Dynamical Contact Problems with Friction: Models, Methods, Experiments and Applications

163 Pages·2002·5.683 MB·English

by  Dr.-Ing. Walter Sextro (auth.)

Lecture Notes in Applied Mechanics
Volume3
Series Editor
Prof. Dr.-Ing. Friedrich Pfeiffer
Springer-Verlag Berlin Heidelberg GmbH
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Engineering
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Dynamical Contact
Problems with Friction
Models, Methods, Experiments
and Applications
Walter Sextro
Springer
Dr.-Ing. WALTER SEXTRO
University of Hannover
Institute for Mechanics
AppelstraBe 11
30167 Hannover
GERMANY
e-mail: [email protected]
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Sextro, Walter:
Dynamical contact problems with friction: models, methods, experiments
and applications I Walter Sextro. -Berlin; Heidelberg; New York ; Barcelona;
Hong Kong; London; Milan; Paris; Tokyo: Springer, 2002
(Lecture notes in applied mechanics; Vol. 3)
(Engineering online library)
ISBN 978-3-662-21834-1 ISBN 978-3-540-46871-4 (eBook)
DOI 10.1007/978-3-540-46871-4
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Preface
Friction contacts are used to transmit forces or to dissipate energy. A better under
standing of friction phenomena can resuIt in improvements Iike the reduction of
noise and maintenance costs, increased life time of machines and improved energy
efficiency. There exists a rich literature on friction. Depending on the features of
the friction contact, different contact models are applied and dependent on the
contact model, different solution methods are preferred. The aim of this book is to
describe an efficient procedure to model dynamical contact problems with friction.
This procedure is applied to different practical problems and verified by experi
ments.
The dynamics of the elastic bodies in contact are described by a reduced order
model through the so called modal description, to speed up calculations. This de
scription is presented in Chap. 2. In Chap. 3 the generalized contact model is de
veloped, which includes the main physical effects Iike contact elasticity, rough
ness, friction characteristics etc .. The contact planes are discretized and a point
contact model is applied to each area element. The thermomechanics of the con
tact is investigated, as weil as the calculation of wear. The application of the com
bined procedure of the point contact model and the modal description of the elas
tic components are illustrated by three different examples. An impact- and friction
oscillator, see Chap. 4, is investigated in the time domain, while the friction
damping of elastic structures with expanded friction contacts is analyzed within
the frequency domain, see Chap. 5. The stationary rolling contact is presumed to
calculate the wear of wheel-rail-systems, see Chap. 6.
This work arose during my research at the Institute of Mechanics of the Univer
sity of Hannover in Germany. Part of the work was supported by the "For
schungsvereinigung Verbrennungskraftmaschinen e.V. (FVV, Frankfurt)" and was
sponsored by the "Bundesministerium für Wirtschaft" through the "Arbeitsge
meinschaft industrieller Forschungsvereinigungen e.V. (AiF, Köln), (AiF Nr.
10684)", a federal collaboration of the turbomachinery-industry and the "Deutsche
Forschungsgemeinschaft (Projekt Nr. SE 895/3-1)".
This book is based on the script, that leads to my "Habilitation" in Mechanics.
The "Habilitation" marks at the end of the education as lecturer. In this context I
would Iike to thank Prof. Dr.-Ing. habil. K. Popp, Prof. Dr.-Ing. habil. P. Wriggers
and Prof. Dr.-Ing. habil. G.-P. Ostermeyer for carefully reading the script and for
their support.
Furthermore, I would like to thank all of my colleagues at the Institute of Me
chanics for the open discussion of any problems and the successful cooperation. I
would especially like to emphasize Prof. Dr.-Ing. habil. K. Popp. During my time
VI Preface
at the institute, he always supported me and therefore most of my thanks belong to
him.
Walter Sextro
Contents
1 lntroduction ........................................................................................................ I
1.1 Problem Deseription .................................................................................... I
1.2 Review ......................................................................................................... 6
1.3 Aim ofthis Work ....................................................................................... 14
2 Dynamical Description of Elastic Bodies ........................................................ 17
2.1 Ki nematies of Elastie Bodies ..................................................................... 17
2.2 Governing Equations for Linear Elastieity ................................................ 19
2.3 Equation 01' Motion 01' an Elastie Body ..................................................... 22
2.4 Modal Deseription of Elastie Bodies ......................................................... 26
3 Point Contact Model ........................................................................................ 29
3.1 Contaet Stitlnesses .................................................................................... 29
3.2 Eigenfrequeneies of the Elastie Layer ....................................................... 34
3.3 Surfaee Roughness .................................................................................... 37
3.4 Hyperbolie Contaet Law ............................................................................ 47
3.5 Validation of the Contaet Model with Roughness ..................................... 49
3.6 Frietion Charaeteristies .............................................................................. 51
3.7 Three-dimensional Point Contaet Element.. .............................................. 55
3.8 Mieroslip Etleets ....................................................................................... 65
3.9 Wear Generation ........................................................................................ 71
4 Dynamics of Oscillators with Elastic Contact and Friction .......................... 77
4.1 System Deseription .................................................................................... 77
4.2 Oseillator with Elastie Contaet .................................................................. 80
4.3 Frietion Oseillator ...................................................................................... 83
5 Friction Damping of Elastic Structures .......................................................... 85
5.1 Foreed Vibrations of Elastie Struetures ..................................................... 85
5.2 Harmonie Balance Method ........................................................................ 89
5.3 Comparison of Measurements and Calculations ........................................ 98
5.4 Optimization of Bladed Dise Assemblies with Shrouds .......................... lOS
VIII Contents
6 Rolling Contact ............................................................................................... 109
6.1 Motivation ............................................................................................... 109
6.2 Normal Contact ....................................................................................... 110
6.3 Tangential Contact.. ................................................................................. 114
6.4 Contact Stiffnesses .................................................................................. 117
6.5 Generalized Contact Forces ..................................................................... 122
6.6 Validation of the Rolling Contact Model ................................................ 127
6.7 Temperature Distribution ........................................................................ 132
6.8 Wear Distribution .................................................................................... 138
7 Conclusion ...................................................................................................... 143
References .......................................................................................................... 145
Nomenclature .................................................................................................... 155
Index ................................................................................................................... 159
1 Introduction
1.1 Problem Description
Friction is the resistal1Ce against sliding and, therefore, friction plays an important
role in dynamical engineering systems. In (Moore 1975) the mechanisms of fric
tion are reviewed in a rich literature and the components of dry friction are sum
marized in (Seireg 1998) as folIows:
• Mechanical interlocking due to the surface roughness, which leads to a higher
static friction coefficient, compared to the sliding friction coefficient and ex
plains the dynamic friction force as the force to lift off the contacts of the upper
surface over the contacts of the lower surface.
• If the developed pressure at the discrete contacts results in local welding. Due
to relative motion the welded surfaces are sheared. Ploughing of the harder
material through the softer material contributes to the friction forces as weIl.
• Molecular attractio!1, which attributes to frictional forces and to energy dissi
pation, if atoms are plucked out of the attraction range,
• and for completeness the electrostaticforces between the surfaces.
On the one hand, there exist dynamic systems, where friction has to be mini
mized, so that wear is reduced and the lifetime as weil as the efficiency of a dy
namic system is increased. The economic loss caused by friction and wear is esti
mated by five percent 01' the gross national product, see (Persson 1994). Hence,
reducing friction and wem saves money. On the other hand, friction is used to
trans mit forces or to reduce vibration amplitudes, see (Popp 1994). A possibility to
reduce the vibration of a machine is to use friction contacts to dissipate energy.
The reduction of vibration amplitudes results in a reduction of alternating stresses
and furthermore in an increase of lifetime and safety. The main part of the dissi
pated energy is transferred to heat. Dependent on the vibration frequencies the
noise development can be reduced as weil. From here, there is a need for efficient
calculation procedures to optimize the dynamics of systems with friction contacts.
Before summarizing the main features of an elastic contact with friction, some
important machines and machine components are presented, where friction plays
an important role.