Table Of ContentRelated title
Handbook of Friction-Vibration Interactions
Xiandong Liu, Gang Sheng Chen
(ISBN: 978-0-85709-458-2)
FRICTION
DYNAMICS
Principles and
Applications
GANG SHENG CHEN
XIANDONG LIU
Amsterdam(cid:129)Boston(cid:129)Cambridge(cid:129)Heidelberg
London(cid:129)NewYork(cid:129)Oxford(cid:129)Paris(cid:129)SanDiego
SanFrancisco(cid:129)Singapore(cid:129)Sydney(cid:129)Tokyo
WoodheadPublishingisanimprintofElsevier
WoodheadPublishingisanimprintofElsevier
TheOfficers’MessBusinessCentre,RoystonRoad,Duxford,CB224QH,UnitedKingdom
50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates
TheBoulevard,LangfordLane,Kidlington,OX51GB,UnitedKingdom
Copyright©2016ElsevierLtd.Allrightsreserved.
Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,
electronicormechanical,includingphotocopying,recording,oranyinformationstorageand
retrievalsystem,withoutpermissioninwritingfromthepublisher.Detailsonhowtoseek
permission,furtherinformationaboutthePublisher’spermissionspoliciesandourarrangements
withorganizationssuchastheCopyrightClearanceCenterandtheCopyrightLicensing
Agency,canbefoundatourwebsite:www.elsevier.com/permissions.
Thisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightby
thePublisher(otherthanasmaybenotedherein).
Notices
Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchand
experiencebroadenourunderstanding,changesinresearchmethods,professionalpractices,
ormedicaltreatmentmaybecomenecessary.
Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgein
evaluatingandusinganyinformation,methods,compounds,orexperimentsdescribedherein.
Inusingsuchinformationormethodstheyshouldbemindfuloftheirownsafetyandthe
safetyofothers,includingpartiesforwhomtheyhaveaprofessionalresponsibility.
Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,or
editors,assumeanyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatter
ofproductsliability,negligenceorotherwise,orfromanyuseoroperationofanymethods,
products,instructions,orideascontainedinthematerialherein.
LibraryofCongressCataloging-in-PublicationData
AcatalogrecordforthisbookisavailablefromtheLibraryofCongress
BritishLibraryCataloguing-in-PublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
ISBN:978-0-08-100285-8(print)
ISBN:978-0-08-100283-4(online)
ForinformationonallWoodheadPublishingpublications
visitourwebsiteathttps://www.elsevier.com/
Publisher:MatthewDeans
AcquisitionEditor:GlynJones
EditorialProjectManager:HarrietClayton
ProductionProjectManager:DebasishGhosh
Designer:GregHarris
TypesetbyTNQBooksandJournals
ABOUT THE AUTHORS
Gang Sheng Chen is the J. Robert Fletcher Associate Professor of
Engineering at Marshall University, West Virginia, USA. He received his
B.S. and M.S. from Shanghai JiaoTong University, P.R., China, and his
Ph.D. degree from Nanyang Technical University, Singapore. He is a
fellow of SAE and ASME. He has written over 100 journal papers, 7 book
chapters and 3 books. Gang has had many years’ industry experience as a
principal engineer and research scientist at DSI Singapore, Sony Singapore
Research Lab, IBM Corp. Technical Division, California and Gates Corp.
Technological Center in Michigan, USA.
Xiandong Liu is a Professor of Automotive Engineering at the School of
TransportationScienceandEngineering,BeihangUniversity,Beijing,P.R.
China. He received his B.S. and M.S. from Jilin University and his
Ph.D. from Beihang University, P.R. China. He teaches noise and vibra-
tioncontrolofvehiclesandhisresearchinterestsincludemechanicalsystem
dynamics, noise and vibration control, strength analysis and lightweight
designofstructure.Hehaspublished104journalpapersand1book,andis
a recipient of 5 patents.
vii
PREFACE
Due to its significance in engineering applications,the friction dynamics of
complex systems has been widely investigated by using modeling, analysis
andexperiments.Thisbookintroducesbasicprinciplesoffrictiondynamics.
Thefrictiondynamicsarepresentedinaunifiedtheoreticalframeworkwith
focusing on some most important engineering applications. The first three
chapters in the book introduce basic concepts and analytical methods of
frictionanddynamics.Thesearedesignedforthereaderswhomayneedto
recap basic knowledge in the relevant areas. The fourth chapter presents
vehiclebrakefrictiondynamics.Inthefifthchapterthefrictiondynamicsof
oil drilling and lifting systems is described. The chapter six presents the
friction dynamics of rotor systems and also touches on the fault diagnosis.
This book provides the information necessary to understand and deal with
friction dynamics by covering the fundamental principles and the most
critical engineering applications which represent the state-of-the-art in the
study of friction dynamics.
Thisbookgivesacomprehensivepictureoffrictiondynamics,intended
for practicing engineers, designers, researchers, and educators to use as a
reference book. It is also a special text of engineering for upper-level
undergraduate and graduate students as an independent study text.
Research students will also find this book useful.
This book has the following key features: widely interested and con-
cernedtopic,frommechanicalengineering,automotiveengineeringtooil&
gas engineering; the first reference of this kind to introduce the framework
of friction dynamics principles; the analysis, experiments and technical
treatment of varied the real systems; broad coverage of contemporary per-
spectives of complex friction dynamics including condition/health moni-
toring and diagnosis; presenting comprehensive and new view of friction
dynamics using modern tools; very useful for users who want to control
friction dynamics or make use of it.
We sincerely hope that this book will help students, teachers, and
researchersindevelopinganappreciationforthetopicoffrictiondynamics.
Any errors, oversights, omissions, or other comments to improve the book
can be communicated to authors and will be greatly appreciated.
We wish to acknowledge the contributions to this book by many
colleagues and students. We here acknowledge those individuals who
ix
x Preface
helped us to develop understanding: Wade Bray, Prof. Mohammed Qatu,
Prof.JonahLee,Dr.BillChen,Dr.FengXiaoandProf.LeroyHulsey.We
would like to thank Dr. T. He, Dr. Y. C. Shan and Dr. H. X. Wang,
Beihang Univeristy, for their help in the preparation of the draft, their
reviews of portions of the manuscript and helpful comments. We also are
gratefultothegraduatestudents,D.Shang,K.Shang,D.Qu,W.H.Chai,
H.Dong,Q.GaoandJ.J.Yi,BeihangUniveristy,fortheirhelpincreating
figures and proofreading of the manuscript.
CHAPTER 1
Introduction
1.1 DEFINITIONS OF FRICTION, DYNAMICS,
AND FRICTION DYNAMICS
Whenthesurfacesoftwoobjectsareplacedincontactandallowedtoslide
against one another, there is a resistance to this motion. This resistance is
known as friction. Friction is one of the most important problems in
tribology, the science and technology of interacting surfaces in relative
motion concerned with friction, wear, and lubrication in interfaces.
Dynamicsdealswiththemotionofrigidordeformablebodiesandtheforces
associatedwithit.Dynamicalsystemswithfrictionoftengiverisetodiverse
forms of motion.
Thecontactandfrictioneventsbetweentwocontactsurfacesconstitute
an energy transition and dissipation process. The kinetic energy of driving
bodies is usually transferred to the driven body through friction and is also
transferred into the dissipative energy of irregular microscopic motion of
the interface asperities, particles, and atoms for deformable bodies. The
friction usually gives rise to motion, oscillatory vibrations, or vibrations
propagating in media.
Up to now, there has been no universally accepted friction model or
theory to cover general friction phenomena due to its multiphysics nature.
Differentmodelshavebeendevelopedforindividualconditions[1e4].Part
ofthereasonforthisisthatfrictionisacomplexprocessinwhichforcesare
transmitted, mechanical energy is converted, surface topography is altered,
interface material can be removed or formed, and physical and even
chemical changes can occur. Actually, friction can be assumed to be a
variableinadynamicalsystemwithaslidinginterface,whichiscomplicated
by the fact that this system’s boundary conditions are not stationary and
deterministic due to interfacial changes in geometrical, mechanical, mate-
rial, physical, and chemical aspects. As such, the coefficients of friction are
not intrinsic properties of materials. Rather, they depend on the properties
of the contact surfaces, their operational conditions, their time history,
environmental conditions, and even their interactions.
FrictionDynamics
ISBN978-0-08-100285-8 ©2016ElsevierLtd.
1
http://dx.doi.org/10.1016/B978-0-08-100285-8.00001-8 Allrightsreserved.
2 FrictionDynamics
Tribology and dynamics used to be two distinct fields. However, with
the recent rapid developments in the related area of friction dynamics,
especially in the application of varied engineering disciplines, engineers are
turning to combining tribology and dynamics for efficient methods to
handle and analyze the vast amounts of practical cases.
This book, Friction Dynamics, offers a combined treatment of modeling,
analyzing, and testing of many problems that application engineers and
scientists are trying to solve. After delineating these mathematical charac-
terizations, it presents several applications currently in use for analyzing
friction dynamics. The emphasis of the text is on the fundamental aspects
and the contemporary knowledge in the area of friction dynamics.
1.2 SIGNIFICANCES AND CHALLENGES OF STUDIES
ON FRICTION DYNAMICS
Friction dynamics exists in numerous engineering systems, including brake
squealing of automobiles and motorcycles, chattering of machine tools,
rubbing impact in rotor systems, and friction whirl of drilling systems, just
to name a few. These examples of friction dynamics cover numerous
phenomena in science and engineering. Even in the interior of a car, from
time to time we may perceive clutch shuddering, wiper squealing, belt
drive chirping, instrument panel squeaking, tire road friction noise, and
other phenomena. This book considers friction dynamics in its broader
meaning, but with a concentration on the fundamentals and engineering
applications.
To give some examples of the problems treated in the book, let’s
consider the immense effort that is being put into dealing with friction
dynamics in the mechanical and automotive industries. The need for
rotatory systems is tremendously great and continues to increase. There is a
variety of mechanical systems with varying rotor systems, from washing
machines to airplane engines. In these contexts, interface friction and
contact-induced friction dynamics and instability have been the most
challenging and critical problems faced by the product designers.
Our lives are highly dependent on vehicles of various types. Most ve-
hicles, like automobiles, motorcycles, trains, and aircraft, use some kind of
brake system for stopping. In these brake systems, friction is a principal
functional/safety performance factor and is also a potential cause of unde-
sirablenoiseandvibration.Thestructuresandprinciplesofthevariedbrake
systems in vehicles are analogous and similar, but noise has been an
Introduction 3
unsolved problem for the last half-century. Friction dynamics affects the
reliability and quality of brake systems in many ways. For instance, brake
squealing, a complex vibration, has been the most challenging issue in
automotive brake systems, as it has been equal to the quality of products
perceived by customers. It has been estimated that the warranty work of
noise and vibration of automotive brake systems costs approximately $1
billion a year in the Detroit area alone. Even in aircraft braking systems,
friction dynamics has been a critical issue. Friction-induced torque oscil-
lations can lead to excessive high loads in the landing gear and brake
structures, and this results in passenger discomfort, component failure, or
both, and thereby warranty claims.
Understanding the nature of friction dynamics and solving the techno-
logical problems associated with it are the essence of these fields. Modeling
of friction dynamics in mechanical and other systems requires an accurate
definition and description of friction. Unfortunately, there is no universally
accepted friction model or theory to cover general friction phenomena due
to the reasons that have already been mentioned. On the other hand, the
resultant dynamics often exhibit various nonlinear, transient/nonstationary,
stochastic and uncertain properties [5e17]. Moreover, small changes in
interfacial parameters could have significant effects on the resultant dy-
namics,andthusthescalesofinfluencingfactorrangefromthemacrometer,
micrometer, and nanometer levels. The boundary conditions of the prob-
lems are not fixed; rather, they depend on environmental conditions,
operation conditions, system interactions, and time. Because of the
complexity of friction dynamics, it has been considered to be an unsolved
problem in many engineering applications. Since the modeling and the
predictions are not very reliable, the trial-and-error approach has been
extensively used.
Recent extensive efforts on modeling, analytical, and experimental in-
vestigations have made much substantial progress in many practical appli-
cations. Many techniques, such as advanced testing, advanced signal
processing, and spectrum analysis and contemporary nonlinear stochastic
dynamics techniques have been used as efficient means to address the
nonlinear, nonstationary, stochastic and uncertain dynamics; it enables fric-
tiondynamicstobequantifiedefficiently.Theemergenceandapplicationof
scanning tunneling microscopy and atomic force microscopy have allowed
for systematic investigation of interfacial problems with high resolution,
which have led to the development of the insight of friction at the micro-,
nano-, molecular-, and even atomic-scale levels. There are several purposes
4 FrictionDynamics
ofresearchintheareaoffrictiondynamics,suchastodevelopafundamental
understanding of friction dynamics, to control the motion of dynamical
systems with friction, to realize some physical processes for products, and to
reduce and eliminate instability in engineering systems caused by friction.
1.3 ORGANIZATION OF THE BOOK
The book has two purposes. The first is to give a general introduction to
the theory of friction and dynamics by offering a physical view of the
fundamental theory. The second is to give examples of the applications of
these theoretical approaches. The author will provide contemporary
coverage of the primary concepts and techniques in the treatment of fric-
tion dynamics.
There are sixchapters. The basic principlesof vibrationsand friction are
discussedinthefirstthreechapters.Thischaptergivesabriefintroductionto
the whole book. Chapter 2 provides a comprehensive analysis of vibrations
and advanced dynamics. The vibration segment of this chapter covers vi-
brations of linear systems, random excited systems, and nonlinear systems,
anddiscussesmostofthemajorareasandapplications,includingtheDuffing
equation, Van der Pol equation, and Mathieu equation. The advanced
dynamics portion presents rigid body dynamics including Euler equation.
Chapter 3 describes contact and friction principles. Chapter 4 presents
the friction dynamics of vehicle brake systems, covering various vibrations
and instability issues of brake systems and numerical and analysis ap-
proaches. Chapter 5 presents the friction dynamics of oil-well drill-strings
and sucker rods. Finally, Chapter 6 presents the friction dynamics of
rotor systems.
Referencesectionsinthebookprovideacomprehensiveperspectiveon
developments in friction dynamics, as well as various applications. For di-
dactic reasons, the text flow is not interrupted by the inclusion of refer-
ences. However, at the end of each chapter, the relevant literatures
published are cited.
REFERENCES
[1] Armstrong-Helouvry,B.,Dupont,P.,CanudasDeWit,C.,1994.Asurveyofmodels,
analysis tools, and compensation methods for the control of machines with friction.
Automatica30(7),1083e1138.
[2] Berger, E.J., 2002. Friction modeling for dynamic system simulation. Appl. Mech.
Rev. 55 (6), 535e576.
