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Contact Mechanics and Friction Contact Mechanics and Friction Valentin L. Popov Contact Mechanics and Friction Physical Principles and Applications 1 3 Professor Dr. Valentin L. Popov Berlin University of Technology Institute of Mechanics Strasse des 17.Juni 135 10623 Berlin Germany [email protected] ISBN 978-3-642-10802-0 e-ISBN 978-3-642-10803-7 DOI 10.1007/978-3-642-10803-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010921669 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Dr. Valentin L. Popov studied physics and obtained his doctorate from the Moscow State Lomonosow University. He worked at the Institute of Strength Physics and Materials Science of the Russian Academy of Sciences. After a guest-professorship in the field of theoretical physics at the University of Paderborn, he has headed the department of System Dynamics and Friction Physics in the Institute of Mechanics at the Ber- lin University of Technology since 2002. His areas of interest, among others, in- clude tribology, nanotribology, tribology at low temperatures, biotribology, the in- fluence of friction through ultrasound, numerical simulation of frictional processes, research regarding earthquakes, as well as themes relating to materials sciences such as the mechanics of elastoplastic media with microstructure, strength of metals and alloys, and shape memory alloys. He is the joint editor of international journals and regularly organizes international conferences and work- shops over diverse tribological themes. Preface to the English Edition The English edition of “Contact Mechanics and Friction” lying before you is, for the most part, the text of the 1st German edition (Springer Publishing, 2009). The book was expanded by the addition of a chapter on frictional problems in earth- quake research. Additionally, Chapter 15 was supplemented by a section on elasto-hydrodynamics. The problem sections of several chapters were enriched by the addition of new examples. This book would not have been possible without the active support of J. Gray, who translated it from the German edition. I would like to thank Prof. G. G. Ko- charyan and Prof. S. Sobolev for discussions and critical comments on the chapter over earthquake dynamics. Dr. R. Heise made significant contributions to the de- velopment and correction of new problems. I would like to convey my affection- ate thanks to Dr. J. Starcevic for her complete support during the composition of this book. I want to thank Ms. Ch. Koll for her patience in creating figures and Dr. R. Heise, M. Popov, M. Heß, S. Kürscher, and B. Grzemba for their help in proof- reading. Berlin, November 2009 V.L. Popov Preface to the German Edition He who wishes to better understand the subject of Contact Mechanics and the Physics of Friction would quickly discover that there is almost no other field that is so interdisciplinary, exciting, and fascinating. It combines knowledge from fields such as the theories of elasticity and plasticity, viscoelasticity, materials sci- ence, fluid mechanics (including both Newtonian and non-Newtonian fluids), thermodynamics, electrodynamics, system dynamics, and many others. Contact Mechanics and the Physics of Friction have numerous applications ranging from measurement and system technologies on a nanoscale to the understanding of earthquakes and including the sheer overwhelming subject of industrial tribology. One who has studied and understands Contact Mechanics and the Physics of Fric- tion will have acquired a complete overview of the different methods that are used in the engineering sciences. One goal of this book is to collect and clearly present, in one work, the most important aspects of this subject and how they relate to each other. Included in these aspects is, first, the entirety of traditional Contact Mechanics including ad- hesion and capillarity, then the theory of friction on a macro scale, lubrication, the foundations of modern nanotribology, system dynamical aspects of machines with friction (friction induced vibrations), friction related to elastomers, and wear. The interplay between these aspects can be very complicated in particular cases. In practical problems, different aspects are always presented in new ways. There is no simple recipe to solve tribological problems. The only universal recipe is that one must first understand the system from a tribological point of view. A goal of this book is to convey this understanding. It is the solid belief of the author that the essential aspects of mechanical con- tacts and friction are often much easier than they appear. If one limits oneself to qualitative estimations, it is then possible to achieve an extensive qualitative un- derstanding of the countless facets of mechanical contacts and friction. Therefore, qualitative estimations are highly valued in this book. In analytical calculations, we limit ourselves to a few classical examples which we can then take as building blocks and apply them to understand and solve a wealth of problems with real applications. A large number of concrete tribological questions, especially if they deal with meticulous optimization of tribological systems, are not solvable in analytical form. This book also offers an overview of methods of Numerical Simulation for Contact Mechanics and Friction. One such method is then explained in detail, which permits a synthesis of several processes related to contact mechanics from different spatial ranges within a single model. Even though this book is primarily a textbook, it can also serve as a reference for the foundations of this field. Many special cases are presented alongside the theoretical fundamentals with this goal in mind. These cases are presented as ex- ercises in their respective chapters. The solutions are provided for every exercise along with a short explanation and results. x Preface to the German Edition The basis of this textbook originates and is drafted from lectures that the author has conducted over Contact Mechanics and the Physics of Friction at the Berlin University of Technology, so that the material can be completed in its entirety in one or two semesters depending on the depth in which it is visited. Thanks This book would not have been possible without the active support of my col- leagues. Several in the department of “System Dynamics and Frictional Physics,” from the Institute for Mechanics, have contributed to the development of the prac- tice exercises. For this, I thank Dr. M. Schargott, Dr. T. Geike, Mr. M. Hess, and Dr. J. Starcevic. I would like to express a heartfelt thanks to Dr. J. Starcevic for her complete support during the writing of this book as well as to Mr. M. Hess, who checked all of the equations and corrected the many errors. I thank Ms. Ch. Koll for her patience constructing figures as well as M. Popov and Dr. G. Putzar for their help with proofreading. I thank the Dean of Faculty V, Transportation and Machine Systems, for granting me a research semester, during which this book was completed. Berlin, October 2008 V.L. Popov Table of Contents 1 Introduction ........................................................................................................1 1.1 Contact and Friction Phenomena and their Applications.............................1 1.2 History of Contact Mechanics and the Physics of Friction..........................3 1.3 Structure of the Book...................................................................................7 2 Qualitative Treatment of Contact Problems – Normal Contact without Adhesion ................................................................................................................9 2.1 Material Properties.....................................................................................10 2.2 Simple Contact Problems ..........................................................................13 2.3 Estimation Method for Contacts with a Three-Dimensional, Elastic Continuum .......................................................................................................16 Problems..........................................................................................................20 3 Qualitative Treatment of Adhesive Contacts.................................................25 3.1 Physical Background .................................................................................26 3.2 Calculation of the Adhesive Force between Curved Surfaces ...................30 3.3 Qualitative Estimation of the Adhesive Force between Elastic Bodies .....31 3.4 Influence of Roughness on Adhesion ........................................................33
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