汽车变速器振动和噪声.pdf

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Vehicle Gearbox Noise and Vibration

Contents

Series Preface

Preface

Acknowledgements

1 Introduction

1.1 Description of the TATRA Truck Powertrain System

1.2 Test Stands

References

2 Tools for Gearbox Noise and Vibration Frequency Analysis

2.1 Theory of Digitisation of Analogue Signals

2.1.1 Types of Signals

2.1.2 Normal Distribution

2.1.3 Mean Value and Standard Deviation (RMS) of a General Signal

2.1.4 Covariance

2.1.5 Mean Value and Standard Deviation (RMS) of a Sinusoidal Signal

2.1.6 Digitalisation of Signals

2.1.7 Signal-to-Noise Ratio

2.1.8 Sampling as a Mapping

2.2 Nyquist-Shannon Sampling Theorem

2.2.1 Antialiasing Filter

2.2.2 Sound and Vibration Measuring Chain

2.3 Signal Analysis Based on Fourier Transform

2.3.1 Time and Frequency Domain

2.3.2 Fourier Series for Periodic Functions

2.3.3 Fourier Transform of the Continuous-Time Functions

2.3.4 Short-Time Fourier Transform

2.3.5 Fourier Transform of the Discrete-Time Functions

2.3.6 Inverse Fourier Transform of the Discrete-Time Functions

2.3.7 DFT of a Constant and a Cosine Signal

2.3.8 Phasors as a Tool for Modelling Harmonic Signals

2.3.9 Example of DFT Calculation

2.3.10 Time and Frequency Scales

2.3.11 Spectral Unit of Autospectrum

2.3.12 Cross-Spectrum

2.3.13 Calculation of the Inverse Discrete Fourier Transform

2.3.14 Fast Fourier Transform

2.3.15 Time Window

2.3.16 Calculation of the Signal Power

2.3.17 Frequency Weighting

2.3.18 Analysis of Random Signals with the Use of Averaging in the Frequency Domain

2.4 Zoom FFT

2.4.1 Real-Time Zoom

2.4.2 Non-Destructive Zoom

2.5 Filtration in the Frequency Domain

2.5.1 Filtering

2.5.2 Integration and Calculation of Derivatives

2.6 Average Power of the Signal

References

3 Gearbox Frequency Spectrum

3.1 Source of Gearbox Noise and Vibration

3.2 Spectrum Signature

3.3 Low Harmonics of the Shaft Speed

3.4 Harmonics of the Fundamental Toothmeshing Frequency and their Sidebands

3.5 Subharmonic Components

3.5.1 Hunting Tooth Frequency

3.5.2 Effect of the Oil Film Instability in Journal Bearings

3.6 Ghost (or Strange) Components

3.7 Gear Rattle

3.8 Periodicity in Signals Measured on a Planetary Gearbox

3.9 Spectrum Components Originating from Faults in Rolling Element Bearings

3.9.1 Calculations for Bearing Defect Frequencies

3.9.2 Envelope Frequency Analysis

References

4 Harmonics and Sidebands

4.1 Harmonics

4.2 Sidebands

4.2.1 Amplitude Modulation

4.2.2 Phase Modulation

4.2.3 Mixed Modulation

4.3 Analytic Signal

4.3.1 Definition of Hilbert Transform

4.3.2 Calculation of Hilbert Transform of Sampled Signals

4.3.3 Demodulation of the Modulated Harmonic Signal

4.3.4 Unwrapping Phase

4.3.5 Normalising Phase

4.3.6 An Alternative Computing the Instantaneous Frequency

4.3.7 Envelope Analysis

4.4 Cepstrum

4.4.1 Effect of Harmonics

4.4.2 Effect of Sideband Components

4.4.3 Advantages of Cepstrum

References

5 Order Analysis

5.1 Speed Rotation Measurements

5.2 Order Analysis Based on External Sampling Frequency

5.3 Digital Order Tracking

5.3.1 Uniformity of Rotation

5.4 Frequency Domain Analysis Methods (Multispectral, Slice Analysis)

5.5 The Use of Order Spectra for Machine Diagnostics

5.6 Averaging in the Time Domain

5.6.1 Principle of Averaging in the Time Domain

5.6.2 Synchronised Averaging as a Comb Filter

5.7 Time Domain as a Tool for Gear Mesh Analysis

5.7.1 Averaging of Resampled Signals

5.7.2 Effect of Load on the Averaged Acceleration Signal

5.7.3 Average Toothmesh

5.7.4 Angular Vibrations

5.7.5 Effect of Averaging

5.7.6 Accuracy of the Incremental Rotary Encoders

5.7.7 Comparison of Averaging in the Time and Frequency Domain

References

6 Tracking Filters

6.1 Interpolation of the Instantaneous Rotational Speed

6.2 Quadrature Mixing as a Method for Amplitude and Phase Demodulation

6.3 Kalman Filter

6.3.1 Examples of the Use of the Kalman Filter

6.4 Vold-Kalman Order Tracking Filtration

6.4.1 Data Equations of the VK-Filter

6.4.2 Structural Equations of the VK-Filter First Generation

6.4.3 Structural Equations of the Second Generation of the VK-Filter

6.4.4 Global Solution of the Single Order Tracking Filtration

6.4.5 The Transfer Function of the VK Filter

6.4.6 Bandwidth of the VK Filter

6.4.7 The Frequency Response of the VK Filter

6.4.8 Global Solution for the Multiorder Tracking Filtration

6.4.9 Analytical Solution for Decoupling of Two Components

6.4.10 Iterative Methods of Solution

6.4.11 PCG Iterative Method

6.4.12 Initial Guess for the Iterative Solution

6.4.13 Comparison of the VK Filter of the First and Second Generation

References

7 Reducing Noise of Automobile Transmissions

7.1 Normal Probability Plot

7.2 Transmission Error Measurements

7.2.1 Averaged Transmission Error for a Circular Pitch Rotation

7.2.2 Transmission Error Measurements during Many Revolutions of Gears

7.3 Case Study

7.3.1 Historical Notes

7.3.2 Vehicle Pass-by Noise Measurements

7.3.3 Estimation of the Doppler Frequency Shift

7.3.4 Pass-by Noise Analysis with the Use of the Vold-Kalman Filter

7.3.5 Factory Limit for the Gearbox SPL

7.4 Gearbox Improvement Aimed at Noise Reduction

7.4.1 Gearbox Housing Stiffness

7.4.2 Geometric Design of Gears

7.5 Effect of Gear Quality on the Gearbox SPL

7.6 Effect of Operation Conditions on the Gearbox Vibrations

7.7 Quality Control in Manufacturing

References

Index

AUTOMOTIVE SERIES VEHICLE GEARBOX NOISE AND VIBRATION MEASUREMENT, SIGNAL ANALYSIS, SIGNAL PROCESSING AND NOISE REDUCTION MEASURES JIRˇÍ TU˚MA

VEHICLE GEARBOX NOISE AND VIBRATION

Automotive Series Series Editor: Thomas Kurfess Vehicle Gearbox Noise and Vibration: Measurement, Signal Analysis, Signal Processing and Noise Reduction Measures Modelling, Simulation and Control of Two-Wheeled Vehicles Modeling and Control of Engines and Drivelines Advanced Composite Materials for Automotive Applications: Structural Integrity and Crashworthiness Guide to Load Analysis for Durability in Vehicle Engineering T˚uma January 2014 Tanelli, Corno and Savaresi March 2014 Eriksson and Nielsen February 2014 Elmarakbi December 2013 Johannesson and Speckert November 2013

VEHICLE GEARBOX NOISE AND VIBRATION MEASUREMENT, SIGNAL ANALYSIS, SIGNAL PROCESSING AND NOISE REDUCTION MEASURES Jiˇr´ı T˚uma VˇSB Technical University of Ostrava, Czech Republic

This edition first published 2014 © 2014, John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. 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, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought. MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. Library of Congress Cataloging-in-Publication Data Tuma, Jiri (Engineer) Vehicle gearbox noise and vibration / by Jiri Tuma. 1 online resource. Includes bibliographical references and index. Description based on print version record and CIP data provided by publisher; resource not viewed. ISBN 978-1-118-79761-7 (ePub) – ISBN 978-1-118-79762-4 (Adobe PDF) – ISBN 978-1-118-35941-9 (cloth) 1. Motor vehicles–Transmission devices–Noise. I. Title. TL262 629.2′440288–dc23 2013051076 A catalogue record for this book is available from the British Library. ISBN: 978-1-118-35941-9 Set in 10/12pt Times by Aptara Inc., New Delhi, India 1 2014

To Magda, Lucie, Peter and Eva To the memory of my parents and brother

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