MODERN TRIBOLOGY HANDBOOK Volume One Principles of Tribology
The MECHANICS and MATERIALS SCIENCE Series Series Editor
Bharat Bhushan
PUBLISHED TITLES Handbook of Micro/Nano Tribology, Bharat Bhushan Modern Tribology Handbook, Bharat Bhushan
FORTHCOMING TITLES Rolling Mills Rolls and Bearing Maintenance, Richard C. Schrama Thermoelastic Instability in Machinery, Ralph A. Burton
MODERN TRIBOLOGY HANDBOOK Volume One Principles of Tribology
Editor-in-Chief
Bharat Bhushan, Ph.D., D.Sc. (Hon.) Department of Mechanical Engineering The Ohio State University Columbus, Ohio
CRC Press Boca Raton London New York Washington, D.C.
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Library of Congress Cataloging-in-Publication Data Modern tribology handbook / edited by Bharat Bhushan. p. cm. — (Mechanics and materials science series) Includes bibliographical references and index. ISBN 0-8493-8403-6 (alk. paper) 1. Tribology — Handbooks, manuals, etc. I. Bhushan, Bharat, 1949- II. Series. TJ1075.M567 2000 621.8′9 — dc21
00-046869
This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. All rights reserved. Authorization to photocopy items for internal or personal use, or the personal or internal use of specific clients, may be granted by CRC Press LLC, provided that $.50 per page photocopied is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 USA. The fee code for users of the Transactional Reporting Service is ISBN 0-8493-8403-6/01/$0.00+$.50. The fee is subject to change without notice. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.
© 2001 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-8403-6 Library of Congress Card Number 00-046869 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper
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Foreword
The very size of this Modern Tribology Handbook reflects the extent to which the subject has developed since the word tribology was introduced in 1966. While much progress has been recorded in recent decades and several research workers, some of whom are authors of chapters in these volumes, have revealed new facets of the subject and generated valuable data, it is as well to remember that the major users of tribological knowledge are the engineers who design, manufacture, and operate machinery. The general engineer who finds much value in handbooks will welcome the addition of this new compendium of tribological knowledge and data. It is important that the reader and user of this handbook be aware of the well-tried approaches to the measurement of friction and wear and the difficulties sometimes encountered in the interpretation of the results. Throughout the long history of tribology, engineers have sought simple guidance on the magnitude of dominant quantities affecting the performance and life of machinery. Engineers in many fields frequently require estimates of the magnitudes of the friction and wear likely to be experienced by different combinations of materials sliding or rolling together in various environments. The presentation of practical information in the form of data banks for friction and wear based upon current knowledge and experience will thus be warmly welcomed. The frustration experienced by practicing engineers when seeking guidance from expert tribologists on representative values of such quantities is legendary! The basic concepts of contact, friction, wear, and lubrication have been embellished in impressive style by recent analytical and experimental approaches to these subjects, and the outcome is thoroughly reviewed in the initial and major section of the handbook dealing with macrotribology. Impressive studies have greatly enhanced our understanding of the physical and chemical nature of surfaces during the latter half of the 20th century, and the subject which underpins many aspects of tribology thus attracts special attention. Some of the topics, such as wear maps and elastohydrodynamic lubrication, are almost as new as the term tribology itself. Effective lubrication remains the ideal way of controlling friction and wear in most mechanical systems. The science and technology of generating fluid-film lubrication to protect tribological components is now firmly established. However, studies of macrotribology have been supplemented by remarkable investigations of micro-, nano-, and even molecular tribology in recent times. This is illustrated by studies of the physical and chemical properties of surfaces; the contact and adhesion between solids; the effects of surface modifications and coatings upon friction and wear; lubricant rheology; very thin elastohydrodynamic lubricating films; and the nature of boundary and mixed lubrication. This alone justifies the substantial and welcome section of the handbook devoted to micro- and nanotribology. While most of the work is devoted to experimental studies, one chapter is devoted to the fascinating subject of molecular dynamics simulations in this field. v
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Both the conventional and the newer tribological materials are considered in the third section of the handbook. This provides a timely opportunity for the reader to extend his or her knowledge of the advantages and limitations of ceramics, diamond, diamond-like carbon and related films, and a wide range of coating composites. The last major section of the handbook is devoted to industrial components and systems. Familiar components which have typically enjoyed a century or more of development, such as slider bearings, rolling element bearings, gears, and seals are all considered, alongside components and systems encountered in road, rail, marine, and space vehicles. The special tribological problems faced in earth-moving and manufacturing equipment attract individual attention. It is refreshing to see newer applications of tribology included in the handbook. The term biotribology was introduced in 1973 to embrace the application of tribology to biological and particularly medical situations. While the success of joint replacement tends to dominate this field, since it represents a remarkable and dominant feature of orthopedic surgery, there are also an increasing number of examples of the successful transfer of tribological knowledge to the biological field. It is, however, the impact of information technology on society that has promoted major progress in tribology in recent times. The role of tribology has undoubtedly been central to the successful development of magnetic storage and retrieval systems. Spectacular achievements have been recorded in relation to computers, printers, cameras, and scanners, and the reader will welcome the chapters devoted to these developments. The Jost Report1 of 1966 emphasized that losses associated with the shutdown of machinery disabled by the failure of tribological components represented a troublesome economic millstone around the necks of machinery and manufacturing systems. Since that time, maintenance of machinery has changed considerably, with emphasis moving away, in many cases, from routine inspection and component replacement to more effective procedures. It is therefore fitting that the closing chapter of the handbook should be devoted to machinery diagnosis and prognosis. It is now well recognized that the tribologist and maintenance engineer must work closely together in monitoring the health of machinery and the performance of tribological components that might so easily compromise the well-being of our industrial society. The Editor-in-Chief and his team are to be warmly congratulated in bringing together this extensive, timely, and useful Modern Tribology Handbook. Duncan Dowson, CBE, FRS, FREng, CEng, FIMechE FCGI Emeritus/Research Professor School of Mechanical Engineering The University of Leeds U.K.
Reference 1. Department of Education and Science, 1966, Lubrication (Tribology) Education and Research, A Report on the Present Position and Industry’s Needs, HMSO, London.
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Preface
Tribology is the science and technology of interacting surfaces in relative motion and of related subjects and practices. The nature and consequences of the interactions that take place at the moving interface control its friction, wear, and lubrication behavior. Understanding the nature of these interactions and solving the technological problems associated with the interfacial phenomena constitute the essence of tribology. The field of tribology incorporates a number of disciplines, including mechanical engineering, materials science, mechanics, surface chemistry, surface physics and a multitude of subjects, such as surface characterization, friction, wear, lubrication, bearing materials, lubricants, and the selection and design of lubrication systems, and it forms a vital element of engineering. The importance of friction and wear control cannot be overemphasized for economic reasons and long-term reliability. It is important that all designers of mechanical systems use appropriate means to reduce friction and wear, through the proper selection of bearings and the selection of appropriate lubricants and materials for all interacting surfaces. It is equally important that those involved with manufacturing understand the tribological origins of unwanted friction, excessive wear, and lubrication failure in their equipment. The lack of consideration of tribological fundamentals in design and manufacturing is responsible for vast economic losses, including shortened life, excessive equipment downtime, and large expenditures of energy. The recent emergence and proliferation of proximal probes (in particular tip-based microscopies and the surface force apparatus) and of computational techniques for simulating tip-surface interactions and interfacial properties has allowed systematic investigations of interfacial problems with high resolution as well as ways and means for modifying and manipulating nanostructures. These advances provide the impetus for research aimed at developing a fundamental understanding of the nature and consequences of the interactions between materials on the atomic scale, and they guide the rational design of material for technological applications. In short, they have led to the appearance of the new field of micro/nanotribology. There are also new applications which require detailed understanding of the tribological processes on macro- and microscales. Since the early 1980s, tribology of magnetic storage systems has become one of the important parts of tribology. Microelectromechanical Systems (MEMS) have begun to appear in the marketplace which present new tribological challenges. Tribology of processing systems such as copiers, printers, scanners, and cameras is important, although it has not received much attention. Along with the new industrial applications, there has been development of new materials, coatings, and treatments, such as synthetic diamond, true diamond, diamond-like carbon films, and chemically grafted films, to name a few. It is clear that the general field of tribology has grown rapidly during the past 50 years or so. Conventional tribology is well established, but micro/nanotribology is evolving and is expected to take center stage for the next decade. New materials are needed, and their development requires fundamental understanding of tribological processes. Furthermore, new industrial applications continue to evolve with their unique challenges. Much of the new tribological information has not made it into the hands vii
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that need to use it. Very few tribology handbooks exist, and these are dated. They have focused on conventional tribology, traditional materials, and already-matured industrial applications. The objective of this handbook is to cover modern tribology with an emphasis on all industrial applications. A large number of leading tribologists from around the world have contributed chapters dealing with all aspects of the subject. The appeal of the subject is expected to be very broad, including researchers and practicing engineers and scientists. The handbook is divided into four sections. The first section, on Macrotribology, covers the fundamentals of conventional tribology. It consists of 15 chapters on topics including surface physics, surface roughness, solid contact mechanics, adhesion, friction, contact temperatures, wear, lubrication and liquid lubricants, friction and wear measurement techniques, design of friction and wear tests, and friction and wear data bank. The second section on Micro/Nanotribology covers the fundamentals of the emerging field of micro/nanotribology. It consists of studies using surface force apparatus, scanning probe microscopy, and molecular dynamic simulations. These studies complement our tribological understanding on the macroscale. The third section on Solid Tribological Materials and Coatings covers the materials; hard, wear-resistant, and solid lubricant coatings; and surface treatments used in tribological applications as well as coating evaluation techniques. The fourth and last section on Tribology of Industrial Components and Systems covers a large range of industrial applications. This section starts out with the most common tribological components followed by tribology of various industrial applications from the “old” and “new” economy. A Glossary of Terms in Tribology is added, which should be of general interest. We embarked on this project in October 1998, and we worked very hard to get all the chapters to the publisher in a record time of a little over 1 year. I wish to sincerely thank the authors for offering to write comprehensive chapters on a tight schedule. This is generally an added responsibility in the hectic work schedules of most researchers today. I also wish to thank the section editors who worked hard to solicit the most competent authors. They are listed in the handbook. I depended on a large number of reviewers who provided critical reviews, in many cases, of more than one chapter in a short time. They are listed in the handbook as well. I also would like to thank Mr. Sriram Sundararajan, a Ph.D. student in my lab, who patiently assisted in the handling of the chapters. I hope the readers of this handbook find it useful. Bharat Bhushan Editor September 2000
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The Editor
Dr. Bharat Bhushan received an M.S. in mechanical engineering from the Massachusetts Institute of Technology in 1971, an M.S. in mechanics and a Ph.D. in mechanical engineering from the University of Colorado at Boulder in 1973 and 1976, respectively, an M.B.A. from Rensselaer Polytechnic Institute at Troy, NY, in 1980, Doctor Technicae from the University of Trondheim at Trondheim, Norway, in 1990, a Doctor of Technical Sciences from the Warsaw University of Technology at Warsaw, Poland, in 1996, and Doctor Honouris Causa from the Metal–Polymer Research Institute of the National Academy of Sciences at Gomel, Belarus. He is a registered professional engineer (mechanical). He is presently an Ohio Eminent Scholar and The Howard D. Winbigler Professor in the Department of Mechanical Engineering as well as the Director of the Computer Microtribology and Contamination Laboratory at the Ohio State University, Columbus. He is an internationally recognized expert in tribology on the macro- to nanoscales, and is one of the field’s most prolific authors. He is considered by some a pioneer in the tribology and mechanics of magnetic storage devices and a leading researcher in the field of micro/nanotribology using single probe microscopy. He has authored 5 technical books, 23 handbook chapters, more than 400 technical papers in reviewed journals, and more than 60 technical reports. He has edited more than 25 books, and holds 10 U.S. patents. He is founding editor-in-chief of the World Scientific Advances in Information Storage Systems Series, the CRC Press Mechanics and Materials Science Series, and the Journal of Information Storage and Processing Systems. He has given more than 200 invited presentations on five continents and more than 50 keynote/plenary addresses at major international conferences. He organized the first symposium on Tribology and Mechanics of Magnetic Storage Systems in 1984 and the first international symposium on Advances in Information Storage Systems in 1990, both of which are now held annually. He is the founder of an ASME Information Storage and Processing Systems Division founded in 1993 and served as the founding chair from 1993 through 1998. His biography has been listed in over two dozen Who’s Who books including Who’s Who in the World, and he has received more than a dozen awards for his contributions to science and technology from professional societies, industry, and U.S. government agencies. Dr. Bhushan is also the recipient of various international fellowships including the Alexander von Humboldt Research Prize for Senior Scientists and the Fulbright Senior Scholar Award. He is a foreign member of the International Academy of Engineering (Russia), the Byelorussian Academy of Engineering and Technology, and the Academy of Triboengineering of the Ukraine, an honorary member of the Society of Tribologists of Belarus, a fellow of ASME and the New York Academy of Sciences, a senior member of IEEE, and a member of STLE, ASEE, Sigma Xi, and Tau Beta Pi. Dr. Bhushan has previously worked for Automotive Specialists, Denver, CO; the R & D Division of Mechanical Technology Inc., Latham, NY; the Technology Services Division of SKF Industries Inc., King of Prussia, PA; the General Products Division Laboratory of IBM Corporation, Tucson, AZ; and the Almaden Research Center of IBM Corporation, San Jose, CA. ix
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Contributors
Dr. Phillip B. Abel
Prof. Herbert S. Cheng
Dr. David I. Fletcher
NASA Glenn Research Center Cleveland, OH
Department of Mechanical Engineering Northwestern University Evanston, IL
Department of Mechanical Engineering The University of Sheffield Sheffield, U.K.
Richard S. Cowan
Dr. Richard S. Gates
Dr. Koshi Adachi Laboratory of Tribology School of Mechanical Engineering Tohoku University Sendai, Japan
Dr. Xiaolan (Alan) Ai The Timken Company Canton, OH
Dr. Niklas Axén Ångström Laboratory Uppsala University Uppsala, Sweden
Prof. Richard C. Benson Department of Mechanical and Nuclear Engineering The Pennsylvania State University University Park, PA
Dr. Alan D. Berman Seagate Technology Costa Mesa, CA
MultiUniversity Center for Integrated Diagnostics Georgia Institute of Technology Atlanta, GA
Prof. Christophe Donnet École Centrale de Lyon Département de Sciences et Techniques des Matériaux et des Surfaces Laboratoire de Tribologie et Dynamique des Systèmes Écully, France
Prof. Rob S. Dwyer-Joyce Department of Mechanical Engineering The University of Sheffield Sheffield, U.K.
Dr. Ali Erdemir
National Institute of Standards and Technology Gaithersburg, MD
William A. Glaeser Battelle Columbus, OH
Lois J. Gschwender Wright Patterson Air Force Base Dayton, OH
Dr. Jeffrey A. Hawk U.S. Department of Energy Albany Research Center Albany, OR
Prof. Sture Hogmark Ångström Laboratory Uppsala University Uppsala, Sweden
Argonne National Laboratory Energy Technology Division Argonne, IL
Dr. Kenneth Holmberg
The Ohio State University Columbus, OH
Dr. Peter J. Blau
Dr. John Ferrante
Dr. Hendrik Hölscher
Bharat Bhushan
Tribomaterials Investigative Systems Oak Ridge, TN
David E. Brewe U.S. Army Vehicle Propulsion Directorate NASA Glenn Research Center Cleveland, OH
Department of Physics Cleveland State University Cleveland, OH
Prof. John Fisher School of Mechanical Engineering The University of Leeds Leeds, U.K.
VTT Manufacturing Technology Espoo, Finland
Institute of Applied Physics University of Hamburg Hamburg, Germany
Dr. Stephen M. Hsu National Institute of Standards and Technology Gaithersburg, MD
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Dr. M. Ishida
Brent K. Lok
Dr. A. William Ruff
Railway Technical Research Institute Tokyo, Japan
Chevron Global Lubricants San Francisco, CA
Consultant Gaithersburg, MD
Prof. Jacob N. Israelachvili
Prof. Kenneth C Ludema
Prof. Richard F. Salant
Department of Chemical Engineering and Materials Department University of California at Santa Barbara Santa Barbara, CA
Prof. Staffan Jacobson Ångström Laboratory Uppsala University Uppsala, Sweden
Mark J. Jansen AYT Corporation Brookpark, OH
Dr. William R. Jones, Jr.
Mechanical Engineering Department University of Michigan Ann Arbor, MI
Department of Mechanical Engineering Georgia Institute of Technology Atlanta, GA
Prof. Othmar Marti Experimentelle Physik Universität Ulm Ulm, Germany
Prof. Allan Matthews Research Centre in Surface Engineering The University of Hull Hull, U.K.
Dr. Daniel Maugis
Dr. K. J. Sawley Transportation Technology Centre Pueblo, CO
Dr. F. Schmid Department of Mechanical Engineering The University of Sheffield Sheffield, U.K.
CNRS Laboratoire des Materiaux et Structures du Genie Civil Champ sur Marne, France
Dr. Karl J. Schmid
NASA Glenn Research Center Cleveland, OH
Dr. Ajay Kapoor
Prof. Eric Mockensturm
Department of Mechanical Engineering The University of Sheffield Sheffield, U.K.
Department of Mechanical and Nuclear Engineering The Pennsylvania State University University Park, PA
Prof. Steven R. Schmid
Prof. Koji Kato
Charles A. Moyer
Laboratory of Tribology School of Mechanical Engineering Tohoku University Sendai, Japan
Prof. Francis E. Kennedy Thayer School of Engineering Dartmouth College Hanover, NH
Dr. Padma Kodali Cummins Inc. Columbus, IN
David C. Kramer Chevron Global Lubricants Richmond, CA
Dr. Mats Larsson Balzers Sandvik Coating AB Stockholm, Sweden
The Timken Company (retired) Canton, OH
John Deere Marine Engines Division Waterloo, IA
Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN
Dr. Shirley E. Schwartz General Motors Powertrain Warren, MI
Dr. Martin H. Müser Institute für Physik Johannes Gutenberg-Universität Mainz, Germany
Dr. Malcolm G. Naylor Cummins Inc. Columbus, IN
Dr. Udo D. Schwarz Institute of Applied Physics University of Hamburg Hamburg, Germany
Dr. Shashi K. Sharma
Dr. Martin Priest
Wright Patterson Air Force Base Dayton, OH
School of Mechanical Engineering The University of Leeds Leeds, U.K.
Dr. Ming C. Shen
Prof. Mark O. Robbins Department of Physics and Astronomy The Johns Hopkins University Baltimore, MD
SULZERMEDICA Austin, TX
Carl E. Snyder, Jr. Wright Patterson Air Force Base Dayton, OH
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Prof. Andras Z. Szeri
Dr. Jerry C. Wang
Dr. Rick D. Wilson
Department of Mechanical Engineering University of Delaware Newark, DE
Cummins Inc. Columbus, IN
U.S. Department of Energy Albany Research Center Albany, OR
Dr. Urban Wiklund
Prof. William R. D. Wilson
Mark L. Sztenderowicz Chevron Global Lubricants Richmond, CA
Dr. Simon C. Tung General Motors Research and Development Center Warren, MI
Ångström Laboratory Uppsala University Uppsala, Sweden
Dr. John A. Williams Engineering Department Cambridge University Cambridge, U.K.
Department of Mechanical Engineering University of Washington Seattle, WA
Prof. Ward O. Winer Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA
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Section Editors Section 1: Macrotribology Bharat Bhushan (The Ohio State University, USA) Francis E. Kennedy (Dartmouth College, USA) Andras Z. Szeri (University of Delaware, USA) Section 2: Micro/Nanotribology Bharat Bhushan (The Ohio State University, USA) Othmar Marti (University of Ulm, Germany) Section 3: Solid Tribological Materials and Coatings Bharat Bhushan (The Ohio State University, USA) Ali Erdemir (Argonne National Laboratory, USA) Kenneth Holmberg (VTT Manufacturing Technology, Finland) Section 4: Tribology of Industrial Components and Systems Bharat Bhushan (The Ohio State University, USA) Stephen M. Hsu (National Institute of Standards and Technology, USA)
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Reviewers Prof. George Adams (Northeastern University, Boston, MA) Dr. Paul Bessette (Nye Lubricants Inc., New Bedford, MA) Prof. B. Bhushan (The Ohio State University, Columbus, OH) Prof. Thierry A Blanchett (Rensselaer Polytechnic Institute, Troy, NY) Dr. Peter J. Blau (Oak Ridge National Laboratory, Oak Ridge, TN) Dr. Ken Budinski (Eastman Kodak Co., Rochester, NY) Dr. Nancy Burnham (École Polytechnique Federal de Lausanne, Switzerland) Dr. Jaime Colchero (Universidad Antonoma de Madrid, Spain) Dr. Christopher Dellacorte (NASA Glenn Research Center, Cleveland, OH) Dr. Urs. T. Duerig (IBM Research Division, Zurich, Switzerland) Dr. John Dumbleton (Biomaterials and Technology Assessment, Ridgewood, NJ) Dr. Norman S. Eiss Jr. (Retired) Dr. Ali Erdemir (Argonne National Laboratory, Argonne, IL) Prof. Traugott E. Fischer (Stevens Institute of Technology, Hoboken, NJ) Mr. William A. Glaeser (Battelle Memorial Institute, Columbus, OH) Prof. Steve Granick (University of Illinois, Urbana, IL) Prof. Judith A. Harrison (U.S. Naval Academy, Annapolis, MD) Dr. Jeffrey A. Hawk (U.S. Department of Energy, Albany, OR) Prof. Sture Hogmark (Uppsala University, Sweden) Dr. Kenneth Holmberg (VTT Manufacturing Technology, Finland) Dr. K. L. Johnson (Cambridge University, Cambridge, U.K.) Dr. William R. Jones (NASA Glenn Research Center, Cleveland, OH) Prof. Koji Kato (Tohoku University, Japan) Prof. Francis E. Kennedy (Dartmouth College, Hanover, NH) Dr. Jari Koskinen (VTT Manufacturing Technology, Finland) Dr. Minyoung Lee (G. E. Corp. R&D, Schenectady, NY) Prof. Frederick F. Ling (University of Texas, Austin, TX) Dr. Jean-Luc Loubet (École Centrale de Lyon, France) Prof. Kenneth C Ludema (University of Michigan, Ann Arbor, MI) Dr. William D. Marscher (Mechanical Solutions Inc., Parsippany, NJ) Prof. Ernst Meyer (Institute für Physik, University of Basel, Switzerland) Dr. Sinan Muftu (Massachusetts Institute of Technology, Bedford, MA) Dr. B. Nau (Fluid Sealing Consultant) Prof. Gerhard Poll (Universität Hannover, Germany) Prof. David E. Rigney (The Ohio State University, Columbus, OH) Dr. A. William Ruff (Consultant, Gaithersburg, MD) Prof. Farshid Sadeghi (Purdue University, W. Lafayette, IN) Prof. Steven R. Schmid (University of Notre Dame, Notre Dame, IN) xvi
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Dr. Shashi K. Sharma (Wright Patterson Air Force Base, Dayton, OH) Dr. Simon Sheu (Alcoa, Pittsburgh, PA) Dr. William D. Sproul (Reactive Sputtering Inc., Santa Barbara, CA) Prof. Andras Z. Szeri (University of Delaware, Newark, DE) Dr. John Tichy (Rensselaer Polytechnic Institute, Troy, NY) Prof. Matthew Tirrell (University of California, Santa Barbara, CA) Dr. Andrey A. Voevodin (Wright Patterson Air Force Base, Dayton, OH) Prof. Mark E. Welland (Cambridge University, U. K.) Prof. J. A. Wickert (Carnegie Mellon University, Pittsburgh, PA) Dr. Pierre Willermet (Ford Motor Co., Dearborn, MI) Dr. John A. Williams (Cambridge University, U. K.) Mr. E. Zaretsky (NASA Glenn Research Center, Cleveland, OH) Dr. Ing. K.-H Zum Gahr (Forschungszentrum Karlsruhe, Germany)
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Contents
Volume One SECTION I Introduction
1
Phillip B. Abel and John Ferrante
Introduction ................................................................................................................................ 5 Geometry of Surfaces .................................................................................................................. 6 Theoretical Considerations ...................................................................................................... 10 Experimental Determinations of Surface Structure................................................................ 19 Chemical Analysis of Surfaces .................................................................................................. 23 Surface Effects in Tribology...................................................................................................... 32 Concluding Remarks ................................................................................................................ 40
Surface Roughness Analysis and Measurement Techniques Bharat Bhushan 2.1 2.2 2.3 2.4
3
Bharat Bhushan, Francis E. Kennedy, and Andras Z. Szeri
Surface Physics in Tribology 1.1 1.2 1.3 1.4 1.5 1.6 1.7
2
Macrotribology
The Nature of Surfaces ............................................................................................................. 49 Analysis of Surface Roughness ................................................................................................. 50 Measurement of Surface Roughness ........................................................................................ 81 Closure..................................................................................................................................... 114
Contact Between Solid Surfaces 3.1 3.2 3.3 3.4 3.5 3.6
John A.Williams and Rob S. Dwyer-Joyce
Introduction ............................................................................................................................ 121 Hertzian Contacts ................................................................................................................... 122 Non-Hertzian Contacts .......................................................................................................... 137 Numerical Methods for Contact Mechanics ......................................................................... 140 Experimental Methods for Contact Mechanics..................................................................... 144 Further Aspects ....................................................................................................................... 150
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4
Adhesion of Solids: Mechanical Aspects 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
5
Friction 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11
6
xx
Koji Kato and Koshi Adachi
Introduction ............................................................................................................................ 273 Change of Wear Volume and Wear Surface Roughness with Sliding Distance .................. 274 Ranges of Wear Rates and Varieties of Wear Surfaces.......................................................... 274 Descriptive Key Terms............................................................................................................ 276 Survey of Wear Mechanisms .................................................................................................. 278 Concluding Remarks .............................................................................................................. 299
Wear Debris Classification 8.1 8.2 8.3 8.4 8.5
Francis E. Kennedy
Surface Temperatures and Their Significance....................................................................... 235 Surface Temperature Analysis................................................................................................ 238 Surface Temperature Measurement....................................................................................... 259
Wear Mechanisms 7.1 7.2 7.3 7.4 7.5 7.6
8
Kenneth C Ludema
Introduction ............................................................................................................................ 205 Qualitative Ranges of Friction................................................................................................ 208 Early Concepts on the Causes of Friction.............................................................................. 213 Adhesion, Welding, and Bonding of the Three Major Classes of Solids.............................. 215 The Formation and Persistence of Friction Controlling Surface Films ............................... 216 Experiments that Demonstrate the Influence of Films on Surfaces..................................... 218 Mechanisms of Friction .......................................................................................................... 219 Measuring Friction.................................................................................................................. 220 Test Machine Design and Machine Dynamics ...................................................................... 227 Tapping and Jiggling to Reduce Friction Effects................................................................... 229 Equations and Models of Friction.......................................................................................... 230
Frictional Heating and Contact Temperatures 6.1 6.2 6.3
7
Daniel Maugis
Introduction ............................................................................................................................ 163 Adhesion Forces, Energy of Adhesion, Threshold Energy of Rupture................................. 164 Fracture Mechanics and Adhesion of Solids.......................................................................... 167 Example: Contact and Adherence of Spheres........................................................................ 175 Liquid Bridges ......................................................................................................................... 183 Adhesion of Rough Elastic Solids — Application to Friction .............................................. 186 Kinetics of Crack Propagation................................................................................................ 188 Adhesion of Metals ................................................................................................................. 197 Conclusion .............................................................................................................................. 198
William A. Glaeser
Introduction ............................................................................................................................ 301 How Wear Debris Is Generated ............................................................................................. 302 Collection of Wear Debris ...................................................................................................... 306 Diagnostics with Wear Debris................................................................................................ 308 Conclusions ............................................................................................................................. 312
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9
Wear Maps 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9
10
Liquid Lubricants and Lubrication Lois J. Gschwender, David C. Kramer, Brent K. Lok, Shashi K. Sharma, Carl E. Snyder, Jr., and Mark L. Sztenderowicz 10.1 10.2 10.3 10.4
11
Andras Z. Szeri
Basic Equations ....................................................................................................................... 384 Externally Pressurized Bearings.............................................................................................. 391 Hydrodynamic Lubrication.................................................................................................... 398 Dynamic Properties of Lubricant Films................................................................................. 422 Elastohydrodynamic Lubrication........................................................................................... 438
Boundary Lubrication and Boundary Lubricating Films and Richard S. Gates 12.1 12.2 12.3 12.4 12.5 12.6
13
Introduction ............................................................................................................................ 361 Lubricant Selection Criteria ................................................................................................... 361 Conventional Lubricants — The Evolution of Base Oil Technology................................... 366 Synthetic Lubricants ............................................................................................................... 373
Hydrodynamic and Elastohydrodynamic Lubrication 11.1 11.2 11.3 11.4 11.5
12
Stephen M. Hsu and Ming C. Shen
Introduction ............................................................................................................................ 317 Fundamental Wear Mechanisms of Materials....................................................................... 318 Wear Prediction ...................................................................................................................... 319 Wear Mapping......................................................................................................................... 320 Wear Maps as a Classification System ................................................................................... 322 Wear Map Construction for Ceramics .................................................................................. 324 Comparison of Materials ........................................................................................................ 328 Modeling Wear by Using Wear Maps.................................................................................... 341 Advantages and Limitations of Current Wear Map Approach ............................................ 354
Introduction ............................................................................................................................ 455 The Nature of Surfaces ........................................................................................................... 457 Lubricants and Their Reactions ............................................................................................. 459 Boundary Lubricating Films................................................................................................... 468 Boundary Lubrication Modeling............................................................................................ 479 Concluding Remarks .............................................................................................................. 486
Friction and Wear Measurement Techniques Sture Hogmark, and Staffan Jacobson 13.1 13.2 13.3 13.4 13.5
Stephen M. Hsu
Niklas Axén,
The Importance of Testing in Tribology ............................................................................... 493 Wear or Surface Damage ........................................................................................................ 494 Classification of Tribotests ..................................................................................................... 497 Tribotest Planning .................................................................................................................. 498 Evaluation of Wear Processes................................................................................................. 500 xxi
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13.6 13.7 13.8 13.9 13.10
14
Simulative Friction and Wear Testing 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8
15
Tribotests — Selected Examples ........................................................................................... 501 Abrasive Wear ........................................................................................................................ 502 Erosive Wear .......................................................................................................................... 504 Wear in Sliding and Rolling Contacts .................................................................................. 505 Very Mild Wear ..................................................................................................................... 508
Friction and Wear Data Bank 15.1 15.2 15.3 15.4
Introduction
Micro/Nanotribology Bharat Bhushan and Othmar Marti
Microtribology and Microrheology of Molecularly Thin Liquid Films Alan D. Berman and J. N. Israelachvili 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9
xxii
A. William Ruff
Introduction........................................................................................................................... 523 Sources of Data ...................................................................................................................... 523 Materials Found in Data Bank .............................................................................................. 527 Data Bank Format.................................................................................................................. 529
SECTION II
16
Peter J. Blau
Introduction........................................................................................................................... 511 Defining the Problem ............................................................................................................ 512 Selecting a Scale of Simulation.............................................................................................. 514 Defining Field-Compatible Metrics...................................................................................... 516 Selecting or Constructing the Test Apparatus...................................................................... 517 Conducting Baseline Testing Using Established Metrics and Refining Metrics as Needed.................................................................................................................................... 517 Case Studies............................................................................................................................ 518 Conclusions............................................................................................................................ 522
Introduction........................................................................................................................... 568 Solvation and Structural Forces: Forces Due to Liquid and Surface Structure.................. 568 Adhesion and Capillary Forces ............................................................................................. 572 Nonequilibrium Interactions: Adhesion Hysteresis ............................................................ 574 Rheology of Molecularly Thin Films: Nanorheology .......................................................... 576 Interfacial and Boundary Friction: Molecular Tribology.................................................... 582 Theories of Interfacial Friction ............................................................................................. 587 Friction and Lubrication of Thin Liquid Films.................................................................... 594 Stick-Slip Friction .................................................................................................................. 600
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Measurement of Adhesion and Pull-Off Forces with the AFM Othmar Marti 17.1 Introduction ............................................................................................................................ 617 17.2 Experimental Procedures to Measure Adhesion in AFM and Applications....................... 624 17.3 Summary and Outlook.......................................................................................................... 633
18
Atomic-Scale Friction Studies Using Scanning Force Microscopy Udo D. Schwarz and Hendrik Hölscher 18.1 Introduction ............................................................................................................................ 641 18.2 The Scanning Force Microscope as a Tool for Nanotribology............................................ 642 18.3 The Mechanics of a Nanometer-Sized Contact ................................................................... 644 18.4 Amontons’ Laws at the Nanometer Scale............................................................................. 646 18.5 The Influence of the Surface Structure on Friction ............................................................. 648 18.6 Atomic Mechanism of Friction............................................................................................. 652 18.7 The Velocity Dependence of Friction................................................................................... 658 18.8 Summary ................................................................................................................................ 660
19
Friction, Scratching/Wear, Indentation, and Lubrication Using Scanning Probe Microscopy Bharat Bhushan 19.1 19.2 19.3 19.4 19.5 19.6 19.7
20
Introduction........................................................................................................................... 667 Description of AFM/FFM and Various Measurement Techniques .................................... 669 Friction and Adhesion ........................................................................................................... 678 Scratching, Wear, and Fabrication/Machining .................................................................... 694 Indentation............................................................................................................................. 703 Boundary Lubrication ........................................................................................................... 708 Closure ................................................................................................................................... 712
Computer Simulations of Friction, Lubrication, and Wear Mark O. Robbins and Martin H. Müser 20.1 20.2 20.3 20.4 20.5 20.6 20.7
Introduction........................................................................................................................... 717 Atomistic Computer Simulations......................................................................................... 718 Wearless Friction in Low-Dimensional Systems.................................................................. 722 Dry Sliding of Crystalline Surfaces ....................................................................................... 734 Lubricated Surfaces................................................................................................................ 740 Stick-Slip Dynamics............................................................................................................... 752 Strongly Irreversible Tribological Processes......................................................................... 755
xxiii
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Volume Two SECTION III Introduction
21
Introduction........................................................................................................................... 827 Tribology of Coated Surfaces ................................................................................................ 828 Macromechanical Interactions: Hardness and Geometry................................................... 835 Micromechanical Interactions: Material Response ............................................................. 839 Material Removal and Change Interactions: Debris and Surface Layers............................ 844 Multicomponent Coatings .................................................................................................... 852 Concluding Remarks ............................................................................................................. 858
Tribology of Diamond, Diamond-like Carbon and Related Films Ali Erdemir and Christophe Donnet 24.1 24.2
xxiv
Ali Erdemir
Introduction........................................................................................................................... 787 Classification of Solid Lubricants ......................................................................................... 792 Lubrication Mechanisms of Layered Solids ......................................................................... 806 High-Temperature Solid Lubricants .................................................................................... 808 Self-Lubricating Composites................................................................................................. 813 Soft Metals.............................................................................................................................. 815 Polymers................................................................................................................................. 817 Summary and Future Directions .......................................................................................... 818
Tribological Properties of Metallic and Ceramic Coatings Kenneth Holmberg and Allan Matthews 23.1 23.2 23.3 23.4 23.5 23.6 23.7
24
Koji Kato and Koshi Adachi
Introduction........................................................................................................................... 771 Pure Metals ............................................................................................................................ 771 Soft Metals and Soft Bearing Alloys...................................................................................... 772 Copper-based Alloys.............................................................................................................. 774 Cast Irons ............................................................................................................................... 774 Steels ....................................................................................................................................... 776 Ceramics................................................................................................................................. 778 Special Alloys.......................................................................................................................... 781 Comparisons Between Metals and Ceramics ....................................................................... 782 Concluding Remarks ............................................................................................................. 783
Solid Lubricants and Self-Lubricating Films 22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8
23
Bharat Bhushan, Ali Erdemir, and Kenneth Holmberg
Metals and Ceramics 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 21.10
22
Solid Tribological Materials and Coatings
Introduction........................................................................................................................... 871 Diamond Films ...................................................................................................................... 872
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24.3 24.4 24.5
25
Self-Assembled Monolayers for Controlling Hydrophobicity and/or Friction and Wear Bharat Bhushan 25.1 25.2 25.3 25.4 25.5
26
Diamond-like Carbon (DLC) Films ..................................................................................... 888 Other Related Films............................................................................................................... 897 Summary and Future Direction............................................................................................ 899
Introduction........................................................................................................................... 909 A Primer to Organic Chemistry............................................................................................ 912 Self-assembled Monolayers: Substrates, Organic Molecules, and End Groups in the Organic Chains ................................................................................................................ 917 Tribological Properties .......................................................................................................... 921 Conclusions............................................................................................................................ 924
Mechanical and Tribological Requirements and Evaluation of Coating Composites Sture Hogmark, Staffan Jacobson, Mats Larsson, and Urban Wiklund 26.1 26.2 26.3 26.4 26.5
Introduction........................................................................................................................... 931 Design of Tribological Coatings............................................................................................ 938 Design of Coated Components............................................................................................. 945 Evaluation of Coating Composites ....................................................................................... 949 Visions and Conclusions ....................................................................................................... 959
SECTION IV Introduction
27
Bharat Bhushan and Stephen M. Hsu
Slider Bearings 27.1 27.2 27.3 27.4
28
Tribology of Industrial Components and Systems
David E. Brewe
Introduction........................................................................................................................... 969 Self-acting Finite Bearings..................................................................................................... 977 Failure Modes....................................................................................................................... 1019 Slider Bearing Materials....................................................................................................... 1027
Rolling Element Bearings 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 28.10
Xiaolan Ai and Charles A. Moyer
Introduction......................................................................................................................... 1041 Rolling Element Bearing Types........................................................................................... 1042 Bearing Materials ................................................................................................................. 1046 Contact Mechanics .............................................................................................................. 1048 Bearing Internal Load Distribution .................................................................................... 1057 Bearing Lubrication ............................................................................................................. 1063 Bearing Kinematics.............................................................................................................. 1067 Bearing Load Ratings and Life Prediction.......................................................................... 1071 Bearing Torque Calculation ................................................................................................ 1074 Bearing Temperature Analysis ............................................................................................ 1079 xxv
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28.11 Bearing Endurance Testing ................................................................................................. 1082 28.12 Bearing Failure Analysis ...................................................................................................... 1083
29
Gears 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8
30
Rotary Dynamic Seals 30.1 30.2 30.3 30.4 30.5
31
Introduction......................................................................................................................... 1187 The Engine ........................................................................................................................... 1188 Transmission and Drive Line.............................................................................................. 1197 The Tire ................................................................................................................................ 1203 The Brakes............................................................................................................................ 1209 Windshield Wipers .............................................................................................................. 1212 Automotive Lubricants........................................................................................................ 1213
Diesel Engine Tribology Jerry C. Wang 33.1 33.2
xxvi
William R. Jones, Jr. and Mark J. Jansen
Introduction......................................................................................................................... 1159 Lubrication Regimes............................................................................................................ 1159 Mechanism Components .................................................................................................... 1161 Liquid Lubricants and Solid Lubricants ............................................................................. 1162 Liquid Lubricant Properties ................................................................................................ 1165 Accelerated Testing and Life Testing .................................................................................. 1175 Summary .............................................................................................................................. 1181
Automotive Tribology Ajay Kapoor, Simon C. Tung, Shirley E. Schwartz, Martin Priest, and Rob S. Dwyer-Joyce 32.1 32.2 32.3 32.4 32.5 32.6 32.7
33
Richard F. Salant
Introduction......................................................................................................................... 1131 Mechanical Seals .................................................................................................................. 1131 Rotary Lip Seal ..................................................................................................................... 1146 Nomenclature ...................................................................................................................... 1154 Defining Terms .................................................................................................................... 1155
Space Tribology 31.1 31.2 31.3 31.4 31.5 31.6 31.7
32
Herbert S. Cheng Introduction......................................................................................................................... 1095 Gear Types............................................................................................................................ 1096 Tribological Failure Modes ................................................................................................. 1097 Full-Film Lubrication Performance.................................................................................... 1101 Mixed Lubrication Characteristics...................................................................................... 1110 Modeling of Tribological Failures in Gears........................................................................ 1115 Failure Tests ......................................................................................................................... 1122 Conclusions.......................................................................................................................... 1124
Malcolm G. Naylor, Padma Kodali, and
Introduction......................................................................................................................... 1231 Power Cylinder Components.............................................................................................. 1233
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33.3 33.4 33.5 33.6 33.7 33.8 33.9
34
Overhead Components ....................................................................................................... 1246 Engine Valves ....................................................................................................................... 1249 Bearings and Bushings......................................................................................................... 1253 Turbomachinery .................................................................................................................. 1255 Fuel System .......................................................................................................................... 1258 Fuels, Lubricants, and Filtration......................................................................................... 1261 Future Trends ...................................................................................................................... 1267
Tribology of Rail Transport Sawley, and M. Ishida
Ajay Kapoor, David I. Fletcher, F. Schmid, K. J.
34.1 Introduction .......................................................................................................................... 1271 34.2 Wheel/Rail Contact.............................................................................................................. 1275 34.3 Diesel Power for Traction Purposes ................................................................................... 1308 34.4 Current Collection Interfaces of Trains.............................................................................. 1314 34.5 Axle Bearings, Dampers, and Traction Motor Bearings.................................................... 1321 34.6 New Developments and Recent Advances in the Study of Rolling Contact Fatigue ....... 1324 34.7 Conclusion ........................................................................................................................... 1325
35
Tribology of Earthmoving, Mining, and Minerals Processing and R. D. Wilson 35.1 35.2 35.3 35.4 35.5 35.6 35.7 35.8
36
37
Introduction......................................................................................................................... 1331 Wear Processes in Mining and Minerals Processing ........................................................... 1333 Equipment Used in Earthmoving Operations ................................................................... 1339 Equipment Used in Mining and Minerals Processing........................................................... 1344 General Classification of Abrasive Wear ............................................................................ 1347 Tribological Losses in the Mining of Metallic Ores, Coal, and Non-metallic Minerals................................................................................................................................ 1359 Financial Cost of Wear in Earthmoving, Mining, and Minerals Processing.................... 1366 Concluding Remarks ........................................................................................................... 1368
Marine Equipment Tribology 36.1 36.2 36.3 36.4 36.5
Steven R. Schmid and Karl J. Schmid
Introduction......................................................................................................................... 1371 Marine Oil Properties and Chemistry ................................................................................ 1371 Diesel Engine Lubrication ................................................................................................... 1374 Steam and Gas Turbines...................................................................................................... 1380 Ancillary Equipment............................................................................................................ 1381
Tribology in Manufacturing 37.1 37.2 37.3 37.4 37.5
Jeffrey A. Hawk
Steven R. Schmid and William R. D. Wilson
Introduction......................................................................................................................... 1385 Unique Aspects of Manufacturing Tribology .................................................................... 1385 Metal Cutting ....................................................................................................................... 1394 Finishing Operations ........................................................................................................... 1398 Bulk Forming Operations ................................................................................................... 1399 xxvii
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Macro- and Microtribology of Magnetic Storage Devices Bharat Bhushan 38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8
39
Macro- and Microtribology of MEMS Materials 39.1 39.2 39.3 39.4
40
Bharat Bhushan
Introduction .......................................................................................................................... 1515 Experimental Techniques ..................................................................................................... 1525 Results and Discussion.......................................................................................................... 1527 Closure................................................................................................................................... 1544
Mechanics and Tribology of Flexible Media in Information Processing Systems Richard C. Benson and Eric M. Mockensturm 40.1 40.2 40.3 40.4 40.5 40.6 40.7 40.8 40.9 40.10 40.11 40.12
41
Introduction .......................................................................................................................... 1413 Magnetic Storage Devices and Components ....................................................................... 1415 Friction and Adhesion .......................................................................................................... 1423 Interface Temperatures......................................................................................................... 1447 Wear....................................................................................................................................... 1448 Lubrication ............................................................................................................................ 1482 Micro/Nanotribology and Micro/Nanomechanics............................................................. 1491 Closure................................................................................................................................... 1501
Introduction .......................................................................................................................... 1549 Introduction to Foil Bearings ............................................................................................... 1550 A Simple Foil Bearing Model................................................................................................ 1553 Other Foil Bearing Models ................................................................................................... 1556 Air Reversers.......................................................................................................................... 1558 Introduction to Wound Rolls............................................................................................... 1561 Air Entrainment in Wound Rolls......................................................................................... 1562 Nip-Induced Tension and J-line Slip in Web Winding ...................................................... 1565 Web Tenting Caused by High Asperities............................................................................. 1570 Mechanisms that Cause a Sheet to Jam, Stall, or Roll Over in a Channel ......................... 1576 Micro-slip of Elastic Belts ..................................................................................................... 1579 Transport of Sheets Through Roller/Roller and Roller/Platen Nips.................................. 1582
Biomedical Applications 41.1 41.2 41.3 41.4 41.5 41.6 41.7
xxviii
John Fisher
Introduction .......................................................................................................................... 1593 Tribology in the Human Body ............................................................................................. 1594 Tribology of Artificial Organs and Medical Devices ............................................................. 1596 Natural Synovial Joint and Articular Cartilage ................................................................... 1599 Total Replacement Joints...................................................................................................... 1603 Wear and Wear Debris Induced Osteolysis......................................................................... 1605 Joint Replacement and Repair in the Next Millennium ..................................................... 1607
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42
Technologies for Machinery Diagnosis and Prognosis and Ward O. Winer 42.1 42.2 42.3 42.4 42.5
Richard S. Cowan
Introduction .......................................................................................................................... 1611 Failure Prevention Strategies................................................................................................ 1611 Condition Monitoring Approaches ..................................................................................... 1616 Tribo-Element Applications................................................................................................. 1634 Equipment Asset Management ............................................................................................ 1639
Glossary .......................................................................................................... 1645 Index ............................................................................................................... 1661
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I Macrotribology Bharat Bhushan The Ohio State University
Francis E. Kennedy Dartmouth College
Andras Z. Szeri University of Delaware 1 Surface Physics in Tribology
Phillip B. Abel, John Ferrante .............................................. 5
Introduction • Geometry of Surfaces • Theoretical Considerations • Experimental Determinations of Surface Structure • Chemical Analysis of Surfaces • Surface Effects in Tribology • Concluding Remarks
2 Surface Roughness Analysis and Measurement Techniques Bharat Bhushan ............. 49 The Nature of Surfaces • Analysis of Surface Roughness • Measurement of Surface Roughness • Closure
3 Contact Between Solid Surfaces John A. Williams, Rob S. Dwyer-Joyce ....................... 121 Introduction • Hertzian Contacts • Non-Hertzian Contacts • Numerical Methods for Contact Mechanics • Experimental Methods for Contact Mechanics • Further Aspects
4 Adhesion of Solids: Mechanical Aspects
Daniel Maugis .............................................. 163
Introduction • Fracture Mechanics and Adhesion of Solids • Example: Contact and Adherence of Spheres • Liquid Bridges • Adhesion of Rough Elastic Solids — Application to Friction • Kinetics of Crack Propagation • Adhesion of Metals • Conclusion
5 Friction Kenneth C. Ludema ............................................................................................ 205 Introduction • Qualitative Ranges of Friction • Early Concepts on the Causes of Friction • Adhesion, Welding, Bonding of the Three Major Classes of Solids • The Formation and Persistence of Friction Controlling Surface Films • Experiments that Demonstrate the Influence of Films on Surfaces • Mechanisms of Friction • Measuring Friction • Test Machine Design and Machine Dynamics • Tapping and Jiggling to Reduce Friction Effects • Equations and Models of Friction
6 Frictional Heating and Contact Temperatures Francis E. Kennedy ............................. 235 Surface Temperatures and Their Significance • Surface Temperature Analysis • Surface Temperature Measurement
7 Wear Mechanisms Koji Kato, Koshi Adachi .................................................................... 273 Introduction • Change of Wear Volume and Wear Surface Roughness with Sliding Distance • Ranges of Wear Rates and Varieties of Wear Surfaces • Descriptive Key Terms • Survey of Wear Mechanisms • Concluding Remarks
1
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Macrotribology
8 Wear Debris Classification
William A. Glaeser .............................................................. 301
Introduction • How Wear Debris Is Generated • Collection of Wear Debris • Diagnostics with Wear Debris • Conclusions
9 Wear Maps
Stephen M. Hsu, Ming C. Shen .................................................................... 317
Introduction • Fundamental Wear Mechanisms of Materials • Wear Prediction • Wear Mapping • Wear Maps as a Classification System • Wear Map Construction for Ceramics • Comparison of Materials • Modeling Wear by Using Wear Maps • Advantages and Limitations of Current Wear Map Approach
10 Liquid Lubricants and Lubrication Lois J. Gschwender, David C. Kramer, Brent K. Lok, Shashi K. Sharma, Carl E. Snyder, Jr., M.L. Sztenderowicz ................................... 361 Introduction • Lubricant Selection Criteria • Conventional Lubricants — The Evolution of Base Oil Technology • Synthetic Lubricants
11 Hydrodynamic and Elastohydrodynamic Lubrication
Andras Z. Szeri ...................... 383
Basic Equations • Externally Pressurized Bearings • Hydrodynamic Lubrication • Dynamic Properties of Lubricant Films • Elastohydrodynamic Lubrication
12 Boundary Lubrication and Boundary Lubricating Films Stephen M. Hsu, Richard S. Gates .................................................................................................................... 455 Introduction • The Nature of Surfaces • Lubricants and Their Reactions • Concluding Remarks
13 Friction and Wear Measurement Techniques Niklas Axén, Sture Hogmark, Staffan Jacobson .................................................................................................................... 493 The Importance of Testing in Tribology • Wear or Surface Damage • Classification of Tribotests • Tribotest Planning • Evaluation of Wear Processes • Tribotests — Selected Examples • Abrasive Wear • Erosive Wear • Wear in Sliding and Rolling Contacts • Very Mild Wear
14 Simulative Friction and Wear Testing Peter J. Blau ...................................................... 511 Introduction • Defining the Problem • Selecting a Scale of Simulation • Defining FieldCompatible Metrics • Selecting or Constructing the Test Apparatus • Conducting Baseline Testing Using Established Metrics and Refining Metrics as Needed. • Case Studies • Conclusions
15 Friction and Wear Data Bank A. William Ruff .............................................................. 523 Introduction • Sources of Data • Materials Found in Data Bank • Data Bank Format
A
great deal of progress has been made in the past 100 years in the understanding of the fundamentals of tribological phenomena at the macroscopic scale. This section begins with a description of solid surfaces, their physical and chemical structures, and their important effect on tribological behavior (Chapter 1). The topography of solid surfaces is treated in Chapter 2, which includes the treatment of the characterization of surface roughness and details techniques for measuring surface roughness at various scales. The deformation and stress that occur when two solid surfaces come into contact and the geometry of contacts are considered for both smooth and rough surfaces in Chapter 3. The fundamentals of adhesion between solid surfaces are presented in Chapter 4, along with a discussion of the effects of surface roughness and the presence of a thin fluid film on the surface. An important concern in sliding contacts is friction. The mechanisms of friction, its major consequences, and means of measuring and controlling friction are covered in Chapter 5. Frictional heating of contacting surfaces, one of the main consequences of friction, is treated in Chapter 6, along with means for determining the surface temperatures that result from frictional heating. Perhaps the most important effect of frictional sliding is wear of the sliding components. The subject of wear is covered in three chapters. Chapter 7 presents a survey of the various mechanisms of wear of metals, ceramics, polymers, and composites; Chapter 8 follows with the analysis of wear debris, particularly as a tool for machine diagnosis. An important tool for understanding and controlling wear is the wear map; basic information about wear maps and their use is given in Chapter 9.
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Macrotribology
3
The primary method for alleviating the detrimental effects of friction is to use lubrication. Chapter 10 presents the fundamentals of liquid lubricants and their use in the various regimes of lubrication. The fundamentals of fluid film lubrication are accessible in Chapter 11; included are treatments of both hydrostatic and hydrodynamic lubrication of conformal contacts, journal and thrust bearing configurations in which the bearing surfaces are considered rigid, and elastohydrodynamic lubrication of counterformal contacts, rolling element bearings and gears with deforming surfaces. Lubrication of surfaces by boundary films is treated in Chapter 12, which includes a discussion of the chemical and physical phenomena occurring at the interface between lubricant and solid surface. There are two chapters dealing with tribotesting methodology: friction and wear measurement methods are presented in Chapter 13, while in Chapter 14 tribotest program design considerations are discussed. The results of many years of tribotests for metals, ceramics, and polymers are compiled in the friction and wear databank in Chapter 15. The editors of Section I hope that this section will prove to be an effective means of transferring basic tribology science and technology to practicing engineers and scientists in need of this information.
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1 Surface Physics in Tribology 1.1 1.2 1.3
Introduction ........................................................................... 5 Geometry of Surfaces............................................................. 6 Theoretical Considerations.................................................. 10
1.4
Experimental Determinations of Surface Structure .......... 19
Surface Theory • Friction Fundamentals Low-Energy Electron Diffraction • High-Resolution Electron Microscopy • Field Ion Microscopy
1.5
Chemical Analysis of Surfaces............................................. 23 Auger Electron Spectroscopy • X-ray Photoelectron Spectroscopy • Secondary Ion Mass Spectroscopy • Infrared Spectroscopy • Thermal Desorption
Phillip B. Abel
1.6
NASA Glenn Research Center
John Ferrante Cleveland State University
Surface Effects in Tribology................................................. 32 Atomic Monolayer Effects in Adhesion and Friction • Monolayer Effects due to Adsorption of Hydrocarbons • Atomic Effects in Metal-Insulator Contacts
1.7
Concluding Remarks............................................................ 40
1.1 Introduction Tribology, the study of the interaction between surfaces in contact, spans many disciplines, from physics and chemistry to mechanical engineering and material science, and is of extreme technological importance. In this first chapter on tribology, the key word will be surface. This chapter will be rather ambitious in scope in that we will attempt to cover the range from microscopic to macroscopic. We will approach this problem in steps: first considering the fundamental idea of a surface, next recognizing its atomic character and the expectations of a ball model of the atomic structures present. We will then consider more realistic relaxed surfaces and then consider how the class of surface, i.e., metal, semiconductor, or insulator, affects these considerations. Finally, we will present what is expected when a pure material is alloyed and the effects of adsorbates. Following these more fundamental descriptions, we will give brief descriptions of some of the experimental techniques used to determine surface properties and their limitations. The primary objective here will be to provide a source for more thorough examination by the interested reader. Finally, we will examine the relationship of tribological experiments to these more fundamental atomistic considerations. The primary goals of this section will be to again provide sources for further study of tribological experiments and to raise critical issues concerning the relationship between basic surface properties with regard to tribology and the ability of certain classes of experiments to reveal the underlying interactions. We will attempt to avoid overlapping the material presented by other authors in this publication. This chapter cannot be a complete treatment of the physics of surfaces due to space
0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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Modern Tribology Handbook
limitations. We recommend an excellent text by Zangwill (1988) for a more thorough treatment. Instead we concentrate on techniques and issues of importance to tribology on the nanoscale.
1.2 Geometry of Surfaces We now examine from a geometric standpoint what occurs when you create two surfaces by dividing a solid along a given plane. We limit the discussion to single crystals, since the same arguments apply to polycrystalline samples except for the existence of grains, each of which could be described by a corresponding argument. This discussion starts by introducing the standard notation for describing crystals given in solid state texts (e.g., Ashcroft and Mermin, 1976; Kittel, 1986). It is meant to be didactic in nature and will not attempt to be comprehensive. In order to establish notation and concepts we limit our discussion to two Bravais lattices, face-centered cubic (fcc) and body-centered cubic (bcc), which are the structures often found in metals. Unit cells, i.e., the structures which most easily display the symmetries of the crystals, are shown in Figure 1.1. The other descriptions that are frequently used are the primitive cells, which show the simplest structures that can be repeated to create a given structure. In Figure 1.1 we also show the primitive cell basis vectors, which can be used to generate the entire structure by the relation
R = n1a 1 + n2a 2 + n3a 3
(1.1)
where n1, n2, and n3 are integers, and a1, a2, and a3 are unit basis vectors. Since we are interested in describing surface properties, we want to present a standard nomenclature for specifying a surface. The algebraic description of a surface is usually given in terms of a vector normal to the surface. This is conveniently accomplished in terms of vectors that arise naturally in solids, namely the reciprocal lattice vectors of the Bravais lattice (Ashcroft and Mermin, 1976; Kittel, 1986). This is convenient since these vectors are used to describe the band structure and diffraction effects in solids. They are usually given in the form
K = hb1 + kb 2 + lb 3
(1.2)
where h,k,l are integers. The reciprocal lattice vectors are related to the basis vectors of the direct lattice by
(
b i = 2π a j × a k
a
) {a ⋅ (a i
j
× ak
)}
(1.3)
b
FIGURE 1.1 (a) Unit cube of face-centered cubic (fcc) crystal structure, with primitive-cell basis vectors indicated. (b) Unit cube of body-centered cubic (bcc) crystal structure, with primitive-cell basis vectors indicated.
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Surface Physics in Tribology
7
a
b
FIGURE 1.2 Projection of cubic face (100) plane for (a) fcc, and (b) bcc crystal structures. In both cases, smaller dots represent atomic positions in the next layer below the surface.
where a cyclic permutation of i,j,k is used in the definition. Typically, parentheses are used in the definition of the plane, e.g., (h,k,l). The (100) planes for fcc and bcc lattices are shown in Figure 1.2 where dots are used to show the location of the atoms in the next plane down. This provides the simplest description of the surface in terms of terminating the bulk. There is a rather nice NASA publication by Bacigalupi (1964) which gives diagrams of many surface and subsurface structures for fcc, bcc, and diamond lattices, in addition to a great deal of other useful information such as surface density and interplanar spacings. A modern reprinting is called for. In many cases, this simple description is not adequate since the surface can reconstruct. Two prominent cases of surface reconstruction are the Au(110) surface (Good and Banerjea, 1992) for metals and the Si(111) surface (Zangwill, 1988) for semiconductors. In addition, adsorbates often form structures with symmetries different from the substrate, with the classic example the adsorption of oxygen on W(110) (Zangwill, 1988). Wood (1963) formalized the nomenclature for describing such structures. In Figure 1.3 we show an example of 2 × 2 structure, where the terminology describes a surface that has a layer with twice the spacings of the substrate. There are many other possibilities, such as structures rotated with respect to the substrate and centered differently from the substrate. These are also defined by Wood (1963). The next consideration is that the interplanar spacing can vary, and slight shifts in atomic positions can occur several planes from the free surface. A recent paper by Bozzolo et al. (1994) presents the results
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Modern Tribology Handbook
FIGURE 1.3 Representation of fcc (110) face with an additional 2 × 2 layer, in which the species above the surface atoms have twice the spacing of the surface. Atomic positions in the next layer below the surface are represented by smaller dots.
1
-3.82% +2.48%
2 3 4 5 Unrelaxed
ECT
FIGURE 1.4 Side view of nickel(100) surface. On the left, the atoms are positioned as if still within a bulk fcc lattice (“unrelaxed”). On the right, the surface planes have been moved to minimize system energy (Bozzolo et al., 1994). The percent change in lattice spacing is indicated, with the spacing in the image exaggerated to illustrate the effect.
for a large number of metallic systems and serves as a good review of available publications. Figure 1.4 shows some typical results for Ni(100). The percent change given represents the deviation from the equilibrium interplanar spacing. The drawing in Figure 1.4 exaggerates these typically small differences in order to elucidate the behavior. Typically, this pattern of alternating contraction and expansion diminishing as the bulk is approached is found in most metals. It can be understood in a simple manner (Bozzolo et al., 1994). The energy for the bulk metal is a minimum at the bulk metallic density. The formation of the surface represents a loss of electron density because of missing neighbors for the surface atoms. Therefore, this loss of electron density can be partially offset by a contraction of the interplanar spacing between the first two layers. This contraction causes an electron density increase between layers 2 and 3 and, thus, the energy is lowered by a slight increase in their interplanar spacing. There are some exceptions to this behavior where the interplanar spacing increases between the first two layers due to bonding effects (Needs, 1987; Feibelman, 1992). However, the pattern shown in Figure 1.4 is the usual behavior for most metallic surfaces. There can be similar changes in position within the planes; however, these are usually small effects (Rodriguez et al., 1993; Foiles, 1987). In Figure 1.5, we show a side view of a gold (110) surface (Good and Banerjea, 1992). Figure 1.5a shows the unreconstructed surface and 1.5b shows a side view of the (2 × 1) missing row reconstruction. Such behavior indicates the complexity that can arise even for metal surfaces and the danger of using ideas which are too simplistic, since more details of the bonding interactions are needed (Needs, 1987; Feibelman, 1992). Real crystal surfaces typically are not perfectly oriented nor atomically flat. Even “on-axis” (i.e., within a fraction of a degree) single crystal low-index faces exhibit some density of crystallographic steps. For
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a
b
FIGURE 1.5 Side view of nickel(110) surface: (a) unreconstructed; (b) 1 × 2 missing row surface reconstruction. (From Good, B.S. and Banerjea, A. (1992), Monte Carlo Study of Reconstruction of the Au(110) Surface Using Equivalent Crystal Theory, in Mat. Res. Soc. Symp. Proc., Vol. 278, pp. 211-216. With permission.)
a gold(111) face tilted one half degree toward the (011) direction, evenly spaced single atomic height steps would be only 27 nm apart. Other surface-breaking crystal defects such as screw and edge dislocations may also be present, in addition to whatever surface scratches, grooves, and other polishing damage remains in a real single crystal surface. Surface steps and step kinks would be expected to show greater reactivity than low-index surface planes. During either deposition or erosion of metal surfaces one expects incorporation into or loss from the crystal lattice preferentially at step edges. More generally on simple metal surfaces, lone atoms on a low index crystal face are expected to be most mobile (i.e., have the lowest activation energy to move). Atoms at steps would be somewhat more tightly bound, and atoms making up a low-index face would be least likely to move. High-index crystal faces can often be thought of as an ordered collection of steps on a low-index face. When surface species and even interfaces become mobile, consolidation of steps may be observed. Alternating strips of two low-index crystal faces can then develop from one high-index crystal plane, with lower total surface energy but with a rougher, faceted topography. Much theoretical and experimental work has been done over the last decade on nonequilibrium as well as equilibrium surface morphology (e.g., Kaxiras, 1996; Williams, 1994; Bartelt et al., 1994; Conrad and Engel, 1994; Vlachos et al., 1993; Redfield and Zangwill, 1992). Semiconductors and insulators generally behave differently (Srivastava, 1997). Unlike most metals for which the electron gas to some degree can be considered to behave like a fluid, semiconductors have strong directional bonding. Consequently, the loss of neighbors leaves dangling bonds which are satisfied by reconstruction of the surface. The classic example of this is the silicon(111) 7 × 7 structure, where rebonding and the creation of surface states gives a complex structure. Until a scanning probe microscope (SPM) provided real-space images of this reconstruction (Binnig et al., 1983) much speculation surrounded this surface. Zangwill (1988) shows both the terminated bulk structure of Si(111) and the relaxed 7 × 7 structure. It is clear that viewing a surface as a simple terminated bulk can lead to severely erroneous conclusions. The relevance to tribology is clear since the nature of chemical reactions between surfaces, lubricants, and additives can be greatly affected by such radical surface alterations. There are other surface chemical state phenomena, even in ultra-high vacuum, just as important as the structural and bonding states of the clean surface. Surface segregation often occurs to metal surfaces and interfaces (Faulkner, 1996, and other reviews cited therein). For example trace quantities of sulfur often segregate to iron and steel surfaces or to grain boundaries in polycrystalline samples (Jennings et al., 1988). This can greatly affect results since sulfur, known to be a strong poisoning contaminant in catalysis, can affect interfacial bond strength. Sulphur is often a component in many lubricants. For alloys, similar geometrical surface reconstructions occur (Kobistek et al., 1994). Again alloy surface composition can vary dramatically from the bulk, with segregation causing one of the elements to be the only component on a surface. In Figure 1.6 we show the surface composition for a CuNi alloy as a function of bulk composition with both a large number of experimental results and some theoretical predictions for the composition (Good et al., 1993). In addition nascent surfaces typically react with the ambient, giving monolayer films and oxidation even in ultra-high vacuum, producing even more pronounced surface composition effects. In conclusion, we see that even in the most simple circumstances, i.e., single-crystal surfaces, the situation can be very complicated.
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Cu (111)
1.0
xCu [surface]
0.8
Y
0.6
0.4
Y
Y
0.2 Y
0.0 0.0
Y
0.2
0.4
0.6
0.8
1.0
xCu [bulk]
BFS [800 K] Ref.31 [923 K] Ref.19 [870-920 K] Ref.19 [823 K] Ref.15 [873 K]
Ref.16 [800 K] Ref.20 [773 K,673 K] Ref.30 [973 K] Y Ref.28 [800 K] ( ) Ref.30 [973 K]
FIGURE 1.6 Copper(111) surface composition vs. copper bulk composition: comparison between the experimental and theoretical results for the first and second planes. (From Good, B., Bozzolo, G., and Ferrante, J. (1993), Surface segregation in Cu–Ni alloys, Phys. Rev. B, Vol. 48, pp. 18284-18287 [and references therein]. With permission © 1993 American Physical Society.)
1.3 Theoretical Considerations 1.3.1 Surface Theory We have shown how the formation of a surface can affect geometry. We now present some aspects of the energetics of surfaces from first-principles considerations. For a long time, calculations of the electronic structure and energetics of the surface had proven to be a difficult task. The nature of theoretical approximations and the need for high-speed computers limited the problem to some fairly simple approaches (Ashcroft and Mermin, 1976). The advent of better approximations for the many body effects, namely for exchange and correlation, and the improvements in computers have changed this situation in the not too distant past. One aspect of the improvements was density functional theory and the use of the local density approximation (LDA) (Kohn and Sham, 1965; Lundqvist and March, 1983). Difficulties arise because, in the creation of the surface, periodicity in the direction perpendicular to the surface is lost. Periodicity simplifies many problems in solid state theory by limiting the calculation to a single unit cell with periodic boundary conditions. With a surface present the wave vector perpendicular to the surface, k⊥ , is not periodic, although the wave vector parallel to the surface, k , still is. Calculations usually proceed by solving the one-electron Kohn–Sham equations (Kohn and Sham, 1965; Lundqvist and March, 1983), where a given electron is treated as though it is in the mean field of all of the other electrons. The LDA represents the mean field in terms of the local electron density at a
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given location. The Kohn–Sham equations are written in the form (using normalized atomic units where the constants appearing in the Schroedinger equation, Planck’s constant and the electron rest mass, along with the electron charge and the speed of light, h = me = e = c ≡ 1).
[−1 2∇ + V(r)]Ψ (k , r) = ε (k ) Ψ (k , r) 2
i
i
i
(1.4)
where Ψi and εi are the one-electron wave function and energy, respectively, and
() ()
[ ( )]
V r = Φ r + Vxc ρ r
(1.5)
where Vxc[ρ(r)] is the exchange and correlation potential, ρ(r) is the electron density (the brackets indicate that it is a functional of the density), and Φ(r) is the electrostatic potential given by
()
()
Φ r = ∫ dr ′ ρ r
r − r′ − Σ j Z j r − R j
(1.6)
in which the first term is the electron–electron interaction and the second term is the electron–ion interaction, Zj is the ion charge and the electron density is given by
( )
()
ρ r = Σ occ Ψi k , r
2
(1.7)
where occ refers to occupied states. The calculation proceeds by using some representation for the wave functions such as the linear muffin tin orbital approximation (LMTO), and iterating self-consistently (Ashcroft and Mermin, 1976). Self-consistency is obtained when either the output density or potential agree to within some specified criterion with the input. These calculations are not generally performed for the semi-infinite solid. Instead, they are performed for slabs of increasing thickness to the point where the interior atoms have essentially bulk properties. Usually, five planes are sufficient to give the surface properties. The values of εi(k) give the surface band structure and surface states, localized electronic states created because of the presence of the surface. The second piece of information needed is the total energy in terms of the electron density, as obtained from density functional theory. This is represented schematically by the expression
[]
[]
[]
[]
E ρ = E ke ρ + Ees ρ + E xc ρ
(1.8)
where Eke is the kinetic energy contribution to the energy, Ees is the electrostatic contribution, Exc is the exchange correlation contribution, and the brackets indicate that the energy is a function of the density. Thus the energy is an extremum of the correct density. Determining the surface energy accurately from such calculations can be quite difficult since the surface, or indeed any of the energies of defects of interest, are obtained as a difference of big numbers. For example, for the surface the energy would be given by
{ ( ) ( )} 2A
Esurface = E a − E ∞
(1.9)
where a is the distance between the surfaces (a = 0 to get the surface energy) and A is the cross-sectional area. The initial solutions of the Kohn–Sham equations for surfaces and interfaces were accomplished by Lang and Kohn (1970) for the free surface and Ferrante and Smith for interfaces (Ferrante and Smith,
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1985; Smith and Ferrante, 1986). The calculations were simplified by using the jellium model to represent the ionic charge. In the jellium model the ionic charge is smeared into a uniform distribution. Both sets of authors introduced the effects of discreteness on the ionic contribution through perturbation theory for the electron–ion interaction and through lattice sums for the ion–ion interaction. The jellium model is only expected to give reasonable results for the densest packed planes of simple metals. In Figures 1.7 and 1.8 we show the electron distribution at a jellium surface for Na and for an Al(111)–Mg(0001) interface (Ferrante and Smith, 1985) that is separated by a small distance. In Figure 1.7 we can see the characteristic decay of the electron density away from the surface. In Figure 1.8 we see the change in electron density in going from one material to another. This characteristic tailing is an indication of the reactivity of the metal surface. In Figure 1.9 we show the electron distribution for a nickel(100) surface for the fully three-dimensional calculations performed by Arlinghouse et al. (1980) and that for a silver layer adsorbed on a palladium(100) interface (Smith and Ferrante, 1985) using self-consistent localized orbitals (SCLO) for approximations to the wave functions. First, we note that for the Ni surface there is a smoothing of the surface density characteristic of metals. For the silver adsorption we can see that there are localized charge transfers and bonding effects indicating that it is necessary to perform three-dimensional calculations in order to determine bonding effects. Hong et al. (1995) have also examined metal ceramic interfaces and the effects of impurities at the interface on the interfacial strength. In Figure 1.10 we schematically show the results of determining the interfacial energies as a function of separation between the surfaces with the energy in Figure 1.10a and the derivative curves giving the interfacial strength. In Figure 1.11 we show Ferrante and Smith’s results for a number of interfaces of jellium metals (Ferrante and Smith, 1985; Smith and Ferrante, 1986; Banerjea et al., 1991). Rose et al. (1981, 1983) found that these curves would scale onto one universal curve and indeed that this result applied to many other bonding situations including results of fully three-dimensional calculations. We show the scaled curves from Figure 1.11 in Figure 1.12. A very useful generalization of the original work can be applied to multicomponent alloy surfaces (Bozzolo et al., 1999). Somewhat surprisingly because of large charge transfer, Hong et al. (1995) found that this same behavior also is applicable to metal–ceramic interfaces. Finnis (1996) gives a review of metal–ceramic interface theory. The complexities that we described earlier with regard to surface relaxations and complex structures can also be treated now by modern theoretical techniques. Often in these cases it is necessary to use “supercells” (Lambrecht and Segall, 1989). Since these structures are extended, it would require many atoms to represent a defect. Instead, in order to model a defect and take advantage of the simplicities of periodicities, a cell is created selected at a size which will mimic the main energetics of the defects. In conclusion, theoretical techniques have advanced substantially and are continuing to do so. They have and will shed light on many problems of interest experimentally.
1.3.2 Friction Fundamentals Friction, as commonly used, refers to a force resisting sliding. It is of obvious importance since it is the energy loss mechanism in sliding processes. In spite of its importance, after many centuries friction surprisingly has still avoided a complete physical explanation. An excellent history of the subject is given in a text by Dowson (1979). In this section we will outline some of the basic observations and give some recent relevant references treating the subject at the atomic level, in keeping with the theme of this chapter, and since the whole topic is much too complicated to treat in such a small space. There are two basic issues, the nature of the friction force and the energy dissipation mechanism. There are several commonplace observations, often considered general rules, regarding the friction force as outlined in the classic discussions of the subject by Bowden and Tabor (1964): 1. The friction force does not depend on the apparent area of contact. 2. The friction force is proportional to the normal load. 3. The kinetic friction force does not depend on the velocity and is less than the static friction force.
FIGURE 1.7 Electron density at a jellium surface vs. position for a Na(011)–Na(011) contact for separations of 0.25, 3.0, and 15.0 au. (From Ferrante, J. (1978), Adhesion of a Bimetallic Interface, NASA TM-78890 National Aeronautics and Space Administration, Washington, D.C.).
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FIGURE 1.8 Electron number density n and jellium ion charge density for an aluminum(111)–magnesium(0001) interface. (From Ferrante, J. and Smith, J.R. (1985), Theory of the bimetallic interface, Phys. Rev. B, Vol. 31, pp. 3427-3434. With permission. © 1985 American Physical Society.)
Historically Coulomb (Dowson, 1979; Bowden and Tabor, 1964), realizing that surfaces were not ideally flat and were formed by asperities (a hill and valley structure), proposed that interlocking asperities could be a source of the friction force. This model has many limitations. For example, if we picture a perfectly sinusoidal interface there is no energy dissipation mechanism, since once the top of the first asperity is attained the system will slide down the other side, thus needing no additional force once set in motion. Bowden and Tabor (1964), recognizing the existence of interfacial forces, proposed another mechanism based on adhesion at interfaces. Again, recognizing the existence of asperities, they proposed that adhesion occurs at asperity contacts and then shearing occurs with translational motion. As can be seen, this model explains a number of effects such as the disparity between true area of contact and apparent area of contact, and the tracking of friction force with load, since the asperities and thus the true area of contact change with asperity deformation (load). The actual arguments are more complex than indicated here and require reading of the primary text for completeness. These considerations also emphasize the basic topic of this chapter, i.e., the important effect of the state of the surface and interface on the friction process. Clearly, adsorbates, the differences of materials in contact, and lubricants greatly affect the interaction. We now proceed to outline briefly some models of both the friction force and frictional energy dissipation. As addressed elsewhere in this volume there have been recently a number of attempts to theoretically model the friction interaction at the atomic level. The general approaches have involved
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FIGURE 1.9 (a) Electronic charge density contours at a nickel(100) surface. (From Arlinghaus, F.J., Gay, J.G., and Smith, J.R. (1980), Self-consistent local-orbital calculation of the surface electronic structure of Ni (100), Phys. Rev. B, Vol. 21, pp. 2055-2059. With permission. © 1980 American Physical Society.) (b) Charge transfer of the palladium (100) slab upon silver adsorption. (From Smith, J.R. and Ferrante, J. (1985), Materials in Intimate Contact, Mat. Sci. Forum, Vol. 4, pp. 21-38. With permission.)
assuming a two-body interaction potential at an interface, which in some cases may only be onedimensional, and allowing the particles to interact across an interface, allowing motion of internal degrees of freedom in either one or both surfaces. Hirano and Shinjo (1990) examine a quasistatic model where one solid is constrained to be rigid and the second is allowed to adapt to the structure of the first, interacting through a two-body potential as translation occurs. No energy dissipation mechanism is included. They conclude that two processes occur: atomic locking where the readjusting atoms change
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FIGURE 1.10 Example of a binding energy curve: (a) energy vs. separation; (b) force vs. separation. (From Banerjea, A., Ferrante, J., and Smith, J.R. (1991), Adhesion at metal interfaces, in Fundamentals of Adhesion, Liang-Huang Lee, (Ed.), Plenum Publishing, New York, pp. 325-348. With permission.)
their positions during sliding, and dynamic locking where the configuration of the surface changes abruptly due to the dynamic process if the interatomic potential is stronger than a threshold value. The latter process they conclude is unlikely to happen in real systems. They also conclude that the adhesive force is not related to the friction force, and discuss the possibility of a frictionless “superlubric” state (Shinjo and Hirano, 1993; Hirano et al., 1997). Matsukawa and Fukuyama (1994) carry the process further in that they allow both surfaces to adjust and examine the effects of velocity with attention to the three rules of friction stated above. They argue, not based on their calculations, that the Bowden and Tabor argument is not consistent with flat interfaces having no asperities. Since an adhesive force exists, there is a normal force on the interfaces with no external load. Consequently, rules of friction one and two break down. With respect to rule three, they find it restricted to certain circumstances. They found
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0
a
-200
-400
-600
-800 (B) Zn(0001)-Zn(0001).
(A) AI(111)-AI(111). 0
-200
ADHESIVE ENERGY, ERG/CM
2
-400
-600
-800 0
.2
.4
.6
.8
1.0
0
.2
.4
.6
.8
1.0
(D) Na(110)-Na(110).
(C) Mg(0001) - Mg(0001).
b -200
-400
Mg(0001) - Na(110)
AI(111) - Mg(0001)
AI(111) - Zn(0001)
-600
-200
-400
AI(111) - Na(110)
Zn(0001) - Mg(0001)
Zn(0001) - Na(110)
-600 0
.2
.4
.6 0
.2
.4
.6
0
.2
.4
.6
SEPARATION a. NM FIGURE 1.11 Adhesive energy vs. separation: (a) commensurate adhesion is assumed; (b) incommensurate adhesion is assumed. (From Rose, J.H., Smith, J.R., and Ferrante, J. (1983), Universal features of bonding in metals, Phys. Rev. B, Vol. 28, pp. 1835-1845. With permission. © 1983 American Physical Society.)
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0 -.1
SCALED ADHESIVE ENERGY, E*
-.2 -.3 AI-AI Zn-Zn Mg-Mg Na-Na AI-Zn AI-Mg AI-Na Mg-Na Zn-Na Zn-Mg
-.4 -.5 -.6 -.7 -.8 -.9 -1.0 -1
0
1
2
3
4
5
6
7
8
SCALED SEPARATION, a*
FIGURE 1.12 Scaled adhesive binding energy as a function of scaled separation for systems in Figure 1.11. (From Rose, J.H., Smith, J.R., and Ferrante, J. (1983), Universal features of bonding in metals, Phys. Rev. B, Vol. 28, pp. 1835-1845. With permission. © 1983 American Physical Society.)
that the dynamic friction force, in general, is sliding velocity dependent, but with a decreasing velocity dependence with increasing maximum static friction force. Hence for systems with large static friction forces, the kinetic friction force shows behavior similar to classical rule three, above. Finally, Zhong and Tomanek (1990) performed a first-principles calculation of the force to slide a monolayer of Pd in registry with the graphite surface. Assuming some energy dissipation mechanism to be present, they calculated tangential force as a function of load and sliding position. Sokoloff (1990, 1992, and references therein) addresses both the frictional force and friction energy dissipation. He represents the atoms in the solids as connected by springs, thus enabling an energy dissipation mechanism by way of lattice vibrations. He also looks at such issues as the energy to create and move defects in the sliding process and examines the velocity dependence of kinetic friction based on the possible processes present, including electronic excitations (Sokoloff, 1995), concluding that both velocity-dependent and independent processes contribute to the force of friction (Sokoloff and Tomassone, 1998). Even a simplified model of flat, sliding, featureless dielectric surfaces can generate velocitydependent friction of a magnitude comparable to Van der Waals forces, according to Pendry (1997). Persson (1991) proposes a model for energy dissipation due to electronic excitations induced within a metallic surface, and concludes (Volokitin and Persson, 1999) that, except possibly for physisorbed layers of atoms sliding on a metal surface, this “van der Waals friction” is negligible compared to friction forces due to real areas of contact between macroscopic bodies. Persson (1993a, 1994, 1995) also addresses the effect of a boundary lubricant between macroscopic bodies, modeling fluid pinning to give the experimentally observed logarithmic time dependence of various relaxation processes. He has devoted an entire book (Persson, 1998) as well as a review article (Persson, 1999) to sliding friction, with emphasis on recent theoretical and experimental results. Interestingly, the concept of “elastic coherence length” in sliding friction theory can also be applied to earthquake dynamics (Persson and Tosatti, 1999). Finally, as more fully covered in other chapters of this volume, much recent effort has gone into modeling
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specifically the lateral force component of a probe tip interaction with a sample surface in scanning probe microscopy (e.g., Hölscher et al., 1997; Diestler et al., 1997, and references therein; Lantz et al., 1997). In conclusion, while these types of simulations may not reflect the full complexity of real materials, they are necessary and useful. Although limited in scope, it is necessary to break down such complex problems into isolated phenomena which, it is hoped, can result in the eventual unification in the larger picture. It simply is difficult to isolate the various components contributing to friction experimentally.
1.4 Experimental Determinations of Surface Structure In this section we will discuss three techniques for determining the structure of a crystal surface, lowenergy electron diffraction (LEED), high-resolution electron microscopy (HREM), and field ion microscopy (FIM). The first, LEED, is a diffraction method for determining structure, and the latter two are methods to view the lattices directly. There are other methods for determining structure, such as ion scattering (Niehus et al., 1993), low-energy backscattered electrons (De Crescenzi, 1995), and even secondary electron holography (Chambers, 1992) which we will not discuss. Other contributors to this volume address scanning probe microscopy and tribology, which are also nicely covered in an extensive review article by Carpick and Salmeron (1997).
1.4.1 Low-Energy Electron Diffraction Since LEED is a diffraction technique, when viewing a LEED pattern you are viewing the reciprocal lattice and not atomic locations on the surface. A LEED pattern typically is obtained by scattering low-energy electrons (0 to ~300 eV) from a single crystal surface in ultra-high vacuum. In Figure 1.13 we show the LEED pattern for the W(110) surface with a half monolayer of oxygen adsorbed on it (Ferrante et al., 1973). We can first notice in Figure 1.13a that the pattern looks like the direct lattice W(110) surface, but this only means that the diffraction pattern reflects the symmetry of the lattice. Notice that in Figure 1.13b extra spots appear at 1/2 order positions upon adsorption of oxygen. Since this is the reciprocal lattice, this means that the spacings of the rows of the chemisorbed oxygen actually are at double the spacing of the underlying substrate. In fact the interpretation of this pattern is more complicated since the structure shown would not imply a 1/2 monolayer coverage, but is interpreted as an overlapping of domains at 90° from one another. In this simple case the coverage is estimated by adsorption experiments, where saturation is interpreted as a monolayer coverage. The interpretation of patterns is further
CLEAN
1/2 MONOLAYER OF OXYGEN
FIGURE 1.13 LEED pattern for (a) clean, and (b) oxidized tungsten(110) with one-half monolayer of oxygen. The incident electron beam energy for both patterns is 119 eV. (From Ferrante, J., Buckley, D.H., Pepper, S.V., and Brainard, W.A. (1973), Use of LEED, Auger emission spectroscopy and field ion microscopy in microstructural studies, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 241-279. With permission.)
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complicated, since with complex structures such as the silicon 7 × 7 pattern, the direct lattice producing this reciprocal lattice is not unique. Therefore it is necessary to have a method to select between possible structures (Rous and Pendry, 1989). We now digress for a moment in order to discuss the diffraction process. The most familiar reference work is X-ray diffraction (Kittel, 1986). We know that for X-rays the diffraction pattern of the bulk would produce what is known as a Laue pattern where the spots represent reflections from different planes. The standard diffraction condition for constructive interference of a wave reflected from successive planes is given by the Bragg equation
2d ⋅ sinθ = nλ
(1.10)
where d is an interplanar spacing, θ is the diffraction angle, λ is the wavelength of the incident radiation, and n is an integer indicating the order of diffraction. Only certain values of θ are allowed where diffractions from different sets of parallel planes add up constructively. There is another simple method for picturing the diffraction process known as the Ewald sphere construction (Kittel, 1986), where it can be easily shown that the Bragg condition is equivalent to the relationship
k − k′ = G
(1.11)
where k is the wave vector (2π/λ) of the incident beam, k′′ is the wave vector of the diffracted beam, and G is a reciprocal lattice vector. The magnitude of the wave vectors k = k′ are equal since momentum is conserved, i.e., we are only considering elastic scattering. Therefore a sphere of radius k can be constructed, which when intersecting a reciprocal lattice point indicates a diffracted beam. This is equivalent to the wave vector difference being equal to a reciprocal lattice vector, with that reciprocal lattice vector normal to the set of planes of interest, and θ the angle between the wave vectors. In complex patterns, spot intensities are used to distinguish between possible structures. The equivalent Ewald construction for LEED is shown in Figure 1.14. We note that the reciprocal lattice for a true two-dimensional surface would be a set of rods instead of a set of points. Consequently the Ewald sphere will always intersect the rods and give diffraction spots resulting from interferences due to scattering between rows of surface atoms, with the number of spots changing with electron wavelength and incident angle. However, for LEED, complexity results from spot intensity modulation by the three-dimensional lattice structure. In X-ray diffraction the scattering is described as kinematic, which means that only single scattering events are considered. With LEED, multiple scattering occurs because of the low energy of the incident electrons; thus, structure determination involves solving a difficult quantum mechanics problem. Generally, various possible structures are constructed, and the multiple scattering problem is solved for each proposed structure. The structure which minimizes the difference between the experimental intensity curves and the theoretical calculations is the probable structure. There are a number of parameters involved with atomic positions and electronic properties, and the best fit parameter is denoted as the “R-factor.” In spite of the complexity, considerable progress has been made, and computer programs for performing the analysis are available (Van Hove et al., 1993). The LEED structures give valuable information about adsorbate binding which can be used in the energy calculations described previously.
1.4.2 High-Resolution Electron Microscopy Fundamentally, materials derive their properties from their make-up and structure, even down to the level of the atomic ordering in alloys. In order to fully understand the behavior of materials as a function of their composition, processing history, and structural characteristics, the highest resolution examination tools are needed. In this section we will limit the discussion to electron microscopy techniques using commonly available equipment and capable of achieving atomic-scale resolution. Traditional scanning electron microscopy (SEM), therefore, will not be discussed, though in tribology SEM has been and should continue to prove very useful, particularly when combined with X-ray spectroscopy. Many modern
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Electron Gun Diffracted Electrons nλ = d sin θ
Fluorescent Screen
θ
1/λ = V/150
Crystal 1/d
Ewald Sphere
Reciprocal Net Rods
FIGURE 1.14 Ewald sphere construction for LEED. (From Ferrante, J., Buckley, D.H., Pepper, S.V., and Brainard, W.A. (1973), Use of LEED, Auger emission spectroscopy and field ion microscopy in microstructural studies, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 241-279. With permission.)
Auger electron spectrometers (discussed in the next section on surface chemical analysis) also have highresolution scanning capabilities, and thus can perform imaging functions similar to a traditional SEM. Another technique not discussed here is photoelectron emission microscopy (PEEM). While PEEM can routinely image photoelectron yield (related to the work function) differences due to single atomic layers, lateral resolution typically suffers in comparison to SEM. PEEM has been applied to tribological materials, however, with interesting results (Montei and Kordesch, 1996). Both transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) make use of an electron beam accelerated through a potential of, typically, up to a few hundred kilovolts. Generically, the parts of a S/TEM consist of an electron source such as a hot filament or field emission tip, a vacuum column down which the accelerated and collimated electrons are focused by usually magnetic lenses, and an image collection section, often comprised of a fluorescent screen or CCD camera for immediate viewing combined with a film transport and exposure mechanism for recording images. The sample is inserted directly into the beam column and must be electron transparent, both of which severely limit sample size. There are numerous good texts available about just TEM and STEM (e.g., Hirsch et al., 1977; Thomas and Goringe, 1979). An advantage to probing a sample with high-energy electrons lies in the De Broglie formula relating the motion of a particle to its wavelength
(
λ = h 2mE k
)
12
(1.12)
where λ is the electron wavelength, h is the Planck constant, m is the particle mass, and Ek is the kinetic energy of the particle. An electron accelerated through a 100 kV potential then has a wavelength of
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0.04 Ångstom, well below any diffraction limitation on atomic resolution imaging. This is in contrast with LEED, for which electron wavelengths are typically of the same order as interatomic spacings. As the electron beam energy increases in S/TEM, greater sample thickness can be penetrated with usable signal reaching the detector. Mitchell (1973) discusses the advantages of using very high accelerating voltages, which at the time included TEM voltages up to 3 MV. More recently, commercially available instruments have taken advantage of the sub-angstrom electron wavelengths with design advances allowing routine achievement of atomic-scale imaging, though image interpretation becomes an issue at that scale (Smith, 1997). As the electron beam traverses a sample, any crystalline regions illuminated will diffract the beam, forming patterns characteristic of the crystal type. Apertures in the microscope column allow the diffraction patterns of selected sample areas to be observed. Electron diffraction patterns combined with an ability to tilt the sample make determination of crystal symmetry and orientation relatively easy, as discussed in Section 1.4.1 above for X-ray Ewald sphere construction. Electrons traversing the sample can also undergo an inelastic collision (losing energy), followed by coherent rescattering. This gives rise to cones of radiation which reveal the symmetry of the reflecting crystal planes, showing up in diffraction images as “Kikuchi lines,” named after the discoverer of the phenomenon. The geometry of the Kikuchi lines provides a convenient way of determining crystal orientation with fairly high accuracy. Another technique for illuminating sample orientation uses an aperture to select one of the diffracted beams to form the image, which nicely highlights sample area from which that diffracted beam originates (“darkfield” imaging technique). One source of TEM image contrast is the electron beam interacting with crystal defects such as various dislocations, stacking faults, or even strain around a small inclusion. How that contrast changes with microscope settings can reveal information about the defect. For example, screw dislocations may “disappear” (lose contrast) for specific relative orientations of crystal and electron beam. An additional tool in examining extended three-dimensional structures within a sample is stereomicroscopy, where two images of the same area are captured tilted from one another, typically by around 10°. The two views are then simultaneously shown, each to one eye, to reveal image feature depth. For sample elemental composition, an X-ray spectrometer and/or an electron energy-loss spectrometer can be added to the S/TEM. Particularly for STEM, due to minimal beam spreading during passage through the sample the analyzed volume for either spectrometer can be as small as tens of nanometers in diameter. X-ray and electron energy-loss spectrometers are somewhat complementary in their ranges of easily detected elements. Characteristic X-rays are more probable when exciting the heavier elements, while electron energy losses due to light element K-shell excitations are easily resolvable. Both TEM and STEM rely on transmission of an electron beam through the sample, placing an upper limit on specimen thickness which depends on the accelerating voltage available and on specimen composition. Samples are often thinned to less than a micrometer, with lateral dimensions limited to a few millimeters. An inherent difficulty in S/TEM sample preparation is locating a given region of interest within the region of visibility in the microscope, without altering sample characteristics during any thinning process needed. For resolution at an atomic scale, columns of lighter element atoms are needed for image contrast, so individual atoms are not “seen.” Samples also need to be somewhat vacuum compatible, or at least stable enough in vacuum to allow examination. The electron beam itself may alter the specimen either by heating, by breaking down compounds within the sample, or by depositing carbon on the sample surface if there are residual hydrocarbons in the microscope vacuum. In short, S/TEM specimens should be robust under high-energy electron bombardment in vacuum.
1.4.3 Field Ion Microscopy For many decades, field ion microscopy (FIM) has provided direct lattice images from sharp metal tips. Some early efforts to examine contact adhesion used the FIM tip as a model asperity, which was brought into contact with various surfaces (Mueller and Nishikawa, 1968; Nishikawa and Mueller, 1968; Brainard and Buckley, 1971, 1973; Ferrante et al., 1973). As well, FIM has been applied to the study of friction
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FIGURE 1.15 Field ion microscope pattern of a clean tungsten tip oriented in the (110) direction. (From Ferrante, J., Buckley, D.H., Pepper, S.V., and Brainard, W.A. (1973), Use of LEED, Auger emission spectroscopy and field ion microscopy in microstructural studies, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 241-279. With permission.)
(Tsukizoe et al., 1985), the effect of adsorbed oxygen on adhesion (Ohmae et al., 1987), and even direct examination of solid lubricants (Ohmae et al., 1990). In FIM a sharp metal tip is biased to a high negative potential relative to a phosphor-coated screen in an evacuated chamber backfilled to about a millitorr with helium or other noble gas. A helium atom impinging on the tip experiences a high electric field due to the small tip radius. This field polarizes the atom, potentially creating a helium ion. Ionization is most probable directly over atoms in the tip where the local radius of curvature is highest. Often, only 10 to 15% of the atoms on the tip located at the zone edges and at kink sites are visible. The helium ions are then accelerated to a phosphorescent screen at some distance from the tip, giving a large geometric magnification. Uncertainty in surface atom positions is often reduced by cooling the tip to liquid helium temperature. Figure 1.15 is a FIM pattern for a clean tungsten tip oriented in the (110) direction. The small rings are various crystallographic planes that appear on a hemispherical single crystal surface. A classic discussion of FIM pattern interpretation can be found in Mueller (1969); a review has been published by Kellogg (1994); and a more extensive discussion of FIM in tribology can be found in Ohmae (1993).
1.5 Chemical Analysis of Surfaces In this section we will discuss four of the many surface chemical analytic tools which we feel have had the widest application in tribology, Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), secondary ion mass spectroscopy (SIMS), and infrared spectroscopy (IR). AES gives elemental analysis of surfaces, but in some cases will give chemical compound information. XPS can give compound information as well as elemental. SIMS can exhibit extreme element sensitivity as well as “fingerprint” lubricant molecules. IR can identify hydrocarbons on surfaces, which is relevant because most lubricants are hydrocarbon based. Hantsche (1989) gives a basic comparison of some surface analytic techniques, and surface characterization advances have been reviewed every 2 years since 1977 in the journal Analytical Chemistry (e.g., McGuire et al., 1999). Before launching into this discussion we wish to present a general discussion of surface analyses. We use a process diagram to describe them given as
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EXCITATION (INTERACTION) ⇓ DISPERSION ⇓ DETECTION ⇓ SPECTROGRAM The first step, excitation in interaction, represents production of the particles or radiation to be analyzed. In light or photon emission spectroscopy a spark causes the excitation of atoms to higher energy states, thus emitting characteristic photons. The dispersion stage could be thought of as a filtering process where the selected information is allowed to pass and other information is rejected. In light spectroscopy this would correspond to the use of a grating or prism, for an ion or electron it might be an electrostatic analyzer. Next is detection of the particle which could be a photographic plate for light or an electron multiplier for ions or electrons. And, finally, the spectrogram tells what materials are present and hopefully how much is there.
1.5.1 Auger Electron Spectroscopy The physics of the Auger emission process is shown in Figure 1.16. An electron is accelerated to an energy sufficient to ionize an inner level of an atom. In the relaxation process an electron drops into the ionized energy level. The energy that is released from this de-excitation is absorbed by an electron in a higher energy level, and if the energy is sufficient it will escape from the solid. The process shown is called a KLM transition, i.e., a level in the K shell is ionized, an electron decays from an L shell, and the final
FIGURE 1.16 Auger transition diagram for an atom. (From Ferrante, J., Buckley, D.H., Pepper, S.V., and Brainard, W.A. (1973), Use of LEED, Auger emission spectroscopy and field ion microscopy in microstructural studies, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 241-279. With permission.)
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electron is emitted from an M shell. Similarly, a process involving different levels will have corresponding nomenclature. The energy of the emitted electron has a simple relationship to the energies of the levels involved, depending only on differences between these levels. The relationships for the process shown are
∆E final = ∆Einitial
(1.13)
Eauger = E K − E L − E M
(1.14)
giving
Consequently, since the energy levels of the atoms are generally known, the element can be identified. There are surprisingly few overlaps for materials of interest. When peaks do overlap, other peaks peculiar to the given element along with data manipulation can be used to deconvolute peaks close in energy. AES will not detect hydrogen, helium, or atomic lithium because there are not enough electrons for the process to occur. AES is surface sensitive because the energy of the escaping electrons is low enough that they cannot originate from very deep within the solid without detectable inelastic energy losses. The equipment is shown schematically in Figure 1.17. The dispersion of the emitted electrons is usually accomplished by any of a number of electrostatic analyzers, e.g., cylindrical mirror or hemispherical analyzers. Although the operational details of the analyzers differ somewhat, the net result is the same. An example spectrum is shown in Figure 1.18 for a wearscar on a pure iron pin worn with dibutyl adipate with 1 wt% zinc-dialkyl-dithiophosphate (ZDDP). This spectrum corresponds to the first derivative of the actual spectral lines (peaks) in the spectrum (Brainard and Ferrante, 1979). Historically, first derivative spectra were taken because the actual peaks were very small compared to the slowly varying background, posing signal to noise problems. The derivative emphasized the more rapidly changing peak, but made quantification more difficult, since the AES peaks are not a simple shape such as Gaussian, where a quantitative relationship exists between the derivative peak-to-peak height and the area under the original peak. The advent of dedicated microprocessors and the ability to digitize the results enable more sophisticated treatment of the data. The signal to background problem can now be handled by modeling the background and subtracting it, leaving an enhanced AES peak. Thus the number of particles present can be obtained by finding the area under the peak, enhancing the quantitative capability of AES. AES can be chemically sensitive in that energy levels may shift when chemical reactions occur. Large shifts can be detected in the AES spectrum or, alternatively, peak shapes may change with chemical reaction. Some examples of these effects will be given later in the chapter.
FIGURE 1.17 Schematic diagram of AES apparatus. (From Ferrante, J. (1982), Practical applications of surface analytic tools in tribology, J. Am. Soc. Lubr. Eng., Vol. 38, pp. 223-236. With permission.)
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FIGURE 1.18 Auger spectrum of wear scar on a pure iron pin run against M2 tool steel disk in dibutyl adipate containing 1-wt% ZDDP. Sliding speed, 2.5 cm/s; load, 4.9 N; atmosphere, dry air. (From Brainard, W.A. and Ferrante, J. (1979), Evaluation and Auger Analysis of a Zinc-Dialkyl-Dithiophosphate Antiwear Additive in Several Diester Lubricants, NASA TP-1544, National Aeronautics and Space Administration, Washington, D.C.)
There are two other techniques that are used in conjunction with AES that should be mentioned: scanning Auger microscopy (SAM) and depth profiling. SAM is simply “tuning” to a particular AES peak and rastering the electron beam in order to obtain an elemental map of a surface. This can be particularly useful in tribology since you are often dealing with rough, inhomogeneous surfaces. We show a sample SAM map in Figure 1.19.
FIGURE 1.19 Example of scanning Auger microscopy results. Sample is silicon carbide fiber reinforced titanium aluminide matrix composite. Single element images as labeled, with higher concentrations represented as brighter regions. (A) SEM mode; (B) silicon; (C) carbon; (D) titanium. (Darwin Boyd, unpublished results.)
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Depth profiling is the process of sputter-eroding a sample by bombarding the surface with ions while simultaneously obtaining AES or other spectra. This enables one to obtain the composition of reactionformed or deposited films on a surface as a function of sputter time or depth, given proper attention to the effects of sputtering itself (Hofman, 1998). Consequently, AES has many applications for studying tribological and other surfaces. Some examples will be given in subsequent sections.
1.5.2 X-ray Photoelectron Spectroscopy The physical processes involved in XPS are simpler than in AES. An X-ray photon ionizes the inner level of an atom directly, and in this case the emitted electron from the ionization is detected, as opposed to AES where several electron energy levels are involved in the final electron production. The dispersion and detection methods are similar to AES. Monochromatic, incoming X-ray photons are generated from an elemental target such as magnesium or aluminum. Measurement of the energy distribution of emitted electrons from the sample permits the identification of the ionized levels by the simple relation
E final = E xray − E binding energy
(1.15)
Since the final energy is measured and the X-ray energy is known one can determine the binding energy and consequently the material. AES peaks are also present in the XPS spectrum. AES peaks can be distinguished from the fact that the energies of the Auger electrons are fixed, since they depend on a difference in energy levels, whereas the XPS electron energies depend on the energy of the incident X-ray. An example XPS spectrum in shown in Figure 1.20, and a schematic diagram of the XPS apparatus would resemble the AES diagram of Figure 1.17, but with incident X-rays replacing electrons impinging on the specimen. XPS can perform chemical as well as elemental analysis. As stated earlier, when an element is in a compound there is a shift in energy levels relative to the unreacted element. Unlike AES where energy level differences are detected, a chemical reaction results in an energy shift of the element XPS peak. For example, the iron peak from Fe2O3 is shifted by nearly 4 eV from an elemental iron peak. Not only are the shifts simpler to interpret, but it is easier to detect peaks directly (as opposed to AES derivative mode
FIGURE 1.20 Example of XPS spectrum. (From Ferrante, J. (1993), Surface analysis in applied tribology, in Surface Diagnostics in Tribology, Miyoshi, K. and Chung, Y.W. (Eds.), World Scientific, Singapore, pp. 19-32. With permission.)
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measurements) since the signal to background in XPS is greater than in AES. In addition, the mode of operation in the dispersion step typically enables higher resolution. The surface sensitivity of XPS is similar to AES because the energies of the emitted electrons are similar. Figure 1.21 shows some examples of oxygen and sulfur peak shifts resulting from reactions with iron and chromium for wear scars on a steel pin run with dibenzyl-disulfide as the lubricant additive (Wheeler, 1978).
SULFUR (2p)
FeSO4
SEVERE WEAR SCAR
FeS
FeS
MILD WEAR SCAR UNWORN SURFACE
170
165
160
155
170
SEVERE WEAR SCAR OXYGEN (1s) FeO ADSORBED O2 535
530
165
160
155
ADSORBED O2
Cr2O3
MILD WEAR SCAR
Fe2O3
UNWORN SURFACE
FeO 535
525
530
525
BINDING ENERGY, eV (a) BEFORE SPUTTERING
(b) AFTER 30 seconds OF SPUTTERING Fe2O3 Cr2O3
FeO
ADSORBED O2
535
530
525
BINDING ENERGY, eV (c) OXYGEN (1s) SPECTRAL LINE FROM WEAR TEST SPECIMEN SHOWING BINDING ENERGIES OF 1s ELECTRON IN SEVERAL COMPOUNDS AND RESOLUTION OF PEAK OBTAINED WITH ANALOG CURVE RESOLVER.
FIGURE 1.21 Sulfur 2p and oxygen 1s XPS peaks from unworn steel surfaces and wear scars run in mineral oil with 1% dibenzyl disulfide. (From Wheeler, D.R. (1978), X-ray photoelectron spectroscopic study of surface chemistry of dibenzyl disulfide on steel under mild and severe wear conditions, Wear, Vol. 47, pp. 243-254. With permission. © 1978 Elsevier Science.)
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1.5.3 Secondary Ion Mass Spectroscopy The physical process involved in SIMS differs from both AES and XPS in that both the excitation source and detected particles are ions. Rather than illuminate the sample surface with either electrons (AES) or photons (XPS), ions are used to bombard the sample surface and knock off (sputter) surface particles. The dispersion phase analyzes the emitted particle masses, instead of energy analyzing the emitted electrons as in AES or XPS. Although using sputtering implies an erosion of the sample surface, a compensating advantage for SIMS is extreme sensitivity. Under advantageous conditions, as few as 1012 atoms per cm3 (ppb) have been detected (Gnaser, 1997), with more typical sensitivities for most elements in the ppm range (Wilson et al., 1989). A comprehensive discussion of the SIMS technique has been published by Benninghoven et al. (1987). The SIMS technique typically used in surface studies gives partial monolayer sensitivity using small incident ion currents (“static” SIMS). Higher ion beam currents, often rastered, give species information as a function of sputter depth (“dynamic” SIMS or SIMS depth profiling). SIMS instrumentation can be roughly categorized by the type of ion detector used, e.g., quadrupole, magnetic sector, or time-of-flight, with their inherent differences in sensitivity, lateral and mass resolution. As well, the incident angle, energy, and type (e.g., noble gas, cesium, or oxygen) of primary ion sputtering beam employed can greatly affect the magnitude and character of the secondary ion yield. SIMS has several complexities. SIMS only detects secondary ions, rather than all of the sputtered species, which can lead to difficulty in quantification. Large molecules on the surface such as hydrocarbon lubricants or typical additives can exhibit complex patterns of possible fragments. A knowledge of the adsorbate and cracking patterns is often needed for interpretation. As well, multiply ionized fragments or simply different species may overlap in the spectra, having nearly identical charge-to-mass ratios. As a simple example, carbon monoxide (CO) and diatomic nitrogen (N2) overlap, requiring examination of other mass fragments to distinguish between the two. As with depth profiling for either AES or XPS, depth resolution “smearing” can occur either due to ion beam mixing of near-surface species or due to the development of surface topography after long times under the ion beam. Despite these potential limitations, SIMS should remain the technique of choice for many low detection limit, high surface sensitivity studies (Zalm, 1995).
1.5.4 Infrared Spectroscopy Infrared spectroscopy (IRS) is particularly useful in detecting lubricant films on surfaces. It can provide binding and chemical information for adsorbed large molecules. It has an additional advantage in that it is nondestructive. Incident electrons in AES can cause desorption and decomposition even for aluminum oxide, and can be very destructive for polymers. Similarly, the emitted electrons can cause destruction of some films for both AES and XPS. In IRS, the specimen is illuminated with infrared light of welldefined energy. If the energy of the incident light corresponds to a transition between vibrational energy levels in the specimen, the light can be absorbed. When compared to the reference light beam that has not passed through a sample, the infrared light interacting with the sample will appear at reduced intensity at these vibrational excitation energies. The dispersion step is similar to dispersion in visible photon spectroscopy in that a grating or prism is used to isolate the wavelengths of interest. A variation of IRS which has advantages in sensitivity and resolution is called Fourier transform infrared spectroscopy (FTIR). In FTIR, the incident beams are passed through a Michelson interferometer in which one of the paths is modulated by moving a mirror. As before, one of the modulated beams is passed through the sample and impinges directly on the detector, which is a heat-sensitive device. When nonmonochromatic radiation is used, the Fourier transform of the spatially modulated beam contains all of the information in one signal, as opposed to the dispersion method where each beam must be analyzed separately. A schematic diagram of the equipment is shown in Figure 1.22. IRS can be surface sensitive and has been used in a diverse range of analytical science applications (McKelvy et al., 1998), which we will not address. A primary interest in tribology is the detection of hydrocarbon or additive films on surfaces. AES and XPS, for contrast, would be useful primarily in
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Fixed Mirror Movable Mirror
Sample Compartment Detector
IR Source Reference or Sample Cell Holders Mirror
Mirror Mirror
FIGURE 1.22 Optical arrangement for a Fourier transform infrared spectrometer. (From Ferrante, J. (1993), Surface analysis in applied tribology, in Surface Diagnostics in Tribology, Miyoshi, K. and Chung, Y.W. (Eds.), World Scientific, Singapore, pp. 19-32. With permission.)
detecting elemental species and are limited to use in ultrahigh vacuum. IRS can be used in air as well as vacuum. The surface sensitivity of IRS can be enhanced by multiple reflections in the surface films and by using grazing incidence angles. Orientation of adsorbed molecules can be obtained by examining the polarization dependence of the spectrum. There are selection rules for what materials can be detected depending on whether the molecule has a dipole moment and the orientation of the molecule on a metal surface. Sample spectra for micron-thick and less than 200-Ångstrom-thick Krytox films on a metal substrate are shown in Figure 1.23 (Herrera-Fierro, 1993).
1.5.5 Thermal Desorption We mention briefly at this point another useful tool for examining the behavior of adsorbates on surfaces, thermal desorption spectroscopy (TDS). We give only a brief description and for a more complete treatment refer the reader to Zangwill (1988). The methods described so far give little information concerning binding energies of adsorbates to surfaces, a topic of importance when choosing stable lubricants or additives. Many species adsorb strongly but do not react chemically, e.g., by forming an oxide. When the surface is heated they can be removed intact or in some decomposed form. A simple view would be that the binding energy would resemble the curves presented in Figure 1.12, and the adsorbates could be removed by giving them sufficient energy to overcome the energy well depth. This would be accomplished by heating a sample following adsorption and then either observing the surface coverage via AES or monitoring pressure increases in the vacuum system. There can be a variety of bonding states depending on the structure of the surface, e.g., at a step edge one would expect a different binding energy from a surface site. Although the real situation may be quite complex, we describe the simplest case, a single bonding state and no decomposition. The rate of desorption can be described by (Meyers et al., 1996)
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Reflectance Spectrum Krytox Lubricant on a 440-C Bearing Ball
ether 2.2
1.8
C-0-C
C-F Stretch
2.0
(a)
Stretch
}
1.6
C-F2
Reflectance
1.4 1.2
Bend
1.0 0.8 0.6 0.4 0.2 0.0 3000
2600
2200
1800
1400
1000
600
1000
600
Wavenumber (cm-1)
0.02
0.01
H 0 2
}
Reflectance
(b)
0.00
3000
2600
2200
1800
1400
Wavenumber (cm-1)
FIGURE 1.23 IR spectrum of a Krytox film on a 440C bearing showing characteristic absorption corresponding to certain functional groups: (a) micron-thick film; (b) less than 200-Ångstrom-thick film; note the increased sensitivity and the bend from absorbed water from 1400 to 2000 cm–1. (From Herrera-Fierro, P.C. private communication, first published in Ferrante (1993).)
(
r = dθ dt = θν ⋅ exp − Ed kT
)
(1.16)
where θ is the coverage, ν is the pre-exponential frequency factor, Ed is the desorption energy, T is the temperature, and k is the Boltzmann constant. By heating to various temperatures and performing an Arrhenius plot one can extract Ed and determine the strength of bonding to a surface. This technique will be seen to be useful in studying monolayer and submonolayer adsorbed film effects on friction between otherwise clean metal surfaces.
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1.6 Surface Effects in Tribology In this section we will deal with a number of issues, analyzing evidence first for effects at the atomic monolayer or submonolayer level in tribology. We will examine monolayer effects both from a fundamental standpoint as well as a more practical viewpoint. This will not be a comprehensive review of the literature, but in keeping with the objectives of this chapter, will be didactic in nature. The references selected, however, will refer to the relevant literature. In this chapter we are not concerned with the effects of lubricants other than their effects of changing shear strength or adhesion at the interface. Consequently we are interested in issues involving boundary lubrication and interfacial properties (Ferrante and Pepper, 1989; Gellman, 1992; Carpick and Salmeron, 1997; McFadden and Gellman, 1997, 1998). There are a number of issues to address which emphasize the difficulties involved in answering fundamental questions concerning bonding (Ferrante and Pepper, 1989). One clear difficulty is the fact that one cannot observe the interface during the interaction. It is necessary to infer what happened at the interface by examining the states of the surfaces before and after interaction. There are often situations where the locus of failure is not the interface, e.g., shear or adhesive failure can occur in the bulk of one of the materials rather than at the interface, or both effects can occur depending on the region in contact. There are uncertainties regarding the measurement of forces, though some recent efforts nicely relate lateral force sensitivity to normal force sensitivity for a commercial SPM cantilever beam, i.e., for a single asperity contact (Ogletree et al., 1996). Clearly, there are elastic effects in any measuring apparatus and in the materials involved that make measurement of the force distribution at the interface difficult. Materials can change mechanical properties as a result of the forces applied. For example, such properties as hardness, ductility, defect formation, plasticity, strain hardening, and creep must be considered. Surface properties may be altered just by contact with the counterface material (Carpick et al., 1996). Generally, even the true area of contact is not known in macroscopic studies due to the fact that asperities determine the contact area on most materials. There is a great deal yet to be learned concerning the basic interfacial properties in tribology. This is in part due to the complexities involved. As an example of such complexities, in Table 1.1 we show some results of Buckley and Pepper (1971) for metallic transfer of dissimilar metals in sliding contact performed using a pin-on-disk apparatus in an ultra-high vacuum system with AES analysis in the wear track. Both pin and disk specimens were ion sputter cleaned. As we can see, all metals transferred to tungsten, and cobalt transferred in all cases. However, iron and nickel did not transfer to tantalum, molybdenum, TABLE 1.1 Metallic Transfer for Dissimilar Metals in Sliding Contact Disk
Rider
Transfer of Metal from Rider to Disk
Tungsten
Iron Nickel Cobalt Iron Nickel Cobalt Iron Nickel Cobalt Iron Nickel Cobalt
Yes Yes Yes No No Yes No No Yes No No Yes
Tantalum
Molybdenum
Niobium
Source: Ferrante, J. (1989), Applications of surface analysis and surface theory in tribology, Surf. Int. Anal., Vol. 14, pp. 809-822. With permission. © John Wiley & Sons.
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or niobium. The surprising result is that the softer metals did not transfer to the harder in all cases. Pepper explained these results in terms of the mechanical properties of the materials. Tungsten, which is the hardest of the materials, fits the expected pattern. However, since nickel and iron strain harden, transfer and deformation are minimized. Cobalt, which has a hexagonal, close-packed structure, has easy slip planes and thus transferred in all cases. Thus simple explanations based on cohesive and interfacial energies can be misleading if mechanical properties are not taken into account. We give a second example performed by Pepper (1974) demonstrating the care necessary in performing studies of polymer films transferred from polymer pins sliding on an S-Monel disk in UHV. Figure 1.24 shows the AES spectra for polytetrafluoroethylene (PTFE), polyvinyl chloride (PVC), and polychlorotrifluoroethylene (PCTFE) pins sliding on S-Monel. The PTFE spectrum shows large fluorine and carbon peaks and large attenuation of the metal peaks. (Care had to be taken due to electron bombardment desorption of the fluorine.) The friction coefficient was low and smooth, suggesting slip. The combined results indicated that PTFE strands were transferring to the metal surface consistent with the models of Pooley and Tabor (1972). For PVC the AES spectrum shows a large chlorine peak and small attenuation of the metal peaks, suggesting decomposition and chlorine adsorption rather than polymer transfer. The friction coefficient, although reduced, remained large and exhibited some stick slip. For PCTFE the spectrum shows chlorine, carbon, and intermediate attenuation of the metal peaks, but with stability under electron bombardment, suggesting the possibility of both decomposition and some polymer transfer. The friction coefficient was high with stick slip. Consequently, it is difficult to anticipate what is happening, again demonstrating the need for more extensive surface characterization.
1.6.1 Atomic Monolayer Effects in Adhesion and Friction Our primary objective in this and following sections is to explore the evidence for atomic effects on friction. The bulk of the discussion in this section will be based on the recent high-quality experiments of Gellman and collaborators (Gellman, 1992; McFadden and Gellman, 1995a,b, 1997, 1998; Ko et al., 1999) while we acknowledge the pioneering contributions of Buckley and the members of his group (Buckley, 1981). Gellman and collaborators have performed a number of adhesion and friction experiments on single crystals in contact, both for clean and adsorbate-covered interfaces, namely Ni(100)–Ni(100), Cu(111)–Cu(111), and even single-grain Al70Pd21Mn9 quasicrystals. The contacting crystals had a slight curvature in order to prevent contact at the edges of the samples where large concentrations of steps were expected, and to ensure point contact. The vacuum system was also vibration isolated, which is very important for reasons to be discussed below. Normally the experiments were repeated for 10 different points. The normals of the crystals were aligned by lasers. The apparatus provided the ability to sputter clean both contacting surfaces, and LEED and AES could be performed on the surfaces in order to guarantee the crystallinity and to measure contamination and determine concentration of adsorbates. The AES measurements were performed with LEED optics in the old retarding field analyzer mode. Following sputter cleaning, the samples were annealed and analyzed with LEED in order to verify the crystal structure and with AES to verify cleanliness. On copper (111) McFadden and Gellman (1995a) examined the effects of sulfur adsorption, since sulfur is a common antiwear additive. It is often used along with phosphorous to prevent metal-to-metal contact when the lubricant breaks down. Both surfaces were dosed with sulfur using hydrogen sulfide, which decomposes upon heating, desorbing the hydrogen and leaving sulfur behind on the surface. At saturation, sulfur forms an ordered superlattice which has a 7 × 7 R19 degree LEED pattern. This corresponds to a close-packed monolayer of sulfide ions (S2–) on top of the copper(111) lattice with an absolute coverage of .43 monolayers relative to the copper(111) substrate. The results of the adhesion experiments are shown in Figure 1.25. The adhesion coefficient, µad = Fad /FN , which is the ratio of pull-off force to normal force, was found to be .69 ± .21. As little as .05 monolayers (11% of saturation) gave a substantial percentage reduction. The saturation value at one monolayer was .26 ± .07. They also found that there was no dependence of the adhesion coefficient on contact time, separation time, temperature, or normal force. There would be
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(B)
(A)
(C)
dN(E)/dE
N (720 V)
Ni , Cu Ni , Cu
C
F
Ni,Cu
100
1000 100 1000 100 1000 E E E (A) SPUTTERED (B) AFTER SLIDING (C) DISK MOVING WITH DISK. PTFE FOR ONE RE- VELOCITY OF 1 MM/SEC UNDER ELECTRON BEAM. VOLUTION. DISK STATIONARY FOR AUGER ANALYSES.
(B)
dN(E)/dE
(A)
C
CI (X1/5) Ni,Cu
100
E
Ni,Cu
E 1000 100 1000 (B) AFTER SLIDING PVC FOR ONE REVOLUTION.
(A) SPUTTERED DISK.
(B)
dN(E)/dE
(A)
Ni ,Cu
100
(C)
C
C CI (X1/5)
CI (X1/5) Ni ,Cu
1000 100
1000 100
Ni ,Cu
1000
E (A) SPUTTERED DISK.
(B) AFTER SLIDING (C) DISK MOVING WITH VELOCITY OF 1 MM/SEC PCTFE FOR ONE REVOLUTION. UNDER ELECTRON BEAM DISK STATIONARY FOR AUGER ANALYSES.
FIGURE 1.24 AES spectra from an S-Monel disk with transfer films from different polymers. (From Pepper, S.V. (1974), Auger analysis of films formed on metals in sliding contact with halogenated polymers, J. Appl. Phys., Vol. 45, pp. 2947-2956. With permission.)
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1.0
0.9
0.8
adhesion coefficient
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0 0
.11
.22
.33
.44
sulfur coverage (ML)
FIGURE 1.25 Adhesion coefficient vs. sulfur coverage by McFadden and Gellman (1995a). Experimental conditions: temperature = 300 K; normal force = 40 to 60 mN; contact time before separation = 15 to 20 s; separation speed = 50 µm/s. At each coverage the standard deviation of the adhesion coefficient calculated from 10 measurements is plotted.
no expected dependence on normal force since higher loads would simply increase the contact area, and the adhesion coefficient therefore would be expected to track with the normal force. Buckley (1981) reported adhesion coefficients much greater than 1.0 for clean single crystals in contact. As mentioned earlier, it is important to control vibrations in the experiments. Bowden and Tabor (1964) showed that when clean metal surfaces were plastically loaded and then translated, the junction grew, i.e., the true contact area increased until shear occurred. In all probability, the large adhesion coefficients observed by Buckley were caused by increased contact area from junction growth caused by vibrations. In any event, there is strong bonding at clean metal interfaces, and as Gellman and others have shown, the adhesion coefficient can be decreased by submonolayer films. McFadden and Gellman (1995a) performed a somewhat different experiment on the copper(111) surface with regard to static friction measurements. The surfaces were exposed to laboratory atmosphere for several days. As determined by AES, the primary contaminants were sulfur and carbon. Although tenuous, the coverage was estimated to be between 10 to 15 Ångstroms. Then a number of cycles of sputtering followed by annealing with static friction measurements after each cycle were performed. The results are shown in Figure 1.26. The friction coefficient, µs, increased with removal of contaminant to the clean-surface value of 4.4 ± 1.3. Again these results imply submonolayer effects by these contaminants. Wheeler (1976) earlier performed static friction experiments with both chlorine and oxygen adsorbed on polycrystalline surfaces of copper, iron, and steel. The measurements were performed with a pin-ondisk apparatus, with AES used to monitor coverage. The results of these studies are shown in Figure 1.27. Wheeler found that there were no differences between the effects of chlorine and oxygen on any of the surfaces if adsorbate coverage was taken into account. Adsorption at partial monolayer coverages reduced the coefficient of friction in all cases. Wheeler found that he could get a good correlation with a junction
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FIGURE 1.26 Static friction coefficient vs. Auger peak ratios as the contaminated copper(111) surfaces are gradually cleaned by ion bombardment. For each contamination level the average and standard deviation of the friction coefficient calculated from 10 measurements are presented. (From McFadden, C.F. and Gellman, A.J. (1995a), Effect of surface contamination on the UHV tribological behavior of the Cu(111)/Cu(111) interface, Tribology Letters, Vol. 1, pp. 201-210. With permission.)
growth model where the surfaces were partially covered during translation. The values of the coefficient were of comparable magnitude to those of Gellman. Clean single-grain Al70Pd21Mn9 quasicrystal surfaces gave a static friction coefficient of only µs = 0.60 ± 0.08 (Ko et al., 1999), in contrast with the high value reported for clean copper(111) above. Formation on the clean quasicrystal surfaces of about a monolayer of oxide following exposure to oxygen or water did discernibly reduce µs, though never as low as for the uncleaned, air-exposed surfaces with µs = 0.11 ± 0.02. Determining reasons for the differing friction coefficients between surfaces remains an ongoing challenge.
1.6.2 Monolayer Effects due to Adsorption of Hydrocarbons In considering the evidence for monolayer effects on friction, we again start by referring to recent publications by Gellman et al. (Gellman, 1992; McFadden and Gellman, 1995a,b, 1998; Meyers et al., 1996) describing a number of friction experiments performed with hydrocarbon adsorbates. First, we present the effects of ethanol adsorption on a sulfur-covered nickel(100) surface. The sulfur was adsorbed as previously described and produced a c2 × 2 structure on the nickel surface. The sulfur overlayer was used since stable results could not be obtained with ethanol alone, which Gellman found desorbed at very low temperatures. There were a number of different friction states depending on ethanol coverage, shown in Figure 1.28 (Gellman, 1992). These are the classic behaviors observed in friction (Buckley, 1981). The first shown is “slip” where, once a certain transverse force is applied, there is simple sliding. The second is “stick-slip” where rebonding occurs and the simple slip process is repeated between rebonding events, with poor definition of a friction coefficient. This behavior probably results from junction growth with the adsorbate only
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2.5 CHLORINE ON COPPER CHLORINE ON IRON OXYGEN ON IRON OXYGEN ON STEEL
2.0
OXYGEN ON COPPER
(MINIMUM µS)
µs
1.5 BOTH SURFACES COVERED
1.0
.5
0
.2
.4
.6
.8
1.0
C' FIGURE 1.27 The effects of oxygen and chlorine adsorption on static friction for a metal–metal contact. (from Wheeler, D.R. (1976), Effect of adsorbed chlorine and oxygen on the shear strength of iron and copper junctions, J. Appl. Phys., Vol. 47, pp. 1123-1130. With permission. © 1976 American Institute of Physics.)
effective in certain regions, as observed by Wheeler (1976). Finally, “stick” is where the surfaces weld, and it is similar to shearing a bulk solid. The results of Gellman’s studies are shown in Figure 1.29 where the key indicates differences in behavior. For copper(111) a saturated, submonolayer sulfur coating barely reduced µs and gave stick behavior (McFadden and Gellman, 1997). Partial coverages of ethanol gave erratic behavior typically exhibiting stick-slip. Finally at one monolayer the ethanol effectively lubricated the surface giving the desired slip as well as low adhesion (McFadden and Gellman, 1995b). Consequently, a monolayer film can effectively lubricate. Similar behavior was observed for 2,2,2-trifluoroethanol (McFadden and Gellman, 1995b) as well as for butanol and heptafluorobutanol adsorbed on clean copper(111) surfaces (McFadden and Gellman, 1998). Again stick-slip was observed for coverages less than a monolayer and slip for coverages greater than or equal to one monolayer. Similarly, high adhesion was observed for low coverages, and low adhesion for higher coverages. We conclude this discussion with some TDS and IR studies of fluorinated hydrocarbons on copper(111) surfaces by Meyers et al. (1996). Fluorinated hydrocarbons are of interest because of their thermal stability, and therefore are useful for higher temperature lubrication. All of the ethers were found to adsorb molecularly and reversibly on the copper(111) surfaces, exhibiting first-order desorption kinetics. These studies found that fluorination of perfluoropolyalkyl ethers (PFPAE) reduced the desorption energy. The general reason for this behavior was felt to be that bonding occurred with the oxygens on the PFPAE’s.
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120K, L = 10, mN, V = 10 µ/s 20 STICK
Friction Force (mN)
15
10 SLIP
SLIP-STICK
5
0
-5 Time
FIGURE 1.28 Friction force vs. time for three types of sliding behavior observed during shearing of interfaces between ethanol-charged nickel(100) surfaces, by Gellman (1992). The loads on the interface are all 10 mN at the beginning of each trace, and shearing begins at the points marked with the arrows. Temperature = 120 K; load = 10 mN; velocity = 10 µm/s.
5 Stick Stick-Slip
Friction Coefficient
4
Slip
3
2
1
0 10-2
10-1
1 101 102 EtOH Coverage (ML)
103
FIGURE 1.29 Coefficients of friction measured at interfaces between nickel(100)–c(2 × 2)–S surface modified by adsorption of ethanol at coverages from 0 to 300 ML. (From Gellman, A.J. (1992), Lubrication by molecular monolayers at Ni–Ni interfaces, J. Vac. Sci. Technol. A, Vol. 10, pp. 180-187. With permission.)
Fluorine is thought to weaken this interaction. In addition, fluorination changed the adsorbate–adsorbate interaction from repulsive to attractive. FTIR studies showed that the diethyl ethers are oriented with their molecular axes parallel to the copper(111) surface.
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We conclude this section with some elegant experiments performed by Krim et al. (Daly and Krim, 1996; Krim et al., 1995; Mak et al., 1994; Sokoloff et al., 1993) for which Widom and Krim (1986; also Krim and Widom, 1988) originally adapted an apparatus for sliding monolayer and thicker physisorbed films on silver substrates. The true contact area is known in these studies and there is no wear of the surfaces, which are silver deposited with a (111) face on a quartz crystal microbalance. These experiments were designed to investigate the nature of the friction forces. Slipping of physisorbed films, e.g., ethane and ethylene, on the silver surfaces causes shifts in the frequency and amplitude of the quartz crystal vibrations, and film characteristic slip times are obtained from shifts in the quality factor, Q, of the oscillator circuit. Friction results from energy losses due to the interactions at an interface. Typically it is assumed that these losses occur through phonons, vibrations of the lattice which dissipate the energy (Sokoloff et al., 1993), though Persson (1991), followed by Sokoloff (1995), demonstrated that electronic excitations could also be an energy dissipation mechanism here. In these experiments the average friction force per unit area is related to the slip time by
Ff = ρν τ
(1.17)
where Ff is the friction force, ρ and ν are the film density and velocity, respectively, and τ is the slip time. Therefore, a longer slip time implies a smaller friction force. Based on electronic effects alone (Persson, 1993b) ethane on silver is expected to have a longer slip time than ethylene and thus lower friction. Krim’s results are consistent with this prediction although the ability of the theory to predict hard numbers is limited. Monolayer oxygen adsorption on the surface increases the slip time and thus lowers the friction coefficient substantially, consistent with the electronic excitation model. Although these experiments are not completely definitive at this time, they open new areas of investigation for probing the little understood energy loss mechanisms in friction.
1.6.3 Atomic Effects in Metal-Insulator Contacts We now discuss a number of results where monolayer effects have been observed in metal-insulator friction experiments performed by Pepper (1976, 1979, 1982). First, we discuss static friction experiments performed with a copper ball on the basal plane of a diamond flat. The diamond surface is known to be terminated by hydrogen atoms. Pepper (1982) found that the hydrogen could be removed by either electron bombardment or heating in UHV. Following removal of the hydrogen, the LEED pattern for the surface changed from a 1 × 1 to a 1 × 2 pattern. The interesting feature is shown in the static friction results for the two situations given in Figure 1.30. We can see that removal of the hydrogen caused an increase in µs. Pepper found that exposing the surface to excited hydrogen could cause readsorption. Following hydrogen readsorption the static friction was again reduced, although not to its original value. Pepper also performed core level ionization energy loss spectroscopy on the diamond surface and found changes in the electronic structure of the valence band. Therefore, these experiments showed results sensitive to the electronic structure of the surface. In Figure 1.31 we show similar studies performed by Pepper (1979) for copper and nickel balls on the basal plane of sapphire with chlorine and oxygen as adsorbates. Again the balls were cleaned by sputtering and the sapphire was cleaned by heating as verified by AES. In both cases, we see that oxygen increased the interfacial friction and chlorine decreased it compared to the clean metal. For the increased shear strength case, one cannot identify the locus of failure, whether at the interface or in the bulk of one of the materials. Unfortunately, the wear scar area was too small to analyze. In any event, again monolayer adsorption was detectable in friction experiments. Perhaps even more surprising were effects shown in Figure 1.32. Here dynamic friction experiments were performed by Pepper (1976) with a polycrystalline sapphire pin on a polycrystalline iron disk in UHV. We see the same behavior reproduced with dynamic friction. After removing the oxygen or chlorine atmospheres, the friction coefficients returned to their original values.
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POLISHED SURFACE TRANSFORMED SURFACE EXPOSED TO EXCITED HYDROGEN TRANSFORMED SURFACE EXPOSED TO HYDROGEN AND THEN ANNEALED
.8
.7
.6 EXPOSED TO EXCITED HYDROGEN
.5 µ
.4
.3
.2
.1
0 750
800
850
900
950
0
ANNEAL TEMPERATURE, C
FIGURE 1.30 Copper–diamond static friction coefficient as a function of diamond annealing temperature. (From Pepper, S.V. (1982), Effect of electronic structure of the diamond surface on the strength of the diamond-metal interface, J. Vac. Sci. Technol., Vol. 20, pp. 643-646. With permission.)
1.7 Concluding Remarks We have attempted to present a description of issues and techniques in the physics of surfaces of interest in tribology. This field of research is exceedingly difficult, with the effects of a wide variety of materials and phenomena to understand. It is further complicated by the inability to observe the interactions directly, resulting in conclusions from inference. It is clear that there is a great deal of research necessary to obtain a comprehensive understanding of tribology at the nanoscale. It is hoped that the demonstrations in this chapter and in this volume indicate that there is the possibility of gaining rational understanding leading to the design of better materials in this technologically important field.
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OXYGEN
2.4
2.0
1.6
1.2 1.0 CHLORINE
µg / µ c
.8
.4 (A) NICKEL
2.8 2.4 2.0
1.6
1.2 1.0 .8
.4
.1
1
10
100
1000
EXPOSURE (L ) (B) COPPER.
FIGURE 1.31 Static friction coefficient after exposure to gas (µg) ratio to static friction coefficient of clean contact (µc), plotted vs. exposure to oxygen or chlorine for: (A) nickel; and (B) copper. (From Pepper, S.V. (1979), Effect of interfacial species on shear strength of metal-sapphire contacts, J. Appl. Phys., Vol. 50, pp. 8062-8065. With permission.)
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1.5
COEFFICIENT OF FRICTION . µ
1.0
.5
1 REVOLUTION
0 EXPOSE TO 1000 L O2 (A) OXYGEN ADSORBED ON IRON DISK.
1.0
.5
0
EXPOSE TO 200 L Cl2 (B) CHLORINE ADSORBED ON IRON DISK.
FIGURE 1.32 Effect of oxygen or chlorine on the dynamic friction of an iron disk sliding on sapphire. (From Pepper, S.V. (1976), Effect of adsorbed films on friction of Al2O3-metal systems, J. Appl. Phys., Vol. 47, pp. 2579-2583. With permission.)
References Arlinghaus, F.J., Gay, J.G., and Smith, J.R. (1980), Self-consistent local-orbital calculation of the surface electronic structure of Ni (100), Phys. Rev. B, Vol. 21, pp. 2055-2059. Ashcroft, N.W. and Mermin, N.D. (1976), Solid State Physics, Holt, Rinehart and Winston, New York. Bacigalupi, R.J. (1964), Surface Topography of Single Crystals of Face-Centered-Cubic, Body-CenteredCubic, Sodium Chloride, Diamond, and Zinc-Blende Structures, NASA TN D-2275, National Aeronautics and Space Administration, Washington, D.C. Banerjea, A., Ferrante, J., and Smith, J.R. (1991), Adhesion at metal interfaces, in Fundamentals of Adhesion, Liang-Huang Lee, (Ed.), Plenum Publishing, New York, pp. 325-348. Bartelt, N.C., Einstein, T.L. and Williams, E.D. (1994), Measuring surface mass diffusion coefficients by observing step fluctuations, Surf. Sci., Vol. 312, pp. 411-421. Benninghoven, A., Rüdenauer, F.G., and Werner, H.W. (1987), Secondary Ion Mass Spectroscopy, Wiley, New York. Binnig, G., Rohrer, H., Gerber, Ch., and Weibel, E. (1983), 7 × 7 Reconstruction on Si(111) resolved in real space, Phys. Rev. Lett., Vol. 50, pp. 120-123. Bowden, F.P. and Tabor, D. (1964), The Friction and Lubrication of Solids, Oxford University Press, London. Bozzolo, G., Rodriguez, A.M., and Ferrante, J. (1994), Multilayer relaxation and surface energies of metallic surfaces, Surf. Sci., Vol. 315, pp. 204-214.
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Bozzolo, G., Ferrante, J., Noebe, R.D., Good, B., Honecy, F.S., and Abel, P.B. (1999), Surface segregation in multicomponent systems: modeling of surface alloys and alloy surfaces, Computational Materials Sci., Vol. 15, pp. 169-195. Brainard, W.A. and Buckley, D.H. (1971), Preliminary Studies by Field Ion Microscopy of Adhesion of Platinum and Gold to Tungsten and Iridium, NASA TN D-6492, National Aeronautics and Space Administration, Washington, D.C. Brainard, W.A. and Buckley, D.H. (1973), Adhesion and friction of PTFE in contact with metals as studied by auger spectroscopy, field ion and scanning electron microscopy, Wear, Vol. 26, pp. 75-93. Brainard, W.A. and Ferrante, J. (1979), Evaluation and Auger Analysis of a Zinc-Dialkyl-Dithiophosphate Antiwear Additive in Several Diester Lubricants, NASA TP-1544, National Aeronautics and Space Administration, Washington, D.C. Buckley, D.H. and Pepper, S.V. (1971), Elemental Analysis of a Friction and Wear Surface during Sliding using Auger Spectroscopy, NASA TN D-6497, National Aeronautics and Space Administration, Washington, D.C. Buckley, D.H. (1981), Surface Effects in Adhesion, Friction, Wear, and Lubrication, Elsevier Scientific Publishing, Amsterdam. Carpick, R.W., Agrait, N., Ogletree, D.F., and Salmeron, M. (1996), Variation of the interfacial shear strength and adhesion of a nanometer-sized contact, Langmuir, Vol. 12, pp. 3334-3340. Carpick, R.W. and Salmeron, M. (1997), Scratching the surface: fundamental investigations of tribology with atomic force microscopy, Chem. Rev., Vol. 97, pp. 1163-1194. Chambers, S.A. (1992), Elastic scattering and interference of backscattered primary, Auger and X-ray photoelectrons at high kinetic energy: principles and applications, Surf. Sci. Reports, Vol. 16, pp. 261-331. Conrad, E.H. and Engel, T. (1994), The equilibrium crystal shape and the roughening transition on metal surfaces, Surf. Sci., Vol. 299/300, pp. 391-404. Daly, C. and Krim, J. (1996), Sliding friction of solid xenon monolayers and bilayers on Ag(111), Phys. Rev. Lett., Vol. 76, pp. 803-806. De Crescenzi, M. (1995), Structural surface investigations with low-energy backscattered electrons, Surf. Sci. Reports, Vol. 21, pp. 89-175. Diestler, D.J., Rajasekaran, E., and Zeng, X.C. (1997), Static frictional forces at crystalline interfaces, J. Phys. Chem. B, Vol. 101, pp. 4992-4997. Dowson, D. (1979), History of Tribology, Longman, New York. Faulkner, R.G. (1996), Segregation to boundaries and interfaces in solids, Int. Mater. Rev., Vol. 41, pp. 198-208. Feibelman, P.J. (1992), First-principles calculation of the geometric and electronic structure of the Be (0001) surface, Phys. Rev. B, Vol. 46, pp. 2532-2539. Ferrante, J., Buckley, D.H., Pepper, S.V., and Brainard, W.A. (1973), Use of LEED, Auger emission spectroscopy and field ion microscopy in microstructural studies, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 241-279. Ferrante, J. (1978), Adhesion of a Bimetallic Interface, NASA TM-78890 National Aeronautics and Space Administration, Washington, D.C. Ferrante, J. (1982), Practical applications of surface analytic tools in tribology, J. Am. Soc. Lubr. Eng., Vol. 38, pp. 223-236. Ferrante, J. and Smith, J.R. (1985), Theory of the bimetallic interface, Phys. Rev. B, Vol. 31, pp. 3427-3434. Ferrante, J., Bozzolo, G.H., Finley, C.W. and Banerjea, A. (1988), Interfacial adhesion: theory and experiment, in Mat. Res. Soc. Symp. Proc., Vol. 118, pp. 3-16. Ferrante, J. (1989), Applications of surface analysis and surface theory in tribology, Surf. Int. Anal., Vol. 14, pp. 809-822. Ferrante, J. and Pepper, S.V. (1989), Fundamentals of tribology at the atomic level, in Mat. Res. Soc. Symp. Proc., Vol. 140, pp. 37-50.
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Ferrante, J. (1993), Surface analysis in applied tribology, in Surface Diagnostics in Tribology, Miyoshi, K. and Chung, Y.W. (Eds.), World Scientific, Singapore, pp. 19-32. Finnis, M.W. (1996), The theory of metal–ceramic interfaces, J. Phys.: Condens. Matter, Vol. 8, pp. 5811-5836. Foiles, S.M. (1987), Reconstruction of fcc (110) surfaces, Surf. Sci., Vol. 191, pp. L779-L786. Gellman, A.J. (1992), Lubrication by molecular monolayers at Ni–Ni interfaces, J. Vac. Sci. Technol. A, Vol. 10, pp. 180-187. Gnaser, H. (1997), SIMS detection in the 1012 atoms cm–3 Range, Surf. Int. Anal., Vol. 25, pp. 737-740. Good, B.S. and Banerjea, A. (1992), Monte Carlo Study of Reconstruction of the Au(110) Surface Using Equivalent Crystal Theory, in Mat. Res. Soc. Symp. Proc., Vol. 278, pp. 211-216. Good, B., Bozzolo, G., and Ferrante, J. (1993), Surface segregation in Cu–Ni alloys, Phys. Rev. B, Vol. 48, pp. 18284-18287. Hantsche, H. (1989), Comparison of basic principles of the surface-specific analytical methods: AES/SAM, ESCA(XPS), SIMS, and ISS with X-ray microanalysis, and some applications in research and industry, Scanning, Vol. 11, pp. 257-280. Herrera-Fierro, P.C. private communication, first published in Ferrante (1993). Hirano, M. and Shinjo, K. (1990), Atomistic locking and friction, Phys. Rev. B, Vol. 41, pp. 11837-11851. Hirano, M., Shinjo, K., Kaneko, R., and Murata, Y. (1997), Observation of superlubricity by scanning tunneling microscopy, Phys. Rev. Lett., Vol. 78, pp. 1448-1451. Hirsch, P., Howie, A., Nicholson, R.B., Pashley, D.W., and Whelan, M.J. (1977), Electron Microscopy of Thin Crystals, Robert E. Krieger Publishing Co., Malabar, Florida. Hofmann, S. (1998), Sputter depth profile analysis of interfaces, Rep. Prog. Phys., Vol. 61, pp. 827-888. Hölscher, H., Schwarz, U.D., and Wiesendanger, R. (1997), Modeling of the scan process in lateral force microscopy, Surf. Sci., Vol. 375, pp. 395-402. Hong, T., Smith, J.R. and Srolovitz, D.J. (1995), Theory of metal–ceramic adhesion, Acta Metall. Mater., Vol. 43, pp. 2721-2730. Jennings, W.D., Chottiner, G.S. and Michal, G.M. (1988), Sulphur segregation to the metal oxide interface during the early stages in the oxidation of iron, Surf. Int. Anal., Vol. 11, pp. 377-382. Kaxiras, E. (1996), Review of atomistic simulations of surface diffusion and growth on semiconductors, Computational Matl. Sci., Vol. 6, pp. 158-172. Kellogg, G.L. (1994), Field ion microscope studies of single-atom surface diffusion and cluster nucleation on metal surfaces, Surf. Sci. Reports, Vol. 21, pp. 1-88. Kittel, C. (1986), Introduction to Solid State Physics, 6th ed., John Wiley & Sons, New York. Ko, J.S., Gellman, A.J., Lograsso, T.A., Jenks, C.J., and Thiel, P.A. (1999), Friction between single-grain Al70Pd21Mn9 quasicrystal surfaces, Surf. Sci., Vol. 423, pp. 243-255. Kobistek, R.J., Bozzolo, G., Ferrante, J., and Schlosser, H. (1994), Multilayer relaxation and surface structure of ordered alloys, Surf. Sci., Vol. 307-309, pp. 390-395. Kohn, W. and Sham, L.J. (1965), Self-consistent equations including exchange and correlation effects, Phys. Rev., Vol. 140, pp. A1133-A1138. Krim, J. and Widom, A. (1988), Damping of a crystal oscillator by an adsorbed monolayer and its relation to interfacial viscosity, Phys. Rev. B, Vol. 38, pp. 12184-12189. Krim, J., Daly, C., and Dayo, A. (1995), Electronic contributions to sliding friction, Tribology Letters, Vol. 1, pp. 211-218. Lambrecht, W.R.L. and Segall, B. (1989), Efficient direct calculation method for dielectric response in semiconductors, Phys. Rev. B, Vol. 40, pp. 7793-7801. Lang, N.D. and Kohn, W (1970), Theory of metal surfaces: charge density and surface energy, Phys. Rev. B, Vol. 1, pp. 4555-4568. Lantz, M.A., O’Shea, S.J., Hoole, A.C.F., and Welland, M.E. (1997), Lateral stiffness of the tip and tip–sample contact in frictional force microscopy, Appl. Phys. Lett., Vol. 70, pp. 970-972. Lundqvist, S. and March, N.H. (Eds.) (1983), Theory of the Inhomogeneous Electron Gas, Plenum Press, New York.
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Mak, C., Daly, C., and Krim, J. (1994), Atomic-scale measurements on silver and chemisorbed oxygen surfaces, Thin Solid Films, Vol. 253, pp. 190-193. Matsukawa, H. and Fukuyama, H. (1994), Theoretical study of friction: one-dimensional clean surfaces, Phys. Rev. B, Vol. 49, pp. 17286-17292. McFadden, C.F. and Gellman, A.J. (1995a), Effect of surface contamination on the UHV tribological behavior of the Cu(111)/Cu(111) interface, Tribology Letters, Vol. 1, pp. 201-210. McFadden, C.F. and Gellman, A.J. (1995b), Ultrahigh vacuum boundary lubrication of the Cu–Cu interface by 2,2,2-trifluoroethanol, Langmuir, Vol. 11, pp. 273-280. McFadden, C.F. and Gellman, A.J. (1997), Metallic friction: the influence of atomic adsorbates at submonolayer coverages, Surf. Sci., Vol. 391, pp. 287-299. McFadden, C.F. and Gellman, A.J. (1998), Metallic friction: the effect of molecular adsorbates, Surf. Sci., Vol. 409, pp. 171-182. McGuire, G.E., Fuchs, J., Han, P., Kushmerick, J.G., Weiss, P.S., Simko, S.J., Nemanich, R.J., and Chopra, D.R. (1999), Surface characterization, Anal. Chem., Vol. 71, pp. 373R-388R. McKelvy, M.L., Britt, T.R., Davis, B.L., Gillie, J.K., Graves, F.B., and Lentz, L.A. (1998), Infrared spectroscopy, Anal. Chem., Vol. 70, pp. 119R-177R. Meyers, J.M., Street, S.C., Thompson, S., and Gellman, A.J. (1996), Effect of fluorine on the bonding and orientation of perfluoroalkyl ethers on the Cu(111) Surface, Langmuir, Vol. 12, pp.1511-1519. Mitchell, T.E. (1973), High voltage electron microscopy of microstructural analysis, in Microstructural Analysis Tools and Techniques, McCall, J.L. and Mueller, W.M. (Eds.), Plenum Press, New York, pp. 125-152. Montei, E.L. and Kordesch, M.E. (1996), Detection of tribochemical reactions using photoelectron emission microscopy, J. Vac. Sci. Technol. A, Vol. 14, pp. 1352-1356. Mueller, E.W. and Nishikawa, O. (1968), Atomic surface structure of the common transition metals and the effect of adhesion as seen by field ion microscopy, Adhesion or Cold Welding of Materials in Space Environment, ASTM Special Tech. Publ. No. 431, American Society for Testing and Materials, Philadelphia, PA, pp. 67-87. Mueller, E.W. (1969), Field Ion Microscopy, American Elsevier, New York. Needs, R.J. (1987), Calculations of the surface stress tensor at aluminum (111) and (110) surfaces, Phys. Rev. Lett., Vol. 58, pp. 53-56. Niehus, H., Heiland, W., and Taglauer, E. (1993), Low-energy ion scattering at surfaces, Surf. Sci. Reports, Vol. 17, pp. 213-303. Nishikawa, O. and Mueller, E.W. (1968), Field ion microscopy of contacts, Proc. of the Holm Seminar on Electric Contact Phenomena, Ill. Inst. Technol., Chicago, IL, pp. 193-206. Ogletree, D.F., Carpick, R.W., and Salmeron, M. (1996), Calibration of frictional forces in atomic force microscopy, Rev. Sci. Instrum., Vol. 67, pp. 3298-3306. Ohmae, N., Umeno, M., and Tsubouchi, K. (1987), Effect of oxygen adsorption on adhesion of W to Au studied by field ion microscopy, ASLE Trans., Vol. 30, pp. 409-418. Ohmae, N., Tagawa, M., Umeno, M., and Koike, S. (1990), High voltage field ion microscopy of solid lubricants, Proc. Jpn. Intl. Tribol. Conf., Nagoya, pp. 1827-1832. Ohmae, N. (1993), Field ion microscopy in tribology studies, in Surface Diagnostics in Tribology, Miyoshi, K. and Chung, Y.W. (Eds.), World Scientific, Singapore, pp. 47-74. Pendry, J.B. (1997), Shearing the vacuum — quantum friction, J. Phys. C: Solid State Phys., Vol. 9, pp. 10301-10320. Pepper, S.V. (1974), Auger analysis of films formed on metals in sliding contact with halogenated polymers, J. Appl. Phys., Vol. 45, pp. 2947-2956. Pepper, S.V. (1976), Effect of adsorbed films on friction of Al2O3-metal systems, J. Appl. Phys., Vol. 47, pp. 2579-2583. Pepper, S.V. (1979), Effect of interfacial species on shear strength of metal-sapphire contacts, J. Appl. Phys., Vol. 50, pp. 8062-8065.
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Pepper, S.V. (1982), Effect of electronic structure of the diamond surface on the strength of the diamondmetal interface, J. Vac. Sci. Technol., Vol. 20, pp. 643-646. Persson, B.N.J. (1991), Surface resistivity and vibrational damping in adsorbed layers, Phys. Rev. B, Vol. 44, pp. 3277-3296. Persson, B.N.J. (1993a), Theory of friction and boundary lubrication, Phys.Rev. B, Vol. 48, pp. 18140-18158. Persson, B.N.J. (1993b), Applications of surface resistivity to atomic scale friction, to the migration of “hot” adatoms, and to electrochemistry, J. Chem. Phys., Vol. 98, pp. 1659-1672. Persson, B.N.J. (1994), Theory of friction: the role of elasticity in boundary lubrication, Phys. Rev. B, Vol. 50, pp. 4771-4786. Persson, B.N.J. (1995), Theory of friction: stress domains, relaxation, and creep, Phys. Rev. B, Vol. 51, pp. 13568-13585. Persson, B.N.J. (1998), Sliding Friction: Theory and Applications, Springer, Heidelberg. Persson, B.N.J. (1999), Sliding friction, Surf. Sci. Reports, Vol. 33, pp. 83-119. Persson, B.N.J. and Tosatti, E. (1999), Theory of friction: elastic coherence length and earthquake dynamics, Solid State Comm., Vol. 109, pp. 739-744. Pooley, C.M. and Tabor, D. (1972), Friction and molecular structure: the behaviour of some thermoplastics, Proc. R. Soc., Vol. A329, pp. 251-274. Redfield, A.C. and Zangwill, A. (1992), Attractive interactions between steps, Phys. Rev. B, Vol. 46, pp. 4289-4291. Richter, R., Gay, J.G., and Smith, J.R. (1985), Spin separation in a metal overlayer, Phys. Rev. Lett., Vol. 54, pp. 2704-2707. Rodriguez, A.M., Bozzolo, G., and Ferrante, J. (1993), Multilayer relaxation and surface energies of fcc and bcc metals using equivalent crystal theory, Surf. Sci., Vol. 289, pp. 100-126. Rose, J.H., Ferrante, J. and Smith, J.R. (1981), Universal binding energy curves for metals and bimetallic interfaces, Phys. Rev. Lett., Vol. 47, pp. 675-678. Rose, J.H., Smith, J.R., and Ferrante, J. (1983), Universal features of bonding in metals, Phys. Rev. B, Vol. 28, pp. 1835-1845. Rous, P.J. and Pendry, J.B. (1989), Applications of tensor LEED, Surf. Sci., Vol. 219, pp. 373-394. Shinjo, K. and Hirano, M. (1993), Dynamics of friction: superlubric state, Surf. Sci., Vol. 283, pp. 473-478. Smith, J.R. and Ferrante, J. (1985), Materials in Intimate Contact, Mat. Sci. Forum, Vol. 4, pp. 21-38. Smith, J.R. and Ferrante, J. (1986), Grain–boundary energies in metals from local-electron-density distributions, Phys. Rev. B, Vol. 34, pp. 2238-2245. Smith, D.J. (1997), The realization of atomic resolution with the electron microscope, Rep. Prog. Phys., Vol. 60, pp. 1513-1580. Sokoloff, J.B. (1990), Theory of energy dissipation in sliding crystal surfaces, Phys. Rev. B, Vol. 42, pp. 760-765. Sokoloff, J.B. (1992), Theory of atomic level sliding friction between ideal crystal interfaces, J. Appl. Phys., Vol. 72, pp. 1262-1269. Sokoloff, J.B., Krim, J., and Widom, A. (1993), Determination of an atomic-scale frictional force law through quartz-crystal microbalance measurements, Phys. Rev. B, Vol. 48, pp. 9134-9137. Sokoloff, J.B. (1995), Theory of the contribution to sliding friction from electronic excitations in the microbalance experiment, Phys. Rev. B, Vol. 52, pp. 5318-5322. Sokoloff, J.B. and Tomassone M.S. (1998), Effects of surface defects on friction for a thin solid film sliding over a solid surface, Phys. Rev. B, Vol. 57, pp. 4888-4894. Srivastava, G.P. (1997), Theory of semiconductor surface reconstruction, Rep. Prog. Phys., Vol. 60, pp. 561-613. Thomas, G. and Goringe, M.J. (1979), Transmission Electron Microscopy of Materials, John Wiley & Sons, New York. Tsukizoe, T., Tanaka, S., Nishizaki, K., and Ohmae, N. (1985), Field ion microscopy of metallic adhesion and friction, Proc. JSLE Intl. Tribol. Conf., Tokyo, pp. 121-126.
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Van Hove, M.A., Moritz, W., Over, H., Rous, P.J., Wander, A., Barbieri, A., Materer, N., Starke, U., and Somorjai, G.A. (1993), Automated determination of complex surface structures by LEED, Surf. Sci. Reports, Vol. 19, pp. 191-229. Vlachos, D.G., Schmidt, L.D., and Aris, R. (1993), Kinetics of faceting of crystals in growth, etching, and equilibrium, Phys. Rev. B, Vol. 47, pp. 4896-4909. Volokitin, A.I. and Persson, B.N.J. (1999), Theory of friction: the contribution from a fluctuating electromagnetic field, J. Phys.: Condens. Matter, Vol. 11, pp. 345-359. Wheeler, D.R. (1976), Effect of adsorbed chlorine and oxygen on the shear strength of iron and copper junctions, J. Appl. Phys., Vol. 47, pp. 1123-1130. Wheeler, D.R. (1978), X-ray photoelectron spectroscopic study of surface chemistry of dibenzyl disulfide on steel under mild and severe wear conditions, Wear, Vol. 47, pp. 243-254. Widom, A. and Krim, J. (1986), Q factors of quartz oscillator modes as a probe of submonolayer-film dynamics, Phys. Rev. B, Vol. 34, pp. 1403-1404. Williams, E.D. (1994), Surface steps and surface morphology: understanding macroscopic phenomena from atomic observations, Surf. Sci., Vol. 299/300, pp. 502-524. Wilson, R.G., Stevie, F.A., and Magee, C.W. (1989), Secondary Ion Mass Spectroscopy, Wiley, New York. Wood, E.A. (1963), Vocabulary of surface crystallography, J. Appl. Phys., Vol. 35, pp. 1306-1312. Zalm, P.C. (1995), Ultra shallow doping profiling with SIMS, Rep. Prog. Phys., Vol. 58, pp. 1321-1374. Zangwill, A. (1988), Physics at Surfaces, Cambridge University Press, Cambridge, U.K. Zhong, W. and Tomanek, D. (1990), First-principles theory of atomic-scale friction, Phys. Rev. Lett., Vol. 64, pp. 3054-3057. Zhu, X.Y., Hermanson, J., Arlinghaus, F.J., Gay, J.G., Richter, R., and Smith, J.R. (1984), Electronic structure and magnetism of Ni (100) films: self-consistent local-orbital calculations, Phys. Rev. B, Vol. 29, pp. 4426-4438.
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2 Surface Roughness Analysis and Measurement Techniques 2.1 2.2
The Nature of Surfaces ........................................................ 49 Analysis of Surface Roughness ............................................ 50 Average Roughness Parameters • Statistical Analyses • Fractal Characterization • Practical Considerations in Measurement of Roughness Parameters
2.3
Mechanical Stylus Method • Optical Methods • Scanning Probe Microscopy (SPM) Methods • Fluid Methods • Electrical Method • Electron Microscopy Methods • Analysis of Measured Height Distribution • Comparison of Measurement Methods
Bharat Bhushan The Ohio State University
Measurement of Surface Roughness................................... 81
2.4
Closure ................................................................................ 114
2.1 The Nature of Surfaces A solid surface, or more exactly a solid–gas or solid–liquid interface, has a complex structure and complex properties depending on the nature of the solids, the method of surface preparation, and the interaction between the surface and the environment. Properties of solid surfaces are crucial to surface interaction because surface properties affect real area of contact, friction, wear, and lubrication. In addition to tribological functions, surface properties are important in other applications, such as optical, electrical and thermal performance, painting, and appearance. Solid surfaces, irrespective of their method of formation, contain irregularities or deviations from the prescribed geometrical form (Whitehouse, 1994; Bhushan, 1996, 1999a,b; Thomas, 1999). The surfaces contain irregularities of various orders ranging from shape deviations to irregularities of the order of interatomic distances. No machining method, however precise, can produce a molecularly flat surface on conventional materials. Even the smoothest surfaces, such as those obtained by cleavage of some crystals, contain irregularities, the heights of which exceed the interatomic distances. For technological applications, both macro- and micro/nanotopography of the surfaces (surface texture) are important (Bhushan, 1999a,b). In addition to surface deviations, the solid surface itself consists of several zones having physicochemical properties peculiar to the bulk material itself (Figure 2.1) (Gatos, 1968; Haltner, 1969; Buckley, 1981). As a result of the forming process in metals and alloys, there is a zone of work-hardened or
0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
49
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FIGURE 2.1
Modern Tribology Handbook
Solid surface details: surface texture (vertical axis magnified) and typical surface layers.
deformed material on top of which is a region of microcrystalline or amorphous structure that is called the Beilby layer. Deformed layers would also be present in ceramics and polymers. These layers are extremely important because their properties, from a surface chemistry point of view, can be entirely different from the annealed bulk material. Likewise, their mechanical behavior is influenced by the amount and depth of deformation of the surface layers. Many of the surfaces are chemically reactive. With the exception of noble metals, all metals and alloys and many nonmetals form surface oxide layers in air, and in other environments they are likely to form other layers (for example, nitrides, sulfides, and chlorides). Besides the chemical corrosion film, there are also adsorbed films that are produced either by physisorption or chemisorption of oxygen, water vapor, and hydrocarbons, from the environment. Occasionally, there will be a greasy or oily film derived from the environment. These films are found on metallic and nonmetallic surfaces. The presence of surface films affects friction and wear. The effect of adsorbed films, even a fraction of a monolayer, is significant on the surface interaction. Sometimes, the films wear out in the initial running period and subsequently have no effect. The effect of greasy or soapy film, if present, is more marked; it reduces the severity of surface interaction often by one or more orders of magnitude. This chapter covers the details on the analysis and measurement of surface roughness.
2.2 Analysis of Surface Roughness Surface texture is the repetitive or random deviation from the nominal surface that forms the threedimensional topography of the surface. Surface texture includes (1) roughness (nano- and microroughness), (2) waviness (macroroughness), (3) lay, and (4) flaws. Figure 2.2 is a pictorial display of surface texture with unidirectional lay (Anonymous, 1985). Nano- and microroughness are formed by fluctuations in the surface of short wavelengths, characterized by hills (asperities) (local maxima) and valleys (local minima) of varying amplitudes and spacings. These are large compared to molecular dimensions. Asperities are referred to as peaks in a profile (two dimensions) and summits in a surface map (three dimensions). Nano- and microroughness include those features intrinsic to the production process. These are considered to include traverse feed marks and other irregularities within the limits of the roughness sampling length. Waviness is the surface irregularity
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FIGURE 2.2 Pictorial display of surface texture. (From Anonymous (1985), Surface Texture (Surface Roughness, Waviness and Lay), ANSI/ASME B46.1, ASME, New York. With permission.)
of longer wavelengths and is referred to as macroroughness. Waviness may result from such factors as machine or workpiece deflections, vibration, chatter, heat treatment, or warping strains. Waviness includes all irregularities whose spacing is greater than the roughness sampling length and less than the waviness sampling length. Lay is the principal direction of the predominant surface pattern, ordinarily determined by the production method. Flaws are unintentional, unexpected, and unwanted interruptions in the texture. In addition, the surface may contain gross deviations from nominal shape of very long wavelength, which is known as errors of form. They are not normally considered part of the surface
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FIGURE 2.3
Modern Tribology Handbook
General typology of surfaces.
texture. A question often asked is whether various geometrical features should be assessed together or separately. What features are included together depends on the applications. It is generally not possible to measure all features at the same time. A very general typology of a solid surface is seen in Figure 2.3. Surface textures that are deterministic may be studied by relatively simple analytical and empirical methods; their detailed characterization is straightforward. However, the textures of most engineering surfaces are random, either isotropic or anisotropic, and either Gaussian or non-Gaussian. Whether the surface height distribution is isotropic or anisotropic and Gaussian or non-Gaussian depends upon the nature of the processing method. Surfaces that are formed by cumulative processes (such as peening, electropolishing, and lapping), in which the final shape of each region is the cumulative result of a large number of random discrete local events and irrespective of the distribution governing each individual event, will produce a cumulative effect that is governed by the Gaussian form. It is a direct consequence of the central limit theorem of statistical theory. Single-point processes (such as turning and shaping) and extreme-value processes (such as grinding and milling) generally lead to anisotropic and non-Gaussian surfaces. The Gaussian (normal) distribution has become one of the mainstays of surface classification. In this section, we first define average roughness parameters, followed by statistical analyses and fractal characterization of surface roughness that are important in contact problems. Emphasis is placed on random, isotropic surfaces that follow Gaussian distribution.
2.2.1 Average Roughness Parameters 2.2.1.1 Amplitude Parameters Surface roughness most commonly refers to the variations in the height of the surface relative to a reference plane. It is measured either along a single line profile or along a set of parallel line profiles (surface maps). It is usually characterized by one of the two statistical height descriptors advocated by the American National Standards Institute (ANSI) and the International Standardization Organization (ISO) (Anonymous, 1975, 1985). These are (1) Ra, CLA (center-line average), or AA (arithmetic average) and (2) the standard deviation or variance (σ), Rq or root mean square (RMS). Two other statistical
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FIGURE 2.4
53
Schematic of a surface profile z(x).
height descriptors are skewness (Sk) and kurtosis (K); these are rarely used. Another measure of surface roughness is an extreme-value height descriptor (Anonymous, 1975, 1985) Rt (or Ry , Rmax , or maximum peak-to-valley height or simply P–V distance). Four other extreme-value height descriptors in limited use, are: Rp (maximum peak height, maximum peak-to-mean height or simply P–M distance), Rv (maximum valley depth or mean-to-lowest valley height), Rz (average peak-to-valley height), and Rpm (average peak-to-mean height). We consider a profile, z(x), in which profile heights are measured from a reference line Figure 2.4. We define a center line or mean line such that the area between the profile and the mean line above the line is equal to that below the mean line. Ra, CLA, or AA is the arithmetic mean of the absolute values of vertical deviation from the mean line through the profile. The standard deviation σ is the square root of the arithmetic mean of the square of the vertical deviation from the mean line. In mathematical form, we write
R a = CLA = AA =
1 L
∫
L
z − m dx
(2.1a)
0
and
m=
1 L
∫
L
z dx
(2.1b)
0
where L is the sampling length of the profile (profile length). The variance is given as
σ2 =
1 L
∫ (z − m) L
2
dx
(2.2a)
0
= R q2 − m2
(2.2b)
where, σ is the standard deviation and Rq is the square root of the arithmetic mean of the square of the vertical deviation from a reference line, or
R q2 = RMS2 =
1 L
∫ (z )dx L
0
2
(2.3a)
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TABLE 2.1 Center-Line Average and Roughness Grades Ra Values up to a Value in µm
Roughness Grade Number
0.025 0.05 0.1 0.2 0.4 0.8 1.6 3.2 6.3 12.5 25.0
N1 N2 N3 N4 N5 N6 N7 N8 N9 N10 N11
For the special case where m is equal to zero,
Rq = σ
(2.3b)
In many cases, the Ra and σ are interchangeable, and for Gaussian surfaces,
σ~
π R ~ 1.25 R a 2 a
(2.4)
The value of Ra is an official standard in most industrialized countries. Table 2.1 gives internationally adopted Ra values together with the alternative roughness grade number. The σ is most commonly used in statistical analyses. The skewness and kurtosis in the normalized form are given as
Sk =
1 σ 3L
∫ (z − m)
1 σ4 L
∫ (z − m)
L
3
dx
(2.5)
dx
(2.6)
0
and
K=
L
4
0
More discussion of these two descriptors will be presented later. Five extreme-value height descriptors are defined as follows: Rt is the distance between the highest asperity (peak or summit) and the lowest valley; Rp is defined as the distance between the highest asperity and the mean line; Rv is defined as the distance between the mean line and the lowest valley; Rz is defined as the distance between the averages of five highest asperities and the five lowest valleys; and Rpm is defined as the distance between the averages of the five highest asperities and the mean line. The reason for taking an average value of asperities and valleys is to minimize the effect of unrepresentative asperities or valleys which occasionally occur and can give an erroneous value if taken singly. Rz and Rpm are more reproducible and are advocated by ISO. In many tribological applications, height of the highest asperities above the mean line is an important parameter because damage may be done to the interface by the few high asperities present on one of the two surfaces; on the other hand, valleys may affect lubrication retention and flow.
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FIGURE 2.5
55
Various surface profiles having the same Ra value.
The height parameters Ra (or σ in some cases) are Rt (or Rp in some cases) are most commonly specified for machine components. For the complete characterization of a profile or a surface, none of the parameters discussed earlier are sufficient. These parameters are seen to be primarily concerned with the relative departure of the profile in the vertical direction only; they do not provide any information about the slopes, shapes, and sizes of the asperities or about the frequency and regularity of their occurrence. It is possible, for surfaces of widely differing profiles with different frequencies and different shapes, to give the same Ra or σ (Rq) values (Figure 2.5). These single numerical parameters are useful mainly for classifying surfaces of the same type that are produced by the same method. Average roughness parameters for surface maps are calculated using the same mathematical approach as that for a profile presented here. 2.2.1.2 Spacing (or Spatial) Parameters One way to supplement the amplitude (height) information is to provide some index of crest spacing or wavelength (which corresponds to lateral or spatial distribution) on the surface. Two parameters occasionally used are the peak (or summit) density, Np (η), and zero crossings density, N0. Np is the density of peaks (local maxima) of the profile in number per unit length, and η is the density of summits on the surface in number per unit area. Np and η are just measures of maxima irrespective of height. This parameter is in some use. N0 is the zero crossings density defined as the number of times the profile crosses the mean line per unit length. From Longuet–Higgins (1957a), the number of surface zero crossings per unit length is given by the total length of the contour where the autocorrelation function (to be described later) is zero (or 0.1) divided by the area enclosed by the contour. This count N0 is rarely used. A third parameter — mean peak spacing (AR) — is the average distance between measured peaks. This parameter is merely equal to (1/Np). Other spacial parameters rarely used are the mean slope and mean curvature, which are the first and second derivatives of the profile/surface, respectively.
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2.2.2 Statistical Analyses 2.2.2.1 Amplitude Probability Distribution and Density Functions The cumulative probability distribution function, or simply cumulative distribution function (CDF), P(h) associated with the random variable z(x), which can take any value between – ∞ and ∞ or zmin and zmax, is defined as the probability of the event z(x) ≤ h, and is written as (McGillem and Cooper, 1984; Bendat and Piersol, 1986)
()
(
P h = Pr ob z ≤ h
)
(2.7)
with P (– ∞) = 0 and P (∞) = 1. It is common to describe the probability structure of random data in terms of the slope of the distribution function given by the derivative
()
pz =
()
dP z
(2.8a)
dz
where the resulting function p(z) is called the probability density function (PDF). Obviously, the cumulative distribution function is the integral of the probability density function p(z), that is,
(
) ∫ p(z)dz = P(h) h
P z≤h =
(2.8b)
−∞
and
(
) ∫ p(z)dz = P(h ) − P(h ) h2
P h1 ≤ z ≤ h 2 =
2
h1
1
(2.8c)
Furthermore, the total area under the probability density function must be unity; that is, it is certain that the value of z at any x must fall somewhere between plus and minus infinity or zmax and zmin. The data representing a wide collection of random physical phenomenon in practice tend to have a Gaussian or normal probability density function,
(
)
z−m − exp pz = 12 2σ 2 σ 2π
()
1
( )
2
(2.9a)
where σ is the standard deviation and m is the mean. For convenience, the Gaussian function is plotted in terms of a normalized variable,
(
)
z* = z − m σ
(2.9b)
which has zero mean and unity standard deviation. With this transformation of variables, Equation 2.9 becomes
( )
p z* =
( )
− z* exp 12 2 2π 1
( )
2
(2.9c)
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which is called the standardized Gaussian or normal probability density function. To obtain P(h) from p(z*) of Equation 2.9c, the integral cannot be performed in terms of the common functions, and the integral is often listed in terms of the “error function” and its values are listed in most statistical textbooks. The error function is defined as
()
erf h =
(2π) ∫ 1
12
0
h
( ) dz *
− z* exp 2
2
(2.10)
An example of a random variable z*(x) with its Gaussian probability density and corresponding cumulative distribution functions is shown in Figure 2.6. Examples of P(h) and P(z* = h) are also shown. The probability density function is bell shaped, and the cumulative distribution function is S-shaped. We further note that for a Gaussian function
( ) P( −2 ≤ z* ≤ 2) = 0.954 P( −3 ≤ z* ≤ 3) = 0.999 P −1 ≤ z* ≤ 1 = 0.682
and
(
)
P −∞ ≤ z* ≤ ∞ = 1 which implies that the probabilities that some number that follows a Gaussian distribution is within the limits of ±1σ, ±2σ, and ±3σ are 68.2, 95.4, and 99.9%, respectively. A convenient method for testing for Gaussian distribution is to plot the cumulative distribution function on probability graph paper to show the percentage of the numbers below a given number; this is scaled such that a straight line is produced when the distribution is Gaussian (typical data to be
FIGURE 2.6
(a) Random function z*(x), which follows Gaussian probability functions.
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FIGURE 2.6 P(z*).
Modern Tribology Handbook
(b) Gaussian probability density function p(z*), and (c) Gaussian probability distribution function
presented later). To test for Gaussian distribution, a straight line corresponding to a Gaussian distribution is drawn on the plot. The slope of the straight line portion is determined by σ, and the position of the line for 50% probability is set at the mean value (which is typically zero for surface height data). The most practical method for the goodness of the fit between the given distribution and the Gaussian distribution is to use the Kolmogorov–Smirnov test (Smirnov, 1948; Massey, 1951; Siegel, 1956). In the Kolmogorov–Smirnov test, the maximum departure between the percentage of the numbers above a given number for the data and the percentage of the numbers that would be above a given number if the given distribution were a Gaussian distribution is first calculated. Then, a calculation is made to determine if the distribution is indeed Gaussian. The level of significance, P, is calculated; this gives the probability of mistakenly or falsely rejecting the hypothesis that the distribution is a Gaussian distribution. Common minimum values for P for accepting the hypothesis are 0.01 to 0.05 (Siegel, 1956). The chisquare test (Siegel, 1956) can also be used to determine how well the given distribution matches a Gaussian distribution. However, the chi-square test is not very useful because the goodness of fit calculated depends too much on how many bins or discrete cells the surface height data are divided into (Wyant et al., 1986).
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For the sake of mathematical simplicity in some analyses, sometimes an exponential distribution is used instead of the Gaussian distribution. The exponential distribution is given as
()
pz =
(
)
z−m 1 exp − σ σ
(2.11a)
or
( )
( )
p z * = exp − z *
(2.11b)
2.2.2.2 Moments of Amplitude Probability Functions The shape of the probability density function offers useful information on the behavior of the process. This shape can be expressed in terms of moments of the function,
mn =
∫
∞
−∞
()
z n p z dz
(2.12)
mn is called the nth moment. Moments about the mean are referred to as central moments,
mnc =
∞
∫ (z − m) p(z) dz n
(2.13)
−∞
The zeroth moment (n = 0) is equal to 1. The first moment is equal to m, mean value of the function z(x), whereas the first central moment is equal to zero. For completeness, we note that
∫
∞
∫
∞
Ra =
()
z − m p z dz
−∞
(2.14)
The second moments are,
m2 =
−∞
()
z 2p z dz = R q2
(2.15)
and
m2c =
∞
∫ (z − m) p(z) dz = σ 2
−∞
= R q2 − m2
2
(2.16a)
(2.16b)
The third moment mc3 is the skewness (Sk). A useful parameter in defining variables with an asymmetric spread, it represents the degree of symmetry of the distribution function (Figure 2.7). It is usual to normalize the third central moment as,
Sk =
1 σ3
∫ (z − m) p(z) dz ∞
−∞
3
(2.17)
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FIGURE 2.7 (a) Probability density functions for random distributions with different skewness, and for (b) symmetrical distributions (zero skewness) with different kurtosis.
Symmetrical distribution functions, including Gaussian, have zero skewness. The fourth moment mc4 is the kurtosis (K). It represents the peakedness of the distribution and is a measure of the degree of pointedness or bluntness of a distribution function (Figure 2.7). Again, it is usual to normalize the fourth central moment as,
K=
1 σ4
∞
∫ (z − m) p(z) dz −∞
4
(2.18)
Note that the symmetric Gaussian distribution has a kurtosis of 3. Distributions with K > 3 are called leptokurtic, and those with K < 3 are called platykurtic. Kotwal and Bhushan (1996) developed an analytical method to generate probability density functions for non-Gaussian distributions using the so-called Pearson system of frequency curves based on the methods of moments (Elderton and Johnson, 1969). (For a method of generating non-Gaussian distributions on the computer, see Chilamakuri and Bhushan [1998].) The probability density functions generated by this method for selected skewness and kurtosis values are presented in Table 2.2. These functions are plotted in Figure 2.8. From this figure, it can be seen that a Gaussian distribution with zero skewness and a kurtosis of three has an equal number of local maxima and minima at a certain height above and below the mean line. A surface with a high negative skewness has a larger number of local maxima above the mean as compared to a Gaussian distribution; for a positive skewness the converse is true, Figure 2.9. Similarly, a surface with a low kurtosis has a larger number of local maxima above the mean as compared to that of a Gaussian distribution; again, for a high kurtosis the converse is true (Figure 2.9).
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TABLE 2.2 Probability Density Functions for Surfaces with Various Skewness and Kurtosis Values Based on the Pearson’s System of Frequency Curves Non-Gaussian Parameters
Number of Type
Probability Density Function, p(z*)
Sk
K
–0.8
3
I
p(z *) = 0.33(1 + z * 3.86)
–0.5
3
I
p(z *) = 0.38(1 + z * 6.36)
–0.3
3
I
p z * = 0.39 1 + z * 10.72
0.0
3
Normal
p(z *) = 0.3989 exp −0.5(z *)
( )
(
2.14
(1 − z * 1.36)
(1 − z * 2.36)
9.21
(
29.80
0.3
3
I
p(z *) = 0.39(1 + z * 4.05)
0.5
3
I
p(z *) = 0.38(1 + z * 2.36)
0.8
3
I
p(z *) = 0.33(1 + z * 1.36)
0.0
2
II
p(z *) = 0.32 1 − (z *) 16
0.0
3
Normal
p(z *) = 0.3989 exp −0.5(z *)
0.0
5
VII
p(z *) = 0.46 1 + (z *) 25
0.0
10
VII
0.0
20
VII
2
(
2
10.64
)
(1 − z * 10.72)
2.79
(1 − z * 6.36)
0.11
(1 − z * 3.86)
)
29.80
9.21
2.14
0.5
( ) p(z *) = 0.49(1 + (z *) 8.20) p(z *) = 0.51(1 + (z *) 5.52) 2
2.79
) (1 − z * 4.05)
10.64
(
0.11
2
)
−4
2
−2.92
2
−2.68
z* = z/σ
In practice, many engineering surfaces have symmetrical Gaussian height distribution. Experience with most engineering surfaces shows that the height distribution is Gaussian at the high end, but at the lower end, the bottom 1 to 5% of the distribution is generally found to be non-Gaussian (Williamson, 1968). Many of the common machining processes produce surfaces with non-Gaussian distribution, Figure 2.10. Turning, shaping, and electrodischarge machining (EDM) processes produce surfaces with positive skewness. Grinding, honing, milling, and abrasion processes produce grooved surfaces with negative skewness but high kurtosis values. Laser polishing produces surfaces with high kurtosis. 2.2.2.3 Surface Height Distribution Functions If the surface or profile heights are considered as random variables, then their statistical representation in terms of the probability density function p(z) is known as the height distribution, or a histogram. The height distribution can also be represented as cumulative distribution function P(z). For a digitized profile, the histogram is constructed by plotting the number or fraction of surface heights lying between two specific heights as a function of height (Figure 2.11). The interval between two such heights is termed the class interval and is shown as dz in Figure 2.11. It is generally recommended to use 15 to 50 class intervals for general random data, but the choice is usually a trade-off between accuracy and resolution. Similarly, from the surface or profile height distribution, the cumulative distribution function is derived. It is constructed by plotting the cumulative number or proportion of the surface height lying at or below a specific height as a function of that height (Figure 2.11). An example of a profile and corresponding histogram and cumulative height distribution on a probability paper for a lapped nickel–zinc ferrite is given in Figure 2.12.
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FIGURE 2.8
Probability density function for random distributions with selected skewness and kurtosis values.
FIGURE 2.9
Schematic illustration for random functions with various skewness and kurtosis values.
Probability density and distribution curves can also be obtained for the slope and curvature of the surface or the profile. If the surface, or profile height, follows a Gaussian distribution, then its slope and curvature distribution also follows a Gaussian distribution. Because it is known that if two functions follow a Gaussian distribution, their sum and difference also follow a Gaussian distribution. Slope and curvatures are derived by taking the difference in a height distribution, and therefore slope and curvatures of a Gaussian height distribution would be Gaussian.
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63
FIGURE 2.10 Typical skewness and kurtosis envelopes for various manufacturing processes (From Whitehouse, D.I. (1994), Handbook of Surface Metrology, Institute of Physics Publishing, Bristol, U.K. With permission.)
FIGURE 2.11 distribution.
Method of deriving the histogram and cumulative distribution function from a surface height
For a digitized profile of length L with heights zi , i = 1 to N, at a sampling interval ∆x=L/(N – 1), where N represents the number of measurements, average height parameters are given as
1 Ra = N
σ2 =
Sk =
1 N
N
∑z −m
(2.19a)
i
i =1
N
∑ (z − m)
1 σ 3N
2
(2.19b)
i
i =1
N
∑ (z − m) i
i =1
3
(2.19c)
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Profile height (nm)
20
10
0
-10 -20 0
56
112
168
224
280
Distance (µm) (a)
Fraction of surface at given height
Rq = 2.2 nm Rt = 34.6 nm 0.4 Histogram
0.3
Gaussian distribution curve
0.2 0.1 0 -20
-10
0 Surface height (nm)
10
20
10
20
Percentage of surface at or below. a given height
99.9 99 90 50 10 1 0.1 -20
-10
0 Surface height (nm) (b)
FIGURE 2.12 ferrite.
(a) Profile and (b) corresponding histogram and distribution of profile heights of lapped nickel–zinc
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K=
N
1 σ 4N
∑ (z − m)
m=
1 N
4
(2.19d)
i
i =1
and N
∑z
(2.19e)
i
i =1
∂z
∂ 2z
Two average spacing parameters, mean of profile slope and profile curvature − 2 of a digitized ∂x ∂x profile, are given as
mean slope =
and mean curvature =
1 N −1
N −1
z i +1 − z i ∆x
∑
1 N−2
i =1
N −1
2z i − z i −1 − z i +1 ∆x 2
∑ i =2
(2.20a)
(2.20b)
The surface slope at any point on a surface is obtained by finding the square roots of the sum of the squares of the slopes in two orthogonal (x and y) axes. The curvature at any point on the surface is obtained by finding the average of the curvatures in two orthogonal (x and y) axes (Nayak, 1971). Before calculation of roughness parameters, the height data are fitted in a least-square sense to determine the mean height, tilt, and curvature. The mean height is always subtracted, and the tilt is usually subtracted. In some cases, curvature needs to be removed as well. Spherical and cylindrical radii of curvature are removed for spherical and cylindrical surfaces, respectively (e.g., balls and cylinders), before roughness parameters are calculated. 2.2.2.4 Bearing Area Curves The real area of contact (to be discussed in the next chapter) is known as the bearing area and may be approximately obtained from a surface profile or a surface map. The bearing area curve (BAC) first proposed by Abbott and Firestone (1933) is also called the Abbott–Firestone curve or simply the Abbott curve. It gives the ratio of air to material at any level, starting at the highest peak, called the bearing ratio or material ratio, as a function of level. To produce a BAC from a surface profile, a parallel line (bearing line) is drawn some distance from a reference (or mean) line. The length of each material intercept (land) along the line is measured and these lengths are summed. The proportion of this sum to the total length, the bearing length ratio (tp), is calculated. This procedure is repeated along a number of bearing lines, starting with the highest peak to the lowest valley, and the fractional land length (bearing length ratio) as a function of the height of each slice from the highest peak (cutting depth) is plotted (Figure 2.13). For a Gaussian surface, the BAC has an S-shaped appearance. In the case of a surface map, bearing planes are drawn, and the area of each material intercept is measured. For a random surface, the bearing length and bearing area fractions are numerically identical. The BAC is related to the CDF. The fraction of heights lying above a given height z (i.e., the bearing ratio at height h) is given by
(
∞
) ∫ p(z) dz
Prob z ≥ h =
h
(2.21a)
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FIGURE 2.13
Modern Tribology Handbook
Schematic of bearing area curve.
which is 1 – P(h), where P(h) is the cumulative distribution function at z ≤ h (Figure 2.6). Therefore, the BAC can be obtained from the height distribution histogram. The bearing ratio histograph at height h is simply the progressive addition of all the values of p(z) starting at the highest point and working down to the height z = h, and this cumulative sum multiplied by the class interval ∆z is
(
)
P z ≥ h = ∆z
∞
∑ p(z)
(2.21b)
z=h
The relationship of bearing ratio to the fractional real area of contact is highly approximate as material is sliced off in the construction of BAC and the material deformation is not taken into account. 2.2.2.5 Spatial Functions Consider two surfaces with sine wave distributions with the same amplitude but different frequencies. We have shown that these will have the same Ra and σ, but with different spatial arrangements of surface heights. Slope and curvature distributions are not, in general, sufficient to represent the surface, as they refer only to one particular spatial size of features. The spatial functions (McGillem and Cooper, 1984; Bendat and Piersol, 1986), namely the autocovariance (or autocorrelation) function (ACVF), structure function (SF), or power spectral (or autospectral) density function (PSDF), offer a means of representing the properties of all wavelengths, or spatial sizes of the feature; these are also known as surface texture descriptors. ACVF has been the most popular way of representing spatial variation. The ACVF of a random function is most directly interpreted as a measure of how well future values of the function can be predicted based on past observations. SF contains no more information than the ACVF. The PSDF is interpreted as a measure of frequency distribution of the mean square value of the function, that is the rate of change of the mean square value with frequency. In this section, we will present the definitions for an isotropic and random profile z(x). Definitions for an isotropic surface z(x,y) can be found in a paper by Nayak (1971). Analysis of an anisotropic surface is considerably complicated by the number of parameters required to describe the surface. For example, profile measurements along three different directions are needed for complete surface characterization of selected anisotropic surfaces. For further details on anisotropic surfaces, see Longuet-Higgins (1957a), Nayak (1973), Bush et al. (1979), and Thomas (1982). Autocovariance and Autocorrelation Functions For a function z(x), the ACVF for a spatial separation of τ is an average value of the product of two measurements taken on the profile a distance τ apart, z(x) and z(x + τ). It is obtained by comparing the function z(x) with a replica of itself where the replica is shifted an amount τ (Figure 2.14),
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FIGURE 2.14
Construction of the autocovariance function.
()
1 L→∞ L
R τ = lim
∫ z(x)z(x + τ)dx L
(2.22a)
0
where L is the sampling length of the profile. From its definition, ACVF is always an even function of τ, that is,
() ( )
R τ = R −τ
(2.22b)
The values of ACVF at τ = 0 and ∞ are,
()
R 0 = R q2 = σ 2 + m2
(2.22c)
and
( )
R ∞ = m2
(2.22d)
The normalized form of the ACVF is called the autocorrelation function (ACF) and is given as
()
C τ = lim
L→∞
[ ( ) ][ ( ) ] [ ( ) ] σ
1 z x − m z x + τ − m dx = R τ − m2 Lσ 2
2
(2.23)
For a random function, C(τ) would be maximum (= 1) at τ = 0. If the signal is periodic, C(τ) would peak whenever τ is a multiple of wavelength. Many engineering surfaces are found to have an exponential ACF,
()
(
C τ = exp − τ β
)
(2.24)
The measure of how quickly the random event decays is called the correlation length. The correlation length is the length over which the autocorrelation function drops to a small fraction of its value at the origin, typically 10% of its original value. The exponential form has a correlation length of β* [C(τ) = 0.1] equal to 2.3 β (Figure 2.15). Sometimes, correlation length is defined as the distance at which value of the autocorrelation function is 1/e, that is 37%, which is equal to β for exponential ACF. The correlation length can be taken as that at which two points on a function have just reached the condition where they can be regarded as being independent. This follows from the fact that when C(τ) is close to unity, two points on the function at a distance τ apart are strongly interdependent. However, when C(τ) attains values close to zero, two points on the function at a distance τ apart are weakly correlated. The correlation length, β* can be viewed as a measure of randomness. The degree of randomness of a surface increases with an increase in the magnitude of β*. The directionality of a surface can be found from its autocorrelation function. By plotting the contours of equal autocorrelation values, one can obtain contours to reveal surface structure. The anisotropy of
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FIGURE 2.15
Modern Tribology Handbook
An exponential autocorrelation function and corresponding power spectral density function.
the surface structure is given as the ratio between the longer and shorter axes of the contour (Wyant et al., 1986; Bhushan, 1996). For a theoretically isotropic surface structure, the contour would have a constant radius; that is, it would be a circle. The autocorrelation function can be calculated either by using the height distribution of the digitized profile or the fast Fourier transform (FFT) technique. In the FFT technique, the first PSDF (described later) is obtained by taking an FFT of the surface height and squaring the results; then an inverse FFT of the PSDF is taken to get ACVF. Structure Function The structure function (SF) or variance function (VF) in an integral form for a profile z(x) is,
()
1 L→∞ L
S τ = lim
∫ [z(x) − z(x + τ)] dx L
2
(2.25)
0
The function represents the mean square of the difference in height expected over any spatial distance τ. For stationary structures, it contains the same information as the ACVF. The two principal advantages of SF are that its construction is not limited to the stationary case, and it is independent of the mean plane. Structure function is related to ACVF and ACF as
() [
( )]
S τ = 2 σ 2 + m2 − R τ
(2.26a)
[ ( )]
= 2σ 2 1 − C τ
(2.26b)
Power Spectral Density Function The PSDF is another form of spatial representation and provides the same information as the ACVF or SF, but in a different form. The PSDF is the Fourier transform of the ACVF, ∞
( ) ( ) ∫ R(τ)exp(−iωτ)dτ
P ω = P −ω = =
∫
∞
−∞
−∞
() (
)
(2.27)
( )
σ 2 C τ exp − iωτ dτ + m2δ ω
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where ω is the angular frequency in length–1 (= 2πf or 2π/λ, f is frequency in cycles/length and λ is wavelength in length per cycle), and δ(ω) is the delta function. P(ω) is defined over all frequencies, both positive and negative, and is referred to as a two-sided spectrum. G(ω) is a spectrum defined over nonnegative frequencies only and is related to P(ω) for a random surface by
( )
( )
G ω = 2P ω , ω ≥ 0
(2.28a)
= 0, ω < 0. Since the ACVF is an even function of τ, it follows that the PSDF is given by the real part of the Fourier transform in Equation 2.27. Therefore, ∞
∞
( ) ∫ R(τ)cos (ωτ)dτ = 2∫ R(τ)cos (ωτ)dτ
Pω =
−∞
(2.28b)
0
Conversely, the ACVF is given by the inverse Fourier transform of the PSDF,
()
Rτ =
1 2π
∞
∫ () ( ) −∞
P ω exp iωτ dω =
1 2π
∞
∫ P(ω)cos (ωτ) dω −∞
(2.29)
For
()
τ = 0, R 0 = R q2 =
1 2π
∞
∫ P(ω) dω
(2.30)
−∞
The equation shows that the total area under the PSDF curve (when frequency in cycles/length) is equal to Rq2 . The area under the curve between any frequency limits gives the mean square value of the data within that frequency range. The PSDF can also be obtained directly in terms of the Fourier transform of the profile data z(x) by taking an FFT of the profile data and squaring the results, as follows:
( )
1 L→∞ L
P ω = lim
z x exp − iωx dx
∫ () ( L
0
)
2
(2.31)
The PSDF can be evaluated from the data either via the ACVF using Equation 2.28 or the Fourier transform of the data (Equation 2.31). Note that the units of the one-dimensional PSDF are in terms of length to the third power, and for the two-dimensional case it is the length to the fourth power. Figure 2.15 shows the PSDF for an exponential ACF previously presented in Equation 2.24. The magnitude of the P(ω) at ω = 1/β is known as the half-power point. For an exponential ACF, the PSDF is represented by white noise in the upper frequencies. The physical meaning of the model is that the main components of the function consist of a band covering the lower frequencies (longer wavelengths). Shorter wavelength components exist, but their magnitude declines with increasing frequency so that, in this range, the amplitude is proportional to wavelength. To cover large spatial range, it is often more convenient with surface data to represent ACF, SF, and PSDF on a log–log scale. Figure 2.16a shows examples of selected profiles. Figures 2.16b and 2.16c show the corresponding ACVF and PSDF (Bendat and Piersol, 1986). (For calculation of ACVF and PSDF, profile length of multiple of wavelengths [a minimum of one wavelength] needs to be used.) The ACVF of a sine wave is a cosine wave. The envelope of the sine wave covariance function remains constant over all time delays,
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FIGURE 2.16 (a) Four special time histories: (i) sine wave, (ii) sine wave plus wide-band random noise, (iii) narrowband random noise, and (iv) wide-band random noise. (b) corresponding idealized autocovariance functions, and (c) corresponding power spectral density functions (From Bendat, J.S. and Piersol, A.G. (1986), Engineering Applications of Correlation and Spectral Analysis, 2nd edition, Wiley, New York. With permission.)
suggesting that one can predict future values of the data precisely based on past observations. Looking at the PSDF of the sine wave, we note that the total mean square value of the sine wave is concentrated at the single frequency, ω0. In all other cases, because of the erratic character of z(x) in Figure 2.16a, a past record does not significantly help one predict future values of the data beyond the very near future. To calculate the autocovariance function for (iii) to (iv) profiles, the power spectrum of the data is considered uniform over a wide bandwidth B. ACVF and PSDF of a sine wave plus wide-band random noise is simply the sum of the functions of the sine wave and wide-band random noise. The moments of the PSDF are defined as
Mn =
1 2π
∫ [P(ω) − m δ(ω)]ω ∞
−∞
2
n
dω
(2.32)
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FIGURE 2.16 (continued)
where Mn are known as the spectral moments of the nth order. We note for a Gaussian function (Nayak, 1971),
M0 = σ 2 =
1 L
∫ (z − m) L
dx
(2.33a)
0
M2 = σ ′ =
( )
1 L
( )
1 L
2
2
∫ (dz dx) dx
(2.33b)
∫ (d z dx ) dx
(2.33c)
L
2
0
and 2
M 4 = σ ′′ =
L
2
2
2
0
where σ′ and σ″ are the standard deviations of the first and second derivatives of the functions. For a surface/profile height, these are the surface/profile slope and curvature, respectively.
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FIGURE 2.16 (continued)
According to Nayak (1971), a random and isotropic surface with a Gaussian height distribution can be adequately characterized by the three-zeroth (M0), second (M2) and fourth moments (M4) of the power spectral density function. Based on the theory of random processes, a random and isotropic surface can be completely characterized in a statistical sense (rather than a deterministic sense) by two functions: the height distribution and the autocorrelation function. A random surface with Gaussian height distribution and exponential autocorrelation function can then simply be characterized by two parameters, two lengths: standard deviation of surface heights (σ) and the correlation distance (β*) (Whitehouse and Archard, 1970). For characterization of a surface with a discrete, arbitrary autocorrelation function, three points C(0), C(h), and C(2h) for a profile, where h is an arbitrary distance and four or more points are needed on the C(τ), depending upon the type of the surface (Whitehouse and Phillips, 1978, 1982). 2.2.2.6 Probability Distribution and Statistics of the Asperities and Valleys Surfaces consist of hills (asperities) of varying heights and spacing and valleys of varying depths and spacing. For a two-dimensional profile, the peak is defined as a point higher than its two adjacent points greater than a threshold value. For a three-dimensional surface map, the summit is defined as a point higher than its four adjacent points greater than a threshold value. A valley is defined in the same way but in reverse order. A threshold value is introduced to reduce the effect of noise in the measured data and ensure that every peak/summit identified is truly substantial. Based on analysis of roughness data
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of a variety of smooth samples, Poon and Bhushan (1995b) recommend a threshold value as one tenth of the σ roughness of smooth surfaces (with σ less than about 50 nm); it should be lower than 10% of the σ value for rougher surfaces. Gaussian surfaces might be considered as comprising a certain number of hills (asperities) and an equal number of valleys. These features may be assessed and represented by their appropriate distribution curves, which can be described by the same sort of characteristics as were used previously for the surface height distributions. Similar to surface height distributions, the height distributions of peaks (or summits) and valleys often follow the Gaussian curve (Greenwood, 1984; Wyant et al., 1986; Bhushan, 1996). Distribution curves can also be obtained for the absolute values of slope and for the curvature of the peaks (or summits) and valleys. Distributions of peak (or summit) curvature follow a log normal distribution (Gupta and Cook 1972; Wyant et al., 1986; Bhushan, 1996). The mean of the peak curvature increases with the peak height for a given surface (Nayak, 1971). The parameters of interest in some analytical contact models of two random rough surfaces to be discussed in the next chapter are the density of summits (η), the standard deviation of summit heights (σp), and the mean radius (Rp) (or curvature, κp) of the summit caps or η, σ, and β*. The former three roughness parameters (η, σp, Rp) can be related to other easily measurable roughness parameters using the theories of Longuet-Higgins (1957a,b), Nayak (1971), and Whitehouse and Phillips (1978, 1982). For a random Gaussian profile, we note that M2(= σ′ 2) and Mr (= σ″ 2) can be calculated from σ, N0, and Np using the following relationship (Longuet-Higgins, 1957a):
σ′ πσ
(2.34a)
σ ′′ 2πσ ′
(2.34b)
N0 = and
Np =
Note that N0 and Np are frequency dependent, for example, if the profile has a high frequency riding on a low frequency, then Np will be higher and N0 will be lower. We now define an auxiliary quantity, bandwidth parameter, α (Nayak, 1971), 2
2N σσ ′′ 2 α = p = 2 N0 σ′
(2.35)
which defines the width of the power spectrum of the random process forming the process from which the profile is taken. The distribution of peak heights and their expected tip curvature as a function of α are shown in Figure 2.17 (Nayak, 1971). z*p (= zp /σ) is the standardized cumulative summit/peak height distribution and κ*p (= κp /σ″) is the standardized mean summit/peak curvature κp . It is observed that high peaks always have a longer expected mean curvature (i.e., a smaller mean radius) than lower peaks. If α = 1, the spectrum consists of a single frequency, where 2Np, total density of peaks and valleys (maxima and minima) equals N0. If α = ∞, the spectrum extends over all frequencies (white noise spectrum). The peak heights have a Gaussian distribution and κp is nearly constant for peaks of all heights and is given by
σp ~ σ
(2.36a)
κ p ~ 1.3 σ ′′
(2.36b)
and
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FIGURE 2.17 (a) Probability density of peak heights and (b) expected dimensionless curvature of peaks. (From Nayak, P.R. (1971), Random process model of rough surfaces, ASME J. Lub. Tech., 93, 398-407. With permission.)
We also note that a profile with a very narrow spectrum has no peaks below a mean line, whereas a white noise profile with infinite spectral width has half of its peaks below this line. From Bush et al. (1976), the standard deviation of the summit/peak height for any α is given by
0.8968 σ p ~ 1 − α
12
σ
(2.37)
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From Nayak (1971), the density of summits per unit area can be related to the spectral moments and number of peaks per unit length by
σ ′′ η = 0.031 σ′
2
(2.38a)
~ 1.2 N p2
(2.38b)
Using discrete random process analysis, Whitehouse and Phillips (1978, 1982) derived the relationship of tribological parameters of interest for a surface that has a Gaussian height distribution. For characterization of a profile, we need standard deviation and just two points on the measured ρ1 and ρ2 spaced h (sampling interval) and 2h from the origin of the normalized autocorrelation function. For characterization of a surface, we need between four and seven points on the ACF, depending upon the type of surface. Tribological parameters that can be predicted are the mean and standard deviation (σp) of the peak height; the mean (κp) and standard deviation (σ″p ) of the peak curvature; the average peak slope; the correlation coefficient between the peak height and its curvature; and the summit density. 2.2.2.7 Composite Roughness of Two Random Rough Surfaces For two random rough surfaces in contact, the composite roughness of interest is defined as the sum of two roughness processes obtained by adding together the local heights (z), the local slope (θ), and local curvature (κ)
z = z1 + z 2 θ = θ1 + θ2
(2.39)
κ = κ1 + κ 2 For two random rough surfaces in contact, an equivalent rough surface can be described of which the values of σ, σ′, σ″, R(τ), P(ω), and M0, M2, and M4 are summed for the two rough surfaces, that is,
σ 2 = σ12 + σ 22 σ ′2 = σ1′ 2 + σ ′2 2 σ ′′2 = σ1′′2 + σ ′′2 2
() () () P(ω ) = P (ω ) + P (ω ) M = (M ) + (M ) R τ = R1 τ + R 2 τ
and
i
1
2
i 1
i 2
(2.40a)
where i = 0, 2, 4. These equations state that variances, autocovariance function, and power spectra are simply additive. Since autocovariance functions of two functions are additive, simple geometry shows that correlation lengths of two exponential ACVFs are related as
1 1 1 = *+ * * β β1 β2
(2.40b)
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FIGURE 2.18
Modern Tribology Handbook
Qualitative description of statistical self-affinity for a surface profile.
2.2.3 Fractal Characterization A surface is composed of a large number of length scales of roughness that are superimposed on each other. As stated earlier, surface roughness is generally characterized by the standard deviation of surface heights. However, due to the multiscale nature of the surface, it is known that the variances of surface height and its derivatives and other roughness parameters depend strongly on the resolution of the roughness measuring instrument or any other form of filter; hence they are not unique for a surface (Ganti and Bhushan, 1995; Poon and Bhushan, 1995a). Therefore rough surfaces should be characterized in such a way that the structural information of roughness at all scales is retained. It is necessary to quantify the multiscale nature of surface roughness. A unique property of rough surfaces is that if a surface is repeatedly magnified, increasing details of roughness are observed right down to nanoscale. In addition, the roughnesses at all magnifications appear quite similar in structure, as is qualitatively shown in Figure 2.18. The statistical self-affinity is due to similarity in appearance of a profile under different magnifications. Such a behavior can be characterized by fractal geometry (Majumdar and Bhushan, 1990; Ganti and Bhushan, 1995; Bhushan, 1999b). The fractal approach has the ability to characterize surface roughness by scale-independent parameters and provides information on the roughness structure at all length scales that exhibit the fractal behavior. Surface characteristics can be predicted at all length scales within the fractal regime by making measurements at one scan length. Structure function and power spectrum of a self-affine fractal surface follow a power law and can be written as (Ganti and Bhushan model)
( 2 D − 3) τ ( 4 −2 D )
()
S τ = Cη
( )
Pω =
(2.41)
( 2 D − 3)
c1η ω
(2.42a)
( 5−2 D )
and
c1 =
(
) [(
)] C
Γ 5 − 2D sin π 2 − D 2π
(2.42b)
The fractal analysis allows the characterization of surface roughness by two parameters D and C which are instrument-independent and unique for each surface. The parameter D (ranging from 1 to 2 for surface profile) primarily relates to the relative power of the frequency contents, and C to the amplitude of all frequencies. η is the lateral resolution of the measuring instrument, τ is the size of the increment (distance), and ω is the frequency of the roughness. Note that if S(τ) or P(ω) are plotted as a function of ω or τ, respectively, on a log-log plot, then the power law behavior results in a straight line. The slope of the line is related to D, and the location of the spectrum along the power axis is related to C.
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FIGURE 2.19 Structure functions for the roughness data measured using AFM and NOP, for a thin-film magnetic rigid disk. (From Ganti, S. and Bhushan, B. (1995), Generalized fractal analysis and its applications to engineering surfaces, Wear, 180, 17-34. With permission.) TABLE 2.3 Surface Roughness Parameters for a Polished Thin-Film Rigid Disk Scan Size (µm × µm)
σ(nm)
D
C(nm)
1(AFM) 10(AFM) 50(AFM) 100(AFM) 250(NOP) 4000(NOP)
0.7 2.1 4.8 5.6 2.4 3.7
1.33 1.31 1.26 1.30 1.32 1.29
9.8 × 10–4 7.6 × 10–3 1.7 × 10–2 1.4 × 10–2 2.7 × 10–4 7.9 × 10–5
AFM — Atomic force microscope NOP — Noncontact optical profiler
Figure 2.19 presents the structure functions of a thin-film magnetic rigid disk measured using an atomic force microscope (AFM) and noncontact optical profiler (NOP). A horizontal shift in the structure functions from one scan to another arises from the change in the lateral resolution. The D and C values for various scan lengths are listed in Table 2.3. Note that fractal dimension of the various scans is fairly constant (1.26 to 1.33); however, C increases/decreases monotonically with σ for the AFM data. The error in estimation of η is believed to be responsible for the variation in C. These data show that the disk surface follows a fractal structure for three decades of length scales.
2.2.4 Practical Considerations in Measurement of Roughness Parameters 2.2.4.1 Short- and Long-Wavelength Filtering Engineering surfaces cover a broad bandwidth of wavelengths, and samples, however large, often exhibit nonstationary properties (in which the roughness is dependent upon the sample size). Surface roughness is intrinsic; however, measured roughness is a function of the bandwidth of the measurement and thus is not an intrinsic property. Instruments using different sampling intervals measure features with different length scales. Roughness is found at scales ranging from millimeter to nanometer (atomic) scales. A surface is composed of a large number of length scales of roughness that are superimposed on each other. Therefore, on a surface, it is not that different asperities come in different sizes but that one asperity comes in different sizes. Distribution of size and shape of asperities is dependent on the short-wavelength limit or the sampling interval of the measuring instrument. When the sampling interval at which the surface is sampled is reduced, the number of asperities detected and their curvature appear to rise without
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FIGURE 2.20
Modern Tribology Handbook
Sinusoidal profiles with different numbers of sampling points per wavelength.
limit down to atomic scales. This means that asperity is not a “definite object.” Attempts are made to identify a correct sampling interval which yields the relevant number of asperities for a particular application. An asperity relevant for contact mechanics is defined as that which makes a contact in a particular application (contacting asperity) and carries some load. The short-wavelength limit or the sampling interval affects asperity statistics. The choice of shortwavelength limit depends on the answer to the following question: what is the shortest wavelength that will affect the interaction? It is now known that it is the asperities on a nanoscale that first come into contact and plastically deform instantly, and subsequently, the load is supported by the deformation of larger-scale asperities (Bhushan and Blackman, 1991; Poon and Bhushan, 1996). Since plastic deformation in most applications is undesirable, asperities on a nanoscale need to be detected. Therefore, the shortwavelength limit should be as small as possible. The effect of the short-wavelength limit on a roughness profile can be illustrated by a sinusoidal profile represented by different numbers of sampling points per wavelength as shown in Figure 2.20. The waveform of the sinusoidal profile is distorted when the number of sampling points decreases. The profile parameters do not change significantly with sampling points equal to 6 or greater per wavelength. Therefore, the minimum number of sampling points required to represent a wavelength structure may be set to 6, i.e., the optimum sampling interval is λ/6, where λ is the wavelength of the sinusoidal profile. By analogy, the suitable sampling interval should be related to the main wavelength structure of a random profile which is represented by β*. However, β* is a function of the bandwidth of the measurement and thus is not an intrinsic property. It is reasonable to select a sampling interval a fraction of β* measured at the long wavelength limit, say 0.25 β* to 0.5 β* (Poon and Bhushan, 1995a). Figure 2.21 demonstrates how the long wavelength limit, also called the cutoff wavelength or sampling length (size), can affect the measured roughness parameters (Anonymous, 1985). The top profile represents the actual movement of the stylus on a surface. The lower ones show the same profile using cutoff wavelength values of 0.8, 0.25, and 0.08 mm. A small cutoff value would isolate the waviness while a large cutoff value would include the waviness. Thomas (1999) has shown that the standard deviation of surface roughness, σ, will increase with an increase in the cutoff wavelength or sampling length L, as given by the following relation,
σ ∝ L1 2
(2.43)
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FIGURE 2.21 The effect of the cutoff wavelength is to remove all components of the total profile that have wavelengths greater than cutoff value.
Ganti and Bhushan (1995) and Poon and Bhushan (1995a) have reported that σ and other roughness parameters initially increase with L and then reach a constant value because engineering surfaces seem to have a long-wavelength limit. Thus, before the surface roughness can be effectively quantified, an application must be defined. Having a knowledge of the application enables a measurement to be planned and in particular for it to be decided to what bandwidth of surface features the information collected should refer. Features that appear as roughness in one application of a surface may well constitute waviness in another. The long-wavelength limit (which is the same as scan size in many instruments) in contact problems is set by the dimensions of the nominal contact area (Figure 2.22). This is simply to say that a wavelength much longer than the nominal contact area will not affect what goes on inside it. In addition, the longwavelength limit of the surface roughness in the nominal contact area, if it exists, should be obtained. The long-wavelength limit can be chosen to be twice the nominal contact size or the long-wavelength limit of the roughness structure in the nominal contact size, if it exists, whichever is smaller. To provide a basis of instrumentation for roughness measurement, a series of cutoff wavelength values has been standardized in a British standard (BS1134-1972), an ANSI/ASME (B46.1-1985), and an ISO Recommendation (R468). The international standard cutoff values are 0.08, 0.25, and 0.8 mm. The preferred value of 0.8 mm is assumed unless a different value is specified. Note that waviness measurements are made without long-wavelength filtering. Long- and short-wavelength filtering in measuring instruments is most commonly accomplished by digital filtering. For example, in a fast Fourier transform (FFT) technique, the FFT of the raw data is taken,
FIGURE 2.22
Contact size of two moving components of different lengths L1 and L2 on the same rough surface.
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FIGURE 2.23
Modern Tribology Handbook
Transmission characteristics of a profiler with low bandpass and high bandpass filters.
the appropriate frequency contents are removed, and the inverse FFT is taken to obtain the filtered data. However, this technique is slow, and one method commercially used is the finite impulse response (FIR) technique. The FIR technique filters by convoluting the trace data with the impulse response of the filter specification. The impulse response is obtained by taking the inverse FFT of the filter specification. Anonymous (1985) also describes the electronic filtering method for short- and long-wavelength filtering, which is accomplished by passing the alternating voltage representing the profile through an electrical wave filter, such as the standard RC filter. The electronic filtering is generally used to filter out short wavelength electronic noise (low band pass filtering). In some profilers (Talysurf by Rank Taylor Hobson, Leicester, England), a skid on a pickup body is traversed along with the stylus arm (Bhushan, 1996). The skid provides a straight reference datum and provides a long-wavelength filtering which is a function of the size and shape of the skid. Mechanical short-wavelength filtering also results from the design and construction of a measuring instrument. For example in the stylus instrument or the atomic force microscope, the stylus removes certain short wavelengths on the order of the stylus tip radius, which is referred to as lateral resolution of the instrument. The stylus is not able to enter the grooves. As the spacing between grooves increases, the stylus displacement will rise, but once it has become sufficient for the stylus to reach the bottom, there will be a full indication. In a digital optical profiler, lateral resolution is controlled by the physical size of the charge-coupled-device (CCD) image sensors at the microscope objective magnifications. A short wavelength limit, if selected, should be at least twice the lateral resolution of the instrument. For the instrument in which a short-wavelength filter is introduced, the output will tend to fall off above a certain frequency, that is below a certain wavelength, for example, as shown by the dotted curve B in Figure 2.23, even though the stylus continues to rise and fall over the irregularities. Dotted curve C in Figure 2.23 also shows the fall off of instrument output at longer wavelength. Only within the range of wavelengths for which the curve is substantially level will the indication be a measure solely of the amplitude and be independent of wavelength curve A in Figure 2.23. 2.2.4.2 Scan Size After the short-wavelength and long-wavelength limits are selected, the roughness measurement must be made on a length large enough to provide a statistically significant value for the chosen locality. The total length involved is called the measuring length, evaluation length, traversing length, or scan length. In some cases, a length of several individual scan lengths (say five) are chosen (Whitehouse, 1994). In most measurements, scan length is the same as the long-wavelength limit. For two-dimensional measurement, a certain area is measured rather than a length. Wyant et al. (1984) and Bhushan et al. (1985) have suggested that in measurement of a random surface, a scan length equal to or greater than 200 β* should be used.
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FIGURE 2.24 SEM micrograph of a trace made by a stylus instrument showing surface damage of electroless Ni–P coating (stylus material, diamond; stylus radius = 0.1 µm; and stylus load = 10 µN or 1 mg). (From Poon, C.Y. and Bhushan, B. (1995a), Comparison of surface roughness measurements by stylus profiler, AFM and non-contact optical profiler, Wear, 190, 76-88. With permission.)
2.3 Measurement of Surface Roughness A distinction is made between methods of evaluating the nanoscale to atomic scale and microscale features of surface roughness. Physicists and physical chemists require fine-scale details of surfaces and often details of molecular roughness. These details are usually provided using methods such as low-energy electron diffraction, molecular-beam methods, field-emission and field-ion microscopy, scanning tunneling microscopy, and atomic force microscopy. On the other hand, for most engineering and manufacturing surfaces, microscopic methods suffice, and they are generally mechanical or optical methods. Some of these methods can also be used to measure geometrical parameters of surfaces (Bhushan, 1996, 1999). Various instruments are available for the roughness measurement. The measurement technique can be divided into two broad categories: (a) a contact type in which during measurement a component of the measurement instrument actually contacts the surface to be measured; and (2) a noncontact type. A contact-type instrument may damage surfaces when used with a sharp stylus tip, particularly soft surfaces (Figure 2.24). For these measurements, the normal loads have to be low enough so that the contact stresses do not exceed the hardness of the surface to be measured. The first practical stylus instruments were developed by Abbott and Firestone (1933). In 1939, Rank Taylor Hobson in Leicester, England, introduced the first commercial instrument called Talysurf. Today, contact-type stylus instruments using electronic amplification are the most popular. The stylus technique, recommended by the ISO, is generally used for reference purposes. In 1983, a noncontact optical profiler based on the principle of two-beam optical interferometry was developed and is now widely used in the electronics and optical industries to measure smooth surfaces. In 1985, an atomic force microscope was developed which is basically a nano-profiler operating at ultra-low loads. It can be used to measure surface roughness with lateral resolution ranging from microscopic to atomic scales. This instrument is commonly used in research to measure roughness with extremely high lateral resolution, particularly nanoscale roughness. There exists a number of other techniques that have been either demonstrated in the laboratory and never commercially used or used in specialized applications. We will divide the different techniques into six categories based on the physical principle involved: mechanical stylus method, optical methods, scanning probe microscopy (SPM) methods, fluid methods, electrical method, and electron microscopy methods. Descriptions of these methods are presented, and the detailed descriptions of only three — stylus, optical (based on optical interferometry), and AFM techniques — are provided. We will conclude this section by comparing various measurement methods.
2.3.1 Mechanical Stylus Method This method uses an instrument that amplifies and records the vertical motions of a stylus displaced at a constant speed by the surface to be measured. Following is a partial list of commercial profilers: Rank
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Taylor Hobson (UK) Talysurf profilers, Tencor Instruments AlphaStep and P-series profilers, Veeco/Sloan Technology Dektak profilers, Gould Inc. Instruments Division profilers, and Kosaka Laboratory, Tokyo (Japan) profilers. The stylus is mechanically coupled mostly to a linear variable differential transformer (LVDT), an optical or a capacitance sensor. The stylus arm is loaded against the sample and either the stylus is scanned across the stationary sample surface using a traverse unit at a constant speed or the sample is transported across an optical flat reference. As the stylus or sample moves, the stylus rides over the sample surface detecting surface deviations by the transducer. It produces an analog signal corresponding to the vertical stylus movement. This signal is then amplified, conditioned, and digitized (Thomas, 1999; Bhushan, 1996). In a profiler, as shown in Figure 2.25a, the instrument consists of a stylus measurement head with a stylus tip and a scan mechanism (Anonymous, 1996a). The measurement head houses a stylus arm with a stylus, sensor assembly, and the loading system. The stylus arm is coupled to the core of an LVDT to monitor vertical motions. The core of a force solenoid is coupled to the stylus arm and its coil is energized to load the stylus tip against the sample. A proximity probe (photo optical sensor) is used to provide a soft limit to the vertical location of the stylus with respect to the sample. The sample is scanned under the stylus at a constant speed. In high precision, ultra-low load profilers, shown in Figures 2.25b and 2.25c, the vertical motion is sensed using a capacitance sensor, and a precision stage transports the sample during measurements (Anonymous, 1996b). The hardware consists of two main components: a stylus measurement head with stylus tip and a scan mechanism. The stylus measurement head houses a sensor assembly, which includes the stylus, the appropriate sensor electronics and integrated optics, and the loading system. The capacitance sensor exhibits a lower noise, has a lower mass, and scales well to smaller dimensions as compared to LVDTs. The capacitive sensor assembly consists of a stylus arm suspended by a flexure pivot, connected to a sensor vane that extends through the center of a highly sensitive capacitive sensor. Vertical movement of the stylus arm results in movement of the vane, which is registered by the capacitance sensor. The analog signal of the capacitance sensor output is digitized and displayed in a surface roughness map. The entire stylus assembly is mounted on a plate, which is driven by a motor for coarse vertical motion. In order to track the stylus across the surface, force is applied to the stylus. The ability to accurately apply and control this force is critical to the profiler performance. The measurement head uses a wire coil to set a programmable stylus load as low as 0.05 mg. Attached above the stylus flexure pivot is an arm with a magnet mounted to the end. The magnet is held in close proximity to the wire coil, and the coil, when energized, produces a magnetic field that moves the magnet arm. This applied force pushes the stylus arm past its null position to a calibrated force displacement, where the horizontal position of the stylus arm represents zero applied force to the stylus. The force coil mechanism and a sophisticated digital signal processor are used to maintain a constant applied force to the stylus. The flexure pivot allows the stylus to move easily, but its tension affects the applied force to the stylus as the stylus arm is moved through its vertical range. To locally correct for the pivot tensions during roughness measurement for a constant stylus force, the force is calibrated by serving the drive current to the force coil to move the stylus several regularly spaced positions, with the stylus not in contact with a sample (zero stylus force). A table of stylus position vs. current settings is generated. A digital signal processor uses these data to dynamically change the force setting as the roughness measurements are made. The scan mechanism shown in Figure 2.25c, holds the sensor assembly stationary while the sample stage is moved with a precision lead screw drive mechanism. This drive mechanism, called the X drive, uses a motor to drive the lead screw, which then moves the sample stage with guide wires along an optical flat via PTFE skids. The motion is monitored by an optical encoder and is accurate to 1 to 2 µm. The optical flat ensures a smooth and stable movement of the stage across the scan length, while a guide bar provides a straight, directional movement. This scanning of the sample limits the measurement noise from the instrument, by decoupling the stage motion from vertical motions of the stylus measured using the sensor. Surface topography measurements can be acquired with high sensitivity over a 205-mm scan. Three-dimensional images can be obtained by acquiring two-dimensional scans in the X direction while
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ce For
l
Coi
t
gne
Ma
ne
r Va
so Sen
d hiel c S w) i t e agn n vie er M sectio ( Out
lus
Sty
s ate xis r Pl nt) o A s t o Sen pare Piv nce trans a t i ac own Cap (sh
Sample Plate (Theta Plate)
X Leadscrew
Y (3D) Leadscrew
Optically Flat Reference
FIGURE 2.25 Schematics of (a) stylus measurement head with loading system and scan mechanism used in Veeco/Sloan Dektak profilers. (Courtesy of Veeco/Sloan Technology, Santa Barbara, CA.) (b) Stylus measurement head with loading system and (c) scan mechanism used in Tencor P-series profilers. (Courtesy of Tencor Instruments, Milpitas, CA.)
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FIGURE 2.26
Modern Tribology Handbook
Schematic of a diamond conical stylus showing its cone angle and tip radius.
stepping in the Y direction by 5 µm with the Y lead screw used for precise sample positioning. When building a surface map by parallel traversing, it is essential to maintain a common origin for each profile. This can be achieved by a flattening procedure in which the mean of each profile is calculated separately and these results are spliced together to produce an accurate surface map. The surface maps are generally presented such that the vertical axis is magnified by three to four orders of magnitude as compared to the horizontal scan axis. Measurements on circular surfaces with long scan lengths can be performed by a modified stylus profiler (such as Talyround) in which a cylindrical surface is rotated about an axis during measurement. Styli are made of diamond. The shapes can vary from one manufacturer to another. Chisel-point styli with tips (e.g., 0.25 µm × 2.5 µm) may be used for detection of bumps or other special applications. Conical tips are almost exclusively used for microroughness measurements (Figure 2.26). According to the international standard (ISO 3274–1975), a stylus is a cone of a 60° to 90° included angle and a (spherical) tip radius of curvature of 2, 5, or 10 µm. The radius of a stylus ranges typically from 0.1 to 0.2 µm to 25 µm with the included angle ranging from 60° to 80°. The stylus is a diamond chip tip that is braised to a stainless steel rod mounted to a stylus arm. The diamond chip is cleaved, then ground and polished to a specific dimension. The radius of curvature for the submicrometer stylus tip, which is assumed to be spherical, is measured with an SEM, or against a standard. The portion of the stylus tip that is in contact with the sample surface, along with the known radius of curvature, determines the actual radius of the tip with regard to the feature size. The stylus cone angle is determined from the cleave and grind of the diamond chip and is checked optically or against a standard. Maximum vertical and spatial (horizontal) magnifications that can be used are on the order of 100,000× and 100×, respectively. The vertical resolution is limited by sensor response, background mechanical vibrations, and thermal noise in the electronics. Resolution for smooth surfaces is as low as 0.1 nm and 1 nm for rough surfaces for large steps. Lateral resolution is on the order of the square root of the stylus radius. The step height repeatability is about 0.8 nm for a step height of 1 µm. The stylus load ranges typically from 0.05 to 100 mg. Long-wave cutoff wavelengths range typically from 4.5 µm to 25 mm. Short-wave cutoff wavelengths range typically from 0.25 µm to several millimeters. The scan lengths can be typically as high as 200 mm, and for three-dimensional imaging, the scan areas can be as large as 5 mm × 5 mm. The vertical range typically ranges from 2 to 250 µm. The scan speed ranges typically from 1 µm/s to 25 mm/s. The sampling rate ranges typically from 50 Hz to 1 kHz. 2.3.1.1 Relocation There are many situations where it would be very useful to look at a particular section of a surface before and after some experiment, such as grinding or run-in, to see what changes in the surface roughness have occurred. This can be accomplished by the use of a relocation table (Thomas, 1999). The table is bolted to the bed of the stylus instrument, and the specimen stage is kinematically located against it at three points and held in position pneumatically. The stage can be lowered and removed, an experiment of some kind performed on the specimen, and the stage replaced on the table. The stylus is then relocated to within the width of the original profile.
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FIGURE 2.27
85
Distortion of profile due to finite dimensions of stylus tip (exaggerated).
2.3.1.2 Replication Replication is used to obtain measurements on parts that are not easily accessible, such as internal surfaces or underwater surfaces. It is used in compliant surfaces because direct measurement would damage or misrepresent the surface (Thomas, 1999). The principle is simply to place the surface to be measured in contact with a liquid that will subsequently set to a solid, hopefully reproducing the detail of the original as faithfully as a mirror image or a negative. Materials such as plaster of paris, dental cement, or polymerizing liquids are used. The vital question is how closely the replica reproduces the features of the original. Lack of fidelity may arise from various causes. 2.3.1.3 Sources of Errors A finite size of stylus tip distorts a surface profile to some degree (Radhakrishnan, 1970; McCool, 1984). Figure 2.27 illustrates how the finite size of the stylus distorts the surface profile. The radius of curvature of a peak may be exaggerated, and the valley may be represented as a cusp. A profile containing many peaks and valleys of radius of curvature of about 1 µm or less or many slopes steeper than 45° would probably be more or less misrepresented by a stylus instrument. Another error source is due to stylus kinematics (McCool, 1984). A stylus of finite mass held in contact with a surface by a preloaded spring may, if traversing the surface at a high enough velocity, fail to maintain contact with the surface being traced. Where and whether this occurs depends on the local surface geometry, the spring constant to the mass ratio, and the tracing speed. It is clear that a trace for which stylus contact has not been maintained presents inaccurate information about the surface microroughness. Stylus load also introduces error. A sharp stylus even under low loads results in an area of contact so small that the local pressure may be sufficiently high to cause significant local elastic deformation of the surface being measured. In some cases, the local pressure may exceed the hardness of the material, and plastic deformation of the surface may result. Styli generally make a visible scratch on softer surfaces, for example, some steels, silver, gold, lead, and elastomers (Poon and Bhushan, 1995a; Bhushan, 1996). The existence of scratches results in measurement errors and unacceptable damage. As shown in Figure 2.24 presented earlier, the stylus digs into the surface and the results do not truly represent the microroughness. It is important to select stylus loads low enough to minimize plastic deformation.
2.3.2 Optical Methods When electromagnetic radiation (light wave) is incident on an engineering surface, it is reflected either specularly or diffusely or both (Figure 2.28). Reflection is totally specular when the angle of reflection is equal to the angle of incidence (Snell’s law); this is true for perfectly smooth surfaces. Reflection is totally
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FIGURE 2.28 Modes of reflection of electromagnetic radiation from a solid surface, (a) specular only, (b) diffuse only, and (c) combined specular and diffuse. (From Thomas, T.R. (1999), Rough Surfaces, 2nd ed., Imperial College Press, London, U.K. With permission.)
diffuse or scattered when the energy in the incident beam is distributed as the cosine of the angle of reflection (Lambert’s law). As roughness increases, the intensity of the specular beam decreases while the diffracted radiation increases in intensity and becomes more diffuse. In most real surfaces, reflections are neither completely specular nor completely diffuse. Clearly, the relationships between the wavelength of radiation and the surface roughness will affect the physics of reflection; thus, a surface that is smooth to radiation of one wavelength may behave as if it were rough to radiation of a different wavelength. The reflected beams from two parallel plates placed normal to the incident beam interfere and result in the formation of the fringes (Figure 2.29). The fringe spacing is a function of the spacing of the two plates. If one of the plates is a reference plate and another is the engineering surface whose roughness is to be measured, fringe spacing can be related to the surface roughness. We have just described so-called twobeam optical interference. A number of other interference techniques are used for roughness measurement. Numerous optical methods have been reported in the literature for measurement of surface roughness. Optical microscopy has been used for overall surveying, which only provides qualitative information. Optical methods may be divided into geometrical and physical methods (Thomas, 1999). Geometrical methods include taper sectioning and light sectioning methods. Physical methods include specular and diffuse reflections, speckle pattern, and optical interference. 2.3.2.1 Taper-Sectioning Method In this technique, a section is cut through the surface to be examined at a shallow angle θ, thus effectively magnifying height variations by a factor cot θ, and is subsequently examined by an optical microscope.
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FIGURE 2.29
87
Optical schematic of two-beam interference.
The technique was first described by Nelson (1969). The surface to be sectioned has to be supported with an adherent coating that will prevent smearing of the contour during the sectioning operation. This coating must firmly adhere to the surface, must have a similar hardness, and should not diffuse into the surface. For steel surfaces, about 0.5-mm-thick electroplated nickel can be used. The specimen is then ground on a surface grinder at a typical taper angle between 1° and 6°. The taper section so produced is lapped, polished, and possibly lightly etched or heat tinted to provide good contrast for the optical examination. The disadvantages of this technique include destruction of the test surface, tedious specimen preparation, and poor accuracy. 2.3.2.2 Light-Sectioning Method The image of a slit (or a straight edge such as a razor blade) is thrown onto the surface at an incident angle of 45°. The reflected image will appear as a straight line if the surface is smooth, and as an undulating line if the surface is rough. The relative vertical magnification of the profile is the cosecant of the angle of incidence, in this case 1.4. Lateral resolution is about 0.5 µm. An automated system for three-dimensional measurement of surface roughness was described by Uchida et al. (1979). Their system consists of using the optical system to project the incident slit beam and then observing the image with an industrial television camera projected through a microscope; the table for the test surface is driven by a stepping motor. 2.3.2.3 Specular Reflection Methods Gloss or specular reflectance (sometimes referred to as sheen or luster) is a surface property of the material, namely, the refractive index and surface roughness. Fresnel’s equations provide a relationship between refractive index and reflectance. Surface roughness scatters the reflected light, thus affecting the specular reflectance. If the surface roughness σ is much smaller than the wavelength of the light (λ) and the surface has a Gaussian height distribution, the correlation between specular reflectance (R) and σ is described by (Beckmann and Spizzichino, 1963) 2 2 4 πσ cos θi 4 πσ cos θi R = exp − ~ 1− R0 λ λ
(2.44)
where θi is the angle of incidence measured with respect to the sample normal, and R0 is the total reflectance of the rough surface and is found by measuring the total light intensity scattered in all
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FIGURE 2.30 Schematic of a glossmeter. (From Budde, W. (1980), A reference instrument for 20°, 40°, and 85° gloss measurements, Metrologia, 16, 1-5. With permission.)
directions including the specular direction. If roughness-induced, light-absorption processes are negligible, R0 is equal to the specular reflectance of a perfectly smooth surface of the same material. For rougher surfaces (σ ≥ λ/10), the true specular beam effectively disappears, so R is no longer measurable. Commercial instruments following the general approach are sometimes called specular glossmeters (Figure 2.30). The first glossmeter was used in the 1920s. A glossmeter detects the specular reflectance (or gloss) of the test surface (of typical size of 50 mm × 50 mm), which is simply the fraction of the incident light reflected from a surface (Gardner and Sward, 1972). Measured specular reflectance is assigned a gloss number. The gloss number is defined as the degree to which the finish of the surface approaches that of the theoretical gloss standard, which is the perfect mirror, assigned a value of 1000. The practical, primary standard is based on the black gloss (refractive index, n = 1.567) under angles of incidence of 20°, 60°, or 85°, according to ISO 2813 or American Society for Testing and Materials (ASTM) D523 standards. The specular reflectance of the black gloss at 60° for unpolarized radiation is 0.100 (Fresnel’s equation, to be discussed later). By definition, the 60° gloss value of this standard is 1000 × 0.10 = 100. For 20 and 85°, Fresnel reflectances are 0.049 and 0.619, respectively, which are again by definition set to give a gloss value of 100. The glossmeter described by Budde (1980), operates over the wavelength range from 380 to 760 nm with a peak at 555 nm. There are five different angles of incidence that are commonly used — 20°, 45°, 60°, 75°, and 85°. Higher angles of incidence are used for rougher surfaces and vice versa. Glossmeters are commonly used in the paint, varnish, and paper-coating industries (Gardner and Sward, 1972). These are also used in magnetic tapes at 45° or 60° incident angles, depending on the level of roughness (Bhushan, 1996). It is very convenient to measure the roughness of magnetic tape coatings during manufacturing by a glossmeter. The advantage of a glossmeter is its intrinsic simplicity, ease, and speed of analysis. Other than accuracy and reproducibility, the major shortcoming of the gloss measurement is its dependence on the refractive index. Specular reflectance of a dielectric surface for unpolarized incident radiation increases with an increase in the refractive index according to Fresnel’s equations (Hecht and Zajac, 1974),
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R=
(R + R ) 1
2
(2.45a)
2
where
( (
2 2 cos θi − n − sin θi R1 = 2 2 cos θi + n − sin θi
) )
12
12
2
(2.45b)
and
( (
2 2 2 n cos θi − n − sin θi R2 = 2 2 2 n cos θi + n − sin θi
) )
12
12
2
(2.45c)
where n is the refractive index of the dielectric material, θi is the angle of incidence with respect to surface normal, and R1 and R2 are the reflectance in the perpendicular and the parallel to the incident plane, respectively. For θi = 0 (normal incidence), Equation 2.45 reduces to
1− n R= 1+ n
2
(2.46)
From Equations 2.45 and 2.46, we can see that a slight change of refractive index of the surface can change the gloss number. A change in the refractive index can come from a change in the supply of the raw material used in manufacturing the test surface (Fineman et al., 1981), a change in the composition of the surface (Wyant et al., 1984), or the aging of the surface (Alince and Lepoutre, 1980; Wyant et al., 1984). We therefore conclude that use of a glossmeter for roughness measurement is not very appropriate; however, for luster or general appearance, it may be acceptable. 2.3.2.4 Diffuse Reflection (Scattering) Methods Vision depends on diffuse reflection or scattering. Texture, defects, and contamination causes scattering (Bennett and Mattson, 1989; Stover, 1995). It is difficult to obtain detailed roughness distribution data from the scattering measurements. Its spatial resolution is based on optical beam size, typically 0.1 to 1 mm in diameter. Because scatterometers measure light reflectance rather than the actual physical distance between the surface and the sensor, they are relatively insensitive to changes in temperature and mechanical or acoustical vibrations, making them extremely stable and robust. To measure large surface areas, traditional methods scan the roughness of several, relatively small areas (or sometimes just a single scan line) at a variety of locations on the surface. On the other hand, with scatterometers, the inspection spot is quickly and automatically rastered over a large surface. The scattering is sometimes employed to measure surface texture. This technique is particularly suitable for on-line roughness measurement during manufacture because it is continuous, fast, noncontacting, nondestructive, and relatively insensitive to the environment. Three approaches have been used to measure defects and roughness by light scattering. Total Integrated Scatter The total integrated scatter (TIS) method is complementary to specular reflectance. Instead of measuring the intensity of the specularly reflected light, one measures the total intensity of the diffusely scattered
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FIGURE 2.31 Schematic of the total integrated scatter apparatus with a diffuse integrated sphere. (From Stover, J.C., Bernt, M., and Schiff, T. (1996), TIS uniformity maps of wafers, disks and other samples, Proc. Soc. Photo-Opt. Instrum. Eng., 2541, 21-25. With permission.)
light (Bennett, 1978; Stover, 1995). In the first TIS instrument, an aluminized, specular Coblentz sphere (90° integrating sphere) was used (Bennett and Porteus, 1961). Another method, shown in Figure 2.31 uses a high-reflectance diffuse integrated sphere. The incident laser beam travels through the integrated sphere and strikes the sample port at a few degrees off-normal. The specular reflection traverses the sphere again and leaves through the exit port where it is measured by the specular detector, D2. The inside of the sphere is covered with a diffuse white coating that rescatters the gathered sample scatter throughout the interior of the sphere. The sphere takes on a uniform glow regardless of the orientation of the scatter pattern. The scatter signal is measured by sampling this uniform glow with a scatter detector, D1, located on the right side of the sphere. The TIS is then the ratio of the total light scattered by the sample to the total intensity of scattered radiation (both specular and diffuse). If the surface has a Gaussian height distribution and its standard deviation σ is much smaller than the wavelength of light (λ), the TIS can be related to σ as given by Equation 2.41 (Bennett, 1978):
TIS =
2 2 R0 − R 4 πσ cos θi 4 πσ cos θi = 1 − exp − ~ R0 λ λ
(2.47a)
2
4 πσ = , if θi = 0 λ
(2.47b)
Samples of known specular reflectance are used to calibrate the reflected power (R0) signals. The same samples, used to reflect the beam onto the sphere interior, can be used to calibrate the scattered power (R0 – R) measurement signals (Stover et al., 1996). Several commercial instruments, such as a Surfscan (Tencor Instruments, Mountain View, CA), Diskan (GCA Corp., Bedford, MA), and Dektak TMS-2000 (Veeco/Sloan Technology, Santa Barbara, CA) are built on this principle. In these instruments, to map a surface, either the sample moves or the light beam raster scans the sample. These instruments are generally used to generate maps of asperities, defects, or particles rather than microroughness distribution. Diffuseness of Scattered Light This approach relies on the observation that, over a large roughness range, the pattern of scattered radiation becomes more diffuse with increasing roughness. Hence, the goal here is to measure a parameter that characterizes the diffuseness of the scattered radiation pattern and to relate this parameter to the surface roughness. The ratio of the specular intensity to the intensity at one off-specular angle is measured.
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Since this ratio generally decreases with increasing surface roughness, it provides a measure of the roughness itself. Peters (1965) used this technique with the detector held 40° off-specular to determine the roughness of cylindrical parts while they were being ground. His results show a good correlation between the diffuseness and Ra over a range up to 0.3 µm. Using a pair of transmitting/receiving fiber-optic bundles set at different angles, the roughness measurements can be made with optics and instrumentation located remotely (North and Agarwal, 1983). Angular Distributions In principle, the entire angular distribution (AD) of the scattered radiation contains a great deal of information about the surface roughness. In addition to σ roughness, measurements of the angular distributions can yield other surface parameters, such as the average wavelength or the average slope. The angle of incidence is normally held constant and the AD is measured by an array of detectors or by a movable detector and is stored as a function of the angle of scattering. The kind of surface information that may be obtained from the AD depends on the roughness regime. For σ > λ and surface spatial wavelength >λ (rough-surface limit), one is working in the geometrical optics regime, where the scattering may be described as scattering from a series of glints or surface facets oriented to reflect light from the incident beam into the scattering direction. This AD is therefore related to the surface slope distribution, and its width is a measure of the characteristic slope of the surface. As σ and surface spatial wavelength decrease, the distribution becomes a much more complicated function of both surface slopes and heights and is difficult to interpret. For σ < λ (smooth-surface limit), the scattering arises from the diffraction of light by the residual surface roughness viewed as a set of sinusoidal diffraction grating with different amplitudes, wavelengths, and directions across the surface. The intensity of the scattered light is determined by the vertical scale of the roughness and its angular width by the transverse scale; both scales are measured in units of the radiation wavelengths. It can be shown theoretically that the AD should directly map the power spectral density function of the surface roughness (Hildebrand et al., 1974; Stover, 1975; Church, 1979). Figure 2.32 shows a sketch of various texture classes (in the smooth surface limit) on the left and their scattering signatures or power spectral densities on the right. The final sketch in the figure is the sum of the preceding ones, representing a real diamond-turned surface. Such signatures can be easily seen by reflecting a beam laser light from the surface onto a distant screen in a dark room (Church, 1979). Figure 2.33 shows the measured scattered intensity distribution from a diamond-turned gold surface using He–Ne laser light. He used a nonconventional method of scanning the scattering angle and the incident angle simultaneously by holding both the source and the detector fixed and rotating the specimen. The upper curve in Figure 2.33 shows the AD in the plane of incidence and perpendicular to the predominant lay of the surface. The sharp peak in the center is the specular reflection; a broad scattering distribution is due to the random component of the roughness; and a series of discrete lines are due to a periodic component roughness caused by the feed rate of the diamond tool. The lower curve in Figure 2.33 is an AD measured parallel to the lay direction, and it shows another broad distribution characteristic of the random roughness pattern in this direction. In principle, then, one can distinguish between effects due to periodic and random roughness components and can detect the directional property of surfaces. A number of experimental systems have been developed. Clarke and Thomas (1979) developed a laser scanning analyzer system to measure rough surfaces; and scattered light was empirically related to the roughness. In their technique, a laser beam is reflected from a polygonal mirror rotating at high speed onto a surface where it is reflected into a fixed photodetector receiver masked to a narrow slit. The angular reflectance function is produced as the spot scans the strip. At a given moment in any scan, the fixed detector receives light scattered from the single point on the strip which happens at that instant to be illuminated by the deflected beam. The spot diameter can be set from 200 µm upward at a scan width of 623 mm, and the scanning speed is 5 kHz maximum.
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FIGURE 2.32 Texture classes and their scattering signatures when illuminated by coherent light. The final sketch is the sum of the preceding ones representing a real diamond-turned surface. (From Church, E.L. (1979), The measurement of surface texture and topography by differential light scattering, Wear, 57, 93-105. With permission.)
In the measurements reported by Clarke and Thomas (1979), all reflection curves were symmetrical and roughly the same shape irrespective of finish and resembled a Gaussian error curve (similar to the upper curve as shown in Figure 2.33). The surface roughness was found to be related to the width of the curve at half the maximum amplitude. Half-width tends to increase fairly linearly with the arithmetic average roughness and varies as about the fourth power of the mean absolute profile slope (Figure 2.34). Vorburger et al. (1984) developed an AD instrument shown in Figure 2.35 in which a beam from an He–Ne laser illuminates the surfaces at an angle of incidence that may be varied. The scattered light distribution is detected by an array of 87 fiber-optic sensors positioned in a semicircular yoke that can be rotated about its axis so that the scattered radiation may be sampled over an entire hemisphere. They compared the angular scattering data with theoretical angular scattering distributions computed from digitized roughness profiles measured by a stylus instrument and found a reasonable correlation. The three scattering methods described so far are generally limited by available theories to studies of surfaces whose σ are much less than λ. With an He–Ne laser as the light source, the preceding constraint means that these techniques have been used mainly on optical quality surfaces where σ < 0.1 µm. Within that limited regime, they can provide high-speed, quantitative measurements of the roughness of both isotropic surfaces and those with a pronounced lay. With rougher surfaces, AD may be useful as a comparator for monitoring both amplitude and wavelength surface properties. The ultimate vertical
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FIGURE 2.33 Experimental AD scattering spectrum of a diamond-turned surface. The upper curve shows a scan mode perpendicular to the lay direction. The lower curve shows a scan parallel to the lay direction. (From Church, E.L. (1979), The measurement of surface texture and topography by differential light scattering, Wear, 57, 93-105. With permission.)
resolution is 1 nm or better, but the horizontal range is limited to fairly short surface wavelengths. Both the vertical and horizontal ranges can be increased by using long wavelength (infrared) radiation, but there is an accompanying loss of vertical and horizontal resolution. 2.3.2.5 Speckle Pattern Method When a rough surface is illuminated with partially coherent light, the reflected beam consists, in part, of random patterns of bright and dark regions known as speckle. Speckle is the local intensity variation between neighboring points in the overall AD discussed earlier. One means of clarifying the distinction between speckle and the AD is to note that speckle is the intensity noise that is usually averaged out to obtain the AD. The technique used to relate speckle and surface roughness is the speckle pattern correlation measurement. Here, two speckle patterns are obtained from the test surface by illuminating it with different angles of incidence or different wavelengths of light. Correlation properties of the speckle patterns are then studied by recording the patterns. Goodman (1963) and others have shown that the degree of correlation between speckle patterns depends strongly on the surface roughness (σ) (see e.g., Ruffing and Fleischer, 1985). 2.3.2.6 Optical Interference Methods Optical interferometry is a valuable technique for measuring surface shape, on both a macroscopic and microscopic scale (Tolansky, 1973). The traditional technique involves looking at the interference fringes and determining how much they depart from being straight and equally spaced. With suitable computer analysis, these can be used to completely characterize a surface. Bennett (1976) developed an interferometric system employing multiple-beam fringes of equal chromatic order (FECO). FECO are formed when a collimated beam of white light undergoes multiple reflections between two partially silvered surfaces, one of which is the surface whose profile is being measured and the other is a super-smooth reference surface. Based upon a television camera for the detection of the positional displacement of the fringes, this technique has yielded accuracies of σ on the order of 0.80 nm for the measurement of surface profiles. Lateral resolution of this system has been reported to be between 2 and 4 µm, over a 1 mm profile length. Both the differential interference contrast (DIC) and the Nomarski polarization interferometer techniques (Francon, 1966; Francon and Mallick, 1971) are commonly used for qualitative assessment of surface roughness. While those interferometers are very easy to operate, and they are essentially insensitive to vibration, they have the disadvantage that they measure what is essentially the slope of the surface
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FIGURE 2.34 Variation of half-width with (a) average roughness and (b) mean absolute slope: A, milled: B, turned; C, spark eroded; D, shaped; E, ground; F, criss-cross lapped; G, parallel lapped. (From Clarke, G.M. and Thomas, T.R. (1979), Roughness measurement with a laser scanning analyzer, Wear, 57, 107-116. With permission.)
errors, rather than the surface errors themselves. A commercial Nomarski type profiler based on the linearly polarized laser beam is made by Chapman Instruments, Rochester, New York. The Tolansky or multiple-beam interferometer is another common interferometer used with a microscope. The surface being examined must have a high reflectivity and must be in near contact with the interferometer reference surface, which can scratch the surface under test. One of the most common optical methods for the quantitative measurement of surface roughness is to use a two-beam interferometer. The actual sample can be measured directly without applying a highreflectivity coating. The surface-height profile itself is measured. The option of changing the magnification can be used to obtain different values of lateral resolution and different fields of view. Shortwavelength visible-light interferometry and computerized phase-shifting techniques can measure surfaceheight variations with resolutions better than 1/100 of a wavelength of light. The short wavelength of visible light is a disadvantage, however, when measuring large surface-height variations and slopes. If a single wavelength is used to make a measurement and the surface-height difference between adjacent measurement
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FIGURE 2.35 Schematic of angular-distribution scatter apparatus. (From Vorburger, T.V., Teague, E.C., Scire, F.E., McLay, M.J., and Gilsinn, D.E. (1984), Surface roughness studies with DALLAS array for light angular scattering, J. Res. of NBS, 89, 3-16. With permission.)
points is greater than one-quarter wavelength, height errors of multiple half-wavelengths may be introduced. The use of white light, or at least a few different wavelengths, for the light source can solve this height ambiguity problem. Two techniques can extend the range of measurement of surface microstructure where the surface slopes are large. One technique, measuring surface heights at two or more visible wavelengths, creates a much longer nonvisible synthetic wavelength, which increases the dynamic range of the measurement by the ratio of the synthetic wavelength to the visible wavelength. Increases in the dynamic range by factors of 50 to 100 are possible. Another more powerful method uses a white-light scanning interferometer, which involves measuring the degree of fringe modulation or coherence, instead of the phase of the interference fringes. Surface heights are measured by changing the path length of the sample arm of the interferometer to determine the location of the sample for which the white-light fringe with the best contrast is obtained. Vertical position at each location gives the surface height map. Various commercial instruments based on optical phase-shifting and vertical scanning interferometry are available (Wyko Corp., Tucson, AZ; Zygo Corp., Middlefield, CT; and Phase Shift Technology, Tucson, AZ). Next, we describe the principles of operation following by a description of a typical commercial optical profiler. Phase Shifting Interferometry Several phase-measurement techniques (Wyant, 1975; Bruning, 1978; Wyant and Koliopoulos, 1981; Creath, 1988) can be used in an optical profiler to give more accurate height measurements than are possible by simply using the traditional technique of looking at the interference fringes and determining how much they depart from going straight and being equally spaced. One mode of operation used in commercial profilers is the so-called integrated bucket phase-shifting technique (Wyant et al., 1984, 1986; Bhushan et al., 1985). For this technique, the phase difference between the two interfering beams is changed at a constant rate as the detector is read out. Each time the detector array is read out, the time variable phase α(t), has changed by 90° for each pixel. The basic equation for the irradiance of a two-beam interference pattern is given by
[ ( ) ( )]
I = I1 + I2 cos φ x , y + α t
(2.48)
where the first term is the average irradiance, the second is the interference term, and φ(x, y) is the phase distribution being measured. If the irradiance is integrated while α(t) varies from 0 to π/2, π/2 to π, and π to 3π/2, the resulting signals at each detected point are given by
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( ) [ ( ) ( )] B( x , y ) = I′ + I′ [− cos φ ( x , y ) − sin φ ( x , y )] C( x , y ) = I′ + I′ [− cos φ ( x , y ) + sin φ ( x , y )] A x , y = I1′ + I2′ cos φ x , y − sin φ x , y 1
2
1
2
(2.49)
From the values of A, B, and C, the phase can be calculated as
( )
[( (
) ( )) (A(x, y ) − B(x, y ))]
φ x , y = tan−1 C x , y − B x , y
(2.50)
The subtraction and division cancel out the effects of fixed-pattern noise and gain variations across the detector, as long as the effects are not so large that they make the dynamic range of the detector too small to be used. Four frames of intensity data are measured. The phase φ(x, y) is first calculated, by means of Equation 2.50, using the first three of the four frames. It is then similarly calculated using the last three of the four frames. These two calculated phase values are then averaged to increase the accuracy of the measurement. Because Equation 2.50 gives the phase modulo 2π, there may be discontinuities of 2π present in the calculated phase. These discontinuities can be removed as long as the slopes on the sample being measured are limited so that the actual phase difference between adjacent pixels is less than π. This is done by adding or subtracting a multiple of 2π to a pixel until the difference between it and its adjacent pixel is less than π. Once the phase φ(x, y) is determined across the interference field, the corresponding height distribution h(x, y) is determined by the equation
λ h x, y = φ x, y 4π
( )
( )
(2.51)
Phase shifting interferometry using a single wavelength has limited dynamic range. The height difference between two consecutive data points must be less than λ/4, where λ is the wavelength of the light used. If the slope is greater than λ/4 per detector pixel, then height ambiguities of multiples of halfwavelengths exist. One technique that has been very successful in overcoming these slope limitations is to perform the measurement using two or more wavelengths λ1 and λ2 , and then to subtract the two measurements. This results in the limitation in height difference between two adjacent detector points of one quarter of a synthesized equivalent wavelength λeq,
λ eq =
λ1λ 2 λ1 − λ 2
(2.52)
Thus, by carefully selecting the two wavelengths it is possible to greatly increase the dynamic range of the measurement over what can be obtained using a single wavelength (Cheng and Wyant, 1985). While using two wavelength phase-shifting interferometry works very well with step heights, it does not work especially well with rough surfaces. A much better approach is to use a broad range of wavelengths and the fringe modulation or coherence peak sensing approach, whose description follows. Vertical Scanning Coherence Peak Sensing In the vertical scanning coherence peak sensing mode of operation, a broad spectral white light source is used. Due to the large spectral bandwidth of the source, the coherence length of the source is short,
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FIGURE 2.36 Irradiance at a single sample point as the sample is translated through focus. (From Caber, P. (1993), An interferometric profiler for rough surfaces, Appl. Opt., 32, 3438-3441. With permission.)
and good contrast fringes will be obtained only when the two paths of the interferometer are closely matched in length. Thus, if in the interference microscope the path length of the sample arm of the interferometer is varied, the height variations across the sample can be determined by looking at the sample position for which the fringe contrast is a maximum. In this measurement there are no height ambiguities and, since in a properly adjusted interferometer the sample is in focus when the maximum fringe contrast is obtained, there are no focus errors in the measurement of surface texture (Davidson et al., 1987). Figure 2.36 shows the irradiance at a single sample point as the sample is translated through focus. It should be noted that this signal looks a lot like an amplitude modulated (AM) communication signal. The major drawback of this type of scanning interferometer measurement is that only a single surface height is being measured at a time and a large number of measurements and calculations are required to determine a large range of surface height values. One method for processing the data that gives both fast and accurate measurement results is to use conventional communication theory and digital signal processing (DSP) hardware to demodulate the envelope of the fringe signal to determine the peak of the fringe contrast (Caber, 1993). This type of measurement system produces fast, noncontact, true threedimensional area measurements for both large steps and rough surfaces to nanometer precision. A Commercial Digital Optical Profiler Figure 2.37 shows a schematic of a commercial phase shifting/vertical sensing interference microscope (Wyant, 1995). For smooth surfaces, the phase shifting mode is used since it gives subnanometer height resolution capability. For rough surfaces and large steps, up to 500-µm surface height variations, the
CCD Camera
Spectral or Neutral Density Filter
Magnification Selector Microscope Objective
White Light Source Test Surface
Translator Mirau Interferometer
FIGURE 2.37 Optical schematic of the three-dimensional digital optical profiler based on phase-shifting/vertical sensing interferometer, Wyko HD-2000. (From Wyant, J.C. (1995), Computerized interferometric measurement of surface microstructure, Proc. Soc. Photo-Opt. Instrum. Eng., 2576, 122-130. With permission.)
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vertical scanning coherence sensing technique is used, which gives an approximately 3-nm height resolution. The instrument operates with one of several interchangeable magnification objectives. Each objective contains an interferometer, consisting of a reference mirror and beams splitter, which produces interference fringes when light reflected off the reference mirror recombines with light reflected off the sample. Determination of surface height using phase-shifting interferometry typically involves the sequential shifting of the phase of one beam of the interferometer relative to the other beam by known amounts, and measuring the resulting interference pattern irradiance. Using a minimum of three frames of intensity data, the phase is calculated and is then used to calculate the surface height variations over a surface. In vertical scanning interferometry when short coherence white light is used, these interference fringes are present only over a very shallow depth on the surface. The surface is profiled vertically so that each point on the surface produces an interference signal and the exact vertical position where each signal reaches its maximum amplitude can be located. To obtain the location of the peak, and hence the surface height information, this irradiance signal is detected using a CCD array. The instrument starts the measurement sequence by focusing above the top of the surface being profiled and quickly scanning downward. The signal is sampled at fixed intervals, such as every 50 to 100 nm, as the sample path is varied. The motion can be accomplished using a piezoelectric transducer. Low-frequency and DC signal components are removed from the signal by digital high bandpass filtering. The signal is next rectified by square-law detection and digitally lowpass filtered. The peak of the lowpass filter output is located and the vertical position corresponding to the peak is noted. Frames of interference data imaged by a video camera are captured and processed by high-speed digital signal processing hardware. As the system scans downward, an interference signal for each point on the surface is formed. A series of advanced algorithms are used to precisely locate the peak of the interference signal for each point on the surface. Each point is processed in parallel and a three-dimensional map is obtained. The configuration shown in Figure 2.37 utilizes a two-beam Mirau interferometer at the microscope objective. Typically the Mirau interferometer is used for magnifications between 10 and 50×, a Michelson interferometer is used for low magnifications (between 1.5 and 5×), and the Linnik interferometer is used for high magnifications (between 100 and 200x) (Figure 2.38). A separate magnification selector is placed between the microscope objective and the CCD camera to provide additional image magnifications. High magnifications are used for roughness measurement (typically 40×), and low magnifications (typically 1.5×), are used for geometrical parameters. A tungsten halogen lamp is used as the light source. In the phase shifting mode of operation a spectral filter of 40-nm bandwidth centered at 650 nm is used to increase the coherence length. For the vertical scanning mode of operation the spectral filter is not used. Light reflected from the test surface interferes with light reflected from the reference. The resulting interference pattern is imaged onto the CCD array, with a size of about 736 × 480 and pixel spacing of about 8 µm. The output of the CCD array can be viewed on the TV monitor. Also, output from the CCD array is digitized and read by the computer. The Mirau interferometer is mounted on either a piezoelectric transducer (PZT) or a motorized stage so that it can be moved at constant velocity. During this movement, the distance from the lens to the reference surface remains fixed. Thus, a phase shift is introduced into one arm of the interferometer. By introducing a phase shift into only one arm while recording the interference pattern that is produced, it is possible to perform either phase-shifting interferometry or vertical scanning coherence peak sensing interferometry. Major advantages of this technique are that its noncontact and three-dimensional measurements can be made rapidly without moving the sample or the measurement tool. One of the limitations of these instruments is that they can only be used for surfaces with similar optical properties. When dealing with thin films, incident light may penetrate the film and can be reflected from the film-substrate interface. This reflected light wave would have a different phase from that reflected from the film surface. The smooth surfaces using the phase measuring mode can be measured with a vertical resolution as low as 0.1 nm. The vertical scanning mode provides a measurement range to about 500 µm. The field of view depends on the magnification, up to 10 mm × 10 mm. The lateral sampling interval is given by the detector spacing divided by the magnification; it is about 0.15 µm at 50× magnification. The optical
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FIGURE 2.38 ferometer.
99
Optical schematics of (a) Michelson interferometer, (b) Mirau interferometer, and (c) Linnik inter-
resolution which can be thought of as the closest distance between two features on the surface such that they remain distinguishable, is given by 0.61 λ/(NA), where λ is the wavelength of the light source and NA is the numerical aperture of the objective (typically ranging from 0.036 for 1.5× to 0.5 for 40×). In practice, because of aberrations in the optical system, the actual resolution is slightly worse than the optical resolution. The best optical resolution for a lens is on the order of 0.5 µm. The scan speed is typically up to about 7 µm/s. The working distance, which is the distance between the last element in the objective and the sample, is simply a characteristic of the particular objective used. Church et al. (1985) measured a set of precision-machined smooth optical surfaces by a mechanicalstylus profiler and an optical profiler in phase measuring mode. They reported an excellent quantitative agreement between the two profilers. Boudreau et al. (1995) measured a set of machined (ground, milled, and turned) steel surfaces by a mechanical stylus profiler and an optical profiler in the vertical scanning mode. Again, they reported an excellent quantitative agreement between the two profilers.
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Typical roughness data using a digital optical profiler can be found in Wyant et al. (1984, 1986), Bhushan et al. (1985, 1988), Lange and Bhushan (1988), Caber (1993), and Wyant (1995).
2.3.3 Scanning Probe Microscopy (SPM) Methods The family of instruments based on scanning tunneling microscopy (STM) and atomic force microscopy (AFM) are called scanning probe microscopies (SPM). 2.3.3.1 Scanning Tunneling Microscopy (STM) The principle of electron tunneling was proposed by Giaever (1960). He envisioned that if a potential difference is applied to two metals separated by a thin insulating film, a current will flow because of the ability of electrons to penetrate a potential barrier. To be able to measure a tunneling current, the two metals must be spaced no more than 10 nm apart. In 1981, Dr. Gerd Binnig, Heinrich Rohrer, and their colleagues introduced vacuum tunneling combined with lateral scanning (Binnig et al., 1982; Binnig and Rohrer, 1983). Their instrument is called the scanning tunneling microscope (STM). The vacuum provides the ideal barrier for tunneling. The lateral scanning allows one to image surfaces with exquisite resolution, laterally less than 1 nm and vertically less than 0.1 nm, sufficient to define the position of single atoms. The very high vertical resolution of the STM is obtained because the tunnel current varies exponentially with the distance between the two electrodes, that is, the metal tip and the scanned surface. Very high lateral resolution depends upon the sharp tips. Binnig et al. overcame two key obstacles for damping external vibrations and for moving the tunneling probe in close proximity to the sample. An excellent review of this subject is presented by Bhushan (1999b). STM is the first instrument capable of directly obtaining three-dimensional images of solid surfaces with atomic resolution. The principle of STM is straightforward. A sharp metal tip (one electrode of the tunnel junction) is brought close enough (0.3 to 1 nm) to the surface to be investigated (second electrode) that, at a convenient operating voltage (10 mV to 2 V), the tunneling current varies from 0.2 to 10 nA, which is measurable. The tip is scanned over a surface at a distance of 0.3 to 1 nm, while the tunnel current between it and the surface is sensed. Figure 2.39 shows a schematic of one of Binnig and Rohrer’s designs. The metal tip was fixed to rectangular piezodrives Px, Py, and Pz made out of commercial piezoceramic material for scanning. The sample was mounted on either a superconducting magnetic levitation or two-stage spring system to achieve the stability of a gap width of about 0.02 nm. The tunnel current JT is a sensitive function of the
FIGURE 2.39 Principle of the operation of the scanning tunneling microscope. (From Binnig, G. and Rohrer, H. (1983), Scanning tunnelling microscopy, Surf. Sci., 126, 236-244. With permission.)
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101
-Y PZT tube scanner -X
Y
X V
Z
Tip i
Sample
FIGURE 2.40 Principle of operation of a commercial STM; a sharp tip attached to a piezoelectric tube scanner is scanned on a sample.
gap width d, that is, JT ∝ VT exp(–Aφ1/2d), where VT is the bias voltage, φ is the average barrier height (work function), and A ~ 1 if φ is measured in eV and d in Å. With a work function of a few eV, JT changes by an order of magnitude for every angstrom change of h. If the current is kept constant to within, for example, 2%, then the gap h remains constant to within 1 pm. For operation in the constant current mode, the control unit (CU) applies a voltage Vz to the piezo Pz such that JT remains constant when scanning the tip with Py and Px over the surface. At the constant work function φ, Vz(Vx, Vy) yields the roughness of the surface z(x,y) directly, as illustrated at a surface step at A. Smearing of the step, δ (lateral resolution) is on the order of (R)1/2, where R is the radius of the curvature of the tip. Thus, a lateral resolution of about 2 nm requires tip radii of the order of 10 nm. A 1-mm-diameter solid rod ground at one end at roughly 90° yields overall tip radii of only a few hundred nanometers, but with closest protrusion of rather sharp microtips on the relatively dull end yields a lateral resolution of about 2 nm. In situ sharpening of the tips by gently touching the surface brings the resolution down to the 1-nm range; by applying high fields (on the order of 108 V/cm) during, for example, half an hour, resolutions considerably below 1 nm can be reached. There are a number of commercial STMs available on the market. Digital Instruments Inc. introduced the first commercial STM, the Nanoscope I, in 1987. In the Nanoscope III STM for operation in ambient air, the sample is held in position while a piezoelectric crystal in the form of a cylindrical tube scans the sharp metallic probe over the surface in a raster pattern while sensing and outputting the tunneling current to the control station (Figure 2.40) (Anonymous, 1992a). The digital signal processor (DSP) calculates the desired separation of the tip from the sample by sensing the tunneling current flowing between the sample and the tip. The bias voltage applied between the sample and the tip encourages the tunneling current to flow. The DSP completes the digital feedback loop by outputting the desired voltage to the piezoelectric tube. The STM operates in both the “constant height” and “constant current” modes depending on a parameter selection in the control panel. In the constant current mode, the feedback gains are set high, the tunneling tip closely tracks the sample surface, and the variation in the tip height required to maintain constant tunneling current is measured by the change in the voltage applied to the piezo tube (Figure 2.41). In the constant height mode, the feedback gains are set low, the tip remains at a nearly constant height as it sweeps over the sample surface, and the tunneling current is imaged (Figure 2.41). A current mode is generally used for atomic-scale images. This mode is not practical for rough surfaces. A three-dimensional picture [z(x,y)] of a surface consists of multiple scans [z(x)] displayed laterally from each other in the y direction. Note that if atomic species are present in a sample, the different atomic species within a sample may produce different tunneling currents for a given bias voltage. Thus the height data may not be a direct representation of the texture of the surface of the sample. Samples to be imaged with STM must be conductive enough to allow a few nanometers of current to flow from the bias voltage source to the area to be scanned. In many cases, nonconductive samples can be coated with a thin layer of a conductive material to facilitate imaging. The bias voltage and the tunneling
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FIGURE 2.41 Scanning tunneling microscope can be operated in either the constant current or the constant height mode. The images are of graphite in air.
current depend on the sample. The scan size ranges from a fraction of a nanometer each way to about 125 µm × 125 µm. A maximum scan rate of 122 Hz can be used. Typically, 256 × 256 data formats are used. The lateral resolution at larger scans is approximately equal to scan length divided by 256. The standalone STMs are available to scan large samples which rest directly on the sample. The STM cantilever should have a sharp metal tip with a low aspect ratio (tip length/tip shank) to minimize flexural vibrations. Ideally, the tip should be atomically sharp, but in practice, most tip preparation methods produce a tip that is rather ragged and consists of several asperities with the one closest to the surface responsible for tunneling. STM cantilevers with sharp tips are typically fabricated from metal wires of tungsten (W), platinum-iridium (Pt–Ir), or gold (Au) and sharpened by grinding, cutting with a wire cutter or razor blade, field emission/evaporator, ion milling, fracture, or electrochemical polishing/etching (Ibe et al., 1990). The two most commonly used tips are made from either a Pt–Ir (80/20) alloy or tungsten wire. Iridium is used to provide stiffness. The Pt–Ir tips are generally mechanically formed and are readily available. The tungsten tips are etched from tungsten wire with an electrochemical process. The wire diameter used for the cantilever is typically 250 µm with the radius of curvature ranging from 20 to 100 nm and a cone angle ranging from 10 to 60° (Figure 2.42a). For calculations of normal spring constant and natural frequency of round cantilevers, see Sarid and Elings (1991). Controlled geometry (CG) Pt/Ir probes are commercially available (Figure 2.42b). These probes are electrochemically etched from Pt/Ir (80/20) wire and polished to a specific shape which is consistent from tip to tip. Probes have a full cone angle of approximately 15° and a tip radius of less than 50 nm. For imaging of deep trenches (>0.25 µm) and nanofeatures, focused ion beam (FIB) milled CG milled probes with an extremely sharp tip radius ( W(1), we would obtain pr(2) > pr(1), h(2) < h(1), and Q(2) < Q(1). Two bearings: Let us assume, for simplicity, that the two bearings, which operate from a single manifold without flow regulators, are geometrically identical but carry loads W (1) and W (2) > W (1), respectively. The required recess pressures are
(1)
pr =
(1)
(2 )
W W (2 ) < = pr af A af A
At the start of operation the pump delivery pressure is increased from zero and reaches the lower of the lift-off pressures pL(1) = W(1)/Ar, where Ar is the area of the recess. Now that the passage is open for the lubricant, the delivery pressure will drop back to pr(1) and there it will stay. There is no way for the pump to reach pL(2) = W(2)/Ar > pL(1) > pr1, the lift required by pad no. 2, i.e., pad no. 2 will not come into operation at all. (ii) Operation with capillary restrictor. The size of the restrictor to be installed in bearing no. 1 of the previous example must be such that ∆p (1) + pr(1) > pL(2) at the required flowrate Q(1).
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TABLE 11.1 Capillary Restrictors for Hydrostatic Pad dC (cm)
lC (cm)
lC/dC
0.38 0.27 0.18 0.12 0.084 0.069 0.051
1184 302 60 12 2.8 1.3 0.38
3120 1100 333 96 18 17 7.4
Example 1. Hydrostatic Pad Design an annular hydrostatic pad with the following requirements:
W = 44, 500 N , R1 = 6.35 cm, R2 = 12.7 cm, h ≥ 50.8 µm, µ = 3.03 × 10 −2 Pa ⋅ s For this geometry Equation 11.36 yields af = 0.54 and qf = 0.755, so that
pr =
44500 = 1.626 MPa 0.54 × 0.1272 π
(5.08 × 10 ) 1.627 × 10 = 5.3115 × 10 Q = 0.755 −6
3
6
3.03 × 10−2
−6
m3 s
We select a pump that delivers 6.309 cm3/sec. At this flowrate the film thickness is an acceptable
6.309 × 10−6 × 3.03 × 10−2 h= 6 0.755 × 1.626 × 10
13
= 53.80 µm > 50.8 µm
We thus need a pump that delivers pL = 44,500/(0.0635)2 π = 3.5129 MPa at zero flow and 1.626 MPa at Q = 6.31 cm3/s. Assume a supply pressure ps = 2.0684 MPa at Q = 6.309 cm3/s, then from the Hagen–Poisseuille law
( )
lC cm =
(
)
π 2.0684 − 1.626 × 106 −2
128 × 3.03 × 10 × 6.309 × 10
−6
( )
dC4 = 5.68 × 104 × dC4 cm
Using this last equation, for standard capillary inside diameters we construct Table 11.1. Only capillaries with 0.084 < dC < 0.18 are satisfactory, and we choose dC = 0.12 cm and lC = 12.0 cm: as lC/dC > 20, the required length is practical, and dC > 0.0635 cm (clogging). The choice of flow restrictors will influence bearing performance under dynamic conditions. Table 11.2 lists advantages and disadvantages of flow restrictors (rating 1 is best or most desirable).
11.3
Hydrodynamic Lubrication
Hydrodynamic lubrication relies on the relative motion of nonparallel bearing surfaces. To generate positive, i.e., load-carrying, pressure, the film must be convergent in the direction of relative motion
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TABLE 11.2
Advantages/Disadvantages of Flow Restrictors
Compensating Elements
Capillary
Orifice
Valve
Initial cost Cost to fabricate, install Space requirement Reliability Useful life Availability Tendency to clog Serviceability Adjustability
2 2 2 1 1 2 1 2 3
1 3 1 2 2 3 2 1 2
3 1 3 3 3 1 3 3 1
(Figure 11.1). No outside agency is required to create and maintain a load-carrying film, provided that adequate lubricant is made available. Hydrodynamic films are easy to obtain; in fact they often occur even when their presence is deemed undesirable, e.g., in hydroplaning of automobile tires on wet pavement. Prototypes of conformal hydrodynamic bearings are journal bearings and thrust bearings; these bearings might also be called “thick film” bearings. A journal bearing at load per projected bearing area of 1.36 MPa, speed 60 rps, and lubricated with an ASTM Grade 315 oil at 52°C would have a minimum film thickness of the order of 88.4 µm. This film is thick in comparison to film found in counterformal bearings, such as ball and roller bearings. Journal bearings are designed to support radial loads on rotating shafts, while thrust bearings, as their name implies, support axial or thrust loads. Although the mode of lubrication is identical in these two bearing types, their geometry is sufficiently distinct for us to discuss them under separate headings; in journal bearings, in general, the clearance geometry is convergent–divergent, and film rupture occurs in the divergent part. Conventional thrust bearings, on the other hand, are purely convergent and their film remains continuous throughout the clearance. The third main heading of this section introduces the idea of lubricant film instability in the dynamic sense; in most cases of application, the thermomechanical load on the bearing varies with time and, as a result, the bearing surfaces undergo cyclic oscillation that can lead to catastrophic film failure.
11.3.1 Journal Bearings In its most elementary form, a journal bearing is a short, rigid, metal cylinder that surrounds and supports the rotating shaft, as in Figure 11.7. The clearance space between bearing and shaft is filled with a lubricant, usually a petroleum oil. Under zero load and negligible body weight, the rotating journal is concentric with its bearing, but as the external load on the journal is increased, the shaft center sinks below the center of the bearing. For
FIGURE 11.7 Schematic of a full journal bearing. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
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FIGURE 11.8 Shaft trajectory during static loading. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
isothermal operations, somewhat of a rarity in practice, the loading conditions on the shaft can be characterized by a single dimensionless group, the Sommerfeld number S, defined by
S=
µN R P C
2
where N is the rotation and R is the radius of the shaft, C is the radial clearance between bearing and shaft, µ is the viscosity of the fluid, and P is the specific load. The specific load has the definition P = W/LD, where L is the length and D is the diameter of the bearing; note that this definition of P is used even for partial arc bearings, for which the projected bearing area might be less than LD. For an unloaded bearing P → 0 and S → ∞, a weightless shaft runs concentric with its bearing. On increasing the external load or decreasing the speed, i.e., on decreasing S, the journal will move away from its concentric position, the journal trajectory approximating a semicircular arc (Figure 11.8). Under extreme load or vanishing speed, S → 0, metal-to-metal contact occurs at the point where the load line cuts the bearing. In most applications there is considerable heat generation, and the viscosity of the lubricant does not remain uniform throughout the film. In such cases we need more than a single dimensionless group to characterize journal bearing operations. In fact, under nonisothermal conditions the number of characterizing parameters is so large that tabulation of bearing performance becomes impractical. Denote the radial clearance, i.e., the difference in radii between cylinder and shaft, by C as before, the radius of the shaft by Rs and the radius of the cylinder by Rb , so that C = Rb – Rs , then in normal design practice (C/R) = O(10–3). This signifies that the lubrication approximation to Equations 11.1 and 11.2 is valid, and we can employ the Reynolds equation for evaluating bearing performance. The small value of C/R further signifies that the curvature of the film can be neglected to the same order, thus the analysis may be performed in an orthogonal Cartesian coordinate system. The (x,z) plane of this coordinate system lies in the surface of the bearing, so that x is the “circumferential” coordinate and z is parallel to the axis of the shaft. The y coordinate is normal to the “plane” of the bearing, i.e., it points toward the center of the bearing arc, yet to the approximation involved here the y arrays appear parallel to one
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another. Because of the smallness of the clearance, it makes no difference whether we put R = Rs or R = Rb in the definition of the Sommerfeld number. Using plane trigonometry and the binomial expansion (Szeri, 1998), it can be shown that the film thickness between eccentric cylinders is well approximated by the formula
(
h = C + e cos θ = C 1 + ε cos θ
)
(11.46)
where e is the eccentricity, h the film thickness, and θ the angle measured from the line of centers in the direction of shaft rotation. When the load-line, and therefore the line of centers, is not fixed but oscillating, as when there is a rotating out of balance force on the shaft, the film thickness relates to the fixed position through the formula
[ (
h = C + e cos Ξ − φ + ψ
)]
(11.47)
Here φ is the angle between load-line and line of centers, the so-called attitude angle, and ψ defines the load-line relative to the fixed position = 0. Equation 11.47 can be used to evaluate the right-hand side of the Reynolds equation, Equation 11.19, to obtain (Szeri, 1998)
∂ h 3 ∂p ∂ h 3 ∂p ∂h + = 6 Rω + 12 e˙ cos θ + e φ˙ + ω W sin θ ∂x µ ∂x ∂z µ ∂z ∂x
[
(
)
]
(11.48)
Here ω and ωW = dψ/dt are the angular frequencies of the shaft and the load vector, respectively. Equation 11.48 is only an approximation to the governing equations of lubricant flow, good to order C/R · · φ, provided that e, and ωW are of the same order of magnitude as ω or smaller. Though Equation 11.48 was arrived at through simplification of the full nonlinear equations, Equations 11.1 and 11.2, its solution is still difficult to obtain except in numerical form. For this reason, before the advent of high-speed computing Equation 11.48 was further simplified to make it amenable to analytical solutions. These simplifications, known as the short-bearing and the long-bearing approximations to the Reynolds equation, must be used with great caution, however, as they may yield incorrect performance parameter values. Before discussing these approximations to Equation 11.49 we shall make the equation nondimensional. The Reynolds equation is nondimensionalized via the substitutions 2
R L x = Rθ, z = z , h = CH = C 1 + ε cos θ , p = µN p 2 C
(
)
(11.49)
· Assuming that e· = φ = ωW = 0 in Equation 11.48, the nondimensional form of the Reynolds equation, valid for journal bearings under static loading, is 2
∂ 3 ∂p D ∂ 3 ∂p ∂H H + H = 12π ∂θ ∂θ L ∂z ∂z ∂θ The individual terms on the left-hand side of Equation 11.50 2
D ∂ 3 ∂p ∂ 3 ∂p H and H ∂θ ∂θ ∂z L ∂z
(11.50)
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represent the rate of average (across the film thickness) pressure flow in the circumferential and axial directions respectively, the sum of which is balanced by the shear flow
12π
∂H ∂θ
By the normalizing transformation, Equation 11.49, each of the variable terms of Equation 11.50 are of the same order of magnitude; thus for long-bearings for which (D/L)2 → 0 the following approximation is acceptable
d 3 d p dH = 12π H dθ dθ ∂θ
(11.51)
whereas for short-bearings (L/D)2 → 0, and we may approximate Equation 11.50 in the form 2
L ∂H ∂ 3 ∂p H = 12π ∂z ∂z D ∂θ
(11.52)
When solved with zero pressure boundary conditions, the pressure distributions specified by Equation 11.50 or its approximations, Equations 11.51 and 11.52, are 2π-periodic functions, antisymmetric with respect to the position of minimum film thickness, θ = π. They yield negative pressures of the same magnitude as positive pressures. However, unless special care is taken to remove all impurities, liquids cannot withstand large negative pressures and the lubricant film will rupture within a short distance downstream from the position of the minimum film thickness. Though the cavitation zone might be preceded by a short range of subambient pressures, in most performance calculations this region of subambient pressures is disregarded. The boundary condition at film-cavity interface is complicated, particularly when dynamic loading conditions prevail, and is still under investigation. Most computer calculations are based on the so-called Swift–Stieber boundary conditions
p=
∂p = 0, at θ = θcav ∂θ
(11.53)
– that preserve flow continuity at the film-cavity interface. Here θcav = θcav (z) denotes the angular position – of the film-cavity interface. Equation 11.50 also implies that p ≥ 0 everywhere in the film. The Swift–Stieber boundary condition cannot be implemented in the short-bearing approximation, – and only with some difficulty in the long-bearing as the latter is governed by a differential equation in z, approximation. The closest we can come to Equation 11.53 when using the short-bearing approximation is to disregard negative (below ambient) pressures in calculating bearing performance, i.e., assume the film to cavitate at the position of minimum film thickness. The conditions
() p(θ) = 0, p θ ≥ 0,
0≤θ≤π π ≤ θ ≤ 2π
(11.54)
are used extensively for performance calculations in both short-bearing and long-bearing approximations and are known as the Gümbel boundary conditions. We will evaluate bearing performance, for both shortbearing and long-bearing approximations, under the conditions specified in Equation 11.54, but for finite bearings we use the Swift–Stieber conditions, Equation 11.35. Figure 11.9 displays pressure distribution under Sommerfeld, Gümbel, and Swift–Stieber boundary conditions.
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FIGURE 11.9 Journal bearing pressure distribution under (a) Sommerfeld, Gümbel, and (b) Swift–Stieber boundary conditions. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
Bearing performance is calculated from the pressure distribution by substitution into the following formulas Load capacity: The force balance (Figure 11.10)
W cos φ + FR = 0
(11.55)
−W sin φ + FT = 0
where FR and FT are the components of the pressure force along the line of centers and normal to it, respectively, and W is the external load on the shaft, yield
( ) ∫ ∫
Rθcav
( ) ∫ ∫
Rθcav
2
FR ≡ f R LDµN R C = 2
FT ≡ fT LDµN R C =
L 2
−L 2 0 L 2
−L 2 0
p cosθdxdz
(11.56a)
p sinθdxdz
(11.56b)
Equations 11.56 define the he nondimensional force components fR , fT . The Sommerfeld number reemerges here as the inverse of the nondimensional pressure force
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FIGURE 11.10 Journal bearing nomenclature. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.) 2
µN R 2 2 S≡ = f R + fT P C
(
)
−1 2
(11.57)
Attitude angle: The attitude angle, i.e., the angle between the load vector and the line of centers is given by
fT fR
φ = arctan
(11.58)
Friction variable: The friction force exerted on the shaft is found from
C Fµ ≡ c µ W = R
L
∫∫ 0
2 πR
0
τ xy h ( x ) dxdz
(11.59)
where τxyh(x) is the shear stress on the shaft and cµ is the friction variable, which is the conventional friction coefficient scaled with (C/R) to numerically convenient values. Lubricant flow: The rate of inflow can be calculated from
Qi ≡ qi NRLC = 2
()
∫ ∫ u(0, y, z )dydz 2 πR
0
h x
0
where u is given by Equation 11.14 and qi is the dimensionless inflow variable.
(11.60)
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TABLE 11.3
Performance of Short- and Long-Bearings Short-Bearing Approximation (Gümbel condition) 2
Long-Bearing Approximation (Gümbel condition)
Equation for pressure, p
∂p 3 dp L ∂H H = 12π D ∂θ ∂z dz
∂ 3 dp ∂H H = 12π ∂θ dθ ∂θ
Boundary condition
p = pa at z = ±1
p(0) = p(2π) = pi
–
2
Pressure, p
L 1 ∂H 2 6 π z − 1 + pa D H 3 ∂θ
Radial force, fR
L 4πε 2 − D 1− ε 2
Tangential force, fT
π 2ε L D (1 − ε )3 2 2
Attitude angle, φ
π 1 − ε2 arctan 4ε
Sommerfeld number, S
1− ε D L πε π 2 1 − ε 2 + 16ε 2
–
(
)
12πε sin θ(2 + ε cos θ)
(2 + ε )(1 + ε cos θ) 2
2
(
)
−
2
( (
Friction variable, cµ Flow variable, qi
2 π 2S
(1 − ε ) 2
2πε
+ pi
12πε 2
(2 + ε )(1 − ε ) 2
2
6π 2ε
2
2
2
(2 + ε )(1 − ε ) 2
2
12
π 1 − ε2 arctan 2ε 2
) )
2
(2 + ε )(1 − ε ) 6πε 4ε + π (1 − ε ) 2
2
ε sin φ +
2
2
2
4π 2 S 1 − ε2
—
Table 11.3 lists the performance characteristics for both short- and long-bearings. These calculations are based on the Gümbel conditions, Equation 11.54. As the cavitated film does not contribute to load capacity but only to unwanted friction, it serves no useful purpose. This leads to the idea of employing partial arc pads instead of 360°, or full, bearings to support the shaft. Different types of fixed pad partial journal bearings, each of arc β, are shown schematically in Figure 11.11.
FIGURE 11.11 Fixed type journal bearings: (a) full 360° bearing, (b) centrally loaded partial bearing, (c) offset loaded partial bearing (offset parameter α/β). (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R., (Ed.), CRC Press, Boca Raton, FL. With permission.)
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11.3.1.1 Finite Journal Bearings The pressure distribution in a finite journal bearing of length L, diameter D and angular extent β, is governed by the Reynolds equation 2
∂ 3 ∂p D ∂ 3 ∂p ∂H H + H = 12π ∂θ ∂θ L ∂z ∂z ∂θ
(11.61)
–
and the boundary conditions (considering p as gauge pressure)
p = 0 at z = ±1
(11.62a)
p = 0 at θ = θ1, θ1 + β
(11.62b)
If (θ1 + β) > π, Equation 11.61 yields both positive and negative pressures, leading to film rupture as previously discussed. At the film-cavity interface the Swift–Stieber conditions, Equation 11.35, are usually applied. Equation 11.61 and its boundary conditions, Equation 11.62, contain three parameters, (L/D), θ1, and β. The only additional parameter of the problem, ε, appears in the definition of the lubricant film geometry
x H = 1 + ε cos θ = 1 + ε cos θ1 + , θ1 ≤ θ ≤ β R
(11.63)
Thus the journal bearing problem is uniquely characterized by the parameter set
{L D, β, ε, θ } 1
(11.64)
The first two parameters of this set define bearing geometry, while the last two characterize the geometry of the film. Having selected parameter set (11.64), we can find the pressure by solving the system consisting of Equations 11.61, 11.62, and 11.63. The nondimensional lubricant force components are obtained from (note the limits of integration on z)
fR =
1 2
∫∫
θcav
fT =
1 2
1
θcav
1
θ1
0
∫∫ 0
θ1
p cosθdθdz
(11.65a)
p sinθdθdz
(11.65b)
and the attitude angle from
φ = arctan
fT fR
(11.66)
Knowledge of the force components {fR, fT } thus enables us to determine both the magnitude, f =
f R + f T , and the direction, φ, of the load the lubricant film will support under the specified conditions. 2
2
Instead of characterizing the oil-film force this way, however, it has been customary to employ an alternate representation of the Sommerfeld number
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S =1 f
(11.67)
and the offset parameter (α/β)
[ (
α 1 = π − θ1 + φ β β
)]
(11.68)
where α is the position of the load-line relative to the leading edge of the pad (Figure 11.11). As shown above, under isothermal conditions the computational problem is defined by the “design parameters” {L/D, β, ε, θ1}, while the computations yield the “performance, parameters” {L/D, β, S, α/β}. The designer, however, must proceed in an inverse manner, so to speak. (In the following, we drop the parameters L/D and β from the list.) What is known at the design stage are the pad geometry and the performance requirements, i.e., the magnitude and direction of the external load, the shaft speed and the viscosity of the lubricant, and it is easy for the designer to define the couple {S, α/β}; but the designer has no way of determining the couple {ε, θ1} that is required in order to compute the minimum film thickness, often the controlling parameter. Let Ω(ε, θ1) and Ψ(ε, θ1) represent the Sommerfeld number and the offset parameter, respectively, obtained by the analyst at some given {ε, θ1}, and let S and α/β be the values that are requested by the designer. The task for the analyst is then to find that particular {ε, θ1} that yields
( )
S − Ω ε, θ1 = 0
(11.69a)
α − Ψ ε, θ1 = 0 β
(11.69b)
(
)
We can solve this pair of nonlinear equations for the unknowns {ε, θ1} by iteration, e.g., using Newton’s method
∂Ω ∂ε ∂Ψ ∂ε
∂Ω n n −1 ∂θ1 ε( ) − ε( ) Ω − S α , n = 1, 2, 3, … (n ) (n−1) = ∂Ψ θ − θ Ψ − 1 1 β ∂θ1
(11.70)
The performance curves in Figure 11.12, taken from Raimondi and Szeri (1984), are for centrally loaded fixed-pad partial bearings of L/D = 1, β = 160° and various values of the Reynolds number. The turbulent data were obtained from Equation 11.21. Example 2. Journal Bearing Calculate the performance of a centrally loaded partial arc journal bearing given the following data
(
)
β = 2.79rad 160° −3
C R = 2 × 10 D = L = 0.508 m
(
N = 40 sec, ω = 251rad sec ISO VG 32, ρ = 831kg m W = 355.84 kN
3
To start the design process, we assume an effective viscosity
µ = 3.447 × 10−2 Pa ⋅ s ;
ν = 0.4148 cm2 s
)
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FIGURE 11.12 Performance of an (L/D) = 1, β = 160° partial journal bearing: (a) minimum film thickness, (b) position of minimum film thickness, (c) power loss, (d) lubricant inflow, (e) lubricant side flow. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R., (Ed.), CRC Press, Boca Raton, FL. With permission.)
For Reynolds and Sommerfeld numbers, respectively, we obtain
Re = S=
25.4 × 251 × 0.0508 = 781 < 1000, the flow is laminar 0.4148
3.447 × 10−2 × 40 1.3789 × 10
6
(500) = 0.25 2
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FIGURE 11.12 (continued)
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FIGURE 11.12 (continued)
Entering Figure 11.12c, d, and e in succession we find
H = 3.05 × 2π × 355.84 × 103 × 40 × 5.08 × 10−4 = 0.1386 MW Q = 3.2 × 0.254 × 5.08 × 10−4 × 40 × 0.508 = 8.39 × 10−3 m 3 s Qs = 1.32 × 2.6219 × 10−3 = 3.46 × 10−3 m 3 s The temperature rise across the bearing is calculated from a simple heat balance, Equation 11.28,
∆T =
1.386 × 105
(
)
1.39 × 106 8.39 − 3.46 2 × 10−3
= 14.97 C
and, assuming an inlet temperature of Ti = 45 C, yields the operating temperature
Ts = Ti + 0.5 × ∆T = 52.5C On Figure 11.13 plot the point A(52.5, 34.47). Note that 1 Pa · s = 1000 cP. Assume another effective viscosity: µ = 6.8948 × 10–3 Pa · s, v = 0.083 cm2/s. The corresponding performance parameters are
Re = 3904 > 1000, turbulent flow S = 0.05 Q = 8.39 × 10−3 m 3 s
)
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411
FIGURE 11.13 ISO viscosity grade for lubricating oils. Points A, B, and the line drawn through them, refer to Example 2. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Q s = 4.93 × 10−3 m 3 s H = 0.123 MW ∆T = 14.94 C The operating temperature is Ts = 45 + 14.94/2 = 52.47 C, and we plot point B(52.5, 6.9) in Figure 11.13. The line drawn from A to B intersects the ISO VG 32 line at
Ts = 52.5 C and µ s = 1.7 × 10−2 Pa ⋅ s giving the effective temperature and effective viscosity that is consistent with the operating conditions of the bearing under the assumption that a single viscosity can portray bearing performance. The final Reynolds number, Sommerfeld number, and minimum film thickness are
Re = 1583, S = 0.123, hn = 0.4 × 0.0508 = 0.0203 cm 11.3.1.2 Pivoted-Pad Journal Bearings In many applications the bearings are constructed of several identical pads. Multipad bearings, in general, dissipate less energy than full bearings. However, they too are unable to damp out unwanted rotor vibrations. This becomes a problem especially when attempting to operate the rotor in the neighborhood of a system critical speed. For this reason the pads are often pivoted in one point or along a line. Pivoted
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FIGURE 11.14 Preloading of a pad: (1) as machined, (2) preloaded (Ob , Oj , Op , bearing, journal, pad center; rb , rp , R, bearing, pad, journal radius). (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
pads are free to swivel and follow the motion of the rotor, maintaining, at all times of normal operation, a load-carrying lubricant film between rotor and pad. Other advantages of pivoted-pad bearings are that the clearance can be closely controlled by making the pivots adjust radially, thus enabling operation with smaller clearances than considered appropriate for a plain journal bearing, and the pads can be preloaded to achieve relatively high stiffness (important with a vertical rotor). Figure 11.14 shows a pad machined to radius R + C (position 1). Assuming the pad does not tilt, the film thickness is uniform and equal to C, and the pad develops no hydrodynamic force. If the pad is now moved inward the distance (C – C′) into position 2, the film thickness will no longer be uniform; the resulting hydrodynamic force preloads the pad. The degree of preload is indicated by the preload coefficient m = (C – C′)/C, the value of which varies between m = 0 for no preload, to m = 1, for metal-to-metal contact between pad and shaft. Figure 11.15 is a schematic of the geometrical relationships in a pivoted-pad journal bearing. The symbols OB and OJ mark the positions of the bearing center and the instantaneous position of the shaft center. The center of the pad is at Ono when the pad is unloaded and moves to On when it is loaded. The pivot point P is located at angle ψ relative to the vertical load line WB . The eccentricity of the journal relative to the bearing center, OB , is e0 = C′ε0 and its attitude angle φ0. Relative to the instantaneous pad center, OJ , the journal eccentricity is e = Cε and the attitude angle φ, the latter measured from the load line that, by necessity, intersects the pivot P. The radii of journal, pad, and pivot circle are R, O n P , and O B P , respectively. From geometric consideration we have (Lund, 1964)
ε n cos φn = 1 −
C′ − ε 0 cos ψ n − φ0 = m − ε 0 cos ψ n − φ0 C
(
)
(
)
(11.71)
where m is the preload coefficient defined earlier, and the index n refers to the nth pad. Once the position of the journal relative to the bearing is specified, i.e., (ε0,φ0) is given, Equation 11.71 together with the constraint that the load must pass through the pivot are sufficient to determine (εn,φn), the position of the nth pad, n = 1,…,N, relative to the journal. Knowing (εn,φn) makes it possible to calculate individual pad performance that can then be summed to yield the performance characteristics of the bearing. Unfortunately (ε0,φ0) is not known at the design stage, and the best the designer can do is assume ε0 and use the condition that WB is purely vertical to calculate the corresponding φ0. This procedure is, at least, tedious. If, however, the pivots are arranged symmetrically with respect to the loadline, the pads are centrally pivoted and are identical, the journal will move along the load line WB and
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FIGURE 11.15 Geometry of a pivoted-pad journal bearing. (From Lund, J.W. (1964), Spring and damping coefficients for the tilting pad journal bearing, ASLE Trans., 7, 342. With permission.)
φ0 ≡ 0. Figure 11.16 plots performance data for a five-pad pivoted-pad journal bearing (ε′0 = ε0/max(ε0), and for the five-pad bearing max(ε0) from geometry). Example 3 Find the performance for a five-pad tilting-pad bearing for a horizontal rotor, given the following data
( )
β = 1.05 rad 60°
W = 11.12 kN
D = 12.7 cm L = 6.35 cm C = C ′ = 0.0127 cm
µ = 1.379 × 10 −2 Pa ⋅ s v = 0.1658 cm2 s N = 60 r sec
Bearing performance is calculated as follows:
Re =
6.35 × 2π × 60 × 0.0127 = 183 < 1000 laminar 0.1658
(
)
2
S=
1.379 × 10 −2 × 60 6.35 = 0.15 1.3789 × 106 0.0127
hn = 0.26 × 0.127 = 0.0033 cm, from Figure 11.16a H = 3.9 × 2π × 11.12 × 10 3 × 60 × 1.27 × 10 −4 = 2.08 kW , from Figure 11.16b ε ′0 = 0.67, from Figure 11.16c The normalized bearing eccentricity ratio ε′0 = ε0/1.236 will be used to obtain stiffness and damping coefficients.
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FIGURE 11.16 Performance of a five-pad pivoted-pad journal bearing (L/D) = 1, β = 160°: (a) minimum film thickness, (b) power loss, (c) normalized bearing eccentricity ratio. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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415
FIGURE 11.16 (continued)
FIGURE 11.17 Schematic of a plain slider. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
11.3.2 Thrust Bearings Thrust bearings in their most elementary form consist of two inclined plane surfaces in relative motion to one another. The geometry of the bearing surfaces is commonly rectangular, to accommodate a linear motion, or sector shaped, to support a rotation, but other geometries are possible. 11.3.2.1 The Plane Slider A schematic of a fixed plane slider is shown in Figure 11.17. The gradient of the pad surface m = (h2 – h1)/B is used to scale Equation 11.18 and its boundary conditions 2
∂ 3 ∂p B ∂ 3 ∂p x = −1 x + 4 ∂x ∂x L ∂z ∂z
(11.72a)
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TABLE 11.4a –
Nondimensional Oil-Film Force: f = Fh12/µULB 2
x1/(L/B)
8/3
2
4/3
1
2/3
1/2
1/3
0.125 0.20 0.25 0.50 0.60 0.80 1.00 1.25 1.67 2.00 2.50 4.00 5.00 10.0
0.0458 0.0700 0.0825 0.1155 0.1205 0.1238 0.1225 0.1179 0.1081 0.1005 0.0901 0.0676 0.0577 0.0330
0.0424 — 0.0755 0.1047 — — 0.1110 — — 0.0903 — 0.0607 0.0518 0.0296
0.0360 — 0.0623 0.0845 — — 0.0879 — — 0.0715 — 0.0479 0.0409 0.0234
0.0303 0.0441 0.0509 0.0675 0.0697 — 0.0692 0.0662 0.0604 0.0559 0.0500 0.0374 0.0319 0.0182
0.0216 0.0303 0.0344 0.0337 0.0447 0.0448 0.0437 0.0415 0.0377 0.0348 0.0311 0.0232 0.0198 0.0113
0.0161 0.0218 0.0243 0.0298 0.0303 0.0301 0.0291 0.0276 0.0249 0.0230 0.0205 0.0153 0.0130 0.074
0.0099 0.0127 0.0139 — 0.0162 0.0159 0.0152 0.0144 0.0129 0.0119 0.0106 0.0078 0.0067 0.0038
Source: Szeri, A.Z. and Powers, D. (1970), Pivoted plane pad bearings: a variational solution, ASME Trans., Ser. F., 92, 466-72.
(
)
p x, ±1 = 0
( ) (
(11.72b)
)
p x1, z = p x2 , z = 0
(11.72c)
Here
x = Bx , y = mBy , z =
6µU L z, p = p 2 Bm2
(11.72d)
The nondimensional force f is calculated from
f≡
Fh12 = 6 x12 µULB2
1
∫∫ 0
x1 +1
( )
p x , z dxdz x1
(11.73)
Its values at various values of x– 1 and aspect ratio (L/B) are displayed in Table 11.4a. The center of pressure, xp, is calculated from
Fx p = –
∫ ∫ xp(x, z )dxdz L 2
x2
− L 2 x1
(11.74)
–
Let xp = x1 + δ represent the dimensionless coordinate of the center of pressure, i.e., the location of the pivot for a pivoted pad, then δ, the dimensionless distance between pad leading edge and pivot, is given by
δ = − x1 +
6 x12 f
1
∫∫ 0
x1 +1 x1
( )
xp x , z dx dz
(11.75)
Table 11.4b lists pivot position δ at various values of x– 1 and aspect ratio (L/B). The nondimensional flow variable at inlet, x2, is listed in Table 11.4c.
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TABLE 11.4b –
Optimum Pivot Position: δ = (x– p – x–1)
x1/(L/B)
8/3
2
4/3
1
2/3
1/2
1/3
0.125 0.20 0.25 0.50 0.60 0.80 1.00 1.25 1.67 2.00 2.50 4.00 5.00 10.0
0.2900 0.3236 0.3397 0.3876 0.3992 0.4161 0.4281 0.4388 0.4510 0.4576 0.4649 0.4568 0.4811 0.4883
0.2858 — 0.3363 0.3851 — — 0.4264 — — 0.4567 — 0.4763 0.4806 0.4878
0.2766 — 0.3286 0.3793 — — 0.4226 — — 0.4544 — 0.4750 0.4796 0.4868
0.2663 0.3021 0.3196 0.3725 0.3854 — 0.4180 0.4302 0.4440 0.4516 0.4599 0.4736 0.4784 0.4854
0.2452 0.2825 0.3009 0.3579 0.3721 0.3931 0.4081 0.4217 0.4372 0.4456 0.4549 0.4704 0.4758 0.4820
0.2268 0.2649 0.2841 0.3444 0.3597 0.3825 0.3988 0.4137 0.4307 0.4399 0.4503 0.4674 0.4735 0.4780
0.2000 0.2388 0.2588 — 0.3408 0.3662 0.3844 0.4013 0.4207 0.4311 0.4431 0.4631 0.4701 —
Source: Szeri, A.Z. and Powers, D. (1970), Pivoted plane pad bearings: a variational solution. ASME Trans., Ser. F, 92, 466-72.
TABLE 11.4c –
Nondimensional Flow at Inlet: qi = Qx=β /ULh1
x1/(L/B)
8/3
2
4/3
1
2/3
1/2
1/3
0.125 0.20 0.25 0.50 0.60 0.80 1.00 1.25 1.67 2.00 2.50 4.00 5.00 10.0
1.6990 1.3390 1.2059 0.9168 0.8621 0.7879 0.7396 0.6990 0.6550 0.6322 0.6083 0.5702 0.5569 0.5293
1.9662 — 1.3318 0.9717 — — 0.7638 — — 0.6427 — 0.5750 0.5607 0.5310
2.4632 — 1.5588 1.0735 — — 0.8078 — — 0.6621 — 0.5838 0.5676 0.5343
2.8866 2.0402 1.7544 1.1584 1.0558 — 0.8449 0.7791 0.7123 0.6783 0.6439 0.5912 0.5733 0.5370
3.4626 2.3825 2.0156 1.2728 1.1485 0.9905 0.8948 0.8176 0.7393 0.7004 0.6611 0.6014 0.5813 0.5409
3.7744 2.5670 2.1584 1.3360 1.1997 1.0270 0.9229 0.8393 0.7549 0.7130 0.6709 0.6072 0.5859 0.5431
4.0710 2.7362 2.2904 — 1.2789 1.0625 0.9505 0.8608 0.7704 0.7260 0.6809 0.6132 0.5906 0.5454
Source: Szeri, A.Z. and Powers, D. (1970), Pivoted plane pad bearings: a variational solution, ASME Trans., Ser. F, 92, 466-72.
Example 4. Plane Slider Calculate the performance of a fixed-pad slider bearing if the following data are specified
W = 16.013 kN ,
L = 20.32 cm,
U = 30.5 m s ,
µ = 0.04137 Pa ⋅ s
B = 7.62 cm,
From Equation 11.73 we obtain the relationship between the external load and the dimensionless lubricant force
f=
16.013 × 10 3 × h12 = 1.0756 × 107 h12 m 0.04137 × 30.5 × 0.2032 × 0.07622
( )
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For (L/B) = 8/3, the dimensionless force has its maximum value of f = 0.1238 at x– 1 = 0.8, yielding the largest value of the exit film thickness at which this bearing can carry the assigned load.
0.1238 h1 = 7 1.0756 × 10
12
= 1.073 × 10 −4 m
The corresponding surface slope is calculated from
m=
1.073 × 10 −4 = 0.00176 0.8 × 7.62 × 10 −2
The film thickness at inlet is h2 = 0.01073 + 0.00176 × 7.62 = 0.024 cm. The lubricant flow-rate at inlet is Q = 0.7879 × 30.5 × 0.2032 × 1.073 × 10–4 = 524 × 10–6 m3/s and the optimum pivot position is xp – x1 = 0.4161 × 7.62 = 3.12 cm from the trailing edge. 11.3.2.2 Annular Thrust Bearing The fixed-pad slider bearing is the most basic configuration. If the pads are arranged in an annular configuration with radial oil distribution grooves, a complete thrust bearing (Figure 11.18a) is achieved.
FIGURE 11.18 Fixed-pad thrust bearing: (a) arrangement of pads, (b) pad geometry. (From Raimondi, A.A. and Szeri, A.Z. (1984) Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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FIGURE 11.19 Pivoted-pad thrust bearing. Source: Raimondi, A. A. and Szeri, A. Z. 1984. Journal and thrust bearings. (From Raimondi, A.A. and Szeri, A.Z. (1984) Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Approximate performance calculations of this bearing can be made by relating the rectangular slider bearing (width B, length L) to the sector configuration (Figure 11.18b). The pads of pivoted-pad thrust bearings are supported on pivots (Figure 11.19). As the location of the pivot fixes the location of the center of pressure, on loading a pad will swivel until it occupies a position that places the center of pressure over the pivot. While performance of a pivoted pad is identical to that of a fixed pad designed with the same surface slope, the pivoted-type bearing has the advantages of (a) being self-aligning, (b) automatically adjusting pad inclination to optimally match the needs of varying speed and load, and (c) having the capability of operating in either direction of rotation. Theoretically, the pivoted pad can be optimized for all speeds and loads by judicious pivot positioning, whereas the fixedpad bearing can have optimum performance only for one operating condition. Although pivoted-pad bearings involve somewhat greater complexity, standard designs are readily available for large machines. The Reynolds equation, Equation 11.19, in cylindrical coordinates (r,θ) takes the form
∂ 3 ∂p 1 ∂ 3 ∂p ∂h rh + h = 6µωr ∂r ∂r r ∂θ ∂θ ∂θ
(11.76)
This equation can be solved numerically. The resulting performance charts (Figures 11.20a to 11.20f) are conveniently entered on a trial basis with an assumed tangential slope parameter mθ and radial slope parameter mr . Load capacity, minimum film thickness, power loss, flow and pivot location (if pivotedpad type) are then determined and the procedure, if necessary, repeated to find an optimum design. Figures 11.20e and 11.20f provide pivot locations for tilting pad sectors. The thrust bearing charts were prepared for a ratio of outside radius to inside radius of 2 and a sector angular length of 40°. While this angle corresponds to seven sectors to form a full thrust bearing, the results should generally give a preliminary indication of performance of other geometries with the same surface area and mean radius. For other pad geometries see Pinkus and Sternlicht (1961). Example 5. Sector Thrust Pad Calculate thrust pad sector performance when given the following:
(
β = 40°
γ r = 0 no radial tilt
R2 = 13.97 cm
γ θ = 5.82 × 10−4 rad
)
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FIGURE 11.20 Performance charts for fixed or tilting pad sector: (a) load capacity, (b) minimum film thickness, (c) power loss, (d) flow, (e) center of pressure (tangential location), and (f) center of pressure (radial location). (From Raimondi, A.A. and Szeri, A.Z. (1984) Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
R1 = 6.985 cm
µ = 1.379 × 10−2 Pa ⋅ s
hc = 50.8 µm, pad center
N = 50 r sec ω = 314 rad sec
(
)
Calculating first
(
mθ = R1 hc
)
(
)
γ θ = 6.985 × 10 −2 50.8 × 10 −6 × 5.82 × 10 −4 = 0.80
Enter Figures 11.20a to 11.20d with mθ = 0.8 and mr = 0.0
(
) (50.8 × 10 )
W = 0.058 × 6 × 1.379 × 10 −2 × 314 × 0.1397 − 0.06985 hmin = 0.45 × 50.8 × 10 −6 = 22.86 µm
4
−6
2
= 13.9 kN
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FIGURE 11.20 (continued)
(
)
H = 3.04 × 1.379 × 10 −2 × 3142 × 0.1397 − 0.06985
(
)
(
)
2
Qin = 0.86 × 50.8 × 10 −6 × 314 × 0.1397 − 0.06985
4
50.8 × 10 −6 = 1.94 kW 6.6931 × 10 −5 m 3 s
2
Qs = 0.35 × 50.8 × 10 −6 × 314 × 0.1397 − 0.06985 = 2.723 × 10 −5 m 3 s Temperature rise can be calculated from Equation 11.28
∆T =
1.94 × 103
(
)
1.39 × 106 × 66.93 − 27.23 2 × 106
= 26.18 C
This temperature rise implies an inlet temperature of Ti = 57 – 26/2 = 44 C. If this did not match the actual oil inlet temperature, a new effective viscosity would be assumed and the steps repeated. From Figures 11.20e and 11.20f, the pivot must be placed at θp /β = 0.39 and (rp – R1)/(R2 – R1) = 0.56, to achieve the above calculated performance. This performance is also achieved with a fixed-type bearing machined to slopes γθ = 0.0333°, γr = 0.0.
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FIGURE 11.20 (continued)
11.4
Dynamic Properties of Lubricant Films
Assuming rigid supports, rotor response to small excitation, say a force imbalance, will be as shown in Figure 11.21a. (The same curve applies with rolling element bearings.) Such rotors cannot be operated at system critical speeds and become “hung” on a critical speed when attempting to drive through. When
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FIGURE 11.20 (continued)
hydrodynamic bearings are used, the lubricant film adds spring, in addition to the shaft spring in bending, and considerable damping to the system. Two effects may be noticed in the rotor response curve on introducing a hydrodynamic film: (1) the critical speed is lowered, and (2) the vibration amplitude is reduced. The rotor-shaft configuration is reduced to a simple dynamical system of springs and dashpots in Figure 11.21b. The four spring coefficients Kxx , Kxy , Kyx , Kyy and the four damping coefficients Cxx , Cxy , Cyx , Cyy (only some shown in Figure 11.21b) enable linear representation of the incremental oil film force when departure from equilibrium is small.
dFx K xx dF = − K y yx
K xy x C xx − K yy y C yx
C xy x˙ C yy y˙
(11.77)
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FIGURE 11.21 Dynamic properties of lubricant films: (a) effect of oil-film on shaft response, (b) Oil film as a simple dynamic system. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
FIGURE 11.22 Force decomposition in journal bearings, a schematic. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
When departure from equilibrium is “large,” lubricant film behavior is highly nonlinear and the representation depicted in Figure 11.21b and Equation 11.77 becomes inaccurate. With the aid of Equation 11.77, the equations of motion of the journal of mass m with periodic excitation Ω can be written as
mx˙˙ + C xx x˙ + C xy y˙ + K xx x + K xy y = F cos Ωt
my˙˙ + C yy y˙ + C yx x˙ + K yy y + K yx x = F sin Ωt
(11.78)
11.4.1 Linearized Spring and Damping Coefficients In the following we illustrate how the element of the stiffness, K, and damping, D, matrices can be calculated under specified loading conditions (Szeri, 1998). For this, we refer to Figure 11.22, which shows a journal in its equilibrium position, OJs, and displaced from it, OJ , and the nomenclature we shall be using. For small values of ∆φ we refer the instantaneous force components Fr , Ft to the line of centers, R, and perpendicular to it, T, in the journal equilibrium position OJs , thus
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FR = Fr − ∆φFt
(11.79)
FT = ∆φFr + Ft The force increments, when referred to the (R,T) axes, are
( )
∆FR = Fr − FR − ∆φFt 0
(11.80)
( )
∆FT = ∆φFr + Ft − FT
0
The instantaneous force component Fr is a perturbation of (FR)0, its magnitude in equilibrium, and thus can be obtained from a (first-order) Taylor expansion centered at equilibrium
∂F ∂F ∂F ∂F Fr = FR + R de + R dφ + R de˙ + R dφ˙ , 0 ∂e 0 ∂φ 0 ∂e˙ 0 ∂φ˙ 0
( )
(11.81)
Substitution of Equation 11.81, and a similar equation for Ft , into Equation 11.80 yields an equation similar to Equation 11.77, but written with reference to the (R,T) coordinate system defined by the shaft equilibrium position
∂FR dFR ∂ε dF = ∂F T T ∂ε
∂FR ∂FR − FT ∂ε˙ d ε ∂φ + ∂FT ∂F dφ + FR T ∂φ ∂ε˙
∂FR ∂φ˙ dε˙ ∂FT dφ˙ ∂φ˙
(11.82)
The elements of the stiffness and damping matrices in Equation 11.82 will be calculated with the aid of the Reynolds equation, Equation 11.48, but for this we write the latter in terms of the “dynamic” · – – – · pressure pˆ = p/(1 – 2φ/ω), rather than the “static” pressure p (note that pˆ as p φ → 0), 2
∂ 3 ∂pˆ D ∂ 3 ∂pˆ ε˙ ω cos θ H + H = −12πε sin θ + 24 π ∂θ ∂θ L ∂z ∂z φ˙ 1 − 2 ω
(11.83)
Employing the notation, (Equation 11.56)
fR =
1 2
θ1
1
∫∫ 0
0
1 pˆ cos θdθdz , fT = 2
θ1
1
∫∫ 0
pˆ sin θdθdz
0
we write the nondimensionalized force components symbolically as
FR ≡
FT ≡
FR LD
( )
µN R C
2
FT LD
( )
µN R C
2
φ˙ ε˙ ω = 1 − 2 f R ε, φ, ω 1 − 2φ˙ ω
(
φ˙ ε˙ ω = 1 − 2 fT ε, φ, ω 1 − 2φ˙ ω
(
)
(11.84a)
)
(11.84b)
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We are now ready to evaluate the force derivatives required in Equation 11.82
∂f R dFR ∂ε = dFT ∂fT ∂ε
∂f R − ε∂φ ∂fT + ε∂φ
∂f R fT ∂ ε˙ ω ε dε + f R εdφ ∂fT ˙ ε ∂ε ω
2 fR ε d ε˙ ω 2 fT εd φ˙ ω − ε
( ) ( )
−
(11.85)
· The derivatives are evaluated in the static equilibrium position, ε = ε0, φ = φ0, ε· = 0, φ = 0. The nondimensional stiffness and damping matrices are defined, respectively, by
∂f R ∂ε k ≡ ∂fT ∂ε
∂f R − ε∂φ ∂fT + ε∂φ
∂f R ∂ε˙ ω c ≡ ∂fT ˙ ∂ε ω
fT ε fR ε
2 fR ε 2f − T ε
(11.86)
c
(11.87)
−
and are related to their dimensional counterparts through
k=
C R LDµN C
c=
k
2
C R LDµN C
2
Table 11.5 contains the analytic stiffness and damping coefficients for both the long-bearing and the short-bearing approximations, calculated under Gümbel conditions from Long-bearing:
1 1 ε sin θ 2 + ε cos θ pˆ = 12π + 2 2 ε 2 + ε 1 + ε cos θ 1 + ε cos θ
( )(
(
fR = −
) )
12πε 2
(
12π
−
(2 + ε )(1 − ε ) (1 − ε ) 2
fT =
2
2
6π2ε
+
32
(2 + ε )(1 − ε ) ( 2
2
12
−
ε˙ ω 2 ˙ 1 + ε 1 − 2φ ω 1
) ( ) ( 2
˙ 8 π − ε ω 2 2 π 2 + ε 1 − 2φ˙ ω
(
24 πε
)(
2 + ε2 1 − ε2
)(
ε˙ ω 1 − 2φ˙ ω
)(
)
)
)
(11.88a)
(11.88b)
(11.88c)
Short-bearing:
(
)
2 1− z2 D ε˙ ω ε sin θ − 2 cos θ p = 6π L 1 + ε cos θ 1 − 2φ˙ ω
(
(
)
(
)
)
2 2π2 1 + 2ε 2 D 4 πε 2 ε˙ ω = − − f R 2 52 2 2 L 1 − 2φ˙ ω 1− ε 1− ε
(
) (
) (
)
(11.89a)
(11.89b)
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TABLE 11.5 Analytical Stiffness and Damping Coefficients (Gümbel conditions) Long-Bearing
k RR
) (2 + ε ) (1 − ε )
(
−24πε 2 + ε 4 2
2
k RT
2
2
2
(1 − ε ) 2
c RT
c TR
c TT
3 2
3 2
)
2
2
2
8πε
(1 − ε )
2
2
24πε
2
8πε
(1 + ε) (1 − ε )
(1 − ε )
2
2
−12π 2
−
1 2
2
L D
2
L D
2
2π 2
(1 − ε ) 2
2
5 2
2
(2 + ε ) (1 − ε )
2
5 2
) 2π (1 + 2ε ) L − (1 − ε ) D
24πε
2
2
(
(
(2 + ε ) (1 − ε )
2
2
−4πε L 2 D 1− ε 2
8 π − 2 π 2 + ε2
2
L D
3 2
2
2
12π
)
2
(2 + ε ) (1 − ε ) 2
(
2
−12πε 2
)
(1 − ε ) π (1 + 2ε ) L (1 − ε ) D
4
2
(
8πε 1 + ε 2 L 2 3 D 1− ε 2 −π 2
1 2
2
2
c RR
2
(2 + ε ) (1 − ε ) 6 π ( 2 − ε + 2ε ) (2 + ε ) (1 − ε ) 2
k TT
−
−6π 2
2
k TR
Short-Bearing
3 2
L D
2
Source: Szeri, A. Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.
2
D π2ε 8πε + fT = 32 L 1 − ε2 1 − ε2
(
)
(
ε˙ ω 1 − 2φ˙ ω
)( 2
–
(11.89c)
)
–
The stiffness and damping matrices will now be referred to the (ξ, η) coordinate system (Figure 11.22)
dFξ ˙ T ξ T ξ = + QkQ QcQ ˙ η η dFη –
cos φ0 Q= sin φ0
− sin φ0 cos φ0
(11.90)
–
where φ0 is measured– from ξ to e0, and ξ = ξ/C, η = η/C. Denoting the stiffness and damping matrices — – – relative to the new (ξ, η) coordinate system by K and C, respectively, we see from Equation 11.90 that
K = −QkQ T , C = −QcQ T
(11.91)
– – Equation 11.91 proves that the stiffness K and damping C are second-order Cartesian tensors. The – – components relative to (ξ, η) are (Lund, 1964):
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K ξξ = −
∂f ∂f R ∂f ∂f sin 2φ f η cos2 φ − T sin2 φ + T + R − sin φ ∂ε ε∂φ ∂ ε ε ∂φ 2 ε
K ξη = −
∂f ∂f R ∂f ∂f sin 2φ f η cos2 φ + T sin2 φ + T − R + cos φ ∂ε ε∂φ ε ε∂φ ∂ε 2
K ηξ = −
∂f ∂f sin 2φ fξ ∂fT ∂f + cos φ cos2 φ + R sin2 φ + T − R ε∂φ ε ∂ε ε∂φ ∂ε 2
K ηη = −
∂f ∂fT ∂f ∂f sin 2φ fξ cos2 φ − R sin2 φ − R + T − cos φ ε∂φ ∂ε ε ε∂φ ∂ε 2
Cξξ = − Cξη =
(11.92)
∂f R ∂f sin 2φ 2 fξ cos2 φ + T − sin φ ∂ε˙ ω ∂ε˙ ω 2 ε
∂fT ∂f sin 2φ 2 fξ + cos φ sin2 φ − R ε ∂ε˙ ω ∂ε˙ ω 2
Cηξ = −
∂fT ∂f sin 2φ 2 f η cos2 φ − R − sin φ ∂ε˙ ω ∂ε˙ ω 2 ε
Cηη = −
∂f R ∂f sin 2φ 2 f η cos φ sin2 φ − T + ˙ ε ∂ε ω ∂ε˙ ω 2
Here we employed the notation:
fξ fR f = Q f T η Example 6. Linearized Force Coefficients The stiffness and damping properties of the bearing in Example 2 are obtained from Figure 11.23a and 11.23b, respectively, with the eccentricity ratio ε = 1 – hn /C = 0.6.
K xx = 3.0 × 355.84 × 10 3 5.08 × 10 −2 = 21.0 MN cm K xy = 3.0 × 355.84 × 10 3 5.08 × 10 −2 = 21.0 MN cm K yx = −0.38 × 355.84 × 10 3 5.08 × 10 −2 = −2.66 MN cm K yy = 1.5 × 355.84 × 10 3 5.08 × 10 −2 = 10.5 MN cm
( (5.08 × 10 (5.08 × 10 (5.08 × 10
) × 251) = 47.4 kN ⋅ s cm × 251) = 47.4 kN ⋅ s cm × 251) = 50.2 kN ⋅ s cm
C xx = 7.0 × 355.84 84 × 10 3 5.08 × 10 −2 × 251 = 195.4 kN ⋅ s cm C xy = 1.7 × 355.84 × 10 3 C yx = 1.7 × 355.84 × 10 3 C yy = 1.8 × 355.84 × 10 3
−2
−2
−2
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FIGURE 11.23 Linearized force coefficients of a partial arc bearing: (a) stiffness, (b) damping. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
11.4.2 Stability of a Flexible Rotor If a rotor-bearing system is undisturbed, the rotor center will remain in its static equilibrium position. It will move out of that position, however, if disturbed. After the disturbance dies out, the rotor center may return to its static equilibrium position, in which case we have a stable system. If the disturbance does not die out, the rotor center will either orbit around its equilibrium position (limit cycle) or spiral outward until metal-to-metal contact occurs. It is of great practical importance to establish the stability boundaries of a given rotor-bearing system. Figure 11.24 illustrates a weightless shaft supporting a disk of mass M at its mid-span. The shaft, in its turn, is supported by identical, single-pad, journal bearings. The geometric center of the bearing is designated by Ob . Under the static load W = Mg the journal center occupies the position OJs while the mass center moves to OM. The equations of motion are: Rotor:
( −k ( y
) − y ) = My˙˙
−k x2 − x1 = Mx˙˙2 2
1
where k is the stiffness of the flexible rotor (both sides).
2
(11.93)
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FIGURE 11.23 (continued)
Modern Tribology Handbook
Note that the symbol Bxx is used here in place of Cxx to represent damping.
FIGURE 11.24 Schematic of rotor-bearing system. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
Bearing:
( + k( y
) −y )=0
2dFx + k x2 − x1 = 0 2dFy
2
1
(11.94)
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To solve Equations 11.93 and 11.94 assume that the centers of both journal and disk undergo harmonic motion according to
x1 X1 υt x2 X 2 υt y = Y e , y = Y e 1 1 2 2
(11.95)
The exponent υ is a complex quantity, υ = R(υ) + iI(υ), and we have
e υt = e
[ ()
( )]
( ) cos I υ t + i sin I υ t
R υ t
The real part of υ is the damping exponent. Stable motion, R(υ) < 0, is separated from unstable motion, R(υ) > 0, by the neutral state of stability, R(υ) = 0. The imaginary part of υ is the orbiting frequency. Substituting Equation 11.95 into the equations of motion, Equations 11.93 and 11.94, and eliminating the amplitude of rotor motion (X2, Y2), we obtain
α + 2K xx + 2 υC xx 2K yx + 2 υC yx
2K xy + 2 υC xy X1 0 = α + 2K yy + 2 υC yy Y1 0
(11.96)
Here we used the nondimensionalization
( ) {K ,C , k }, C
LDµN R C
{K , ωC , k} = {X ,Y } = C{x , y }, ij
1
ij
1
1
1
2
ij
ij
(11.97)
υ = ωυ, ω = ω N ω ,
and the abbreviation
α=
k υ 2ω 2 υ 2ω 2 + 1
(a real number)
For Equation 11.96 to have nontrivial solutions, the system determinants must vanish. Separating the real and imaginary parts of the determinant we have
α + 2K xx 2K yx
2K xy 2C + υ 2 xx α + 2K yy 2C xy
2C xx
2K xy
2C yx
α + 2K yy
υ+
2C yx =0 2C yy
α + 2K xx
2C xy
2K yx
2C yy
(11.98a)
υ=0
(11.98b)
)
(11.99)
On expansion, Equation 11.98a yields
α=
while Equation 11.98b results in
(
2 K xyC yx + K yxC xy − K yyC xx − K xxC yy
(C
xx
+ C yy
)
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FIGURE 11.25 Stability of a single mass rotor supported by full journal bearings. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
υ =− 2
(
)
(
α 2 + 2 K xx + K yy α + 4 K xx K yy − K xy K yx
(
4 C xxC yy − C yxC xy
)
)
(11.100)
Using the definition for α, we find the instability threshold value of the normalized frequency as
ωc2 =
α υ k −α 2
(
)
(11.101)
In the state of neutral stability, υ is purely imaginary, thus the whirl ratio υwhirl /ω is given by
υ whirl = − υ2 ω
(11.102)
– Figure 11.25 plots the stability parameter M = CMω2/W against the Sommerfeld number S. (Note that both ωc and υ are functions of the stiffness and damping evaluated in the static equilibrium position, which, in turn, is characterized by the Sommerfeld number alone.) Example 7. Rotor-Bearing Stability Determine the bearing-rotor stability for the following conditions:
D = 12.7 cm
µ = 1.38 × 10−2 Pa ⋅ s
L = 6.35 cm
K s ≡ k = 8.76 MN cm
C = 0.0127 cm
2W = 22.24 kN
N = 90 r s
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Calculate
P=
11.12 × 103 = 1.38 MPa 0.127 × 0.0635
S=
1.38 × 10−2 × 90 5002 = 0.225 1.38 × 106 2
L S = 0.0563 D C 1.27 × 10−4 8.76 × 108 = 10 Ks = W 11.12 × 103 1.27 × 10−4 22.24 × 103 2 C 2 × × 2π × 90 = 8.28 Mω = 3 . 9 807 W 11.12 × 10
(
)
Since the point (0.0563, 8.28) lies below the curve for (C/W)Ks = 10, the rotor is free of oil-whip instability. 11.4.2.1 Pivoted-Pad Bearings Calculating linearized force coefficients and stability characteristics of tilting-pad bearings is made difficult by having to take into account the motion of the pads as well as the rotor. The pad assembly method (Shapiro and Colsher, 1977) calculates the stiffness and damping coefficients associated with all degrees of freedom of a single pad over the whole range of eccentricities and stores them according to pivot film thickness. The performance characteristics of the tilting-pad bearing are then calculated in the following steps (viz., Figure 11.15): 1. Calculate individual pad performance data for a wide range of eccentricities and store according to pivot film thickness. 2. Fix position of journal (ψ = 0 for symmetric arrangement of identical, centrally pivoted pads). 3. Calculate film thickness over each pivot from bearing geometry and interpolate from previously stored pad data to obtain pad characteristics at operating conditions. 4. Form vectorial sum of individual pad characteristics to obtain bearing characteristics. Excitation frequency and pad inertia enter the analysis of the rotor-bearing system only when specific pad motion, necessary for the reduction of the results of the pad assembly method to “standard” 4 × 4 stiffness and damping matrices, is postulated. For this illustration of the pad assembly method the rotor is assumed rigid (2 degrees of freedom) and the bearings comprise N pads, each pad assuming its own orientation δi , i = 1, …, N (1 degree of freedom each). The equations of motion are as follows Rotor: N
Mx˙˙ + K xx x + K xy y + C xx x˙ + C xy y˙ +
∑ (K i =1
N
My˙˙ + K yx x + K yy y + C yx x˙ + C yy y˙ +
∑ (K i =1
)
(11.103a)
)
(11.103b)
δ + C xδi δ˙ i = 0
xδi i
δ + C yδi δ˙ i = 0
yδi i
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TABLE 11.6
–∆Fx –∆Fy –∆M1 –∆M2 –∆M3 –∆M4 –∆M5
Stiffness Matrix for a Five-Pad Bearing
∆x
∆y
∆δ1
∆δ2
∆δ3
∆δ4
∆δ5
Kxx Kyx Kδ1x Kδ2x Kδ3x Kδ4x Kδ5x
Kxy Kyy Kδ1y Kδ2y Kδ3y Kδ4y Kδ5y
Kxδ1 Kyδ1 Kδ1δ1 0 0 0 0
Kxδ2 Kyδ2 0 Kδ2δ2
Kxδ3 Kyδ3 0 0 Kδ3δ3 0 0
Kxδ4 Kyδ4 0 0 0 Kδ4δ4 0
Kxδ5 Kyδ5 0 0 0 0 Kδ5δ5
0 0 0
ith pad, i = 1, …, N:
I pδ˙˙ i + K δiδi δ i + Cδiδi δ˙ i + K δi x x + K δi y y + Cδi x x˙ + Cδi y y˙ = 0
(11.104)
The stiffness and damping terms in Equations 11.104 have the definitions
K xx = −
∆Fx ∆F ∆F ∆F ,…, C xx = − x ,…, K xδi = − x ,…, C xδi = − ˙ x ,… ∆x ∆x˙ ∆δ i ∆δ i
K δiδi = −
∆M i ∆M ∆M i ∆M i ,…, Cδiδi = − ˙ i ,…, K δi x = − ,…, Cδi x = − ,… ∆δ i ∆δ i ∆x ∆x˙
The coefficients Kxx,…,CδN y are calculated by perturbing the equilibrium of the shaft while keeping the pads in their respective position of static equilibrium. The coefficients Kxδ1,…,CδNδN, on the other hand, result from constraining the shaft to static equilibrium and perturbing the pitch angle or the angular velocity of the ith pad, i = 1,…,N. Table 11.6 displays the full stiffness matrix for a five-pad bearing. A pad supported on a rigid pivot will track journal vibration by rocking (pitching) about the pivot. However, the influence of pad inertia on dynamic spring and damping coefficients is negligible except when approaching pad resonance, which is characterized by the rotor motion and pad motion being 90° out of phase. Onset of pad resonance can be determined from the critical pad mass parameter, and requires calculation of the pad moment of inertia, Ip , about the pivot. Figures 11.26a through 11.26e plot the performance characteristics for a five-pad journal bearing. The pads are centrally loaded, the preload is zero, and shaft excitation occurs at the running speed. Critical pad mass is calculated from 2
CK ηη CωCηη + CWB M CRIT 1 WB WB = 2 CK ηη 4 πS 2 2 R µDL C WB
2
and is plotted in Figure 11.26e. Example 8. Pivoted-Pad Bearing Performance Find the performance of the five-pad journal bearing, given the following:
(11.105)
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FIGURE 11.26 Performance of five-pad tilting-pad bearing: (a) vertical stiffness, (b) horizontal stiffness, (c) damping (here, B), (d) critical pad–mass parameter. (From Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. With permission.)
( )
β = 1.05 rad 60°
W = 11.12 kN
D = 12.7 cm
µ = 0.0138 Pa ⋅ s
L = 6.35 cm
ρ = 832.3 kg m 3
N = 60 r s
v = 0.1658 cm2 s
C = C ′ = 0.0127 cm
m = 0.0
The Sommerfeld and Reynolds numbers are calculated as
S=
0.0138 × 60 1.3789 × 106
Re =
× 5002 = 0.15
0.0635 × 2π × 60 × 1.27 × 10−4 1.658 × 10−5
(
= 183 < 1000 laminar
)
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FIGURE 11.26 (continued)
Entering Figure 11.16a at S = 0.15 we find hn /C = 0.26. The power loss is obtained from Figure 11.16b, H/(2πWNC) = 3.9, and the normalized bearing eccentricity, ε′ = ε0 /1.2361 = 0.67, from Figure 11.16c. To obtain the linearized force coefficients enter Figures 11.25a through 11.25c at ε′ = 0.67
)
hn = 0.0033 cm
H = 2.08 kW
K xx = 4.4 MN cm
K yy = 2.1 MN cm
C xx = 8.4 kN ⋅ s cm
C yy = 4.7 kN ⋅ s cm
The critical pad mass can be estimated from Figure 11.25d
M crit =
[
0.45 × 0.0138 × 0.127 × 0.0635 × 5002 1.27 × 10−4 × 11.12 × 103
]
2
= 246.7 kg
and the critical pad polar moment of inertia is (Ip)crit = 246.7 × 0.06352 = 0.9946 kg · m2.
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FIGURE 11.26 (continued)
If t is the thickness of the pad, rp + t1 is the radius of the pivot circle, i.e., distance between pivot point and center of pad, and α1, α2 represent the angular distance of pivot from the edges of the bearing. The polar moment of inertia of the pad can be obtained from
(
)
sin α + sin α 1 2 I p = 2rp2 M p 1 + f1 − f2 β
(11.106)
where 2 2 t1 1 t1 1 t 1 t f1 = + + + 2 rp 2 rp 4 rp r p 2 t t 1 t 1 f2 = 1 + 1 + + 2 rp r rp p
1 t 1 + 2 rp
For α1 = α2 = 30° and t = t1 = 0.0 we have rp = D/2 and (Ip)actual = 2rp2 M [1 – 2 sin 30°/1.05] = 3.84 × 10–4M. If the actual pad mass is less than 0.9946/3.84 × 10–4 = 2590 kg, there is no danger of pad resonance.
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FIGURE 11.26 (continued)
11.5
Elastohydrodynamic Lubrication
Elastohydrodynamic lubrication (EHL) is the name given to hydrodynamic lubrication when applied to solid surfaces of low geometric conformity that deform elastically. In bearings utilizing this mode of lubrication, the pressure and film thickness are of order 1 GP and 1 µm, respectively — under such conditions, conventional lubricants exhibit material behavior distinctly different from their bulk properties at normal pressure. In fact, without taking into account the viscosity–pressure characteristics of the liquid lubricant and the elastic deformation of the bounding solids, hydrodynamic theory is incapable of explaining the existence of continuous lubricant films in highly loaded gears and rolling contact bearings. The principal features of EHL contacts are: (1) the film thickness is nearly uniform over the contact zone, but displays a sudden decrease just upstream of the trailing edge, (2) the pressure distribution curve follows the Hertzian ellipse over most of the contact zone, but a sharp second pressure maximum manifests itself at high speeds and light loads (Figures 11.27 and 11.28). The principal variable of interest in EHL lubrication is the minimum film thickness, but to estimate this we need simultaneous solutions of the Reynolds equation, the equations of elasticity, and the viscosity–pressure relationship of the lubricant. Contact mechanics has been discussed in detail elsewhere in this handbook; here we list only formulas required in our sample calculations of minimum film thickness.
11.5.1 Contact Mechanics When two convex, elastic bodies come into contact under zero load, they touch along a line (e.g., cylinder on a plane) or in a point (e.g., two spheres). However, on increasing the normal contact load, the bodies
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FIGURE 11.27 Pressure and film thickness in EHL contact for (a) steel and mineral oil and (b) bronze and mineral – oil under high load, p = p/E′, H = h/R. (From Dowson, D. and Higginson, G.R. 1960. Effect of material properties on the lubrication of elastic rollers, J. Mech. Eng. Sci., 2, 188-94. Reprinted by permission of the Council of the Institution of Mechanical Engineers.)
deform to yield small, though finite, areas of contact, ensuring finiteness of the surface stresses. The shape of this finite contact zone is an infinite strip for nominal line contact, and an ellipse for nominal point contact. To facilitate further discussion, we replace our bodies in the neighborhood of the point of contact by ellipsoids that have the same principal curvatures, r1x, r1y , and, r2x, r2y , as bodies 1 and 2, respectively. The principal relative radii of curvature, Rx, Ry , are specified by
1 1 1 = + , Rx r1 x r2 x
1 1 1 = + Ry r1 y r2 y
The contours of constant gap h between the undeformed surfaces are the ellipses
x2 2hR x
2
+
y2 2hR y
2
=1
(11.107)
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FIGURE 11.28 Pressure and film thickness in EHL contact for (a) steel-mineral oil and (b) bronze-mineral oil – under low load, p = p/E′, H = h/R. (From Dowson, D. and Higginson, G.R. 1960. Effect of material properties on the lubrication of elastic rollers, J. Mech. Eng. Sci., 2, 188-94. Reprinted by permission of the Council of the Institution of Mechanical Engineers.)
the ratio of whose axes are given by (Ry /Rx)1/2. When pressed together, the bodies deform in the neighborhood of the point of their first contact, and touch over a finite area. Though the contact area also has the shape of an ellipse, the ratio of whose semi axes, κ = b/a, depends on (Ry /Rx)1/2 alone, κ = (Ry /Rx)1/2 only in the limit (Ry /Rx) → 1. The ratio of the semi axes, κ, is called the ellipticity parameter; it can be calculated from the approximate formula
R κ ≈ α r2 π , α r = y Rx
(11.108a)
The elastic deflection of the surfaces δ is given by (Harris, 1991) 2 9 w δ = F 2ER πκE ′
1 3
where the composite modulus, E′, and the composite radius of curvature, R, are defined by
(11.108b)
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TABLE 11.7 Parameters Employed in EHL Design Formulas Type of Contact
Parameter Film Thickness, H Load, W Speed, U Materials, G Ellipticity, κ
Point
Line
h/Rx w/Rx2 E′ µoV/E′Rx αE′ b/a
h/Rx w/RxLE′ ˜ ′R x µ0u/E αE′ —
u˜ = (u1 + u2)/2, V = (u2 + v2)1/2
1 1 1 − v12 1 − v22 = + , E ′ 2 E1 E2
1 1 1 = + R Rx Ry
The functions F and E are elliptic functions of αr that can be conveniently approximated by the formulas
π E ≈ 1 + − 1 α r , 2
F≈
π π + − 1 ln α r 2 2
11.5.2 Dimensional Analysis The EHL problem is characterized by such a multitude of independent parameters that tabulation of EHL solutions is impractical. The number of these parameters can, however, be significantly reduced through an application of dimensional analysis. Assuming pressure dependence of lubricant viscosity in the form µ = µo exp(αp), dimensional analysis of the EHL problem yields
(
)
Φ H , U , W , G, κ = 0
(11.109)
For the two types of contacts, viz., nominal line and nominal point, the parameters in Equation 11.109 have somewhat differing definitions, as shown in Table 11.7. We also note that the ellipticity parameter κ does not appear in Equation 11.109 when application is to line contacts (Arnell et al., 1991; Hamrock and Dowson, 1981). Although we have reduced the number of independent variables through application of dimensional analysis, the film thickness variable H is still dependent on four nondimensional groups U, W, G, and κ, and tabulation of H is still a formidable task. However, with little sacrifice to accuracy of representation, the number of nondimensional groups involved in determining the film thickness can be further reduced by employing another set of nondimensional groups, constructed by combining the elements of the sets in Table 11.7. The new parameters, gH , gE , gV , and κ have the added advantage that they are easily identified with the main characteristics of EHL: they represent film thickness, deviation from isoviscosity, deviation from rigidity, and the geometry of the contact: 1. gV = 0, gE = 0, Rigid – Isoviscous Regime: The pressure is low enough to leave the viscosity unaltered; neither does it cause significant elastic deformation of the surfaces. This is the condition encountered in hydrodynamic journal and thrust bearings and in lightly loaded counterformal contacts. 2. gV ≠ 0, gE = 0, Rigid — Piezoviscous Regime: The pressure is high enough to effectively change the lubricant’s viscosity (for certain types of lubricants) from its inlet value, yet not as high as to initiate significant elastic deformation in the bearing material.
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3. gE ≠ 0, gV = 0, Elastic — Isoviscous Regime: Characterized by significant elastic deformation but the pressure is not high enough to affect the viscosity of the particular lubricant employed (also, soft EHL). 4. gE ≠ 0, gV ≠ 0, Elastic — Piezoviscous Regime: The elastic deformation of the surfaces can be orders of magnitude larger than the thickness of the film and the lubricant viscosity orders of magnitude higher than its bulk value (also, hard EHL). The dimensionless groups gH , gE, gV , and κ are not formed identically for line and point contacts and will be listed separately. 2
W gH = H U GW 3 gV = 2 U W gH = H U W 3 2G gV = 1 2 U
0.636 R κ = 1.0339 y Rx g E = W 8 3U 2
gE =
nominal point contact
(11.110)
nominal line contact
(11.111)
W U1 2
We now have the relationship
(
g H = Ψ g V , g E ,κ
)
(11.112)
in place of Equation 11.109, and the task is to find the function Ψ(gV , gE , κ) over practical ranges of its arguments (in nominal line contact, drop κ from the list). This is accomplished by solving the EHL problem for a number of inputs (gV , gE , κ) and then curve fitting to the surface gH = Ψ(gV , gE , κ) in fourdimensional parameter space. For a nominal line contact, for example, the EHL problem is defined by a system composed of the following equations and boundary conditions: 1. Reynolds equation and its boundary condition:
h−h dp = 12µu˜ 3 o dx h p = 0 at x = xi p = 0,
dp = 0 at x = xo dx
2. Viscosity–pressure correlation of Roeland (z is a material parameter):
µ = exp ln µ 0 + 9.67
(
)−1 + (1 + 5.1 × 10 p) −9
z
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3. Lubricant density–pressure correlation of Dowson and Higginson (p in MPa):
0.6 × 10−3 p ρ = ρo 1 + −3 1 + 1.7 × 10 p 4. Elastic deformation:
()
h x = hw +
x2 2 − 2Rx πE ′
∫ () ( ) x0
2
p s ln x − s ds
xi
5. Force balance (w′ is the external load)
∫ p(x )dx x0
w′ =
xi
The various lubrication regimes are depicted in Figures 11.29 and 11.30.
11.5.3 Film-Thickness Design Formulas Nominal Line Contact (Arnell et al., 1991) 1. Rigid-Isoviscous regime: gH = 2.45 2. Rigid-Piezoviscous regime: gH = 1.05 gV2/3 3. Elastic-Isoviscous regime: gH = 2.45 gE0.8 4. Full EHL regime: gH = 1.654 gV0.54 gE0.06
(11.113)
Nominal Point Contact (Hamrock and Dowson, 1981) 2
α 1. Rigid-Isoviscous regime: g H = 128α r λ2b 0.131 tan −1 r + 1.683 , λ b = 1 + 2 3α r 2
[
2. Rigid-Piezoviscous regime: g H = 141g V0.375 1 − e −0.0387α r
[
] ]
(
)
−1
(11.114)
3. Elastic-Isoviscous regime: g H = 8.70 g E0.67 1 − 0.85e −0.31κ
[
4. Full EHL regime: g H = 3.42 g V0.49 g E0.17 1 − e −0.68κ
]
11.5.4 Minimum Film Thickness Calculations Example 9. Nominal Line Contact (Table 11.8) Cylindrical roller bearing geometry is depicted in Figure 11.31. Stribeck’s formula calculates the load on the most heavily loaded roller as
wmax =
4w = 4.8kN n
The radii of curvature at contact on the inner and outer race, respectively, are
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10000
gh = 500 gh = 300 gh = 200
1000
gh = 100 gh = 70
Rigid piezoviscous u ti c c o a s is El zov e pi
Viscosity parameter gv
gh = 50 gh = 30
100
s
gh = 20 gh = 10 10
gh = 7
gh = 5
a El
st
ic
i
us co is v so
1.0 Rigid isoviscous
gh = 4.9 0.1 0.1
1.0
10
100
10,000
Elasticity parameter ge
FIGURE 11.29 Map of lubrication regimes for nominal line contact. (From Arnell, R.D., Davies, P.B., Halling, J., and Whomes, T.L. (1991), Tribology Principles and Design Applications, Springer Verlag. With permission.)
1 1 1 5 = + = Rx , i 0.08 0.032 0.032
1 1 1 5 = − = Rx , o 0.08 0.048 0.048
yielding Rx,i = 0.0064 m, and Rx,o = 0.0096 m. The effective modulus E′ and the pitch diameter de are
E′ =
2 1− v 1− v + E1 E2 2 1
2 2
= 228 GPa,
de =
d0 + di = 0.08 m 2
Assuming pure rolling, the surface velocity for cylindrical rollers is calculated from (Hamrock, 1991)
u˜ =
ω i + ω 0 × de2 − d 2 4de
= 10.061 m s
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FIGURE 11.30 Map of lubrication regimes for nominal point contact, (a) κ = 1, (b) κ = 3, (c) κ = 6. (From Hamrock, B.J. and Dowson, D. (1981), Ball Bearing Lubrication, John Wiley & Sons. With permission.)
Calculation will be performed for the inner-race contact alone. The relevant parameters are
U=
µ 0u˜ 0.01 × 10.061 = 6.895 × 10−11 = 11 E ′Rx , i 2.28 × 10 × 0.0064
W=
wmax 4800 = = 2.0559 × 10−4 11 E ′LRx , i 2.28 × 10 × 0.016 × 0.0064
G = αE ′ = 2.2 × 10−8 × 2.28 × 1011 = 5.016 × 103 The effects of viscosity change and elastic deformation are indicated by the parameters
gV =
W 2 3G = 1.7804 × 103 , U1 2
gE =
W = 24.759 U1 2
The point (gV , gE) characterizing conditions at the inner contact can be plotted in Figure 11.29, showing that full EHL conditions apply. Thus the minimum film thickness calculations are
g H = 1.6549 g V0.54 g 0E.06 = 114.15
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FIGURE 11.30 (continued)
U H min = g H = 3.8284 × 10−5 W hmin = Rx , i H min = 0.245 µm Example 10. Nominal Point Contact (Table 11.9) Spherical roller bearing geometry is depicted in Figure 11.32. The inner-race contact calculations are as follows. The pitch diameter is
de =
(d + d ) = 0.065 m o
e
2
and the equivalent radii and curvature are
Rx = Ry =
(
d de − d cos β 2de
) = 0.00511 m
rd i = 0.165 m 2ri − d
1 1 1 = + = 201.76 R Rx Ry
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FIGURE 11.30 (continued)
TABLE 11.8 Problem
Data for Nominal Line Contact
Inner-race diameter Outer-race diameter Roller diameter Roller axial length No. Rollers per bearing Radial load per roller Inner-race angular velocity Outer-race angular velocity Absolute viscosity Viscosity–pressure coefficient Elastic modulus (rollers, races) Poisson’s ratio
di = 0.064 m do = 0.096 m d = 0.016 m l = 0.016 m n=9 w = 10.8 kN ωi = 524 rad/s ωi = 0 µ0 = 0.001 Pa · s α = 2.2 × 10–8 Pa–1 E = 207.5 GPa v = 0.3
yielding R = 4.956 × 10–3 m, αR = RY/Rx = 32.29, and an ellipticity parameter
κ = α r2 3 = 9.1348
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FIGURE 11.31 Schematic of a cylindrical roller bearing. (From Szeri, A.Z. (1998) Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
TABLE 11.9 Problem
Date for Nominal Point Contact
Inner-race diameter Outer-race diameter Ball diameter No. of balls per bearing Inner-groove radius Outer-groove radius Contact angle Radial load Inner-race angular velocity Outer-race angular velocity Absolute viscosity Viscosity–pressure coefficient Modulus of elasticity Poisson’s ratio
di = 0.052291 m do = 0.077706 m d = 0.012700 m n=9 ri = 0.006604 m ro = 0.006604 m β=0 wz = 8.9 kN ωi = 400 rad/s ωo = 0 µ0 = 0.04 Pa · s α = 2.3 × 10–8 Pa–1 E = 200 GPa v = 0.3
The approximate formulae for the elliptic integrals give
π E = 1 + − 1 α r = 1.0177 2 F=
π π + − 1 ln α r = 3.5542 2 2
Using E′ = 219.8 MPa for effective modulus and Stribeck’s estimate for the maximum load
wmax = the deformation is estimated from
5w z = 4.944 kN n
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FIGURE 11.32 Schematics of a ball bearing. (From Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press. With permission.)
2 9 wmax δ=F 2ER πκE ′
13
= 29.087 µm
Assuming pure rolling, the surface velocity is calculated from (Hamrock, 1991)
u˜ =
wo − wi de2 − d 2 4de
= 6.252 m s
and the design parameters are
U=
µ 0u˜ 0.04 × 6.252 = 2.227 × 10−10 = E ′Rx 2.198 × 1011 × 5.11 × 10−3
G = αE ′ = 2.3 × 10−8 × 2.198 × 1011 = 5.055 × 103 W=
wmax E ′Rx2
=
4944.0
(
2.198 × 10 × 5.11 × 10 11
−3
)
2
= 8.6141 × 10−4
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The minimum film thickness variable is
[
g H = 3.42 g V0.49 g E0.17 1 − e −0.68κ
]
(11.115)
Substituting
GW 3 g V = 2 = 6.5149 × 1013 U g E = W 8 3U 2 = 1.3545 × 1011 into Equation 11.115 we find
g H = 1.5645 × 109 U2 H = g H = 1.0457 × 10−4 W and
hmin = rx H = 0.00511 × 1.0457 × 10−4 = 0.5345 µm
References Arnell, R.D., Davies, P.B., Halling, J., and Whomes, T.L. (1991), Tribology Principles and Design Applications, Springer-Verlag, New York. Dowson, D. and Higginson, G.R. (1960), Effect of material properties on the lubrication of elastic rollers, J. Mech. Eng. Sci., 2, 188-94. Hamrock, B.J. (1991), Fundamentals of Fluid Film Lubrication, NASA Reference Publication 1255. Hamrock, B.J. and Dowson, D. (1981), Ball Bearing Lubrication, John Wiley & Sons, New York. Harris, T.A. (1991), Rolling Bearing Analysis, John Wiley & Sons, New York. Kaufman, H.N., Szeri, A.Z., and Raimondi, A.A. (1978), Performance of a centrifugal disk-lubricated bearing, Trans. ASLE, 21, 314-22. Lund, J.W. (1964), Spring and damping coefficients for the tilting pad journal bearing, ASLE Trans., 7, 342. Patir, N. and Cheng, H.S. (1978), An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, ASME J. Lub. Tech., 100, 12-7. Patir, N. and Cheng, H.S. (1979), Application of average flow model to lubrication between rough sliding surfaces, ASME J. Lub. Tech., 101, 220-30. Raimondi, A.A. and Szeri, A.Z. (1984), Journal and thrust bearings, in CRC Handbook of Lubrication, Vol. 2, Booser, E.R. (Ed.), CRC Press, Boca Raton, FL. Shapiro, W. and Colsher, R. (1977), Dynamic characteristics of fluid-film bearings, Proc. 6th Turbomachinery Symp., Texas A&M University, 39-54. Suganami, T. and Szeri, A.Z. (1979a), A thermohydrodynamic analysis of journal bearings, ASME J. Lub. Tech., 101, 21-7. Szeri, A.Z. (1998), Fluid Film Lubrication, Theory and Design, Cambridge University Press, Cambridge. Szeri, A.Z. and Powers, D. (1970), Pivoted plane pad bearings: a variational solution, ASME Trans., Ser. F., 92, 466-72.
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451
Recommendations for Further Reading The treatment of fluid film bearings in this chapter essentially follows that in Szeri, A.Z.: Fluid Film Bearings, Theory and Design, Cambridge University Press, 1998. However, while results are often only quoted here without derivation, they are rigorously derived in the book. For the other than casual reader, we strongly recommend the above-cited book by Szeri. Extensive treatment of the elastohydrodynamic problem can be found in Hamrock, B.J. and Dowson, D.: Ball Bearing Lubrication, John Wiley & Sons, 1981; Hamrock, B. J.: Fundamentals of Fluid Film Lubrication, NASA, 1991, and in the series of papers by these two authors that appeared in the ASME Journal of Lubrication Technology (now, Journal of Tribology) during the 1970s. For a thorough treatment of rolling element bearings we recommend Harris, T.A.: Contact Bearing Analysis, John Wiley & Sons, 1991. This book discusses not only the more practical aspects of rolling element bearings, but also gives a lucid exposition of the underlying contact mechanics. For readers interested in the thermal aspects of fluid film lubrication, the French language book Lubrification Hydrodynamique by Frene, J., Nicolas, D., Degueurce, B., Berthe, D., and Godet, M. is recommended. Another extensive treatment of THD lubrication can be found in Pinkus, O.: Thermal Aspects of Fluid Film Tribology, ASME Press, 1990.
Nomenclature A B C C′ Cxx ,…,Cyy Cξξ ,…,Cηη D E′ F, FR, FT Fµ G H Hp , Hf , HT Kxx ,…,Kyy Kξξ ,…,Kηη L Mcrit N P Q Qs R, I RB, RJ RP R1, R2 RB, RC Rx, Ry S
area of hydrostatic pad slider dimension (in direction of motion) radial clearance pivot circle clearance bearing damping coefficients fixed pad damping coefficients bearing diameter effective elastic modulus oil film force, radial and tangential components friction force material parameter film thickness parameter, dimensionless film thickness pumping power, shear power, total power bearing spring coefficients fixed pad spring coefficients bearing length critical pad mass shaft speed lubricant force per projected bearing area rate of flow side leakage real, imaginary part radius of bearing, journal radius of pivot circle hydrostatic pad inner and outer radii resistance resulting from bearing, capillary relative principal radii of curvature Sommerfeld number
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T U U, V UM V0 W af a, b gE mr , mθ h, hc , h1, h2 hf gH gV pH rix, riy c cµ dc f, fR, fT lc m p, pc pr, pa, ps pi qi qf t ui (u, v, w) u˜ v xi (x, y, z) xp Γ1, Γ2 α β δ ε θ θ1, θ2 λ µ ρ σ τ φ ω ωw ε0 ξ, η φ0
Modern Tribology Handbook
temperature velocity parameter surface velocity components maximum surface velocity squeeze velocity external load, load parameter area factor semi-axes of elliptical contact elasticity parameter radial, azimuthal tilt parameter film thickness, at pad center, minimum, maximum friction factor film parameter viscosity parameter maximum Hertzian pressure principal radii of curvature specific heat coefficient of friction diameter of capillary restrictor dimensionless lubricant force, radial and tangential components length of capillary restrictor slope of bearing surfaces, preload parameter pressure, center line pressure recess, ambient, supply pressures inlet pressures inflow variable flow factor time lubricant velocity components effective velocity lubricant velocity vector orthogonal Cartesian coordinates pivot position recess boundary, pad external boundary angular coordinate position of load relative to pad leading edge, pressure-viscosity coefficient pad angle dimensionless pivot position, surface deflection eccentricity ratio angular coordinate measured from line of centers angular coordinates of pad leading edge, trailing edge dimensionless bearing stiffness lubricant viscosity lubricant density standard deviation shear stress attitude angle shaft angular velocity angular frequency of applied load eccentricity ratio with respect to the bearing center coordinates of journal center with respect to the pad attitude angle with respect to the bearing load line
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ψn αr κ ( )
( )cav
angle from vertical (negative x-axis) to pad pivot point ratio Ry /Rx ellipticity parameter dimensionless quantity evaluated at fluid-cavity interface
453
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12 Boundary Lubrication and Boundary Lubricating Films 12.1
Introduction ..................................................................... 455 Definitions
12.2
The Nature of Surfaces .................................................... 457 Surface Structures and Compositions • Surface Energy and Reactivity • Surface Emission under Stress • Surface Roughness and Relative Conformity
12.3
Lubricants and Their Reactions ...................................... 459 Lubricant Basestocks and Additives • Relationship Between Oxidation Reactions and Film Formation • Organometallic Chemistry and Tribochemistry
12.4
Physical and Chemical Properties • The Detection of Organometallic Compounds in Films • Mechanical Properties of Boundary Lubricating Films • Advances in Measurement Techniques
Stephen M. Hsu National Institute of Standards and Technology
12.5
Richard S. Gates National Institute of Standards and Technology
12.1
Boundary Lubricating Films ........................................... 468
Boundary Lubrication Modeling .................................... 479 Wear • Flash Temperatures • Asperity-Asperity Understanding • Molecular Dynamics Modeling
12.6
Concluding Remarks ....................................................... 486
Introduction
Lubrication may be defined as any means capable of controlling friction and wear of interacting surfaces in relative motion under load. Gases, liquids, and solids have been used successfully as lubricants. Boundary lubrication usually occurs under high load and low speed conditions in bearings, gears, cam and tappet interfaces, piston rings and liner interfaces, pumps, transmissions, etc. In many cases, it is the critical lubrication regime that governs the life of the components subject to wear. Because of its industrial significance, many studies have been conducted in the past. The most comprehensive was the 1969 assessment by the American Society of Mechanical Engineers (ASME) Research Committee on Lubrication (Ling et al., 1969). The study included critical reviews on surface physics, chemistry, fluid mechanics, contact mechanics, and materials science. The major conclusion in that review was that more research was needed to understand the complex chemical, physical, and material interactions. Since then, topical symposia have been organized by different researchers on lubricant chemistry, contact mechanics, microelastohydrodynamic lubrication (µ-EHL), analytical techniques, boundary films, and molecular dynamics simulations. Cross communication and integration of the significant advances in analytical chemistry, surface analysis, materials sciences, and molecular modeling, however, have seldom been made. This chapter attempts to provide a bird’s eye view across these disciplines. 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
455
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12.1.1 Definitions When the contact geometry and the operating conditions are such that the load is fully supported by a fluid film, the surfaces are completely separated. This is generally referred to as the hydrodynamic lubrication. Theory for fluid film design is well developed based on Reynolds’ equations and continuum mechanics (Reynolds, 1886). When the load is high and/or the speed is low, the hydrodynamic or hydrostatic pressure may not be sufficient to fully support the load, and the surfaces come into contact. The contact occurs at the peaks and hills of the surfaces, and these are referred to as asperities. The amount and the extent of the asperity contact depend on many factors: surface roughness, fluid film pressure, normal load, hardness, and elasticity of the asperities, etc. Many of the asperities undergo elastic deformation under the contacting conditions, and the normal load is supported by the asperities and the thin fluid film. This condition is generally referred to as the elastohydrodynamic lubrication (EHL) (Dowson and Higginson, 1959). The EHL theories are reasonably well developed and are capable of describing the surface temperatures, fluid film thickness, and the fluid film pressures supporting the load. The theory assumes continuum mechanics and does not take into account the effects of wear and the presence of a third body (wear debris). No chemical effect between the asperity and the lubricant is taken into account. Further increase in the contact pressure beyond the EHL conditions causes the contacting asperities to deform plastically and the number of contacts to increase as well as for the fluid film thickness to decrease. When the average fluid film thickness falls below the average relative surface roughness, surface contact becomes a major part of the load supporting system. Mechanical interactions of these contacts produce wear, deformation, abrasion, adhesion, and fatigue under dry sliding conditions. Chemical reactions between the lubricant molecules and the asperity surface, due to frictional heating, often produce a boundary chemical film which can be either beneficial or detrimental in terms of wear. The combination of the load sharing by the asperities and the occurrence of chemical reactions constitutes the lubrication regime commonly referred to as the boundary lubrication (BL) regime. Figure 12.1 shows an approximation of the relationship for these regimes as they relate to coefficient of friction and contact severity. Under boundary lubrication conditions, interactions between the two surfaces take place in the form of asperities colliding with each other. These collisions produce a wide range of consequences at the asperity level, from elastic deformation to plastic deformation to fracture. These collisions produce friction, heat, and sometimes wear. Chemical reactions between lubricant molecules and surfaces usually accompany such collisions producing organic and inorganic surface films. It has long been thought that surface films protect against wear. Closer examination (Hsu, 1991) suggests that some films are protective (antiwear), some films are benign, and some films are detrimental (prowear). A theory for a comprehensive view on boundary lubrication is currently lacking; however, models on lubricant chemistry and contact mechanics do exist (Klaus et al., 1991; Blencoe et al., 1998; Yang et al., 1996; Cheng and Lee, 1989). Recently, molecular dynamics models have been developed to describe atomic interactions under simplified boundary lubricated conditions (Stuart and Harrison, 1999). The detailed physical and chemical processes occurring in the contact zone are still not well understood. Where does EHL end and BL begin? Since the surfaces have a range of asperity height distributions, two surfaces in contact produce a range of distribution of stresses within the contact zone. Therefore, in practical systems there is often no pure EHL or BL lubrication regime, and a mixed lubrication regime exists. Some asperities are in the hydrodynamic mode, some asperities in EHL, and some asperities in BL mode. As wear occurs, surface topography also changes. Depending on the nature and extent of chemical reactions, conformity of surfaces can either develop or disappear. This changes the real area of contact and, hence, the asperity stress distribution. The following sections will attempt to present the current view of boundary lubrication and address some of the important issues. We will discuss the following topics: the nature of surfaces, lubricants and their reactions, boundary lubricating film formation, and modeling and prediction of boundary lubrication.
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FIGURE 12.1
12.2
457
Comparison of lubrication regimes encountered under different contact severities.
The Nature of Surfaces
12.2.1 Surface Structures and Compositions Engineering materials usually go through a series of manufacturing/fabrication and machining/polishing steps to become load-bearing components in machinery. These steps invariably change the surface structure and sometimes the chemical composition. For most engineering surfaces, the surface is covered with oxides. In the case of iron-based alloys, for example, the surface is covered with oxides of iron such as FeO, Fe3O4 , and Fe2O3. The subsurface beneath the oxide is often a deformed or case-hardened layer, often called the Beilby layer, which is the result of the machining and polishing steps and/or heat treatment the material has undergone during the manufacturing process. The microstructure of this layer generally is a microcrystalline phase dispersed in an amorphous phase for most steels. Specific compositions depend on the particular alloying elements present.
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Contaminants in the alloying elements often diffuse to the surface during the manufacturing process, resulting in higher concentrations of the minor elements near the surface than the bulk material. The atoms in solids are bonded together by different forces. They are: covalent, ionic, metallic, hydrogen and van der Waals. Covalent bonds are strong bonds that are formed when electrons are shared between atoms of similar electronegativity. They have an intrinsic directional nature. Ionic bonds result when complete electron transfer takes place between atoms of different electronegativity. Coulombic attraction between the resulting charged ions results in strong bonds. Metallic bonds are the result of attractive coulombic forces between positive metallic atoms with commonly shared free negative electrons resulting in high electrical and thermal conductivity. Hydrogen bonds refer to when hydrogen acts as a bridge between its primary bond to an electronegative atom and another electronegative atom. van der Waals forces are weaker long-range forces that result from dipole–dipole interactions between atoms; they influence bonding strengths in some solids. These bonds have different strengths and require different amounts of energy to break them. Additionally, in a solid, complex atomic and molecular units must fit together with a periodicity that minimizes electrostatic repulsive forces. When different bonds are broken (by mechanical or chemical means), the resulting surface energy and reactivity are different. For single crystalline solids, different crystalline planes often exhibit different physical, mechanical, and chemical properties. Frictional studies have shown that different crystalline phases produce different frictional resistance to sliding when subjected to the same conditions (Buckley, D.H., 1981). Thus, polycrystalline solids as well as polymeric solids often have anisotropic properties. This adds to the complexity of the surface structure/properties relationships. Under boundary lubricated conditions, different crystalline phases also exhibit different reactivity to lubricants, moisture, oxidation, and surface contaminants under sliding conditions.
12.2.2 Surface Energy and Reactivity Surface energy for most engineering surfaces is difficult to determine. Rabinowicz (Rabinowicz, 1965) has suggested that the surface energy of a solid can be approximated by using the surface energy of the liquid at the melting point of the material. The agreement between this approximation and experimentally determined value for simple pure materials is surprisingly good. It was further shown that the ratio of the surface energy to penetration hardness could be correlated to friction, i.e., lower the ratio, lower the friction. Thermodynamically, the higher the surface energy, the more reactive the surface will be. Therefore knowing the surface energy will give an indication of the potential chemical reactivity toward oxygen, water, and lubricants. Unfortunately, as has been discussed before, the surface is covered with oxides, other impurities, and mechanically altered layers. When the surface roughness is superimposed on it, the energy of the engineering surface is very difficult to estimate. Additionally, as with any solids, there are defects. Atomic misalignment, lattice mismatch defects, dislocations, voids, and phase segregations abound in solids. When these defects are on the surface, including steps, twists, kinks for crystalline solids, they provide high-energy sites at which chemical reactions, adsorption, and catalysis take place preferentially (Yates et al., 1996). Experimentally, contact angle measurements with a series of well-known liquids have been used to estimate “surface energy” of a smooth solid surface. Results are useful to understand wettability and spreading of liquids on that solid surface, but caution must be used in generalizing to other surfaces.
12.2.3 Surface Emission under Stress When atomic bonds are broken at the surface by mechanical processes, energy is both consumed and released. This often changes the surface energy state. When all the oxides and other mechanically deformed layers are broken through by scratches, nascent surface emerges. The energy state of such nascent surfaces is high compared with the “normal” surfaces.
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Simoi et al. (1968) suggested that the rubbing of metal surfaces produced highly localized electron clouds, referred to as the “exo-electrons.” The presence of these electrons had also been detected by others (Ramsey, 1967; Rosenblum et al., 1977). How this electron cloud could induce reactions that otherwise would not occur remained to be proven. Lenahan (1990) reported the measurement of dangling bonds on silicon nitride, suggesting that rubbing might produce dangling bonds on crystalline surfaces, and these dangling bonds were highly energetic and reactive. Nakayama (1991) detected the emissions of charged particles, electrons, and photons from scratched silicon-based ceramics. Dickinson et al. (1993) observed the emission of particles and electrons from fracture of crystalline surfaces. In repeated single-pass experiments, Ying (1994) observed the surface to be highly strained and ordered for various metals. Strain-induced fracture and deformation appeared to be the dominant mechanisms under lubricated conditions for metals. Would this highly strained state upon fracture produce electrons and charged particles?
12.2.4 Surface Roughness and Relative Conformity Surfaces have microscopic roughnesses which are often random in nature. Under concentrated contact, these asperities are deformed either elastically or plastically to form the interface. So the initial interface depends on the relative hardness and the relative roughness of the two surfaces in contact. If the two surfaces conform perfectly to each other and all the asperities are deformed 100%, then the real contact area is equal to the apparent contact area. Of course, this is not the case for most engineering contacts. For highly loaded steel bearing surfaces under sliding conditions, the real area of contact may be only 15 to 25% of the apparent area of contact (Wang et al., 1991) depending on other parameters, such as relative surface roughness and the relative surface hardness. If the normal force acting on the surface is very high, then some plastic deformation will also occur. Greenwood and Williamson and others have studied this topic extensively (Greenwood and Williamson, 1966; McCool, 1986). On each asperity, there are subasperities which are smaller in scale. On each subasperity, there are sub-subasperities, and so on. If the distribution of asperity heights is Gaussian in nature, such as in the case of ball bearings, the typical surface roughness parameters such as average roughness (Ra), root mean square roughness (RMS), skewness, and kurtosis, will be adequate in describing the surface roughness. However, if the asperity height distribution is not Gaussian, as for example, when two or three major peaks have many smaller-scale subasperities, then the multimodal characteristics of the load-bearing asperities become important. In lubrication, the surface roughness is an important indicator as well as a significant parameter in the calculation of oil film thickness. Wang et al. (1991) suggested that in a lubricated case, even though the surfaces may be rough, if they conform to each other under plastic yielding, then the relative surface roughness may be quite small. Oil film calculations based on elastohydrodynamics may yield significantly smaller film thickness than is actually present. Conformity has been demonstrated to change with time, materials, chemical additives, and wear modes (Wang et al., 1991).
12.3
Lubricants and Their Reactions
In lubricated systems, liquid lubricants are commonly used. When liquid lubricants are used in engines and machineries, they serve multiple functions. They control friction and wear, cool the surfaces, remove debris and contaminants, generate hydrodynamic pressures to support load, and redistribute stresses over the surface. Since most of the liquid lubricants are hydrocarbons, they tend to oxidize, thermally decompose, and polymerize. These reactions produce high-molecular-weight reaction products which lead to the formation of “friction polymers.” To understand the interplay between these reactions and wear, we need to understand the chemical reactions that take place as well as the chemical composition of the lubricants.
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12.3.1 Lubricant Basestocks and Additives Modern liquid lubricants are compounded from lubricating basestocks and chemical additives. Selective combination of the two produces a myriad of special lubricants designed for different applications. There are two major classes of basestocks: (a) petroleum or mineral-oil derived; and (b) specially synthesized basestocks. 12.3.1.1 Petroleum Basestocks Petroleum basestocks are selected hydrocarbon fractions derived from crude oils. They generally consist of molecules containing 18 to 40 carbon atoms in three basic hydrocarbon types: (a) paraffins, (b) aromatics, and (c) naphthenes (cycloparaffins). Most of the molecules are of the mixed type containing two or more basic hydrocarbon structures. These basestocks also contain a small percentage of compounds containing heteroatoms, such as sulfur, nitrogen, or oxygen, substituted into the various hydrocarbon structures. Typical molecular structures are illustrated in Figure 12.2. Stereochemical possibilities provide an astronomical number of structural variations in such molecules. This is one of the reasons why the effects of molecular structure on lubrication are not well understood today. In typical basestocks, the mass fraction of aromatics usually ranges from 5 to 40% with the average about 20%; straight chain paraffins usually range from 10 to 20%; and cycloparaffins make up the difference. Molecules containing heteroatoms (N, S, O) usually range from 0.5 to 4% depending on crude source, processing technology, and viscosity grade. Although the heteroatoms are a small fraction of the basestock mixture, they have a significant influence on basestock stability and friction. The aromatics provide solvency for additives and oxidized products, but they tend to react to form oil insoluble products.
FIGURE 12.2
Base oil molecular structures.
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12.3.1.2 Synthetic Basestocks Synthetic basestocks are mostly long-chain molecules produced by chemical reactions in order to obtain specific characteristics. They are made from petrochemicals, animal and vegetable oils, and coal-derived feed stocks. There are five major classes of synthetic basestocks: synthesized hydrocarbons, esters, ethers, halogenated compounds and silicone polymers. Others include sodium–potassium eutectics, and inorganic polymers of boron, phosphorus, and nitrogen, for highly specialized applications. More comprehensive descriptions of synthetic lubricants are available in the literature (Gunderson and Hart, 1962; Shubkin, 1993). a. Synthesized Hydrocarbons Synthesized hydrocarbons include alkylbenzenes, cycloaliphatics, poly-α-olefins, and polybutenes. Alkylbenzenes are mainly used in low-temperature applications as hydraulic oils, greases, and sometimes engine oils. Poly-α-olefins have found increasing acceptance due to their similarity to and compatibility with petroleum base oils, good thermal stability, and excellent viscosity–temperature relationship. b. Esters Esters are by far the most common synthetic basestock. Large quantities of materials with various structures are readily available from chemical manufacturers. They consist of monoesters, dibasic acid esters (adipates, azelates, dodecanedioates), polyol esters (neopentyl esters), polyesters, phosphate esters, and silicate esters. Most of these exhibit high boiling points, excellent viscosity–volatility characteristics, and high-temperature stability. Esters generally exhibit good solvency and have good friction and wear characteristics. They tend to react to form acidic species (acid esters and half acid esters) faster than paraffins. c. Polyethers Among polyethers, polyglycol ethers provide a variety of viscosity and molecular-weight grades. They are used mostly in water-based fire retardant hydraulic fluids, brake fluids, and rubber molding lubricants. They are available in water-soluble and oil-soluble forms. They have low pour points, good compatibility with rubber, and good sludge and varnish resistance. The volatility and oxidation stability of the polyethers are generally similar to those of petroleum basestocks. They have a unique property in that their decomposition products are low-molecular-weight compounds similar in physical properties to the original starting material. Polyphenyl ethers represent a thermally stable class of aromatic compounds containing no paraffinic side chains. These materials exhibit relatively poor viscosity–temperature and low-temperature fluidity properties. d. Halogenated Compounds In halogenated compounds the hydrogen is replaced by chlorine, fluorine, or bromine. This generally results in reduced flammability. Nonflammability may be achieved by incorporating more than 60% of halogen into the molecule. Toxicity has placed severe limitations on the use of chlorinated and brominated compounds. Perfluoropolyethers are examples of halocarbons that are in current use as lubricants. These materials show excellent oxidation stability and good viscosity and volatility properties. The very high cost of these materials has limited their use in commercial applications. e. Silicone Polymers Silicone polymers were one of the earliest compound types investigated for lubricant applications. They are mainly dimethyl silicone polymers and methylphenyl silicone polymers with various chain lengths. Methyl silicones were developed in the 1940s as the liquids with the best physical properties (viscosity–temperature) for lubricant application. Since then a series of modified structures, including phenyl, phenyl methyl, chlorophenyl methyl, fluoromethyl, and alkyl (C4-C5) silicones have been developed to overcome the major problems of the silicones, which is the lack of boundary lubricity on ferrous bearing
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systems. Silicones have excellent fluid properties and have been used as lubricants in systems designed to run under hydrodynamic and elastohydrodynamic conditions where the bearing systems are nonferrous. They have probably the best viscosity–temperature characteristics of any synthetics, with very low volatility and excellent oxidative and thermal stability. However, their solvency is poor and they are not miscible with petroleum oils. 12.3.1.3 Additives Most lubricants contain special chemical additives to impart specific properties to the basestocks to enhance performance and inhibit degradation. A wide variety of additive chemicals has been developed. There are 10 major classes of additions, categorized according to their functions: antiwear additives; friction modifiers; extreme-pressure additives; detergents; dispersants; antioxidants; corrosion inhibitors; pour-point depressants; defoamants; and viscosity-index improvers. There are also other additives such as tackiness agents, fatty oils, thickening agents, and color stabilizers. Smalheer and Smith (1967) describe many chemical types in each class. For additional information, see Booser (1984). Recent advances in the additive area are available through patent summaries published periodically (for example, Ranney, 1980; Satriana, 1982). a. Antiwear Additives Additives are used to reduce wear under elastohydrodynamic and boundary lubrication conditions. The most widely used are zinc dithiophosphates and tricresyl phosphate. Each of these additives has a family of derivatives modified for different temperature and stability requirements. Other additives used for wear control are acid phosphates, phosphites, sulfurized terpenes, sulfurized sperm oils, metal dithiocarbamates, and occasionally some sulfides. The antiwear additives generally function by adsorbing on or reacting with metal surfaces to form a protective film that is easily shearable. Since direct reactions or interactions are sometimes involved, additive–metal compatibility is important. One lubricant with an antiwear additive may function very well for one material pair but may fail in another material combination. b. Friction Modifiers Additives are also used to modify the frictional characteristics of the material under boundary lubrication contact. Fatty oils are sometimes used, such as lard oil, tallow, sperm whale oil, porpoise-jaw oil, and blown rapeseed oil. Recent research on friction modifiers has centered on glycerides, oil-soluble molybdenum compounds, finely dispersed graphite in oil, and synthetic esters of various fatty acids. c. Extreme-Pressure Additives Extreme-pressure (EP) additives are used under highly loaded conditions to prevent seizure, scoring, and welding. In metal forming and cutting applications, wear of one contacting surface is acceptable. The additives therefore are chemically active compounds containing chlorine, phosphorus, and/or sulfur. Examples are chlorinated wax, sulfurized fatty oils, sulfurized mineral oil, chlorinated mineral oil, phosphosulfurized fatty oils, benzyl and chlorobenzyl disulfides, and some phosphites. d. Detergent/Dispersant Additives Detergent/dispersant additives may be separated into two classes of compounds: metal-containing (ashcontaining) high-temperature detergents and ashless low-temperature dispersants. Their common function is to prevent deposits from forming on metal surfaces due to oil oxidation, contamination, or polymerization. The detergents function as surfactants that tend to adsorb on surfaces forming micelles around the insoluble material from the degradation of the oil. A stable microemulsion results from this process. Modern automotive and diesel engine lubricants contain some “overbasing” associated with the detergents. Calcium carbonate is added in the form of micelles to the detergent. This form of overbase can thus neutralize acidic components from either the environment or oxidation of the lubricant. There are many classes of detergents: metal sulfonates, metal phenates, metal salicylates, and metal phosphonates and thiophosphonates. Most of these can be overbased to varying degrees. Metals commonly used in detergents are calcium, magnesium, barium, and zinc.
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Dispersants are primarily additives used to disperse oxidized oil-insoluble products, water, fuel, or other contaminants at relatively low temperatures (100°C or below). Because they do not contain metal, they sometimes are referred to as ashless dispersants. There are two main families: Mannich reaction products and succinimides. Mannich reaction products are reaction products from polybutene and phenol; they are treated with amines and boric acid. Succinimides are usually n-substituted long-chain alkenyl succinimides. The detailed mechanism of the dispersion is not well understood, but most researchers agree that they adsorb on the oil-insoluble submicrometer particles and keep them finely dispersed in oil without further aggregation. e. Antioxidants There are numerous antioxidants available for lubricant use. The limiting factor sometimes is oil solubility. The important classes are hindered phenols, amines, and sulfur and phosphorus compounds. Hindered phenols are phenols in which the hydroxyl group is sterically blocked or hindered, such as 2,6di-tert-butyl-4-methylphenol. They act as peroxide-radical traps to interrupt the oxidation chain reaction. Amines such as N-phenyl α-naphthylamine are also widely used. Sulfur and phosphorus compounds are usually used at high temperatures in the presence of metals, which often catalyze oxidation of hydrocarbons. Some researchers speculate that sulfur and phosphorus compounds inhibit oxidation by passivating the metal surface with a protective film. Some phosphorus compounds, such as zinc dialkyldithiophosphate, also act as peroxide-radical traps to stop the oxidation chain reaction. Johnson (1975) lists over 100 antioxidants used in lubricants. f. Corrosion Inhibitors Corrosion inhibitors are additives that protect metal components used in engines and bearings against attack from acidic contaminants in the lubricant. Rust inhibitors are a subset of corrosion inhibitors designed specifically to protect ferrous materials against attack. Corrosion inhibitors function by forming a tight passive film on the metal surfaces to withstand the detergent or dispersant often present in the same lubricant. The most common corrosion inhibitors are zinc dithiophosphate, zinc dithiocarbamate, sulfurized terpenes, and phosphosulfurized terpenes. Common rust inhibitors are alkenyl succinic acids, alkyl thioacetic acids and their derivatives, imidazolines, amine phosphates, and acid phosphate esters. In high-temperature applications such as the internal-combustion engine, calcium or magnesium sulfonates are usually used. g. Viscosity-Index Improvers Viscosity-index (VI) improvers are polymers with molecular weights on the order of 100,000 or more, which thicken the oil at high temperatures. There are numerous variants of these additives, but the most widely used include three types: polymethacrylates, olefin copolymers, and polyisobutenes. These VI improvers are currently used in automotive crankcase oils, automatic transmission fluids, hypoid gear oils, and hydraulic fluids. The polymers tend to break down permanently with use and the viscosity of the polymer solution is decreased irreversibly at high shear rates. The stability requirements for the various areas of application are met by careful control of the molecular weight and concentration of the polymer used. In order to change the viscosity–temperature relationship sufficiently, relatively large dosage is required (5 to 10% neat polymer). 12.3.1.4 Lubricant Formulation Technology The large array of available petroleum basestocks, synthetics, and various chemical additives makes numerous combinations possible. Lubricant formulators, when confronted with a particular lubrication problem, select a certain basestock to satisfy the viscosity–temperature requirements and a particular set of additives to give different characteristics. However, additives often interact with the basestocks as well as with other additives in ways that are not understood. Therefore, most lubricants are developed by actual equipment testing through trial and error. O’Connor (1968) lists over 30 major types of lubricants and their requirements and some typical additives used in each application.
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12.3.2 Relationship Between Oxidation Reactions and Film Formation The relationship between lubricant reactions and wear has long been observed in engines. Historically, however, the link between the two technical areas is very weak. This is because the studies are largely conducted by two separate communities. One group focuses on the oxidation mechanism and bench test development; the other emphasizes the boundary lubrication mechanisms. 12.3.2.1 Chemical Reactions The chemistry in the contact is complex and abundant. There are oxidation and thermal reactions of hydrocarbons, polymerization to form high-molecular-weight products, adsorption and corrosion reactions, and catalysis by metal surfaces. In addition, tribochemistry, tribomechanical reactions, surface oxide reactions, phase transitions, and mechanochemical effects also come into play. For semiconductors, double-layer surface charges complicate the matter by introducing potential electrochemical reactions. 12.3.2.2 Oxidation and Thermal Reactions It is well known that hydrocarbons oxidize via a free radical mechanism. The basic reaction mechanisms are simple in principle but complex in reality. It follows primarily four steps: initiation, propagation, branching, and termination (Hucknell, 1974): RH → R• + H
1. Initiation 2. Propagation
R• + O2 → ROO• ROO• + RH → ROOH + R• ROOH → RO• + HO• RO• + RH → ROH + R• HO• + RH → H2O + R•
3. Branching
4. Termination
alcohols R• +R• aldehydes R• +ROO• ⇒ ROO• +ROO• ketones acids RO• +R•
12.3.2.3 Metal Catalyzed Oxidation Reactions Many metals, such as iron, chromium, copper, and nickel, have known catalytic activities with hydrocarbons. In lubricant oxidation studies, metal coupons are routinely used to simulate the catalytic reactions encountered in actual applications. Studies reveal that the hydrocarbons react with oxygen and form polar species such as carboxylic acids which adsorb onto the metal surface and react with the metal forming metal complexes (Hsu et al., 1988). These metal complexes are soluble in oil, and both homogeneous and heterogeneous catalytic reactions take place. Such reactions generally follow the reaction mechanism (Hucknell, 1974): Initiation: Propagation:
Termination:
Rn M + RH → R• + RH + Rn–1 M R• + O2 → ROO• RO• + RH → ROOH + R• Rn–1MH + ROOH → ROO• + Rn–1MH Rn–1MH + ROOH → RO• + Rn–1M + H2O Rn–1MH + ROH → R• + Rn–1M + H2O Rn–1M + C – O/C = O → RC•O + Rn–1M + H2O R• + Rn–1MH → Rn–1M + ROH and further oxidation products R• + RnM → R – R + Rn–2M ROO• + Rn–1M → Rn–1M – ROO
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FIGURE 12.3
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Catalytic effect of different metals on oxidation rate.
The role of metal catalysis on lubricant oxidation is a complex one. Since the molecular species in a lubricant are numerous, the possible reaction pathways and the number of isomers are astronomical. Because the fundamental reaction mechanisms are functions of the molecular structures, the mechanism described above can only serve as an illustration of the general directions of the reaction steps. Detailed understanding of the catalysis mechanism is currently not available. Different metals exhibit different degrees of catalytic activities on lubricant oxidation. Figure 12.3 illustrates the effects of different metal surfaces on the rate of oxidation (Lahijani et al., 1981). Low carbon steel has the highest “catalytic” effect in terms of causing the lubricant to oxidize. 12.3.2.4 Polymerization Reactions Lubricant molecules upon oxidation always tend to go in two different directions: smaller molecules through beta carbon scission and/or decomposition; high-molecular-weight “polymers” through condensation reactions. Because of the myriad molecular species present in the lubricant molecular mixtures, there is a statistical averaging effect in terms of product mix and distribution among all lubricants. A typical aldol condensation reaction is shown below:
O O OH | CH3–C–CH3 + CH3–C–CH3 → CH3–C–CH3 → CH3–C–CH3 + H2O | CH2 CH | | CO CO CH3 CH3 The conjugated double bonds of the products are characteristic of the condensation reactions. They have been experimentally detected by NMR on surface films produced under base oil lubricated contacts (Naidu et al., 1984). These conjugated double bonds then provide the impetus for further polymerization to higher-molecular-weight products. Naidu et al. (1984) demonstrated that the chemistry proceeds in the following sequence: primary oxidation step; formation of organic acids; aldol condensation reactions to form high-molecular-weight compounds. When the molecular weight reaches the solubility limit (about 100,000), the reaction products become insoluble and deposit on the surface. Figure 12.4 shows the molecular weight increase as a function of oxidation time. The lubricant is subjected to thin film oxidation at temperatures of 225 and
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FIGURE 12.4
Modern Tribology Handbook
Effect of oxidation on high-molecular-weight reaction product formation.
275°C for different oxidation durations. The surface reaction products are dissolved in a polar solvent, typically tetrahydrofuran (THF), and analyzed by passing through a gel permeation column for molecular size separation. The detailed procedure is described elsewhere (Cho and Klaus, 1983). As shown in Figure 12.4 (Cho and Klaus, 1983), the original lubricant has an average molecular weight of about 400, which is indicated by the solid zero minute line. As the oxidation continues, the highermolecular-weight fraction increases in magnitude. At a higher temperature of 275°C, the increase in molecular weight is much faster, but the trend is the same. Similar behavior has been observed under dynamic wearing conditions, as will be discussed in a later section on organometallic compounds. As one can see, oxidation reactions are complex, and they are necessary to form the polar species, which in turn react with the metal surfaces, forming polymers which lubricate the surface. The linkage between oxidation and wear has long been suspected, but the detailed mechanistic explanation is lacking. It has long been postulated by the lubricant researchers’ community that more oxidation-resistant oils are intrinsically more wear resistant. But as we shall demonstrate, the relationship between oxidation
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FIGURE 12.5
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Effect of oxidation on wear for IIID reference oils.
reactions and film formation tendencies is complex. Figure 12.5 shows the relationship between oxidation and wear for a set of five reference oils (ASTM sequence III engine dynamometer test for oxidation and wear; high wear reference oils produce higher wear in the engine dynamometer tests, low wear reference oils produce lower wear). Four-ball wear test results are measured before and after oil thickening tests (OTT) on the lubricants (oil thickening tests conditions: 60 mL/min air flow rate, 171°C, 5% drain oil as catalyst). As can be seen, the high wear reference oils (77B and 77C) have a much higher response to oxidation than the low wear reference oils.
12.3.3 Organometallic Chemistry and Tribochemistry In examining the nature of chemical reactions occurring in a contact, the direct reaction between the surface and lubricant molecules has been alluded to. In this section, we will discuss the role of chemical reactions induced by mechanical rubbing (tribochemistry). 12.3.3.1 Direct Reactions with Metals Buckley (1974) has suggested that the nascent surfaces of metals behave differently than oxide-covered surfaces. Morecroft (1971) performed high-vacuum experiments to show chemical reactions occurred on freshly exposed metal surfaces. Exoelectrons have been measured and used to explain the enhance reactivity of the freshly exposed metal surfaces. These early works sparked research into the effects of nascent surfaces on chemical reactivity. In general, it was found that nascent surfaces under high-vacuum conditions, readily reacted with any hydrocarbon, decomposing the molecules into fragments. No polymerization reactions have been reported. A conclusion may be that freshly exposed metal surfaces will readily react, form oxides, and decompose hydrocarbons. In reality, engineering surfaces are almost always oxide covered. How this observation fits into lubrication theory is not certain. Hsu and Klaus (1978) used chemical reaction kinetics to back-calculate the reaction temperatures necessary to generate the observed amount of products from the wear processes and the thermally induced simulations. The reaction temperatures determined for steel systems are very similar, 379 ± 28°C for the static case (oxide-covered surfaces) and 349 ± 8°C for the dynamic rubbing case (fresh metal surfaces exposed). Hsu concluded that, based on these results, the nascent surface effects on reaction rates under atmospheric conditions are minimal. Thermal effect is the dominant factor for controlling the boundary chemical reactions for steels.
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FIGURE 12.6
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Comparison of antiwear effectiveness of different additives with SiC and Si3N4 .
12.3.3.2 Tribochemistry Observed for Ceramics For ceramics, such as aluminas, silicon nitrides, and silicon carbides, the situation turns out to be different. Fundamentally, these are polycrystalline solids with very well-defined crystalline structures and bonding energies. When the surfaces are disrupted, dangling bonds are created. Since these bonds are atom specific, they are not only more reactive but also tend to be more reaction specific than thermally controlled reactions. Hydroxide formation was first reported by Gates et al. (1989) for aluminas, and subsequently, hydration reactions were reported in wearing systems as well as in static systems for other ceramics (Tomizawa and Fischer, 1986; Mizuhara and Hsu, 1992). Gates and Hsu (1995), in studying alcohols lubricating silicon nitrides, discovered that the alkoxide reactions dominated the tribochemistry, and these reactions cannot be simulated by thermal conditions. In studying the surface reactions, Deckman (1995) compared the reactions of silicon nitride with silicon carbide under identical conditions. Even though the surface species are predominantly the same, namely silicon oxides and oxynitrides, the response to different chemistry under rubbing experiments is totally different. Figure 12.6 illustrates the lack of correlation between the two materials responding to the same chemical compounds under the same conditions. While these results are puzzling, they point to the importance of tribochemistry. In metal systems the thermal reactions dominate and the nascent surface effects are minor. For crystalline materials, not only is the reactivity different, but the nature of the reaction pathways is different. The cause for this difference may be suggested by some recent results reported by Nakayama and Hashimoto (1991) and Dickinson et al. (1993). They independently studied the charged particle emission from crystalline surfaces and found under deformation and fracture conditions, different materials emit different amounts of particles (electrons, molecules, charged particles). Figure 12.7 shows that different materials under rubbing conditions emit different amounts of charged particles. The amount of emission for silicon carbide is much lower than silicon nitride. This observation may not explain directly the difference in reactivity observed for the two materials, but it does point to a direction for some future research to resolve this issue.
12.4 Boundary Lubricating Films As early as 1958, Hermance and Egan (1958) noted that the lubrication of metallic surfaces was often accompanied by opaque organic deposits on and around the contact surfaces. Analysis revealed that these were high-molecular-weight “polymeric” materials. Over the years, the term “friction polymers” was coined over the objections of polymer chemists. The early perception is that this film is responsible for successful lubrication of the surface, and its formation is controlled by the chemical additives in the lubricants. Therefore, many research efforts have been focused on the mechanical properties of these films, the nature of them, and in their information mechanisms.
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FIGURE 12.7 Charged particle emission of different surfaces under rubbing conditions. (From Nakayama, K. and Hashimoto, H. (1991), Triboemission from Various Materials in Atmosphere, Wear, 147 (2):335-343. With permission.)
Recent data suggest that not all films are protective (Hsu, 1991). Depending on the nature of the solid surfaces, many films can be formed. Some of them are protective, some of them are corrosive, and some are simply the reaction product residue, which does not affect the friction and wear.
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Direct visual observation of formation of ZDP films in a contact during rubbing has provided additional insight into the complex dynamic nature of the process (Sheasby et al., 1991). Similarly, in an elastohydrodynamic regime, Gunsel and Spikes measured ZDP film thickness as a function of test duration and temperature (Gunsel et al., 1993; Spikes, 1996).
12.4.1 Physical and Chemical Properties There have been many studies conducted to analyze the physical and chemical properties of boundary lubricating films (Belin et al., 1989; Briscoe et al., 1992; Gates et al., 1989; Godfrey, 1962; Hsu and Klaus, 1979; Klaus et al., 1987; Klaus et al., 1985; Lindsay et al., 1993; Martin et al., 1986; Morecroft, 1971; Mori and Imaizumi, 1988; Tonck et al., 1986). Results of these studies suggest that the chemical compositions of the films are mainly micron- and submicron-sized particles of iron and iron oxides intertwined with high-molecular-weight organometallic compounds of 3000 to 100,000 MW (Gates et al., 1989). If antiwear additives such as zinc dialkyldithiophosphate or tricresylphosphate are present in the lubricants, iron phosphates and phosphate glasses can be formed and become part of the boundary film (Belin et al., 1989; Martin et al., 1986). The appearance and morphology of the films can be patchy, continuous, or discrete, and have different colors, from green to brown to black (Lindsay et al., 1993; Klaus et al., 1987). This is probably due to the different chemical compositions as well as the thickness of the films. Different thicknesses reflect and refract part of the light spectrum resulting in different colors being observed (Choa et al., 1994). Overall, there is no general correlation between the appearance and morphology of the films to effective boundary lubrication. Several boundary lubricating films are illustrated in Figure 12.8. These are photomicrographs taken of the wear scars from ball-on-three-flat tests conducted on silicon nitride at 2 GPa mean pressures (Gates and Hsu, 1995). The films range from fluid-like, observed for 2-ethyl hexyl ZDP (Figure 12.8a) and calcium phenate (Figure 12.8b), to the more solid-like films of tricresyl phosphate (Figure 12.8c) and magnesium sulfonate (Figure 12.8d). The film formed from ZDP appears to be flexible, as shown by Figure 12.9. There are several mechanisms by which boundary lubricating films function: sacrificial layer, low shear interlayer, friction modifying layer, shear resistant layer, and load bearing glasses. The sacrificial layer is based on the fact that the reaction product layer is weakly bound and easily removable; thereby providing a low shear interfacial layer against the rubbing. So instead of the surfaces being worn by the shear stresses, this layer is removed instead. For such films to be effective, the rate of film formation has to be higher than the rate of film removal to protect the surface. An example is the oxide layer in the case of steels (Quinn et al., 1984). The oxide layer forms rapidly and is easily removed, thus protecting the steel surfaces. The low shear interlayer mechanism can best be illustrated by the use of solid lubricant molecules. The solid lubricant molecules have weak interlattice attraction between shear planes; therefore, the lubricating film can slide easily along the low shear planes within the film, thus accommodating the motion and shear. Another mechanism is that the molecules or reaction products form an ordered structure at the interface, and the sliding of the two surfaces is accomplished between the two weakly bonded absorbed layers in the ordered structure. This is how friction modifiers such as fatty acids function. Of course, the other alternative mechanism is to have a strongly adhered bonded layer which is shear resistant by itself. Under certain conditions, the lubricant layer will behave like a solid exhibiting limiting shear and shear band fracture (Bair et al., 1993). These mechanisms operate in different regimes controlled by the environment and operating conditions. What works for one system may not work for another. Within the same system, what works within one set of operating conditions may not work when the operating conditions change significantly. Figures 12.10 and 12.11 illustrate different film morphologies and appearances for two different materials. Figure 12.10 shows very thin dense films that work for silicon nitride. These films are similar in appearances and textures to the steel-on-steel systems. Figure 12.11 shows effective films for the silicon carbide system. The same chemicals in Figure 12.10 do not work for silicon carbide. Because of the brittleness of silicon carbide, thicker films are needed to protect the system.
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FIGURE 12.8 Optical micrographs of wear scars from wear tests on silicon nitride using paraffin oil containing (A) 1% 2-ethylhexyl ZDP; (B) 1% Ca phenate. Optical micrographs of wear scars from wear tests on silicon nitride using paraffin oil containing (C) 1% tricresyl phosphate; (D) 1% Mg sulfonate.
FIGURE 12.9 SEM micrographs of film from wear tests on silicon nitride using paraffin oil containing 1% 2-ethylhexyl ZDP.
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FIGURE 12.10 SEM photomicrographs of wear scars from wear tests on silicon nitride using paraffin oil containing 1% 2-ethylhexyl ZDP.
12.4.2
The Detection of Organometallic Compounds in Films
Oil-soluble metal-containing compounds were first identified as being generated in lubricants under oxidizing conditions (Klaus and Tewksbury, 1973). These compounds were later identified to be highmolecular-weight organometallic compounds using gel permeation chromatography coupled with atomic absorption spectroscopy (Gates et al., 1989). Figures 12.12 through 12.15 show the results for two cases: static oxidation test conditions and dynamic wear test conditions. Under static oxidation test conditions, a thin oil film about 40 µm thick was deposited on a steel disk and oxidized at a temperature of 225°C for 20 to 30 minutes. Afterwards, the surface reaction products were dissolved by a solvent (tetrahydrofuran). The solution was then injected into the GPC columns for molecular size separation. The effluent flowed through two detectors, refractive index and ultraviolet detector. After the detectors, the effluent stream was collected in a autosampler vial for the determination of metal content in the effluent stream by atomic absorption spectroscopy analysis. The same procedures were followed to examine the films formed on worn surfaces after wear experiments. Figure 12.12 shows that organometallic compounds are formed when lubricants are reacted with the metal surfaces under static oxidation conditions. The top curves denote the molecular weight distributions of the lubricant (a 150 N paraffinic base oil) after 30 minutes of reaction time at 225°C on steel and copper surfaces. The original molecular weight distribution centers around 300 (similar to the molecular weight distribution curve for the copper surface). The lower two curves are the results of the atomic absorption signals as a function of the discrete volumetric increments of the effluent from the
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FIGURE 12.11 SEM photomicrographs of wear scars from wear tests on silicon carbide using paraffin oil containing 1% benzyl phenyl sulfide.
gel permeation column. So these signals indicate the amount of organometallic compounds as a function of molecular weight. In these two cases, one can see that the steel surface, under identical reaction conditions, forms a larger quantity of high-molecular-weight products and produces a large quantity of organo-iron compounds. The copper surface, on the other hand, produces a much smaller amount of organo-copper compounds (note the scale difference between steel and copper) even though the molecular weights of the organometallic compounds are about the same. The molecular weight distribution curves also suggest that copper did not cause the original molecular weight distribution to change substantially, i.e., the lubricant is not significantly oxidized. Figure 12.13 shows the formation of organo-iron compounds as a function of time under static oxidizing conditions. As one can see, the iron peak intensity increases with time. This indicates that the amount of organo-iron compounds are increasing as a function of time. The data also indicate that there is an induction time under static oxidation conditions for the organo-iron compounds to form. The analytical procedures used here are sensitive to ppm level of iron, and the amount of organometallic compounds detected depends on the solvent and the extraction procedure. Figure 12.14 shows the result when the same procedure is applied to the dynamic wear case for a superrefined mineral oil base stock in a four-ball wear tester. The wear procedure used is a modified procedure in that only 6 µL of lubricant is available to the contacts. This way, the reaction products and the reaction sequence are concentrated for ease of analysis. A broad spectrum of organo-iron compounds of various molecular weights is found, with molecular weights ranging up to about 100,000. Higher-molecularweight compounds are not detected, suggesting that the solubility limit has been reached Figure 12.15 shows the results for a fully formulated lubricant (containing antiwear additives, detergents, dispersants, etc.) as a function of time. In this case, the amount of organo-iron compounds is much less, but the presence of organo-iron compounds can be detected very rapidly. Optical pictures reveal that the boundary
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FIGURE 12.12 Molecular weight distribution of organometallic compounds from oxidation tests conducted on iron and copper surfaces.
lubricating film is fully formed after only 1 minute of wearing contact. There seems to be a shearing action reducing the molecular weight of the products and shifting the maximum amount of organo-iron to a molecular weight of about 3000. These organometallic compounds are also found on cam and tappet parts in an ASTM engine dynamometer test, the sequence III oxidation wear test. Cam and tappet parts were taken from ASTM test stand calibration runs and analyzed for surface reaction products. Similar patterns were observed. This suggests that organometallic compounds play an important role in the formation of the boundary lubricating films.
12.4.3 Mechanical Properties of Boundary Lubricating Films Let us hypothesize that these high-molecular-weight organometallic compounds form the glue to provide cohesive strength with dispersed fine particles of iron and iron oxides. The bonding via the iron organometallic bonds provides the adhesive strength. Then once the film is formed, one should be able to measure the shear strength of these films. In the last few decades, many researchers have attempted to measure the film strength. There have been some limited successes. Briscoe et al. (1973) studied the shear strength of thin films under a range of high pressure (MPa to GPa). They found that at these pressures shear strengths increased with increasing pressure for calcium and copper stearate and polyethylene films. Increasing temperature reduced shear strength. Researchers at École Centrale de Lyon have devised clever ways to measure the shear strength of thin films by a microslip method (Tonck et al., 1986). These strengths are tabulated in Table 12.1. Generally, the film strength increases with load for base fluids, zinc dithiophosphates, and
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FIGURE 12.13 at 250°C.
475
Molecular weight distribution of organometallic compounds from static oxidation tests conducted
calcium sulfonates but decreases with load in the case of a friction modifier. This is reasonable since friction modifiers depend on multilayer adsorption and easily sheared planes between the molecular layers. As load increases, the film thickness will decrease. Monomolecular film studies have also been done (Briscoe and Evans, 1982). The measured shear strength for stearic acid was found to be on the order of about 10 MPa on a steel surface. Comparison of these two results is difficult because of the differences in measurement techniques, film chemistry, and film thickness. Yet in terms of an order of magnitude comparison, it is instructive to note that a monolayer is relatively weak and the complex films generated by lubricants are relatively strong. Another observation is that not all films lubricate (Deckman, 1995). Hsu (1991) suggested that there is an optimum reactivity for a film to lubricate the surfaces based on the commonly observed constant renewal, sacrificial lubrication mechanisms. The ability of the film to lubricate the surfaces depends on the adhesive and cohesive strengths of the film with respect to the surface. Warren et al. (1998) used scanning force microscopy to determine nanomechanical properties of ZDP films from both static (heating) and wear tests. They found that films generated in the highly loaded regions of the wear test were markedly different in nanomechanical response than films from a lightly loaded region and films from a static test. We have attempted to show the linkage among the oxidation reactions, polymerization reactions, and the effects of different materials in effecting lubrication. The picture that is emerging is complex but traceable to molecular phenomena on the surface. The surface is an integral part of the reacting system. Since surfaces depend on many variables including machining, defects, crystalline configurations, oxide layers, hydride layers, etc., the resulting reaction pathways sometimes are difficult to predict. But knowing
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Intensity, arb. units
Apparatus: 4-ball wear tester Speed: 600 rpm Load: 40 kg Atmosphere: 0.25 l/min dry air Lubricant: 6ml superrefined mineral oil Duration: 30 minutes Material: 52100 steel
Molecular weight distribution (refractive index detector)
Fe peak intensities
106
105
104
103
102
101
100
Molecular Weight
FIGURE 12.14
Molecular weight distribution of organometallic compounds from dynamic wear tests.
the surface layer composition precisely, and the operating conditions, the future of predicting boundary lubrication is foreseeable, albeit with the existence of many formidable obstacles. With the many studies on boundary film formation, some generalizations can also be made. Figure 12.16 shows the general diagram for the formation of boundary films. The area of tribochemistry needs many more studies to understand the intricate interactions between surfaces and molecules under rubbing conditions. The role of surface defects as well as dangling bonds (Lenahan and Curry, 1990) needs to be identified and characterized in order to gain important insights into surface reactions which have wide implications for other areas of research as well.
12.4.4 Advances in Measurement Techniques There are several new techniques that have been applied to boundary lubrication issues, ranging from new wear and property measurement to specialized surface and film analysis. In general, these new techniques have followed a trend toward smaller-scale as well as more specific property measurement. At the small end of the scale — atomic-level property measurement — the surface forces apparatus (SFA), pioneered by Israelachvili (Israelachvili, 1986), is being used to probe the properties of the first monolayer of molecules on surfaces. Significant progress has been made on the properties of confined films, even though the technique is limited to transparent, atomically smooth, materials like mica. Scanning probe microscopy (SPM), first introduced as a technique for looking at the topography of surfaces at the nanometer level, is also now being used essentially as a “nanotribometer.” Many different forms of the nanotribometer SPM have been used to measure friction, adhesion, and wear at this ultrasmall scale (Mate, 1995; Feldman et al., 1998; Bhushan et al., 1995). At this scale however, issues of calibration and control are critical and continuously evolving, with recent designs for instruments such as the NIST “calibrated” atomic force microscope (Schneir et al., 1994) as well as commercial “metrology” instruments making their way into use. The issue of cantilever calibration, so critical to obtaining accurate absolute values for forces is being approached from several angles such as finite element analysis (Hazel
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FIGURE 12.15
Molecular weight distribution of organometallic compounds from wear tests of different duration. TABLE 12.1 Mechanical Properties of Surface Films Measured by Microslip Technique: Cast Iron on 52100 Steel Measure Shear Moduli at Selected Normal Load (GPa) Film
1N
2N
5N
10N
Film A, 120 nm dodecane Film b, 60 nm ZDP Film C, 60 nm Ca sulfonate 5% Film D, FM complex ester 1%
3 3.5 1.9 3.4
3.3 3.8 2.1 2.9
3.6 4.7 3.1 2.5
4.3 4.2 3.2 1.8
Data from Tonck, A., Kapsa, Ph., and Sabot, J. (1986), Mechanical behavior of tribochemical films under a cyclic tangential load in a ball flat contact, J. Tribology, Vol. 108, 117.
and Tsukruk, 1998), resonance methods (Cleveland et al., 1993), and reference cantilevers (Gibson et al., 1996). A simple, accurate, calibration for both normal and tangential forces is still elusive. The issue of relevance of these nanoscale measurements to larger “real world” devices is still being debated. Interestingly enough, the relevance issue is being bridged by the fact that actual devices are now shrinking down to the scale of measurement — as in the rapidly developing fields of micromachines and microelectromechanical systems (MEMS). Some very interesting contributions are being made on slightly larger scales with modified SFA and SPM apparatus. These tribometers and indenters make very small-scale measurements of surfaces and films in the nanometer and micrometer scale contact regime. One of the simplest SPM modifications,
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FIGURE 12.16
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Overall framework for boundary lubricating film formation.
first made by Ducker (Ducker et al., 1991), was the attachment of very small spheres to the end of an SPM cantilever. Instead of a contact with 10 nm radius of contact that might just push a film aside, the contact could be enlarged to micrometer dimensions. In another approach, the research group at L’École Central (Bec et al., 1996; Tonck et al., 1986; Georges et al., 1998) have developed an apparatus that utilizes a variety of diamond and sphere tips to apply controlled forces to surfaces and measure their effects. They have made considerable progress in probing the properties of important boundary lubricating thin films such as ZDP on surfaces. In boundary lubrication research, the key has always been unlocking the understanding of the underlying chemistry taking place during lubrication. In many cases this means using the combination of wear testing and key analytical instrumentation designed to elucidate the chemical mechanism responsible for lubrication. In the area of analytical measurements of surface films, the workhorse techniques of FTIR, Raman, XPS, and Auger are being augmented with highly sensitive and specific techniques such as near edge X-ray absorption fine structure (NEXAFS) spectroscopy, which utilizes a synchrotron radiation source to generate soft X-ray beams to measure the presence and orientation of molecularly thin films on surfaces. This technique was first applied to stearic acid on copper and was able to provide a detailed understanding of the surface bonding under both static and dynamic rubbing conditions (Fischer et al., 1997a,b). The technique was also recently applied to nanometer-thin layers of perfluoropolyether
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containing phosphazene on magnetic hard disks to show the presence of unsaturated carbon bonds at the interface (Kang et al., 1999). Time of flight secondary ion mass spectrometry (TOF SIMS) has been used to probe the chemical composition of relatively high-molecular-weight films formed from silicon nitride lubricated by a monoalcohol (Gates and Hsu, 1995). The technique showed unambiguously that silicon alkoxides were being produced by tribochemical reactions during rubbing and helped to define the tribochemical mechanism of boundary lubrication of silicon nitride by alcohols. Other techniques such as microellipsometry and surface reflectivity are being utilized in direct response to specific industrial needs. In the case of the hard disk industry, surface reflectivity techniques are being refined in such a way that depletion of the nanometer-thin lubricant film and wear of the protective carbon overcoat layer can be measured in situ during component testing (Meeks et al., 1995).
12.5 Boundary Lubrication Modeling Boundary lubrication effectiveness has long been considered to be essential in modern machine designs for proper operation. As the demands for better energy efficiency, tighter tolerances, and the availability of new materials, the need to predict lubrication effectiveness in this regime increases. What do we mean by effective predictive models? Given the materials pair, speed, load, surface roughness, lubricant type (viscosity, additive chemistry), and duty cycles, can we predict length of service, amount of wear, time to scuffing, seizure? According to this definition, we currently do not have any such model. At the same time, we can describe fairly well average film thickness, elastohydrodynamic support, and even some wear. It is instructive, therefore, to examine the current predictive ability on some of these parameters: wear, flash temperatures at the tips of the asperities, lubrication transition temperatures, and some discussion on the subject of molecular dynamic simulation.
12.5.1 Wear Wear is a system function. It depends on the system, which includes the materials, surface roughness, lubricants, environment, operating conditions, temperatures, etc. To predict wear a priori, i.e., without experimental fitting constants, is very difficult. Yet wear is such an important parameter, so studies abound to describe the wear processes (Choa et al., 1994). Under boundary lubrication regime, one of the most critical initial system parameters is the real area of contact. This parameter controls the real load the asperities are under and the subsequent stress/strain relationship beneath the contact. As discussed in the chapter titled, “Wear Maps,” the fundamental wear process for most metals is controlled by the accumulation of strain. Greenwood and Williamson (1966) proposed several models to describe the initial real area of contact, which is usually a small fraction of the apparent area of contact between two engineering surfaces. One version, which assumes a distribution of peak heights can be written as:
()
A = π ηβσ F1 h
where η = number of asperities β = asperity radius σ = standard deviation of the peak height distributions and ∞
( ) ∫ (s − h) φ * (s)ds
Fm h =
h
where φ* (s) is a probability density.
m
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However, once the sliding takes place, the real area of contact changes with wear. Under steady-state mild wear condition the real contact area could be quite high when the two surfaces conform to one another. The next step is to model the lubricant rheology in the contact. Under boundary lubrication conditions, traditionally, bulk fluid viscosity does not play a role since the asperities are bearing the load. However, recent studies of fluid molecules under confined space exhibit radically different mechanical and flow properties as compared to those in the bulk (Coy, 1998; Granick, 1991a,b; Granick, 1999; Israelachvili, 1993, 1986; Israelachvili et al., 1988). The viscosity near the wall (nanometers) is much higher than those of the bulk. This also implies that viscosity of the fluid trapped inside the contact among the asperities under sliding conditions may be higher, hence giving rise to the elastohydrodynamic life at the local level. Some of this viscosity and polymer solution behavior near the wall can be simulated by dissipative particle dynamics (DPD) (Hoogerbrugge and Koelman Jmva, 1992; Kong et al., 1997), which is an accelerated molecules dynamics method. Once the rheology is defined, fluid film thickness can be estimated by Dowson and Higginson’s (Dowson and Higginson, 1959) equation:
η0.7 α 0.54 V 0.7 R0.43 h = 1.63 0 00.13 L E ′ 0.03 There are several computer programs available to calculate the contact stresses, fluid flow, temperatures, and elastohydrodynamic lifts (Lee and Cheng, 1992), but to link these calculations to wear is a big step. Bell (Bell and Colgan, 1991; Bell and Willemse, 1998) used component cam-follower wear data to correlate with oil film thickness and calculate the oil film thickness using a finite element program. The wear contours and approximate amount of wear of the cam-follower contact in an engine was successfully simulated. Chemical film formation as a function of additive concentrations and temperatures was not taken into account but simulated by the bench tests.
12.5.2 Flash Temperatures Engineering surfaces are not atomically smooth. Under contact conditions, the hills (asperities) of each surface bump into the hills of the other surface. When they move relative to one another, frictional energy producers heat, and the transient temperatures at the tips of asperities are called flash temperatures. They are a microsecond in duration and highly localized (Furey, 1964). When one surface begins to move over another surface, the contact phenomena are controlled by asperity interactions and the interfacial layer (liquid lubricant or oxide). At very light loads, the friction is controlled by the surface forces which include van der Waals forces, hydration force, electrostatic or double layer forces (depending on the materials), and elastic contacts of the asperities and the viscous drag of the oil film. The elastic contacts will sometimes produce chatter, or stick slip phenomena as observed by frictional force traces. Under high load, the asperity contacts result in plastic deformation of the asperities. This changes the surface features of the interface. The asperity–asperity contacts lead to deformation of the asperities, and this process provides the majority of the frictional resistance. Other processes contributing to friction and heat release are adhesion, plowing, and abrasion. In boundary lubrication, chemical films are produced to provide surface protection. The films for steel systems are produced mostly by frictional heating. Therefore, if one is able to predict the asperity temperatures in the contact one can calculate the chemical reaction rate to generate the films. Historically, two approaches have been used to estimate the flash temperature. One is chemical; the total amount of reaction products is measured and compared to constant temperature reaction rates at different temperatures. Given the time and temperatures, from the total reaction products, the average surface reaction temperatures can be estimated. The other approach is mechanical; asperity contacts are
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modeled to take into account the elasticity, frictional heating, fluid flow, heat transfer characteristics as a function of load, speed, surface roughness, and materials properties. To compare these two approaches, Hsu, Klaus, and Cheng (1988) used a simple experiment on a fourball wear tester. The chemistry of the lubricant was kept simple by using a purified paraffinic base oil. A microsample test procedure was used to allow maximum lubricant degradation. The composition of the lubricant during and after the test was analyzed to show molecular weight changes. The total amount of reaction products generated during the wear test was measured. Knowing the kinetics of the reaction, the temperatures in the contact were calculated. The temperatures were also determined by using a mechanical contact model given the surface roughness, material properties, and physical properties of the lubricant. These two temperatures were then compared. Klaus et al. (1980) demonstrated that conditions within a thin-film micro-oxidation test closely resemble those within a sliding contact. The test used a thin lubricant film on a metal catalyst cup in a nitrogen–oxygen mixture, thus both temperature and oxygen availability may be controlled. Subsequent work (Clark et al., 1985; Klaus et al., 1982) demonstrated that the oxidation reactions followed the Arrhenius relationship. The equation has the form:
k = m e − E RT where T = temperature m = a fitting coefficient E = the activation energy (cal/mode) R = gas constant Naidu et al. (1986) described a global rate model based on the consumption of lubricant within a microoxidation test, subjected to conditions similar to those encountered in a sliding contact. The model describes the primary oxidation step as well as the subsequent condensation polymerization step, which results in lubricant viscosity increase and insoluble sludge formation. These reactions can be described as follows:
where A E B F P D k
= original oil = evaporated original oil = low-molecular-weight oxidation products = evaporated low-molecular-weight products = high-molecular-weight liquid polymerization products = insoluble deposits = reaction rate constants
The estimated contact temperature required to produce polymerization in 10% of the total lubricant volume is shown in Figure 12.17, as a function of film thickness. As the mean separation between the opposing surfaces decreases, the theoretical oil temperature increases exponentially, as less oil is able to enter the contact junction. The mean boundary film thickness between the opposing surfaces is approximately 0.06 µm (600 Å), as calculated from the asperity contact model detailed in the following section. The required film temperature at this separation is 375°C. Figure 12.18 shows the calculated lubricant life at this temperature
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Estimated Temperature, °C
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Film Thickness, µm
FIGURE 12.17
Estimated lubricant temperature as a function of film thickness.
400
Time to Failure, minutes
600 rpm 40 kg 300
3 75
200
°C
100
0 0
1
2
3
4
5
Lubricant Volume, µl
FIGURE 12.18 Calculated oil film temperature required to provide the lubricant oxidation measured during microsample wear tests with different volumes of lubricant.
as a function of lubricant volume, along with experimentally determined values for comparison. As may be seen, the predicted values are in general agreement with the experimental data. The asperity temperatures within the contact zone of two rough surfaces were calculated using the model developed by Lee and Cheng (1992). The input data include two groups: (1) experimental conditions such as sample geometries, load, speed, the material’s elastic constants, and lubricant properties, and (2) measured data such as friction and surface roughness profiles of the worn samples. Given roughness profiles of the opposing surfaces, the calculations include three sequential steps: (1) contact modeling to determine the relationship between average contact pressure and the average distance (gap) between the two surfaces, (2) rough-EHD analysis to calculate the average film thickness and the load distribution between hydrodynamic film support and asperity contacts, and (3) temperature calculation to determine the asperity temperature distribution within the contact zone.
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Surface Roughness Top Ball (inverted)
RMS: 0.19
Lower Ball
RMS: 0.31 Calculation Region
Relative
RMS: 0.23
Test: 2160R Load: 40kg Scale, µm Speed: 600rpm Time: 60 minutes 1 Lubricant: Paraffin Oil Material: 52100 steel 100 Measurements taken perpendicular to direction of sliding
FIGURE 12.19
Profiles taken from opposing worn surfaces.
To model two surfaces in contact, one has to describe the surface roughness and simulate the contact geometry under static load mathematically. The contact model used assumes that both surfaces have longitudinal roughness. The validity of this assumption has been demonstrated (Sugimura and Kimura, 1984; Wang et al., 1991) for wear scars formed after a four-ball wear test. Figure 12.19 shows the surface roughness profiles taken from the top ball (inverted) and the lower balls after the prewear test. These profiles were measured perpendicular to the sliding direction. To ensure accurate representation of the wear scar on the top ball, its roughness trace was determined by averaging digitized profiles in three angular directions (θ = 0°, θ = 120°, θ = 240°). An average trace for the lower balls was similarly determined, one profile being taken from each of the lower balls. Subsequently, the profiles from the top ball and the lower balls were derived, by subtraction, to form a composite profile, denoted as “relative” trace in Figure 12.19. The contact between the top ball and the lower balls was then simulated by analyzing the contact between the composite profile and a rigid plane. Taking into account the elastic deformation, the local high spots (asperities) of the composite profile would deform and become flattened when the profile is pressed against the rigid plane. The distance measured from the rigid plane to the mean line (plane) of the deformed composite profile defines the average gap between the mean lines (planes) of the two rough surfaces under the same load. Meanwhile, the average pressure of those deformed asperities defines the average contact pressure. By increasing the severity of loading, the average gap becomes smaller, while the contact pressures of the individual asperities increase. Depending on the local geometries, some of the asperities may yield as the contact severity increases. When this happens, the model assumes that the contact pressure stays at the yield pressure and does not increase further. If one varies the loading mathematically, one could determine the relationship between the average contact pressure and the average gap, as illustrated in Figure 12.20. For this particular simulation, since the balls are preworn, the maximum Hertzian pressure under an applied load of 40 kg is estimated to be 0.847 GPa. The average gap in the central portion of the contact is about 0.06 µm, according to Figure 12.20. The r.m.s. value of the “relative” roughness shown in Figure 12.19 is 0.23 µm. After the relationship between average contact pressure and average gap has been determined, the rough-EHD analysis was then carried out. In the rough-EHD analysis, a line-contact between two rough cylinders is assumed, and only the inlet half of the contact is analyzed (Lee and Cheng, 1992). The pressure along the centerline of the line contact is assumed to be the same as the maximum Hertzian pressure determined by considering the preworn geometry. The film thickness solution of the rough-EHD analysis is based on the average gap. Since the analysis is based on two rough surfaces in contact, the two cylinders are subjected to two types of pressures; one from hydrodynamic lift, the other from asperity contact pressures. The relationship between average contact pressure and average gap determined in the contact simulation previously is therefore utilized
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6
Average Pressure, GPa
5
4
3
2
1
0 0.0
0.1
0.3
0.2
Average Gap, µm
FIGURE 12.20
Average contact pressure as a function of gap between mean lines of opposing surfaces.
1.0
Fraction of Centerline Pressure
0.8
Asperity Pressure
0.6
0.4
0.2 Hydrodynamic Pressure 0.0 -1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
X/b
FIGURE 12.21
Normal pressure as a function of normalized distance from contact center.
in the calculation of the overall pressure distribution of the contact. Figure 12.21 illustrates the loadsharing characteristics between asperity contact and hydrodynamic lift, as a function of the normalized distance from the center of the contact. The parameter b is the Hertzian contact radius. Clearly, asperity contacts carry most of the normal load, thus, sliding friction between the opposing asperity contacts will be responsible for most of the heat generated. Besides the pressure estimations, the rough-EHD analysis also calculates the average friction coefficient from the asperity contacts based on the measured friction value (Lee and Cheng, 1992). In this case, the measured friction coefficient was 0.11, and the average asperity contact friction was determined to be 0.112. From the rough-EHD calculations, the size and shape of the asperities within the contact zone can be determined. Each asperity contact forms roughly an elongated ellipse, with its major axis orientated in the sliding direction. Also, the pressure distribution on each asperity as a function of distance from the contact centerline can be determined. Before the temperature calculations are performed based on Jaeger’s work (Jaeger, 1942), some further simplifications are taken. Each asperity contact is approximated to be rectangular, and its average contact pressure is used for temperature calculations. Frictional heating is
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Temperature, °C
180
160
140
120
100 0.0
0.1
0.2
0.3
0.4
0.5
Contact Area Ratio
FIGURE 12.22
Cumulative temperature distribution within the Hertzian contact.
considered as the heat source, which includes both the average asperity contact friction and the hydrodynamic film friction. The resulting temperature within each asperity contact is a function of the location measured from the centerline of the nominal contact zone. The maximum temperature of each asperity contact is sought and will be considered as the representative temperature for that asperity. Figure 12.22 shows the cumulative temperature distribution under the conditions included in Figure 12.19. The highest temperature attainable is approximately 220°C covering about 3% of the nominal area. These results also reveal that the asperity contacts cover approximately 45% of the nominal area, and the bulk temperature is ~150°C. The results of the temperature analysis show that the temperatures within the contact zone are in the range of 150 to 220°C. This is in general agreement with other continuum models (Francis, 1970; Fein, 1960) which, for the present test conditions, predict the maximum contact temperature to be 157 and 160°C, respectively. By using the current model, the considerations of asperity contacts, thus local high contact pressures, and a slightly higher average friction than the measured overall friction appear to have already increased the temperature estimates. However, the reaction kinetics model estimates an average temperature of 375°C in the lubricant film is necessary to degrade 10% of the total lubricant. Also, measurements carried out by Bos (Bos, 1975) under slightly more severe conditions using a subsurface thermocouple, demonstrated that the true surface temperatures during a four-ball wear test are in excess of 300°C. Clearly, the predicted contact temperatures based on the current mechanical model are considerably lower than that required by the chemical reaction model. The discrepancy is large enough to be significant. For a more detailed discussion on the subject, see reference Hsu et al., 1994.
12.5.3 Asperity-Asperity Understanding One can effectively argue that most wear events under effective lubrication conditions are occurring at the asperity level. Conversely, lubrication means protecting the asperities. When asperities are touching and sliding over each other, both mechanical events and chemical events occur, but the wear is dominated by the mechanical events in the form of contact pressures, stresses, and strain accumulation rate. If the load is so high that fracture of the asperity is inevitable, lubrication has little impact. For lower loads, the protective mechanisms are: load-bearing interface; easily shearable layer; interfilm shear; and adhesion barrier. Under high pressure, the lubricant or the chemical film behaves like a solid between the contact, enlarging the real area of contact, hence reducing the contact pressure, redistributing the stresses, and therefore reducing the strain buildup rate for metals or the stress intensity for brittle solids. Since wear of brittle solids depends primarily on stress intensity, lowering it minimizes wear. If the film
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is easily shearable and has sufficient thickness, then the magnitude of the tensile stresses imposed by the asperity will be significantly reduced. If the film is thick enough and can allow interfilm shear to take place easily, such as solid lubricating films with weak planar attractive forces, the relative motion can be accommodated by interfilm movement. If the molecules are large, have strong bonding to the surface to resist shear, and cover the asperity surface reasonably well, the presence of such film will prevent nascent surface contact forming cold welding or adhesion. Under current boundary lubrication technology, many of these protective mechanisms are being used to protect the surfaces.
12.5.4 Molecular Dynamics Modeling In the last decade, molecular dynamics modeling of contacts and friction between materials has been used to understand the atomic and molecular origin of friction and wear (Harrison et al., 1995; Perry and Harrison, 1996; Stuart and Harrison, 1999). Concurrently, experimental measurements at the atomic and molecular level have been conducted (Granick, 1991a,b; Granick, 1999; Krim, 1996; Mate, 1995). These results are providing insights into the fundamental processes of friction and wear. 12.5.4.1 The Issue of Scale While the molecular dynamic calculations and the atomic scale measurements are providing valuable insights into the basic processes, the issue of scale emerges. Proponents of atomic scale investigations point out that if we understand the friction at the molecular level, then we can apply this knowledge to the micro- and macroscale events and significantly improve the technology. At this time, this has not taken place. Let us examine the issue from an engineering point of view. On each asperity, there are subasperities, which are smaller in scale. On each subasperity, there are sub-subasperities, and so on. At what scale should the contact of two surfaces be considered? For most engineering applications, the critical scale for friction is at the micron scale. The sub- subasperities need not be considered. Can one describe fully the asperity deformation process from the deformation of subasperities, sub-subasperities … down to the molecular or atomic level? The asperity deformation process is a complex system containing many stress domains, defects, and various dislocation zones. Within each zone, there are many energy levels existing at the molecular level. It is not clear how atomic simulations can reach the proper scale factor to simulate what is happening at the interface. But if a constitutive relationship can be developed from the molecular dynamic models, it may help to explain phenomena difficult to observe experimentally. 12.5.4.2 Molecular Dynamics Models The basic calculation procedure has been laid out (Harrison et al., 1993). Take a collection of atoms or molecules, calculate the interatomic forces, integrate equations of motion within a boundary from an initial position, according to the temperature, pressure, stress, and energy transfer mechanisms specified by the model. Periodic boundaries are used to simulate an extended array of atoms. Reactions and molecular attachment are dictated by energy levels and pairwise potentials (Brenner, 1990). An example of this technique is shown in Figure 12.23 for the simulated tribochemical wear of diamond (Harrison and Brenner, 1994). As the model diamond surfaces pass one another under contact (from a → d), we observe C–C bond formation (adhesion), and subsequent bond breakage resulting in the transfer of atoms from one surface to the other. This area of study is rapidly evolving to handle complex situations more relevant to boundary lubrication; however, the current significance to practical lubrication is not clear at this time.
12.6
Concluding Remarks
Significant progress has been made in the field of boundary lubrication research in the past 20 years. Much of this is focused on understanding the factors that influence lubrication effectiveness. We can identify the effects of tribochemistry, lubrication film formation, and the failure mechanisms of boundary
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FIGURE 12.23 Molecular dynamics model simulation of tribochemical interaction between diamond surfaces. (From Harrison, J.A. and Brenner, D.W. (1994), Simulated tribochemistry — an atomic-scale view of the wear of diamond, Journal of the American Chemical Society, 116 (23):10399-10402. With permission.)
lubrication much better; however, our ability to predict lubrication effectiveness in any given instance for a particular system still needs development.
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Ranney, M.W. (1980) Synthetic Oils and Additives for Lubricants: Advances since 1977, Noyes Data Corp., Park Ridge, N.J. Reynolds, O. (1886), On the theory of lubrication and its application to Mr Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil, Phil. Trans. R. Soc., 117:157-234. Rosenblum, F., Braunlich P., and Himmel, L. (1977), Spontaneous emission of charged particles and photons during tensile deformation of oxide-covered metals under ultrahigh vacuum conditions, J. Appl. Phys., Vol. 48, 5262. Satriana, M.J. (1982) Synthetic Oils and Additives: Advances Since 1979, Noyes Data Corp., Park Ridge, N.J. Schneir, J., Mcwaid, T.H., Alexander, J., and Wilfley, B.P. (1994), Design of an atomic-force microscope with interferometric position control, Journal of Vacuum Science & Technology B, 12 (6):3561-3566. Sheasby, J.S., Caughlin, T.A., and Habeeb, J.J. (1991), Observation of the antiwear activity of zinc dialkyldithiophosphate additives, Wear, 150 (1-2):247-257. Shubkin, R.L. (1993), Synthetic Lubricants and High Performance Functional Fluids, Marcel Dekker, New York. Simoi, C., Hrianca, I., and Cracium, P. (1968), Exoemission of electrons without photo-stimulation, Phys. Status Solidi, Vol. 29, 761. Smalheer, C.V. and Smith, R.K. Lubricant Additives, Lezius-Hiles, Cleveland, OH. Spikes, H.A. (1996), Direct observation of boundary layers, Langmuir, 12 (19):4567-4573. Stuart, S.J. and Harrison, J.A. (1999), Molecular dynamics study of lubrication by small hydrocarbons, Abstracts of Papers of the American Chemical Society, 217:U589. Sugimura, J. and Kimura, Y. (1984), Characterization of topographical changes during lubricated wear, Wear, Vol. 98, 101. Tomizawa, H. and Fischer, T. (1986), Friction and wear of silicon nitride and silicon carbide in water: hydrodynamic lubrication at low sliding speed obtained by tribochemical wear, ASLE Trans., Vol. 30, 41. Tonck, A., Kapsa, Ph., and Sabot, J. (1986), Mechanical behavior of tribochemical films under a cyclic tangential load in a ball flat contact, J. Tribology, Vol. 108, 117. Wang, F.X., Lacey, P., Gates, R.S., and Hsu, S.M. (1991), A study of the relative surface conformity between 2 surfaces in sliding contact, Journal of Tribology — Transactions of the ASME, 113 (4):755-761. Warren, O.L., Graham, J.F., Norton, P.R., Houston, J.E., and Michalske, T.A. (1998), Nanomechanical properties of films derived from zinc dialkyldithiophosphate, Tribology Letters, 4:189-198. Yang, Y.Y., Torrance, A.A., and Oxley, P.L.B. (1996), Modelling mechanical wear processes in metallic sliding friction, Journal of Physics D — Applied Physics, 29 (3):600-608. Yates, J.T., Dohnalek, Z., Yang, W., and Choyke, W.J. (1996), Defect site effects on chlorine chemistry on silicon, Abstracts of Papers of the American Chemical Society, 211:18-PHYS. Ying, T.N. (1994), Wear mechanisms for ductile and brittle materials in a microcontact, Ph.D. Thesis, Department of Materials and Nuclear Engineering, University of Maryland, College Park, MD.
For Further Information The reader is directed to the following important resources for further information on the topics discussed in this chapter on boundary lubrication. Boundary Lubrication: An Appraisal of World Literature, F.F. Ling, E.E. Klaus, and R.S. Fein, Editors, ASME, NY [1969]. CRC Handbook of Lubrication, Theory and Practice of Tribology, Volume II: Theory and Design, Richard Booser, Editor, CRC Press, Boca Raton, FL [1984]. Limits of Lubrication, selected papers from the Limits of Lubrication Conference in Williamsburg, VA, April 14-18, 1996. Tribology Letters 3(1) [1997]. Tribochemistry, Heinke, G., Hanser Press, Munich, Germany [1984].
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Defining Terms Additive: Chemical compounds dissolved or dispersed in a base fluid to impart or extend desirable properties to the lubricant. Basestocks: Main fluid component of a lubricant. Can be derived from naturally occurring, or synthetic sources. Boundary Lubrication: Lubrication regime involving contact between asperities in relative motion in which chemical reactions dominate the mechanism of reduction of friction and wear. Dangling Bonds: Highly reactive sites on atoms resulting from inability of the atom to form proper bonds with nearest neighbor atoms. Can occur when bonds in a structure are broken by mechanical forces. Friction Polymer: High-molecular-weight product formed in some contacts under boundary lubricating conditions. Kurtosis: Surface roughness parameter describing the narrowness of the peak height distribution. Nascent Surfaces: Fresh surfaces formed during rubbing. Highly reactive. Organometallic: Chemical compounds consisting of metal atoms bonded to organic molecules. Ra: Surface roughness parameter describing the average surface roughness, also known as centerline average roughness. RMS: Surface roughness parameter describing the root mean square surface roughness. Skewness: Surface roughness parameter describing the asymmetry of the peak height distribution of a surface. Tribochemistry: Chemical reactions that are induced by rubbing, usually referring to reactions that are not observed by purely thermal means.
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13 Friction and Wear Measurement Techniques
Niklas Axén Uppsala University
Sture Hogmark Uppsala University
Staffan Jacobson Uppsala University
13.1
13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10
The Importance of Testing in Tribology ........................ 493 Wear or Surface Damage ................................................. 494 Classification of Tribotests .............................................. 497 Tribotest Planning............................................................ 498 Evaluation of Wear Processes.......................................... 500 Tribotests — Selected Examples ..................................... 501 Abrasive Wear................................................................... 502 Erosive Wear ..................................................................... 504 Wear in Sliding and Rolling Contacts ............................ 505 Very Mild Wear ................................................................ 508
The Importance of Testing in Tribology
Friction and wear are caused by complicated and multiplex sets of microscopic interactions between surfaces that are in mechanical contact and slide against each other. These interactions are the result of the materials, the geometrical and topographical characteristics of the surfaces, and the overall conditions under which the surfaces are made to slide against each other, e.g., loading, temperature, atmosphere, type of contact, etc. All mechanical, physical, chemical, and geometrical aspects of the surface contact and of the surrounding atmosphere affect the surface interactions and thereby also the tribological characteristics of the system. Therefore, friction and wear are not simply materials parameters available in handbooks; they are unique characteristics of the tribological system in which they are measured. For most surfaces in relative sliding or rolling contact, the area of real contact is much smaller than the nominal contact area. The applied load is carried by a number of small local asperities making up the area of real contact, and the friction and wear behavior results from the interactions between these local contact asperities. At the regions of these local contacts, the conditions are characterized by very high pressures and shear stresses, often well above the yield stress of the materials, high local (flash) temperatures of short duration, and maybe also very high degrees of deformation and high shear rates. Under such conditions, the local mechanical properties of the materials may be very different from what is found, for example, in normal tensile testing. The importance of oxide layers, small amounts of contaminants, local phase transformations, etc., is also much greater than in large-scale mechanical testing. Consequently, the properties of a material in the real contact areas may be far from those measured in normal mechanical testing procedures, and the coupling between wear and friction properties and traditional mechanical properties, such as elastic modulus and yield strength, is weak. See Zum Gahr (1987) and Hutchings (1992). 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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It also follows from the systems aspect of friction and wear (and the insight into how complicated a surface contact consisting of interacting local asperities, rather than of flats, really may be) that modeling of friction and wear becomes very difficult. Unfortunately, there are very few reliably and reasonably comprehensive models describing the wear or friction processes. This dearth of good models strongly complicates the interpretation of measured wear and friction data. There is also generally no simple correlation between wear and friction; for example, low friction does not automatically imply low wear rates. See Czichos (1987). Still, the effect of system parameters on tribological properties should not be exaggerated. Many materials do produce low friction or high wear resistance in most practical situations, and may therefore very well be referred to as low-friction materials or wear-resistant materials. Diamond or Teflon® (PTFE) produce low friction in most sliding systems, but exceptions can certainly be found. Cemented carbides are wear-resistant materials, but they may wear very quickly in corrosive environments. But, because of the system nature of tribological parameters, tabulated friction or wear values for these or any other materials are only meaningful if test conditions are very carefully documented. Conclusively, because tribological properties are not materials but system parameters, tribotesting has to be an integral part of both the process of developing tribomaterials and in the selection of materials for applications involving friction and wear.
13.2
Wear or Surface Damage
According to DIN 50 320, or similarly in other terminology standards, wear is the progressive removal of material from a surface in sliding or rolling contact against a countersurface. As described in many textbooks, e.g., Zum Gahr (1987) and Hutchings (1992), different types of wear may be separated by referring to the basic material removal mechanisms, the wear mechanisms, that cause the wear on a microscopic level. There are many attempts to classify wear by wear mechanisms, but a commonly accepted first order classification distinguishes between adhesive wear, abrasive wear, wear caused by surface fatigue, and wear due to tribochemical reactions. Over a longer sliding distance, either one mechanism alone, or a combination of several of these wear mechanisms, causes a continuous removal of material from the mating surfaces, and thereby also adds to the friction force that opposes the sliding. Such continuous, steady-state wear and friction conditions may be quantified in terms of wear rates, i.e., removed material mass or volume per sliding distance or time, or its inverse, the wear resistance, and in terms of friction forces or friction coefficients. However, not all types of tribological failures are due to wear in the sense of a continuous material removal from tribosurfaces, and the tribological properties of the materials in a component are not always best described by their wear resistances or friction properties. Instead a broader study of the various types of surface damages that occur may be more meaningful. If for example the lubrication of a piston-cylinder system fails, the result will generally be an increased temperature leading to softening or even melting of the surface asperities, followed by an increasing adhesion, material transfer, and local surface welds between the piston and cylinder surfaces; the engine seizes, as exemplified in Figure 13.1. Or, taking cutting tools as another example, the reason for lost cutting performance may very well not be a continuous wear of the cutting edges. Instead a few sudden, catastrophic and discrete events, such as grain pull-outs, edge fractures, or sudden local overheating causing plastic deformation, may lead to lost edge geometry followed by reduced tolerances, unacceptable surface finish, or increased cutting forces. In both these examples the actual wear rate may be very low and perhaps of no importance for the occurrence of the seizure or the lost cutting edge performance; but still, the effect of the events on the performance of the tribosystems is dramatic. Often, the wear process will undergo several stages as sliding proceeds; at least three stages are commonly identified: The wear starts with what could be called a run-in stage, during which steady-state conditions are building up (Figure 13.2). The running-in may be very important for some sliding systems, as for many types of bearings and gears. During this stage the mating surfaces conform to each other in
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FIGURE 13.1
Seized piston from combustion engine.
FIGURE 13.2
Typical wear stages appearing over longer service times in sliding contacts.
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such a way that the load is more favorably distributed over the surfaces. During the early running-in stages, the wear rates may be relatively high; running-in should, however, be short compared to the whole lifetime of the component. Steady-state conditions with low wear rates and stable friction values should prevail for most of the lifetime of the system, but low steady-state wear rates will eventually alter clearances or surface properties to the extent that components fail, during a brief, final, catastrophic stage during which wear rates are high and severe surface damage occurs. Only wear rates or friction forces measured during the stable, steady-state conditions are useful in characterizing the long-term properties of the system. Damages to a failed component, which occurred just shortly before the failure, are not characteristic of the continuous wear of the materials, and can therefore not explain the series of events leading to failure. Identifying the stage during which a component’s surface damages (or their precursors) did appear, and what their importance is to overall performance of the component, is one of the more difficult parts of analyzing the failure of tribological components, and probably also the point at which many analyses go wrong. To predict the onset of severe wear regimes is a challenge. The variety of surface damage types that may occur is vast. An attempt to provide some organization of all the possible types of surface damages is found in Hogmark et al. (1992). The following classes of surface damage of tribological importance are there described (Figure 13.3):
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FIGURE 13.3
Classification of surface damages and wear.
• Structural changes of the surface, for example phase transformations, formation of diffusion zones or recrystallization. Such surface changes may occur solely because of mechanical deformation of the surface, or be the result of heat generation causing diffusion or chemical reactions. Structural surface changes do not necessarily imply wear, but they may alter the mechanical properties of the outer surface layers and may constitute the initial stages of wear or other types of failures. • Plastic deformation caused by mechanical stresses or by thermal gradients at the surface. Although plastic deformation of surface asperities or of an entire surface zone does not necessarily need to be associated with gradual wear, it is of the utmost importance in the creation of any surface damage that may eventually lead to catastrophic failures. • Cracking in the surface zone may also be caused by exaggerated surface stresses, fatiguing cyclic deformations, or of repeated thermal alterations. Cracking may also be an initial mechanism that eventually leads to large-scale damage without causing any progressive wear during the service stage. • Corrosion or other chemical attacks may represent the main wear mechanism, but more frequently they assist in mechanical wear processes. Frequently, chemical attacks are the cause of lost surface finish and accelerated crack propagation.
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• Wear or surface damage involving continuous material loss due to various types of microscopic material removal mechanisms, causing material to leave the surface as debris. The wear mechanisms may ultimately be both mechanical and chemical. • Gain of material, such as material transfer from the countersurface, resulting from excessive heating of the surfaces, agglomeration of debris such as may appear in seizure, or embedment during erosion. The resulting “third-body” layers are typical of conformal sliding contacts. Very commonly, the damage observed on a tribologically loaded surface is a result of two or more coexisting or interacting surface damage types. Interacting damage types may lead to unproportionally high wear rates, as for example in oxidation-enhanced surface cracking; adhesive wear may however also be suppressed by oxidation. In the selection and design of tribological test systems, and in the choice of test parameters, great care must be taken in considering whether measured wear rates or friction forces are the best characterization parameters for the system. Perhaps the study should focus on the occurring types of surface damage instead. Generally a combination of the two is most rewarding. Likewise, it is important to consider what stages in the life-cycle of a tribosurface a test should evaluate: wear rates or wear mechanisms during steady-state conditions or surface damages responsible for the failure. In many cases microscopy or other surface characterization techniques may be more important than wear rate or friction measurements. As further described below, a selected tribotest always has to reproduce the specific type of wear mechanisms or surface damages that appear in the intended application. An approach to this is also described in Chapter 14.
13.3
Classification of Tribotests
Tribological tests can be performed in an almost endless number of ways. As the outcome of a tribotest is strongly related not only to the characteristics of the materials couple, but also to the whole mechanical system and its environment, the process of selecting the most appropriate test for a specific purpose is fundamental to making meaningful interpretations; it is crucial to plan tribotesting in detail, as shall be further described below. A rational tribotest classification facilitates the tribotest planning. It is convenient to classify tribological test methods according to their degree of realism, i.e., how closely they imitate the conditions of a real application. Generally a high degree of realism is aimed for, but there are also many reasons to evaluate materials in tests far from any application. Consider for example the aspects of cost, test time, and the accurate control of test conditions, or the wish to perform a scientific study of individual, isolated wear mechanisms. For such evaluations, clearly the simulation of an application does not have the highest priority. One of the most accepted ways of classifying tribotests, found for example in the DIN 50 322 German industrial standards or Zum Gahr (1987), identifies five levels of simple tests in addition to the field test of the entire system (Figure 13.4). If for example the wear characteristics of the cylinder–piston system in a car engine are to be investigated, a field test would include the whole vehicle driven under realistic service conditions. The whole vehicle could, however, also be evaluated in a bench test, which to improve the degree of test condition control is performed in a laboratory or other controlled milieu. Serving the purpose of reducing cost, only the important subsystem (which is still a real system and not a model), the engine in this example, may be tested under controlled conditions in a laboratory. To simplify even further, only the important machine components can be evaluated in a component test. Although a wellplanned component test might at first seem similar to any bench or field test, the alterations in the system’s complicated environments are likely to affect the test conditions significantly; heat dissipation, vibrations, conditions of lubrication, etc., will not be entirely identical. To further increase efficiency and the degree of control over the test conditions, a simplified component test or a full-model test may be explored. With a simple model test a large range of materials can be easily, quickly, and cheaply evaluated, under well-controlled test conditions. The degree of realism, however, in the data and the surface damage features, and also the possibility of making reliable conclusions about performance or usability in an application, decreases when we go from the field test to the simpler model test.
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Classification
FIGURE 13.4
Decreasing cost and Increasing control
Increasing test realism
Field test
Bench test Tribocouple test Sub-system test
Component test
Simplified component test
Semi-tribocouple test
Model test
Model test
Classification of tribotests according to the degree of realism.
Any model test may be further classified according to the characteristics of the tribosystem, as illustrated in Figure 13.4. This classification originates from the frequent wish to evaluate new materials or new designs for one or two components in already existing machinery. Because of cost and time schedules, the evaluations should be performed in some kind of simplistic test equipment; the components are real, but the rest of the tribosystem has to be simulated. In such situations one may distinguish between tests with full tribocouples, thus involving the real components in both of the sliding surfaces, or semitribocouple tests in which only one of the surfaces represents an actual component. In a pure model test both tribosurfaces are replaced by simulated components. In addition, tribotests may be classified as open or closed, with respect to the type of tribological contact situation. If one tribosurface continuously follows the same track on the counterbody, the system is closed, whereas the sliding track is continuously renewed in an open system. (Open or closed may also refer to systems with fresh or recycled particles or oil.) One can also distinguish between tests involving unidirectional or reciprocal sliding, or specify whether the contact involves impacts. Sometimes it may be convenient to distinguish between conformal or nonconformal (alternatively counterformal) contacts. For counterformal geometries, the contact area changes (often increases) as wear proceeds, leading to varied contact conditions, as for example, when a sphere is worn against a flat. Further test configurations are outlined in a later section on selected examples of tribotests.
13.4
Tribotest Planning
It follows from the systems aspect of wear and friction, i.e., the insight that tribological properties depend on the whole tribosystem and not merely on the materials, that any tribological testing should be preceded by a thorough evaluation of the characteristics of the system to be evaluated and the purposes of the test;
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FIGURE 13.5
499
Reasons to perform tribotests.
a tribotest should always be designed to meet a defined need (Figure 13.5). One such need to perform a tribotest may be to rank a set of materials in terms of their friction and wear properties in a certain, welldefined system, either with the purpose of selecting a material for an existing piece of machinery, which the tribotest then should imitate, or to select a tribological material for a construction under development, for which field tests or component tests are impossible. Alternatively, the purpose of tribotesting may be to increase the fundamental and general understanding of how a material behaves in tribological applications. For that purpose, the response of that material to each individual type of wear mechanism has to be studied; this includes the exposure of the material to a variety of model tests simulating different mechanisms under systematically varied loading conditions. For each mechanism, the materials are characterized in terms of wear resistance, friction properties and typical types of surface damage — what may be called the tribological profile of the material. This is the scientific procedure to evaluate the tribological properties of new materials, and the purpose may be to recommend tribological applications for a new material. In evaluating materials for specific applications, the tribotest selection procedure becomes critical. Always choose the highest possible level of realism in the tests (i.e., higher test level according to Figure 13.4), considering the aspects of time, cost, and test condition control. As the degree of realism in the test increases, the interpretation of the test results becomes more reliable and can be more safely applied to the application in mind. A lower test level ranking means that more care must be taken to ensure that the friction and wear mechanisms of the service component are indeed simulated in the test, and surface damage analysis thereby becomes an important part of the tribotesting procedure. Also in terms of test parameters, the closest possible resemblance to the application should be aimed for. Imitate the loading situation, the contact pressures, sliding speeds, contact frequencies, ambient temperatures, atmospheres, lubricants, etc. (Hogmark et al., 1991). Consequently, the first step in the tribotest planning process is to study the application carefully in order to simulate the loading conditions as closely as possible. Secondly, the appearing wear mechanisms, specific for the service conditions have to be identified, and as a third step, a tribotest may be selected, possibly following an iterative process of wear mechanism control (Figure 13.6). The most basic and important criterion for ensuring the relevance of a model test is the close reproduction of the wear mechanisms appearing in the application during service conditions. The imitation of the actual wear mechanism is decisive for the friction and wear behavior of the tested materials. The wear mechanism, or set of wear mechanisms that a tested material is exposed to, are determined by the properties of the counterface material together with all test parameters. Temperature in particular may greatly influence wear behavior, even if the mechanism itself is under control. Maintaining the proper temperature may be difficult even if all other conditions are satisfactory, e.g., because the test pieces may be smaller than the actual components, providing a smaller heat capacity, or because heat dissipation from the tribocontact or cooling rates through the atmosphere or lubricant might differ.
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FIGURE 13.6
Recommendations for the planning of a tribotest.
Very often laboratory model tests are deliberately designed to increase, or accelerate, the wear rate of a test in order to speed up the evaluation. This is most generally achieved by exaggerating either contact pressure or sliding speed, or both. Unfortunately, test acceleration by exaggerating the contact pressure and sliding speed often alters the wear type, particularly through changing the temperature conditions, and accelerated tests that do not reproduce the true wear mechanisms are of limited value. For wear types that result from a large number of microevents, the obvious example being erosion by hard particles, the test procedure can be accelerated by increasing the rate at which the events appear, for example by increasing the rate of erodent hits, or the density of grit in an abrasive type of wear. For simulation of tribosystems with intermittent contact, a decrease in the duration of the noncontact phase may be a good way of accelerating a test. Another, often neglected part of tribotesting, also emerging from the system aspect of tribological properties, is the importance of using reference materials. Strictly seen, tribological properties are only comparative parameters, and even in a tribosystem as well characterized as it realistically can be, a wear rate or friction value measured for a sole material shall be used with skepticism. The selection of reference materials may follow different routes. In the ranking procedure for existing machineries, of course materials commonly used in the application are adequate references, but in a general tribological evaluation of an uncharacterized material, reference materials well known for specific behaviors, e.g., ductility, resistance to surface fatigue, low friction, etc., may be selected for comparison purposes. To gain knowledge about the wear mechanisms and to facilitate the overall ranking of materials, it may even pay to include materials which are known to behave poorly in the application.
13.5
Evaluation of Wear Processes
The most commonly used techniques to evaluate wear are weighing and measurement of changes in dimensions. Weighing may often be difficult if the worn volumes are small compared to the weight of the component, as is further discussed in the later section on mild wear. The wear may also be unevenly distributed over a surface, making the measurement of local wear damage more relevant than the total mass loss. Laboratory model tests may allow a continuous recording of the wear, whereas this may be more problematic in the evaluation of actual components, for which estimations of wear scar dimensions with microscopy is more realistic. The identification of wear mechanisms and surface damages is an important part of any tribotesting procedure and should accompany the measuring of wear and friction values. Therefore, the study of worn surfaces, for example with microscopy or surface topography techniques, becomes an integral part of the evaluation procedure. When examining a worn surface it is important to be attentive to the type of surface damage which sets the life time of the component; this may not be the most spectacular feature appearing on the wear scar. In other words, the identification of the most important mechanisms of a
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FIGURE 13.7
501
Recommendations for the evaluation of wear processes
wear process is an important part of the evaluation process. For large components, the use of replica techniques may prove fruitful. This identification procedure may be very difficult and there are no universal procedures to follow (Figure 13.7). Be attentive to what has caused the failure and identify the location of the damage on the surface. Consider whether the failure is the result of continuous wear, or of suddenly appearing damage. Also be aware that a worn out or failed detail seldom gives information about the wear mechanism which caused the wear during service, since these may be hidden by damage that occurred during the end phase of the failure. Study components that have not yet failed, and compare worn and unworn components. This helps to differentiate between surface features which appeared during the manufacturing, and those caused by the service conditions. Study the worn surface in cross-section. This provides information about the depth of the damage, crystallographic changes caused by temperature; the lack of surface zones may indicate chemical wear. Study the countersurface. This may provide further hints about the wear process, such as transferred layers of material or embedded hard particles. Try to collect wear debris; its size, shape, and chemical content may provide ideas about wear mechanisms and surface temperatures. Because of the number of parameters influencing friction and wear, and their potential fluctuations and time dependence, scatter of data is one of the prime problems in tribotesting. The influence of both systematic and random deviations has to be taken into account. The causes of scatter may be found far from the materials or the tribometer itself; surface preparations, heat treatments, variations between batches, humidity variations, etc., may all strongly affect the measured values of friction and wear. Therefore the number of tests required to achieve a reliable result is a matter of constant debate among tribologists. It is no understatement that the result of a single measurement should be considered with great prudence. To minimize the number of influencing parameters, it is generally favorable if all tests in an evaluation procedure can be run by the same operator during a limited time period.
13.6
Tribotests — Selected Examples
Large amounts of test equipment for the evaluation of wear and friction properties, often referred to as tribometers, have been designed over the years for a variety of purposes. In this context, only a small number of model tests will be presented; these tests merit particular attention either because of being frequently used, or for representing interesting recent developments in the field of tribotesting. In addition to model tests, a large number of more application-oriented tests are in use, particularly in the industrial sector. As part of the development of materials for cutting and grinding tools, bearings, seals, etc., accelerated application-close trial tests are frequently used. For further examples of tribotests, see Blau (1992) and Normung (1986). The tribotest examples below are organized according to the main wear mechanism they are designed to simulate.
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Abrasive Wear
Among the basic wear mechanisms, pure abrasion, which is grooving by hard particles or hard asperities on a countersurface, is probably the most meticulously studied. Compared to other types of wear, the analytical models developed to describe abrasion are much more reliable and comprehensive, which strongly facilitates the interpretation of test results. For well-characterized materials, rough material rankings are sometimes possible without any testing at all. In pure abrasion there is a linearity between wear volume and sliding distance (as long as the wear of the abrasives is negligible), which is in strong contrast to many sliding contact situations. For relatively ductile materials, including most metals, a proportionality between abrasive wear resistance and indentation hardness is also generally observed, although the dependence on hardness is strongly different for different groups of ductile materials. There are also functional analytical models for the effect of grit shape and size, and for the abrasion properties of materials consisting of several phases (see Zum Gahr [1987] and Axén et al. [1996]). Since the abrasion rate depends very strongly on the shape, size, hardness, and friability of the abrasive particles, the choice of grit is particularly important in the evaluation of abrasion properties. A strong decrease in wear rate occurs when the sample hardness exceeds the grit hardness (Hutchings, 1992). Also, abrasion with loose particles, called three-body abrasion, produces fundamentally different wear types compared to tests with fixed abrasives (two-body abrasion). Three-body abrasion becomes intimately sensitive to the properties, particularly the hardness, of the counterbody. A strong shift in the wear rate has been identified at unity ratio of grit hardness to workpiece hardness (see Figure 13.8 and Axén et al., 1994). Also the degree of freedom of motion of the grit, the compliance of the support, etc., affect the characteristics of an abrasion test. Thus, also for pure abrasion, materials may behave, and also rank differently depending on the details of the test procedure. Most common tests to evaluate the resistance of materials to abrasive wear explore either wearing surfaces with fixed abrasives, e.g., grinding papers or grinding wheels, or use loose abrasives which are fed into the contact between the sample and a countersurface, for example a rotating wheel or disk. The configuration details for abrasion tests vary widely (Figure 13.9). The pin-on-disk (a) or pin-on-drum (c) configurations are very common, the latter forming the basis of a tribometer defined in the German Industrial standards in DIN 53516, and being commonly used for polymers. Rectilinear sliding of pins
Ring Slurry
Specific wear resistance [ mm/(N km) ]
Block 1.5
two-body abrasion-
Ring Block 1.0
0.5 Three-body abrasion
0 0.01
0.1 1 10 100 Hardness of ring/hardness of block
FIGURE 13.8 Wear rate as a function of the hardness ratio of the two sliding surfaces in an abrasion test with initially loose particles, evaluating a tool steel and an aluminum alloy heat treated to different hardnesses.
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FIGURE 13.9
FIGURE 13.10
503
Common abrasive wear test configuration.
Schematics of common crater grinding tests configurations.
over flats is also in use (Figure 13.9b). Figure 13.9d illustrates the frequently applied rubber wheel abrasion test, defined in the U.S. standard ASTM G65. The specimen, in the form of a block is pressed with a constant load against a rotating wheel, the rim of which is covered with a thick layer of replaceable rubber. In tests with fixed particles, the wear rate decreases with the number of passes over the same track due to the degradation of the abrasives. Therefore many apparatuses move the test pins along spiral tracks to make them meet constantly fresh abrasives. The three-body tests avoid this problem to some degree, but becomes more sensitive to the properties of the counterbody providing the grit support. Also more application-close abrasion tests have been developed. One example is the laboratory scale jawcrusher, used to simulate the gouging abrasion which occurs in mining operations. This test has been adopted to the U.S. standard and is described in ASTM G81. In contrast to these fairly coarse abrasion tests, the recent development of a finer type of abrasion test, often referred to as the dimple grinder test or the ball crater test, has attracted much attention. With the help of a rotating wheel or ball, small craters, often less than 1 mm in diameter and with depths of less than 10 microns, are ground on the sample surfaces using grit slurries (Figure 13.10). The tests have proved very practical because of their simplicity of operation, the good control of test conditions, the simplicity of measuring the wear volumes, and because of the fact that the small wear scars make the tests virtually nondestructive. Crater grinding tests have been evaluated on hard coatings, ceramics and metals bulks, thin amorphous metal bands, small ceramic crystallites, and on soft coatings of paint, in most cases with very promising results (Kassman et al., 1991 or Rutherford et al., 1996). A test procedure to evaluate the abrasion properties of multiphase materials consisting of hard phases in a softer matrix is outlined in Axén et al. (1996). This procedure has found industrial use for the evaluation of the wear resistances of the hardphase in grinding tools and multiphase materials with
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Composite wear resistance, Ω
Ωp
r
ea
w al
tim
Op
Minimal wear resistance
Ωm 0
FIGURE 13.11
ce
an
ist
s re
Amount of hardphase
1
Load-specific composite wear resistance as a function of the amount of reinforcement.
superhard reinforcements used in the machining and drilling of rock. The work is based on the concept of load distribution between the phases in a multiphase material, and it clarifies how the load applied to the sliding surfaces may be shared between the different phases of a multiphase material. Generally, a more wear-resistant phase takes a higher load and thereby contributes more to the wear and friction properties of the composite material, as described in detail in Axén et al. (1996). The wear resistant phase may also carry low load shares and contribute very little to the wear resistance of a multiphase material. By identifying the upper and lower limits for how well a hard phase can carry load, the possible load distribution limits, and thereby the optimal and minimal wear resistance of a composite, can be predicted. In practice, measured values of the wear resistance and friction of the individual phases, or extrapolated values measured for materials with very low or high amounts of reinforcements, are used to calculate upper and lower limits for the wear and friction properties of the multiphase material. The contribution of hard reinforcing phases to the properties of the composite is thereafter quantified in terms of load distribution coefficients relating to the possible maximum or minimum values. The procedure is practical in the evaluation of reinforcements because it is based rather on measurable values of load distributions between the phases, and is less dependent on the subjective study of wear mechanisms (Figure 13.11). In the context of abrasion tests, which are basically multiple-tip grooving tests, single-tip scratch tests also merit being mentioned. Equipment to slide a diamond stylus over the sample surface under controlled loading and speed conditions is commercially available and commonly used to evaluate both bulk materials and coatings. Often hardness indentors of the Rockwell C or Vickers types are slid over the sample surface to produce a controlled groove along which failure mechanisms can be studied with microscopy, or by the use of acoustic emission detection units and friction recordings (Axén et al., 1997).
13.8
Erosive Wear
Solid particle erosion is the wear caused by hard particles bombarding a surface. Like abrasion, erosive wear can involve both plastic deformation and brittle fracture, and the details of the appearing wear mechanism depends on both the wearing material, the erodents, and the condition of the impacts, primarily particle mass, velocity, and impingement angle. The erosion behavior of materials is closely linked to the properties of the eroding grit; shape, hardness, toughness, and size all strongly affect the erosion rate of any test material. Deterioration of the erodents during testing has to be taken into account, and testing with recycled particles should be avoided, unless appropriate for the application being
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FIGURE 13.12
505
Basic test configurations for erosive wear.
investigated. The erosion rate increases with the speed of the eroding particles and their mass and tends to fall with the hardness of the wearing material, although the hardness dependence may be weak for certain groups of materials (Söderberg et al., 1981). The effect of impact angle is fundamentally different for materials of different mechanical properties. The erosion rates of brittle materials generally increase continuously with impact angle, from the particles streaming close to parallel to the surfaces, to the case of orthogonal impacts. Ductile materials, however, tend to erode the fastest at an intermediate impact angle, often at around 20 to 30° measured from the eroded surface tangent (Kosel, 1992; Hutchings, 1992). Erosion properties thus also depend on the details of the test configuration, and there is a need to control test conditions accurately. Test methods for laboratory evaluation of erosion can be classified according to the principles for the propulsion of the eroding particles toward the samples. Most commonly the particles are carried either by a fast gas or liquid stream exiting through a nozzle directed toward the test materials; alternatively they are propelled by the rotary motion of a disk or propeller. Figure 13.12 shows different types of testing methods. In the jet impingement or gas-blast method illustrated in Figure 13.12a, particles are accelerated toward the sample by a stream of gas or fluid along a nozzle. Gasblasting methods are standardized in the ASTM G76 and the DIN 50332 industrial standards. Systems exploring a loop through which gas-born particles or slurries are pumped are used to establish wear properties of pipework components (Figure 13.12b), e.g., pneumatic or hydraulic components. The centrifugal techniques, illustrated in Figure 13.12c, or rigs based on whirling arms have the advantage of allowing accurate calculation of particle speeds; in the gas or liquid carrier methods, particle speed has to be measured by separate systems. Centrifugal techniques also facilitate the evaluation of large numbers of samples in each test run. Also there is detonation gun equipment for single particle impacts. Some attempts have been made to use erosion for the evaluation of the durability of coatings. Thick, thermally sprayed coatings can be tested along the same principles as bulk materials. For thin coatings, Shipway (1995) has developed a procedure capable of extracting the erosion resistance of the coating material from deep wear scars involving simultaneous wear of coating and substrate. The technique is based on assumptions about the variation of particle flux along the radius of the circular wear scars produced by a stream of particles leaving a long parallel nozzle. The radius of the area corresponding to the exposed substrate, or the start of the coating, thereby also indicates the mass of particles required just to remove the coating. By following the rate at which this radius widens with the dose of erodents, values for what Shipway called the “erosion durability” can hence be established. The technique has been shown to be sensitive to the adhesion of the coating to the substrate.
13.9
Wear in Sliding and Rolling Contacts
Sliding or rolling wear do not specify any wear mechanisms, but refer to the types of contact between two surfaces in relative motion. Instead numerous types of material removal mechanisms may appear in
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Illustrations of common sliding wear test configuration.
these types of contacts. Surface damages or wear based on adhesion or on surface fatigue are common, but also grooving by surface asperities, i.e., abrasion, tribochemical wear types and other mechanisms are possible. Nevertheless, wear and friction in sliding and rolling contacts are naturally of great interest because of their common occurrence in many machine elements. Therefore, numerous tests for sliding and rolling wear evaluations have been produced. Because of the vast variety of surface interactions and types of surface damages that may occur in sliding contacts, apparently minor alterations in the test conditions can lead to radical and sharp changes in the dominant wear mechanisms and the associated wear and friction values. When choosing model tests for materials ranking, it therefore becomes important to simulate the conditions of the application in detail. Contact stress, thermal conditions, sliding speed, and chemical environment are all vital test parameters in sliding and rolling wear. The interpretation of sliding wear test results is generally much more difficult than for abrasion or erosion. While these types of wear by hard particles are the result of a very large number of microevents, a sliding contact may initiate a variety of interacting phenomena whose character changes as the test proceeds. As a consequence, wear rate is often not proportional to the sliding distance, and correlations to any bulk materials properties, such as hardness, toughness, etc., cannot generally be taken for granted. Sliding wear tests may be performed with a large variety of geometrical configurations (Figure 13.13). It is practical to distinguish between tests where the test bodies are symmetrically or asymmetrically arranged. Figure 13.13a and c illustrate symmetrical versions for which self-mated materials should ideally give identical results. Symmetrical arrangements are not often used in model tests; an example, however, are rings arranged as in Figure 13.13c simulating the symmetrical and conformal contact of axial seals. Asymmetrical configurations, exemplified in Figure 13.13d to f are more common, and because of the noncontinuity of the contact, they produce different results depending on the positioning of the test sample. Probably because of their simplicity and flexibility in terms of test conditions and specimen shape, rigs of the asymmetrical pin-on-disk configuration (Figure 13.13e) have become some of the most popular model tests for evaluating sliding wear. Pin-on-disk rigs with attached heat stages and cover boxes enabling tests in controlled atmospheres are commercially available. Also pin- or block-on-cylinder configurations (Figure 13.13d) are frequently used. The configuration of a stationary pin loaded against
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a sliding block, or vice versa, primarily finds use for friction measurements in monopass tests. Very important for all these configurations is to make the distinction between conformal and nonconformal (counterformal) contacts. The contact may initially be of the point or line type, and then continuously grow as wear proceeds, or the contact may from the start be extended over a large area which remains constant as the test proceeds, as illustrated in Figure 13.14. Several sliding wear test configurations are specified in national standards. Tests based on the block-on-ring (ASTM G77), crossed cylinders (ASTM G83), pin-on-disk (ASTM G99), and sphereon-disk (DIN 50 324) are examples of American and German industrial standards. However, standardizations in tribology only serve the purpose of facilitating comparisons between results from different laboratories; the system aspect of wear and friction is unavoidable, being particularly apparent in sliding wear tests. In one recently developed apparatus to evaluate the sliding behavior of components, the orientation of the test specimens and their motion during testing is arranged in such a way that the contact spot on each specimen moves along a contact path during testing (Jacobson, 1998). In the test two specimens are loaded against each other to form a well defined contact spot on each specimen. The primary novelty of this technique is that, during testing, each contact spot on both specimens only makes contact to one specific spot on the other specimen, and vice versa. The test configuration is typically that of two crossed test bars, cylinders, or similar geometries. During testing the point of contact between the bars is for both bars moving from one end to the other (Figure 13.15 and 13.16). Testing is either performed as a single stroke operation or by reciprocally sliding the specimens across each other under controlled loading conditions. The load can be kept constant or increased gradually or stepwise. Independently of the loading, each point along the contact path of both test rods will only experience a unique load, both if the test is performed as a single stroke or reciprocally.
FIGURE 13.14 Counterformal (a) and conformal (b) contacts.
Contact path
Stationary specimen
Lower, moving specimen
End position
Intermediate position
Start position
FIGURE 13.15 Schematics of equipment loading and sliding two test rods against each other. The contact spot path resulting form the movement of the lower specimen moves along the contact path (full black line) on both specimens.
FIGURE 13.16 Typical friction graph obtained for a metal in the equipment presented in Figure 13.15. The friction shows a sudden increase at the load of seizure.
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Very Mild Wear
In situations of mild wear, such as the wear of most tribological components involving lubricated sliding or rolling contact, the mass loss is often very small in relation to the total mass of the worn component. For many machine elements it can be assumed that the wear appears on an atomistic scale. A precision balance typically has a resolution of 10–6 of the maximum load (e.g., 0.1 mg resolution at 100 g load), which naturally sets a limit to the minimum load possible to quantify in relation to the total weight of the component. Often this excludes the weighing of components before and after wear testing as a method of quantifying wear. Further, weighing gives no information about the distribution of the wear over the worn surface. In most cases this is a serious disadvantage, since the service life is often limited by the maximum wear at some critical location, rather than by the total wear. For further information, Ruff (1992) has given an overview of wear measurement techniques. As discussed above, acceleration of the wear situation may lead to changes of the wear mechanisms, and so provide unreliable results, and tests involving normal wear rates may require unrealistically long test times. In such situations modern topographical methods may be the best way to evaluate the wear. With the introduction of high-resolution instruments such as the atomic force microscope (AFM) and optical interferometry, techniques capable of determining height differences in the subnanometer range (with lateral resolutions of about 1 nm and 1 µm, respectively) and storing the obtained topographical data digitally, it is now possible to measure the volume of topographical features in the sub µm3 range. (The mass of 1 µm3 of steel equals ca. 10–11 g) Another benefit of this kind of instrument is that the topographical data are used directly to render images of the surface, including shading and color-coded heights. Recently a new method to map and quantify wear was presented by Gåhlin and Jacobson (1998). They used the technique, called the topographical difference method, to evaluate the very minute initial wear of a hydraulic motor cam roller (Gåhlin et al., 1998). The topographical difference method for evaluation of wear comprises two techniques: topographic image subtraction for wear distribution mapping, and bearing volume subtraction for local wear volume determination. Topographical image subtraction is suitable mainly for qualitative presentation of the distribution of wear over the surface and to indicate the magnitude of the individual wear events. This information is obtained by taking the topographical image of a worn surface and subtracting the previously recorded unworn (or less worn) topographical image of the same surface. This procedure effectively eliminates all unaltered surface features, leaving corresponding areas flat, and exhibits lost material as elevations over this flat surface and gained (plastically displaced) material as depressions. To get a good mapping, the lateral matching of the two images has to be very precise. On the other hand, the technique does not require a height reference, but only the existence of unaltered parts of the surface that become flat after subtraction and thus indicate the “zero wear” level. Bearing volume subtraction is used to quantitatively determine the volume loss over the local studied area. This is achieved by using bearing histograms to calculate the volume of material left above a common fixed surface level (Figure 13.17). The more the surfaces are worn, the less material is left above this reference level. To obtain the bearing volumes from the topographical data, each measured point (surface element) of the specified surface area is multiplied by its height over the reference level. The accumulated wear volume is then calculated by subtracting this bearing volume by the corresponding volume obtained after the wear test. In contrast to topographical image subtraction, bearing volume subtraction involves no point-to-point comparison and thus does not depend on a precise lateral matching of the two images. The first application of this method to actual components involved wear evaluation of a hydraulic motor. The wear of the cam rollers was successfully mapped and measured (Figure 13.18), using a standalone-type AFM. For this application typical average wear depths of 30 nm were registered after a sliding distance of about 15 km (2165 h test time), corresponding to a total wear of about 1 mg of the 600 g roller. The wear distribution map revealed that this minute wear was localized at the uppermost parts of the grinding ridges (Figure 13.19). These results were obtained on rollers, where the curved geometry put extra demands on the experimental technique. This clearly demonstrates that the topographical difference method is not restricted to simplified laboratory tests.
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FIGURE 13.17 A computer-generated two-dimensional profile of a surface showing the effect of wear with and without plastic deformation. The wear distribution maps produced by subtracting profiles and the changes of corresponding bearing histograms are shown. The magnitude of the initial bearing volume and the two bearing volume differences are also indicated.
FIGURE 13.18 Topography and corresponding bearing histograms of a chromium steel roller before and after sliding against silicon nitride in a full-scale hydraulic motor test. The average wear depth is about 40 nm, corresponding to a mass loss of 10–9 g. (10× larger magnification in the height direction.) (a) Initial and (b) worn 2165 h.
FIGURE 13.19 Wear distribution map of the roller obtained by subtracting the initial surface by the worn surface. (10× larger magnification in the height direction.)
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In conclusion, extremely high resolution methods such as the one described above, promise to improve tribological testing of real machine elements by reducing the need for excessively accelerated tests or extremely long test times.
References Axén, N., Kahlman, L., and Hutchings, I.M. (1997), Correlations between tangential force and failure mechanisms in scratch testing of ceramics, Tribol. Int., 30, 7, 467-474. Axén, N. and Hutchings, I.M. (1996), Analysis of the abrasive wear and friction behaviour of composites, Mater. Sci. Technol., 12, 757-765. Axén, N., Jacobson, S., and Hogmark, S. (1994), Influence of hardness of the counterbody in three-body abrasive wear — an overlooked hardness effect, Tribol. Int., 27, 4, 233-236. Blau, P. (Ed.) (1992), ASM Handbook on Friction, Lubrication and Wear Technology Technology, ASM International, vol. 18, 362. Czichos, H. (1987), Tribology — A System Approach to the Science and Technology of Friction, Lubrication and Wear, Elsevier, Amsterdam, 351. Gåhlin, R. and Jacobson, S. (1998), A novel method to map and quantify wear on a micro-scale, Wear, 222, 93–102. Gåhlin, R., Larker, R., and Jacobson, S. (1998), Wear volume and wear distribution of hydraulic motor cam rollers studied by a novel AFM technique, Wear, 220, 1–8. Hogmark, S., Jacobson, S., and Vingsbo, O. (1992), ASM Handbook on Friction, Lubrication and Wear Technology, Blau, P. (Ed.), 18, 176-183. Hogmark, S. and Jacobson, S. (1991), Hints and guidelines for tribotesting and evaluation, Journal of the Society of Tribologists and Lubrication Engineers, 48, 5, 401-409 Hutchings, I.M. (1992), Tribology — Friction and Wear of Engineering Materials, Edward Arnold, London. Hutchings, I.M. (1998) Abrasive and erosive wear tests for thin coatings: a unified approach, Proceedings of the World Tribology Congress, London, 269-278. Jacobson, S. and Hogmark, S. (1998), Swedish Patent no. 9802017-6. Kassman, Å., Jacobson, S., Erickson, L., Hedenqvist, P., and Olsson, M. (1991), A new test method for intrinsic abrasion resistance of thin coatings, Surf. Coat. Technol., 50, 75-84. Kosel, T.H. (1992), Solid particle erosion, in ASM Handbook on Friction, Lubrication and Wear Technology, Blau, P. (Ed.), 18, 199. Normung, D.I. (1986), Wear Testing Categories, Beuth Verlag, Berlin. Ruff, A.W. (1992), Friction, Lubrication and Wear Technology, ASM International, Blau, P. (Ed.), Vol. 18, ASM Handbook, 362. Rutherford, K.L. and Hutchings, I.M. (1996), A micro-abrasive wear test, with particular application to coated systems, Surf. Coat. Technol., 79, 231-239. Shipway, P.H. and Hutchings, I.M. (1995), Measurement of coating durability by solid particle erosion, Thin Solid Films, 137, 65-77. Söderberg, S., Hogmark, S., Engman, U., and Swahn, H. (1981), Erosion classification of materials using a centrifugal erosion tester, Tribology International, 14, 6, 333-343. Zum Gahr, K.-H. (1987), Microstructure and Wear of Materials, Tribology Series 10, Elsevier, Amsterdam.
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14 Simulative Friction and Wear Testing 14.1 14.2 14.3
Introduction ..................................................................... 511 Defining the Problem ...................................................... 512 Selecting a Scale of Simulation ....................................... 514
14.4 14.5 14.6
Defining Field-Compatible Metrics................................ 516 Selecting or Constructing the Test Apparatus ............... 517 Conducting Baseline Testing Using Established Metrics and Refining Metrics as Needed ....................... 517 Case Studies...................................................................... 518
Levels of Tribosimulation
14.7
An Oil Pump Gear Set with Several Wear Modes • Wear of Gravure Rollers on Doctor Blades • Scoring of Spur Gears • Wear of Plastic Parts in an Optical Disk Drive • Wear of Rotary Slitter Knife Blades • Erosive Wear of Piping
Peter J. Blau Tribomaterials Investigative Systems
14.8
Conclusions ...................................................................... 522
14.1 Introduction The selection of lubricants, materials, or surface treatments for friction and wear-critical applications often involves validation or screening tests before final decisions are made. Testing is particularly valuable during the development of new machines for which operating conditions are much different than existing designs. An example of the latter might be a new design that cannot use off-the-shelf bearings or gears because the temperatures are too high or the surrounding environments are too corrosive. The steps involved in developing tribosimulations of current or newly designed systems are, with only one significant exception, essentially the same. The exception is that for an existing friction of wear problem, there is prior experience in the response of the materials and lubricants to the operating conditions. In a new design, however, there may be no direct prior experience in the behavior of candidate materials, although there may be some relevant experience from machinery of a similar kind. There are two types of tribosimulations: computer simulations and physical simulations. The computer simulation uses a virtual mechanical assembly that consists of several components defined in terms of a set of properties, spatial relationships, and assumed rules of interaction. Known or estimated properties of the materials and/or lubricants are provided to the model, and the expected responses of the virtual tribosystem to such variables as load cycles, deflections, temperature excursions, etc., are calculated. Such programs have been prepared by both academic researchers and industry engineers for tribological components like bearings, face seals, brakes, and gears. Component designers have also developed sophisticated design tools for automotive valve trains, engines, and pumping systems as well. The second type of tribosimulation is the physical simulation. Here, materials and lubricants are screened in an apparatus that is intended to provide the essential operating characteristics of the intended
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application. An additional use of virtual and physical simulations is to observe how a certain material or lubricant might react in a situation when the opportunity to observe the material or lubricant is not practical. For example, bearings for use in unmanned orbiting satellites might be observed in an ultrahigh vacuum, space-like environmental chamber created in the laboratory for that purpose. This article focuses on the development and use of physical tribosimulations. It describes the process involved in developing and validating laboratory bench-scale simulations for friction and wear-critical machine components. The steps in developing a physical tribosimulation are similar in some respects to those used to set up a computer simulation. They are: 1. 2. 3. 4. 5. 6. 7.
Define the nature of the friction or wear problem to be investigated Select a scale of simulation Define field-compatible metrics to use to assess the results of the simulation Select or build the apparatus (the model, in the case of the computer simulation) Conduct baseline tests to establish the repeatability and characteristics of the method Analyze baseline test results using the established metrics Refine as needed to achieve an acceptable engineering confidence level
14.2 Defining the Problem Defining the nature of the friction or wear problem is critical before any test method can be selected, developed, or successfully employed. Rushing ahead to testing without proper analysis of the problem is akin to sitting down at a table to play cards without knowing what game is to be played and what its rules are. At the first level of problem definition, one answers the following questions: 1. 2. 3. 4.
What are the physical attributes of the tribosystem? Is it an open or closed tribosystem? What form or forms of friction or wear are likely to be involved? What quantitative measures, if any, are there to describe the behavior of the materials in the situation of interest? 5. What materials or lubricants are currently under consideration for this application? 6. What time and resources are available to use to solve the current problem? By defining the physical limits of the tribosystem, we are forced to make the first judgment. At what distance from the tribological interface will the surroundings still affect the tribological function? For example, if we limit our focus to a pair of wearing gears in isolation from their surroundings, we might inadvertently neglect externally produced mechanical vibrations, sources of abrasive debris, or temperature excursions from surrounding components as potential contributions to the gears’ wear environment. Thus our simulation could omit critical, wear life-limiting elements which come from the surroundings, elements which might in fact be just as important to include in the simulation as the imposed load on the gear teeth or the speed of relative rotation. Closed tribosystems involve, for example, recirculating lubricants or contact environments which are contained within a certain portion of the machine. Open tribosystems are more complicated and difficult to simulate because materials of unforeseen origin might enter the area of contact from sources external to the machine and cause strong friction or wear responses. An example of an open tribosystem is the bucket teeth on construction equipment that must dig through all kinds of dirt, soil, and rock under wet and dry, hot and cold conditions. The forms of friction or wear must be defined early. It is common to observe more than one type of wear or mechanical surface damage in different locations, even on the same part. Therefore, the locations and wear types most damaging to the satisfactory operation of the component must be identified and prioritized. It is possible that more than one type of test will be required to ensure that the proposed materials or lubricants will respond suitably to all the critical contact conditions on various surfaces of the component. For example, the side of a pump gear may slide against its case while the teeth of the same gear may experience contact fatigue worsened by a small amount of tangential slip.
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TABLE 14.1
Elements of a TriboSystem Analysis (TSA)
Element Tribosystem — open or closed? Macro contact and conformity Microcontact and surface finish Type of relative motion Speed of relative motion Contact load and pressure Temperature Contact environment and lubrication
Third bodies Type(s) of wear Performance degradation Experience Metrics
Description Is the system open to the environment, like the teeth of earthmoving equipment, or closed, like a sealed recirculation system? To what degree do the shapes of the contacting bodies conform to one another? How can the geometry be described: convex curve-on-convex curve, flat-on-flat, particles-on-flat, etc.? Is the contact open on the edges or closed so as to confine wear debris? Surface texture of the interacting bodies — roughness, waviness, and lay. How long does the initial finish persist in service? Is the motion unidirectional, reciprocating, intermittent, or continuous? What is the characteristic constant distance (stroke length, etc.)? Fretting or long-distance sliding? Sliding velocity or impingement velocity, if particles are involved. How is the load distributed on the surfaces? What is the magnitude of the normal force? How does it vary? Does the temperature change during operation or remain constant? Is frictional heating an issue? What chemical environment does the contact area experience? Is there a lubricant? What lubricant regime is present (dry, starved, boundary, mixed, hydrodynamic)? What are the lubricant characteristics? Are there contaminants in the lubricant? Is the lubricant agitated so as to entrain air? Are there vibrations or other mechanical contributions to negative performance? Are there particles involved in the wear, and if so, what are their characteristics? Are particles generated by wear or externally to the contact area? Using surface analysis and microscopy, what is/are the dominant form(s) of wear? To solve the problem, the negative manner in which wear or friction affect the operation must be defined. What are the current materials and lubricants, and which others have been tried? What quantitative measures are used to described the wear or friction of the subject component?
In existing applications, identifying the type of wear involves examining field-worn parts which have been protected from the environment after having been removed from the machine. Surfaces of worn parts which have stood unprotected for some time may be corroded and difficult to analyze. Other complications include removing surface deposits of degraded or heat-altered lubricants without destroying the most telling clues as to the dominant mode of wear damage. In new designs, the engineer is placed in a position of speculating what the environment of the tribosystem will be, and adjusting the simulation appropriately. Some guidance can, however, be obtained by analyzing existing systems with similar mechanical, thermal, and chemical aspects in the key areas of tribocontact. TriboSystem Analysis (TSA) [3] is a means to define the operating conditions of a system to be simulated. It involves a systematic analysis, aspect-by-aspect, of the operating environment of the subject component(s). Table 14.1 lists key elements for analyzing a tribosystem. Often, not all of the operating parameters are known. Therefore it is doubly important to understand the characteristic wear features or other key aspects of the tribosystem that will help to define metrics for the simulation (see Section 14.4). Understanding the properties and behavior of the currently used materials, or those used in an application which has key operating aspects in common with the component of interest, is important. Knowing what materials have and have not worked in the given application is equally valuable because it could save a great deal of time and effort. Simply asking the questions embodied in a thorough tribosystem analysis can go a long way toward solving the problem. Verifying the answers to those questions with a second opinion or a measurement can also be helpful. Sometimes people incorrectly assume that certain operating conditions exist. Tribosimulations sometimes need to be sensitive enough to distinguish between different variants of the same material. For example, there are many ways to heat-treat steels. A wear problem may occur if a component supplier changes the heat treatment, perhaps for reasons of economy, or changes the material supplier without notifying the customer (see the later example of gear scoring). The simulation in that case must be sensitive enough to detect the differences due to different heat treatments. Detecting
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small variations in friction or wear using short-term laboratory tests can be challenging, but it can be facilitated through the use of statistical methods for data analysis. Therefore, multiple tests of each material or lubricant combination are needed to establish the characteristics of the laboratory test method; particularly, if the test method is new and has no historical record of performance. Using ASTM and other standardized tests offers the benefit of having previous data available from tests conducted in the same manner.
14.3 Selecting a Scale of Simulation Field-trials evaluate materials and lubricants under actual operating environments. Sometime field trials involve monitoring components as they are used in normal service. These instrumented components can be subjected to certain prescribed patterns of use. For example, some automotive companies have instrumented the brakes of test vehicles and returned those vehicles to their owners for a period of time, treating the driver’s behavior as a variable. In other cases, instrumented vehicles have been run in several cities, but over carefully prescribed driving routes. Both types of field tests provide valuable information, but interpreting the wealth of data that obtains in these situations is difficult and complicated due to the many uncontrolled variables present in the field. For example, test drivers on city routes might be forced to break rapidly to avoid hitting a child or a dog. They could wind up behind a slow moving vehicle. In truth, the more “channels of information” that are collected, the more challenging is the task of interpreting the results and determining the underlying relationships in material and lubricant behavior. Like the automotive and truck brakes in the foregoing example, a great many tribological components are not operated under steady-state conditions. Some machine parts may experience short start-up and slow-down intervals but spend most of their lives under constant conditions. A classic example is the piston ring in an internal combustion engine that experiences hydrodynamic fluid film breakdown at the ends of the stroke. Other interfaces may be in a constant state of change and never reach what might be termed steady-state. Perhaps the contact pressure is not constant, the contact velocity is not constant, the temperature is not constant, and the direction of relative motion is not constant. In addition, tribosystems tend to age. Lubricants change properties as their additives degrade on exposure to high temperatures, react with the surfaces and other chemical species in the environment, and become contaminated with wear particles. The degree to which these factors affect the validity of a tribosimulation’s results is not easy to determine a priori, but they can be taken into account to some degree in a well-designed tribosimulation.
14.3.1 Levels of Tribosimulation For the purposes of this chapter, we shall consider four levels of tribosimulation. Figure 14.1 shows these levels, indicating the parallels between physical and computer tribosimulations. Generally, the more realistic the simulation, the more costly and complicated it becomes. Level 1 tribosimulations use full-scale machines, such as entire automobiles, trucks, aircraft, ships, manufacturing machinery, and consumer products. These machines may be instrumented to measure loads, temperatures, strains, power demands on motors, and vibrations. In physical simulations, fullscale machines are operated under controlled conditions, such as on a test stand or inside an environmental chamber. For example, an entire communications satellite might be placed in a high-vacuum chamber and its antennas caused to rotate to determine whether the bearing lubricants will perform effectively in space. A truck might be rolled onto a chassis dynamometer and its wheels subjected to various braking loads and cycles. However, even the high-level simulations of Level 1 might omit certain factors present in the field. For example, the effects of zero-gravity on the aforementioned satellite cannot be completely simulated in a vacuum chamber on Earth. The effects of random potholes, loose gravel, and uneven road surfaces cannot easily be simulated on a test stand, but recent developments in computercontrolled test stands are making such simulations increasingly realistic.
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FIGURE 14.1
515
The levels of tribosimulation.
Level 2 tribosimulations use subassemblies which are subjected to near-operating conditions. Examples include brake pads and rotor combinations on dynamometers, fluid pumps in closed-loop pump test rigs, and jet engines in engine test cells. Nearly as expensive as Level 1 tests, Level 2 tests offer additional control of the externally applied test parameters. At the same time, fewer of the field-associated effects on performance are faithfully simulated. For example, the effects of road-induced vibrations on piston motions, the vehicle-specific flow of air past brake components, and the introduction of environmental contaminants into wheel bearing grease may be omitted in subassembly tests. In dynamometer tests of break component materials it is common to apply a series of test stages in an attempt to simulate specific types of frictional phenomena, like fade effects at elevated temperatures. Even staged Level 2 tests as complex as these cannot totally simulate the full range of habits of individual drivers and driving conditions. In some cases, however, Level 2 tribosimulations can be very effective in screening materials or lubricants because the operating conditions of the system are more clearly known. For example, loopby-loop ballpoint pen testers can show how long the products will continue to write effectively and establish failure statistics for the entire pen, whose satisfactory performance depends on the ability of the point to deliver a clear, uniform line of writing fluid to the paper. One tribosimulation area of particular medical interest is that of computerized hip and knee joint testing. Attention here is given to mimicking the forces, types of motion, and impact loads to which bioimplants are subjected. This subject area can make effective use of both physical and virtual component Level 2 simulations. The selection of the fluids to simulate synovial fluid and to correlate with clinical results is an important issue. Material swelling in situ, in the case of polymeric materials, and the role of debris particles as they interact with the soft tissues surrounding the joints, are also of interest. Level 3 tribosimulations involve test rigs designed to test specific components, like bearings and gears. For example, bearing test rigs have been successful in developing empirical design and selection guidelines for rolling element bearings of many kinds. Multiple-station rigs, automated to take data or to ascertain critical failure conditions, like excessive heat or vibration, can be run unattended, enabling the compilation of lifetime statistics and related performance data for consumer products or machine components. Level 4 tribosimulations involve test coupons of simple shapes. Examples include pin-on-disk tests, block-on-ring tests, four-ball lubricant tests, dry-sand-rubber-wheel abrasion tests, and vibratory cavitation tests. These tests are described elsewhere in this volume and in the wear testing literature [e.g., ASM (1992, 1997)]. Their usefulness is based on their ability to simulate the key contact conditions of the components of interest. For example, a cam roller follower in the engine of a certain diesel engine might be simulated by two disks turning at different speeds to impart a desired degree of slip to the
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TABLE 14.2
Modern Tribology Handbook
Common Metrics for Assessing Friction and Wear Situations
Situation Field component
Tribological Problem High friction
Surface damage Wear
Laboratory specimen
High friction Surface damage Wear
Typical Metrics Seizure; galling or scuffing marks; power draw of a motor; overheating of bearings or slideways; irregular motions; excessive wear of bearing or sealing surfaces; unusual noises or vibrations; marring of a formed product’s surface, as in metalworking; irregular speed fluctuations in a bearing Scuffing marks; galling and other visual indications Fluid leakage in a seal; loss of compression in a piston; erosive perforation of a pipe elbow; presence of wear particles in a lubricant; loss of fit between parts; excessive or unusual noise from gears or bearings; excessive or unusual vibrations; changes in the appearance of contact surfaces (abrasive grooves, scuff marks, etc.); signal drop-out in electrical contacts; loss of cutting performance of a tooling insert. Friction force or torque measurements Visual inspection or profilometric measurements Weight loss; displacement relative to another specimen or reference plane, wear scar size; wear depth; wear volume calculated by surface measurements or by weight change; visual examination; changes in friction force, surface temperature, or vibrations as detected by sensors; surface reflection characteristics measured by sensors
contact. Furthermore, the test disks could be supplied with a lubricant and heated to simulate engine conditions. The linkage between tribosimulation levels can be important to establish the validation of Level 3 and 4 tests as effective screening methods. For example, if a set of Level 4 rankings agrees with relative rankings of the same set of materials or lubricants in Level 3 tests, and the validity of Level 3 tests in a certain application has been confirmed, then the usefulness of Level 4 tests will be greatly extended.
14.4 Defining Field-Compatible Metrics A metric is a measurable quantity or unique observational feature that can be used to rank or otherwise distinguish the performance of a material or lubricant in a tribosystem. Table 14.2 lists a few metrics commonly used in the field and in tribology laboratories. Wear and friction measurement methods are described in more detail elsewhere in this volume and in ASM publications (ASM, 1992, 1997). Ideally, metrics for assessing friction or wear problems should be quantitative, accurate, straightforward to measure, and not subject to the investigator’s judgment. In practice, however, some or all of the foregoing criteria cannot be met. Furthermore, as Table 14.2 shows, there is often a significant difference between the parameters or observations that can be made in the field and those that can be made in the laboratory. Therefore, an important issue in assessing the usefulness and validity of simulations involves arriving at a set of common metrics which laboratory investigators and field engineers can agree on. There is no point in developing a laboratory test if field engineers refuse to believe that the results of the tests are relevant or cannot relate the test results to what they observe. Some key wear and surface damage metrics, in order of preference, follow: 1. Quantitative measures, like weight loss or dimensional changes, that can be measured both in the field and in the laboratory 2. A series of reference materials that rank in similar order of merit in the field and laboratory tests. 3. Visual wear features that appear similar in field-worn and laboratory-generated surfaces. 4. Wear debris that looks similar in field and laboratory-collected samples.
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14.5 Selecting or Constructing the Test Apparatus Well-equipped tribology laboratories usually contain a variety of testing machines, capable of testing for a range of tribological behavior. One or more of these machines might be suitable for conducting the given tribosimulation. Commercially manufactured wear testing machines may be a cost-effective alternatives to designing and building new, special-purpose machines for the problem at hand. But commercial machines should be used only if they serve the required purposes, including simulating specific wear of friction conditions. It may also be possible to modify an existing machine to perform the requisite simulation. It is beyond the scope of this chapter to provide guidance on the design and construction of friction and wear testing machines because there is an enormous number of alternative designs. Well-equipped tribology laboratories also contain auxiliary equipment for measuring and characterizing wear, such as precision microbalances, profiling instruments, hardness testers, and microscopes of various types. Special techniques and highly trained personnel experienced in cross-sectioning wear surfaces or performing surface chemical analysis populate a well-equipped tribology laboratory. When selecting or designing a friction or wear testing apparatus for a specific purpose, it is important that the reason for testing, and the metrics selected for validating the results, are firmly in mind. For example, if weight loss is a metric, specimen fixturing and handling procedures should be designed to avoid sources of error in mounting specimens, treating them after exposure to wear, and transferring them to the weighing system. If surface appearance is a metric, protection of wear features from demounting and handling artifacts must be a part of the procedure.
14.6 Conducting Baseline Testing Using Established Metrics and Refining Metrics as Needed Baseline tests with the materials and lubricants in current use, or believed to be the leading candidates for a new application, are helpful in establishing the repeatability and characteristics of the test method itself. It is worthwhile to conduct a series of replicated tests to establish the repeatability of the baseline conditions. Knowing this, the performance of other materials or lubricants can be analyzed to determine if it is statistically different from the normal scatter in the test results. One test per materials couple or set of test conditions does not provide very strong evidence on which to make engineering decisions. If wear is measured quantitatively, then the wear factors or other metrics from baseline tests can be used in the denominator of a figure of merit. For example, the lifetime of a baseline cutting tool material, expressed as the number of workpieces produced before tool replacement is required, is divided into the lifetime of another candidate tool material to give the relative lifetime of the candidate. The higher the number is above 1.0, the greater the wear benefits of substitution, other factors being equal. An alternative engineering metric might be the tooling cost per unit part machined. Sometimes suitable quantitative metrics cannot be found. It may then be possible to compare the appearance of the test specimen to a worn part to establish the success of the simulation. An example is given in 14.7.1. It is likely that laboratory simulations will not be able to reproduce every aspect of the part operating conditions. Therefore, it is, in general, unreasonable to expect that precisely the same wear rates or metrics will be obtained in the laboratory and in the field. From the standpoint of screening, however, it is very important that candidate materials rank in very much the same order in the field and in the laboratory. Since there are many ways to measure wear in the laboratory (weight loss, wear profile, wear scar dimensions, etc.), there may be one metric that correlates better with the field wear results than another. Therefore if one method of laboratory wear measurement does not correlate well with field results, another may work better. The following section describes several laboratory simulations that used different kinds of metrics and testing procedures depending on the nature of the parts being simulated.
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14.7 Case Studies Six case studies on the selection and use of simulative friction and wear tests are provided below. The first case, which is described by Blau (1998), involves an automotive application in which new simulative test fixtures and procedures were developed. In the latter five case studies, summarized from an article by Blau and Budinski (1999), existing or slightly modified ASTM test methods were used to solve industrial plant wear issues and product-related wear problems.
14.7.1 An Oil Pump Gear Set with Several Wear Modes An initiative was undertaken to replace certain steel fluid pump gears with a lighter-weight, aluminumbased alloy. One criterion for the acceptability of the new gear material was that it possess acceptable wear characteristics when substituted for the current steel. The gears were of a gerotor type in which a wedge of fluid is trapped between the teeth of eccentrically mounted inner and outer gears. As the gears turn, the fluid is forced between them, pressurized, and then out of a pocket in the pump housing. This type of pump is typical of automotive oil pumps and automatic transmission fluid pumps. Based on the results of a TSA, described in Section 14.2, and with input from both pump part makers and pump users, the two wear-critical areas were determined to be the teeth contact points and the flat gerotor gear faces which can rub intermittently against the inside faces of the housing. In the latter case, little or nothing was known about the surface contact pressures or loads. In addition, specimens of gears run in actual service and in full-sized gear pump test rigs were carefully examined by optical microscopy and cross-sectioned for subsurface study. Based on the relatively small quantities of candidate materials available for use in the material selection process, it was necessary to devise a simulative test method which used small, round disks, about 20 mm in diameter and 10 mm thick. These were about 1/4 the diameter of the actual gear disks. To simplify the testing process and make the best use of limited materials, it was decided to use the same specimen dimensions for tests of both tooth wear and the flat face-on-casing wear. It was desired to use quantitative metrics to screen the various candidate materials, but as described later, some of the wear metrics turned out to be only semiquantitative. Several testing configurations were developed. Eventually, the wear simulation evolved into a configuration that emphasized tooth-to-tooth slip which resulted in combined adhesive and three-body abrasive wear and subsequent loss of the gear tooth profile. One disk was rigidly held vertically with its curved outer diameter, simulating the curvature of the tooth face. It was oscillated against the flat face of a second disk of the same material (Figure 14.2). Hot, lubricated tests were performed at temperatures similar to that of the application. The length of the test was determined by the time needed to produce wear features similar to those seen in actual gears. The width of the wear scar on the curved disk’s outer diameter was measured and converted to a wear volume. This wear volume was normalized by dividing by the product of the applied load and the number of cycles to obtain a wear rate (mm3/N-cycle). The gear face-on-casing sliding wear mode was simulated by placing the flat faces of two disk specimens together in a thrust-washer-type geometry (Figure 14.3). Circular insets were machined into one or both disk specimens to produce an annular contact. The upper specimen was held fixed in a spring-loaded arrangement to assure good flat-on-flat seating with the lower rotating disk. The rotating disk was made of the candidate lightweight gear material and the upper was made of typical casting alloy. Tests were run with oil-coated surfaces. Each test consisted of four segments in which the test was stopped and oil was replenished on the contact surfaces. Weight losses and dimensional changes were unsatisfactory quantities for measuring the small amount of wear produced in this type of flat-on-flat test. Therefore, a semiquantitative method for determining the wear severity was used. This involved cataloging the types of wear damage, such as scuffing, abrasion, gouging, etc., and assigning several severity levels to each. Table 14.3 shows the wear damage rating scale. Each level was defined sufficiently well so that two people independently obtained the same numerical rankings on the same test specimens. The wear damage ratings for each disk specimen were determined,
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FIGURE 14.2
Curve-on-flat geometry used to simulate tooth-on-tooth rubbing contact.
FIGURE 14.3
Flat-on-flat geometry used to simulate gear-on-casing sliding.
519
and then a composite rating for each couple was determined (the sum of the two specimen ratings). Each test was duplicated to establish the repeatability of the results, and to enhance the investigators’ confidence in the differences between the wear ratings of different material couples. Figure 14.4 compares the wear seen on an actual part with that produced in laboratory experiments of several candidate alloys. Results from these two kinds of simulative tests, coupled with full-scale pump rig tests at a manufacturer’s facility, cost modeling, and alloy processing trials, were used to select the leading alloy and surface treatment for this application.
14.7.2 Wear of Gravure Rollers on Doctor Blades In a certain industrial coating process, dimpled cylinders (gravure rollers) are used to pick up and deliver a solution to another surface. These cylinders are cyclically wiped by steel doctor blades to remove the
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TABLE 14.3
Modern Tribology Handbook
Wear Damage Rating (WDR) Scale Used to Assess Flat-on-Flat Wear
Factor
Severity
Description
Light abrasion
1.0
Moderate abrasion Severe abrasion
4.0 6.0
Light scuffing
1.5
Moderate scuffing Scoring
3.0 5.0
Pull-out
5.0
Delamination
5.0
Burning Severe metallic wear Microwelding Major transfer
5.0 6.0
Faint, widely spaced grooves aligned parallel to the sliding direction. Grooves may not be continuous around the track and are similar in depth to the original grinding marks. Multiple, parallel wear grooves extending across a substantial portion of the contact area. Some of the original surface finish visible between the abrasion grooves. Deep abrasive wear grooves across the entire contact face. Little or no trace of the original surface finish. Polished-looking areas with little or no original surface finish within their boundaries. Scuffed area < 25% of the nominal contact area. Scuffed area 25 to 75% of the nominal contact area. Localized, relatively deep grooves ( depth of original machining marks), suggesting plowing by large hard particles. Removal of particles or entire grains from the surface. Regions of pull-out may be associated with scoring by the removal material. Detachment of thin, flat platelets; typically associated with fatigue crack growth parallel to the free surface. Production of dark oxides or tarnishes suggestive of exposure to excessive frictional heating. Significant plastic deformation accompanied by deep grooving. No traces of the original surface finish. Often accompanied by shiny flake-like wear particles. Presence of tiny flecks of highly adherent, transferred material from the opposing surface. Presence of relatively large particles or patches of highly adherent material from the opposing surface.
1.0 2.0
excess coating material, and were experiencing unacceptable wear as a result. It was decided to try ionimplanting the surfaces of the rollers to improve their wear. ASTM standards G-99 (pin-on-disk test) was used to compare the implanted and unimplanted (current) materials. While the wear of the roller material was markedly improved, the wear of the doctor blade material increased to an unacceptable level. Therefore, it was decided that ion implantation would not be an acceptable solution in this case. While the pin-on-disk method was not an exact simulation of the doctor blade operating conditions, it was felt to be adequate to evaluate one potential solution for this wear problem, and to determine that alternative methods of surface engineering or materials substitution would be required.
14.7.3 Scoring of Spur Gears An expensive steel gear set in production equipment began to exhibit signs of significant scoring. It was learned that the supplier had modified his processing and that the hardness of the new gears varied from that of the previous sets. ASTM standard G-98 (the button-on-block galling test) was used to determine the critical level of Rockwell hardness to avoid the onset of galling. This ASTM test method is based on using visual observations to obtain a numerical metric; namely, the threshold stress for galling. Using observations of test coupon surfaces subjected to increasing levels of normal force, one assesses the normal pressure at which galling begins. It turned out that a difference of only 1 or 2 units on the Rockwell C hardness scale made the difference between steel gears that ran acceptably and those that did not. Costly future failures were therefore avoided by tightening the hardness specifications on the gear steels. Increasing the hardness of a material to improve its surface durability and wear resistance is a longstanding, intuitive notion that is not always substantiated by testing. That is because other factors, such as the type of wear being experienced, the material’s fracture toughness, fatigue resistance, and chemical reactivity with the environment can also affect the surface response to contact conditions. In the present fortuitous example, the suitability of the steels for use as gear teeth could be directly correlated to their Rockwell hardness numbers with the help of a standardized test method that captured the essential elements of surface contact in the application.
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FIGURE 14.4 (a) Wear features on a gear side face tested in a commercial producers’ testing facility under severe operating conditions. (b–d) Different levels of wear damage observed on laboratory test specimens in the flat-onflat simulator test shown in Figure 14.3.
14.7.4 Wear of Plastic Parts in an Optical Disk Drive Not only wear, but the presence of wear products (debris particles) can seriously affect the performance of imaging and computer equipment. This was the case for contacting plastic parts in an optical disk drive. The ASTM G-133 reciprocating pin-on-flat test was used to screen plastic pairs for those which not only had the best material-to-material compatibility, but also produced the least harmful debris insofar as the surrounding machinery was concerned. Therefore, an additional metric was an observationally bases scale of the distribution of wear debris in the vicinity of the contact area on the pin and flat specimens.
14.7.5 Wear of Rotary Slitter Knife Blades Rotary slitter knives were used to cut plastic sheeting to size. The edges of the knives slid against one another repeatedly as they worked. Excessive wear led to unsatisfactory performance, costly equipment shutdowns, and product damage. In this case, the development of acceptable metrics for laboratory screening was complicated by the lack of a clear definition for the blade “sharpness.” A decrease in product cut-edge quality is the result of worn blades, but edge quality is difficult to quantify in a way that can be used in cost-effective laboratory tests. The ASTM G-83 crossed cylinders wear test was eventually selected to screen materials for knife blade applications. This test produces a concentrated contact at the intersection of two orthogonal cylindrical
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specimens. While not exhibiting the exact geometry of the application, the small, highly-loaded contact between test specimens contained enough of the essential elements of rotary slitter knife interactions to produce a useful screening test. Wear volume is used as the metric and is computed from the test materials’ densities and their weight losses. By examining a great deal of crossed-cylinders laboratory wear test data that would have been impractical to obtain on the production floor, it was discovered that at least one of the blades had to be composed of carbide material in order for the slitter knives to perform satisfactorily. Since more than one material combination with satisfactory wear rates was identified in the course of the testing campaign, it was possible to select the most affordable solution to the problem from among several alternatives.
14.7.6 Erosive Wear of Piping During the process of designing a new plant involving the piping of dicalcium phosphate, it was necessary to know what material would be the best choice for the piping. Issues were not only erosion resistance, but corrosion resistance as well. The G-32 solid particle impingement erosion test was selected. Several candidate materials were exposed to dicalcium phosphate and other erodants using a pressurized air jet apparatus, such as that prescribed in the standard. It was determined that a soft stainless steel would work adequately in this application, and the decision was made to use that material for construction. Significantly, higher hardness did not ensure wear resistance, as it did in the case described in Section 14.7.3. Therefore, the selection of materials for wear applications based on properties like hardness depends on the type of wear involved and on other performance requirements.
14.8 Conclusions The development of simulative friction and wear tests requires an interdisciplinary approach, beginning with a tribosystem analysis to define the problem and to establish key metrics that can be used to test the validity of simulations. Laboratory simulations using either custom-designed apparatus or standard test methods can be successfully applied to save time and money in solving friction and wear problems. No single test method will solve all problems, and proper test selection is critical for success. Sometimes, more than one test method will be needed to establish an engineering solution; especially, if more than one form of wear or surface damage is present in the application of interest.
References ASM Handbook (1992), Friction Lubrication and Wear Technology, 18, ASM International Materials Park, OH. ASM (1997), Source Book on Friction and Wear Testing, ASM International, Materials Park, OH. Blau, P.J. (1998), Development of bench-scale test methods for screening P/M aluminum alloys for wear resistance, in Powder Metallurgy Aluminum and Light Alloys for Automotive Applications, Jandeska, Jr., W.F. and Chernenkoff, R.A. (Eds.), Metal Powder Industries Federation, Princeton, NJ, 97. Blau, P.J. and Budinski, K.G. (1999), Use of ASTM standard wear tests for solving practical industrial wear problems, Wear, 225-229, 1159.
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15 Friction and Wear Data Bank 15.1 15.2 15.3
Introduction ..................................................................... 523 Sources of Data ................................................................ 523 Materials Found in Data Bank........................................ 527 Metals for Fluid (Oil) Film Bearings • Porous Metals • Plastics • Carbon–Graphites • Miscellaneous Nonmetallic Materials • Materials under Abrasive Wear
A. William Ruff Consultant
15.1
15.4
Data Bank Format............................................................ 529 Material Data • Tribological Data • Data Field Definitions
Introduction
Tribology is a critical science that has a key role in U.S. technology and competitiveness. Increased knowledge in tribology attained through research, both fundamental and applied, can lead to improved system reliability and durability, as well as decreased energy and material losses, throughout industrial technology. Transfer of tribology research results into general engineering practice is essential and can be assisted through the dissemination and use of critical tribological data. Tribology encompasses crossdisciplinary research and practice in materials, lubricants, and design (Zum Gahr, 1987). As a result, tribology research results are published in a number of specialized journals. This fact coupled with the diversity of tribology conditions of interest makes it difficult for researchers and engineers who work in different fields to locate pertinent information. As a result, advances in tribology have sometimes only slowly been incorporated into engineering practice. One approach to reduce this problem is the creation of tribological data and information banks. Many equipment manufacturing companies have taken steps to create proprietary data banks for their own use in design and material selection. In the public sector, the National Institute of Standards and Technology began in 1985 to develop a computerized tribology information system that would be widely available (Jahanmir et al., 1988). That system, termed ACTIS, was planned in accordance with recommendations from the international tribology community. The system was constructed to be computer-based and suitable for PCs generally available at that time. Within the limits of available funding, a total of 11 individual modules of code and data were developed and marketed. Recently, seven modules of the system, including databases and design codes, have been made available to the public without charge (see Further Information). The data included in this publication are drawn from those databases.
15.2
Sources of Data
Data generation in tribology involves a wide variety of experimental systems. In a compilation of 157 different wear test systems used to report data at the ASME Wear of Materials Conferences over the
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SLIDING VELOCITY v (m/s) 10-4 2.0
10-2
1
102
STEEL
COEFFICIENT OF FRICTION µ
COEFFICIENT OF FRICTION µ
The range of possible values for roughened disks
1.0
roughened disks
Mirror-smooth disks
0 FIGURE 15.1 Variation in coefficient of friction with sliding velocity for unlubricated steel–steel combinations.
period 1977 to 1985 (Glaeser et al., 1986) found that predominant systems were pin/disk (32%), pin/flat (29%), and block/ring (17%). Since each of these test geometries has different mechanical and thermal contact characteristics, it should be expected that measured tribological data will reflect those differences. Interlaboratory comparisons in fact show significant differences in wear results using basically similar pin/disk systems (Czichos et al., 1987) and even larger differences using dissimilar pin/disk systems (Almond et al., 1987). There is not yet any known way to adjust data from any test geometry to some reference measurement condition. Since results from laboratory tribology measurements are determined by the properties and conditions of the specific test system (Czichos, 1978), it is essential that the conditions used are appropriate to the final application intended. This requirement has been well stated (Barwell et al., 1983): “For … experiment to have meaning, it must reproduce the circumstances surrounding the occurrence of the phenomena under study. Otherwise the results … will be irrelevant to the purpose of the investigation.” Ashby and co-workers (Lim et al., 1987) have gathered friction data and wear rate data from the literature pertaining to pin/disk test systems involving steel/steel contacts. The results for system friction are shown in Figure 15.1, plotted vs. sliding velocity. Clearly there is a significant spread of friction values at any velocity. A simple functional relationship is difficult to justify using these data, and it is impossible to determine a single representative friction value. The authors discuss possible reasons for the wide variation. Similar difficulties were found in handling wear data collected from the literature. The scatter inherent in tribology data has been noted by many authors (Rabinowicz, 1981; Ruff, 1989). Figure 15.2 summarizes findings reported from a laboratory study of sliding UHMW polyethylene against stainless steel (Walbridge et al., 1987). By repeatedly interrupting a long-term test, the investigators were able to follow the progression of the wear coefficient as a function of time. The statistical distribution of those wear
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525
FIGURE 15.2 The distribution of calculated wear coefficient values of measured wear loss for UHMW polyethylene sliding against type 316L stainless steel.
coefficients was found to be a lognormal distribution. In most of the cases, there was significant difference between the most frequent value and the mean value. That suggests that descriptions of wear data by mean value and standard deviation analysis, while customary, may not always be suitable. This particular point needs to be more widely examined as tribological data are evaluated and added to data banks. Two specific examples of data gathering and evaluation for quite different tribological situations will be discussed. Two different modes of wear, mild and severe, are involved. Example 1. Mild Sliding Wear Mild wear situations are commonly experienced in service. This mode of damage might be considered as an extreme upper limit to tolerable behavior in many tribological systems. Ashby and co-workers have published wear rate results gathered from the literature on selected material combinations. Figure 15.3 shows their findings for pin/disk unlubricated sliding wear of low carbon steel against itself (Lim et al., 1987). In order to simplify the figure, contour lines have been drawn here guided by the actual data values that were in the original plot. In this graph the variables, normalized pressure and normalized velocity, cover a wide range of 4 decades and 6 decades, respectively, while the wear rates cover 6 decades. This clearly represents a physical situation of extremely large range in design and use conditions. For example, in certain regions of the plot, a change by a factor of 2 in pressure or velocity can produce a change by a factor of 10 in wear rate. This may be due to changes in the controlling wear mechanisms, or due to inherent sensitivity of wear to conditions in that region. In order to examine data from a more systematic, controlled perspective, consider two carefully controlled interlaboratory studies that have been reported. The VAMAS studies (Czichos et al., 1987) reported the wear constant for steel sliding against steel, as summarized in Figure 15.4. Results for six U.S. laboratories are individually indicated along with, separately, the average for the U.S. and for the world laboratories. The individual number of measurements is indicated in each case. It is seen that while the average values for the U.S. and world groups agree very well, there is considerable variation among the individual U.S. labs, up to a factor of 6 times in the average values reported. A similar situation is seen in a second set of interlaboratory data developed by a U.K. effort (Almond et al., 1987) and summarized in Figure 15.5. Both single-pin/disk tests, carried out with conditions similar to the VAMAS tests, and tri-pin/disk tests were done. Looking at the single- pin test results, one sees a large difference in average wear constant value among the individual labs, up to a factor of 4 times. The comparison between the single-pin test average and the tri-pin test average disagrees by a factor of about 2 times. The large individual differences in average wear constant shown, in spite of the care taken to control test specimen and test condition uniformity, suggest that both bias and precision of the data must be substantial concerns in any effort to construct data banks.
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SLIDING VELOCITY v (m/s) 10
10
-4
10
-2
1
10
2
LOW CARBON STEEL
~ NORMALIZED PRESSURE F
WEAR-RATE DATA-MAP
-4 10
-1
-5 -6
-4
-7
-5 10
-3
-6
-8
-7 -9 -6
-6 -7 -8 10
-9
-10
-5
FIGURE 15.3 Contours of constant wear rate order-of-magnitude values (mm3/m) for steel–steel unlubricated sliding conditions vs. normalized pressure and velocity. (Adapted from Lim, S.C. and Ashby, M.F. (1987), Wearmechanism maps, Acta Metallurgica, 35, 1-24.)
FIGURE 15.4 Wear constant results from VAMAS interlaboratory measurements of steel–steel combinations in unlubricated sliding. Each bar is a mean value topped by one standard deviation. The number of individual measurements is shown above each bar.
Example 2. Severe Abrasive Wear The second example involves a comparison of laboratory abrasive wear data obtained using two different test methods. Figure 15.6 shows a comparison (Moore et al., 1983) between two laboratory methods, pin/abrasive disk sliding, and dry sand abrasion, for a high hardness steel. The data for the rounded Ottawa sand follow a 1:1 relation comparing measurements from the two tests. However, the results using crushed quartz abrasive deviate significantly from that relationship, up to about 50%. The authors interpreted this spread to show the significance of different abrasive shape and composition characteristics on wear.
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FIGURE 15.5 Wear constant results from U.K. interlaboratory measurements of steel–steel combinations in unlubricated sliding. Each bar is a mean value topped by one standard deviation. The number of individual measurements is shown above each bar.
FIGURE 15.6 Comparison of relative wear resistances between two abrasion test methods using two types of abrasive.
One can conclude from these and other examples that extreme care must be used in selecting test results for data bank construction, so that substantial bias and variability are not introduced into the data collection.
15.3
Materials Found in Data Bank
A brief discussion of the material types found in the database, Table 15.1, is in order.
15.3.1 Metals for Fluid (Oil) Film Bearings This group of metals is primarily composed of alloys with a high content of lead, tin, copper, silver, cadmium, indium, aluminum, or zinc. They are compatible against steel journals and thrust surfaces. Friction and wear data are for dry operation with carbon steel. For dynamic lubricated operation with
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the load supported on a full oil film, the coefficient of friction commonly lies in the 0.001 range and is determined by characteristics of the oil film rather than by the bearing material. With a boundary film, both dynamic friction and wear rates will attain intermediate levels between dry and full oil film values. The softest material capable of meeting the load and temperature requirements is the common choice for optimum embedding of foreign particles and tolerating misalignment. Even where fatigue load capacity is inadequate with a soft material such as babbitt, the material can be used when it is applied as a thin layer on a backing of either steel or a stronger bearing material. Note carefully the conditions used when the data were obtained since most materials are sensitive to changes in conditions.
15.3.2 Porous Metals These materials are employed extensively in boundary lubricated service for operation within the tabulated load, speed, and temperature limits while using the oil supply self-contained within the pores. While a PV limit of 1.75 MPa m/s (50,000 psi ft/min) is commonly quoted for use of porous metals, conservative values should again be held to 10 to 20% of that limit for long-time service. A PV limit of 0.35 MPa m/s (10,000 psi ft/min) is usually suggested for application of porous metals in thrust bearing applications. Operating life at the 135°C (275°F) temperature limit given for porous bearing materials will reflect primarily the oxidation life of the oil impregnating the pores. Much longer life is possible in the 82°C (180°F) range and at even lower temperatures. With continuous feed of oil, porous metals can be used as fluid (oil) film bearing materials in a wide variety of higher speed and higher load applications. Note carefully the conditions used when the data were obtained since most materials are sensitive to changes in conditions.
15.3.3 Plastics Plastic materials are used for dry (unlubricated) or boundary lubricated, slow speed sliding and intermittent operation within the tabulated limits of temperature, P, V, and PV values, where P is unit loading on the projected bearing area in N/m2, V is surface velocity in m/s, and their product PV gives some measure of the temperature rise and wear severity for the contact. For acceptable wear performance in long-term operation, PV values should be held to about 10 to 20% of the maximum PV value listed, which is for short-time running under a most severe condition. The limiting PV given here was usually determined at approximately V = 0.5 m/s (100 ft./min.) in a short-time laboratory bench test. Tabulated P, V, and PV limits are either for dry operation on steel or for operation with the lubricants originally incorporated (where possible) in the plastic. With a supplementary supply of lubrication, much more demanding requirements may be accommodated. Friction and wear data for the plastics are for sliding against carbon steel surfaces. Manufacturers can often supply further guidelines for running against aluminum or various plastics. Note carefully the conditions used when the data were obtained, since most materials are sensitive to changes in conditions.
15.3.4 Carbon–Graphites These materials are widely used for dry operation at high temperature, and also for bearings and seals running with low-viscosity fluids such as water, solvents, and fuels; such fluids are inadequate for lubrication of fluid (oil) film bearing metals. These hard and brittle carbon–graphites require hardened mating surfaces and tolerate dirt contamination poorly. P, V, and PV data are given for application of carbon–graphites in dry operation. When used with water, fuels, solvents, and many process fluids, the carbon–graphites are excellent fluid-film bearing materials. In such cases, operating limits are commonly much higher than those given here, and performance characteristics depend largely on the nature of the fluid film involved in the bearing. Note carefully the conditions used when the data were obtained, since most materials are sensitive to changes in conditions.
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15.3.5 Miscellaneous Nonmetallic Materials Almost all materials used in the construction of mechanical systems have been employed at some time as bearing surfaces. Included are examples of the growing group of ceramics and composites which find use in special applications and as high temperature sliding surfaces. Also included in this group are rubber and wood, which find use with water, slurries, and a variety of low-viscosity liquids. Note carefully the conditions used when the data were obtained since most materials are sensitive to changes in conditions, particularly test pressure and load values for ceramics.
15.3.6 Materials under Abrasive Wear Abrasive wear data were obtained from laboratory tests using the dry sand/rubber wheel abrasion test as described in ASTM standard G-65. The tests involved abrading a specimen with rounded silica sand of controlled size. The abrasive was introduced between the specimen and a rotating wheel with a rubber rim of specified material. The specimen was pressed against the rotating wheel by a specified normal force. A controlled stream of abrasive was fed by gravity into the contact region. The wear mode is usually referred to in the literature as low stress, scratching, three-body abrasion. The data were obtained in a series of interlaboratory tests using the particular conditions given. The test conditions used were carefully chosen to provide uniform and reproducible wear. The test method has been used to provide relative rankings of materials to wear. In some reported cases a good correlation has been found between actual abrasive wear performance in service and that measured using this test. However, the severity of abrasive wear will depend on the particulars of abrasive size and shape, and on the system parameters of load and environment. Note carefully the conditions used when the data were obtained, since most materials are sensitive to changes in conditions.
15.4
Data Bank Format
The database, Table 15.1, contains data records of two types: materials data and tribological data.
15.4.1 Material Data These records contain properties data (composition, processing, physical, mechanical) on a group of materials frequently used in tribological applications. Since the materials are used in a variety of different tribological applications, specific tribological performance data are not given for records of this type.
15.4.2 Tribological Data These records contain critically evaluated tribological data for a group of materials measured under specific tribological use or test conditions. The counterface material, the contact environment, and other parameters associated with the data are specified to the extent that such information was available in the original report. Blank spaces in the data records indicate data not available. Note carefully the conditions used when the data were obtained, since most materials are sensitive to changes in conditions. Note that the materials data in records of this type may not be complete in all cases because they depend on the original source.
15.4.3 Data Field Definitions The definitions, given here in alphabetical order, in most cases follow ASTM definitions. Class: Common name: Component name: Component weight percent:
A major material class, e.g., metal, ceramic, polymer, etc. A name frequently given to a particular material, e.g., nylon. The set of components (elements) present, in order present. The weight percent of each component (element) in order.
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Contact environment: Contact geometry: Counterface description: Counterface material: Data source: Density: Distance: Expansion coefficient: Form: Fracture toughness (Mode I, plane strain): Friction coefficient: Grade: Hardness: Heat capacity: Load: Maximum operating temperature: Maximum pressure: Maximum velocity: Melting point: P(ressure) V(elocity) limit: Principal component: Processing conditions: Processing and treatment: Resistivity: Second component: Specification: Specimen shape: Standard test: Sub-class: Temperature: Tensile strength: Thermal conductivity: Velocity: Wear coefficient: Wear constant: Wear rate:
Modern Tribology Handbook
Terms describing the local environment at the contact, e.g., atmosphere, lubricant, abrasive, etc. Terms describing the geometry such as pin/disk, etc. Further identification of the counterface. Identification of the opposing surface material, e.g., rubber, steel. Source of data for this record (consult data sources at end of table). Mass per unit volume, in kilograms per cubic meter. Sliding distance used in the test, in meters. Increase in dimensions of a body due to change in temperature, in micrometers per meter per degree C. The material form, e.g., rod, sheet, cast, etc. Resistance to extension of a crack, given here by KIC, the critical stress intensity factor for plane strain, linear–elastic conditions, in MPa m1/2. Dimensionless ratio of the force resisting motion to the normal force pressing two moving bodies together. Designation given a material by a manufacturer. Resistance of a material to indentation. The usual methods for hardness determinations include Rockwell C, Vickers, etc. Amount of heat necessary to change the temperature of unit mass by one degree, in kilojoules per kilogram per degree C. Normal contact load used in the test, in Newtons. Maximum permitted contact temperature, in degrees C. Maximum permitted contact pressure, in MPa. The maximum permitted sliding velocity, in m/s. Temperature at which a solid changes to liquid state at one standard atmosphere, in degrees C. Maximum permitted value of the product contact pressure times sliding velocity, in MPa m/s. The principal component (element) designation. Specific process conditions used, e.g., 200°C temperature. A descriptive phrase on the process method, e.g., cast. Electrical resistance measured between opposite faces of a centimeter cube of material, in units of micro-ohm cm. The second component (element) present. A precise statement of a set of requirements to be satisfied by a material, promulgated by an organization, e.g., ASTM-###, SAE-###, etc. The shape of the test specimen, e.g., block, pin. Test designation, i.e., ASTM, SAE, etc. Subdivisions of a class, e.g., ferrous, boride, etc. Test temperature, in degrees C. Maximum amount of tensile load per unit original cross-section area that a material attains when tested to rupture, in MPa. Time rate of steady heat flow through unit area per unit temperature gradient, in watts per meter per degree C. Relative speed of motion between the two contacting surfaces, in m/s. Dimensionless coefficient calculated by the relationship: (wear volume)∗(hardness)/(load)/(sliding distance). Volume rate of material removal per unit sliding distance per unit load, in cubic millimeters per Newton-millimeter. Volume rate of material removal per unit sliding distance, in cubic millimeters per meter.
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Wear type:
Young’s modulus:
531
Five possible types are considered: abrasive, adhesive, fatigue, fretting, or lubricated, defined as: (1) abrasive — wear being caused by the action of hard particles or protuberances between the contacting surfaces; (2) adhesive — wear caused by surface interactions usually involving deformation; (3) fatigue — wear due to time-dependent, accumulative fatigue processes at or beneath the contacting surfaces; (4) fretting — wear under oscillating conditions at small sliding amplitudes; (5) lubricated — wear under conditions in which a lubricant is present. Ratio of tensile or compressive stress to corresponding strain below the proportional limit of the material, in MPa.
References Almond, E.A. and Gee, M.G. (1987), Results from a U.K. interlaboratory project on dry sliding wear, Wear, 120, 101-116. Barwell, F.T. and Jones, M.H. (1983), Role of laboratory test machines, in Industrial Tribology, Jones, M.H. and Scott, D. (Eds.), Elsevier, NY. Czichos, H. (1978), Tribology: A Systems Approach to the Science and Technology of Friction, Lubrication, and Wear, Elsevier, NY. Czichos, H., Becker, S., and Lexow, J. (1987), Multilaboratory tribotesting: results from the VAMAS program on wear test methods, Wear, 114, 109-130. Glaeser, W. and Ruff, A.W. (1986), private communication. Jahanmir, S., Ruff, A.W., and Hsu, S.M. (1988), A computerized tribology information system, in Proceedings ASM Conference on Engineered Materials for Advanced Friction and Wear Applications, ASM International, OH, 243-247. Lim, S.C. and Ashby, M.F. (1987), Wear-mechanism maps, Acta Metallurgica, 35, 1-24. Moore, M.A. and Swanson, P.A. (1983), The effect of particle shape on abrasive wear: a comparison of theory and experiment, in Proceedings of Wear of Materials Conference — 1983, American Society of Mechanical Engineers, NY, 1-11. Peterson, M.B. and Winer, W.O. (1980) (Eds.), Wear Control Handbook, American Society of Mechanical Engineers, NY. Rabinowicz, E. (1981), The wear coefficient — magnitude, scatter, uses, Transactions of the American Society of Mechanical Engineers, 103, 188-194. Ruff, A.W. (1989), Comparison of standard test methods for non-lubricated sliding wear, in Proceedings of Wear of Materials Conference — 1989, American Society of Mechanical Engineers, NY, 717-721. Walbridge, N.C. and Dowson, D. (1987), Distribution of wear rate data and a statistical approach to sliding wear theory, in Proceedings of Wear of Materials Conference — 1987, American Society of Mechanical Engineers, NY, 101-110. Zum Gahr, K.-H. (1987), Microstructure and Wear of Materials, Elsevier, NY.
For Further Information Free copies of the PC-based code and database modules developed for the ACTIS system are available by contacting: NIST Office of Standard Reference Data, North Building, Gaithersburg, MD 20899. A thorough description of the development process that led to the ACTIS system is found in the reference of Jahanmir et al., 1988. Good, accessible sources of tribological data include Wear Control Handbook (Peterson, M. B. and Winer, W. O. (1980), Eds., American Society of Mechanical Engineers, NY); ASM Handbook — Friction, Lubrication, and Wear Technology, Vol. 18, (Blau, P. J. (1998), Ed., ASM International), and Wear of Materials Conference Proceedings, 1977–1999 (published biannually by ASME, NY, and Elsevier, NY).
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TABLE 15.1 NUMBER
Modern Tribology Handbook
Tribo-Materials Database (Part A) COMMON NAME
CLASS
SUBCLASS
PRINCIPAL COMPONENT
SECOND COMPONENT
GRADE
1 2 3 4 5 6 7 8 9 10
TITANIUM DIBORIDE BORON CARBIDE CHROMIUM CARBIDE SILICON CARBIDE TITANIUM CARBIDE TITANUM CARBIDE TUNGSTEN CARBIDE TUNGSTEN CARBIDE CARBON CARBON
CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC
BORIDE CARBIDE CARBIDE CARBIDE CARBIDE CARBIDE CARBIDE CARBIDE CARBON CARBON
TIB2 B4C CR3C2 SIC TIC TIC WC WC C C
11 12 13 14 15 16 17 18 19 20
CARBON CARBON CARBON CARBON CARBON CARBON CARBON CARBON GRAPHITE CARBON GRAPHITE-BABBITT CARBON GRAPHITE-COPPER
CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC
CARBON CARBON CARBON CARBON CARBON CARBON CARBON CARBON CARBON CARBON
C C C C C C C C C C
21 22 23 24 25 26 27 28 29 30
CARBON GRAPHITE-GLASS CARBON GRAPHITE-LITHIUM FLUORIDE CARBON GRAPHITE-RESIN CARBON GRAPHITE-SILVER GRAPHITE QUARTZ GLASS SODA GLASS SILICON NITRIDE TITANIUM NITRIDE ALUMINUM OXIDE
CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC
CARBON CARBON CARBON CARBON CARBON GLASS GLASS NITRIDE NITRIDE OXIDE
C C C C C SIO2 SIO2 SI3N4 TIN AL2O3
SIO2 LIF
31 32 33 34 35 36 37 38 39 40
ALUMINUM OXIDE – TITANIUM OXIDE BERYLLIUM OXIDE PARTIALLY STABILIZED ZIRCONIA PARTIALLY STABILIZED ZIRCONIA PARTIALLY STABILIZED ZIRCONIA PARTIALLY STABILIZED ZIRCONIA PARTIALLY STABILIZED ZIRCONIA SILICON DIOXIDE TITANIUM DIOXIDE WOOD/OIL IMPREGNATED
CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC CERAMIC COMPOSITE
OXIDE OXIDE OXIDE OXIDE OXIDE OXIDE OXIDE OXIDE OXIDE CELLULOSE
AL2O3 BEO ZRO2 ZRO2 ZRO2 ZRO2 ZRO2 SIO2 TIO2 WOOD
TIO2
SPK SN80
Y2O3
TZ3Y 1027 MS 2016 Z191
41 42 43 44 45 46 47 48 49 50
MOLYBDENUM DISULFIDE COMPOSITE DU (BRONZE/PTFE) STEEL/TiC TUNGSTEN CARBIDE – COBALT TUNGSTEN CARBIDE – COBALT CAST IRON CAST IRON CAST IRON CAST IRON CAST IRON
COMPOSITE COMPOSITE COMPOSITE COMPOSITE COMPOSITE METAL METAL METAL METAL METAL
COMPOSITE METAL MATRIX METAL MATRIX METAL MATRIX METAL MATRIX FERROUS FERROUS FERROUS FERROUS FERROUS
MOS2 CU FE WC WC FE FE FE FE FE
TA PTFE TiC CO CO NI CR SI NI CR
51 52 53 54 55 56 57 58 59 60
CAST IRON CAST IRON, OIL-FILLED IRON IRON-COPPER, OIL-FILLED IRON-COPPER, OIL-FILLED IRON, OIL-FILLED MILD STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
C C
C CR CR CR
440CM 304HN 316
61 62 63 64 65 66 67 68 69 70
STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
440C 440C 17-4PH 304 316 347 17-4 PH 316 316 17-4 PH
71 72 73 74 75 76 77 78
STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STAINLESS STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR
410 15-5PH 410 21-55N 310 52100 52100 52100
HOT PRESSED K 162B
AG
2690 P-5AG S-95 T-0054 P-9 G-1 P-03 P-2W P-5 P-15
CU
AG
MGO Y2O3
OIL PM-103 H-46 K-714 NI-RESIST 1 NI-HARD 4 DURIRON NI-HARD HC250 MEEHANITE
CU CU
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TABLE 15.1
Tribomaterials Database (Part B) SPECIFICATION
FORM
PROCESSING CONDITIONS
PROCESSING AND TREATMENT
SELF BOND
MOULDED
CO BONDED CARBPM GRAPHITE, HIGH TEMP. TREATED SILVER IMPREGNATED
MOULDED BAKED MOULDED BAKED BAKED BAKED, IMPREGNATED BABBITT IMPREGNATED
SILVER IMPREGNATED EXTRUDED CAST CAST SELF BOND HOT PRESS
SAE 863; ASTM B-439-70, GR4; MIL-B-5687C, 2B SAE 862; ASTM B-439-70, GR3; MIL-B-5687C, 2B SAE 850; ASTM B-439-70, GR1; MIL-B-5687C, 2A1
MOULDED COATING ON STEEL
MOLYBDENUM DISULFIDE, BONDED SINTERED
PLATE
SINTERED
CAST CAST CAST CAST CAST
ANNEALED
CAST POROUS, 8% ELECTROLYTIC POROUS, 20% POROUS, 20% POROUS, 20%
ANNEALED
COLD ROLLED
BAR BAR BAR BAR
ANNEALED HT WROUGHT, H900 ANNEALED ANNEALED HOT WORKED, ANNEALED HT ANNEALED ANNEALED HT
BAR BAR BAR
ANNEALED WROUGHT, H900 HT ANNEALED ANNEALED HT HT HT
600F TEMPER
925F:4h H-900 H-900 H-1100
1000 TEMPER
350F TEMPER 350F TEMPER 350F TEMPER
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TABLE 15.1
Modern Tribology Handbook
Tribo-Materials Database (Part A)
NUMBER
COMMON NAME
CLASS
SUBCLASS
PRINCIPAL COMPONENT
SECOND COMPONENT
GRADE
79 80
STEEL STEEL
METAL METAL
FERROUS FERROUS
FE FE
CR CR
52100 52100
81 82 83 84 85 86 87 88 89 90
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR C MN CR CR CR CR
52100 52100 52100 52100 1090 1020 52100 52100 52100 52100
91 92 93 94 95 96 97 98 99 100
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 52100 52100 52100 52100 52100 52100 52100 52100
101 102 103 104 105 106 107 108 109 110
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR C CR CR CR
52100 52100 52100 52100 52100 52100 1090 52100 52100 52100
111 112 113 114 115 116 117 118 119 120
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 52100 52100 52100 52100 52100 52100 52100 52100
121 122 123 124 125 126 127 128 129 130
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR C CR
52100 52100 52100 52100 52100 52100 52100 52100 1090 52100
131 132 133 134 135 136 137 138 139 140
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 52100 52100 52100 52100 52100 52100 52100 52100
141 142 143 144 145 146 147 148 149 150
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 52100 52100 52100 52100 52100 52100 52100 52100
151 152 153 154 155
STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE
CR CR CR CR CR
52100 52100 52100 52100 52100
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TABLE 15.1
Tribomaterials Database (Part B) SPECIFICATION
FORM
PROCESSING AND TREATMENT
PROCESSING CONDITIONS
BAR BAR
HT HT
350F TEMPER 350F TEMPER
BAR BAR BAR BAR SHEET SHEET BAR BAR BAR BAR
HT HT HT HT NORMALIZED ANNEALED HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 1650F 1610F:1h, FURNACE COOLED 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR
HT HT HT HT HT HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR SHEET BAR BAR BAR
HT HT HT HT HT HT NORMALIZED HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 1650F 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR
HT HT HT HT HT HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR SHEET BAR
HT HT HT HT HT HT HT HT NORMALIZED HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 1650F 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR
HT HT HT HT HT HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR
HT HT HT HT HT HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR
HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
8403/frame/ch15-Tbl 15.1(AB) Page 536 Friday, October 27, 2000 4:18 PM
536
TABLE 15.1
Modern Tribology Handbook
Tribo-Materials Database (Part A)
NUMBER
COMMON NAME
CLASS
SUBCLASS
PRINCIPAL COMPONENT
SECOND COMPONENT
GRADE
156 157 158 159 160
STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE
CR CR CR CR CR
52100 52100 52100 52100 52100
161 162 163 164 165 166 167 168 169 170
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 SS UNILOY 19-9DL 52100 52100 52100 52100 52100 52100 52100
171 172 173 174 175 176 177 178 179 180
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
CR CR CR CR CR CR CR CR CR CR
52100 52100 52100 52100 52100 52100 52100 SS A-286 52100 52100
181 182 183 184 185 186 187 188 189 190
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
C C C C C C C CR MN CR
81B45 9310 51100 50100 4820 C1080 9310 52100 C1080 FERRO TIC
191 192 193 194 195 196 197 198 199 200
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
C C C CR MN MN C C CR AL
8620 81B45 4820 52100 1118 1118 8620 4340 SS UHB AEB-L SUPER NITRALLOY
201 202 203 204 205 206 207 208 209 210
STEEL STEEL STEEL STEEL STEEL STEEL TOOL STEEL TOOL STEEL TOOL STEEL TOOL STEEL
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS FERROUS
FE FE FE FE FE FE FE FE FE FE
AL CR C C C CR W CR CR Cr
SUPER NITRALLOY 52100 4340 1040 1040 52100 MOD M2 D2 M50 M50
211 212 213 214 215 216 217 218 219 220
TOOL STEEL TOOL STEEL TOOL STEEL TOOL STEEL ALUMINUM ALUMINUM ALUMINUM ALUMINUM ALUMINUM ALLOY ALUMINUM BRONZE
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
FERROUS FERROUS FERROUS FERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
FE FE FE FE AL AL AL AL AL CU
CR CR CR CR SI
H13 D2 D2 H11 380
SI FE CD AL
390 1100
221 222 223 224 225 226 227 228 229 230
ALUMINUM BRONZE ALUMINUM BRONZE ALUMINUM BRONZE ALUMINUM-BIMETAL ALUMINUM-LEAD ALUMINUM-SILICON ALUMINUM-TIN ALUMINUM, OIL-FILLED ANTIMONY BERYLLIUM COPPER
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
CU CU CU AL AL AL AL AL SB CU
AL AL AL SN PB SI SN CU
C61000
231 232
BERYLLIUM COPPER BRONZE
METAL METAL
NONFERROUS NONFERROUS
CU CU
BE SN
C61000
C60800
BE
C93200
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Friction and Wear Data Bank
TABLE 15.1
Tribomaterials Database (Part B) SPECIFICATION
FORM
PROCESSING AND TREATMENT
PROCESSING CONDITIONS
BAR BAR BAR BAR BAR
HT HT HT HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR
HT HT HOT ROLLED HT HT HT HT HT HT HT
350F TEMPER 350F TEMPER
HT HT HT HT HT HT HT QUENCHED, TEMPERED HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR BAR
CAST
BAR
HT CARBURIZED, HT ANNEALED ANNEALED ANNEALED ANNEALED ANNEALED ANNEALED HT
ANNEALED ANNEALED CARBURIZED, HT HT CARBURIZED, HT ANNEALED CARBURIZED, HT HT
350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER 350F TEMPER
350F TEMPER 900F TEMPER 400F TEMPER 300F, TEMPER
400F TEMPER
300F TEMPER 350F TEMPER 300F TEMPER 300F TEMPER 260C TEMPER
PH
BAR
BAR
BAR BAR
PH,NITRIDED HT ANNEALED HT ANNEALED ANNEALED HT HT HT ANNEALED HT HT HT HT
CAST ANNEALED CAST SAE 781 HARDENED CAST
ANNEALED
CAST
ANNEALED
CDA 954 SAE 780
SAE 783 POROUS, 19%
SAE 660
CAST
ANNEALED AGE HARDENED
CAST CAST
ANNEALED ANNEALED
350F TEMPER 300F TEMPER
300F TEMPER 1850F, TEMPER 400F, 1 h 600F TEMPER
25min.1875F, 2 TEMPER 1100F,2h 600F TEMPER 1850F, TEMPER 400F, 1 h 500F TEMPER
8403/frame/ch15-Tbl 15.1(AB) Page 538 Friday, October 27, 2000 4:18 PM
538
TABLE 15.1
Modern Tribology Handbook
Tribo-Materials Database (Part A)
NUMBER
COMMON NAME
CLASS
SUBCLASS
PRINCIPAL COMPONENT
233 234 235 236 237 238 239 240
BRONZE BRONZE BRONZE BRONZE, OIL-FILLED BRONZE, OIL-FILLED CADMIUM CADMIUM ALLOY CAST ALUMINUM ALLOY
METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
CU CU CU CU FE CD CD AL
241 242 243 244 245 246 247 248 249 250
COPPER COPPER-LEAD COPPER-LEAD ELECTROLESS NICKEL ELECTROLESS NICKEL GOLD GUN METAL HASTELLOY INCONEL INDIUM
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
CU CU CU NI NI AU CU NI NI IN
251 252 253 254 255 256 257 258 259 260
LEAD LEAD BABBITT LEAD BABBITT LEAD BABBITT LEAD BABBITT LEADED GUN METAL LEAD-TIN BRONZE LEAD-TIN BRONZE MANGANESE BRONZE MOLYBDENUM
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
PB PB PB PB PB CU CU CU CU MO
261 262 263 264 265 266 267 268 269 270
MONEL NAVY GUN METAL NICKEL-CHROMIUM ALLOY NICKEL-CHROMIUM ALLOY PHOSPHOR BRONZE PHOSPHOR BRONZE SEMIPLASTIC BRONZE SILICON BRONZE SILVER STELLITE
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
271 272 273 274 275 276 277 278 279 280
STELLITE STELLITE STELLITE STELLITE STELLITE STELLITE STOODY Ti-6Al-4V Ti-6Al-4V TIN
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
281 282 283 284 285 286 287 288 289 290
TIN BABBITT TIN BABBITT TIN BABBITT TIN BABBITT TRIBALOY TRIBALOY TRIBALOY TUNGSTEN VANASIL WASPALOY
291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310
SECOND COMPONENT PB PB SN SN CU
GRADE C98600 C94300 C93700
NI SN OFHC PB PB P P SN MO CR
C 718
SB SB SB SB SN SN SN ZN TI
15 13 7 8
NI CU FE FE CU CU CU CU AG CO
CU SN NI NI SN SN SN SI
K500
CR
S1016
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
CO CO CO CO CO CO CO TI TI SN
CR CR CR CR CR CR CR AL AL
1 6 F STAR J S1016 S1016 6
METAL METAL METAL METAL METAL METAL METAL METAL METAL METAL
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
SN SN SN SN CO CO NI W SI NI
SB SB SB SB MO MO MO NI NI CR
3 2 1
WASPALOY WAUKESHA ZINC ZINC-11 ALUMINUM ZINC-27 ALUMINUM ZIRCALLOY ACETAL ACRYLONITRILE-BUTADIENE-STYRENE (ABS) ARMALON DUROID
METAL METAL METAL METAL METAL METAL POLYMER POLYMER POLYMER POLYMER
NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS NONFERROUS
NI NI ZN ZN ZN ZR
CR SN
23
AL AL SN
12 27 2
FEP IPC NYLON NYLON NYLON 6/6 PHENOLIC POLYCARBONATE POLYESTER POLYETHYLENE POLYIMIDE
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
C86300 0.5 TI
16-25-6 16-25-6 C51100 C87200
T-800 T-400 T-700 77
5600
1832 6 TF
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Friction and Wear Data Bank
TABLE 15.1
Tribomaterials Database (Part B) SPECIFICATION
FORM
SAE 64 SAE 841; ASTM b-438-73, GR1 TYPE II; MIL-B-5678C, 1A ASTM B-612-70, GR3
CAST CAST CAST POROUS, 20% POROUS, 20%
SAE 770
CAST
PROCESSING AND TREATMENT
PROCESSING CONDITIONS
ANNEALED ANNEALED ANNEALED
ANNEALED
ANNEALED SAE 480 PLATED PLATED
HEATED TO 400C AS DEPOSITED ANNEALED
CAST CAST
ANNEALED AGED ANNEALED
SAE 62, CDA 902
ANNEALED SAE 15 SAE 13 ASTM 7 ASTM B23/8 SAE 63, CDA 927 SAE 40, CDA 836 CDA943
CAST CAST CAST CAST
CAST ARC CAST
ANNEALED
CAST SAE 620, CDA 903 HOT ROLLED, HARDENED HOT ROLLED, ANNEALED SAE 64, SAE 792; SAE 797, CDA 937 COLD WORKED SAE 67, CDA 938 CAST BAR CAST CAST CAST CAST BAR BAR CAST CAST
ASTM B23/3 ASTM B23/2
ANNEALED ANNEALED WELD
OXY/ACETY
WELD WELDED
OXY/ACETY OXY/ACETY
ANNEALED BORONIZED, HT ANNEALED
CAST CAST CAST
SAE 11 CAST CAST CAST PM CAST CAST CAST CAST
SINTER, DRAWN AGE HARDENED ANNEALED HT, PH ANNEALED
ASTM B-669-82
CAST CAST CAST
MOULDED CAST CAST CAST LAMINATED
ANNEALED
8403/frame/ch15-Tbl 15.1(AB) Page 540 Friday, October 27, 2000 4:18 PM
540
TABLE 15.1 NUMBER
Modern Tribology Handbook
Tribo-Materials Database (Part A) COMMON NAME
CLASS
SUBCLASS
311 312 313 314 315 316 317 318 319 320
POLYIMIDE (FILLED) POLYPHENYLENE OXIDE POLYPHENYLENE SULFIDE POLYPROPYLENE POLYSULFONE POLYURETHANE PTFE TORLON UHMWPE RUBBER
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
ELASTOMER
321 322 323 324 325 326 327 328 329 330
ACETAL-CARBON ACETAL-GLASS ACETAL-PTFE ACETAL-SILICONE ACRYLONITRILE-BUTADIENE-STYRENE (ABS) EPOXY-CELLULOSE NYLON 6/6-CARBON NYLON 6/6-GLASS NYLON 6/6-PTFE NYLON 6/6-SILICONE
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED
331 332 333 334 335 336 337 338 339 340
PEEK-GRAPHITE PHENOLIC-COTTON LAMINATE PHENOLIC-WOOD FLOUR POLYCARBONATE-CARBON POLYCARBONATE-GLASS POLYCARBONATE-PTFE POLYESTER-CARBON POLYESTER-GLASS POLYESTER-PTFE POLYESTER-SILICONE
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED
341 342 343 344 345 346 347 348 349 350
POLYETHYLENE-PTFE POLYIMIDE-GLASS POLYIMIDE-GRAPHITE POLYPHENYLENE OXIDE-GLASS POLYPHENYLENE OXIDE-PTFE POLYPHENYLENE SULFIDE-CARBON POLYPHENYLENE SULFIDE-GLASS POLYPHENYLENE SULFIDE-PTFE POLYPROPYLENE-PTFE POLYSULFONE-CARBON
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED
351 352 353 354 355 356 357 358 359 360
POLYSULFONE-GLASS POLYSULFONE-PTFE POLYURETHANE-GLASS POLYURETHANE-PTFE PTFE-FABRIC PTFE-GLASS PTFE-GRAPHITE RULON RYTON VESPEL
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED FILLED
361 362 363 364 365 366 367 368
VESPEL BUTYL NEOPRENE NITRILE SILICONE RUBBER URETHANE VITON FABROID
POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER POLYMER
FILLED RUBBER RUBBER RUBBER RUBBER RUBBER RUBBER WOVEN
PRINCIPAL COMPONENT
SECOND COMPONENT
GRADE T-0454
PTFE
LD R4 SP1 SP21
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Friction and Wear Data Bank
TABLE 15.1
Tribomaterials Database (Part B) SPECIFICATION
FORM
PROCESSING AND TREATMENT
MOULDED
MOULDED
MOULDED SINTERED
SINTERED MOULDED MOULDED MOULDED MOULDED MOULDED MOULDED WOVEN
PROCESSING CONDITIONS
8403/frame/ch15-Tbl 15.1(CD) Page 542 Friday, October 27, 2000 4:17 PM
542
Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part C) Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Component Weight Percent
Component Names
Density (kg/m3) 4,429 2,510 6,643 3,045 4,429 5,536 6,089 3,045 1,938 2,353
C C, Ag
8,304 1,850 1,661 1,938 1,938 1,661 1,661 1,700 2,350 2,400
C C C C C C C, Babbitt C, copper
21 22 23 24 25 26 27 28 29 30
C, glass C, lithium fluoride C, resin C, silver C
31 32 33 34 35 36 37 38 39 40
Al2O3, TiO2
41 42 43 44 45 46 47 48 49 50
MoS2, Ta PTFE, Pb, bronze TiC,Cr,Mo,C,Fe
34.6,6.6,2,.8,56
C,Si,Ni,Cu,Cr,Fe C,Si,Mn,Ni,Cr,Fe C,Si,Mn,P,S,Fe C,Si,Ni,Cr,Fe C,Cr,Fe
3,1.5,15,6,2,71.5 3.5,1.5,0.5,6,8,80.5 .85,14.5,.5,.07,.08,84 3.5,.5,4,2,89.5 2.8,28,69.2
51 52 53 54 55 56 57 58 59 60
C,Mn,Si,Cu,Ni,Mo,Fe C, Fe C,Fe Cu, Fe Cu, Fe Fe
3,2,1.8,.5,2,.5,90.2 3, 97 .006,99.98 20, 80 10, 90
C,Mn,Si,Cr,Ni,Mo,Ti,Va,Fe C,Mn,P,S,Si,Cr,Ni,N,Fe C,Cr,Ni,Mo,Fe
.08,1,.6,15,26,1,2,.3,54 .08,2,.045,.03,1,18,8,.2,70.6 .1,18,14,3,65
7,197 6,700 7,861 6,000 6,100 6,000 7,800 7,473 8,027 8,027
61 62 63 64 65 66 67 68 69 70
C,Mn,Si,P,S,Cr,Mo,Fe C,Mn,Si,P,S,Cr,Mo,Fe C,Cr,Ni,Cu,Fe C,Cr,Ni,Fe C,Cr,Ni,Mo,Fe C,Mn,Si,Cr,Fe C,Cr,Ni,Cu,Fe C,Cr,Ni,Mo,Fe C,Cr,Ni,Mo,Fe C,Cr,Ni,Cu,Fe
1,1.25,1,.04,.04,18,.75,78 1,1.25,1,.04,.04,18,.75,78 .05,16.5,4.0,4.0,75.5 .08,19,10,71 .1,18,14,3,65 .15,1.0,.5,12,86.5 .07,17,4,4,74 .08,18,14,3,64 .08,18,14,3,64 .07,17,4,4,74
71 72 73 74 75 76 77 78
C,Mn,Si,Cr,Fe C,Mn,P,S,Si,Cr,Ni,Cu,Cb,Fe C,Mn,P,S,Si,Cr,Ni,Cb&Ta C,Mn,Si,Cr,Ni,N,Fe C,Mn,Si,Cr,Ni,Fe C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
.15,1.0,.5,12,86.5 .07,1.0,.04,.03,1,14.5,4,3,.3,76 .08,2,.045,.03,1,18,11,.1 .52,9,.15,21,3.85,.45,65 .25,2,1.5,25,20,47 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
Y2O3,ZrO2
5.3,94
ZrO2, MgO Y2O3,Zr02
Melting Point (C)
2,400 1,890 2,699 3,140
2,800
3,652
2,000 1,900 1,900 2,400 1,570 2,491 2,491 3,045 5,536 3,875
1,538 1,122 1,899 2,950 1,849
4,152 2,214 6,089
1,750 2,570 2,700
5,536 3,97
5,813 3,045 4,152 1,200
2,593 1,710 1,838
5,900 7,750 14,200 14,200 7,197 7,473 7,197 7,473 7,473
1,269
Expansion Coefficient (µm/m)
Thermal Conductivity (watt/m/C)
Heat Capacity (kJ/kg C)
8 5 10 4 8 9 10 6 1 5
26 19 19 147 26 17 19 2 36 26
1.0 2.0 1.0 1.0 1.0 1.0
4 5 4 8 8 10 9 5 5 5
138
5 9 5 5 2 57 10 2 8 7
78 17 9 14 170 2 1 15 66 35
8 36 10 20 10
25 2 3
10 16 9 5
3 164 5
9 19
43 42
6 6 10 10 12 9 9
87 87 40
12 2 69 17 9 9 13 14
0.0
1.0
1.0 1.0 1.0 1.0 0.0 1.0 2.0 1.0
2
1.0 1.0 2.0
1.0 17
8 16 12 12 13 10 23
29 28 50
1,427 1,427
17 11
16 16
0.0 0.0
7,473 7,473 7,750 8,030 8,027 7,889 7,750 8,027 8,027 7,750
1,538 1,538 1,400
29 29 18
1,427 1,427
11 11 11 17 11 19 11 11 11
0.0 0.0 0.0 1.0 0.0 1.0 1.0 0.0 1.0 1.0
7,750 7,750 7,750 7,750 7,970 7,800 7,800 7,800
1,482
12 12 16 16 12 12 12
25 18 25
0.0
1,482
16 43 43 43
1.0 0.0 0.0 0.0
1,537
1,427 1,400
1,427 1,475 1,475 1,475
0.0 54
16 16 21 16 16
0.0
0.0
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Friction and Wear Data Bank
TABLE 15.1 Tribomaterials Database (Part D) Resistivity (u-ohm-cm)
Hardness
Youngs Modulus (MPa)
Fracture Toughness (MPa-m1/2)
896 41 69
650 HV 650 HV 480 HV 170 HV 600 HV 320 HV 680 HV 85 SHORE 70 SHORE 95 SHORE
97 59 28 21 38 28 41 41 62 62
13,800 14,500 14,500 20,700 12,400 6,890 13,800 16,600 32,344 32,348
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Booser Booser Booser
90 SHORE 90 SHORE 90 SHORE 90 SHORE 3 HV
52 48 59 69 12 110
262
15,200 20,700 32,612 32,560 12,900 129,744 130,340 310,000 248,000 372,000
Booser Booser Booser Booser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser
545 103 1,172 276 689 172 1,020 103 52 8
358,000 379,000 200,000 200,000 200,000 172,000 205,000 379,000 234,000 12,400
675 HV
69
138,000
330 HV 85 HRA 90 HRA 150 HV 560 HV 530 HV 655 HV 530 HV
1,034 1,100 1,103 207 620 110 379 689
196 HV 30 HB 45 HV 83 HB 50 HB 150 HB
310 138 276 221 207 83 414
72 74
200 HV 200 HV
689 758
200,000 200,000 200,000 196,000
60 60 77
257 HV 650 HV 400 HV 160 HV 150 HV 150 HV 44 HRC 97 HRB 97 HRB 44 HRC
862 1,379 1,379 586 586 620 1,379 760 680 1,379
200,000 200,000 196,000 193,000 196,000 193,000 196,000 196,000 196,000 196,000
135 HV 420 HV 257 HV 264 HV 150 HV 62 HRC 62 HRC 62 HRC
517 1,379 758 862 654 1,640 1,640 1,640
196,000 196,000 196,000 193,000 200,000 199,000 199,000 199,000
2
4 3 2 5 4
820 HV
1.00E+12
60
0580 HV 1300 HV 2000 HV 1500 HV
1800 HV 1158 HV 1600 HV
1.46E+20 400 4.01E+13
71
10
74 72 77 74 74 77 57 77 57 78 20 20 20
286 HV 853 HV 900 HV
172 262 103 896 345
524
7 6
Data Source
345,000 441,000 372,000 379,000 483,000 414,000 407,000 552,000 6,890 32,344
100 100
3500 HV 3200 HV 2600 HV 2700 HV 3000 HV 3000 HV 1400 HV 1500 HV
Tensile Strength (MPa)
5
12
1 1 4 4 5 7 10 9 10 9 1 3
607,000 607,000 103,000 172,000 172,000 221,000
98
124,000 129,528 207,000
140
48
48
48
81 60
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser
Wear Coefficient
3.0E-06
Glaeser Glaeser Glaeser Glaeser Glaeser Hughes/Rowe Hughes/Rowe Hughes/Rowe
9.5E-07 649 260
6.1E-05
371 650 288 204 538 288 316 316 190 260
2.4E-04
649 260 260 260 425 1,650 1,480 1,760
1,370 1,370 1,480 2,400 71 400 204 649 3.0E-05
4.5E-04 538 538 816 816 427
Glaeser Booser Glaeser Booser Booser Booser Booser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser ASTM G2,RR3,5/18/76,3 labs,n=3 ASTM G2,RR2,12/9/75,5 labs,n=5 ASTM G2,RR1,5/23/75,2 labs,n=2 ASTM G2,RR9,6/10/82,8 labs,n=32
Wear Rate (mm3/m)
1,650
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Booser Glaeser Glaeser Glaeser ASTM G2,RR2,12/9/75,5 labs,n=5 Booser Glaeser Glaeser Glaeser Glaeser Glaeser
Maximum Operating Temperature (C)
399 135 135 135 135 538
649
3.0E-05 7.6E-06
316 316 870 649 815
2.0E-03 9.0E-04 4.0E-04 3.0E-03
6.0E-05 1.7E-03
1.7E-02 1.9E-02 8.7E-03 8.5E-02 649
1.5E-05 3.7E-09 8.0E-09 3.0E-07
649 538 927 200 200 200
3.8E-03 3.0E-08 1.2E-07 2.4E-06
8403/frame/ch15-Tbl 15.1(CD) Page 544 Friday, October 27, 2000 4:17 PM
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Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part C) Number
Component Names
Component Weight Percent
Density (kg/m3)
Melting Point (C)
Expansion Coefficient (µm/m)
Thermal Conductivity (watt/m/C)
Heat Capacity (kJ/kg C)
79 80
C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800
1,475 1,475
12 12
43 43
0.0 0.0
81 82 83 84 85 86 87 88 89 90
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Mn,P,S,Fe C,Mn,P,S,Fe C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 .9,.9,.04,.05,98 .2,.6,.04,.05,99 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,750 7,750 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,482 1,482 1,475 1,475 1,475 1,475
12 12 12 12 11 11 12 12 12 12
43 43 43 43 50 50 43 43 43 43
0.0 0.0 0.0 0.0 1.0 1.0 0.0 0.0 0.0 0.0
91 92 93 94 95 96 97 98 99 100
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12 12 12 12
43 43 43 43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
101 102 103 104 105 106 107 108 109 110
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Mn,P,S,Fe C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 .9,.9,.04,.05,98 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,750 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,482 1,475 1,475 1,475
12 12 12 12 12 12 11 12 12 12
43 43 43 43 43 43 50 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0
111 112 113 114 115 116 117 118 119 120
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12 12 12 12
43 43 43 43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
121 122 123 124 125 126 127 128 129 130
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Mn,P,S,Fe C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 .9,.9,.04,.05,98 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,750 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,482 1,475
12 12 12 12 12 12 12 12 11 12
43 43 43 43 43 43 43 43 50 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0
131 132 133 134 135 136 137 138 139 140
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12 12 12 12
43 43 43 43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
141 142 143 144 145 146 147 148 149 150
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12 12 12 12
43 43 43 43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
151 152 153 154 155
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475
12 12 12 12 12
43 43 43 43 43
0.0 0.0 0.0 0.0 0.0
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Friction and Wear Data Bank
TABLE 15.1 Tribomaterials Database (Part D) Resistivity (u-ohm-cm)
Hardness
Tensile Strength (MPa)
Youngs Modulus (MPa)
Fracture Toughness (MPa-m1/2)
Data Source
Wear Coefficient
Maximum Operating Temperature (C)
Wear Rate (mm3/m)
20 20
62 HRC 62 HRC
1,640 1,640
199,000 199,000
Hughes/Rowe Hughes/Rowe
3.0E-08 2.0E-08
200 200
2.2E-06 2.4E-07
20 20 20 20 19 19 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 27 HRC 60 HRB 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe ASTM G2,RR4,11/4/76,5 labs,n=5 ASTM G2,RR8,5/20/81,7 labs,n=28 Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
1.0E-08 1.2E-07 1.2E-07 2.4E-07 4.0E-04 7.0E-04 2.4E-07 2.4E-07 4.0E-09 2.0E-09
200 200 200 200
400 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 207,000 207,000 199,000 199,000 199,000 199,000
200 200 200 200
1.2E-07 1.1E-06 1.2E-06 1.8E-06 1.9E-02 8.4E-02 1.9E-06 3.8E-06 5.9E-08 1.4E-08
20 20 20 20 20 20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
9.5E-07 9.5E-07 4.0E-09 3.7E-09 5.0E-09 4.0E-08 8.0E-08 2.0E-08 7.4E-09 2.0E-08
200 200 200 200 200 200 200 200 200 200
6.7E-06 3.9E-06 5.9E-08 3.0E-08 3.8E-08 3.3E-07 6.6E-07 2.4E-07 6.0E-08 1.3E-07
20 20 20 20 20 20 19 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 27 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe ASTM G2,RR5,3/7/78,6 labs,n=30 Hughes/Rowe Hughes/Rowe Hughes/Rowe
1.2E-07 8.0E-09 4.0E-09 3.7E-09 3.0E-07 2.4E-07 4.0E-04 1.2E-07 4.0E-08 3.0E-08
200 200 200 200 200 200
1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000 199,000 207,000 199,000 199,000 199,000
200 200 200
1.2E-07 1.2E-07 3.0E-08 2.8E-08 3.8E-06 1.5E-06 7.3E-03 9.3E-07 3.5E-07 2.3E-07
20 20 20 20 20 20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
1.2E-07 1.0E-03 2.0E-10 2.4E-07 2.4E-07 1.0E-02 2.0E-08 4.0E-09 1.5E-05 1.2E-07
200 200 200 200 200 200 200 200 200 200
1.1E-05 8.5E-03 1.7E-09 1.9E-06 1.9E-06 8.5E-02 1.6E-07 5.9E-08 1.2E-04 9.4E-07
20 20 20 20 20 20 20 20 19 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 27 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe ASTM G2,RR4,11/4/76,5 labs,n=5 Hughes/Rowe
1.2E-07 1.0E-08 3.7E-09 3.7E-09 5.9E-08 3.0E-07 2.0E-09 4.0E-09 5.0E-04 5.0E-09
200 200 200 200 200 200 200 200
1,640
199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 207,000 199,000
200
9.4E-07 1.2E-07 3.0E-08 3.0E-08 4.7E-07 2.4E-06 1.8E-08 5.9E-08 8.3E-03 3.8E-08
20 20 20 20 20 20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
3.0E-08 7.4E-09 5.9E-08 2.0E-09 3.0E-07 8.0E-08 4.7E-07 2.4E-07 4.0E-08 5.0E-09
200 200 200 200 200 200 200 200 200 200
2.3E-07 6.0E-08 4.7E-07 1.8E-08 2.9E-06 9.5E-07 3.8E-06 1.9E-06 3.5E-07 5.9E-08
20 20 20 20 20 20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
3.7E-09 1.2E-07 4.7E-07 1.0E-08 4.0E-09 1.2E-07 9.2E-10 6.0E-07 7.0E-07 5.9E-08
200 200 200 200 200 200 200 200 200 200
3.0E-08 9.4E-07 3.0E-06 1.2E-07 5.9E-08 9.5E-07 5.0E-09 5.3E-06 7.6E-06 4.7E-07
20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
1.0E-09 4.0E-09 5.9E-08 5.0E-09 4.0E-09
200 200 200 200 200
1.5E-08 3.6E-08 4.5E-07 5.9E-08 3.6E-08
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Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part C) Number
Component Names
Component Weight Percent
Density (kg/m3)
Melting Point (C)
Expansion Coefficient (µm/m)
Thermal Conductivity (watt/m/C)
Heat Capacity (kJ/kg C)
156 157 158 159 160
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,800 7,800 7,800
1,475 1,475 1,475 1,475 1,475
12 12 12 12 12
43 43 43 43 43
0.0 0.0 0.0 0.0 0.0
161 162 163 164 165 166 167 168 169 170
C,Cr,Mn,Si C,Cr,Mn,Si C,Mn,Si,Cr,Ni,Mo,W,Cb+Ta,Fe C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si
1.0,1.5,.5,.3 1.0,1.5,.5,.3 .4,1,.5,19,9,1.5,1.5,.4,67 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3
7,800 7,800 7,916 7,800 7,800 7,800 7,800 7,800 7,800 7,800
1,475 1,475
12 12
43 43
0.0 0.0
1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12
43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0
171 172 173 174 175 176 177 178 179 180
C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Cr,Mn,Si C,Mn,Si,Cr,Mo,Va,Fe C,Cr,Mn,Si C,Mn,P,S,Si,Cr,Fe
1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1.0,1.5,.5,.3 1,1,1,15,4,.15,87.25 1.0,1.5,.5,.3 1,.5,.025,.025,.3,1.5,96.5
7,800 7,800 7,800 7,800 7,800 7,800 7,800 8,248 7,800 7,800
1,475 1,475 1,475 1,475 1,475 1,475 1,475
12 12 12 12 12 12 12
43 43 43 43 43 43 43
0.0 0.0 0.0 0.0 0.0 0.0 0.0
1,475 1,475
12 12
43 43
0.0 0.0
181 182 183 184 185 186 187 188 189 190
C,Mn,Si,Ni,Cr,Mo,B,Fe C,Mn,Si,Cr,Ni,Mo,Fe C,Mn,Si,Cr,Fe C,Mn,Si,Cr,Fe C,Mn,P,S,Si,Ni,Mo,Fe C,Mn,Si,Fe C,Mn,Si,Cr,Ni,Mo,Fe C,Mn,P,S,Si,Cr,Fe C,Mn,Si,Fe C,Mn,Si,Cr,Ni,Mo,V,Cb+Ta,Fe
.45,.8,.3,.3,.4,.1,.0005,98 .1,.5,.2,1.2,3.2,1,94.2 1,.3,.2,.5,98.1 1,.3,.2,1,97.5 .2,.6,.035,.04,.3,3.5,.25,95 .8,.7,.2,98 .1,.5,.2,1.2,3.2,1,94.2 1,.5,.025,.025,.3,1.5,96.5 1.0,12,.2,87 .15,.6,.4,12,.4,.6,.3,.3,85
7,750 7,750 7,800 7,800 7,861 7,750 7,750 7,800 7,750 6,366
13 15 12 12 16 15 15 12 15
47 43 43 45 47 47 43 47
1.0 0.0 0.0
191 192 193 194 195 196 197 198 199 200
C,Mn,Si,Cr,Ni,Mo,Fe C,Mn,Si,Ni,Cr,Mo,B,Fe C,Mn,P,S,Si,Ni,Mo,Fe C,Cr,Mn,Si C,Mn,Fe C,Mn,Fe C,Mn,Si,Cr,Ni,Mo,Fe C,Mn,P,S,Si,Ni,Cr,Mo,Fe C,Mn,Si,Cr,Fe C,Mn,Si,Ni,Cr,Mo,Al,Va,Fe
.2,.8,.2,.5,.6,.2,97.5 .45,.8,.3,.3,.4,.1,.0005,98 .2,.6,.035,.04,.3,3.5,.25,95 1.0,1.5,.5,.3 .16,1.4,98.44 .16,1.4,98.44 .2,.8,.2,.5,.6,.2,97.5 .4,.7,.025,.025,.3,1.7,.8,.25,96 .68,.6,.38,13.2,85.2 .2,.3,.2,5,.5,.2,2,.1,92
7,750 7,750 7,861 7,800 7,805 7,805 7,750 7,750 7,750 7,750
38
0.0
201 202 203 204 205 206 207 208 209 210
C,Mn,Si,Ni,Cr,Mo,Al,Va,Fe C,Cr,Mn,Si C,Mn,P,S,Si,Ni,Cr,Mo,Fe C,Mn,P,S,Si,Fe C,Mn,P,S,Si,Fe C,Mn,Si,Cr,Fe C,W,Mo,Cr,V,Fe C,Cr,V,Si,Mn,Fe C,Mn,Si,P,S,Cr,Ni,V,Mo,Fe C,Mn,Si,P,S,Cr,Ni,V,Mo,Fe
.2,.3,.2,5,.5,.2,2,.1,92 1.0,1.5,.5,.3 .4,.7,.025,.025,.3,1.7,.8,.25,96 .4,.7,.04,.05,.2,98.6 .4,.7,.04,.05,.2,98.6 1,1,.6,1,96.4 .8,6,5,4,2,82.2 1.6,13,1,.6,.6,83 .8,.25,.25,.015,.015,4,.1,1,4.5,89 .8,.25,.25,.015,.015,4,.1,1,4.5,89
7,750 7,800 7,750 7,750 7,750 7,800 8,027 7,750 7,890 7,890
211 212 213 214 215 216 217 218 219 220
C,Cr,Mo,V,Si,Fe C,Cr,Mo,V,Si,Mn,Fe C,Cr,V,Si,Mn,Fe C,Si,Mn,Cr,V,Mo,Fe Cu,Si,Fe,Mn,Mg,Zn,Ni,Al Al Cu,Si,Fe,Mn,Mg,Zn,Ti,Al Si + Fe, Cu, Mn, Zn, Al Al, Si, Cd Cu,Al
.35,5,1.5,1,1,91 .35,5,1.5,.4,.9,.3,91.6 1.6,13,1,.6,.6,83 1.5,.4,.3,12,.4,1,96.5 3.5,8,2,.5,.1,1,.5,84.5
7,750 7,750 7,750 7,750 2,768 2,685 2,491 2,713
221 222 223 224 225 226 227 228 229 230
Cu,Al Cu, Al, Fe Cu,Al Al, Sn, Cu, Ni, Si Al, Pb, Si, Sn, Cu Al, Si, Cu Al, Sn, Cu Al, Cu, Sn, Pb Sb Be,Co,Ni,Cu
92,8 85, 11, 4 95,5 90, 6.5, 1, 0.5, 1.5 85, 8.5, 4, 1.5, 0.5 88, 11, 1 79, 20, 1 87, 5, 4, 4
231 232
Be,Co,Ni,Cu Cu,Sn,Pb,Zn
1,475 1,475
1,475
1,507 1,510 1,475
1,482 649
1,475 1,482 1,482 1,482 1,475
15 13 16 12 12 12 15 15 12
45 43 52 52 38 38 28 52
12 12 15 11 11 12 10
52 43 38 50 51 43 38
0.0 1.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 1.0 0.0
11 11 16 10
29
650 649 510 649
16 40 24 11 22
29 97 221 134 221
1.0
7,760
1,041
18
69
0.0
7,760 7,500 8,304
1,041 1,045 1,054
18 16 18
69 59 80
0.0
1.8,,.2,99.5
2,300 6,643 8,304
631 982
23 9 17
137 18 121
1.8,,.2,99.5 83,7,7,3
8,304 8,857
982 1,038
17 10
121 58
4.5,17,1,.1,.5,.1,.2,77.5 1, .1, .05, .1, 99 95, 4, 1 92,8
1.0 1.0
0.0
0.0 0.0
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Friction and Wear Data Bank
TABLE 15.1 Tribomaterials Database (Part D) Resistivity (u-ohm-cm)
Hardness
Tensile Strength (MPa)
Youngs Modulus (MPa)
Fracture Toughness (MPa-m1/2)
Data Source
Wear Coefficient
Maximum Operating Temperature (C)
Wear Rate (mm3/m)
20 20 20 20 20
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 1,640 1,640 1,640
199,000 199,000 199,000 199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
2.4E-07 1.2E-07 5.9E-08 1.2E-07 7.4E-09
200 200 200 200 200
1.5E-06 9.8E-07 7.6E-06 6.1E-07 5.9E-08
20 20
62 HRC 62 HRC 217 HV 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC
1,640 1,640 751 1,640 1,640 1,640 1,640 1,640 1,640 1,640
199,000 199,000
Hughes/Rowe Hughes/Rowe Glaeser Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe
5.0E-09 1.0E-09
200 200 760 200 200 200 200 200 200 200
4.0E-08 1.5E-08
62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 62 HRC 330 HV 62 HRC 413 HV
1,640 1,640 1,640 1,640 1,640 1,640 1,640 1,000 1,640 1,379
199,000 199,000 199,000 199,000 199,000 199,000 199,000
9.0E-08 2.0E-09 4.0E-09 2.0E-08 2.0E-10 2.4E-07 5.0E-09
200 200 200 200 200 200 200 760 200 260
7.3E-07 1.4E-08 5.9E-08 1.6E-07 1.7E-09 1.5E-06 5.9E-08
199,000 199,000
Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Hughes/Rowe Glaeser Hughes/Rowe Glaeser
617 HV 694 HV 200 HV 225 HV 230 HV 224 HV 200 HV 200 HV 404 HV 695 HV
2,041 1,241 689 689 758 820 689 689 1,303
207,000 207,000 207,000 207,000 207,000 207,000 207,000 199,000 207,000 290,000
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser
180 HV 195 HV 424 HV 62 HRC 210 HV 140 HV 789 HV 350 HV 310 HV 435 HV
607 641 1,379 1,640 758 448 1,296 1,723 689 1,420
207,000 207,000 207,000 199,000 207,000 207,000 207,000 207,000 207,000 207,000
740 HV 62 HRC 260 HV 540 HV 150 HV 200 HV 765 HV 60 HRC 760 HV 160 HV
1,640 979 896 552 689 2,758 1,930 2,758 683
207,000 199,000 207,000 207,000 207,000 199,000 207,000 207,000 202,000 202,000
3
50 HRC 590 HV 60 HRC 598 HV 80 HB 15 HV 145 HV 30 HV
1,930 1,930 2,068 296 52 310 90
207,000 207,000 207,000 207,000 71,000 130,340 82,000 130,044
12
165 HV
448
79,300
12 23 10
100 HV 180 HB 70 HV 92 HRH
358 621 414 179
79,300 124,000 121,000 129,744
60 HB 35 HB 55 HRH 40 HV 393 HV
179 110 103 10 1,380 483 276
20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
20 20 28 18 20 18
30 28 20 14 14 30 30 28 28 20 30 19 19
18
8 5
70 5
80 HV 80 HV
199,000 199,000 199,000 199,000 199,000 199,000 199,000
125
38
77 77
33
20 55
Glaeser Glaeser Glaeser Hughes/Rowe Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Hughes/Rowe Glaeser Glaeser Glaeser Glaeser Glaeser ASTM G2,RR6,6/6/78,,9 labs,n=40 Glaeser Glaeser
3.0E-07 5.0E-09 4.0E-09 2.0E-09 2.0E-09 1.2E-07 9.0E-08
1.2E-07
260
8.0E-08
4.0E-09
200 260
8.0E-03 3.1E-05 4.0E-04
9.5E-07
5.9E-08
2.0E-02 260 538
3.0E-05 8.0E-03
427 427
1.0E-04
78,332 131,000
Glaeser Booser Glaeser Booser Booser Booser Booser Booser Glaeser Glaeser
131,000 103,000
Glaeser Glaeser
64,800
200
260
2.0E-03 3.0E-05 4.0E-04 8.0E-04
275
9.5E-07
260 260
ASTM G2,RR11,7/13/83,10 labs,n=50 Glaeser ASTM G2,RR6,6/26/80,6 labs,n=6 Glaeser Glaeser Glaeser Glaeser Glaeser Booser Glaeser
60
2.4E-07 3.8E-08 5.9E-08 1.4E-08 1.5E-08 8.6E-08 9.4E-07
538
538
3.9E-02 4.4E-05 8.3E-03 5.0E-04
149 150 260 260 260 260 150 150 150 150 135
1.1E-03
6.1E-05
427
6.1E-05
2.0E-04
427 149
3.0E-03
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TABLE 15.1 Tribomaterials Database (Part C) Number
Component Names
Component Weight Percent
233 234 235 236 237 238 239 240
Cu,Sn,Pb Cu,Pb,Sn Cu,Sn,Pb Cu, Sn, c Fe, Cu, Sn, C Cd Cd, Ni Al, Sn, Cu, Ni
65,.5,34.5 70,25,5 80,10,10 89, 10,1 59, 36, 4, 1
241 242 243 244 245 246 247 248 249 250
Cu Cu, Pb Cu, Pb P,Ni P,Ni Au Cu, Sn, Zn C,W,Fe,Cr,Mo,Va,Mn,Si,Ni C,Si,Mn,Cu,Ni,Cr,Co,Mo,Al,Ti,Fe In
99.94 70, 30 65, 35 1-12,88-99 1-12,88-99
251 252 253 254 255 256 257 258 259 260
Pb Pb,Sb,Sn,As,Cu Pb,Sb,Sn,As,Cu Pb,Sb,Sn,As,Cu Pb,Sb,Sn,As,Cu Cu, Sn, Pb Cu, Sn, Pb, Zn Cu, Sn, Pb Al,Cu,Fe,Mn,Zn C,Ti,Mo
261 262 263 264 265 266 267 268 269 270
Ni,Al,Fe,Mn,C,Si,Ti,Cu Cu, Sn, Zn C,Mn,Si,Cr,Ni,Mo,Fe C,Mn,Si,Cr,Ni,Mo,Fe Cu, Sn, Pb Cu,Sn,P Cu, Sn, Pb Cu,Si,Sn,Zn,Fe,Al,Mn Ag
271 272 273 274 275 276 277 278 279 280
98.5, 1.5 91, 6.5, 1, 1
Density (kg/m3) 9,134 9,300 8,857 6,600 6,200 8,664 8,600 2,900
Melting Point (C)
925 1,038
321
Expansion Coefficient (µm/m)
Thermal Conductivity (watt/m/C)
20 19 19 17 13 31 31 24
294 63 47 29 31 92 92 206
17
393
12 12 14 20 13 13 25
294 4 4 294 74 135 14 69
9,134 9,000 9,000 8,027 8,027 32,692 8,700 8,860 8,027 7,197
1,083 985 955
11,350 10,200 10,800 9,688 10,520 8,800 8,700 9,000 7,833 10,240
327 281 240 240
29 25
975
18 18 19 22 15
65,3,2,1.5,.25,1.0,.5,27 88, 8, 4 .12,2,1,16,25,6,49.9 .12,2,1,16,25,6,49.9 80, 10, 10 95.6,4.2,.2 78, 6, 16 87,4,1,4,2,1,1
8,304 8,700 8,027 8,027 8,900 8,857 9,200 8,359 10,520
1,316 975
Cr,C,Si,Mo,Fe,Ni,W,Co C,Mn,Si,Fe,Ni,Cr,W,Co
30,2.5,1,1,3,3,12,47.5 1.4,1,1.5,3,3,31,5,54
C,Mn,SI,Fe,Ni,Cr,W,Co
2.5,1,1,3,2.5,32,17,41
9,134 8,304 9,000 8,857
C,Si,Fe,Ni,Cr,W,Co C,Al,V,Ti C,Al,V,Ti SN
1.2,1.2,1,1,30,5,60.5 .1,6,4,90 .1,6,4,90
281 282 283 284 285 286 287 288 289 290
Sn,Sb,Cu Sn,Sb,Cu Sn,Sb,Cu Sn, Sb, Cu Co,Mo,Cr,Si,C Co,Mo,Cr,Si,C Ni,Mo,Cr,Si,C Ni,Cu,W Si,Zn,Cu,Fe,Ti,Mn,Ni,Mg,Va C,Mn,Si,Cr,Ni,Mo,Co,Ti,Al,Zr
84,8,8 89,7.5,3.5 91,4.5,4.5 86, 7.5, 6.5 52,28,17,3,.08 62,28,8,2,.08 50,32,15,3,.08 7,3,90 22,.1,1.5,.75,.15,.1,2.2,1,.1 .1,.5,.75,20,57,4,13,3,1,.1
291 292 293 294 295 296 297 298 299 300
C,Mn,Si,Cr,Ni,Mo,Co,Ti,Al,Zr Ni,Pb,Sn,Zn,Mn Zn Zn,Al,Cu,Mg Zn,Al,Cu,Mg Sn,Fe,Cr,Ni,Zr
.1,.5,.75,20,57,4,13,3,1,.1 80,4,8,7,1
PTFE-40 % ceramic fibre filled
301 302 303 304 305 306 307 308 309 310
fluorinated ethylene propylene polyphenylene sulfide resin, fibrefilled polyamide polyamide polyamide
88, 10, 2 .15,4,6,16,17,.3,1,1,54.6 .1,.75,.5,.75,50,18,5,3,.8,1,20
82.5,15,1,1,.6 83,10,6,.25,.5 75,15,10,.5,.5 80,15,5,.5,.5 88, 10, 2 85, 5, 5, 5 70, 5, 25 5,63,3,3,25 .02,.5,99.4
88.2,11,.75,.02 70.8,27,2.2,.015 1.5,.1,.1,.05,98.4
8,304 4,429 4,429 7,307
1,064 975 1,304 1,370 179
923
750 1,060 971 961
14 18 16 16 19 18 19 17 19
1,275
0.0
0.0
0.0
0.0 0.0 0.0 0.0
35 24 24 24 24 69 71 62 35 128
0.0
14 74
0.0
47 84 52 28 415
0.0 0.0 0.0
0.0 0.0
0.0 0.0 0.0
176 14
1,600 231
7,470 7,473 7,473
420 241 273
8,664 9,134 8,857 17,000 2,768 8,138
1,288 1,288 1,243 3,410 538
8,138 8,857 7,141 6,089 4,982 6,700 1,410 1,050
12
Heat Capacity (kJ/kg C)
14 9 9 24
7 7 64
23
52
1.0 1.0 0.0
54.0 19 18 7 16 14
171 176 136 167 126 12
1.0
14 5 31 28 12 7 85 90
12 26 112 115 124 15 0.0
2.0
1,900
18
0.0
1.0
2,140 1,661 1,130 1,107 1,140 1,384 1,200 1,310 940 1,430
180 22 80
0.0
1.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2.0
419 404 427
258 104
81 29 67 95 110 49
1.0 0.0
2.0 1.0
1.0 1.0
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TABLE 15.1 Tribomaterials Database (Part D) Resistivity (u-ohm-cm)
Hardness 28 HV 48 HV 60 HV 40 HB
7
2
90 90 2 140 13 9 24
7
50
4 9
2
91
171 171 12
6
21 HV 35 HB 45 HB 42 HV 28 HB 25 HB 1050 HV 500 HV 35 HV 75 HB 216 HV 410 HV 1 HV
Tensile Strength (MPa) 59 186 207 90 103 69 138 193 59 55
Youngs Modulus (MPa)
Fracture Toughness (MPa-m1/2)
64,688 129,744 129,528 11,000
Data Source Glaeser Glaeser Glaeser Booser Booser Glaeser Booser Booser
65,440 65,440 129,044 103,000
Glaeser Booser Booser Glaeser Glaeser Glaeser Booser Glaeser Glaeser Glaeser
689 138 310 551 1,380 3
200,000 200,000 74,500 103,000 197,000 200,000 11,000
14 HV 20 HV 20 HV 22 HV 11 HV 77 HB 60 HB 48 HB 225 HV 264 HV
41 69 69 69 69 290 241 186 793 689
13,800 29,000 29,000 29,000 29,000 130,560 64,764 62,204 131,068 324,000
Glaeser Glaeser Glaeser Glaeser Glaeser Booser Booser Booser Glaeser Glaeser
320 HV 70 HB 320 HV 202 HV 60 HB 145 HV 57 HB 85 HV 34 HV 52 HRC
689 310 1,103 827 241 552 214 310 207
179,000 96,500 197,000 197,000 64,744 110,000 129,744 103,000 71,000
Glaeser Booser Glaeser Glaeser Booser Glaeser Booser Glaeser Glaeser ASTM G2,RR2,12/9/75,5 labs,n=5
834
241,000 210,000
517
255,000
Glaeser Glaeser Glaeser Glaeser ASTM G2,RR5,3/7/78,8 labs,n=38 ASTM G2,RR1,5/23/75,3 labs,n=3 Glaeser Glaeser Glaeser Glaeser
562 HV 395 HV 383 HV 675 HV 52 HRC 52 HRC 526 HV 301 HV 1700 HV 8 HV 26 HV 24 HV 17 HV 26 HB 739 HV 655 HV 485 HV 257 HV 140 HV 157 HV
12
689 896 15 81 81 81 117
207,000 110,000 110,000 41,400 51,000 64,688 64,764
689 276 827
241,000 269,000 214,000 276,000 93,000 211,000
1,280 586 103 296 414 517 61 55
211,000 159,000 130,340 82,940 129,528 129,528 2,550 2,760
689
71
Glaeser Glaeser Glaeser Booser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser
5.48E+11
5 HV
18
13,800
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Booser Booser Glaeser Glaeser
4.01E+19
5 HV 15 HV 15 HV
5.02E+12 1.00E+11 2.80E+14 7.15E+16 1.00E+15 1.00E+13
121 HRR 115 HV 66 HRM 70 HRM 65 HRR 52 HRE
21 69 80 55 81 62 62 59 28 90
689 11,000 3,700 2,070 2,830 6,890 2,280 2,340 965 3,170
Glaeser Glaeser Glaeser Glaeser Booser Glaeser Booser Booser Booser Booser
6 28 30 74
373 HV 165 HV 47 HV 93 HV 107 HV 185 HV 80 HRM 103 HRR
96
21 21
Wear Coefficient
Maximum Operating Temperature (C)
Wear Rate (mm3/m)
176 1.0E-04
2.1E-03 121 135 135
3.0E-05
2.9E-03 260 150
1.0E-04
5.1E-03 177 177 320 320 260 649
204 232 232 232 260 232 204 538 538 260 649 649 232 232 4.0E-03 2.0E-04
204
6.1E-05 1.0E-03 1.5E-05
2.4E-01 4.4E-03 9.8E-04 1.1E-03 9.7E-04
649 2.0E-04 1.0E-04
3.8E-03 3.4E-03 400 400
1.0E-04 7.0E-05 7.0E-06
220 238 221 150 704 704 649
5.5E-03 1.4E-03 2.4E-04
260 871 871 649 5.0E-02
2.3E+00 121 149 400 93 82 260 204 204 85 60 88 121 116 149 82 316
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TABLE 15.1 Tribomaterials Database (Part C) Number
Component Weight Percent
Component Names
311 312 313 314 315 316 317 318 319 320
polyimide filled, self lubricating
graphite, PTFE, polyamide/imide ultra high molecular weight polyethylene
12, 3, 85
321 322 323 324 325 326 327 328 329 330
carbon fiber, acetal glass fiber, acetal PTFE, acetal silicone, acetal PTFE, ABS cellulose carbon fiber, nylon 6/6 glass fiber, nylon 6/6 PTFE, nylon 6/6 silicone, nylon 6/6
20, 80 30, 70 15, 85 2, 98 15, 85
331 332 333 334 335 336 337 338 339 340
polyetheretherketone cotton laminate wood flour carbon fiber, polycarbonate glass fiber, polycarbonate PTFE, polycarbonate carbon fiber, polyester glass fiber, polyester PTFE, polyester silicone, polyester
341 342 343 344 345 346 347 348 349 350
PTFE, polyethylene glass fiber, polyimide graphite, polyimide glass fiber, polyphenylene oxide PTFE, polyphenylene oxide carbon fiber, polyphenylene sulfide glass fiber, polyphenylene sulfide PTFE, polyphenylene sulfide PTFE, polypropylene carbon fiber, polysulfone
351 352 353 354 355 356 357 358 359 360
glass fiber, polysulfone PTFE, polysulfone glass fiber, polyurethane PTFE, polyurethane fabric, PTFE glass fiber, PTFE graphite, PTFE mineral filled PTFE polyphenylene sulfide resin graphite, polyimide
30, 70 15, 85 30, 70 15, 85
361 362 363 364 365 366 367 368
polyimide, graphite Isobutylene-isoprene chloroprene butadiene-acrylonitrile polysiloxane disocyanate polyester vinylidene fluoride-hexafluoropropylene PTFE - Glass woven fabric
40, 60
Density (kg/m3) 1,520 1,060 1,340 910 1,240 1,250 2,180 1,460 930 1,200
20, 80 30, 70 20, 80 2, 98
1,460 1,630 1,490 1,400 1,140 1,200 1,230 1,370 1,260 1,120
30, 70 30, 70 15, 85 30, 70 30, 70 20, 80 2, 98
1,430 1,330 1,400 1,330 1,430 1,280 1,410 1,520 1,440 1,290
20, 80
Melting Point (C)
160
Expansion Coefficient (µm/m) 8 59 54 72 56 72 55 25 200 77
334
20 22 40 16 23 70 9 22 99 95 128 14 49 25 63 11 27 59 76 11 25 59 45
15, 85 15, 85
1,450 1,320 1,460 1,330 2,500 2,190 2,080
121 126
15, 85
1,661 1,384
63
1,384 830 1,107 1,107 1,384 1,107 1,500
0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0
Heat Capacity (kJ/kg C)
1.0 1.0 0.0 1.0 2.0 2.0
40 43 94 90 94 52 25 32 83 81
1,080 1,900 1,510 1,280 1,150 1,450 1,650 1,450 1,020 1,370
15, 85 30, 70 15, 85 30, 70 40, 60 20, 80 20, 80 30, 70
Thermal Conductivity (watt/m/C)
0.0 0.0
0.0
1.0
0.0
1.0
0.0
0.0 0.0 1.0 0.0 1.0
23 10 32 16 25 125
0.0 0.0 0.0 0.0 0.0
23
0.0
2.0
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TABLE 15.1 Tribomaterials Database (Part D) Resistivity (u-ohm-cm)
1.00E+17 5.00E+16 1.00E+12 1.00E+17 8.03E+13 5.01E+14 1.70E+16
Hardness
95 HRR
60 SHORE D 40 HV 50 HV 65 SHORE A
118 HRR
95 HRM
105 HRM 85 HRE 118 HRR
100 HRM
120 HRM 88 HRM
5.56E+14
123 HRR
1.40E+14
5068 HV
1.00E+12
35 HV 2 HV 2 HV 2 HV 3 HV 6 HV 3 HV
3.50E+10 1.40E+14 2.00E+11 2.00E+12
Tensile Strength (MPa)
Youngs Modulus (MPa)
Fracture Toughness (MPa-m1/2)
Data Source
Wear Coefficient
Maximum Operating Temperature (C)
56 66 76 35 70 14 23 164 41 16
10,400 2,480 4,140 1,240 2,690 103 620 6,600 689 41
Glaeser Booser Booser Booser Booser Booser Booser Glaeser Glaeser Booser
288 116 188 77 171 110 260 260 77 66
81 135 48 55 45 90 193 179 62 75
9,310 8,960 2,070 2,410 2,550 2,410 16,600 8,960 2,550 2,760
Booser Booser Booser Booser Booser Booser Booser Booser Booser Booser
149 138 138 88 88
207 69 48 166 128 48 152 138 45 55
17,000
Glaeser Booser Booser Booser Booser Booser Booser Booser Booser Booser
220 138 138 116 116 116 204 204 149 149
26 186 66 128 55 186 159 59 28 159
896 3,790 7,930 2,280 32,260 12,400 3,790 1,170 14,100
Booser Booser Booser Booser Booser Booser Booser Booser Booser Booser
82 316 316 127 116 188 188 188 77 171
124 54 57 12
8,270 2,620 1,310 97
20
1,100 1,380
171 171 110 110 204 260 260
131 83
11,700 3,450
Booser Booser Booser Booser Booser Booser Booser Glaeser Glaeser Glaeser
62 21 21 21 7 34 14
4,140
Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser Glaeser
371 149 116 149 316 116 232 204
827 13,100 8,270 2,070 15,900 8,270 1,720 2,280
93
260 371
Wear Rate (mm3/m)
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TABLE 15.1 Tribomaterials Database (Part E) Number
P*V Limit (MPa*m/s)
Maximum Pressure (MPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78
Wear Constant (mm3/mm*N)
Friction Coefficent
Maximum Velocity (m/s)
2.0E-10
Contact Geometry
PIN-ON-RING
Load (N)
Temp. (C)
3.9
Velocity (m/s)
Distance (m)
Specimen Shape
1.8
1.0E+04
PIN
2.7
1.1E+07
RING PIN PIN PIN
0.25
83 207 0.35 0.7 0.7
6.0E-09 3.0E-09 2.0E-09 1.0E-09
0.15 2.5 0.16
0.7 0.53 0.7
6.0E-10 4.0E-09
0.16
2.5
RING-ON-RING PIN-ON-CYLINDER PIN-ON-CYLINDER PIN-ON-CYLINDER
37
PIN-ON-CYLINDER PIN-ON-CYLINDER PIN-ON-CYLINDER PIN-ON-CYLINDER
PIN PIN PIN PIN
0.012
0.17
0.42
13.8
1.75
41
0.1 4.0E-09
BLOCK-ON-RING
1.75
14.5
2.3
1.23 1.05 1.05
27.6 51.7 20.7 1.38
1.1
124
24
2.4
4250
BLOCK
2 7.0E-06
4.0E-09
BLOCK-ON-RING
2.0E-09
BLOCK-ON-RING
657
9.8
3.0E-07 4.0E-07 2.0E-07 6.0E-07
BLOCK-ON-RING BLOCK-ON-RING BLOCK-ON-RING BLOCK-ON-RING
45 45 45 130
5.0E-09 4.0E-13 1.0E-12 4.0E-11
BLOCK-ON-RING FOUR BALL FOUR BALL FOUR BALL
657 60 60 60
1
3.6E+06
BLOCK
0.05
1.2
BLOCK
24 24 24 24
2.4 2.4 2.4 2.4
4310 4250 4280 1440
BLOCK BLOCK BLOCK BLOCK
50 50 50
0.05 0.58 0.58 0.58
1.2 2100 2100 2100
BLOCK BALL BALL BALL
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TABLE 15.1 Tribomaterials Database (Part F) Contact Environment
Standard Test
Counterface Material
Counterface Description
Wear Type
AIR
AIR
TUNGSTEN CARBIDE
ADHESIVE
AIR AIR
CARBON STEEL CARBON STEEL
ADHESIVE ADHESIVE
AIR AIR AIR AIR
CAST IRON CARBON STEEL CARBON STEEL CARBON STEEL
ADHESIVE ADHESIVE ADHESIVE ADHESIVE
AIR AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
ADHESIVE ADHESIVE ADHESIVE ADHESIVE
AIR
CARBON STEEL
ADHESIVE
AIR
CARBON STEEL
AIR
AIR
CARBON STEEL
AFS 50/70 sand; 471 g/min AIR
CHLOROBUTYL CARBON STEEL
Boundary lubricated, oil-filled material
CARBON STEEL
LUBRICATED
Boundary lubricated, oil-filled material Boundary lubricated, oil-filled material Boundary lubricated, oil-filled material AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
LUBRICATED LUBRICATED LUBRICATED ADHESIVE
AIR
MILD STEEL
ADHESIVE
AIR
M2 TOOL STEEL
ADHESIVE
AFS 50/70 sand; 435 g/min AFS 50/70 sand; 471 g/min AFS 50/70 sand; 234 g/min AFS 50/70 sand; 329 g/min; 49% RH
AIR Paraf.Oil;
[email protected];Addit:DibutylPhosphate;Cyclohexyl NH2;4 mmol/100g Paraf.Oil;
[email protected];Addit:DibutylPhosphate;Benzyl NH2;4 mmol/100g Paraf.Oil;
[email protected] ASTM G65-D ASTM G65-B
ADHESIVE A60 SHORE HARDNESS
ABRASIVE
CHLOROBUTYL CHLOROBUTYL CHLOROBUTYL CHLOROBUTYL
A57 SHORE HARDNESS A59 SHORE HARDNESS A62 SHORE HARDNESS A60 SHORE HARDNESS
ABRASIVE ABRASIVE ABRASIVE ABRASIVE
M2 TOOL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL
ADHESIVE LUBRICATED LUBRICATED LUBRICATED
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TABLE 15.1 Tribomaterials Database (Part E) Number
P*V Limit (MPa*m/s)
Maximum Pressure (MPa)
Wear Constant (mm3/mm*N)
Friction Coefficent
Maximum Velocity (m/s)
Contact Geometry
Load (N)
Temp. (C)
Velocity (m/s)
Distance (m)
Specimen Shape
60 60
50 50
0.58 0.58
2100 2100
BALL BALL
60 60 60 60 130 130 60 60 60 60
50 50 50 50 24 24 50 50 50 50
0.58 0.58 0.58 0.58 2.4 2.4 0.58 0.58 0.58 0.58
2100 2100 2100 2100 4310 1440 2100 2100 2100 2100
BALL BALL BALL BALL BLOCK BLOCK BALL BALL BALL BALL
79 80
4.0E-12 3.0E-12
FOUR BALL FOUR BALL
81 82 83 84 85 86 87 88 89 90
1.0E-12 2.0E-11 2.0E-11 3.0E-11 1.0E-07 6.0E-07 3.0E-11 3.0E-11 5.0E-13 2.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL BLOCK-ON-RING BLOCK-ON-RING FOUR BALL FOUR BALL FOUR BALL FOUR BALL
91 92 93 94 95 96 97 98 99 100
1.0E-10 6.0E-11 5.0E-13 4.0E-13 6.0E-13 6.0E-12 1.0E-11 3.0E-12 9.0E-13 2.0E-12
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60 60 60 60
50 50 50 50 50 50 50 50 50 50
0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58
2100 2100 2100 2100 2100 2100 2100 2100 2100 2100
BALL BALL BALL BALL BALL BALL BALL BALL BALL BALL
101 102 103 104 105 106 107 108 109 110
1.0E-11 1.0E-12 5.0E-13 5.0E-13 4.0E-11 3.0E-11 2.0E-07 2.0E-11 6.0E-12 4.0E-12
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL BLOCK-ON-RING FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 45 60 60 60
50 50 50 50 50 50 24 50 50 50
0.58 0.58 0.58
2100 2100 2100
0.58 2.4 0.58 0.58 0.58
2100 4310 2100 2100 2100
BALL BALL BALL BALL BALL BALL BLOCK BALL BALL BALL
111 112 113 114 115 116 117 118 119 120
2.0E-11 1.0E-07 3.0E-14 3.0E-11 3.0E-11 1.0E-06 3.0E-12 5.0E-13 1.0E-09 1.0E-11
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60 60 60 60
50 50 50 50 50 50 50 50 50 50
0.58
2100
0.58 0.58
2100 2100
0.58 0.58
2100 2100
0.58
2100
BALL BALL BALL BALL BALL BALL BALL BALL BALL BALL
121 122 123 124 125 126 127 128 129 130
1.0E-11 2.0E-12 4.0E-13 4.0E-13 7.0E-12 4.0E-11 3.0E-13 5.0E-13 2.0E-07 6.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL BLOCK-ON-RING FOUR BALL
60 60 60 60 60 60 60 60 45 60
50 50 50 50 50 50 50 50 24 50
0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 2.4 0.58
2100 2100 2100 2100 2100 2100 2100 2100 4310 2100
BALL BALL BALL BALL BALL BALL BALL BALL BLOCK BALL
131 132 133 134 135 136 137 138 139 140
4.0E-12 9.0E-13 8.0E-12 3.0E-13 5.0E-11 1.0E-11 5.0E-11 3.0E-11 6.0E-12 8.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60 60 60 60
50 50 50 50 50 50 50 50 50 50
0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58
2100 2100 2100 2100 2100 2100 2100 2100 2100 2100
BALL BALL BALL BALL BALL BALL BALL BALL BALL BALL
141 142 143 144 145 146 147 148 149 150
4.0E-13 1.0E-11 5.0E-11 1.0E-12 5.0E-13 1.0E-11 8.0E-14 9.0E-11 9.0E-11 7.0E-12
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60 60 60 60
50 50 50 50 50 50 50 50 50 50
0.58 0.58 0.58 0.58 0.58 0.47 0.47 0.58 0.58 0.47
2100 2100 2100 2100 2100 1680 1680 2100 2100 1680
BALL BALL BALL BALL BALL BALL BALL BALL BALL BALL
151 152 153 154 155
2.0E-13 6.0E-13 7.0E-12 7.0E-13 6.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60
50 50 50 50 50
0.56 0.56 0.47 0.56 0.56
2010 2010 1680 2010 2010
BALL BALL BALL BALL BALL
8403/frame/ch15-Tbl 15.1(EF) Page 555 Friday, October 27, 2000 4:17 PM
555
Friction and Wear Data Bank
TABLE 15.1 Tribomaterials Database (Part F) Contact Environment
Standard Test
Counterface Material
Counterface Description
Wear Type
Paraf.Oil;
[email protected];Addit:Phosphate ;Diethyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphate ;Di-n-butyl;4 mmol/100g
STEEL STEEL
52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED
Paraf.Oil;
[email protected];Addit:Phosphate ;Di-n-dodecyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-n-Dodecyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Butyl,H;4 mmol/100g Mineral Oil;
[email protected] AFS 50/70 sand; 380 g/min AFS 50/70 sand; 323 g/min Paraf.Oil;
[email protected];Addit:Disulfide;Di-(para-t-nonylphenyl);18 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-n-Octyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Dibuytlphoshoramidate;n-Butyl,H;4 mmol/100g Paraf.Oil;
[email protected];Addit:DibutylPhosphate;n-Octyl NH2;4 mmol/100g
STEEL STEEL STEEL STEEL CHLOROBUTYL CHLOROBUTYL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL A60 SHORE HARDNESS A60 SHORE HARDNESS 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED ABRASIVE ABRASIVE LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Paraf.Oil;
[email protected];Addit:Disulfide;Diethyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-n-Butyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphate ;Di-2-ethylhexyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:DibutylPhosphate;2-Ethylhexyl NH2;4 mmol/100g Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;Benzyl NH2;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphate ;Tributyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-n-Hexadecyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;Methyl NH2;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Lauryl,H;4 mmol/100g Min.Oil;
[email protected];Addit:Dibuytlphoshoramidate;Ethyl,Ethyl;4 mmol/100g
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Paraf.Oil;
[email protected];Addit:Diesterdisulfide;[-SCH2COOC2H5]2;2.3mmol/100g Paraf.Oil;
[email protected];Addit:Dibuytlphoshoramidate;Phenyl,H;4 mmol/100g Min.Oil;
[email protected];Addit:Dibuytlphoshoramidate;t-Butyl,H;4 mmol/100g paraffin oil;tricresyl phosphate paraffinic oil Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;n-Octyl NH2;4 mmol/100g AFS 50/70 sand; 239 g/min Par.Oil;
[email protected];Add:Diesterdisulfide;[-S(CH2)2COOC2H5]2;2.3mmol/100g Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;n-Butyl NH2;4mmol/100g Par.Oil;
[email protected];Add:Di2EthylhexylPhosphate;n-PropylNH2;4mmol/100g
STEEL STEEL STEEL STEEL STEEL STEEL CHLOROBUTYL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL A60 SHORE HARDNESS 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED ABRASIVE LUBRICATED LUBRICATED LUBRICATED
Paraf.Oil;
[email protected];Addit:Disulfide;Di-(para-t-butylphenyl);18 mmol/100g dry air Formulated Engine Oil Paraf.Oil;
[email protected];Addit:Phosphonate;Ethyl,H;4 mmol/100g Paraf.Oil;
[email protected] dry argon Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;Ethyl NH2;4 mmol/100g Par.Oil;
[email protected];Add:Di2EthylhexylPhosphate;CyclohexylNH2;4mmol/100g Cyclohexane Paraf.Oil;
[email protected];Addit:Di2EthylhexylPhosphate;Dodecyl NH2;4 mmol/100g
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Par.Oil;
[email protected];Add:Di2EthylhexylPhosphate;2-EthylhexylNH2;4mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;2-Ethylhexyl,H;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphate ;Tricresyl;4 mmol/100g Min.Oil;
[email protected];Addit:Dibuytlphoshoramidate;Ethyl,H;4 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-n-Octadecyl;18 mmol/100g Paraf.Oil;
[email protected] Min.Oil;
[email protected];Addit:Dibuytlphoshoramidate;n-Dodecyl,H;4 mmol/100g Paraf.Oil;
[email protected];Addit:Dibuytlphoshoramidate;n-Dodecyl,H;4 mmol/100g AFS 50/70 sand; 380 g/min Paraf.Oil;
[email protected];Addit:Dibuytlphoshoramidate;Allyl,H;4 mmol/100g
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL CHLOROBUTYL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL A60 SHORE HARDNESS 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED ABRASIVE LUBRICATED
Paraf.Oil;
[email protected];Addit:Phosphonate;Ethyl,Benzyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Ethyl,o-Nitrophenyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Diphenyl;18 mmol/100g Min.Oil;
[email protected];Addit:Dibuytlphoshoramidate;Octadecyl,H;4 mmol/100g Par.Oil;
[email protected];Add:Disulfide;Di-2,4,4Trimethylpentyl;18mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Dibenzyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-t-Octyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Dicyclohexyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Butyl,Phenyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Cyclohexyl,H;4 mmol/100g
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Min.Oil;
[email protected];Add:Dibuytlphoshoramidate;n-Octyl,n-Octyl;4mmol/100g Paraf.Oil;
[email protected];Addit:Phosphonate;Butyl,Hexyl;4 mmol/100g Paraf.Oil;
[email protected];Addit:Disulfide;Di-2-Ethylhexyl;18 mmol/100g Paraf.Oil;
[email protected];Addit:Phosphate ;Dilauryl;4 mmol/100g Paraf.Oil;
[email protected];Addit:DibutylPhosphate;Dodecyl NH2;4 mmol/100g Min.Oil;Addit:1-Chloro Hexadecane;2.0 Wt% Min.Oil;Addit:Tricresyl Phosphate + Oleic Acid;1.5+1.5 Wt% Paraf.Oil;
[email protected];Addit:Diesterdisulfide;[-S(CH2)3OC2H5]2;2.3mmol/100g Paraf.Oil;
[email protected];Addit:Diesterdisulfide;[-S(CH2)2OC2H5]2;2.3mmol/100g Min.Oil;Addit:Antimony Diakyldithiocarbamate;2.0 Wt%
STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Min.Oil;Addit:ZnDialkylphos'o-dithioate;Isopropyl/p-Octylphenyl;.056Wt%P Min.Oil;Addit:ZnDialkylphosphoro-dithioate;Isobutyl/Pentyl;0.056 Wt% P Min.Oil;Addit:Lead Naphthenate;1.0 Wt% Min.Oil;Addit:ZnDialkylphosphoro-dithioate;C6-C10;0.056 Wt% P Min.Oil;Addit:ZnDialkylphosphoro-dithioate;2-Ethylhexyl;0.056 Wt% P
STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
ASTM G65-A ASTM G65-B
ASTM G65-D
ASTM G65-D
8403/frame/ch15-Tbl 15.1(EF) Page 556 Friday, October 27, 2000 4:17 PM
556
Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part E) Number
P*V Limit (MPa*m/s)
Maximum Pressure (MPa)
Wear Constant (mm3/mm*N)
Friction Coefficent
Maximum Velocity (m/s)
Contact Geometry
Load (N)
Temp. (C)
Velocity (m/s)
Distance (m)
Specimen Shape
156 157 158 159 160
3.0E-11 2.0E-11 7.0E-12 1.0E-11 8.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60
50 50 50 50 50
0.58 0.58 0.58 0.58 0.56
2100 2100 2100 2100 2010
BALL BALL BALL BALL BALL
161 162 163 164 165 166 167 168 169 170
7.0E-13 2.0E-13
FOUR BALL FOUR BALL
60 60
50 50
0.56 0.56
2010 2010
BALL BALL
4.0E-12 6.0E-13 5.0E-13 2.0E-13 2.0E-13 1.0E-11 1.0E-11
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60
50 50 50 50 50 50 50
0.58 0.56 0.56 0.56 0.56 0.47 0.47
2100 2010 2010 2010 2010 1680 1680
BALL BALL BALL BALL BALL BALL BALL
171 172 173 174 175 176 177 178 179 180
1.0E-11 2.0E-13 5.0E-13 3.0E-12 3.0E-14 2.0E-11 7.0E-13
FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL FOUR BALL
60 60 60 60 60 60 60
50 50 50 50 50 50 50
0.47 0.56 0.56 0.47 0.47 0.47 0.56
1680 2010 2010 1680 1680 1680 2010
BALL BALL BALL BALL BALL BALL BALL
1.0E-11
FOUR BALL
60
50
0.56
2010
BALL
1.0E-11
FOUR BALL
60
50
0.47
1680
BALL
5.0E-13
FOUR BALL
60
50
0.58
2100
BALL
5.0E-06
PIN-ON-RING
3.9
1.8
1.0E+04
PIN
3.0E-09 6.0E-08
BLOCK-ON-RING BLOCK-ON-RING
9.8 130
1 2.4
3.6E+06 4.3E+03
BLOCK BLOCK
3.0E-07 4.0E-09 6.0E-08 2.0E-07
BLOCK-ON-RING BLOCK-ON-RING BLOCK-ON-RING PIN-ON-RING
130 9.8 130 3.9
2.4 1 2.4 1.8
1.4E+03 3.6E+06 4.3E+03 1.0E+04
BLOCK BLOCK BLOCK PIN
BLOCK-ON-RING
9.8
1
3.6E+06
BLOCK
181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232
24
24 24
34.5
206 41.4
1.75
1.0E-07 3.0E-07
34.5 34.5 34.5 34.5 13.8
0.46
6.1
344
1.0E-08
PIN-ON-RING
3.9
1.8
1.0E+04
PIN
17
3.0E-07
BLOCK-ON-RING
9.8
1
3.6E+06
BLOCK
8403/frame/ch15-Tbl 15.1(EF) Page 557 Friday, October 27, 2000 4:17 PM
557
Friction and Wear Data Bank
TABLE 15.1 Tribomaterials Database (Part F) Contact Environment
Standard Test
Counterface Material
Counterface Description
Wear Type
Par.Oil;
[email protected];Add:Diesterdisulfide;[-S(CH2)10COOC2H5]2;2.3mmol/100g Par.Oil;
[email protected];Add:Diesterdisulfide;[-S(CH2)2COOC10H21]2;2.3mmol/100g Par.Oil;
[email protected];Add:Diesterdisulfide;[-S(CH2)3COOC2H5]2;2.3mmol/100g Par.Oil;
[email protected];Add:Diesterdisulfide;[-S(CH2)5COOC2H5]2;2.3mmol/100g Min.Oil;Addit:ZnDialkylphosphoro-dithioate;1-Methylheptyl;0.056 Wt% P
STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Min.Oil;Addit:ZnDialkylphosphoro-dithioate;n-Butyl;0.056 Wt% P Min.Oil;Addit:ZnDialkylphosphoro-dithioate;Isobutyl;0.056 Wt% P
STEEL STEEL
52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED
Paraffin Oil;
[email protected] Min.Oil;Addit:ZnDialkylphosphoro-dithioate;2,2-Dimenthylpnetyl;0.12Wt%P Min.Oil;Add:ZnDialkylphos'o-dithioate;2-Ethylhexyl/p-Octylphenyl;.056Wt%P Min.Oil;Addit:ZnDialkylphosphoro-dithioate;p-Octylphenyl;0.056 Wt% P Min.Oil;Addit:ZnDialkylphos'o-dithioate;Isobutyl/p-Octylphenyl;.056Wt%P Mineral Oil Min.Oil;Addit:Hexachloro-1, 3-Butandiene;2.0 Wt%
STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Min.Oil;Addit:Oleic Acid;2.0 Wt% Min.Oil;Addit:ZnDialkylphosphoro-dithioate;Isopropyl;0.056 Wt% P Min.Oil;Addit:ZnDialkylphosphoro-dithioate;n-Dodecyl;0.12 Wt% P Min.Oil;Addit:Tricresyl Phosphate;1.5 Wt% Min.Oil;Addit:Zinc 0, 0-Dialkylphosphorodithioate;2.0 Wt% Min.Oil;Addit:Bis-(B-Chloroethyl) vinylphosphonate;1.0 Wt% Min.Oil;Addit:ZnDialkylphosphoro-dithioate;Sec-Butyl;0.056 Wt% P
STEEL STEEL STEEL STEEL STEEL STEEL STEEL
52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL 52100 STEEL
LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED LUBRICATED
Mineral Oil
STEEL
52100 STEEL
LUBRICATED
Min.Oil;Addit:Perfluoroctanoic Acid;0.05 Wt%
STEEL
52100 STEEL
LUBRICATED
Paraf.Oil;
[email protected];Addit:Phosphonate;Stearyl,H;4 mmol/100g
STEEL
52100 STEEL
LUBRICATED
AIR
MILD STEEL
AIR AFS 50/70 sand; 353 g/min
MILD STEEL CHLOROBUTYL
AIR
AFS 50/70 sand; 324 g/min; 51% RH AIR AFS 50/70 sand; 300 g/min AIR
ASTM G65-A
ASTM G65-B ASTM G65-A
CHLOROBUTYL MILD STEEL CHLOROBUTYL TOOL STEEL
ADHESIVE
A60 SHORE HARDNESS
A60 SHORE HARDNESS A60 SHORE HARDNESS
ADHESIVE ABRASIVE
ABRASIVE ADHESIVE ABRASIVE ADHESIVE
AIR
CARBON STEEL
AIR AIR
MILD STEEL CARBON STEEL
ADHESIVE ADHESIVE
AIR AIR AIR AIR Boundary lubricated, oil-filled material
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
LUBRICATED
AIR
HARD STEEL
ADHESIVE
AIR
440C STAINLESS STEEL
ADHESIVE
8403/frame/ch15-Tbl 15.1(EF) Page 558 Friday, October 27, 2000 4:17 PM
558
Modern Tribology Handbook
TABLE 15.1 Tribomaterials Database (Part E) Number 233 234 235 236 237 238 239 240
P*V Limit (MPa*m/s)
Maximum Pressure (MPa)
Maximum Velocity (m/s)
2.0E-07 1.75 1.23
Contact Geometry
BLOCK-ON-RING
10 13.8 17.2 13.8 34.5
Load (N)
Temp. (C)
Velocity (m/s)
Distance (m)
Specimen Shape
9.8
1
3.6E+06
BLOCK
6.1 4.1 1.0E-07 2.0E-08
3.0E-07 13.8 13.8
PIN-ON-RING
19.6
1.9
6.7E+04
PIN
PIN-ON-RING
19.6
0.13
9.7E+03
PIN
1.9 2.4
6.7E+04 4.3E+03
PIN BLOCK
0.15 0.15 0.15
220 220 220
BLOCK BLOCK BLOCK
2.4 2.4
4310 4360
BLOCK BLOCK
0.15 0.15 0.15
220 220 220
BLOCK BLOCK BLOCK
1.9
6.7E+04
PIN
0.21 0.21 0.13 0.13
27.6
251 252 253 254 255 256 257 258 259 260
24 26 28 27 27.6 24.1 20.7
261 262 263 264 265 266 267 268 269 270
2.0E-07
0.18
20.7
2.0E-07
0.21
34.5
1.0E-05 4.0E-08
PIN-ON-RING BLOCK-ON-RING
19.6 124
7.0E-09 8.0E-09 2.0E-09
BLOCK-ON-RING BLOCK-ON-RING BLOCK-ON-RING
134 137 402
3.0E-08 3.0E-08
BLOCK-ON-RING BLOCK-ON-RING
130 124
1.0E-08 1.0E-08 2.0E-09
BLOCK-ON-RING BLOCK-ON-RING BLOCK-ON-RING
401 137 137
1.0E-04
PIN-ON-RING
27.6
27.6
271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290
301 302 303 304 305 306 307 308 309 310
Friction Coefficent
14
241 242 243 244 245 246 247 248 249 250
291 292 293 294 295 296 297 298 299 300
Wear Constant (mm3/mm*N)
10.3 33 26 10.3 248 124 124
24
24 24
19.6
1
0.12
6.89
1.0E-09 7.0E-08
0.21 0.35
2
BUSHING-SHAFT BUSHING-SHAFT
24 24
0.5 0.5
BUSHING BUSHING
3
BUSHING-SHAFT
24
0.5
BUSHING
5.1
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24
0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING
1.052 0.05
1.23 0.702 0.09 0.0175
827 41 21 6.89 34 6.89
4.0E-09 5.0E-08 4.0E-09 3.0E-10 2.0E-09
0.15 0.28 0.38 0.25 0.37
1.5 8.1
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TABLE 15.1 Tribomaterials Database (Part F) Contact Environment
Standard Test
Counterface Material
Counterface Description
Wear Type
AIR
MILD STEEL
ADHESIVE
Boundary lubricated, oil-filled material Boundary lubricated, oil-filled material AIR AIR AIR
CARBON STEEL CARBON STEEL MILD STEEL CARBON STEEL CARBON STEEL
LUBRICATED LUBRICATED ADHESIVE ADHESIVE
AIR AIR AIR
STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
AIR
CARBON STEEL
AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL
ADHESIVE
AIR
CARBON STEEL CARBON STEEL
ADHESIVE
AIR
CARBON STEEL
AIR
CARBON STEEL
AIR AFS 50/70 sand; 471 g/min
SILVER CHLOROBUTYL
AIR AIR AIR
4620 CARBURIZED STEEL 4620 CARBURIZED STEEL 4620 CARBURIZED STEEL
AFS 50/70 sand; 239 g/min AFS 50/70 sand; 197 g/min
ASTM G65-A
CHLOROBUTYL CHLOROBUTYL
ADHESIVE
A60 SHORE HARDNESS
ADHESIVE ABRASIVE ADHESIVE ADHESIVE ADHESIVE
A60 SHORE HARDNESS A62 SHORE HARDNESS
ABRASIVE ABRASIVE
AIR AIR AIR AIR
CARBON STEEL 4620 CARBURIZED STEEL 4620 CARBURIZED STEEL 4620 CARBURIZED STEEL
ADHESIVE ADHESIVE ADHESIVE
AIR
ZINC
ADHESIVE
AIR AIR
CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE
CARBON STEEL
ADHESIVE
CARBON STEEL
ADHESIVE
AIR
CARBON STEEL CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE
AIR AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE ADHESIVE
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TABLE 15.1 Tribomaterials Database (Part E) Number 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368
P*V Limit (MPa*m/s)
Maximum Pressure (MPa)
Wear Constant (mm3/mm*N)
Friction Coefficent
0.017 0.11
6.0E-08 1.0E-08
0.07 0.39 0.24
0.18 0.053 0.049
3.0E-08 7.0E-09 4.0E-07
0.37 0.37 0.1 0.15
8.0E-10 5.0E-09 4.0E-10 5.0E-10 6.0E-09
0.14 0.34 0.16 0.12 0.16
8.0E-10 8.0E-10 2.0E-10 8.0E-10
0.2 0.31 0.18 0.09
3.45
Maximum Velocity (m/s)
0.25
Contact Geometry
Load (N)
Temp. (C)
Velocity (m/s)
Distance (m)
Specimen Shape
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24 24 24
0.5 0.5 0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24 24
0.5 0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING BUSHING
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24
0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24 24 24 24
0.5 0.5 0.5 0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24 24 24 24 24 24 24
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING
BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT BUSHING-SHAFT
24 24 24 24 24 24 24
0.5 0.5 0.5 0.5 0.5 0.5 0.5
BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING BUSHING
7 0.3 0.7 0.44 0.32 0.14 0.88 0.35 0.61 0.21
0.53 1.58 0.3
13.8 13.8
50 41.4
0.7 0.77 0.54
0.7 0.56 0.18 0.3
1.23 0.53 0.56 0.351
4.1
0.2
2.0E-09 3.0E-09 2.0E-09 5.0E-10 2.0E-09 3.0E-10 1.0E-09
0.26 0.17 0.22 0.15 0.15 0.27 0.17 0.16
9.0E-10
0.13
6.0E-10 5.0E-09 2.0E-09 3.0E-09 5.0E-09 1.0E-09 7.0E-10 2.0E-09
0.27 0.16 0.2 0.29 0.1 0.11 0.14
3.0E-09 9.0E-10 3.0E-09 1.0E-09 4.0E-11 1.0E-10 6.0E-11
8.1
0.22 0.14 0.34 0.32
0.0105
138 17.2 17.2 7 41 55
0.0119
55
0.24
0.877
414
0.03
0.09 0.07
1 5.1 5.1
0.3
Notes: 1. This Table is a row/column array of size 368 rows by 43 columns. Each row is a database record (the results of one or more tests); each column is a database field (a significant test or material parameter). In printed form, it is necessary to subdivide the array to suit the printed page size. This was accomplished by division of the array into 6 parts (A, B, C,…F) each containing 6 or more columns, and further dividing each part into 5 pages, resulting in 30 pagesized sub-arrays. The first sub-array is set of columns and rows starting at the upper left corner of the array. The next sub-array fits below the first, etc. Each page contains appropriate headings and seventy to eighty records that are numbered in the left-most column so that they can be followed across the array. Every tenth record is followed by a solid line to facilitate reading. 2. The data records are sorted alphabetically by class, sub-class, and common name in that order. The common name field is shown first. 3. Each record contains material description data and many but not all records have tribological test data. 4. All records that contain tribological data result from sliding test conditions. All records refer to air environment testing unless special evironmental conditions were established at the tribological contact and are so stated. 5. The user is cautioned about use of any record where important test parameters are not given. This results from lack of reporting by the original source of data. The significance of an incomplete description of test conditions or material description, and any resulting effect on the reported data, must be judged by the individual user. Data Sources: Alloy Digest, (Alloy Digest, Inc, Orange, N.J.). Ashby, M. F. and Jones, D. R. H., Engineering Materials, Pergammon, Oxford, (1980). ASM, International, Metals Handbooks, 8th edition (ASM Intern., Metals Park, OH 44073). ASM, International, Aluminum-Properties, Physical Metallurgy, Phase Diagrams, Vol.1(1967).
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TABLE 15.1 Tribomaterials Database (Part F) Contact Environment
Standard Test
Counterface Material
AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
AIR AIR AIR AIR AIR AIR AIR AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
AIR AIR AIR AIR AIR AIR AIR AIR AIR
AIR AIR AIR AIR AIR AIR
Counterface Description
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
Wear Type ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
AIR AIR AIR AIR AIR AIR AIR AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
AIR AIR AIR AIR AIR AIR AIR
CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL CARBON STEEL
COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin COLD-ROLLED, 20 HRC, 16uin
ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE ADHESIVE
CARBON STEEL
ADHESIVE
CARBON STEEL
ADHESIVE
CARBON STEEL
ADHESIVE
ASME, Wear of Materials, Conference Proceedings, (ASME, NY, 1977-1987). ASTM, unpublished data in ASTM Research Report relative to Standard G-65, (ASTM, W. Conshohocken, PA) ASME, Metals Properties, ASME Handbook (1954). Battelle Tribology Laboratory, Columbus, Ohio., private communication of unpublished data. Booser, E. R., ed. Handbook of Lubrication, Vol. I (1983) and Vol. II (1984) (CRC Press, Boca Raton, FL 33431). CRC Publ. Co., Handbook of Chemistry and Physics, 69th Edition, (1988). Encyclopedia of Chemical Technology, 3rd Edition, Vols. 3,4,16,18,23. Glaeser, W., pp. 313-326, in Wear Control Handbook, Peterson, M. B. and Winer, W. O., eds., ASME, New York, NY, 1980. Hertzberg, R. W., Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., Wiley, NY, (1989). Lynch, C. T., Engineering Properties of Ceramics, AFML Report TR-66-52, WPAFB, (1966). Modern Plastics Encyclopedia-88 (McGraw Hill, NY, 1988). Morey, C. Properties of Glass, (1938). National Center of Tribology, Polymer Materials for Bearing Surfaces, (Risley, UK, 1983). NIST-Thermo-Physical Data Center, Thermophysical Properties of Matter; Data Series, Vols, 1,4 (1970). Rowe, C. N., pp. 143-160 in Wear Control Handbook, Peterson, M. B. and Winer, W. O., eds., ASME, New York, NY, 1980. Shah, Vishu, ed. Handbook of Plastics Testing Technology, (Wiley, 1984). Smithells Metal Reference Book, (Butterworths, London, 1955). Smithsonian Physical Tables, 9th Edition, (1964). Standards Handbook: Copper — Brass — Bronze, Alloy Data/7 and Alloy Data/2 (Copper Development Association Inc, 1985). Touloukin, Y. S. et al., Thermophysical Properties of Matter, (IFI Plenum, NY, 1972).
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II Micro/Nanotribology Bharat Bhushan The Ohio State University
Othmar Marti University of Ulm 16 Microtribology and Microrheology of Molecularly Thin Liquid Films Alan D. Berman and Jacob N. Israelachvili ......................................................................... 567 Introduction • Solvation and Structural Forces: Forces Due to Liquid and Surface Structure • Adhesion and Capillary Forces • Nonequilibrium Interactions: Adhesion Hysteresis • Rheology of Molecularly Thin Films: Nanorheology • Interfacial and Boundary Friction: Molecular Tribology • Theories of Interfacial Friction • Friction and Lubrication of Thin Liquid Films • Stick-Slip Friction
17 Measurement of Adhesion and Pull-Off Forces with the AFM Othmar Marti ......... 617 Introduction • Experimental Procedures to Measure Adhesion in AFM and Applications • Summary and Outlook
18 Atomic-Scale Friction Studies Using Scanning Force Microscopy Udo D. Schwarz and Hendrik Hölscher ............................................................................................ 641 Introduction • The Scanning Force Microscope as a Tool for Nanotribology • The Mechanics of a Nanometer-Sized Contact • Amontons’ Laws at the Nanometer Scale • The Influence of the Surface Structure on Friction • Atomic Mechanism of Friction • The Velocity Dependence of Friction • Summary
19 Friction, Scratching/Wear, Indentation, and Lubrication Using Scanning Probe Microscopy Bharat Bhushan ................................................................................. 667 Introduction • Description of AFM/FFM and Various Measurement Techniques • Friction and Adhesion • Scratching, Wear, and Fabrication/Machining • Indentation • Boundary Lubrication • Closure
20 Computer Simulations of Friction, Lubrication, and Wear Mark O. Robbins and Martin H. Müser ........................................................................................................... 717 Introduction • Atomistic Computer Simulations • Wearless Friction in Low-Dimensional Systems • Dry Sliding of Crystalline Surfaces • Lubricated Surfaces • Stick-Slip Dynamics • Strongly Irreversible Tribological Processes
563
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M
Micro/Nanotribology
icro/nanotribology involve studies of friction and wear processes ranging from microscopic to atomic levels, whereas classical tribology and rheology deal with large sample volumes which can be viewed as a continuum. The experiments in the field of micro/nanotribology are conducted using either surface force apparatus or a variety of scanning probe microscopes (SPMs). Surface force apparatus is generally used to study rheology of molecular thick liquid films sandwiched between atomically smooth (many times, optically transparent) surfaces. At most solid–solid interfaces of technological relevance, contact occurs at numerous asperities. In a scanning probe microscope, a sharp tip sliding on a surface simulates just one such contact. Atomic force/friction force microscopes (AFM/FFM), a form of SPM, are used to study various tribological phenomena. AFM/FFM techniques are increasingly used for tribological studies of engineering surfaces at scales ranging from atomic and molecular to microscale; studies include surface roughness, adhesion, friction, scratching, wear, indentation, detection of material transfer and boundary lubrication. Molecular dynamic simulations are carried out to model interfacial processes on a nanoscale. The techniques dealt with in this section are on the borderline between the atomistic/molecular view and the classical one. The first chapter of this section deals with questions of dissipation in nanoscopic volumes using surface force apparatus. Micro- and nanorheology help us to understand how liquid or liquid-like films only a few molecules in thickness behave under shearing stress. It is found that the nature and shape of the molecules profoundly alter the shearing behavior of the systems. Specifically, the shear stiffness is a periodic function of the film thickness, with the diameter of the molecules determining the period. The findings, obtained with the surface force apparatus, give important design parameters for the lubrication of hard disks, for example. The possibility to measure the shear response at large shear rates with vanishingly small probe volumes may help in a first screening of new substances. The loading force of a contact is not only given by the external force, but also by the interfacial adhesion forces between the two bodies in contact. The next chapter outlines the measurement of adhesion and pull-off forces by the scanning probe microscope. It is shown that heterogeneous samples can be segmented into their components by the adhesion force. Again one of the important questions still open is that of the applicability of continuum mechanics models. Molecular interaction might have a non-negligible influence for small tips. Increasing the resolution of the instrument, the chapter on the atomic scale friction measurements explains the theory and experimental details of this technique. On an atomic level, one can have dissipative, but not plowing friction. Mapping of the samples enables the seasoned researcher to extract important information on the surface and its interaction potential with the tip. This means that the very nature of the surface determines friction coefficients. Since the wear part of the friction is mostly not present at atomic scales, the friction can be much lower than in the macroscopic case. Even though the AFM can be operated in the wearless regime it is also possible to operate the instrument at higher loads for friction studies as well as for scratch/wear and indentation studies. The nanoindentation and the nanoscratch operation allow us to probe the elastic/plastic response of nanometer films and of small amounts of material. The experiments are similar to the failure mechanism one would expect if a hard disk slider touched a surface or if a MEMS device were to undergo the first steps of a catastrophic failure. An overview of various tribological studies being conducted by scanning probe microscopy are given in the next chapter. Investigations of scratching, wear, and indentation on nanoscales using the AFM can provide insights into failure mechanisms of materials. Coefficients of friction, wear rates, and mechanical properties such as hardness have been found to be different on the nanoscale than on the macroscale; generally, coefficients of friction and wear rates on micro- and nanoscales are smaller, whereas hardness is greater. Therefore, micro/nanotribological studies may help define the regimes for ultra-low friction and near zero wear. The last chapter of this section gives an overview on the theoretical concepts behind simulations. Results derived from these simulations are compared to the theory. First a brief overview of common simulation methods concentrates on the relative strengths and weaknesses and the fields of application of these methods. The friction between two crystalline surfaces is calculated using simple spring models. Adsorbed layers are added to make the simulation more realistic. In a final step, friction between metals is considered. This part shows nicely where the difficulties lie when trying to bridge the gap between the
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565
world of atoms and single molecules and the macroscopic world. Then lubrication on an atomic scale is considered. This part of the chapter is a complement to the first chapter. This is also true for the wall induced structures, which were shown to be of utmost importance to understand the shear behavior in the first chapter. The flow boundary condition on the walls and the solidification of liquids in extremely constrained structures are additional features found both in the simulations and the experiment. Stickslip motion is finally explained using molecular models. This section gives an overview of the status of both the experimental and the theoretical work. It is clear that tremendous progress has been made, but there is a gap between the theoretical models and experimental data that needs to be bridged.
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16 Microtribology and Microrheology of Molecularly Thin Liquid Films 16.1 16.2
Introduction ..................................................................... 568 Solvation and Structural Forces: Forces Due to Liquid and Surface Structure .......................................... 568 Effects of Surface Structure • Effect of Surface Curvature and Geometry
16.3
Adhesion and Capillary Forces ....................................... 572
16.4 16.5
Nonequilibrium Interactions: Adhesion Hysteresis....... 574 Rheology of Molecularly Thin Films: Nanorheology ................................................................... 576
Adhesion Mechanics
Different Modes of Friction: Limits of Continuum Models • Viscous Forces and Friction of Thick Films: Continuum Regime • Friction of Intermediate Thickness Films
16.6
Interfacial and Boundary Friction: Molecular Tribology........................................................................... 582 General Interfacial Friction • Boundary Friction of Surfactant Monolayer Coated Surfaces • Boundary Lubrication of Molecularly Thin Liquid Films • Transition from Interfacial to Normal Friction (with Wear)
16.7
Theories of Interfacial Friction....................................... 587 Theoretical Modeling of Interfacial Friction: Molecular Tribology • Adhesion Force Contribution to Interfacial Friction • Relation Between Boundary Friction and Adhesion Energy Hysteresis • External Load Contribution to Interfacial Friction • Simple Molecular Model of Energy Dissipation ε
16.8
Smooth and Stick-Slip Sliding • Role of Molecular Shape and Liquid Structure
Alan D. Berman Seagate Removable Storage Solutions
Jacob N. Israelachvili University of California
0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
Friction and Lubrication of Thin Liquid Films............. 594
16.9
Stick-Slip Friction ............................................................ 600 Rough Surfaces Model • Distance-Dependent Model • Velocity-Dependent Friction Model • Phase Transitions Model • Critical Velocity for Stick-Slip • Dynamic Phase Diagram Representation of Tribological Parameters
567
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16.1 Introduction When a bow is gently pulled across a violin string to produce a rich C note, it sounds very elegant and simple. In analyzing the source of the sound — the sliding of a bow with resin over a tuned string — the physics seems simple. At first glance is would appear that the “lubricating” resin would be undergoing Couette flow between the bow and the string, but such dynamics would not produce the resonance in the string. Instead, it is the far more complex stick-slip type of frictional sliding between the moving parts that excites the resonance and creates the sound. Other similar examples such as door hinges or wheel bearings are ideally described by engineering hydrodynamics. However, when the door creaks or the wheel squeaks, there is a transition from a system described by bulk lubrication to a system controlled by microtribology (or what is now referred to as nanotribology). These latter two cases of lubrication failure result in the sliding surfaces interacting directly, or with a very thin lubricating film that behaves differently from the bulk lubricant in the “quiet” condition. This chapter seeks to explore the transition from bulk lubrication to microscale rheology and tribology, and how such systems are better described. As lubricating layers become thinner, their properties change not only quantitatively, but also qualitatively, as surface forces become dominant and liquid properties change under confinement. The effects of these on the tribology and rheology of thin films will be described.
16.2 Solvation and Structural Forces: Forces Due to Liquid and Surface Structure When a liquid is confined within a restricted space, for example, a very thin film between two surfaces, it ceases to behave as a structureless continuum. Likewise, the forces between two surfaces close together in liquids can no longer be described by simple continuum theories. Thus, at small surface separations — below about 10 molecular diameters — the van der Waals force between two surfaces or even two solute molecules in a liquid (solvent) is no longer a smoothly varying attraction. Instead, there now arises an additional “solvation” force that generally oscillates with distance, varying between attraction and repulsion, with a periodicity equal to some mean dimension σ of the liquid molecules (Horn and Israelachvili, 1981). Figure 16.1 shows the force-law between two smooth mica surfaces across the hydrocarbon liquid tetradecane, whose inert chain-like molecules have a width of σ ≈ 0.4 nm. The short-range oscillatory force-law, varying between attraction and repulsion with a molecular-scale periodicity is related to the “density distribution function” and “potential of mean force” characteristic of intermolecular interactions in liquids. These forces arise from the confining effect that two surfaces have on the liquid molecules between them, forcing them to order into quasi-discrete layers which are energetically or entropically favored (and correspond to the free energy minima) while fractional layers are disfavored (energy maxima). The effect is quite general and arises with all simple liquids when they are confined between two smooth surfaces, both flat and curved. Oscillatory forces do not require that there be any attractive liquid–liquid or liquid–wall interaction. All one needs is two hard walls confining molecules whose shapes are not too irregular and which are free to exchange with molecules in the bulk liquid reservoir. In the absence of any attractive forces between the molecules, the bulk liquid density may be maintained by an external hydrostatic pressure. In real liquids, attractive van der Waals forces play the role of the external pressure, but the oscillatory forces are much the same. Oscillatory forces are now well understood theoretically, at least for simple liquids, and a number of theoretical studies and computer simulations of various confined liquids, including water, which interact via some form of the Lennard–Jones potentials have invariably led to an oscillatory solvation force at surface separations below a few molecular diameters (Snook and van Megan, 1979, 1980, 1981; van Megan and Snook, 1979, 1981; Kjellander and Marcelja, 1985a,b; Tarazona and Vicente, 1985; Henderson and Lozada-Cassou, 1986; Evans and Parry, 1990).
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569
FIGURE 16.1 Solid curve: Forces between two mica surfaces across saturated linear chain alkanes such as n-tetradecane (Christenson et al., 1987; Horn and Israelachvili, 1988; Israelachvili and Kott, 1988; Horn et al., 1989). The 0.4 nm periodicity of the oscillations indicates that the molecules align with their long axis preferentially parallel to the surfaces, as shown schematically in the upper insert. The theoretical continuum van der Waals force is shown by the dotted line. Dashed line: Smooth, nonoscillatory force-law exhibited by irregularly shaped alkanes, such as branched isoparaffins, that cannot order into well-defined layers (lower insert) (Christenson et al., 1987). Similar nonoscillatory forces are also observed between “rough” surfaces, even when these interact across a saturated linear chain liquid. This is because the irregularly-shaped surfaces (rather than the liquid) now prevent the liquid molecules from ordering in the gap. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
In a first approximation, the oscillatory force laws may be described by an exponentially decaying cosine function of the form
(
)
E ≈ Eo cos 2πD σ e − D σ
(16.1)
where both theory and experiments show that the oscillatory period and the characteristic decay length of the envelope are close to σ (Tarazona and Vicente, 1985). It is important to note that once the solvation zones of two surfaces overlap, the mean liquid density in the gap is no longer the same as that of the bulk liquid. And since the van der Waals interaction depends on the optical properties of the liquid, which in turn depend on the density, one can see why the van der Waals and oscillatory solvation forces are not strictly additive. Indeed, it is more correct to think of the solvation force as the van der Waals force at small separations, with the molecular properties and density variations of the medium taken into account. It is also important to appreciate that solvation forces do not arise simply because liquid molecules tend to structure into semi-ordered layers at surfaces. They arise because of the disruption or change of this ordering during the approach of a second surface. If there were no change, there would be no solvation force. The two effects are of course related: the greater the tendency toward structuring at an isolated surface, the greater the solvation force between two such surfaces, but there is a real distinction between the two phenomena that should always be borne in mind.
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Concerning the adhesion energy or force of two smooth surfaces in simple liquids, a glance at Figure 16.1 and Equation 16.1 shows that oscillatory forces lead to multivalued, or “quantized,” adhesion values, depending on which energy minimum two surfaces are being separated from. For an interaction energy that varies as described by Equation 16.1, the quantized adhesion energies will be Eo at D = 0 (primary minimum), Eo /e at D = σ (second minimum), Eo /e2 at D = 2σ, etc. Such multivalued adhesion forces have been observed in a number of systems, including the interactions of fibers. Most interesting, the depth of the potential energy well at contact (–Eo at D = 0) is generally deeper but of similar magnitude to the value expected from the continuum Lifshitz theory of van der Waals forces (at a cutoff separation of D0 ≈ 0.15 to 0.20 nm), even though the continuum theory fails to describe the shape of the force-law at intermediate separations. There is a rapidly growing literature on experimental measurements and other phenomena associated with short-range oscillatory solvation forces. The simplest systems so far investigated have involved measurements of these forces between molecularly smooth surfaces in organic liquids. Subsequent measurements of oscillatory forces between different surfaces across both aqueous and nonaqueous liquids have revealed their subtle nature and richness of properties (Christenson, 1985; Christenson and Horn, 1985; Israelachvili, 1987; Christenson, 1988a; Israelachvili and McGuiggan 1988), for example, their great sensitivity to the shape and rigidity of the solvent molecules, to the presence of other components, and to the structure of the confining surfaces. In particular, the oscillations can be smeared out if the molecules are irregularly shaped (e.g., branched) and therefore unable to pack into ordered layers, or when the interacting surfaces are rough or fluid-like (e.g., surfactant micelles or lipid bilayers in water) even at the Ångstrom level (Gee and Israelachvili, 1990).
16.2.1 Effects of Surface Structure It has recently been appreciated that the structure of the confining surfaces is just as important as the nature of the liquid for determining the solvation forces (Rhykerd et al., 1987; Schoen et al., 1987, 1989; Landman, et al., 1990; Thompson and Robbins, 1990; Han et al., 1993). Between two surfaces that are completely smooth or “unstructured,” the liquid molecules will be induced to order into layers, but there will be no lateral ordering within the layers. In other words, there will be positional ordering normal but not parallel to the surfaces. However, if the surfaces have a crystalline (periodic) lattice, this will induce ordering parallel to the surfaces as well, and the oscillatory force then also depends on the structure of the surface lattices. Further, if the two lattices have different dimensions (“mismatched” or “incommensurate” lattices), or if the lattices are similar but are not in register and are at some “twist angle” relative to each other, the oscillatory force-law is further modified. McGuiggan and Israelachvili (1990) measured the adhesion forces and interaction potentials between two mica surfaces as a function of the orientation (twist angle) of their surface lattices. The forces were measured in air, in water, and in an aqueous salt solution where oscillatory structural forces were present. In air, the adhesion was found to be relatively independent of the twist angle θ due to the adsorption of a 0.4-nm-thick amorphous layer of organics and water at the interface. The adhesion in water is shown in Figure 16.2. Apart from a relatively angle-independent “baseline” adhesion, sharp adhesion peaks (energy minima) occurred at θ = 0°, ±60°, ±120° and 180°, corresponding to the “coincidence” angles of the surface lattices. As little as ±1° away from these peaks, the energy decreases by 30 to 50%. In aqueous salt (KCl) solution, due to potassium ion adsorption, the water between the surfaces becomes ordered, resulting in an oscillatory force profile where the adhesive minima occur at discrete separations of about 0.25 nm, corresponding to integral numbers of water layers. The whole interaction potential was now found to depend on orientation of the surface lattices, and the effect extended at least four molecular layers. Although oscillatory forces are predicted from Monte Carlo and molecular dynamic simulations, no theory has yet taken into account the effect of surface structure, or atomic “corrugations,” on these forces, nor any lattice mismatching effects. As shown by the experiments, within the last one or two nanometers, these effects can alter the adhesive minima at a given separation by a factor of two. The force barriers,
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FIGURE 16.2 Adhesion energy for two mica surfaces in a primary minimum contact in water as a function of the mismatch angle θ about θ = 0° between the two contacting surface lattices (McGuiggan and Israelachvili, 1990). Similar peaks are obtained at the other “coincidence” angles: θ = ±60°, ±120°, and 180° (inset). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
or maxima, may also depend on orientation. This could be even more important than the effects on the minima. A high barrier could prevent two surfaces from coming closer together into a much deeper adhesive well. Thus, the maxima can effectively contribute to determining not only the final separation of two surfaces, but also their final adhesion. Such considerations should be particularly important for determining the thickness and strength of intergranular spaces in ceramics, the adhesion forces between colloidal particles in concentrated electrolyte solutions, and the forces between two surfaces in a crack containing capillary condensed water. The intervening medium profoundly influences how one surface interacts with the other. As experimental results show (McGuiggan and Israelachvili, 1990), when two surfaces are separated by as little as 0.4 nm of an amorphous material, such as adsorbed organics from air, then the surface granularity can be completely masked and there is no mismatch effect on the adhesion. However, with another medium, such as pure water which is presumably well ordered when confined between two mica lattices, the atomic granularity is apparent and alters the adhesion forces and whole interaction potential out to D > 1 nm. Thus, it is not only the surface structure but also the liquid structure, or that of the intervening film material, that together determine the short-range interaction and adhesion. On the other hand, for surfaces that are randomly rough, the oscillatory force becomes smoothed out and disappears altogether, to be replaced by a purely monotonic solvation force. This occurs even if the liquid molecules themselves are perfectly capable of ordering into layers. The situation of symmetric liquid molecules confined between rough surfaces is therefore not unlike that of asymmetric molecules between smooth surfaces (see Figure 16.1). To summarize some of the above points, for there to be an oscillatory solvation force, the liquid molecules must be able to be correlated over a reasonably long range. This requires that both the liquid molecules and the surfaces have a high degree of order or symmetry. If either is missing, so will be the oscillations. A roughness of only a few Ångstroms is often sufficient to eliminate any oscillatory component of a force law.
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16.2.2 Effect of Surface Curvature and Geometry It is easy to understand how oscillatory forces arise between two flat, plane parallel surfaces (Figure 16.2). Between two curved surfaces, e.g., two spheres, one might imagine the molecular ordering and oscillatory forces to be smeared out in the same way that they are smeared out between two randomly rough surfaces. However, this is not the case. Ordering can occur so long as the curvature or roughness is itself regular or uniform, i.e., not random. This interesting matter is due to the Derjaguin approximation (Derjaguin, 1934), which relates the force between two curved surfaces to the energy between two flat surfaces. If the latter is given by a decaying oscillatory function, as in Equation 16.1, then the energy between two curved surfaces will simply be the integral of that function, and since the integral of a cosine function is another cosine function, with some appropriate phase shift, we see why periodic oscillations will not be smeared out simply by changing the surface curvature. Likewise, two surfaces with regularly curved regions will also retain their oscillatory force profile, albeit modified, so long as the corrugations are truly regular, i.e., periodic. On the other hand, surface roughness, even on the nanometer scale, can smear out any oscillations if the roughness is random and the liquid molecules are smaller than the size of the surface asperities.
16.3 Adhesion and Capillary Forces When considering the adhesion of two solid surfaces or particles in air or in a liquid, it is easy to overlook or underestimate the important role of capillary forces, i.e., forces arising from the Laplace pressure of curved menisci which have formed as a consequence of the condensation of a liquid between and around two adhering surfaces (Figure 16.3). The adhesion force between a spherical particle of radius R and a flat surface in an inert atmosphere is
FS = 4 πRγ SV
(16.2)
but in an atmosphere containing a condensable vapor, the above becomes replaced by
(
FS = 4 πR γ LV cos θ + γ SL
)
(16.3)
where the first term is due to the Laplace pressure of the meniscus and the second is due to the direct adhesion of the two contacting solids within the liquid. Note that the above equation does not contain the radius of curvature, r, of the liquid meniscus (Figure 16.3). This is because for smaller r the Laplace pressure γ LV/r increases, but the area over which it acts decreases by the same amount, so the two effects cancel out. A natural question arises as to the smallest value of r for which Equation 16.3 will apply. Experiments with inert liquids, such as hydrocarbons, condensing between two mica surfaces indicate that Equation 16.3 is valid for values of r as small as 1 to 2 nm, corresponding to vapor pressures as low as 40% of saturation (Fisher and Israelachvili, 1981; Christenson, 1988b). With water condensing from vapor or from oil it appears that the bulk value of γ LV is also applicable for meniscus radii as small as 2 nm. The capillary condensation of liquids, especially water, from vapor can have additional effects on the whole physical state of the contact zone. For example, if the surfaces contain ions, these will diffuse and build up within the liquid bridge, thereby changing the chemical composition of the contact zone as well as influencing the adhesion. More dramatic effects can occur with amphiphilic surfaces, i.e., those containing surfactant or polymer molecules. In dry air, such surfaces are usually nonpolar — exposing hydrophobic groups such as hydrocarbon chains. On exposure to humid air, the molecules can overturn so that the surface nonpolar groups become replaced by polar groups, which renders the surfaces hydrophilic. When two such surfaces come into contact, water will condense around the contact zone and the adhesion force will also be affected — generally increasing well above the value expected for inert hydrophobic surfaces.
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FIGURE 16.3 Sphere on flat in an inert atmosphere (top) and in an atmosphere containing vapor that can “capillary condense” around the contact zone (bottom). At equilibrium the concave radius, r, of the liquid meniscus is given by the Kelvin equation. The radius r increases with the relative vapor pressure, but for condensation to occur, the contact angle θ must be less than 90° or else a concave meniscus cannot form. The presence of capillary condensed liquid changes the adhesion force, as given by Equations 16.2 and 16.3. Note that this change is independent of r so long as the surfaces are perfectly smooth. Experimentally, it is found that for simple inert liquids such as cyclohexane, these equations are valid at Kelvin radii as small as 1 nm — about the size of the molecules themselves. Capillary condensation also occurs in binary liquid systems, e.g., when small amounts of water dissolved in hydrocarbon liquids condense around two contacting hydrophilic surfaces, or when a vapor cavity forms in water around two hydrophobic surfaces. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
It is clear that the adhesion of two surfaces in vapor or a solvent can often be largely determined by capillary forces arising from the condensation of liquid that may be present only in very small quantities, e.g., 10 to 20% of saturation in the vapor, or 20 ppm in the solvent.
16.3.1 Adhesion Mechanics Modern theories of the adhesion mechanics of two contacting solid surfaces are based on the Johnson–Kendall–Roberts (JKR) theory (Johnson et al., 1971; Pollock et al., 1978; Barquins and Maugis, 1982). In the JKR theory two spheres of radii R1 and R2, bulk elastic moduli K, and surface energy γ per unit area, will flatten when in contact. The contact area will increase under an external load or force F, such that at mechanical equilibrium the contact radius r is given by
r3 =
R F + 6 πRγ + 12πRγF + 6 πRγ K
(
) 2
(16.4)
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where R = R1R2 /(R1+R2). Another important result of the JKR theory gives the adhesion force or “pull off ” force:
FS = −3πRγ S
(16.5)
where, by definition, the surface energy γS, is related to the reversible work of adhesion W, by W = 2γS. Note that according to the JKR theory a finite elastic modulus, K, while having an effect on the loadarea curve, has no effect on the adhesion force — an interesting and unexpected result that has nevertheless been verified experimentally (Johnson et al., 1971; Israelachvili, 1991). Equations 16.4 and 16.5 are the basic equations of the JKR theory and provide the framework for analyzing the results of adhesion measurements of contacting solids, known as “contact mechanics” (Pollock et al., 1978; Barquins and Maugis, 1982), and for studying the effects of surface conditions and time on adhesion energy hysteresis (see next section).
16.4 Nonequilibrium Interactions: Adhesion Hysteresis Under ideal conditions the adhesion energy is a well-defined thermodynamic quantity. It is normally denoted by E or W (the work of adhesion) or γ (the surface tension, where W = 2γ), and it gives the reversible work done on bringing two surfaces together or the work needed to separate two surfaces from contact. Under ideal, equilibrium conditions these two quantities are the same, but under most realistic conditions they are not: the work needed to separate two surfaces is always greater than that originally gained on bringing them together. An understanding of the molecular mechanisms underlying this phenomenon is essential for understanding many adhesion phenomena, energy dissipation during loading–unloading cycles, contact angle hysteresis, and the molecular mechanisms associated with many frictional processes. It is wrong to think that hysteresis arises because of some imperfection in the system, such as rough or chemically heterogeneous surfaces or because the supporting material is viscoelastic; adhesion hysteresis can arise even between perfectly smooth and chemically homogenous surfaces supported by perfectly elastic materials, and can be responsible for such phenomena as “rolling” friction and elastoplastic adhesive contacts (Bowden and Tabor, 1967; Greenwood and Johnson, 1981; Maugis, 1985; Michel and Shanahan, 1990) during loading–unloading and adhesion–decohesion cycles. Adhesion hysteresis may be thought of as being due to mechanical or chemical effects, as illustrated in Figure 16.4. In general, if the energy change, or work done, on separating two surfaces from adhesive contact is not fully recoverable on bringing the two surfaces back into contact again, the adhesion hysteresis may be expressed as
W
R Receding
> WA Advancing
or
(
)
∆W = WR − WA > 0
(16.6)
where WR and WA are the adhesion or surface energies for receding (separating) and advancing (approaching) two solid surfaces, respectively. Figure 16.5 shows the results of a typical experiment that measures the adhesion hysteresis between two surfaces (Chaudhury and Whitesides, 1991; Chen et al., 1991). In this case, two identical surfactant-coated mica surfaces were used in a Surface Forces Apparatus. By measuring the contact radius as a function of applied load both for increasing and decreasing loads, two different curves are obtained. These can be fitted to the JKR equation, Equation 16.4, to obtain the advancing (loading) and receding (unloading) surface energies.
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MECHANICAL ADHESION HYSTERESIS
A
S′
Approach (Advance)
S′
WA
S
Separation (Recede) Contact
Macroscopic jumps S′
Molecular jumps Out In
Popped bond
KS
B
WR
D
S S‘
Repulsion Distance, D
0
C
FORCE
Jump in
DR DA
o
pe
Sl
=
KS Attraction
Jump out D0
D CHEMICAL ADHESION HYSTERESIS FIGURE 16.4 Origin of adhesion hysteresis during the approach and separation of two solid surfaces. (A) In all realistic situations the force between two solid surfaces is never measured at the surfaces themselves, S, but at some other point, say S′, to which the force is elastically transmitted via the backing material supporting the surfaces. (B, left) “Magnet” analogy of how mechanical adhesion hysteresis arises for two approaching or separating surfaces, where the lower is fixed and where the other is supported at the end of a spring of stiffness KS. (B, right) On the molecular or atomic level, the separation of two surfaces is accompanied by the spontaneous breaking of bonds, which is analogous to the jump apart of two macroscopic surfaces or magnets. (C) Force–distance curve for two surfaces interacting via an attractive van der Waals-type force law, showing the path taken by the upper surface on approach and separation. On approach, an instability occurs at D = DA, where the surfaces spontaneously jump into “contact” at D ≈ Do. On separation, another instability occurs where the surfaces jump apart from ~Do to DR. (D) Chemical adhesion hysteresis produced by interdiffusion, interdigitation, molecular reorientations and exchange processes occurring at an interface after contact. This induces roughness and chemical heterogeneity even though initially (and after separation and reequilibration) both surfaces are perfectly smooth and chemically homogeneous. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Hysteresis effects are also commonly observed in wetting/dewetting phenomena (Miller and Neogi, 1985). For example, when a liquid spreads and then retracts from a surface, the advancing contact angle θA is generally larger than the receding angle θR. Since the contact angle, θ, is related to the liquid–vapor surface tension, γ, and the solid–liquid adhesion energy, W, by the Dupré equation:
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FIGURE 16.5 Measured advancing and receding radius vs. load curves for two surfactant-coated mica surfaces of initial, undeformed radii R ≈ 1 cm. Each surface had a monolayer of CTAB (cetyl-trimethyl-ammonium-bromide) on it of mean area 60 Å2 per molecule. The solid lines are based on fitting the advancing and receding branches to the JKR equation, Equation 16.4, from which the indicated values of γA and γR were determined, in units of mJ/m2 or erg/cm2. The advancing/receding rates were about 1 µm/sec. At the end of each unloading cycle the pull-off force, Fs, can be measured, from which another value for γR can be obtained using Equation 16.5. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
(1+ cosθ) γ
L
=W
(16.7)
we see that wetting hysteresis or contact angle hysteresis (θA > θR) actually implies adhesion hysteresis, WR > WA , as given by Equation 16.6. Energy dissipating processes such as adhesion and contact angle hysteresis arise because of practical constraints of the finite time of measurements and the finite elasticity of materials which prevent many loading–unloading or approach–separation cycles from being thermodynamically reversible, even though if these were carried out infinitely slowly they would be reversible. By thermodynamic irreversibility one simply means that one cannot go through the approach–separation cycle via a continuous series of equilibrium states because some of these are connected via spontaneous — and therefore thermodynamically irreversible — instabilities or transitions (Figure 16.4C) where energy is liberated and therefore “lost” via heat or phonon release (Israelachvili and Berman, 1995). This is an area of much current interest and activity, especially regarding the fundamental molecular origins of adhesion and friction, and the relationships between them.
16.5 Rheology of Molecularly Thin Films: Nanorheology 16.5.1 Different Modes of Friction: Limits of Continuum Models Most frictional processes occur with the sliding surfaces becoming damaged in one form or another (Bowden and Tabor, 1967). This may be referred to as “normal” friction. In the case of brittle materials, the damaged surfaces slide past each other while separated by relatively large, micron-sized wear particles. With more ductile surfaces, the damage remains localized to nanometer-sized, plastically deformed asperities. There are also situations where sliding can occur between two perfectly smooth, undamaged surfaces. This may be referred to as “interfacial” sliding or “boundary” friction, and is the focus of the following sections. The term “boundary lubrication” is more commonly used to denote the friction of surfaces that contain a thin protective lubricating layer, such as a surfactant monolayer, but here we shall use this term more broadly to include any molecularly thin solid, liquid, surfactant, or polymer film.
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TABLE 16.1 The Three Main Tribological Regimesa Characterizing the Changing Properties of Liquids Subjected to an Increasing Confinement Between Two Solid Surfacesb Regime
Conditions for Getting into This Regime
Static/Equilibrium Propertiesc
Bulk
• Thick films (>10σ, Rg), • Low or zero loads • High shear rates
Bulk, continuum properties: • Bulk liquid density • No long-range order
Mixed or Intermediate
• Intermediately thick films (4–10 molecular diameters, ~Rg for polymers) • Low loads
Boundary
• Molecularly thin films ( 0 for shear thickening (dilatent) fluids, and n < 0 for shear thinning (pseudoplastic) fluids (the latter become less viscous, i.e., flow more easily, with increasing shear rate, e.g., Figure 16.7B). An additional effect on η can arise from the higher local stresses
FIGURE 16.7 Typical rheological behavior of liquid film in the mixed lubrication regime. (A) Increase in effective viscosity of dodecane film between two mica surfaces with decreasing film thickness (Granick, 1991). Beyond 40 to 50 Å, the effective viscosity ηeff approaches the bulk value ηbulk. (B) Non-Newtonian variation of ηeff with shear rate of a 27 Å thick dodecane film (data from Luengo et al., 1996). The effective viscosity decays as a power law, as in Equation 16.10. In this example, n = 0 at the lowest γ,· then transitions to n = –1 at higher γ.· For bulk thick films, dodecane is a low-viscosity Newtonian fluid (n = 0). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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(pressures) experienced by the liquid film as γ· increases. Since the viscosity is generally also sensitive to the pressure (usually increasing with P), this effect also acts to increase ηeff and thus the friction force. A second effect that occurs at high shear rates is surface deformation, arising from the large hydrodynamic forces acting on the sliding surfaces. For example, Figure 16.6B shows how two surfaces elastically deform when the sliding speed increases to a high value. These deformations alter the hydrodynamic friction forces, and this type of friction is often referred to as elastohydrodynamic lubrication (EHD or EHL) as mentioned in Table 16.1. One natural question is: How thin can a liquid film be before its dynamic, e.g., viscous flow, behavior ceases to be described by bulk properties and continuum models? Concerning the static properties, we have already seen that films composed of simple liquids display continuum behavior down to thicknesses of 5 to 10 molecular diameters. Similar effects have been found to apply to the dynamic properties, such as the viscosity, of simple liquids in thin films. Concerning viscosity measurements, a number of dynamic techniques have been developed (Chan and Horn, 1985; Israelachvili, 1986a; Van Alsten and Granick, 1988; Israelachvili and Kott, 1989) for directly measuring the viscosity as a function of film thickness and shear rate across very thin liquid films between two surfaces. By comparing the results with theoretical predictions of fluid flow in thin films, one can determine the effective positions of the shear planes and the onset of non-Newtonian behavior in very thin films. The results show that for simple liquids, including linear chain molecules such as alkanes, their viscosity in thin films is the same, within 10%, as the bulk even for films as thin as 10 molecular diameters (or segment widths) (Chan and Horn, 1985; Israelachvili, 1986a; Israelachvili and Kott, 1989). This implies that the shear plane is effectively located within one molecular diameter of the solid–liquid interface, and these conclusions were found to remain valid even at the highest shear rates studied (~2 × 105 s–1). With water between two mica or silica surfaces (Chan and Horn, 1985; Israelachvili, 1986a; Horn et al., 1989; Israelachvili and Kott, 1989), this has been found to be the case (to within ±10%) down to surface separations as small as 2 nm, implying that the shear planes must also be within a few Ångstrom of the solid–liquid interfaces. These results appear to be independent of the existence of electrostatic “double layer” or “hydration” forces. For the case of the simple liquid toluene confined between surfaces with adsorbed layers of C60 molecules, this type of viscosity measurement has shown that the traditional noslip assumption for flow at a solid interface does not always hold (Campbell, et al., 1996). For this system, the C60 layer at the mica–toluene interface results in a “full slip” boundary, which dramatically lowers the viscous drag or “effective” viscosity for regular Couette or Poiseuille flow. With polymeric liquids (polymer melts) such as polydimethylsiloxanes (PDMS) and polybutadienes (PBD), or polystyrene (PS) adsorbed onto surfaces from solution, the far-field viscosity is again equal to the bulk value, but with the non-slip plane (hydrodynamic layer thickness) being located at D = 1 to 2 Rg away from each surface (Israelachvili, 1986b; Luengo et al., 1997a), or at D = L for polymer brush layers of thickness L per surface (Klein et al., 1993). In contrast, the same technique was used to show that for nonadsorbing polymers in solution, there is actually a depletion layer of nearly pure solvent that exists at the surfaces that affects the confined solution flow properties (Kuhl et al., 1997). These effects are observed from near contact to surface separations in excess of 200 nm. Further experiments with surfaces closer than a few molecular diameters (D < 20 to 40 Å for simple liquids, or D < 2 to 4 Rg for polymer fluids) indicate that large deviations occur for thinner films, described below. One important conclusion from these studies is that the dynamic properties of simple liquids, including water, near an isolated surface are similar to those of the bulk liquid already within the first layer of molecules adjacent to the surface, only changing when another surface approaches the first. In other words, the viscosity and position of the shear plane near a surface are not simply a property of that surface, but of how far that surface is from another surface. The reason for this is that when two surfaces are close together, the constraining effects on the liquid molecules between them are much more severe than when there is only one surface. Another obvious consequence of the above is that one should not make measurements on a single, isolated solid–liquid interface and then draw conclusions about the state of the liquid or its interactions in a thin film between two surfaces.
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16.5.3 Friction of Intermediate Thickness Films The properties of liquid films between 6 and 10 molecular diameters thick can be significantly different from those of bulk films. But the fluids remain recognizable as fluids; in other words, they do not undergo a phase transition into a solid or liquid-crystalline phase. This regime has been studied by Granick and co-workers (Van Alsten and Granick, 1990a,b, 1991; Granick, 1991; Hu et al., 1991; Hu and Granick, 1992; Klein and Kumacheva, 1995), who used a different type of friction attachment (Van Alsten and Granick, 1988, 1990b) to the SFA where the two surfaces are made to vibrate laterally past each other at small amplitudes. This method provides information on the real and imaginary parts (elastic and dissipative components, respectively) of the shear modulus of thin films at different shear rates and film thickness. Granick (1991) and Hu et al. (1991) found that films of simple liquids become non-Newtonian in the 25 to 50 Å regime (about 10 molecular diameters; see Figure 16.7), whereas polymer melts become non-Newtonian at much thicker films, depending on their molecular weight (Luengo et al., 1997a). Klein and Kumacheva (1998; Kumacheva and Klein, 1998) studied the interaction forces and friction of small quasispherical liquid molecules such as cyclohexane between molecularly smooth mica surfaces. They concluded that surface epitaxial effects can cause the liquid film to solidify at 6 molecular diameters, resulting in a sudden (discontinuous) jump to high friction at low shear rates. Such “dynamic” firstorder transitions, however, may depend on the shear rate. A generalized friction map (Figure 16.8) has been proposed by Luengo et al. (1996) that illustrates the changes in ηeff from bulk Newtonian behavior (n = 0, ηeff = ηbulk) through the transition regime where n reaches a minimum of -1 with decreasing shear rate, to the solid-like creep regime at very low γ· where n returns to 0. The data in Figure 16.9 show the transition for thicker polymer films from bulk behavior to the tribological regime where n reaches –1 (Luengo et al., 1997a). With further decreasing shear rates the exponent n increases from –1 to 0, as illustrated in Figure 16.7B for a dodecane system. A number
FIGURE 16.8 Proposed generalized friction map of effective viscosity plotted against effective shear rate on a loglog scale (data from Luengo et al., 1996). Three main classes of behavior emerge: (1) Thick films; elastohydrodynamic sliding. At zero load (L = 0), approximating bulk conditions, ηeff is independent of shear rate except when shearthinning may occur at sufficiently large γ.· (2) Boundary layer films, intermediate regime. A Newtonian regime is again observed (ηeff = constant, n = 0 in Equation 16.10) at low loads and low shear rates, but ηeff is much higher than the bulk value. As the shear rate γ· increases beyond γ·min, the effective viscosity starts to drop with a power-law dependence on the shear rate (see Figure 16.7B), with n in the range of –1/2 to –1 most commonly observed. As the shear rate γ· increases still more, beyond γ·max, a second Newtonian plateau is again encountered. (3) Boundary layer films, high load. The ηeff continues to grow with load and to be Newtonian provided that the shear rate is sufficiently low. Transition to sliding at high velocity is discontinuous (n < –1) and usually of the stick-slip variety. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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FIGURE 16.9 Effective viscosity plotted against effective shear rate on log-log scales for polybutadiene (MW = 7000) at four different separations, D (adapted from Luengo et al., 1997a). Open data points were obtained from sinusoidally applied shear at zero load (L = 0) at the indicated separations. Solid points were obtained from friction experiments at constant sliding velocities. These tribological results extrapolate, at high shear rate, to the bulk viscosity. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
of results from experimental, theoretical, and computer simulation work have shown values of n from –1/2 to –1 for this transition regime for a variety of systems and assumptions (Hu and Granick, 1991; Granick, 1991; Thompson et al., 1992; Thompson et al., 1995; Urbakh et al., 1995; Rabin and Hersht, 1993). The intermediate regime appears to extend over a narrow range of film thickness, from about 4 to 10 molecular diameters or polymer radii of gyration. Thinner films begin to adopt “boundary” or “interfacial” friction properties (described below; see also Table 16.1). Note that the intermediate regime is actually a very narrow one when defined in terms of film thickness, for example, varying from about D = 20 to 40 Å for hexadecane films (Granick, 1991). A fluid’s effective viscosity ηeff in the intermediate regime is usually higher than in the bulk, but ηeff usually decreases with increasing sliding velocity, v (known as shear thinning). When two surfaces slide in the intermediate regime, the motion tends to thicken the film (dilatency). This sends the system into the bulk EHL regime where, as indicated by Equation 16.8, the friction force now increases with velocity. This initial decrease, followed by an increase, in the frictional forces of many lubricant systems is the basis for the empirical Stribeck Curve of Figure 16.6A. In the transition from bulk to boundary behavior there is first a quantitative change in the material properties (viscosity and elasticity) which can be continuous, then discontinuous qualitative changes which result in yield stresses and non-liquid-like behavior. The rest of this chapter is devoted to friction in the interfacial and boundary regimes. The former (interfacial friction) may be thought of as applying to the sliding of two dry, unlubricated surfaces in true molecular contact. The latter (boundary friction) may be thought of as applying to the case where a lubricant film is present, but where this film is of molecular dimensions — a few molecular layers or less.
16.6 Interfacial and Boundary Friction: Molecular Tribology 16.6.1 General Interfacial Friction When a lateral force, or shear stress, is applied to two surfaces in adhesive contact, the surfaces initially remain “pinned” to each other until some critical shear force is reached. At this point, the surfaces begin
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to slide past each other either smoothly or in jerks. The frictional force needed to initiate sliding from rest is known as the static friction force, denoted by Fs , while the force needed to maintain smooth sliding is referred to as the kinetic or dynamic friction force, denoted by Fk . In general, Fs > Fk . Two sliding surfaces may also move in regular jerks, known as “stick-slip” sliding, which is discussed in more detail in Section 16.9. Note that such friction forces cannot be described by equations, such as Equation 16.10, used for thick films that are viscous and therefore shear as soon as the smallest shear force is applied. Experimentally, it has been found that during both smooth and stick-slip sliding the local geometry of the contact zone remains largely unchanged from the static geometry, and that the contact area vs. load is still well described by the JKR equation, Equation 16.4. The friction force of two molecularly smooth surfaces sliding while in adhesive contact with each other is not simply proportional to the applied load, L, as might be expected from Amontons’ Law. There is an additional adhesion contribution that is proportional to the area of contact, A, which is described later. Thus, in general, the interfacial friction force of dry, unlubricated surfaces sliding smoothly past each other is given by
F = Fk = Sc A + µL
(16.11)
where Sc is the “critical shear stress” (assumed to be constant), A = πr2 is the contact area of radius r given by Equation 16.4, and µ is the coefficient of friction. For low loads we have:
R 2 F = Sc A = Sc πr = Sc π L + 6 πRγ + 12πRγL + 6 πRγ K
(
2
)
2 3
(16.12)
while for high loads, Equation 16.11 reduces to Amontons’ law:
F = µL
(16.13)
Depending on whether the friction force, F, in Equation 16.11 is dominated by the first or second terms, one may refer to the friction as “adhesion-controlled” or “load-controlled,” respectively. Figure 16.10 shows a plot of contact area, A, and friction force, F, both plotted against the applied load, L, in an experiment where two molecularly smooth surfaces of mica in adhesive contact were slid past each other in an atmosphere of dry nitrogen gas. This is an example of the low load, adhesioncontrolled limit, which is excellently described by Equation 16.12. In a number of different experiments, Sc was measured to be 2.5 × 107 N/m2, and to be independent of the sliding velocity. Note that there is a friction force even at negative loads, where the surfaces are still sliding in adhesive contact.
16.6.2 Boundary Friction of Surfactant Monolayer Coated Surfaces The high friction force of unlubricated sliding can often be reduced by treating the solid surface with a “boundary layer” of some other solid material that exhibits lower friction, such as a surfactant monolayer, or by ensuring that during sliding, a thin liquid film remains between the surfaces. The effectiveness of a solid boundary lubricant layer on reducing the forces of friction is illustrated in Figure 16.11. Comparing this with the friction of the unlubricated/untreated surfaces (Figure 16.10) shows that the critical shear stress has been reduced by a factor of about 10: from 2.5 × 107 to 3.5 × 106 N/m2. At much higher applied loads or pressures, the friction force is proportional to the load rather than the area of contact (Briscoe et al., 1977), as expected from Equation 16.11. Yamada and Israelachvili (1998) studied the adhesion and friction of fluorocarbon surfaces (surfactantcoated boundary lubricant layers), which were compared to those of hydrocarbon surfaces. They concluded that well-ordered fluorocarbon surfaces have a high friction, in spite of their lower adhesion energy (in agreement with previous findings). The low friction coefficient of PTFE (Teflon®) must
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FIGURE 16.10 Friction force F and contact area A vs. load L for two mica surfaces sliding in adhesive contact in dry air. The contact area is well described by the JKR theory, Equation 16.4, even during sliding, and the frictional force is found to be directly proportional this area, Equation 16.12. The vertical dashed line and arrow show the transition from “interfacial” to “normal” friction with the onset of wear (lower curve). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
FIGURE 16.11 Sliding of mica surfaces each coated with a 25 Å thick monolayer of calcium stearate surfactant in the absence of damage (obeying JKR type boundary friction) and in the presence of damage (obeying Amontons’ type “normal” friction) (data from Homola et al., 1989, 1990). At much higher applied loads the undamaged surfaces also follow Amontons’ type sliding, but for different reasons. Lower line: interfacial sliding with a monolayer of water between the mica surfaces, shown for comparison. Note that in both cases, after damage occurs, the friction force obeys Amontons’ law with the same coefficient of friction of µ ≈ 0.3. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
therefore be due to some effect other than a low adhesion, for example, the softness of PTFE which allows material to flow at the interface, behaving like a fluid lubricant. On a related issue, Luengo et al. (1997b) found that C60 surfaces also exhibited low adhesion but high friction. In both cases the high friction appears to arise from the bulky surface groups — fluorocarbon compared to hydrocarbon groups in the former, large fullerene spheres in the latter. Apparently, the fact that C60 molecules rotate in their lattice does not make them a good lubricant: the molecules of the opposing surface must still climb over them in order to move, and this requires energy which is independent of whether the surface molecules are fixed or freely rotating. Larger particles, such as ~25 nm sized nanoparticles (also known as “inorganic
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FIGURE 16.12 Two mica surfaces sliding past each other while immersed in a 0.01 M KCl salt solution. In both cases the water film is molecularly thin: 2.5 to 5.0 Å thick, and the interfacial friction force is very low: Sc ≈ 5 × 105 N/m2, µ ≈ 0.015 (before damage occurs). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
fullerenes”) do appear to produce low friction by behaving like molecular ball bearings, but the potential of this promising new class of solid lubricant has still to be explored (Rapoport et al., 1997).
16.6.3 Boundary Lubrication of Molecularly Thin Liquid Films A liquid lubricant film is usually much more effective at lowering the friction of two surfaces than a solid boundary lubricant layer. However, to successfully use a liquid lubricant, it must “wet” the surfaces; that is, it should have a high affinity for the surfaces so that the liquid molecules do not become squeezed out when the surfaces come close together, even under a large compressive load. Another important requirement is that the liquid film remains a liquid under tribological conditions, i.e., that it does not epitaxially solidify between the surfaces. Effective lubrication usually requires that the lubricant be injected between the surfaces, but in some cases the liquid can be made to condense from the vapor. Both of these effects are illustrated in Figure 16.12 for two untreated mica surfaces sliding with a thin layer of water between them. We may note that a monomolecular film of water (of thickness 2.5 Å per surface) has reduced Sc by a factor of more than 30, which may be compared with the factor of 10 attained with the boundary lubricant layer (of thickness 25 Å per surface). The effectiveness of a water film only 2.5 Å thick to lower the friction force by more than an order of magnitude is attributed to the “hydrophilicity” of the mica surface (mica is “wetted” by water) and to the existence of a strongly repulsive short-range hydration force between such surfaces in aqueous solutions which effectively removes the adhesion-controlled contribution to the friction force (Berman et al., 1998a). It is also interesting that a 2.5 Å thick water film between two mica surfaces is sufficient to bring the coefficient of friction down to between 0.01 and 0.02, a value that corresponds to the unusually low friction of ice. Clearly, a single monolayer of water can be a very good lubricant — much better than most other monomolecular liquid films, for reasons that will be discussed below.
16.6.4 Transition from Interfacial to Normal Friction (with Wear) Frictional damage can have many causes such as adhesive tearing at high loads or overheating at high sliding speeds. Once damage occurs, there is a transition from “interfacial” to “normal” or load-controlled friction as the surfaces become forced apart by the torn-out asperities (wear particles). For low loads, the friction changes from obeying F = ScA to obeying Amontons’ law: F = µL, as shown in Figures 16.10 to
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FIGURE 16.13 Friction forces as a function of load for smooth (undamaged) and rough (damaged) surfaces (data from Berman et al., 1998b). Untreated alumina surfaces (curve a) exhibit the lowest friction due to a thin physisorbed layer of lubricating contaminants, but these are easily damaged upon sliding, resulting in rough surface (curve b) with a higher friction. Monolayer coated surfaces (curve c) slide with higher friction at lower loads than untreated alumina, but remain undamaged even after prolonged sliding, keeping the friction and wear substantially lower than rough surfaces at high loads. Smooth sliding was “adhesion controlled,” i.e., the contact area A is well described by the JKR equation (Equation 16.4), and F/A = constant (Equation 16.12). In addition, F is finite at L = 0. Rough, damaged sliding was “load controlled,” i.e., the “real” contact area is undefined, and F ∝ L (Equation 16.13) with F ≈ 0 at L = 0. Experimental conditions: sliding velocity V = 0.05 to 0.5 µm/s; undeformed radius of curved surfaces, R ≈ 1 cm; temperature T = 25°C; contact pressure range, P = 0 to 10 MPa; relative humidity, RH = 0% (curves a and c), RH = 0% and 100% (curve b). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
16.13, and sliding now proceeds smoothly with the surfaces separated by a 100 to 1000 Å forest of wear debris (mica or alumina flakes in this case). The wear particles keep the surfaces apart over an area that is much greater than their size, so that even one submicroscopic particle or asperity can cause a significant reduction in the area of contact and therefore in the friction (Homola et al., 1990). For this type of frictional sliding, one can no longer talk of the molecular contact area of the two surfaces, although the macroscopic or “apparent” area is still a useful parameter. A further discussion on the impact of normal load and contact area is found in Section 16.7.4. One remarkable feature of the transition from interfacial to normal friction of brittle surfaces is that while the strength of interfacial friction, as reflected in the values of Sc, is very dependent on the type of surface and on the liquid film between the surfaces, this is not the case once the transition to normal friction has occurred. At the onset of damage, it is the material properties of the underlying substrates that control the friction. In Figures 16.10 to 16.12 the friction for the damaged surfaces is that of any damaged mica–mica system, while in Figure 16.13 the damaged surfaces friction is that of general alumina–alumina sliding (with a friction coefficient that agrees with literature values for the bulk materials), independent of the initial surface coatings or liquid films between the surfaces. In order to practically modify the frictional behavior of such brittle materials, it is important to use coatings that will both alter the interfacial tribological character and remain intact and protect the surfaces from damage during sliding (Berman et al., 1998b). An example of the friction behavior of a strongly bound octadecyl phosphonic acid monolayer on alumina surfaces is shown in Figure 16.13. In this case, the friction is higher than untreated, undamaged α-alumina surfaces, but the bare surfaces easily damage upon sliding, resulting in an ultimately higher friction system with greater wear rates than the more robust monolayer-coated surfaces.
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Clearly, the mechanism and factors that determine normal friction are quite different from those that govern interfacial friction. These mechanisms are described in the theoretical section below, but one should point out that this effect is not general and may only apply to brittle materials. For example, the friction of ductile surfaces is totally different and involves the continuous plastic deformation of contacting surface asperities during sliding rather than the rolling of two surfaces on hard wear particles (Bowden and Tabor, 1967). Furthermore, in the case of ductile surfaces, water and other surface-active components do have an effect on the friction coefficients under “normal” sliding conditions.
16.7 Theories of Interfacial Friction 16.7.1 Theoretical Modeling of Interfacial Friction: Molecular Tribology The following friction model, first proposed by Tabor (1982) and developed further by Sutcliffe et al. (1978), McClelland (1989), and Homola et al. (1989), has been quite successful at explaining the interfacial and boundary friction of two solid crystalline surfaces sliding past each other in the absence of wear. The surfaces may be unlubricated, or they may be separated by a monolayer or more of some boundary lubricant or liquid molecules. In this model, the values of the critical shear stress Sc , and coefficient of friction µ, of Equation 16.11 are calculated in terms of the energy needed to overcome the attractive intermolecular forces and compressive externally applied load as one surface is raised and then slid across the molecular-sized asperities of the other. This model (variously referred to as the interlocking asperity model, Coulomb friction, or the cobblestone model) is akin to pushing a cart over a road of cobblestones where the cart wheels (which represent the molecules of the upper surface or film) must be made to roll over the cobblestones (representing the molecules of the lower surface) before the cart can move. In the case of the cart, the downward force of gravity replaces the attractive intermolecular forces between two material surfaces. When at rest the cartwheels find grooves between the cobblestones where they sit in potential energy minima and so the cart is at some stable mechanical equilibrium. A certain lateral force (the “push”) is required to raise the cart wheels against the force of gravity in order to initiate motion. Motion will continue as long as the cart is pushed, and rapidly stops once it is no longer pushed. Energy is dissipated by the liberation of heat (phonons, acoustic waves, etc.) every time a wheel hits the next cobblestone. The cobblestone model is not unlike the old Coulomb and interlocking asperity models of friction (Dowson, 1979) except that it is being applied at the molecular level and the external load is augmented by attractive intermolecular forces. There are thus two contributions to the force pulling two surfaces together: the externally applied load or pressure, and the (internal) attractive intermolecular forces which determine the adhesion between the two surfaces. Each of these contributions affects the friction force in a different way, and we start by considering the role of the internal adhesion forces.
16.7.2 Adhesion Force Contribution to Interfacial Friction Consider the case of two surfaces sliding past each other as shown in Figure 16.14. When the two surfaces are initially in adhesive contact the surface molecules will adjust themselves to fit snugly together, in a manner analogous to the self-positioning of the cart wheels on the cobblestone road. A small tangential force applied to one surface will therefore not result in the sliding of that surface relative to the other. The attractive van der Waals forces between the surfaces must first be overcome by having the surfaces separate by a small amount. To initiate motion, let the separation between the two surfaces increase by a small amount ∆D, while the lateral distance moved is ∆d. These two values will be related via the geometry of the two surface lattices. The energy put into the system by the force F acting over a lateral distance ∆d is
Input energy: F × ∆d
(16.14)
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L ∆d
F
∆D
Impact
D0
FIGURE 16.14 Schematic illustration of how one molecularly smooth surface moves over another when a lateral force F is applied. As the upper surface moves laterally by some fraction of the lattice dimension ∆d, it must also move up by some fraction of an atomic or molecular dimension ∆D, before it can slide across the lower surface. On impact, some fraction ε of the kinetic energy is “transmitted” to the lower surface, the rest being “reflected” back to the colliding molecule (upper surface). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
This energy may be equated with the change in interfacial or surface energy associated with separating the surfaces by ∆D, i.e., from the equilibrium separation D = D0 to D = (D0 + ∆D). Since γ ∝ D–2, the surface energy cost may be approximated by
Surface energy change: 2γA 1 − D20
(D
0
)
(
2 + ∆D ≈ 4 γA ∆D D0
)
(16.15)
where γ is the surface energy, A the contact area, and where D0 is the surface separation at equilibrium. During steady-state sliding (kinetic friction), not all of this energy will be “lost” or absorbed by the lattice every time the surface molecules move by one lattice spacing: some fraction will be reflected during each impact of the “cart wheel” molecules (McClelland, 1989). Assuming that a fraction ε of the above surface energy is lost every time the surfaces move across the characteristic length ∆d (Figure 16.14), we obtain, after equating the above two equations,
Sc =
F 4 γε ⋅ ∆D = A D0 ⋅ ∆d
(16.16)
For a typical hydrocarbon or a van der Waals surface, γ ≈ 25 × 10–3 J/m2. Other typical values would be: ∆D ≈ 0.5 Å, D0 ≈ 2 Å, ∆d ≈ 1 Å, and ε ≈ 0.1 to 0.5. Using the above parameters, Equation 16.16 predicts
(
)
Sc ≈ 2.5 − 12.5 × 107 N m2
for van der Waals surfaces
This range of values compares very well with typical experimental values of 2 × 107 N/m2 for hydrocarbon or mica surfaces sliding in air or separated by one molecular layer of cyclohexane (Homola et al., 1989). The above model suggests that all interfaces, whether dry or lubricated, dilate just before they shear or slip. This is a small but important effect: the dilation provides the crucial extra space needed for the molecules to slide across each other or flow. This dilation has been measured by Granick et al. (1999) and computed by Robbins and Thompson (1991). This model may be extended, at least semiquantitatively, to lubricated sliding, where a thin liquid film is present between the surfaces. With an increase in the number of liquid layers between the surfaces, D0
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increases while ∆D decreases, hence a lower friction force. This is precisely what is observed. But with more than one liquid layer between two surfaces the situation becomes too complex to analyze analytically. (Actually, even with one or no interfacial layers, the calculation of the fraction of energy dissipated per molecular collision ε is not a simple matter.) Sophisticated modeling based on computer simulations is now required, as described in the following section.
16.7.3 Relation Between Boundary Friction and Adhesion Energy Hysteresis While the above equations suggest that there is a direct correlation between friction and adhesion, this is not the case. The correlation is really between friction and adhesion hysteresis, described in Section 16.4. In the case of friction, this subtle point is hidden in the factor ε, which is a measure of the amount of energy absorbed (dissipated, transferred, or “lost”) by the lower surfaces when it is impacted by a molecule from the upper surface. If ε = 0, all the energy is reflected and there will be no kinetic friction force, nor any adhesion hysteresis, but the absolute magnitude of the adhesion force or energy would remain finite and unchanged. This is illustrated in Figure 16.15. The following simple model shows how adhesion hysteresis and friction may be quantitatively related. Let ∆γ = (γR – γA) be the adhesion energy hysteresis per unit area, as measured during a typical loading–unloading cycle (see Figure 16.15C, D). Now consider the same two surfaces sliding past each other
FIGURE 16.15 Top: Friction traces (data from Chen et al., 1991) for two fluid-like monolayer-coated surfaces at 25°C showing that the friction force is much higher between dry monolayers (A) than between monolayers whose fluidity has been enhanced by hydrocarbon penetration from vapor (B). Bottom: Contact radius vs. load (r 3 – L) curves measured for the same two surfaces as above and fitted to the JKR Equation 16.4 — shown by the solid lines. For dry monolayers (C) the adhesion energy on unloading (γR = 40 mJ/m2) is greater than that on loading (γA = 28 mJ/m2), indicative of an adhesion energy hysteresis of ∆γ = γR – γA = 12 mJ/m2. For monolayers exposed to saturated decane vapor (D) their adhesion hysteresis is zero (γA = γR), and both the loading and unloading curves are wellfitted by the thermodynamic value of the surface energy of fluid hydrocarbon chains, γ ≈ 24 mJ/m2. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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and assume that frictional energy dissipation occurs through the same mechanism as adhesion energy dissipation, and that both occur over the same characteristic molecular length scale σ. Thus, when the two surfaces (of contact area A = πr2) move a distance σ, equating the frictional energy (F × σ) to the dissipated adhesion energy (A × ∆γ), we obtain
Friction force: F =
A ∆γ πr 2 γ −γA = σ σ R
(
)
(16.17)
or
Friction stress: Sc = F A = ∆γ σ
(16.18)
which is the desired expression and which has been found to give order of magnitude agreement between measured friction forces and adhesion energy hysteresis (Chen et al., 1989). If we equate Equation 16.18 with Equation 16.16, since 4∆D/D0∆d ≈ σ, we obtain the intuitive relation
ε≈
∆γ γ
(16.19)
Figure 16.15 illustrates the relationship between adhesion hysteresis and friction for surfactant-coated surfaces under different conditions. This effect, however, is much more general, and has been shown to hold for other surfaces as well (Vigil et al., 1994; Israelachvili et al., 1994, 1995). Direct comparisons between absolute adhesion energies and friction forces show little correlation. In some cases higher adhesion energies for the same system under different conditions correspond with lower friction forces. For example, for hydrophilic silica surfaces it was found that with increasing relative humidity the adhesion energy increases, but the adhesion energy hysteresis measured in a loading–unloading cycle decreases, as does the friction force (Vigil et al., 1994). For hydrophobic silica surfaces under dry conditions, the friction at load L = 5.5 mN was F = 75 mN. For the same sample, the adhesion energy hysteresis was ∆γ = 10 mJ/m2, with a contact area of A ≈ 10–8 m2 at the same load. Assuming a value for the characteristic distance σ on the order of one lattice spacing, σ ≈ 1 nm. Inserting these values into Equation 16.17, the friction force is predicted to be F ≈ 100 mN for the kinetic friction force, which is close to the measured value of 75 mN. Alternatively, we may conclude that the dissipation factor is ε = 0.75, i.e., that almost all the energy is dissipated as heat at each molecular collision.
16.7.4 External Load Contribution to Interfacial Friction When there is no interfacial adhesion Sc is zero. Thus, in the absence of any adhesive forces between two surfaces, the only “attractive” force that needs to be overcome for sliding to occur is the externally applied load or pressure. For a preliminary discussion of this question, it is instructive to compare the magnitudes of the externally applied pressure to the internal van der Waals pressure between two smooth surfaces. The internal van der Waals pressure is given by P = A/6πD03 ≈ 104 atm (using a typical Hamaker constant of A = 10–12 erg, and assuming D0 ≈ 2 Å for the equilibrium interatomic spacing). This implies that we should not expect the externally applied load to affect the interfacial friction force F, as defined by Equation 16.11, until the externally applied pressure L/A begins to exceed ~1000 atm. This is in agreement with experimental data (Briscoe et al., 1977) where the effect of load became dominant at pressures in excess of 1000 atm. For a more general semiquantitative analysis, again consider the cobblestone model as used to derive Equation 16.16, but now include an additional contribution to the surface energy change of Equation 16.15 due to the work done against the external load or pressure, L∆D = PextA·∆D. (This is equivalent to the work done against gravity in the case of a cart being pushed over cobblestones.)
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Thus:
Sc =
F 4 γε ⋅ ∆D Pext ε ⋅ ∆D = + ∆d A D0 ⋅ ∆d
(16.20)
which gives the more general relation
Sc = F A = C1 + C 2Pext
(16.21)
where Pext = L/A, and where C1 and C2 are constants characteristic of the surfaces and sliding conditions. The constant C1 = (4γε·∆D/D0 ·∆d) depends on the mutual adhesion of the two surfaces, while both C1 and C2 = ε·∆D/∆d depend on the topography or atomic bumpiness of the surface groups (Figure 16.14) — the smoother the surface groups, the smaller the ratio ∆D/∆d and hence the lower the value of C2. In addition, both C1 and C2 depend on ε — the fraction of energy dissipated per collision which depends on the relative masses of the shearing molecules, the sliding velocity, the temperature, and the characteristic molecular relaxation processes of the surfaces. This is by far the most difficult parameter to compute, and yet it is the most important since it represents the energy transfer mechanism in any friction process, and since ε can vary between 0 and 1, it determines whether a particular friction force will be large or close to zero. Molecular simulations offer the best way to understand and predict the magnitude of ε, but the complex multibody nature of the problem makes simple conclusions difficult to draw. Some of the basic physics of the energy transfer and dissipation of the molecular collisions can be drawn from simplified models (Urbakh et al., 1995; Rozman et al., 1996, 1997) such as a one-dimensional three-body system (Israelachvili and Berman, 1995). This system, described in more detail in Section 16.7.5, offers insight into the mechanisms of energy transfer and relates them back to the familiar parameter De, the Deborah number. Finally, the above equation may also be expressed in terms of the friction force F:
F = Sc A = C1A + C 2L
(16.22)
Equations similar to Equations 16.21 and 16.22 were previously derived by Derjaguin (1988, 1934) and by Briscoe and Evans (1982), where the constants C1 and C2 were interpreted somewhat differently than in this model. In the absence of any attractive interfacial force, we have C1 ≈ 0, and the second term in Equations 16.21 and 16.22 should dominate. Such situations typically arise when surfaces repel each other across the lubricating liquid film, for example, when two mica surfaces slide across a thin film of water (Figure 16.11). In such cases the total frictional force should be low, and it should increase linearly with the external load according to
F = C 2L
(16.23)
An example of such lubricated sliding occurs when two mica surfaces slide in water or in salt solution, where the short-range “hydration” forces between the surfaces are repulsive. Thus, for sliding in 0.5 M KCl it was found that C2 = 0.015 (Berman et al., 1998a). Another case where repulsive surfaces eliminate the adhesive contribution to friction is for tethered polymer chains attached to surfaces at one end and swollen by a good solvent (Klein et al., 1994). For this class of systems C2 < 0.001 for a finite range of polymer layer compressions (normal loads, L). The low friction between the surfaces in this regime is attributed to the entropic repulsion between the opposing brush layers with a minimum of entanglement between the two layers. However, with higher normal loads, the brush layers become compressed and begin to entangle, resulting in higher friction.
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It is important to note that Equation 16.23 has exactly the same form as Amontons’ law
F = µL
(16.24)
where µ is the coefficient of friction. When damage occurs, there is a rapid transition to “normal” sliding in the presence of wear debris. As previously described, the mechanisms of interfacial friction and normal friction are vastly different on the submicroscopic and molecular levels. However, under certain circumstances both may appear to follow a similar equation (see Equations 16.23 and 16.24) even though the friction coefficients C2 and µ are determined by quite different material properties in each case. At the molecular level, a thermodynamic analog of the Coulomb or cobblestone models (see Section 16.7.1) based on the contact value theorem (Berman et al., 1998a; Berman and Israelachvili, 1997; Israelachvili, 1991) can explain why F ∝ L also holds at the microscopic or molecular level. In this analysis we consider the surface molecular groups as being momentarily compressed and decompressed as the surfaces move along. Under irreversible conditions, which always occur when a cycle is completed in a finite amount of time, the energy lost in the compression/decompression cycle is dissipated as heat. For two nonadhering surfaces, the stabilizing pressure Pi acting locally between any two elemental contact points i of the surfaces may be expressed by the contact value theorem (Israelachvili, 1991):
Pi = ρi k B T = k B T Vi
(16.25)
where ρi = 1/Vi is the local number density (per unit volume) or activity of the interacting entities, be they molecules, atoms, ions, or the electron clouds of atoms. This equation is essentially the osmotic or entropic pressure of a gas of confined molecules. As one surface moves across the other, as local regions become compressed and decompressed by a volume ∆Vi, the work done per cycle can be written as ε Pi ∆Vi where ε (ε ≤ 1) is the fraction of energy per cycle lost as heat, as defined earlier. The energy balance shows that for each compression/decompression cycle, the dissipated energy is related to the friction force by
Fi x i = ε Pi ∆Vi
(16.26)
where xi is the lateral distance moved per cycle, which can be the distance between asperities or the distance between surface lattice sites. The pressure at each contact junction can be expressed in terms of the local normal load Li and local area of contact Ai as Pi = Li /Ai . The volume change over a cycle can thus be expressed as ∆Vi = Aizi, where zi is the vertical distance of confinement. Plugging these back into Equation 16.26, we get
(
Fi = ε Li z i x i
)
(16.27)
which is independent of the local contact area Ai . The total friction force is thus
(
) (
)
F = Σ Fi = Σ ε Li z i x i = ε z i x i Σ Li = µ L
(16.28)
where it is assumed that on average, the local values of Li and Pi are independent of the local “slope” zi /xi . Therefore, the friction coefficient µ is a function only of the average surface topography and the sliding velocity, but is independent of the local (real) or macroscopic (apparent) contact areas. While this analysis explains nonadhering surfaces, there is still an additional explicit contact area contribution for the case of adhering surfaces, as in Equation 16.22. The distinction between the two cases arises because the initial assumption of the contact value theorem, Equation 16.25, is incomplete
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A
m1
k1
m2
k2
593
m3
v0 Interaction Energy
Energy transferred from mass 1
B
1
C
0.8 0.6 0.4 0.2 0 0.01
0.1
1
10
100
Deborah Number, De (System relaxation time/ Collision time)
FIGURE 16.16 (a) Schematic diagram of a basic three-body collision. Mass 1 approaches the other masses with an initial velocity, v0. The kinetic energy of mass 1 after the collision is compared to its initial kinetic energy. The characteristic times of the m1–m2 and m2–m3 interactions are functions of the respective masses and the strengths of the connecting springs k1 and k2 (b). The Deborah number for this system is the ratio of the collision time between masses 1 and 2 to the harmonic oscillating frequency of masses 2 and 3. (c) The energy transferred from mass 1 to the rest of the system (masses 2 and 3) is plotted as a function of the Deborah number. In this calculation k1 = 1, k2 = 10, m1 = 1, and masses m2 = m3 were varied. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
for adhering systems. A more appropriate starting equation would reflect the full intermolecular interaction potential, including the attractive interactions in addition to the purely repulsive contributions of Equation 16.25, much as the van der Waals equation of state modifies the ideal gas law.
16.7.5 Simple Molecular Model of Energy Dissipation ε The simple three-body system of balls and springs illustrated in Figure 16.16a provides molecular insight into dissipative processes such as sliding friction and adhesion hysteresis. Mass m1 may be considered to constitute one body or surface that approaches another at velocity v0 . Masses m2 and m3 represent the other surface. As shown in Figure 16.16b, the masses of the second surface are bound together via a parabolic (Hookian spring) potential, while masses m1 and m2 interact via a nonadhesive repulsion modeled as a half-parabola. Although this system is simple in appearance, it is rich in physics. Different relative values of the masses and spring constants lead to very different collision outcomes where the initial translational or kinetic energy of m1 is distributed among the final kinetic, translational, and vibrational energies of m1 and the m2–m3 couple. The collision is a molecular analogy, and perhaps a good microscopic representation of an adhesive loading–unloading cycle (see Figure 16.4) or a frictional sliding process. The finer molecular model of Figure 16.16a allows us to determine exactly how the energy is being dissipated in these cycles. In a
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loading–unloading process, m1 represents the surface molecules of one body approaching the surface molecules of a second body (m2 and m3). Solutions to the equations of motion show that in the collision the first mass can be reflected, stopped, or even continue forward at a different velocity. In the case of lateral sliding, the molecules of the two surfaces can still be considered to interact in this way; the surface groups from the slider continually collide with those of the opposing surface, with the amount of the energy transferred during the collisions defining the friction. Analysis of this problem shows that the essential determinant of the amount of energy transferred from m1 is based on the ratio of the collision time to the characteristic relaxation time of the system, in other words, to the Deborah number
De = Relaxation time Measuring time
(16.29)
Thus, it is found that m1 loses most of its energy to the m2–m3 couple when the collision time is close to the characteristic vibration time of the m2–m3 harmonic system, which corresponds to De = 1. When the collision time is much larger or smaller than the system characteristic time, mass m1 is found to retain most of its original kinetic energy (Figure 16.16c). In this simple example the interaction times are functions only of the three masses, the intermolecular potential between m1 and m2, and the potential or spring constant of the m2–m3 couple. In more complex systems with more realistic interaction potentials (i.e., attractive interactions between m1 and m2), the velocity v0 becomes an important factor as well, and also affects the Deborah number. It is important to note that in this simple one-dimensional analysis, additional energy modes and degrees of freedom of the molecules have not been considered. These modes, when present, will also be involved in the interaction, affecting the energy transferred from m1 and sharing in the final distribution of the energy transferred. In addition, different types of energy modes (e.g., rotational modes) will generally have different relaxation times, so that their energy peaks will occur at different measuring times. Such real systems may be considered to have more than one Deborah number. The three-body system sheds some light on the molecular mechanisms of energy dissipation and the impact of the Deborah number on the dissipation parameter ε, but because of its simplicity, does not offer predictive capabilities for real systems. More sophisticated models have been presented by Urbakh et al. (1995) and Rozman et al. (1996, 1997).
16.8 Friction and Lubrication of Thin Liquid Films When a liquid is confined between two surfaces or within any narrow space whose dimensions are less than 5 to 10 molecular diameters, both the static (equilibrium) and dynamic properties of the liquid, such as its compressibility and viscosity, can no longer be described even qualitatively in terms of the bulk properties. The molecules confined within such molecularly thin films become ordered into layers (“out-of-plane” ordering), and within each layer they can also have lateral order (“in-plane” ordering). Such films may be thought of as behaving more like a liquid crystal or a solid than a liquid. As described in Section 16.2, the measured normal forces between two solid surfaces across molecularly thin films exhibit exponentially decaying oscillations, varying between attraction and repulsion with a periodicity equal to some molecular dimension of the solvent molecules. Thus, most liquid films can sustain a finite normal stress, and the adhesion force between two surfaces across such films is “quantized,” depending on the thickness (or number of liquid layers) between the surfaces. The structuring of molecules in thin films and the oscillatory forces it gives rise to are now reasonably well understood, both experimentally and theoretically, at least for simple liquids. Work has also recently been done on the dynamic, e.g., viscous or shear, forces associated with molecularly thin films. Experiments (Israelachvili et al., 1988; Gee et al., 1990; Hirz et al., 1992; Homola et al., 1991) and theory (Schoen et al., 1989; Thompson and Robbins, 1990; Thompson et al., 1992) indicate that even when two surfaces are in steady-state sliding they still prefer to remain in one of their stable potential energy minima, i.e., a sheared film of liquid can retain its basic layered structure. Thus,
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even during motion the film does not become totally liquid-like. Indeed, if there is some “in-plane” ordering within a film, it will exhibit a yield-point before it begins to flow. Such films can therefore sustain a finite shear stress, in addition to a finite normal stress. The value of the yield stress depends on the number of layers comprising the film and represents another “quantized” property of molecularly thin films. The dynamic properties of a liquid film undergoing shear are very complex. Depending on whether the film is more liquid-like or solid-like, the motion will be smooth or of the stick-slip type. During sliding, transitions can occur between n layers and (n – 1) or (n + 1) layers, and the details of the motion depend critically on the externally applied load, the temperature, the sliding velocity, the twist angle between the two surface lattices and the sliding direction relative to the lattices.
16.8.1 Smooth and Stick-Slip Sliding Recent advances in friction-measuring techniques have enabled the interfacial friction of molecularly thin films to be measured with great accuracy. Some of these advances have involved the surface forces apparatus technique (Israelachvili et al., 1988; Gee et al., 1990; Hirz et al., 1992; Homola et al., 1989, 1990, 1991), while others have involved the atomic force microscope (McClelland, 1989; McClelland and Cohen, 1990). In addition, molecular dynamics computer simulations (Schoen et al., 1989; Landman et al., 1990; Thompson and Robbins, 1990; Robbins and Thompson, 1991) have become sufficiently sophisticated to enable fairly complex tribological systems to be studied for the first time. All these advances are necessary if one is to probe such subtle effects as smooth or stick-slip friction, transient and memory effects, and ultra-low friction mechanisms at the molecular level. Figure 16.17 shows typical results for the friction traces measured as a function of time (after commencement of sliding) between two molecularly smooth mica surfaces separated by three molecular layers of the liquid OMCTS, and how the friction increases to higher values in a quantized way when the number of layers falls from n = 3 to n = 2 and then to n = 1. With the much added insights provided by recent computer simulations of such systems, a number of distinct molecular process have been identified during smooth and stick-slip sliding. These are shown
FIGURE 16.17 Measured change in friction during interlayer transitions of the silicone liquid octamethylcyclotetrasiloxane (OMCTS, an inert liquid whose quasispherical molecules have a diameter of 8 Å) (Gee et al., 1990). In this system, the shear stress Sc = F/A, was found to be constant so long as the number of layers n remained constant. Qualitatively similar results have been obtained with other quasispherical molecules such as cyclohexane (Israelachvili et al., 1988). The shear stresses are only weakly dependent on the sliding velocity v. However, for sliding velocities above some critical value vc, the stick-slip disappears and sliding proceeds smoothly in the purely kinetic value. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
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stress
Applied stress
(a) AT REST stress
(b) STICKING
(c) SLIPPING (whole film melts)
stress Slip planes
(c') SLIPPING (one layer melts)
(c") SLIPPING (interlayer slip)
(d) REFREEZING
FIGURE 16.18 Idealized schematic illustration of molecular rearrangements occurring in a molecularly thin film of spherical or simple chain molecules between two solid surfaces during shear. Note that, depending on the system, a number of different molecular configurations within the film are possible during slipping and sliding, shown here as stages (c) total disorder as whole film melts, (c′) partial disorder, and (c″) order persists even during sliding with slip occurring at a single slip-plane either within the film or at the walls. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
schematically in Figure 16.18 for the case of spherical liquid molecules between two solid crystalline surfaces. The following regimes may be identified: Surfaces at rest — Figure 16.18a: Even with no externally applied load, solvent–surface epitaxial interactions can induce the liquid molecules in the film to solidify. Thus at rest the surfaces are stuck to each other through the film. Sticking regime (frozen, solid-like film) — Figure 16.18b: A progressively increasing lateral shear stress is applied. The film, being solid, responds elastically with a small lateral displacement and a small increase or “dilatency” in film thickness (less than a lattice spacing or molecular dimension, σ). In this regime the film retains its frozen, solid–like state — all the strains are elastic and reversible, and the surfaces remain effectively stuck to each other. However, slow creep may occur over long time periods. Slipping and sliding regimes (molten, liquid-like film) — Figure 16.18c, c′, c″: When the applied shear stress or force has reached a certain critical value Fs, the static friction force, the film suddenly melts (known as “shear melting”) or rearranges to allow for wall-slip or film-slip to occur, at which point the two surfaces begin to slip rapidly past each other. If the applied stress is kept at a high value, the upper surface will continue to slide indefinitely. Refreezing regime (resolidification of film) — Figure 16.18d: In many practical cases, the rapid slip of the upper surface relieves some of the applied force, which eventually falls below another critical value Fk, the kinetic friction force, at which point the film resolidifies and the whole stick-slip cycle is repeated. On the other hand, if the slip rate is smaller than the rate at which the external stress is applied, the surfaces will continue to slide smoothly in the kinetic state and there will be no more stick-slip. The critical velocity at which stick-slip disappears is discussed in more detail in Section 16.9.
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Experiments with linear chain (alkane) molecules show that the film thickness remains quantized during sliding, so that the structure of such films is probably more like that of a nematic liquid crystal where the liquid molecules have become shear aligned in some direction enabling shear motion to occur while retaining some order within the film. Computer simulations for simple spherical molecules (Thompson and Robbins, 1990) further indicate that during the slip, the film thickness is roughly 15% higher than at rest (i.e., the film density falls), and that the order parameter within the film drops from 0.85 to about 0.25. Both of these are consistent with a disorganized liquid–like state for the whole film during the slip, as illustrated schematically in Figure 16.18c. At this stage, we can only speculate on other possible configurations of molecules in the slipping and sliding regimes. This probably depends on the shapes of the molecules (e.g., whether spherical or linear or branched), on the atomic structure of the surfaces, on the sliding velocity, etc. Figure 16.18c, c′, and c″ show three possible sliding modes wherein the shearing film either totally melts, or where the molecules retain their layered structure and where slip occurs between two or more layers. Other sliding modes, for example, involving the movement of dislocations or disclinations are also possible, and it is unlikely that one single mechanism applies in all cases.
16.8.2 Role of Molecular Shape and Liquid Structure The above scenario is already quite complicated, and yet this is the situation for the simplest type of experimental system. The factors that appear to determine the critical velocity vc (Section 16.9.5) depend on the type of liquid between the surfaces (as well as on the surface lattice structure). Small spherical molecules such as cyclohexane and OMCTS have been found to have very high vc, which indicates that these molecules can rearrange relatively quickly in thin films. Chain molecules, and especially branched chain molecules, have been found to have much lower vc, which is to be expected, and such liquids tend to slide smoothly rather than in a stick-slip fashion (see Table 16.2). With highly asymmetric molecules, such as multiply branched isoparaffins and polymer melts, no regular spikes or stick-slip behavior occurs at any speed since these molecules can never order themselves sufficiently to “solidify.” Examples of such liquids are perfluoropolyethers and polydimethylsiloxanes (PDMS) (Figure 16.19). Recent computer simulations (Gao, et al., 1997a,b; He et al., 1999) of the structure, interaction forces, and tribological behavior of chain molecules between two shearing surfaces indicate that both linear and singly or doubly branched chain molecules order between two flat surfaces by aligning into discrete layers parallel to the surfaces. However, in the case of the weakly branched molecules the expected oscillatory forces do not materialize because of a complex cancellation of entropic and enthalpic contributions to the interaction free energy which results in a monotonically smooth interaction, exhibiting a weak energy
TABLE 16.2
Effect of Molecular Shape and Short-Range Forces on Tribological Propertiesa
Liquid (dry)
Short-Range Force
Type of Friction
Friction Coefficient
Bulk Liquid Viscosity (cP)
Quantized stick-slip Quantized stick-slip Stick-slip ↔ smooth Stick-slip ↔ smooth Smooth Smooth
1 1.5 1.0 0.3 0.4 0.03
0.6 0.5 2.3 5.5 50 800
Organic Cyclohexane Octane Tetradecane Octadecane (branched) PDMSb (M = 3700, melt) PBDb (M = 3500, branched)
Oscillatory Oscillatory Oscil ↔ smooth Oscil ↔ smooth Oscil ↔ smooth Smooth
Water Water (KCl solution) a b
Smooth
Smooth
0.01–0.03
For molecularly thin liquid films between two shearing mica surfaces at 20°C. PDMS: polydimethylsiloxane, PBD: polybutadiene, OMCTS: octamethylcyclotetrasiloxane.
1.0
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Stiction spike
Fs
Friction force
Fk
Stop sliding
Start sliding Time FIGURE 16.19 Stiction is the high starting frictional force Fs experienced by two moving surfaces which causes them to jerk forward rather than accelerate smoothly from rest. It is a major cause of surface damage and wear. The figure shows a typical “stiction spike” or “starting spike,” followed by smooth sliding in the kinetic state. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
minimum rather than the oscillatory force profile that is characteristic of linear molecules. During sliding, however, these molecules can be induced to align further, which can result in a transition from smooth to stick-slip sliding. Table 16.2 shows the trends observed with some organic and polymeric liquids between smooth mica surfaces. Also listed are the bulk viscosities of the liquids. From the data of Table 16.2 it appears that there is a direct correlation between the shapes of molecules and their coefficient of friction or effectiveness as lubricants (at least at low shear rates). Small spherical or chain molecules have high friction with stick-slip because they can pack into ordered solid–like layers. In contrast, longer chained and irregularly shaped molecules remain in an entangled, disordered, fluid-like state even in very thin films, and these give low friction and smoother sliding. It is probably for this reason that irregularly shaped branched chain molecules are usually better lubricants. It is interesting to note that the friction coefficient generally decreases as the bulk viscosity of the liquids increases. This unexpected trend occurs because the factors that are conducive to low friction are generally conducive to high viscosity. Thus, molecules with side groups such as branched alkanes and polymer melts usually have higher bulk viscosities than their linear homologues for obvious reasons. However, in thin films the linear molecules have higher shear stresses because of their ability to become ordered. The only exception to the above correlations is water, which has been found to exhibit both low viscosity and low friction (see Figure 16.12). In addition, the presence of water can drastically lower the friction and eliminate the stick-slip of hydrocarbon liquids when the sliding surfaces are hydrophilic. If an “effective” viscosity ηeff were to be calculated for the liquids in Table 16.2, the values would be many orders of magnitude higher than those of the bulk liquids. This can be demonstrated by the following simple calculation based on the usual equation for Couette flow (see Equation 16.8):
ηeff = Fk D Av
(16.30)
where Fk is the kinetic friction force, D is the film thickness, A the contact area, and v the sliding velocity. Using typical values for experiments with hexadecane (Yoshizawa and Israelachvili, 1993): Fk = 5 mN, D = 1 nm, A = 3 × 10–9 m2 and v = 1 µm/sec, yields ηeff ≈ 2000 N m–2 s, or 20,000 Poise, which is ~106 times higher than the bulk viscosity ηbulk of the liquid. It is instructive to consider that this very high effective viscosity nevertheless still produces a low friction force or friction coefficient µ of about 0.25. It is interesting to speculate that if a 1 nm film were to exhibit bulk viscous behavior, the friction coefficient under the same sliding conditions would be as low as 0.000001. While such a low value has never been
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FIGURE 16.20 Schematic view of interfacial film composed of spherical molecules under a compressive pressure between two solid crystalline surfaces. If the two surface lattices are free to move in the XYZ directions so as to attain the lowest energy state, they could equilibrate at values of X, Y, and Z, which induce the trapped molecules to become “epitaxially” ordered into a solid-like film. (B) Similar view of trapped molecules between two solid surfaces that are not free to adjust their positions, for example, as occurs in capillary pores or in brittle cracks. (C) Similar to (A) but with chain molecules replacing the spherical molecules in the gap. These may not be able to order as easily as do spherical molecules even if X, Y, and Z can adjust, resulting in a situation that is more akin to (B). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
reported for any tribological system, one may consider it as a theoretical lower limit that could, conceivably, be attained under certain experimental conditions. Various studies (Van Alsten and Granick, 1990a,b, 1991; Granick, 1991; Hu and Granick, 1992) have shown that confinement and load generally increase the effective viscosity and/or relaxation times of molecules, suggestive of an increased glassiness or solid-like behavior. This is in marked contrast to studies of liquids in small confining capillaries, where the opposite effects have been observed (Warnock et al., 1986; Awschalom and Warnock, 1987). The reason for this is probably that the two modes of confinement are different. In the former case (confinement of molecules between two structured solid surfaces), there is generally little opposition to any lateral or vertical displacement of the two surface lattices relative to each other. This means that the two lattices can shift in the x-y-z space (Figure 16.20A) to accommodate the trapped molecules in the most crystallographically commensurate or “epitaxial” way, which would favor an ordered, solid-like state. In contrast, the walls of capillaries are rigid and cannot easily move or adjust to accommodate the confined molecules (Figure 16.20B), which will therefore be forced into a more disordered, liquid-like state (unless the capillary wall geometry and lattice is exactly commensurate with the liquid molecules, as occurs in certain zeolites). Experiments have demonstrated the effects of surface lattice mismatch on the friction between surfaces (Hirano et al., 1991; Berman, 1996). Similar to the effects of lattice mismatch on adhesion (Figure 16.2, Section 16.2.1), the static friction of a confined liquid film is maximum when the lattices of the confining surfaces are aligned. For OMCTS confined between mica surfaces (Berman, 1996) the static friction was found to vary by more than a factor of 4 (Figure 16.21), while for bare mica surfaces the variation was by a factor of 3.5 (Hirano et al., 1991). In contrast to the sharp variations in adhesion energy over small twist angles, the variations in friction as a function of twist angle were much more broad — both in magnitude and angular spread. Similar variations in friction as a function of twist or misfit angles have also been observed in computer simulations (Gyalog and Thomas, 1997).
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FIGURE 16.21 Static friction of a 2-nm-thick OMCTS film as a function of the lattice twist angle between the two confining crystalline mica surfaces. The variation in friction is comparable to variations in an unlubricated mica–mica system (Hirano et al., 1991). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Robbins and co-workers (He et al., 1999) computed the friction forces of two clean crystalline surfaces as a function of the angle between their surface lattices. They found that for all nonzero angles (finite “twist” angles) the friction forces fell to zero due to incommensurability effects. They further found that submonolayer amounts of organic or other impurities trapped between two incommensurate surfaces can generate a finite friction force, and they therefore concluded that any finite friction force measured between incommensurate surfaces is probably due to such “third-body” effects. With rough surfaces, i.e., those that have random protrusions rather than being periodically structured, we expect a smearing out of the correlated intermolecular interactions that are involved in film freezing and melting (and in phase transitions in general). This should effectively eliminate the highly regular stick-slip and may also affect the location of the slipping planes. The stick-slip friction of “real” surfaces, which are generally rough, may therefore be quite different from those of perfectly smooth surfaces composed of the same material (see next section). We should note, however, that even between rough surfaces, most of the contacts occur between the tips of microscopic asperities, which may be smooth over their microscopic contact area.
16.9 Stick-Slip Friction An understanding of stick-slip is of great practical importance in tribology (Rabinowicz, 1965) since these spikes are the major cause of damage and wear of moving parts. But stick-slip motion is a much more common phenomenon and is also the cause of sound generation (the sound of a violin string, a squeaking door, or the chatter of machinery), sensory perception (taste texture and feel), earthquakes, granular flow, nonuniform fluid flow such as the “spurting” flow of polymeric liquids, etc. In the previous section the stick-slip motion arising from freezing–melting transitions in thin interfacial films was described, but there are other mechanisms that can give rise to stick-slip friction, which will now be considered. However, before proceeding with this, it is important to clarify exactly what one is measuring during a friction experiment. Figure 16.22 shows the basic mechanical coupling and equivalent mechanical circuit characteristic of most tribological systems and experiments. The distinction between F and F0 is important because in almost all practical cases, the applied, measured, or detected force, F, is not the same as the “real” or “intrinsic” friction force, F0, generated at the surfaces. F and F0 are coupled in a way that depends on
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A. Typical system geometry Friction force F measured here
Sliding velocity V Mechanical coupling K
Friction force F 0 generated here
B. Equivalent mechanical circuit load L
X=Vt
F Spring stiffness K
F0
Drive
Stage (M) V0=X0 Surfaces
Contact area A Surface energy ϒ Film thickness D Film viscosity η
FIGURE 16.22 (A) Schematic geometry of two shearing surfaces illustrating how the friction force, F0, which is generated at the surfaces, is generally measured as F at some other place. The mechanical coupling between the two may be described in terms of a simple elastic stiffness or compliance, K, or in terms of more complex nonelastic coefficients, depending on the system. Here, the mechanical coupling is simply via the backing material supporting one of the surfaces. (B) Equivalent mechanical circuit for the above set-up applicable to most tribological systems. Note that F0 is the force generated at the surfaces, but that the measured or detected force is F = (X – Xo)K. The differences between the forces, the velocities, and the displacements at the surfaces and at the Drive (or detector) are illustrated graphically in Figures 16.24 through 16.27. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
the mechanical construction of the system, for example, the axle of a car wheel which connects it to the engine. In Figure 16.22A, this coupling is shown to act via the material supporting the upper surface, which can be modeled (Figure 16.22B) as an elastic spring of stiffness K and mass M. This is the simplest type of mechanical coupling and is also the same as in SFA- and AFM-type experiments, illustrated in Figure 16.23. More complicated real systems can be reduced to a system of springs and dashpots, as described by Luengo et al. (1997a). We now consider four different models of stick-slip friction. These are illustrated in Figures 16.24 to 16.27, where the mechanical couplings are assumed to be of the simple elastic spring type as shown in Figures 16.22 and 16.23. The first two mechanisms (Figures 16.24 and 16.26) may be considered as the “traditional” or “classical” mechanisms or models (Rabinowicz, 1965); the third (Figure 16.27) is essentially the same as the freezing–melting phase-transition model described in Section 16.8.
16.9.1 Rough Surfaces Model Rapid slips can occur whenever an asperity on one surface goes over the top of an asperity on the other surface. As shown in Figure 16.24, the extent of the “slip” will depend on asperity heights and slopes, on the speed of sliding, and on the elastic compliance of the surfaces and the moving stage. We may note that, as in all cases of stick-slip motion, the driving velocity (V) may be constant, but the resulting motion at the surfaces (V0) will display large slips as shown in the inset. This type of stick-slip has been described by Rabinowicz (1965). It will not be of much concern here since it is essentially a noise-type fluctuation, resulting from surface imperfections rather than from the intrinsic interaction between two surfaces. Actually, at the atomic level, the regular atomic-scale corrugations of surfaces can lead to periodic stickslip motion of the type shown here. This is what is sometimes measured by AFM tips (McClelland, 1989; McClelland and Cohen, 1990).
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FIGURE 16.23 (A) Schematic geometry of two contacting asperities separated by a thin liquid film. This is also the geometry adopted in most pin-on-disc, SFA and AFM experiments. In the SFA experiments described here, typical experimental values were: undeformed radius of surfaces, R ≈ 1 cm; radius of contact area, r = 10 to 40 µm; film thickness, D ≈ 10 Å; externally applied load, L = –10 to +100 mN; measured friction forces, F = 0.001 to 100 mN; contact pressures, p = 0 to 0.5 GPa; sliding or driving velocity, V = 0.001 to 100 µm/s; surface or interfacial energy, γ = 0 to 30 mJ/m2 (erg/cm2); effective elastic constant of supporting material, K = 108 N/m; elastic constant of frictionmeasuring spring, K = 500 N/m; temperature, T = 15 to 40°C. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
FIGURE 16.24 Figures 16.24 through 16.27 show three different models of friction and the stick-slip friction force vs. time traces they give rise to. Figure 16.24 shows Rabinowicz’ model (Rabinowicz, 1965) for rough surfaces which produces irregular stick-slip (inset) when the elastic stiffness of the system (reflected by the slopes of the SLIP lines) is not too high. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
16.9.2 Distance-Dependent Model Another theory of stick-slip, observed in solid-on-solid sliding, is one that involves a characteristic distance (but also a characteristic time, τs, this being the characteristic time required for two asperities to increase their adhesion strength after coming into contact). Originally proposed by Rabinowicz (1965, 1958), this model suggests that two rough macroscopic surfaces adhere through their microscopic asperities of characteristic length Dc. During shearing, each surface must first creep a distance Dc — the size of the contacting junctions — after which the surfaces continue to slide, but with a lower (kinetic) friction force that the original (static) value. The reason for the decrease in the friction force is that even though, on average, new asperity junctions should form as rapidly as the old ones break, the time-dependent adhesion and friction of the new ones will be lower than the old ones. This is illustrated in Figure 16.25.
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Dry
603
Lubricated
t=0 Contact
t=τs Creep Dc
FIGURE 16.25 Distance-dependent friction model (also known as the creep model) in which a characteristic distance Dc has to be moved to break adhesive junctions. The model also has a characteristic, τs, this being the time needed for the adhesion and friction forces per junction to equilibrate after each contact is made. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
The friction force therefore remains high during the creep stage of the slip, but once the surfaces have moved the characteristic distance Dc, the friction rapidly drops to the kinetic value. Any system where the kinetic friction is less than the static force (or one that has a negative slope over some part of its F0–V0 curve) will exhibit regular stick-slip sliding motion for certain values of K, m, and driving velocity, V. This type of friction has been observed in a variety of dry (unlubricated) systems such as paper-onpaper (Baumberger et al., 1994; Heslot et al., 1994) and steel-on-steel (Rabinowicz, 1958; Sampson et al., 1943; Heymann et al., 1954). This model is also used extensively in geologic systems to analyze rock-onrock sliding (Dieterich, 1978, 1979). While originally described for adhering macroscopic asperity junctions, the distance-dependent model may also apply to molecularly smooth surfaces. For example, for polymer lubricant films, the characteristic length Dc would now be the chain–chain entanglement length, which could be much larger in a confined geometry than in the bulk.
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FIGURE 16.26 The lower part of the figure shows the Stage or surface displacement X0, surface velocity V0 (= dX0/dt · or X0), and measured friction force F, as functions of time t for surfaces whose intrinsic friction force is F0. In general, F0 is a function of X0, V0, and t. Three specific examples are shown here corresponding to F0 either increasing monotonically (Case a), remaining constant (Case b), or decreasing monotonically (Case c) with V0. The latter case corresponds to a film that exhibits “shear thinning.” Only when F0(V0) has a negative slope is the resulting motion of the stick-slip type, characterized by very different motions and friction forces being detected at the surfaces (the Stage) and the detector (the Drive). (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
16.9.3 Velocity-Dependent Friction Model This is the most studied mechanism of stick-slip and, until recently was considered to be the only cause of intrinsic stick-slip. If a friction force decreases with increasing sliding velocity, as occurs with boundary films exhibiting shear-thinning, the force (Fs) needed to initiate motion will be higher than the force (Fk) needed to maintain motion. Such a situation is depicted in Figure 16.26 (Case c) where a decreasing intrinsic friction force F0 with sliding velocity V0 results in the sliding surface or stage moving in a periodic fashion where, during each cycle, rapid acceleration is followed by rapid deceleration (see curves for X0 and V0 in Figure 16.26). So long as the drive continues to move at a fixed velocity V, the surfaces will continue to move in a periodic fashion punctuated by abrupt stops and starts whose frequency and amplitude depend not only on the function F0(V0) but also on the stiffness K and mass M of the moving stage, and on the starting conditions at t = 0. More precisely, referring to Figures 16.22 and 16.26, the motion of the sliding surface or stage can be determined by solving the following differential equation:
(
)
(
)
˙˙ = F − F = F − X − X K MX 0 0 0 0
(16.31)
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SLIP
STICK
STICK
Liquidlike state
Solidlike State
605
Solidlike state
Increasing velocity
V>Vc
V 0, where V = constant
(16.33)
In other systems, the appropriate driving condition may be F = constant. Various forms for F0 = F0(X0,V0,t) have been proposed, mainly phenomenological, to explain various kinds of stick-slip phenomena. These models generally assume a particular functional form for the friction as a function of velocity only, F0 = F0(V0), and they may also contain a number of mechanically coupled elements comprising the stage (Tomlinson, 1929; Carlson and Langer, 1989). One version is a two-state model characterized by two friction forces, Fs and Fk, which is a simplified version of the phase transitions model (next section). More complicated versions can have a rich F–v spectrum, as proposed by Persson (1994). Unless the experimental data are very detailed and extensive, these models cannot generally distinguish between different types of mechanisms. Neither do they address the basic question of the origin of the friction force, since this is assumed to begin with.
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Experimental data have been used to calculate the friction force as a function of velocity within an individual stick-slip cycle (Nasuno et al., 1997). For a macroscopic granular material confined between solid surfaces, the data show a velocity-weakening friction force during the first half of the slip. However, the data also show a hysteresis loop in the friction–velocity plot, with a different behavior in the deceleration half of the slip phase. Similar results were observed for a 1 to 2 nm liquid lubricant film between mica surfaces (Berman, Carlson, and Ducker, unpublished results). These results indicate that a purely velocity-dependent friction law is insufficient to describe such systems, and an additional element such as the state of the confined material must be considered (next section).
16.9.4 Phase Transitions Model Recent molecular dynamics computer simulations have found that thin interfacial films undergo firstorder phase transitions between solid-like and liquid-like states during sliding (Thompson and Robbins, 1990; Robbins and Thompson, 1991) and have suggested this is responsible for the observed stick-slip behavior of simple isotropic liquids between two solid crystalline surfaces. With this interpretation, stickslip is seen to arise because of the abrupt change in the flow properties of a film at a transition (Israelachvili et al., 1990; Thompson et al., 1992) rather than the gradual or continuous change as occurs in the previous example. Such simulations have accounted for many of the observed properties of shearing liquids in ultrathin films between molecularly smooth surfaces, and have so far offered the most likely explanation for experimental data on stick-slip friction, such as shown in Figure 16.28. A novel interpretation of the well-known phenomenon of decreasing coefficient of friction with increasing sliding velocity has been proposed by Thompson and Robbins (1990) based on their computer simulation. This postulates that it is not the friction that changes with sliding speed v, but rather the time various parts of the system spend in the sticking and sliding modes. In other words, at any instant during sliding, the friction at any local region is always Fs or Fk, corresponding to the “static” or “kinetic” values. The measured frictional force, however, is the sum of all these discrete values averaged over the whole contact area. Since as v increases each local region spends more time in the sliding regime (Fk) and less in the sticking regime (Fs), the overall friction coefficient falls. One may note that this interpretation reverses the traditional way that stick-slip has been explained, for rather than invoking a decreasing friction with velocity to explain stick-slip, it is now the more fundamental stick-slip phenomenon that is producing the apparent decrease in the friction force with increasing sliding velocity. This approach has been studied analytically by Carlson and Batista (1996), with a comprehensive rate-and-state dependent friction force law. This model includes an analytic description of the freezing–melting transitions of a film, resulting in a friction force that is a function of sliding velocity in a natural way. This model predicts a full range of stick-slip behavior observed experimentally. An example of the rate- and state-dependent model is observed when shearing thin films of OMCTS between mica surfaces (Berman et al., 1996a,b). In this case the static friction between the surfaces is dependent on the time that the surfaces are at rest with respect to each other, while the intrinsic kinetic friction Fk0 is relatively constant over the range of velocities (Figure 16.29). At slow driving velocities, the system responds with stick-slip sliding, with the surfaces reaching maximum static friction before each slip event, and the amplitude of the stick-slip, Fs – Fk, is relatively constant. As the driving velocity increases, the static friction decreases as the time at relative rest becomes shorter with respect to the characteristic time of the lubricant film. As the static friction decreases with increasing drive velocity, it eventually equals the intrinsic kinetic friction Fk0, which defines the critical velocity Vc, above which the surfaces slide smoothly, without the jerky stick-slip motion. The above classifications of stick-slip are not exclusive, and molecular mechanisms of real systems may exhibit aspects of different models simultaneously. They do, however, provide a convenient classification of existing models and indicate which experimental parameters should be varied to test the different models.
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FIGURE 16.28 Exact reproductions of chart-recorded traces of friction forces at increasing sliding velocities V (in µm/s) plotted as a function of time for a hydrocarbon liquid (A) and a boundary monolayer (B). In general, with increasing sliding speed, the stick-slip spikes increase in frequency and decrease in magnitude. As the critical sliding velocity Vc is approached the spikes become erratic, eventually disappearing altogether at V = Vc. At higher sliding velocities the sliding continues smoothly in the kinetic state. Such friction traces are fairly typical for simple liquid lubricants and dry boundary lubricant systems, and may be referred to as the “conventional” type of static–kinetic friction. (A) Liquid hexadecane (C16H34) film between two untreated mica surfaces. Experimental conditions (see Figure 16.23): contact area, πr2 = 4 × 10–9 m2; load, L≈1 gm; film thickness, D = 0.4 to 0.8 nm; V = 0.08 to 0.4 µm/sec; Vc ≈ 0.3 µm/sec; atmosphere: dry N2 gas; T = 18°C. (B) Close-packed surfactant monolayers on mica (dry boundary lubrication) showing behavior qualitatively similar to that obtained above with a liquid hexadecane film. In this case, Vc ≈ 0.1 µm/sec. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
16.9.5 Critical Velocity for Stick-Slip For any given set of conditions, stick-slip disappears above some critical sliding velocity Vc, above which the motion continues smoothly in the liquid-like or kinetic state. The critical velocity is found to be well described by two simple equations. Both are based on the phase transition model, and both include some parameter associated with the inertia of the measuring instrument. The first equation is based on both experiments and simple theoretical modeling (Yoshizawa and Israelachvili, 1993):
Vc ≈
(F − F ) S
k
5Kτo
(16.34)
where το is the characteristic nucleation time or freezing time of the film. For example, inserting the following typically measured values for a ~10 Å thick hexadecane film between mica: (Fs – Fk) ≈ 5 mN, spring constant K ≈ 500 N/m, and nucleation time (Yoshizawa and Israelachvili, 1993) τo ≈ 5 sec, we obtain Vc ≈ 0.4 µm/s, which is close to typically measured values (Figure 16.28). The second equation is based on computer simulations (Robbins and Thompson, 1991):
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FIGURE 16.29 Measured friction Fs and Fk for increasing drive velocity V with OMCTS confined between two mica surfaces. Fs (solid circles) decreases with increasing velocity because at higher drive speeds the sticking time is shorter, resulting in less complete freezing of the lubricant layer. The observed Fk (open circles) increases as Fs decreases, resulting in a nearly constant intrinsic friction force Fk (triangles) ≈ (Fs + Fk)/2 for these underdamped conditions. The critical velocity is reached when Fs decreases to the intrinsic friction Fk. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
Vc ≈ 0.1
∆F ⋅ σ M
(16.35)
where σ is a molecular dimension and M is the mass of the stage. Again, inserting typical experimental values into this equation, viz., M ≈ 20 gm, σ ≈ 0.5 nm, and (Fs – Fk) ≈ 5 mN as before, we obtain Vc ≈ 0.3 µm/s, which is also close to measured values. Stick-slip also disappears above some critical temperature Tc, which is not the same as the melting temperature of the bulk fluid. Certain correlations have been found between Vc and Tc , and between various other tribological parameters, that appear to be consistent with the principle of “time-temperature superposition,” similar to that occurring in viscoelastic polymer fluids (Ferry, 1980). We end by considering these correlations.
16.9.6 Dynamic Phase Diagram Representation of Tribological Parameters Both friction and adhesion hysteresis vary nonlinearly with temperature, often peaking at some particular temperature, T0. The temperature-dependence of these forces can therefore be represented on a “dynamic” phase diagram such as that shown in Figure 16.30. Experiments have shown that T0, and the whole bellshaped curve, are shifted along the temperature-axis (as well as in the vertical direction) in a systematic way when the load, sliding velocity, etc., are varied. These shifts also appear to be highly correlated with one another; for example, an increase in temperature produces effects that are similar to decreasing the sliding speed or load. Such effects are also commonly observed in other energy-dissipating phenomena such as polymer viscoelasticity (Ferry, 1980), and it is likely that a similar physical mechanism is at the heart all of such phenomena. A possible molecular process underlying the energy dissipation of chain molecules during
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FIGURE 16.30 Schematic “friction phase diagram” representing the trends observed in the boundary friction of a variety of different surfactant monolayers (Yoshizawa et al., 1993). The characteristic bell-shaped curve also correlates with the monolayers’ adhesion energy hysteresis. The arrows indicate the direction in which the whole curve is dragged when the load, velocity, etc., is increased. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
A
Solidlike
B
Amorphous
C
Liquidlike
FIGURE 16.31 Different dynamic phase states of boundary monolayers during adhesive contact and/or frictional sliding. Low adhesion hysteresis and friction is exhibited by solid-like and liquid-like layers (A and C). High adhesion hysteresis and friction is exhibited by amorphous layers (B). Increasing the temperature generally shifts a system from the left to the right. Changing the load, sliding velocity, and other experimental conditions can also change the “dynamic phase state” of surface layers, as shown in Figure 16.30. (From Berman, A. and Israelachvili, J.N. (1999), Surface forces and microrheology of molecularly thin liquid films, in Handbook of Micro/Nanotribology, 2nd ed., Bhushan, B. (Ed.), CRC Press, Boca Raton, FL. With permission.)
boundary layer sliding is illustrated in Figure 16.31, which shows the three main “dynamic” phase states of boundary monolayers. In contrast to the characteristic relaxation time associated with fluid lubricants, for unlubricated (dry, solid, rough) surfaces it has been established that there is a characteristic “memory distance” which must be exceeded before that system loses all memory of its initial state (original surface topography). The underlying mechanism for a characteristic distance was first used to successfully explain rock mechanics and earthquake faults (Ruina, 1983) and, more recently, the tribological behavior of unlubricated surfaces of ceramics, paper, and elastomeric polymers (Berthoud et al., 1999; Baumberger et al., 1999). Recent experiments (Israelachvili et al., 1999) suggest that fluid lubricants composed of complex branched-chain or polymer molecules may also have “characteristic distances” (in addition to characteristic relaxation times) associated with their tribological behavior — the “characteristic distance” being total sliding distance that must be exceeded before the system reaches its steady-state tribological conditions.
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Acknowledgment This work was supported by ONR grant N00014-931D269.
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He, G., Müser, M.H., and Robbins, M.O. (1999), Adsorbed layers and the origin of static friction, Science, Vol. 284, pp. 1650-1652. Helm, C., Knoll, W. and Israelachvili, J.N. (1991), Measurement of ligand-receptor interactions, Proc. Natl. Acad. Sci. USA, Vol. 88, pp. 8169-8173. Henderson, D. and Lozada-Cassou, M. J. (1986), A simple theory for the force between spheres immersed in a fluid, J. Colloid Interf. Sci., Vol. 114, pp. 180-183. Heslot, F., Baumberger, T., Perrin, B., Caroli, B., and Caroli, C. (1994), Creep, stick-slip, and dry-friction dynamics: experiments and a heuristic model, Phys. Rev. E, Vol. 49, pp. 4973-4988. Heymann, F., Rabinowicz, E., and Rightmire, B. (1954) Friction apparatus for very low-speed sliding studies, Rev. Sci. Instr., Vol. 26, pp. 56-58. Hirano, M., Shinjo, K., Keneko, R., and Murata, Y. (1991), Anisotropy of frictional forces in muscovite mica, Phys. Rev. Lett., Vol. 67, pp. 2642-2645. Hirz, S.J., Homola, A.M., Hadziioannou, G., and Frank, C.W. (1992), Effect of substrate on shearing properties of ultrathin polymer films, Langmuir, Vol. 8, pp. 328–333. Holly, F.J. and Refojo, M.J. (1975), Wettability of hydrogels. I. Poly (2-hydroxyethyl methylcrylate), J. Biomed. Mater. Res., Vol. 9, pp. 315-326. Homola, A.M., Israelachvili, J.N., Gee, M.L., and McGuiggan, P.M. (1989), Measurements of and relation between the adhesion and friction of two surfaces separated by thin liquid and polymer films, J. Tribology, Vol. 111, pp. 675-682. Homola, A.M., Israelachvili, J.N., McGuiggan, P.M. and Gee, M.L. (1990), Fundamental experimental studies in tribology: the transition from “interfacial” friction of undamaged molecularly smooth surfaces to “normal” friction with wear, Wear, Vol. 136, pp. 65-83. Homola, A.M., Nguyen, H.V., and Hadziioannou, G. (1991), Influence of monomer architecture on the shear properties of molecularly thin polymer melts, J. Chem. Phys., Vol. 94, pp. 2346-2351. Horn, R.G. and Israelachvili, J.N. (1981), Direct measurement of structural forces between two surfaces in a nonpolar liquid, J. Chem. Phys., Vol. 75, pp. 1400-1411. Horn, R.G. and Israelachvili, J.N. (1988), Molecular organization and viscosity of a thin film of molten polymer between two surfaces as probed by force measurements, Macromolecules, Vol. 21, pp. 2836-2841. Horn, R.G., Smith, D.T., and Haller, W. (1989), Surface forces and viscosity of water measured between silica sheets, Chem Phys. Lett., Vol. 162, pp. 404-408. Hu, H-W. and Granick, S. (1992), Viscoelastic dynamics of confined polymer melts, Science, Vol. 258, pp. 1339-1342. Hu, H-W., Carson, G., and Granick, S. (1991), Relaxation time of confined liquids under shear, Phys. Rev. Lett., Vol. 66, pp. 2758-2761. Israelachvili, J.N. (1986a), Measurement of the viscosity of liquids in very thin films, J. Colloid and Interface Sci., Vol. 110, pp. 263-271. Israelachvili, J.N. (1986b), Measurements of the viscosity of thin films between two surfaces with and without absorbed polymers, Colloid and Polymer Science, Vol. 264, pp. 1060-1065. Israelachvili, J.N. (1989), Techniques for direct measurements of forces between surfaces in liquids at the atomic scale, Chemtracts — Anal. Phys. Chem., Vol. 1, pp. 1 — 12. Israelachvili, J.N. (1991), Intermolecular and Surface Forces, 2nd ed., Academic Press, London. Israelachvili, J. and Berman, A. (1995), Irreversibility, energy dissipation, and time effects in intermolecular and surface interactions, Israel Journal of Chemistry, Vol. 35, pp. 85-91. Israelachvili, J.N. and Kott, S. (1989), Shear properties and structure of simple liquids in molecularly thin films: the transition from bulk (continuum) to molecular behavior with decreasing film thickness, J. Colloid Interface Sci., Vol. 129, pp. 461-467. Israelachvili, J.N. and Kott, S.J. (1988), Liquid structuring at solid interfaces as probed by direct force measurements: the transition from simple to complex liquids and polymer fluids, J. Chem. Phys., Vol. 88, pp. 7162-7166. Israelachvili, J.N. and Wennerström, H.K. (1992), Entropic Forces Between amphiphilic Surfaces in Liquids, J. Phys. Chem., Vol. 96, pp. 520-531.
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Israelachvili, J., Chen, Y.-L., and Yoshizawa, H. (1995), Relationship between adhesion and friction forces, in Fundamentals of Adhesion and Interfaces, Rimai, D.S., DeMejo, L.P., and Mittal, K.L. (Eds.), VSP, pp. 261-279. Israelachvili, J., Chen, Y.-L., and Yoshizawa, H. (1994), Relationship between adhesion and friction forces, J. Adhesion Science & Technology, Vol. 8, pp. 1-18. Israelachvili, J.N., Gee, M.L., McGuiggan, P., Thompson, P., and Robbins, M. (1990), Melting-freezing transitions in molecularly thin liquid films during shear, in Dynamics in Small Confining Systems, Proc. 1990 Fall Meeting of the Materials Research Society, Drake, J.M., Klafter, J., and Kopelman, R. (Eds.), MRS Publications, pp. 3-6. Israelachvili, J., Giasson, S., Kuhl, T., Drummond C., Berman, A., Luengo, G., Pan, J.-M., Heuberger, M., Ducker, W. and Alcantar, N. (1999), Some fundamental differences in the adhesion and friction of rough versus smooth surfaces, in Thinning Films and Tribological Interfaces, Proc. of the 26th LeedsLyon Symposium, Tribology Series 38, Elsevier, pp. 3-12. Israelachvili, J.N., McGuiggan, P., Gee, M., Homola, A., Robbins, M., and Thompson, P. (1990), Liquid dynamics in molecularly thin films, J. Phys.: Condens. Matter, Vol. 2, pp. SA89-SA98. Israelachvili, J.N. (1987), Solvation forces and liquid structure — as probed by direct force measurements, Accounts of Chemical Research, Vol. 20, pp. 415-421. Israelachvili, J.N. (1988), Measurements and relation between the dynamic and static interactions between surfaces separated by thin liquid and polymer films, Pure and Appl. Chem., Vol. 60, pp. 1473-1478. Israelachvili, J.N. and McGuiggan, P.M. (1988), Forces between surfaces in liquids, Science, Vol. 241, pp. 795-800. Israelachvili, J.N. and McGuiggan, P.M. (1990), Adhesion and short-range forces between surfaces. I — new apparatus for surface force measurements, J. Mater. Res., Vol. 5, pp. 2223-2231. Israelachvili, J.N., Homola, A.M., and McGuiggan, P.M. (1988), Dynamic properties of molecularly thin liquid films, Science, Vol. 240, pp. 189-191. Johnson, K.L., Kendall, K., and Roberts, A.D. (1971), Surface energy and the contact of elastic solids, Proc. R. Soc. London A, Vol. 324, pp. 301-313. Kjellander, R. and Marcelja, S. (1985a), Perturbation of hydrogen bonding in water near polar surfaces, Chem. Phys. Lett., Vol. 120, pp. 393-396. Kjellander, R. and Marcelja, S. (1985b), Polarization of water between molecular surfaces: a molecular dynamics study, Chem. Scr., Vol. 25, pp. 73-80. Klein, J. and Kumacheva, E. (1995), Confinement-induced phase transitions in simple liquids, Science, Vol. 269, pp. 816-819. Klein, J., and Kumacheva, E. (1998), Simple liquids confined to molecularly thin layers. I. Confinementinduced liquid-to-solid phase transitions, J. Chem. Phys., Vol. 108, pp. 6996-7009. Klein, J., Kumacheva, E., Mahalu, D., Perahia, D., and Fetters, L.J., (1994), Reduction of frictional forces between solid surfaces bearing polymer brushes, Nature, Vol. 370, pp. 634-636. Klein, J., Kamiyama, Y., Yoshizawa, H., Israelachvili, J.N., Fredrickson, G.H., Pincus, P., and Fetters, L.J., (1993), Lubrication forces between surfaces bearing polymer brushes, Macromolecules, Vol. 26, pp. 5552-5560. Kuhl, T.L., Berman, A.D., Israelachvili, J.N., and Hui, S.W. (1997), Part I: Direct measurement of depletion attraction and thin film viscosity between lipid bilayers in aqueous polyethylene glycol solutions, Macromolecules, Vol. 31, pp. 8250-8257. Kumacheva, E. and Klein, J. (1998), Simple liquids confined to molecularly thin layers. II. Shear and Frictional behavior of solidified films, J. Chem. Phys., Vol. 108, pp. 7010-7022. Landman, U., Luedtke, W.D., Burnham, N.A., and Colton, R.J. (1990), Atomistic mechanisms and dynamics of adhesion, nanoindentation, and fracture, Science, Vol. 248, pp. 454-461. Lawn, B.R. and Wilshaw, T.R. (1975), Fracture of Brittle Solids, Cambridge Univ. Press, London. Leckband, D.E., Schmitt, F-J., Knoll, W., and Israelachvili, J.N. (1992), Long-range attraction and molecular rearrangements in receptor–ligand interactions, Science, Vol. 255, pp. 1419–1421. Luengo, G., Israelachvili, J., and Granick, S. (1996), Generalized effects in confined fluids: new friction map for boundary lubrication, Wear, Vol. 200, pp. 328-335.
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Luengo, G., Schmitt, F.-J., Hill, R., and Israelachvili, J. (1997a), Thin film rheology and tribology of confined polymer melts: contrasts with bulk properties, Macromolecules, Vol. 30, pp. 2482-2494. Luengo, G., Campbell, S.E., Srdanov, V.I., Wudl, F., and Israelachvili, J.N. (1997b), Direct measurement of the adhesion and friction of smooth C60 surfaces, Chemistry of Materials, Vol. 9, pp. 1166–1171. Maugis, D. (1985), Subcritical crack growth, surface energy, fracture toughness, stick-slip, and embrittlement, J. Materials Sci., Vol. 20, pp. 3041-3073. McClelland, G.M. (1989), in Adhesion and Friction. Springer Series in Surface Sciences, Grunze, M. and Kreuzer, H.J. (Eds.), Springer, Berlin, Germany, Vol. 17, pp. 1-16. McClelland, G.M. and Cohen, S. R. (1990), Chemistry and Physics of Solid Surfaces VIII, Springer, Berlin, pp. 419-445. McGuiggan, P. and Israelachvili, J.N. (1990), Adhesion and short-range forces between surfaces. Part II: effects of surface lattice mismatch, J. Mater. Res., Vol. 5, pp. 2232-2243. Michel, F. and Shanahan, M.E.R. (1990), Kinetics of the JKR experiment, C. R. Acad. Sci. Paris, Vol. 310II, pp. 17-20. Miller, C.A. and Neogi, P. (1985), Interfacial Phenomena: Equilibrium and Dynamic Effects, Marcel Dekker, New York. Nasuno, S., Kudrolli, A., and Gollub, J. (1997), Friction in granular layers: hysteresis and precursors, Phys. Rev. Lett., Vol. 79, pp. 949-952. Peachey, J., Van Alsten, J., and Granick, S. (1991), Design of an apparatus to measure the shear response of ultrathin liquid films, Review of Scientific Instruments, 62(2), pp. 463-473. Persson, B.N.J. (1994), Theory of friction — the role of elasticity in boundary lubrication, Phys. Rev. B, Vol. 50, pp. 4771-4786. Pollock, H.M., Barquins, M., and Maugis, D. (1978), The force of adhesion between solid surfaces in contact, Appl. Phys. Lett., Vol. 33, pp. 798-799. Rabin, Y. and Hersht, I. (1993), Thin liquid layers in shear-non-Newtonian effects, Physica. A, Vol. 200, pp. 708-712. Rabinowicz, E. (1958), The intrinsic variables affecting the stick-slip process, Proc. Phys. Soc., Vol. 71, pp. 668-675. Rabinowicz, E. (1965), Friction and Wear of Materials, John Wiley & Sons, New York. Rapoport, L., Bilik, Y., Feldman, Y., Homyonfer, M., Cohen, S.R., and Tenne, R. (1997), Hollow Nanoparticles of WS2 as potential solid-state lubricants, Nature, Vol 387, pp. 791-793. Rhykerd, C., Schoen, M., Diestler, D., and Cushman, J. (1987), Epitaxy in simple classical fluids in micropores and near-solid surfaces, Nature, Vol. 330, pp. 461-463. Robbins, M.O. and Thompson, P.A. (1991), Critical velocity of stick-slip motion, Science, Vol. 253, pp. 916-916. Rozman, M.G., Urbakh, M., and Klafter, J. (1996), Origin of stick-slip motion in a driven two-wave potential, Phys. Rev. E, Vol. 54, pp. 6485-6494. Rozman, M.G., Urbakh, M., and Klafter, J. (1997), Stick-slip dynamics as a probe of frictional forces, Europhys. Lett., Vol. 39, pp. 183-188. Ruina, A. (1983), Slip instability and state variable friction laws, J. Geophys. Res., 88, 10359-10370. Sampson, J., Morgan, F., Reed, D., and Muskat, M. (1943), Friction behavior during the slip portion of the stick-slip process, J. Appl. Phys., Vol. 14, pp. 689-700. Schoen, M., Dietsler, D.J., and Cushman, J.H. (1987), Fluids in micropores. I. Structure of a simple classical fluid in a slit-pore, J. Chem. Phys., Vol. 87, pp. 5464-5476. Schoen, M., Rhykerd, C., Diestler, D., and Cushman, J. (1989), Shear forces in molecularly thin films, Science, Vol. 245, pp. 1223-1225. Shanahan, M.E.R., Schreck, P., and Schultz, J. (1988), Effets de la réticulation sur l’adhésion d’un élastomére, C.R. Acad. Sci. Paris, Vol. 306II, pp. 1325-1330. Snook, I.K. and van Megen, W. (1979), Structure of dense liquids at solid interfaces, J. Chem. Phys., Vol. 70, pp. 3099-3105.
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Snook, I.K. and van Megen, W. (1980), Solvation forces in simple dense fluids. I, J. Chem. Phys., Vol. 72, pp. 2907-2913. Snook, I.K. and van Megen, W. (1981), Calculation of solvation forces between solid particles immersed in simple liquid, J. Chem. Soc. Faraday Trans. II, Vol. 77, pp. 181-190. Sutcliffe, M.J., Taylor, S.R., and Cameron, A. (1978), Molecular asperity theory of boundary friction, Wear, Vol. 51, pp. 181-192. Tabor, D. (1982), The role of surface and intermolecular forces in thin film lubrication, in Microscopic Aspects of Adhesion and Lubrication, Societe de Chimie Physique, Paris, pp. 651-679. Tarazona, P. and Vicente, L. (1985), A model for the density oscillations in liquids between solid walls, Mol. Phys., Vol. 56 pp. 557-572. Thompson, P.A., Grest, G.S., and Robbins, M.O. (1992), Phase transitions and universal dynamics in confined films, Phys Rev Letters, Vol. 68, pp. 3448–3451. Ibid. (1993), in Thin Films in Tribology, Proceedings of the 19th Leeds-Lyon Symposium on Tribology, Dawson, D., Taylor, C.M., and Godet, M. (Eds.), Elsevier, Amsterdam, pp. 1–14. Thompson, P. and Robbins, M. (1990), Origin of stick-slip motion in boundary lubrication, Science, Vol. 250, pp. 792-794. Thompson, P.A., Robbins, M.O., and Grest, G.S. (1995), Structure and shear response in nanometerthick films, Israel Journal of Chemistry, Vol. 35, pp. 93-106. Tomlinson, G. A. (1929), A molecular theory of friction, Phil. Mag., Vol. 7, pp. 905-939. Urbakh, M., Daikhin, L., and Klafter, J. (1995), Dynamics of confined liquids under shear, Phys. Rev. E, Vol. 51, pp. 2137-2141. Van Alsten, J. and Granick, S. (1988), Molecular tribometry of ultrathin liquid films, Phys. Rev. Lett., Vol. 61, pp. 2570-2573. Van Alsten, J. and Granick, S. (1990a), The origin of static friction in ultrathin liquid films, Langmuir, Vol. 6, pp. 876-880. Van Alsten, J. and Granick, S. (1990b), Shear rheology in a confined geometry — polysiloxane melts, Macromolecules, Vol. 23, pp. 4856-4862. van Megen, W. and Snook, I.K. (1979), Calculation of solvation forces between solid particles immersed in a simple liquid, J. Chem. Soc. Faraday Trans. II, Vol. 75, pp. 1095-1102. van Megen, W. and Snook, I.K. (1981), Solvation forces in simple dense fluids. II. Effect of chemical potential, J. Chem. Phys., Vol. 74, pp. 1409-1411. Vigil, G., Xu, Z., Steinberg, S., and Israelachvili, J. (1994), Interactions of silica surfaces, J. Colloid Interf. Sci., Vol. 165, pp. 367-385. Warnock, J., Awschalom, D.D., and Shafer, M.W. (1986), Orientational behavior of molecular liquids in restricted geometries, Phys. Rev. B, Vol. 34, pp. 475-478. Weisenhorn, A.L., Hansma, P.K., Albrecht, T.R., and Quate, C.F. (1989), Forces in atomic force microscopy in air and water, Appl. Phys. Lett., Vol. 54, pp. 2651-2653. Wilchek, M. and Bayer, E.B. (1990), Methods in Enzymology, Vol. 184: Avidin–Biotin Technology, Academic Press, Orlando, FL, pp. 5-45. Yamada, S. and Israelachvili, J. (1998), Friction and adhesion hysteresis of fluorocarbon surfactant monolayer-coated surfaces measured with the surface forces apparatus, J. Phys. Chem. B, Vol. 102, pp. 234–244. Yoshizawa, H. and Israelachvili, J.N. (1993), Fundamental mechanisms of interfacial friction II: stick-slip friction of spherical and chain molecules, J. Phys. Chem., Vol. 97, pp. 11300-11313. Yoshizawa, H., Chen, Y.L., and Israelachvili, J. (1993), Fundamental mechanisms of interfacial friction I: relation between adhesion and friction, J. Phys. Chem., Vol. 97, pp. 4128-4140. Zisman, W.A. (1963), Influence of constitution on adhesion, Ind. Eng. Chem., Vol. 55(10), pp. 19-38. Zisman, W.A. and Fox, J. (1952), The spreading of liquids on low-energy surfaces. III. Hydrocarbon surfaces, J. Colloid Sci., Vol. 7, pp. 428-442.
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17 Measurement of Adhesion and Pull-Off Forces with the AFM 17.1
Introduction ..................................................................... 617 Importance of Adhesion Measurements • Review of Adhesion Properties
17.2
Tip Properties • Surface Topography • Force–Distance Curves • Influence of Pull-Off Force on Tapping Mode • Pulsed-Force Mode
Othmar Marti University of Ulm
Experimental Procedures to Measure Adhesion in AFM and Applications..................................................... 624
17.3
Summary and Outlook.................................................... 633
17.1 Introduction The key to the successful operation of an AFM (Binnig et al., 1986) in the materials sensitive regime (Burnham and Colton, 1989; Miyamoto et al., 1990; Mizes et al., 1991) is the measurement of the interaction forces between the tip and the sample surface. The tip would ideally consist of only one atom, which is brought in the vicinity of the sample surface. A crude estimation shows that the interaction forces between the AFM tip and the sample surface should be smaller than about 10–7 N for bulk materials and preferably well below 10–9N for organic macromolecules. On the other hand, there are indications that the measured values, especially of the pull-off force, are considerably off from the theoretically expected values. The reasons are manifold: the shape and size of the tip is not well known (Godowski et al., 1995; Lekka et al., 1997; Ramirez-Aguilar and Rowlen, 1998). The composition of the surfaces of the tip and the sample might differ strongly from their bulk values. Another possibility is that the continuum mechanical models (Johnson, 1992; 1996; Johnson et al., 1971; Maugis, 2001) usually employed to analyze the data might fail. Pull-off force measurements (Creuzet et al., 1992; Mizes et al., 1991; Weisenhorn et al., 1992), often called adhesion measurements, have been carried out for some years. The number of published papers shows that the method has become more and more popular. The theories of contact mechanics that are used in these investigations date back to the time when the only available test bodies were macroscopic. The remarkable precision with which these theories work in the sub-mm regime was first questioned by Stalder and Dürig (Dürig and Stalder, 1997; Stalder and Dürig, 1996). This chapter will discuss the measurement of adhesion with the AFM and the data interpretation with respect to macroscopic theories. The discussion of limiting cases will pinpoint possible limitations.
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FIGURE 17.1 Contact angle measurement. Surface energies are often measured by the contact angle method. A drop of liquid is placed on the sample. The surface energies of the liquid vs. the gas, of sample surface vs. the gas, and of the sample surface vs. the liquid have to balance tangentially, resulting in the equation given above.
17.1.1 Importance of Adhesion Measurements The tip in an AFM is in contact, in intermittent contact, or close to the sample surface. The interaction of the tip and the sample therefore depends on the surface properties of both bodies. The physics of the interaction therefore dominates the imaging process in an AFM. Moreover it strongly affects the measurement of other quantities, such as the tapping phase (Sarid et al., 1998). The adhesion properties of sample surfaces are important in many applications. Adhesive tapes, for instance, require a high adhesive force almost independent of the opposite material (Jiaa et al., 1994; Koinkar and Bhushan, 1996a). Magnetic tapes and computer hard disks, on the other hand, work best if the adhesion with the read and write heads is minimal. Micromechanical devices (MEMS) require a careful control of adhesion (Bhushan, 1996). Bearings should have low adhesion, parts where two materials are joined should have a higher adhesion. As these examples have shown, if it is necessary to control adhesion properties, it is also necessary to measure adhesion which is often correlated with surface energies. Figure 17.1 shows the classical way to measure adhesive properties. A drop of a liquid with a known surface energy is put on the sample. As Figure 17.1 shows, there has to be a balance of forces parallel to the sample surface. This results in the drop having a contact angle Θ with the sample. The equilibrium is reached when
γ S = γ SL + γ L cosΘ
(17.1)
Here the subscript S denotes surface energy of the sample with respect to the ambient medium, SL denotes the surface energy of the sample and the liquid, and L the surface energy of the liquid with respect to the ambient. This measurement method works reliably, but it is almost impossible to characterize areas with micrometer diameters. Therefore it is necessary to use a microscopic tool such as the AFM for these measurements.
17.1.2 Review of Adhesion Properties Adhesion is one of the main forces holding bodies of different materials together. As outlined above, adhesion is measured using test bodies. This chapter summarizes the literature (Dürig and Stalder, 1997; Johnson, 1992, 1996, 1997; Maugis, 2001), as it applies to AFM. The most common test body is the sphere. Figure 17.2 shows a sketch of such an interaction. The spherical body (radius R) is in contact with the sample with a circular region with radius Rc . A force F is applied to the body. A positive force means that the body is pressed against the surface. A negative force means that the adhesion keeps the contact, although the force is trying to separate sample and test body. The indentation of the spherical test body into the sample is called δ. 17.1.2.1 Hertz The laws of indentation and adhesion are highly nonlinear. Hertz was the first to formulate the laws of interaction of a spherical test body with a planar surface (Hertz, 1881). Figure 17.2 shows the definitions
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FIGURE 17.2 Definition of the quantities for the indentation of a spherical test body. The sphere has the radius R. The radius of the contact area is RC . The indentation depth is δ.
for the equations. Hertz formulated his theory of indentation without any adhesive or other long-range forces. The contact radius Rc is then
Rc3 = DRF
(17.2)
2 1 − ν2 3 E
(17.3)
D=
where F is the applied force, R the radius of the spherical test body, E the Young’s modulus, and ν the Poisson number. Figure 17.3 shows the function. The indentation depth δ is then given by
δ3 =
D2 F 2 R
(17.4)
2.00
Yield line
1.80 1.60
JKR 1.40
Rc/R0
1.20
DMT
1.00 0.80
Hertz
0.60 0.40 0.20 0.00 -1.50
-1.00
-0.50
0.00
0.50
1.00
f/f0
FIGURE 17.3 Curves from different contact mechanics theories. The thin line shows the Hertz theory; the fat solid line, the main branch of the JKR theory; the faint fat line is the second branch of the JKR theory; the long-dashed line is the DMT theory; and the dotted line is the yield stress line. The values were calculated for polypropylene, as shown in Table 17.1.
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Equation 17.4 shows that there is a nonlinear law connecting the indentation depth and the applied force. Also the indentation depth is inversely proportional to the tip radius. The force, although depending in a nonlinear fashion on the indentation, is a single-valued function. Therefore any interaction will be well behaved with no hysteresis. The contact stiffness kc is then given by 1
F FR 3 R 3 kc = = 2 = c δ D D
(17.5)
This equation is the basis for the conversion of the indentation δ and the applied force F to the contact radius Rc . 17.1.2.2 DMT The Derjaguin Muller–Toporov–Theory (Derjaguin et al., 1975) is closely related to the Hertz theory. In addition to the Hertz theory, DMT takes into account adhesion inside the junction. This leads to the equation
Rc3 FDR 2π%γR2D
(17.6)
The indentation depth is then given by the same Equation 17.4 as for the Hertz case. Figure 17.3 shows this curve. The force as a function of the contact radius is given by
Rc3 − 2π∆γ R DR
F=
(17.7)
17.1.2.3 JKR One of the most popular models for contact mechanics which includes adhesion effects is the model by Johnson, Kendall, and Roberts (Johnson et al., 1971). The adhesion is included by defining the pull-off force F0
F0
3 πR%γ 2
(17.8)
where ∆γ is the surface energy difference between the spherical test body and the sample surface. The minimum contact area is
R0 = DRF0
(17.9)
The applied force F and the contact radius Rc are connected by the following equation
F Rc3 = DR F + 2F0 1 ± 1 + F0
(17.10)
Figure 17.3 shows this function. The branch with the + sign is the stable one, whereas the other can not be probed by a force controlled setup. The equation can be solved for F. One then obtains 2
R3 c F = − F0 − F0 DR
(17.11)
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17.1.2.4 Maugis The theory of Maugis (2001) gives a smooth interpolation between the two extreme cases shown above: the DMT theory and the JKR theory. Generally, the real sample behaves in the intermediate range of the two theories. Chapter 4 gives a detailed account of this theory. 17.1.2.5 Effect of Tensile Stress Adhesion measurement in AFM is closely related to the measurement of pull-off forces. The interactions of the tip with the sample as well as the deformation of the sample before the separation influence the measurement. The speed of separation does influence materials made of long molecules. Therefore we limit our discussion to the case of tensile stress on the sample, the situation just before the breaking of the adhesive junction with the tip. Compressive stress and the dwell time in the indentation regime affect the contact area. This section is intended to raise the reader’s awareness of the fact that the deformation of the sample may not be neglected. When the spherical test body is pulling on the sample, the tensile stress might exceed the yield stress of the junction (Dürig and Stalder, 1997). The tensile yield stress H relates to the force Fyield with the following equation
Fyield = − σ π Rc2
(17.12)
where Rc is the radius of the contact area, which is assumed to be circular. The JKR or the DMT theory relates Rc to the applied force. Assuming that the starting force is set at a constant value such as is the case in the pulsed force mode (Krotil et al., 1999; Rosa-Zeiser et al., 1997) the starting contact area is kept constant. Since the two force laws (Equations 17.12 and 17.11 or 17.6) have a different dependence on the contact radius, only the law which has the lower contact radius Rc will prevail. Hence there will be a crossover force Fmax which is given by
( )
Fmax = Fyield = F Rc
(17.13)
This equation always has a solution for the DMT theory. By equating Equations 17.13 and 17.7 one obtains an implicit equation for the maximum force:
[
F 3 = −π 3 σ 3 D 2 FR + 2π∆γ R2
]
2
(17.14)
The crossing of the two curves is given by the solution of the above equation. This value in the same time is the maximum negative force sustainable by the junction. For the JKR theory we can do a similar calculation. The point where the two curves cross is given by 2
3 F Fmax = − σπ Rc2 = − σπ D R Fmax + 2F0 1 ± 1 + max F0 2 3
2 3
(17.15)
This is an implicit equation for the force F. Due to its nonlinear behavior it must be solved numerically. Large tensile yield stresses mean that the curve Equation 17.12 crosses curve Equation 17.10 on the negative branch. This is the situation where the finite tensile yield stress of the junction is not relevant. However, if the curve Equation 17.12 crosses curve Equation 17.10 exactly at F0 we have the limiting case. In that case the equation can be solved. 2
2
2
− F0 = −π D 3 R 3 σF03
(17.16)
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Critical Radius for Different Materials
Quantity
Symbol
PP
HDPE
LDPE
PVC
PS
PMMA
Nylon 6
V2A Steel
Young’s modulus Poisson ratio Yield stress Ratio JKR Ratio DMT Max force before yield Critical radius (20)
E ν σ αJKR αDMT Fmax Rcrit
1.4 GPa 0.43 32 MPa 35% 16% 1.5 nN 31 µm
1 GPa 0.47 30 MPa 36% 19% 2.3 nN 21 µm
0.2 GPa 0.49 8 MPa 28% 13% 1 nN 46 µm
2.6 GPa 0.42 48 MPa 35% 16% 1.5 nN 31 µm
3.4 GPa 0.38
3.2 GPa 0.40
1.9 GPa 0.44 50 MPa 42% 22% 3.1 nN 15 µm
195Gpa 0.28
Break stress Ratio JKR Ratio DMT Max force before break Critical radius (20)
B αJKR αDMT Fmax Rcrit,B
33 MPa 34% 16% 1.7 nN 28 µm
30 MPa 36% 19% 2.3 nN 21 µm
10 MPa 37% 20% 2 nN 24 µm
50 MPa 33% 15% 1.7 nN 27 µm
50 MPa 28% 13% 1.1 nN 43 µm
65 MPa 39% 18% 2.6 nN 18 µm
75 MPa 57% 29% 10 nN 4.5 µm
700MPa 28% 13% 1.1 nN 45 µm
The critical radius is calculated both for the yield and the break stress. The ratio values were calculated with R = 100 nm and ∆γ = 1 N/m. They give the pull-off force as a percentage of the pull-off force one would measure if DMT or JKR were applicable references: polymers: van Kevele, 1976; steel: Vogel, 1995.
From this equation one can calculate the maximum sustainable force for a tip with the radius R
Fmax = π 3 σ 3 D 2 R2
(17.17)
Likewise one can calculate for a given force the critical tensile yield stress H.
σ crit =
3 ∆γ 1 3 F0 1 3 πR∆γ = 3 2 2 2 = 3 22 2 2 2 π D R π D R π D R
(17.18)
For H > Hcrit the contact mechanics shows full JKR behavior. However, for softer materials this is no longer true. One can also solve Equation 17.18 for the radius Rcrit of the spherical test body.
Rcrit =
F0 = 3 2 3 π D σ
3 2
π Rcrit ∆γ
π 3 D2 σ 3
(17.19)
Solving Equation 17.19 for the critical tip radius Rcrit , one obtains
Rcrit =
3∆γ 2π D 2 σ 3 2
(17.20)
For a tip radius R < Rcrit , the junction becomes unstable before the JKR limit is reached. Hence for certain materials there will always be a deviation from JKR behavior. Table 17.1 shows results for selected materials, mainly from the polymers group. The critical tip radius Rcrit gives the radius of curvature which must be exceeded to observe the JKR behavior to the end. Table 17.1 clearly demonstrates that the pull-off force is a distinct function of the tensile yield stress σ. The measured pull-off forces are as small as 10% of what one would have detected without the yield barrier. The “max force before break” or the “max force before yield” values show that the JKR theory is applicable without any corrections, provided the pull-off force is below the value shown. The simple JKR theory Equation 17.8 gives for the surface energy
∆γ = −
2 Fmax 3π R
(17.21)
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FIGURE 17.4 Correction factors to compensate for the effect of the finite yield stress of materials. Shown is a calculation for a tip radius of 100 nm and the sample material polypropylene (see Table 17.1) The squares show the result for the DMT theory; the diamonds represent the JKR theory.
The DMT theory Equation 17.7, on the other hand, predicts
∆γ = −
1 Fmax 2π R
(17.22)
If one includes the effects of the finite tensile yield stress σ, one must use Equation 17.15. Whereas it is not possible to find a simple solution for the pull-off force Fmax , one can easily solve Equation 17.15 for F0 and hence for ∆γ
2 Fmax ∆γ = D − 3π πσ
−3
2
3 2 F 1 − max −F πσ DR max
2
(17.23)
Likewise one can also solve for the DMT value of the surface energy using Equation 17.14 3 1 Fmax 1 Fmax 2 ∆γ = − + 2 − 2π R R D πσ
(17.24)
Hence, even though the tensile yield stress reduces the pull-off forces in an AFM experiment, there is an analytical way to correct for these problems. Curves calculated with Equations 17.23 and 17.24 are shown in Figure 17.4. The surface energy for samples obeying the DMT laws is always below the correct value and has to be corrected. The measurement of the surface energy for a JKR-type sample is correct when
2 ∆γ < π2 σ 3 D 2 R 3
(17.25)
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is measured. Equivalently, one might state that the surface energy is correct according to JKR if
Fmax < π 3 σ 3D 2 R2
(17.26)
You find a calculation of this force in Table 17.1. What does it mean if the contact mechanics equations say that tensile stress will be the failure mechanism of the tip–sample junction? • When the pull-off force is larger than predicted by the yield stress argument, one can conclude that continuums theories such as JKR, DMT, or Hertz do not adequately describe the physics of the separation. It was shown by several authors (Cross et al., 1998; Landman et al., 1992; Rubio et al., 1996; Stalder and Dürig, 1996b) both theoretically and experimentally that the tensile stress on the junction shortly before the separation from the tip can exceed the limits set by continuums mechanical theories. Hence a comparison of the actual data with the Dürig (Dürig and Stalder, 1997) theory discussed above gives a criterion for the applicability of standard theories. • In an intermediate regime of AFM tip radii of 50 nm, it is often the case that the yield stress is reached before the crazing mechanism usually responsible for the detachment of the tip and the sample sets in. As a consequence, one expects (and also finds in certain cases) that the tips are contaminated by the sample.
17.2 Experimental Procedures to Measure Adhesion in AFM and Applications The forces of an AFM tip in contact with the sample should in principle be given by the contact mechanics. The tip of the AFM, however, is usually small. Hence the ideas outlined above show that one needs to know the shape and the surface properties of the tip. The ideas above were deduced assuming a flat surface. Real sample topographies are usually rough. Hence one has to calculate the effect of steps on the pull-off force image. This is done using a simple theory based on continuum mechanics. Finally, we discuss force–distance curves, the influence of pull-off force on the tapping mode, and pulsed force mode techniques for AFM. The measurement in the AFM are further complicated by the compliance of the cantilever necessary to measure forces.
17.2.1 Tip Properties Cantilevers are made from a wide range of materials (Akamine et al., 1990; Grütter et al., 1990; Marti, 1998; Pitsch et al., 1989; Wolter et al., 1991). Most cantilevers are made of Si and of Si3N4 . The realizable thickness depends on the fabrication process and the material properties. Grown materials such as Si3N4 can be made thinner than those fabricated out of the bulk. Cantilevers come basically in two flavors. Straight dashboard-like types are preferentially used for lateral force measurements and noncontact modes. Their properties are rather easy to calculate. Triangular shaped cantilevers are easier to align, but harder to handle numerically. They are usually made of silicon nitride. Their response to lateral forces is more complicated. Whereas triangular cantilevers must be calculated using finite element methods, one can get a good estimate of the normal force compliance of the straight ones using analytical methods. Using the equation for straight cantilevers
kN =
F Eb h = z 4 l
3
(17.27)
2 and observing that the length of the two joined cantilever beams in a triangular cantilever are leff = l2 + 2 (w/2) , where w is the width of the base of the cantilever, one gets for the compliance
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Ebh 3 2 w 2 kN = l + 2 4
3
625
2
(17.28)
The radius of curvature of silicon nitride cantilevers is limited to about 30 to 50 nm, because of the manufacturing process. The imperfections of the etch pits and the filled in silicon nitride limit the sharpness. Silicon nitride tips can be sharpened during the production by thermal oxidation (Akamine and Quate, 1992). Instead of directly depositing silicon nitride on the wafers with the pyramidal etch pits, an oxide layer is deposited first. Then the silicon nitride is added. When the oxide is removed with buffered oxide etch, a sharpening effect is observed. Details of the process are described by the inventors (Akamine and Quate, 1992). A second method is to grow in an electron microscope a so-called “supertip” on top of the silicon nitride. It is well known that in scanning electron microscopes with a base pressure of more than 10-10 mbar, hydrocarbon residues are present. These residues are cracked at the surface of the sample by the electron beam, leaving carbon in a presumed amorphous state on the surface. It is known that prolonged imaging in such an instrument degrades the surface. If the electron beam is not scanned, but stays at the same place, one can build up tips with a diameter comparable to the electron beam diameter and with a height determined by the dwell time. These tips are extremely sharp and can reach radii of curvature of a few nanometers. Therefore, they allow imaging with a very high resolution. In addition they enable the microscope to image the bottoms of small crevasses and ditches on samples. Unprocessed silicon nitride tips are not able to do this, since their sides enclose an angle of 90°, due to the crystal structure of the silicon. Alternatives to silicon nitride cantilevers are those made of silicon. The basic manufacturing idea is the same as for silicon nitride. Masks determine the shape of the cantilevers. Processes from the microelectronics fabrication are used. Since the thickness of the cantilevers is determined by etching and not by growth, wafers have to be more precise than for the manufacturing of the silicon nitride cantilevers. The manufacturing process of silicon cantilevers guarantees that the tip asperity has a well defined radius of curvature of 2 to 5 nm. Since the thickness of the silicon cantilever is determined by etching, it cannot be made as thin as the silicon nitride cantilever. The lower limit is typically 1 µm. Therefore the stiffness of silicon cantilevers is higher, ranging from 1 to 100 N/m. Since the material is a single crystal, unlike the silicon nitride, it has a very high quality of resonance. Values exceeding 100,000 have been observed in vacuum. Therefore silicon cantilevers are often used for noncontact or tapping mode experiments. The cantilevers have two drawbacks when working in contact mode. First, they have a very high affinity to organic materials. They often destroy such samples. Second, their index of refraction matches that of water rather closely. Silicon cantilevers have a very poor reflectivity in aqueous environments. Occasionally cantilevers are made with tungsten wire (Marti et al., 1987) or thin metal foils, with tips of diamond (Marti et al., 1988) or other materials glued to them. The radius of curvature of a tip is not well defined. As outlined above and in the literature, the tip shape and the tip radius of curvature are often the results of uncontrollable processes. The initial variation of the tip radius is further increased by wear during use. Therefore the tip radius is one of the least known parameters in an AFM experiment. In many experiments one does not pay attention to the tip shape or radius. To obtain quantitative results it is imperative to inspect the tip before and after the AFM experiment. The size and shape of the tip influence the measured adhesion values (Bhushan and Sundararajan, 1998). Silicon nitride cantilevers were used to probe the adhesion forces vs. a silicon (100) sample. It was found that tip sizes in the order of 1 to 10 µm affect the adhesive forces. At high humidity, capillary forces increase the adhesion considerably. The main properties of an AFM tip are its surface energy and its radius. The surfaces of most cantilevers are made of silicon or silicon nitride. Since cantilevers are usually stored in air, their surfaces are often covered by a thin oxide layer. The surface energy of silicon ranges between 1 and 1.4 N/m (Burdorf, 1999). That of silicon oxide might be as high as 3.5 N/m. Silicon nitride, on the other hand, has a surface energy of 0.7 N/m.
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→
FIGURE 17.5 Geometry of the model calculation. The distance r between a point in the tip and a point in the → → sample is a combination of the distance z between the tip and the sample and the positions of the point in the tip rt → and of the point in the sample rS.
17.2.2 Surface Topography It was mentioned above that the models usually used to describe adhesion do not include effects of the topography (Bhushan, 1999; Koinkar et al., 1996). Therefore a model investigation was done at the University of Ulm. A model based on continuum mechanics and taking into account only interactions due to the shape of the tip and surface topography was established (Stifter et al., 1998). Interactions between the atoms of the tip and the sample were summed up (Figure 17.5). In the model, atoms are represented by a spherically symmetric potential that cannot account for chemical bonding. The interaction is composed of the attractive van der Waals force and the repulsive Pauli force. Both are combined in the Lennard–Jones potential
Vatom
r r r r r r = Vattr r + Vrep r = ε 0 − 2 0 r r
()
()
()
12
6
(17.29)
or
r a b Vatom r = − 6 + 12 r r
()
(17.30)
Here r0 is the position of the potential minimum and ε the depth of the potential minimum. The two potential parameters a and b are defined by
a = 2εr06 and b = εr012 →
(17.31) →
The vector r consists of a contribution of the tip–sample distance z and the local positions of the tip → → and sample, rs and rt , respectively. Equation 17.30 is used for the Lennard–Jones potentials because the two parts of the potential — attractive and repulsive — can be treated separately. Integrating the Lennard–Jones potential over the volume of the tip and the volume of the sample gives the interaction potential between the tip and sample. The integration is performed in two steps, first on the tip and then on the sample, to simplify changes in the surface shape. To simulate an SFM operating in the constant force mode, the force acting in the direction perpendicular to the sample surface is calculated. The
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FIGURE 17.6 Principle of the measurement of force–distance curves. Far away from the sample surface the cantilever spring is not deflected from the zero position (right side of the image). When the tip approaches the sample, an instability for soft cantilevers occurs. The tip snaps to the sample (“snap on peak”). The cantilever is deflected toward the sample (middle of the image), indicating a tensile stress at the tip–sample junction. Finally, at close approach the tip penetrates slightly into the sample. The cantilever spring is deflected away from the sample. When retracting the cantilever from the sample, the tip–sample junction breaks at a value larger than the snap-on peak. This force we call the pull-off force.
coordinate in this direction is the z axis. The x and y axes are in the plane of the sample surface. Figure 17.5 shows the coordinate system used for these calculations. The derivative of the potential with respect to z gives the force between the tip and the sample. For a (x, y) position on the sample, the z-feedback of the SFM determines the value the tip has to be moved to realize the preset force. The calculation works in the same way. For a given (x, y) position and a fixed force value Ffix , the surface distance ztopo was calculated. The pull-off force in the experiment is the maximal negative force appearing as the tip is removed from the surface. This corresponds to the minimum of the force Fmax curve vs. z (see Figure 17.6). A commonly used model for the tip is a sphere with radius R. The sample is represented as a plane. This model was solved in the literature (Stifter et al., 1998). Then the model can be expanded to include the effects of a surface step. The step represents a sharp topographical change. Only forces along a line perpendicular to the step have to be calculated. To get the force for the step, it was necessary to make two volume integrations. To simplify the calculation, the attractive and the repulsive parts of the Lennard–Jones potential (Equation 17.30) are treated separately. The first integration — over the volume of the tip — can be done analytically. The result of the integration is the potential between an atom in the surface and a sphere with radius R. The second integration is split into two parts: the infinite plane is handled analytically, and the terrace (a semiinfinite slab) is treated numerically. The step changes the interaction of the sample with the tip. Because of the curvature, the tip can approach closer to the surface. Its interaction changes. Figure 17.7 shows the influence of the material on the appearance of a step. The figure, calculated with the model outlined above, using a tip radius of 10 nm and a step height of 1 nm, nicely demonstrates that, within this theoretical framework which treats surfaces as infinitely stiff, the surface potential, given by parameters A and B, determines the adhesion. For a materials pairing with equal adhesive properties, a characteristic rim of higher adhesion appears. This feature is also present when the terrace has a higher adhesion. The conclusion from Figure 17.7 is that adhesion forces or pull-off forces are only meaningful at the flat parts of the sample. Figure 17.8 is a measurement by AFM of the adhesion across a step. The measurement confirms the theoretical model.
17.2.3 Force–Distance Curves The easiest way to measure pull-off force properties of a sample surface is to perform force–distance curves. Force–distance curves are obtained by slowly (1 nm/s to 1 µm/s) lowering the tip onto the sample.
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FIGURE 17.7 Adhesion at a step as a function of the material composition. The top part of the image shows the topography. The bottom part depicts the calculated adhesion trace across the step. A Lennard–Jones-type model was used. The three curves are calculated for the binding energy ε and binding distance R0 indicated in the figure. The tighter the tip is bound to the sample, the larger are the artifacts at the steps. The parameters for the sample away from the step correspond to Curve 2.
FIGURE 17.8 Pull-off force of a graphite step. The image size is 210 × 300 nm. The data were measured in a 1 mM solution of NaClO4. The simulations were calculated with a tip radius of 100 nm and a step size of 1.55 nm (multi step). Details of the calculation can be found in Stifter et al. (1998).
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FIGURE 17.9 Correction of the influence of the cantilever compliance. The cantilever compliance is the reason for the double minimum potential landscape when the tip interacts with the sample. On a stiff surface, the change of force when the cantilever base approaches the sample is given by the cantilever compliance. This compliance must be subtracted from the measured force–distance curves. On the adhesive part, the cantilever compliance creates a multivalued force curve, giving rise to adhesive hysteresis. The corrected curve has been calculated from the uncorrected curve. Both have the same underlying potential.
Figure 17.6 shows the principle of such an experiment. Far away from the sample, no force will act on the cantilever. When coming close to the sample, the nonlinear interaction of the tip with the sample will result in an, at least, double well potential. This potential has two stable positions. Which one will be realized depends on the history. At the point where the tip snaps to the surface, it jumps from one minimum to the second one. Upon further approaching the tip, the sample becomes indented. The slope of the force distance curve is now mainly given by the compliance kt of the cantilever. Assume that the sample has a compliance ks and the tip kt
1 1 1 = + keff ks kt
(17.32)
Hence the effective compliance of a soft cantilever and a stiff sample is almost entirely given by the soft cantilever. The effect of the cantilever can be compensated for. If one knows the sensitivity of the detection system (which deflection is necessary to measure a certain force), one can correct the slopes by subtracting the deflection of the cantilever from the position one imposed on the cantilever from the outside (Figure 17.9).
z true = z measured −
F k
(17.33)
The true z-position ztrue is calculated from the measured one zmeasured with Equation 17.33. The force F is determined by the AFM calibration, the compliance of the cantilever k has to be determined independently, or, as a first guess, to be taken from the manufacturer’s data sheets. The corrected curve should then be the real force interaction. As an example, Figure 17.10 shows a measured and corrected force–distance curve on a polystyrene sample. The cantilever compliance and response have been measured with a silicon sample. The values
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FIGURE 17.10 Measured force–distance curve. Shown on the horizontal axis is the distance to the sample surface. Zero is just before the position where the approach curve has its snap-on peak. The vertical axis depicts the force. There is a considerable hysteresis in the retract (unloading) curve. The molecules in the polystyrene samples seem to adhere to the tip; the tensile forces can considerably stretch the molecules before their adhesion bonds to the tip fail.
obtained in this way were used for the correction. The data clearly show that the simple model outlined here is not sufficient. First, the piezo actuators in the AFMs are hampered by hysteretic behavior. This behavior is not easily cast into equations. Therefore a good nano-indentation experiment would need a position control for z. Second, if plastic deformations occur in the sample (which, according to the reasoning above are almost inevitable), dissipation will separate the approach and the retract curves. The pull-off force in Figure 17.10 is about 30% of what the JKR theory predicts. This is why the pull off force has about the same magnitude as the snap-in force. The latter should not depend on the yield stress of the sample, since there is no contact before the sudden change in force.
17.2.4 Influence of Pull-Off Force on Tapping Mode A popular imaging mode in scanning force microscopy is the tapping mode (Anczykowski et al., 1996a,b, 1998; Sarid et al., 1996; Spatz et al., 1995, 1997; Winkler et al., 1996; Zhong et al., 1993). It was realized that adhesion can play an important role in the imaging properties (Evans and Ritchie, 1997; Izrailev et al., 1997; Sarid et al., 1998; Schmitz et al., 1997). In the tapping mode operation (also called dynamic mode operation) the cantilever of the AFM is operated at or near its resonance. The amplitude and phase of the oscillation are complex functions of the drive amplitude, frequency, and of the interaction potential between the tip and the sample. Experience showed that the phase was very sensitive to changes in the materials properties. The equation of motion for the cantilever can be formulated as follows:
∂2 mz˙˙ + 2δz˙ + 2 U z − d − z 0 cos ω 0t z − z 0 cos ω 0t = 0 ∂z
(
)(
)
(17.34)
where z is the position of the end of the cantilever, z0 the drive amplitude, d the separation of the cantilever reference point and the sample. δ is the damping of the cantilever, m its reduced mass, and U(z) the interaction potential. ω0 is the drive frequency. The instantaneous resonance frequency now changes along the trajectory of the tip. The resulting amplitude and phase will be an averaged function of the second derivative of the potential energy of the tip over a full period.
∂2 z˜ t = z ω 0 , f zU z 2 ∂z
()
() ()
(17.35)
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FIGURE 17.11 Phase change as a function of the adhesion properties for a polymer with E = 100 GPa. The solid and dashed lines show the theoretical calculation for the tapping-mode phase with and without taking adhesion into account. (From Sarid, D., Hunt, J.P., Workman, R.K., Yao, X., and Peterson, C.A. (1998), The role of adhesion in tapping-mode atomic force microscopy, Applied Physics A Materials Science & Processing, 66, S283-S286. With permission.)
The potential U(z) is weighted by some function f(z), which has a complicated dependence on the interaction details. From Equations 17.34 and 17.35, it is clear that the compliance of the sample will affect the resonance frequency. Since the tapping mode is usually performed with a constant resonance frequency, this means that the mechanical properties of the sample will show up in the amplitude, and also more prominently in the phase. Hard samples will increase the potential on the average, hence increasing the resonance frequency of the tip–sample system. Samples which exert a nonvanishing adhesive force on the tip lower the average potential for the tip–sample system. In a mean-field reasoning, the resonance frequency has to go down. The stronger the adhesion, the larger the phase shift of the system. Figure 17.11 shows data from Sarid et al. (1998). The phase change for a given set point as a function of the adhesion is clearly visible. A strong adhesive force can create multiwell potential landscapes. The oscillation of the cantilever can then be confined to one or the other well. Jumps between the wells can occur. This behavior has been observed, for instance by Anczykowski et al. (1998) (Figure 17.12). The jumps from one potential well to the other occur when the original well becomes unstable, i.e., loses its confinement. The result is a hysteresis when the set-point of the microscope is brought closer to the sample surface and then back again. It is not trivial to extract meaningful quantitative adhesion data from tapping-mode phase measurements. The effects of the finite yield stress of the material certainly have an influence on the depth of the potential wells. They will reduce the effects of adhesion. On the other hand, adhesion for macromolecules is always connected with a rearrangement of molecules. This rearrangement has its own time constants. In principle it should be calculated with molecular dynamics methods. Unfortunately these methods are not yet able to calculate the dynamics on the time scale relevant for a tapping-mode experiment.
17.2.5 Pulsed-Force Mode A third method to measure pull-off force properties (or better, pull-off forces) is the pulsed-force mode (PFM). A sinusoidal z-modulation is used to continuously acquire force vs. distance curves. The PFM is one of the so-called intermittent contact modes in AFM. The key to the operation of the PFM (and the tapping mode) is the frequency dependence of the elastic moduli of samples. The apparent shear modulus increases when the frequency of the acquisition of force-distance curves is increased. The time the tip is in contact with the surface can be directly estimated by the modulation frequency. Typically the AFM
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FIGURE 17.12 Influence of multiple potential wells on the tapping mode amplitude and phase behavior, experimental data. The cantilever was driven at the harmonic resonance frequency. A bias voltage was applied for the measurement at the right side to increase the attractive part of the potential. When combining the harmonic potential related to a Hookian spring with the interaction potential for two bodies, e.g., the Lennard–Jones potential or similar potentials, a double-well potential landscape is formed. Shown are the amplitude of the tapping-mode oscillation on the top and the phase on the bottom. In every part the sample surface is at zero z-position. (From Anczykowski, B., Cleveland, J.P., Kruger, D., Elings, V., and Fuchs, H. (1998), Analysis of the interaction mechanisms in dynamic mode SFM by means of experimental data and computer simulation, Appl. Phys. A Materials Science & Processing, 66, S885-S889. With permission.)
cantilever in the PFM is brought into contact at a rate of 1 to 10 kHz. Thus, the PFM has a contact time of about 10 µs (as measured from oscilloscope traces), compared to > 10 ms when measuring force–distance curves and ≈1 µs in tapping mode. Delicate samples can be measured this way, with a resolution and gentleness comparable to that of the tapping mode. Electronic circuitry (Krotil et al., 1999; Miyatani et al., 1998; Rosa-Zeiser et al., 1997) creates the sinusoidal modulation frequency, which is applied either to the z-electrode of the scan piezo or to a special modulation piezo. The sinusoidal shape is necessary to avoid the excitation of resonances in the microscope. The cantilever-base moves up and down, as depicted in Figures 17.13 and 17.14. The resulting force signal, as detected by the AFM head, is a repetitive measurement of force–distance curves. The peak positive force (1 in Figure 17.14) is detected by a “sample and hold” circuit. It serves as the input of the control loop and is fed into the AFM control electronics, faking a constant force measurement. The feedback loop now maintains a constant peak positive force. The PFM allows an exact determination of the peak interaction force independent of the operating environment.
FIGURE 17.13 Movement of the tip in the pulsed-Force mode measurement. In a typical setup the cantilever is mounted on a piezo. This piezo moves the cantilever base up and down with a predefined curve form. Most often a sinusoidal movement is used. As long as the cantilever is free, it is not bent, indicating that no interaction force is present. Indentation causes the cantilever to bend upwards, tensile forces before pull-off deflect the cantilever beam downwards.
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FIGURE 17.14 Operation of the pulsed force mode measurement (Krotil et al., 1999; Rosa-Zeiser et al., 1997). At point 1 a sample and hold circuit measures the peak indentation force. This force is kept constant by the feedback control circuits of the microscope. The peak force (Fmax) minus the force measured at 3 (Fis) is a function of the local sample stiffness and the cantilever stiffness kc. The force at 2 is the zero point value. It is constant if there are no long-range forces. It varies if magnetic, electrostatic, or other forces are present. Finally, the force at 4 measured by a peak picker circuit is the pull-off force.
The PFM automates the measurement of surface properties at every point on the sample by additionally sampling a few characteristic values of the force–distance curves using additional “sample and hold” circuits. It has a minimal impact on the data acquisition rate. Data taken from the curve are the local stiffness, the local pull-off force (adhesion), and local charges (Figure 17.14). The pull-off force output is the difference between the output of a peak-detector for negative forces and a sample and hold measuring the zero base line. These quantities are complementary to what one would get from tapping mode, where the phase signal is related to the energy dissipation and, sometimes, to the adhesion on the sample surface. As pointed out above, the measured pull-off forces have to be corrected for the finite yield stress of the samples. If this is done, then reliable values for the surface energies can be extracted. Figure 17.15 shows the effect of a changing Young’s modulus of the sample surface. The force curve on the hard material is shorter; the pull-off force is less. This is the behavior one would expect from the JKR theory. As an example, we show a measurement of spherulites in polypropylene (Hild et al., 1998; Marti et al., 1999). The images in Figure 17.16 were acquired in the PFM with a frequency of 1.6 kHz. The left side shows the topography; the right side, the pull-off force. The amorphous parts in the topography images appear to be lower than the crystalline areas. This can be explained by differences in local stiffness. For a given force, the tip indentation in the softer material is larger than in the harder one. Because of the different indentation at a given applied force, harder parts of a surface appear to be higher. In the pulloff force image, the amorphous parts between the crystalline lamellae exert a high force on the tip (dark color). The data on the right side of Figure 17.16 have not been corrected for the yield stress phenomenon.
17.3 Summary and Outlook The measurement of pull-off forces with the AFM is widespread nowadays. The interaction of the AFM tips and the sample surfaces yields valuable information on the surface energies of the samples. However, in day-to-day work, one is using methods like tapping mode, force–distance curves, and pulsed-force-mode
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FIGURE 17.15 Signals in the pulsed-force mode measurement. The top trace shows the movement of the piezo, which is the same as that of the mounting point of the cantilever spring. The bottom trace shows a typical force vs. time curve. The left side simulates the behavior on a stiff surface; the right side shows a typical trace obtained on a compliant, nonviscous surface. The measurement system determines the peak force Fmax and a second force value at a fixed time offset, Fis. The difference between these two forces depends on the stiffness of the sample.
FIGURE 17.16 Spherulite of polypropylene. The left image shows the topography; the right image, the pull-off force measurement. The scan size of both images is 1200 × 1200 nm. The height range in the left image is 35 nm (white corresponds to high lying areas; black to low lying areas). The pull-off force values range from –40 to –90 nN (white corresponds to low pull-off forces).
to get a quick overview of the sample. Usually one is interested in finding differences in the morphology of the samples. The quantitative nature of the pull-off force measurement is usually not necessary. However, experiments trying to correlate pull-off force measurements with theories sometimes fail. Usually one is able to range samples correctly with different methods. For polymer samples, often the absolute surface energies calculated from reasonable assumptions of the tip shape do not agree with measurements by contact angles. The idea of Stalder and Dürig (Dürig and Stalder, 1997) that the yield stress is an important quantity for the determination of surface energies has not been fully exploited yet. From the considerations in this chapter it is clear that probably no AFM, independent of the operating mode, works in the “adhesion” dominated regime. It rather operates in the yield stress or break stress dominated regime. The theoretical considerations show that the shape of the force–distance curve, if the movement of the z-piezo were linear, and the pull-off force together are sufficient to extract both the surface energy and the yield (break) stress from the data.
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If the shape of force–distance curves is not known, then one can use the macroscopic yield stress to infer the surface energy. One wonders why the tips of an AFM do not show substantial contamination with the sample material, since the failure of an AFM–sample junction seems to be located entirely within the sample. In the case of polymers, the situation is not as simple as one might guess. The macromolecules have typical gyration radii of up to 30 nm. Hence a junction might consist of only a few molecules. The yield-stress limit is an indication of the point up to which continuum mechanics apply. For smaller tips, one will have to take into account the discrete nature of the interaction. When one has to measure adhesion forces, or more specifically pull-off forces, one has to select the methods according to the priorities of the experiment. If a fast overview on the variations of surface properties and on the spatial distribution of them is desired, tapping-mode phase imaging is the method of choice. However, its physics is not easily handled. Extensive calculations and, probably, modeling of the sample–tip system are required to get quantitative data. The force–distance curves, on the other hand, allow a rather precise measurement of the pull-off forces, at the expense of speed. Imaging is almost impossible. Force–distance curves give the shape of the interaction, making it comparatively easy to calculate quantitative data. The pulsed-force mode is a compromise between the previous two measurement modes. It only acquires some selected values of the force–distance curve. This is done efficiently and poses no obstacle to imaging in reasonable time. Data from force–distance curves and from the pulsed-force mode can be corrected for the yield-stress effect. There is still considerable research necessary to sort out all the effects besides the adhesion forces in pull-off force measurements. Nevertheless, meaningful measurements can be done, provided the experiment is carefully planned. Therefore the AFM has a good chance to become a versatile mechanical testing device for ultra-small amounts of materials.
Acknowledgments The overview presented here is based on the contributions of many persons. I would like to thank Thomas Stifter, Hans-Ulrich Krotil, Sabine Hild, and Charly Imhof for the measurements. I had long discussions with Martin Pietralla, Sabine Hild, Thomas Stifter, Gerd-Ingo Asbach, and Bharat Bhushan on this subject. Gerhard Volswinkler built the electronics. This work was funded in part by the Deutsche Forschungsgemeinschaft (SFB 239), the Land Baden-Württemberg, and by Witec GmbH Ulm.
References Akamine, S., Barrett, R.C., and Quate, C.F. (1990), Improved atomic force microscope images using microcantilevers with sharp tips, Appl. Phys. Lett., 57, 316. Akamine, S. and Quate, C.F. (1992), Low temperature thermal oxidation sharpening of microcast tips, J. Vac. Sci. Technol., B10 (6), 2307-2311. Anczykowski, B., Cleveland, J.P., Kruger, D., Elings, V., and Fuchs, H. (1998), Analysis of the interaction mechanisms in dynamic mode SFM by means of experimental data and computer simulation, Appl. Phys. A Materials Science & Processing, 66, S885-S889. Anczykowski, B., Kruger, D., Babcock, K.L., and Fuchs, H. (1996), Basic properties of dynamic force spectroscopy with the scanning force microscope in experiment and simulation, Ultramicroscopy, 66 (3-4), 251-259. Anczykowski, B., Kruger, D., and Fuchs, H. (1996), Cantilever dynamics in quasinoncontact force microscopy: spectroscopic aspects, Phys. Rev. B Condensed Matter, 53 (23), 15485-15488. Bhushan, B. (1996), Nanotribology and nanomechanics of MEMS devices, in Proceedings of the 9th Annual Workshop on Micro-Electro-Mechanical Systems, IEEE, New York, 91. Bhushan, B. (1999), Principles and Applications of Tribology, John Wiley & Sons, New York. Bhushan, B. and Sundararajan, S. (1998), Micro/nanoscale friction and wear mechanisms of thin films using atomic force and friction force microscopy, Acta Metallurgica, 46 (11), 3793-3804. Binnig, G., Quate, C.F., and Gerber, C. (1986), Atomic force microscope, Phys. Rev. Lett. 56 (9), 930-933.
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Burdorf, K. (1999), Silicon-direct-bonding: packaging technology on wafer level, Institute for Microsensors, -actuators and -systems (IMSAS), University of Bremen, http://www.imsas.unibremen.de/service/sdb.html. Burnham, N.A. and Colton, R.J. (1989), Measuring the nanomechanical properties and surface forces of materials using an atomic force microscope, J. Vac. Sci. Technol. A (Vacuum, Surfaces, and Films), 7 (4), 2906-13. Creuzet, F., Ryschenkow, G., and Arribart, H. (1992), A new tool for adhesion science: the atomic force microscope, J. Adhes., 40 (1), 15-25. Cross, G., Schirmeisen, A., Stalder, A., Grütter, P., Tschudy, M., and Dürig, U. (1998), Adhesion interaction between atomically defined tip and sample, Phys. Rev. Lett., 80 (21), 4685-4688. Derjaguin, B.V., Muller, V.M., and Toporov, Y.P. (1975), Effect of contact deformations on the adhesion of particles, J. Colloid Interface Sci., 53, 314-320. Dürig, U. and Stalder, A. (1997), Adhesion on the nanometer scale, in Micro/Nanotribology and Its Applications, Bhushan, B. (Ed.), Kluwer, Dordrecht, Vol. E330, 61. Evans, E. and Ritchie, K. (1997), Dynamic strength of molecular adhesion bonds, Biophys. J., 72 (4), 1541-1555. Godowski, P.J., Maurice, V., and Marcus, P. (1995), Analytical problems in atomic force microscopy: distortion of surface structures during imaging, Chem. Anal., 40, 231-242. Grütter, P., Rugar, D., Mamin, H.J., Castillo, G., Lambert, S.E., Lin, C.-J., Valletta, R.M., Wolter, O., Bayer, T., and Greschner, J. (1990), Batch fabricated sensors for magnetic force microscopy, Appl. Phys. Lett., 57, 1820. Hertz, H. (1881), Über die Berührung fester elastischer Körper, J. Reine Angew. Math., 92, 156-171. Hild, S., Rosa, A., and Marti, O. (1998), Deformation induced changes in surface properties of polymers investigated by scanning force microscopy, in Scanning Probe Microscopy of Polymers, Ratner, B.D. and Tsukruk, V.V. (Eds.), Oxford University Press, Vol. 694, 110. Izrailev, S., Stepaniants, S., Balsera, M., Oono, Y., and Schulten, K. (1997), Molecular dynamics study of unbinding of the avidin–biotin complex, Biophys. J., 72 (4), 1568-1581. Jiaa, C.L., Nguyen, P., Teng, E., and Eltoukhy, A. (1994), The role of surface properties in the mechanical performance of thin film rigid disks, Thin Solid Films, 248 (1), 41-6. Johnson, K.L. (1992), Introduction to contact mechanics: a summary of the principal formulae, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I.L. and Pollock, H.M. (Eds.), Kluwer Academic Publishers, Dordrecht, Vol. 220, 589. Johnson, K.L. (1996), A continuum mechanics model of adhesion and friction in a single asperity contact, in Micro/Nanotribology and its Applications, Bhushan, B. (Ed.), Kluwer Academic Publishers, Dordrecht. Johnson, K.L. (1997), Adhesion and friction between a smooth elastic spherical asperity and a plane surface, Proceedings of the Royal Society of London Series A Mathematical Physical and Engineering Sciences, 453 (1956), 163-179. Johnson, K.L., Kendall, K., and Roberts, A.D. (1971), Surface energy and the contact of elastic solids, Proc. R. Soc. London, Ser. A, 324, 301-313. Koinkar, V.N. and Bhushan, B. (1996a), Micro/nanoscale studies of boundary layers of liquid lubricants for magnetic disks, J. Appl. Phys., 79 (10), 8071-5. Koinkar, V.N. and Bhushan, B. (1996b), Microtribological studies of unlubricated and lubricated surfaces using atomic force friction force microscopy, J. Vac. Sci. Technol. A Vacuum Surfaces and Films, 14 (4), 2378-2391. Krotil, H.-U., Stifter, T., Waschipky, H., Weishaupt, K., Hild, S., and Marti, O. (1999), Pulsed force mode: a new method for the investigation of surface properties, Surface and Interface Analysis, 27, 336-340. Landman, U., Luedtke, W.D., and Ringer, E.M. (1992), Atomistic mechanisms of adhesive contact formation and interfacial processes, Wear, 153 (1), 3-30.
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Lekka, M., Laidler, P., Gil, D., Cleff, B., and Stachura, Z. (1997), Elastic surface properties studied using scanning force microscopy, Electron Technology, 30 (2), 173-6. Marti, O. (1998), AFM instrumentation and tips, in Handbook of Micro/Nanotribology, Bhushan, B. (Ed.), CRC Press, Boca Raton, 81. Marti, O., Drake, B., and Hansma, P.K. (1987), Atomic force microscopy of liquid-covered surfaces: atomic resolution images, Appl. Phys. Lett., 51 (7), 484-486. Marti, O., Ribi, H.O., Drake, B., Albrecht, T.R., Quate, C.F., and Hansma, P.K. (1988), Atomic force microscopy of an organic monolayer, Science, 239, 50-52. Marti, O., Waschipky, H., Quintus, M., and Hild, S. (1999), Scanning probe microscopy of heterogeneous polymers, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 154 (1-2), 65-73. Maugis, D. (2001), Adhesion of solids: mechanical aspects, in Modern Tribology Handbook, Bhushan, B. (Ed.), CRC Press, Boca Raton. Miyamoto, T., Kaneko, R., and Ando, Y. (1990), Interaction force between thin film disk media and elastic solids investigated by atomic force microscope, J. Tribol., 112 (3), 567-72. Miyatani, T., Okamoto, S., Rosa, A., Marti, O., and Fujihira, M. (1998), Surface charge mapping of solid surfaces in water by pulsed-force-mode atomic force microscopy, Appl. Phys. A Materials Science & Processing, 66, S349-S352. Mizes, H.A., Loh, K.-G., Miller, R.J.D., Ahuja, S.K., and Grabowski, E.F. (1991b), Submicron probe of polymer adhesion with atomic force microscopy: dependence on topography and material inhomogeneities, Appl. Phys. Lett., 59, 2901-2903. Pitsch, M., Metz, O., Kohler, H.-H., Heckmann, K., and Strnad, J. (1989), Atomic resolution with a new atomic force tip, Thin Solid Films, 175, 81. Ramirez-Aguilar, K.A. and Rowlen, K.L. (1998), Tip characterization from AFM images of nanometric spherical particles, Langmuir, 14 (9), 2562-2566. Rosa-Zeiser, A., Weilandt, E., Hild, S., and Marti, O. (1997), The simultaneous measurement of viscoelastic, electrostatic and adhesive properties by SFM: pulsed force mode operation, Measurement Science and Technology, 8, 1333-1338. Rubio, G., Agraït, N., and Vieira, S. (1996), Atomic-sized metallic contacts: mechanical properties and electronic transport, Phys. Rev. Lett., 76 (13), 2302-2305. Sarid, D., Hunt, J.P., Workman, R.K., Yao, X., and Peterson, C.A. (1998), The role of adhesion in tappingmode atomic force microscopy, Applied Physics A Materials Science & Processing, 66, S283-S286. Sarid, D., Ruskell, T.G., Workman, R.K., and Chen, D. (1996), Driven nonlinear atomic force microscopy cantilevers: from noncontact to tapping modes of operation, J. Vac. Sci. Technol. B, 14 (2), 864-867. Schmitz, I., Schreiner, M., Friedbacher, G., and Grasserbauer, M. (1997), Phase imaging as an extension to tapping mode AFM for the identification of material properties on humidity-sensitive surfaces, Appl. Surf. Sci., 115 (2), 190-198. Spatz, J.P., Sheiko, S., Möller, M., Winkler, R.G., and Marti, O. (1995), Forces affecting a substrate in tapping mode, Nanotechnology, 6, 40-44. Spatz, J.P., Sheiko, S., Möller, M., Winkler, R.G., Reineker, P., and Marti, O. (1997), Tapping scanning force microscopy in air — theory and experiment, Langmuir, 13, 4699-4703. Stalder, A. and Dürig, U. (1996a), Study of plastic flow in ultrasmall Au contacts, J. Vac. Sci. Technol. B, 14 (2), 1259-1263. Stalder, A. and Dürig, U. (1996b), Study of yielding mechanics in nanometer-sized Au contacts, Appl. Phys. Lett., 68 (5), 637-639. Stifter, T., Weilandt, E., Marti, O., and Hild, S. (1998), Influence of the topography on adhesion measured by SFM, Appl. Phys. A Materials Science & Processing, 66, S597-S605. van Kevele, D.W. (1976), Properties of Polymers, Elsevier, Amsterdam, 303. Vogel, H. (1995), Gerthsen: Physik, 18 ed. Springer, Heidelberg.
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Weisenhorn, A.L., Maivald, P., Butt, H.-J., and Hansma, P.K. (1992), Measuring adhesion, attraction, and repulsion between surfaces in liquids with an atomic-force microscope, Physical Review B, 45 (19), 11226-11232. Winkler, R.G., Spatz, J.P., Sheiko, S., Moller, M., Reineker, P., and Marti, O. (1996), Imaging material properties by resonant tapping-force microscopy: A model investigation, Phys. Rev. B Condensed Matter, 54 (12), 8908-8912. Wolter, O., Bayer, T., and Gerschner, J. (1991), Micromachined silicon sensors for scanning force microscopy, J. Vac. Sci. Technol., B9, 1353. Zhong, Q., Inniss, D., Kjoller, K., and Elings, V.B. (1993), Fractured polymer/silica fiber surface studied by tapping mode atomic force microscopy, Surf. Sci., 290 (1-2), L688-92.
Symbols Symbol
Unit
Meaning
z~ a b b D
m Nm7 m Nm13 m -----N
Compliance factor
E
N ------2 m
Modulus of elasticity, Young’s modulus
F F(z) F0 Fmax Fyield h Hcrit
N — N N N m
Force applied to spherical test body Weight function for averaging the potential Pull-off force (JKR) Maximum force in the junction before yielding Yield force Thickness of cantilever
N ------2 m
Critical yield stress
k
N ---m
Cantilever compliance
kc
N ---m
Contact stiffness
keff
N ---m
Effective compliance of the junction
kN
N ---m
Compliance of the cantilever for normal forces
kS
N ---m
Sample compliance
kT
N ---m
Tip compliance
l m R r0 R0 Rc Rcrit U(z) Vatom
m kg m m m m m Nm Nm
Length of cantilever Effective mass of cantilever Radius of the spherical test body Distance of potential minimum in the Lennard–Jones potential Minimum contact radius Contact radius Critical radius of spherical test body for yield failure Interaction potential between tip and sample Potential of a single atom
Averaged movement of tip Coefficient of attractive part of the Lennard–Jones potential Width of cantilever Coefficient of repulsive part of the Lennard–Jones potential
2
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Vattr Vrep w z zmeasured ztrue ∆γ
Nm Nm m M M M
Attractive component of the potential of a single atom Repulsive component of the potential of a single atom Base width of a triangular cantilever Coordinate perpendicular to sample or cantilever Measured displacement of the cantilever end-point True displacement of the cantilever end-point
N ---m
Difference in the contact potential
Θ δ ε γL
rad m Nm
Contact angle Indentation depth Magnitude of the potential in the Lennard–Jones potential
N ---m
Contact potential of the test liquid vs. air
N ---m
Contact potential of the sample vs. air
—
Poisson number
N ------2 m
Yield stress
N ------2 m
Critical yield stress for a given tip radius
1 --s
Angular frequency of excitation
γS ν σ
σcrit ω0
639
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18 Atomic-Scale Friction Studies Using Scanning Force Microscopy 18.1 18.2 18.3 18.4 18.5
Frictional Contrast Caused by Local Changes in the Chemical Composition • Friction of Surfaces Possessing Identical Chemical Composition • Direction Dependence of Sliding Friction
Udo D. Schwarz University of Hamburg
Hendrik Hölscher University of Hamburg
Introduction ..................................................................... 641 The Scanning Force Microscope as a Tool for Nanotribology .................................................................. 642 The Mechanics of a Nanometer-Sized Contact ............. 644 Amontons’ Laws at the Nanometer Scale....................... 646 The Influence of the Surface Structure on Friction ...... 648
18.6 18.7 18.8
Atomic Mechanism of Friction....................................... 652 The Velocity Dependence of Friction............................. 658 Summary .......................................................................... 660
18.1 Introduction Although frictional forces are familiar to everyone from daily life experiences, little progress has been made in finding an exact physical description of friction since the following phenomenological friction laws were established by Amontons (1699) and Coulomb (1783): 1. Friction is proportional to the load (i.e., to the applied normal force). 2. Friction is independent of the (apparent) contact area. 3. Sliding friction is independent of the sliding velocity. These laws hold surprisingly well in the case of dry friction or Coulomb friction, if there is no lubrication between the two interacting bodies. Nevertheless, they could not be derived from first principles up to now. Moreover, the understanding of the fundamental mechanisms of friction on the atomic scale is poor since most macroscopic and microscopic frictional effects are normally dominated by the influence of wear, plastic deformation, lubrication, surface roughness, and surface asperities. Macroscopic friction experiments (see Figure 18.1a), especially if performed under ambient conditions are therefore difficult to analyze in terms of a universal theory. Moreover, the complexity of the phenomena prevented the observation of pure wearless friction for many years, thus disabling all attempts to understand the origins of friction on the molecular and atomic scale. In the last decades, however, the field of nanotribology was established by introducing new experimental tools which opened the nanometer and the atomic scale to tribologists. One of the basic ideas of
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FIGURE 18.1 (a) The well-known experimental setup to confirm the frictional laws (1) and (2) of dry friction on the macroscopic scale. (b) The apparent contact area observed on the macroscopic scale consists of many individual small asperities. A nanometer-sized single asperity contact (“point contact”) can be realized in a scanning force microscope.
nanotribology is that for a better understanding of friction in macroscopic systems, the frictional behavior of a single asperity contact should be investigated first. Macroscopic friction could then possibly be explained with the help of statistics, i.e., by adding the interactions of a large number of individual contacts, which together form the macroscopic roughness of the interface between the two bodies which are in relative motion (see Figure 18.1b for illustration). The first big step toward such experiments at the atomic level was taken when the surface force apparatus was equipped with special stages enabling the measurement of lateral forces between two molecularly smooth surfaces sliding against each other (Israelachvili and Tabor, 1973; Briscoe and Evans, 1982). The biggest step concerning the reduction of the asperity size was accomplished with the development of the friction force microscope (FFM) (Mate et al., 1987). The FFM is derived from the scanning force microscope (SFM) (Binnig et al., 1986) and enables the local measurement of lateral forces by moving a sharp tip, representing (approximately) a point contact, over a sample surface. In this chapter, we intend to describe how the FFM can contribute to the understanding of the origin and nature of the fundamental laws of friction by the investigation of atomic-scale frictional effects. As shown in the following sections, friction at the nanometer scale manifests itself in a significantly different manner than the Coulomb friction at the macroscopic scale. The friction laws (1) and (2) are found to be not valid for point contact friction, since the frictional forces on the nanometer scale are proportional to the actual area of contact, which is generally not proportional to the load (Section 18.4). On the other hand, friction law (3) could be confirmed for moderate sliding velocities also on this scale (Section 18.7). The analysis of the frictional behavior of such approximate point contacts in terms of a simple mechanical model exhibits a two-dimensional nature of friction on the atomic scale, which is determined by a “stickslip” type movement of the foremost tip atoms (Section 18.6). Molecular-scale effects involving wear or lubrication, however, will be discussed in the next chapter.
18.2 The Scanning Force Microscope as a Tool for Nanotribology The principle of scanning force microscopy is rather simple and resembles that of a record player. A force microscope (Figure 18.2) detects forces acting between a sample surface and a sharp tip which is mounted on a soft leaf spring (the cantilever). A feedback system which controls the vertical z-position of the tip on the sample surface keeps the deflection of the cantilever (and thus the force between tip and sample) constant. Moving the tip relative to the sample in the x–y-plane of the surface by means of piezoelectric drives, the actual z-position of the tip is recorded as a function of the lateral x–y-position with (ideally)
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laser
photo diode
A C
B
z x y
D cantilever tip sample Fx
Fz
x-, y-, z-scanner
Fy
a)
b)
FIGURE 18.2 (a) Principle of the scanning force microscope. Bending and torsion of the cantilever are measured simultaneously by measuring the lateral and vertical deflection of a laser beam while the sample is scanned in the x–y-plane. The laser beam deflection is determined using a four-quadrant photo diode: (A+B)–(C+D) is a measure for the bending and (A+C)–(B+D) a measure for the torsion of the cantilever, if A, B, C, and D are proportional to the intensity of the incident light of the corresponding quadrant. (b) The torsion of the cantilever (middle) is solely due to lateral forces acting in the x-direction, whereas both forces acting normal to the surface (Fz) as well as acting in plane in the y-direction (Fy) cause a bending of the cantilever (bottom).
sub-Ångström precision. The obtained three-dimensional data represent a map of equal forces; the necessary conversion of the cantilever deflection into the normal force is basically performed by applying Hook’s law. The data can be analyzed and visualized through computer processing. A more detailed description of the method and the generally used instrumentation is given, e.g., by Meyer and Heinzelmann (1992), Wiesendanger (1994), Bhushan and Ruan (1994), or Schwarz (1997). The experimental setup for the deflection detection measurement, which is most frequently used in SFM studies on friction, is the beam deflection scheme sketched in figure 18.2a (Marti et al., 1990; Meyer and Amer, 1990). With this detection scheme, not only the deflection, but also the torsion of the cantilever can be measured (see the caption of Figure 18.2a for further details). Force microscopes, which can record bending and torsion of the cantilever simultaneously, are often referred to as friction force microscopes (FFMs) or lateral force microscopes (LFMs). What are the specific advantages of friction force microscopy in comparison with other methods? As we have seen in the introduction, macroscopic friction experiments are often difficult to analyze due to the complexity of the experimental system. For the unambiguous analysis of physical phenomena, the experiments performed to clarify their nature are preferably arranged as simply as possible. Friction force microscopy is an especially suitable tool for nanotribological investigations because it meets this requirement quite well: 1. Measurements within the purely elastic regime prevent plastic deformation or wear of tip or sample. Consequently, all experiments presented in this chapter were performed at loading forces which were sufficiently low such that no effects due to plastic deformation could be observed. 2. The contact area of the sliding tip with the sample surface is very small (typically some nm2), thus enabling the localized detection of frictional forces. 3. The apparent and the actual contact area are identical. Therefore, problems occurring from surface roughness and surface asperities can be neglected if the experiments are performed on atomically smooth surfaces. 4. If measured under controlled conditions (e.g., in ultra-high vacuum or in an argon atmosphere), an influence of adsorbates on the measured friction can be reduced or completely avoided.
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FIGURE 18.3 (a) Macroscopic tip–sample contact; Fl denotes the externally applied loading force. The contact area-load dependence is difficult to describe due to the irregular shape of both tip and sample surface. (b) Geometry of a Hertzian contact (see text). R = radius of the tip apex; a = radius of the contact area.
Finally, two more points should be noted: (1) During scanning, the torsion of the cantilever is exclusively induced by lateral forces acting in the x-direction (Fx), whereas for corrugated samples, the bending of the cantilever is mainly caused by forces acting perpendicular to the sample surface in the z-direction (Fz). Nevertheless, a bending of the cantilever induced by lateral forces acting in the y-direction (Fy) cannot be excluded (see Figure 18.2b, bottom). For atomically flat surfaces, Fujisawa et al. (1993a,b; 1995) pointed out that the variation of Fz is so small that the measured signal of an SFM equipped with the beam deflection method is mostly determined by lateral forces. Therefore, on the atomic scale, the lateral forces both in scan direction and perpendicular to the scan direction are measured. (2) The correct calibration of the bending and the torsion of the cantilever in terms of lateral forces is much more difficult than the conversion of the cantilever deflection into the normal force, which can simply be performed by applying Hook’s law. Many parameters such as the cantilever dimensions, the elastic moduli of the cantilever material, the tip length, the position on the cantilever backside where the laser beam is reflected and the sensitivity of the four-quadrant photo diode have to be known. Different procedures for the quantitative analysis of lateral force microscopy experiments are described, e.g., by Marti et al. (1993), Bhushan and Ruan (1994), Lüthi et al. (1995), Putman et al. (1995), Ogletree et al. (1996), and Schwarz et al. (1996a).
18.3 The Mechanics of a Nanometer-Sized Contact Since it is the attempt of nanotribology to reconstruct the macroscopic frictional behavior from the frictional properties of an individual nanometer-sized contact, it is clear that a knowledge of the mechanics of such small single asperity contacts is essential. For example, the exact contact area of tip and sample as a function of the applied loading force has to be known in order to compare the data obtained by scanning force microscopy with theoretical models, as we will see in Section 18.4. Scanning force microscopy, however, does not allow an independent measurement of the contact area. In order to circumvent this restriction, it is a common approach in SFM to use tips with a geometrically well-defined apex and to calculate the effective contact area (and other important parameters such as deformation or stiffness of the contacts) on the basis of continuum elasticity theory. A detailed description of contact mechanics is given by Johnson (1994). Here, we will restrict ourselves to the mathematically simplest and most frequently used case of a spherical tip which is in contact with a flat surface (the so-called Hertzian contact, Figure 18.3), in spite of the fact that there also exist extensions to other geometries (see, e.g., Carpick et al., 1996). Without adhesion, the contact area of such a Hertzian contact can be determined using the Hertzian theory (Hertz, 1881), which was already developed in 1881. It predicts a contact area-load dependence of the following form:
RF A = π l K
2 3
(18.1)
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Here, R is the radius of the tip, Fl the loading force, and
4 1 − ν12 1 − ν22 K= + E2 3 E1
−1
(18.2)
the “effective elastic modulus” (with E1,2 and ν1,2 as Young’s moduli and Poisson’s ratios of sphere and flat, respectively). Other useful quantities are, e.g., the contact radius a of the interface region
a3 =
RFl K
(18.3)
the vertical displacement δ of the two bodies in contact
δ=
a 2 Fl = R Ka
(18.4)
and the pressure or stress distribution p(r) within the contact region 2
r r 3Fl 3Ka pr = 1− = 1− 2 2πR a a 2πa
()
2
(18.5)
Since the early 1970s, however, theories have been developed which include attractive forces (Johnson et al., 1971; Derjaguin et al., 1975; Muller et al., 1983; Maugis, 1987; Fogden and White, 1990; Maugis, 1992; Maugis and Gauthier-Manuel, 1994). The general mathematical formulation of the contact areaload dependence of a Hertzian contact including adhesion cannot be solved analytically (Fogden and White, 1990; Maugis, 1992). Nevertheless, depending on how the attractive forces act, approximations can be derived. In order to decide which of the above-mentioned approximations applies under which conditions, Tabor (1977) introduced the nondimensional parameter Φ
9Rγ 2 Φ= 2 3 4K z0
13
(18.6)
(γ: surface energy of sphere and flat [for equal surfaces] and z0: equilibrium distance in contact), which represents basically a measure for the magnitude of the elastic deformation outside the effective contact area compared with the range of the surface forces. When Φ is large (Φ > 5 [Johnson, 1997]), the Johnson–Kendall–Roberts (JKR) theory (Johnson et al., 1971) applies, which has been confirmed in many experiments (see, e.g., Israelachvili et al. [1980] and Homola et al. [1990]). If Φ < 0.1, however, contacts should be appropriately described by the analysis of Derjaguin, Muller, and Toporov (DMT) (Derjaguin et al., 1975; Muller et al., 1983). Nevertheless, since the small value of Φ indicates that there is only negligible elastic deformation outside the effective contact area, the influence of attractive forces can in further simplification be considered by introducing an effective normal force Fn = F1 + F0, where F0 is the sum of all acting attractive forces. Replacing F1 with Fn in Equation 18.1 leads to
(
)
R Fl + F0 A = π K
2 3
RF = π n K
2 3
(18.7)
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FIGURE 18.4 Three examples of tip specially prepared in a transition electron microscope with spherical tip apexes of (a) 21 ± 5 nm, (b) 35 ± 5 nm, and (c) 112 ± 5 nm radius.
This model will be referred to as the Hertz-plus-offset model in the following to distinguish between the original and more precise DMT formalism and the present further simplification. Detailed mathematical derivations of Equation 18.7 for the case of capillary forces were published by Fogden and White (1990) and Maugis and Gauthier-Manuel (1994). By introducing typical values for contacts as they occur in SFMs into Equation 18.6 (R = 30 nm, γ = 25 mJ/m2 [typical for van der Waals surfaces], K = 50 GPa, and z0 = 3 Å), we find a value for Φ of ≈ 0.09. Therefore, Equation 18.7 should represent the correct contact area-load dependence for typical contacts found in SFMs. A more detailed discussion of the contact mechanics of a nanometer-sized Hertzian contact is given by Schwarz et al. (1996a, 1997a). However, Equation 18.7 only applies for tips with exactly spherical apex. Using SFM tips as supplied by the manufacturer, such a shape is only accidentally realized, and thus all kinds of power laws A ∝ Fn with n ranging from n ≈ 0.4 to n ≈ 1.2 have been found (Schwarz et al., 1997a). Consequently, tips of exactly defined spherical tip apex and a tip radius which is known with nanometer accuracy are mandatory for quantitatively reproducible friction force measurements. Mainly two different methods to prepare such well-defined tips have been introduced in the past. The first method is to heat a very sharp tip in high vacuum (Binh and Uzan, 1987; Binh and Garcia, 1992). Surface diffusion will then induce migration of atoms from regions of higher curvature to regions of lower curvature. Another method was realized by covering doped single-crystalline silicon tips (apex radii 5 to 15 nm without coating) with a layer of amorphous carbon in a transmission electron microscope (Schwarz et al., 1997b). Molecules from the residual gas are ionized in the electron beam and accelerated to the tip end. There, the molecules spread out evenly due to their charge, forming a well-defined spherical tip end. With this method, tips with radii from 7 nm up to 112 nm could be successfully produced. Three examples of tips prepared using the second method described above are shown in Figure 18.4.
18.4 Amontons’ Laws at the Nanometer Scale Amontons’ macroscopic friction laws (1) and (2) can be condensed in the well-known equation
Ff = µFn
(18.8)
where Ff denotes the observed friction force. µ represents a value which is constant for a given material combination in a wide range of applied normal forces Fn and which is usually referred to as the friction coefficient. Nevertheless, for the description of the frictional behavior of materials at the nanometer scale, it is practical to introduce the mean friction per unit area (the so-called shear stress S)
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FIGURE 18.5 The frictional force Ff as a function of the normal force Fn, measured on amorphous carbon with geometrically well-defined spherical tips in argon atmosphere (Schwarz et al., 1997a). The data presented in (a) were obtained using a tip with a radius of R = 17 ± 5 nm; the data in (b) using a tip with R = 58 ± 10 nm. Both curves are in excellent agreement with fits according to Equation 18.10 (solid lines); the dashed lines illustrate the deviation from the linear macroscopic model (Equation 18.8). The offsets of the solid lines from the zero point of the normal force are caused by the experimental uncertainty in the determination of the zero point by means of force-vs.-distance curves.
S = Ff A
(18.9)
Combining Equations 18.7 and 18.9, we find
R Ff = πS K
2 3
Fn2 3 = µ˜ R2 3 Fn2 3
(18.10)
with µ˜ = πS/K 2/3. There have already been many reports in the literature when the frictional force has been measured as a function of the normal force using an FFM (Mate et al., 1987; Mate, 1993; Hu et al., 1995; Bhushan and Kulkarni, 1995; Carpick et al., 1996; Meyer et al., 1996; Lantz et al., 1997; Schwarz et al., 1997a; Enachescu et al., 1998). In most of these reports, the frictional force showed a strongly nonlinear dependence on the normal force. Figure 18.5 features results published by Schwarz et al. (1997a), which were acquired in argon atmosphere on amorphous carbon with tips showing exactly spherical tip apexes (tip radii of 17 ± 5 nm [a] and 58 ± 10 nm [b], respectively). The fits according to Equation 18.10 show excellent agreement between the experimental results and theory. The dashed lines illustrate the deviation of the present friction law from the macroscopic linear law Equation 18.8. It is interesting to note that not only can the relationship Ff ∝ F n2/3 be confirmed, but also the Ff ∝ 2/3 R -dependence. Comparing Figure 18.5a with 18.5b, much higher friction is observed in (b); the frictional force at Fn = 10 nN, for example, is about three times larger (≈15 nN) than the frictional force of only 5.5 nN observed in (a). However, the calculated numerical value of µ˜ = 0.17 ± 0.07 GPa1/3 for the second measurement is in good agreement with the value of µ˜ = 0.17 ± 0.09 GPa1/3 obtained in the first measurement. Summarizing the main results obtained from the different research groups on a large variety of materials, it was found that the friction as a function of the normal load showed good agreement of experimental data and theoretical fits using Equation 18.9 combined with contact mechanical models appropriate for the specific tip-sample contact, if S is set constant. This finding leads to the following remarkable consequences:
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• The observed frictional force Ff is in opposition to law (2) proportional to the crack area A (see Equation 18.9). In the special case of a Hertzian contact, this leads to a Ff(Fn)-dependence of Ff ~ F 2/3 n . • The shear stress S depends only on the materials used and on environmental conditions such as temperature and humidity, but not on the mean contact pressure p = Fn/A.* • The independence of the shear stress S from the mean contact pressure p = Fn/A is in flagrant contradiction to Amontons’ law (1). • The continuum elasticity theory also applies at the nanometer scale. Since the continuum elasticity theory also applies at the nanometer scale, Equation 18.7 can be used to calculate the actual contact area of an SFM tip and the sample surface. Typical normal forces Fn occurring in an SFM during measurement are between 1 nN and 100 nN. This results in contact areas of a few nm2, with the effect that only some tens or some hundreds of atoms are in direct contact. The deformations of tip and sample are then fully elastical, i.e., fully reversible. Therefore, with an SFM, it is indeed possible to study wearless friction of a quasipoint contact. Another outcome from the above considerations is the finding that it is obviously useless to determine “friction coefficients” µ (see Equation 18.8) from point contact measurements, since these values will heavily depend on the specific geometry of the tip–sample contact. For a classification of the microscopic frictional properties of materials, Schwarz et al. (1997a) have therefore proposed the factor µ˜ = πS/K2/3 (see Equation 18.10), which combines the frictional and elastic properties of tip and sample and which can be regarded as an effective friction coefficient for point contact-like single-asperity friction in the case of a nanometer-sized Hertzian contact. The definition of such a coefficient is advantageous for two main reasons: (1) If materials with identical intrinsic frictional properties (i.e., the materials show the same friction per unit area) but different Young moduli are examined in measurements performed with identical tips and normal forces, higher friction will be found on the softer material due to the larger ˜ however, will always show the same friction during an contact area. Materials which have the same µ, experiment. (2) If the same sample is investigated with tips featuring different apex radii, lower friction will be found in the experiment carried out with the sharper tip. Nevertheless, consideration of the ˜ as we have seen in Figure 18.5. geometry by the calculation of µ˜ will lead to identical values of µ, How can the above results now be correlated with the macroscopic laws of friction? As we have seen in the introduction, it is the general attempt of nanotribology to conclude from the frictional properties of an individual nanocontact to the behavior of macroscopic bodies by the statistical adding of the interactions of a large number of individual contacts with represent the macroscopical roughness of the contact interface. This means for the given situation that the contradiction between Amontons’ laws (1) and (2) and their corresponding counterparts on the nanometer scale could be entirely eliminated if the effective contact area of such a macroscopic contact increased proportionally to the externally applied loading force. Then, the observed frictional force would also increase linearly with the load, according to the nanoscopic friction law found above. Such a linear Ff(Aeff )-dependence for macroscopically flat, but microscopically rough surfaces has indeed been demonstrated by Greenwood (1967, 1992). Interestingly, the apparent contact area of the two bodies does not matter in this case.
18.5 The Influence of the Surface Structure on Friction In the preceding sections, we dealt with the mechanical and tribological properties of nanometer-sized contacts. Questions concerning the fundamental mechanisms of friction at the atomic scale, however, *The same result has been found by Carpick et al. (1997) and Enachescu et al. (1998) with different approaches, which both circumvent the assumption of a specific contact mechanical model. Additionally, experiments performed with the surface force apparatus and consequently much larger contact areas A also show the same behavior (Israelachvili and Tabor, 1973; Homola et al., 1990).
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FIGURE 18.6 (a) Topography and (b) lateral force map of an AgBr thin film deposited on NaCl(001) at room temperature (image size: 1.4 µm × 1.4 µm). The AgBr islands are 1 to 6 monolayers high and partially cover the NaCl substrate. In the lateral force map, the AgBr islands are revealed as areas with about ten times higher friction than the corresponding friction observed on the NaCl surface. (From Meyer, E., Lüthi, R., Howald, L., and Güntherodt, H.-J., 1995. Friction force microscopy, in Forces in Scanning Probe Methods, Güntherodt, H.-J., Anselmetti, D., and E. Meyer (Eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 285. With permission.)
are still unanswered. Since we focus in this chapter on the analysis of wearless friction on atomically flat surfaces without defects, it is reasonable to expect that the origin for the different friction observed on the different materials can be found in the local arrangement of the atoms at the tip–sample contact area. If this expectation holds, it should be possible to distinguish areas of different chemical composition by lateral force microscopy. This ability is sometimes called “chemical imaging”; examples for such investigations will be discussed in Section 18.5.1. Another interesting consequence of the above expectation is that the friction should depend on the direction with which the tip profiles the sample surface. This frictional anisotropy is especially easy to verify experimentally if a material exhibiting an asymmetric surface potential is used as a sample, as presented in Section 18.5.3. Finally, we will see in Section 18.5.2 that even small conformational (i.e., purely geometrical) changes within a surface unit cell give rise to different friction in lateral force maps.
18.5.1 Frictional Contrast Caused by Local Changes in the Chemical Composition The ability of the FFM to provide a contrast between surfaces of different chemical composition is not only important for tribologists, but also of considerable general interest for users from the whole field of scanning force microscopy, where contrast mechanisms are needed which provide information in addition to the pure topography. Since the lateral forces acting on the FFM tip are not independent of the topography,* atomically or molecularly flat terraces give the most unambiguous results. Consequently, chemical contrast has first been demonstrated for Langmuir–Blodgett films, which can easily be prepared and investigated under atmospheric conditions and exhibit large, molecularly flat surfaces. See, for example, Overney et al. (1992), or Meyer et al. (1992). However, in this chapter we will restrict the discussion to the atomic-scale frictional effects at crystalline surfaces. In order to check the frictional behavior for such systems, Lüthi et al. (1995) partially covered the surface of an NaCl(001) single crystal with 1 to 6 monolayers of AgBr (Figure 18.6a), which has the same crystalline structure as NaCl. In the corresponding FFM investigations (Figure 18.6b), they found a strong frictional contrast between the AgBr islands and the NaCl substrate due to the different chemical composition of the two materials. *Scanning “up hill” causes more torsion of the cantilever than scanning “down hill”; see, for example, Grafström et al. (1993), Fujisawa et al. (1993b), Ruan and Bhushan (1994a), or Aimé et al. (1995).
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According to the same principle, basically all areas of different chemical composition can be distinguished in force microscopical investigations. Fompeyrine et al. (1998), for example, could differentiate areas terminated by SrO from areas terminated by TiO2 on an SrTiO3 single crystal. This ability of the SFM is sometimes called “chemical imaging.” It should be noted, however, that chemical imaging does not mean chemical identification. The reason for this has been discussed in Section 18.4. If the contact mechanics of the tip–sample contact is not exactly known, the results obtained are difficult to interpret without additional information. In order to circumvent this restriction at least partially, chemically modified tips have been used to sensitize the tip to certain functional groups which have been patterned on suitable sample surfaces. See, for example, Frisbie et al. (1994) or Sasaki et al. (1998). A theoretical study on the bases of “chemical force microscopy” on organic monolayers has been published recently by Fujihira and Ohzono (1999).
18.5.2 Friction of Surfaces Possessing Identical Chemical Composition After what has been discussed above, it seems promising to analyze the influence of differences in the structure of surfaces possessing identical chemical composition on the friction observed by a point probe. Probably the first observation on this issue was published by Ruan and Bhushan (1994b). They observed graphite(0001) areas with unusually high friction, which could be identified as areas exhibiting graphite planes of different orientations (other than [0001]) as well as amorphous carbon. Comparative quantitative studies for different carbon compounds have been performed by Mate (1993) and Schwarz et al. (1997a) on diamond, graphite, C60 thin films, and amorphous carbon. High frictional forces have been found especially on the C60 thin films, whereas friction nearly vanishes on graphite. These examples demonstrate that even on materials that consist of the same chemical species, large variations in the observed friction might occur. As a consequence, it follows that it is not the specific atomic species which form a crystal, but factors such as the crystalline structure, the charge distribution, and/or the binding conditions that might decide the frictional properties of a material. The “chemical differentiation” postulated in Section 18.5.1 is therefore based more on structural and electronical differences between the materials than on the fact that they represent chemically different species. This issue will be further illustrated with the example of the ferroelectric material guanidinium aluminum sulfate hexahydrate (GASH) in the following. Since the Curie point of GASH is above its decomposition temperature, the crystals always show the ferroelectric phase. The surfaces of positively and negatively charged domains not only have the same chemical composition, the surface atoms are also bound in the exact same manner on both domains. The difference is that the surface undergoes a conformational (i.e., geometrical) change of the surface structure if the polarity of a certain surface area is flipped. Certain aluminum ions which are octahedrally coordinated by water molecules stick on the positive domain more out from the surface (by 0.5 Å) than they do no the negative domain, resulting in a different surface corrugation. Bluhm et al. (1998) showed in a combination of voltage-dependent friction force microscopy experiments and electrostatic force microscopy experiments that the domain contrast observed in FFM images is not caused by the electrostatic interaction between a charged tip and the electric field of the sample, but is explained by the geometrical differences exhibited by the surfaces of domains with opposite polarity (Figure 18.7). This example elegantly demonstrates that even small changes in the arrangement of the atoms located at the sample surface influence the friction occurring during the sliding of nanocontacts.
18.5.3 Direction Dependence of Sliding Friction In the above sections, we have seen that friction is very sensitive to the structure of the surface. In everyday life, it is often observed that friction depends on the sliding direction. This phenomenon can be observed rubbing by one’s hand over certain pieces of cloth. Another example is that of a saw; there, how much
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FIGURE 18.7 (a) Topographical image of GASH(0001) (image size: 30 µm × 30 µm). The surface is featureless and without any steps. (b) Friction force map of the same surface spot as in (a) (slight zoom-out; image size: 40 µm × 40 µm). A well-expressed contrast is visible. (c) Image acquired with electrostatic force microscopy at the same surface area as in (a), showing the structure and absolute sign of the ferroelectric domains. By comparison of (b) and (c), it can be concluded that the contrast in the friction image represents the domain structure of GASH.
FIGURE 18.8 Principle of FFM contrast formation. (a) On materials that have no directional dependence of friction (i.e., the friction coefficient µ is the same in the forward and backward scan directions), the contrast between surface areas exhibiting different µ is reversed when scanning forward compared to scanning backward since the FFM signal is a measure for the torsion of the cantilever. At the surface steps, peaks occur in the FFM signal due to some torque of the tip. (b) FFM tip probing the frictional force of a surface with asymmetric surface potential, illustrated by a sawtooth-like structure. The surface structure on the lower terrace is rotated by 180° along the surface normal compared to the structure on the upper terrace. The friction coefficient of one single terrace is, e.g., µ→ in the forward scan direction, whereas it changes to µ← for the backward scan direction due to effects as described in the text; i.e., the friction coefficient is direction-dependent. The contrast recorded in the FFM signal is the same for both directions. The direction dependence, however, has no influence on the torque of the FFM tip at the surface steps.
one has to pull or push depends on the direction. It is now instructive to investigate how this mechanism also applies on the atomic scale. The basic idea of this issue is illustrated in Figure 18.8 by contrasting the behavior of a tip moving (a) in a symmetric and (b) in an asymmetric surface potential. The asymmetric surface potential is represented by a sawtooth-like structure. Intuitively, one might assume that a sharp tip which profiles such an asymmetric potential would experience a larger lateral force at the steep sides of the sawtooth than
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FIGURE 18.9 Perspective view of the (010) surface of a negative domain exhibiting a surface step of half of the unit cell height.
on the less inclined sides.* Therefore, lower friction is expected for the upper terrace in comparison with the lower terrace for the “forward” scan direction. Additionally, the frictional contrast between the upper and the lower terrace should vanish if the tip is moved along the grooves of the sawtooth, i.e., perpendicular to the sketched figure. For the first time, effects due to the atomic-scale asymmetry of a surface potential were reported by Overney et al. (1994) for a lipid bilayer on oxidized Si(100). A similar domain contrast was also found by Gourdon et al. (1997) and Liley et al. (1998) with a thiolipid monolayer on mica. As a possible explanation, the observed contrast was considered to be caused by different molecular tilts within the individual domains. On crystalline surfaces, however, such effects can be studied in a more controlled manner. Here, we will use the ferroelectric material triglycine sulfate (TGS) as an example; similar results have recently been published by Shindo et al. (1999) for alkaline earth sulfate crystals. Figure 18.9 displays a perspective view on two neighboring terraces separated by a b/2 step within a negative domain. The glycine molecules form a sawtooth-like pattern perpendicular to the c-axis. The most remarkable feature of the surface structure in this context is that the arrangement of the molecules on the upper terrace is rotated by 180° compared to the structure on the lower terrace. This sawtoothlike surface structure is very similar to the case considered above, and an asymmetry in friction is therefore expected. Measurements by Bluhm et al. (1995) fully confirm the expected behavior. Figure 18.10 shows the relative frictional contrast between neighbored terraces (i.e., the difference of the friction on the upper and on the lower terrace) in arbitrary units as a function of the sample rotation angle; 0° is orthogonal to the a-axis. Due to a 105° angle between the a and the c-axis of the TGS crystal, the sample orientation is for 165° and 345° parallel to the grooves of the sawtooth structure. For these angles, the frictional contrast vanishes as predicted. A detailed discussion of the frictional anisotropy on TGS(010), including a simple theoretical model, can be found by Schwarz et al. (1996b).
18.6 Atomic Mechanism of Friction Although the experiments described above were performed with sliding distances in the micrometer range, it is clear that the origins for the studied effects can only be found on the atomic scale. In Section 18.2, we have seen that it is possible to measure frictional forces with a scanning force microscope down to the atomic scale. The analysis of such measurements gives interesting insight into the basic mechanism of friction. *Such a correlation between surface slope and lateral force can indeed not only be observed on the macroscopic scale, but has also been demonstrated at length scales of some 10 or 100 nanometers (Fujisawa et al., 1993b; Grafström et al., 1993; Bhushan et al., 1994; Ruan and Bhushan, 1994a), making our assumption even more substantial.
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FIGURE 18.10 Relative frictional contrast for neighbored terraces on the negative domain of TGS(010) as a function of the sample rotation angle.
FIGURE 18.11 (a) A simple model for a tip sliding on an atomically flat surface based on the Tomlinson model. A point-like tip is coupled elastically to the body M by a spring with spring constant cx in the x-direction; xt represents its position within an external potential V(xt) with periodicity a. If xt = xM, the spring is in its equilibrium position. For sliding, the body M is moved with the velocity νM in the x-direction. (b) A schematic view of the tip movement in a sinusoidal interaction potential. If condition (18.13) holds, the tip shows the typical stick-slip-type movement, i.e., it jumps from one potential minimum to another. (c) If the tip moves with stick-slips over the sample surface, the lateral force Fx manifests as a sawtooth-like function.
Many issues observed on the atomic scale can be illustrated by using a simple but instructive mechanical model based on the so-called Tomlinson (Tomlinson, 1929) or independent oscillator (IO) model (Prandtl, 1928; McClelland, 1989; Helman et al., 1994). A schematic view of this simple spring model is shown in Figure 18.11. A point-like tip is coupled elastically to the main body M with a spring possessing a spring constant cx in the x-direction, and it interacts with the sample surface via a periodic potential Vint(xt), where xt represents the actual position of the tip. During sliding, the body M is moved with the sliding velocity νM in the x-direction. All energy dissipation — independent of the actual dissipation channel . (phonons or electronic excitations) — is considered by a simple velocity-dependent damping term (–γx x t). Within this model, the point-like tip represents the average of the real tip–sample contact or single asperity contact, where up to hundreds of atoms might be involved (see Section 18.4). In principle, the real tip–sample contact could also be treated as a system consisting of many individual atomically sharp tips interacting through springs, leading to more complex models of friction. However, we will restrict ourselves to the simple model introduced above, which has proven to describe successfully the tip motion for many materials (Table 18.1). The resulting equation of motion for the tip in the interaction potential is given by
(
)
m x x˙˙t = c x x M − x t −
( ) − γ x˙
∂ Vint x t ∂x t
x t
(18.11)
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TABLE 18.1 Some Examples of Materials where the Tomlinson or Independent Oscillator Model Has Been Successfully Applied to Simulate Experimental Data Sample
Reference
Graphite(0001)
KBr(001) MoS2(001) β-MoTe2(001) NaF(001) Organic Monolayers
Sasaki et al., Phys. Rev. B, 54, 2138 (1996) Toussaint et al., Surf. Interface Anal., 25, 620 (1997) Hölscher et al., Phys. Rev. B, 57, 2477 (1998) Lüthi et al., J. Vac. Sci. Technol. B, 14, 1280 (1996) Hölscher et al., Surf. Sci., 375, 395 (1997) Hölscher et al., Phys. Rev. B, 59, 1661 (1999) Hölscher et al., Europhys. Lett., 39, 19 (1996) Ohzono et al., Jpn. J. Appl. Phys., 37, 6535 (1999)
where mx is the effective mass of the system, xM = νMt the equilibrium position of the spring, and γx the damping constant. The solution of this differential equation is the path of the tip xt(t). The lateral force Fx to move the tip in the x-direction can be calculated from Fx = cx(xM – xt), whereas the friction force Ff is defined as the averaged lateral force (Fx). If the sliding velocities are very low, analytical solutions of Equation 18.11 can be derived. In this case, the tip will always be in its stable equilibrium position, and Equation 18.11 can be solved for x¨ t = 0 and . xt = 0:
(
)
c x xM − xt =
( )
∂ Vint x t
(18.12)
∂x t
From this equation, a path xt(xM) can be determined.* For a stiff spring, there is only one solution for all xM, resulting in a continuous tip movement and vanishing friction, since the averaged lateral force (Fx) is zero (Figure 18.12). However, the tip movement changes dramatically if the condition
∂2 Vint cx < − 2 ∂x t min
(18.13)
is fulfilled. Now the tip moves discontinuously in a stick-slip-type motion over the sample surface and jumps from one potential minimum to another. This specific movement of the tip results in a sawtoothlike function for the lateral force Fx (see Figures 18.11c and 18.12). Since the averaged lateral force (Fx) is nonzero in this case, the friction force Ff is necessary to move the body M in the x-direction. To simulate experimental data obtained with a scanning force microscope, it is important to remember that an SFM can measure the lateral forces along and perpendicular to the scan direction (Section 18.2). Therefore, it is necessary to extend the one-dimensional model introduced above to two dimensions in a manner that considers explicitly the tip movement perpendicular to the scan direction (Gyalog et al., 1995). In the further analysis, we will show that this two-dimensional movement of the tip is significant and thus has a considerable effect on SFM images. The extension of the model to two dimensions leads to the following coupled second-order differential equation
(
)
m x x˙˙t = c x νMt − x t −
(
∂ Vint x t , y t ∂x t
) − γ x˙
x t
(18.14)
*An alternative way to determine the path of the tip is to calculate the minimum of its energy (McClelland, 1989).
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FIGURE 18.12 The tip movement in the Tomlinson model, illustrated with the example of the simple sinusoidal potential displayed in (a). If the tip moves in such a potential, its path can be determined from the solution of Equation 18.12. The graphical solution of this equation is shown in (b) for two different cases. For a stiff spring, ∂V x δx t
sin t there is only one point of intersection between cx(xM – xt) (dotted lines in [b]) and --------------(solid line). Consequently,
the obtained path xt(xM) and the lateral force Fx — displayed by dotted lines in (c) and (d) — are continuous, with the effect that the lateral force averages to zero and no friction occurs. If condition (18.13) holds, however, there is more than one point of intersection for certain support positions xM (dashed lines in [b]). This leads to instabilities, which manifest as “jumps” of the tip, as shown in (c) and (d). The occurrence of more than one intersection in (b) means that more than one value xt is possible for the same support position xM (dashed line in [c]). Thus, xt jumps for increasing xM instantaneously from one stable value to the next (solid line with arrows), leading to a discontinuous lateral force which looks like a sawtooth (solid line with arrows in [d]). The averaged lateral force Ff is now nonzero.
(
)
m y y˙˙t = c y y M − y t −
(
∂ Vint x t , y t ∂y t
)−γ
y˙
(18.14)
y t
which describes the movement of the tip in the tip–sample potential of an idealized SFM (Hölscher et al., 1997). The simulation of experimental data is performed by moving the support M with constant velocity νM in the “forward” direction (i.e., from left to right) as well as the “backward” direction (i.e., from right to left) continuously along a certain line in the x-direction while yM is held constant. Calculating the position of the tip (xt, yt) from Equation 18.14, the lateral forces Fx = cx(xM – xt) and Fy = cy(yM – yt) can be determined as a function of the support position (xM, yM). Then, after increasing yM, a new scan line is computed parallel to the previous line. The application of the model to a realistic sample system (and thus the movement of a sharp singleasperity tip in general) is illustrated in the following with the example of the MoS2(001) surface, where the simulated results are compared with experimental data of Fujisawa et al. (1994, 1995). For the calculations, it is necessary to choose a suitable tip–sample interaction potential Vint(xt, yt), which has to be used to solve Equation 18.14. The exact tip–sample interaction potential is difficult to determine, since the precise structure of the tip is usually unknown. However, it can be shown that all basic features of SFM measurements are reproduced by the simulation as long as Vint reflects the translational symmetry
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FIGURE 18.13 A schematic view of the MoS2 surface structure. The spheres represent the positions of the sulfate surface atoms. The dashed line marks the position yM = 0 used in Figure 18.15.
of the sample surface. A comparison with the surface structure of the MoS2(001) sample surface displayed in Figure 18.13 shows that this requirement is met by
2π 2π VMoS2 x t , y t = V0 cos x t cos y t ax ay
(
)
(18.15)
where ax = 3.16 Å and ay = 5.48 Å; the actual value of V0 depends on the loading force. With this potential, numerical solutions of Equation 18.14 were computed. The resulting images and line plots presented here were obtained with the following set of parameters: V0 = 1 eV, cx = cy = 10 N/m, mx = my = 10–8 kg, νM = 400 Å/s, γx = γy = 10–3 Ns/m ~ 2 c x ⁄ m x (critical damping is assumed). These parameters have typical magnitude, but qualitatively similar results are obtained with other choices. Figure 18.14 shows a comparison of lateral force images calculated using the two-dimensional IOmodel with experimental data acquired in the [100]- and [120]-directions. The good agreement demonstrates that the presented method has the capability to simulate experimental lateral force maps. Moreover, it suggests that the model is able to describe the basic mechanism of atomic-scale friction, although it is based on comparably simple assumptions. A better insight into the scan process allows Figure 18.15a, where both lateral forces Fx and Fy are plotted as a function of the support position xM for the [100]-direction and scan positions yM = 0.0, 0.2, 1.0, 1.3, 1.4, 1.7, 2.5, and 2.7 Å (from left to right) according to the definition of yM given in Figure 18.13. The lateral force in scan direction Fx(xM) exhibits a sawtooth-like shape, whereas the force perpendicular to the scan direction, Fy(xM), looks like a step function. All features of the calculated forces are in good agreement with experimental data, which is shown for comparison in Figure 18.15b. The origin of this behavior is analyzed in Figure 18.16. Figure 18.16a shows the paths of the tip in the potential of VMoS2(xt , yt) for different values of yM. For yM = 0 Å, no movement of the tip perpendicular to the scan direction can be observed, as expected from Figure 18.15. However, with increasing yM-values, the path of the tip becomes zigzag. A smaller area of the potential is shown in Figure 18.16b, where the path of the tip for yM = 1.4 Å and 0.7 Å is plotted “time-resolved” by points of equal time distance with ∆t = 62.5 µs. It can be seen that the tip only moves slowly as long as it is in the areas which are framed by white lines. These areas are obtained by calculating the surface areas where the tip has a stable position for very slow scan velocities (νM → 0) (Gyalog et al., 1995). If the tip leaves these “areas of stability,” it becomes unstable and jumps into the next “area of stability.” This explains the stick-slip-type behavior of the lateral force Fx as well as the “step-function”-like shape of the force Fy .
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FIGURE 18.14 A comparison between the simulated (top) and measured (bottom) lateral force images for the scan directions indicated in Figure 18.13. The movement of the support was in positive x-direction (“forward”); the scan size was 25 Å × 25 Å. (Data from Fujisawa, S., Kishi, E., Sugawara, Y., and Morita, S. (1995), Atomic-scale friction observed with a two-dimensional frictional-force microscope, Phys. Rev. B, 51, 7849-7857.)
a) Fx [nN]
4
-4
Fy [nN]
2
0
o
xM [A]
25
LFM (fx)
o
b)
o 1.1x10-10 N (1.5A) 4.8x10-7N (8.8A )
-2
AFM (fY ) o
25 A
FIGURE 18.15 A comparison between the calculated (a) and measured (b) lateral forces Fx and Fy for a scan in the [100]-direction and different support positions yM as defined in Figure 18.13. (Data from Fujisawa, S., Kishi, E., Sugawara, Y., and Morita, S. (1995), Atomic-scale friction observed with a two-dimensional frictional-force microscope, Phys. Rev. B, 51, 7849-7857.)
One consequence of this behavior is that the maximum of Fx might appear at different positions than the maximum values of Fy (see Hölscher et al., 1998), as it was first observed experimentally by Ruan and Bhushan (1994a). Another consequence is that a large part of the surface is skipped by the tip and, therefore, no information about these skipped surface areas can be extracted from the acquired images. This latter behavior has been experimentally verified for mica by Kawakatsu and Saito (1996); a visualization of this issue based on the MoS2 data presented in Figures 18.14 and 18.15 is shown in Figure 18.16c. Here, the “position probability density” of the tip during the scan is plotted, i.e., only the parts of the surface that show a high density of black points have contact with the tip for a significant time; the white areas are skipped by the tip.
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FIGURE 18.16 (a) The interaction potential V(xt, yt) (image size: 25 Å × 25 Å) and the calculated paths of the tip (xt(t), yt(t)) in this potential for the support positions yM = 0.0, 0.2, 0.7, 1.0, and 1.4 Å (from top to bottom; for the definition of yM see Figure 18.13). If yM ≠ 0, the tip performs a zigzag movement. (b) A detail of (a) (image size: 10 Å × 10 Å). The contours of the “areas of stability” (see text) are marked by white lines. In order to show that the tip stays in these areas most of time, the path of the tip is drawn for yM = 1.4 Å (top) and 0.7 Å (bottom) by points separated by equal time intervals ∆t = 62.5 µs. (c) Visualization of the tip position during the scanning of the sample. All calculated paths (54 lines per period) are plotted as in (b). Consequently, the density of points can be interpreted as the “position probability density” of the tip on the surface during the scan. The “areas of stability” are framed by black lines. Only parts of the stable areas — the dark areas — are in contact with the tip for a significant time.
At the end of this section, the question arises of how far the situation described above corresponds with the tribological behavior of a nanocontact which is not connected to a cantilever. By the comparison of experiment and simulation, however, it can be demonstrated that elastic deformations between the atoms at or close to the tip–sample contact area are responsible for the stick-slip movement of the tip; astonishingly the cantilever has only a minor influence. Additionally, in molecular dynamics simulations, atomic stick-slips as found in the above analysis are found to take place as a direct consequence of the interplay between the surface forces and interatomic interactions within tip and sample (Landman et al., 1989; Harrison et al., 1992, 1993a; Schimizu et al., 1998). Even the zigzagging of the tip atoms in the interaction potential of the surface has been reproduced (Harrison et al., 1993a,b; Shluger et al., 1999). Thus, it can be concluded that the scanning force microscope indeed measures the “real” frictional behavior of a nanocontact.
18.7 The Velocity Dependence of Friction So far, we have discussed different phenomenological aspects as well as theoretical concepts of friction on the nanometer scale, but we still have to find an explanation for Coulomb’s law (3) on the independence of sliding friction from the sliding velocity νM. As already mentioned in the introduction, this law has also been confirmed on the nanometer scale within a wide velocity range for crystalline surfaces (Hu et al., 1995; Bouhacina et al., 1997; Zwörner et al., 1998).* Figure 18.17 shows two examples of experimental data sets for amorphous carbon and diamond. It is found that the friction force Ft is nearly constant for the velocities that can be reached with an SFM. To get a basic idea of the mechanism which causes the velocity independence of the frictional forces, we again apply the simple mechanical model introduced in Section 18.6. For this purpose, we are interested in the solutions of Equation 18.11 for moderate scan velocities. The qualitative behavior within the one-dimensional case is shown for a sinusoidal potential Vint(xt) = V0sin(2πxt). All data presented here are obtained with the parameters V0 = 1.0 eV, a = 3 Å, cx = 10 N/m (condition [13] holds for these *There is, however, experimental evidence that friction has a logarithmic or even more complicated dependence on the sliding velocity for noncrystalline overlayers (e.g., polymeric, self-assembled, or Langmuir–Blodgett-type layers), probably due to a certain viscosity of the layers due to a liquid-like structure (Liu et al., 1994; Koinkar and Bhushan, 1996; Bouhacina et al., 1997). Additionally, it should be mentioned that there have been reports where even on crystalline surfaces, a slight logarithmic dependence of the friction on the sliding velocity was observed by SFM (Liu et al., 1994; Koinkar and Bhushan, 1996).
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FIGURE 18.17 The friction forces Ff as a function of the sliding velocity νM measured with a silicon tip on (a) amorphous carbon, and (b) diamond. Ff is independent of the sliding velocity in good approximation.
parameters, i.e., stick-slips will occur), mx = 10–10 kg (with this effective mass, the system [tip and sample in contact] has a typical resonance frequency of 1/(2π) c x ⁄ m x ≈ 50 kHz, which is typical for SFM experiments), and γx = 2 c x ⁄ m x (critical damping). With this set of parameters, we calculate the numerical solutions of Equation 18.11 and determine the lateral forces Fx as well as the frictional force Ff for different sliding velocities (νM = 10 nm/s … 100 µm/s). In Figure 18.18, the calculated lateral force Fx is displayed for different sliding velocities νM. It is obvious that the obtained results change only little within the wide range of sliding velocities νM = 10 nm/s … 10 µm/s. Only for high sliding velocities, where the solution of Equation 18.11 is dominated by the velocity-dependent damping term (see Fx for 100 µm/s in Figure 18.18), the lateral force increases significantly. Consequently, since the friction force is the average of the lateral force, Ff is approximately independent of the sliding velocity in a wide range. What is now the reason for the relative independence of the lateral forces on the sliding velocities at moderate values of νM? This issue is illustrated in Figure 18.11b. We have seen above that the tip usually moves in a stick-slip-type motion over the sample surface. With this type of motion, the tip stays in the minima of the interaction potential most of the time where it slides very slowly or “sticks.” Therefore, almost no energy is dissipated in this “stick”-state, since we assumed that the damping is proportional to the sliding velocity. In the “slip”-state, however, the tip “jumps” from one to another minimum. During this jump, the tip reaches very high peak velocities and dissipates significant amounts of energy due to the velocity-dependent damping mechanism. It is now important to note that the maximum velocity reached during the slip depends for low values of νM in first approximation only on the spring constant cx, the height and the shape of the potential, the chosen damping constant, and the effective mass of the system, but not on the sliding velocity νM. As a consequence, the total amount of energy dissipated during sliding does not change significantly as long as νM is much smaller than the slip velocity of the tip. From Figure 18.18, we obtain a slip velocity of about 60 µm/s for sliding speeds up to 10 µm/s.* For larger sliding velocities, the mechanism of energy dissipation through the “stick-slip” effects breaks down, as can be seen for νM = 100 µm/s. However, despite its success, the model introduced above is still unsatisfactory from an atomistic view, since it is fully phenomenological in the way that it does not give any insight into the dissipation mechanism involved. It is clear that the energy dissipation process will be much more complicated in a real physical system than that considered here; more complete theories can be found in, for example, Sokoloff (1990, 1993) or Colchero et al. (1996). *The numerical value of the slip velocity obtained within this simple mechanical model is determined by the onedimensional interaction potential and the chosen numerical values of the parameters, which partially might vary in a very large range without changing the obtained results qualitatively. Consequently, the slip velocity of 60 µm/s is not a prediction for an experimental measurement and could actually be much higher without contradiction of the general mechanism discussed here.
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FIGURE 18.18
Modern Tribology Handbook
The lateral force Fx and the tip velocity νt for different sliding velocities νM = 10 nm/s … 100 µm/s.
18.8 Summary In this chapter, we have reviewed some of our present understanding of atomic-scale friction gained from scanning force microscopy experiments. Our analysis, however, has always been restricted to fundamental aspects of wearless Coulomb friction (i.e., dry friction); effects due to boundary lubrication and wetting of surfaces were not considered. It has been shown that the main advantage of the SFM in this context is its ability to enable detailed studies of the friction of “point contacts” (which have been found to exhibit, in reality, contact areas of some nm2, depending on the applied load, the elastic properties of tip and sample, and the tip radius) with high spatial resolution as a function of the contact geometry, the applied load, the effective contact area, the sliding velocity, and the surface structure of the profiled sample. Remarkably, it has been found that some phenomena manifest similarly on the nanometer scale compared to their macroscopic behavior, whereas others show a very different behavior. Most strikingly, friction on the nanometer scale is proportional to the effective contact area, contrary to the macroscopic case. Consequently, the concept of the “friction coefficient,” which is independent of the actual contact geometry, fails on this scale. In the corresponding experiments, contact pressures of up to 1 GPa are easily reached. Such pressures are already above the yield stress of many materials and therefore seem very high at first sight, but might match the “realistic” pressures of individual nanocontacts within a macroscopical contact far better than lower contact pressures. However, despite these high
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pressures and the small dimensions of the individual contact with only some tens or some hundreds of atoms in intimate contact, contact mechanics, which has been derived from continuum elasticity theory, has proved to be still valid. Another interesting point is that the shear stress is independent of the mean contact pressure — at least in the case of nanometer-sized Hertzian or approximately Hertzian contacts. Again, very high shear stresses of up to 1 GPa are found, orders of magnitude more than typically obtained from other friction experiments. These high values can possibly be accounted for as representing approximately the theoretical shear stress of the contact, which is about 1/30 of the shear modulus of the contact (Cottrell, 1953) and therefore has about the correct order of magnitude. Much more difficult to answer is the question of which factors determine whether a given contact shows high or low friction. In many experiments, it has been demonstrated that friction is very sensitive to even small changes in the surface structure and might additionally show a strong dependence on the sliding direction relative to the crystal lattice. This feature has been used frequently to distinguish between chemically different areas of samples or to obtain a contrast between individual domains that differ due to structural effects, but has not yet resulted in significant progress in our understanding of why certain surfaces have higher friction than others. Nevertheless, studying such issues, the atomic-scale movement of the individual atoms which are in intimate contact has been clarified to a certain degree. By comparison with theoretical models, it can be shown that the tip atoms move in a “stick-slip”-type motion over the sample surface, “jumping” from one minima of the tip–sample interaction potential to the next. Since they try to avoid passing over the position of a sample atom which represents a maximum of the interaction potential, their paths often resemble a zigzag curve. Due to this specific behavior, it follows that the “atomically resolved” images of contact force microscopy represent solely the periodicity of the potential minima of the interaction potential, which does not generally match the atomic structure of a sample for nontrivial unit cells. Another intention of this chapter was to bridge the gap between the macroscopic and the microscopic/nanoscopic scale. As we have seen in the introduction, it is one of the basic aims of nanotribology to explain the macroscopic frictional behavior of materials and contacts with fundamental processes occurring on the atomic scale. And it seems indeed possible to derive Amontons’ and Coulomb’s laws of friction from nanoscopic effects. Greenwood (1967, 1992) showed that the effective contact area between macroscopically flat bodies, which nevertheless exhibit a statistical microscopical roughness, increases linearly with the load, which eliminates any contradiction between the corresponding macroscopic and the nanoscopic friction laws. Moreover, the relative independence of friction on the sliding velocity on both the macroscopic and the nanoscopic scale might be explained with the stick-slip-type motion of the atoms in the tip–sample interaction potential. As long as the relative velocity of the two bodies is much lower than the intrinsic “slip velocity” of the atoms, the dissipated energy will be independent of variations in the sliding velocity. To conclude, nanotribology is a young field which has developed rapidly during the last one or two decades. Considerable progress has been made during this time in our understanding of fundamental frictional processes on the nanometer scale, as we hope to have demonstrated above, and first attempts to connect the atomic-scale effects with macroscopic phenomena seem to be successful. However, in spite of this progress, there are still many more open than answered questions. For example, it is still impossible with our present knowledge to predict the frictional properties of a specific contact from first principles. Nevertheless, the optimization of the frictional properties of surfaces for a given purpose will be increasingly important in the future for the further miniaturization of motors and other moving parts in, for example, hard discs or micro electromechanical systems. A further unsolved question is how energy is dissipated during wearless friction. It seems that the excitation of phonons represents the main channel for energy dissipation, even though electronic processes might be equally important in the case of conducting materials. Thus, the exact control of the dissipation channels might be a prerequisite for the tailoring of surfaces with given frictional properties — and simultaneously offers plenty of room for original and innovative nanotribological research.
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Fujisawa, S., Kishi, E., Sugawara, Y., and Morita, S. (1995), Atomic-scale friction observed with a twodimensional frictional-force microscope, Phys. Rev. B, 51, 7849-7857. Gourdon, D., Burnham, N.A., Kulik, A., Dupas, E., Oulevey, F., Gremaud, G., Stamou, D., Liley, M., Dienes, Z., Vogel, H., and Duschl, C. (1997), The dependence of friction anisotropies on the molecular organisation of LB films as observed by AFM, Tribol. Lett., 3, 317-324. Grafström, S., Neitzert, M., Hagen, T., Ackermann, J., Neumann, R., Probst, O., and Wörtge, M. (1993), The role of topography and friction for the image contrast in lateral force microscopy, Nanotechnology, 4, 143-151. Greenwood, J.A. (January 1967), The area of contact between rough surfaces and flats, J. Lub. Technol., 81-91. Greenwood, J.A. (1992), Contact of rough surfaces, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I. L. and Pollock, H.M. (Eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 37. Gyalog, T., Bammerlin, M., Lüthi, R., Meyer, E., and Thomas, H. (1995), Mechanism of atomic friction, Europhys. Lett., 31, 269-274. Harrison, J.A., Colton, R.J., White, C.T., and Brenner, D.W. (1993a), Effect of atomic-scale surface roughness on friction: a molecular dynamics study of diamond surfaces, Wear, 168, 127-133. Harrison, J.A., White, C.T., Colton, R.J., and Brenner, D.W. (1993b), Effects of chemically-bound, flexible hydrocarbon species on the frictional properties of diamond surfaces, J. Chem. Phys., 97, 6573-6576. Helman, J.S., Baltensberger, W., and Holyt, J.A. (1994), Simple model for dry friction, Phys. Rev. B, 49, 3831-3838. Hertz, H. (1881), Über die Berührung fester elastischer Körper, J. Reine Angew. Math., 92, 156-171. Hölscher, H., Schwarz, U.D., and Wiesendanger, R. (1997), Modelling of the scan process in lateral force microscopy, Surf. Sci., 375, 395-402. Hölscher, H., Schwarz, U.D., Zwörner, O., and Wiesendanger, R. (1998), Consequences of the stick-slip movement for the scanning force microscopy imaging of graphite, Phys. Rev. B, 57, 2477-2481. Homola, A.M., Israelachvili, J.N., McGuiggan, P.M., and Gee, M.L. (1990), Fundamental experimental studies in tribology: the transition from “interfacial” friction of undamaged molecularly smooth surfaces to “normal” friction with wear, Wear, 136, 65-83. Hu, J., Xiao, X.-D., Ogletree, D.F., and Salmeron, M. (1995), Atomic scale friction and wear of mica, Surf. Sci., 327, 358-370. Israelachvili, J.N. and Tabor, D. (1973), The shear properties of molecular films, Wear, 24, 386-390. Israelachvili, J.N., Perez, E., and Tandon, R.K. (1980), On the adhesion force between deformable surfaces, J. Colloid Interface Sci., 78, 260-261. Johnson, K.L. (1994), Contact Mechanics, Cambridge University Press, Cambridge, U.K. Johnson, K.L. (1997), Adhesion and friction between a smooth elastic spherical asperity and a plane surface, Proc. R. Soc. Lond. A, 453, 163-179. Johnson, K.L., Kendall, K., and Roberts, A.D. (1971), Surface energy and the contact of elastic solids, Proc. R. Soc. London A, 324, 301-313. Kawakatsu, H. and Saito, T. (1996), Scanning force microscopy with two optical levels for detection of deformations of the cantilever, J. Vac. Sci. Technol. B, 14, 872-876. Koinkar, V.N. and Bhushan, B. (1996), Microtribological studies of unlubricated and lubricated surfaces using atomic force/friction force microscopy, J. Vac. Sci. Technol. A, 14, 2378-2391. Landman, U., Luedtke, W.D., and Nitzan, A. (1989), Dynamics of tip–substrate interactions in atomic force microscopy, Surf. Sci., 210, L177-L184. Lantz, M.A., O’Shea, S.J., Welland, M.E., and Johnson, K.L. (1997), Atomic-force-microscope study of contact area and friction on NbSe2, Phys. Rev. B, 55, 10776-10785. Liley, M., Gourdon, D., Stamou, D., Meseth, U., Fischer, T.M., Lautz, C., Stahlberg, H., Vogel, H., Burnham, N.A., and Duschl, C. (1998), Friction anisotropy and asymmetry of a compliant monolayer induced by a small molecular tilt, Science, 280, 273-275. Liu, Y., Wu, T., and Evans, D.F. (1994), Lateral force microscopy study on the shear properties of selfassembled monolayers of dialkylammonium surfactant on mica, Langmuir, 10, 2241-2245.
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Lüthi, R., Meyer, E. Haefke, H., Howald, L., Gutmannsbauer, W., Guggisberg, M., Bammerlin, M., and Güntherodt, H.-J. (1995), Nanotribology: an UHV–SFM study on thin films of C60 and AgBr, Surf. Sci., 338, 247-260. Marti, O., Colchero, J., and Mlynek, J. (1990), Combined scanning force and friction microscopy of mica, Nanotechnology, 1, 141-144. Marti, O., Colchero, J., and Mlynek, J. (1993), Friction and forces on the atomic scale, in Nanosources and Manipulation of Atoms Under High Fields and Temperatures: Applications, Binh V.T. et al. (Eds.) Kluwer Academic Publishers, Dordrecht, The Netherlands, 253. Mate, C.M., McClelland, G.M., Erlandsson, R., and Chiang, S. (1987), Atomic-scale friction of a tungsten tip on a graphite surface, Phys. Rev. Lett., 59, 1942-1945. Mate, C.M. (1993), Nanotribiology studies of carbon surfaces by force microscopy, Wear, 168, 17-20. Maugis, D. (1987), Adherence of elastomers: fracture mechanics aspects, J. Adhesion Sci. Technol., 1, 105-134. Maugis, D. (1992), Adhesion of spheres: the JKR–DMT transition using a Dugdale model, J. Colloid Interface Sci., 73, 294-269. Maugis, D. and Gauthier-Manuel, B. (1994), JKR–DMT transition in the presence of a liquid meniscus, J. Adhesion Sci. Technol., 8, 1311-1322. McClelland, G.M. (1989), Friction at weakly interacting interfaces, in Adhesion and Friction, Grunze, M. and Kreuzer, H.J. (Eds.), Springer Series in Surface Science, Vol. 17, Springer Verlag, Heidelberg, 1. Meyer, E., Overney, R., Brodbeck, D., Howald, L., Lüthi, R., Frommer, J., and Güntherodt, H.-J. (1992), Friction and wear of Langmuir–Blodgett films observed by friction force microscopy, Phys. Rev. Lett., 69, 1777-1780. Meyer, E. and Heinzelmann, H. (1992), Scanning force microscopy, in Scanning Tunneling Microscopy II, Wiesendanger, R. and Güntherodt, H.-J. (Eds.), Springer Series in Surface Science, Vol. 28, Springer-Verlag, Heidelberg, 99. Meyer, E., Lüthi, R., Howald, L., Bammerlin, M., Guggisberg, M., and Güntherodt, H.-J. (1996), Sitespecific friction force microscopy, J. Vac. Sci. Technol. B, 14, 1285-1288. Meyer, G. and Amer, N.M. (1990), Simultaneous measurement of lateral and normal forces with opticalbeam-deflection atomic force microscope, Appl. Phys. Lett., 57, 2089-2091. Muller, V.M., Yuschenko, V.S., and Derjaguin, B.V. (1983), General theoretical consideration of the influence of surface forces on contact deformations and the reciprocal adhesion of elastic spherical particles, J. Colloid Interface Sci., 92, 92-101. Ogletree, D.F, Carpick, R.W., and Salmeron, M. (1996), Calibration of frictional forces in atomic force microscopy, Rev. Sci. Instrum., 67, 3298-3306. Overney, R.M., Meyer, E., Frommer, J., Brodbeck, D., Lüthi, R., Howald, L. Güntherodt, H.-J., Fujihira, M., Takano, H., and Gotoh, Y. (1992), Friction measurements on phase-separated thin films with a modified atomic force microscopy, Nature, 359, 133-135. Overney, R.M., Takano, H., Fujihira, M., Paulus, W., and Ringsdorf, H. (1994), Anisotropy in friction and molecular stick-slip motion, Phys. Rev. Lett, 72, 3546-3549. Prandtl, L. (1928), Ein Gedankenmodell zur kinetischen Energie der festen Körper, Z. Angew. Math. Mech., 8, 85-106. Putman, C., Igarashi, M., and Kaneko, R. (1995), Quantitative determination of friction coefficients by friction force microscopy, Jpn. J. Appl. Phys., 34, L264-L267. Ruan, J. and Bhushan, B. (1994a), Atomic-scale and microscale friction studies of graphite and diamond using friction force microscopy, J. Appl. Phys., 76, 5022-5035. Ruan, J. and Bhushan, B. (1994b), Frictional behavior of highly oriented pyrolytic graphite, J. Appl. Phys., 76, 8117-8120. Sasaki, K., Koike, Y., Azehara, H., Hokari, H., and Fujihara, M., (1998), Lateral force microscope and phase imaging of patterned thiol self-assembling monolayer using chemically modified tips, Appl. Phys. A, 66, S1275-S1277. Schluger, A.L., Livshits, A.I., Foster, A.S., and Catlow, C.R.A. (1999), Models of image contrast in scanning force microscopy on insulators, J. Phys: Condens, Matter, 11, R295-R322.
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Schwarz, U.D. (1997), Scanning force microscopy, in Handbook of Microscopy II, Amelinckx, S., Van Dyck, D., Van Landuyt, J.F., and Van Tendeloo, G., (Eds.), VCH Verlagsgesellschaft, Weinheim, Germany, 827. Schwarz, U.D., Köster, P., and Wiesendanger, R. (1996a), Quantitative analysis of lateral force microscopy experiments, Rev. Sci. Instrum., 67, 2560-2567. Schwarz, U.D., Bluhm, H., Hölscher, H., Allers, W., and Wiesendanger, R. (1996b), Friction in the lowload regime: studies on the pressure and direction dependence of frictional forces by means of friction force microscopy, in Physics of Sliding Friction, Persson, B.N.J. and Tosatti, E. (Eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 369. Schwarz, U.D., Zwörner, O., Köster, P., and Wiesendanger, R. (1997a), Quantitative analysis of the frictional properties of solid materials at low loads. I. Carbon compounds, Phys. Rev. B, 56, 6987-6996. Schwarz, U.D., Zwörner, O., Köster, P., and Wiesendanger, R. (1997b), Preparation of probe tips with well-defined spherical apexes for quantitative scanning force spectroscopy, J. Vac. Sci. Technol. B, 15, 1527-1530. Shimizu, J., Eda, H., Yoritsune, M., and Ohmura, E. (1998), Molecular dynamics simulation of friction on the atomic scale, Nanotechnology, 9, 118-123. Shindo, H., Shitagami, T., and Kondo, S.-I. (1999), Evidence of the contribution of molecular orientations on the surface force friction of alkaline earth sulfate crystals, Phys. Chem. Chem. Phys., 1, 1597-1600. Sokoloff, J.B. (1990), Theory of energy dissipation in sliding crystal surfaces, Phys. Rev. B, 42, 760-765. Sokoloff, J.B. (1993), Fundamental mechanisms for energy dissipation at small solid sliding surfaces, Wear, 167, 59-68. Tabor, D. (1977), Surface forces and surface interactions, J. Colloid Interface Sci., 58, 2-13. Tomlinson, G.A. (1929), A molecular theory of friction, Philos. Mag. S., 7, 7, 905-939. Wiesendanger, R. (1994), Scanning Probe Microscopy and Spectroscopy: Methods and Applications, Cambridge University Press, Cambridge, U.K. Zwörner, O., Hölscher, H., Schwarz, U.D., and Wiesendanger, R. (1998), The velocity dependence of frictional forces in point-contact friction, Appl. Phys. A, 66, S263-S267.
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19 Friction, Scratching/Wear, Indentation, and Lubrication Using Scanning Probe Microscopy 19.1 19.2
Introduction ..................................................................... 667 Description of AFM/FFM and Various Measurement Techniques ........................................................................ 669 Surface Roughness and Friction Force Measurements • Adhesion Measurements • Scratching, Wear, and Fabrication/Machining • Surface Potential Measurements • Nanoindentation Measurements • Boundary Lubrication Measurements
19.3
Friction and Adhesion ..................................................... 678 Atomic-Scale Friction • Microscale Friction • Comparison of Microscale and Macroscale Friction Data • Effect of Tip Radii and Humidity on Adhesion and Friction
19.4
Scratching, Wear, and Fabrication/Machining............... 694 Nanoscale Wear • Microscale Scratching • Microscale Wear • Nanofabrication/Nanomachining
19.5
Indentation ....................................................................... 703
19.6 19.7
Boundary Lubrication ..................................................... 708 Closure .............................................................................. 712
Picoindentation • Nanoscale Indentation
Bharat Bhushan The Ohio State University
19.1 Introduction The atomistic mechanisms and dynamics of the interactions of two materials during relative motion need to be understood in order to develop a fundamental understanding of adhesion, friction, wear, indentation, and lubrication processes. At most solid–solid interfaces of technological relevance, contact occurs at many asperities. Consequently, the importance of investigating single asperity contacts in studies of the fundamental micromechanical and tribological properties of surfaces and interfaces has long been recognized. The recent emergence and proliferation of proximal probes, in particular scanning probe microscopies (the scanning tunneling microscope and the atomic force microscope) and the surface force apparatus, and of computational techniques for simulating tip–surface interactions and interfacial properties, has allowed systematic investigations of interfacial problems with high resolution as well as ways and means for modifying and manipulating nanoscale structures. These advances have led to the appearance of the new field of micro/nanotribology, which pertains to experimental and theoretical investigations of interfacial processes on scales ranging from the atomic- and molecular- to the microscale, occurring during adhesion, friction, scratching, wear, nanoindentation, and thin-film lubrication at
0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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TABLE 19.1 Comparison of Typical Operating Parameters in SFA, STM, and AFM/FFM Used for Micro/Nanotribological Studies Operating Parameter
SFA
Radius of mating surface/tip Radius of contact area Normal load Sliding velocity
~10 mm 10–40 µm 10–100 mN 0.001–100 µm/s
Sample limitations
Typically atomically smooth, optically transparent mica; opaque ceramic, smooth surfaces can also be used
STM*
AFM/FFM
5–100 nm N/A N/A 0.02–2 µm/s (scan size ~1 nm × 1 nm to 125 µm x 125 µm; scan rate 0. The number of metastable solutions increases as λ increases. As illustrated in Figure 20.2b, once an atom is in a given metastable minimum it is trapped there until the center of mass moves far enough away that the second derivative of the potential vanishes and the minimum becomes unstable. The atom then pops forward very rapidly to the nearest remaining metastable state. This metastability makes it possible to have a finite static friction even when the surfaces are incommensurate. If the wall is pulled to the right by an external force, the atoms will only sample the metastable states corresponding to the thick solid portion of the force from the substrate potential in Figure 20.2b. Atoms bypass other portions as they hop to the adjacent metastable state. The average over the solid portion of the curve is clearly negative and thus resists the external force. As λ increases, the dashed lines in Figure 20.2b become flatter and the solid portion of the curve becomes confined to more and more negative forces. This increases the static friction which approaches N f1 in the limit λ → ∞ (Fisher, 1985). A similar analysis can be done for the one-dimensional Frenkel–Kontorova model (Frank et al., 1949; Bak, 1982; Aubry, 1979, 1983). The main difference is that the static friction and ground state depend strongly on η. For any given irrational value of η there is a threshold potential strength λc . For weaker potentials, the static friction vanishes. For stronger potentials, metastability produces a finite static friction. The transition to the onset of static friction was termed a breaking of analyticity by Aubry (1979) and is often called the Aubry transition. The metastable states for λ > λc take the form of locally commensurate regions that are separated by domain walls where the two crystals are out of phase. Within the locally commensurate regions, the ratio of the periods is a rational number p/q that is close to η. The range of η where locking occurs grows with increasing potential strength (λ) until it spans all values.
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At this point there is an infinite number of different metastable ground states that form a fascinating “Devil’s staircase” as η varies (Aubry, 1979, 1983; Bak, 1982). Weiss and Elmer (1996) have performed a careful study of the one-dimensional Frenkel–Kontorova–Tomlinson model where both types of springs are included. Their work illustrates how one can have a finite static friction at all rational η and an Aubry transition at all irrational η. They showed that magnitude of the static friction is a monotonically increasing function of λ and decreases with decreasing commensurability. If η = p/q then the static friction rises with corrugation only as λq. Successive approximations to an irrational number involve progressively larger values of q. Since λc < 1, the value of Fs at λ < λc drops closer and closer to zero as the irrational number is approached. At the same time, the value of Fs rises more and more rapidly with λ above λc . In the limit q → ∞ one has the discontinuous rise from zero to finite values of Fs described by Aubry. Weiss and Elmer also considered the connection between the onsets of static friction, of metastability, and of a finite kinetic friction as v → 0 that is discussed in the next section. Their numerical results showed that all these transitions coincide. Work by Kawaguchi and Matsukawa (1998) shows that varying the strengths of competing elastic interactions can lead to even more complex friction transitions. They considered a model proposed by Matsukawa and Fukuyama (1994) that is similar to the one-dimensional Frenkel–Kontorova–Tomlinson model. For some parameters the static friction oscillated several times between zero and finite values as the interaction between surfaces increased. Clearly the transitions from finite to vanishing static friction continue to pose a rich mathematical challenge.
20.3.3 Metastability and Kinetic Friction The metastability that produces static friction in these simple models is also important in determining the kinetic friction. The kinetic friction between two solids is usually fairly constant at low center of mass velocity differences vCM. This means that the same amount of work must be done to advance by a lattice constant no matter how slowly the system moves. If the motion were adiabatic, this irreversible work would vanish as the displacement was carried out more and more slowly. Since it does not vanish, some atoms must remain very far from equilibrium even in the limit vCM → 0. The origin of this non-adiabaticity is most easily illustrated with the Tomlinson model. In the low velocity limit, atoms stay near to the metastable solutions shown in Figure 20.2. For λ < 1 there is a unique metastable solution that evolves continuously. The atoms can move adiabatically, and the kinetic friction vanishes as vCM → 0. For λ > 1 each atom is trapped in a metastable state. As the wall moves, this state becomes unstable and the atom pops rapidly to the next metastable state. During this motion the atom experiences very large forces and accelerates to a peak velocity vp that is independent of vCM. The value of vp is typically comparable to the sound and thermal velocities in the solid and thus cannot be treated as a small perturbation from equilibrium. Periodic pops of this type are seen in many of the realistic simulations described in Section 20.4. They are frequently referred to as atomic-scale stick-slip motion (Sections 20.4 and 20.6), because of the oscillation between slow and rapid motion (Section 20.6). The dynamic equation of motion for the Tomlinson model (Equation 20.8) has been solved in several different contexts. It is mathematically identical to simple models for Josephson junctions (McCumber, 1968), to the single-particle model of charge-density wave depinning (Grüner et al., 1981), and to the equations of motion for a contact line on a periodic surface (Raphael and DeGennes, 1989; Joanny and Robbins, 1990). Figure 20.3 shows the time-averaged force as a function of wall velocity for several values of the interface potential strength in the overdamped limit. (Since each atom acts as an independent oscillator, these curves are independent of η.) When the potential is much weaker than the springs (λ < 1), the atoms cannot deviate significantly from their equilibrium positions. They go up and down over the periodic potential at constant velocity in an adiabatic manner. In the limit vCM → 0 the periodic force is sampled uniformly and the kinetic friction vanishes, just as the static friction did for incommensurate walls. At finite velocity the kinetic friction is just due to the drag force on each atom and rises linearly with velocity. The same result holds for all spring constants in the Frenkel–Kontorova model with equal lattice constants (η = 1).
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FIGURE 20.3 Force vs. velocity for the Tomlinson model at the indicated values of λ. The force is normalized by the static friction N f1 and the velocity is normalized by v0 f1/γ where γ is the phenomenological damping rate. (From Robbins, M.O. (2000), Jamming, friction, and unsteady rheology, in Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales, Liu, A.J. and Nagel, S.R. (Eds.), Taylor and Francis, London. With permission; adapted from Joanny, J.F. and Robbins, M.O. (1990), Motion of a contact line on a heterogeneous surface, J. Chem. Phys., 92, 3206-3212.)
As the potential becomes stronger, the periodic force begins to contribute to the kinetic friction of the Tomlinson model. There is a transition at λ = 1, and at larger λ the kinetic friction remains finite in the limit of zero velocity. The limiting Fk (v = 0) is exactly equal to the static friction for incommensurate walls. The reason is that as vCM → 0 atoms spend almost all of their time in metastable states. During slow sliding, each atom samples all the metastable states that contribute to the static friction and with exactly the same weighting. The solution for commensurate walls has two different features. The first is that the static friction is higher than Fk (0). This difference is greatest for the case λ < 1 where the kinetic friction vanishes, while the static friction is finite. The second difference is that the force/velocity curve depends on whether the simulation is done at constant wall velocity (Figure 20.3) or constant force. The constant force solution is independent of λ and equals the constant velocity solution in the limit λ → ∞. The only mechanism of dissipation in the Tomlinson model is through the phenomenological damping force, which is proportional to the velocity of the atom. The velocity is essentially zero except in the rapid pops that occur as a state becomes unstable and the atom jumps to the next metastable state. In the overdamped limit, atoms pop with peak velocity vp ~ f1 /γ – independent of the average velocity of the center of mass. Moreover, the time of the pop is nearly independent of vCM, and so the total energy dissipated per pop is independent of vCM. This dissipated energy is of course consistent with the limiting force determined from arguments based on the sampling of metastable states given above (Fisher, 1985; Raphael and DeGennes, 1989; Joanny and Robbins, 1990). The basic idea that kinetic friction is due to dissipation during pops that remain rapid as vCM → 0 is very general, although the phenomenological damping used in the model is far from realistic. A constant dissipation during each displacement by a lattice constant immediately implies a velocity independent Fk, and vice versa.
20.3.4 Tomlinson Model in Two Dimensions: Atomic Force Microscopy Gyalog et al. (1995) have studied a generalization of the Tomlinson model where the atoms can move in two dimensions over a substrate potential. Their goal was to model the motion of an atomic-force microscope (AFM) tip over a surface. In this case the spring constant k reflects the elasticity of the cantilever, the tip, and the substrate. It will in general be different along the scanning direction than along the perpendicular direction. The extra degree of freedom provided by the second dimension means that the tip will not follow the nominal scanning direction, but will be deflected to areas of lower potential energy. This distorts the
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image and also lowers the measured friction force. The magnitude of both effects decreases with increasing stiffness. As in the one-dimensional model there is a transition from smooth sliding to rapid jumps with decreasing spring stiffness. However, the transition point now depends on sliding direction and on the position of the scan line along the direction normal to the nominal scan direction. Rapid jumps tend to occur first near the peaks of the potential, and extend over greater distances as the springs soften. The curves defining the unstable points can have very complex, anisotropic shapes. Hölscher et al. (1997) have used a similar model to simulate scans of MoS2. Their model also includes kinetic and damping terms in order to treat the velocity dependence of the AFM image. They find marked anisotropy in the friction as a function of sliding direction, and also discuss deviations from the nominal scan direction as the position and direction of the scan line vary. Rajasekaran et al. (1997) considered a simple elastic solid of varying stiffness that interacted with a single atom at the end of an AFM tip with Lennard–Jones potentials. Unlike the other calculations mentioned above, this paper explicitly includes variations in the height of the atom and maintains a constant normal load. The friction rises linearly with load in all cases, but the slope depends strongly on sliding direction, scan position, and the elasticity of the solid. The above papers and related work show the complexities that can enter from treating detailed surface potentials and the full elasticity of the materials and machines that drive sliding. All of these factors can influence the measured friction and must be included in a detailed model of any experiment. However, the basic concepts derived from one-dimensional models carry forward. In particular, (1) static friction results when there is sufficient compliance to produce multiple metastable states, and (2) a finite Fk(0) arises when energy is dissipated during rapid pops between metastable states. All of the above work considers a single atom or tip in a two-dimensional potential. However, the results can be superimposed to treat a pair of two-dimensional surfaces in contact, because the oscillators are independent in the Tomlinson model. One example of such a system is the work by Glosli and McClelland (1993) described in Section 20.4.2. Generalizing the Frenkel–Kontorova model to two dimensions is more difficult.
20.3.5 Frenkel–Kontorova Model in Two Dimensions: Adsorbed Monolayers The two-dimensional Frenkel–Kontorova model provides a simple model of a crystalline layer of adsorbed atoms (Bak, 1982). However, the behavior of adsorbed layers can be much richer because atoms are not connected by fixed springs, and thus can rearrange to form new structures in response to changes in equilibrium conditions (i.e., temperature) or due to sliding. Overviews of the factors that determine the wide variety of equilibrium structures, including fluid, incommensurate and commensurate crystals, can be found in Bruch et al. (1997) and Taub et al. (1991). As in one dimension, both the structure and the strength of the lateral variation or “corrugation” in the substrate potential are important in determining the friction. Variations in potential normal to the substrate are relatively unimportant (Persson and Nitzan, 1996; Smith et al., 1996). Most simulations of the friction between absorbed layers and substrates have been motivated by the pioneering quartz crystal microbalance (QCM) experiments of Krim et al. (1988, 1990, 1991). The quartz is coated with metal electrodes that are used to excite resonant shear oscillations in the crystal. When atoms adsorb onto the electrodes, the increased mass causes a decrease in the resonant frequency. Sliding of the substrate under the adsorbate leads to friction that broadens the resonance. By measuring both quantities, the friction per atom can be calculated. The extreme sharpness of the intrinsic resonance in the crystal makes this a very sensitive technique. In most experiments the electrodes were the noble metals Ag or Au. Deposition produces fcc crystallites with close-packed (111) surfaces. Scanning tunneling microscope studies show that the surfaces are perfectly flat and ordered over regions at least 100 nm across. At larger scales there are grain boundaries
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and other defects. A variety of molecules have been physisorbed onto these surfaces, but most of the work has been on noble gases. The interactions within the noble metals are typically much stronger than the van der Waals interactions between the adsorbed molecules. Thus, to a first approximation, the substrate remains unperturbed and can be replaced by a periodic potential (Smith et al., 1996; Persson, 1998). However, the mobility of substrate atoms is important in allowing heat generated by the sliding adsorbate to flow into the substrate. This heat transfer into substrate lattice vibrations or phonons can be modeled by a Langevin thermostat (Equation 20.3). If the surface is metallic, the Langevin damping should also include the effect of energy dissipated to the electronic degrees of freedom (Schaich and Harris, 1981; Persson, 1991; Persson and Volokitin, 1995). With the above assumptions, the equation of motion for an adsorbate atom can be written as
mx˙˙α = − γ α x˙ α + Fαext −
∂ U + fα t ∂xα
()
(20.10)
where m is the mass of an adsorbate atom, γα is the damping rate from the Langevin thermostat in the α → direction, fα(t) is the corresponding random force, F ext is an external force applied to the particles, and U is the total energy from the interactions of the adsorbate atoms with the substrate and with each other. Interactions between noble gas adsorbate atoms have been studied extensively, and are reasonably well described by a Lennard–Jones potential (Bruch et al., 1997). The form of the substrate interaction is less well-known. However, if the substrate is crystalline, its potential can be expanded as a Fourier series in → the reciprocal lattice vectors Ql of the surface layer (Bruch et al., 1997). Steele (1973) has considered Lennard–Jones interactions with substrate atoms and shown that the higher Fourier components drop → off exponentially with increasing Q and height z above the substrate. Thus most simulations have kept only the shortest wavevectors, writing:
r
r U sub r , z = U 0 z + U1 z
( )
()
( ) ∑ cos[Q ⋅ rr] l
(20.11)
l
→
→
where r is the position within the plane of the surface, and the sum is over symmetrically equivalent Q l. For the close-packed (111) surface of fcc crystals there are six equivalent lattice vectors of length 4π/ 3a where a is the nearest neighbor spacing in the crystal. For the (100) surface there are four equivalent lattice vectors of length 2π/a. Cieplak et al. (1994) and Smith et al. (1996) used Steele’s potential with an additional four shells of symmetrically equivalent wavevectors in their simulations. However, they found that their results were almost unchanged when only the shortest reciprocal lattice vectors were kept. Typically the Lennard–Jones , σ, and m are used to define the units of energy, length and time, as described in Section 20.2.1. The remaining parameters in Equation 20.10 are the damping rates, external force, and the substrate potential, which is characterized by the strength of the adsorption potential U0(z), and the corrugation potential U1(z). The Langevin damping for the two directions in the plane of the substrate is expected to be the same and will be denoted by γ . The damping along z, γ⊥, may be different (Persson and Nitzan, 1996). The depth of the minimum in the adsorption potential can be determined from the energy needed to desorb an atom, and the width is related to the frequency of vibrations along z. In the cases of interest here, the adsorption energy is much larger than the Lennard–Jones interaction or the corrugation. Atoms in the first adsorbed layer sit in a narrow range of z near the minimum z0. If the changes in U1 over this range are small, then the effective corrugation for the first monolayer is U10 U1(z0). As discussed below, the calculated friction in most simulations varies rapidly with U10 but is insensitive to other details in the substrate potential. The simplest case is the limit of weak corrugation and a fluid or incommensurate solid state of the adsorbed layer. As expected based on results from one-dimensional models, such layers experience no
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static friction, and the kinetic friction is proportional to the velocity: Fk = –Γv (Persson, 1993a; Cieplak et al., 1994). The constant of proportionality Γ gives the “slip time” ts m/Γ that is reported by Krim and co-workers (1988, 1990, 1991). This slip time represents the time for the transfer of momentum between adsorbate and substrate. If atoms are set moving with an initial velocity, the velocity will decay exponentially with time constant ts. Typical measured values of ts are of order nanoseconds for rare gases. This is surprisingly large when compared to the picosecond time scales that characterize momentum transfer in a bulk fluid of the same rare gas. (The latter is directly related to the viscosity.) The value of ts can be determined from simulations in several different ways. All give consistent results in the cases where they have been compared, and should be accurate if used with care. Persson (1993a), Persson and Nitzan (1996), and Liebsch et al. (1999) have calculated the average velocity as a function → of F ext and obtained Γ from the slope of this curve. Cieplak et al. (1994) and Smith et al. (1996) used this approach and also mimicked experiments by finding the response to oscillations of the substrate. They showed ts was constant over a wide range of frequency and amplitude. The frequency is difficult to vary in experiment, but Mak and Krim (1998) found that ts was independent of amplitude in both fluid and crystalline phases of Kr on Au. Tomassone et al. (1997) have used two additional techniques to determine ts. In both cases they used no thermostat (γα = 0). In the first method all atoms were given an initial velocity and the exponential decay of the mean velocity was used to determine ts. The second method made use of the fluctuation–dissipation theorem, and calculated ts from equilibrium velocity fluctuations. A coherent picture has emerged for the relation between ts and the damping and corrugation in Equations 20.10 and 20.11. In the limit where the corrugation vanishes, the substrate potential is translationally invariant and cannot exert any friction on the adsorbate. The value of Γ is then just equal to γ . In his original two-dimensional simulations Persson (1993a) used relatively large values of γ and reported that Γ was always proportional to γ . Later work by Persson and Nitzan (1996) showed that this proportionality only held for large γ . Cieplak et al. (1994), Smith et al. (1996), and Tomassone et al. (1997) considered the opposite limit, γ = 0 and found a nonzero Γph that reflected dissipation due to phonon excitations in the adsorbate film. Smith et al. (1996) found that including a Langevin damping along the direction of sliding produced a simple additive shift in Γ. This relation has been confirmed in extensive simulations by Liebsch et al. (1999). All of their data can be fit to the relation
( )
Γ = γ + Γph = γ + C U10
2
(20.12)
where the constant C depends on temperature, coverage, and other factors. Cieplak et al. (1994) and Smith et al. (1996) had previously shown that the damping increased quadratically with corrugation and developed a simple perturbation theory for the prefactor C in Equation 20.12. Their approach follows that of Sneddon et al. (1982) for charge-density waves, and of Sokoloff (1990) for friction between two semi-infinite incommensurate solids. It provides the simplest illustration of how dissipation occurs in the absence of metastability, and is directly relevant to studies of flow boundary conditions discussed in Section 20.5.1. The basic idea is that the adsorbed monolayer acts like an elastic sheet. The atoms are attracted to regions of low corrugation potential and repelled from regions of high potential. This produces density → → modulations ρ(Ql) in the adsorbed layer with wavevector Ql . When the substrate moves underneath the adsorbed layer, the density modulations attempt to follow the substrate potential. In the process, some of the energy stored in the modulations leaks out into other phonon modes of the layer due to anharmonicity. The energy dissipated to these other modes eventually flows into the substrate as heat. The rate of energy loss can be calculated to lowest order in a perturbation theory in the strength of the corrugation if the layer is fluid or incommensurate. Equating this to the average energy dissipation rate given by the friction relation, gives an expression for the phonon contribution to dissipation. The details of the calculation can be found in Smith et al. (1996). The final result is that the damping rate is proportional to the energy stored in the density modulations and to the rate of anharmonic
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coupling to other phonons. To lowest order in perturbation theory the energy is proportional to the square of the density modulation and thus the square of the corrugation as in Equation 20.12. The density → modulation is experimentally accessible by measuring the static structure factor S(Q)
r SQ
( ) ≡ ρ(Qr ) N
2
(20.13)
ad
where Nad is the number of adsorbed atoms. The rate of anharmonic coupling is the inverse of an effective lifetime for acoustic phonons, tphon, that could also be measured in scattering studies. One finds
Γph m =
( )
cS Q
1 N ad t phon →
(20.14)
where c is half of the number of symmetrically equivalent Ql . For an fcc crystal, c = 3 on the (111) surface and c = 2 on the (100) surface. In both cases the damping is independent of the direction of sliding, in agreement with simulations by Smith et al. (1996). Smith et al. performed a quantitative test of Equation 20.14 showing that values of S(Q) and tphon from equilibrium simulations were consistent with nonequilibrium determinations of Γph . The results of Liebsch et al. (1999) provide the first comparison of (111) and (100) surfaces. Data for the two surfaces collapse onto a single curve when divided by the values of c given above. Liebsch et al. (1999) noted that the barrier for motion between local minima in the substrate potential is much smaller for (111) than (100) surfaces and thus it might seem surprising that Γph is 50% higher on (111) surfaces. As they state, the fact that the corrugation is weak means that atoms sample all values of the potential and the energy barrier plays no special role. The major controversy between different theoretical groups concerns the magnitude of the substrate damping γ that should be included in fits to experimental systems. A given value of Γ can be obtained with an infinite number of different combinations of γ and corrugation (Robbins and Krim, 1998; Liebsch et al., 1999). Unfortunately both quantities are difficult to calculate and to measure. Persson (1991, 1998) has discussed the relation between electronic contributions to γ and changes in surface resistivity with coverage. The basic idea is that adsorbed atoms exert a drag on electrons that increases resistivity. When the adsorbed atoms slide, the same coupling produces a drag on them. The relation between the two quantities is somewhat more complicated in general because of disorder and changes in electron density due to the adsorbed layer. In fact, adsorbed layers can decrease the resistivity in certain cases. However, there is a qualitative agreement between changes in surface resistivity and the measured friction on adsorbates (Persson, 1998). Moreover, the observation of a drop in friction at the superconducting transition of lead substrates is clear evidence that electronic damping is significant in some systems (Dayo et al., 1998). There is general agreement that the electronic damping is relatively insensitive to nad, the number of adsorbed atoms per unit area or coverage. This is supported by experiments that show the variation of surface resistivity with coverage is small (Dayo and Krim, 1998). In contrast, the phonon friction varies dramatically with increasing density (Krim et al., 1988, 1990, 1991). This makes fits to measured values of friction as a function of coverage a sensitive test of the relative size of electron and phonon friction. Two groups have found that calculated values of Γ with γ = 0 can reproduce experiment. Calculations for Kr on Au by Cieplak et al. (1994) are compared to data from Krim et al. (1991) in Figure 20.4a. Figure 20.4b shows the comparison between fluctuation–dissipation simulations and experiments for Xe on Ag from Tomassone et al. (1997). In both cases there is a rapid rise in slip time with increasing coverage nad . At liquid nitrogen temperatures, krypton forms islands of uncompressed fluid for nad < 0.055 Å–2 and the slip time is relatively constant. As the coverage increases from 0.055 to 0.068 Å–2, the monolayer is compressed into an incommensurate crystal. Further increases in coverage lead to an increasingly dense crystal. The slip time increases by a factor of seven during the compression of the monolayer.
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FIGURE 20.4 Slip times vs. coverage for (a) Kr on Au (Cieplak et al., 1994, Krim et al., 1991) and (b) Xe on Ag (Tomassone et al., 1997). Calculated values are indicated by symbols, and experimental results by solid lines. Experimental data for three different runs are shown in (b). The dashed lines in (a) indicate theoretical values obtained by fitting experiments with 1/3, 1/2, or 9/10 (from bottom to top) of the friction at high coverage coming from electronic damping. (From Robbins, M.O. and Krim, J. (1998), Energy dissipation in interfacial friction, MRS Bull., 23(6), 23-26. With permission.)
For low coverages, Xe forms solid islands on Ag at T = 77.4 K. The slip time drops slightly with increasing coverage, presumably due to increasing island size (Tomassone et al., 1997). There is a sharp rise in slip time as the islands merge into a complete monolayer that is gradually compressed with increasing coverage. Figure 20.4 shows that the magnitude of the rise in ts varies from one experiment to the next. The calculated rise is consistent with the larger measured increases. The simulation results of the two groups can be extended to nonzero values of γ , using Equation 20.12. This would necessarily change the ratio between the slip times of the uncompressed and compressed layers. The situation is illustrated for Kr on Au in Figure 20.4a. The dashed lines were generated by fitting the damping of the compressed monolayer with different ratios of γ to Γph . As the importance of γ increases, the change in slip time during compression of the monolayer decreases substantially. The comparison between theory and experiment suggests that γ is likely to contribute less than 1/3 of the friction in the compressed monolayer, and thus less than 5% in the uncompressed fluid. The measured increase in slip time for Xe on Ag is smaller, and the variability noted in Figure 20.4b makes it harder to place bounds on γ . Tomassone et al. (1997) conclude that their results are consistent with no contribution from γ . When they included a value of γ suggested by Persson and Nitzan (1996) they still found that phonon friction provided 75% of the total. Persson and Nitzan had concluded that phonons contributed only 2% of the friction in the uncompressed monolayer. Liebsch et al. (1999) have reached an intermediate conclusion. They compared calculated results for different corrugations to a set of experimental data and chose the corrugation that matched the change
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in friction with coverage. They concluded that most of the damping at high coverages is due to γ and most of the damping at low coverages is due to phonons. However, the data they fitted had only a factor of 3 change with increasing coverage, and some of the data in Figure 20.4b changes by a factor of more than 5. Fitting to these sets would decrease their estimate of the size γ . The behavior of commensurate monolayers is very different than that of the incommensurate and fluid layers described so far. As expected from studies of one-dimensional models, simulations of commensurate monolayers show that they exhibit static friction. Unfortunately, no experimental results have been obtained because the friction is too high for the QCM technique to measure. In one of the earliest simulation studies, Persson (1993a) considered a two-dimensional model of Xe on the (100) surface of Ag. Depending on the corrugation strength, he found fluid, 2×2 commensurate, and incommensurate phases. He studied 1/Γ as the commensurate phase was approached by lowering temperature in the fluid phase, or decreasing coverage in the incommensurate phase. In both cases he found that 1/Γ went to zero at the boundary of the commensurate phase, implying that there was no flow in response to small forces. When the static friction is exceeded, the dynamics of adsorbed layers can be extremely complicated. In the model just described, Persson (1993a,b, 1995) found that sliding caused a transition from a commensurate crystal to a new phase. The velocity was zero until the static friction was exceeded. The system then transformed into a sliding fluid layer. Further increases in force caused a first order transition to the incommensurate structure that would be stable in the absence of any corrugation. The velocity in this phase was also what would be calculated for zero corrugation, F = γ v (dashed line). Decreasing the force led to a transition back to the fluid phase at essentially the same point. However, the layer did not return to the initial commensurate phase until the force dropped well below the static friction. The above hysteresis in the transition between commensurate and fluid states is qualitatively similar to that observed in the underdamped Tomlinson model or the mathematically equivalent case of a Josephson junction (McCumber, 1968). As in these cases, the magnitude of the damping affects the range of the hysteresis. The major difference is the origin of the hysteresis. In the Tomlinson model, hysteresis arises solely because the inertia of the moving system allows it to overcome potential barriers that a static system could not. This type of hysteresis would disappear at finite temperature due to thermal excitations (Braun et al., 1997a). In the adsorbed layers, the change in the physical state of the system has also changed the nature of the potential barriers. Similar sliding-induced phase transitions were observed earlier in experimental and simulation studies of shear in bulk crystals (Ackerson et al., 1986; Stevens et al., 1991, 1993) and in thin films (Gee et al., 1990; Thompson and Robbins, 1990b). The relation between such transitions and stick-slip motion is discussed in Section 20.6. Braun and collaborators have considered the transition from static to sliding states at coverages near to a commensurate value. They studied one- (Braun et al., 1997b; Paliy et al., 1997) and two- (Braun et al., 1997a,c) dimensional Frenkel–Kontorova models with different degrees of damping. If the corrugation is strong, the equilibrium state consists of locally commensurate regions separated by domain walls or kinks. The kinks are pinned because of the discreteness of the lattice, but this Peierls–Nabarro pinning potential is smaller than the substrate corrugation. In some cases there are different types of kinks with different pinning forces. The static friction corresponds to the force needed to initiate motion of the most weakly pinned kinks. As a kink moves through a region, atoms advance between adjacent local minima in the substrate potential. Thus the average velocity depends on both the kink velocity and the density of kinks. If the damping is strong, there may be a series of sudden transitions as the force increases. These may reflect depinning of more strongly pinned kinks, or creation of new kink–antikink pairs. At high enough velocity, the kinks become unstable, and a moving kink generates a cascade of new kink–antikink pairs that lead to faster and faster motion. Eventually the layer decouples from the substrate and there are no locally commensurate regions. As in Persson (1995), the high velocity state looks like an equilibrium state with zero corrugation. The reason is that the atoms move over the substrate so quickly that they cannot respond. Although this limiting behavior is interesting, it would only occur in experiments between flat crystals at velocities comparable to the speed of sound.
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FIGURE 20.5 The effect of crystalline alignment and lattice constant on commensurability is illustrated by projecting atoms from the bottom (filled circles) and top (open circles) surfaces into the plane of the walls. In A through C the two walls have the same structure and lattice constant but the top wall has been rotated by 0°, 8.2°, or 90°, respectively. In D the walls are aligned, but the lattice constant of the top wall has been reduced by a small amount. Only case A is commensurate. The other cases are incommensurate, and atoms from the two walls sample all possible relative positions with equal probability. (From He, G., Müser, M.H., and Robbins, M.O. (1999), Adsorbed layers and the origin of static friction, Science, 284, 1650-1652. With permission. © 1999 American Association for the Advancement of Science.)
20.4 Dry Sliding of Crystalline Surfaces The natural case of interest to tribologists is the sliding interface between two three-dimensional objects. In this section we consider sliding of bare surfaces. We first discuss general issues related to the effect of commensurability, focusing on strongly adhering surfaces such as clean metal surfaces. Then simulations of chemically passivated surfaces of practical interest are described. The section concludes with studies of friction, wear, and indentation in single-asperity contacts.
20.4.1 Effect of Commensurability The effect of commensurability in three-dimensional systems has been studied by Hirano and Shinjo (1990, 1993). They noted that even two identical surfaces are likely to be incommensurate. As illustrated in Figure 20.5, unless the crystalline surfaces are perfectly aligned, the periods will no longer match up. Thus one would expect almost all contacts between surfaces to be incommensurate. Hirano and Shinjo (1990) calculated the condition for static friction between high symmetry surfaces of fcc and bcc metals. Many of their results are consistent with the conclusions described for lower dimensions. They first showed that the static friction between incommensurate surfaces vanishes exactly if the solids are perfectly rigid. They then allowed the bottom layer of the top surface to relax in response to the atoms above and below. The relative strength of the interaction between the two surfaces and the stiffness of the top surface plays the same role as λ in the Tomlinson model. As the interaction becomes stronger, there is an Aubry transition to a finite static friction. This transition point was related to the condition for multistability of the least stable atom. To test whether realistic potentials would be strong enough to produce static friction between incommensurate surfaces, Hirano and Shinjo (1990) applied their theory to noble and transition metals. Contacts between various surface orientations of the same metal (i.e., (111) and (100) or (110) and (111)) were tested. In all cases the interactions were too weak to produce static friction. Shinjo and Hirano (1993) extended this line of work to dynamical simulations of sliding. They first considered the undamped Frenkel–Kontorova model with ideal springs between atoms. The top surface was given an initial velocity and the evolution of the system was followed. When the corrugation was small, the kinetic friction vanished, and the sliding distance increased linearly with time. This “superlubric” state disappeared above a threshold corrugation. Sliding stopped because of energy transfer from the center of mass motion into vibrations within the surface. The transition point depended on the initial
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velocity, since that set the amount of energy that needed to be converted into lattice vibrations. Note that the kinetic friction only vanishes in these simulations because atoms are connected by ideal harmonic springs (Smith et al., 1996). The damping due to energy transfer between internal vibrations (e.g., Equation 20.14) is zero because the phonon lifetime is infinite. More realistic anharmonic potentials always lead to an exponential damping of the velocity at long times. Simulations for two-dimensional surfaces were also described (Shinjo and Hirano, 1993; Hirano and Shinjo, 1993). Shinjo and Hirano noted that static friction is less likely in higher dimensions because of the ability of atoms to move around maxima in the substrate potential, as described in Section 20.3.4. A particularly interesting feature of their results is that the Aubry transition to finite static friction depends on the relative orientation of the surfaces (Hirano and Shinjo, 1993). Over an intermediate range of corrugations, the two surfaces slide freely in some alignments and are pinned in others. This extreme dependence on relative alignment has not been seen in experiments, but strong orientational variations in friction have been seen between mica surfaces (Hirano et al., 1991) and between a crystalline AFM tip and substrate (Hirano et al., 1997). Hirano and Shinjo’s conclusion that two flat, strongly adhering but incommensurate surfaces are likely to have zero static friction has been supported by two other studies. As described in more detail in Section 20.4.3, Sørensen et al. (1996) found that there was no static friction between a sufficiently large copper tip and an incommensurate copper substrate. Müser and Robbins (2000) studied a simple model system and found that interactions within the surfaces needed to be much smaller than the interactions between surfaces in order to get static friction. Müser and Robbins (2000) considered two identical but orientationally misaligned triangular surfaces similar to Figure 20.5C. Interactions within each surface were represented by coupling atoms to ideal lattice sites with a spring constant k. Atoms on opposing walls interacted through a Lennard–Jones potential. The walls were pushed together by an external force (~3 MPa) that was an order of magnitude less than the adhesive pressure from the LJ potential. The bottom wall was fixed, and the free diffusion of the top wall was followed at a low temperature (T = 0.1/kB). For k ≤ 10σ –2, the walls were pinned by static friction for all system sizes investigated. For k ≥ 25σ –2, Fs vanished, and the top wall diffused freely in the long time limit. By comparison, Lennard–Jones interactions between atoms within the walls would give rise to k ≈ 200σ –2. Hence, the adhesive interactions between atoms on different surfaces must be an order of magnitude stronger than the cohesive interactions within each surface in order to produce static friction between the flat, incommensurate walls that were considered. The results described above make it clear that static friction between ideal crystals can be expected to vanish in many cases. This raises the question of why static friction is observed so universally in experiments. One possibility is that roughness or chemical disorder pins the two surfaces together. Theoretical arguments indicate that disorder will always pin low-dimensional objects (e.g., Grüner, 1988). However, the same arguments show that the pinning between three-dimensional objects is exponentially weak (Caroli and Nozieres, 1996; Persson and Tosatti, 1996; Volmer and Natterman, 1997). This suggests that other effects, like mobile atoms between the surfaces, may play a key role in creating static friction. This idea is discussed in Section 20.5.3.
20.4.2 Chemically Passivated Surfaces The simulations just described aimed at revealing general aspects of friction. There is also a need to understand the tribological properties of specific materials on the nanoscale. Advances in the chemical vapor deposition of diamond hold promise for producing hard protective diamond coatings on a variety of materials. This motivated Harrison et al. (1992b) to perform molecular-dynamics simulations of atomic-scale friction between diamond surfaces. Two orientationally aligned, hydrogen-terminated diamond (111) surfaces were placed in sliding contact. Potentials based on the work of Brenner (1990) were used. As discussed in Section 20.7.3, these potentials have the ability to account for chemical reactions, but none occurred in the work described here. The lattices contained ten layers of carbon atoms and two layers of hydrogen atoms, and each layer
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consisted of 16 atoms. The three outermost layers were treated as rigid units, and were displaced relative to each other at constant sliding velocity and constant separation. The atoms of the next five layers were coupled to a thermostat. Energy dissipation mechanisms were investigated as a function of load, temperature, sliding velocity, and sliding direction. At low loads, the top wall moved almost rigidly over the potential from the bottom wall, and the average friction was nearly zero. At higher loads, colliding hydrogen atoms on opposing surfaces locked into a metastable state before suddenly slipping past each other. As in the Tomlinson model, energy was dissipated during these rapid pops. The kinetic friction was smaller for sliding along the grooves between nearest-neighbor hydrogen terminations, [110], than in the orthogonal direction, [112], because hydrogen atoms on different surfaces could remain farther apart. In a subsequent study, Harrison et al. (1993) investigated the effect of atomic-scale roughness by randomly replacing 1/8 of the hydrogen atoms on one surface with methyl, ethyl, or n-propyl groups. Changing hydrogen to methyl had little effect on the friction at a given load. However a new type of pop between metastable states was observed: Methyl groups rotated past each other in a rapid turnstile motion. Further increases in the length of the substituted molecules led to much smaller Fk at high loads. These molecules were flexible enough to be pushed into the grooves between hydrogen atoms on the opposing surface, reducing the number of collisions. Note that Harrison et al. (1992b, 1993) and Perry and Harrison (1996, 1997) might have obtained somewhat different trends using a different ensemble and/or incommensurate walls. Their case of constant separation and velocity corresponds to a system that is much stiffer than even the stiffest AFM. Because they used commensurate walls and constant velocity, the friction depended on the relative displacement of the lattices in the direction normal to the velocity. The constant separation also led to variations in normal load by up to an order of magnitude with time and lateral displacement. To account for these effects, Harrison et al. (1992b, 1993) and Perry and Harrison (1996, 1997) presented values for friction and load that were averaged over both time and lateral displacement. Studies of hydrogenterminated silicon surfaces (Robbins and Mountain) indicate that changing to a constant load and lateral force ensemble allows atoms to avoid each other more easily. Metastability sets in at higher loads than in a constant separation ensemble, the friction is lower, and variations with sliding direction are reduced. Glosli and co-workers have investigated the sliding motion between two ordered monolayers of longer alkane chains bound to commensurate walls (McClelland and Glosli, 1992; Glosli and McClelland, 1993; Ohzono et al., 1998). Each chain contained six monomers with fixed bond lengths. Next-nearest neighbors and third-nearest neighbors on the chain interacted via bond bending and torsional potentials, respectively. One end of each chain was harmonically coupled to a site on the 6 × 6 triangular lattices that made up each wall. All other interactions were Lennard–Jones (LJ) potentials between CH3 and CH2 groups (the united atom model of Section 20.2.1). The chain density was high enough that chains pointed away from the surface they were anchored to. A constant vertical separation of the walls was maintained, and the sliding velocity v was well below the sound velocity. Friction was studied as a function of T, v, and the ratio of the LJ interaction energy between endgroups on opposing surfaces, 1, to that within each surface, 0. Many results of these simulations correspond to the predictions of the Tomlinson model. Below a threshold value of 1/0 (0.4 at kBT/0 = 0.284), molecules moved smoothly, and the force decreased to zero with velocity. When the interfacial interactions became stronger than this threshold value, “plucking motion” due to rapid pops between metastable states was observed. Glosli and McClelland (1993) showed that at each pluck, mechanical energy was converted to kinetic energy that flowed away from the interface as heat. Ohzono et al. (1998) showed that a generalization of the Tomlinson model could quantitatively describe the sawtooth shape of the shear stress as a function of time. The instantaneous lateral force did not vanish in any of Glosli and McClelland’s (1993) or Ohzono et al.’s (1998) simulations. This shows that there was always a finite static friction, as expected between commensurate surfaces. For both weak (1/0 = 0.1) and strong (1/0 = 1.0) interfacial interactions, Glosli and McClelland (1993) observed an interesting maximum in the T-dependent friction force. The position of this maximum coincided with the rotational “melting” temperature TM where orientational order at the interface
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was lost. It is easy to understand that F drops at T > TM because thermal activation helps molecules move past each other. The increase in F with T at low T was attributed to increasing anharmonicity that allowed more of the plucking energy to be dissipated.
20.4.3 Single Asperity Contacts Engineering surfaces are usually rough, and friction is generated between contacting asperities on the two surfaces. These contacts typically have diameters of order a µm or more (e.g., Dieterich and Kilgore, 1996). This is much larger than atomic scales, and the models above may provide insight into the behavior within a representative portion of these contacts. However, it is important to determine how finite contact area and surface roughness affect friction. Studies of atomic-scale asperities can address these issues, and also provide direct models of the small contacts typical of AFM tips. Sørensen et al. performed simulations of sliding tip–surface and surface–surface contacts consisting of copper atoms (Sørensen et al., 1996). Flat, clean tips with (111) or (100) surfaces were brought into contact with corresponding crystalline substrates (Figure 20.6). The two exterior layers of tip and surface were treated as rigid units, and the dynamics of the remaining mobile layers was followed. Interatomic forces and energies were calculated using semiempirical potentials derived from effective medium theory (Jacobsen et al., 1987). At finite temperatures, the outer mobile layer of both tip and surface was coupled to a Langevin thermostat. Zero temperature simulations gave similar results. To explore the effects of commensurability, results for crystallographically aligned and misoriented tip–surface configurations were compared. In the commensurate Cu(111) case, Sørensen et al. observed atomic-scale stick-slip motion of the tip. The trajectory was of zigzag form, which could be related to jumps of the tip’s surface between fcc and hcp positions. Similar zigzag motion is seen in shear along (111) planes within bulk fcc solids (Stevens and Robbins, 1993). Detailed analysis of the slips showed that they occurred via a dislocation mechanism. Dislocations were nucleated at the corner of the interface, and the moved rapidly through the contact region. Adhesion led to a large static friction at zero load. The static friction per unit area, or critical yield stress, dropped from 3.0GPa to 2.3GPa as T increased from 0 to 300K. The kinetic friction increased linearly with load with a surprisingly small differential friction coefficient µ˜ k ∂Fk /∂L ≈ .03. In the load regime investigated, µ˜ k was independent of temperature and load. No velocity dependence was detectable up to sliding velocities of v = 5 m/s. At higher velocities, the friction decreased. Even though the interactions between the surfaces were identical to those within the surfaces, no wear was observed. This was attributed to the fact that (111) surfaces are the preferred slip planes in fcc metals. Adhesive wear was observed between a commensurate (100) tip and substrate (Figure 20.6). Sliding in the (011) direction at either constant height or constant load led to interplane sliding between (111) planes inside the tip. As shown in Figure 20.6, this plastic deformation led to wear of the tip, which left a trail of atoms in its wake. The total energy was an increasing function of sliding distance due to the extra surface area. The constant evolution of the tip kept the motion from being periodic, but the sawtooth variation of force with displacement that is characteristic of atomic-scale stick-slip was still observed. Nieminen et al. (1992) observed a different mechanism of plastic deformation in essentially the same geometry, but at higher velocities (100m/s vs. 5m/s) and with Morse potentials between Cu atoms. Sliding took place between (100) layers inside the tip. This led to a reduction of the tip by two layers that was described as the climb of two successive edge dislocations, under the action of the compressive load. Although wear covered more of the surface with material from the tip, the friction remained constant at constant normal load. The reason was that the portion of the surface where the tip advanced had a constant area. While the detailed mechanism of plastic mechanism is very different than in Sørensen et al. (1996), the main conclusions of both papers are similar: When two commensurate surfaces with strong interactions are slid against each other, wear occurs through formation of dislocations that nucleate at the corners of the moving interface. Sørensen et al. (1996) also examined the effect of incommensurability. An incommensurate Cu(111) system was obtained by rotating the tip by 16.1° about the axis perpendicular to the substrate. For a small tip (5 × 5 atoms) they observed an Aubry transition from smooth sliding with no static friction at
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FIGURE 20.6 Snapshots showing the evolution of a Cu(100) tip on a Cu(100) substrate during sliding to the left. (From Sørensen, M.R., Jacobsen, K.W., and Stoltze, P. (1996), Simulations of atomic-scale sliding friction, Phys. Rev. B, 53, 2101-2113. With permission. © 1996 American Physical Society.)
low loads, to atomic-scale stick-slip motion at larger loads. Further increases in load led to sliding within the tip and plastic deformation. Finite systems are never truly incommensurate, and pinning was found to occur at the corners of the contact, suggesting it was a finite-size effect. Larger tips (19 × 19) slid without static friction at all loads. Similar behavior was observed for incommensurate Cu(100) systems. These results confirm the conclusions of Hirano and Shinjo (1990) that even bare metal surfaces of the same material will not exhibit static friction if the surfaces are incommensurate. They also indicate that contact areas as small as a few hundred atoms are large enough to exhibit this effect. Many other tip–substrate simulations of bare metallic surfaces have been carried out. Mostly, these simulations concentrated on indentation, rather than on sliding or scraping (see Section 20.7.2). Among the indentation studies of metals are simulations of a Ni tip indenting Au(100) (Landman et al., 1990), a Ni tip coated with an epitaxial gold monolayer indenting Au(100) (Landman et al., 1992), an Au tip indenting Ni(100) (Landman and Luedtke, 1989, 1991), an Ir tip indenting a soft Pb substrate (RaffiTabar et al., 1992), and an Au tip indenting Pb(110) (Tomagnini et al., 1993). These simulations have been reviewed in detail within this series by Harrison et al. (1999).
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0
A
(a)
Fz(nN)
Au / Ni
K I
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G
E
C
J
-20
H B
F
-30 D
-47230
Ep(eV)
(b)
-47300
0
4
0
dhs (A)
8
FIGURE 20.7 Normal force Fz and potential energy Ep of an Au tip lowered toward a Ni(001) surface as a function of separation dhs, which is defined to be zero after the jump to contact has occurred. As indicated by arrows, upper lines were obtained by lowering the tip; lower lines are obtained by raising the tip. The points marked C, E, G, I, and K correspond to ordered configurations of the tip, each containing an additional layer. (Data from Landman, U. and Luedtke, W.D. (1991), Nanomechanics and dynamics of tip–substrate interactions, J. Vac. Sci. Technol. B, 9, 414-423.)
In general, plastic deformation occurs mainly in the softer of the two materials, typically Au or Pb in the cases above. Figure 20.7 shows the typical evolution of the normal force and potential energy during an indentation at high enough loads to produce plastic deformation (Landman and Luedtke, 1991). As the Au tip approaches the Ni surface (upper lines), the force remains nearly zero until a separation of about 1 Å. The force then becomes extremely attractive and there is a jump to contact (A). During the jump to contact, Au atoms in the tip displace by 2 Å within a short time span of 1 ps. This strongly adhesive contact produces reconstruction of the Au layers through the fifth layer of the tip. When the tip is withdrawn, a neck is pulled out of the substrate. The fluctuations in force seen in Figure 20.7 correspond to periodic increases in the number of layers of gold atoms in the neck. Nanoscale investigations of indentation, adhesion and fracture of nonmetallic diamond (111) surfaces have been carried out by Harrison et al. (1992a). A hydrogen-terminated diamond tip was brought into contact with a (111) surface that was either bare or hydrogen-terminated. The tip was constructed by removing atoms from a (111) crystal until it looked like an inverted pyramid with a flattened apex. The model for the surface was similar to that described in Section 20.4.2, but each layer contained 64 atoms. The indentation was performed by moving the rigid layers of the tip in steps of 0.15 Å. The system was then equilibrated before observables were calculated. Unlike the metal/metal systems (Figure 20.7), the diamond/diamond systems (Figure 20.8) did not show a pronounced jump to contact (Harrison et al., 1992a). This is because the adhesion between diamond (111) surfaces is quite small if at least one is hydrogen-terminated (Harrison et al., 1991). For effective normal loads up to 200 nN (i.e., small indentations), the diamond tip and surface deformed elastically and the force distance curve was reversible (Figure 20.8A). A slight increase to 250 nN, led to plastic deformation that produced hysteresis and steps in the force distance curve (Figure 20.8B) (Harrison et al., 1992a).
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FIGURE 20.8 Total potential energy of a hydrogen-terminated diamond–diamond system as a function of separation during indentation to a maximum load of (A) 200 nN or (B) 250 nN. Arrows indicate the direction of the motion. (Data from Harrison, J.A., White, C.T., Colton, R.J., and Brenner, D.W. (1992a), Nanoscale investigation of indentation, adhesion and fracture of diamond (111) surfaces, Surf. Sci., 271, 57-67.)
20.5 Lubricated Surfaces Hydrodynamics and elastohydrodynamics have been very successful in describing lubrication by microthick films (Dowson and Higginson, 1968). However, these continuum theories begin to break down as atomic structure becomes important. Experiments and simulations reveal a sequence of dramatic changes in the static and dynamic properties of fluid films as their thickness decreases from microns down to molecular scales. These changes have important implications for the function of boundary lubricants. This section describes simulations of these changes, beginning with changes in flow boundary conditions for relatively thick films, and concluding with simulations of submonolayer films and corrugated walls.
20.5.1 Flow Boundary Conditions Hydrodynamic theories of lubrication need to assume a boundary condition (BC) for the fluid velocity at solid surfaces. Macroscopic experiments are generally well-described by a “no-slip” BC; that is that the tangential component of the fluid velocity equals that of the solid at the surface. The one prominent exception is contact line motion, where an interface between two fluids moves along a solid surface. This motion would require an infinite force in hydrodynamic theory, unless slip occurred near the contact line (Huh and Scriven, 1971; Dussan, 1979). The experiments on adsorbed monolayers described in Section 20.3.5 suggest that slip may occur more generally on solid surfaces. As noted, the kinetic friction between the first monolayer and the substrate can be orders of magnitude lower than that between two layers in a fluid. The opposite deviation from no-slip BC is seen in some Surface Force Apparatus experiments — a layer of fluid molecules becomes immobilized at the solid wall (Chan and Horn, 1985; Israelachvili, 1986). In pioneering theoretical work, Maxwell (1867) calculated the deviation from a no-slip boundary condition for an ideal gas. He assumed that at each collision molecules were either specularly reflected or exchanged momentum to emerge with a velocity chosen at random from a thermal distribution. The calculated flow velocity at the wall was nonzero, and increased linearly with the velocity gradient near the wall. Taking z as the direction normal to the wall and u as the tangential component of the fluid velocity relative to the wall, Maxwell found
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∂u u z 0 = S ∂z z
( )
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(20.15) 0
where z0 is the position of the wall. The constant of proportionality, S, has units of length and is called the slip length. It represents the distance into the wall at which the velocity gradient would extrapolate to zero. Calculations with a fictitious wall at this position and no-slip boundary conditions would reproduce the flow in the region far from the wall. S also provides a measure of the kinetic friction per unit area between the wall and the adjacent fluid. The shear stress must be uniform in steady state, because any imbalance would lead to accelerations. Since the velocity gradient times the viscosity µ gives the stress in the fluid, the kinetic friction per unit area is u (z0)µ/S. Maxwell found that S increased linearly with the mean free path and that it also increased with the probability of specular reflection. Early simulations used mathematically flat walls and phenomenological reflection rules like those of Maxwell. For example, Hannon et al. (1988) found that the slip length was reduced to molecular scales in dense fluids. This is expected from Maxwell’s result, since the mean free path becomes comparable to an atomic separation at high densities. However work of this type does not address how the atomic structure of realistic walls is related to collision probabilities and whether Maxwell’s reflection rules are relevant. This issue was first addressed in simulations of moving contact lines where deviations from noslip boundary conditions have their most dramatic effects (Koplik et al., 1988, 1989; Thompson and Robbins, 1989). These papers found that even when no-slip boundary conditions held for single fluid flow, the large stresses near moving contact lines led to slip within a few molecular diameters of the contact line. They also began to address the relation between the flow boundary condition and structure induced in the fluid by the solid wall. The most widely studied type of order is layering in planes parallel to the wall. It is induced by the sharp cutoff in fluid density at the wall and the pair correlation function g(r) between fluid atoms (Abraham, 1978; Toxvaerd, 1981; Nordholm and Haymet, 1980; Snook and van Megen, 1980; Plischke and Henderson, 1986). An initial fluid layer forms at the preferred wall-fluid spacing. Additional fluid molecules tend to lie in a second layer, at the preferred fluid–fluid spacing. This layer induces a third, and so on. Some of the trends that are observed in the degree and extent of layering are illustrated in Figure 20.9 (Thompson and Robbins, 1990a). The fluid density is plotted as a function of the distance between walls for a model considered in almost all the studies of flow BCs described below. The fluid consists of spherical molecules interacting with a Lennard–Jones potential. They are confined by crystalline walls containing discrete atoms. In this case the walls were planar (001) surfaces of an fcc crystal. Wall and fluid atoms also interact with a Lennard–Jones potential, but with a different binding energy wf . The net adsorption potential from the walls (Equation 20.11) can be increased by raising wf or by increasing the density of the walls ρw so that more wall atoms attract the fluid. Figure 20.9 shows that both increases lead to increases in the height of the first density peak. The height also increases with the pressure in the fluid (Koplik et al., 1989; Barrat and Bocquet, 1999a) since that forces atoms into steeper regions of the adsorption potential. The height of subsequent density peaks decreases smoothly with distance from the wall, and only four or five well-defined layers are seen near each wall in Figure 20.9. The rate at which the density oscillations decay is determined by the decay length of structure in the bulk pair-correlation function of the fluid. Since all panels of Figure 20.9 have the same conditions in the bulk, the decay rate is the same. The adsorption potential only determines the initial height of the peaks. The pair correlation function usually decays over a few molecular diameters except under special conditions, such as near a critical point. For fluids composed of simple spherical molecules, the oscillations typically extend out to a distance of order 5 molecular diameters (Magda et al., 1985; Schoen et al., 1987; Thompson and Robbins, 1990a). For more complex systems containing fluids with chain or branched polymers, the oscillations are usually negligible beyond ~3 molecular diameters (Bitsanis and Hadziianou, 1990; Thompson et al., 1995; Gao et al., 1997a, 1997b). Some simulations with realistic
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FIGURE 20.9 Panels (a) through (c) show density as a functions of position z relative to two walls whose atoms are centered at z/σ = ±6.4. Values of wf are indicated. Solid lines are for equal wall an fluid densities, and dotted lines are for ρw = 2.52ρ. Squares in panels (d) through (f) show the average velocity in each layer as a function of z, and solid and dotted lines are fits through these values for low- and high-density walls, respectively. For these data the walls were moved in opposite directions at speed U = 1σ/tLJ. The dashed line in (e) represents the flow expected from hydrodynamics with a no-slip BC (S = 0). As shown in (f), the slope (dashed line) far from the walls is used to define S. For this case, the first two layers stick, and S is negative. (Panels d through f from Thompson and Robbins, 1990a).
potentials for alkanes show more pronounced layering near the wall because the molecules adopt a rodlike conformation in the first layer (Ribarsky et al., 1992; Xia et al., 1992). Solid surfaces also induce density modulations within the plane of the layers (Landman et al., 1989; Schoen et al., 1987, 1988, 1989; Thompson and Robbins, 1990a, 1990b). These correspond directly to the modulations induced in adsorbed layers by the corrugation potential (Section 20.3.5), and can also be quantified by the two-dimensional static structure factor at the shortest reciprocal lattice vector Q of the substrate. When normalized by the number of atoms in the layer, Nl, this becomes an intensive variable that would correspond to the Debye–Waller factor in a crystal. The maximum possible value, S(Q)/Nl = 1, corresponds to fixing all atoms exactly at crystalline lattice sites. In a strongly ordered case such as ρw = ρ in Figure 20.9c, the small oscillations about lattice sites in the first layer only decrease S(Q)/Nl to 0.71. This is well above the value of 0.6 that is typical of bulk three-dimensional solids at their melting point and indicates that the first layer has crystallized onto the wall. This was confirmed by computer simulations of diffusion and flow (Thompson and Robbins, 1990a). The values of S(Q)/Nl in the second and third layers are 0.31 and 0.07, respectively, and atoms in these layers exhibit typical fluid diffusion. There is some correlation between the factors that produce strong layering and those that produce strong in-plane modulations. For example, chain molecules have several conflicting length scales that tend to frustrate both layering and in-plane order (Thompson et al., 1995; Gao et al., 1997a,b; Koike and Yoneya, 1998, 1999). Both types of order also have a range that is determined by g(r) and a magnitude that decreases with decreasing wf /. However, the dependence of in-plane order on the density of substrate atoms is more complicated than for layering. When ρw = ρ, the fluid atoms can naturally sit on the sites of a commensurate lattice, and S(Q) is large. When the substrate density ρw is increased by a factor of 2.52, the fluid atoms no longer fit easily into the corrugation potential. The degree of induced
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in-plane order drops sharply, although the layering becomes stronger (Figure 20.9). Sufficiently strong adsorption potentials may eventually lead to crystalline order in the first layers, and stronger layering. However, this may actually increase slip, as shown below. Figure 20.9 also illustrates the range of flow boundary conditions that have been seen in many studies (Heinbuch and Fischer, 1989; Koplik et al., 1989; Thompson and Robbins, 1990a; Bocquet and Barrat, 1994; Mundy et al., 1996; Khare et al., 1996; Barrat and Bocquet, 1999a). Flow was imposed by displacing the walls in opposite directions along the x-axis with speed U (Thompson and Robbins, 1990a). The average velocity Vx was calculated within each of the layers defined by peaks in the density (Figure 20.9), and normalized by U. Away from the walls, all systems exhibit the characteristic Couette flow profile expected for Newtonian fluids. The value of Vx rises linearly with z, and the measured shear stress divided by ∂Vx /∂z equals the bulk viscosity. Deviations from this behavior occur within the first few layers, in the region where layering and in-plane order are strong. In some cases the fluid velocity remains substantially less than U, indicating slip occurs. In others, one or more layers move at the same velocity as the wall, indicating that they are stuck to it. Applying Maxwell’s definition of slip length (Equation 20.15) to these systems is complicated by uncertainty in where the plane of the solid surface z0 should be defined. The wall is atomically rough, and the fluid velocity cannot be evaluated too near to the wall because of the pronounced layering. In addition, the curvature evident in some flow profiles represents a varying local viscosity whose effect must be included in the boundary condition. One approach is to fit the linear flow profile in the central region and extrapolate to the value of z* where the velocity would reach +U (Figure 20.9f). The slip length can then be defined as S = z* – ztw where ztw is the height of the top wall atoms. This is equivalent to applying Maxwell’s definition (Equation 20.15) to the extrapolated flow profile at ztw . The no-slip condition corresponds to a flow profile that extrapolates to the wall velocity at ztw as illustrated by the dashed line in Figure 20.9e. Slip produces a smaller velocity gradient and a positive value of S. Stuck layers lead to a larger velocity gradient and a negative value of S. The dependence of slip length on many parameters has been studied. All the results are consistent with a decrease in slip as the in-plane order increases. Numerical results for ρw = ρ and wf = 0.4 (Figure 20.9d) are very close to the no-slip condition. Increasing wf leads to stuck layers (Koplik et al., 1988, 1989; Thompson and Robbins, 1989, 1990a; Heinbuch and Fischer, 1989), and decreasing wf can produce large slip lengths (Thompson and Robbins, 1990a; Barrat and Bocquet, 1999a). Increasing pressure (Koplik et al., 1989; Barrat and Bocquet, 1999a) or decreasing temperature (Heinbuch and Fischer, 1989; Thompson and Robbins, 1990a) increases structure in g(r) and leads to less slip. These changes could also be attributed to increases in layering. However, increasing the wall density ρw from ρ to 2.52 ρ increases slip in Figure 20.9. This correlates with the drop in in-plane order, while the layering actually increases. Changes in in-plane order also explain the pronounced increase in slip when wf / is increased to 4 in the case of dense walls (Figure 20.9f). The first layer of fluid atoms becomes crystallized with a very different density than the bulk fluid. It becomes the “wall” that produces order in the second layer, and it gives an adsorption potential characterized by rather than wf . The observed slip is consistent with that for dense walls displaced to the position of the first layer and interacting with . Thompson and Robbins (1990a) found that all of their results for S collapsed onto a universal curve when plotted against the structure factor S(Q)/Nl. When one or more layers crystallized onto the wall, the same collapse could be applied as long as the effective wall position was shifted by a layer and the Q for the outer wall layer was used. The success of this collapse at small S(Q)/Nl can be understood from the perturbation theory for the kinetic friction on adsorbed monolayers (Equation 20.14). The slip length is determined by the friction between the outermost fluid layer and the wall. This depends only on S(Q)/Nl and the phonon lifetime for acoustic waves. The latter changes relatively little over the temperature range considered, and hence S is a single-valued function of S(Q). The perturbation theory breaks down at large S(Q), but the success of the collapse indicates that there is still a one-to-one correspondence between it and the friction.
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In a recent paper, Barrat and Bocquet (1999b) have derived an expression relating S and S(Q) that is equivalent to Equation 20.14. However, in describing their numerical results* they emphasize the correlation between increased slip and decreased wetting (Barrat and Bocquet, 1999a,b). In general the wetting properties of fluids are determined by the adsorption term of the substrate potential U0 (Equation 20.11). This correlates well with the degree of layering, but has little to do with in-plane order. In the limit of a perfectly structureless wall one may have complete wetting and yet there is also complete slip. The relation between wetting and slip is very much like that between adhesion and friction. All other things being equal, a greater force of attraction increases the effect of corrugation in the potential and increases the friction. However, there is no one-to-one correspondence between them. In earlier work, Bocquet and Barrat (1993, 1994) provided a less ambiguous resolution to the definition of the slip length than that of Thompson and Robbins (1990a). They noted that the shear rate in the central region of Couette flow depended only on the sum of the wall position and the slip length. Thus one must make a somewhat arbitrary choice of wall position to fix the slip length. However, if one also fits the flow profile for Poiseuille flow, unique values of slip length and the effective distance between the walls h are obtained (Barrat and Bocquet, 1999a). Bocquet and Barrat (1993, 1994) also suggested and implemented an elegant approach for determining both S and h using equilibrium simulations and the fluctuation–dissipation theorem. This is one of the first applications of the fluctuation–dissipation theorem to boundary conditions. It opens up the possibility of calculating flow boundary conditions directly from equilibrium thermodynamics, and Bocquet and Barrat (1994) were able to derive Kubo relations for z0 and S. Analytic results for these relations are not possible in general, but, as noted above, in the limit of weak interactions they give an expression equivalent to Equation 20.14 for the drag on the wall (Barrat and Bocquet, 1999b). Mundy et al. (1996) have proposed a nonequilibrium simulation method for calculating these quantities directly. In all of the work described above, care was taken to ensure that the slip boundary condition was independent of the wall velocity. Thus both the bulk of the fluid and the interfacial region were in the linear response regime where the fluctuation–dissipation theorem holds. This linear regime usually extends to very high shear rates (>1010s–1 for spherical molecules). However, Thompson and Troian (1997) found that under some conditions the interfacial region exhibits nonlinear behavior at much lower shear rates than the bulk fluid. They also found a universal form for the deviation from a linear stress/strain-rate relationship at the interface. The fundamental origin for this nonlinearity is that there is a maximum stress that the substrate can apply to the fluid. This stress roughly corresponds to the maximum of the force from the corrugation potential times the areal density of fluid atoms. The stress/velocity relation at the interface starts out linearly and then flattens as the maximum stress is approached. The shear rate in the fluid saturates at the value corresponding to the maximum interfacial shear stress and the amount of slip at the wall grows arbitrarily large with increasing wall velocity. Similar behavior was observed for more realistic potentials by Koike and Yoneya (1998, 1999).
20.5.2 Phase Transitions and Viscosity Changes in Molecularly Thin Films One of the surprising features of Figure 20.9 is that the viscosity remains the same even in regions near the wall where there is pronounced layering. Any change in viscosity would produce a change in the velocity gradient since the stress is constant. However, the flow profiles in panel (d) remain linear throughout the cell. The profile for the dense walls in panel (f) is linear up to the last layer, which has crystallized onto the wall. From Figure 20.9 it is apparent that density oscillations by at least a factor of 7 can be accommodated without a viscosity change. The interplay between layering and viscosity was studied in detail by Bitsanis et al. (1987), although their use of artificial flow reservoirs kept them from addressing flow BCs. They were able to fit detailed *They considered almost the same parameter range as Thompson and Robbins (1990a), but at a lower temperature (kBT/ = 0.7 vs. 1.1 or 1.4) and at a single wall density (ρ = ρw).
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flow profiles using only the bulk viscosity evaluated at the average local density. This average was taken over a distance of order σ that smeared out the rapid density modulations associated with layering, but not slower variations due to the adsorption potential of the walls or an applied external potential. In subsequent work, Bitsanis et al. (1990) examined the change in viscosity with film thickness. They found that results for film thicknesses h > 4σ could be fit using the bulk viscosity for the average density. However, as h decreased below 4σ, the viscosity diverged much more rapidly than any model based on bulk viscosity could explain. These observations were consistent with experiments on nanometer-thick films of a wide variety of small molecules. These experiments used the surface force apparatus (SFA), which measures film thickness with Å resolution using optical interferometry. Films were confined between atomically flat mica sheets at a fixed normal load, and sheared with a steady (Gee et al., 1990) or oscillating (Granick, 1992) velocity. Layering in molecularly thin films gave rise to oscillations in the energy, normal force, and effective viscosity (Horn and Israelachvili, 1981; Israelachvili, 1991; Georges et al., 1993) as the film thickness decreased. The period of these oscillations was a characteristic molecular diameter. As the film thickness decreased below seven to ten molecular diameters, the effective viscosity increased dramatically (Gee et al., 1990; Granick, 1992; Klein and Kumacheva, 1995). Most films of one to three molecular layers exhibited a yield stress characteristic of solid-like behavior, even though the molecules formed a simple Newtonian fluid in the bulk. Pioneering grand canonical Monte Carlo simulations by Schoen et al. (1987) showed crystallization of spherical molecules between commensurate walls separated by up to six molecular diameters. However, the crystal was only stable when the thickness was near to an integral number of crystalline layers. At intermediate h, the film transformed to a fluid state. Later work (Schoen et al., 1988, 1989) showed that translating the walls could also destabilize the crystalline phase and lead to periodic melting and freezing transitions as a function of displacement. However, these simulations were carried out at equilibrium and did not directly address the observed changes in viscosity. SFA experiments cannot determine the flow profile within the film, and this introduces ambiguity in the meaning of the viscosity values that are reported. Results are typically expressed as an effective viscosity . . µeff τs /γeff where τs is the measured shear stress and γeff v/h represents the effective shear rate that would be present if the no-slip condition held and walls were displaced at relative velocity v. Deviations from the no-slip condition might cause µeff to differ from the bulk viscosity by an order of magnitude. However, they could not explain the observed changes of µeff by more than five orders of magnitude or the even more dramatic changes by 10 to 12 orders of magnitude in the characteristic viscoelastic relaxation time determined from the shear rate dependence of µeff (Gee et al., 1990; Hu et al., 1991). Thompson et al. (1992) found very similar changes in viscosity and relaxation time in simulations of a simple bead-spring model of linear molecules (Kremer and Grest, 1990). Some of their results for the effective viscosity vs. effective shear rate are shown in Figure 20.10. In (a), the normal pressure P⊥ was fixed and the number of atomic layers, ml, was decreased from eight to two. In (b), the film was confined by increasing the pressure at fixed particle number. Both methods of increasing confinement lead to dramatic changes in the viscosity and relaxation time. The shear rate dependence of µeff in Figure 20.10 has the same form as in experiment (Hu et al., 1991). A Newtonian regime with constant viscosity µ0 is seen at the lowest shear rates in all but the uppermost . curve in each panel. Above a characteristic shear rate γc the viscosity begins to decrease rapidly. This shear thinning is typical of viscoelastic media and indicates that molecular rearrangements are too slow to . . respond to the sliding walls at γeff > γc . As a result, the structure of the fluid begins to change in a way that facilitates shear. A characteristic time for molecular rearrangements in the film can be associated . with 1/ γc . Increasing confinement by decreasing ml or increasing pressure, increases the Newtonian viscosity and relaxation time. For the uppermost curve in each panel, the relaxation time is longer than the longest simulation runs (>106 time steps) and the viscosity continues to increase at the lowest accessible shear rates. Note that the ranges of shear rate covered in experiment and simulations differ by orders of magnitude. However, the scaling discussed below suggests that the same behavior may be operating in both.
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FIGURE 20.10 Plots of µeff vs. γeff at (a) fixed normal pressure P⊥ = 4σ –3 and varying numbers of layers ml , and (b) fixed ml = 4 and varying P⊥ (Thompson et al., 1992). Dashed lines have slope –2/3. Panel (c) shows that this and other data can be collapsed onto a universal response function (Robbins and Baljon, 2000). Results are for decreasing temperature in bulk systems (circles), increasing normal pressure at a fixed number of fluid layers (triangles), or decreasing film thickness at fixed pressure with two different sets of interaction potentials (squares and crosses). The dotted line has a slope of –0.69. (Panels a and b from Thompson et al., 1992; panel c from Robbins and Baljon, 2000.)
For the parameters used in Figure 20.10, studies of the flow profile in four layer films showed that one layer of molecules was stuck to each wall and shear occurred in the middle layers. Other parameter sets produced varying degrees of slip at the wall/film interface, yet the viscoelastic response curves showed the same behavior (Thompson et al., 1995). Later work by Baljon and Robbins (1996, 1997) shows that lowering the temperature through the bulk glass transition also produces similar changes in viscoelastic response. This suggests that the same glass transition is being produced by changes in thickness, pressure or temperature. Following the analogy to bulk glass transitions, Thompson et al. (1993, 1995) have shown that changes . in equilibrium diffusion constant and γc can be fit to a free volume theory. Both vanish as exp(–h0 /(h – hc )) where hc is the film thickness at the glass transition. Moreover, at h < hc , they found behavior characteristic of a solid. Films showed a yield stress and no measurable diffusion. When forced to slide, shear localized . at the wall/film interface and µeff dropped as 1/ γ, implying that the shear stress is independent of sliding velocity. This is just the usual form of kinetic friction between solids. The close relation between bulk glass transitions and those induced by confinement can perhaps best be illustrated by using a generalization of time–temperature scaling. In bulk systems it is often possible to collapse the viscoelastic response onto a universal curve by dividing the viscosity by the Newtonian . value, µ0, and dividing the shear rate by the characteristic rate, γc . Demirel and Granick (1996a) found that this approach could be used to collapse data for the real and imaginary parts of the elastic moduli of confined films at different thicknesses. Figure 20.10c shows that simulation results for the viscosity of thin films can also be collapsed using Demirel and Granick’s approach (Robbins and Baljon, 2000). Data for different thicknesses, normal pressures, and interaction parameters taken from all parameters considered by Thompson et al. (1992, 1995) collapse onto a universal curve. Also shown on the plot (circles) are data for different temperatures that were obtained for longer chains in films that are thick enough
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to exhibit bulk behavior (Baljon and Robbins, 1996, 1997). The data fit well onto the same curve, providing a strong indication that a similar glass transition occurs whether thickness, normal pressure, or temperature is varied. The high shear rate region of the universal curve shown in Figure 20.10c exhibits power law shear . thinning: µeff ∝ γ –x with a best fit exponent x = 0.69 ± .02. In SFA experiments, Hu et al. (1991) found shear thinning of many molecules was consistent with x near 2/3. However, the response of some fluids followed power laws closer to 0.5 as they became less confined (Carson et al., 1992). One possible explanation for this is that these measurements fall onto the crossover region of a universal curve like Figure 20.10c. The apparent exponent obtained from the slope of this log-log plot varies from 0 to 2/3 as µeff drops from µ0 to about µ0 /30. Many of the experiments that found smaller exponents were only able to observe a drop in µ by an order of magnitude. As confinement was increased, and a larger drop in viscosity was observed, the exponent increased toward 2/3. It would be interesting to attempt a collapse of experimental data on a curve like Figure 20.10c to test this hypothesis. Another possibility is that the shear thinning exponent depends on some detail of the molecular structure. Chain length alone does not appear to affect the exponent, since results for chains of length 16 and 6 are combined in Figure 20.10c. Manias et al. (1996) found that changing the geometry from linear to branched also has little effect on shear thinning. In most simulations of simple spherical molecules, crystallization occurs before the viscosity can rise substantially above the bulk value. However, Hu et al. (1996) have found a set of conditions where spherical molecules follow a –2/3 slope over two decades in shear rate. Stevens et al. (1997) have performed simulations of confined films of hexadecane using a detailed model of the molecular structure and interactions. They found that films crystallized before the viscosity rose much above bulk values. This prevented them from seeing large power law scaling regimes, but the apparent exponents were consistently less than those for bead spring models. It is not clear whether the origin of this discrepancy is the inability to approach the glass transition, or whether structural changes under shear lead to different behavior. Hexadecane molecules have some tendency to adopt a linear configuration and become aligned with the flow. This effect is not present in simpler bead-spring models. Shear thinning typically reflects changes in structure that facilitate shear. Experiments and the above simulations were done at constant normal load. In bead-spring models the dominant structural change is a dilation of the film that creates more room for molecules to slide past each other. The dilations are relatively small, but have been detected in some experiments (Dhinojwala and Granick). When simulations are done at constant wall spacing, the shear-thinning exponent drops to x = 0.5 (Thompson et al., 1992, 1995; Manias et al., 1996). Kröger et al. (1993) find the same exponent in bulk simulations of these molecules at constant volume, indicating that a universal curve like that in Figure 20.10c might also be constructed for constant volume instead of constant pressure. Several analytic models have been developed to explain the power law behavior observed in experiment and simulations. All the models find an exponent of 2/3 in certain limits. However, they start from very different sets of assumptions, and it is not clear if any of these correspond to the simulations and experiments. Two of the models yield an exponent of 2/3 for constant film thickness (Rabin and Hersht, 1993; Urbakh et al., 1995) where simulations give x = 1/2. Urbakh et al. (1995) also find that the exponent depends on the velocity profile, while simulations do not. The final model (DeGennes) is based on scaling results for the stretching of polymers under shear. While it may be appropriate for thick films, it cannot describe the behavior of films which exhibit plug-like flow. It remains to be seen if the 2/3 exponent has a single explanation or arises from different mechanisms in different limits. The results described in this section have interesting implications for the function of macroscopic bearings. Some bearings may operate in the boundary lubrication regime where the separation between asperities decreases to molecular dimensions. The dramatic increase in viscosity due to confinement may play a key role in preventing squeeze-out of the lubricant and direct contact between asperities. Although the glassy lubricant layer would not have a low frictional force, the yield stress would be lower than that for asperities in contact. More important, the amount of wear would be greatly reduced by the glassy film. Studies of confined films may help to determine what factors control a lubricant’s ability to form
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a robust protective layer at atomic scales. As we now discuss, they may also help explain the pervasive observation of static friction.
20.5.3 Submonolayer Lubrication Physisorbed molecules, such as the short hydrocarbon chains considered above, can be expected to sit on any surface exposed to atmospheric conditions. Even in ultra-high vacuum, special surface treatments are needed to remove strongly physisorbed species from surfaces. Recent work shows that the presence of these physisorbed molecules qualitatively alters the tribological behavior between two incommensurate walls (He et al., 1999; Müser and Robbins, 2000) or between two disordered walls (Müser et al., 2000). As noted in Section 20.4, the static friction is expected to vanish between most incommensurate surfaces. Under similar conditions, the static friction between most amorphous, but flat, surfaces vanishes in the thermodynamic limit (Müser et al., 2000). In both cases, the reason is that the density modulations on two bare surfaces cannot lock into phase with each other unless the surfaces are unrealistically compliant. However, a submonolayer of molecules that form no strong covalent bonds with the walls can simultaneously lock to the density modulations of both walls. This gives rise to a finite static friction for all surface symmetries: commensurate, incommensurate, and amorphous (Müser et al., 2000). A series of simulations were performed in order to elucidate the influence of such “between-sorbed” particles on tribological properties (He et al., 1999; Müser and Robbins, 2000). A layer of spherical or short “bead-spring” (Kremer and Grest, 1990) molecules was confined between two fcc (111) surfaces. The walls had the orientations and lattice spacing shown in Figure 20.5, and results are labeled by the letters in this figure. Wall atoms were bound to their lattice sites with harmonic springs as in the Tomlinson model. The interactions between atoms on opposing walls, as well as fluid–fluid and fluid–wall interactions, had the LJ form. Unless noted, the potential parameters for all three interactions were the same. The static friction per unit contact area, or yield stress τs, was determined from the lateral force needed to initiate steady sliding of the surfaces at fixed pressure. When there were no molecules between the surfaces, there was no static friction unless the surfaces were commensurate. As illustrated in Figure 20.11a, introducing a thin film led to static friction in all cases. Moreover, all incommensurate* cases (B through D) showed nearly the same static friction, and τs was independent of the direction of sliding relative to crystalline axes (e.g., along x or y for case D). Most experiments do not control the crystallographic orientation of the walls relative to each other or to the sliding direction, yet the friction is fairly reproducible. This is hard to understand based on models of bare surfaces which show dramatic variations in friction with orientation (Hirano and Shinjo, 1993; Sørensen et al., 1996; Robbins and Smith, 1996). Figure 20.11 shows that a thin layer of molecules eliminates most of this variation. In addition, the friction is insensitive to chain length, coverage, and other variables that are not well controlled in experiments (He et al., 1999). The kinetic friction at low velocities is typically 15 to 25% lower than the static friction in all cases (He and Robbins). Of course experiments do observe changes in friction with surface material. The main factor that changed τs in this simple model was the ratio of the characteristic length for wall–fluid interactions σwf to the nearest-neighbor spacing on the walls, d. As shown in Figure 20.11b, increasing σwf /d decreases the friction. The reason is that larger fluid atoms are less able to penetrate between wall atoms and thus feel less surface corrugation. Using amorphous, but flat, walls produced a somewhat larger static friction. Note that τs rises linearly with the imposed pressure in all cases shown in Figure 20.11. This provides a microscopic basis for the phenomenological explanation of Amontons’ laws that was proposed by Bowden and Tabor (1986). The total static friction is given by the integral of the yield stress over areas of the surface that are in molecular contact. If τs = τ0 + αP, then the total force is Fs = αL + τ0Areal where – L is the load and Areal is the total contact area. The coefficient of friction is then µs = α + τ0 /P *Although perfectly incommensurate walls are not consistent with periodic boundary conditions the effect of residual commensurability was shown to be negligible (Müser and Robbins, 2000).
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FIGURE 20.11 Yield stress as a function of normal pressure for various systems. In (a) the letters correspond to the labels of wall geometries in Figure 20.5, and system D was slid in both x and y directions. Panel (b) shows the effect of increasing the wall/fluid coupling wf , decreasing or increasing the wall/fluid length σwf , and increasing the nearest-neighbor spacing d on the friction of system B. The unit of pressure and stress, σ –3 corresponds to about 30 to 50 MPa. (From He, G., Müser, M.H., and Robbins, M.O. (1999), Adsorbed layers and the origin of static friction, Science, 284, 1650-1652. With permission. © 1999 American Association for the Advancement of Science.) –
where P ≡ L/Areal is the mean contact pressure. Amontons’ laws say that µs is independent of load and – the apparent area of the surfaces in contact. This condition is satisfied if τ0 is small or if P is constant. The latter condition is expected to hold for both ideal elastic (Greenwood and Williamson, 1966) and plastic (Bowden and Tabor, 1986) surfaces. The above results suggest that adsorbed molecules and other “third-bodies” may prove key to understanding macroscopic friction measurements. It will be interesting to extend these studies to more realistic molecular potentials and to rough surfaces. To date, realistic potentials have only been used between commensurate surfaces, and we now describe some of this work. The effect of small molecules injected between two sliding hydrogen-terminated (111) diamond surfaces on kinetic friction was investigated by Perry and Harrison (1996, 1997). The setup of the simulation was similar to the one described in Section 20.4.2. Two sets of simulations were performed. In one set, bare surfaces were considered. In another set, either two methane (CH4) molecules, one ethane (C2H6) molecule, or one isobutane (CH3)3CH molecule was introduced into the interface between the sliding diamond surfaces. Experiments show that the friction between diamond surfaces goes down as similar molecules are formed in the contact due to wear (Hayward, 1991). Perry and Harrison found that these third bodies also reduced the calculated frictional force between commensurate diamond surfaces. The reduction of the frictional force with respect to the bare hydrogenterminated case was most pronounced for the smallest molecule, methane. The molecular motions were analyzed in detail to determine how dissipation occurred. Methane produced less friction because it was small enough to roll in grooves between the terminal hydrogen atoms without collisions. The larger ethane and isobutane collided frequently. As for the simple bead-spring model described above, the friction increased roughly linearly with load. Indeed, Perry and Harrison’s data for all third bodies correspond to α ≈ 0.1, which is close to that for
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commensurate surfaces in Figure 20.11a. One may expect that the friction would decrease if incommensurate walls were used. However, the rolling motion of methane might be prevented in such geometries. Perry and Harrison (1996, 1997) compared their results to earlier simulations (Harrison et al., 1993) where hydrogen terminations on one of the two surfaces were replaced by chemisorbed methyl (–CH3), ethyl (–C2H5), or n-propyl (–C3H7) groups (Section 20.4.2). The chemisorbed molecules were seen to give a considerably smaller reduction of the friction with respect to the physisorbed molecules. Perry and Harrison note that the chemisorbed molecules have fewer degrees of freedom, and so are less able to avoid collisions that dissipate energy.
20.5.4 Corrugated Surfaces The presence of roughness can be expected to alter the behavior of lubricants, particularly when the mean film thickness is comparable to the surface roughness. Gao et al. (1995, 1996) and Landman et al. (1996) used molecular dynamics to investigate this thin film limit. Hexadecane (n-C16H34) was confined between two gold substrates exposing only (111) surfaces (Figure 20.12). The two outer layers of the substrates were completely rigid and were displaced laterally with a constant relative velocity of 10 to 20m/s at constant separation. The asperities on both walls were modeled by flat-topped pyramidal ridges with initial heights of 4 to 6 atomic layers. The united atom model (Section 20.2.1) was used for the interactions within the film, and the embedded atom method was used for Au–Au interactions. All other interactions were modeled with suitable 6-12 Lennard–Jones potentials. The alkane molecules and the gold atoms in the asperities were treated dynamically using the Verlet algorithm. The temperature was kept constant at T = 350 K by rescaling the velocities every 50th time step. Simulations were done in three different regimes, which can be categorized according to the separation ∆haa that the outer surfaces of the asperities would have if they were placed on top of one another without deforming elastically or plastically. The cases were (1) large separation of the asperities ∆haa = 17.5 Å, (2) a near-overlap regime with ∆haa = 4.6 Å, and (3) an asperity-overlap regime with ∆haa = –6.7 Å. Some selected atomic and molecular configurations obtained in a slice through the near-overlap system are shown in Figure 20.12. In all cases, the initial separation of the walls was chosen such that the normal pressure was zero for large lateral asperity separations. One common feature of all simulations was the formation of lubricant layers between the asperities as they approached each other (Figure 20.12). This is just like the layering observed in equilibrium between flat walls (e.g., Figure 20.9), but the layers form dynamically. The number of layers decreased with decreasing lateral separation between the asperities, and the lateral force showed strong oscillations as successive layers were pushed out. This behavior is shown in Figure 20.13 for the near-overlap case. For large separation, case (1), four lubricant layers remained at the point of closest approach between the asperities, and no plastic deformation occurred. In case (2), severe plastic deformation occurred after local shear and normal stresses exceeded a limiting value of close to 4 GPa. This deformation led to direct intermetallic junctions, which were absent in simulations under identical conditions but with no lubricant molecules in the interface. The junctions eventually broke upon continued sliding, resulting in transfer of some metal atoms between the asperities. In this and the overlap case (3), great densification and pressurization of the lubricant in the asperity region occurred, accompanied by a significant increase in the effective viscosity in that region. For the near-overlap system, local rupture of the film in the region between the departing asperities was seen. A nanoscale cavitated zone of length scale ≈ 30 Å was observed that persisted for about 100 ps. The Deborah number D was studied as well. D can be defined as the ratio of the relaxation time of the fluid to the time of passage of the fluid through a characteristic distance l. D ≈ 0.25 was observed for the near-overlap system, which corresponds to a viscoelastic response of the lubricant. The increased confinement in the overlap system, resulted in D = 2.5, which can be associated with highly viscoelastic behavior, perhaps even elastoplastic or waxy behavior. Gao et al. (1996) observed extreme pressures of 150 GPa in the near-overlap case when the asperities were treated as rigid units. Allowing only the asperities to deform reduced the peak pressure by almost
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FIGURE 20.12 Atomic and molecular configurations obtained in a slice through the near-overlap system at times 156, 250, 308, 351, 400, 461, 614, and 766 ps. Time increases from top to bottom in the left column and then in the right. (From Gao, J., Luedtke, W.D., and Landman, U. (1995), Nano-elastohydrodynamics: structure, dynamics, and flow in non-uniform lubricated junctions, Science, 270, 605608. With permission. © 1995 American Association for the Advancement of Science.)
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FIGURE 20.13 Total force in driving direction fx and normal to the walls fz plotted vs. time. Solid lines correspond to the net force between lubricant and gold surface, dashed lines to direct forces between opposing gold surfaces. The numbers in panel A give the number of layers between the asperity ridges. (From Gao, J., Luedtke, W.D., and Landman, U. (1995), Nano-elastohydrodynamics: structure, dynamics, and flow in non-uniform lubricated junctions, Science, 270, 605-608. With permission. © 1995 American Association for the Advancement of Science.)
two orders of magnitude. However, even these residual pressures are still quite large, and one may expect that a full treatment of the elastic response of the substrates might lead to further dramatic decreases in pressure and damage. Tutein et al. (1999) have recently compared friction between monolayers of anchored hydrocarbon molecules and rigid or flexible nanotubes. Studies of elasticity effects in larger asperities confining films that are several molecules thick are currently in progress (Persson and Ballone, 2000).
20.6 Stick-Slip Dynamics The dynamics of sliding systems can be very complex and depend on many factors, including the types of metastable states in the system, the times needed to transform between states, and the mechanical properties of the device that imposes the stress. At high rates or stresses, systems usually slide smoothly. At low rates the motion often becomes intermittent, with the system alternately sticking and slipping forward (Rabinowicz, 1965; Bowden and Tabor, 1986). Everyday examples of such stick-slip motion include the squeak of hinges and the music of violins. The alternation between stuck and sliding states of the system reflects changes in the way energy is stored. While the system is stuck, elastic energy is pumped into the system by the driving device. When the system slips, this elastic energy is released into kinetic energy, and eventually dissipated as heat. The system then sticks once more, begins to store elastic energy, and the process continues. Both elastic and kinetic energy can be stored in all the mechanical elements that drive the system. The whole coupled assembly must be included in any analysis of the dynamics. The simplest type of intermittent motion is the atomic-scale stick-slip that occurs in the multistable regime (λ > 1) of the Tomlinson model (see Figure 20.2b). Energy is stored in the springs while atoms are trapped in a metastable state, and converted to kinetic energy as they pop to the next metastable state. This phenomenon is quite general and has been observed in several of the simulations of wearless
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FIGURE 20.14 Time profiles of the (a) frictional force per unit area F/A, (b) displacement of the top wall, xW , (c) wall spacing h, and (d) Debye–Waller factor S(Q)/N during stick-slip motion of spherical molecules that form two crystalline layers in the static state. Note that the system dilates (c) during each slip event. The coinciding drop in Debye–Waller factor shows a dramatic decrease from a typical crystalline value to a characteristic value for a fluid. (From Robbins, M.O. and Baljon, A.R.C. (2000), Response of thin oligomer films to steady and transient shear, in Microstructure and Microtribology of Polymer Surfaces, Tsukruk, V.V. and Wahl, K.J. (Eds.), American Chemical Society, Washington, DC, 91. With permission. © 2000 American Chemical Society.)
friction described in Section 20.4 as well as in the motion of atomic force microscope tips (e.g., Carpick and Salmeron, 1997). In these cases, motion involves a simple ratcheting over the surface potential through a regular series of hops between neighboring metastable states. The slip distance is determined entirely by the periodicity of the surface potential. Confined films and adsorbed layers have a much richer potential energy landscape due to their many internal degrees of freedom. One consequence is that stickslip motion between neighboring metastable states can involve microslips by distances much less than a lattice constant (Thompson and Robbins, 1990b; Baljon and Robbins, 1997; Robbins and Baljon, 2000). An example is seen at t/tLJ = 620 in Figure 20.14b. Such microslips involve atomic-scale rearrangements within a small fraction of the system. Closely related microslips have been studied in granular media (Nasuno et al., 1997; Veje et al., 1999) and foams (Gopal and Durian, 1995). Many examples of stick-slip involve a rather different type of motion that can lead to intermittency and chaos (Ruina, 1983; Heslot et al., 1994). Instead of jumping between neighboring metastable states, the system slips for very long distances before sticking. For example, Gee et al. (1990) and Yoshizawa and Israelachvili (1993), observed slip distances of many microns in their studies of confined films. This distance is much larger than any characteristic periodicity in the potential, and varied with velocity, load, and the mass and stiffness of the SFA. The fact that the SFA does not stick after moving by a lattice constant indicates that sliding has changed the state of the system in some manner, so that it can continue sliding even at forces less than the yield stress. Phenomenological theories of stick-slip often introduce an unspecified “state” variable to model the evolving properties of the system (Dieterich, 1979; Ruina, 1983; Batista and Carlson, 1998).
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One simple property that depends on history is the amount of stored kinetic energy. This can provide enough inertia to carry a system over potential energy barriers even when the stress is below the yield stress. Inertia is readily included in the Tomlinson model and has been thoroughly studied in the mathematically equivalent case of an underdamped Josephson junction (McCumber, 1968). One finds a hysteretic response function where static and moving steady-states coexist over a range of force between Fmin and the static friction Fs . There is a minimum stable steady-state velocity vmin corresponding to Fmin. At lower velocities, the only steady state is linearly unstable because ∂v/∂F < 0 — pulling harder slows the system. It is well-established that this type of instability can lead to stick-slip motion (Bowden and Tabor, 1986; Rabinowicz, 1965). If the top wall of the Tomlinson model is pulled at an average velocity less than vmin by a sufficiently compliant system, it will exhibit large-scale stick-slip motion. Confined films have structural degrees of freedom that can change during sliding, and this provides an alternative mechanism for stick-slip motion (Thompson and Robbins, 1990b). Some of these structural changes are illustrated in Figure 20.14, which shows stick-slip motion of a two-layer film of simple spherical molecules. The bounding walls were held together by a constant normal load. A lateral force was applied to the top wall through a spring k attached to a stage that moved with fixed velocity v in the x-direction. The equilibrium configuration of the film at v = 0 is a commensurate crystal that resists shear. Thus at small times, the top wall remains pinned at xW = 0. The force grows linearly with time, F = kv, as the stage advances ahead of the wall. When F exceeds Fs , the wall slips forward. The force drops . rapidly because the slip velocity xW is much greater than v. When the force drops sufficiently, the film recrystallizes, the wall stops, and the force begins to rise once more. One structural change that occurs during each slip event is dilation by about 10% (Figure 20.14c). Dhinojwala and Granick have recently confirmed that dilation occurs during slip in SFA experiments. The increased volume makes it easier for atoms to slide past each other, and is part of the reason that the sliding friction is lower than Fs. The system may be able to keep sliding in this dilated state as long as it takes more time for the volume to contract than for the wall to advance by a lattice constant. Dilation of this type plays a crucial role in the yield, flow, and stick-slip dynamics of granular media (Thompson and Grest, 1991; Jaeger et al., 1996; Nasuno et al., 1997). The degree of crystallinity also changes during sliding. As in Sections 20.3.5 and 20.5.1, deviations from an ideal crystalline structure can be quantified by the Debye–Waller factor S(Q)/N (Figure 20.14d), where Q is one of the shortest reciprocal lattice vectors of the wall and N is the total number of atoms in the film. When the system is stuck, S(Q)/N has a large value that is characteristic of a three-dimensional crystal. During each slip event, S(Q)/N drops dramatically. The minimum values are characteristic of simple fluids that would show a no-slip boundary condition (Section 20.5.1). The atoms also exhibit rapid diffusion that is characteristic of a fluid. The periodic melting and freezing transitions that occur during stick-slip are induced by shear and not by the negligible changes in temperature. Shear-melting transitions at constant temperature have been observed in both theoretical and experimental studies of bulk colloidal systems (Ackerson et al., 1986; Stevens and Robbins, 1993). While the above simulations of confined films used a fixed number of particles, Lupowski and van Swol (1991) found equivalent results at fixed chemical potential. Very similar behavior has been observed in simulations of sand (Thompson and Grest, 1991), chain molecules (Robbins and Baljon, 2000), and incommensurate or amorphous walls (Thompson and Robbins, 1990b). These systems transform between glassy and fluid states during stick-slip motion. As in equilibrium, the structural differences between glass and fluid states are small. However, there are strong changes in the self-diffusion and other dynamic properties when the film goes from the static glassy to sliding fluid state. In the cases just described, the entire film transforms to a new state, and shear occurs throughout the film. Another type of behavior is also observed. In some systems shear is confined to a single plane — either a wall/film interface, or a plane within the film (Baljon and Robbins, 1997; Robbins and Baljon, 2000). There is always some dilation at the shear plane to facilitate sliding. In some cases there is also in-plane ordering of the film to enable it to slide more easily over the wall. This ordering remains after sliding stops and provides a mechanism for the long-term memory seen in some experiments (Gee et al., 1990; Yoshizawa and Israelachvili, 1993; Demirel and Granick, 1996b). Buldum and Ciraci (1997) found
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stick-slip motion due to periodic structural transformations in the bottom layers of a pyramidal Ni(111) tip sliding on an incommensurate Cu(110) surface. The dynamics of the transitions between stuck and sliding states are crucial in determining the range of velocities where stick-slip motion is observed, the shape of the stick-slip events, and whether stickslip disappears in a continuous or discontinuous manner. Current models are limited to energy balance arguments (Robbins and Thompson, 1991; Thompson and Robbins, 1993) or phenomenological models of the nucleation and growth of “frozen” regions (Yoshizawa and Israelachvili, 1993; Heslot et al., 1994; Batista and Carlson, 1998; Persson, 1998). Microscopic models and detailed experimental data on the sticking and unsticking process are still lacking. Rozman et al. (1996, 1997, 1998) have taken an interesting approach to unraveling this problem. They have performed detailed studies of stick-slip in a simple model of a single incommensurate chain between two walls. This model reproduces much of the complex dynamics seen in experiments and helps to elucidate what can be learned about the nature of structural changes within a contact using only the measured macroscopic dynamics.
20.7 Strongly Irreversible Tribological Processes Sliding at high pressures, high rates, or for long times can produce more dramatic changes in the structure and even chemistry of the sliding interface than those discussed so far. In this concluding section, we describe some of the more strongly irreversible tribological processes that have been studied with simulations. These include grain boundary formation and mixing, machining, and tribochemical reactions.
20.7.1 Plastic Deformation For ductile materials, plastic deformation is likely to occur throughout a region of some characteristic width about the nominal sliding interface (Rigney and Hammerberg, 1998). Sliding-induced mixing of material from the two surfaces and sliding-induced grain boundaries are two of the experimentally observed processes that lack microscopic theoretical explanations. In an attempt to get insight into the microscopic dynamics of these phenomena, Hammerberg et al. (1998) performed large-scale simulations of a two-dimensional model for copper. The simulation cell contained 256 × 256 Cu atoms that were subject to a constant normal pressure P⊥. Two reservoir regions at the upper and lower boundaries of the cell were constrained to move at opposite lateral velocities ±up . The initial interface was midway between the two reservoirs. The friction was measured at P⊥ = 30 GPa as a function of the relative sliding velocity v. Different behavior was seen at velocities above and below about 10% of the speed of transverse sound. At low velocities, the interface welded together and the system formed a single work-hardened object. Sliding took place at the artificial boundary with one of the reservoirs. At higher velocities the friction was smaller, and decreased steadily with increasing velocity. In this regime, intense plastic deformation occurred at the interface. Hammerberg et al. (1998) found that the early time-dynamics of the interfacial structure could be reproduced with a Frenkel–Kontorova model. As time increased, the interface was unstable to the formation of a fine-grained polycrystalline microstructure, which coarsened with distance away from the interface as a function of time. Associated with this microstructure was the mixing of material across the interface.
20.7.2 Wear Large scale, two- and three-dimensional molecular dynamics simulations of the indentation and scraping of metal surfaces were carried out by Belak and Stowers (1992). Their simulations show that tribological properties are strongly affected by wear or the generation of debris. A blunted diamond tip was first indented into a copper surface and then pulled over the surface. The tip was treated as a rigid unit. Interactions within the metal were modeled with an embedded atom potential, and Lennard–Jones potentials were used between C and Cu atoms.
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In the two-dimensional simulation, indentation was performed at a constant velocity of about 1 m/s. The contact followed Hertzian behavior up to a load L ≈ 2.7 nN and an indentation of about 3.5 Cu layers. The surface then yielded on one side of the tip, through the creation of a single dislocation edge on one of the easy slip planes. The load needed to continue indenting decreased slightly until an indentation of about five layers. Then the load began to rise again as stress built up on the side that had not yet yielded. After an indentation of about six layers, this side yielded, and further indentation could be achieved without a considerable increase in load. The hardness, defined as the ratio of load to contact length (area), slightly decreased with increasing load once plastic deformation had occurred. After indentation was completed, the diamond tip was slid parallel to the original Cu surface. The work to scrape off material was determined as a function of the tip radius. A power law dependence was found at small tip radii that did not correspond to experimental findings for microscraping. However, at large tip radii, the power law approached the experimental value. Belak and Stowers found that this change in power law was due to a change in the mechanism of plastic deformation from intragranular to intergranular plastic deformation. In the three-dimensional simulations, the substrate contained as many as 36 layers or 72,576 atoms. Hence long-range elastic deformations were included. The surface yielded plastically after an indentation of only 1.5 layers, through the creation of a small dislocation loop. The accompanying release of load was much bigger than in two dimensions. Further indentation to about 6.5 layers produced several of these loading–unloading events. When the tip was pulled out of the substrate, both elastic and plastic recovery was observed. Surprisingly, the plastic deformation in the three-dimensional studies was confined to a region within a few lattice spacings of the tip, while dislocations spread several hundred lattice spacings in the two-dimensional simulations. Belak and Stowers concluded that dislocations were not a very efficient mechanism for accommodating strain at the nanometer length scale in three dimensions. When the tip was slid laterally at v = 100 m/s during indentation, the friction or “cutting” force fluctuated around zero as long as the substrate did not yield (Figure 20.15). This nearly frictionless sliding can be attributed to the fact that the surfaces were incommensurate and the adhesive force was too small to induce locking. Once plastic deformation occurred, the cutting force increased dramatically. Figure 20.15 shows that the lateral and normal forces are comparable, implying a friction coefficient of about one. This large value was expected for cutting by a conical asperity with small adhesive forces (Suh, 1986).
20.7.3 Tribochemistry The extreme thermomechanical conditions in sliding contacts can induce chemical reactions. This interaction of chemistry and friction is known as tribochemistry (Rabinowicz, 1965). Tribochemistry plays important roles in many processes, the best known example being the generation of fire through sliding friction. Other examples include the formation of wear debris and adhesive junctions, which can have a major impact on friction. Harrison and Brenner (1994) were the first to observe tribochemical reactions involving strong covalent bonds in molecular dynamics simulations. A key ingredient of their work is the use of reactive potentials that allow breaking and formation of chemical bonds. Two (111) diamond surfaces terminated with hydrogen atoms were brought into contact as in Section 20.4.2. In some simulations, two hydrogen atoms from the upper surface were removed, and replaced with ethyl (–CH2CH3) groups. The simulations were performed for 30 ps at an average normal pressure of about 33 GPa. The sliding velocity was 100 m/s along either the [110] or [112] crystallographic direction. Sliding did not produce any chemical changes in the hydrogen-terminated surfaces. However, wear and chemical reactions were observed when ethyl groups were present. For sliding along the [112] direction, wear was initiated by the shearing of hydrogen atoms from the tails of the ethyl groups. The resulting free hydrogen atoms reacted at the interface by combining with an existing radical site or abstracting a hydrogen from either a surface or a radical. If no combination with a free hydrogen atom occurred, the reactive radicals left on the tails of the chemisorbed molecules abstracted a hydrogen from
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FIGURE 20.15 Normal (bottom) and lateral (top) force on a three-dimensional, pyramidal diamond tip on a copper surface as a function of time. No plastic flow was reported up to 1000 time steps. The indentation stopped at about five layers after 2000 time steps (From Belak, J. and Stowers, I.F. (1992), The indentation and scraping of a metal surface: a molecular dynamics study, in Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I.L. and Pollock, H.M. (Eds.), Kluwer Academic Publishers, Dordrecht, 511. With permission. © 1992 Kluwer Academic Publishers.)
the opposing surface, or they formed a chemical bond with existing radicals on the opposing surface (Figure 20.16). In the latter case, the two surface bonds sometimes broke simultaneously, leaving molecular wear debris trapped at the interface. It is interesting to note that the wear debris, in the form of an ethylene molecule CH2CH2, did not undergo another chemical reaction for the remainder of the simulation. Similarly, methane CH4, ethane C2H6, and isobutane (CH3)3CH were not seen to undergo chemical reactions when introduced into a similar interface composed of hydrogen-terminated (111) diamond surfaces (Section 20.5.3) at normal loads up to about 0.8 nN/atom (Perry and Harrison, 1996; 1997; Harrison and Perry, 1998). At higher loads, only ethane reacted. In some cases a hydrogen broke off of the ethane. The resulting free H atom then reacted with an H atom from one surface to make an H2 molecule. The remaining C2H5 could then form a carbon–carbon bond with that surface when dragged close enough to the nascent radical site. The C–C bond of the ethane was also reported to break occasionally. However, due to the proximity of the nascent methyl radicals and the absence of additional reactive species, the bond always reformed. Sliding along the (110) direction produced other types of reaction between surfaces with ethyl terminations. In some cases, tails of the ethyl groups became caught between hydrogen atoms on the lower surface. Continued sliding sheared the entire tail from the rest of the ethyl group, leaving a chemisorbed CH 2• group and a free CH 3• species. The latter group could form a bond with an existing radical site, it could shear a hydrogen from a chemisorbed ethyl group, or it could be recombined with the chemisorbed CH 2• .
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FIGURE 20.16 Adhesion of the two diamond surfaces via the formation of a carbon–carbon bond. The C atoms forming the bond originated from an ethyl group chemisorbed on the upper diamond surface. (From Harrison, J.A. and Brenner, D.W. (1994), Simulated tribochemistry: an atomic scale view of the wear of diamond, J. Am. Chem. Soc., 116, 10399-10402. With permission. © 1994 American Chemical Society.)
Acknowledgment Support from the National Science Foundation through Grants No. DMR-9634131 and DMR-0083286 and from the German–Israeli Project Cooperation, “Novel Tribological Strategies from the Nano to Meso Scales,’’ is gratefully acknowledged. We thank Gang He, Marek Cieplak, Miguel Kiwi, Jean-Louis Barrat, Patricia McGuiggan, and especially Judith Harrison for providing comments on the text. We also thank Jean-Louis Barrat for help in improving the density oscillation data in Figure 20.9, and Peter A. Thompson for many useful conversations and for his role in creating Figure 20.14.
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Rajasekaran, E., Zeng, X.C., and Diestler, D.J. (1997), Frictional anisotropy and the role of lattice relaxation in molecular tribology of crystalline interfaces, in Micro/Nanotribology and its Applications, Bhushan, B. (Ed.), Kluwer, The Netherlands, 371. Raphael, E. and DeGennes, P.G. (1989), Dynamics of wetting with non-ideal surfaces — the single defect problem, J. Chem. Phys., 90, 7577-7584. Ribarsky, M.W. and Landman, U. (1992), Structure and dynamics of normal-alkanes confined by solidsurfaces. 1. Stationary crystalline boundaries, J. Chem. Phys., 97, 1937-1949. Rigney, D.A. and Hammerberg, J.E. (1998), Unlubricated sliding behavior of metals, MRS Bull., 23(6), 32-36. Robbins, M.O. (2000), Jamming, friction, and unsteady rheology, in Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales, Liu, A.J. and Nagel, S.R. (Eds.), Taylor and Francis, London. Robbins, M.O. and Baljon, A.R.C. (2000), Response of thin oligomer films to steady and transient shear, in Microstructure and Microtribology of Polymer Surfaces, Tsukruk, V.V. and Wahl, K.J. (Eds.), American Chemical Society, Washington, DC, 91. Robbins, M.O. and Krim, J. (1998), Energy dissipation in interfacial friction, MRS Bull., 23(6), 23-26. Robbins, M.O. and Mountain, R.D., unpublished. Robbins, M.O. and Smith, E.D. (1996), Connecting molecular-scale and macroscopic tribology, Langmuir, 12, 4543-4547. Robbins, M.O. and Thompson, P.A. (1991), Critical velocity of stick-slip motion, Science, 253, 916. Rozman, M.G., Urbakh, M., and Klafter, J. (1996), Stick-slip motion and force fluctuations in a driven two-wave potential, Phys. Rev. Lett., 77, 683-686. Rozman, M.G., Urbakh, M., and Klafter, J. (1997), Stick-slip dynamics as a probe of frictional forces, Europhys. Lett., 39, 183-188. Rozman, M.G., Urbakh, M., Klafter, J., and Elmer, F.-J. (1998), Atomic scale friction and different phases of motion of embedded molecular systems, J. Phys. Chem. B, 102, 7924-7930. Ruina, A. (1983), Slip instability and state variable friction laws, J. Geophys. Res., 88, 10359-10370. Ryckaert, J.P. and Bellemans, A. (1978), Molecular dynamics of liquid alkanes, Discuss. Faraday Soc., 66, 95-106. Sarman, S.S., Evans, D.J., and Cummings, P.T. (1998), Recent developments in non-Newtonian molecular dynamics, Phys. Rep., 305, 1-92. Schaich, W.L. and Harris, J. (1981), Dynamic corrections to van der Waals potentials, J. Phys. F: Met Phys., 11, 65-78. Schneider, T. and Stoll, E. (1978), Molecular dynamics study of a three-dimensional one-component model for distortive phase transitions, Phys. Rev. B, 17, 1302-1322. Schoen, M., Cushman, J.H., Diestler, D.J., and Rhykerd, C.L. (1988), Fluids in micropores II: self-diffusion in a simple classical fluid in a slit-pore, J. Chem. Phys., 88, 1394-1406. Schoen, M., Rhykerd, C.L., Diestler, D.J., and Cushman, J.H. (1987), Fluids in micropores. I. Structure of a simple classical fluid in a slit-pore, J. Chem. Phys., 87, 5464-5476. Schoen, M., Rhykerd, C.L., Diestler, D.J., and Cushman, J.H. (1989), Shear forces in molecularly thin films, Science, 245, 1223-1225. Shinjo, K. and Hirano, M. (1993), Dynamics of friction: superlubric state, Surf. Sci., 283, 473-478. Smith, E.D., Cieplak, M., and Robbins, M.O. (1996), The friction on adsorbed monolayers, Phys. Rev. B, 54, 8252-8260. Sneddon, L., Cross, M.C., and Fisher, D.S. (1982), Sliding conductivity of charge-density waves, Phys. Rev. Lett., 49, 292-295. Snook, I.K. and van Megen, W. (1980), Solvation in simple dense fluids. I, J. Chem. Phys., 72, 2907-2914. Sokoloff, J.B. (1990), Theory of energy dissipation in sliding crystal surfaces, Phys. Rev. B, 42, 760-765. Sørensen, M.R., Jacobsen, K.W., and Stoltze, P. (1996), Simulations of atomic-scale sliding friction, Phys. Rev. B, 53, 2101-2113. Steele, W.A. (1973), The physical interaction of gases with crystalline solids. I. Gas-solid energies and properties of isolated absorbed atoms, Surf. Sci., 36, 317-352.
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Stevens, M.J., Mondello, M., Grest, G.S., Cui, S.T., Cochran, H.D., and Cummings, P.T. (1997), Comparison of shear flow of hexadecane in a confined geometry and in bulk, J. Chem. Phys., 106, 7303-7314. Stevens, M.J. and Robbins, M.O. (1993), Simulations of shear-induced melting and ordering, Phys. Rev. E, 48, 3778-3792. Stevens, M.J., Robbins, M.O., and Belak, J.F. (1991), Shear-melting of colloids: a non-equilibrium phase diagram, Phys. Rev. Lett., 66, 3004-3007. Suh, N.P. (1986), Tribophysics, Prentice-Hall, Englewood Cliffs. Taub, H., Torzo, G., Lauter, H.J., and S.C. Fain, J. (1991), Phase Transitions in Surface Films 2, Plenum Press, New York. Thompson, P.A. and Grest, G.S. (1991), Granular flow: friction and the dilatancy transition, Phys. Rev. Lett., 67, 1751-1754. Thompson, P.A., Grest, G.S., and Robbins, M.O. (1992), Phase transitions and universal dynamics in confined films, Phys. Rev. Lett., 68, 3448-3451. Thompson, P.A. and Robbins, M.O. (1989), Simulations of contact-line motion: slip and the dynamic contact angle, Phys. Rev. Lett., 63, 766-769. Thompson, P.A. and Robbins, M.O. (1990a), Shear flow near solids: epitaxial order and flow boundary conditions, Phys. Rev. A, 41, 6830-6837. Thompson, P.A. and Robbins, M.O. (1990b), Origin of stick-slip motion in boundary lubrication, Science, 250, 792-794. Thompson, P.A., Robbins, M.O., and Grest, G.S. (1993), Simulations of lubricant behavior at the interface with bearing solids, in Thin Films in Tribology, Dowson, D., Taylor, C.M., Childs, T.H.C., Godet, M., and Dalmaz, G. (Eds.), Elsevier, Amsterdam, 347. Thompson, P.A., Robbins, M.O., and Grest, G.S. (1995), Structure and shear response in nanometerthick films, Israel J. of Chem., 35, 93-106. Thompson, P.A. and Troian, S.M. (1997), A general boundary condition for liquid flow at solid surfaces, Nature, 389, 360-363. Tomagnini, O., Ercolessi, F., and Tosatti, E. (1993), Microscopic interaction between a gold tip and a Pb(110) surface, Surf. Sci., 287/288, 1041-1045. Tomassone, M.S., Sokoloff, J.B., Widom, A., and Krim, J. (1997). Dominance of phonon friction for a xenon film on a silver (111) surface, Phys. Rev. Lett., 79, 4798-4801. Tomlinson, G.A. (1929), A molecular theory of friction, Phil. Mag. Series, 7, 905-939. Toxvaerd, S. (1981), The structure and thermodynamics of a solid-fluid interface, J. Chem. Phys., 74, 1998-2008. Tschöp, W., Kremer, K., Batoulis, J., Bürger, T., and Hahn, O. (1998a), Simulation of polymer melts. I. Coarse graining procedure for polycarbonates, Acta Polym., 49, 61-74. Tschöp, W., Kremer, K., Batoulis, J., Bürger, T., and Hahn, O. (1998b), Simulation of polymer melts. II. From coarse grained models back to atomistic description, Acta Polym., 49, 75-79. Tutein, A.B., Stuart, S.J., and Harrison, J.A. (1999), Indentation analysis of linear-chain hydrocarbon monolayers anchored to diamond, J. Phys. Chem. B, 103, 11357-11365. Urbakh, M., Daikhin, L., and Klafter, J. (1995), Dynamics of confined liquids under shear, Phys. Rev. E, 51, 2137-2141. Veje, C.T., Howell, D.W., and Behringer, R.P. (1999), Kinematics of a two-dimensional granular Couette experiment at the transition to shearing, Phys. Rev. E, 59, 739-745. Volmer, A. and Natterman, T. (1997), Towards a statistical theory of solid dry friction, Z. Phys. B, 104, 363-371. Weiss, M. and Elmer, F.-J. (1996), Dry friction in the Frenkel–Kontorova–Tomlinson model: static properties, Phys. Rev. B, 53, 7539-7549. Xia, T.K., Ouyang, J., Ribarsky, M.W., and Landman, U. (1992), Interfacial alkane films, Phys. Rev. Lett., 69, 1967-1970. Yoshizawa, H. and Israelachvili, J.N. (1993), Fundamental mechanisms of interfacial friction. 1. Stickslip friction of spherical and chain molecules, J. Phys. Chem., 97, 11300-11313.
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III Solid Tribological Materials Bharat Bhushan The Ohio State University
Ali Erdemir Argonne National Laboratory
Kenneth Holmberg VTT Manufacturing Technology 21 Metals and Ceramics Koji Kato and Koshi Adachi ......................................................... 771 Introduction • Pure Metals • Soft Metals and Soft Bearing Alloys • Copper-based Alloys • Cast Irons • Steels • Ceramics • Special Alloys • Comparisons Between Metals and Ceramics • Concluding Remarks
22 Solid Lubricants and Self-Lubricating Films
Ali Erdemir ............................................ 787
Introduction • Classification of Solid Lubricants • Lubrication Mechanisms of Layered Solids • High-Temperature Solid Lubricants • Self-Lubricating Composites • Soft Metals • Polymers • Summary and Future Directions
23 Tribological Properties of Metallic and Ceramic Coatings Kenneth Holmberg and Allan Matthews .............................................................................................................. 827 Introduction • Tribology of Coated Surfaces • Macromechanical Interactions: Hardness and Geometry • Micromechanical Interactions: Material Response • Material Removal and Change Interactions: Debris and Surface Layers • Multicomponent Coatings • Concluding Remarks
24 Tribology of Diamond, Diamond-Like Carbon, and Related Films Ali Erdemir and Christophe Donnet ......................................................................................................... 871 Introduction • Diamond Films • Diamond-like Carbon (DLC) Films • Other Related Films • Summary and Future Direction
25 Self-assembled Monolayers for Controlling Hydrophobicity and/or Friction and Wear Bharat Bhushan ................................................................................................ 909 Introduction • A Primer to Organic Chemistry • Self-assembled Monolayers: Substrates, Organic Molecules, and End Groups in the Organic Chains • Tribological Properties • Conclusions
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26 Mechanical and Tribological Requirements and Evaluation of Coating Composites Sture Hogmark, Staffan Jacobson, Mats Larsson, and Urban Wiklund ..... 931 Introduction • Design of Tribological Coatings • Design of Coated Components • Evaluation of Coating Composites • Visions and Conclusions
D
uring the industrial revolution, more importantly in the past 50 years, solid tribological materials and coatings have continued to play important roles in many engineering areas, mainly because mechanical systems rely on them for high performance, durability, and efficiency. In particular, the development of advanced coatings with low friction and high wear resistance has become a leading research activity in tribology and is now called “surface engineering.” The increasingly multifunctional needs and more stringent operating conditions envisioned for future mechanical systems will certainly make solid tribological materials and advanced coatings far more important in the near future. To meet the increasing tribological needs of these advanced systems, researchers are constantly exploring new materials and developing novel coatings. As a result, great strides have been made in recent years in the fabrication and diverse utilization of new tribomaterials and coatings that are capable of satisfying the multifunctional needs of more advanced mechanical systems. Major developments in solid tribological materials include coatings with superlow friction and extreme hardness, providing very long wear life to sliding or rolling contact surfaces. Some of these novel coatings are now available for key industrial applications with high thermal/mechanical loadings and harsh tribological environments. Overall, the state-of-the-art in advanced material and coating technologies has now reached the point at which a tribocomponent can be fabricated from bulk ceramics or coated with a hard ceramic film to provide improved tribological performance and durability. Progress in solid lubricants and self-lubricating films (such as transition-metal dichalcogenides, diamond, diamond-like carbon, and composites) has led to significant improvements in the wear lives of bearings, gears, seals, and cutting tools that typically operate under severe tribological conditions. With recent advances in fabrication methods, the cost of these new tribomaterials and coatings has become very affordable. This section focuses on the latest developments in solid tribological materials and coatings. Readers will find a wealth of information, ranging from mechanistic modeling and understanding of the friction and wear behavior of various materials and coatings to how, where, and when these materials and coatings can be used to solve a challenging tribological problem. Chapters in this section cover all aspects of the metals, alloys, ceramics, composites, solid lubricants, and novel materials and coatings developed, tested, and used for tribological purposes. Each chapter has been written by leading experts in the field. Tribological studies on traditional metals and alloys have continued at a steady pace during the last decade. The major research emphasis has been on further understanding the friction and wear mechanisms of these materials. During the same period, interest in ceramics and composites has increased tremendously, and these materials have become the major focus of tribological research, mainly because ceramics and composites offer perhaps the best prospect for realization of some new and advanced tribosystems (e.g., heat engines, high-speed bearings, high-temperature seals, and cutting tools). Obviously, ceramics and composites combine a wide range of attractive mechanical, thermal, and chemical properties that are not available in most metals and alloys. In-depth studies on ceramics have led to a better understanding of their friction and wear mechanisms, and this understanding has been used to design and develop a new generation of tribocomponents whose performance and durability far exceed that of traditional metal- and alloy-based tribocomponents. Koji Kato and Koshi Adachi provide an overview of the recent developments in the tribology of traditional metals and alloys, emphasizing the importance of advanced ceramic materials for demanding tribological applications (Chapter 21). Solid lubricants and self-lubricating films have been around for a long time and are used largely to combat friction and wear under severe tribological conditions in which liquid or grease lubricants cannot function. In recent years, great strides have been made in the processing, fabrication, and diverse utilization of solid lubricants. Chapter 22 by Ali Erdemir is devoted to solid lubricants and self-lubricating films. Recent progress in understanding the lubricating mechanisms of both traditional and new solid
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lubricants is presented. The state-of-the-art in advanced solid lubrication methods and application practices is discussed, with particular emphasis on synthesis and applications of solid lubricant films on tribological surfaces through advanced surface-engineering processes. Recent advances in surface engineering have led to the development of novel metallic and ceramic coatings that can meet the increasingly multifunctional needs of advanced mechanical systems. These advances were the result of dedicated research directed toward the modeling and mechanistic understanding of the tribological properties of these coatings. A chapter by Kenneth Holmberg and Allan Matthews is devoted to the recent progress made in tribological coatings and in understanding the friction and wear mechanisms of these coatings (Chapter 23). Special emphasis was placed on multilayered, compound, or gradient coatings used under both the dry and lubricated conditions. Diamond, diamond-like carbon, and other related coatings (such as carbon nitride and cubic boron nitride) are some of the hardest tribomaterials known and offer perhaps some of the lowest friction and wear coefficients under dry sliding conditions. A widespread application of diamond-like carbon coating is magnetic rigid disks and metal evaporated tapes used in magnetic storage devices. Chapter 24 by Ali Erdemir and Christophe Donnet provides an in-depth review of the recent progress made in the synthesis, tribology, and industrial uses of these coatings. Emphasis is on the state-of-the-art in understanding their friction and wear mechanisms, as well as on the uses of these coatings for diverse tribological applications. Referring to the structural and fundamental tribological knowledge gained during past decades, the authors stress the importance of surface physical and chemical effects on the friction and wear properties of these materials. Tribological issues associated with metal cutting and contact sliding are also addressed in detail. Self-assembled monolayers are organized, dense molecular-scale layers of long-chain organic molecules that are being developed for lubrication purposes. These films are synthesized such that the functional groups of the organic molecules chemisorb onto a solid surface, which results in the spontaneous formation of robust, highly ordered and oriented, dense monolayers chemically attached to the surface. The films with nonpolar end groups on the free end result in films with hydrophobic properties. These films have been successfully tried in the laboratory for microdevice applications. A chapter by Bharat Bhushan provides an in-depth review of the state-of-the-art of the science and technology of selfassembled monolayers (Chapter 25). Recent developments in deposition technologies have provided the flexibility needed for design and development of multifunctional coatings that afford low friction and long wear life under demanding tribological conditions. These exotic coatings with nanocomposite structures or multilayer architectures are quite tough and are resistant to cracking during sliding contact. They also work extremely well in aggressive environments. Chapter 26 by Sture Hogmark, Staffan Jacobson, Mats Larsson, and Urban Wiklund focuses on tribological needs and design considerations for such multifunctional films. Important tribological issues addressed in this chapter include premature coating delamination, coating deformation, brittle fracture and spalling, abrasive scratching, material pickup or transfer, and coating wear due to abrasive, erosive, and tribochemical interactions. New techniques used in the mechanical, structural, and tribological characterization of multifunctional coatings are also discussed. Several examples are provided to highlight the effectiveness of these coatings in metal-cutting and -forming operations and other tribological fields. The use of thin surface coatings (such as diamond, diamond-like carbon, molybdenum disulfide, nitrides, carbides, and their composites and dopants) has substantially improved the tribological performance of rolling, rotating, or sliding mechanical parts and components in recent years. Specifically, friction and wear of sliding contact interfaces has decreased by orders of magnitude. Compared to any material combinations used in the past, some of these new coatings were able to reduce friction coefficients to as low as 0.001, and wear rates to levels that in some cases are almost impossible to measure. A key reason for these remarkable developments is that researchers are now better equipped and have a deeper understanding of the fundamental mechanisms that control friction and wear. A second factor is that the thin coatings are now applied on solid surfaces that are in perfect compliance with the chemical,
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mechanical, and thermal properties of the coating materials themselves, thus ensuring that premature failures due to thermal, mechanical, or chemical incompatibility are nonexistent. In short, while recent advances in new tribomaterials and coatings have been phenomenal, there remain several key challenges for future tribologists and surface engineers. In this field, there are almost unlimited numbers of material combinations, surface parameters, and application conditions that one can manipulate or use to his/her advantage in a tribological application to achieve better performance and longer durability. Pioneers and dedicated researchers in the tribology field have already made great strides in this respect, despite the very intricate and multifaceted nature of the field. Today, as we embrace a new millennium with great hopes and expectations, we should look forward to opening up new possibilities for a highly industrialized and modern society. To move forward in this direction, we must develop new surface-engineered materials and coatings, together with novel design concepts in tribology. Specifically, we need to devise new ways to build composite structures or systems that are based on multilayers or nanocomposites. We should also tailor or model the surface tribological properties of these structures and coating materials to achieve even higher performance and durability in future tribosystems. The tools (analytical, computational, and intellectual) for the successful execution of this task are now available. The greatest challenge for the future seems to be the formulation of new ideas and concepts and the integration of the vast knowledge base accumulated over the years in advanced tribological research and development. From the very beginning, mankind has been in search of new tribomaterials to achieve better and faster mobility. There should be no doubt that this trend will continue at a much accelerated pace in the new millennium, intensifying the need for new solid tribological materials and coatings.
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21 Metals and Ceramics
Koji Kato Tohoku University
Koshi Adachi Tohoku University
21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 21.10
Introduction ..................................................................... 771 Pure Metals ....................................................................... 771 Soft Metals and Soft Bearing Alloys ............................... 772 Copper-based Alloys ........................................................ 774 Cast Irons.......................................................................... 774 Steels.................................................................................. 776 Ceramics ........................................................................... 778 Special Alloys.................................................................... 781 Comparisons Between Metals and Ceramics................. 782 Concluding Remarks ....................................................... 783
21.1 Introduction Friction and wear can be kept low if the contact interface is well-lubricated. Even when the contact interface is not supplied with lubricants, friction and wear are changed by adsorbed gasses (Bowden et al., 1954) or by frictional repetition. This means that tribological properties are responses of a tribosystem that is lubricated on purpose or is under the effects of surroundings. Therefore, material properties of only one of two contacting bodies cannot be independently related to the tribological properties in a direct way. At the frictional contact surfaces, there exist frictional heating, high flash temperature, severe plastic shear deformation under contact pressure, and the agglomeration of wear particles to form the tribolayer (Rigney et al., 1977). These produce new surface properties that are different from the bulk material properties. Friction and wear take place at the contact interface between such unsteady surfaces. Nevertheless, metal and ceramic materials can be classified into groups for different applicational purposes, and the tribological usefulness of each group in practice can be qualitatively explained, to a certain extent, by the bulk material properties. These explanations are described in the following sections, which can be guides in the first step of material selection for tribo-elements.
21.2 Pure Metals Pure metals are generally soft and ductile. Therefore, the contact junctions of asperities between them show large amounts of junction growth in sliding if the contact interface is not lubricated. Table 21.1 shows the friction coefficients µ observed with eight pure metals sliding on themselves in different atmospheres (Bowden et al., 1954). In air, oxygen, or water vapor, the friction coefficients of these eight frictional pairs vary from 0.8 to 3.0. Gold, nickel, platinum, and silver show relatively large values, which means that the adhesion is relatively strong at the contact interfaces of these metals and contact junctions grow sufficiently to generate such large values. In hydrogen or nitrogen, copper, gold,
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TABLE 21.1 Friction of Metals (Spectroscopically Pure) Outgassed in Vacuum (When clean, there is gross seizure.) Coefficient of Friction after Admitting Metals Aluminum on aluminum Copper on copper Gold on gold Iron on iron Molybdenum on molybdenum Nickel on nickel Platinum on platinum Silver on silver
H2 or N2
Air or O2
Water Vapor
— 4 4 — — 5 — —
1.9 1.6 2.8 1.2 0.8 3 3 1.5
1.1 1.6 2.5 1.2 0.8 1.6 3 1.5
Data from Bowden, F.P. and Tabor, D. (1954), Friction and Lubrication of Solids, I, Clarendon Press, Oxford.
FIGURE 21.1 Effect of hardness on the relative wear resistance of pure metals. (From Khruschov, M.M. (1957), Resistance of metals to wear by abrasion as related to hardness, Proc. Conf. Lubrication and Wear, Inst. Mech. Engr., 655-659. With permission.)
and nickel show large µ values (between 4 and 5), which means adhesion is stronger in the inert gases than in air. The high friction of pure metals shown in Table 21.1 is applied in friction bonding of noble metals such as gold. Abrasive wear resistance of such pure metals linearly increases with hardness as shown in Figure 21.1 (Khruschov, 1957). On the other hand, adhesive wear does not show a clear relationship with hardness.
21.3 Soft Metals and Soft Bearing Alloys When hard metals such as steels slide on themselves without lubricants, high friction, gross seizure, and severe wear take place in air or vacuum. A soft-metal thin film at the sliding interface between hard materials can reduce friction to the level of µ = 0.1 to 0.2. Gold, silver, lead, and indium are representative soft metals whose hardness values vary from about 0.3 GPa to about 0.5 GPa. In practical cases of soft metal-lubricated tribosystems, sliding velocities are relatively small and soft metals are not expected to work in the molten state.
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FIGURE 21.2 Thin film lubrication of soft pure metals in sliding of an Si3N4 pin on SUS440C stainless steel disk in high vacuum. (From Kato, K., Kim, H., Adachi, K., and Furuyama, H. (1996), Basic study of lubrication by tribocoating for space machines, Trans. Japan Soc. Mech. Eng., 62(600), 3237-3243. With permission.)
Figure 21.2 shows the lubricating properties of Ag, Au, Bi, In, Pb, Sb, and Sn observed with the friction pair of an Si3N4 pin against an SUS440C stainless steel disk in a vacuum of 10–6 Pa (Kato et al., 1996). It is recognized that the soft-film thickness has its optimum value for the minimum friction coefficient (Bowden et al., 1954), but such optimum film thickness can be held during running only when the soft metal is supplied continuously to repair the worn parts of the film (Kato et al., 1990). When a soft-metal film of a certain thickness is precoated on a hard material substrate, the life of the tribocomponent is determined by the wear life of the film. Soft-metal film lubrication is, therefore, convenient for relatively small and replaceable tribocomponents such as ball bearings. When a bearing system is expected to run in a state of hydrodynamic lubrication with oil, an unexpected solid contact is generated by the introduction of hard abrasive particles, misalignment, high load, or slow speed at the sliding contact interface. Soft alloys such as lead- or tin-based babbitts and aluminum-based alloys work well as bearing materials in such contact conditions. Lead-based babbitts contain a high percentage (>80 wt%) of lead with 1 to 10 wt% tin and 10 to 15 wt% antimony, and have a hardness value of about 0.2 GPa. An Sb-Sn phase is distributed as fine cubes throughout the structure. This material has the weakness of low fatigue strength because of segregation of the Sb-Sn phase during solidification. Tin-based babbitts contain a high percentage (>85 wt%) of tin with 5 to 8 wt% antimony and 4 to 8 wt% copper, and have hardness values of about 0.2 GPa. They have the phase of Sb-Sn or Cu6Sn5, and the presence of either or both of these intermetallic phases increases fatigue strength below 130°C (Glaesure, 1992). These babbitts are soft enough to embed dirt or hard particles, but also provide good conforming under misalignment or high load. Even when the supply of oil is interrupted, babbitts flow or melt to protect the shaft from damage. The dry friction coefficient against steel remains at ~0.55 to 0.80 (Bowden et al., 1954). They are used below the contact pressure of 30 to 40 MPa and their fatigue strength is ~20 to 30 MPa. Aluminum-based alloys are used for bearings that require large fatigue strength and higher operating temperature than babbitt bearings. Aluminum-tin alloys show a fatigue strength three times larger than tin- or lead-based babbitts (Pratt, 1969) and provide better compatibility with steels. Aluminum-20 wt% lead alloy is less expensive and has fatigue strength almost equal to that of aluminum-20 wt% tin alloy and better wear resistance (Bierlein et al., 1969). Although these aluminum-based alloys exhibit better fatigue strength, corrosion resistance, wear resistance, and compatibility with steel than babbitts, their embeddability and seizure resistance are not as good as that of babbitts and a thin overlay of lead-tin becomes necessary. By considering all the tribological properties of babbitts and aluminum-based alloys, as well as the material costs, soft alloys are used for the oil-lubricated bearings. Because these alloys have relatively
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TABLE 21.2
Copper-based Alloys and Hardness Values
Alloy
Cu
Pb
Sn
P
Al
Be
Hardness BHN, GPa
Copper-lead alloy Lead bronze Tin bronze Phosphor bronze Aluminum bronze Beryllium copper
>60 >80 >80 >85 >78 99.5
25–35 1–10 — — — —
50 µm) composites Thin-film (0.25 µm) lubricant film. This is the area of hydrodynamic lubrication where friction is determined by the rheology of the lubricant. For nonconformal, concentrated contacts where loads are high enough to cause elastic deformation of the surfaces and pressure-viscosity effects on the lubricant, another regime — elastohydrodynamic lubrication (EHL) — occurs. Film thickness in this regime ranges from 0.025 to 1.250 µm. As this parameter decreases, film thickness decreases and surface interactions start taking place. This regime, in which both surface interactions and fluid film effects occur, is referred to as the mixed regime. Finally, at low values of ZN/P, the boundary lubrication regime is entered. The boundary lubrication regime is a highly complex arena involving metallurgy, surface topography, physical and chemical adsorption, corrosion, catalysis, and reaction kinetics (Godfrey, 1980; Jones, 1982). The most important aspect of this regime is the formation of protective surface films to minimize wear and surface damage. For space mechanisms, AISI 440C stainless steel is the most common bearing material. The formation of lubricating films is governed by the chemistry of both the film former as well as the bearing surface and other environmental factors. The effectiveness of these films in minimizing wear is
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determined by their physical properties. These include shear strength, thickness, surface adhesion, film cohesion, melting point or decomposition temperature, and solubility in the bulk lubricant. Typically, the EHL, mixed, and boundary lubrication regimes occur in lubricated space mechanisms, with the boundary lubrication regime being the most stringent. However, a subdivision of EHL — starvation theory — was described a number of years ago (Wedeven et al., 1971). It describes the situation occurring in ball bearings having a restricted oil supply, in which pressure buildup in the inlet region of the contact is inhibited, resulting in a film thickness thinner than calculated by classical EHL theory (Dowson and Higginson, 1959; Hamrock and Dowson, 1981). However, starvation theory fails to adequately describe instrument bearing behavior because there is no oil meniscus. Another subdivision of EHL — parched elastohydrodynamics — describes a behavior where there is no free bulk oil in the system (Kingsbury, 1985; Schritz et al., 1994). The lubricant films in this regime are so thin that they are immobile outside the Hertzian contact zone. This regime is of particular importance to space mechanisms because parched bearings require the least driving torque and have the most precisely defined spin axis. Finally, another area of EHL that is of importance to space mechanisms involves transient or nonsteady-state behavior. Unlike steady-state EHL behavior, non-steady-state behavior is not well-understood. However, many practical machine elements (e.g., rolling element bearings, gears, cams, and traction drives) operate under non-steady-state conditions. This is where load, speed, and contact geometry are not constant over time. In particular, stepper motors, which are commonly used in many space mechanisms, operate in this regime. This regime has been studied theoretically for line contacts (Wu and Yan, 1986; Ai and Yu, 1988; Hooke, 1994) and experimentally for point contacts (Sugimura et al., 1998).
31.3 Mechanism Components Spacecraft contain a variety of instruments and mechanisms that require lubrication. Devices include solar array drives; momentum, reaction, and filter wheels; tracking antennas; scanning devices; and sensors. Each of these devices has unique hardware, and therefore lubrication requirements. Gyroscopes, which are used to measure changes in orientation, operate at high speeds, typically between 8000 and 20,000 rpm, with high accuracy. This makes the bearings the most important element of a gyroscope. Fluctuations in the bearing reaction torque, noise, and excess heat generation can cause a loss of null position in the gyroscope. The ideal lubricant for a gyroscope provides a high level of wear protection, produces minimal friction, and has a low evaporation rate (Kalogeras et al., 1993). Also, a fixed, small (3 mg) amount of lubricant is used and must provide lubrication throughout the life of the gyroscope. Gyroscope gimbal supports are low-speed applications and the bearings operate in the boundary regime only. Momentum wheels, which typically operate between 3000 and 10,000 rpm, pose their own lubricant selection criteria. Currently, the majority of problems experienced by momentum wheels are related to the lubricant. Inadequate lubrication, loss of lubricant, and/or lubricant degradation are the reasons for the majority of wheel failures (Kalogeras et al., 1993). As higher speed wheels are designed, lubricants will be subjected to higher operating temperatures, which can increase creep or degradation rates. Current design practices to ease lubricant problems include use of improved synthetic lubricants, labyrinth seals and barrier coatings, lubricant-impregnated retainers, and a lubricant resupply system. Reaction wheels have similar design concepts as momentum wheels, but operate at lower speeds. The support bearings spend more time in the mixed lubrication regime. Therefore, lubricants chosen for reaction wheel use must also have good boundary lubrication characteristics. Control momentum gyroscopes (CMGs) combine the aspects of the gyroscope and the momentum wheel to provide attitude control of a spacecraft. Therefore, considerations of both groups must be weighed when selecting a lubricant for use in a CMG (Kalogeras et al., 1993). Devices that utilize scanning or rotating sensors represent another space mechanism that requires lubrication. An example would be a scanning horizon sensor. This device detects the Earth’s horizon,
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which allows spacecraft to orient themselves. Moderate operational speeds (400 to 1600 rpm) and low loads in the bearings make lubricant selection easy. On the other hand, sensors that use oscillatory motion place a high demand on the lubricant. Typically, the angle of oscillation is slight and the bearing operates in the boundary lubrication regime only. With the small oscillatory angle, no new lubricant is brought in the contact zones (Postma, 1999). Slip rings are another example of a common mechanism used in space applications that requires lubricants. Low-speed operation and electrical conductivity are two important factors that affect lubricant selection. Excessive electrical noise is the most common failure mechanism in slip rings (Kalogeras et al., 1993). This is usually due to surface contamination, which can be reduced by proper lubricant selection. Many other mechanisms that require lubrication are used in space applications. Some examples include solar array drives (SADs), which rotate a spacecraft’s solar arrays; ball, roller, and acme screws; and many types of gears and transmission assemblies (Sarafin and Larson, 1995).
31.4 Liquid Lubricants and Solid Lubricants Both liquid and solid lubricants are used for space applications. The choice is often left to the designer. However, each class has merits and deficiencies. The relative merits have been tabulated by Roberts and Todd (1990) and appear in Table 31.1.
31.4.1 Liquid Lubricants Many different chemical classes of liquid lubricants have been used for space applications in the last 3 decades. These include mineral oils, silicones, polyphenyl ethers, esters, and perfluoropolyethers. Recently, a synthetic hydrocarbon (Pennzane™) has replaced many of the older lubricant classes. Each of these types is discussed briefly herein. However, because the great majority of current spacecraft use either a formulated Pennzane or one of the PFPE materials, these two classes are discussed in much greater detail. 34.4.1.1 Mineral Oils This class of lubricants consists of a complex mixture of naturally occurring hydrocarbons with a fairly wide range of molecular weights. Examples include V-78, BP 110, Apiezon C, Andok C (Coray 100) (Bertrand, 1991), and the SRG series of super-refined mineral oils, which includes KG-80 (Dromgold and Klaus, 1968). These latter fluids have been highly refined, either by hydrogenation or percolation through bauxite to remove polar impurities. This makes them poorer neat lubricants, but greatly improves their response to additives. Apiezon C is still available commercially, but production of all others was discontinued many years ago. Nevertheless, the SRG oils have been stockpiled by some companies and are still used to lubricate bearings for momentum and reaction wheels. Their estimated shelf life is in excess of 20 years (Dromgold and Klaus, 1968). TABLE 31.1
Relative Merits of Solid and Liquid Space Lubricants
Dry Lubricants Negligible vapor pressure Wide operating temperature Negligible surface migration Valid accelerated testing Short life in moist air Debris causes frictional noise Friction speed independent Life determined by lubricant wear Poor thermal characteristics Electrically conductive
Wet Lubricants Finite vapor pressure Viscosity, creep, and vapor pressure all temperature dependent Sealing required Invalid accelerated testing Insensitive to air or vacuum Low frictional noise Friction speed dependent Life determined by lubricant degradation High thermal conductance Electrically insulating
From Roberts, E.W. and Todd, M.J. (1990), Wear, 136, 157-167. With permission.
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FIGURE 31.2 Screening test results (scanner and mechanism). (From Kalogeras, C., Hilton, M., Carré, D., Didziulis, S., and Fleischauer, P. (1993), The use of screening tests in spacecraft lubricant evaluation, Aerospace Corp. Report No. TR-93(3935)-6.)
31.4.1.2 Esters British Petroleum developed a triester-based lubricant in the 1970s designated BP 135. This material was laboratory tested but production was stopped and it never “flew.” Another ester used in the past is designated as NPT-4 (neopentylpolyol ester), but is no longer marketed. Nye Lubricants markets another series of low-volatility neopentylpolyol esters (UC4, UC7, and UC9). Esters are inherently good boundary lubricants and are available in a wide viscosity range. 31.4.1.3 Silicones This fluid class was used early in the space program. They are poor boundary lubricants for steel on steel systems. Versilube F-50, a chloroarylalkylsiloxane, was an early example. Comparisons of this fluid in boundary lubrication tests with a PFPE and a PAO have been reported (Kalogeras et al., 1993). Relative life is shown in Figure 31.2. The silicone performed poorly by degrading into an abrasive polymerized product. 31.4.1.4 Synthetic Hydrocarbons There are two groups of synthetic hydrocarbons available today: polyalphaolefins (PAO) and multiply alkylated cyclopentanes (MACs). The first class is made by the oligomerization of linear α-olefins having six or more carbon atoms (Shubkin, 1993). Nye Lubricants markets a number of PAOs for space applications. Properties for three commercial PAOs appear in Table 31.2. The other class of hydrocarbons is known as MACs. These materials are synthesized by reacting cyclopentadiene with various alcohols in the presence of a strong base (Venier and Casserly, 1993). The products are hydrogenated to produce the final product, which is a mixture of di-, tri-, tetra-, or pentaalkylated cyclopentanes. Varying reaction conditions controls the distribution. For the last several years, only one product has been available for space use — primarily the tri-2-octyldodecyl-substituted cyclopentane (Venier and Casserly, 1991). This product is known as Pennzane SHF-X2000, marketed as Nye Synthetic Oil 2001A. Various formulated versions are also available. A primarily disubstituted (lower viscosity, but higher volatility) version is also now available. Properties of the 2001A product appear in Table 31.3. Recent experience with this fluid appears in Carré et al. (1995). A 6-year life test of a CERES elevation bearing assembly using a Pennzane/lead naphthenate formulation yielded excellent results (Brown et al., 1999).
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TABLE 31.2 Typical Properties for Three Commercial Polyalphaolefins Property Viscosity at:
210°F, SUS 210°F, cs 100°F, SUS 100°F, cs 0°F, cs
Flash point Pour point Evaporation 61/2 hours at 350°F Specific gravity @ 25°C
Oil 132
Oil 182
Oil 186
39 3.9 92 18.7 350 440°F –85°F 2.2% 0.828
62.5 10.9 348 75.0 2700 465°F –60°F 2.0% 0.842
79.5 15.4 552 119 7600 480°F –55°F 1.9% 0.847
TABLE 31.3 Typical Properties of Nye Synthetic Oil 2001A (SHF X-2000) Viscosity at 100°C Viscosity at 40°C Viscosity at –40°C Viscosity index Flash point Fire point Pour point Specific gravity at 25°C Specific gravity at 100°C Coefficient of thermal expansion Evaporation, 24 hr at 100°C Refractive index at 25°C Vapor pressure at 25°C
TABLE 31.4
14.6 cSt 108 cSt 80,500 cSt 137 300°C 330°C –55°C 0.841 0.796 0.0008 cc/cc/°C None 1.4671 10–11–10–10 Torr
Physical Properties of Four Commercial PFPE Lubricants and Pennzane SHF X-2000
Lubricant
Average Molecular Weight
Fomblin™ Z-25 Krytox™ 143AB Krytox™ 143AC Demnum™ S-200 Pennzane SHF X-2000
9500 3700 6250 8400 1000
Viscosity at 200°C (cSt) 255 230 800 500 330
Viscosity Index 355 113 134 210 137
Pour Point (°C) –66 –40 –35 –53 –55
Vapor Pressure (Pa) At 20°C 3.9 2.0 2.7 1.3 2.2
× 10 × 10–4 × 10–6 × 10–8 × 10–11 –10
At 100°C 1.3 × 10–6 4.0 × 10–2 1.1 × 10–3 1.3 × 10–5 1.9 × 10–8
31.4.1.5 Perfluoropolyethers These fluids, designated as either PFPE or PFPAE, have been commercially available since the 1960s and 1970s in the form of a branched fluid (Krytox™) manufactured by DuPont (Gumprecht, 1966); a linear fluid (Fomblin™ Z) (Sianesi et al., 1973); and a branched fluid (Fomblin™ Y) (Sianesi et al., 1971), the latter two manufactured by Montefluous. Another linear fluid (Demnum™) was developed in Japan by Daikin (Ohsaka, 1985). The preparation and properties of these fluids appear in Synthetic Lubricants and High-Performance Functional Fluids, (Shubkin, 1993). Some typical properties of these fluids appear in Table 31.4. 31.4.1.6 Silahydrocarbons A new type of space lubricant has been developed by the Air Force Materials Laboratory (Snyder et al., 1992). These materials contain only silicon, carbon, and hydrogen, and therefore do not exhibit the poor
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FIGURE 31.3 Kinematic viscosity as a function of temperature for a series of silahydrocarbons. (From Jones, W., Shogrin, B., and Jansen, M. (1998a), Research on liquid lubricants for space mechanisms, in Proc. 32nd Aerospace Mechanisms Symp., Cocoa Beach, FL, NASA/CP-1998-207191, 299-310.)
boundary lubricating ability observed with silicones. In addition, these unimolecular materials have exceptionally low volatility and are available in a wide range of viscosities. There are three types, based on the number of silicon atoms present in the molecule (i.e., tri, tetra, or penta) (Paciorek et al., 1990, 1991). A series of silahydrocarbons have been synthesized and their kinematic viscosities as a function of temperature have been measured (Figure 31.3) (Jones et al., 1998). For comparison, a Pennzane plot has been included. As can be seen, the viscosity properties of the silahydrocarbons bracket the Pennzane data. EHL properties of two members of this class have been measured (Spikes, 1996). A trisilahydrocarbon had an α value of 16 GPa–1 (±0.3) at 21°C, while a pentasilahydrocarbon had an α value of 17 GPa–1 (±0.3). At 40°C, the trisilahydrocarbon had an α value of 11 GPa–1 (±1) and the penta, 13.5 GPa–1 (±1). For comparison, the α value for Pennzane at 30°C is 9.8 GPa–1 (±0.3), estimated by the same method. Therefore, these silahydrocarbons will generate thicker EHL films than Pennzane under the same conditions.
31.5 Liquid Lubricant Properties Numerous reviews of liquid lubricants for space applications have been published (Fusaro and Khonsari, 1991; Stone and Bessette, 1998; Zaretsky, 1990). Liquid lubricant data also appear in some handbooks (Fusaro et al., 1999; Roberts, 1999; McMurtrey, 1985). Because most applications today use either PFPEs or Pennzane (MAC) formulations, these two classes will be presented in more detail.
31.5.1 Perfluoropolyethers and MACs A liquid lubricant must possess certain physical and chemical properties to function properly in a lubricated contact. To be considered for space applications, these lubricants must have vacuum stability (i.e., low vapor pressure), low tendency to creep, high viscosity index (i.e., wide liquid range), good elastohydrodynamic and boundary lubrication properties, and resistance to radiation and atomic oxygen. Optical or infrared transparency is important in some applications.
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FIGURE 31.4 Relative evaporation rates of aerospace lubricants. (From Conley, P. and Bohner, J.J. (1990), Experience with synthetic fluorinated fluid lubricants, in Proc. 24th Aerospace Mech. Symp., NASA CP-3062, 213-230. With permission.)
31.5.1.1 Volatility Although labyrinth seals are extensively used in space mechanisms, lubricant loss can still be a problem for long-term applications (Hilton and Fleischauer, 1990). For a fixed temperature and outlet area, lubricant loss is directly proportional to vapor pressure. For a similar viscosity range, the PFPE fluids are particularly good candidates compared to conventional lubricants, as shown in Figure 31.4 (Conley and Bohner, 1990). Vapor pressure data for four commercial PFPE fluids and Pennzane appear in Table 31.4. 31.5.1.2 Creep The tendency of a liquid lubricant to creep or migrate over bearing surfaces is inversely related to its surface tension. Therefore, PFPE fluids, which have unusually low surface tensions (γLV , 17 to 25 dynes/cm at 20°C), are more prone to creep than conventional fluids such as hydrocarbons, esters, and silicones. However, these fluids may be contained in bearing raceways by using low surface energy fluorocarbon barrier films on bearing lands (Kinzig and Ravner, 1978). However, there is a tendency for PFPE fluids to dissolve these barrier films with prolonged contact (Hilton and Fleischauer, 1993). Therefore, they are not effective in preventing the migration of PFPEs. Pennzane-based lubricants have higher surface tensions and are thus less prone to creep. 31.5.1.3 Viscosity-Temperature Properties Although liquid lubricated space applications do not involve wide temperature ranges, low temperatures (i.e., –10 to –20°C) are sometimes encountered. Therefore, low pour point fluids that retain low vapor pressure and reasonable viscosities at temperatures to 75°C are desirable. The viscosity-temperature slope of PFPE unbranched fluids is directly related to the carbon-to-oxygen ratio (C:O) in the polymer repeating unit, as shown in Figure 31.5 (Jones, 1995). Here, the ASTM slope is used for the correlation. High values of the ASTM slope indicate large changes of viscosity with temperature. In addition, branching (e.g., the trifluoromethyl pendant group in the Krytox fluids) causes deterioration in viscometric properties. A comparison of ASTM slopes for three commercial fluids appears in Figure 31.6. Here, the low C:O ratio fluid Fomblin Z has the best viscometric properties. The Demnum fluid, with a C:O ratio of 3, has intermediate properties, while the branched Krytox fluid has the highest slope. 31.5.1.4 Elastohydrodynamic Properties The operation of continuously rotating, medium- to high-speed bearings relies on the formation of an elastohydrodynamic (EHL) film. This regime was briefly discussed in the introduction. A more detailed
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FIGURE 31.5 Viscosity-temperature slope as a function of carbon-to-oxygen ratio. (From Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. With permission.)
FIGURE 31.6 Viscosity-temperature slope (ASTM D 341-43) as a function of kinematic viscosity at 20°C for Krytox™ (K), Demnum™ (D), and Fomblin™ (Z) fluids. (From Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. With permission.)
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38°C
99°C
149°C
1.3 1.8 1.8 2.5 3.1 4.2
1.0 1.5 1.5 1.5 1.7 3.2
0.85 1.1 1.3 (extrapolated) 1.3 0.94 3.0
Note: α* given in units of Pa–1 × 108. From Jones, W.R., Jr., Johnson, R.L., Winer, W.O., and Sanborn, D.M. (1975), ASLE Trans., 18(4), 249-262. With permission.
discussion appears in Wedeven (1975). The two physical properties of the lubricant that influence EHL film formation are absolute viscosity (µ) and the pressure-viscosity coefficient (α) (Hamrock and Dowson, 1981). Both molecular weight and chemical structure influence viscosity. Except for low-molecular-weight fluids, α values are only related to structure (Spikes et al., 1984). Pressure-viscosity coefficients can be measured directly with conventional high-pressure viscometers (Jones et al., 1975; Vergne and Reynaud, 1992) or indirectly from optical EHL experiments (Cantow et al., 1987; Aderin et al., 1992). Conventional viscometry normally uses the Barus equation (Barus, 1893) for correlations.
µ p = µ oe αp
(31.1)
where µp = Absolute viscosity at pressure, p µo = Absolute viscosity at atmospheric pressure α = A temperature-dependent but pressure-independent constant This implies that a plot of log µp vs. p should yield a straight line of slope α. Unfortunately, this simple relationship is seldom obeyed. The pressure-viscosity properties that are important in determining EHL film thickness occur in the contact inlet where pressures are much lower than in the Hertzian region. Therefore, the slope of a secant drawn between atmospheric pressure and 0.07 GPa is typically used for film thickness calculations. Some researchers (Jones et al., 1975) favor the use of another pressure-viscosity parameter, the reciprocal asymptotic isoviscous pressure (α*) based on work by Roelands (1966). Pressure-viscosity coefficients (α*) for several lubricants at three temperatures (38°, 99°, and 149°C) are given in Table 31.5. Figure 31.7 contains α values for the branched PFPE, Krytox 143AB. Data obtained by conventional (low shear) pressure-viscosity measurements are denoted with open symbols. Indirect measurements from EHL experiments (effective α values) are shown with solid symbols. There is good agreement between the different sources as well as different measurement techniques. Figure 31.8 contains similar data for the unbranched PFPE Fomblin Z-25 as a function of temperature. Here, there is a definite grouping of the data, with effective α values being substantially lower than values from conventional measurements. Two possibilities exist for this discrepancy. First, inlet heating can occur during the EHL measurements, thus leading to lower viscosities, lower film thicknesses, and resulting in lower calculated α values. The second possibility is a non-Newtonian shear thinning effect, which can occur with polymeric fluids. Shear rates in EHL inlets can range from 105 to 107 sec–1 (Foord et al., 1968). However, the EHL measurements do represent actual film thicknesses that may be expected in practice. Effective α values for several nonPFPE space lubricants, including Pennzane base fluid and some Pennzane formulations, appear in Table 31.6 (Spikes, 1997).
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FIGURE 31.7 Pressure-viscosity coefficients for PFPE Krytox™ 143 AB as a function of temperature. (From Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. With permission.)
FIGURE 31.8 Pressure-viscosity coefficients for PFPE Fomblin™ Z-25 as a function of temperature. (From Jones, W.R., Jr. (1995), Properties of perfluoropolyethers for space applications, Trib. Trans., 38(3), 557-564. With permission.)
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TABLE 31.6 Measured Viscosities and Calculated Pressure-Viscosity Coefficients (α Values) for Several Space Lubricants Temp (°C)
Pennzane 2001: Synth. Oil
PAO-186: Synth. Oil
40 80 100 120
88 19 12 8
90 21 13 8
NPE UC-7: Ester
Pennzane 2001+5% Pb Naphthenate
Pennzane 2001+3% Pb Naphthenate
98 21 12 8
96 21 12 8
12.0 9.0 6.5 6.0
10.0 9.0 7.0 7.0
Viscosity (cP) 37 10 6 4 α (GPa–1) 40 80 100 120
11.0 9.5 7.0 7.0
12.5 9.0 7.0 5.0
6.5 5.0 5.0 5.0
From Spikes, H.A. (1997), Film Formation and Friction Properties of Five Space Fluids, Imperial College (Tribology Section), London, U.K., Report TSO37/97.
FIGURE 31.9 Lubricant parameters for PFPE Y and Z fluids. (From Spikes, H.A., Cann, P., and Caporiccio, G. (1984), Elastohydrodynamic film thickness measurements of perfluoropolyether fluids, J. Syn. Lubr., 1(1), 73-86. With permission.)
From EHL theory, the greatest film thickness at room temperature should be obtained with a lubricant having the largest α value, assuming approximately equal inlet viscosities. However, for many applications, lubricants must perform over a wide temperature range. In this case, the EHL inlet viscosity can be the overriding factor if the temperature coefficient of viscosity is high. This can cause a crossover in film thickness as a function of temperature for some PFPE fluids, as shown by Spikes et al. (1984) in Figure 31.9. 31.5.1.5 Boundary Lubrication As described in the introduction, boundary lubrication is the regime where surfaces are not completely separated, which results in surface asperity interactions. The most important aspect of this regime is the formation of protective surface films to minimize wear and surface damage. The formation of these films
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is governed by the chemistry of both the film former as well as the contacting surfaces. Non-additive hydrocarbons, mineral oils, and esters will react in a boundary contact to produce “friction polymer” (Lauer and Jones, 1987). Except for electrical contacts, this material is usually beneficial, but does represent a lubricant loss mechanism. However, these conventional lubricants are never required to act alone and almost all are formulated with anti-wear, anti-corrosion, extreme pressure, or anti-oxidant additives to enhance their performance. Contrast this with a PFPE boundary lubricant, a relatively inert, very pure fluid, which in past years contained no additives. If these fluids were really inert, they would not provide any surface protection except for some local fluid film effects (micro-EHL) and some removal of wear debris. However, these fluids do react with bearing surfaces, producing a series of corrosive gases and friction polymer which, in turn, react with existing surface oxides to produce metallic fluorides (Mori and Morales, 1989; Carré, 1986; Herrera-Fierro et al., 1993). These fluorides are effective in situ solid lubricants that reduce friction and prevent catastrophic surface damage (Mori and Morales, 1989). Unfortunately, these fluorides are also strong Lewis acids (electron acceptors) that readily attack and decompose PFPE molecules (Herrera-Fierro et al., 1993; Carré and Markowitz, 1985; Kasai, 1992). This causes the production of additional reactive species, which, in turn, produce more surface fluoride, resulting in an autocatalytic reaction. This can cause a lubricated contact to fail abruptly, as shown in Figure 31.10a. In contrast, a non-PFPE space lubricant, such as Pennzane, has a greater lubricated lifetime and a much slower progression to failure. This is usually characterized by a gradually increasing friction
Friction Coefficient
0.3
0.2
0.1
0.0 0
1
2
3
4
5
6
7
Time (hrs) (a) KrytoxTM 143AC
Friction Coefficient
0.3
0.2
0.1
0.0 0
20
40
60
80
100
120
140
Time (hrs) (b) PennzaneTM
FIGURE 31.10 Coefficient of friction as a function of time for (a) Krytox™ 143AC and (b) Pennzane™ 2001A (spiral orbit rolling contact tribometer).
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FIGURE 31.11 Eccentric bearing screening test results for PFPE, PAO, and MAC oils. (From Carré, D.J., Kalogeras, C.G., Didziulis, S.V., Fleishauer, P.D., and Bauer, R. (1995), Recent Experience with Synthetic Hydrocarbon Lubricants for Spacecraft Applications, Aerospace Report TR-95(5935)-3.)
coefficient, as shown in Figure 31.10b. Therefore, the very reaction that allows the use of pure PFPE fluids in boundary contacts eventually leads to their early destruction and accompanying bearing failure. Of course, the progression of this mechanism is highly dependent on the local contact conditions (i.e., degree of surface passivation, type and thickness of surface oxides, amount of surface contamination, temperature, load, speed, etc.). Substantial improvements in bearing lifetimes can be obtained if ceramic or ceramic-coated balls are substituted for the standard bearing steels. TiC-coated balls (Boving et al., 1988) have shown considerable promise in alleviating some of these lubricant degradation problems. Gill et al. (1992) have observed a ninefold increase in bearing lifetime with a PFPE (Fomblin Z25 when TiC balls were used instead of 52100 steel balls. In accelerated life tests (Jones et al., 1999) using a spiral orbit tribometer, lubricant lifetimes with another PFPE (Krytox 143AC) were extended by factors of two to four, depending on the stress level. 31.5.1.5.1 Wear Characteristics and Relative Life Various Pennzane formulations have been compared to other hydrocarbons (PAOs) and PFPEs in eccentric bearing tests (Carré et al., 1995). The data shown in Figure 31.11 indicated that a Pennzane formulated with antimony dialkyldithiocarbamate yielded a lifetime of several times that of a PFPE (Krytox 143AB). Linear ball screw tests at ESTL (European Space Tribology Laboratory) (Gill, 1997) compared several lubricants. These included: Fomblin Z-25 oil, Braycote™ 601 grease, Pennzane SHF X-2000 oil, sputter coated MoS2, ion-plated lead, and Braycote 601 + ion-plated lead. The two PFPE lubricants failed rapidly, but the use of Braycote 601 and ion-plated lead reached the full test requirement of 2 million cycles. Ionplated lead alone failed at 400K cycles, while the MoS2 survived the full test, but some polishing of the contact zone was noted. The Pennzane oil completed the test but wear of the lead screw occurred and some dewetting was noted. Earlier work at ESTL (Gill, 1994) compared the performance of several solid and liquid lubricants in oscillating ball bearings. Three liquid/grease lubricants were tested with phenolic cages: Fomblin Z-25, Braycote 601, and Pennzane SHF X-2000. Torque levels were measured over 10 million oscillations. For a low angle of oscillation (±0.5°), Fomblin Z-25 yielded average torque levels 1.5 times that of Braycote and approximately 3 times that of Pennzane. At ±5°, mean torque measurements were similar for all three lubricants, but Pennzane did exhibit the lowest levels. Finally, at ±20°, the Z-25 yielded the highest torque, Braycote intermediate, and again Pennzane the lowest.
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FIGURE 31.12 Mean wear rates of various space lubricants using a vacuum four-ball tribometer. (From Jones, W., Shogrin, B., and Jansen, M. (1998a), Research on liquid lubricants for space mechanisms, in Proc. 32nd Aerospace Mechanisms Symp., Cocoa Beach, FL, NASA/CP-1998-207191, 299-310.)
Long-term, angular-contact bearing tests were also reported by Gill and Rowntree (1995). Pennzane SHF X-2000 was tested at 200 and 1400 rpm for 108 and 109 revolutions, respectively. The bearings did not fail, but they did suffer from oil starvation due to evaporation losses. It was not clear if this was due to insufficient sealing or related to a lubricant batch problem. However, it was stated that similar tests with PFPE oils have never failed due to starvation by oil evaporation. A vacuum four-ball tribometer (Jones et al., 1998) has been used to rank various space lubricants according to wear rates (Figure 31.12), including three PFPEs, Pennzane base fluid, a formulated Pennzane, and two other unformulated fluids (a silahydrocarbon and a PAO). In general, higher wear rates represent lower lifetimes in space. 31.5.1.6 PFPE Formulations Although no liquid PFPE additive formulations are currently being used for any space application, many additives, soluble in PFPEs, have been developed in the last few years. These include anti-wear, anticorrosion, and anti-rust additives (Gschwender et al., 1993; Helmick et al., 1997; Jones et al., 1996; Masuko et al., 1995; Nakayama et al., 1996; Sharma et al., 1990; Shogrin et al., 1997; Srinivasan et al., 1993; Williams et al., 1994). Several different additives exhibited anti-wear behavior in a Krytox basestock in vacuum four-ball tests (Figure 31.13) (Shogrin et al., 1997). 31.5.1.7 Greases Greases based on PFPEs with PTFE thickeners (Krytox 240 series and Braycote 600 series) have been used extensively in space mechanisms. In addition, hydrocarbon greases based on Pennzane and marketed by Nye Lubricants under the name Rheolube™ 2000 are also now available. The performance of various Pennzane-based greases appears in Rai et al. (1999). Recently, new PFPE formulations (commercially designated as Braycote 700 and 701) incorporating a boundary additive have yielded much improved wear characteristics (Figure 31.14) (Jones, D.G.V. et al., 1999). 31.5.1.8 Solid Lubricants A number of different solid lubricants have been used in space over the last 30 years. These include lamellar solids, soft metals, and polymers. Lamellar solids include transition-metal dichalcogenides like molybdenum disulfide and tungsten disulfide. Soft metals include lead, gold, silver, and indium. Polyimides and polytetrafluoroethylene are polymeric materials that possess lubricating properties. Unlike
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FIGURE 31.13
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Anti-wear behavior of several additives in Krytox™ base stock using a vacuum four-ball tribometer.
FIGURE 31.14 Mean wear rates of various PFPE formulated greases using a vacuum four-ball tribometer. (From Jones, D.G.V., Fowzy, M., Landry, J.F., Jones, W.R., Jr., Shogrin, B., and Nguyen, Q. (1999a), An Additive to Improve the Wear Characteristics of Perfluoropolyether Based Greases, NASA TM-1999-209064.)
liquid lubricants, the metals and lamellar solids are applied as thin films (i.e., less than a micron). Ion plating (Roberts, 1990; Spalvins, 1987, 1998) and sputtering (Roberts, 1990; Spalvins, 1992; Fox et al., 1999) are preferred methods of applying these materials. Another method of applying lubricants to surfaces involves bonded films (Fusaro, 1981; Dugger et al., 1999). In this case, lubricants are mixed with an organic binder and applied to the surface via spraying or dipping. The films, which are typically greater than 10 microns, are then cured at high temperature. Self-lubricating polymers and polymer
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composites (Fusaro, 1990; Gardos, 1986) are sometimes utilized. The most common form of usage is as a cage or retainer in a rolling element bearing or as a bushing. By far the most common solid lubricants used in today’s space mechanisms are ion-plated lead and various forms of sputter-deposited MoS2. 31.5.1.8.1 Ion-plated Lead This is the lubricant of choice for precision spacecraft bearings in Europe. It is normally used in conjunction with a leaded bronze cage. Lead coatings and cages saw early success in cryogenic space applications (Brewe et al., 1974). Successful applications have been used on GIOTTO (Todd and Parker, 1987), OLYMPUS (Sheppard, 1983), and GERB (Fabbrizzi et al., 1999). Although not as common in the United States, this combination has recently been applied to encoder bearings for SABER. Extensive data have been published (Arnell, 1978) on the effects of speed, thickness, and substrate surface roughness. One disadvantage of this lubricant is its limited life in laboratory air. Much higher wear rates occur in air, producing copious amounts of lead oxide. This debris can also cause torque noise. 31.5.1.8.2 Molybdenum Disulfide MoS2 has been successfully used in space for many years (Lince and Fleishauer, 1997; Hilton and Fleischauer, 1994; Loewenthal et al., 1994; Hopple et al., 1993). These films display very low friction under vacuum conditions (i.e., 0.01 or less). Optimized thin films (1 micron or less) are deposited by sputtering. The tribological performance of these films is extremely dependent on the sputtering conditions. The sputtering conditions control the microstructure, which in turn determines crystallinity, morphology, and composition (Didziulis et al., 1992). For example, the presence of oxygen in the sputtering environment can affect both friction and wear life (Lince et al., 1990). For more details about the sputtering process, see Spalvins (1992). In addition, substrate surface roughness also has a pronounced effect on friction and wear. For steel bearing surfaces, optimum durability occurs at a nominal surface roughness of 0.2 µm (cla) (Roberts et al., 1992). The test environment also greatly affects the frictional behavior and life of MoS2 films. In ultra-high vacuum, these films display ultra-low friction (less than 0.01), as shown in Figure 31.15. Under normal vacuum conditions, the friction can range from 0.01 to 0.04, with exceptionally low wear and long endurance lives. When tested in humid air, these films have initial friction coefficients near 0.15 and very limited life (Roberts, 1987; Lince and Fleischauer, 1998). Because many space mechanisms must be ground-tested before launch, sometimes in room air, there has been much research to improve the performance of these films under atmospheric conditions. One method has been to modify MoS2 films by layering or co-depositing metals such as Au (Spalvins, 1984; Roberts and Price, 1995). In this work, inclusions of Au doubled the film durability in dry nitrogen and tripled or quadrupled it in air. Co-deposition with other metals (i.e., Cr, Co, Ni, and Ta) have also shown synergistic effects (Stupp, 1981). Ion implantation with Ag has also been reported to be beneficial (Liu et al., 1995) but not when co-deposited (Stupp, 1981). The properties of MoS2 films can also be improved by co-deposition with titanium (Renevier et al., 1999). These films were much less sensitive to atmospheric water vapor than pure MoS2 films. Studies have shown that the problems that occur in moist air are associated with adsorption of water molecules at edge sites on the MoS2 lattice (Fleishauer, 1984). Another method of enhancing MoS2 endurance in ball bearings is to use a PTFE composite as the retainer material (Suzuki and Prat, 1999). In gimbal bearing life tests (Hopple and Loewenthal, 1994), lives in excess of 45 million cycles were demonstrated with advanced MoS2 films combined with PTFEbased retainers.
31.6 Accelerated Testing and Life Testing Because of increasing demands of spacecraft mechanisms, new lubricants and additives are always under development. These materials must undergo ground-based testing to ensure they will meet the long duty cycle requirements and stringent conditions required by today’s space missions. In the past, two approaches to qualify lubricants for space were taken. The first approach was to perform system-level tests on actual flight hardware. The second was to attempt to duplicate the conditions
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0.20
Humid air
0.15
0.10
0.05
0.04
0.30
0.20
Ultra low friction
Vacuum
0.015
0.01 Super-ultra low friction
FIGURE 31.15 Frictional variation of sputtered MoS2 films. (From Spalvins, T. (1992), Lubrication with sputtered MoS2 films: principles, operation and limitations, J. Mater. Eng. and Perf., 1, 347-352. With permission.)
of flight system operation (Kalogeras et al., 1993). Although this type of testing produces results, they are costly, both in time and money. Therefore, only a few candidate lubricants are selected for testing. This has led to most lubricants being chosen through “heritage” or actual flight experience. Accelerated life testing is an approach that allows quick screening of several lubricants. Generally, test results cannot be extrapolated to predict lifetimes of components that are lubricated similarly but operate under different conditions (Conley, 1998). Instead, accelerated life testing allows for a better selection of candidate lubricants to undergo full-scale tests. Accelerated tests typically do not involve actual flight hardware, but rather utilize a setup that subjects the lubricant to an extreme condition. Test acceleration is achieved by varying various test parameters such as speed, load, temperature, contaminants, quantity of lubricant available, and surface roughness (Murray and Heshmat., 1995). When selecting which parameters to vary, it is important to have a thorough understanding of contact conditions and the lubricant used. In a liquid-lubricated environment, a significant change in speed or temperature could introduce a change of the lubrication regime. As speed increases or temperature decreases, film thickness also increases, taking the bearing from the boundary regime, through the mixed regime, and into the EHL regime. As described previously, each lubrication regime has specific and different wear characteristics. Also, time-dependent parameters such as creep, loss of lubricant through evaporation and centrifugal forces, and lubricant degradation are not modeled with accelerated life tests (Conley, 1998).
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TABLE 31.7
Strengths and Weaknesses of Accelerated Life Testing
Weakness Wetting condition with temperature Chemistry changes with temperature and pressure Oxidation changes with temperature and pressure Hydrodynamics region changes Wear/friction polymers change Coating fracture under high load (solid lube) Non-standardized Dynamic changes in cages and components Low confidence
Strength Easy to monitor Use to enhance design Use to validate model Rapid baseline data generation
From Murray, S. and Heshmat, H. (1995), Accelerated Testing of Space Mechanisms, NASA Contractor Report 198437.
Accelerated life testing with solid lubricants is somewhat easier. If a system uses solid lubricants exclusively and is a fairly low-speed application (99%), at the same time maintaining a low restriction to air flow. In the initial stages, the dust particles coat the fibers, building up a layer. As the amount of contaminant captured increases with time, a continuous cake forms on the surface of the filter medium and the restriction to flow increases to the point that the filter needs to be replaced. Some filters contain a mechanical valve that activates a “flag” when the restriction reaches a predetermined limit and before serious loss of engine performance is experienced.
33.8.5 Filtration: Lubricating System In contrast to the air system, the lubricating system is relatively closed; that is, the fluid is controlled and the system is not frequently open to the outside environment. There are two common approaches to filtration in the lubricating system: single or two-stage filtration. For a single-stage or full-flow filter, all of the lubricating oil is continuously pumped through the filter. The disadvantage of this approach is that if a high level of efficiency is desired, the filter can reach a high flow restriction very rapidly, leading to short filter life. There are a variety of two-stage filter systems in current use, but the general approach is to use a relatively open, full-flow section while a portion of the flow (usually about 5 to 10%) is shunted or bypassed into a very high-efficiency second stage. This system produces high efficiency with longer life. Most full-flow filter elements are of pleated construction and the filter media include cellulose, glass, and polymeric materials. In some cases, blends and layers of different materials are used to produce a gradient density medium. The design of a lubricating filtration system is a trade-off between efficiency and capacity or life, and the use of different filtration materials can help control that balance. The second stage, or bypass section, can be a surface-type medium such as a higher efficiency fullflow type material in a pleated configuration or a depth medium constructed of stacked disks or packed fibers. Cellulose is the most common and effective second-stage material due to its affinity for the organic contaminants. Centrifuges are sometimes used as permanent, cleanable second-stage filters because of their high capacity.
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The most commonly encountered contaminants in the lubricating system are much more complex than in the air system. Analysis of contaminants extracted from used filters shows that at least 90% of the total contaminants are organic in nature. These are soot, sludge, tars, resins, and oxidation products. The inorganic portion includes spent additives, wear metals, neutralization products, and external dust. The organic material, if not removed, would increase the oil viscosity to the point where lubricity would be degraded. This material tends to coat the fibers of the filter, increasing the apparent fiber diameter and gradually reducing the pore size and increasing the restriction to flow (Stehouwer, 1996; Truhan and Stehouwer, 1998). When two-stage filtration is employed, the second stage collects the bulk of the contaminant, allowing the full-flow section to continue filtering. When longer service intervals are desired, such as for on-highway applications, extended filter life can be achieved by increasing the capacity of the second stage. Filter performance is closely related to oil quality, with better quality oils reducing wear for a given filter efficiency and longer filter life by keeping the organic contaminants dispersed.
33.8.6 Filtration: Fuel System The fuel system, like air, is an open system but with better control over the fluid quality. The fuel system, however, is still vulnerable to loads of fuel with biocontamination and water, which can foul injectors and create corrosive by-products. Because diesel fuel has poorer inherent lubricity compared to lubricating oil and tolerances in the fuel hardware are very close, fuel cleanliness is proportionately more important. Fuel filter elements are constructed similar to oil filters in that they are of a pleated configuration. They can be housed in a spin-on can or in a permanent housing that includes other features such as clear bowls and fuel heaters. Both spin-on and permanent housings may have drain valves to allow the removal of water separated by the filter medium. The filters can be mounted on either side of the fuel pump, depending on the engine design; and, in some cases, a lower efficiency primary filter is used to protect the pump and a higher efficiency secondary filter is used to protect the fuel injectors. As with lubricating oil filters, filter media include cellulose, glass, and polymeric fibers. The types of contaminants that fuel filters remove are similar to lubricating oil filters; that is, they are primarily organic, with a small inorganic component of wear metals, precipitates, and external dust (Martin, 1998). Because only a portion of the fuel is burned at a time, the remainder of the fuel flow is recirculated in the system to provide cooling. This recirculated fuel increases in temperature and can, with an unstable fuel, produce partial oxidation products called asphaltenes. This organic material will plug a fuel filter just as a lubricating oil filter, limiting its life. As mentioned previously, organisms growing in poorly stored fuel can cause occasional problems by prematurely plugging a filter. Because most injector systems operate at high pressure, most engine manufacturers require the use of a fuel/water separator, particularly for electronically controlled engines. Fuel/water separation is accomplished using a filter medium to which the fuel will wet and water will not. The water falls to the bottom of the filter by virtue of its higher density, where it can be collected and drained. Cellulose requires a coating to achieve this separation; however, this coating will degrade with use and the buildup of organic material. Polymeric fibers have the inherent ability to reject water and do not require additional surface treatments. Consequently, they are more durable for longer service operations.
33.8.7 Filtration: Cooling System Although not universally employed on diesel engines, coolant filtration is beneficial nonetheless (Hudgens and Hercamp, 1988). The cooling system is a partially closed system because the additional external plumbing, hoses, and clamps make it prone to leakage. Consequently, the system must be opened periodically for inspection and refilling if necessary, making it vulnerable to outside contamination. Internally, particulates can result from corrosion, scaling, or precipitation if the coolant is of poor quality. These particulates can cause erosion in pumps and internal passages. Lubricating oil can contaminate the coolant if internal seals fail and this oil can coat heat-rejecting surfaces, impeding heat transfer. Although cellulose is the most commonly used filter material, polypropylene has an affinity for oil, and
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filter fibers made from it will effectively remove oil if the quantities are not large. Coolant filters often have the additional job of adding supplemental additives to the coolant, which help prevent corrosion and scaling, keeping internal particulate formation under control.
33.9 Future Trends Future advanced diesel engine designs will require substantial improvements in the areas of emissions control, performance, and fuel economy. One effect of these requirements will be to place much greater stress on tribological systems in the engine through higher loads and temperatures with more marginal lubrication. Also, the use of exhaust gas recirculation will require improved wear and corrosion resistance, particularly for power cylinder components. These requirements, plus customer expectations of improved durability and reliability, dictate improvements in wear and friction performance of several key engine components and subsystems. Several future trends in engine design will impact valve system durability: 1. Higher cylinder pressures will lead to increased valve/seat contact pressures and tangential stresses and greater valve/seat deflection, resulting in increased wear. 2. Increasing power density will cause higher temperatures and pressures, resulting in increased thermal and mechanical distortion of the seats. 3. Reduced particulate emissions will require the use of tighter valve stem seals, which will reduce lubrication to the stem/guide and valve/seat interfaces. 4. The use of exhaust gas recirculation will potentially result in intake stem/guide corrosion due to condensation of sulfuric/nitric acids. The outcome of these changes will probably include: a. Reduction in seat angles for improved valve/seat wear b. Development of exhaust valve materials with improved high-temperature fatigue properties 5. Increased use of powder metal guide materials for wear and scuff resistance. 6. The use of improved seat insert materials for wear resistance and temperature capability. Future trends affecting bearing requirements include: 1. Increased unit loads (peak oil film pressure, POFP) due to higher cylinder pressure, packaging constraints, and lower oil viscosity, which will increase fatigue and wear 2. Greater flexibility of housings 3. Greater precision/reduced tolerancing for maximum bearing area 4. Greater emphasis on longevity and life prediction 5. Modeling capabilities for analysis of bearing features/structures 6. Increased bearing back temperatures due to higher unit loads and higher oil temperature, which will increase fatigue, wear, and corrosion 7. Reduced oil viscosity for improved fuel economy, which will reduce film thicknesses and increase wear 8. Environmental concerns over lead (Pb) in used oil and in manufacturing processes These trends will require further advances in bearing materials/processing technologies and will probably occur at the expense of conformability/embeddability, which will entail further improvements in dimensional tolerances and manufacturing cleanliness for bearing systems.
Acknowledgments The authors would like to thank Dr. J.J. Truhan, Dr. D.M. Stehouwer, Dr. D.E. Richardson, and Mr. M.A. Luehrmann for their contributions of materials and constructive comments; and Cummins Inc. for permission to write this chapter.
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References ASTM D5967-97 (1997), Standard Test Method for Evaluation of Diesel Engine Oils in T-8 Diesel Engine, ASTM Standards. Booser, E.R. (1992), CRC Handbook of Lubrication, 8th ed., CRC Press, Boca Raton, FL. Bovington, C. and Caprotti, R. (1993), Latest diesel fuel additive technology development, 4th Int. Symp. Perf. Eval. Auto. Fuels and Lubr., CEC/93/EF13, Birmingham, U.K., May. Cusano, C.M. and Wang, J.C. (1995), Corrosion of copper and lead containing materials by diesel lubricants, Lubr. Engr., 51(1), 89-95. Challen, B. and Baranescu, R. (1999), Diesel Engine Reference Book, 2nd ed., Society of Automotive Engineers, Warrendale, PA. Dennis, A.J., Garner, C.P., and Taylor, D.H.C. (1999), The Effect of EGR on Diesel Engine Wear, SP-1427, 45-57, Society of Automotive Engineers, Warrendale, PA. Glassey, S.F., Stockner, A.R., and Flinn, M.A. (1993), HEUI — A New Direction for Diesel Engine Fuel Systems, SAE Tech. Paper No. 930270. Hudgens, R.D. and Hercamp, R.D. (1988), Filtration of Coolants for Heavy Duty Engines, SAE Tech. Paper No. 881270. Jaroszczyk, T., Wake, J., and Conner, M. (1993), Factors affecting the performance of engine air filters, J. Eng. Gas Turbines and Power, 115, 693-699. Kim, C., Passut, C., and Zang, D.M. (1992), Relationships among Oil Composition Combustion-Generated Soot, and Diesel Engine Valve Train Wear, SAE Tech. Paper No. 922199. Kitamura, K., Takebayashi, H., Ikeda, M., and Percoulis, H.M. (1997), Development of Ceramic Cam Roller Followers for Engine Application, SAE Tech. Paper No. 972774. Kodali, P., Truhan, J. J., Richardson, D. E. (1999), 3rd Int. Conf. Filtration, Southwest Research Institute. Korte, V., Barth., R., Kirschner, R., and Schulze, J. (1997), Camshaft/Follower-Design for Different Stress Behavior in Heavy Duty Diesel Engines, SAE Tech. Paper No. 972776. Kuo, C.C., Passut, C.A., and Jao, T.C. (1998), Wear Mechanism in Cummins M-11 High Soot Diesel Test Engines, SAE Tech. Paper No. 981372, Sp. Pub. No. 1368. Lacey, P.I. (1994), Development of a lubricity test based on the transition from boundary lubrication to severe adhesive wear in fuel, Lubr. Eng., 50(10), 749-757. Martin, H. (1998), A comparison of the chemical and physical characteristics of field returned fuel filter plugging contaminants vs. a laboratory generated fuel filter plugging contaminant, Proc. 2nd Int. Filtration Conf., Southwest Research Institute, San Antonio, TX, 203-211. McGeehan, J.A., and Kulkarni, A.V. (1987), Mechanism of Wear Control by the Lubricant in Diesel Engines, SAE 872029, Society of Automotive Engineers, Warrendale, PA. Miba Gleitlager AG, Technical Information, Laakirchen, Austria. Owen, K. and Coley, T. (1995), Automotive Fuels Reference Book, 2nd ed., Society of Automotive Engineers, Warrendale, PA. Rastegar, F. and Craft, A.E. (1993), Piston ring coatings for high-horse power diesel engines, Surf. Coat. Technol., 61, 36-42. Rastegar, F., Graham, M., and Chang, P. (1997), Scuff Resistance Rig test for Piston Ring Face Coatings, SAE 970819, Society of Automotive Engineers, Warrendale, PA. Richardson, D.E. (1999), Review of Power Cylinder Friction for Diesel Engines, ASME, ICE-Vol. 32-3, Paper No.99-ICE-196. Rodriques, H. (1997), Sintered valve seat inserts and valve guides: features affecting design, performance and machinability, Proc. Int. Symp. Valvetrain Sys. Des. Mater., Dearborn MI, April 14-15, 129-139. Schaefer, S.K., Larson, J.M., Jenkins, L.F., and Wang, Y. (1997) Evaluation of heavy duty engine valvesmaterial and design, Proc. Int. Symp. Valvetrain Sys. Des. Mater., Dearborn MI, April 14-15. Shen, Q. (1987), Development of Material Surface Engineering to Reduce the Friction and Wear of the Piston Ring, SAE 970821, Society of Automotive Engineers, Warrendale, PA.
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Shurvell, H.F., Clague, A.D.H., and Southby, M.C. (1997), Method for determination of the combustion of diesel engine deposits by infrared spectroscopy, Appl. Spectrosc., 61(6), 827-835. Shuster, M., Mahler, F., Crysler, D. (1999), Metallurgical and metrological examination of the cylinder liner-piston ring surfaces after heavy duty diesel engine testing, Tribol. Trans., 42(1), 116-125. Stehouwer, D.M. (1996), The effects of extended service intervals on filters in diesel engines, Proc. 1st Int. Filtration Conf., Southwest Research Institute, San Antonio, TX, 211-214. Truhan, J.J., Covington, C.B., and Wood, L.M. (1995), The Classification of Lubricating Oil Contaminants and their Effect on Wear in Diesel Engines as Measured by Surface Layer Activation, SAE 952558, Society of Automotive Engineers, Warrendale, PA. Truhan, J.J. and Stehouwer, D.M. (1998), Engine measured filter performance, Proc. 2nd Int. Filtration Conf., Southwest Research Institute, San Antonio, TX, 152-157. Wang, J.C. and Cusano, C.M. (1995), Predicting Lubricity of Low Sulfur Diesel Fuel, SAE Tech. Paper No. 952564. Waterhouse, R.B. (1992), Fretting wear, ASM Handbook, 18, 242-256, ASM. Wei, D. and Spikes, H.A. (1986), The lubricity of diesel fuels, Wear, 111, 217-235. Weiss, E.K., Busenthuer, B.B., Hardenberg, H.O. (1987), Diesel Fuel Sulfur and Cylinder Liner Wear of a Heavy-duty Diesel Engine,” SAE 872148, Society of Automotive Engineers, Warrendale, PA.
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34 Tribology of Rail Transport 34.1
Introduction ................................................................... 1271 Historical Background • Wheel/Rail Interface and Axle Loads • Axle Load Increases
34.2
Wheel/Rail Contact........................................................ 1275 Wheel/Rail Materials • Forces at the Contact Patch • Adhesion • Repeated Contact — Plasticity, Shakedown, and Ratcheting • Consequences of Rail/Wheel Contact: Wear • Consequences of Rail/Wheel Contact: Rolling Contact Fatigue • Interaction of Wear and RCF • Grinding • Rail Corrugation
34.3
Generation of Mechanical Power • Tribological Issues in the Design of Diesel Engines • Supply of Combustion Air • Transmissions and Drives • Gas Turbines
Ajay Kapoor The University of Sheffield
34.4
The University of Sheffield
34.5
Axle Bearings, Dampers, and Traction Motor Bearings .......................................................................... 1321
34.6
New Developments and Recent Advances in the Study of Rolling Contact Fatigue.................................. 1324
The University of Sheffield
K.J. Sawley
Axle Bearings • Dampers for Suspension Systems
Transportation Technology Centre
Friction Modifiers • Wheelset Steering and Individually Driven and Controlled Wheels • Integrated Study of Rolling Contact Fatigue
M. Ishida Railway Technical Research Institute
Current Collection Interfaces of Trains........................ 1314 Earth Brushes • Current Collection Shoe and Gear • Pantographs • Registration Arms
David I. Fletcher F. Schmid
Diesel Power for Traction Purposes ............................. 1308
34.7
Conclusion...................................................................... 1325
34.1 Introduction For effective and economical railway operation, important tribological issues must be addressed at the wheel/rail interface, within the engines of locomotives and, for electric trains, at the current collection point (Figure 34.1). In this chapter, the authors present the background to these issues and follow this with a brief discussion of some recent developments in wheel/rail tribology and related research. Important tribological issues also affect other systems involved in rail transport, and some of these aspects are discussed toward the end of this chapter.
34.1.1 Historical Background Long before railway transport developed into the effective and complex system as generally understood today, rails were used to guide horse-drawn vehicles (Wickens, 1998) and by 1767 iron rails had been 0-8493-8403-6/01/$0.00+$.50 © 2001 by CRC Press LLC
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FIGURE 34.1
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Tuen Mun light rapid transit system (Courtesy of Tuen Mun, Hong Kong New Territories).
introduced (Snell, 1973). At the start of the 19th century, mechanically powered rail transport had started to develop, initially by modification and transfer onto wheels of stationary steam engines, which had by that time become commonplace. Engine design was initially derived from that of stationary steam engines, with the driving cylinders placed inside the boiler (Figure 34.2). However, over time, the designs evolved to satisfy more completely the requirements of a railway engine (Russell, 1998). Over a similar time period, passenger vehicle design also evolved, having initially been based almost entirely on stagecoach design (Russell, 1998). By the mid-1800s, the general form of rail and wheel had developed into something very similar to those in use today (Figure 34.3) but it was late in the 19th century when Hertz (1896) developed the first scientific description of the wheel/rail contact. Hertz developed an analysis method to describe the elastic contact of glass lenses but, following its publication, it was found that it could also be used to describe contacts within rolling element bearings, between gear teeth, and between rails and wheels (Johnson, 1985). Hertzian contacts between three-dimensionally curved bodies have an elliptical form, and pressure within this contact region varies with an elliptical distribution (Figure 34.4). The distribution is described by Equation 34.1, in which p0 is the maximum pressure within the contact, a and b are the semi-axes of the contact patch, and x and y are coordinates with their origin in the plane of the contact and at its center.
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Trevithick(1804-1805) Hackworth (1827)
Blenkinsop (1812) Stephenson (1815-1825)
Hedley (1813)
Stephenson (1828)
Stephenson (1830 on)
FIGURE 34.2 Evolution of boiler position on early steam trains. (From Russell, C.A. (1998), The developing relations between science, technology and the railways, Proc. Instn. Mech. Engs., 212(F), 201-208. With permission.)
FIGURE 34.3
The steel wheel rolling on a steel rail is the basis of almost all railway systems.
x 2 y2 p = p0 1 − 2 − 2 b a
12
(34.1)
With some additions, the theory is still in use today, and it forms the basis of much current work on the contact mechanics of rail and wheel.
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FIGURE 34.4
Modern Tribology Handbook
Elliptical, Hertzian contact patch.
34.1.2 Wheel/Rail Interface and Axle Loads Since the adoption of steel rather than iron as the material of choice for rails, the wheel/rail system has remained virtually unchanged. However, this does not imply that the system is ideal. The wheel/rail contact area is typically the size of a small coin and, commonly, eight such contacts (i.e., eight wheels) support a vehicle weighing from 30 t (lightweight passenger coach) to 140 t and more (heavy freight). The material in and around the contact area is therefore highly stressed. High rates of wear might be expected for such a contact but, in addition, because the load is applied and removed many times during the passage of each train, there is the possibility of fatigue of the rail surface. Further details of these loads and their effects on steel rails and wheels are discussed below. The ideal material, which does not wear or suffer fatigue and yet is economically viable as a rail or wheel material, has not yet been found. The axle-load examples given refer to the static loads applied in the contact patch area when a train is stationary. Dynamic loads (e.g., at rail-joints or in turnouts [points]) are much higher, with vertical accelerations reaching values of 100 g (1000 m/s2). This is a consequence of the high stiffness of the wheel/rail interface. Well-designed primary suspensions are essential to minimize the impact of these loads on track life and wheel life. Heavy freight trains are generally limited to 60 to 90 km/hr, the top speed being determined by gradients, aerodynamic considerations, and the capability of rolling stock. On high-speed passenger routes such as the French LGV (ligne grande vitesse or high-speed line), axle loads are limited to 15 t, a constraint necessary because of the much higher dynamic forces at 300 km/hr.
34.1.3 Axle Load Increases The requirement for efficiency dictates the use of ever-greater axle loads. In Europe, axle loads of freight vehicles were limited for many years to 18 t, but have now been standardized to 22.5 t by UIC.* In America, 30 t has been common for many years and moves are afoot in Sweden to increase the axleloads on the iron ore railway from Kiruna to Narvik from 25 t to 30 t. Also, on standard gauge, BHP Iron Ore (formerly Mount Newman Mining) in the Pilbara region of Australia, operates ore trains of 36,000 t, formed of 240 wagons with an axle load of 37.5 t. These are powered by two diesel locomotives *Union Internationale des Chemins de Fer, the international standard-setting body for the railways based in Paris, France.
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at the front and two at the rear, with a combined rating of 13,000 kW. Queensland Railways in Australia operates trains of similar size over hundreds of kilometers in their coal corridors, albeit on 1067-mm gauge track.
34.2 Wheel/Rail Contact Steel wheels rolling on steel rails is the principal characteristic that distinguishes railways from other forms of transport (Figure 34.3). Wheel and rail meet at a contact patch that is small (typically about 100 mm2) and carries the full wheel load through which all steering, traction, and braking forces are transmitted. This contact patch sees a severe working environment. Stresses normal to the plane of contact can reach values several times the wheel or rail tensile strength, and sometimes shear stresses in the plane of contact can exceed the shear yield stress. Rapid temperature rises, caused by relative slip between the wheel and rail, can reach several hundred degrees Celsius in routine operation, and over 1000°C in extreme circumstances. These stress and temperature conditions inevitably lead to wear, deformation, and damage to the wheels and rails; and a major goal of railroads is to arrange service conditions and maintenance procedures to minimize deterioration and hence extend component life. This is important because rails — and to a lesser extent wheels — constitute a large part of a railroad’s asset base. For example, there are about 1.4 million freight vehicles and some 25,000 locomotives in service in North America, which give a total population of about 13 million wheels. North American railroads also own over 170,000 miles of track, which equates to about 35 million tons of steel rail. Railways have more money invested in rail than in any other asset, excepting land and perhaps bridges. Extending the life of these components, and especially that of the rail, has a major impact on railroad profitability. An understanding of the tribology of the wheel/rail system is essential if wheel/rail life is to be extended. This system is complex, and its behavior depends on interactions between the materials (wheel, rail, and any third body introduced, such as lubricant/debris mixtures) and the stress-temperature environment (among other things, a function of vehicle weight, vehicle/track interaction, wheel/rail profiles, wheel/rail adhesion, and speed).
34.2.1 Wheel/Rail Materials The resistance of a train to rolling has several components, including grade and acceleration resistance, aerodynamic and wind drag, bearing resistance, and wheel/rail contact resistance. Only this last resistance is influenced by the choice of wheel and rail materials. Several factors contribute to wheel/rail contact resistance (Castelli, 1996). First, during rolling, the wheel and rail surfaces are elastically deflected such that relative motion can occur. Second, energy can be dissipated by plastic deformation. Third, surface adhesion phenomena can dissipate energy. To a first approximation, contact resistance is proportional to the length of the contact patch and, hence, resistance is minimized if, for a given geometry, the contact area is kept small by choosing materials with a high elastic modulus. Of the common and inexpensive metals, steel has one of the highest values of elastic modulus. For this reason — and because steel is relatively inexpensive and offers a very attractive combination of strength, ductility, and wear resistance — almost all wheels and rails worldwide are made from plain carbon-manganese pearlitic steel, which has a lamellar structure of iron and iron carbide. Table 34.1 illustrates typical wheel and rail chemistries and hardness values. In general, passenger vehicle wheels tend to have lower carbon content and hardness than heavy axle load freight vehicles. Steel of about 300 Brinell hardness is typically used for rail in straight track, while rail in the hardness range 340 to 390 Brinell tends to be used for curved track where the stress environment is more severe. Although numerous studies have examined the use of higher hardness materials, such as bainitic and martensitic steels, for wheel and rail materials (Clayton and Devanathan, 1992; De Boer et al., 1995; Hårkonen, 1985), few materials can compete on wear resistance with pearlitic steel, first used for wheels and rails last century.
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TABLE 34.1 and Rails
Typical Chemistries and Hardnesses of Freight and Passenger Wheels
Rails Passenger wheels Freight wheels
Standard Hardened Standard Hardened Standard Hardened
C (wt%)
Mn (wt%)
S (wt%)
P (wt%)
Hardness (Brinell)
0.75 0.75 0.50 0.55 0.62 0.72
0.90 0.90 0.80 0.80 0.72 0.72
0.02 0.02 0.04 max 0.04 max 0.05 max 0.05 max
0.02 0.02 0.04 max 0.04 max 0.05 max 0.05 max
290 370 260 270 300 340
34.2.2 Forces at the Contact Patch Within the wheel/rail contact patch, a force exists normal to the plane of the contact, mainly due to the load (weight) of the wheel on the rail. In addition, tractions are produced in the plane of contact by the vehicle steering forces (see below). This force system produces complex hydrostatic and shear stresses in the rail and wheel (Johnson, 1985). Of most interest is the compressive contact stress normal to the plane of contact, which has a generally elliptical distribution and affects both wheel/rail wear and rolling contact fatigue (see Section 34.2.6). The maximum value of the contact stress p0, occurs at the center of the ellipse, and is given by (Johnson, 1985):
6 PE *2 p0 = 3 2 π Re
13
[F (R′ R′′)]
−2 3
(34.2)
where P is the normal load, E * depends on the wheel and rail elastic moduli, F(R′/R″) is a function of the wheel and rail radii of curvature, and Re is the equivalent relative curvature of the wheel/rail system, defined as Re = (R′R″)1/2. Although studies of vehicles with independently rotating wheels have been made (Elkins, 1988), the solid axle with fixed coned (or nearly coned) wheels operating on inclined rails is used almost exclusively on main line railway vehicles worldwide (Figure 34.5). With this arrangement, each wheelset (axle plus two wheels) is effectively self-steering through the action of forces produced in the contact patches.
Left
R RL
Right
R RR
FIGURE 34.5 Self-steering is provided by the use of fixed coned wheels on solid axles. In this example, when the wheelset is offset to the left, the left wheel effective rolling radius increases (to RL), and the right wheel radius decreases (to RR), enabling the wheelset to steer back to a central position. The angles of the rails and the wheel shapes are exaggerated for clarity.
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Computer models are available to predict the steering forces, which depend on vehicle and track characteristics as well as the detailed wheel and rail profile shapes (Wilson et al., 1995). However, the theory behind the models is complex and cannot be described here. An understanding of how these contact patch forces arise can be gained by considering the difference in rolling radius between the left and right wheels of Figure 34.5. With the wheelset centered on straight track, if the left and right wheel rolling radii are equal (R), the wheelset can roll normally. However, if the wheelset is shifted laterally to the left, the left wheel rolling radius increases to RL while the right wheel radius decreases to RR . Because the two wheels must rotate at the same angular velocity, this difference in rolling radius produces longitudinal micro-slip (termed creep) between the wheels and rails which, in turn, leads to a longitudinal force on each wheel to steer the wheelset back to the center of the track. In a similar manner, lateral forces are produced on each wheel if the wheelset runs at an angle to the track. Equal and opposite forces are produced on the rails. Creep is a natural consequence of having fixed wheels on a solid axle, and is defined with respect to the forward and lateral wheel and rail velocities:
V F − VWF Longitudinal creep s x = 2 RF F VR + VW
(34.3)
V L −V L W Lateral creep s y = 2 RF F VR + VW
(34.4)
( )
( )
where V refers to velocity; subscripts R and W refer to the wheel and rail, respectively; and superscripts F and L refer to the forward and lateral directions. There is a further type of creep, known as spin creep, that is caused by a relative rotation of the wheel and rail around an axis normal to the plane of contact. This type of creep (Equation 34.5) is also implicated in wheel and rail damage.
Ω − ΩW Spin creep ω z = 2 RF F VR + VW
( )
(34.5)
In general, a wheelset will always be moving laterally with respect to the rail (producing lateral creep at each contact patch), and each wheel will not be moving at the forward speed of the vehicle (thereby producing longitudinal creep at each contact patch). All three types of creep will usually be present, although one may dominate. While total creep can increase continually, the steering forces are limited by the available adhesion between the wheels and rails, and this is discussed in detail in Section 34.2.3. Thus, the steering force on a wheel saturates at a value equal to the wheel load times the adhesion coefficient. This saturation occurs at a resultant creep of about 0.01. Relationships between these three types of creep and the resultant forces and moments have been derived by Kalker (1979). The steering forces caused by creep lead to surface and near-surface shear stresses that produce deformation in the contact patch. This deformation increases rolling resistance, and, more importantly, contributes to increased wear and rolling contact fatigue.
34.2.3 Adhesion In railway systems, the force acting at the wheel/rail contact, in the direction of the vehicle’s velocity, is called traction force or brake force. Variation of the traction coefficient, defined as traction force divided by vertical (normal) load, with slip (creep) ratio is shown in Figure 34.6 (Tevaarwerk, 1982). The results shown in this figure are based on work of Johnson and co-workers (Johnson and Roberts, 1974; Johnson and Tevaarwerk, 1977; Johnson and Cameron, 1967) and Tevaarwerk (1982), who have summarized the
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Modern Tribology Handbook
REGION-C REGION-B REGION-A
THERMAL
NONLINEAR
LINEAR
SLIDE ROLL RATIO DU/U
FIGURE 34.6 Typical traction/slip curve. (From Tevaarwerk, J.L. (1982), Traction in lubricated contacts, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 121-132. With permission.)
general characteristics of the traction curve. There are three regions identified on the curve and the behavior in each of these regions can best be described by the Deborah (De) number. This number is the ratio of the relaxation time, for a simple Maxwell viscoelastic model, to the mean transit time. 1. The linear low slip region, thought to be isothermal in nature, is caused by the shearing of a linear viscous fluid (low De) or linear elastic solid (high De); see Johnson and Cameron (1967). 2. The nonlinear region is still isothermal in nature but now the viscous element responds nonlinearly. For low De, this portion of the traction curve can be described by a suitable nonlinear viscous function alone. For high De, a linear elastic element interacts with the nonlinear viscous element, as reported by Johnson and Tevaarwerk (1977). 3. At yet higher values of slip, the traction decreases with increasing slip and it is no longer possible to ignore the dissipative shearing and the heat that it generates in the film. Johnson and Cameron (1967) showed that the shear plane hypothesis advanced by Smith (1965) accounted for most of their experimental observations in this region. More recently, Conry et al. (1979) have shown that a nonlinear viscous element, together with a simple thermal correction, can also describe this region. In railways, the maximum traction coefficient is commonly called the adhesion coefficient. The adhesion coefficient is primarily used to estimate the brake performance of a vehicle and, accordingly, the phenomenon of adhesion between steel wheels and steel rails is a very important tribological issue for improving the performance of the railway as a transportation system. 34.2.3.1 Characteristics of Adhesion and Traction Coefficients under Dry Conditions Ohyama (1987) has shown the relationship between Hertzian pressure and adhesion coefficient to be a function of surface roughness (Figure 34.7). The data vary widely but the tendency of the adhesion coefficient to decrease with increasing Hertzian pressure can be estimated. Generally, under dry conditions, the friction coefficient does not depend on loading force (this is Amontons-Coulomb’s law). However, from results of experiments with carbon steels, Shaw (1960) concluded that, while AmontonsCoulomb’s law covers the case of light loading, at high loading the friction coefficient decreases. Also, a report of the Office for Research and Experiments (ORE, now known as the European Railway Research Institute, ERRI, 1978) described how adhesion coefficients decreased when axle loads increased; however, the influence of surface roughness on the adhesion coefficient, under dry conditions, was not so significant. Krause and Poll (1982) demonstrated a relationship between the initial gradients of dsx /dfx (where sx is the longitudinal creepage and fx is the longitudinal traction coefficient), the mean roughness Rz , and a parameter Rp /Rz (the ratio of the maximum smoothing depth to the mean roughness, Figure 34.8).
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0.4
f max
0.3
0.2 320- #320 240- #240 #320- #180 #
V= 200 km/h
#
0.1
0 0
100
200
300
400
500
600
700
Pmax
MPa
800
900
FIGURE 34.7 Relationship between adhesion and maximum Hertzian pressure. (From Ohyama, T. (1987), Study on influence of contact condition between wheel and rail on adhesion force and improvement at higher speeds, RTRI Rep., 1(2). With permission.)
0.48
6.10-3
0.27
0.39
0.20
0.23
0.18 4.10-3
Rp Rz
dsx
= 0.33
0.12
dfx 2.10-3
0
6
12
18 R
z
24
30
36
[µm]
FIGURE 34.8 Dependency of the initial gradients of dsx/dfx on the mean roughness Rz, parameter Rp/Rz, test rig I (type Bugarcic). (From Krause, H. and Poll, G. (1982), The influence of real material and system properties on the traction/creep relationships in rolling contact, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 353-372. With permission.)
With greater values of Rz , there is a tendency for a particular value of friction force at higher creepage. This is in agreement with Ohyama (1987). 34.2.3.2 Adhesion and/or Traction Coefficients with Water Lubrication Experimental measurements of the adhesion coefficient for the Shinkansen lines (the Japanese bullet train) with water lubrication are shown in Figure 34.9 (Ohyama, 1991). The measured values are very scattered, some of them smaller than the values used for vehicle component design. Because the railway system is open to the atmosphere, there are a variety of factors that might account for this scatter. These include temperature variation and the source of the water (i.e., rain, snow, and ice). Variation in the quantity of water falling on the rail during rain may also affect the results because experience shows that
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0.14 Net condition
Adhesion coefficient
f
max
Series - 200
0.12 0.10 0.08 Planned Value f
max =
13.6
V +85
0.06 0.04 0.02 0
0
20
40
60
80 100 120 140 160 180 200 220 240 260 280 Speed V (km/h)
FIGURE 34.9 Adhesion coefficient measured on Shinkansen under wet conditions. (From Ohyama, T. (1991), Tribological studies on adhesion phenomena between wheel and rail at high speeds, Wear, 144, 263-275. With permission.)
light rain is an excellent lubricant, whereas heavy rain can clean the rails sufficiently for steel-to-steel contact to develop, leading to high levels of adhesion. However, the general trend of the data indicates that the adhesion coefficient decreases as the train speed increases (up to 270 km/hr). The wide spread of these field-test measurements agrees with the laboratory-based experimental results of Ohyama and Maruyama (1982) and Krause and Poll (1982). The relationship between adhesion coefficient and rolling speed, including the effect of differing surface roughnesses and Hertzian contact pressures, was investigated by Ohyama and Maruyama (1982) (Figure 34.10). As for the field measurements discussed above, the adhesion coefficient was found to decrease appreciably with an increase in rolling speed. Surface roughness has a significant influence on the adhesion coefficient, with smoother surfaces giving lower adhesion coefficients at a given Hertzian pressure. In addition: the higher the Hertzian pressure, the larger the adhesion coefficient, based on a given surface roughness (except for the case of #80; Figure 34.10). This suggests that relatively rough surfaces do not have a large influence on the adhesion coefficient for cases of large Hertzian pressure, perhaps because asperities at the surface are heavily deformed. Ohyama (1987) examined the relationship between the mean surface roughness and the adhesion coefficient for a rolling speed of 200 km/hr and Hertzian pressures of 588 MPa and 784 MPa (Figure 34.11). The data show some variation but, by rough estimation, the adhesion coefficient increases with an increase in Rz . This means that the heights of asperities and the number of asperities may have a significant effect on the traction and/or adhesion coefficients. More recently, Ohyama has focused on EHL (elastohydrodynamic lubrication) theory, investigating Johnson’s EHL regime (Johnson, 1970) and studying the application of EHL theory to water lubrication between wheel and rail. Using EHL theory, Chen et al. (1998) have examined the effects of rolling speed and pressure on water film thickness as a function of water temperature (Figures 34.12 and 34.13). For a Hertzian pressure of 800 MPa, water film thickness increases with an increase in rolling speed and with a decrease in water temperature. For a rolling speed of 300 km/hr, water film thickness increases with a decrease in Hertzian pressure as well as with a decrease in water temperature. Indeed, the water temperature has a significant effect on the water film thickness. A comparison of adhesion coefficients obtained from field tests on revenue railway lines with the results of numerical calculation is shown in Figure 34.14. The numerical calculation, using basic EHL theory, can predict (approximately) the adhesion coefficients
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0.20
f max Maximum traction coefficient
A B C D E F
G
0.15
# 600 # 600 # 320 # 320 # 80 # 80
G DIA.
490 MPa 785 MPa 490 MPa 785 MPa 490 MPa 785 MPa 490MPa
E F
0.10
D A
B C
0.05
0
0
50
0
100 20
30
150 40
200 50
300 (km/h)
250
60
70
80 (m/s)
Rolling speed FIGURE 34.10 Relationship between maximum traction coefficient and rolling speed with varied surface roughness and Hertzian pressure under water lubrication. (From Ohyama, T. and Maruyama, H. (1982), Traction and slip at higher rolling speeds: some experiments under dry friction and water lubrication, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 395-418. With permission.) V= 200km/h
f max
0.2
0.1
: 588MPa : 784MPa
0
0
1.0
2.0
3.0
4.0
Rz
(µm)
FIGURE 34.11 Relationship between Rz and adhesion coefficient. (From Ohyama, T. (1987), Study on influence of contact condition between wheel and rail on adhesion force and improvement at higher speeds, RTRI Rep., 1(2). With permission.)
for water lubrication. The mechanism by which the adhesion coefficient decreases with an increase in rolling speed can be explained as an increase of water film thickness leading to a decrease in real contact area (i.e., the number of asperities making contact and supporting load decreases). 34.2.3.3 Influence of Contaminants on the Traction and Adhesion Coefficients In practice, the wheel/rail contact is exposed to significant contamination, not just the wet conditions described above. Tevaarwerk (1982) calculated example theoretical traction curves based on the method of Johnson and co-workers. Figure 34.15 shows typical theoretical curves for a low-viscosity mineral oil.
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FIGURE 34.12 Effects of rolling speed and temperature on water film thickness. (From Chen, H., Yoshimura, A., and Ohyama, T. (1998), Numerical analysis for the influence of water film on adhesion between rail and wheel, Proc. Inst. Mech. Engs., 212 (Part J), 359-368. With permission.)
FIGURE 34.13 Effects of pressure and temperature on water film thickness. (From Chen, H., Yoshimura, A., and Ohyama, T. (1998), Numerical analysis for the influence of water film on adhesion between rail and wheel, Proc. Inst. Mech. Engs., 212 (Part J), 359-368. With permission.)
Figure 34.16 shows theoretical traction curves for the same data and oil as used in Figure 34.15, but with the addition of 3% spin. By comparison of the two figures, the effects of rolling speed and spin on the adhesion coefficient and the initial gradient of the traction curve can be seen to be significant. Through rolling experiments with various materials, Bugarcic and Lipinsky (1982) focused on the influence of the complex reaction in the physicochemical boundary layer and obtained the variation of the adhesion coefficient with respect to relative humidity. Figure 34.17 shows the variation of the adhesion coefficient in clean air with 200 ppm SO2. At higher humidity levels, titanium alloy resulted in an improved adhesion coefficient in rolling experiments with various materials. This interesting effect was a result of reactions between the metallic surface, H2O, and SO2, accompanied by hydrogen embrittlement and hardening. Ohyama (1987) examined the effect of Hertzian pressure on the adhesion coefficient, for varying creepage, using paraffin lubrication (Figure 34.18). For a rolling speed of 200 km/hr, the initial gradient of the traction curve increases with an increase of Hertzian pressure, up to 0.15% creepage. Also, Krause and Poll (1982) examined the relationship between traction coefficient and creepage for various
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FIGURE 34.14 Adhesion coefficients obtained by the field tests and numerical calculation, where the calculating conditions are: load per unit length = 4.5 MN/m, temperature of water = 15 Fi, friction coefficient of asperity contact = 0.14. (From Bugarcic, H. and Lipinsky, K. (1982), Mechanical and tribological research on two newly developed rolling friction test rigs at the Technical University of Berlin, Germany, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 445-462. With permission.)
FIGURE 34.15 Typical theoretical traction curve. (From Tevaarwerk, J.L. (1982), Traction in lubricated contacts, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 121-132. With permission.)
contaminants on the running surface (Figure 34.19). The gradient dsx /dfx increases with increasing solid content of the contaminant. The solid interface media have the primary effect of a reduction in the real contact area (compared to the Hertzian area) but, depending on the rheological properties of the powders or solid contaminants, the decrease in the initial gradient of the traction curve can be significant. Ohyama (1987) summarized the effects of Hertzian pressure under dry conditions; and the effects of surface roughness, rolling speed, and contamination of the running surface, with water lubrication. The decrease in traction and/or adhesion coefficients could be explained as an effect of contact rigidity in each case. 34.2.3.4 Locomotive Adhesion Control For non-powered passenger vehicles and freight cars, traction forces between wheel and rail need be no higher than those required to ensure that the vehicles steer adequately on straight and curved track. Indeed, to reduce wear, it is generally arranged, either through lubrication or the use of improved suspension bogies, to minimize wheel/rail adhesion to a level that provides satisfactory vehicle steering.
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FIGURE 34.16 Slip ratio as a function of aspect ratio and slip/spin ratio. (From Tevaarwerk, J.L. (1982), Traction in lubricated contacts, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 121-132. With permission.)
FIGURE 34.17
The variation of adhesion coefficient.
However, good adhesion performance is still required for braking purposes and compromises between low friction running and good braking performance are therefore unavoidable. The situation is different for locomotives, in that high adhesion is required for the high tractive effort, either to pull the train away from a standstill or to maintain high speeds. The maximum tractive effort a locomotive can supply is limited by the product of locomotive weight and wheel/rail adhesion. High levels of locomotive adhesion are essential on heavy-haul railroads, where locomotives are often used that consist of up to five units to haul total train weights in excess of 10,000 t. A more detailed description of modern diesel electric traction arrangements can be found in Section 34.3.3.3, which also includes a comparison between DC and AC traction.
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ρmax : 784 MPa
0.04
0.03
637 MPa 0.02 490 MPa
0.01
P 350 V : 200 km/h (55.6 m/s) 0
0
0.05
0.10
ξ
0.15 %
FIGURE 34.18 Relationship between slip ratio and traction coefficient in micro-slip region. (From Ohyama, T. (1987), Study on influence of contact condition between wheel and rail on adhesion force and improvement at higher speeds, RTRI Rep., 1(2). With permission.)
60 F
R
x [N] 40
20
x
x x - 0.08
- 0.04
0.04
x
0.08
0.12
0.16
sx [%]
0.2
x
-20
FIGURE 34.19 Relationship between longitudinal friction force FRx and longitudinal creep sx for various contaminants on the running surfaces, test rig I (type Bugarcic). (From Krause, H. and Poll, G. (1982), The influence of real material and system properties on the traction/creep relationships in rolling contact, Proc. Contact Mechanics and Wear of Rail/Wheel Systems, University of Waterloo Press, 353-372. With permission.)
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FIGURE 34.20 The increase in maximum locomotive adhesion demand with time, and the increased adhesion produced by AC traction technology. (From Iden, M.E. (1998), The AC traction revolution: putting rail-wheel adhesion to work, presented to ARM Rail/Wheel Interface Seminar: Crosstalk 1998, Session 13, Chicago. With permission.)
34.2.3.4.1 Increased Adhesion Through Creep Control The enhanced wheel slip control offered by modern DC and AC drive locomotives can be used to increase tractive effort through better control of wheel/rail adhesion. Figure 34.20 illustrates how maximum locomotive adhesion demand (locomotive tractive effort divided by weight) has risen over the past 50 years in North America, and how it is estimated to increase in the near future. Throughout most of the 1950s and 1960s, locomotives were designed to operate at a maximum adhesion of less than 0.2, an easily satisfied demand. During the 1970s and 1980s, the required adhesion levels rose to approximately 0.3, achieved with conventional DC traction systems. A step change in the exploitation of available adhesion arrived in North America with the general introduction of high-horsepower AC traction locomotives, which are currently using adhesion in the range 0.35 to 0.40 and are likely to reach 0.45. These high values of adhesion are achieved predominantly at low speed (substantially less than 15 km/hr), by the use of what is termed “creep control.” That is, the motors are used to run the wheels at a peripheral speed up to 25% greater than the forward speed of the vehicle. This high degree of rolling/sliding motion of the wheel scrubs the wheel/rail interface, promoting steel-on-steel contact and thus high adhesion. The long-term effect of high adhesion locomotives on wheel and rail performance is not yet known, but it is likely that wear and rolling contact fatigue damage will increase. As already noted, wheel and rail wear are both related to the energy dissipated in the contact patch, which is the product of traction force and creepage. High adhesion locomotives increase both force and creepage, and hence can be expected to increase wear. A greater problem may be increased rolling contact fatigue, manifested as cracks, spalls, and shells on the rail surface (see Section 34.2.6). An increase in adhesion leads to an increase in the shear forces that produce ratcheting of the surface layers of the rail, leading to an increase in surface cracks. An additional factor is that, as shown in Figure 34.21, shakedown limits decrease with increased traction coefficient. Thus, a given level of contact stress is more damaging at high traction coefficients than at low coefficients. 34.2.3.4.2 Thermal Damage with High Adhesion Locomotives A final problem is that of thermal damage to the wheel and rail surface layers. Although wear is related to the energy dissipated in the contact patch, most of the energy is dissipated as frictional heating. Tanvir (1980), for example, has produced explicit equations describing the temperature rise in a rail as a function of, among other things, contact stress and creep, as have Knothe and Liebelt (1995). Equation 34.6 (Tanvir, 1980) predicts rail temperature rise (∆T) for the case when the wheel is moving faster than the rail:
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Ratchetting Load
Plastic shakedown limit
(a )
FIGURE 34.21
(b)
stici ty
aked Elas tic sh
Elast ic
Elastic limit
Cyc lic p la
own
Elastic shakedown limit
Deflexion
Ratchetting threshold (c)
( d)
Response of material to repeated (cyclic) loading.
2.203 p0µ aαV ∆T = ⋅ π K
12
v 1 2 ⋅ 1 + s − 1 V
(34.6)
(p0 is the maximum contact stress, µ is the maximum adhesion demanded, a is the contact semi-length, V is the forward speed of the vehicle, vS is the slip speed, K is thermal conductivity, and α is thermal diffusivity.) Assuming typical values for the thermal constants, a contact stress of 2000 MPa, a creep of 0.2 (20%), a contact semi-length of 8 mm, an adhesion of 0.4, and a forward vehicle speed of 10 mph, the maximum predicted rail temperature rise is approximately 1500°C. This is a flash temperature, and heating and cooling are very rapid, leading to non-equilibrium transformation kinetics (Archard and Rowntree, 1988). The kinetics are also affected by the high hydrostatic pressures in the contact patch. However, such high temperatures may increase the production of the hard and brittle “white phase” that is seen to form on the surface of rails and has been seen to contribute to spalls in rails. It is clear that combinations of high contact stress and high creep lead to potentially high levels of frictional heating, possibly sufficient to cause thermal transformations of the wheel and rail surfaces. It is likely, therefore, that high adhesion AC (and some DC) locomotives will cause increased wear and fatigue damage to the wheel and rail, although, in mitigation, increased rail wear and damage will occur primarily in areas where high tractive effort is applied, for example, where trains pull away from standing and on steep grades. AC locomotives also generate higher dynamic braking effort, and wear and damage will thus also increase in areas where dynamic braking is continuously employed. However, this is also mostly a low-speed phenomenon because the available levels of dynamic braking are relatively low at higher speeds. The operational advantages of high adhesion AC locomotives are such that there is likely to be continuous business demand to increase adhesion, at least for the heavy-haul freight environment. Much work needs to be done in this area, and it is the job of the tribologist to understand and quantify the likely scale of damage, and to seek ways to mitigate the damage. 34.2.3.5 Improving Adhesion for Traction and Braking Rain, snow, ice, and leaf mulch on the rails often reduce adhesion levels below acceptable limits for safe braking and reliable acceleration. Sliding during braking leads to longer brake distances and wheel-flats, while high levels of wheel-slip during acceleration can lead to localized abrasion of the rail surface with increased risk of rail breaks. Rail surfaces are therefore cleaned with mechanical scrubbers, water jets, and high-pressure air, and some railway administrations routinely apply adhesion-enhancing substances
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such as Sandite in the U.K., during the leaf-fall season. Other railroad operators rely on substantial sanding for braking and small applications of sand to enhance adhesion during acceleration. The composition of the sand must be monitored closely if it is not to cause damage to the wheel and rail surfaces. Light rail operations frequently rely on magnetic track brakes to guarantee stopping under adverse rail surface conditions. These devices are pressed against the rail surface using a permanent magnet or an electromagnet, and rely on cast iron rubbing blocks to achieve high levels of friction.
34.2.4 Repeated Contact — Plasticity, Shakedown, and Ratcheting Wheels and rails are subjected to large numbers of repeated contacts. For example, a wheel on a passenger coach can travel 200,000 miles per year, equivalent to about 100 million revolutions. Although these contacts are scattered across the width of the wheel tread, a small area on the wheel is still likely to see more than 10 million contacts per year. This repeated rolling or sliding contact stresses the material cyclically, and it responds in one of the following four ways, as illustrated in Figure 34.21: 1. Perfectly elastic behavior if the contact pressure does not exceed the elastic limit during any load cycle (Figure 34.21a). 2. Elastic shakedown, in which plastic deformation takes place during the early cycles, but, due to the development of residual stresses and sometimes strain hardening, the steady-state behavior is perfectly elastic (Figure 34.21b). This process is known as shakedown, and the contact pressure below which this is possible is referred to as the elastic shakedown limit. 3. Plastic shakedown, in which the steady state is a closed elastic-plastic loop, but with no net accumulation of plastic deformation. This behavior is sometimes referred to as cyclic plasticity (Figure 34.21c), and the corresponding limit is called the plastic shakedown limit or the ratcheting threshold. 4. Above the ratcheting threshold, the steady state consists of open elastic-plastic loops, and the material accumulates a net unidirectional strain during each cycle, a process known as ratcheting (Figure 34.21d). The rational design criterion for heavily loaded tribological contacts is the avoidance of repeated plasticity and thus, by implication, of accelerating rates of wear and surface degradation. For frictionless sliding of a two-dimensional line contact, the elastic limit is 3.14 k, k being the shear yield stress, and the shakedown limit is 4 k, as shown in Figure 34.22. The load supported is proportional to the square of the maximum contact pressure (Johnson, 1985) and, thus, the use of the shakedown limit as the operation limit would lead to a 60% improvement in allowable loading, or corresponding savings in material and cost. 34.2.4.1 Surface Engineering and Shakedown Shakedown limits are well-established for solids whose properties do not alter with depth. In both wheels and rails, however, work-hardening due to rolling contact produces hardened surface layers which, with increasing depth, soften back to the base hardness. In head-hardened rails, such hardened layers are also produced directly during manufacture to reduce wear. For wheel/rail contact, therefore, it is important to understand the shakedown behavior of layers with varying strength. Most work on the shakedown of layers with variable strength has been done on surface-engineered components, but this work is directly applicable to wheel/rail tribology. Surface engineering, now part of established industrial practice, improves tribological performance, principally by enhancing the hardness (and thus the shear yield strength k) of material at or near the load-bearing surfaces. In some cases (e.g., ion-nitrided BD2 steel), the hardness drops almost linearly from a high value at the surface to a lower value in the core, while in others (e.g., nitrided and tempered En40B), this variation is rather gentler (Child, 1980). Variations in hardness imply corresponding changes in the value of the shear yield stress k. However, diffusion treatments of this sort will not change the elastic constants E and ν. Kapoor and Williams (1994a,b) have investigated the way in which the shakedown limit depends on such variations in the shear yield strength. The model is shown in Figure 34.23,
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5 sub-surface flow
surface and sub-surface flow
load intensity po/k
4
repeated plastic flow elastic shakedown
3
surface flow elastic
2 elastic limit elastic-perfectly plastic shakedown limit
1
kinematic hardening shakedown limit
0 FIGURE 34.22
0.1
0.2
0.3
0.4
0.5
Shakedown limits for line contact.
2a Po P
q
x
shear yield stress
h
1
k1 k2
2 z
z
(a) FIGURE 34.23
(b)
Heat-treated half-space. The case depth is h. The shear yield strength varies linearly with depth.
where the shear yield strength drops linearly from a higher value at the surface to a lower value in the core, over a case depth of h. Figure 34.24 shows the results of the analysis in terms of the shakedown limit ps /k2; that is, the maximum contact pressure normalized by the shear yield stress of the core. These are plotted against the case depth, which has been non-dimensionalized by the contact semi-width (i.e., h/a), for a range of surface to core shear yield stress ratios (i.e., values of k1/k2). Data are shown for two values of the coefficient of sliding friction µ, 0.1 and 0.5, typical of boundary lubricated and dry contact conditions, respectively. When µ = 0.1, increasing the case depth from a value of zero gives no immediate increase in the shakedown limit from its value of 3.65 k2, which is appropriate for a uniform half-space carrying this surface traction. Only if the case depth h is greater than about 0.5a does the shakedown limit start to grow. Increasing
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16
µ = 0.1 µ = 0.5
12
2
4 3 4 2 3 2 1 1
8 4
0
FIGURE 34.24
( kk1 )
0
1
2
3 Case depth (h/a)
4
5
Shakedown limits for line contact on a hardened half-space.
the case depth further results in an almost linear increase in the shakedown limit: this has a maximum value set by the factor k1/k2. For example, if this is equal to 3, then the maximum value of ps /k2 is just under 10, and is achieved when the case thickness h is just over three times the semi-contact width a. Increasing the case depth beyond this critical value will result in no further improvement in the shakedown limit. The initial behavior of the data for µ = 0.1 is readily explicable if it is appreciated that at this value of traction coefficient, the maximum shear stress occurs below the surface: specifically, when µ = 0.1, the maximum occurs at a depth of 0.45a. Increasing the shear yield stress of a surface layer of thickness of less than 0.45a cannot strengthen the critically stressed material, so that there is no increase in the shakedown limit. This is true for all values of the ratio k1/k2. When µ is greater than about 0.3, however, a value where the maximum shear stress occurs at the surface, hardening even a thin layer strengthens the critically stressed material and this increases the shakedown limit. The dotted curve for µ = 0.5 in Figure 34.24 shows an improvement even when the case depth is very small. As with a uniform halfspace, the shakedown limit drops with an increase in the coefficient of sliding friction. This is clear from Figure 34.24, in which the dotted curves for µ = 0.5 are significantly below those corresponding to µ = 0.1. The shakedown limits for a material that undergoes strain hardening have also been estimated for line and elliptical contacts (Jones et al., 1996; Dyson et al., 1999, respectively) (Figure 34.25). An important finding is that the friction coefficient beyond which plastic flow occurs at the surface (where it is most damaging), rather than in the body of the steel, moves from a value of about 1/3 to about 1/2. This happens because strain hardening of the material near the surface raises the shear yield strength of the steel in this region, making it more resistant to plastic flow. The surface friction coefficient, and therefore near-surface stresses within the steel, can therefore rise to a higher level than for a non-strain hardened steel, without yield taking place. Kapoor and co-workers have also analyzed the effect of coatings (Wong and Kapoor, 1996) and coating adhesion (Kapoor and Williams, 1997) on the shakedown limit by incorporating the variations of Young’s modulus and Poisson’s ratio with depth in the analysis. This remains a current area of research. 34.2.4.2 Roughness and Shakedown Limit As well as developing surface layers whose hardness varies with depth, both wheels and rails have surfaces that are not perfectly smooth. Roughness, even at the micro-level, affects the near-surface stresses and strains that affect performance. Kapoor and Johnson (1992) analyzed the effect of repeated sliding on roughness. A soft (elastic-plastic) surface was repeatedly loaded by a sliding harder (elastic) counterface. During the initial contact, some asperities (roughness bumps) experience a contact pressure greater than the shakedown limit. They undergo plastic deformation and their height and shape change; wear also assists in this process. Based on the hypothesis that the shape and height change such that the load is supported elastically (Johnson and Shercliffe, 1992), the new asperity heights were related to the original roughness and load. The changes in a Gaussian roughness distribution are displayed in Figure 34.26.
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FIGURE 34.25 (solid line).
Shakedown limits for a line contact: perfectly plastic material (dashed line) strain hardening material
(R1C/σ)
