Contact Mechanics and Friction: Physical Principles and Applications

396 Pages·2017·14.72 MB·English

by  Valentin L. Popov (auth.)

Valentin L. Popov
Contact Mechanics
and Friction
Physical Principles
and Applications
Second Edition
123
Contact Mechanics and Friction
Valentin L. Popov
Contact Mechanics
and Friction
Physical Principles and Applications
Second Edition
Valentin L. Popov
TU Berlin Inst. Mechanik
Berlin, Germany

ISBN 978-3-662-53080-1 ISBN 978-3-662-53081-8 (eBook)
DOI 10.1007/978-3-662-53081-8

Library of Congress Control Number: 2017933487

© Springer-Verlag GmbH Germany 2010, 2017
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or
information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar
methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, 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.
The publisher, the authors and the editors are safe to assume that the advice and information in this
book are believed to be true and accurate at the date of publication. Neither the publisher nor the
authors or the editors give a warranty, express or implied, with respect to the material contained herein
or for any errors or omissions that may have been made. The publisher remains neutral with regard to
jurisdictional claims in published maps and institutional affiliations.

Printed on acid-free paper

This Springer imprint is published by Springer Nature
The registered company is Springer-Verlag GmbH Germany
The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany
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.

v
Preface to the Second English Edition

The second English edition of “Contact Mechanics and Friction” was substantially
revised compared to the 1st edition. This is especially related to the chapters on
“contact mechanics” (normal contact with and without adhesion, tangential con-
tact, and contact with elastomers), which were supplemented with many solutions
for axially-symmetric contact problems. The chapter on “wear” now includes a
discussion on fretting. The section of elasto-hydrodynamic lubrication was com-
pletely rewritten and enriched by several problems. Furthermore, the chapter on
numerical simulation methods in contact mechanics has been overhauled and now
contains the basic ideas of the application of the boundary element method to ad-
hesive contacts.
I would like to thank M. Hess and R. Pohrt for their help in writing new sec-
tions and problems. Also, thanks go to M. Hess and M. Popov for their corrections
of this book, Ms. Wallendorf for drawing new figures, and Dr. J. Starcevic for ex-
tensive support in the completion of the book.

Berlin, September 2016 V.L. Popov

vii
From the Preface to the First English Edition

The English edition of “Contact Mechanics and Friction” ....... 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 earthquake re-
search. 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

ix
Preface to the First 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.
xi
xii Preface to the First 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 ................................................. 27
3.1 Physical Background ................................................................................. 28
3.2 Calculation of the Adhesive Force between Curved Surfaces ................... 32
3.3 Qualitative Estimation of the Adhesive Force between Elastic Bodies ..... 33
3.4 Influence of Roughness on Adhesion ........................................................ 35
3.5 Adhesive Tape ........................................................................................... 36
3.6 Supplementary Information about van der Waals Forces and Surface
Energies ........................................................................................................... 37
Problems .......................................................................................................... 38
4 Capillary Forces ............................................................................................... 43
4.1 Surface Tension and Contact Angles ......................................................... 43
4.2 Hysteresis of Contact Angles ..................................................................... 47
4.3 Pressure and the Radius of Curvature ........................................................ 47
4.4 Capillary Bridges ....................................................................................... 48
4.5 Capillary Force between a Rigid Plane and a Rigid Sphere ...................... 49
4.6 Liquids on Rough Surfaces ........................................................................ 50
4.7 Capillary Forces and Tribology ................................................................. 51
Problems .......................................................................................................... 52
5 Rigorous Treatment of Contact Problems – Hertzian Contact .................... 57
5.1 Deformation of an Elastic Half-Space being Acted upon by Surface Forces.58
5.2 Hertzian Contact Theory ............................................................................ 61
5.3 Contact between Two Elastic Bodies with Curved Surfaces ..................... 62
5.4 Contact between a Rigid Cone-Shaped Indenter and an Elastic Half-Space..65
xiii