Contact Mechanics. Johnson , Kenneth Langstreth Johnson. This treatise is concerned with the stresses and deformation of solid bodies in contact with each other, along curved surfaces which touch initially at a point or along a line. Examples are a railway wheel and rail, or a pair of gear wheel teeth.

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This book describes the stresses and deformations of solid bodies in contact with each other, along curved surfaces which touch initially at a point of contact or along a line.

Examples are a railway track and the wheels running on it, or a pair of meshed gear teeth. The book commences with the development o f the theory since t h e problem was first described in Next there is a discussion of the influence of friction and the topographical roughness of surfaces, and this is built into the theory.

Ah important feature of the text is the treatment of plastic and viscoetastic bodies. An appreciable section of the book is on bodies in sliding or rolling contact. The mathematical treatment assumes that users of the book are graduates in engineering; it is a book written by a distinguished engineer for other professionals and their graduate students.

Briscoe, Tribology lnternational. The book is a unique introduction to the subject. Cover design: Jan van de Watering.

ISBN 0- 3. Contact mechanics. The Edinbun.! N;w York. NY Melbourne Cambridge University Press This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements. Printed in Malta by lntcrprilll Limited. A catalogue record for this book is available from the British Library. Library of Congress Cataloguing in Publication data available. ISBN 0 3 paperback. Frame of reference. Relative motion of the surfaces -sliding, rolling and spin.

Forces transmitted at a point of contact. Surface tractions. Examples I involute spur gears. The elastic half-space. Concentrated normal force. Concentrated tangential force. Distributed normal and tangential tractions. Displacements specified in the loaded reg10n. Point loading of an elastic half-space. Potential functions of Boussinesq and Cerruti. Pressure applied to a polygonal region. Pressure applied to a circular region. Pressure applied to an elliptical region.

Axi-symmctrical tractions. Rolling contact of iilelnstic bodies Elastic hystcresis Elastic-plas tic niaterials: sli akedown Rolliiig of a rigld cyliiider on a perfectly plastic Iialf-spacc Rolling contact of viscoelastic bodics Rolling friction.

An elastic strip betwcen rollcrs Onset of plastic flow iii a tliiii strip Plastic rolling of strip Lubrication of rollcrs. Dynamic effects and impact Stress wavcs in solids Dynamic loading of an dastic lialf-spzice Contact resonalice Elastic iiiipac t Inclastic irnpact Travelling loads - high specd sliding an d roUing.

T hermoelastic contact Introduction Ternperature distributions in a coiiducting Iidf-spacc Stcady therriioelastic distortion of a lialf-space Contact bctwecn bodics nt diffcrent tcinperatures Frictional heating and tliermoelastic instability. Refcrences and aiithor index. Siibjcct indcx. Pre face. Tlie subject of contact mechanics niay be said to have startcd in witii the publication by Heinrich Hertz of his classic paper the corltact of elastic solicls.

At that time Hertz was oniy 24, and was workiiig as a research assistant to Helrnholtz in tlie University of Berliii. Ilis interest in the problem was aroused by experirncnts on optical interference between glass lenses. Tlie question arose whethcr clastic deformation of tlic lenses under the action of the force holding tliern in contact could havc a significant influence on the pattern of interferencc fhges.

It is easy to imagine how the hypothesis of an elliptical area of contact could Iiave been prometed by observations of interference fringes such as tliose stiown in Fig. His knowlcdgc of clectrostatic potential thcory then enabled hini to sliow, by arialogy, that an ellipsoidd - F-Iertzian - distribution of contact pressure would produce elastic displacenients in thc two bodics whicli wcrc canipatible with tlie proposcd elliptical arca of contact.

The Hertz tlieory is restricted to frictionless surfaces and perfectly clastic solids. Progress ili contact nicclianics in tlie sccond haif of this ceritury Iias been associated largely witli tlie rcmoval of tliese restrictiolis.

A proper trcatriient of friction at the interface of bodics in contact has enabled the elastic tlieory to be extended to both slipping aiid rolliiig contact in a realistic way. At the same time developrnerit of tlie theories of plasticity and linear viscoelasticity have eriabled the stresses and deforniations at tJie contact of inclastic bodies to be exaniined. Somewhat surprisingly, in view of the technological importance of the subject, books on contact mechanics have been few.

In the book by L. Contact Problems in the Theory of Elasticity, appeared in Russian summarising. An up-to-date and thorough treatment of the same field by Gladwell, Contact Problerns in the Classical Them:v of Elasticity, was published in These books exclude rolling contacts and arc restricted to perfectly clastic solids.

Analyses of the contact of inelastic solids arc scattered through the technical journals or arc given brief treatment in the books on the Theory of Plasticity. Jn these circumstances the contact stresses comprise. The contact stresses then become part of the general stress distribution throughout the bodies and cannot be separated from it.

We shall not be concerned with conformal contact problems of tllis sort. This book is written by an engineer primarily for the use of professional engineers. Where possible the mathematical treatment is tailored to the level of. The approach which has been followed is to build. Complex potentials and integral transform. In this respect the more mathematically sophisticated reader will find Gladwell's book a valuable complement to Chapters This is a user's book rather than a course text-book.

The material is grouped according to application: stationary contacts, sliding, rolling and impact, rather than the usual academic division into clastic, plastic and viscoelastic problems. Results derived there arc used. These chapters may be regarded as appendices which are not necessary for a qualitative understanding of the later chapters.

Mindlin, whose pioneering work on the influence of tangential forces on elastic contacts stimulated my early interest in the subject, and to D. Tabor whose revealing experiments and physical insight into surface interactions gave rise to many challenging contact problems.

Several chapters of the book have been read and improved by colleagues whose knowledge and experience in those areas greatly exceeds my own: Dr J. Barber, Prof. Duffy, Prof. Gladwell, Dr J. Greenwood, Prof.

Kalker, Prof. Reid, Dr W. Stronge and Dr T. The complete manuscript was read by DrS. Grassic who made many valuable suggestions for improvements in presentation. Responsibility for errors, however, is mine alone and I should be very grateful if readers would inform me of any errors which they detect. The diagrams were carefully drawn by Mr A.

Finally my wife assisted in innumerable ways; without her patience and encouragement the book would never have reached completion. Motioii and forces at a point of cotitact. A coiitact is said to be coiiforrning if tlie sur faces of tlie two bodies 'fit' exactly or even closcly together witlioiit deforrnation.

Flat sljdcr bcarings and journal bearings are 2xaniplcs of confoniiing contact. Bodics whicli liave dissiniilar profiles are said to be nori-conforniing. Line contact ariscs tvlien tlic profiles of tlic bodies are conforniiiig in one directioii and iion- conforinirig in tlie perpendiculpr direction.

Thesc are ttie circurnstances with wliich we sliall be rnainly concerned iri this book. For cxample, tlie poiiit of coritact between a pair of gcar teeth itsclf niovcs in spacc, whilc at that poiiit the two surfaces Inove rclativc to eacli othcr witli a motian which conibiries both rollirig aiid sliding.

We take this point 0 as origin of rectangular coordinate axes Oxyz. The two bodies, lower and upper as shown in Fig. The Oz axis is chosen to coincide with the common normal to the two surfaces at 0.

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Contact Mechanics K L Johnson



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