SERIES ON STABILITY, VIBRATION AND CONTROL OF SYSTEMS Volume Series B Dynamics with Friction Modeling, Analysis and Experiment Part II Editors Ardeshir Guran, Friedrich Pfeiffer & Karl Popp onol Joint with s '""° ^ ? C We[...]... and Karl Popp Contributors xi DYNAMICS WITH FRICTION: MODELING, ANALYSIS E X P E R I M E N T S , P A R T II AND C h a p t e r 1: I n t e r a c t i o n of V i b r a t i o n a n d Friction at D r y Sliding C o n t a c t s Daniel P Hess 1 1 Introduction 1 2 Normal Vibration and Friction at Hertzian Contacts 3 3 Normal Vibration and Friction at Rough Planar Contacts 7 4 Normal and Angular Vibrations at Rough... Conclusions xvii 254 256 265 269 273 280 281 282 283 295 297 5 Acknowledgment 298 6 References 298 Subject Index 309 Author Index 313 Dynamics with Friction: Modeling, Analysis and Experiment, Part II, pp 1-27 edited by A Guran, F Pfeiffer and K Popp Series on Stability, Vibration and Control of Systems, Series B, Vol 7 © World Scientific Publishing Company INTERACTION OF VIBRATION A N D FRICTION A T... lubrication is present as tendons slide within synovial sheaths at sites of wear, and the articulating surfaces of joints are bathed in synovial fluid Despite this tremendous importance of contact mechanics and frictional phenomena, we still hardly understand it The present part II of this volume on Dynamics with Friction is a continuation of the previous part I, and is designed to help synthesize our... disc with a rotating mass-spring-damper system 3.2 Rotating disc with a stationary mass-spring-damper system 3.3 Instability mechanisms 39 40 45 46 4 Follower Force Friction Models 4.1 Follower force analysis in brake design 4.2 Sensitivity analysis 4.3 Distributed frictional load 4.4 Friction with a negative /z-velocity characteristic 48 48 49 50 51 5 Friction- Induced Parametric Resonances 52 xiii xiv... models of smooth and rough contacts are examined, in which the assumed sliding conditions, the kinematic constraints, and the mechanism of friction are well-defined Instantaneous and average normal and frictional forces are computed The results are compared with experiments It appears t h a t when contacts are in continuous sliding, quasi-static friction models can be used to describe friction behavior,... given and general features of the problem are discussed Some comparisons are made with experiments and with part of the work of Martins et al.10, in which a similar problem using a phenomenological constitutive contact model is examined Before proceeding, we comment on the interpretation of the coefficient of friction under dynamic conditions If both the load and the friction force at a contact vary with. .. friction force decreases When F, P and [i all vary with time, the coefficient of friction seems to be of limited value Particular difficulties arise when P{t)~0 For defining average friction, the definition of Eq (2) is preferred Sometimes, in friction testing, only the instantaneous friction force is measured Even this requires a measurement system with sufficient frequency bandwidth to accurately measure... Stability Analysis 13 6 Chaotic Vibration and Friction 20 7 Conclusions 25 8 References 26 C h a p t e r 2: V i b r a t i o n s and Friction- Induced Instability in D i s c s John E Mottershead 29 1 Introduction 29 2 Disc Vibrations and Critical Speeds 2.1 Flexural vibrations 2.2 Vibration of a spinning membrane 2.3 Combined effects of centrifugal and flexural rigidity 2.4 Travelling waves and critical... Structures, and Intelligent Machines: Theory and Applications in Engineering and Science) The proceedings of ISIFSM papers are rigorously reviewed and appeared in volumes published in this series Today, research continues vigorously in the description and design of systems with friction models, in quest to understand nature, machines, structures, transportation systems, and other processes We hope this book... current knowledge regarding the role of friction in mechanical and structural systems as well as everyday life We understand that in the preface of the first part in this book we promised the readers to have a final review chapter with a complete list of references in friction dynamics However, we soon realized that the knowledge in this field in written form is expanding very rapidly at a considerable ... Control of Machines with Friction (Kluwer Academic Publishers, Boston, 1991) Dynamics with Friction: Modeling, Analysis and Experiment, Part II, pp 29-74 edited by A Guran, F Pfeiffer and K Popp Series... STABILITY, VIBRATION AND CONTROL OF SYSTEMS < < ^ ^ > Series B Volume Series Editors: Ardeshir Guran & Daniel J Inman Dynamics with Friction Modeling, Analysis and Experiment Part II Editors Ardeshir... British Library DYNAMICS WITH FRICTION: MODELING, ANALYSIS AND EXPERIMENT, PART II Copyright © 2001 by World Scientific Publishing Co Pte Ltd All rights reserved This book, or parts thereof, may