjunction temperature of 453 (180 C) was observed at scuffing. On the other hand, Fein's [491 extensive study of transition temperatures and scuffing in pure sliding with the four-ball machine showed the same type of response to the velocity/load ratio that he found with the two-disk machine 1441. The sliding speeds ranged from 0.0002 to 68.6 cm/s, the loads from 19.6 to 88.2 N (2-90 kg). Two kinds of steel specimen sets were used: hardened A I S I 52100, diamond pyramid hardness 740, and heat-treated AISI 4140, hardness 270. There were 13 di.fferent lubricants, with the properties shown in Table 15-7. At low rubbing speeds the interfacial flash temperatures were negligible and the bulk temperatures of the lubricant were taken to be the transition temperatures. At speeds above 0.359 cm/s a particularized form of the flash temperature equation was used to calculate the contribution from interfacial rubbing to be added to the bulk temperature to obtain the transition temperature. A s shown in Fig. 15-20, the results cluster around a

straight

line

463

TABLE 15-7.

LUBRICANTS USED IN STUDY OF TRANSITION TEMPERATURES

Lubricant

Cetane Squalane Paraffin wax Dinonylnaphthalene Stearic acid, commercial Stearic acid, pure White oil Mineral oil Mineral oil Mineral oil Bright stock 0 . 4 3 % Pure stearic acid in cetane 0 . 4 3 % Pure stearic acid in squalane

Viscosity

Symbol (Fig. 1 5 - 2 0 )

Pa-s at 309.0 K

Pa-s at 372.1 K

0.00232 0.0165 0.0100 1.632 0.026

0.00087 0.00323 0.00289 0.0221 0.0051

0.0642 0.0186 0.0274 0.213 0.666 0.00232

0.00645 0.00354 0.00425 0.0154 0.0288 0.00087

0.0165

0.00323

on 5 2 1 0 0 steel

on 4 1 4 0 steel

it, d X

Data by R. S. Fein 1491.

Figure 15-20. Dependence of transition temperature on viscosity lubricant, rubbing speed and load. From data by R. S. Fein [ 4 9 1 .

of

464

representing the reciprocal of the transition temperature (in degrees Kelvin) as the inverse function of the parameter l o g ( q V / W ) . In some instances the fit of the data to this relation is excellent, as for example the case of 0 . 4 3 % stearic acid in cetane tested in a pin-on-disk machine with specimens of AISI 4 1 4 0 steel [ 5 0 1 and on a four-ball apparatus with Similar bespecimens of either AISI 5 2 1 0 0 or AISI 4 1 4 0 steel [ 5 0 , 5 1 1 . havior was observed with a light solvent-refined mineral oil. Rather than a simple response of the durability of the oil film to interfacial temperature, Fein sees the critical transition temperature as the result of competing influences such a s lubricant viscosity, true pressure at asperity contacts, duration of contact between asperities, chemical interactions at asperity contacts, etc. When chemical activity is minimal, the other influences affect the manner in which a thick film of lubricant (as distinguished from a monomolecular film) is trapped and squeezed out between interacting asperities. The critical transition temperature does not depend on the behavior of the lubricant alone. Fig. 1 5 - 2 1 shows the relations found by Fein, Rowe and Kreuz [ 5 0 1 between the critical temperature and the speed/load ratio for specimens of AISI 4 1 4 0 steel, copper and silver, lubricated by 0 . 4 3 % stearic acid in cetane.

Transition temperatures for various metals in pin and disk Figure 1 5 - 2 1 . experiments. Lubricant: 0 . 4 3 % stearic acid in cetane. From data by Fein, Rowe and Kreuz [ 5 0 ] .

15.5.

EFFECTS OF TEMPERATURE ON LUBRICATION AND LUBRICANTS

I n the discussions of the preceding section the breakdown of lubrication and the onset of scuffing at the critical temperature was accepted as an empirical fact, wirh little inquiry into the details of how and why temptrature should affecE the lubrication process. True, given

465

such parameters as the geometry of the rubbing interface, the speed of rubbing, the loading, the viscosity and other appropriate properties of the lubricant, one can calculate the temperature at which a hydrodynamic or elastohydrodynamic oil film will become so thin that it will not separate the rubbing surfaces effectively. But the interaction of temperature and lubricant goes beyond the stability of the fluid film. Consider the thermodynamic approach to the lubricating action of an adsorbed film of boundary lubricant ( c d . Chapter 10, Section 10.4.3) as given by the relation R

7

(15-46) where 4 is the fractional coverage of the rubbing surface by the boundary lubricant additive, C its concentration in the carrier oil, AH' and AS' are the standard heat and entropy of adsorption respectively, and R is the thermodynamic gas constant. The critical temperature, T c , is in degrees Kelvin. I f it is observed empirically that t n C is a linear function of l/Tc,

tn C

=

- KT/Tc

+

K'

(

15-47)

then. for Eqns 15-46 and 15-47 to be equivalent, + / ( l - 4 ) as well as AH' and AS" must be constants. Also, the carrier oil must not compete with the additive for adsorption sites on the surface. These are the formal requirements to be met i f the thermodynamic treatment of transition temperatures is to be strictly valid. I n practice, the variance in A H ' , AS' and @/(l - 4 ) that can be tolerated is determined by the limits of experimental precision. However, the real adsorption of boundary additives on metal surfaces frequently departs from the simple behavior to which Eqn 15-46 applies. For example, Spikes and Cameron [521 found that the adsorption of noctadeylamine from cetane onto stainless steel powder was not completely reversible, and they were therefore force to settle for the isosteric heat of adsorption, y h t , from the equation

(

15-48)

where the subscript r defines the extent of surface coverage by the adsorbate. Equation 15-48 therefore defines a family of straight lines for given surface coverages r . At low temperatures (+'

Data by Andr6 and O'Neal [ l l ] .

in dewaxed lubricating oils are branched, with situated near the end of the pr ncipal chain.

the

branches

short

and

The aromatic constituents of raw lubricant distillate are of little direct interest to the lubricat on engineer except for that portion which is not removed from the iubricating oil by commercial extraction or other processing. The character of this material is shown in some detail in Table 16-9. Organosulfur, organonitrogen and oxygenated material tends to go with the aromatic fractions ( s e e Tables 16-3 and 16-9). Mair and Martingz-Picg [ 141 isolated and identified 4-methyldibenzothiophene, 4,6dimethyldibenzothiophene and benzo[b]naphtho[2,1-d]-thiophene. Mikhailov and co-workers [15] reported the presence of 1.5-2.7% of benzothiophenes in Russian 100 VI lubricating stocks of 0.85-0.92% sulfur content.

491

16.4. TYPE STRUCTURES IN LUBRICATING OILS BY CORRELATION PROPERTIES: INDIRECT METHODS

WITH

PHYSICAL

Macroscopic separation of a lubricat ng oil into fractions is tedious and laborious, and from the viewpoint of petroleun technology and lubrication engineering, characterization of an oil by methods which require such separations is not practical for ordinary purposes. Consequently, side by side with procedures directly based on fundamental data, there are also indirect methods of assaying petroleum lubricating oils for type structures via trends displayed by physical properties such as viscosity, density and refractive index. The development of the necessary correlations, involving a s it does a great deal of curve fitting and outright empiricism, will not be shown in detail here. There is no unified reference which treats all the significant correlation systems adequately, and the interested reader must therefore go to the individual sources. King, Kust and Kurtz 1161 list six different methods, the essentials of which are outlined in Table 16-10. ?he n-d-M method (n is refractive index, d is density and M is molecular weight), which is one of the methods most frequently cited, is described in detail in the book by van Nes and van Westen [ 1 7 1 . The equations of correlation f o r this method define total ring content, percentage of carbon in rings, aromatic ring content and percentage of carbon in aromatic rings; hence the naphthenic and paraffinic carbon content can be calculated by difference. The working equations are given in Table 16-11. For best accuracy the equation applicable to an oil with high content of aromatics is different from the equation for an oil of iow aromatic content. The calculations have been derived for values of

TABLE 16-10. PHYSICAL CORRELATION METHODS FOR CARBON TYPE ANALYSIS Designation

Physical properties utilized

n-d-M

Refractive index, density, molecular weight

Refractivity interceptkinetic viscositygravity constant

Refractive index, density, viscosity (in centistokes)

(hi-KVGC)

Refractivity interceptRefractive index, density, viscosity viscosity-gravity constant (in Saybolt seconds) ( hi-

VGC )

Refractivity interceptdensity (hi-density)

Refractive index, density, number of carbon atoms (from viscosity)

Boelhouwer-Waterman

Refractive index, density, viscosity

Cornelissen-Waterman

Refractive index, density, viscosity

ri-\

W

N

TABLE 16-11. Formula for

low range 0.44 + 0.080

RA % ‘A

‘A

R

high range

M

(2.51 An

-

Ad)

3660/M + 670 (2.51 An - Ad) 0.41

RA

%

FORMULAS OF THE n-d-M METHOD

+

0.080

M

(2.42 An - Ad)

3360/M + 720 (2.42 An - Ad) 1.33

+

0.180

M (Ad - 1.11 An)

0.44

+

3660/M

0.055

Temperature (a)

M

(2.51 An

0.41 + 0.055

M

(2.42 An - Ad)

410 (2.42 An - Ad)

c

20

c

70 C 70 C

+

1.33

0.146M

Ad - 1.11 An)

20

820

A d - 1.11 An)

20

+

10OOO/M

R

1.55 + 0 . 1 8 0 M (Ad - 1.11 An)

1.55 + 0.146M

Ad

% CR

12100/M + 1440(Ad

11500/M

Ad

1.11 An)

20

3660/M

10600/M + 1440(Ad - 1.11 An)

-

Ad)

430 (2.51 An - Ad)

+

% C

R

-

+

+

775

-

c c

1.11 An)

70 C

1.11 An)

70 C

(a) For refractive index and density data. R = total number of rings per molecule. RA = aromatic rings per molecule. % CR = percent of carbon in total rings. % CA = percent of carbon in aromatic rings. n = refractive index. d = density. M = molecular weight. Formulas by van Nes and van Westen [ 1 7 1 , p. 323.

493

the refractive index and density taken at either 2 0 C o r 7 0 C . The formulas for the n-d-M method

were

obtained

by

an

elaborate

scheme of empirical calibration based on the observed behavior of many different oil fractions. F o r a given fraction, the mean molecular weight and the density are determined, and the fraction is then hydrogenated completely; the number of aromatic rings can be computed from the It was shown by van Nes and van Westen [ 1 7 1 that the hydrogen uptake. number of rings in a particular structural category (aromatic, naphthenic or total rings) can be expressed by a relation of the form

R = a'

+

b'MAd

+

c'MAn

and the percentage of carbon occurring as the ring structure by

a %C =

-

+ bad + c A ~

M

where a, a ' , b , b ' , c , c ' are constants and Ad and An are the differences between the measured values of the density and the refractive index and the extrapolated values of these physical properties for the limiting paraffin, i . e . the hypothetical n-alkane of infinite chain length in the liquid state. Manipulation of the specific relations in the two formats given above yield the numerical equations shown in Table 1 6 - 1 1 . The h i - K V G C and the f i i - V G C methods do not require determination of the molecular weight. The refractivity intercept is calculated by the formula (16-1)

where n;' is the refractive index at 20 C and d i 0 is the density at 20 C in grams per cubic centimeter 1 1 8 1 . The viscosity-gravity constant is an oil characteristic recognized by ASTM I 1 9 1 and is computed from the relation l o g A p - 1 . 0 7 5 2 Log ( v n - 3 8 )

VGC

=

10 - Locj ( v *

-

38)

(16-2)

where g is the specific gravity at 6 0 / 6 0 F and v h is the viscosity in hlJ Saybolt seconds at 100 F. The kinematic viscosity-gravity constant is Its formula is described by Smith [ Z O ] .

KVGC =

d i O - 0.1384 Lay ( v

-

20)

- Log ( v

-

2011

0.1526

r7.14

+

0.579

(16-3)

where v is the kinematic viscosity in centistokes at 2 0 C. Within a limited but useful range of composition the viscosity-gravity constant (either VGC or K V G C ) and the refractivity intercept are linearly related

494

to the percentages of aromatic naphthenic and paraffinic carbon in an oil. By combining the two linear relations in a triangular composition diagram, Kurtz and co-workers [ 2 3 developed a method whereby determination of refractive index, density and viscosity could be used to assay the hydrocarbon types in an oil. The method, of course, required empirical calibration. A similar approach was used by Kurtz, King, Stout and Peterkin [22] to develop a correlation method for which the input data were density and refractivity intercept. The Boelhouwer-Waterman method [23] and the Cornelissen-Waterman method [241 depend on correlations similar to those used for the hi-KVGC method. The typical output of an indirect correlation analysis gives the rings, percentage of the total carbon distributed among aromatic naphthenic rings and paraffinic (alkyl) chains. There are a number of assumptions implicit in such results, depending on how the particular correlation method was calibrated. The usual assumption is that the percentage of carbon atoms in aromatic rings and the total number of rings are known exactly, since this part of the calibration depends on the direct data obtained from hydrogenation of the oil. Calculation of the number of aromatic ring and of the percentage of carbon in naphthenic rings assumes that the ring systems are built up of six-membered katacondensed rings. Percentage of paraffinic carbon is taken to be the Boelhouwer-Waterman and residual difference from 100%. The n - d - M , Cornelissen-Waterman methods use all these assumptions. The hi-VGC method and the hi-density method use the assumptions about aromatic carbon atoms and total rings but in addition have special calibrating assumptions about the size and the degree of condensation of rings which stem from analysis of properties of hydrocarbons of known structure. The h . - KVGC method is calibrated from experimental data obtained from A. aromatic-free petroleum oils and pure compounds. King, Kust and Kurtz [161 compared the results of the analysis of 44 different petroleum oils and oil fractions by the six correlation methods listed in Table 16-10. The deviations of the average results for all the oils by each method from the average "best analysis" for all the oils ranged from -0.2 to +1.8 for percent aromatic carbon ( % CA), -3.0 to + 0 . 5 for percent naphthenic carbon ( % C,) and -2.3 to +1.6 for percent paraffinic carbon ( % Cp). The magnitudes of the standard deviations from the "best analysis" were somewhat larger: 1.5 to 3.1 for % C A , 2.6 to 4.7 for The six methods were also applied to 154 % CN, and 2.1 to 4.6 for % Cp. pure hydrocarbons of known structure. The figures for the deviations of the average results from the correct analysis are: %CA, -2.1 to + 0 . 1 ; % CN, -0.7 to +5.2; % Cp, -4.7 to +0.7. The range of the standard deviations is somewhat broader: % CA, 3.4 to 11.0; % CN, 9.6 to 17.5; % Cp, 7.1 to 15.5. I t is not surprising that the six correlation methods work

495

as well as they do for petroleum oil, since these methods were calibrated with selected petroleum fractions. The less satisfactory results obtained for pure hydrocarbons indicate that cyclic hydrocarbons adequately characteristic of those found in petroleum lubricating oils have not yet been synthesized and tested. 16.5. TYPE LUBRICANTS

STRUCTURES

AND

THE

PERFORMANCE

OF

PETROLEUM

OILS

AS

For the lubrication technologist the significance of chemical structures in the composition of petroleum oils goes beyond mere classification of such oils as paraffinic, naphthenic or aromatic. Because their borderlines are not precisely distinguishable, these classification categories serve mostly as general indicators of what the lubrication engineer might anticipate about the behavior of the oil in use. The utility of classificatory designations can be extended by examining the details of the relations between the structural types upon which the classifications are based and the functioning of the oil as a lubricant.

50-1

I

I

I

I

I

I

I-

1, lp] I

(b)

0

40

80

120

160 0

40

80

120

160

Viscosity Index

Figure 16-3. Viscosity index and structural types in lubricating oil. (a) Commercial solvent-extracted lubricating stocks. (b) Aromatic-free fractions. 1: Non-condensed cycloalkanes. 2 : Condensed cycloalkanes. 3: Isoparaffins. 4: Aromatics. From data by Andr; and O'Neal [ 1 1 1 .

Viscosity index is a familiar item of technological interest in the physical properities of a lubricating oil. I t is by common experience that aromatics are associated with low values of the viscosity index; when the aromatic-rich extract is separated from raw lubricant distillate, the viscosity index of the extract is lower and that of the raffinate is higher than the original viscosity index of the raw distillate. The diagrams of Fig. 16-3 show the relations betveen viscosity index and structural types in refined oil. Figure 16-3a shows the summed-up contents of the various type categories in Table 16-9 plotted against the values of viscosity index a s given in Table 16-8. Figure 16-3b shows a related plot for the saturated portion of these oils after the aromatic hydrocarbons have been removed. Although the basis for computing volume-

496

percentage is different in Fig. 16-3a than in Fig. 16-3b, it is still obvious that the removal of aromatics from the oils raised the viscosity index. The linear relations depicted in Figs. 16-3a and 16-3b may be forced. The data from which these plots were constructed have some deficiencies in precision and self-consistency. Data of good precision are available from the work of Melpolder c: aL.[lO] on thermally diffused fractions of a petroleum oil, as listed in Tables 16-6 and 16-7;

180 160 140 120 100 % 5 80 8 60

g

-

5 40

20 [ i d , 0

,

,s ,i,1 I

10 20 30 40 50 60 70 Volume-Percent Component Figure 16-4. Viscosity index of fractions from thermally diffused lubricating oil. (a) Isoparaffins. (b) Condensed cycloalkanes. (c) Non-condensed cycloakanes. (d) Aromatics. From data by Melpolder e t

0

ae.

[lo].

Fig. 16-4 is a plot of viscosity index against molecular type made from these data. The relation of viscosity index to isoparaffin content is not linear until the VI attains a value of 100; below that value the viscosity index increases strongly with increasing concentration of isoparaffin and there is a pronounced transition to the linear terminal The relation between viscosity index and conportion of the graph. centration of condensed-ring naphthenes is inversely linear over much of the graph but shows a sharp drop in the VI range 20 to 8. Monocyclic and non-condensed cycloalkanes fluctuate somewhat with VI but lie within the concentration range 33% to 42% for viscosity index values between 10 and 160. The aromatic content drops sharply with increasing viscosity index, but i t should be noted that for this series of oil fractions the maximum level of aromatics is only 7% at a VI of 1 1 . Critical examination of the data plotted in Figs. 16-3 and 16-4 reveals that aromatic content is not the only constituent which influences the viscosity index. Table 16-12 shows data taken from these graphs for the structural type content of various oil fractions at three different levels of viscosity index. I t is obvious that the rise in the viscosity index from 100 to 140 for saturated oils as plotted in Fig. 16-3b cannot be ascribed to decrease in aromatic content. The decrease in the content of condensed-ring naphthenes from 34% to 18% and

497

TABLE 1 6 - 1 2 .

INFLUENCE OF MOLECULAR TYPES ON VISCOSITY INDEX

Molecular type

\'olume-% constituent 1 (a)

I1 (b)

I11 (c)

Viscosity index 3 0 Isoparaffins Aromatics Condensed naphthenes Non-condensed rings

3 29 34 34

3 6 58 33

Viscosity index 100 I soparaf f ins Aromatics Condensed naphthenes Non-condensed rings

13 20 20 45

15 -34 51

17 3.5 38.5 41

Viscosity index 1 4 0 I soparaff ins Aroma t i c s Condensed naphthenes Non-condensed rings

22 16 17 45

32

48

18 50

16 35

-_

1

(a) Commercially refined oils: see Fig. 16-3a. (b) Saturated fraction: see Fig. 1 6 - 3 b . (c) Thermally diffused fractions: see Fig. 1 6 - 4 .

the increase in isoparaffin content from 15% to 3 2 % are highly suggestive of two interrelated influences responsible for the rise in viscosity index. The content of monocyclic and non-condensed cycloalkanes remains virtually unchanged at 5 0 - 5 1 % . The data for the two oils of 30 VI indicate that aromatics and condensed-ring naphthenes are equivalent in their adverse effect on the viscosity index. The positive effect of isoparaffin content is strongest at the lower values of viscosity index: thus, in Fig. 1 6 - 4 we observe that an increase of viscosity index from 11 to 6 5 is characterized by a rise in isoparaffin content from 3% to 6 % (a two-fcld change), while the condensed-ring naphthenes decreased from 5 6 % to 5 2 % (a change of only 7 parts in a hundred) and the aromatics decreased from 7 % to 4% (a change of almost one and one-half times). But, as other evidence shows, the aramatics and condensed-ring naphthenes are equivalent in lowering the viscosity index; hence the observed rise in VI must be attributed directly to the strong positive influence of the modest increase in isoparaffin content rather than to the effect of the matching decrease in aromatics. The data in Tables 1 6 - 6 and 16-7 also show that the magnitude of the viscosity as well as the viscosity index changes systematically with the molecular composition of the oil. This effect must be ascribed to molecular structure rather than molecular size, given the substantially

uniform level of molecular weight of all the fracti0n.s listed tables.

in

these

If it is accepted that the viscous behavior of oils is reponsive to the proportions of rings and chains and their arrangement within the molecular structures, then the lubrication engineer with exacting requirements will be interested in how the oil was refined. Solvent extraction or acid treatment removes a portion of the cyclic components from the raw oil and thus affects the proportion of rings and chains in the raffinate. Strong hydrogenation converts aromatic rings to naphthenes; the type of rings is altered by this treatment but no portion of the cyclic compounds are removed from the raffinate. Thus, replacement of acid treatment by hydrogenation in the processing of naphthenic

oils has a noticeable influence on the properties of market.

such

oil

for

the

Another important area of technological utility influenced by the Two structure of petroleum lubricating oils is oxidation stability. modes of behavior must be considered. One is the resistance to the initiation of oxidation, ususlly defined by the period of induction before the uptake of oxygen proceeds at an appreciable rate. The other is the post-induction rate of oxidation and the kind of oxidation products formed thereby. There are no easy generalities about the relation of structure to these two aspects of oxidation. Such empirical relations as have been established are successful because the refining procedures produce oils of consistently stable properties in a broad sense. But changes in refining technique can result in unexpected alterations in the oxidation stability of the oil. For example, the light hydrotreating of paraffinic oils to improve color and color stability has as an undesirable side effect reduction of oxidation stability. Among the minor components of ordinary lubricant stocks strongly affected by light hydrotreating are the sulfur compounds which occur as polynuclear hererocycles. These are known to be oxidation inhibitors naturally occuring in the oil. Reduction of the sulfur level from 0.1-0.2% to 0.04-0.08% by hydrogenation has an adverse effect on the oxidation resistance of the treated oil Pour point is another lubricating oil characteristic of .technological interest. Although it has no specifically identified direct influence on the lubricating performance of the oil, there is an obvious disadvantage if the oil at rest in the sump cannot flow or be pumped to the sites where it is needed. Improvement of pour point is the reason for dewaxing oil. The insolubility and the crystallinity of paraffin waxes can be attributed to the straight-chain structure of their constituent alkane hydrocarbons, which promotes their removal in the dewaxing process. Branched-chain alkanes and long chains substituted on a

499

cycloparaffin ring are more likely to be found in the "microcrystalline" type of waxes, which are softer and more plastic than the higher-melting paraffin waxes. The high pour points of the first five fractions listed in Tables 16-6 and 16-7 can be attributed to the combination of isoparaffins and substituted monocyclic naphthenes. The minimum pour point, at Fraction 21, seems to be characterized by substantially equivalent levels of isoparaffins and bicyclic condensed naphthenes; then as the pour point progressively rises with the fraction number, the isoparaffins decrease and the polycyclic condensed cycloparaffins increase. From this it appears that in an oil of homogeneous molecular weight with a heterogeneous array of molecular constitutive types, the pour point minimum is governed by the smoothing of the distribution among the isoparaffins, the r?.onocyclicconstituents and the condensed polycyclic constituents, rather than the predominant influence of any one particular molecular type. REFERENCES 1.

2.

3. 4. 5. 6. 7. 8.

9. 10. 11.

12. 13. 14. 15. 16.

17. 18.

19.

F. D. Rossini, J. Chem. Ed., 37 (1960) 554-561. ASTM Method D 1298-67, Density, Specific Gravity o r API Gravity of Crude Petroleum o r Liquid Petroleum Products by Hydrometer Method, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. W. Carruthers and J. W. Cool, J. Chem. SOC. London, (1954) 20472052. R. J. Moore, R. E. Thorpe and C. L. Mahoney, J. Am. Chem. SOC., 75 (1953) 2259. B. J. Mair, S. T. Schicktanz and F. W. Rose, jr., J. Res. Natl. Bur. Standards, 15 (1935) 557-573. B. J. Mair and S. T. Schicktanz, J. Res. Natl. B u r . Standards, 17 (1936) 909-922. B . J. Mair and S. T. Schicktanz, Ind. Eng. Chem., 28 (1936) 14461451. F. D. Rossini, B. J. Mair and A. J. Streiff, Hydrocarbons from Petroleum, Reinhold Publishing Co., New York, 1953, Chapter 22. B. J. Mair and F. D. Rossini, Ind. Eng. Chem., 47 (1955) 1062-1068. F. W. Melpolder, R. A. Brown, T. A. Washall, W. Doherty and C. E. Headington, Anal, Chem., 28 (1956) 1936-1945. M. L. Andre' and M. J. O'Neal, jr., Anal. Chem., 31 (1959) 164-169. L. P. Lindeman. PreDrints. ACS Div. Petroleum Chemistry. _ . 14 (1969) No. 3, B186lB198. A. Hood, R. J. Clerc and M. J. O'Neal,. j- r . , J. Inst. Petroleum, 45 (1959) 168-173. B. J. Mair and J. L. Martingz-Pic;, Proc. Am. Petroleum Inst., 42 (1962) 1 1 1 , 173-185. I. A. Mikhailov, A. A. Polyakova, N. P. Izotova, E. S. Brodskii, M. M. Chern'isheva and I. M, Uvarova, Khim. Tekh. Topliv Masel, 17 (1972) No. 7, 13-17. R. W. King, M. A. Kust and S. S. Kurtz, j r . , Anal. Chem., 32 (1960) 738-745. K. van Nes and H. A. van Westen, Aspects of the Constitution of Mineral Oils, Elsevier Publishing Co., New York-Amsterdam-LondonBrussels, 1951. S. S. Kurtz, jr., in Chemistry of Petroleum Hydrocarbons, B. T. Brooks (Editor), Reinhold Publishing Co., New York, 1954, Vol. I , Chapter 1 1 . ASTM Method D 2501-66, Calculation of Viscosity-Gravity Constant ( V G C ) of Petroleum Oils, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia.

500

20. 21. 22. 23. 24.

E. E. Smith, Ohio State Univ. Eng. Exptl. Station Bulletin 152, May, 1953. S. S. Kurtz, j r . , R. W. King, W. J. Stout, D. G. Partikian and E. A. Skrabek, Anal. Chem., 28 (1956) 1928-1936. S. S. Kurtz, jr., R. W. King, W. J. Stout and M. E. Peterkin, Anal. Chem., 3 0 (1958) 1224-1236. C. Boelhouwer and H. I. Waterman, J. Inst. Petroleum, 4 0 (1954) 116121. J. Cornelissen and H. I. Waterman, J. Inst. Petroleum, 43 (1957) 48.

501

Chapter 17 NON-PETROLEUM LIQUIDS A S LVBRICANTS

A s pointed out in the preceding chapter, petroleum oils offer many advantages a s lubricants. In no other single class of liquids d o we find so many desirable attributes, such as versatility of performance, ready availability and economically bearable price. However, occasions arisewith increasing frequency a s the needs of modern machinery become more demanding-when the properties of petroleum oils are inadequate for the service required. These requirements, for the most part connected with higher service temperatures, include better viscosity behavior, better oxidative and thermal stability, and lower volatility. In particular, hydraulic fluids that must function at high pressures and elevated temperatures should have resistance to ignition without sacrifice of antiwear performance.

When the need for improved performance outweighs restrictions on price and desire for availability which ordinarily dominate the procurement of lubricants, then the purview expands to include fluids that can be made by synthetic chemistry. Even if we restrict ourselves to those fluids that promise reasonable potential for usefulness, there are as many a s 20 broad generic classes which can come under consideration, and within each class there may be 10 or more subclasses gradated according to some property such as viscosity or molecular weight. A comprehensive survey of all the synthetic fluids with potential for practical u s e would be a major undertaking. In this chapter, therefore, we shall restrict ourselves to the examination of those types of synthetic lubricants that have been tested well enough to establish their usefulness and their limitations. 17.1.

CHEMICAL TYPES AND STRUCTURES

In Table 17-1 are listed seven of the more important types of chemic a l structures according to which the non-petroieum liquids discussed in this

chapter may be classified. All of these lubricants are synthetic: ~ . e their . structures are the result of substantial chemical alteration of the starting material, in contradistinction to the refining of natural petroleum oils, which principally separates the crude oil into fractions and removes the unwanted portions thereof. Even though synthetic lubricants o f the hydrocarbon type may have had their origin in raw materials obtained from petroieum, they are the products of substantial

502

TABLE 17-1.

IMPORTANT CHEMICAL TYPES OF SYNTHETIC LUBRICANTS

Hydrocarbons Fluorocarbons and fluorohydrocarbons 3. Other hydrocarbon halides 4. Carboxylic esters 5 . Other esters 6. Ethers and glycols 7. Silicon derivatives 1.

2.

chemical alteration of the starting substances. Olefinic hydrocarbons of low molecular weight are among the byproducts of the cracking of petroleum stocks. Attempts to make synthetic lubricants by the polymerization of such olefins date back to but these efforts were not truly successful, either techthe 1 9 3 0 ' s , Polymers of butene and isobutene with nologically or economically. molecular weights of 100,000 and greater were developed, but such large molecules were found unsuitable as lubricant base stocks although they perform effectively as viscosity-improving additives. Similar polymers of ethylene and propylene are familiar and need no special mention. In order that olefin polymers be suitable for use a s lubricant fluids they must be u L i y u m e n . 5 : that is, they must be made up of relatively few basic repeating units so that the molecular weight of the polymer fluid lies within the range 300-500, which empirically has been found associated with desirable values of properties such as viscosity, pour point, volatility, etc. As the chain length and the branching of the parent olefin increases, the structural variations possible in the polymerized product proliferate. One of the ostensible objectives of synthesizing lubricants is better control over the structure and hence of the properties of the product, and such control starts at the beginning with the choice of the olefin to be polymerized. Olefins with terminal unsaturation are preferred: e . g . 1-alkenes, whether normal o r branched. In the examples below, the structure shown for the normal terminal olefin i s general, but that for the branched-chain terminal olefin is only one of several possible types. The values of x and y may both be zero, in which case the branched-chain olefin is isobutene (2-methylpropene-1):

R CH=CH2

R(CH2)xCH.(R')*(CH

)

2 Y

CH=CH2

CH 3 )C=CH2

CH3 Normal w-alkene

Iso-w-alkene

2-Methylpropene-1

Commercial olefin polymerizations are currently carried out in catalytic systems, and in many of them the course of reaction goes via a

503

Cha n

carbonium-ion mechanism. olef in proceeds

+

propagation

for

the

normal

terminal

+

R.C-CH3 + R.CH=CH2 H

I! + R-C-CH, C-CH3, etc. H

H

as the most likely course. Initiation of the chain requires that a hydrogen ion be furnished by the catalytic system: chain termination requires its removal. Control of the reaction to keep the molecular weight of the product in the desired range is a matter of specific technique. The ultimate oligomer has the general structure:

Isomers restilting f r o m wandering of the site of the electron deficiency and shifting of the double bond are not excluded. For a branched-chain structure, the reaction scheme outlined below for isobutene may be taken as representative:

Catalyzed free-radical mechanisms are also modes the chain is poiymerization. F o r the type olefin R.CH=CH, principally by the radical attack

R-C=CH2

+

R-CH=CH, j [H2C=C-;-;H R H

.

of olefin propagated

(b)

Configuration (a) is the favored one for the propagation giving the oligomeric product with the structure

of

the

chain,

H,C=CR.(CH2-CH);CH2-CH2R R

However, the structure H2C=CR*(CH-CH,);CH-CH3 R R generated from configuration (b) is not excluded.

All of the hydrocarbon oligomers whose structures have been drawn above are olefinic with one double bond per molecule. Hydrogenation to

504

produce a completely saturated hydrocarbon is the usual finishing step in the preparation of synthetic lubricant fluids from olefinic oligomers. The choice of synthetic hydrocarbons for lubricant use is not restricted to olefin oligomers. I t is entirely credible that among the thousands of hydrocarbons of various structures will be found many whose properties make them worthy of attention as possible lubricants. For example, Wilgus, Ettling and Pino [ l ] investigated the potential usefulness as high-temperature, radiation-resistant hydraulic fluids of a series of diarylalkanes of the general type

where X,, X2 and Y may be either H or an alkyl group. Schmidt-Collgrus, Krimmel and Bohner [ 2 ] reported on the properties of substituted bi- and terphenyls:

That so few of the synthetic hydrocarbons already known and synthesized have been investigated as possible lubricants is not only a matter of whether their properties are suitable; the overriding conditions are for the most part economics and availability. Halogen-substituted hydrocarbons in general do not show much promise as lubricant fluids. However, some of the properties reported for one class of hydrocarbon halides, namely the substituted w,w'-diphenylalkanes

where either x or y may be zero, make lubricants for special uses 131.

them

of

interest

as

synthetic

Fluorine heads the halogen group in the periodic table of the chemical elements, but fluorocarbons fall into a class distinct from other halogen-substituted hydrocarbons because of their distinctive properties. The carbon-fluorine bond in fluoroalkanes is among the strongest of alkyl bonds, and the fl'uoroalkane surface is among those with the lowest energy and the least wettability. In mixed fluorohydrocarbons, e . 9 . alkyl fluorides of empirical formula C H F (x+y=2n+2), the number of possible n x y structural combinations increases rapidly with increasing n. One general type is the terminally fluorinated chain: CH~(CH~)~CF~

505

Other types are illustrated by the structures shown below: CH, (CH2)n (CF2),CF3

and

CF3 (CF2),(CH2

)n ( C F 2 ),CF3

Ring-substituted fluoroaromatics and fluorocycloalkanes are tures to be considered.

also

struc-

Carboxylic esters today are mostly associated with the lubrication of jet turbine aircraft engines, but the practical use of an ester as a lubricar,t antedates the jet age. Castor oil, the iegendary h i g h viscosity crankcase oil for racing car engines, is a mixture of fatty esters whose principal constituent is triricinolein:

CH,OOC(CH,)~.CH=CH.CH~CH(OH).(CH~)~CH~

I I

CHOOC(CH2),*CH=CH.CH2CH(OH).(CH2)5CH3

CH200C(CH2)7-CH=CH.CH2CH(OH).(CH2)5CH3 But the requirements of jet engine lubrication call for properties quite different than those which governed the selection of castor oil as a crankcase lubricant, and it is these altered requirements that have their influence on the correlations between physical properties and chemical structures which determine the modern development of ester lubricant fluids. Of the numerous possibilities arising from the esterification of polycarboxylic acids by polyhydroxylic alcohols, fortunately only a few need be considered seriously from the viewpoint of utility as synthetic ester lubricants. Most of the esters that find application as lubricant fluids are products of the reaction of m,>nohydroxylic alcohols and dicarboxylic acids; for example, the simple type structure shown below:

ROOC.(CH2),*COOR Or, the reactants may be a monocarboxylic acid cohol :

and

a

dihydroxylic

al-

RCOO(CH2)m00CR Complex esters can be made by the interaction of a dihydroxylic alcohol and a dicarboxylic acid: for example, HO(CH2)~OOC~(CH2)n~COO~CH2)mOH which is then capped with a monocarboxylic acid to give RCOO(CH2)m00C* (CH2)n.COO(CH2)m00CR By blending diesters and complex esters, versatile control of the viscosity of the lubricant can be achieved. The illustrative formulas above were restricted to straight-chain w,w'-structures for both the dihydroxylic alcohol and the dicarboxylic acid, but there is no necessity for such a restriction, theoretically or practically. The combination of w,o'-straight-chain dicarboxylic acid and branched-chain monohydroxylic

506

alcohol is encountered more often than the reverse combination because Of the comparative availability of acid and alcohol. Among the non-carboxylic esters that have been investigated for lubricant service are tetra-alkyl orthosilicates, (R0)4Si; trialkyl orthophosphates, (RO)3P=O; phosphonates, (R0)2.PR'-O; phosphinates, RO*PR'.O. The phosphates, phosphonates and phosphinates were studied as lubricant liquids p e h n e and not as additives. Polyalkylene glycols of sufficient chain length can function acceptably a s lubricants. The simplest in structure are the polyethylene glycols: HO(CH2CH20);CH2CH20H Isobutylene epoxide gives polyoxyglycols with the structure

Polyoxyalkylene glycols have also been prepared from propylene epoxide and 1,2-epoxybutane. Structurally the polyoxyalkylene glycols are both ethers and glycols. The polyphenyl ethers constitute a class of oxygenated liquid lubricants without free hydroxyl or carbonyl groups. Some typical structures are shown below: c r 0 0 0 ~ 0 c >

bis(p-Phenoxyphenyl) Ether

m-Phenoxyphenyl p-Phenoxyphenyl Ether

Phenoxy-n-(m-phenoxy)benzene

n = 0,

1,

2

... etc.

In addition to the orthosilicates already mentioned, two other types of silicon derivatives have been studied as lubricants. The most familiar are the poly(diorganosi1oxanes); these are the well-known silicones: R R R-SiO (-iiO) -Si-R R R

The organic groups need not necessarily be all alike. are the tetraorganosilanes

In the other class

R R-Si-R R proposed as high-temperature lubricants by Baum and Tamborski 1 4 1 .

Here,

507

too, the organic groups are not necessarily alike. Since the polyoxyalkylene glycols are dihydroxylic alcohols as well as polyethers, they can be reacted with acids to give ester-type e . y . , carboxylates, phosphates, silicates, etc. lubricant fluids: Another type of chemical multifunctionality in synthetic lubricants is introduced by halogen substitution: for example, fluorine-substituted polyphenyl ethers; o r alkyl-aryl silicones with chlorine substituted for hydrogen on the aryl ring. 17.2.

CHEMICAL TYPES AND PROPERTIES OF SYNTHETIC LUBRICANTS

The criteria for the evaluation of a given synthetic liquid as a lubricant will depend upon the functional demands of the service required Some of these demands may not be directly connected with the of it. function as a lubricating fluid: for instance, odor, toxicity, o r attack on paints and'finishes. Those properties that are pertinently connected with lubricant service can be classified into the five categories listed below: 1.

FLaw Pnapehtien: Under this heading come the viscosity of the fluid and the effect of temperature on viscosity, The latter might be a theoretically derived function, or an arbitrary function such as the viscosity index, o r even a grossly empirical evaluation of the viscosity at two or more selected temperatures. Low temperature flow properties are frequently evaluated by the ASTM pour point determination [ 5 1 , but the inadequacies of this method of evaluation have led to the use of pumpability tests which have a better empirical relation to service conditions.

2.

H i y h Tempehatuhe Phopehtien: The high temperature domain may be arbitrarily taken to lie above 3 7 3 K ( 1 0 0 c ) . The chief properties of interest at such temperatures are resistance to thermal cracking, particularly in the presence of metals; absence o r low level of polymerized or carbonaceous residue; resistance to flammability; and low loss by volatilization.

3.

Oxidation Chahactehinticn: These characteristics include resistance to oxidation at ordinary and at high temperatures, the nature and the properties of the oxidation products, and response to oxidation inhibi tors.

4.

C o h n a n i o n Chahactehinticn: In general, rubbing parts to be lubricated are made of metal. The corrosiveness of the lubricant p e h n e and the corrosiveness of any degradation products resulting from oxidation, thermal decomposition or hydrolysis must be considered.

5.

Weak and S e i z u h e Chahactehinticn: The behavior o f the fluids themselves in various bench tests for antiwear or antiseizure performance

508

is of interest, as is also the behavior of antiwear and antiseizure additives when dissolved in the fluids. The criteria listed above are also used to judge petroleum oils; therefore evaluating synthetic lubricants by these criteria tests whether they perform better than petroleum oils under the conditions required by service. I n hydrodynamic lubrication considerable emphasis is placed on the temperature coefficient of viscosity. Figure 17-1 illustrates the extent of the control that can be exercised over this important parameter in the synthesis of hydrocarbon oligomers. Viscosity data are plotted o n the

10,000 5,000 2,000 1,000 B c 500 0

2 200

u)

s

n

ZI 0

g f 0

100

80 60

50 45 40 35 30 50 75 100 125 150 175 200

250 300

Temperoture,degrees Fahrenheit

Figure 17-1. Effect of temperature on the viscosity of mineral oils and hydrocarbon oligomers. 1: Mineral oil, VI 92. 2: Mineral oil, VI 92, 5: molecular weight 418. 3: White oil, VI 101. 4: Mineral oil, VI 29. Polybutene, VI 47. 6: Hydrogenated polyoctene, VI 113, molecular weight 420. 7: Hydrogenated polyoctene, VI 142, molecular weight 1100. 8: Hydrogenated polyoctene, VI 155, molecular weight 1300. From data by Duling, Griffith and Stearns [ 6 1 . viscosity-temperature scale for three of the hydrogenated oligomers The supeof octene-1 prepared by Duling, Griffith and Stearns [ 6 1 . riority of these synthetic hydrocarbons over the best of the solventrefined petroleum oils and over white oil is immediately evident from the slope of the temperature dependence function. Not so evident is the fact that the molecular weight of the synthetic hydrocarbon for a given viscosity at 372 K (210 Fj is higher than that of the corresponding naphthenic-paraffinic hydrocarbon; hence the synthetic oil has the better ASTM

volatility characteristics. The pour points for this series of synthetic hydrocarbons lie mostly at the level 211-214 K ( - 7 5 to -80 C ) . These values reflect the lack of

509

Figure 17-2. Viscosity-temperature behavior of various types of synthetic lubricants. 1: White oil, VI 101. 2: 4'-Undecyl-m-terphenyl. 5: Polyphenyl ether. 3: Fluoroalkane. 4: w,o'-Di(chloropheny1)pentane. 6 : Polyoxyalkylene glycol. 7: Di(2-ethylhexyl) sebacate. 8: Dimethyl silicone

.

crystallinity inherent in the molecular geometry of the polymerizates. Figure 17-2 shows the influence of temperature o n the viscosity of representative examples of synthetic fluids of various chemical types. Direzt comparisons can be made when individual fluids have the same viscosity at a given temperature: e . 5 . white oil and polyoxyalkylene glycol at 301 K (83 F). The viscosity of the glycol fluid at 372 K (210 F) i s 6 Saybolt seconds higher than that of white oil, which is a significant difference that immediately shows the better viscosity behavior of the synthetic fluid. In similar fashion, w,w'-di(chlorophenyl)pentane, di(2ethylhexyl) sebacate and a dimethyl silicone all have a viscosity of 120 Saybolt seconds at 340 K (153 F ) ; but at 372 K there is a spread of 15.7 Saybolt seconds in the viscosity behavior of these fluids. Table 17-2 shows some relations between structure and flow properties. The data for the substituted terphenyls are from the work of Schmidt-CollLrus, Krimmel and Bohner [ 2 ] ; those for the polyphenyl ethers are by Mahoney and his co-workers 171. For the substituted terphenyls the location of the alkyl group rather than the linkage of the aromatic r i n g s has the stronger influence on the viscosity behavior and the pour point. The viscosity at 310.8 K (100 F) for the n-heptylterphenyls substituted in the 2-position is 2.3 to 2.7 times that of the isomer substituted in another position, and the pour point for the 2-substituted isomer is also consistently higher. Unfortunately this trend in pour point is opposite to what is desired. The data for the polyphenyl ethers

510

TABLE 17-2. STRUCTURE AND PHYSICAL PROPERTY RELATIONS FOS n-HEPTYL-SUBSTITUTED TERPHENYLS AND POLYPHENYL ETHERS Pour point

Viscosity, cs

310 8 K(a) 372.0 K(b) 422.0 K(c) OK

O F

2-n-Heptyl-o-terphenyl 3-n-Heptyl-o-terphenyl 2-n-Heptyl-m-terphenyl 3-n-Heptyl-m-terphenyl 4-n-Heptyl-m-terphenyl

29 55.2 73 65 65

6.55 5.14 7.61 6.29 6.29

2.3 1.9 2.65 2.59 2.59

4'-n-Heptyl-m-terphenyl 2-n-Heptyl-p-terphenyl bis(m-Phenoxyphenyl) ether m-bis(m-Phenoxyphenoxy) benzene

64.9 110 60.9

6.18 7.03 5.98

2.5 2.65 2.45

264 15 -10 250 272 30 244 -20 liquid at room temperature 250 -10 278 40 261 10

3.85

278

12.7

332

40

From data (a) 100 F. (b) 210 F. (c) 300 F; extrapolated values. Schmidt-Collgrus, Krimmel and Bohner [2] and by Mahoney e t aL.[7].

by

-

u) 5

10 20

30 40 50 60 70 Degree of Polymerization

Figure 17--3. Structure and viscosity of silicones. 1: Polydimethylsiloxane. 2: Polyoctylmethylsiloxane. 3, 3': Polymethylphenylsiloxane. From data by Jakobsen, Sanborn and Winer [a].

show the strong influence of the number of rings in the structure. The viscosity behavior of the four-ring bis(m-phenoxyphenyl) ether is similar to that of the n-heptylterphenyls, whereas the five-ring m-bis(mphenoxyphen0xy)benzene is considerably more viscous.

Silicones have the least sensitive response of viscosity to temperature change of any of the synthetic fluids used as lubricants (see Fig. 17-2). The viscosity level depends on the nature of the organic groups linked to the silicon atom in each siloxane unit and on the number of organosiloxane units per molecule, as illustrated by Fig. 17-3 from

511

data by Jakobsen, Sanborn and Winer [81 for dimethylsiloxane, octylmethylsiloxane and methylphenylsiloxane polymers. The influence of the size of the organic substituent groups is so strong that 15 repeating units carrying one methyl and one octyl group per unit confers a higher viscosity than 70 units substituted with only methyl groups. The two curves for methylphenylsiloxane in Fig. 17-3 illustrate the difficulty of controlling the polymerization process to obtain uniform distribution of structural units in the product. Resistance to cracking, reactive condensation and oxidation, in conjunction with acceptable viscosity behavior, is a behavioristic property that often determines the choice of a given fluid as a high-temperature lubricant. A technique for evaluating thermal stability is to measure the temperature at which the gas pressure of an enclosed system rises at some given rate: e . g . 0.014 torr per second. McHugh and Stark [9] obtained the following rating by this method for various chemical classes: polyphenyls, 783 K (950 F); polyphenyl ethers 716-727 K (830-850 F); silicones, 655-661 K (720-730 F); aromatic ethers, 655 K (720 F): silicate esters, 616 K (650 F); super-refined mineral oil, 611 K (640 F); The diesters, 555 K uncatalyzed, 500 K metal-catalyzed (540 F, 440 F). individual members of the various classes were not specifically identified. Table 17-3 shows thermal stability data obtained by Brown, Aftergut and Blackington [ I 0 1 for three classes of aromatic compounds: unsubstituted polyphenyl hydrocarbons, polyphenyl ethers, and silanes sub-

TABLE 17-3.

THERMAL STABILITY OF VARIOUS AROMATIC COMPOUNDS Decomposition temperature for 0.014 torr per second

Polyphenyls p-Quaterphenyl m-Polyphenyls, mixed (a) Tetraarylsilanes p-Biphenylyltriphenylsilane o-Biphenylyl-p-biphenylyldiphenylsilane o-Biphenyloxytriphenylsilane o-Biphenylyl-m-phenoxyphenyldiphenylsilane bis(m-Phenoxypheny1)diphenylsilane Polyphenyl ethers bis(p-Phenoxyphenyl) ether m-Phenoxyphenyl-p-phenoxyphenyl ether [Phenoxytri(m-phenoxy1ene)lbenzene [Phenoxytetra(m-phenoxy1ene)lbenzene [Phenoxypenta(m-phenoxy1ene)lbenzene (a) Contains 2% halide by weight. ington [lo].

aeg. K

deg. F

714 663

826 734

699 727 708 707 679

799 850 815 814 763

713 71 i 717 703 716

824 82 7 832 806 830

Data by Brown, Aftergut and

Black-

512

stituted by phenyl, polyphenyl o r phenoxy groups. The high level of the decomposition temperatures can be ascribed to the absence of alkyl I n contrast, Baum and Tamborski [41 reported 586 K (595 F ) for groups. the decomposition temperature of tetra(n-dodecyl)silane, and SchmidtCollgrus e t aL. [2] recorded 5 4 6 K (523 F) for 4'-n-amyl-rn-terphenyl. Schiefer, Awe and Whipple [ 1 1 ] found decomposition temperatures of 705 and 677 K ( 8 1 0 , 760 F) for two different methylphenylsilicones. Mahoney and co-workers 171 compared di(2-ethylhexyl) sebacate, an aliphatic hydrocarbcn and the two aromatic ethers, bis(m-phenoxyphenyl) ether and m-bis(m-phenoxyphen0xy)benzene. They found the following temperatures for 1% decomposition per hour: ester, 583 K (590 F); hydrocarbon, 616 K (650 F); polyphenyl ethers, 739 K (671 F).

Heating for a given time at a fixed temperature is another technique for evaluating thermal stability. Duling, Griffith and Stearns [61 found that a sebacate diester fluid was significantly less stable at 644 K (700 F) than petroleum oil or synthetic alkanes from olefin oligomers. Wilgus, Ettling and Pino [ l ] observed that in a static heating test at 644 K for 20 hours a polyoxyalkylene glycol fluid was characterized by a large change i n viscosity and evolution of much gas; di(2-ethylhexyl) sebacate set to a solid; and a silicone fluid evolved more gas than naphthenic white oil, substituted biphenyl, substituted diphenyl ether or w,w'-diphenylalkane. Baum and Tamborski [41 on testing various teraalkylsilanes by a closed-tube static procedure for 9 hours at 644 K observed some loss of viscosity, but the extent of change was at an acceptable level. The effect of high-temperature oxidation on lubricant fluids is usually monitored by changes in viscosity and acidity, by the amount and Very nature of deposits and sludge, and by corrosive attack o n metals. few lubricants can withstand high-temperature oxidation without antioxidant additives. Hence in making comparisons it is the interaction of base fluid and additive which usually is being tested, and interpretation of the results is thereby complicated. The silicones are an outstanding exception, being resistant to oxidative degradation without the aid of an antioxidant additive. Murphy, Saunders and Smith [121 studied the oxidation of three methyl phenyl silicones and compared the results with those of a previous investigation of dimethyl silicone [ 1 3 1 . Their findings for uncatalyzed oxidation are summarized in Table 17-4 a s viscosity increase, loss of weight and evolution of formic acid and formaldehyde. Data for metal-catalyzed oxidation can be found in the original reference [ 1 2 ] . Baum and Tamborski [41 studied the oxidation of tetraalkyl silanes at 4 7 7 K (400 F) and reported that the oxidative resistance and antioxidant response of these substances were poor. Table 17-5 gives some comparisons of polyphenyl ethers with other synthetic lubricants in a 50 hour oxiaation-corrosion test [ 7 1 . A l l the

TABLE 17-4.

HIGH-TEMPERATURE OXIDATION OF SILICONES Temperature

Time, % Viscosity Wt. loss, Millimoles HCOOH hours increase at percent + H C H - 0 per gm 310.8 K(a) deg. C deg. K

Polydimethylsiloxane

200 225 P o l y m e t h y l p h e n y l s i l o x a n e s 200 225 250 250 250 275 300

c)

d) d) d)

473 498 473 498 523 523 523 548 573

168 168 168 168 168 168 168 168 168

48 gelled (b) (b) 85-124 165 34 137-209 336-577

2 2 (b) (b) 3.5 4 1 1.5 6

In air unless otherwise noted. (a) 100 F. (b) Unchanged. helium. From data by Murphy, Saunders and Smith [12]. TABLE 17-5.

(c)

1.7 0.003-0.015 0.015 0.004 0.002-0.006 0.007

In

oxygen.

% Viscosity

Acid number

(d)

In

OXIDATION TESTS: POLYPHENYL ETHERS AND OTHER FLUIDS Temperature deg. C

bis(m-Phenoxyphenyl) ether bis(p-Phenoxyphenyl) ether m-bis(m-Phenoxyphenoxy)benzene

m-bis(m-(m-Phenoxyphenoxy)phenoxy)benzene m-Terphenyl Methyl phenyl silicone Chlorophenyl silicone Diphenyldi-n-dodecylsilane Diester base oil (c) Mineral oil

589 589 589 589 589 589 533 533 505 477

increase, deg. F 372 K(a) 600 600 600 600 600 600 500 500 450 400

7 5.0(b) 29 84 8 1020 250 410 80 (d)

0.8 0.6 1.8 3.2 0.7 -

6.0 14 16

Deposits

None None None None None None None Heavy Very heavy Heavy and solidified

50 hour test; 200 cm3 air per hour; Cu, Mg, Fe, Ag, Al, Ti coupons immersed in fluid. (a) Data by 210 F. (b) At 421 K (300 F). (c) Formulated oil. (d) Oxidized oil is solid. Mahoney, Barnum, Kerlin and Sax [71.

514

fluids tested were unformulated except the diester, which was made up into a compounded jet aircraft engine oil. The influence of the aromatic structure of the polyphenyl ethers and of the m-terphenyl on oxidation resistance is shown by the low level of the acid numbers and the absence of deposits on metal coupons which were immersed in the fluids during the tests. Even the highest level of viscosity increase was not excessive. On the other hand, a petroleum oil oxidized at 477 K (400 F) set up to a solid, and the diester fluid (formulated with antioxidants) ran up a high acid number and left very heavy deposits. The instability of the tetrasubstituted silane is also apparent. The silicones survived the test with no deposits but with large increases in viscosity. AS long as the service conditions which the lubricant sees are compatible with the existence of a fluid film, there is no reason to believe that the characteristics which govern the behavior of a synthetic fluid in hydrodynamic or elastohydrodynamic lubrication are any different than those which hold for a petroleum oil: namely, viscosity, compressibility, and the temperature and pressure dependence thereof. But when failure of the fluid film is suspected and the possibility of metal-to-metal contact arises, the intrinsic antiwear and antiseizure behavior of the synthetic fluid becomes pertinent. Logically these problems should be studied by behavior under conditions related to service; in practice, as is mostly the case in the evaluation of conventional lubricants, they are dealt with usually in terms of the commonly used arbitrary bench tests.

Table 17-6 indicates that concern with the intrinsic influence of the specific lubricant on wear is valid. The fluids listed there are of low viscosity because they were investigated for low-temperature hydraulic service [141. However, the extent of wear shows no direct relation to viscosity; the silicate fluid, which permits the most wear, is not the least viscous of the fluids tested, and the silicone, which is the most viscous, is not the one which gives the best antiwear rating. Figure 17-4 shows intrinsic lubricant behavior in a different version of TABLE 17-6. FOUR-BALL WEAR WITH SOME SYNTHETIC LUBRICANT FLUIDS Viscosity, cs 310.8 K (a) Silicate ester Dimethyl silicone Fluorohydrocarbon Fluorinated polyether Hydraulic fluid (d)

1.66 12.09 2.38 0.99

-

Four-ball wear scar diam., mm (c) 372.0 K (b)

0.80 5.01 1. 14 0.43 -

1.06 0.56 0.44 0.39 0.28

(a) 100 F. (b) 210 F. (c) 10 kg load, 2 hours, I200 rpm, 348 K (167 F). (d) Fully formulated commercial fluid. From data by C. S. Armstrong [ i41.

515

10 5 E E

r30 40

10 20 Load, kg

5

Figure 17-4. Four-ball testing of various lubricant fluids. One hour at 2 4 0 0 rpm, 4 7 7 K ( 4 0 0 F). A: Di(2-ethylhexyl) sebacate. B: bis(p-Phenoxyphenyl) ether. Data by Mahoney e t aL. 1 7 1 . the four-ball wear test. While the consistent difference in the size of the wear scars obtained with di(2-ethylhexyl) sebacate and with polyphenyl ether might be ascribed to viscosity effects, such a reason cannot be advanced for the extremely high wear found with m-terphenyl. The behavior with white oil is probably indicative of a load-governed wear transition. The

data

in

Table

17-7,

taken from work by Klaus, Tewksbury and

Fenske [ 1 5 ] , compare the behavior of silicate ester and silicone fluids with that of dicarboxylate ester and mineral oil in four-ball antiwear testing. At 3 4 8 K ( 1 6 7 F ) under moderately heavy load of 1 0 kg the silicate ester and the silicone are comparable to the other two fluids in anTABLE 1 7 - 7 . ANTIWEAR PERFORMANCE OF SILICATE ESTER AND SILICONE FLUIDS IN THE FOUR-BALL TEST Temper at ur e deg. K Silicate ester Silicone Dicarboxylate ester Mineral oil

One hour at 6 2 0 rpm.

348 533 589 348 533 589 348 533 58 9 340 533 589

deg. F 167 500 600 167 500 600 167 500 600 167 500 600

Avge. wear scar diameter, mm 10 kg

4 0 kg

0.22 0.22

0.44 1.04 1.17 0.31 0.77 1.38 0.56 0.68 0.63

0.28 0.31 0.20

0.47 0.57

0.63 1.62 1.19 0.67 1.56 1.30 0.69 0.96 1.10 0.60 1.38 1.71

1

k9

0.21

0.72 0.78 0.18 0.39 0.29 0.34

0.42

From data by Klaus, Tewksbury and Fenske 1 1 5 1 .

516

tiwear action, but at 5 8 9 K ( 6 0 0 F) the silicate definitely inferior. Under 40 kg load the similarly.

and the silicone are fluids all behave quite

The relation between structural types in silicones and wear or friction control has been studied from several points of view. Brown 1 1 6 1 prepared a series of methyl alkyl polysiloxanes whose properties are shown in Table 1 7 - 8 . The results of their wear testing in the four-ball machine is seen in Fig. 17-5. The sharp drop in wear as the size of the

TABLE 17-8.

I

PROPERTIES OF METHYL ALKYL POLYSILOXANES c

YH3 CH -Si-0-

7

r 3

-Si-0-

1.7'3

I

3 1 CH 3

nCH3

Alkyl group, R

Ethyl n-Propyl n-Butyl n-Amy1 n-Hexyl n-Octyl n-Decyl n-Dodecyl n-Tetradecyl

3

-Si--CH

Viscosity, cs 310.8 K (a)

3 7 2 . 0 K (b)

67 67 82 98 99 147 195 246 298

22 21 27 29 29 37 44 51 58

(a) 100 F. (b) 210 F. Data by E. D. Brown, jr. [ 1 6 ] .

L

0.5 -

0

L - 4R,-Number- 8of -Carbon-Atoms 12 kin Side 7Chain

Figure 17-5. Effect of alkyl group size on antiwear action of methyl alkyl silicones in four-ball testing. One hour at 6 0 0 rpm, 5 0 kg load, 3 4 8 K ( 1 6 7 F). Data by E. D. Brown, jr. [ 1 6 ] .

517

alkyl group R increases from methyl to octyl and the levelling off for R > 8 is not likely to be a viscosity effect because the viscosity differences are greater for the higher temperature. Brown attributed the influence of the size of the alkyl chain to general bulkiness of the polymer molecule at the rubbing interface, a point of view for which Tabor and Willis [ 1 7 ] found some support on the basis of friction results. Halogen substitution on the phenyl group in methyl phenyl silicones can improve their antiwear function, but the character of such effects is governed by the test device as well as the test conditions. Descriptions of testing and experimental results are found in work reported by Gainer [ 1 8 ] and by Bowers, Cottington, Thomas and Zisman [191. Figure 1 7 - 6 from work reported by Schiefer [ 2 0 ] shows four-ball wear under various conditions with a methyl silicone copolymer that has dichlorophenyl groups in its structure. The abscissa, which is scaled in of chlorine content, is a measure of the proportion of terms dichlorophenyl groups in the makeup of the silicone. At 4 kg load and a temperature of 3 4 8 K ( 1 6 7 F), a chlorine content of C U . 6 - 7 % gives minimum wear, whereas at 4 7 7 K ( 4 0 0 F) wear increases steadily with chlorine content. With a load of 40 kg increase of chlorine content in the range 6 to 17 percent progressively reduces wear at both 3 4 8 and 4 7 7 K, but even at the lower temperature the smallest wear scar is still in the high-wear domain. Fluorine-substituted silicones do not behave like halophenyl methyl silicones. Figure 1 7 - 7 shows four-bali wear with ccpolymers containing 2.4 2.2

2 .o 1.8

E E, 1.6 c

& t E

.. .

p-

0'.

0

6

1.4

1.2

b 1.0 0

u,

p

0.8 0.6

0.4

-

0

0.2 0

0

4

8 12 Percent Chlorine

16

Figure 1 7 - 6 . Four-ball wear with methyl dichlorophenyl silicones. One hour at 1 2 0 0 rpm. From data by H. M. Schiefer [ 2 0 ] .

-

10 15 20 25 30 35 Percent Fluorine Figure 1 7 - 7 . Four-ball wear with methyl trifluoropropyl silicones. One hour at 1200 rpm. From data by H. M. Schiefer [ 2 0 1 .

0

5

518

methyl and triflouropropyl groups; 35% fluorine on the abscissa corresponds to a polymer with the siloxane chain completely filled with trifiuoropropyl groups. The absence of a sharp downward inflection in the curve for 40 kg load at 348 K probably indicates that fluorine, unlike chlorine in the chlorophenyl copolymers ( c d . Fig. 17-6), does not react chemically in the lubrication process. Tabor and Willis [17] found that trifluoropropyl silicones fell on functional curves for the behavior of methyl alkyl silicones in sliding friction and contact resistance as though the trifluoropropyl group were equivalent to an octyl group. 17.3.

APPLICATIONS OF SYNTHETIC LUBRICANTS

I n this section we shall examine some of the more important areas where synthetic non-petroleum liquids find utility as lubricants because One such area where the use of of their specialized properties. synthetic lubricants is particularly well-established is the lubrication of jet aircraft engines. The principal requirements for this service are good resistance to thermal and oxidative degradation, absence of hightemperature deposits, suitable viscosity throughout the range of service temperatures, solubility of additives, and availability. The parts to be lubricated are rolling element bearings and geared drives for auxiliary equipment such as pumps, etc. The synthetic fluid first widely used for this service was di(2-ethylhexyl) sebacate, and it is still accepted a s the typical fluid to which new developments are compared. I t has a wide range of satisfactory fluidity, with the viscosity lying in the range 1450 centistokes at 233 K (-40 F) to 3.350 centistokes at 310.8 K ( 2 1 0 F). I t dissolves complex esters and polymers which are used to augment its high-temperature viscosity. I t responds to oxidation inhibitors and antiwear additives. I t does not deposit excessive amounts of varnish or sludge and it does not thicken excessively after service at high temperatures. Experience with synthetic esters for jet engine iubrication has been so good that improvement has been concentrated on optimization of ester structures to push the durability of the base fluid into the higher temperature field as the demands of jet engine lubrication become more severe. The reader is referred to the patent literature and the open reports of various engineering laboratories for specific information about this highly specialized endeavor.

The intrinsic control possible with synthetic lubricants comes to the forefront in the formulation of nonflammable or fire-resistant hydraulic fluids. The lubricating function of the fluid must protect the pump which pressurizes the hydraulic system against wear. Some typical ranges of operating temperatures within which the fluid must function are: 220 to 505 K (-65 to 450 F); 233 to 561 K (-40 to 550 F); 255 to 644 K ( 0 to 700 F). In addition to acceptable viscosity, the fluid must have good thermal stability above 505 K, high autogenous ignition

519

temperature, and resistance to flame propagation. Blake and co-workers [ 3 1 reviewed the properties of 47 synthetic fluids with respect to these requirements; the following chemical types were represented: partially fluorinated hydrocarbons, fluorinated carboxylic esters, fluorosilicates, fluoroamines, halogenated tetrasubstituted silanes, fluoroaromatic ethers, halogenated w,w'-diphenylalkanes, and phosphorus esters (phosphates, phosphonates, phosphinates). I t turns out to be very difficult to optimize all the desired properties; low volatility and flame resistance are for the most part incompatible with the viscosity and pour point requirements. Phosphate esters, a much-recommended type of fire resistant hydraulic fluid, are not truly suited for high-temperature service because of excessive thermal decomposition at as low as 486 K ( 4 1 5 F). Surprisingly enough, although hydraulic pump tests are easy to carry out and probably thousands have been run routinely, few usable comTable parisons of synthetic fluids are recorded in the open literature. 17-9 shows the results of some comparative work carried out by W. H. Millett [ 2 1 ] with a vane pump. The polyglycol fluid gave the best allaround antiwear protection; however, fluids of this type have relatively low flash and fire points, of the order of 5 1 9 to 5 6 1 K ( 4 7 5 to 5 5 0 F). They show good antigumming behavior, a property which is very important for servov.alves with close clearances. The phosphate fluid had the poorest antiwear behavior of the three tested.

TABLE 17-9.

WEAR TESTING BY HYDRAULIC VANE PUMP (a) Petroleum oi 1

Phosphate ester fluid

Polyalkylene glycol fluid

Wear loss of pump part, mg Ring Rotor Vanes Bushings Total

400 20 460 30 910

540 260 130 110 1050

23 17 11

1 52

Viscosity, SLJS/lOO F 32 1

(a) 7 5 0 hours, 1000 psi, 1 2 0 0 rpm, 150 F. [211.

153

From data by

302

W.

H.

Millett

Service tests have not always confirmed the potential as hightemperature lubricant fluids one would expect from silicones on the basis of their properties and their behavior in laboratory investigations. As early a s 1 9 4 6 a study by Fitzsimmons, Pickett, Militz and Zisman [ 2 2 ]

520

reported. the poor durability of steel on steel and steel on cast iron in hydraulic pumps working with dimethyl silicone as the fluid. Some of the non-ferrous combinations, however, did not show this disadvantage. The benefits of the high-temperature stability of silicones may be illusory, for the small quantities of degradation products that do form may be wear-promoting o r may generate enough gel to clog filter elements. I n some instances synthetic fluids are proposed f o r lubricating service on the basis of their resistance to degradation in a radioactive environment. These are likely to be unsubstituted or short-chain substituted polyphenyls or polyphenyl ethers. Their radiation stability outweights their disadvantages in other respects, such a s high pou'r point and poor temperature coefficient of viscosity.

REFERENCES 1.

D. R. Wilgus, A. C. Ettling and M. A. Pino, J. Chem.

Eng.

Data,

6

( 1 9 6 1 ) 106-111.

2.

J.

3.

E n g . Data, 6 ( 1 9 6 1 ) 1 1 8 - 1 2 4 . E. S . Blake, G. A. Richardson, J. A. Webster and

4. 5.

6.

J.

Schmidt-CollGrus, J.

A. Krimmel and G. E. Bohner, J. Chem.

R. E. DeBrunner, ASLE Trans., 9 ( 1 9 6 6 ) 4 7 - 5 8 . G. Baum and C. Tamborski, J. Chem. Eng. Data., 6 ( 1 9 6 1 ) 1 4 2 - 1 4 5 . ASTM Method D 9 7 - 6 6 , Standard Method of Test for Pour Point, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. I. N. Duling, J. Q. Griffith and R. S. S t e a m s , ASLE Trans., 9 (1966)

1-12.

9. 10.

C. L. Mahoney, E. R. Barnum, W. W. Kerlin and K. J. Sax, ASLE Trans., 3 ( 1 9 6 0 ) 8 3 - 9 2 . J. Jakobsen, D. M. Sanborn and W. 0. Winer, J. Lubrication Tech. (Trans. ASME), 96F ( 1 9 7 4 ) 4 1 0 - 4 1 7 . K. L. McHugh and L. R. Stark, ASLE Trans., 9 ( 1 9 6 6 ) 1 3 - 2 3 . G. P. Brown, S. Aftergut and R. J , Blackington, J. Chem. Eng. Data,

11.

H.

12.

C. M. Murvhv. C. E. Saunders and D. C. Smith. Ind.

7.

8.

6 (1961)

M.

(1961)

125-127.

Schiefer, R. W. Awe and C. L. Whipple, J. Chem. Eng. Data, 6 155-160.

Enq.

Chem..

42

(1950) 24g2-2468. 13.

D.

C.

Atkins, C. M. Murphy and C. E. Saunders, I n d . Eng. Chem., 3 9

( 1 9 4 7 .) 1 .. 395-1401. 14. 15.

C. S. Armstrong, ASLE Trans., 9 ( 1 9 6 6 ) 5 9 - 6 6 . E. E. Klaus, E. J. Tewksbury and M. R. Fenske, J. Chem. Eng. Data, 6

16. 17. 18. 19.

E. D. Brown, jr., ASLE Trans., 9 ( 1 9 6 6 ) 3 1 - 3 5 . D. Tabor and R. F. Willis, Wear, 11 ( 1 9 6 8 ) 1 4 5 - 1 6 2 . G. C. Gainer, Ind. Eng. Chem., 4 6 ( 1 9 5 4 ) 2 3 5 5 - 2 3 6 2 . R. C. Bowers, R. L. Cottington, T. M. Thomas and W. A. Zisman, Ind. Eng. Chem., 4 8 ( 1 9 5 6 ) 9 4 3 - 9 5 0 . H. M. Schiefer, ASLE Trans., 9 ( 1 9 6 6 ) 3 6 - 4 6 . W. H. Millett, Ind. Eng. Chem., 4 2 ( 1 9 5 0 ) 2 4 3 6 - 2 4 4 1 . V. G. Fitzsimmons, D. L. Pickett, R. 0. Militz and W. A. Zisman, Trans. ASME, 68 ( 1 9 4 6 ) 3 6 1 - 3 6 9 .

( 1 9 6 1 ) 99-106.

20. 21. 22.

521

Chapter 18 LUBRICATING GREASE

In its general sense grease refers to a fatty solid, firm enough to hold its shape under its own weight but soft enough to flow under a low stress. These two characteristics determine what is known as the consistency of the grease. The consistency of a grease is the basis of its special utility as a lubricant and enables it to be applied to locations which cannot be supplied by a flow of liquid. In earlier times lubricating greases were actually solid fats, but modern greases are basically made up of a liquid oil and a solid thickener or gellant. The systematic study of the structure and the rheology of greases The falls mostly in the domain of colloid and physical chemistry. manufacture of greases is adequately treated in specialized books. A thorough treatment of greases in lubrication technology would require a None of these objectives can be specialized monograph of its own. achieved in the space of the single chapter t o follow, but the fundamental principles governing grease structure and the relations between structure and the utilization of greases are known well enough to be dealt with informatively. 18.1.

BASIC ASPECTS OF LUBRICATING GREASE STRUCTURE

The consistency of a grease is a complex of related properties, easily demonstrable empirically but difficult to define precisely. We can single out yield stress as a truly definable, pertinent property and then have a quantitative parameter in terms of which we can treat consistency. Criddle and Dreher [ l ] observed typical solid-body stress-strain behavior in greases, with an elastic region, a region of plastic deformation and an ultimate yield or rupture point. At rest grease behaves like a solid body; provided the specimen is not too big, i t will not flow under the force of gravity.* As stated above, a grease contains two basic components: an oil, which has the flow properties of a liquid; and a thickener o r gellant, which is a solid insoluble in the oil. I t will be shown later that the

*The behavior described above is idealized and simplified. In fact the yield point is affected by the rate of strain and there is slow creep at pressures within the nominal elastic range.

oil behaves as the continuous phase in this system. We must therefore explain the structure and the behavior of the system in which the continuous phase is a liquid and which responds to initial stress as an elastic solid. The structure and behavior is that of a gel. Following the reasoning of Hotten [ 2 ] , we shall call the solid component the g e e Lanf rather than the thickeneh. In this way we emphasize the fundamental structure of the grease as a gel and call attention to the difference between the action of a gellant and that of a polymeric viscosity improver, which functions by dissolving in the oil. Many different solids can be used to gel oils into greases. However, the gelling agents around which the standard technology of grease-making developed historically are the metallic soaps of fatty acids, and the bulk of the present-day output of greases consists of soap-gelled products. Therefore, when the nature of the grease is not explicitly specified otherwise, it will be understood that the gelling agent is fatty soap. The usual technique in making a soap-gelled grease is to form and disperse the soap in the oil at an appropriately elevated temperature and then to cool the mixture. The desired consistency in the finished product is achieved by a vigorous stirring and shearing process, known as milling. One of the forms in which soaps crystallize is a long-fiber phase. The structure of the soap phase in a grease is affected by the intrinsic nature of the fibers p e h b e , by the network which they form as they are generated and dispersed in the oil, and by the rearrangement of the fiber structure when the grease is milled. With the aid of electron microscopy, pictures showing soap fibers in great detail have become commonplace. Figure 18-1 shows some views of soap fibers separated from greases and converted to replicas by vacuum-shadowing with metals. The technique for making these replicas involves leaching the oil phase away from the soap with a volatile hydrocarbon solvent. While this treatment preserves the structure of the individual soap fibers adequately, it destroys the three-dimensional structure of the soap phase as a whole, upon which the characteristics of the grease depend. To preserve the structure of the soap network as it exists in the grease, the o i l phase must be displaced by a liquid that has the correct combination of critical temperature and critical pressure, so that i t can be evaporated from the oil-free soap without dissolving any of it and without forming a liquid film on the surface of the fibers which would disrupt their structure by surface tension forces. The soap skeleton resulting from this treatment is often termed an aerogel. Peterson and Bondi [31 described the sodium soap aerogel obtained from a grease by displacement of the oil with butylene as a chalky, pithy, rather brittle, opaque, white, porous

523

Figure 1 8 - 1 . Soap fibers from greases, photographs of replicas taken by electron microscopy. (a), ( b ) Lithium 12-hydroxystearate. ( c ) Lithium 1 nm oleate. ( d ) Calcium-sodium soap. Fiduciary marks:

524

solid which had maintained the bulk volume of the original grease to Determination of the surface area of the aerogel by nitrogen within 1%. adsorption and comparison with the area calculated from fiber diameter The grease which indicated the absence of pores in the fibers petr b e . was reconstituted by allowing the oil to permeate the aerogel in vacua experienced some shrinkage in gel volume. Key properties such as cone penetration value and durability of consistency in the roll test differed little for the original and the reconstituted grease. McClelland and Cortes [ 4 ] prepared aerogel specimens which could be examined directly in the electron microscope. These preparations were compared with soap specimens which had been prepared by the conventional solvent-washing techniques. All specimens prepared by the aerogel technique showed the typical closely interlocked network structure, whereas the soap structures resulting from solvent-washing were broken down, with dispersed fibers. Aerogels were also studied for non-soap gellants such as treated bentonite, purified attapulgite clay, esterified silicic acid and carbon black. I f structure is imparted by the gellant, what part does the oil play in the behavior of a grease? Let us think of an ideal grease as one with the fibers of the gellant interlocked to form a uniformly arranged system of passages filled with liquid oil as a continuous phase. Then let us consider a cubical element of this grease, restrained from gross motion as a whole but with the liquid phase free to move through the cube under the influence of the hydrostatic pressure p in the direction from face There will be an efABCD to face A'B'C'D', as illustrated in Fig. 18-2.

D

A,

61

Figure 18-2. Gel structure of a grease and the flow of the oil phase. The oil will nove through the pores of the gel structure under the pressure p.

525

flux of oil through the pores of the gellant structure and out of the cubical element at the face A ' B ' C ' D ' . As a simplified analogue of a passage in the gel structure of grease let us examine the behavior of a liquid in a straight capillary tube of circular cross-section. I f we start with the capillary filled with liquid and displace a volume V in the capillary to form a drop, as shown in Fig. 18-3, two general cases arise. I f the liquid wets the wall of the

Figure 18-3. a grease.

Capillary analogue of oil flow through the gel structure of

capillary but movement of the column a distance h leaves the exposed wall dry, then the work done by the moving liquid must be equal to the work of wetting plus the work of creating new surface in the exuded drop. The energy thus required is given by the general relation n t2p h = Z n t h E , + A A E ~ (18-1) where p is the hydrostatic pressure, t the radius of the capillary, A A the increase in the surface area due to the exuded drop, E l the energy of wetting per unit area and E2 the surface energy of the liquid per unit area. I f the movement of the liquid in the capillary does not de-wet the wall, then ntI2ph

=

(2nt'h

+

aA')E2

(18-2)

Zqn 1 8 - 2 probably represents the behavior actually encountered, as complete de-wetting by retraction of the liquid is unlikely.

The basic model of a grease, then, is that of a self-supporting structure of interlocked fibers or aggregates of gellant, within which liquid is held by capillary forces. This model is consistent with the two characteristics most typical of grease: resistance to change of

526

shape below the yield stress and relatively easy flow at higher stresses. However we shall find that the actual behavior of real greases has a number of nuances and complexities which require modification and sophistication of this basic model. 18.2.

THE MANUFACTURE OF LUBRICATING GREASE

In principle the manufacture of a grease comprises two simple operations: dispersion of the gelling agent in the oil, and mechanical working o r stirring of the gel to give the grease the desired consistency. In practice there are many technological complexities, as the reader can discover by consulting a specialized text on the subject [ 5 1 . Our interest in the influence of technological manipulations in the manufacturing process on the properties of the grease is motivated by our concern with the relations between the properties of greases and their function as lubricants. The most important greases are those gelled by metal soaps of fatty acids. Table 1 8 - 1 gives a schematic outline of the typical processes by which soap-gelled greases are manufactured. These processes can have TABLE 1 8 - 1 .

SCHEMATIC OUTLINE OF MANUFACTURE OF SOAP-GELLED GREASE

I. Soap formed in the oil A. Saponification of glyceride

fats or other fatty acid esters

B. Saponification of fatty acids

1 . Dehydration 2. Dissolution or tempering of soap in the o i l 3 . Cooling and crystallization of the soap 4. Milling for consistency 11. Preformed soap added to the oil

1. Dissolution o r tempering Cooling and crystallization 3. Milling 2.

direct influences on the properties of the greases which they produce. For example, the direct saponification of a glyceride fat in the oil which is to be gelled into a grease means that the water which participates in the saponification and the glycerol released from the fat must be removed from the mixture. How well this is done is a function of the time allotted and of the configuration of the equipment. Thus, a grease gelled by preformed dry soap could have properties different from one made with soap saponified in b i t U and not fully purged of small amounts of retained water o r glycerol. After the soap has been made and dehydrated, the reaction mixture

is

527

tempered thermally to obtain the desired gel structure. To economize on heat in the commercial manufacturing process, the dehydrated soap is not dissolved. in the oil and then crystallized o n cooling. Instead, a thermal soak which gives the desired crystal structure to the soap in the solid phase is employed. The phase transitions involved in the production of lithium soap greases were investigated by Suggit 161, who showed that soaps prepared below a critical temperature characteristic for each fatty acid anion species crystallize as platelets which are mediocre gellants for grease. I f held above this critical temperature, the platelets are transformed to the type of fiber structure seen in Fig. 18-1. Suggit found the critical temperature for lithium stearate to be 468 K (195 C). The phase diagram for lithium stearate and white oil (390-440 molecular weight) as determined by Cox 171 and shown in Fig. 18-4 has 458 K (185 C) as the temperature of transition from the field representing a mixture of lithium stearate crystal I and isotropic solution to the field representing a waxy phase. I

250

I

I

I

I

I

I

I

E

I

~

/

00 200-/cLD

1 \

0

v

\

150-

-II

B+E

3

Eg 100E

I-"

50, I

A+ E I I I

I

'

I

I

I

-

Mole-% Lithium Stearate

Figure 18-4. Phase diagram for the system lithium stearate-white oil. Crystalline lithium stearate I. B: Crystalline lithium stearate 11. C: Waxy phase. D: Liquid crystal phase. E: Isotropic solution. Data by D. B. Cox [71. A:

Both Suggit [6] and Cox [7] discussed those structural aspects of the waxy phase which would favor the formation of fibrous soap crystals. It is obvious that the fibrous soap structure desired in a grease at room temperature must be in a metastable, supercooled state. Cox commented'on the strong supercooling of the waxy phase 171. Vold, 3 z u and Bils 181 were able to demonstrate supercooling directly by comparison of heating and cooling curves in differential scanning calorimetry of the system lithium stearate in white oil. In modern greasemaking oil mixture is subjected to break up clumps of soap the grease. This stiffens

technology the to milling: i . and distribute the grease, a s

gel formed by cooling the soape . , passage through narrow gaps

the fibers uniformly throughout i s evidenced by decrease in the

cone penetration values; but even more important, it reduces gross leakage of oil out of the gel structure [91. Evidently reduction of the proportion of large passages in the free space of the soap structure is an important aspect of improving the utility of a grease. At least 90% of the grease produced in this country is gelled with soaps, and in these soaps the most prevelant cationic constituents are calcium, lithium and sodium. At the most, only 10% of the soaps have other cations, principally aluminum, barium, strontium, and perhaps lead. Glyceride fats are most likely to be tallow, animal grease,* hydrogenated lard oil, hydrogenated vegetable oils, liquid vegetable oils, or fish oils (liquid and hydrogenated). Mixed acids from fats and*oils are available commercially, as well as individual constituent acids such as stearic acid, palmitic acid, oleic acid, myristic acid, lauric acid, etc. fr fatty acid of particular importance is 12-hydroxystearic acid. Commercial grade fatty acids are usually contaminated by their nearest homologues. Commercial 12-hydroxystearic acid is likely to be the mixed hydrogenated acids from castor oil. It is thus apparent that one of the chief technological difficulties of making grease reproducibly is control of the quality of the starting materials. Non-soap gellants for grease add u p to a n impressive list, examples of which include the following: treated bentonite clays, treated attapulgite clays, terephthalamate salts, treated silica, aryl ureas, indanthrene, phthalocyanines, carbon blacks. The same general principles which govern soap-gelled grease structure hold for these non-soap gellants, but individual techniques for making the grease differ from one type of gellant to another. Another variation in grease formulation is the substitution of a synthetic organic liquid for the petroleum oil phase, particularly for use in severe environments. Silicones of various types-dimethyl, methyl phenyl, trifluoropropyl-have been incorporated into greases for such service. 18.3.

FURTHER CONSIDERATION OF GREASE STRUCTURE

Now that we have some idea about the composition of greases and how In they are made, let us inquire into their structure a little further. particular we wish to establish a basic connection between the structure of a grease and the reason it is used for lubrication service. 18.3.1.

Bleeding and Permeability

Booser and Wilcock 1101 viewed the function of grease in ball bearing lubrication as a controlled release of oil to the zone of contact of the balls with the races and the cage. Following this line of thought, A. E.

*A mixture of solid stearine and liquid olein; not the lubricating grease made by gelling liquid lubricating oil.

529

Baker [ 1 1 1 regarded test data on the bleeding of oil out of a grease a s a significant evaluation of its lubricating quality. The bleeding test employed to arrive at this conclusion is a simple one [121. Ten grams of grease are placed in a wire mesh cone hung in a closed vessel which catches the oil that bleeds from the grease. Temperature and time can be fixed to suit the experimenter's requirements. Obviously the test is grossly empirical, and moreover its significance is obscured by complications which will be discussed later in this section. As pointed out in Secrion 18.1, grease is composed of a network of solid gellant fibers that hold the continuous liquid phase by interfacial and surface forces. Spontaneous exudation of liquid from this structure requires the unbalancing of these forces. The method of Sisko and Brunstrum 1 1 3 1 for measuring the permeability of grease to the movement of oil depends on driving the exudation artificially; the apparatus is illustrated in Fig. 18-5. The sample of grease is filled into the volume bounded by the retaining ring and the screen-supported Millipore filter;

Burette-

n

a

Gaskets Retainingring

Screens and millipore filters

Grease'Sample Figure 18-5. Apparatus for the grease by oil

determination

of

the

permeability

of

the thickness and the cross-sectional area of the sample are then known. clamp fastens the sample to the adapter that carries the burette. The adapter and the burette are filled with oil, preferably the same oil from which the grease was made. Under these conditions, the only liquid surfaces and interfaces of any consequence are those at the bottom surface of the sample tisk, and even those can be reduced to negligible proportions by having the bottom of the sample holder in contact with a pool of oil in a receiver. Movement of the oil will be governed by the viscous resistance of the passages in the gel structure and Darcy's law for the flow of liquids through porous beds is taken to be applicable: A

530

where u is the velocity of oil flow through the sample, p is the pressure is the viscosity of the oil. The perdrop across the thickness a, and meability B has the dimensions of area, but it can also be interpreted as the volumetric flow rate of the liquid through the unit cube of porous material under unit pressure drop. The experimental determination of permeability by the method of Sisko and Brunstrum [13] is obtained from the rate of fall of the level of the oil in the burette. Then from Eqn 18-3 we get h2

dh

- - _ = -

K2 d t

Bpgh

(18-4)

qa

where n is the radius of the burette, R the radius of the grease sample, h the height of the oil column above the sam le, p the density of the oil and cj the acceleration of gravity. Equation 18-4 can be rearranged to

g = -

2.303 vanL d(Racj h )

5R2

dt

where v is the kinematic viscosity.

(18-5) Collect ng the constants gives us

d(toy h)

B = - k

dt

(18-6)

The validity of E q n 18-5 was tested experimentally by Ewbank and his co-workers 1141. They found that plots of h against t on semilogarithmic coordinates were consistently linear. The viscosity of the permeating 2 oil was varied over the range 0.00003-0.001 m / s (30-1000 cs), but fluctuations in the value of 8 stayed within the range 5-10% i f the oil was of the same general chemical type. Change in the type of oil sometimes gave deviations of up to 40% in the permeability. In some cases sensitivity to the thickness of the sample bed caused as much as 30% deviation, especially when the permeability of the qrease was intrinsically low * I t is a mistake, however, to ascribe deviations from the results expected by Darcy's law to weakness of the experimental technique. A more productive point of view is to assume that Darcy's law holds for the ideal gelled grease structure and to interpret deviations from predicted behavior as informative of the actual structure. For instance, Brown and Ewbank [15] proposed that permeation takes place predominantly through the larger pores of the grease structure and cited evidence that only about 25-50% of the oil held by a grease can be made to flow out of the structure. Persistent retention of the oil can be ascribed to physicochemical interaction with soap fibers, the effect of which is

531

relatively more pronounced in the narrower passages. Thus the strong effects of oil viscosity and oil type reported by Zakin and T u [ 1 6 1 can be given a rational explanation. Greases are often used to lubricate bearings at elevated temperatures, sometimes 4 7 8 K ( 2 0 5 C ) or higher. Therefore oil bleeding tests are frequently carried out at the anticipated working temperature of the grease. Two factors affect the influence of temperature on oil separation. One is the decrease in the viscosity of the oil as the temperature rises, thereby facilitating filtration of the separated oil away from the grease. The other factor is the phase state of the oil-soap system at from data by Hotten and Birdsall the test temperature. Figure 1 8 - 6 , [ 1 7 ] , shows the combined effect of these two influences on the bleeding of greases made with various lithium soaps in naphthenic oil. A l l the

I , , , , , , , ,

0 25 5 0 75 100 125 150 175 200

~

!5

Ternperature,deg . C

Figure 18-6. Eff ect of temperature on oil separation from greases made with lithium soaps: 1 2 % of the lithium soap in naphthenic oil: 3 hours vacuum filtration at the indicated temperature. Data by biotten and Birdsall [ ! 7 1 . greases exhibit an increase in the amount of oil separable by 3 hours vacuum filtration as the temperature rises to a critical value which depends on the soap. The maximum in the bleeding curve is followed by a decrease which is quite sharp for the greases made with oleate, stearate The grease or myristate soap but less so for the laurate soap grease. gelled with lithium 12-hydroxystearate shows the least sensitivity of bleeding to temperature and also has a high critical temperature. The sharp decrease in bleeding is probably associated with a transition to the waxy phase. I n Fig. 1 8 - 6 the dip in the oil separation curve is at

532

453 K ( 1 8 0 C); in Fig. 18-4 the transition for the system lithium stearate-white oil is at 463 K ( 1 9 0 C). The sharp rise in the bleeding of oil from the lithium 12-hydroxystearate grease is due to transformations to the liquid crystal and the isotropic liquid states. If controlled bleeding of oil is desired for the lubrication of bearings, then Fig. 1 8 - 6 illustrates the importance of the phase behavior of the soap component of grease with change of temperature. The reason for the superior utility of lithium hydroxystearate greases is apparent from the bleeding behavior. 18.3.2.

Consistency and Penetration

It has already been pointed out that the consistency of a grease is the characteristic most overtly connected with its functionality. In qualitative terms consistency can be thought of a s resistance to unwanted flow; in terms of performance it is manifest as antislumping behavior, the correct degree of channeling, resistance to ejection from a bearing by centrifugal force, etc. The physical test by which consistency is evaluated quantitatively is the ASTM cone penetration determination [ l a ] , which is illustrated schematically by Fig. 18-7. The cone and its attachments weigh 0.1500 kg. At the start of the test the cone and dial

I !

Figure 18-7.

initial position of the cone

Cone penetration of greases

assembly is adjusted so that the tip of the cone just touches the level, undisturbed surface of the grease sampie (AA') when the dial reads zero. The cone is then released and sinks into the grease. The distance A , read on the dial in tenths of millimeters, is the penetration value of the grease. The test is usually carried out at 298 K (25 C). The softer the grease the greater the penetration value. Table 18-2 gives the relation between the National Lubricating Grease Institute classification system and penetration values.

533

TABLE 18-2.

PENETRATION VALUES FOR NLGI GREASE GRADES

NLGI Grade NO. 000 00 0 1 2

3 4 5 6

Penetration at 2 9 8 K (a) 445-475 400-430 335-385 310-340 265-295 220-250 175-205 130- 1 6 0 85-115

(a) ASTM D 2 1 7 (worked 6 0 strokes). The ASTM penetration value is not a measure of yield stress. The theoretical difficulties in the determination of the true yield stress of a grease have been discussed by Evans, Xutton and Matthews [ 1 9 1 . Greases do not really have a sharp stress boundary between elastic and plastic deformation; there i s always some residual creep although the flow rate may be slow enough to be treated as zero for practical purposes. The apparent viscosity of grease is dependent on rate of shear, and slow lowering of.the penetrator at a uniform rate will give results different from those of the quick-release ASTM method. Also, the buoyancy due to the behavior of the grease a s a fluid must be taken into account. Evans e t al. developed a relation for a simple right circular 90' cone as an indenter:

w

Pb =

- W'

-

where on the in the ing as

A

(18-7)

pb is the bearing pressure which supports the cone, W is the load cone, W ' is the buoyancy force and A is the cross-sectional area plane of AA'. I f T~ denotes the yield stress of the grease behava plastic solid, then

where c is a constant of proportionality which in theory is obtainable Therefore p b is from the solution of the plastic deformation problem. fundamentally proportional to the yield stress of the grease, whereas the empirical ASTM penetration value is not. Nevertheless, it is the ASTM penetration numbers that are the generally accepted measure of the consistency of greases, and numerous investigations are on record where the penetration values are used to assess the influence of the type of gellant, the concentration of the gellant, the method of manufacture, the working of the grease (milling, shearing, flow), etc. The empirical character of such information has

534

TABLE 18-3.

EFFECT OF FIBER LENGTH ON GREASE CONSISTENCY ~~~

Nylon fibers

Soda soap grease

Axial ratio

Micropenetration, fiber diameter of

L/D

300/1 100/1 70/1 50/1 6/ 1

95

Axial ratio L/D

118 125 -

165 208 208 Fluid

Micropenetration

170/1 80/1

120 200

Data by Bondi e t a L . [ 2 0 ] . not seriously affected its utility for technological purposes. A direct demonstration that the geometry of the gellant fibers influences the penetration response of grease is found in the work of Bondi and his collaborators [20], who gelled a turbine oil into a grease by incorporating 10% of completely insoluble nylon fibers. The consistency of the resulting product depended on the ratio of length to diameter ( L / D ) of the suspended nylon particles, as shown by the data in Table 18-3. The same trend holds for a grease gelled by a soda soap. R. H. Leet [211 obtained the ratio of the average fiber length L to the average diameter V for nine greases of different composition, samples of which were worked i n various ways o r allcwed to harden by aging and then tested for penetration. The relations between ASTM penetration value and L / V are shown diagrammatically in Fig. 18-8. The influence of the individual nature of the grease is evident, but there is also a consistent linear

400

I

I

c

g e c C

fv)a a"

& \ \ \ 0 0 3 g

200

A ,

535

relation between ASTM penetration and L/D for each grease. Other data showing the influence of L / D on penetration for a grease gelled by 7% lithium 12-hydroxystearate have been reported by Borg and Leet [22]. All greases suffer a degradation in consistency when subjected to prolonged shearing action. One of the devices commonly used to shear greases in stability testing is the ASTM grease worker, a full description of which is given in the ASTM penetration Method D 217 [l8]. In essence the grease worker is a circular plate 2-15/16 inches in diameter with 41 1/4-inch holes. The plate is worked up and down with a stroke length of 2-5/8 inches through the grease sample in a cup 3.000 inches in diameter. The instructions f o r standard working call for 60 double strokes [18]. Prolonged working may amount to 100,000 strokes or more. Table 18-4 gives data by Woods and Trowbridge [231 showing the effect of prolonged working on penetration value for six different types of soapgelled greases. Another method of working greases is with the roll tester [241, which consists of a cylinder 3-35/64 inches i n diameter and 7-3/32 inches long, i n which are placed a 50-gram sample of grease and a solid roller 2-3/8 inches in diameter, 6-15/16 inches long, weighing 5 kg. The cylinder is driven o n a set of idlers at 165 rpm. The grease is sheared by the motion of the roller on the inner surface of the cylinder. Loss of consistency is monitored by a quarter-scale penetration test. Figure 18-9 shows some characteristic behavior. Comparison of Fig. 18-9 with Table 18-4 shows that the results of the roller test and the grease worker test do not rank the greases in the same relative order. 18.4.

THE FLOW OF GREASES

I n lubrication with a liquid, the rheology of the lubricant at the functioning site is the dominant behavior; transportation of the lubricant to that site, e . 5 . a bearing o r a gear, by piping or spray nozzle is on the whole a routine matter and rarely affects the selection

TABLE 18-4.

EFFECT OF WORKING ON PENETRATION OF SOAP-GELLED GREASES

Type of soap

ASTM penetration 60 strokes

100,000 strokes

277 295 282 270 269 268

286 335 354 358 370 380

Li 12-hydroxystearate Ca tallow Na tallow/stearate A 1 stearate Li stearate Na tallow Data by Woods and Trowbridge [231.

536

240

200

s s

E

160

W C

a

2

P 120 80

I0

I 24

I

t

48 72 Rolling Time, hours

96

Figure 18-9. Roll testing of grease consistency. Gellants: A . Lithium stearate. B. Lithium 12-hydroxystearate. C. Calcium tallow soap. D. Sodium tallow-stearate. E. Aluminum stearate. From data by Woods and Trowbridge [23].

of the lubricant. But when the lubricant is a grease, rheological problems associated with getting i t to the functioning site are often a s important as those directly connected with its primary lubricating action. These two aspects of grease behavior are frequently at variance with each other. For instance, in a bearing it is preferred that the grease remains packed in place and not be bodily moved around by stress, whereas for transportation in a piping system, gross flow is desired. Let us look at the behavior wanted of grease in a rolling element bearing. Some lubricant must get into the conjunction zone between the ball or the roller and the race, small though the quantity required may be. There are a number of reasonable models f o r how the lubricant gets into the conjunction zone. If we postulate that it is the total grease which flows into the conjunction and functions there as the lubricant

0

2.5

a Q 2.0

(u

< 1.5

1 E 3i 8

F First cycle

300 seconds

E--

Sleady stale after 1000 sec preshearmg

1.0

8 0.5

10

0.0

I 8

I

1

I

I 1

I

160 8 160 8 Rote of Sheor,.i, lo3 sec-'

I 16

Figure 18-10. Flow behavior for lithium stearate grease. Bauer, Finkelstein and Wiberly [261.

From

data

by

537

without segregating into oil and soap, then the principles of elastohydrodynamic lubrication can be applied. A detailed analysis is given by Kauzlarich and Greenwood [ 2 5 ] ; what interests us particularly in this work is the viscosity function used for the grease. An informative study of the flow behavior of soap-gelled grease is that of Bauer, Finkelstein and Wiberly [ 2 6 ] . Figure 1 8 - 1 0 shows the relation between the rate of shear and shear stress for a grease gelled with 12% lithium stearate. The three diagrams show the behavior for the first cycle of shearing, the second cycle, and the ultimate steady State. The first cycle is characterized by pronounced hysteresis as the rate of shear is increased from zero to the maximum of the viscometer and then decreased back to zero. In the second cycle the hysteresis loop is much smaller. A shearing time of 100 seconds at a shear rate of approximately 975 5-l removed the hysteresis loop from the flow curve having a cycle period of 300 seconds. With the hysteresis eliminated, the flow diagram clearly shows the existence of a yield stress. Bauer and his co-workers [ 2 6 ] proposed the following equation for the flow relation of greases: T

-

To

= Cli

+

-n C2y

where c l and c2 are constants and T~ is the yield stress. Greenwood [ 2 5 1 generalized the flow function to T

-

To =

f(i)n

(18-9)

Kauzlarich and

(18-10)

in order to facilitate manipulation of the elastohydrodynamic computations. The evaluation of f(:)n required for a specific problem can be obtained from experimental data by graphic or numerical methods. Usually it is assumed that hysteresis has been eliminated. But obviously it is incorrect to use steady-state grease rheology when measuring starting torque.after a long rest or evaluating flow resistance in slow reciprocation. The thixotropic properties of grease and the relation of structure to thixotropy, as exemplified by the work of Eyring and his collaborators C27, 2 8 1 , can be highly pertinent aspects of the flow of grease, although the details of an adequate treatment are too involved for the space available here. Just a s complex is the viscoelasticity of grease. The work of Forster and Kolfenbach [291 indicates a relation between viscoelastic behavior and structure. The flow of grease in piping or tubing brings up two questions of technological importance: (a) How much pressure drop is there along the run of pipe? (b) Given the driving pressure at the pump, what is the flow rate at any selected distance along the piping? Both of these questions can be treated adequately in terms of the general principles of

538

viscometry discussed in Chapter 4 and the flow relations for grease given above. The following expression (see Chapter 4, Eqn 4 - 1 4 ) can be used to obtain 2, the volumetric rate of flow through a tube:

where A p is the driving pressure, R the radius of the tube, L its length is a functional relation between the shear stress and the rate and T"/+ By one means of shear such as shown in the flow diagram of Fig. 1 8 - 1 0 . or another the steady-state flow diagram can be made to yield a value for A capillary flow determination such as ASTM Method D the exponent n'. 1092 I 3 0 1 yields values of 2 for preselected values of Ap, R and L . Furthermore, Eqn 4 - 1 of Chapter 4 gives the expression below for the shear stress at the wall of the tube o r piping through which the grease is flowing: ApR

T = -

2L Substitution into Eqn 1 8 - 1 0 gives APR T - T o = -

(18-12)

2L

The yield stress T~ can be obtained by the rotational viscometry technique as shown in Chapter 4. Thus from two sets of rheological determinations, one the capillary flow technique and the other rotational viscometry, enough information can be obtained to treat the problems associated with the flow of grease in pipes. A quantity cited fairly often in discussing the properties of greases is the apparent viscosity. This is the empirical ratio of measured shear stress to rate of shear: T

nappatlent =

Y

(18-13)

Apparent viscosity is useful as an evaluation of the difficulty of pumping a grease. Since greese moves by non-Newtonian flow, knowledge of the rate of shear and also of the yield stress required to initiate flow is necessary for apparent viscosity value to have any utility. 18.5.

GREASE AS A LUBRICANT IN SERVICE.

Greases are used as lubricants i n a wide range of service conditions, The lubricathe more important of which are summarized in Table 1 8 - 5 . tion of high-speed rolling-element bearings is probably the most familiar service use of grease, but other applications are the lubrication of

539

TABLE 18-5.

TYPES OF SERVICE FOR LUBRICATING GREASES ~

Motion and contact

Examples

Unidirectional Fast, continuous Slow, continuous Slow, intermittent

Rolling element bearings Bearings, cams Gears, cams

Oscillatory or reciprocating Slow to moderately fast

Suspensions, linkages, cams

slow-speed plain bearings a s well as of large, slow-acting gears which i t is impractical to enclose in a case that holds an oil lubricant. Automotive suspensions, which cannot be sealed adequately against oil leakage, are also advantageously lubricated with grease. Basically the lubrication of a high-speed rolling element bearing is no different with grease than with oil. Booser and Wilcock [ l o ] studied the running life of No. 306 ball bearings turning at 3600 rpm under a radial load of 7 1 1 . 7 N 1 1 6 0 lb) when lubricated with oil in submilligram quantities. With less than 0.35 mg of oil on the bearing, running life was gi’ven by the expression

t

=

0.66

w

2 being the life of the bearing in hours and

milligrams. given by

LU the quantity of oil in For quantities of oil greater than 0 . 3 5 mg, bearing life was

I t was calculated that 0 . 3 5 rng of oil would cover the balls, races and F o r bearings retainer pockets with a film 51 nm ( 2 rnicroinches) thick. of conventional precision (Grade ABEC-1) lubricated with one milligram of oil, a running time of 4 . 7 hours was observed, and with high-precision Grade ABEC-5 bearings the running time was 1 4 . 5 hours. With fully packed open bearings lubricated with grease the life times were 2000 and 4000 hours respectively. The grease is believed to function a s a source of oil by controlled bleedincj a s it is worked by the motion of the roIling elements in the bearing.

However, there are n o a phiahi grounds for excluding the possibility that the whole grease instead of just the exuded oil is the functioning lubricant. Dyson and Wilson I 3 1 1 and also S . Y. Poon [ 3 2 1 have published film thickness data for the elastohydrodynamic lubrication of rolling disks with grease. This may be regarded a s a close experimental approximation of a roller acting against a race in a bearing. Figure 18-11 is a diagram of typical results obtained. Curve A shows the ratio of

540

0

oc"=

1.0

ln ln 0,

c

1

0

._ E LL

0.0 0 10

20

30 40

50 90

Time, minutes

Figure 18-11. Elastohydrodynamic film ments. 10% Lithium 12-hydroxystearate sure; 335.3 cm/s surface velocity at base oil film thickness 2.201 Um. A : before experimental r u n . Data by Poon

behavior of grease in disk experigrease; 965.3 MPa contact pres800 rpm; temperature 308 K (35 C ) ; Original grease. B: Presheared [321.

measured film thicknesses for a grease gelled with 10% lithium 12hydroxystearate and for the base oil a s a function of the duration of running. At the beginning, the thickness of the grease film was 1.6 times that of the base oil, but after approximately 50 minutes running the ratio dropped to a steady 0.7. The part that degradation of gel structure by flow through the conjunction zone played was assessed by preshearing the grease in a gear mill before the disk experiment. The initial film thickness ratio for grease/oil decreased to 1.1 and a final ratio of 0.7 was attained in 30 minutes. The film thickness of the ungelled base oil was 2.201 urn ( e 7 microinches); hence a ratio of 0.7 c o r responds to 1.549 Urn ( 6 1 microinches) for the grease film. Even though the film of grease was thinner than that of the base oil, it was still thick enough to prevent contact of the bearing surfaces. Poon [321 explained the film behavior of grease in terms of viscoelastic behavior a s the lubricant passes through the conjunction zone. Kauzlarich and Greenwood [251 suggested that because of its gel structure grease heats u p by shear faster than oil and loses the heat by conduction more slowly. I n their estimation, a thermal rather than an isothermal treatment of the elastohydrodynamic problem is required. Elastohydrodynamic action of the total grease and selective bleeding of the oil are not mutually exclusive mechanisms in the lubrication of I n this respect grease i s a versatile rolling-element bearings. lubricant, for i f the flow of the grease a s a whole suffers a temporary interruption, then the residual oil coating the bearing can protect the system from damage for a while. Still another mechanism for lubrication by soap-gelled greases stems from the fact that soap is a "boundary" lubricating agent. Using a slow-

541

speed pin-on-disk type tribometer, Godfrey [33] showed that the friction with dry soaps such as calcium stearate or sodium stearate, as influenced by temperature in the range 373-473 K (100-200 C), resembled that of the greases made with these soaps and was quite distinct from that of the base oil. Simple dispersions of silica, bentonite o r calcium carbonate in the base oil showed maxima in the coefficient of friction at 473 K , whereas the soaps and the greases made with them gave minima at that temperature. Horth, Sproule and Pattenden [341 compared the frictional torque of a 120' journal bearing lubricated with greases against the torque obtained with the base oil; their results are summarized in Fig. 18-12. Speed-governed transitions to hydrodynamic action are apparent for the base oil and for the greases gelled with aluminum soap,

I

1

I

I

I

L

I

1

I

,

0.05 0.1 0.2 0.5 1.0 2.0 5.0 10 Journal Speed, cm/s Figure 18-12. Speed-dependent torque behavior of greases in a journal bearing, steel journal in bronze bearing: load 3718 N , temperature 311 K (37.8 C ) . A: Base oil 300 SUS at 37.8 C. B: Aluminum soap grease. C: Calcium soap grease. D: Sodium soap grease. E: Lithium soap grease. Data by Horth, Sproule and Pattenden [341.

calcium soap or sodium soap, but there seems to be no identifiable transition speed for the lithium soap grease. When the torque values are converted to coefficients of friction in the non-hydrodynamic region, there is a reliable difference between the friction with the base oil hnd the greases. Interpretation of these data would be even better i f flow curves of shear stress vs. rate of shear were available for the greases. Although elastohydrodynamic transport of grease through the conjunction between the rolling element and the race is the operative mode of flow for the basic lubrication process, the overall movement of the lubricant in a grease-packed rolling-element bearing is more complicated in than that. Consider the ball bearing shown diagrammatically Fig. 18-13a. The movement of the inner ring rotates the ball in the direction shown, but there is also partition of sliding so that the entire ball assembly held by the retainer will also rotate slowly. The

542

Grease within

Shield vent-

-&

Retainer Inner ring

Figure 18-13. Diagram of ball bearing. (a) View showing modes o f motion which interact with grease lubrication. (b) Cross-sectional view with shields mounted. grease packed into the bearing between the rings is subject to gross stirring by the following kinds of action: (a) There will be viscous shear, most probably turbulent, of the grease in the gap between the inner and the outer rings as the inner ring rotates. (b) There will be turbulent mixing of the grease as the ball and retainer assembly plows (c) Superimposed on the movement of the grease due to the through it. rotating of the bearing components around the axis of the shaft there will be movement due to the rotation of the balls around their individual axes. In addition to these large-scale movements of the grease there are two other modes of motion, which under favorable circumstances should proceed by streamline flow of grease through the conjunctions between the balls and the races, and flow of grease between the balls and the retainer. The gross flow of soap-gelled grease in rolling-element bearings was studied by O'Halloran, Kolfenbach and Leland [ 3 5 ] . They used a shielded ball bearing, a cross-sectional diagram of which is shown in Fig. 18-13b. A weighed sample of grease treated with two kinds of dye, one an'oilsoluble blue and the other a water-soluble sodium fluorescein which dissolved in the soap phase, was packed into the bearing proper, and a weighed portion of undyed grease was put on the shields. The mixing of the qrease was monitored by assaying the migration of the dye into the grease on the shields. The results showed that the grease moved as an entity; i.e. soap and oil moved at the same rate. Soft greases mixed readily, whereas with harder greases the moving components of the bearing tended to plow channels and leave portions of the grease unmixed.

543

0

10 20 30 40 50 Running Time, minutes

60

Figure 18-14. Grease consistency and the running temperature of a rolling element bearing. I: Grease with initial worked penetration 200. 11: Grease with initial worked penetration 260. Spindle speed 10,000 rpm. Data by Horth, Norton and Pattenden [361.

TABLE 18-6.

DISTRIBUTION OF GREASE IN SHIELDED BEARINGS Grease I (a)

Grease I 1 (a)

Total original packing

3.00 grams

3.00 grams

Total grease in bearing within cage outside cage

1.10 0.32 0.78

1.43 0.34 1.08

Total grease on shields on shield faces in shield cups

1.92 1.04 0.87

1.53 1.15 0.37

(a) One hour at 10,000 rpm. 1361.

Data by

Horth,

Norton

and

Pattenden

The extent cf mixing is reflected in the gross temperature behavior of the running bearing. Figure 18-14 shows the two extreme types of behavior as observed by Horth, Norton and Pattenden [361. In Curve i the temperature of the bearing quickly rises to a maximum and then gradually stabilizes at a level less than 2.9 K above ambient. The time interval t ' is often designated as the clearing time because i t is associated with the expulsion of the excess grease from locations where it can be churned by the moving components of the bearing and thus generate heat. In Curve I1 the clearing phenomenon is absent: the temperature of the bearing rises to a level 33 K above ambient. Horth e k a e . 1361 demonstrated that the distribution of grease in the disassembled bearings was consistent with this explanation of the temperature behavior (see Table 18-6). With Grease I , once the excess was displaced from the path of the moving ball/ retainer assembly, little back mixing took place, whereas Grease I 1 readily slumped back into the inter-ring annulus. This was demonstrated

544

by dye-partition experiments, which showed that there was only 33% back mixing of Grease I from the faces of the shields into the bearing in the course of an hour's running, but 100% back mixing of Grease 11. The worked penetration of Grease I when i t was packed into the bearing was 200, that of Grease I 1 260. However, Horth e t at. 1361 found that the penetration value was not sufficient by itself to predict the behavior of a grease in an operating bearing. Soap content is another important parameter which is related to the tendency of a grease to channel in the bearing and therefore to r u n cooler. Channeling greases are characterized by sharply defined yield stress, by shear hardening in the bearing and by short fibers. It is the entire complex of rheological properties which influences the functioning of a grease in service. SO far n o all-encompassing generalizations have been developed. In lieu of an overall rationale, there are numerous empirical tests for evaluating greases as lubricants for rolling-element bearings. A. Schilling [37] published descriptions of 14 different bearing tests with outlines of the failure criteria and diagrams of the operating principles of the testers. These tests are concerned with the ability of the grease to prevent bearing failure o r its ability to withstand prolonged shearing without intolerable loss of consistency o r both. Bearing failure may be signalized by increased power required to drive the test rig at the rated speed, o r a sharp increase in the temperature of the bearing after establishment of steady-state operation, o r persistent unusual noise. Other manifestations of failure are: scuffed locations on the races o r the rolling elements (balls or rollers), spalled races, spalled balls o r rollers, worn o r broken retainers, excessive wear of races o r rolling el emen t s

.

Breakdown of grease by prolonged shear to the point of excessive l o s s of the whole grease by leakage o r of the oil by bleeding is undesirable because of the danger of leaving the bearing inadequately lubricated and because of soiling or contamination of the surroundings by the leaking A standard test for this type of leakage is ASTM Method lubricant. D 1263 [38]. This test is a credible analogue of service in an automotive front wheel bearing assembly. Stokely and Calish [391 noted that shearing the grease in an ASTM worker o r the roll tester does not necessarily predict its behavior in an overpacked bearing. The ASTM leakage test is carried out with an overpacked assembly. In contradistinction to rolling-element bearings, the lubrication of automotive suspensions, which is the second major service area for greases, is characterized by lower contact pressures, lower rubbing speeds and intermittent o r oscillatory motion. In 1960 Brunstrum and Hayne [ 4 0 ] published the results of a road test with four different greases used on 15 different vehicles. Cumulative plots of the distribu-

545

tion of wear showed no consistent trend assignable to a particular grease or a particular vehicle. Wear was low, c a . 4 mg average l o s s per 1000 miles at the most sensitive locations in the suspension. Tests with these four greases in a laboratory oscillatory contact rig also showed no differentiation among the four greases, but in the same type of test a special lithium grease gave a cumulative distribution diagram with a significantly lower level of wear. Another point of view on the function of grease in automotive suspensions is found in the laboratory ball joint tests reported by Gilbert, Verdura and Rounds [ 4 1 1 . A convex surface is oscillated against a concave housing under load to simulate the ball joint action in an automotive front wheel suspension. The desired standard of performance is torque stability at a predetermined level: high, erratic torque is symptomatic of “ride harshness,” but torque at too low a level adversely affects the damping required in the suspension system. Results obtained with various commercial greases indicated significant differences in perf ormance. There are three ASTM extreme-pressure bench tests specifically applicable to greases [ 4 2 1 . Considerable empirical bench test data is to be found in the literature for greases compounded with extreme-pressure additives. A particularly interesting study along such lines was carried out by Silver and Stanley [ 4 3 1 . Greases were made u p from a base oil with various concentrations of lithium 12-hydroxystearate or a treated bentonite a s gellants and with the following substances as additives: dibenzyl disulfide, chlorinated wax, and tricresyl phosphate. A special set of greases was made up with 15% ground graphite a s the gellant. The behavior of these greases in the four-ball machine was tested by two procedures: a one-hour wear test under 15 kg load and the standard ASTM extreme-pressure test. Table 18-7 shows the results. The data in Table 1 8 - 7 do not permit a firm interpretation of additive action in a complex system such as grease but they do offer a number of suggestive hints. For the greases without additives there is no discernible relation between penetration or gellant concentration and the 15-kg wear scar. With the exception of graphite, which seems to have no influence whatsoever on the 15-kg wear, the type of gellant makes only minor differences in the wear results. But in the EP test graphite has the strongest influence, while the mean Hertz loads for the other two gellants group at substantially the same level. The basic behavior of additives in the ungelled oil is given by the following ranking of effecdibenzyl disulfide = tiveness in terms of the 15-kg wear test: chlorinated wax < tricresyl phosphate. Ranking in terms of the mean Hertz load is tricresyl phosphate < chlorinated wax < dibenzyl disulfide. Adsorption of the additive by the gellant was determined by filtering

546

TABLE 18-7.

FOUR BALL TESTING OF GREASES COKPOUNDED WITH E? ADDITIVES No additive

Gellant

Dibenzyl disulfide (a)

Chlorinated wax (b)

Tricresyl phosphate (c)

Wear scar, mm (d) None Bentonite (treated), 2.5% worked penetration >385 Bentonite (treated), 5.0% worked penetration 197 Bentonite (treated), 7.5% worked penetration 167 Li 12-hydroxystearate, 4% worked penetration >385 Li 12-hydroxystearate, 8% worked penetration 320 Li 12-hydroxystearate, 12% worked penetration 219 Graphite, 15% worked penetration >385

0.77 0.55

0.61 0.63

0.63 0.47

0.26 0.33

0.67

0.63

0.43

0.47

0.56

0.54

0.48

0.50

0.56

0.60

0.52

0.29

0.61

0.65

0.46

0.49

0.53

0.59

0.37

0.48

0.72

0.61

0.53

0.43

% Left ~

~~~

None Bentonite (treated), 2.5% 5.0% 7.5% Li 12-hydroxystearate, 4% 8% 12% Graphite, 15%

__ __ -_ -__ __ ---

in oil (e)

__

__

__

95 68 69 98 89 96 86

86 81 65 99 92 95 96

70 44 20 87 83 87 67

~~

Mean Hertz load, kg None Bentonite (treated). 2.5% 5.0% 7.5% Li 12-hydroxystearate, 4% t 8% I 12% Graphite, 15% 11

,I

16.6 22.3 22.8 23.7 20.3 21.4 21.0 27.4

41.4 30.7 34.0 41.1 28.9 36.4 33.3 55.1

37.7 34.0 27.0 31 .O 28.3 30.8 32.7 48.0

27.6 22.4 19.6 23.3 20.8 24.5 24.5 34.1

(a) 1 .7% in grease. ( b ) 51% C1, 1.7% in grease. (c) 1.7% in grease. (d) 1 hour, 15 kg load, 1500 rpm, 50 C. (e) At end of wear test, after' separation of oil from gellant by 0.45 pm Millipore filter. Data by Silver and Stanley [431.

off a known proportion of the oil and assaying it for additive content. The treated bentonite was the strongest adsorbent for all the additives. But close scrutiny of Table 18-7 reveals enough irregularity and anomaly to make the simple concept of reduction of the effective concentration of the EP additive by competitive adsorption on the gellant untenable. Each system seems to have its individual characteristics. For instance, the effect of interaction between gellant and dibenzyl disulfide seems to be

541

minor with respect to the 15-kg wear test and irregular with respect to the mean Hertz load. The antiwear action of tricresyl phosphate in the 15-kg test is noticeably inhibited when i t is compounded in a grease: the same holds true for the mean Hertz load except for the grease thickened with graphite. The reader will have noted that the emphasis in this chapter has been on basic modes of behavior and that specific discussion of grease of particular compositions and types has been limited. This is not for lack of available information. However, a great deal of such information is empirical and non-systematic. The fundamental aspects of a complex colloidal system such as grease are difficult to investigate; therefore it is not surprising that the major attention has been directed to studies with direct technological applications. The intent of the presentation in this chapter is to equip the reader with enough basic background so that he can examine the results published in the technical literature of grease composition, manufacture and use with the insight to appreciate a l l the implications he finds there. REFERENCES 1. 2. 3. 4.

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

D. W. Criddle and J. L. Dreher, NLGI Spokesman, 2 3 ( 1 9 5 9 ) 9 7 - 1 0 1 . B. W. Hotten, in Advances in Petroleum Chemistry and Refining, J. J. McKetta, Editor, Interscience, New York, 1 9 6 4 , Volume 9, Chapter 3. W. H. Peterson and A. Bondi, J. Phys. Chem., 57 ( 1 9 5 3 ) 3 0 - 3 5 . A . L. McClelland and 3. Cortes, jr., NLGI Spokesman, 2 0 ( 1 9 5 6 ) NO. 6 , 1 2 - 1 6 . C. J. Boner, Manufacture and Application of Lubricating Greases, Reinhold Publishing Co., New York, 1 9 5 4 . R. M. Suggit, NLGI Spokesman, 24 ( 1 9 6 0 ) 3 6 7 - 3 7 5 . D. B. Cox, J. Phys. Chem., 6 2 ( 1 9 5 8 ) 1 2 5 4 - 1 2 5 6 . M. J. Vold, Y. Uzu and R. F. Bils, NLGI Spokesman, 3 2 ( 1 9 6 9 ) 3 6 2 367. S. F.

E.

Calhoun, NLGI Spokesman, 2 9 ( 1 9 6 6 ) 3 2 8 - 3 3 2 . R. Booser and D. F. Wilcock, Lubrication Eng., 9 ( 1 9 5 3 ) 140-143,

156- 1 5 8 . A . E. Baker, NLGI Spokesman, 2 2 ( 1 9 5 8 ) 2 7 1 - 2 7 7 . A . E. Baker, E. G. Jackson and E. R. Booser, (1953) 249-253.

Lubrication

Eng.,

9

kT. Sisko and L. C. Brunstrum, NLGI Spokesman, 2 5 ( 1 9 6 1 ) 7 2 - 7 6 . W. J. Ewbank, J. Dye, J. Gargaro, K. Doke and J. Beattie, NLGI Spokesman, 2 7 ( 1 9 6 3 ) 7 5 - 8 2 . W. L. Brown and W. J. Ewbank, NLGI Spokesman, 2 9 ( 1 9 6 5 ) 7 7 - 8 3 . J. L. Zakin and E. H. Tu, NLGI Spokesman, 2 9 ( 1 9 6 6 ) 3 3 3 - 3 3 7 . B. W. Hotten and D. H. Birdsall, Ind. Eng. Chem., 4 7 ( 1 9 5 5 ) 4 4 7 - 4 5 1 . ASTM Method D 2 1 7 - 6 7 , Cone Penetration of Lubricating Grease, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. D. Evans, J. F. Hutton and J. B. Matthews, Lubrication Eng., 13 A.

( 1 9 5 7 ) 341-346. 20. 21. 22. 23.

A. Bondi, A. M. Cravath, R. J. Moore and W. H. Peterson, NLGI Spokesman, 13 ( 1 9 5 0 ) No. 12, 1 2 - 1 8 . R. H. Leet, NLGI Spokesman, 19 ( 1 9 5 5 ) No. 1, 2 0 - 2 3 . A . C. Borg and R. H. Leet, Lubrication Eng., 15 ( 1 9 5 9 ) 4 5 0 - 4 5 4 . H. A. Woods and H. M. Trowbridge, NLGI Spokesman, 19 ( 1 9 5 5 ) No. 5, 2 6 - 3 1.

548

24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42.

43.

ASTM Method D 1831-64, Roll Stability of Lubricating Grease, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. J. J. Kauzlarich and J. A. Greenwood, ASLE Trans., 15 (1972) 269277. W. H. Bauer, A. P. Finkelstein and S. E. Wiberly, ASLE Trans., 3 (1960) 215-224. S. J. Hahn. T. Ree and H. Evrins, NLGI SDokesman 23 (1956) 129-136. H. Utsugi; K. Kim, T. Ree-and-H. Eyring, NLGI Spokesman, 25 (1961) 125- 13 1. E. 0. Forster and J. J. Kolfenbach, ASLE Trans., 2 11959) 13-24. ASTM Method D 1092-62, Apparent Viscosity of Lubricating Greases, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. A. Dyson and A. R. Wilson, Proc. Inst. Mech. Eng., 184 (1969/1970), Part 3F, 1 - 1 1 . S. Y. Poon, J. Lubrication Tech. (Trans. ASME), 94F (1972) 27-34. D. Godfrey, ASLE Trans., 7 (1964) 24-31. A. C. Horth, L. W. Sproule and W. C. Pattenden, NLGI Spokesman, 32 (1968) 155-161. R. O'Halloran, J. J. Kolfenbach and H. L. Leland, Lubrication Eng., 14 (1958) 104-107, 117. A. C. Horth, J. H; Norton and W. C. Pattenden, Lubrication Eng., 27 (1971) 380-385. A. Schilling, NLGI Spokesman, 30 (1967) 388-400, 420-432. ASTM Method D 1263-61, Leakage Tendencies of Automotive Wheel Bearing Greases, ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. J. M. Stokely and S. R. Calish, NLGI Spokesman, 19 (1955) No. 9, 1215. L. C. Brunstrum and W. L. Hayne, jr,, NLGI Spokesman, 23 (1960) 394400. A. W. Gilbert, T. M. Verdura and F. G. Rounds, NLGI Spokesman, 29 (1966) 356-365. (a) ASTM Method D 2266-67, Wear Preventive Characteristics of Lubricating Grease (Four Ball Method). (b) ASTM Method D 2509-66, Measurement of Extreme-Pressure Properties of Lubricating Grease (Timken Method). (c) ASTM Method D 2596-67, Measurement of Extreme-Pressure Properties of Lubricating Grease (Four Ball Method). ASTM Standards Book, Part 17-Petroleum Products, American Society for Testing and Materials, Philadelphia. H. B. Silver and I. R. Stanley, Tribology Int., 7 (1974) 113-118.

549

Chapter 19 LUBRICATION BY SOLIDS

19.1.

CLASSIFICATION AND TERMINOLOGY

Lubrication by solids is a well-recognized branch of lubrication technology, and the experienced practitioner finds little difficulty with the meaning of this designation when he sees it. But careful scrutiny shows that the distinction between lubrication by solids and other aspects of lubrication is not one of fundamental principles. Instead, the term as it is generally understood is applied to a collection of techniques characterized by one common feature: the lubrication process is governed by the presence of a deliberately inserted solid substance in the rubbing interface. There are many nuances in this concept. Consider the definition of "...any solid used bea solid lubricant proposed by W. E. Campbell [ 1 1 : tween two surfaces to provide protection from damage during relative movement and/or to reduce friction or wear." As a definition it is straightforward and logical. Using it as a guideline, we would be able to recognize without doubt any instance of lubrication by a solid substance. But it turns out to be ambiguous in practice because it does not say anything about the original condition of the two surfaces to be lubricated. F o r example, i f the surfaces are steei exposed to ambient air and thus carrying the usual film of oxides and adsorbed moisture, are we to regard these surface constituents as lubricants with respect to oxide-free iron? And with respect to which initial surface condition, the oxide-free or the contaminated state, should the lubricating action of purposively introduced solid substances be evaluated? The theoretical ambiguities posed by these questions do not seriously affect actual practice. In situations of technological significance, the lubrication engineer usually h a s some knowledge of the initial surface condition of the unlubricated rubbing parts. His criterion of the effectiveness Of the solid lubricant is the improvement in tribologicai behavior with respect t o such initial condition. It is essentially from this point of view that lubrication by solids will be treated here. By and large, the initial conditions of the surfaces as encountered in practice will be taken as the reference state in assessing the behavior of lubricating solids in their interaction with these surfaces, both at rest and during rubbing.

550

As a specific example of some of the subtleties involved, consider an oriented condensed film of long-chain fatty acid formed on an ordinary oxide-covered steel surface by chemisorption from a compounded lubricating oil. This type of film has been discussed at length in the treatment of additive action and it has been demonstrated that such a film may be regarded as the two-dimensional analogue of a solid lattice laid down on the underlying surface. Thus it fits Campbell's definition of a solid lubricant [ I ] , and yet the experienced lubrication engineer is not disturbed by semantics when he excludes fatty acid films from his pragmatic category of solid lubricants. In a suspension of molybdenum disulfide in oil, the additive is overtly recognizable as a solid, while in a solution of stearic acid in oil, the additive is unquestionably not in the solid state. The use of solid lubricants is governed largely by practical considerations, and the need for them may be put in the following words: the engineer l o o k s to solid lubricants for "low and, above all, constant friction and increased durability of the lubricating film under extreme environmental conditions" [ 2 ] . Among the extreme environmental conditions are high temperature, high contact pressure, hard vacuum and corrosive atmospheres. At the low atmospheric pressure of the stratosphere o r the high vacuum of outer space, the most important function of the lubricant is to insure absence of seizure and to maintain reliable movement of rubbing parts. I t is apparent why solids are particularly suited as lubricating substances in these circumstances. Even though the technology of lubrication by solids is largely empirical, it is useful to systematize classification and terminology. Substances that are used as solid lubricants can be grouped into the six

TABLE 15-1.

TYPES OF SOLID LUBRICANTS Inorganic MoS2, graphite,

Layer-lattice

graphite fluoride Other inorganic solid compounds

CaF2, PbO

Soft metals

Pb, Ag, Au Organic ~~

Soaps, fats, waxes

Calcium stearate, dimethylstearamide

Polymeric plastics

Polytetrafluoroethylene, pol ymide

Layer-lattice solids

Phthalocyanines

551

general types shown in Table 19-1, witn examples to illustrate each type. The methods of lubricating with solids fall into three broad categories:

( i )pretreatments which put a film of solid lubricant parts before they are brought into rubbing contact:

on

(ii) systems which feed solid lubricant as such to parts during operation;

rubbing

the

the

(iii) systems which bring the solid lubricant to the rubbing parts suspended in a carrier oil o r in a gas stream. Pretreatment can be divided into two sub-categories. In the first, a protective film is formed by physical adhesion of the externally applied solid lubricant to the surfaces. Burnishing or rubbing may be used to develop the adhesicn of the applied solid, but as far as is known, the adhesion does not depend on chemical reactivity; deliberate intent to alter the surface by chemical reaction is not an intrinsic part of this method of applying the lubricant Silm. The second category of pretreatment, on the other hand, specifically involves the formation of solid lubricating films on surfaces by chemical treatments such as phosphatizing, suifidizing, anodizing, acid etching, etc. The question of when the coating thus formed is to be regarded as a lubricant and when as an initial condition of the rubbing surfaces cannot be answered unequivocally. For instance, carburizing might be viewed as a technique of solid lubrication, but it is usually considered to be a way of modifying the material properties of steel. The same viewpoint might be taken towards ion implantation. Midgley and Wilman [ 3 1 have shown that though the film put 01: mild steel by phosphatizing is worn away during initial rubbing, the surface is rendered more responsive to protection by oil on subsequent rubbing, an observation which makes it difficult to classify the action of the phosphate film in terms of formal nomenclature. The efficacy of a pre-applied, self-adherent solid film depends on its durability during rubbing. Deficiencies in durability can be overcome by supplying material for the maintenance of the film by methods (in) or (iii) listed above. For instance, material can be transferred to the lubricating film by a compact of the solid lubricant in rubbing contact with one of the surfaces o r by dropping powdered solid as needed. The film can also be maintained by using the solid lubricant as an additive in a carrier o i l or in a gas stream. 19.2.

LAYER-LATTICE INORGANIC SOLIDS AS LUBRICANTS

Many inorganic solids crystallize in layer-lattice structures; cadmium iodide is frequently cited as the type example. The cadmium ions are arranged hexagonally in sneets, each with a sheet of hexagonally arranged iodide ions above and below. The separation of adjacent sheets of

552

iodide ions is greater than the spacing between a sheet of iodide ions and its neighboring sheet of cadmium ions. Many of the inorganic substances which have layer-lattice crystalline structure can be cleaved into thin sheets and therefore are termed lamellar solids, but the ability to be cleaved into lamellae is not necessarily a property of all solids with layer-lattice crystalline structure. As pointed out by A. J. Haltner [41, the nature of the bonding between the sheets of ions whose separation defines the layer-lattice structure is what determines the cleavage behavior. Thus, the easily cleaved phlogophite and muscovite micas are characterized by the presence of K + ions, whereas in a brittle ++ mica such as margarite, Ca acts as an ionic cement. Haltner also stated that cleavage of a layer-lattice solid is more akin to a tensile Hence a solid which can be easily failure than it is to shearing. cleaved into lamellae is not necessarily a lubricating substance, particularly in the sense of reducing friction. The easily cleaved micas are riot really useful as lubricants. Lubrication is associated with low tangential force at the rubbing interface; therefore those lamellar solids that function a s lubricants are characterized by low interlamellar slip force. 19.2.1.

Molybdenum Disulfide as a Lubricating Lamellar Solid

Of the lamellar solids which do show lubricating action, the two most familiar tc the lubrication engineer are molybdenum disulfide (MoS2) and graphite. The lubricant-grade MoS2 of commerce is made by processing

TABLE 19-2. CHEMICAL ANALYSIS OF MOLYBDENUM DISULFIDE H20, Oil,

MoS2,

Fe,

Moo3,

%

%

m

x

0.12 0.059 0.072

0.03 0.014 0.025

0.00 0.047 0.035 0.024

Lubricant grade 98.04 Sample A 99.6 Sample B

%

- -

C,

Acid insoluble,

%

%

1.22 0.200

-

0.50 0.022 0.032

From data by Risdon, Maurer and Barry 151.

and purifying mined natural molybdenite. Table 19-2 compares the chemical analyses of lubricant grade MoS2 and two specimens which were purified further 151. Treatment of the commercial grade material reduces the silica (acid insoluble) and iron content, a s shown for Samples A and B. The presence of Moo3 is a characteristic feature of MoS2 surfaces which have been exposed to air; sulfuric acid is a concomitantly occurring contaminant [ 6 , 71. The oil and carbon content, which comes from the flotation agents used in processing mine-run lowered by milling and solvent extraction.

molybdenite,

can

be

553

Milled MoS2 is available in a wide range of particle sizes, from as small as 0.3 urn up to 100 urn and larger. Scanning electron microscopy of 50 Vrn powder at magnifications up to lOOOX by Holinski and Glnsheimer 18, 91 revealed that the grains are not single crystals and do not consist of flat platelets; also grains this size have flakes of more finely divided material adhering to their surfaces. A single traverse of a loaded steel ball across a plate sprinkled with powdered MoS2 was sufficient to flatten the grains into a compact aggregate of platelets. Platelets as thin as 15 nm ( 2 4 atomic layers of MoS2) were formed on prolonged running. The process by which the granules characteristic of milled MoS2 are transformed into platelets and the platelets are further compacted into adherent films was studied during the course of 1000 revolutions of the ring in a ring-on-block apparatus under a loading pressure of 1 . 1 1 kPa (1.1 kg/cm2). Provided that the initial supply is sufficient, burnishing by repeated traverses puts a compacted film of MoS2 on the substrate surface. This film may be several microns thick. Such behavior of MoS2 granules during rubbing under load is consistent with the layer-lattice structure shown in Fig. 19-1. On either side of each sheet of molybdenum atoms in a planar hexagonal arrangement is a The sheet of sulfur atoms, also in a planar hexagonal arrangement.

Figure 19-1. The unit cell of hexagonal sions in nanometers.

molybdenum

disulfide.

Dimen-

554

molybdenum-sulfur distances (0.241 nm) correspond to the atomic bonding radii, but the sulfur-sulfur distances in adjacent layers (0.349 nm) are greater than the combined atomic sulfur radii. These widely separated adjacent sheets of sulfur atoms are oriented parallel to the basal planes of the crystal, which are the planes of easiest shear characteristic of solids that crystallize in the hexagonal system. Evidence for the orientation of crystallites in rubbed films of MoS2 along their basal planes is seen in X-ray and electron diffraction spectra [lo, 11, 12, 13, 14, 151.

The full details of the formation of burnished films of MoS2 and their adhesion to substrates are not well understood. H. E. Sliney [161 observed the generation of a burnished film of MoS2 from 10 Um powder during the sliding of a tool steel ball on a glass plate. The MoS2 adhered to the rubbing surfaces of both the ball and the track on the plate. Y. Tsuya 1171 reported that the adherent MoS2 film on the rubbing tracks of metallic substrates could not be removed by the butylcellosolve transfer technique. The strong adhesion of burnished films of MoS2 to the underlying metal is at odds with the postulate of easy sliding on the basal planes of the crystal. Brudnyi and Karmadonov [15] presented evidence that the edge planes (1700, 1070, 0170) of MoS2 are harder and have a higher surface energy than the basal (0001) planes; Andrews, Groszek and Hairs 1181, on the basis of adsorptive behavior postulated that the edge planes are polar in nature and hence are high energy surfaces. According to Brudnyi and Karmadonov’s picture of the burnished film, strong attachment to the metallic substrate is via the suitably oriented (1700, 1070, 0170) faces of the crystallites in a randomly arranged layer directly on the metal surface; the basal planes of the crystallites on the surface of this layer become oriented in the direction of sliding during the course of rubbing. Chemical bonding via the reaction 2FeS + MO MoS2 + 2Fe has been suggested, but according to GHnsheimer and Holinski I141 this reaction does not take place below 700 C. Johnston and Moore [121 did not detect the presence of FeS at the junction of a surface which had been burnished with MoS2 at 300 C nor did Spengler and Peltzer 1191 find evidence of FeS or mixed crystals at the rubbing surface by X-ray diffraction. J. K. Lancaster [20] proposed mechanical embedding of MoS2 in the substrate as a mechanism of film attachment. The lubricating performance of MoS2 is evaluated by various criteria: magnitude of the coefficient of friction, rate of wear of the rubbing parts, durability of the antifriction or antiwear effect, magnitude of the scuffing load. Experimental studies and testing procedures are governed by the criterion adopted. Since MoS2 frequently comes under

555

consideration as a lubricant for severe conditions and hostile environments, such as high temperatures, vacuum or corrosive atmospheres, these conditions are often deliberately part of the experiment o r test, Because

of

the

usefulness of MoS2 in high vacuum (more precisely,

extremely low ambient pressure), the influence of the constituents of ordinary ambient air is an important factor to evaluate. Basically it resolves into identifying the intrinsic tribological behavior of MoS2 and distinguishing it from the rubbing behavior in a particular ambient environment. Rubbing in hard vacuum is the experimental approach used to study the basic behavior of MoS2 sliding against itself, the favored technique being to generate a transfer film from a pellet in contact with a moving countersurface, usually of metal. The generation of the oriented transfer film also orients the material in the surface of the pellet, so that the rubbing is along the basal planes of the MoS2 in each surface. Coefficients of friction ranging from 0.02 to 0.15 have been reported for such experiments [21, 22, 23, 241, as shown in Table 19-3. Results by Matsunaga, Hoshimoto and Uchiyama [251 and by Jamison and Weber 1261 for a metallic slider against a burnished film on a metallic substrate are shown for comparison. It might be thought that cleaning treatment such as washing with NH40H solution and refluxing with organic solvents, followed by conditioning in a hard vacuum environment, would give MoS2 a clean surface with stable tribological properties, but experimental results do not consistently substantiate this. Johnson and Vaughn [21] observed that on resumption of rubbing after quiescent standing in vacuum, the initial TABLE 19-3. COEFFICIENTS OF FRICTION OF MoS2 SLIDING ON MoS2 IN HARD VACUUM Reference source

uk

Pressure, torr

Speed, cm/s

Temperature, deg. C

Substrate

t211

0.07-0.09

1 Ow6

310

25-60

Stainless steel lapped with 600 mesh carborundum

[221

0.06-0.09

10-7-10-9

0.4-68

25

HCOF copper

[231

0.07

2

-

room

Copper

“241

0.03-0.12

5 x

lo-’

0.05a

room

Copper

t251

0.02-0.10

5 x lo-’

0.05a

room

Copper b

[261

0.07-0.10

1 f71 O-’

0. 042a

room

Copper

(a) Average speed, reciprocating Stainless steel slider.

motion.

(b)

Copper

slider.

(c)

556

0.04 0 0 1. 2

3 04

5

66 7

8

9 L

Running Time, min.

Figure 19-2. The effect of rest time I n vacuum on the friction of molybdenum disulfide. Rest time: I , 16 hrs.; 1 1 , 15 hrs.; 1 1 1 , 185 min.; IV, 134 min.; V, 90 min.; VI, 8 5 min. Data by Johnson and Vaughn 1211.

coefficient of friction was higher than the steady-state value characteristic of prolonged rubbing, as shown in Fig. 19-2. This kind of behavior was confirmed by Haltner [22] and in part by Matsunaga e t ae. [24, 251. Johnson and Vaughn [21] attributed the low steady-state coefficient of friction to the generation of a superficial coating of sulfur from the tribological decomposition of MoS2. The reaction 4MoS2

+ 2M02S3

+

S2 (9)

is known and has been studied [27], Johnson and Vaughn postulated that cessation of rubbing in vacuum allows the MoS2 surface to be denuded of the adsorbed sulfur by evaporation. Haltner [22], in view of the rate at which sulfur evaporates i n v a c u a , expressed doubts that sulfur generated by the tribological decomposition of MoS2 would remain on the surface long enough to influence the kinetic coefficient of friction. To complicate the picture further, Matsunaga and Nakagawa [28] claimed that the cleanest MoS2 surfaces were obtained from powder deposited electrophoretically from acetone suspension onto a copper substrate and baked for 4 hours at 280 C in a vacuum of lo-' torr; the steady-state coefficient of friction they observed for a run-in film so prepared was 0.15. Matsunaga and Nakagawa [281 found that hydrogen, nitrogen, argon o r helium could be put into the system at pressures ranging from to 100 torr and pumped away without at any time changing the coefficient of friction from its clean-surface value of 0.15, as measured by their reciprocating technique. Haltner [221 reported a steady-state value of uk = 0.081 f o r a pellet of compacted MoS2 rubbing against a transfer film

557

5 .' t .-

. I -

0.12

-

0.10

-

-

0.08 -

-

-

-

0.04 -

-

.I-

," 0.06 c

I

1

0, .-

2 8

.I-

0,

0.02 0,OO

6

-

o Admission

-

Evacmiion

I

I

I

I

I

I

on copper in an atmosphere of nitrogen at 175 C, almost the same value that was observed in hard vacuum. The effect of water vapor as observed by Matsunaga and Nakagawa [28] is shown in Fig. 19-3; an analogous minimum and hysteresis effect was seen f o r n-butanol. Admission of oxygen produced a sharp rise in friction at c a . 1 torr pressure, with a marked hysteresis effect on pumping off; ethane qave a sharp drop in friction with even stronger hysteresis in the pump-off. Interpretation of the tribological behavior of MoS2 in air is often complicated by uncertainty about its initial surface condition. Salomon, de Gee and Zaat [29] observed the sequential evolution of the following gases chromatographically when MoSZ powder was heated i n v a c u a : oxygen, nitrogen, carbon dioxide (above 300 C ) , methane (above 400 C ) , and hydrogen (from 450 C up). Commercial milling of MoS2 to particle sizes useful f o r lubrication permits oxidation of the surface and adsorption of water vapor from air. J. W. Midgley [301 equilibrated MoS2 of 1-3 um particle diameter with air of 60% relative humidity at room temperature and then heated it to 120 C. The MoS2 lost 1.1% of its equilibrium When moist, equilibrated MoS2 powder was used to lubricate the weight. humidity, the value of uk rubbing of steel i n air of 60% relative dropped from 0.2 to 0.05 in the course of three hours, during which time the temperature of the steel specimen piece near the rubbing surface rose from 2 2 C to 50 C. When the system was cooled to room temperature in dry air ( < 0 . 1 % relative hunidity) and then rubbii.9 was resumed, u k stayed at 0.05; but i f quiescent cooling and subsequent rubbing occurred at 60% relative humidity, uk rose to 0.15. This effect was attributed to the adsorption of water on the surface of the MoS2 crystallites. Haltner and Oliver [311 observed a strong influence of the relative humidity between 0 and 40% on the increase of the friction of a MoS2 compact rubbing against a transfer film on copper in an atmosphere of nitrogen.

558

0.6

0.5

0 ._ c

0.3 .c

0

,

0

.

0 0

K)

20 30 40 50 6070

% Relative Humidity at Specimen

Temperature

Figure 10-4. Effect of relative humidity on the static friction of molybdenum disulfide films. Data by Pritchard and Midgley 1321.

Pritchard and Midgley [321 found that the coefficient of static friction of steel lubricated by a burnished film of MoS2 was influenced by the relative humidity over a range of temperatures as shown in Fig. 19-4. Haltner and Oliver [31] observed a sharp rise of vk from 0.12 to 0.22 in the range 0-37% relative humidity for a MoS2 compact against a transfer film. Ballou and Ross [331 demonstrated hysteresis effects in the adsorption and desorption of water vapor on and from MoS2, depending on the past treatment of the surfaces; about 6 0 % of the adsorbed water vapor was retained when the relative pressure was reduced from 50% of saturaJohnston and Moore [71 observed that the adsorption equition to 5%. librium of atmospheric water vapor at 30 C with the surface of a sample of commercial MoS2 powder was reversible; however, if the powder was heated i n vacua to 350 C, the adsorption/desorption isotherms in air at 30 C showed a strong hysteresis effect o n the first cycle but subsequent adsorption/desorption cycles were reversible. I f the MoS2 is not heated higher that 800 C , decomposition to Mo2S3 and elemental sulfur does not occur. Heating in v a c u a at 350 C drives off any H2S04 contaminating the MoS2 surface hut leaves Moo3. Thus the second adsorption/desorption cycle in air (measured a s gain or loss of weight with a thermogravimetric balance system) starts with the base line established by chemisorption during the first cycle. It is thus seen that the interaction of molybdenum disulfide with its ambient surroundings in a tribological context involves complexities that have not been fully resolved. It has not been established why the friction of rubbed MoS2 should be adversely affected by adsorbed water vapor. Speculations range from the formation of intercalation structures

559

within the lattice [ 8 , 9 , 341 to reactions which alter the nature of surface, such as MoS2 + 2H20 + [O] -+Moo3

+

the

2H2S

the occurrence of which was demonstrated by Haltner and Oliver [31]. Atkinson and Swift [ 3 5 J observed decrease in sulfur and increase in oxygen by the X-ray photoelectron spectroscopy of MoS2 films rubbed in ambient air. Another unresolved aspect of the tribological behavior of MoS2 is whether the sliding occurs between the exposed basal-plane faces of one crystallite against another or whether it occurs by shear of the (0001) slip planes within the individual crystallites. The first alternative should be sensitive to the influence of ambient atmosphere because the basal planes are always exposed, whereas the internal slip along the ( 0 0 0 1 ) plane within a crystallite should be governed by the true shear strength of MoS2 in that direction. The two modes of behavior are not mutually exclusive. Furthermore, the observations of Sliney [16] indicate that under sufficient pressure individual crystallites of MoS2 can be compressed into larger single-body aggregates by plastic flow. In view of the complications connected with the intrinsic tribological behavior of MoS2 discussed above, interpretation of its overt response to experimental parameters such as load and rubbing speed and of its behavior in empirical testing is obviously not straightforward. F o r example, Fig. 19-5 shows the results by Haltner and Oliver 1361 for the effect of load and rubbing speed on the coefficient of friction for a steel ball rubbing against a burnished film of MoS2 on a chromium-plated steel disk. Because of the absence of a speed-dependent effect, Haltner and Oliver discounted the influence of release of adsorbed vapor and interpreted the load-dependent behavior in terms of Bowden and Tabor's mechanism f a r a thin, soft film of solid on a hard substrate [37] (see

(a)

(b)

0.2 -

:

D **em

0.00

I

I

I

I

0.0,

I

I

I

I

, *

I

.

560

Section 19.3). I n a detailed study by S. A . Karpe, [381 using a steel ball sliding with reciprocating motion at an average speed of 0.1 cm/s against burnished MoSZ on a steel plate in air of 30% relative humidity at 2 5 C, the effect of loading pressure on the coefficient of kinetic friction showed essentially the same pattern observed by Haltner and Oliver [36]: a strong decrease over the lower range of loading and a gradual transition to a much slower rate of decrease over the rest of the graph. This response of pk to contact pressure followed the course calculated for Bowden and Tabor's thin-film model. Akaoka and Nitanai [39] found similar effects of contact pressure in the continuous sliding of torr) at 16.7 steel against burnished MoS2 on steel in vacua (2 x cm/s. Haltner and Oliver's experiments on the effect of rubbing speed were carried out in an environment of nitrogen [361. Barry and Binkelman [ 4 0 ] observed a similar lack of rubbing-speed effect on friction in dry air and also insensitivity to applied load for the friction of films of MoS2 on metals such as steel, molybdenum, tungsten, copper, brass, bronze and silver. But in ambient air of 50% relative humidity at room temperature, the coefficient of friction decreased with increasing speed or load, to a greater or less extent, for films of MoS2 on various metals. J. GQ'nsheimer [13, 411 found the systematic effect of applied load and relative humidity to be that shown in Fig. 19-6: increasing the load stepwise lowers the coefficient of friction, decreasing the load raises it,

0.12

0.10

0.08 0.06 c

c

.-0

0.04

5

0.02

0)

F V

0.00

0

10

20

30

40

50

60

70

Time,minutes

Figure 19-6. Effect of relative humidity on the frictional behavior of molybdenum disulfide. 1:16.2% R.H.; 2:6.56% R.H.; 3:0.12% R.H.; 4: dry air. Data by J. Ghsheimer [13].

561

I

!

0.00I

I

I

1

I

1

133

1467 2801 1467 133 k ~ o a d4 -iw 0 a d m g - - + ( Load,newtons

Figure 1 9 - 7. Effect of vapors on the frictional behavior of molybd enum disulf i de (e) (a) n-Butanol. (b) Water. (c) Benzene. (d) Heptane. Dry a i r. Vapors at saturation pressure, 20 C. Data by J. Gznshe imer

.

[411.

0.3 Contact pressure ,MI 0

0.08

n 0.17 0

0.25

v 0.33 0 0.42

1

1

0.5

1.0

I

I

I

1.5

2.0

2.5

I

3.OxlC

Frictional Heat,uPV (J/m2d

Coefficient of friction of molybdenum disulfide as a funcFigure 19-8. tion of frictional heat. u = coefficient of friction; P = pressure; V = sliding speed. Data by Tanaka, Nakagawa and Matsunaga 1 4 2 1 .

562

and the effect is stronger at higher levels of relative humidity. In dry air change of load has a negligible effect. This lack of load effect is not altered by the presence of hydrocarbon vapors such as benzene o r heptane at saturation pressure in dry air, but the admission of the vapor of a hydroxylic compound such as butanol has an effect like that of water vapor, as shown in Fig. 19-7. Tanaka, Uchiyama, Nakagawa and Matsunaga [421 carried out experiments on the sliding of a MoS2 compact against its transfer film on steel in air of 50-60% relative humidity at 23-26 C with loads ranging from 10 to 50 N (8-420 kPa) and at speeds from 85 to 583 cmis. As shown in Fig. 19-8, the coefficient of friction decreases with increasing rate of heat input per unit area; i . e . friction decreases with increasing surface temperature. Thus there is a significant body of evidence which can be put together to show that influence of contact pressure and rubbing speed on the coefficient of friction observed with transfer films of MoS2 involves the effect of the surface temperature on the moisture content of the film. The antiwear and antiscuff action of MoS2 and the durability of its lubricating efficacy involves the behavior of the film interposed between the two rubbing bodies as well as the intrinsic tribology of MoS2 itself. I f each surface of the rubbing bodies carries an intact film of MoS2, neither body will suffer attritive wear and the friction observed will be that of MoS2 sliding on itself under the conditions prevailing. But i f any part of the film fails to adhere to either of the two rubbing bodies, then there will be a local occurrence of friction between the exposed substrate material and the MoS2 film on the other substrate and wear of the exposed material rubbed by the MoS2 as well as wear of MoS2. Local breakdown of the MoS2 film which results in contact between both substrate bodies results in metal-tometal wear at that site; i f the breakdown is extensive enough, the wear augments to scuffing. The lubricating effect of MoS2 on the wear of soft steel (English EN 2 A , equivalent to A I S I 1 0 2 0 ) as observed by J. K. Lancaster [43] is shown by the comparison of wear rates in Table 19-4. The film of Mo2 was maintained dynamically by rubbing a compact of MoS2 against the sliding track at a location diametrically opposite the contact of the steel rider with the rotating disk in the experimental apparatus. The easiest interpretation of these results is to assume that the MoS2 film blocked enough metal-to-metal contacts to reduce the wear rate by four or five orders of magnitude relative to that of unlubricated steel. But it cannot be assumed 'that there is no intrinsic wear of metal by MoS2 sliding against it. Lancaster rubbed riders of copper against compacts of MoS2 in a manner which minimized reiterated traversals of the sliding path on MoS2, thereby minimizing the abrasive effects of copper particles which might have transferred to the compact; nevertheless significant wear of the copper rider was observed [441. Using this technique for copper sliding

563

TABLE 19-4. EFFECT OF A DYNAMICALLY MAINTAINED FILM OF MOS2 ON THE WEAR OF STEEL Wear rate, cm3/Nm Load: 58.8 N

Load: 255 N

Unlubricated

0.561 x

0.561 x

MoS2 film

0.5404 x 10-l'

0.714 x

Rubbing speed: 0.60 m/s.

TABLE 19-5.

Data by J. K. Lancaster [431.

SCUFFING LOADS FOR A DYNAMICALLY MAINTAINED FILM OF MoS2

Speed, m/s

Steady-state

pk

Contact pressure at scuffing, MPa

0.10 0.60 3.00

0.1 0.1 0.1

139 126 51

0.60

0. 04a

126

(a) MoS2 on phosphated steel surface. From data by J. K. Lancaster [431.

against clean massive polytetrafluoroethylene, Lancaster reported a wear cm2/Nm, but with a film of MoS2 on rate for copper of less than 2 x the PTFE the wear of the copper was increased by more than 10-fold 1201. Table 19-5 shows the scuffing loads Lancaster observed for mild steel rubbing at various speeds in atmospheric air against a dynamically maintained film of MoS2 on mild steel [43]; load was applied in incrernental steps until the coefficient of friction increased drastically above the steady-state value. The effect of maintaining the film by transfer from a compact is seen in Fig. 19-9, where the scuffing pressure is compared with that for a preformed film which is not renewed by transfer. The role of the compact in maintaining the film is also shown by a decrease in the electrical contact resistance from 38 ohms to 10 ohms when the compact was lifted from the rubbing track for 400 seconds and restoration of the contact resistance to 38 ohms in 1400 seconds when the compact was replaced, the steel rider meanwhile rubbing against the track under a sub-scuffing load. The rate of transfer from the compact to the track decreases as the surface of the compact is conditioned by rubbing, and eventually the film becomes too thin to protect against scuffing under the particular load employed. Akaoka and Nitanai [391 observed a

564

G1o4-

I

I

4

c

f0

0 u)

with qac+\

without compact

p 3-

-

v)

0

8

-I

Sliding Distance to Scuffing ,km

Figure 19-9. Effect of a maintained film of scuffing. From data by J. K. Lancaster [ 4 3 1 .

molybdenum

disulfide

on

L

2 15c

1

0

% Relative Humidity at Rubbing Surface I

10

I

I

I

30 50 70 % Relative Humidity of Air

I

90

Figure 19-10. Influence of relative humidity on the friction coefficient and the durability of a molybaenum disulfide film. Load: 613 N. Speed: 100 cm/s. The humidity of the surrounding atmosphere (lower scale) is higher than that at the rubbing surface (upper scale) because the rubbing surface is warmer than the atmosphere. The friction coefficient (right-hand scale) increases with humidity and is higher at the beginning ( p i ) than the termination (p,) of the run. Data by Salomon, de Gee and Zaat [29!. sharp decrease in the endurance of preformed burnished films of MoS2 with high contact pressure for the lubrication of steel i n vacuo and attributed failure to fatigue of the film. Environmental conditions such as relative humidity and the composition of the ambient atmosphere influence the durability of the MoS2 film. Figure 19-10, from work by Salomon, de Gee and Zaat [29], shows the effect of relative humidity on the smooth-running life of steel rubbing

565

against steel lubricated by a burnished film of MoS2. No explanation is advanced for the strong beneficial effect of 7% relative humidity at the surface; it seems to coincide with the maximum value of the temperature of the ring. The rapid decrease in durability with increase of relative humidity beyond this level is attributed to tribologically catalyzed chemical reactions, such as the evolution of H2S reported by Haltner and Oliver [311; Salomon and his co-workers observed that large quantities of H2S were evolved when rubbing experiments were carried out at 90% relative humidity and 25 C in an atmosphere of argon o r nitrogen. Pritchard and Midgley [321 found a strong decrease in the durability of MoS2 films as the relative humidity rose from 7% to 20%. The effect of oxygen as observed by Salomon e t a L . [291 is shown in Table 19-6. They also obof large served g r o s s visual evidence of film failure-formation blisters-which seemed to be promoted by oxygen. Tanaka e X aL. 1421

TABLE 19-6.

INFLUENCE OF OXYGEN ON THE DiiRABILITY OF A MOS2 FILM

Atmosphere

Durability, hrs.

Oxygen Air Argon (0.05% 0 2 )

Steel specimens; 613 N; 1 m/s; Gee and Zaat [291.

measured the response of

wear

2-4 6-9 >150

dry atmospheres. From data by Salomon,

rate

of

steel

lubricated

by

Mo2

de

(in

reciprocating motion) to the influence of ambient atmosphere from to lo5 Pa (7.5 x lo-’ to 750 torr) and found a sharp increase at about 2 0 0 0 Pa (15 torr).

R. L. Fursaro [45] made a detailed study of the durability of burnished films of MoS2 on 440 C stainless steel disks of surface roughness (0.09 pml to 0.3 um by the sliding of ranging from polished hemispherically-ended pins (0.467 cm radius) with an applied thrust of 9.8 N at a rubbing speed of 2.6 m/s. Table 19-7 shows the results obtained in moist air (50% relative humidity at 25 C) and in dry argon. The initial wear rates for the first 1000 cycles of traverse are relatively high but the corresponding coefficients of friction were found to lie in the range 0.09-0.13. This portion of the wear process seems to be associated with the formation of transfer films of MoS2 on the rider and localized depletion of this film at the rubbing interface. The steadystate rubbing process appears to be controlled by MoS2 supplied from the rubbing track, particularly from pockets and grooves in the surfaces of

566

TABLE 19-7.

DURABILITY OF BURNISHED MOLYBDENUM DISULFIDE FILMS

Traverses, kilocycles

Rider wear rate, Sandblasted,

Abraded,

1.2

0.30

urn

urn

m3/m Polished, 0 . 0 9 ym

Moist air 0- 1 1-5

5-10 5-15 10-30 15-60 60-70 70- 100

8.80

2.00

1 .8

0.64

0.55

3.6*

0.07 0.11

1.60* 0.22

2.40* 0.49

-

-

Dry argon 0- 1 1-15 15-60 60-200 200-400 400-700 700-940 700- 1500 1500- 1 8 6 0 1500-2700 2700-3700 3700-4450

4.500 0.048 0.013 0.003 0.006

0.490 0.062 0.019 0.012 0.012 0.008

0.100 0.038 0.018 0.004 0.002 0.002

-

-

0.100*

0.010

0.011

-

0.018*

0.009

0.012 0.009 0.046*

*Failure: uh 2 0.30. Data by R. L. Fusaro [ 4 5 1 .

the abraded and the sandblasted disks. The lower durability of the films in moist air is ascribed to chemical degradation of MoS2 (probably to Moo3) with adverse effects on the ability of MoS2 to flow under pressure and maintain the film. 19.2.2.

Graphite as a Solid Lubricant

Graphite is a lamellar solid with the layer-lattice structure shown in Fig. 1 9 - 1 1 . The distance between neighboring carbon atoms in each layer is 0 . 1 4 2 nm, very close to the 0.140 nm for the C-C distance in benzene; the distance between layers is 0 . 3 3 5 nm. This long interlayer spacing was the basis of an early postulate [ 4 6 1 that the low friction observed for the rubbing of graphite against solid surfaces in ordinary ambient air could be ascribed to weak interatomic forces between the

561

Figure 19-11. nanometers.

Layer-lattice

structure

of

graphite.

Dimensions

in

parallel sheets of carbon atoms. R. H. Savage [ 4 7 1 demonstrated that the friction observed for graphite in air is strongly influenced by gases and vapors and that i n vucuu the friction of clean graphite rubbing against a copper surface can attain a value as high as pl: = 0.8. This brought about a radically altered view of the intrinsic nature of graphite and its frictional behavior. The electronic and orbital structure of graphitic carbon is such that TI bonds are formed between the unused p orbitals of adjacent carbon atoms in two neighboring layers [481. In MoS2, because of its different electronic and orbital structure, there is no interlayer sulfur-sulfur bonding; its lubricating properties are thus a direct consequenc9 of its intrinsically low interlamellar surface energy, even though the 0.299 nm sulfur-sulfur distance between layers is less than the 0.335 nm interlayer distance in graphite. Bryant, Gutshall and Taylor [ 4 9 1 , by cleaving flakes in vacuum, found a value of 1.750 J/m2 for the interlayer energy of graphite, and by using the quantum mechanical calculations of R. 0. Brennan [50] they computed a value of 2.500 J/m2. Girifalco and Lad [511 carried out interaction calculations with a Lennard-Jones 6-12 potential function and computed a value of 0.330 J/m2 for the surface energy, which Good, Girifalco and Kraus [521 claimed was confirmed by the average values of 0.234-0.260 J/m2 computed from heats of immersion. But there are doubts about applying heat of immersion data obtained in air to the calculation of the surface energy of clean graphite. Bryant e i d.[ 4 9 1 observed that admission of oxygen to a bifilar specimen of graphite cleaved in vacuum and maintained in strain by the original cleaving force caused further propagation of the cleavage crack because adsorption of the gas lowered the binding energy of the strained surfaces. The reader is also referred to the description of the cleavage of mica and the influence of atmosThe pheric gases on the surface energy (Chapter 10, Section 1 0 . 4 . 4 ) .

568

best interpretation of the evidence indicates that the intrinsic inter2 layer energy of graphite is of the order of 1.75-2.50 J / m

.

The influence of gases on the tribological behavior of graphite is described in detail by Savage [ 4 7 1 . The rate of rubbing wear i n vacuo against a copper disk at a speed of 1 3 7 0 cm/s under a contact pressure of 4 9 0 kPa was reduced by 5 0 % when water was admitted at an ambient vapor pressure of 0.5 torr. At an ambient pressure of 3 torr, the wear rate was very low mm/s) and the coefficient of friction was 0.18. Savage found that hydrogen, nitrogen or carbon monoxide did not change the wear of graphite from that observed i n v a c u o , that oxygen required an ambient pressure of 4 0 0 - 6 0 0 torr to equal the effectiveness of water vapor at 3 torr, and that easily condensable vapors such as ammonia, acetone, benzene, ethanol, diethyl ether, hexamethyldisiloxane or hexane

1.6-

cE 1.2 E

I 1

I

3

4

I

5

I

I

6 *

e

8

-

-

7

-

-

zO.8 al

-

a

b

g0.4-

-

-

.,

0.0. lo-*

to-'

I

10

Vapor Pressure, torr

Figure 1 9 - 1 2 . Bromopentane. tetrachloride. Schaefer 1531.

Effect of vapors on the wear of graphite. 1: 12: n-Heptane. 3: n-Propanol. 4 : n-Pentane. 5: Carbon 6: Methanol. 7: Propane. 8: Water. Data by Savage and

0.6

,g 0.5 0 E 04

-

f

O

03

i'D .- 0.2 r w-

8

0

0.1

0 0

0.1

0.2 0.3 0.4 05 Vapor Pressure, torr

0.6 0.7

Figure 19-13. Effect of vapors on the friction Nitrogen. 2: Hydrogen. 3: Water. 4: Dry air. 5: Heptane. 7: Oxygen. From data by G . W. Rowe 1 5 4 1 .

of graphite. Ethanol. 6:

1:

n-

569

were effective at pressures below 5 torr. Figure 19-12 shows the behavior observed by Savage and Schaefer I531 with the vapors of 1bromopentane, n-heptane, n-propanol, n-pentane, carbon tetrachloride, methanol, propane and water. G. W. Rowe [54], working with graphite sliding against graphite at low velocity, obtained the results shown in Fig. 19-13; under these conditions, both hydrogen and oxygen were effective in lowering friction at low ambient pressure. Savage found that the beneficial effect of water vapor at 3 torr for graphite sliding against itself held only at rubbing speeds below 200 cm/s; higher pressures were Although required at higher speeds: e . y . 6 to 7 torr at 800 cm/s 1471. the numbers vary somewhat with the specific experimental conditions, the general observation by various investigators is that the friction and wear of graphite are high i n wacuo and much lower in air. G. W. Rowe [541 found that the high friction of graphite i n vacuo (11 0.45) persisted up to temperatures of c a . 1123 K (850 C ) , above which it fell, dropping at a steady rate to )I = 0.32 at 1623 K (1350 C ) . This effect was attributed to the weakening of the TI bonding at the higher temperatures. A . P. Semenov 1551 observed a gradual decrease in the coefficient of friction of out-gassed graphite i n vucuo from u = 0.70 at room temperature to u = 0.65 at 675 K , followed by a sharper rate of decline t o u = 0.30 at 975 K and a slow, steady decrease to p = 0.15 at 2175 K . On cooling, the friction increased at this terminal rate to ca. p = 0.35 at 575 K and then at a faster rate to restore the value of p = 0.70 at room temperature. For the friction of a platinum rider against a rubbed layer of graphite on a platinum substrate in ordinary air Deacon and Goodman [ l l ] saw a substantially slow decrease in friction from u = 0.25 to u = 0.10 in the temperature range 298-623 K (25-350 C ) , followed = 0.4 with stick-slip over the by increase in friccion from u = 0 . 1 to Then there was a short interval of interval 623-823 K (350-550 C ) . smooth sliding at p = 0.25, and finally a sharp rise to p = 0.8 at 873 K which was related to the oxidation of graphite as shown by the course of thermogravimetric analysis. =

Savage and Brown [56] found that the dust generated by the wear of graphite i n vacuo consisted of laminar platelets, some thinner than 10 nm. Surfaces of rubbed polycrystalline graphite compacts abraded with fine emery paper show orientation along the (0001) direction of the hexagonal crystal structure, with about 10' tilt of the platelets against the direction of rubbing [57, 58, 591. Thus, although the basal planes are not intrinsically directions of easy slip within the body of a crystal or crystallite, once an exposed surface is generated on the basal plane, it becomes associated with easy sliding behavior in a favorable ambient environment. The properties of the basal-plane surface are different from those of the edge-plane surface, a s shown, for example, by the differential adsorption of n-dotriacontane and butanol from solution

570

in n-heptane 6 0 1 . A s an illustration of how ambient environment can influence the surface properties of graphite, material whose surface area was increased from 5 m 2 /g to 658 m 2 /g (as evaluated by BET adsorption of nitrogen) by milling in air showed an average value of 3.6 2 0.6 for the ratio of basal-plane to edge-plane surface; the same type of graphite milled under heptane increased its surface area to only 9 2 m 2 /g but the ratio of basal-plane to edge-plane surface was 51.8. Such a high ratio of basal-plane to edge-plane surface signifies preferential cleavage of crystallites along the ( 0 0 0 1 ) direction by the milling process. Judged by its frictional and wear behavior when rubbing against itself, graphite is not a lubricant intrinsically; its tribological action The is strongly influenced by constituents in the ambient atmosphere. lubrication of metals by graphite is governed by the formation of films on the substrate surfaces and by the behavior of these films in the rubbing process. Thus the study of graphite as a lubricant resolves itself into the study of the formation and properties of the films in relation to the basic behavior of graphite and the specific conditions of rubbing, which include, in addition to mechanical parameters such as load and speed, the condition of the substrate surfaces and the nature of the ambient atmosphere. Most of the information available is for films of graphite on copper because of the use of graphite brushes against copper commutators in electrical machinery. Savage [ 4 7 1 reported estimates of films 33 nm thick laid down by electrographitic compacts rubbing on copper. Electrographites are made by the thermal treatment of non-graphitic carbons such as petroleum coke or carbon black, and depending on the degree of graphitization, may consist of randomly oriented crystallites up to several hundred gngtroms in size, either interlocked among themselves or bonded by a non-graphitic carbon cement. The film transferred to copper by rubbing is strongly oriented in the direction of rubbing [61, 621. The equilibrium film generated by rubbing electrographite against copper (635 nm surface roughness) at 1800 cm/s rubbing speed. and 550 kPa pressure for 11,400 reiterations i n air was c a . 1000 nm thick [611 and was maintained in that condition by an average depth-wear rate of 3.6 nm per traverse of the graphite slider. The transfer process involved the formation of a soft surface layer ( 6 kg/mm2 VPN) on the relatively hard electrographic compact ( 1 0 0 0 kg/mm2 VPN), as was demonstrated by rubbing electrographite against itself. When an unrubbed compact of electrographite was run against fresh copper at 1800 cm/s, it required 80 reiterations to initiate transfer, whereas transfer from a previously rubbed compact to fresh copper occurred during the first traverse of the track 1 6 2 1 . The role of the transferred graphite film in the lubrication of steel was studied by Lancaster [ 4 3 1 , using the technique of dynamic maintenance described in Section 9 . 2 . 1 for MoS2. The wear at a rubbing speed

571

TABLE 19-8.

SCUFFING LOADS FOR A DYNAMICALLY MAINTAINED FILM OF GRAPHITE

I

Speed, m/s

Compact load, N

Steady-state

ph

Contact pressure at scuffing, MPa

Compacted natural graphite powder 0.10 0.60 0.60 0.60 3.00

-

9.8 0.98 2.94 9.8 9.8

100.95 16.10 16.10 28.49 16.10

0.18 0.12 0.15

Electrographite

0.60

9.8

0.25

16.10

Data by J. K. Lancaster [431.

to4

6

c

I o with

5

=*

0

compact without compocl

I0 n 0)

5

-

lo,-\

5

VJ

0

8

-I

lo*

I

of 0.6 m/s was reduced from an unlubricated rate of 0.561 x cm3/Nm cm3/Nm to 0.3059 x 10-l' cm3/Nm at a load of 58.8 N and to 0.2754 x at 255 N. Table 19-8 shows the influence of the dynamically maintained film on the scuffing behavior under various conditions. The load on the compact that maintains the film dynamically does not affect the scuffing load when the speed is held constant at 0.6 m / s , whereas there is a pronounced influence of rubbing speed on scuffing load for a constant compact load of 9.8 N, particularly at the lowest speed used, 0.1 cm/s. The durability of preformed films of graphite on steel in relation to the applied load on the rubbing specimens, as measured by the sliding distance to the onset of scuffing, is shown in Fig. 19-14. Once the transfer film is established, the presence of the compact has no effect on its durability under these conditions. Powdered natural graphite does not aggregate into coherent films on rubbing as easily as MoS2, according to the observations of Sliney 1161.

512

Nor does graphite adhere to

the substrate surface as well as MoS2: graphite films can be stripped from the rubbing track on a copper substrate by the usual techniques for making replicas for electron microscopy, whereas MoS2 films cannot [17]. A mechanism for the adhesion of carbon to metals in ordinary air proposed by Buckley and Johnson [631 involves chemisorptive formation of a carbonate-like metal-oxygen-carbon J. K. Lancaster [ 4 4 ] advocated the following mechanical linkage. process: direct embedding of the lubricating solid into a softer substrate, deposition of the solid into surface depressions generated by the abrasive action of the solid p e t b e , and deposition of the solid into surface depressions characteristic of the original surface finish of the substrate ( e . g . grind marks). Lancaster [43] suggested that the failure of the transferred film can be ascribed to desorption of water vapor and other protective adsorbed gases as the surface temperature increases during rubbing. When a steel rider was rubbed against a preformed film of graphite on a steel substrate, the coefficient of friction increased with temperature and scuffing failure occurred at 390 K (117 C) after 0.36 km of rubbing; under the same load (196 N ) at room temperature, the critical rubbing distance for scuffing was 10 km. It can be inferred from such behavior that the influence of protective vapors on the wear of a transferred film of graphite parallels their influence on the “dusting” wear of graphite in bulk. 19.2.3.

Graphite Fluoride as a Solid Lubricant

Graphite fluoride is the name applied to material with the generic formula (CFx!n resulting from the action of elemental fluorine on graphitic carbon. The value of x can range from 0.68 to 1.12; since (CFx),, is a giant macromolecule, the exact value of n is unknown but is very high. The preparation of graphite fluoride was first reported in 1934 by Ruff, Br.etschneider and Ebert [641, who obtained material with the empirical formula CF0.921 by the reaction of fluorine with graphite at 693 K. W. Rcdorff and G. RGdorff [651 prepared specimens with formulas ranging from CFo.676 to CF0.988, depending on the temperature (693823 K ) and the time of reaction (1-15 hours). Lagow., Badachhape, Wood and Margrave [661 found that material with the formula CF1.,* could be prepared consistently at reaction temperatures of 900 f 3 K by careful attention to the experimental details. Strictly speaking, the designation graphite fluoride is a misnomer, for the various materials with the formula (CFxIn do not have graphitic structures or graphitic properties; f o r example, they do not conduct electricity. The consensus of the available evidence [65, 66, 67, 68, 691 is for the structure shown in Fig. 19-15, in which the carbon

573

@ C a r b o n 0 Fluorine

Figure 19-15. Layer-lattice structure of graphite fluoride. in nanometers.

Dimensions

skeleton is that of a giant "hydroaromatic" molecule with a carbon-carbon bond distance of 0.154 nm and interlayer distances variously reported a s 0.60 nm [671, 0.66 nm [681, 0.58 nm [661 and 0.616 nm 1631. The carbon skeleton is usually assigned the cyclohexane "chair" configuration, probably on the basis of thermodynamic stability 1661; however, Ebert, Brauman and Huggins [691 suggest that nuclear magnetic resonance calculations favor the "boat" structure. According to Lagow e t uL. 1661, stacking of the layers is such that the locations of the carbon atoms are staggered. The carbon-fluorine bonds are covalent, which accounts for the high electrical resistivity of graphite fluoride. Infrared absorption spectra of samples with the empirical composition C F l a 1 2show stretching frequencies assignable to tertiary carbon linkages and to CF2 bonding [661. The CF2 bonding occurs with the carbon atoms located on the periphery of the polynuclear sheet. Heavy fluorination can open the polynuclear structure Light with the formation of volatile fluorocarbons CnFnc2 1651. fluorination would leave patches of graphite unreacted. The possibility that a particular preparation is a mixture of underfluorinated and superfluorinated structures must also be considered. T h u s , there is no particular merit in the designation poly(carbon monofluoride) [701 for substances with the empirical formula (CFxIn (n c u . 1). Graphite fluoride, whatever its shortcomings as a name in other respects, does not have any implications of precision as regards the composition or nature of the material and hence will be used here as the designation of materials with the composition (CFxIn.

574

Lagow e t n l . 1661 reported that preparations with the composition CF1.12 were stable in air up to a temperature of 873 K and decomposed at 1073 K. Under high vacuum graphite fluoride decomposes at 693-853 K to form a series of polyolefinic fluorocarbons 1711. Ruff e t a l . [64] found the fluorocarbons CF4, C2F4, C2F,-, etc. as the products of the thermal decomposition of their preparations. Depending on the particular method of preparation, RGdorff and RGdorff [651 reported critical temperatures of decomposition in the range 743-773 K. Gisser, Petronio and Shapiro f721 observed a change in (CF0.9)n at 678 K by differential thermal analysis.

8

0

100 200 300 400 500 600 Temperature, deg. C

Figure 19-16 Comparison of the effect of temperature on the durability and the frict on of films of graphite fluoride and molybdenum disulfide. 440 C stain ess steel riders against burnished films on 440 C stainless steel disks. Load: 4.6 N. Sliding speed: 1.6 m/s. Atmosphere: dry air. A: Friction f unlubricated metal. B: Onset of thermal decomposition of (CF1.12)n. Data by Fusaro and Sliney [731.

Although graphite fluoride has been known since 1934, its properties as a solid lubricant were not investigated until 35 years later. Fusaro and Sliney [731 studied the behavior of burnished films on stainless steel with a pin and disk apparatus. Figure 19-16 shows a comparison of the effect of temperature on the durability and the friction behavior of films of (CF1.12)n and MoS2 on 440 C stainless steel in dry air, the criterion of film failure being the strong increase of friction to that of the,unlubricated metal. Under these conditions (CFlVl2),, exhibits better durability than MoS2 up to the temperature at which thermal decomposition of graphite fluoride is appreciable. The relation between durability and temperature can be expressed as a linear function of temperature by

Log L

= bog

L o - he

(19-1)

TABLE 19-9.

Disk

440C 440C 440C 440C

BEHAVIOR OF GRAPHITE FLUORIDE A S A SOLID LUBRICANT

u

(a)

(CF1.12 ’n

Dry air

506

0.03-0,15

Dry air

99

0.02-0.04

Moist air (e)

__

0.06

1200

Moist air (e)

-

0.15

30

Dry air

200

MOS

(CF1.12)n MO 5

2

(CF1.12)n

310

Graphite

Dry air

310

M0S2

Dry air

310

h

Atmosphere

310

310

Lo, min.

Lubricant

(CF1.12)n

Graphite

Moist air (e) Moist air (e)

~

Dry argon

_ .

MoS2

Dry argon

310

~

(b)

450 70

250

Fa i lure(g)

~

Graphite

310

min.

Failure(g)

-

53

(CF1.12)n

0.02-0.07

I _

Dry argon

310

0. 004222(f

L,

0.002?71(h)

0.05

700’

0.09

350

0.02-0.04

50