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Theory and Practice
This book is based on the well-known
CONTENTS Rubber in Engineering Practice by
Davey and Payne, which was published
Part I: Properties of Elastomeric in 1965 and has become a major work
of Engineering with
Materials. on the subject. The book has been
1. Introduction and review of prop largely rewritten and with the per
erties. spective of 12 years of hew advances
2. Static load-deformation properties. and applications it has been possible to
3. Dynamic force-deformation prop provide a considerably more substantial
Rubber
erties. link between theory and practice and to
Part II: Theory and Practice of Design. deal in detail with the origins and
4. Analysis of the deformation of limitations of the analytical techniques
rubber units under equilibrium used extensively in design. The book is
loading conditions. divided into three sections, furnishing
5. Vibration isolation and trans- the reader with a logical progression
missibility. from physical properties to the design
6. Isolation of shock and transient of load bearing rubber units and then
vibration. to the use of rubber units in a range of
7. Practical design details and typical applications. The layout is arranged to
forms of rubber mountings. provide the user with a means of rapid
8. Practical mounting arrangements reference to specific items and to supply
using rubber springs. the practising engineer with concise
Part III: Applications. information in a form easily related to
9. Rubber in packaging. design problems.
10. Flexible couplings
Р. К. FREAKLEY
11. Bridge bearings.
12. Piers and fenders.
13. Rubber in buildings.
and
14. Transport engineering.
15. Industrial shock and vibration
isolation. A. R. PAYNE
16. Noise control and structural
damping.
17. Rubber in fluid sealing.
18. Flexible composites.
Appendices:
I. Properties of vulcanised rubber.
II. Note on expressions for damping.
III. Note on the decibel system.
IV. Hardness testing of rubbers.
Index.
APPLIED SCIENCE PUBLISHERS
THEORY AND PRACTICE OF
ENGINEERING WITH RUBBER
P. K. FREAKLEY
Institute of Polymer Technology,
Loughborough University, UK
and
A. R. PAYNE
Formerly Director, Shoe and Allied
Trades Research Association, UK
APPLIED SCIENCE PUBLISHERS LTD
LONDON
APPLIED SCIENCE PUBLISHERS LTD
RIPPLE ROAD, BARKING, ESSEX, ENGLAND
British Library Cataloguing in Publication Data
Freakley, P К
Theory and practice of engineering with rubber.
1. Rubber
I. Title II. Payne, Arthur Robert
620. 1'94 TA455.R8
ISBN 0-85334-772-7
WITH 34 TABLES AND 443 ILLUSTRATIONS
© APPLIED SCIENCE PUBLISHERS LTD 1978
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system, or transmitted in any form or by any means, electronic, mechanical, photocopy
ing, recording, or otherwise, without the prior written permission of the publishers,
Applied Science Publishers Ltd, Ripple Road, Barking, Essex, England
Typeset by The European Printing Corporation Limited
Printed in Great Britain by Galliard (Printers) Ltd, Great Yarmouth
Acknowledgements
In the text the authors have been happy to acknowledge the contri
butions made by many workers in the field of ‘engineering with
rubber’ and are grateful for their kind permission and that of their
publishers to reproduce various material. Without this it would not
have been possible to contemplate producing a book of this form.
It is proper to mention here the unique and sustained contribution
made by the staff of the Malaysian Rubber Producers’ Research
Association (MRPRA). The scope of this contribution has resulted in
Chapters 2 and 4 being based largely upon MRPRA publications.
The extensive work of Professor J. C. Snowdon in the field of
vibration and shock isolation, resulting in numerous references in the
text, must also be mentioned.
In order to update the sections and chapters dealing with com
mercially available products and their application to particular cases,
the help of numerous manufacturers was sought and in most cases
given, enthusiastically and unstintingly. The authors wish to ac
knowledge, with many thanks, the assistance of the following persons
and companies among the many who helped them in the preparation
of this book: Mr E. T. Dawson and Dunlop, Polymer Engineering
Division; Mr W. R. Brake and BTR-Silvertown Ltd; Mr D. O’Brien,
Mr A. T. Smith and Cementation Muffelite; Mr R. P. Torr and the
Andre Rubber Co Ltd; Mr D. Turner, Mr R. A. Dove and the Avon
Rubber Co. Ltd; Dr D. Holland and BTR-Solarbridge; Mr D. A.
Rayner, Mr M. K. Snow and J. H. Fenner Co. Ltd; Mr G. N. Wright
and Lord Kinematics; Mr J. Fee and Firestone Industrial Products;
Mr J. E. Long and PSC-Equipment Ltd; Mr T. Rogers and Vauxhall
Motors Ltd; Mr M. P. Hill and Rolls Royce Ltd; Mr P. Ward and
Britten Norman Ltd; Mr J. Adam and Scottish Aviation Ltd.
Finally, our thanks are due to Miss Linda Malins, who spent many
hours at her typewriter in order to produce the final manuscript.
V
Foreword
The use of rubbers in engineering applications has increased
markedly in the last two decades. This increase, however, is small
compared to the potential, and a major factor restricting growth is the
low level of appreciation of the engineering properties of rubber and
design procedures based on these.
The research work necessary to underwrite the rational use of
rubber in critical applications has, in large measure, been completed
and it remains to inform and convince the engineer that design
procedures are available and reliable.
Pioneering work has been carried out in a few centres in the UK
and the late Dr A. R. Payne was an early missionary, his efforts
culminating in the book Rubber in Engineering Practice (co-author A.
B. Davey). Dr A. R. Payne was an Industrial Professor at Lough
borough University of Technology and it is fitting that this book,
updating the earlier one and which was in preparation at the time of
his death, should have been completed by the new co-author and
member of the staff of the University, Philip Freakley, in the face of
considerable difficulties resulting from the tragic event of 20 August,
1976.
A. W. BlRLEY
Director,
Institute of Polymer Technology,
Loughborough, UK
vii
Preface
Work carried out in the field of engineering design with rubber has, in
the past ten years, followed two main paths. The first is an extension
and consolidation of the subject matter of the book by A. B. Davey
and A. R. Payne, entitled Rubber in Engineering Practice. The second
path is essentially computer oriented, using the modern digital
computer’s capacity and speed to good advantage in solving complex
problems.
It was decided, at the conception of this book, to deal only with
those methods which are capable of being handled using traditional
mathematical methods or a pocket calculator (although the increasing
sophistication of pocket calculators may blur this dividing line with
the passage of time), thus producing an updated version of the earlier
book. This decision was made on the basis that the majority of
engineering problems are solved without recourse to a computer and
that this text is designed to present the engineer, practising and
potential, with a clear and precise review of the application of
conventional analytical skills to the field of engineering with rubber.
Indeed, the combination of analytical and computer methods in a
single text dealing with a subject matter which is itself a departure
from conventional engineering was thought to detract from the
requirement for a logical progression from material properties to
applications.
The application of the digital computer to engineering with rubber
has extended the capabilities of some of the available analytical
methods detailed in the text. The problems best solved using
computer methods are indicated and it is hoped that these will be the
subject of a further text to be produced in the not too distant future.
P. K. Freakley
ix
Contents
Acknowledgements............................................................ v
Foreword .......................................................................... vii
Preface............................................................................... ix
List of Symbols................................................................. xvii
PART I: PROPERTIES OF ELASTOMERIC MATERIALS
Chapter 1 Introduction and Review of Properties
1.1 Definition of ‘Rubber’.......................................... 3
1.2 Molecular Nature of Rubber................................ 3
1.3 Prediction of Stress-Strain Properties .... 6
1.4 Relations Among Time, Temperature and Rate of
Deformation ........................................................ 8
1.5 Energy Absorption and Loss ............................ 9
1.6 Other Properties................................................... 10
1.7 Raw Elastomeric Materials ................................ 15
1.8 Vulcanisation and Compounding ....................... 18
1.9 Processing Techniques.......................................... 21
Chapter 2 Static Load-Deformation Properties
2.1 Introduction ........................................................ 24
2.2 Statistical or Kinetic Theory of Rubber Elasticity • 24
2.3 Phenomenological Theory of Rubber Elasticity . . 30
2.4 Effect of Carbon Black on Poisson’s Ratio and Rela
tions Among E0 ,G and К (Bulk Modulus) . . . 32
2.5 Creep and Stress Relaxation................................ 35
2.6 Rupture of Rubber.............................................. 50
2.7 Effect of Ozone................................................... 53
xi
xii CONTENTS
Chapter 3 Dynamic Force-Deformation Properties
3.1 Introduction ........................................................ 56
3.2 Linear Viscoelastic Behaviour............................ 56
3.3 Non-linear Viscoelastic Behaviour ................... 74
3.4 Energy Dissipation and Heat Build-up in Rubber
Units...................................................................... 85
3.5 Wave Effects in Rubber ..................................... 88
3.6 Dependence of Ultimate Strength and Extension on
Rate, Temperature and Hysteresis....................... 93
3.7 Failure of Rubber Under Conditions of Cyclic Load
ing—Fatigue............................................................ 97
PART II: THEORY AND PRACTICE OF DESIGN
Chapter 4 Analysis of the Deformation of Rubber
Units Under Equilibrium Loading
Conditions
4.1 Application on Deformation Theories................... 113
4.2 Compression of Rubber Blocks............................ 113
4.3 Shear of Rubber Blocks ....................... 119
4.4 Combined Compression and Shear ................... 120
4.5 Torsion Disk........................................................ 121
4.6 Annular Rubber Units in Axial Shear................... 125
4.7 Annular Rubber Units in Rotary Shear .... 129
4.8 Annular Rubber Units in Radial Compression . . 134
4.9 Annular Rubber Units in Transverse Loading . . 138
4.10 Elastic Stability and Buckling of Rubber Compression
Units...................................................................... 140
4.11 Compression of Laterally Unrestrained Toroidal
Rubber Rings........................................................ 146
4.12 Radial Compression of Long Hollow Circular Cylin
ders ...................................................................... 148
4.13 Radial Deformation of Rubber-covered Rollers . . 154
4.14 Compression of a Rubber Sphere Between Plane
Surfaces ............................................................ 156
4.15 Radial Compression of Half-Cylindrical and D-section
Units...................................................................... 158
4.16 Hollow Cylinders in Axial Compression .... 162
4.17 Conclusions ........................................................ 164
CONTENTS xiii
Chapter 5 Vibration Isolation and Transmissibility
5.1 Introduction ........................................................ 166
5.2 Vibration of a Simple Single-degree-of-freedom
System................................................................. 166
5.3 Vibration of Systems Having Parallel Mountings 174
5.4 Vibration of Systems Mounted on Non-rigid Foun
dations ................................................................. 179
5.5 Vibration of Systems Having Two Degrees of
Freedom ............................................................ 183
5.6 Vibration of Systems Having Many Degrees of
Freedom ............................................................ 187
5.7 Vibration of Systems Having a Distributed Mass . 189
5.8 Vibration of Systems Mounted on Non-linear Units 195
5.9 Vibration of Systems Having a Dynamic Absorber 198
5.10 Vibration Wavelength Effects on Rubber Mountings 203
Chapter 6 Isolation of Shock and Transient Vibration
6.1 Introduction ........................................................ 208
6.2 Transient Vibration of the Simple Linear System . 208
6.3 Transient Vibration of the Non-linear Simple System 217
6.4 Concepts of Mounting Performance...................... 223
6.5 Practical Considerations for Shock Isolation . . 230
Chapter 7 Practical Design Details and Typical Forms
of Rubber Mountings
7.1 Introduction ........................................................ 236
7.2 Avoidance of Excessive Stress in the Rubber . . 236
7.3 Dimensional Tolerances and Clearances .... 243
7.4 Design for Stability.............................................. 248
7.5 Design for Manufacture ..................................... 255
7.6 Precautions to be Taken During Installation . . 258
7.7 Causes of Failure and Suitable Remedies . . . 260
7.8 Typical Forms of Rubber Mountings................... 264
Chapter 8 Practical Mounting Arrangements Using
Rubber Springs
8.1 Parallel Mounting Arrangements ....................... 300
8.2 ‘Parallel Ring’ Type (Conventional) ................... 303
8.3 Convergent Arrangements ................................ 304
8.4 Other Arrangements .......................................... 310
