Mechanical Instability E-Book

Tomasz Krysinski

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 237

Veröffentlichungsjahr: 2013

Beschreibung

This book presents a study of the stability of mechanical systems, i.e. their free response when they are removed from their position of equilibrium after a temporary disturbance. After reviewing the main analytical methods of the dynamical stability of systems, it highlights the fundamental difference in nature between the phenomena of forced resonance vibration of mechanical systems subjected to an imposed excitation and instabilities that characterize their free response. It specifically develops instabilities arising from the rotor–structure coupling, instability of control systems, the self-sustained instabilities associated with the presence of internal damping and instabilities related to the fluid–structure coupling for fixed and rotating structures. For an original approach following the analysis of instability phenomena, the book provides examples of solutions obtained by passive or active methods.

Leseprobe

Table of Contents

Foreword

Preface

Chapter 1. Notions of Instability

1.1. Introduction

1.2. Comparison of Notions of Resonance and Instability

1.3. Instability Due to Self-Sustained Excitation

1.4. Parametric Instability

1.5. Summary of Methods Used to Ensure or Increase the Stability of a System

Chapter 2. Rotor/Structure Coupling: Examples of Ground Resonance and Air Resonance

2.1. Introduction to Ground Resonance

2.2. Ground Resonance Modeling

2.3. Active Control of Ground Resonance

2.4. Air Resonance

Chapter 3. Torsional System: Instability of Closed-Loop Systems

3.1. Introduction

3.2. Governing Principle

3.3. Industrial Cases

Chapter 4. Self-Sustaining Instability for Rotating Shafts

4.1. Introduction to Self-Sustaining Instability

4.2. Modeling of Effect of Internal Damping on Rotating Systems

Chapter 5. Fluid-Structure Interaction

5.1. Introduction

5.2. Flutter of an Airfoil in an Airstream

5.3. Whirl Flutter

Bibliography

Index

First published 2011 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Adapted and updated from Instabilité mécanique published 2009 in France by Hermes Science/Lavoisier © LAVOISIER 2009

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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© ISTE Ltd 2011

The rights of Tomasz Krysinski and François Malburet to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Krysinski, Tomasz.

  [Instabilité mécanique. English]

  Mechanical instability/Tomasz Krysinski, François Malburet.

       p. cm.

  Includes bibliographical references and index.

  ISBN 978-1-84821-201-5

  1. Dynamics. 2. Mechanics, Applied. 3. Mechanical engineering. 4. Stability. 5. Vibration. I. Malburet, François. II. Title.

  TA352.K7913 2011

  620.1--dc22

2010042672

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-84821-201-5

Foreword

In a previous work, Mechanical vibrations – Origin and control, published in 2003, Tomasz Krysinski, Dynamics Specialist, former Head of the Vibration and Internal Noise Department at Eurocopter Engineering and Design Department, and François Malburet, Teacher-Researcher at the Ecole nationale supérieure d’arts et métiers of Aix-en-Provence, analyze the forced response of deformable mechanical systems subjected to periodic vibratory forces as well as to the dynamic optimization methods, and active and passive antivibration devices designed to limit the related effects.

In this work, which supplements the preceding one, the same authors are interested in the stability of mechanical systems, that is in their free response when they are moved away from their equilibrium position subsequent to a disturbance.

After a brief reminder of the main methods of analysis of the dynamic stability of systems, the authors highlight the fundamental difference in kind between the forced vibration resonance phenomena of mechanical systems subjected to an imposed excitation, and the instability phenomena which characterize their free response. If both types of phenomenon may lead to great deformation amplitudes and fatigue damage to the structure, the unstable phenomena are potentially much more hazardous since they may lead to sudden destruction of the structure in the event of divergent oscillations.

Sometimes also, unstable dissipative systems are subjected to self-sustained oscillations initially divergent but which saturate due to system behavior nonlinearities, thus resulting in a periodic permanent rating termed limit cycle. This is probably why the resonance phenomena and instabilities are sometimes mistaken for each other although the relevant analysis methods and mechanisms are very different, such as shown by the authors through the numerous examples presented.

The authors devote an entire chapter to the analysis of the phenomenon known as ground resonance of helicopters, which is in fact a potentially destructing self-sustaining instability resulting from coupling between the lag motion of the rotor blades and the motion of the aircraft standing on its landing gear.

Dynamic adaptation of the structure ensures the stability of the phenomenon by selecting the stiffness and damping characteristics for the landing gear, and lag adapters in order to correctly position the eigenfrequencies of the fuselage standing on its landing gear, and the blade lag eigenfrequency by preventing mode crossing within the normal rotor speed operating range while providing the damping necessary for the system stability (Coleman’s criterion).

Active control of ground resonance (and air resonance) is then approached. It consists in controlling the fuselage roll oscillations, measured by means of accelerometers placed in the structure, through the rotor main servocontrols which directly act on the cyclic pitch and hence on the blade flapping response, and indirectly on the lag, through the inertial coupling induced by the Coriolis forces.

The next chapter is devoted to the stability of drive shafts of rotating machines, and especially to a form of instability which is expressed through appearance of self-sustained bending vibrations on nonsynchronous frequencies of the shaft rotational speed, and which often lead to a limit cycle resulting from saturation of the forces. The authors show that the energy which supplies the vibrations originates from an external source and, and that such instability is related to the presence of damping internal to the rotating system whereas the original external damping reduces the risk of instability.

The last chapter concerns the problems of stability which may result from the interaction of a fluid with a flexible structure whose deformations change the fluid flow. Such aeroelastic coupling may give rise to self-sustained oscillations whose amplitude increases upon every cycle until their divergence leads to failure of the structure. In other cases, a limit cycle will be reached when there is an energy equilibrium state characterized by oscillation amplitude such that the energy dissipated by the structure compensates for the external energy supply.

Such flutter phenomena concern a substantial number of structures subjected to the effect of wind, like engineering structures, bridges, buildings and electric line cables, airplane wings or else helicopter blades and several cases which are approached in that chapter.

Whirl flutter of the rotors of tilting rotor convertible craft is the subject of a special study which details the relevant mechanisms and shows the effect of all system characteristics on the critical speed at which instability occurs.

We obviously recommend reading of this work, fruit of the collaboration between an industrial engineer and a university teacher, to all people who wish to deepen their knowledge as regards rotary wing dynamics.

Philippe ROESCH

VP Technology & Product Innovation

Eurocopter

Preface

The unstable behavior of structures has always constituted a substantial concern for designers. A simplified definition would consist in saying that the equilibrium of a dynamic system is stable when it remains close to its equilibrium position after any disturbance. Conversely, the system is unstable when it tends to leave its equilibrium position after such a disturbance. This definition will be specified and extended in Chapter 1.

The unstable behavior of structures caused much destruction in several industrial sectors, whether in naval construction, mechanical construction, land construction or air construction. In this foreword, we propose several examples of damage caused by instabilities:

– flutter of airplane stabilizers;

– whirl flutter of rotors;

– ground resonance phenomenon leading to destruction of helicopters;

– instability caused by a hydrodynamic bearing, resulting in damage to a turbine;

– instability due to coupling between a governing system and the behavior of a rotating system.

Airplane Stabilizer Flutter

The aeroelastic coupling phenomenon occurring on airplane wings or stabilizers, termed flutter, caused many disasters.

The most recent example which was made public concerns the E-6A aircraft, Navy’s version of the Boeing 707-320 airplane. In February 1989, that airplane lost the upper section of the tail fin and the rudder control surface in flight, Figure 1.

Figure 1.Crash due to flutter on Boeing E-6A tail fin

The problem was solved by rigidifying the tail fin by extending the spar up to the tail fin tip and reducing the hydraulic pressure in the rudder control surface.

These aeroelastic phenomena constitute, for the aeronautics manufacturers, and especially for the civil aircraft manufacturers, a concern from the design phase to certification, including flight tests [LAC 95]. This problem becomes increasingly crucial due to the emergence of flexible aircraft combining size increase and optimization of the structural index (ratio of the total weight to the empty weight).

Rotor Whirl Flutter

Whirl flutter concerns the aeroelastic coupling of a rotating system with blades or vanes in an airstream. The difficulty in controlling this phenomenon can be illustrated by a historical approach. It appeared on the first constructions of tiltrotor planes, it was hard to model and, consequently, very hard to predict on the first aircraft. The tiltrotor concept and the origin of are explained in .