Automotive Tire Noise and Vibrations: Analysis, Measurement and Simulation [1 ed.] 0128184094, 9780128184097

Table of contents :
Cover
Automotive Tire Noise and Vibrations: Analysis, Measurement and
Simulation
Copyright
Contents
List of Contributors
Preface
1 Background introduction
References
2 Tire/road noise separation: tread pattern noise and road texture noise
2.1 Introduction
2.2 Close proximity measurement
2.3 Tire/road noise separation
2.3.1 Two noise components
2.3.2 Order tracking analysis
2.3.3 Noise separation results
2.4 Tire/road wheel noise separation and combination
2.5 Conclusion
Acknowledgments
References
3 Influence of tread pattern on tire/road noise
3.1 Introduction
3.2 Tire/road noise separation
3.3 Tread pattern parameterization
3.3.1 Tread profile spectrum
3.3.2 Air volume velocity spectrum
3.4 Correlation between tread pattern and tire noise
3.5 Conclusion
Acknowledgments
References
4 Influence of road texture on tire/road noise
4.1 Introduction
4.2 Rough and smooth pavement
4.2.1 Total noise
4.2.2 Tread pattern noise
4.2.3 Nontread pattern noise
4.2.4 Percent contribution from the two noise components
4.3 Pavement texture characterization
4.4 Spectral trend between pavement texture and tire/road noise
4.5 Transfer function and regression model
4.6 Conclusion
Acknowledgments
References
5 Measurement methods of tire/road noise
5.1 Introduction
5.2 Tire noise and vibrations: indoor testing
5.2.1 Indoor testing: structural borne noise characterization
5.2.1.1 Indoor structural borne noise characterization: stationary tire
5.2.1.2 Indoor structural borne noise characterization: rolling tire impact test
5.2.1.3 Indoor structural borne noise characterization: high frequency structural borne noise characterization
5.2.2 Indoor airborne noise characterization
5.3 Outdoor testing
5.3.1 Outdoor testing: subjective evaluation
5.3.2 Outdoor testing: objective evaluation
5.3.2.1 Outdoor objective evaluation: structural borne noise
5.3.2.2 Outdoor objective evaluation: airborne noise
5.3.2.3 Outdoor objective evaluation: pass-by noise measurement
5.4 Summary
References
Further reading
6 Generation mechanisms of tire/road noise
6.1 Introduction
6.2 Tire structural borne noise and airborne noise
6.2.1 Tire structural borne noise
6.2.2 Tire airborne noise
6.3 Tire noise and vibration: generation mechanisms
6.3.1 Impact induced noise and vibration
6.3.2 Air pumping
6.3.3 Friction-induced noise and vibration
6.3.4 Tire nonuniformity as a vibration source
6.4 Tire structural borne noise transmission mechanism
6.4.1 Low frequency transmissibility (below 30Hz)
6.4.2 Mid-frequency transmissibility from 30 to 500Hz
6.4.3 Effect of rolling on tire transmissibility
6.5 Tire noise and vibration amplification by acoustic resonance
6.5.1 Tire cavity resonance
6.5.2 Tire pipe resonance
6.5.3 Tire horn effect
6.6 Summary
References
Further reading
7 Suspension vibration and transfer path analysis
7.1 Introduction
7.2 Excitations of suspension system from road and tire
7.2.1 Excitation from road roughness
7.2.2 Excitation generated by tire
7.3 Theoretical basis of transfer path analysis method
7.3.1 Traditional transfer path analysis method
7.3.1.1 Frequency response function
7.3.1.2 Identification of structural load
7.3.1.3 Analysis of transfer path
7.3.2 Operational transfer path analysis
7.4 Transfer path analysis of suspension vibration
7.4.1 Frequency response function of suspension and car body system
7.4.2 Identification of load between suspension and car body
7.4.3 Transfer path analysis of suspension vibration
7.5 Transfer path analysis of structure-borne tire/road noise
7.5.1 Transfer function of structure-borne noise
7.5.2 Identification of load on path point and principal component analysis
7.5.3 Analysis of interior noise from tire/road interaction based on transfer path analysis
7.5.3.1 Transfer path analysis of structure-borne tire/road noise based on test
7.5.3.2 Control of structure-borne tire/road noise based on simulation
7.6 Summary
Nomenclatures
References
8 Structure-borne vibration of tire
8.1 Introduction
8.2 Modal characteristics of tire vibration and influencing parameters
8.2.1 Modal characteristics of tire vibration
8.2.2 Influencing parameters of modal characteristics of tire vibration
8.2.2.1 Influence of tire pressure
8.2.2.2 Influence of tread pattern
8.2.2.3 Influence of tire mass
8.2.2.4 Influences of belt angle and Young’s moduli of belt cord and tread compound
8.3 Modal test methods of a tire
8.4 Analytical calculation method of tire mode
8.4.1 Two-dimensional ring model of a tire
8.4.1.1 Strain of ring
8.4.1.2 Initial stress
8.4.1.3 Velocity of point at middle surface of ring
8.4.1.4 Work of inflation pressure
8.4.2 Three-dimensional ring model of tire
8.4.2.1 Stress and strain of tire crown
8.4.2.2 Equations of motion of three-dimensional ring model
8.4.2.3 In-plane free vibration mode of a tire
8.4.2.4 Out-of-plane free vibration mode of a tire
8.5 Modal analysis of a tire based on finite element method
8.5.1 Differential equations of a dynamic system
8.5.2 Methods of solving natural frequency and modal shape
8.5.3 Establishment of finite element model of a tire
8.5.4 Natural frequency and modal shape of a tire
8.6 Summary
Nomenclature
References
9 Structural-acoustic analysis of tire cavity system
9.1 Introduction
9.2 Frequency and wave number
9.3 Tire cavity resonance
9.4 Tire-cavity-wheel system
9.5 Tire cavity resonance frequency
9.5.1 Degenerate tire cavity modes
9.6 Tire tread natural frequency and mode shape
9.7 Structural-acoustic coupling of tire tread and cavity
9.7.1 Impedance-mobility approach
9.8 Finite element simulation of tire structural resonance
9.9 Finite element simulation of structural-acoustic coupling of tire cavity
9.10 Experiment using model from FEM
9.11 Effect of loaded tire
9.12 Road experiment using internal microphone
9.13 Summary
Nomenclature
References
10 Computer-aided engineering findings on the physics of tire/road noise
10.1 Introduction
10.2 Computer-aided engineering simulation methodologies
10.2.1 Deterministic methods at low frequency
10.2.1.1 Finite element method
10.2.1.2 Boundary element method
10.2.1.3 Waveguide finite element method
10.2.2 Energy methods at high frequency
10.2.2.1 Statistical energy analysis
10.2.2.2 Energy finite element analysis
10.2.3 Hybrid methods in the mid frequency range
10.3 Other computer-aided engineering simulation methodologies
10.3.1 Computational fluid dynamics
10.3.2 Transfer path analysis
10.4 Vehicle suspension corner module simulation
10.5 Mechanisms of the wheel imbalance induced vibration
10.6 Tire–road interaction caused by dynamic force variation induced by a hexagon tire
10.7 Tire–road interface impact force and friction force-induced vibration
10.8 Finite element modeling of tire–pavement interaction
10.9 Auralization models of tire/road noise
10.10 Trends and challenges in computer-aided engineering modeling of tire/road noise
10.11 Summary
Nomenclature
References
11 Tire cavity noise mitigation using acoustic absorbent materials
11.1 Introduction
11.2 Sound absorption coefficient theory
11.2.1 Airflow resistivity
11.2.2 Empirical models
11.2.3 Effect of airflow resistivity
11.2.4 Effect of layer thickness
11.3 Absorption coefficient measurement methodologies
11.3.1 Impedance tube method
11.3.2 Alpha cabin
11.4 Tire cavity damping loss
11.5 Sound absorption with perforated plates, porous materials, and air gaps
11.6 Application to tire cavity
11.7 Multilayer configuration design
11.8 Analytical simulation of the multilayer sound absorber
11.9 Using finite element simulation
11.10 Experiments on tires
11.11 Experimental modal test (impact hammer test)
11.12 Experimental modal analysis test with a shaker excitation
11.13 Design of experiment (Taguchi)
11.14 Summary
Nomenclature
References
12 Statistical energy analysis of tire/road noise
12.1 Introduction
12.2 Basic principle of statistical energy analysis
12.2.1 Power balance equation of statistical energy analysis
12.2.2 Energy description of subsystem
12.2.3 Damping loss factor and coupling loss factor
12.3 Simulation of tire high-frequency vibration and tire cavity resonance noise
12.3.1 Statistical energy analysis model and simulation of tire structure
12.3.1.1 Subsystem partition and statistical energy analysis model of a tire
12.3.1.2 Parameters in statistical energy analysis model of a tire
12.3.1.3 Simulation results and analysis
12.3.2 Statistical energy analysis model and simulation of tire cavity system
12.3.2.1 Statistical energy analysis model of tire with cavity
12.3.2.2 Parameters of statistical energy analysis model and external excitation
12.3.2.3 Simulation of tire cavity system using statistical energy analysis
12.4 Tire/road noise modeling and simulation using statistical energy analysis
12.4.1 Generation and propagation of tire/road noise
12.4.2 Statistical energy analysis model of a car body
12.4.3 Input power in statistical energy analysis model
12.4.4 Parameters in statistical energy analysis model
12.4.5 Simulation of tire/road noise
12.5 Summary
Nomenclature
References
13 Pass-by noise: regulation and measurement
13.1 Introduction
13.2 Generation mechanisms and characteristics of the tire/road pass-by noise
13.2.1 Generation mechanisms of the tire/road pass-by noise
13.2.2 Pass-by noise frequency content
13.2.3 The effect of the air temperature on the pass-by noise
13.3 ISO 362-1/ECE R51.03
13.3.1 ISO 362-1/ECE R51.03 acceleration test targets
13.3.2 ISO 362-1/ECE R51.03 acceleration test gear selections
13.3.3 ISO 362-1/ECE R51.03 acceleration test
13.3.4 ISO 362-1/ECE R51.03 constant speed cruise test
13.3.5 Interpretation of test results under ISO 362-1/ECE R51.03
13.3.6 ISO 362-3 indoor pass-by noise test and simulation development
13.4 Source and contribution identification of pass-by noise
13.5 Other pass-by noise research and development
13.6 Summary
Nomenclature
References
14 Pass-by noise: simulation and analysis
14.1 Introduction
14.2 Pass-by noise prediction model
14.3 Sensitivity analysis and propagation of uncertainty
14.4 Substitution monopole technique
14.4.1 Method of correlated equivalent monopoles
14.4.2 Method of uncorrelated equivalent monopoles
14.4.2.1 Source strength definition of uncorrelated monopoles
14.4.2.2 Transfer functions
14.4.2.3 Determination of the source strength of uncorrelated monopoles
14.4.2.4 Validation experiments
14.5 Airborne source quantification method
14.6 Transmissibility approach
14.7 Numerical prediction methods for the pass-by noise
14.7.1 Neural networks approach
14.7.2 Boundary element method
14.8 Summary
Nomenclature
References
15 Summary and future scope
References
Index
Back Cover

Citation preview

Automotive Tire Noise and Vibrations

Automotive Tire Noise and Vibrations Analysis, Measurement and Simulation

Edited by

XU WANG School of Engineering, RMIT University, Melbourne, VIC, Australia

Butterworth-Heinemann is an imprint of Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright © 2020 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-12-818409-7 For Information on all Butterworth-Heinemann publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Matthew Deans Acquisitions Editor: Carrie Bolger Editorial Project Manager: Rachel Pomery Production Project Manager: Kamesh Ramajogi Cover Designer: Victoria Pearson Typeset by MPS Limited, Chennai, India

Contents List of contributors Preface

1.

Background introduction

xiii xv

1

Xu Wang

2.

References

6

Tire/road noise separation: tread pattern noise and road texture noise

7

Tan Li

3.

2.1 Introduction 2.2 Close proximity measurement 2.3 Tire/road noise separation 2.3.1 Two noise components 2.3.2 Order tracking analysis 2.3.3 Noise separation results 2.4 Tire/road wheel noise separation and combination 2.5 Conclusion Acknowledgments References

7 7 12 12 14 16 20 24 25 25

Influence of tread pattern on tire/road noise

27

Tan Li 3.1 Introduction 3.2 Tire/road noise separation 3.3 Tread pattern parameterization 3.3.1 Tread profile spectrum 3.3.2 Air volume velocity spectrum 3.4 Correlation between tread pattern and tire noise 3.5 Conclusion Acknowledgments References

27 29 31 32 35 37 39 39 39

v

vi

4.

Contents

Influence of road texture on tire/road noise

43

Tan Li

5.

4.1 Introduction 4.2 Rough and smooth pavement 4.2.1 Total noise 4.2.2 Tread pattern noise 4.2.3 Nontread pattern noise 4.2.4 Percent contribution from the two noise components 4.3 Pavement texture characterization 4.4 Spectral trend between pavement texture and tire/road noise 4.5 Transfer function and regression model 4.6 Conclusion Acknowledgments References

43 45 46 47 48 50 50 56 58 61 62 62

Measurement methods of tire/road noise

65

Yousof Azizi

6.

5.1 Introduction 5.2 Tire noise and vibrations: indoor testing 5.2.1 Indoor testing: structural borne noise characterization 5.2.2 Indoor airborne noise characterization 5.3 Outdoor testing 5.3.1 Outdoor testing: subjective evaluation 5.3.2 Outdoor testing: objective evaluation 5.4 Summary References Further reading

65 67 67 76 83 83 83 89 89 90

Generation mechanisms of tire/road noise

91

Yousof Azizi 6.1 Introduction 6.2 Tire structural borne noise and airborne noise 6.2.1 Tire structural borne noise 6.2.2 Tire airborne noise 6.3 Tire noise and vibration: generation mechanisms 6.3.1 Impact induced noise and vibration 6.3.2 Air pumping 6.3.3 Friction-induced noise and vibration

91 93 94 94 95 95 97 98

Contents

6.3.4 Tire nonuniformity as a vibration source 6.4 Tire structural borne noise transmission mechanism 6.4.1 Low frequency transmissibility (below 30 Hz) 6.4.2 Mid-frequency transmissibility from 30 to 500 Hz 6.4.3 Effect of rolling on tire transmissibility 6.5 Tire noise and vibration amplification by acoustic resonance 6.5.1 Tire cavity resonance 6.5.2 Tire pipe resonance 6.5.3 Tire horn effect 6.6 Summary References Further reading

7.

Suspension vibration and transfer path analysis

vii 100 102 103 105 107 108 108 110 111 113 113 113

115

Xiandong Liu and Qizhang Feng 7.1 Introduction 7.2 Excitations of suspension system from road and tire 7.2.1 Excitation from road roughness 7.2.2 Excitation generated by tire 7.3 Theoretical basis of transfer path analysis method 7.3.1 Traditional transfer path analysis method 7.3.2 Operational transfer path analysis 7.4 Transfer path analysis of suspension vibration 7.4.1 Frequency response function of suspension and car body system 7.4.2 Identification of load between suspension and car body 7.4.3 Transfer path analysis of suspension vibration 7.5 Transfer path analysis of structure-borne tire/road noise 7.5.1 Transfer function of structure-borne noise 7.5.2 Identification of load on path point and principal component analysis 7.5.3 Analysis of interior noise from tire/road interaction based on transfer path analysis 7.6 Summary Nomenclatures References

8.

Structure-borne vibration of tire

115 116 117 119 123 123 129 132 133 134 135 137 138 139 140 144 145 146

149

Xiandong Liu and Qizhang Feng 8.1 Introduction

149

viii

Contents

8.2 Modal characteristics of tire vibration and influencing parameters 8.2.1 Modal characteristics of tire vibration 8.2.2 Influencing parameters of modal characteristics of tire vibration 8.3 Modal test methods of a tire 8.4 Analytical calculation method of tire mode 8.4.1 Two-dimensional ring model of a tire 8.4.2 Three-dimensional ring model of tire 8.5 Modal analysis of a tire based on finite element method 8.5.1 Differential equations of a dynamic system 8.5.2 Methods of solving natural frequency and modal shape 8.5.3 Establishment of finite element model of a tire 8.5.4 Natural frequency and modal shape of a tire 8.6 Summary Nomenclature References

9.

Structural-acoustic analysis of tire cavity system

151 151 151 157 160 161 165 173 174 174 175 177 180 181 182

185

Zamri Mohamed Introduction Frequency and wave number Tire cavity resonance Tire-cavity-wheel system Tire cavity resonance frequency 9.5.1 Degenerate tire cavity modes 9.6 Tire tread natural frequency and mode shape 9.7 Structural-acoustic coupling of tire tread and cavity 9.7.1 Impedance-mobility approach 9.8 Finite element simulation of tire structural resonance 9.9 Finite element simulation of structural-acoustic coupling of tire cavity 9.10 Experiment using model from FEM 9.11 Effect of loaded tire 9.12 Road experiment using internal microphone 9.13 Summary Nomenclature References 9.1 9.2 9.3 9.4 9.5

185 186 188 189 190 194 196 199 200 203 206 207 211 212 212 214 215

Contents

ix

10. Computer-aided engineering findings on the physics of tire/road noise 217 Laith Egab 10.1 Introduction 10.2 Computer-aided engineering simulation methodologies 10.2.1 Deterministic methods at low frequency 10.2.2 Energy methods at high frequency 10.2.3 Hybrid methods in the mid frequency range 10.3 Other computer-aided engineering simulation methodologies 10.3.1 Computational fluid dynamics 10.3.2 Transfer path analysis 10.4 Vehicle suspension corner module simulation 10.5 Mechanisms of the wheel imbalance induced vibration 10.6 Tire road interaction caused by dynamic force variation induced by a hexagon tire 10.7 Tire road interface impact force and friction force-induced vibration 10.8 Finite element modeling of tire pavement interaction 10.9 Auralization models of tire/road noise 10.10 Trends and challenges in computer-aided engineering modeling of tire/ road noise 10.11 Summary Nomenclature References

11. Tire cavity noise mitigation using acoustic absorbent materials

217 219 219 223 227 229 229 229 230 233 233 234 235 238 239 240 240 242

245

Zamri Mohamed and Laith Egab 11.1 Introduction 11.2 Sound absorption coefficient theory 11.2.1 Airflow resistivity 11.2.2 Empirical models 11.2.3 Effect of airflow resistivity 11.2.4 Effect of layer thickness 11.3 Absorption coefficient measurement methodologies 11.3.1 Impedance tube method 11.3.2 Alpha cabin 11.4 Tire cavity damping loss 11.5 Sound absorption with perforated plates, porous materials, and air gaps 11.6 Application to tire cavity

245 246 246 247 248 250 250 251 252 253 254 255

x

Contents

11.7 Multilayer configuration design 11.8 Analytical simulation of the multilayer sound absorber 11.9 Using finite element simulation 11.10 Experiments on tires 11.11 Experimental modal test (impact hammer test) 11.12 Experimental modal analysis test with a shaker excitation 11.13 Design of experiment (Taguchi) 11.14 Summary Nomenclature References

12. Statistical energy analysis of tire/road noise

256 258 260 261 262 263 264 268 268 269

271

Xiandong Liu and Qizhang Feng 12.1 Introduction 12.2 Basic principle of statistical energy analysis 12.2.1 Power balance equation of statistical energy analysis 12.2.2 Energy description of subsystem 12.2.3 Damping loss factor and coupling loss factor 12.3 Simulation of tire high-frequency vibration and tire cavity resonance noise 12.3.1 Statistical energy analysis model and simulation of tire structure 12.3.2 Statistical energy analysis model and simulation of tire cavity system 12.4 Tire/road noise modeling and simulation using statistical energy analysis 12.4.1 Generation and propagation of tire/road noise 12.4.2 Statistical energy analysis model of a car body 12.4.3 Input power in statistical energy analysis model 12.4.4 Parameters in statistical energy analysis model 12.4.5 Simulation of tire/road noise 12.5 Summary Nomenclature References

13. Pass-by noise: regulation and measurement

271 273 274 276 277 279 279 283 288 289 289 289 291 291 293 294 295

297

Xu Wang 13.1 Introduction 13.2 Generation mechanisms and characteristics of the tire/road pass-by noise 13.2.1 Generation mechanisms of the tire/road pass-by noise

297 297 298

Contents

13.2.2 Pass-by noise frequency content 13.2.3 The effect of the air temperature on the pass-by noise 13.3 ISO 362-1/ECE R51.03 13.3.1 ISO 362-1/ECE R51.03 acceleration test targets 13.3.2 ISO 362-1/ECE R51.03 acceleration test gear selections 13.3.3 ISO 362-1/ECE R51.03 acceleration test 13.3.4 ISO 362-1/ECE R51.03 constant speed cruise test 13.3.5 Interpretation of test results under ISO 362-1/ECE R51.03 13.3.6 ISO 362-3 indoor pass-by noise test and simulation development 13.4 Source and contribution identification of pass-by noise 13.5 Other pass-by noise research and development 13.6 Summary Nomenclature References

14. Pass-by noise: simulation and analysis

xi 303 305 308 312 314 314 314 315 316 321 322 330 330 331

333

Xu Wang Introduction Pass-by noise prediction model Sensitivity analysis and propagation of uncertainty Substitution monopole technique 14.4.1 Method of correlated equivalent monopoles 14.4.2 Method of uncorrelated equivalent monopoles 14.5 Airborne source quantification method 14.6 Transmissibility approach 14.7 Numerical prediction methods for the pass-by noise 14.7.1 Neural networks approach 14.7.2 Boundary element method 14.8 Summary Nomenclature References 14.1 14.2 14.3 14.4

15. Summary and future scope

333 333 338 340 341 342 348 352 354 354 355 357 358 360

361

Tan Li References Index

368 369

List of Contributors Yousof Azizi Bridgestone Americas, Akron, OH, United States Laith Egab School of Engineering, RMIT University, Melbourne, VIC, Australia Qizhang Feng Beihang University, Beijing, P.R. China Tan Li Maxxis Technology Center, Suwanee, GA, United States; Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, United States Xiandong Liu Beihang University, Beijing, P.R. China Zamri Mohamed Faculty of Mechanical and Automotive Engineering Technology, Universiti Malaysia Pahang, Pekan, Malaysia Xu Wang School of Engineering, RMIT University, Melbourne, VIC, Australia

xiii

Preface As developed powertrains become quieter and quieter, tire/road noise cannot be masked by the powertrain noise anymore. Therefore, tire/road noise of motor vehicles is increasingly important for the automotive industry and is a major concern for both vehicle manufacturers and component suppliers since legislation on noise pollution is driving down vehicle exterior noise, and customers are becoming more concerned about vehicle interior noise. This book provides a review of tire/road noise generation mechanisms, characteristics, frequency contents, traffic regulation, control methods, advanced experimental and modeling techniques. A comprehensive reference list is provided in order to direct further studies and assist readers to develop in-depth knowledge of the sources and transmission mechanisms of the tire/road noise. The book aims to provide the information needed for university undergraduates and postgraduates, research students, scientific researchers, academia in mechanical or automotive engineering, highway and automotive engineers, and government officers related to environmental policies. The book could also be used as a textbook for postgraduate by course students in a program of mechanical or automotive engineering. The tire/road noise is a challenging problem, and methods for improvement are not straightforward. This book is intended to present the fundamentals of the generation and transmission mechanisms of the tire/road noise in vehicle suspension and road system, and to summarize the state-of-the-art knowledge of the tire/road noise research. The book includes chapters to describe: • The tire/road noise generation mechanisms • The tire/road noise measurement and evaluation methods • Transfer path analysis and control of structure-borne tire/road noise • Transfer path analysis and control of airborne tire/road noise • Current technologies and analysis methods used to develop the reduced interior tire/road noise • Pass-by tire/road noise and traffic regulation The authors include specialist engineers from major automotive manufacturers and tire component suppliers and researchers from universities.

xv

xvi

Preface

An additional aim of this book is to improve automotive engineering education and to bridge the gap between the automotive industry and universities. The uniqueness of this book is to study the tire/road noise in the system of road, tire, and vehicle as a whole which is different from other books related to this topic. This book only covers the interior and exterior tire/road noise study under the dry road conditions.

CHAPTER 1

Background introduction Xu Wang

School of Engineering, RMIT University, Melbourne, VIC, Australia

Sound results from small, fast pressure variations and propagates in a fluid medium. Acoustics is a science of sound that studies generation, propagation, and reception of sound in all aspects. Noise is refereed as unwanted sound. In the case of the tire/pavement noise, the unwanted sound propagates in the medium of the air. Thus any air pressure variation resulting from the tire/road interaction will generate noise in the air. The traffic noise was commonly already complained in the Roman Empire. Nearly 2000 years later, in 1869, the problem seemed not to be changed much, as noted by Sir Norman Moore, a British physician, who described the noise graphically in a London street: “Most of the streets were paved with granite sets and on them the wagons with iron-tired wheels made a din that prevented conversation while they passed by. The roar of London by day was almost terrible—a never varying deep rumble that made a background to all other sounds” [1]. Tire/road noise (TRN) is the noise emitted from a rolling tire as a result of the interaction between the tire and road surface [2]. TRN is also known as the tire road interaction noise, tire pavement interaction noise (TPIN), tire pavement noise, or tire noise. The term tire/tyre was used even before the pneumatic tire was known representing the outer part of the wheel. In the days of iron-shredded wheel/tires, the interaction of metal (tire as well as horse shoes) and stone (pavement) created noise. TRN includes two aspects, one is the interior TRN, which has been concerned with vehicle engineers and tire industry from the 1930s, and the other is exterior TRN, which was first studied experimentally in 1955 [3]. The success in reducing the vehicle interior TRN has been remarkable. For example, the interior dominated TRN levels in the 1.5 1.8 liter Japanese cars driven at 100 km/h had been reduced by 8 dB(A) in the time period 1976 85 [4]. Sound pressure levels (SPLs) and sound quality Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00001-5

© 2020 Elsevier Inc. All rights reserved.

1

2

Automotive Tire Noise and Vibrations

of the interior TRN have been reduced and improved. The reason for the remarkable reduction of interior noise is that the acoustic comfort within a vehicle cabin is one of the important product quality attributes reflecting the brand image: vehicles that are quiet inside are considered comfortable and give the owner a feeling of luxury. Interior TRN is affected by tire, road, and vehicle suspension system. The TRN is generated by four subsources/mechanisms: tread impact, air pumping, slip-stick, and stick-snap. At the tire pavement interaction, the mechanisms create energy, which is eventually radiated as sound. The four TRN source generation mechanisms are all important for certain combinations of the tire and pavement. Different source mechanisms may dominate the sound generation for different applications making it difficult to develop the TRN reduction strategies for all cases. If source mechanisms are similar in strength, a strategy to suppress one mechanism will not have a large effect on the overall noise level because other mechanisms will become dominant. Sound enhancement mechanisms are the characteristics of the TPIN that causes that energy to be converted to sound and radiated efficiently. The sound enhancement mechanisms consist of the horn effect, organ pipes, the Helmholtz resonators, carcass vibration, and internal acoustic cavity resonance. The enhancement mechanisms further complicate the strategies for reducing the TRN. The contributions from the various sound enhancement mechanisms or from the source mechanisms are often difficult to distinguish from each other. It is not clear which mechanisms are important for various surfaces and conditions. Many of the mechanisms for generation or enhancement of the sound from tires and road are directly integrated with the tire/road characteristics required for safety, durability, and cost. The road traffic noise is a main contributor to environmental noise, which represents a burden to people resulting in annoyance, sleep disturbance, or cardiovascular disease [5]. Hence, legislation intends to reduce and limit vehicle exterior noise [6] in order to increase health and life quality. Modeling/analysis, measurement, and simulation techniques of the exterior TRN have been extensively studied since the 1970s. The emission limits introduced first in the 70s were very liberal, but later tightening of limits has been rather tough, at least for trucks and busses. Exterior vehicle noise has been reduced very little at high speeds but largely at low speeds for heavy vehicles. But the exterior TRN of the passenger car tires may have increased somewhat rather than decreased; the reasons for this issue are believed to be caused by no requirements being

Background introduction

3

in place and a general trend toward wider tires with design optimizations more and more focused on their extreme high-speed performance. In 1982 Samuels [7] conducted systematically experimental studies and theoretical study named as air-pumping theoretical model, and derived some important conclusions, which are now also correct and guiding: (1) Roadside noise level increased with increasing vehicle speed, road surface macrotexture roughness, and tire tread roughness. (2) The road surface macrotexture was found to be the most dominant of the above three parameters. (3) The roadside noise contributed from different road and tire components occurred over different frequency ranges. Speed, road, and tire are the three most important and dominant factors for exterior TRN. No other single factor has a more prominent influence on TRN than the speed. It is well known that the noise relationship with vehicle speed very closely follows the ideal relation Lp 5 A 1 B 3 log(V) as V is the vehicle speed in unit of km/h. However, the speed influence is not our focus for the solution. Therefore the noisespeed relation is seldom outlooked any further. With regard to the road surface, different road surfaces may give a large variation in noise levels, say up to 17 dB(A) [8]. A driver can easily have this driving experience on different road surfaces. The rougher the texture is, the higher the noise emission becomes. The mean profile depth (MPD) for the road surface texture has been found to be a good measure of the road surface texture for describing its influence on wet friction, but unfortunately it appears that the relation between the noise level and MPD is far from being clear. Tire influence has a SPL range of 10 dB(A) between the best and the worst tires in a sample of nearly 100 tires of approximately similar sizes (the tires were all new or newly retreaded and available in tire shops) [8]. In addition to the SPL range quoted above, other variables like tire width and state of wear also affect the TRN levels and will increase the flouncing range of the TRN SPLs. When taking all such effects into account, it seems that the flouncing range of the TRN SPLs for tires is approximately as large as that for road surfaces. The TRN emission should always be eliminated at the source. It is natural to look first at the possibilities for the noise reduction through the measures relating to tires. It is important to understand the root causes and generation mechanisms of the TRN to reduce the noise. Background introduction of TRN is concluded here. Chapter 2, Tire/ Road Noise Separation: Tread Pattern Noise and Road Texture Noise,

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Automotive Tire Noise and Vibrations

will introduce close proximity (CPX) method to measure the near-field TRN and break down the tire noise into the tread pattern and nontread pattern noise components. This method can also be expanded to lab drum test applications where the noise can be separated into tread pattern noise, road-drum noise, and aerodynamic noise. Chapter 3, Influence of Tread Pattern on Tire/Road Noise, studies the contribution of tread pattern to TRN through two major mechanisms: (1) tread impact due to the interaction between the tread blocks and the road and (2) air pumping due to the air compression/expansion in the tread grooves. Chapter 4, Influence of Road Texture on Tire/Road Noise, investigates influence of road surface on the TRN. It was found that smoother pavement tends to cause higher tread pattern noise but lower nontread pattern noise. Good correlation can be found between pavement texture velocity spectrum and tire nontread pattern noise spectrum. Chapter 5, Measurement Methods of Tire/Road Noise, studies measurement methods of the TRN as not only objective measurements but also advanced subjective evaluations will have to be conducted to evaluate and quantify the TRN. Different indoor and outdoor tests developed over years and used by industry and academia are presented to evaluate tire noise and vibration performance in regard to their generation and transmission. Chapter 6, Generation Mechanism of Tire/Road Noise, studies the generation mechanisms of the TRN. The tire noise and vibration and their different mechanisms involved in generation, transmission, as well as amplification of the structural borne noise and the airborne noise to the vehicle cabin and the environment will be illustrated. Chapter 7, Suspension Vibration and Transfer Path Analysis, will study the excitation of suspension, which mainly comes from the tire road roughness and tire or tire pavement interaction. Chapter 7, Suspension Vibration and Transfer Path Analysis, will also study the method of transfer path analysis (TPA) and the application of TPA method in analysis of structure-borne TRN. Chapter 8, Structure-Borne Vibration of Tire, will investigate the modal characteristics of tire and the influences of some key parameters on the modal characteristics, including the inflation pressure, tread pattern, tire mass, belt angle, and Young’s moduli of belt cord and tread compound. The modal testing method, analytical modal models, and finite element model of a tire (including 2D and 3D ring models) will be also studied. Chapter 9, Structural-Acoustic Analysis of Tire-Cavity System, will explore tire-cavity noise by means of analytical, finite element, and experimental methods.

Background introduction

5

Chapter 10, Computer-Aided Engineering Findings on the Physics of Tire/Road Noise, will report the progress and improvement in the theory and algorithms that is being used to simulate and predict the TRN including the key CAE simulation methods like finite element method (FEM), boundary element method (BEM), waveguide finite element method (WFEM), statistical energy analysis (SEA), energy finite element analysis (EFEA), computational fluid dynamics (CFD), and TPA. This chapter also studies the auralization models of the TRN and uncovers the current trends and challenges in the CAE modeling of TRN. Chapter 11, Tire/Road Noise Mitigation Using Acoustic Absorbent Materials, will study the acoustic properties of felt material by means of theoretical calculation, finite element simulation, and laboratory experiment. Chapter 11, Tire/Road Noise Mitigation Using Acoustic Absorbent Materials, will also investigate possibility of the use of felt and multilayer trim materials for increasing the acoustic damping and sound absorption coefficient of cavities through a given mathematical solution and several empirical models found in the literature and verify it by the impedance tube measurement results. Chapter 12, Statistical Energy Analysis of Tire/Road Noise, will study the basic principle of SEA and the application of SEA method in analyzing TRN, which includes the subsystem parameter identification, and the mean energy prediction of all the airborne and structure-borne TRN subsystems in the mid-high frequency range. Chapter 13, Pass-by Noise: Regulation and Measurement, will study general vehicle pass-by noise with a focus on generation mechanisms, characteristics, and frequency components of the pass-by TRN. Chapter 14, Pass-by Noise: Simulation and Analysis, will introduce the simulation, analysis, regulation testing, and numerical prediction methods of the pass-by noise for source identification and sensitivity study based on the TPA method. Chapter 15, Summary and Future Scope, will make conclusions for this book. The TRN is generated by the impact of road surface texture on the tire tread and by the impact of the tire tread pattern on the road surface, both of these exciting radial vibrations in the tire. In addition, the displacement of air in and out of the tire pavement interaction contact patch contributes to the noise emission. Chapter 15, Summary and Future Scope, will also illustrate the future research scope of the TRN including how electric vehicles and regulations/requirements/expectations will shape the future of the tire/automobile industry.

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References [1] Crocker MJ. (e.d.) Introduction chapter in the book “Noise Control”. New York: Van Nostrand Reinhold Co. Inc.; 1984. [2] Sandberg U, Ejsmont JA. Tyre/road noise reference book. Kisa, Sweden; Harg, Sweden: INFORMEX; 2002. ISBN 9789163126109, 9163126109. [3] Luetgebrune H. Reifengeräusche - Fahrzeuggeräusche. Kautschuk und Gummi 1955;4:91 6. [4] Namba S. Noise—quantity and quality. In: Proceedings of inter-Noise 94, Yokohama, Japan; 1994. p. 3 22. [5] “Quiet Pavement” project underway and news. Arizona Department of Transportation. www.quietroads.com [accessed July 2004]. [6] ANSI S1.18. Template method for ground impedance. Acoustical Society of America. [7] Samuels S. The generation of tyre/road noise. ISSN 0518-0728; 1982. [8] Sandberg U. Tire/road noise-myths and realities. In: Proceedings of the 2001 international congress and exhibition on noise control engineering. The Netherlands: The Hague; 2001.

CHAPTER 2

Tire/road noise separation: tread pattern noise and road texture noise Tan Li1,2 1

Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, United States Maxxis Technology Center, Suwanee, GA, United States

2

2.1 Introduction Tire/road noise is also known as tire road interaction noise, tire pavement interaction noise (TPIN), tire pavement noise, or tire noise, which is defined as the noise emitted from a rolling tire as a result of the interaction between the tire and the road surface [1]. However, few literatures have reported the mechanisms about this interaction, or the individual contributions from tread pattern and road texture [2,3]. In this chapter, case studies will be demonstrated to reveal the tire pavement interaction mechanisms.

2.2 Close proximity measurement In this section, the experimental setup for tire noise data collection is introduced, including test tires, test pavement, test equipment, and test conditions [4,5]. The 37 tires tested are listed in Table 2.1. Their tread pattern pictures are shown in Fig. 2.1 where the red arrow indicates the rotation direction for directional tires in the test. All the tires are tubeless radial tires. Most of the tires are passenger car tires, including all-season tires, winter/snow tires. Tire 42 is for light truck (LT); Tire 53 is for trailer only. Some tires are just for lab purpose but not for sale (Tires 39 and 49). Some tires have the same size and aspect ratio (e.g., Tires 1 19 of 215/60R16) but different tread patterns. Tire 20 is the Standard Reference Test Tire (SRTT). Tires 19, 25, 27, and 29 are the same tire for repeatability evaluation. Tires 12, 24, and 26 are the same tire but in different rotation directions. Tire 43 has long and narrow tread blocks instead of square blocks Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00002-7

© 2020 Elsevier Inc. All rights reserved.

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Automotive Tire Noise and Vibrations

Table 2.1 Specifications of the test tires. No.

Size

Condition

Number of pitches

Number of plies (tread/ sidewall)

Rubber hardness (Shore A)

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 29 37 39 42 43 45 49 53 54 55 57

215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 225/60R16 225/60R16 225/60R16 215/60R16 215/60R16 215/60R16 215/60R16 215/60R16 265/70R17 255/55R18 235/85R16 215/60R16 235/55R19 205/70R15 235/80R16 245/40R18 235/70R16 225/60R16

All-season All-season All-season All-season All-season All-season All-season All-season Winter/snow All-season All-season Winter/snow All-season All-season All-season All-season All-season All-season Winter/snow All-season All-season All-season Winter/snow Winter/snow Winter/snow Winter/snow Winter/snow All-season Not for sale All-season (LT) All-season All-season Not for sale Trailer All-season All-season Worn

70 64 72 64 76 70 76 56 62 72 72 77 66 68 72 72 72 65 60 81 60 60 77 60 77 60 60 50 85 66 28 80 65 67 64 72 66

5/2 4/1 4/2 4/1 4/1 4/1 4/1 4/2 3/1 4/1 4/1 4/1 4/1 4/1 4/1 4/1 4/1 5/2 5/2 3/1 5/2 5/2 4/1 5/2 4/1 5/2 5/2 5/2 5/2 5/2 5/2 6/2 4/2 5/2 5/2 4/2 5/2

66.0 63.3 67.5 66.5 68.5 64.5 70.3 63.7 59.0 63.7 61.7 57.5 64.3 64.0 56.5 67.0 59.3 65.8 66.0 66.0 65.0 65.0 61.3 67.3 59.0 68.0 66.8 71.5 76.5 72.0 70.0 71.0 74.0 79.0 68.5 61.5 76.5

Tire/road noise separation: tread pattern noise and road texture noise

9

Figure 2.1 Tread patterns of the test tires (arrow indicates rotation direction).

commonly seen in the other tires. Tire 57 has the same tread pattern as Tire 13 but different tire size and tread depth. It is also noted that Tires 1 30 are of the same size (215/60R16), except Tires 20 23 of 225/ 60R16 that is very similar size to the former. Tires 31 60 have various sizes. The number of pitches, as shown in Table 2.1, is the total number of tread elements (or usually tread blocks) around the full tire circumference. The number of plies in the tread band and the sidewall differs for different tires, indicating that the structure of the tires varies. However, the number of plies is shown to be not very different for the tires tested, thus it is not of interest in this study. The tread rubber hardness was the average of several measurements and it is generally accepted that the tolerance for rubber hardness measurements is 6 2 Shore A. Most of the tires are pretty new and well stored in the lab, and the rubber hardness is generally in the range between 60 and 70 Shore A. Some tires, especially the bigger tires, are very old (over 10 years) and the rubber hardness is usually over 70 Shore A due to the age hardening effect. The test pavement is U.S. Route 460 near Virginia Tech (between Toms Creek Rd. and North Main St. with one-way distance of around 1.3 mile), as shown in Fig. 2.2. It is a nonporous asphalt pavement that is commonly seen in USA. Both eastbound section and westbound section

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Automotive Tire Noise and Vibrations

Figure 2.2 Test pavement. From Google Street View.

Table 2.2 Different tire sizes tested. Tire size

Section width (mm)

Aspect ratio (%)

Rim diameter (in.)

Section height (mm)

Inner diameter (mm)

Outer diameter (mm)

205/70R15 215/60R16 225/60R16 235/55R19 235/70R16 235/80R16 235/85R16 245/40R18 255/55R18 265/70R17

205 215 225 235 235 235 235 245 255 265

70 60 60 55 70 80 85 40 55 70

15 16 16 19 16 16 16 18 18 17

143.50 129.00 135.00 129.25 164.50 188.00 199.75 98.00 140.25 185.50

381.00 406.40 406.40 482.60 406.40 406.40 406.40 457.20 457.20 431.80

668.00 664.40 676.40 741.10 735.40 782.40 805.90 653.20 737.70 802.80

were tested, but only results on eastbound section will be discussed; the results on westbound section show the same trends. The testing vehicle used for testing depends on the tire size, to be more specific, the tire outer diameter. The 10 different tire sizes tested are shown in Table 2.2. For the smaller tires with outer diameter smaller than 700 mm, a 2012 Chevrolet Impala LT (front-wheel drive) was used, as shown in Fig. 2.3 (left). For larger tires, a 2017 Chevrolet Tahoe LT was used (all-wheel drive), as shown in Fig. 2.3 (right). The equipment used for collecting noise data was an on-board sound intensity (OBSI) system based on standard AASHTO TP-76 [6]. The setup of the OBSI system is shown in Fig. 2.4. The system was installed at the rear right tire with a camber angle close to zero. The conventional OBSI system has two sound intensity probes, one at the leading edge of the tire road contact patch, the other at the trailing edge. The distance

Tire/road noise separation: tread pattern noise and road texture noise

11

Figure 2.3 Test vehicles (left: Chevy Impala; right: Chevy Tahoe).

Figure 2.4 On-board sound intensity (OBSI) with optical sensor installed on the test vehicle.

between the two probes is 210 mm (8.25 in.); the distance between the probes and the tire sidewall is 114 mm (4.5 in.); the distance between the probes and the ground is 89 mm (3.5 in.). Each probe consists of two microphones to record the sound pressure. The sound intensity along the direction of the two microphones (away from the tire) is then calculated. Therefore a typical OBSI has four microphones: leading inboard (Mic 1), leading outboard (Mic 2), trailing inboard (Mic 3), and trailing outboard (Mic 4). In this chapter, only the data from Mic 1 are used. To that purpose, the OBSI system can be substituted with a close proximity (CPX) system [7]. The present OBSI system also has an optical sensor (tachometer) installed, as shown in Fig. 2.4. The optical sensor radiates a beam onto the surface of the black disk rotating with the tire, and once the beam encounters the retroreflective tape and gets reflected to the optical

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Automotive Tire Noise and Vibrations

sensor, the optical sensor generates a pulse. Therefore a pulse signal is recorded at the exact time the tire completes one revolution. The optical signal (once-per-revolution signal) can be used to accurately calculate vehicle speed, acceleration, as well as used for the order tracking analysis, which will be discussed later. The microphone and optical signals were recorded simultaneously at 25.6 kHz. For each tire, the noise data were collected under five different vehicle speeds, that is, 72, 80, 89, 97, and 105 km/h (45, 50, 55, 60, and 65 mph). In addition, an acceleration test was also conducted where the vehicle accelerated from 72 to 105 km/h (45 65 mph) within 10 seconds. The inflation pressure was set to 221 kPa (32 psi) for the tires on Impala, and to 276 kPa (40 psi) for tires on Tahoe. The ambient temperature range during the test days was 37° F 86°F (3°C 30°C). For repeatability evaluation, Tire 19 was tested in multiple test sets as indicated by Tires 25, 27, and 29; very good repeatability was shown (error ,1 dB), indicating the temperature within the normal range does not have much influence on the near-field tire/road noise.

2.3 Tire/road noise separation 2.3.1 Two noise components The unweighted sound pressure level spectrogram (dB) for Tire 12 during the acceleration test from 72 to 105 km/h (45 65 mph) within 10 seconds is shown in Fig. 2.5. This figure is used to illustrate that there exist two main noise components in the dominant part of the spectrum, that is, 600 1200 Hz. The first component is clearly associated with the vehicle speed or tire speed with the center band frequency going from 700 to 1000 Hz as the vehicle speed increases from 45 to 65 mph. The second

Figure 2.5 Spectrogram of Mic 1 (leading inboard) for Tire 12 accelerating from 72 to 105 km/h (45 65 mph).

Tire/road noise separation: tread pattern noise and road texture noise

13

Figure 2.6 Illustration of two excitation sources and tire noise components. (A) Slick tire on smooth road, (B) patterned tire on smooth road, (C) slick tire on rough road, (D) patterned tire on rough road.

component is independent of the vehicle speed (or tire rotation) with the spectral content encompassed always within the fixed frequency range between 600 and 1200 Hz. To separate the tire noise components, the noise generation mechanisms need to be investigated, as illustrated in Fig. 2.6. Assuming a tire with no tread pattern (e.g., slick tire) on a purely smooth pavement (e.g., steel drum), as shown in Fig. 2.6A, there will be negligible tire noise generated due to no excitation source. Assuming a tire with tread pattern on a purely smooth pavement, as shown in Fig. 2.6B, the tire noise generated is basically due to tread pattern excitation, that is, tread pattern noise. Assuming a tire with no tread pattern on a rough pavement, as shown in Fig. 2.6C, the tire noise generated is basically due to pavement texture excitation, that is, pavement texture noise (road texture noise or road noise). Under normal conditions, that is, a tire with tread pattern on a rough pavement, as shown in Fig. 2.6D, the tire noise generated is basically due to two excitation sources: (1) tread pattern excitation that is periodic (self-repeated per tire revolution) and (2) pavement texture excitation that is random. The characteristics of response (noise generated) are supposed to be the same as those of the excitation source. Therefore the tread pattern noise is periodic while the pavement texture noise is random, based on which the two noise components can be separated.

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Automotive Tire Noise and Vibrations

Both, the tread impact and the air pumping, are periodic with the rotation of the tire and tread pattern. This noise component is, thus, referred to as tread pattern related noise or tread pattern noise. The second component is clearly not related to the periodic tread pattern and it is most likely due to tire structural vibration excited by the roughness of the pavement. Some other mechanisms might also belong to the second component, such as the air pumping due to small cavities in the pavement, the nonperiodic scrubbing of tread elements due to pavement randomness. However, for the sake of generality, this second noise component is referred to here as nontread pattern related noise or nontread pattern noise. It should be noted that, the tread pattern noise and nontread pattern noise are categorized by the excitation source (periodic tread pattern or nonperiodic pavement) rather than the vibration response position (tire tread or sidewall). Both tire tread noise and tire sidewall noise are originally sourced from the tread pattern and nontread pattern noise. To be more specific, the tire tread noise includes two parts: (1) tread pattern excited noise that is periodic and more related to the geometry/layout of the tread elements and (2) vibration induced noise of tread elements that is randomly excited by the pavement and more related to the stiffness of the tread elements, which is not considered as tread pattern related, thus belongs to the nontread pattern related noise. Likewise, the tire sidewall noise also consists of tread pattern related noise and nontread pattern related noise.

2.3.2 Order tracking analysis The technique used for separation of the tread pattern and nontread pattern noise components using the optical sensor signal (tachometer) is a conventional approach called order tracking analysis or order synchronous averaging [8]. This separation technique is briefly described here. Fig. 2.7A shows a typical time history from the optical sensor. The time elapsed between successive pulses represents the time period of a full revolution of the wheel-tire being tested. Since the optical signal was simultaneously recorded with the microphone sound pressure signals, these pulses were then used to identify the microphone signal windows corresponding to each wheel-tire revolution as shown in Fig. 2.7B. Each individual microphone signal was windowed and resampled to have the same number of data points (1800 points here), independent of their actual time length. The resampled and windowed microphone signals were then

Tire/road noise separation: tread pattern noise and road texture noise

15

Figure 2.7 Illustration of separation of tread pattern noise and nontread pattern noise (60 mph test for Tire 12). (A) Optical sensor signal, (B) total noise signal (each window representing one wheel-tire revolution), (C) tread pattern related noise signal, (D) nontread pattern related noise signal.

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Automotive Tire Noise and Vibrations

Fourier transformed (FT) and coherently averaged, thus rejecting the noise signal not related to the tire rotation (i.e., only focusing on tread pattern related noise). The averaged complex FT value is then converted back to the time domain by taking the inverse Fourier transform as illustrated in Fig. 2.7C. The nontread pattern related noise component, as shown in Fig. 2.7D, is computed by subtracting (window by window) the tread pattern related noise time signal from the total (or original) resampled signal, that is, difference between Fig. 2.7B and C.

2.3.3 Noise separation results Example results for Tires 9, 12, 15, and 19 are shown in Fig. 2.8. The noise levels and tread pattern noise contribution for Tires 1 23 (same/ similar tire size) are displayed in Table 2.3. It can be observed that the tread pattern noise component is significant (10% 50% of total noise) for Tires 1, 9, 12, 16, and 19. For the other tires, the tread pattern noise is significantly lower than the nontread pattern noise, like Tire 15 in Fig. 2.8 where the total noise spectrum nearly coincides with the

Figure 2.8 Total noise, tread pattern noise, and nontread pattern noise spectra at 97 km/h (60 mph) for Tires 9, 12, 15, and 19 (A-weighted, 5 Hz resolution).

Tire/road noise separation: tread pattern noise and road texture noise

17

Table 2.3 Overall A-weighted sound pressure level of noise components (bold indicates winter/snow tire). Tire no.

Total noise level (dBA)

Tread pattern noise level (dBA)

Nontread pattern noise level (dBA)

Tread pattern noise contribution (%)

01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 22 23

104.1 103.7 102.8 102.9 104.5 103.8 105.1 104.4 106.3 103.8 103.3 103.4 104.4 102.4 102.1 102.8 102.8 105.2 102.4 105.0 102.6 104.6

95.8 88.1 90.2 87.4 89.2 88.7 87.6 86.7 102.7 86.8 85.5 97.1 88.4 87.4 86.6 92.9 88.0 90.6 93.1 90.7 88.2 92.6

103.3 103.6 102.6 102.7 104.3 103.6 105.0 104.3 103.5 103.8 103.2 102.3 104.3 102.2 102.0 102.3 102.7 105.1 101.8 104.8 102.5 104.2

15.1 2.7 5.4 2.9 3.0 3.1 1.8 1.7 45.4 2.0 1.7 23.4 2.5 3.2 2.8 10.3 3.3 3.5 12.0 3.8 3.6 6.5

nontread pattern noise spectrum. It is also implied that winter tires (Tires 9, 12, and 19) tend to have large tread pattern noise. It is noted that, comparing Fig. 2.7D and C, it looks like the nontread pattern noise is much larger than the tread pattern noise. This is because these time domain plots are from raw data and not A-weighted, and the large amplitude of nontread pattern noise is mostly due to the lowfrequency contents in the frequency below 200 Hz. In the frequency domain, after A-weighting is applied, the amplitude difference between the two noise components is not so obvious, as shown in Fig. 2.8 (Tire 12). It is important to mention that the relative contribution of the tread pattern and nontread pattern noise components is dependent on the pavement. Thus the results presented here are only valid for the pavement tested. Data from testing on a newer and smoother asphalt pavement

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Automotive Tire Noise and Vibrations

show that the nontread pattern noise can be greatly reduced, leading to an increase of the percentage contribution of the tread pattern noise, for example, to B50% of the total tire noise for Tire 12, and to B70% of the total tire noise for Tire 09. This will be discussed in detail in Chapter 4, Influence of Road Texture on Tire/Road Noise. Two extreme scenarios for a typical patterned tire can be expected: (1) on an extremely smooth pavement, such as the steel surface of the lab drum, the tread pattern noise contribution should be completely dominant, as there is basically no pavement excitation and (2) on an extremely rough pavement, such as the gravel road, the nontread pattern noise should be overwhelmingly dominant, as the tread pattern has marginal influence on the interaction between the tire (with a gentle tread pattern) and the pavement (with more aggressive texture). It is noted that in the second scenario, the relatively marginal tread pattern noise does not necessarily suggest that the tread noise is marginal. Table 2.3 also shows that the nontread pattern noise level ranges from 101.8 to 105.1 dBA (3.3 dBA difference), not as large as the tread pattern noise ranging from 85.5 to 102.7 dBA (17.2 dBA difference). For the tires that have a large component of tread pattern noise, more oblique spectral contents will occur in the spectrogram of acceleration test when the speed increases, as shown in Fig. 2.5. For the tires that have a small component of tread pattern noise, the spectral contents in the spectrogram of acceleration test will remain nearly constant level. This explains why the results contradicted each other in some of the literature [9,10]. Alt et al. [9] showed that the dominant frequencies of TPIN do not change with speed while Schumacher [10] indicated that they do. For the interest, human ears tend to be more sensitive to the progressive sound frequency change than the progressive amplitude change. For example, for tones in the frequency around 1000 Hz, the just noticeable difference for frequency is B5.4 Hz where only 0.54% speed change is needed. When a speed exponent of four is assumed [11], the just noticeable difference for intensity is B1 dB where 5.9% speed change is needed. Therefore the tread pattern noise is more noticeable during acceleration than that at constant speed [12,13]. The nontread pattern noise can be potentially considered as the minimum tire noise for a specific tire when the tread pattern is perfectly randomized and the tread pattern noise is reduced to zero. The total tire noise (TTN), tread pattern noise (TPN), and nontread pattern noise (NTPN) spectra for all test tires at 97 km/h (60 mph) are displayed in Fig. 2.9. The spectral peaks for Tire 49 seem to be cropped,

Tire/road noise separation: tread pattern noise and road texture noise

19

Figure 2.9 Total, tread pattern, and nontread pattern noise spectra at 97 km/h (60 mph) with 10 Hz frequency resolution. (A) Total noise spectra, (B) tread pattern noise spectra, (C) nontread pattern noise spectra.

because the amplitude is too large ( . 0.8). Fig. 2.9A shows that the total noise has a dominant frequency range between 400 and 1400 Hz for all the tires, but the location and amplitude of spectral peaks differ. Fig. 2.9B shows that the tread pattern noise varies a lot for different tires, which is expected because the tread pattern noise is dependent on the tread pattern. Fig. 2.9C (left) shows that, after the tread pattern noise is removed from the total noise, all the nontread pattern noise spectra of the test tires are similar, which makes sense because nontread pattern noise is supposed to be independent on the tread pattern, but dependent on the pavement and tire structure, and all the tires have similar structure (sizes of 215/ 60R16 or 225/60R16) and were tested on the same pavement. Fig. 2.9C (right) shows that the spectral distribution of the nontread pattern noise (e.g., central frequency) varies for different tires, indicating the tire sizes may have an influence on the nontread pattern noise [14].

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Automotive Tire Noise and Vibrations

2.4 Tire/road wheel noise separation and combination Roadwheel is also called lab drum, usually equipped with replica road surfaces or sandpaper. Roadwheel surface is different from real random road surfaces, because its texture repeats itself per revolution (i.e., periodic). Therefore interaction between tire and drum will generate three noise components: periodic with tire, periodic with drum, and nonperiodic with tire or drum, as shown in Fig. 2.10. The first noise component is mostly from tread pattern excitation (tread impact and air pumping), and maybe slightly from tire nonuniformity; thus it is referred to as tread pattern noise. The second noise component is called roadwheel noise (like road texture noise), because it is basically generated from roadwheel surface excitation and maybe marginally from drum bearing. The third noise component is turbulence noise, which is due to tire/drum displacing air randomly or stick/slip (friction) if the tire is not pure rolling [3,15]. Using the same order tracking techniques described previously in Section 2.3.2, the three noise components can be separated. The tachometer signal monitoring tire revolution can be used to extract the tread pattern noise component; the tachometer signal monitoring drum revolution can be used to extract the roadwheel noise component; the turbulence noise component can be obtained by subtracting the aforementioned two

Figure 2.10 Illustration of tire/roadwheel noise components.

Tire/road noise separation: tread pattern noise and road texture noise

21

Figure 2.11 Tire/roadwheel combination.

components from the total noise. Intuitively, the nontread pattern noise is composed of the roadwheel noise and the turbulence noise. In order to investigate the mechanisms of TPIN, four cases need to be covered, as shown in Fig. 2.11. The four cases include combinations of two types of tire treads (patterned and nonpatterned) and two types of drum surfaces (ISO 10844 replica and smooth steel), which also corresponds to four scenarios in Fig. 2.6 except that the pavement excitation here is also periodic. The tires used are normal passenger car radial tires with size 195/65R15, and they have the same tire construction/structure. In the following, the four cases are referred to as Patterned on ISO, Patterned on Steel, NP on ISO, and NP on Steel. The total noise measurement results for the four cases are shown in Figs. 2.12 and 2.13. The results of the coast-down tests run from 100 to 40 km/h are shown in Fig. 2.12 and the results of the constant speed cruise tests run at 80 km/h are shown in Fig. 2.13. The noise spectrograms shown were measured at the leading edge of tire contact patch where a frequency resolution of 25 Hz was used for data processing. It is noted that the sound pressure levels and amplitudes shown in this section are scaled by a specific factor due to the confidentiality considerations. It can be seen that the amplitude of the total noise spectrogram for NP on Steel is negligible, which indicates that the lab test rig/background noise will not practically contaminate tire noise measurement. In Fig. 2.12, Patterned on Steel seems to have higher tonal noise than Patterned on ISO, especially at higher frequencies. The pipe resonance frequencies due to longitudinal grooves can also be observed at around

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Figure 2.12 Total noise spectrogram for coast-down from 100 to 40 km/h.

Figure 2.13 Total noise spectrum for constant speed at 80 km/h.

1.1 and 2.2 kHz for the two Patterned cases, and more dominantly for Patterned on Steel than Patterned on ISO. This agrees with the literature reporting that the pipe resonance effect could be reduced if the pavement texture is very rough. This is because the shape of pipe will not form easily [16] due to the rough pavement texture. It is noted that the pipe resonance is not a noise generation mechanism but a noise amplification mechanism, that is, the longitudinal tread grooves will not generate noise itself without external excitation. Therefore the pipe resonance noise is

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Figure 2.14 Total noise spectrum summation of the three noise components for the constant speed cruise test at 80 km/h and its comparison with the measured noise spectrum of the Patterned on ISO.

actually composed of and coupled with the three noise components categorized by their generation mechanisms which are the tread pattern noise, the roadwheel noise, and the turbulence noise. In Fig. 2.13, simple calculation reveals that Patterned on ISO (OASPL 57.9 dBA) is about 1.3 dBA lower than the sound pressure level summation of the other three cases (57.6 dBA 1 53.7 dBA 1 41.7 dBA 5 59.2 dBA), which implies that TPIN is not the simple summation of pure tire tread pattern noise and pure pavement texture noise. This phenomenon is better shown in Fig. 2.14 where the noise at B1000 Hz seems underestimated while noise at 1500 3000 Hz overestimated. Noise component separation provides further insights into this mechanism, as shown in Fig. 2.15. For the tread pattern noise, Patterned on ISO and Patterned on Steel are very similar at lower frequencies because the two cases have the same tire tread pattern. However, the noise for Patterned on ISO is greatly damped at high frequencies over 1500 Hz as roadwheel texture is introduced. This is likely because the ISO replica surface is softer than steel, and the cavities in ISO surface attenuates tread pattern noise through smearing tread impact with pavement texture impact and disturbing air pumping. In addition, NP tire has little tread pattern noise on either ISO or Steel surface because NP has no tread pattern.

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Figure 2.15 Separation of three noise components for the constant speed cruise tests at 80 km/h.

For the roadwheel noise, Patterned on ISO and NP on ISO are very similar at lower frequencies because the two cases have the same ISO replica surface. However, the noise for NP on ISO is greatly damped at high frequencies around 1000 Hz due to thicker/heavier tread of NP. In addition, the roadwheel noise component is shown to be negligible for Patterned and NP tire tested on the steel drum, because the steel surface has little texture excitation. For the turbulence noise, it is shown that Patterned on ISO has the most dominant noise from turbulence and amplified by pipe resonance (B1000 Hz due to the longitudinal tread grooves). The air turbulence can be caused by tire tread, tire sidewall, or roadwheel surface. By comparing with Patterned on Steel, it also implies that both the tread blocks and pavement texture stir the air flow in the longitudinal grooves; pavement texture might contribute a greater part. The coupling of tire tread pattern and pavement texture amplifies the turbulent pipe resonance. In addition, the NP on ISO has noticeable stick/slip noise at high frequencies from 2000 to 4000 Hz compared to the NP on Steel.

2.5 Conclusion Using order tracking techniques, tire/road noise can be separated into different noise components. The noise contributions from the tread pattern, road texture, and their interactions can be clearly identified.

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Acknowledgments This chapter is based on the study (Project Code: MODL-2015-B3-8) partially supported by the Center for Tire Research (CenTiRe), an NSF-I/UCRC (Industry/University Cooperative Research Centers) program led by Virginia Tech. Special thanks go to Dr. Ricardo Burdisso and Dr. Corina Sandu for advising on this project. The present author thanks Maxxis for permission to publish some of the internal data. Credits are also given to Maxxis associates who conducted the NVH testing. Some commercial information was intentionally omitted in this chapter.

References [1] Sandberg U, Ejsmont JA. Tyre/road noise reference book. Kisa, Sweden; Harg, Sweden: INFORMEX; 2002. [2] Li T, Burdisso R, Sandu C. Literature review of models on tire pavement interaction noise. J Sound Vib 2018;420:357 445. Available from: https://doi.org/ 10.1016/j.jsv.2018.01.026. [3] Li T. A review on physical mechanisms of tire pavement interaction noise. SAE Int J Veh Dyn Stab NVH 2019;3. [4] Li T, Feng J, Burdisso R, Sandu C. The effects of tread pattern on tire pavement interaction noise. In: 45th international congress and exposition on noise control engineering: towards a quieter future, INTER-NOISE 2016 Hamburg, Germany, August 21 24, 2016; 2016. p. 2185 96. [5] Li T, Feng J, Burdisso R, Sandu C. The effects of speed on tire pavement interaction noise (tread-pattern-related noise and non-tread-pattern-related noise). In: 35th annual meeting and conference on tire science and technology, September 13 14, 2016, Akron, OH; 2016. [6] AASHTO. Standard method of test for measurement of tire/pavement noise using the on-board sound intensity (OBSI) method. AASHTO TP 76; 2013. [7] Li T. A state-of-the-art review of measurement techniques on tire pavement interaction noise. Meas J Int Meas Confed 2018;128:325 51. Available from: https:// doi.org/10.1016/j.measurement.2018.06.056. [8] Fyfe KR, Munck EDS. Analysis of computed order tracking. Mech Syst Signal Process 1997;11:187 205. [9] Alt N, Wolff K, Eisele G, Pichot F. Fahrzeug Außen Geräuschsimulation (Vehicle exterior noise simulation). Automobiltechnische Z 2006;108:832 6. [10] Schuhmacher A. Blind source separation applied to indoor vehicle pass-by measurements. SAE Int J Passeng Cars Mech Syst 2015;8:1034 41. [11] Zwicker E, Flottorp G, Stevens SS. Critical band width in loudness summation. J Acoust Soc Am 1957;29:548 57. Available from: https://doi.org/10.1121/ 1.1908963. [12] Pratt H, Starr A, Michalewski HJ, Dimitrijevic A, Bleich N, Mittelman N. Auditory-evoked potentials to frequency increase and decrease of high- and lowfrequency tones. Clin Neurophysiol (Irel) 2009;120:360 73. [13] Song L, McGee J, Walsh EJ. Frequency- and level-dependent changes in auditory brainstem responses (ABRs) in developing mice. J Acoust Soc Am 2006;119:2242 57.

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[14] Li T, Burdisso R, Sandu C. The effect of rubber hardness and tire size on tire pavement interaction noise. In: 36th annual meeting and conference on tire science and technology, September 12 13, 2017, Akron, OH; 2017. [15] Li T. Tire braking/cornering noise analysis: stick/slip mechanism. In: NoiseCon 2019, August 26 28, 2019, San Diego, CA; 2019. [16] Koike H, Fujikawa T, Oshino Y, Tachibana H. Generation mechanism of tire/road noise. Part 2: Pipe resonance in tread groove of tire. Inter-Noise 1999;99.

CHAPTER 3

Influence of tread pattern on tire/road noise Tan Li1,2 1

Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, United States Maxxis Technology Center, Suwanee, GA, United States

2

3.1 Introduction As of 2004, there were approximately 16,000 different tread patterns used on tires [1] and the number continues increasing with time. The tire tread pattern is designed as a compromise between traction, handling, ride, noise, safety, and tire longevity criteria [1]. As regulations for silent tires and vehicles are introduced internationally together with increasing customer needs for driving comfort [2], a number of attempts have been made to reduce the tire/road noise, a.k.a., tire pavement interaction noise (TPIN) [3]. Among the important aspects investigated, the tread pattern design is of great interest [4 6]. Sandberg and Ejsmont [7] presented three approaches to reduce the tire/road noise related to tread pattern: (1) pattern randomization to reduce tread impact concentrated at specific frequencies; (2) groove ventilation to reduce air pumping; and (3) modification of the geometry and dimension of grooves (length, width, depth, and angle). For the first approach, randomization often does not reduce overall tire noise levels, but it distributes the spectral energy over a wider frequency range and makes the sound more pleasant, that is, less tonal. Iwao and Yamazaki [8] showed that, for a car at a speed of 56 km/h with randomized tire tread pattern, the pattern sound associated with the first-order component of the wheel-tire or its tread block passage frequency (excites the side wall having low-dynamic stiffness) with a central frequency of 500 Hz is spread out into the frequency range from 400 to 600 Hz. The pattern sound associated with the second-order component of the wheel-tire (excites the tread surface) with a central frequency of 1000 Hz is spread out into the frequency range from 800 to 1200 Hz. For the second approach, it is good practice to avoid closed pockets (air pumping), cavities with narrow Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00003-9

© 2020 Elsevier Inc. All rights reserved.

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outlets and long grooves without ventilated side channels (pipe resonance). Cusimano [9] patented a quiet tire design with strategic placement of grooves such that the amount of groove void across the trailing and/or leading edges of the footprint is substantially uniform across the circumference of the tire to reduce the air volume change and resulting pumping. For the third approach, it was shown that increased groove length reduces the frequency of pipe resonance but will usually cause higher amplitude due to the coincidence with the impact frequency [10]. As groove width increases, tire noise increases due to increased air cavity between blocks. However, after the groove width reaches beyond 9 mm, tire noise decreases, probably due to the tread stiffness reduction [7]. Increased groove depth also increased air pumping. It was reported that groove depth is more important than groove width [11]. Tire noise decreases with the increased groove angle with respect to the lateral direction because it avoids simultaneous impact over the tread width. However, it cannot explain why TPIN is not sensitive to groove angle once it is over 20 degrees. Several models were developed to correlate tread patterns with tire noise. These models can be categorized into three types: deterministic, statistical, and hybrid models [12]. For deterministic models, Kido et al. [13] and Bremner et al. [14] analyzed the effect of tread impact; Chen et al. [15] and Kim et al. [16] mainly focused on air pumping; De Roo and Gerretsen [17] and Plotkin and Stusnick [18] investigated both tread impact and air pumping. For statistical models, both Che et al. [19] and Li et al. [20] utilized soft computing method, the former artificial neural network and the latter fuzzy genetic algorithm. For hybrid models, Kuijpers and Blokland [21] calculated the static contact pressure distribution from the tire tread profiles while Cao et al. [22] assumed physically explainable formulas with coefficients to be statistically determined and calculated the tread impact noise and air pumping noise separately. Unfortunately, the tread pattern parameters, such as constant groove width or angle, in most of these models cannot be applied to an arbitrary tread pattern because these parameters usually vary over the entire tire circumference. Therefore it is desired to create tread pattern parameters that are able to comprehensively quantify any tread patterns. It is believed among the general public that the slick tire is the quietest tire because the tread impact and air pumping are reduced to the minimum [22]. Alt et al. [23] also showed that noise from a patterned tire (also known as treaded tire) has more spectral content around 1000 Hz

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than a slick tire. This is true on very smooth road. However, FEHRL [24] found that a slick tire might be the noisiest tire if tested on rough pavement. Fong [25] also found that the sound levels from smooth tires (P175/70R13) were slightly greater than the patterned tire over all the chip-seal pavements. Data collected by the present author also show that the slick tire and heavily worn tire generate larger noise at high frequencies from 1000 to 2500 Hz on the pavement that is not very smooth due to the nontread pattern noise contribution [26]. Therefore it is necessary to extract the tread pattern noise from the total tire noise in order to correlate it with tread pattern parameters.

3.2 Tire/road noise separation Using the tire/road noise separation technique described in Chapter 2, Tire/Road Noise Separation: Tread Pattern Noise and Road Texture Noise, the total, tread pattern, and nontread pattern noise spectra for the 22 tires (Tires 1 20, 22 23 of same/similar tire size, Tire 21 not included due to different tire category) are shown in Fig. 3.1. Most of the tires have five ribs/rows separated by four circumferential/longitudinal grooves, as shown in Fig. 2.1. Additional information about the tires is listed in Table 2.1. Fig. 3.1A shows that the total noise has a dominant frequency range between 400 and 1400 Hz for all the tires, but the location and amplitude of spectral peaks differ. Fig. 3.1B shows that the tread pattern noise varies a lot for different tires, which is expected because the tread pattern noise is dependent on the tread pattern. Fig. 3.1C shows that, after the tread pattern noise is removed from the total noise, all the nontread pattern noise spectra of the test tires are similar, which makes sense because nontread pattern noise is supposed to be independent on the tread pattern, but dependent on the pavement and tire structure, and all the tires have similar structure and were tested on the same pavement. The variations in the nontread pattern noise for different tires are likely due to the pipe resonance effect which is different among different tread patterns (e.g., geometry and position of longitudinal grooves). The tread pattern noise is usually tonal noise with frequencies around pitch passing frequency, which sounds annoying to human ears. The nontread pattern noise is more like broadband noise, which sounds more pleasant even though it is generally louder than the tread pattern noise. As a matter of fact, the broadband nontread pattern noise can have a masking effect on the tonal tread pattern noise due to human hearing perception [27 29].

Figure 3.1 Total, tread pattern, and nontread pattern noise components at 60 mph for all tires (A-weighted, 5 Hz resolution). (A) Total noise spectra; (B) tread pattern noise spectra; (C) nontread pattern noise spectra.

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3.3 Tread pattern parameterization As mentioned in Chapter 2, Tire/Road Noise Separation: Tread Pattern Noise and Road Texture Noise, tread pattern contributes to the TPIN through two major mechanisms: (1) tread impact due to the interaction between the tread blocks and the pavement texture and (2) air pumping due to the air compression/expansion in the tread grooves. In this section, two tread pattern spectra, that is, tread profile spectrum and air volume velocity spectrum, are calculated from the three-dimensional (3D) tread profile to characterize the two mechanisms of tread impact and air pumping, respectively. The 3D tread pattern/profile was obtained using a CTWIST laser scanning machine. An example of the digitized 3D profile is illustrated in Fig. 3.2. The measurement resolution is B0.5 mm in the length/width direction and ,0.01 mm in the height direction. The tread profiles for a specific circumferential section and a specific transverse section are illustrated in Fig. 3.2. It can be seen from the circumferential section profile that the distance between adjacent lateral grooves is not constant due to pitch sequence randomization. The transverse section profile shows that

Figure 3.2 Illustration of 3D tread profile of Tire 12.

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the profile drops off in the range of 10 35 mm compared to the other shoulder, suggesting that the tread pattern is not exactly symmetric.

3.3.1 Tread profile spectrum The tread impact mechanism of the tire/road noise generation is the sudden impulse contact between tire tread blocks and pavement. The resulting sound can be considered as the contribution of hundreds of small hammer strokes each second [30]. At the leading edge, the impact mechanism occurs as the tread block is pushed in toward the tire center; at the trailing edge, the release of the tread block can be considered as an inverse impact [31]. This mechanism is caused by the irregularities of the tire tread assuming the pavement surface is smooth. The parameter used to quantify the irregularities of the tire tread is the tread profile spectrum characterizing the height variations of the tire tread. The tread profile height for each circumferential section is converted from the spatial domain (height vs length) to the time domain (height vs time) assuming a vehicle speed, for example, 97 km/h (60 mph). The time domain signal is then Fourier transformed, yielding complex data that contain both amplitude and phase, and then the power spectrum is computed. Fig. 3.3A illustrates the resulting profile spectra for all circumferential sections versus tire width as a 2D color plot. In this plot, the tread pattern pitch passing frequency (tread block passage frequency) is easily observed at around 1000 Hz. The pitch passing frequency is computed as the number of pitches (77) times the tire angular velocity in Hz (B13 Hz at 60 mph). As shown in Fig. 3.3A, the value of tread profile spectrum at the center of tire width is close to zero. This is because at the center of tire width for Tire 12, there is only a circumferential groove without tread blocks, so there is no tread profile variation, as shown in Fig. 3.3B. In addition, if there is not any tread groove along a specific circumferential section, its tread profile spectral value will also be zero due to no tread profile variation, like the circumferential lines next to the center circumferential groove. By comparing Fig. 3.3A and B, it is clear to see that the dominant tread impact source at around 1000 Hz is at the tire width position of 50 and 110 mm where longitudinal/lateral grooves intersect and large cavities exist. There are two options to reduce the 2D spectral information in Fig. 3.3A to a single representative spectrum. The simplest approach is to compute the average spectrum across the tire width, that is, incoherent

Influence of tread pattern on tire/road noise

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Figure 3.3 Tread profile spectral analysis at 60 mph for Tire 12 (12.5 Hz resolution). (A) Tread profile spectra for all circumferential sections; (B) tread pattern image; (C) incoherent tread profile spectrum; (D) coherent tread profile spectrum.

addition, as illustrated in Fig. 3.3C. This approach ignores the phase information (i.e., offsets between different ribs of tread elements). If the tread block offset information is to be accounted for, the averaging process across the tire width must be performed using the Fourier transform complex data with both phase and amplitude information included. This average power spectrum is called coherent tread profile spectrum since it accounts for the relative phase between circumferential tread profiles along the tire width. As an illustration, the coherent tread profile spectra for Tire 12 are displayed in Fig. 3.3D. It can be observed that peaks occur around the pitch passing frequency (77 3 13 5 1001 Hz) indicating that the number of pitches has a great influence on the tread profile spectrum. The incoherent and coherent tread profile spectra are displayed in Fig. 3.4 for all test tires. It is shown that, the coherent tread profile spectrum is nearly an order of magnitude smaller than that of incoherent tread profile, indicating that the process of tread element/rib offset plays a great role in making the tread pattern less aggressive, especially for Tires 02, 18,

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Figure 3.4 Incoherent and coherent tread profile spectra at 97 km/h (60 mph) for all tires (legend includes tire number and pitch passing frequency). (A) Incoherent tread profile spectrum; (B) coherent tread profile spectrum.

and 20, where the incoherent tread profile spectra are among the largest while the corresponding coherent tread profile spectra are much smaller. Based on the coherent tread profile spectrum, the most “aggressive” tread patterns are Tires 09, 12, and 19, which are winter tires. Their tread patterns tend to be symmetric with respect to the central line of the tire tread band. They are called directional tires where there are insufficient

Influence of tread pattern on tire/road noise

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cancellation effects (destructive interference) between ribs in the tread pattern. On the contrary, the noise produced by these ribs adds constructively since they produce the noise nearly in phase. It is later found that on the smooth surface where the tread pattern noise is dominant, the coherent tread profile spectrum is better correlated with tread pattern noise than the incoherent tread profile spectrum at lower frequencies, but worse at higher frequencies. This is likely because the noise generated from different ribs does not maintain well in phase at higher frequencies. Therefore both the coherent and incoherent tread profile spectra should be considered for tread impact noise.

3.3.2 Air volume velocity spectrum The air pumping mechanism is caused by the variation of the air volume enclosed between the tread and the road surface in the contact patch. As the tire rotates, the air volume in the contact patch changes with time becoming a noise source. This noise generation mechanism is known as air pumping [30,32]. In terms of acoustics [33], noise is produced by the rate of change of air volume (volume velocity). Fig. 3.5 illustrates the approach implemented to estimate the volume velocity time history and spectrum for the tires tested. Firstly, a simple rectangular-shaped contact patch geometry is assumed, as seen in Fig. 3.5A. This contact patch shape can be improved to better represent the actual tire footprint geometry. Secondly, the tire is assumed to rotate at 97 km/h (60 mph), so that the contact patch also moves along the tire circumference at 97 km/h (60 mph), for example, to the right in Fig. 3.5A. Next, utilizing the 3D digitized tread profile, the air volume in the tread grooves within the contact patch at each moment of time is calculated and illustrated as air volume versus time in Fig. 3.5B. Then, the air volume signal is differentiated with respect to time to yield the volume velocity trace in Fig. 3.5C. Finally, the air volume velocity spectrum is obtained by taking the Fourier transform shown in Fig. 3.5D. This process can also be improved by accounting for the deformation of tread rubber due to loading that might change the air volume. The air volume velocity spectra for the test tires are shown in Fig. 3.6. Similar to the tread profile spectra, the dominant part of the air volume velocity spectrum also occurs around the pitch passing frequency. However, there is no significant spreading of the energy around the pitch passing frequency, that is, usually a single dominant peak at the pitch passing frequency. The spectral content agreement between the tread profile

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Figure 3.5 Illustration of calculation of air volume velocity spectrum (Tire 12, 12.5 Hz resolution). (A) Contact patch geometry on the tread pattern, (B) time history of air volume in the contact patch, (C) air volume velocity time history, (D) air volume velocity spectrum.

Figure 3.6 Air volume velocity spectrum at 97 km/h (60 mph) for all tires (legend includes tire number and pitch passing frequency).

Influence of tread pattern on tire/road noise

37

and air volume velocity spectra indicates that the tread impact and air pumping are originated from and related to the tire tread pattern. The tread impact and air pumping mechanisms have the same dominant frequency ranges. This is expected as they are both produced by the same periodic tread pattern. In addition, the air volume velocity spectral shape seems to be more similar to the coherent tread profile spectral shape than the incoherent one, likely because the first two spectra both consider the phase information whereas the last one does not.

3.4 Correlation between tread pattern and tire noise To correlate the tread pattern to the tire noise, the spectral content of the tire tread pattern and the tire noise are compared. Specifically, the coherent tread pattern profile and air volume velocity spectral shapes are compared with the tread pattern noise spectral shape. The results for Tires 12 and 19 are shown in Figs. 3.7 and 3.8, respectively.

Figure 3.7 Comparison between the tread pattern spectra and the A-weighted tire noise spectra for Tire 12 at 97 km/h (60 mph) (frequency resolution 5 5 Hz; Mic 1 is at the leading edge of the contact patch). (A) Tread profile vs total noise; (B) tread profile vs tread pattern noise; (C) air volume velocity vs total noise; (D) air volume velocity vs tread pattern noise.

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Figure 3.8 Comparison between the tread pattern spectra and the A-weighted tire noise spectra for Tire 19 at 97 km/h (60 mph) (frequency resolution 5 5 Hz; Mic 1 is at the leading edge of the contact patch). (A) Tread profile vs total noise; (B) tread profile vs tread pattern noise; (C) air volume velocity vs total noise; (D) air volume velocity vs tread pattern noise.

From general inspection of these figures, it is clear that the tread pattern spectra (coherent profile and air volume velocity) do not completely match the total noise spectrum. However, a very good match can be observed between the tread pattern spectral shape when compared to only the tread pattern noise component. It is supposed that both tread impact and air pumping contribute to the tread pattern noise. The separation of the two mechanisms can be investigated in the future. It is also important to note that the tread profile spectral content at high frequencies around 2000 Hz (twice the pitch passing frequency) do not generate corresponding tread pattern noise. However, this is valid only for the pavement tested. On a very smooth surface such as smooth steel, the tread pattern noise at high frequencies might also occur, as shown in Fig. 2.15. The interaction between different tread rubber and

Influence of tread pattern on tire/road noise

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paving materials behaves like different acoustic filters, generating different tire/road noise (amplifying or attenuating at specific frequencies) even for the same tread pattern and pavement texture. The agreement between Figs. 3.1B, 3.4, and 3.6 also indicates that the tread profile spectrum and the air volume velocity spectrum have strong correlations with the tread pattern noise spectrum.

3.5 Conclusion Any tire tread pattern can be digitized into 3D data and then converted to tread profile and air volume velocity spectra. Very good match was found between the tread profile spectrum, the air volume velocity spectrum, and the tread pattern noise spectrum, supporting the conclusion that the tread pattern in the spectral perspective leads to the tread pattern noise, including tread impact and air pumping.

Acknowledgments This chapter is derived from the study (Project Code: MODL-2015-B3-8) partially supported by the Center for Tire Research (CenTiRe), an NSF-I/UCRC (Industry/ University Cooperative Research Centers) program led by Virginia Tech. Special thanks go to Dr. Ricardo Burdisso and Dr. Corina Sandu for advising on this project.

References [1] Hanson DI, James RS, NeSmith C. Tire/pavement noise study. NCAT Report 0402, United States; 2004. p. 49. [2] Nijland R, Vos E, Hooghwerff J. The Dutch noise innovation program road traffic (IPG). In: The 32nd international congress and exposition on noise control engineering, inter-noise 2003; 2003. [3] Li T. Literature review of tire-pavement interaction noise and reduction approaches. J Vibroeng 2018;20:2424 52. [4] Li T. Influencing parameters on tire pavement interaction noise: review, experiments and design considerations. Designs 2018;2:38. [5] Li T, Feng J, Burdisso R, Sandu C. The effects of tread pattern on tire pavement interaction noise. In: 45th international congress and exposition on noise control engineering: towards a quieter future, INTER-NOISE 2016 Hamburg, Germany, August 21 24, 2016; 2016. p. 2185 96. [6] Li T, Burdisso R, Sandu C. An artificial neural network model to predict tread pattern-related tire noise. In: SAE 2017 noise and vibration conference and exhibition, June 12 15, 2017, Grand Rapids, Michigan, SAE Technical Paper 2017-01-1904; 2017. [7] Sandberg U, Ejsmont JA. Tyre/road noise reference book. Kisa, Sweden; Harg, Sweden: INFORMEX; 2002.

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[8] Iwao K, Yamazaki I. A study on the mechanism of tire/road noise. JSAE Rev 1996;17:139 44. [9] Cusimano FJI. Low noise pneumatic tire tread and method for producing same. European Patent EP0513676 A1, Google Patents; 1992. p. 1 14. [10] Ejsmont JA, Sandberg U, Taryma S. Influence of tread pattern on tire/road noise. Passenger Car Meeting, October 1, 1984 October 4, 1984, Technical University of Gdansk, Poland Swedish Road and Traffic Research Institute. Linköping, Sweden: SAE International; 1984. p. 9. https://doi.org/10.4271/841238. [11] Zhou H. Investigate into influence of tire tread pattern on noise and hydroplaning and synchronously improving methods [PhD dissertation]. China: Jiangsu University; 2013. p. 1 178. [12] Li T, Burdisso R, Sandu C. Literature review of models on tire-pavement interaction noise. J Sound Vib 2018;420:357 445. Available from: https://doi.org/10.1016/j. jsv.2018.01.026. [13] Kido I, Ueyama S, Hashioka M, Yamamoto S, Tsuchiyama M, Yamaoka H. Tire and road input modeling for low-frequency road noise prediction. SAE Technical Papers, vol. 4, Warrendale, PA; 2011. p. 1277 82. [14] Bremner P, Huff J, Bolton JS. A model study of how tire construction and materials affect vibration-radiated noise. SAE Technical Papers, Warrendale, PA; 1997. [15] Chen C, Kuan Y, Chen C, Sung M. Using CFD. Technique to investigate the effect of tire roiling-noise with different pattern design. Appl Mech Mater 2014;575:469 72. [16] Kim S, Jeong W, Park Y, Lee S. Prediction method for tire air-pumping noise using a hybrid technique. J Acoust Soc Am 2006;119:3799 812. [17] De Roo F, Gerretsen E. TRIAS—tyre road interaction acoustic simulation model. In: InterNoise 2000, the 29th international congress and exhibition on noise control engineering, August 27 30, 2000, Nice, France, vol. 4; 2000. p. 2488 96. [18] Plotkin KJ, Stusnick E. A unified set of models for tire/road noise generation. Report: WR-81-26, Environmental Protection Agency, Arlington, VA. Office of Noise Abatement and Control, United States; 1981. p. 63. [19] Che Y, Xiao W, Chen L, Huang Z, Yong C, Wangxin X, et al. GA-BP neural network based tire noise prediction. Adv Mater Res 2012;443 444:65 70. [20] Li X-H, Liu J, Liu D-Q, Sun K-M. Application of tread patterns noise-reduction based on self-adaptive fuzzy genetic algorithm. Comput Eng Appl 2009;45. [21] Kuijpers A, van Blokland G. Tyre/road noise modeling: the road from a tyre’s point-of-view. In: Proceedings of inter-noise 2003, the 32nd international congress and exposition on noise control engineering, Jeju International Convention Center, Seogwipo, Korea, August 25 28, 2003; 2003. p. 249. [22] Cao P, Yan X, Xiao W, Chen L. A prediction model to coupling noise of tire tread patterns and road texture. Proceedings of the 8th international conference of Chinese logistics and transportation professionals—logistics: the emerging frontiers of transportation and development in China. Chengdu, China: American Society of Civil Engineers; 2008. p. 2332 8. Available from: https://doi.org/10.1061/40996 (330)344. [23] Alt N, Wolff K, Eisele G, Pichot F. Fahrzeug Außen Geräuschsimulation (Vehicle exterior noise simulation). Automobiltechnische Z 2006;108:832 6. [24] FEHRL (Forum of European National Highway Research Laboratories). Tyre/road noise. FEHRL final report SI2.408210; 2001. [25] Fong S. Tyre noise predictions from computed road surface texture induced contact pressure. In: Proceedings of INTER-NOISE 98 Christchurch, New Zealand; 1998. p. 137 40.

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[26] Li T. Tire-pavement interaction noise (TPIN) modeling using artificial neural network (ANN) [PhD dissertation]. Virginia Tech; 2017. [27] Houtsma AJM. A note on pure-tone masking by broadband noise under free-field and insert-phone conditions (L). J Acoust Soc Am 2005;117:490 1. [28] Fidell S, Horonjeff R, Teffeteller S, Green DM. Effective masking bandwidths at low frequencies. J Acoust Soc Am 1983;73:628 38. [29] Hawkins JE J, Stevens SS. The masking of pure tones and of speech by white noise. J Acoust Soc Am 1950;22:6 13. [30] Rasmussen RO, Bernhard RJ, Sandberg U, Mun EP. The little book of quieter pavements. Report No FHWA-IF-08-004; 2007. [31] Negrus EM, Teodorescu C. ISBN 973-648-027-5 Testing and evaluation of tyre like component part of motor vehicle. Bucharest: BREN Publisher? 2002. p. 102p. [32] McDaniel R, Shah A, Dare T, Bernhard R. Hot mix asphalt surface characteristics related to ride, texture, friction, noise and durability; 2014. [33] Kinsler LE, Frey AR, Coppens AB, Sanders JV. ISBN 0-471-84789-5Fundamentals of acoustics. 4th Edition Wiley-VCH? 1999. p. 560. Available from: https://doi.org/ 10.1002/9780470612439.

CHAPTER 4

Influence of road texture on tire/road noise Tan Li1,2 1

Maxxis Technology Center, Suwanee, GA, United States Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, United States

2

4.1 Introduction Pavement parameters might be more important than tire parameters in terms of tire pavement interaction noise (TPIN) [1]. As a matter of fact, two-thirds of literature focus on the pavement parameter effects while only one-third focus on the tire parameter effects [2]. Different pavement parameters affect different noise generation and propagation mechanisms. The pavement related parameters could be categorized into primary parameters, secondary parameters, and tertiary parameters [3]. The primary parameters are those for pavement design or mixture properties, such as grading size distribution, content of binder and thickness; the secondary parameters are characteristics that show up and remain relatively constant after the pavement is built, such as porosity, texture, and stiffness/ impedance [4]; the tertiary parameters are those that might change with time, such as wetness, wear/age, and surface rating. It is generally accepted that pavement texture is the most dominant parameter for tire/road noise. Porosity or sound absorption is another important factor, but its variety is not as commonly seen as for pavement texture. Road surface usually refers to the pavement texture. Pavement texture is defined as “the deviation of a pavement surface from a true planar surface” within a specific wavelength range [5]. Therefore the texture cannot be fully described using one single metric. It is divided into a group of parameters representing different aspects of the texture based on the wavelength of the texture features: microtexture (,0.5 mm), macro-texture (0.5 50 mm), mega-texture (50 500 mm), unevenness (0.5 50 m), and topographical undulation ( . 50 m) [6]. Microtexture is a function of the surface texture of the aggregate particles. Microtexture of high amplitude provides high frictional resistance Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00004-0

© 2020 Elsevier Inc. All rights reserved.

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and water skid resistance by disrupting the continuity of the water film. It can be analogous to sand paper with a gritty surface. Microtexture of higher amplitude increases stick/slip (friction) noise generation mechanism but decreases stick/snap generation mechanism. These conflicting changes might explain why it is difficult to find clear relations between the microtexture amplitude and TPIN [2]. Microtexture amplitude was shown to influence TPIN above 1000 Hz [7,8]. However, very few literature have reported strong correlation between pavement microtexture and tire/road noise. One possible reason might be the lack of accurate measurement of the microtexture and the lack of appropriate methods for interpreting/ characterizing the microtexture data. Another reason might be that the effect of macro-texture is usually so dominant (especially for rough pavement) that the microtexture effect is masked. Macro-texture represents the overall properties of the pavement surface and has the greatest influence on TPIN among the texture characteristics. It depends on the type of asphalt surface (e.g., dense vs porous), the gradation of the aggregates in the mixture, and presence of air voids at the surface [9]. Higher macro-texture amplitude reduces hydroplaning by providing channels at the surface through which water can travel away from the contact area. Higher macro-texture amplitude (wavelength 10 50 mm) increases the texture impact TPIN generation mechanism. It also influences the air pumping generation mechanism by changing the volume of air cavities in the pavement. It has certain influence on the stick/slip, pipe resonance, and Helmholtz resonance mechanisms. Macro-texture was shown to affect TPIN levels in the range of 630 1000 Hz [10]. However, higher macrotexture amplitude (wavelength 0.5 10 mm) was reported to decrease the TPIN levels at higher frequencies [11]. Generally, mega-texture, unevenness, or topographical undulation has little influence on the TPIN level, except in cases of extreme roughness such as potholes, joints, and bumps. Texture profile can be measured using a laser profilometer standardized in ISO 13473 [12]. Texture spectrum analysis [13 15] can then be applied to the pavement texture investigations standardized in ISO/TS 13473-4 [16]. TPIN has different sensitivities to the different components of the texture spectrum, and certain range of the spectrum might be ignored or cannot be recognized by tire/road interaction [17]. Sandberg and Ejsmont [2] demonstrated that TPIN at low frequencies (below 1000 Hz) increases with the texture amplitude within the texture wavelength range of 10 500 mm. TPIN at high frequencies (above 1000 Hz)

Influence of road texture on tire/road noise

45

decreases with texture amplitude within the texture wavelength range of 0.5 10 mm. Li et al. [18] reported the similar trends. However, Domenichini et al. [19] reported that the phenomenon (TPIN above 1000 Hz decreases with texture amplitude centered on 5 mm wavelength) holds only when the total texture spectral line (wavelength of 4, 5, and 6.3 mm) is less than 200. It should be pointed out that the correlation between TPIN and pavement texture of short wavelengths is still uncovered. Many researchers failed to measure texture amplitude levels with enough precision at such short wavelengths as micrometer level, so the results were usually debatable [20]. For most of the cases, power spectrum of the texture is used, which will lose the phase information. However, Hamet and Klein [21] claimed that two pavements with identical power spectrum or amplitude spectrum of the texture do not necessarily show the same acoustical behavior. Both the amplitude and phase information should be taken into account.

4.2 Rough and smooth pavement In this section, the acoustic characteristics of five tires on a rough pavement section and a smooth pavement section (Fig. 4.1) are analyzed and compared. The on-vehicle experimental setup for the tire noise data collection is the same as in Chapter 2, Tire/Road Noise Separation: Tread Pattern Noise and Road Texture Noise and Chapter 3, Influence of Tread Pattern on Tire/Road Noise. Noise separation techniques are used

Figure 4.1 Two road sections (left) and five tread patterns (right). From (left) Google Street View.

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to investigate the effect of road surface texture on tread pattern noise and nontread pattern noise individually.

4.2.1 Total noise The total noise spectra at 97 km/h (60 mph) for the rough and smooth road sections are compared and shown in Fig. 4.2. The differences in TPIN spectra between rough and smooth road sections depend on the tread pattern; no general trends can be found. For Tires 07 and 08, all the amplitudes of the TPIN spectral contents increase on the rough section compared to the smooth section, especially for Tire 07. For Tires 09, 12, and 19, the amplitudes of the TPIN spectral contents only increase over part of the frequencies while at certain frequencies the amplitudes of the TPIN spectral contents are higher on the smooth road section than on the rough road section, for example, in the frequency range of 700 800 Hz for Tire 09, in the frequency range of 900 1000 Hz for Tire 12, and 700 Hz for Tire 19. The overall A-weighted sound pressure levels (OASPLs) of the total noise on the rough and smooth road sections are shown in Table 4.1. Generally, the OASPL is 2 3 dBA larger on the rough road section than on the smooth road section. However, the OASPL difference for Tire 07 is as large as 5.8 dBA while for Tire 09 only 0.9 dBA. In Table 4.1, the rank of tires from quietest to noisiest is also displayed. Tire 19 is the

Figure 4.2 Total noise spectra at 97 km/h (60 mph) (5 Hz resolution). (A) Tire 07, (B) Tire 08, (C) Tire 09, (D) Tire 12, (E) Tire 19.

Influence of road texture on tire/road noise

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Table 4.1 OASPL of total noise on rough and smooth sections. Tire no.

07 08 09 12 19

OASPL (dBA)

Rank (from quiet to noisy)

Rough

Smooth

Difference (rough 2 smooth)

Rough

Smooth

105.5 104.3 104.9 104.1 101.7

99.7 101.5 104.0 101.2 99.3

5.8 2.8 0.9 2.9 2.4

5 3 4 2 1

2 4 5 3 1

Figure 4.3 Tread pattern noise spectra at 97 km/h (60 mph) (5 Hz resolution). (A) Tire 07, (B) Tire 08, (C) Tire 09, (D) Tire 12, (E) Tire 19.

quietest on both the smooth and rough road sections. It is interesting to note that Tire 07 is the noisiest tire on the rough section but turns out to be among the quietest on the smooth section. In order to better explain the differences in total noise due to different pavement sections, the noise separation is performed to identify the noise component due to the tread pattern and the noise component due to the pavement in the following.

4.2.2 Tread pattern noise The tread pattern noise spectra at 97 km/h (60 mph) for the rough and smooth road sections are shown in Fig. 4.3, and the corresponding

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Table 4.2 OASPL of the tread pattern noise on the rough and smooth road sections. Tire no.

07 08 09 12 19

OASPL (dBA)

Rank (from quiet to noisy)

Rough

Smooth

Difference (rough 2 smooth)

Rough

Smooth

91.0 89.0 98.4 94.2 91.9

90.2 89.8 102.0 97.6 93.7

0.8 2 0.8 2 3.6 2 3.4 2 1.8

2 1 5 4 3

2 1 5 4 3

OASPL values are shown in Table 4.2. It can be seen that the spectral shape of the tread pattern noise component on the two road sections is almost the same, which makes sense because the tread pattern noise is generated due to the tire tread pattern independent of the pavement. However, it is demonstrated that the amplitude of the tread pattern noise on the smooth section is generally larger (up to 3.6 dBA for Tire 09) than that on the rough section. It is likely because the smoother texture has no noise masking of the nontread pattern noise and makes the tread pattern noise more distinguishable. The total noise spectral amplitude tested on the smooth section is larger than that tested on the rough section at the dominant frequencies of the tread pattern noise spectra, as discussed above and shown in Fig. 4.2. For Tire 07, the trend is opposite, probably because its tread pattern noise is much smaller than the nontread pattern noise on the smooth road section. As shown in Table 4.2, the ranking of the tires is consistent on either rough or smooth pavement. It is implied that the tire with the lowest tread pattern noise has the best tread pattern design in terms of noise reduction, regardless of the pavement.

4.2.3 Nontread pattern noise The nontread pattern noise spectra at 97 km/h (60 mph) for the rough and smooth road sections are shown in Fig. 4.4, and its corresponding OASPL values are displayed in Table 4.3. It can be seen that the amplitude of the nontread pattern noise spectra on the rough section is generally larger than that on the smooth section over all the frequencies. The nontread pattern noise is supposed to be excited by the isotropic pavement texture, which is considered to be random, homogeneous, and

Influence of road texture on tire/road noise

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Figure 4.4 Nontread pattern noise spectra at 97 km/h (60 mph) (5 Hz resolution). (A) Tire 07, (B) Tire 08, (C) Tire 09, (D) Tire 12, (E) Tire 19.

Table 4.3 OASPL values of the nontread pattern noise on the rough and smooth road sections. Tire no.

07 08 09 12 19

OASPL (dBA)

Rank (from quiet to noisy)

Rough

Smooth

Difference (rough 2 smooth)

Rough

Smooth

105.5 104.3 103.7 103.6 101.3

99.0 101.2 99.5 98.6 97.8

6.5 3.1 4.2 5.0 3.5

5 4 3 2 1

3 5 4 2 1

broadband; the nontread pattern noise increases as the spectral contents (rough . smooth) of the pavement texture increase. The ranking of tires for the nontread pattern noise is inconsistent on the two pavement sections. For example, Tire 07 is fairly quiet on the smooth section whereas it becomes the noisiest on the rough section in terms of nontread pattern noise. This is likely because its tire components such as the pipe/cavity resonance or structural modes not related to the tread pattern is more prone to resonate at higher pavement texture excitation.

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4.2.4 Percent contribution from the two noise components As discussed above, on the smoother pavement, the tread pattern noise increases and the nontread pattern noise decreases. As such, the percent contribution from tread pattern noise component increases on the smoother pavement (around three times), as shown in Table 4.4. For example, more than half (64%) of the TPIN comes from the tread pattern for Tire 09 on the smoother section while only 23% on the rough section. It is implied that on the smoother pavement, the tread pattern noise is more important in terms of the noise reduction. Smoother pavement is more feasible for ranking the quietness of a tire or its tread pattern noise. For an extreme example, the lab drum with a very smooth steel surface as a pavement is supposed to generate the lowest nontread pattern noise, and meantime the generated tread pattern noise is dominant [22]. It also agrees with the observation that the tread pattern noise component that shifts with speed is more easily seen for the tires tested on the lab drum [23] than that on real pavement [24]. In Table 4.4, it also exhibits that, for Tires 07 and 08 (all-season tires), the periodic tread pattern noise contributes marginally to the total tire noise, especially on the rough section (below 5%), which means the tread pattern is well designed and randomized. For Tires 09, 12, and 19 (snow/ winter tires), of which the tread pattern looks aggressive, the tread pattern noise contributes considerably to the total tire noise, especially on the smooth section.

4.3 Pavement texture characterization To illustrate the characteristics of different pavement textures, four pavement sections were used as examples, as shown in Fig. 4.5. The vertical upwards direction is the vehicle traveling direction. Pavements A and B Table 4.4 Percent contribution from the tread pattern noise component. Tire no.

07 08 09 12 19

Tread pattern noise contribution (%)

Rank (from small to large)

Rough

Smooth

Rough

Smooth

3.4 2.9 22.8 10.3 10.3

11.6 6.8 64.0 44.3 28.0

2 1 5 3 3

2 1 5 4 3

Influence of road texture on tire/road noise

51

Figure 4.5 Four pavement sections with different textures. (A) Pavement A texture, (B) Pavement B texture, (C) Pavement C texture, (D) Pavement D texture.

are basically isotropic while Pavements C and D are not. Pavement A seems smoother than Pavement B. Pavement C has random cracks in random directions. Pavement D has evenly spaced lateral grooves. The texture height measurement results using laser profilometer for the four pavement sections (1-m length for each) are shown in Fig. 4.6. The spatial resolution is about 0.5 mm. The features of each pavement mentioned above can be clearly identified. Mean profile depth (MPD) and shape factor (g-factor) can be calculated from the raw texture height data, as shown in Figs. 4.7 and 4.8. Each data point is the average for 0.1-m pavement length. MPD can be considered as the average depth of a section of pavement and indicates mainly the macro-texture [25], as illustrated in Fig. 4.9 [5]. TPIN has good positive correlation with MPD and the correlation increases with vehicle speed [26]. However, some researchers claimed that the correlation is sometimes weak, because MPD filters out the spectral contents of short wavelengths and cannot be representative of texture characteristics. The shape factor is derived from the Abbott curve, and is used to identify

Figure 4.6 Texture height measurement for four pavement sections.

Figure 4.7 Mean profile depth (MPD) for four pavement sections.

Figure 4.8 Shape factor (g-factor) for four pavement sections.

Influence of road texture on tire/road noise

53

Figure 4.9 Illustration of MPD definition. Modified from ISO. Characterization of pavement texture by use of surface profiles—Part 1: Determination of mean profile depth. ISO 13473-1; 1997.

convex and concave (a.k.a., positive and negative) textures [27], as illustrated in Fig. 4.10. The shape factor is considered as the ratio of peaks above the mean texture height. It is noted that the texture of Fig. 4.10B is simply a flipped version of Fig. 4.10A upside down. A lower value of shape factor indicates more convex/positive texture, which usually generates louder TPIN such as Pavement B. To capture the texture features of different wavelength, the best parameter is the texture spectrum; 200-m measurement was conducted for each pavement to obtain statistically stable spectrum. Fig. 4.11 shows three texture spectra: texture height (displacement), first derivative of texture height with respect to distance (velocity), and second derivative of texture height with respect to distance (acceleration). All spectra are in the frequency domain assuming a traveling speed of 80 km/h for a convenient correlation with the noise spectrum in the following. The frequency resolution is 1 Hz. The displacement spectrum has higher amplitude at lower frequencies while the acceleration spectrum has higher amplitude at higher frequencies. The velocity spectrum is basically flat, indicating the fractal (white noise) characteristics of the pavement texture. Low amplitude is shown at very low frequencies below 200 Hz for the velocity spectrum due to the limitations of the laser profilometer that is not able to measure long-wavelength unevenness features.

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Figure 4.10 (A) Convex (positive) texture with low shape factor; (B) concave (negative) texture with high shape factor.

It can be seen that Pavement B is rougher than Pavement A equally at all frequencies. Pavement C is rougher at lower frequencies but smoother at higher frequencies. Pavement D is smoother at lower frequencies but rougher at higher frequencies. In addition, Pavement D has sharp tones at certain frequencies. It is noted that flipping the texture profile upside down will yield a different MPD and g-factor (equal to one minus the original) but exactly the same texture spectrum, which indicates that the weakness of texture spectrum is the incapability of capturing positive/negative texture features. In addition, for anisotropic pavement texture, multiple lines in the vehicle traveling direction should be measured and texture spectra should be averaged coherently, which is similar to the coherent tread profile spectrum described in Chapter 3, Influence of Tread Pattern on Tire/Road Noise. This process is not further discussed in this chapter.

Figure 4.11 Spectra for pavement texture height (top), first derivative of texture height (middle), and second derivative of texture height (bottom).

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Automotive Tire Noise and Vibrations

4.4 Spectral trend between pavement texture and tire/road noise To determine which spectrum in Fig. 4.11 has the best correlation with the tire/road noise, the effect of the speed on tire/road noise is first investigated. Fig. 4.12 shows the nontread pattern noise spectra at different speeds for a 195/65R15 tire on Pavement B using the Close-Proximity Method (CPX) method at the leading edge of tire contact patch. The nontread pattern noise is very close to the total tire noise because the tread pattern of the tire tested is very quiet compared to the road roughness. It is shown that the noise spectral distribution does not change with speed [28], which indicates that the pavement texture causing the nontread pattern noise should have a flat spectrum, that is, first derivative of texture height with respect to distance (texture velocity spectrum). The texture velocity spectrum is used to correlate with tire noise spectrum at 80 km/h, as shown in Fig. 4.13. Consistent trend can be observed at low frequencies below 1000 Hz in terms of amplitude ranking order.

Figure 4.12 Effect of the speed on the nontread pattern noise for Pavement B.

Figure 4.13 Trend analysis between pavement texture velocity spectrum and tire nontread pattern noise spectrum at 80 km/h (1 Hz frequency resolution).

Influence of road texture on tire/road noise

57

Figure 4.14 Vehicle interior noise spectrum at driver left ear at 80 km/h (1 Hz frequency resolution).

Figure 4.15 Trend analysis between the pavement texture velocity spectrum and tire nontread pattern noise spectrum for Pavement D at different speeds (1 Hz frequency resolution).

However, noise at higher frequencies over 1500 Hz seems to be less dependent on the pavement, likely because the tire envelopes the high-frequency components of the pavement texture [29]. It is noted that the noise data in this section are scaled by a factor due to confidentiality considerations. Vehicle interior noise spectrum also shows consistent trend with texture velocity spectrum at low frequencies, as shown in Fig. 4.14. The high-frequency envelopment for different pavements is also observed in vehicle interior noise spectrum, which agrees with vehicle exterior noise spectrum (CPX). Unlike the other pavements, Pavement D does not have a flat or fractal texture velocity spectrum, which implies that the spectral peaks/tones will shift with speed, as shown in Fig. 4.15. It is also implied that the ISO replica surface on the lab drum is not fractal either considering the frequencies of roadwheel noise also shift with speed, as described in Chapter 2, Tire/Road Noise Separation: Tread Pattern Noise and Road Texture Noise. This is likely due to the

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Automotive Tire Noise and Vibrations

Figure 4.16 Total tire noise spectrogram for the coast-down test from 100 to 40 km/ h on the ISO replica drum and smooth road.

lack of high frequency texture components (such as sand/dirt and other tiny/sharp asperities) in the ISO replica surface. Fig. 4.16 also shows that the nonpatterned (NP) tire only has a broadband noise on a real smooth road whereas the same NP tire can generate tonal noise that shifts with speed on an ISO replica surface. The noise results for the patterned tire on the smooth road shows both tonal noise that shifts with speed due to the tread pattern and broadband noise at around 1 and 2 kHz partially due to the pipe resonance.

4.5 Transfer function and regression model Transfer function (TF) can be simply calculated by the ratio (subtraction if in dB scale) of the noise spectrum to the pavement texture spectrum. In this section, 10 different pavements are tested using the same tire and setup discussed in Section 4.4, assuming the speed of 80 km/h. The first derivative of pavement texture height (pavement texture velocity spectrum) is shown in Fig. 4.17. The picture and type for each pavement is omitted due to confidentiality. The exterior noise spectrum (tire nontread pattern noise by CPX) and interior noise spectrum (at driver left ear) are shown in Fig. 4.18, which uses the same color code as Fig. 4.17. It is shown that for the same tire, the

Influence of road texture on tire/road noise

59

Figure 4.17 Pavement texture velocity spectrum for 10 different pavements at 80 km/h (1 Hz frequency resolution).

Figure 4.18 Exterior and interior noise spectra for 10 different pavements at 80 km/ h (1 Hz frequency resolution).

Figure 4.19 Transfer function between exterior/interior noise and pavement texture velocity for 10 different pavements at 80 km/h (1 Hz frequency resolution).

exterior tire/road noise can be 30 dB different at 300 1000 Hz for different pavements while the interior noise can vary by 25 dB at 100 500 Hz. The variations at higher frequencies over 1500 Hz are likely due to the anisotropic pavement features such as rain grooves, joints, and cracks. The transfer function between exterior/interior noise and pavement texture velocity for the 10 different pavements are shown in Fig. 4.19. If

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Automotive Tire Noise and Vibrations

Table 4.5 Metrics of pavement texture and noise for 10 different pavements at 80 km/h (results partially presented due to confidentiality). Pavement no.

1

2 3 4 Min Max

Overall exterior noise (dBA)

Overall interior noise (dBA)

Overall pavement texture (dB)

MPD (mm)

Shape Factor (%)

116.8 111.5 113.4 116.2 115.5 105.3 113.8 105.8 110.4 113.4 105.3 116.8

86.4 82.1 84.7 89.0 90.1 75.1 87.2 75.6 77.3 85.7 75.1 90.1

76.9 62.1 67.7 75.6 76.1 58.7 67.5 59.7 72.8 58.0 58.0 76.9

3.02 1.16 1.82 4.11 5.00 0.33 2.52 0.54 0.46 1.08 0.33 5.00

84.1 70.8 75.3 62.3 49.5 65.3 67.4 77.1 92.9 46.6 46.6 92.9

there exists a good correlation (cause and effect relationship) between the two spectra, the TF curves for the 10 pavements should overlap/converge. Therefore, the convergence of the TF curves at specific frequencies indicates the dominating effect of pavement texture on exterior noise at 300 1000 Hz and on interior noise at 100 500 Hz, which agrees with Fig. 4.18. The decay of the TF amplitude at higher frequencies implies the tire envelopment effect on noise for small-scale pavement features. For each pavement, the MPD, shape factor, and overall levels of pavement texture velocity and exterior/interior noise are calculated and partially presented in Table 4.5. The overall level of pavement texture velocity is calculated by summing up all its spectral contents. The statistical analysis results are shown in Fig. 4.20. The MPD and shape factor are considered as factors while the overall levels of pavement texture velocity and exterior/interior noise are considered as responses. Fig. 4.20A shows that both exterior and interior noise have positive correlation with MPD but negative correlation with shape factor; interior noise has slightly stronger linear correlation. Fig. 4.20B and C shows that exterior and interior noise will decrease at very high MPD and increase at very high shape factor, which indicates nonlinear correlation. This also suggests that to design a quiet pavement, it is good practice to have a low MPD and moderate shape factor (i.e., avoid major bumps and slots in the pavement).

Influence of road texture on tire/road noise

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Figure 4.20 (A) Linear correlation between metrics; (B) quadratic model for overall exterior noise level; (C) quadratic model for overall interior noise level; (D) linear model for overall pavement texture velocity level.

Fig. 4.20D implies that the pavement texture velocity is positively dominated by both MPD and shape factor.

4.6 Conclusion The comparisons of TPIN between a rough road and a smooth road show that smoother pavement tends to excite higher tread pattern noise but lower nontread pattern noise. Good correlation can be found between pavement texture velocity spectrum and tire nontread pattern noise spectrum at lower frequencies. Higher-frequency components of pavement texture usually do not generate the corresponding tire noise under rolling conditions due to the tire tread envelopment and damping.

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Acknowledgments This chapter is based on the study (Project Code: MODL-2015-B3-8) partially supported by the Center for Tire Research (CenTiRe), an NSF-I/UCRC (Industry/University Cooperative Research Centers) program led by Virginia Tech. Special thanks go to Dr. Ricardo Burdisso and Dr. Corina Sandu for advising on this project. The present author thanks Maxxis for permission to publish some of the internal data. Credits are also given to Maxxis associates who helped with the NVH measurements and statistical analysis. Some commercial information was intentionally omitted in this chapter.

References [1] Li T. Tire-pavement interaction noise (TPIN) modeling using artificial neural network (ANN) [PhD dissertation]. Virginia Tech; 2017. [2] Sandberg U, Ejsmont JA. Tyre/road noise reference book. Kisa, Sweden; Harg, Sweden: INFORMEX; 2002. [3] Li T. Influencing parameters on tire pavement interaction noise: review, experiments and design considerations. Designs 2018;2:38. [4] Li M, Molenaar A, van de Ven M, Huurman R, van Keulen W. New approach for modelling tyre/road noise. In: Inter-Noise 2009; 2009. [5] ISO. Characterization of pavement texture by use of surface profiles—Part 1: Determination of mean profile depth. ISO 13473-1; 1997. [6] Saemann E-U, Dimitri G, Kindt P. Tire requirements for pavement surface characteristics. Presented at 7th symposium on pavement surface characteristics: SURF 2012 Norfolk, VA; 2012. p. 1 33. [7] Dare T, Bernhard R. Predicting tire-pavement noise on longitudinally ground pavements using a nonlinear model. In: 38th international congress and exposition on noise control engineering 2009, Inter-Noise 2009, vol. 1, Ottawa, ON, Canada; 2009. p. 405 15. [8] Sandberg U, Ejsmont JA. Texturing of cement concrete pavements to reduce traffic noise. Noise Control Eng J 1998;46:231. [9] McDaniel R, Shah A, Dare T, Bernhard R. Hot mix asphalt surface characteristics related to ride, texture, friction, noise and durability; 2014. [10] Rasmussen R, Karamihas S, Mun E, Chang G. Relating pavement texture to tirepavement noise. In: Institute of Noise Control Engineering of the USA—35th international congress and exposition on noise control engineering, Inter-Noise 2006, vol. 1, Honolulu, HI; 2006. p. 422 31. [11] FHWA. Technical advisory T 5040.36—surface texture for asphalt and concrete pavements. Washington, DC: FHWA; 2005. [12] ISO. Characterization of pavement texture by use of surface profiles—Part 3: Specification and classification of profilometers. ISO 13473-3; 2002. [13] He D-C, Wang L. Texture features based on texture spectrum. Pattern Recognit 1991;24:391 9. Available from: https://doi.org/10.1016/0031-3203(91)90052-7. [14] Lee YG, Lee JH, Hsueh YC. Texture classification using fuzzy uncertainty texture spectrum. Neurocomputing 1998;20:115 22. Available from: https://doi.org/ 10.1016/S0925-2312(97)00095-7. [15] Wang L, He D-C. Texture classification using texture spectrum. Pattern Recognit 1990;23:905 10. Available from: https://doi.org/10.1016/0031-3203(90)90135-8. [16] ISO. Characterization of pavement texture by use of surface profiles—Part 4: Spectral analysis of surface profiles. ISO/TS 13473-4; 2008.

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[17] Biermann J, von Estorff O, Petersen S, Schmidt H. Computational model to investigate the sound radiation from rolling tires. Tire Sci Technol 2007;35:209 25. [18] Li M, van Keulen W, Ceylan H, Tang G, van de Ven M, Molenaar A. Influence of road surface characteristics on tire-road noise for thin-layer surfacings. J Transp Eng 2015;141. [19] Domenichini L, Fracassa A, La Torre F, Loprencipe G, Ranzo A, Scalamandrè A. Relationship between road surface characteristics and noise emission. In: First international colloquium on vehicle tyre road interaction, Rome, Italy, Paper 99.03; 1999. p. 1 22. [20] Fong S. Tyre noise predictions from computed road surface texture induced contact pressure. In: Proceedings of Inter-Noise 98, Christchurch, New Zealand; 1998. p. 137 40. [21] Hamet J-F, Klein P. Road texture and tire noise. In: Proceedings of Inter-Noise 2000, Nice, France; 2000. p. 178 83. [22] Gautam P, Chandy AJ. A three-dimensional numerical investigation of air pumping noise generation in tires. J Vib Acoustics Trans ASME 2016;138. [23] Schuhmacher A. Blind source separation applied to indoor vehicle pass-by measurements. SAE Int J Passeng Cars Mech Syst 2015;8:1034 41. [24] Alt N, Wolff K, Eisele G, Pichot F. Fahrzeug Außen Geräuschsimulation (Vehicle exterior noise simulation). Automobiltechnische Z 2006;108:832 6. [25] ASTM. Standard practice for calculating pavement macrotexture mean profile depth. ASTM E1845; 2009. [26] Saykin VV. Pavement macrotexture monitoring through sound generated by the tire-pavement interaction [Master’s thesis]. Northeastern University; 2011. [27] Beckenbauer T, Kuijpers A. Prediction of pass-by levels depending on road surface parameters by means of a hybrid model. In: Proceedings of Inter-Noise 2001, The Hague, Holland; 2001. p. 2528 33. [28] Li T, Feng J, Burdisso R, Sandu C. Effects of speed on tire pavement interaction noise (tread-pattern related noise and non tread-pattern related noise). Tire Sci Technol 2018;46:54 77. Available from: https://doi.org/10.2346/tire.18.460201. [29] Goubert L, Sandberg U. Enveloping texture profiles for better modelling of the rolling resistance and acoustic qualities of road pavements. In: 8th symposium on pavement surface characteristics (SURF), 2018, Brisbane, QLD, Australia; 2018.

CHAPTER 5

Measurement methods of tire/road noise Yousof Azizi

Bridgestone Americas, Akron, OH, United States

5.1 Introduction Designing a new tire is a process comprising of different steps. The process is usually begins with a virtual tire model, with different levels of fidelity, to design the tire with the desired characteristics. Based on the virtual designs, physical prototypes are then manufactured and evaluated in different cycles. The design objectives cover a range of performance areas including: 1. NVH, 2. rolling resistance, 3. handling, 4. snow, wet, dry traction, 5. durability, 6. wear, and several more. Multiple tire subsystem component geometries and material properties are tuned and designed to achieve the design objectives and to deliver the desired performance. It is important to evaluate the tire to ensure it meets the intended design. Over years, different experimental procedures have been developed to test each performance area mentioned earlier. Some of these physical experiments have been replaced by virtual simulations and tests. However, in most of the cases, running physical tests is inevitable. In order to evaluate the tire NVH performance, multiple indoor and outdoor tests have been designed and developed by tire industry. Indoor tests are usually at component level to measure tire wheel system airborne noise radiation and structural borne noise generation and transmission. Here the tire and wheel system is mounted on especial experimental setup and acoustic and vibration data is collected. Outdoor tests are usually at system, that is, vehicle, level and tire NVH performance is Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00005-2

© 2020 Elsevier Inc. All rights reserved.

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evaluated to characterize the tire impacts on the overall vehicle in-cabin noise and vibration and pass-by noise. Unlike indoor tests which are mostly objective tests, the outdoor tests include both subjective and objective evaluations of the vehicle noise and vibration. In order to collected objective data, the vehicle is instrumented with different accelerometers, microphones, and intensity probes and the desired acoustic and vibration data is collected. For subjective evaluations, professional evaluators test the vehicle and decide if the noise and vibrations of a tested tire is acceptable according to the preset NVH targets. Comparison of the outdoor system level test data with the indoor component test data can help the engineers to find the root cause of the tire NVH problems, to identify the tire NVH performance gaps, and to solve the tire NVH problems. Some countries and regions have also established some local legislative regulations to keep pass-by noise level of the passenger and commercial vehicles below a certain limit. Since the pass-by noise target is a system level target, outdoor automotive homologation testing is essential. Some examples of these tests are shown in Fig. 5.1. In this chapter, some of the major testing techniques that have been developed and used by the tire industry are introduced. In Section 5.2, the indoor testing methods will be presented. As mentioned these tests are mostly focused on understanding the dynamic and acoustic performance of the tire wheel assembly system. In Section 5.3, common outdoor tests will be reviewed. These outdoor tests are applied to evaluate the regulatory requirement, such as the pass-by noise levels, or evaluate and understand the tire noise and vibration performance of the tire wheel vehicle as a system.

Figure 5.1 Different indoor and outdoor tire NVH tests.

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5.2 Tire noise and vibrations: indoor testing Indoor NVH tests aim to understand the dynamic behavior of tire wheel assembly system and to quantify the tire wheel structural borne noise transmissibility and the tire airborne noise radiation. Under operational conditions, a tire is inflated to a certain internal pressure and loaded and rolled on the road surface at different speeds and angles, e.g. camber. It is known that tire inflation pressure, load, and speed can greatly impact tire characteristics including noise radiation, vibration generation, and transmission. The ultimate goal is to characterize the tire under the same realistic operational conditions. Since tire is a complicated structure, with different layovers of nonlinear viscoelastic materials with complex geometries and contact properties, it is often more practical to first study the tire dynamic behavior under the conditions that are simpler than actual operational conditions. For example, tire vibration transmissibility and modal behavior can be first measured under the unloaded condition, which is far from the tire operational condition. However, the tire’s unloaded and stationary dynamic behavior is well known and understood. Therefore, it is much easier to interpret the tire’s unloaded and stationary test data and relate it to the tire construction and design. Tire can also be tested under realistic loaded and rolling conditions. The results of these tests are helpful in diagnosing tire NVH problems and gaps. They can also help engineers to understand how changing tire’s load and speed impact the noise radiation and vibration transmission. Compared to stationary tire, rolling tire’s vibratory and dynamic response is more complicated due to introduction of the footprint and complex nonlinear contact and centrifugal dynamic and thermal effects. In the past two decades, some researchers have studied these complex phenomena of a loaded rolling tire and how tire construction and design impacts the tire dynamic behavior of a rolling tire. In the rest of this section, multiple common tests developed to study tire structural borne noise, vibration transmissibility, and airborne noise radiation are presented.

5.2.1 Indoor testing: structural borne noise characterization It is known that tire dynamic behavior is a function of frequency. At lower frequencies, a tire basically acts as a spring dashpot system whose stiffness is a function of tire construction and inflation pressure. In the

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frequency range between 50 and 500 Hz, the tire dynamic behavior is influenced by multiple resonances which dictate the vibration energy transmission. At higher frequencies, tire vibrations mostly contribute to the airborne noise generation. With that information, a few different structural borne noise tests have been developed over years to study the tire vibration transmissibility and modal behavior in the frequency ranges of interest. In these tests, the tire is subjected to different inputs which replicate the road inputs. Road excitation inputs are usually considered to be broadband in nature. But depending on the event such as tread band impact and road texture, road inputs only excite the tire effectively up to a certain frequency limit. Some of these testing methods and input types will be reviewed in the following section. 5.2.1.1 Indoor structural borne noise characterization: stationary tire The most basic dynamic test conducted on a tire is to measure frequency response functions and vibration transmissibility of a static and unloaded tire where the modal parameters of the tire are identified. It is noticed that the term transmissibility is intentionally used instead of transfer function as the transfer function has a very specific definition in engineering and is used for linear systems. A tire is nonlinear due to its material composition of rubber hyperelasticity, and geometry and complex footprint contact mechanics induced nonlinearity. Tire dynamic test is run in different forms. In its simplest way, a tire is mounted on an appropriate wheel and the assembly is mounted and fixed on the test bedplate. Shown in Fig. 5.2 is one example of such test setup. The setup consists of a load cell to measure the spindle force. The setup is well isolated to minimize external disturbances and it needs to be designed to ensure its resonance frequency occurs outside the measurement frequency range of interest, for example, above 800 Hz. In this test the mounted tire is impacted by a modal force hammer, both the input and spindle forces are measured and recorded. To relax the fixed boundary condition, the free boundary condition is achieved by hanging the tire with bungee cords that act as weak springs, see Fig. 5.1. The tire is then impacted by a modal hammer and tire surface acceleration, or velocity, can be measured. The effect of the free boundary condition on the response is estimated knowing the bungee cord stiffness and geometry. In both tests, the modal force hammer is usually selected based on the tire size and amount of energy needed to excite the tire. Fig. 5.3 shows an example of a modal force hammer used to excite a passenger vehicle tire.

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Figure 5.2 Modal analysis test stand for measurement of tire transmissibility.

Figure 5.3 PCB modal force hammer.

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Since the tire is mostly made of rubber, applying a force impact to excite the response of high frequencies is challenging. One common solution is to use an appropriate impact force hammer cap/tip. In some cases, small modal exciters or shakers are used instead of the modal force hammer to perform the modal analysis test. This can especially be useful when it is difficult to excite the response of high frequencies with the force hammer. The test setups can be used to perform modal analysis test on the tire. Here, usually a series of accelerometers are placed at strategic locations on the tire, and the modal force hammer is used to impact the tire at the selected location. Alternatively, noncontact measurement methods such as the laser Doppler vibrometery and digital image correlation methods can be used to measure the tire response and for the application of tire modal analysis testing. Signal processing techniques are used to calculate the tire wheel system vibration transmissibility and frequency response. Techniques such as Quadrature Picking can be used to estimate the tire mode shapes and modal natural frequencies. One example of the measured force transmissibility and modal frequency response functions of an unloaded static tire is shown in Fig. 5.4 where the accelerometer is mounted on the tire crown. From the force transmissibility data, it is seen that the tire cavity mode peak (around 210 Hz) and tire vertical mode peak (around 90 Hz) are clear.

Figure 5.4 Sampled force transmissibility of an unloaded static tire. Top: transmissibility from the hammer to the accelerometer. Bottom: transmissibility from the hammer to the spindle.

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The test setup shown in Fig. 5.2 can be used to study the static tire dynamic behavior when a tire is loaded by a hydraulic shaker which is able to apply static or dynamic loads on the tire. The static load is applied by the shaker, or other mechanical mechanisms, to the desired level. Modal force hammer can again be used to impact the tire and to perform modal analysis test in order to measure the transmissibility as described before. This test is useful to understand how introducing footprint and external loads affect the tire dynamic behavior. If the test setup is equipped with a dynamic shaker, dynamic force inputs can be applied to the tire at a desired location which is usually the tire footprint. A tire can be excited with the desired force input and the generated output force is measured at the spindle to calculate the transmissibility from the footprint to spindle. The dynamic shaker can be used to excite the tire footprint in the vertical, fore-aft, or lateral directions. One example of the measured transmissibility and modal frequency response functions of a loaded static tire is shown in Fig. 5.5 where the major mode peak identified at 90 Hz is the tire’s vertical mode similar to the one seen in Fig. 5.4. Comparing Fig. 5.4 with Fig. 5.5, it is seen that additional modes are introduced due to the existence of the footprint. Cavity resonance frequency is a function of tire size, cavity geometry, and filling gas property. The cavity resonance mode can be seen around 200 Hz in both Figs. 5.4 and 5.5.Tire cavity resonance and its impact on the tire transmissibility will be studied in different chapters of this book.

Figure 5.5 A sampled force transmissibility of a loaded static tire from the shaker force to spindle force.

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5.2.1.2 Indoor structural borne noise characterization: rolling tire impact test The static tire impact modal analysis tests are usually very fast and effective in developing a basic understanding of tire dynamic behavior. It is known that tire rolling can affect the dynamic behavior observed in the static tests. In practice, the dynamic behavior of a rolling tire is characterized by different tests that can be distinguished from each other based on their force or displacement inputs. In each test, the tire is tested on different road surfaces, with unique features and textures, which excite the tire at different known frequency ranges and input amplitudes. Rolling tire impact test is one example in which the tire is subjected to impact while it is rolling. A sample test setup developed to run this test is shown in Fig. 5.6. In this setup the tire wheel system is mounted on a fixed spindle equipped with load cells to measure the spindle forces, and in some more advanced cases spindle torques. The tire is then loaded against a surface which replicates the road surface. The road surface is represented by a road wheel drum or a stiff belt with different surface textures depending on the test. In the case of drum, it is important to design the drum diameter so that the footprint is not largely affected by the drum curvature. To apply the impact to the tire while it is rolling, a square or trapezoid metal obstacle, known as cleat, is bolted to the drum

Figure 5.6 Impact test setup of a rolling tire.

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or belt surface. As the tire starts rolling on the drum, cleat impacts and excites the tire. Sample results are show in Fig. 5.7. It is straight forward to show that the frequency spectrum content of the cleat impact is a function of the cleat size, tire footprint length, and tire rolling speed.

Figure 5.7 A sample of the measured tire cleat impact transient time response.

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For standard passenger and commercial vehicle tires, the maximum cleat impact excitation frequency is below 300 Hz and most of the excitation energy is at lower frequencies. Therefore, this test is suitable for understanding the tire’s low frequency dynamic behavior. The collected frequency response data is usually very important for characterizing how the tire impacts automotive ride and harshness. 5.2.1.3 Indoor structural borne noise characterization: high frequency structural borne noise characterization To characterize tire dynamic behavior at high frequencies, a tire needs to be subjected to different road inputs from the ones described before. The road drum or belt described earlier can be covered by asphalt aggregates, or coarse surface shells replicating the real road excitation input where the frequency spectrum contents and amplitude of the asphalt aggregates, or coarse surface shells are similar to those of the real road pavement surface. Like the real road pavement surface, a variety of artificial coarse surfaces with unique textures are available in the market for this testing application. Standard surfaces are effective to excite the tire modes up to 700 800 Hz with most of the excitation frequency below 200 Hz. One example of such coarse surfaces is shown in Fig. 5.8. Rest of the setup is similar to the one described in the previous section. The spindle forces and moments are measured and used to characterize tire dynamic response. As observed before in Section 5.2.1.1 for the stationary tires, the spindle force and acceleration outputs are normalized by the input

Figure 5.8 Test drum with different coarse surfaces.

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excitation force, measured by the modal force hammer or dynamic excitation shaker, to estimate the transmissibility and frequency response functions. However, for the rolling tire tests, we only measure the spindle force. Therefore, the measured force response is not transmissibility and is “polluted” by the road excitation input, in other words, the forced steady state or transient responses are measured. Therefore, when interpreting the data, one needs to be conscious that measured frequency response does not only contain the tire related information. Thus, it is not recommended to compare the measured results collected for the tires tested under different conditions. Examples of measured tire responses are shown in Fig. 5.9. Cavity mode as well as tire radial modes and higher order lateral bending modes are clear in the data. Bearing hub/spindle is fixed in all the setups described so far in this section, in other words, the spindle is fixed. Testing a tire wheel system with completely fixed spindle is useful to understand the tire dynamic behavior. Under operational conditions, the spindle of the tire wheel system is not fixed where the boundary condition of the spindle is determined by the suspension dynamic properties and behaviors. To test the

Figure 5.9 Measured frequency response of the spindle forces for the tire rolling on a drum of a coarse surface. Top: lateral spindle force. Bottom: vertical spindle force. Test data for the tire rolling at 80 kph.

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Figure 5.10 Quarter-vehicle suspension test rig.

tire wheel system under a more realistic condition, the tire wheel assembly system can be mounted on a realistic quarter-vehicle suspension setup. The complete quarter-car suspension setup can then be used to study the dynamic behavior of a stationary or rolling tire [3]. In the former, a static tire is excited by a dynamic shaker similar to the setup described in Section 5.2.1.1, while for the latter the tire is rolling on a road wheel drum or belt similar to the setup in Sections 5.2.1.2 and 5.2.1.3. One example of such test setups is shown in Fig. 5.10. There are also some other simpler solutions in which the rolling tire wheel is not completely fixed at the spindle but the wheel and spindle are constrained by external mechanisms so that only one vertical degree of freedom is achieved for the spindle.

5.2.2 Indoor airborne noise characterization Tire airborne noise impacts in-cabin noise and the vehicle comfort. There are several legislative regulations which require the far-field tire airborne noise, or the pass-by noise, to remain under certain dB levels. For these reasons, characterizing the airborne noise generation and propagation is of great interest. As tire engineers have limited control over the noise propagation and transmission, they are mainly interested in characterizing the tire airborne noise generation and radiation. Tire design such as tread band geometries and material properties can be tuned to influence noise generation and radiation.

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The tire airborne noise generation mechanism is categorized into two types: 1. vibration-induced airborne noise and 2. aero-acoustics noise. Most of the tire airborne noise sources are located close to the tire footprint. Multiple experimental methods/procedures have been developed and standardized to measure the radiated tire airborne noise. These methods are usually categorized into four main types: 1. near-field sound pressure measurement, 2. sound intensity measurement, 3. far-field sound pressure measurement, and 4. radiated sound power measurement. Near-field sound pressure measurement is conducted to understand the tire’s radiated airborne noise, especially close to the footprint where most of the sound sources are located. The sound pressure measurement can also help to gain some understanding about the near-field pressure distribution. Sound intensity measurements can be implemented to estimate the radiated sound power. Also, since the sound intensity is a directional quantity, it is often used to characterize, isolate, and locate a specific airborne noise source. This is important as there are multiple sound sources which contribute to the overall noise radiation and sound pressure level. When the other noise sources are present, sound intensity measurement can be conducted to minimize the effect of other noise sources on the radiated tire airborne noise measurements. Free-field or far-field sound pressure measurement is usually undertaken outdoor to study the vehicle system noise radiation for vehicle homologation. One example of the farfield (free-field) sound measurement will be studied in the next section. Sound power measurement is conducted to characterize the overall airborne noise radiated by the tire. This method is not usually as useful as to study local effects such as the noise mechanisms and sound sources. But it contains useful information to evaluate how tires are different in radiating the noise. The setup used to measure tire noise radiation should usually be located in a full anechoic, semianechoic, or reverberant chamber. Anechoic chambers are commonly used to conduct experiments in nominally free-field conditions where the generated tire noise will be traveling away from the tire with almost none reflected. Different experiments such as near-field sound pressure measurement, sound power measurement, directivity of noise radiation measurement, and tire to cabin noise transfer function characterization can be conducted in anechoic chambers. The reverberant chamber can

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be used to measure tire radiated sound power. Only a few pressure measurements are required in the reverberant rooms to compute radiated sound power. Many more sound pressure measurements are required to do so in an anechoic room. However, for practical reasons, it is common to use an anechoic or semianechoic chamber in the tire industry. The standard setup used to measure the radiated sound pressure and sound power is similar to that described in the previous section consisting of a road wheel drum, load cell and a mechanism to load the tire. The drum surface is either smooth, mimicking smooth road surface like concrete, or coarse, simulating road surface with coarse aggregates. Knowing the important role of the footprint in the airborne noise generation, we need to ensure that the footprint shape and size is close to the ones under real road operational conditions. So, the drum diameter needs to be large enough to minimize the curvature effect on the tire footprint. One example of such test setup is shown in Fig. 5.11.

Figure 5.11 Test setup for tire airborne noise measurement.

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Figure 5.12 Frequency response of A-weighting filter.

Microphones are located around the tire at different locations within about two wavelengths from the noise source to measure the near-field sound pressure. In practice, at least three microphones are placed close to the leading edge, trailing edge, and side of the footprint. In the next chapter, it will be shown that most of the tire airborne noise sources are close to the footprint. The “signature” of the tire airborne noise generated by some of these mechanisms can be observed from the sound pressure measured by one of the three microphones, enabling the engineers to determine the dominant noise generation mechanism(s). It is common to modify the measured data by passing the signal through an A-weighting filter to account for how the sound is perceived by the human ear. Frequency response of an Aweighting filter is shown in Fig. 5.12. Example of a measured sound pressure level for a sample tire is shown in Fig. 5.13. In all three plots in Fig. 5.13, the peaks around 1000 Hz are identified as the tread pipe resonance frequency of the impact induced noise which will be illustrated in the next chapter. In order to estimate the tire noise sound power, microphones are placed on an imaginary surface enclosing the airborne noise source, that is, the tire. There are a few standards describing the sound power measurement such as ANSI S12.34-1988. Fig. 5.14 shows an example of the sound power measurement setup and how the microphones are placed around the tire. Total radiated sound power is calculated from the measured sound pressure and the imaginary area where each measurement microphone is located. The sound power spectrum data is plotted in 1/3

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Figure 5.13 Measured sound pressure level. Top: the sound pressure level measured by the microphone at the leading edge. Middle: the sound pressure level measured by the side microphone. Bottom: the sound pressure level measured by the microphone at the trailing edge.

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Figure 5.14 Setup for measuring sound power of a tire.

Figure 5.15 Measured sound power.

octave bands. Presenting the sound power spectrum data in 1/3 octave bands has multiple benefits. It facilitates the comparison between different sets of sound power spectrum data since there are fewer sound power spectrum data points for comparison. A sample measured sound power in third octave bands is shown in Fig. 5.15. Most of the indoor tests are at component level with some exception where the full vehicle is tested indoor to directly characterize the tire impact on vehicle noise and vibrations. For example, like the tire transmissibility test, the road to cabin structural borne noise transmissibility can be measured. This is done by exciting the tire, already mounted on the vehicle with a shaker and by measuring the in-cabin noise and vibrations. The vehicle can be excited at just one tire or all four tires with the broadband road profile spectrum inputs. If the in-cabin airborne noise is being measured, the vehicle should be tested in an anechoic chamber.

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Similar to the tire airborne noise radiation measurement test (at the component level), the tire noise radiation can be measured while the tire is mounted on the vehicle. For this test, the vehicle should be tested in the anechoic chamber with the tires are rolling on four wheel road drums which are similar to the drum described in the previous section. Then the overall airborne noise radiation is measured. In this test, the vehicle is driven by an external electric motor power source such as the road wheel drum. Thus, the measured tire noise sound pressure is not affected by the sound pressure of the other type of vehicle noise, such as the powertrain or exhaust noise. Alternatively, the in-cabin sound pressure can be estimated by measuring the tire radiated noise and vehicle transmissibility. Tire to cabin airborne noise transmissibility can be experimentally measured for the vehicle of interest in an anechoic chamber. For the vehicle of interest, the tire is replaced by a sound source of known sound power and the interior sound pressure is measured at different locations in the cabin. The airborne noise transmissibility can be estimated given the source power and measured sound pressure using the reciprocity principle of the transmissibility. With the transmissibility identified, the in-cabin sound pressure can be obtained by summarizing the measured radiated sound power from different tires multiplied by the measured transmissibility in all the noise transfer paths. See [4] for more details. Fig. 5.16 illustrates the procedures.

Figure 5.16 In-cabin tire airborne noise prediction given the measured tire sound power.

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5.3 Outdoor testing In the previous section different tests and experimental setups, used to characterize the tire dynamic behavior, structural borne noise transmission, and airborne noise radiation, were introduced and studied. Although some vehicle level tests can also be performed indoor, it is desired to test and evaluate the vehicle outdoor for multiple practical reasons. In general, vehicle indoor testing, such as indoor pass-by noise measurement, can become difficult and expensive as it often requires acoustic measurement environments, a lot of advanced instrumentation, staff training, and experience.

5.3.1 Outdoor testing: subjective evaluation When the vehicle is tested outdoor, the airborne noise and structural borne noise can be directly measured and recorded. Standard objective metrics, based on the recorded data, have been developed over years to evaluate in-cabin noise and vibrations. One of the advantages of evaluating the tire and vehicle for the radiated noise outside the lab is the possibility of subjective evaluation of the structural borne noise and airborne noise. Professional evaluators can drive the vehicle, with different mounted tires in multiple test rounds, and rate the in-cabin noise and vibrations. The evaluators can usually distinguish between tire originated noise and vibrations and the ones originated from other sources. The criteria used for subjective evaluation of vehicle and tire noise and vibrations are usually proprietary and belong to the vehicle or tire manufacturer. The criteria are also different with different vehicle or tire manufacturers. Therefore, they will not be further discussed in this chapter.

5.3.2 Outdoor testing: objective evaluation The objective of the outdoor noise and vibration tests is to understand how the tire impacts: 1. in-cabin airborne noise, structural borne noise and vibrations, and 2. pass-by noise under real vehicle operational conditions, which is difficult to achieve in the lab environment. 5.3.2.1 Outdoor objective evaluation: structural borne noise The vehicle is usually tested on different road surfaces. These surfaces, with different textures and features, replicate different real-world roads with different road profile excitation frequencies and amplitudes. For example, the surfaces with bumps and positive and negative cleats are used to study low

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frequency ride performance when the tire is subjected to larger excitation inputs. Another example of a road surface commonly used is a coarse asphalt paved surface. Similar to the described indoor test set-up, the coarse surface and aggregates contents and types dictate the excitation frequency and amplitude.. Usually based on the design objectives, different asphalt surfaces with different properties are used to characterize how a tire filters this road excitation input and how the resultants of the in-cabin structural noise and vibrations are measured. Later in the chapters of this book, it will be shown that the tire is effective in filtering these mid frequency road inputs. However, if a tire is not well designed, the tire can amplify the road excitation inputs at its resonance frequencies such as the tire cavity mode. This can even lead to more complicated scenarios if there is a coupling between tire and vehicle component resonance modes. Another common road surface used for the outdoor tire evaluation is smooth pavement, for example, concrete or very smooth asphalt. The surface is used to test the tire airborne noise radiation and how the noise is perceived in-cabin. Other surfaces such as the surfaces with potholes, rain groove, and chopped surfaces are some other examples commonly used in the industry. Fig. 5.17 shows some examples of these surfaces and their layouts. In order to avoid any undesired coupling between the tire and vehicle components, engineers need to understand how each component along the structural borne noise transmission path affect the overall system transmissibility. Therefore, it is a common practice in industry to instrument

Figure 5.17 Different outdoor surface and roads used for evaluating tire noise and vibration generation, radiation, and transmission.

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Figure 5.18 Structural borne noise measurement along the transmission path. Top left: at knuckle, Top right: at shock absorber mount, Bottom left: at chassis floor under body, and Bottom right: at seat frame.

Figure 5.19 Frame acceleration for a sample vehicle tested on a coarse road. Top: lateral acceleration, Middle: fore-aft acceleration, and Bottom: vertical acceleration.

the vehicle with multiple accelerometers along the path starting from wheel and hub to cabin floor, seat frame, and steering column. In some cases, wheel transducer is used to measure tire force. Since the wheel transducer is usually heavy, special attentions need to be paid to understand how the dynamic behavior of the transducer influences the collected data at higher speeds. Fig. 5.18 shows an example some measurement points on an instrumented vehicle. Some sample results are shown in Fig. 5.19. Here, previously discussed tire cavity mode and some of the higher order bending modes can be observed in the data.

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5.3.2.2 Outdoor objective evaluation: airborne noise To measure the in-cabin airborne noise, the vehicle is tested with constant speeds on a desired road surface (such as the Glen Eagles, concrete and smooth road surfaces), and the sound pressure level is measured by microphones placed at the ear positions strategically in the cabin where the occupants are seated. For more accurate and realistic measurement, the head measurement system (Head Acoustics HMS system) is used. With this method, the airborne noise is measured for objective evaluation and the noise can also be played back for subjective evaluation. Fig. 5.20 shows an example of a microphone location and a head measurement system developed by Head Acoustics. The recorded in-cabin noise is used to understand how the tire impact in-cabin noise. Similarly, the recorded incabin noise when the vehicle is tested on other surfaces, such as coarse surfaces, is used to understand how the structural borne noise is perceived and heard in the cabin. Fig. 5.21 shows some sample sound pressure spectrum results measured near the driver’s ear. The results are shown for the same vehicle and tire but for two different road surfaces. As expected, the sound pressure spectrum amplitude under the coarse surface excitation input to the tire at lower frequencies is larger than the one under the smoother road surface excitation input to the tire, which leads to almost 16 dB difference between the two results below 500 Hz. When the incabin measured noise is analyzed, it is often beneficial to study the indoor tire noise radiation spectrum data, if available. The tire noise spectrum data can help to identify the tire noise contribution to the overall measured noise spectrum data and understand how the tire radiated noise is affected by the vehicle. It is important to understand that unlike the indoor tests which are conducted in a fully controlled environment, different external noise sources and factors may contaminate the measured in-cabin airborne noise. Therefore, when the outdoor test results are being used to evaluate the tire airborne noise radiation, these external factors need to be considered. For example, when two tires are evaluated and compared for the tire noise, it is important that the two tires are tested on the same vehicle and under similar conditions. External noise or excitation sources can greatly influence the collected airborne noise spectrum data which may lead to misjudgment. On-board sound intensity (OBSI) measurement method is another common outdoor test method to characterize the tire/road noise. In this

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Figure 5.20 Top: example of microphone location for the in-cabin airborne noise measurement. Bottom: head measurement system made by HEAD Acoustics.

method, the sound intensity probes are mounted near the contact patch at the leading edge, trailing edge, and side of the footprint of a rotating tire. The setup is illustrated in Fig. 5.22 where an encoder is usually equipped to correlate the measured sound intensity with the tire rotational speed. This method is effective in characterizing the tire tread pattern related airborne noise radiation.

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Figure 5.21 Example of the in-cabin airborne noise spectrum data. Top: on smooth road; Bottom: on coarse road.

Figure 5.22 OBSI system developed by AVEN, Inc.

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Data collected from this test is very similar to the data collected in the lab as described in the previous section. This method often serves as an alternative to indoor tire airborne noise test when the infrastructure does not exist. A method similar to the one in Fig. 5.16 has been developed to estimate the in-cabin noise based on the data collected by OBSI. 5.3.2.3 Outdoor objective evaluation: pass-by noise measurement Tire pass-by noise measurement is another common outdoor test which is frequently run by the tire manufacturers and OEMs. There are a few variations of this legislative government regulated test. For example, recently, a revision of PBN vehicle homologation (UNECE Reg. 51.02) was passed by EU (COM 856/2011). Contrarily to Reg. 51.02 (assessing max vehicle noise), new Reg. 51.03 aims to assess the vehicle noise in urban traffic conditions. There are two chapters in this book dedicated to the pass-by noise and its measurement methods. Readers are referred to Chapter 13, Pass-by Noise: Regulation and Measurement and Chapter 14, Pass-by Noise: Simulation and Analysis, for more details.

5.4 Summary In this chapter multiple testing methods developed to characterize the tire airborne noise radiation and structural borne noise transmission have been developed. The testing methods are presented in two groups: The first group includes the indoor tire noise tests which are most focused on characterizing the tire wheel system. Tests in the second group focus on understanding the tire noise and vibration when the tire is mounted onto a vehicle and becomes a part of the vehicle. Some examples of the collected sound pressure spectrum data for both the indoor and outdoor tests have been presented. In the next chapter, different mechanisms contributing to the tire noise and vibration generation and transmission will be presented.

References [1] Yi J, Liu X, Shan Y, Dong H. Characteristics of sound pressure in the tire cavity arising from acoustic cavity resonance excited by road roughness. Appl Acoust 2019;146 (2):218 26. [2] Wei Y, Yongbao Y, Yalong C, Hao W, Dabing X, Zhichao L. Analysis of coast-by noise of heavy truck tires. J Traffic Transp Eng 2016;3(2):172 9.

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[3] Sandu C, Andersen ER, Southward S. Multibody dynamics modelling and system identification of a quarter-car test rig with McPherson strut suspension. Veh Syst Dyn 2011;49(1):153 79. [4] Saguchi T, Yumii K, Zakelj P. Vehicle interior noise prediction using tire characteristics and vehicle transmissibility. SAE Technical Paper, No. 2007-01-1533; 2007.

Further reading Cerrato G, Goodes P. Practical approaches to solving noise and vibration problems. Sound Vib 2011;45(4):18 22. Constant M, Leyssens J, Penne F, Freymann R. Tire and car contribution and interaction to low frequency interior noise. SAE Technical Paper, No. 2001-01-1528; 2001. De Klerk D, Ossipov A. Operational transfer path analysis: theory, guidelines and tire noise application. Mech Syst Signal Process 2010;24(7):1950 62. Feng, Z., Gu, P., Chen, Y., Li, Z. Modeling and experimental investigation of tire cavity noise generation mechanisms for a rolling tire. SAE Int. J. Passeng. Cars Mech. Syst. 2009;2(1):1414 1423. Genuit K. Vehicle interior noise—combination of sound, vibration and interactivity. Sound Vib 2009;43(12):8 12. Guo R, Cao C, Mi Y, Huang Y. Experimental investigation of the noise, vibration and harshness performances of a range-extended electric vehicle. J Automobile Eng 2016;230(5):650 63. Junoh AK, Muhamad WZAW, Fouladi MA. A study on the effects of tyre vibration to the noise in passenger car cabin. Adv Model Optim 2011;13(3):567 81. Kindt P, Berckmans D, De Coninck F, Sas P, Desmet W. Experimental analysis of the structure-borne tyre/road noise due to road discontinuities. Mech Syst Signal Process 2009;23(8):2557 74. Kindt P, De Coninck F, Sas P, Desmet W. Test setup for tire/road noise caused by road impact excitations: first outlines. In: Proceedings of ISMA; 2006. p. 4327 4336. Mohamed Z, Wang X, Jazar R. A survey of wheel tyre cavity resonance noise. Int J Veh Noise Vib 2013;9(3):276 93. Ni EJ, Snyder DS, Walton GF, Mallard NE, Barron GE, Browell JT, et al. Radiated noise from tire/wheel vibration. Tire Sci Technol 1997;25(1):29 42. Park J, Gu P, Juan J, Ni A, Van Loon J. Operational spindle load estimation methodology for road NVH applications. SAE transactions 2001; Paper No. 2001-01-1606. Park J, Gu P, Lee MR, Ni A. A new experimental methodology to estimate tire/wheel blocked force for road NVH application. SAE Technical Paper 2005-01-2260; 2005.

CHAPTER 6

Generation mechanisms of tire/road noise Yousof Azizi

Bridgestone Americas, Akron, OH, United States

6.1 Introduction It is well known that the tire noise and vibrations are generated by either tire tread and road surface interactions or some internal dynamic effects. There are many theoretical mechanical and acoustical mechanisms that can contribute to the generated noise and vibrations. There is an agreement that the source of the tire vibrations and structural borne noise is the broadband road inputs which excite the tire. The forced controlled and displacement controlled road and tire mechanical interactions excite the tire. The nature of the broadband input is a function of various parameters including road surface textures and properties as well as tire contact patch geometries and characteristics. In practice researchers have strived to identify the specific mechanisms which contribute the most to the overall generated noise. Reviewing the literature, there are several studies correlating a specific noise generation mechanism with the overall tire noise. However, in many examples such studies have been designed and engineered to inherently neglect other existing mechanisms. To avoid any premature judgment, different theoretical generation mechanisms are introduced in this chapter. Similar to other acoustic problems and applications, tire generated noise can be categorized into two main groups: 1. Aero-acoustic induced noise 2. Vibration-induced noise In the former, the acoustic pressure fluctuations are induced by aeroacoustic noise sources like aerodynamic effects. In the latter the acoustic pressure fluctuations are generated by structural vibration and its close coupling and interactions with the surrounding air. Of course, there are multiple mechanisms in each group that need to be studied and evaluated to accurately understand the tire noise generation mechanism. Also, Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00006-4

© 2020 Elsevier Inc. All rights reserved.

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different factors such as the road surface, tire speed, load, geometry, and construction can dictate which category is more important. For example, when the tire is rolling on a coarse bitumen road surface, the low frequency vibro-acoustic mechanisms become more dominant. However, in the case of the smoother concrete road surfaces, the aero-acoustic mechanisms become important. It is also important to remember that tire noise and vibrations are transmitted through several mediums and paths/parts until they reach vehicle cabin, or in the case of the pass-by noise, they radiate into the environment. The transmission paths filter the generated tire vibrations and structural borne noise. For example, the generated structural vibrations are propagated through and filtered by the tire carcass, wheel, spindle, and other suspension components. The generated tire noise transmits in the air to the environment as the pass-by noise or through the unsealed gaps or holes on vehicle body panels and windows into the cabin. These mediums and transmission paths can also amplify the transmitted noise at certain frequencies. Therefore, understanding the transmission mechanisms is always as important as generation mechanisms. This knowledge can often help the engineers to minimize and control the cabin noise and vibration and pass-by noise by tuning design parameters of the transmission path. This becomes very important as it is frequently more feasible to tune the transmission path design parameters than to change the noise and vibration source. Fig. 6.1 shows some of these mechanisms.

Figure 6.1 Some examples of tire structural borne noise and airborne noise generation and amplification mechanisms.

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Tire induced noise and vibration can be felt in the cabin as structural borne noise or perceived as noise as airborne noise. Next in this chapter, the tire structural borne noise and the airborne noise concepts will be introduced. Later in this chapter different tire airborne noise and structural borne noise generation mechanisms are introduced. Then, different structural borne noise transmission mechanisms are reviewed. Airborne noise amplification mechanisms are presented in the last section.

6.2 Tire structural borne noise and airborne noise Road noise, that is, tire noise and vibrations can be categorized into two types: 1. Structural borne noise and vibration (SBN) 2. Airborne noise (ABN) Depending on the frequency range of interest, one type can dominate the other type. The tire structural borne noise dominates the overall generated noise at lower frequencies while the airborne noise is more important at higher frequencies. Experimental studies have shown that there is a transition region around 500 Hz where the airborne mechanisms start to become more dominant than the structural borne noise mechanisms. Fig. 6.2 shows this transition region and dominant frequency ranges of the airborne and structural borne noise.

Figure 6.2 The dominant frequency range of the structural borne noise and airborne noise.

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6.2.1 Tire structural borne noise Structural borne noise is vibration induced. As the tire rolls on the road, at the tire pavement interface, the tire is excited by the imperfections in the road. In some cases, the tire can also be excited by some internal mechanisms such as tire nonuniformity. These external and internal excitations, in addition to local tread band deformations, can cause local strains that propagate in the tire carcass. External road inputs and excitations are usually considered to be broadband up to 200 500 Hz for standard road surfaces. When analyzing the tire structural borne noise, it is often beneficial to picture the tire as a dynamic system which filters and modifies the broadband road inputs. The filtered road inputs and tire vibrations propagate in the tire and transmitted through bead area and tire wheel interface to the wheel. The propagated vibration can further be transmitted through the spindles, vehicle suspension, steering mechanisms, and chassis to the vehicle cabin. The transmitted vibrations can be felt in the cabin at the steering wheel, foot rest, and seats. The vibrations can also excite the components to radiate audible noise in the cabin. To improve tire generated structural borne noise, tire engineers “tune” this dynamic system by designing the tire construction to filter out the road broadband inputs at certain frequencies. Like other dynamic systems, different materials, constructions, and designs need to be adopted to achieve a desired dynamic system transmissibility. This tuning process is usually achieved considering the dynamic behaviors of different components along the transmission path.

6.2.2 Tire airborne noise Airborne noise can be vibration induced or it can be generated by aeroacoustic noise sources. Airborne noise dominants the overall tire noise at higher frequencies as illustrated in Fig. 6.2. Tire structural vibrations can excite the air surrounding the tire to generate pressure fluctuations due to the air-structure coupling. It is well known that certain vibration modes and waves, for example, supersonic flexural waves, are very effective in radiating airborne noise. Several studies have shown the tire vibrations near tire contact patch are especially effective in exciting the surrounding air and radiating noise. The aero-acoustic noise sources can also generate the airborne noise. Here the aerodynamic sources, such as tire tread groove deformation and

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air coupling, cause some pressure fluctuations and acoustic waves that can propagate in the space which propagates in the air and reaches the people outside the car. This radiated tire airborne noise is a part of vehicle passby noise which is regulated by the government in certain regions mandating the overall vehicle pass-by noise to stay below a certain level. Similarly, the airborne noise can transmit through the unsealed gaps and holes in the automotive body structures into the cabin, which directly impacts the cabin comfort and passenger’s perception of the ride quality. The tire vibration induced airborne noise can be controlled by reducing the tire structural vibrations. As indicated earlier, certain vibration modes are more effective in radiating noise. Tire construction can be tuned to impact these modes with higher radiation efficiency. Tire aeroacoustic noise radiation can usually be controlled by changing tire geometric features such as the tire shape, tread sequence, pitch count, and pattern.

6.3 Tire noise and vibration: generation mechanisms There are different mechanisms that contribute to the tire structural borne and airborne noise. In most of these mechanisms, tire noise and vibrations are originated from the tire and road interactions at the tire contact patch or some internal dynamic effects. Tire road interactions were discussed in Chapter 3, Influence of Tread Pattern on Tire/Road Noise, andChapter 4, Influence of Road Texture on Tire/Road Noise. In this section, we will show how these interactions contribute to the tire noise generation. Tire mass and stiffness nonuniformity can also act as tire internal vibration generation mechanism. Tire nonuniformity mechanism is also discussed in this section.

6.3.1 Impact induced noise and vibration One of the airborne noise generation mechanisms is tread impact. As the tire lugs enter and leave the footprint area, the local deformations of a tire due to the tire road interactions excite the tire. This excitation input propagates in the tire carcass resulting in some forced and natural vibration responses of the tire. Different experimental methods, such as laser Doppler vibrometer and digital image correlation-based methods, have been used to observe how these bending waves propagate in the carcass. These studies have shown the vibration in the tread in front of and behind the contact patch is dominated by bending waves. Due to rubber

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Figure 6.3 Tire lug impact induced noise and vibration.

viscoelastic and high damping properties, the vibrations cannot propagate all through the tire and the vibrations are only observed near the contact patch where they are originated. These bending waves in the tread band are very effective in radiating noise. It is believed that controlling these waves, by changing the tread material which impacts the wave phase speed and controlling the inputs which cause these waves at the first place, can help to improve the tire noise radiation. This mechanism is illustrated in Fig. 6.3. It is seen from Fig. 6.3 that the vibration wave attenuates as it travels away further away from the contact patch. In addition to the out-of-plane vibrations, the tangential and axial vibrations were also reported. In general, these modes cannot serve as effective noise radiators and are often neglected. Similar behavior was also observed in the tire sidewall. When these bending waves are high in frequency or supersonic, they can effectively radiate noise. There are several studies suggesting the sidewall vibrations and radiated noise impact the pass-by noise. It is difficult to associate any of these mechanisms, for example, sidewall vibrations, with the overall radiated noise. It is always recommended that both the sidewall and tread band vibrations and their contributions to the tire noise radiation should be considered when a tire is designed. This generation mechanism is effective in the frequency range between 500 and 3000 Hz depending on the tire speed, tire design, and construction such as tire pitch count. The effect of the forced vibrations, for example, mostly governed by the excitation input to the tire, can be perceived by the spindle force as well as the measured near-field sound pressure at the leading edge, trailing edge, and even sides of the contact

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patch. For a single pitch tire, frequency of the generated forced vibration can be simply calculated by, f 5 Nω where f is the frequency in Hz, N is the pitch count, and ω is the tire rotational speed in radius/s. For a mono-pitch tire where all tread elements are of the same circumference size, a tonal noise can be produced. To overcome the tonal noise, it is common to randomize the pattern of tread elements around the tire. For a passenger vehicle tire with 70 pitch count, this frequency can be around 1000 Hz at a highway speed. Later in this chapter, the generated noise at this frequency will be shown to be amplified by some other mechanisms.

6.3.2 Air pumping One of the tire noise mechanisms which has been studied in detail is the tire air pumping. For a treaded tire, there are multiple air volumes/cavities and pockets formed by the grooves and the tread slots. As the tire rolls on the road surface, these volumes are compressed or expanded, which forces the air in and out of the pockets at the leading edge, trailing edge, and sides of the tire footprint/contact patch. This phenomenon is called the tire air pumping which leads to local pressure fluctuations propagating in the air. The air-pumping mechanism and different steps of air-pumping mechanism are illustrated in Fig. 6.4.

Figure 6.4 Tire air-pumping noise generation mechanism [1].

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Similar to other aero-acoustic noise source, air pumping is reported to be effective in the high frequencies from 2000 to 10,000 Hz. The importance of the air-pumping mechanism has been questioned by some researchers as its effective frequency range overlaps with that of some other known mechanisms. It is shown from the experimental measurement of the near-field sound pressure that the sound pressure level of the air-pumping noise at the leading edge of the tire footprint/contact patch are higher than those at the trailing edge. Some researchers Have used this data to conclude that the air-pumping noise is more dominant at the leading edge than that at the trailing edge. Although, it is difficult to conclude that the elevated sound pressure level at the leading edge is solely caused by the air-pumping noise while neglecting the noise generated by the other generation mechanisms in effect. There are also several numerical and analytical models to simulate the tire air-pumping noise generation mechanism. One of the advantages of using these models to simulate the tire air-pumping noise is the ability to isolate the tire noise generated by the other mechanisms. It has been shown from one of these studies that the tire air-pumping noise can be reasonably modeled by a point monopole for very small volume changes, that is, small loads. In more sophisticated numerical models, the tire is modeled as a rigid structure to isolate the impact induced tire noise or vibration and the tire air-pumping noise is modeled as pure aero-acoustic phenomena. Most of these simulation models and studies confirm the mentioned frequency range of the tire noise generated by the aeroacoustic noise sources. It is also suggested by some researchers that the whole tire aeroacoustics noise source can be treated as another tire noise generation mechanism. But there is no evidence that shows this tire noise generation mechanism strongly contributes to the overall airborne noise compared to the other tire noise mechanisms.

6.3.3 Friction-induced noise and vibration Friction between the tire and road surface induces vibrations which can induce the noise. Friction induced vibration is generated by either the stick slip mechanism or tread adhesion. As the tire rolls on the road surface and the tread lugs enter the footprint, the lugs get compressed, deformed, and stick to the road surface due to vehicle load. As the lugs exit the footprint, the lugs start to recover from the deformation. The

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lugs undergo shear due to the tire rotation and the friction force between the tire and road surface. As the tire rotate and the shear force exceeds a threshold, the lugs slip on the road surface. Depending on the shear threshold, maximum tire deformation as well as the tire tread stiffness, the lugs will start to vibrate. This can result in the tire airborne noise radiation depending on the mobility of the tread vibration. The lug vibration can also excite the tread band and propagate in the tire and radiate the noise similar to that generated by the mechanism described in Section 6.3.1. To reduce friction induced vibration, stiffer tread lugs with higher viscoelastic damping are desired. This is an example of the contradicting requirements of designing the tire, that is, the requirement to reduce impact induced noise desires the softer lugs, while the requirement to reduce the friction induced vibration desires the stiffer tread lugs with higher viscoelastic damping. Also, to maintain the tire’s rolling resistance targets, the tread with lower viscoelastic properties is desired. Fig. 6.5 depicts the generation mechanism of the friction induced noise and vibration. Note that this schematic only shows a basic representation of what is happening at the footprint when tread lugs leave the footprint. The actual behavior is more complicated. It is seen that the friction induced vibration is damped as the lug exists the footprint. Researches have shown that the tire noise generated by the stick slip and adhesion mechanism usually has frequencies measured from 800 to 3500 Hz. The tire noise generated by the stick slip and adhesion

Figure 6.5 Generation mechanism of the friction induced noise.

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mechanism is dominant close to trailing edge of the rotating tire as expected from the physics of the mechanism. Road surface texture plays a significant role in the existence and importance of this mechanism. It can easily be observed by rubbing one’s finger against different surfaces and listing to the generated friction induced noise. In practice, the noise generated by these friction-based mechanisms is sometime called sizzling and squealing noise (depending on the road surface conditions). It is interesting to note that all three major tire noise generation mechanisms discussed in this section are effective in similar frequency ranges. The fact that these mechanisms overlap has caused confusions and questions about the existence of certain mechanisms such as tire airpumping noise generation mechanism. It is not recommended by the author to ignore any of the aforementioned mechanisms. The airborne noise may be generated by all of these mechanisms, and maybe even a few more that we have not covered in this section! Depending on different factors such as the tire construction, material, road surface texture, tread design, pattern, and pitch counts, one of the mechanisms may dominate the other ones. Therefore, it is impossible to conclude which mechanism is more effective in the tire noise generation.

6.3.4 Tire nonuniformity as a vibration source Tire noise and vibration generated by all the mechanisms mentioned in this chapter are originated from the tire road interactions. Tire structure can also be internally excited by the geometric and material nonuniformities of the tire structure. Tire nonuniformity can occur in different ways including the nonuniformity in mass, stiffness, or geometry. Mass nonuniformity, shown in Fig. 6.6, is characterized by nonuniform distribution of mass in the tire. Mass imbalance can be introduced into a tire by improper manufacturing, extreme pitch sequence or patterns, irregular wear or during the extreme events such as harsh braking. Depending on the location of the imbalance mass, the centrifugal force effect can cause the radial or lateral vibrations which can be felt by the vehicle occupants. Geometric nonuniformity is due to either the tire radial or lateral runout as geometry of a tire is not always perfect as shown in Fig. 6.7. Although, the manufacturers always try to maintain imperfections of a tire at a minimum level, the imperfections or undesired features of the tire shape are introduced during the manufacturing process. These geometric

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Figure 6.6 Tire nonuniformity due to improper mass distribution.

Figure 6.7 Geometric nonuniformity of a tire.

run-outs lead to the variations of the radial and lateral forces which cause structural vibrations. The generated forces are functions of run-out as shown in Fig. 6.7 as Rmin, Rmax, dmin, and dmax. Stiffness nonuniformity is due to the undesired variation of tire radial and lateral stiffness values. The undesired variation can be caused by the manufacturing flaws or simply the tread sequence and pattern design. Similar to the outcomes in the previous cases, the stiffness nonuniformity

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Figure 6.8 Tire radial stiffness nonuniformity.

leads to the variations of the tire radial and lateral forces consequently resulting in the undesired vibrations. Fig. 6.8 shows an example of tire radial stiffness nonuniformity. The self-excitation frequencies due to tire nonuniformity are a function of tire rotating speed and the nature of the nonuniformity. However, the self-excitation frequencies usually are lower and below 150 Hz. One practical way for identifying the noise and vibration generation mechanism out of the tire nonuniformity is to measure and monitor the tire vibration response including the spindle force at different speeds. Since the generated centrifugal force is a quadratic function of the tire rotating speed, it is possible to track and identify the vibrations caused by the tire nonuniformity. In the next section, tire structural borne noise transmission mechanisms will be presented where the road excitation input or tire nonuniformity induced vibration can be amplified at the resonant frequencies of the components along the transmission path.

6.4 Tire structural borne noise transmission mechanism A tire is subjected to different external and internal excitations as it starts rolling on the road surface. The resultant free and forced vibratory responses propagate through the tire structure. As described earlier, the tire structure can act as a filter which reduces or amplifies the input energies at different frequencies. Considering that today’s tires are composite structures, made of multiple elastomeric components and reinforcement layers, the tire’s dynamic behavior such as transmissibility, can be tuned by

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Figure 6.9 Tire noise and vibration transmissibility and propagation path.

changing the material, construction, and geometry of tire lay-up layers and components. Fig. 6.9 depicts how a tire filters road excitation inputs. For many years, the tire’s transmissibility has been studied using experimental studies, analytical models of different complexities including the ring or shell models, and high fidelity numerical models, for example, finite element analysis or statistical energy analysis. Most of the studies are restricted to the cases of the unloaded and static tires. Some studies have shown some correlations between the rolling loaded tire transmissibility and static unloaded tire transmissibility. However, these studies usually offer limited information about the actual tire dynamic behavior. Under realistic loaded and rolling operating conditions, dynamic effects, such as the gyroscopic effects, cause the transmissibility of a rolling tire to be different from that of a static tire. In this section, the transmissibility of a static unloaded tire is studied. Although understanding the dynamic behavior of a rolling tire transmissibility is beyond the scope of this chapter, the effect of rolling on the static tire transmissibility is briefly discussed in this section.

6.4.1 Low frequency transmissibility (below 30 Hz) Tire noise and vibration transmissibility is a function of frequency. Tire’s overall dynamic behavior can be studied for different frequency ranges of interest for automotive applications. Below 30 Hz, a tire acts as a springdashpot system where the tire radial stiffness and damping play significant roles in the overall tire noise and vibration transmissibility. Tire

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sidewall stiffness directly impacts the radial stiffness. Therefore, sidewall construction parameters can be tuned to impact the transmissibility in this frequency range. In this frequency range, tire is usually designed considering the vehicle behavior, for example, suspension properties. The well-known wheel hop mode or resonance occurs in this frequency range which can be controlled by tuning the tire and suspension stiffness values. In the frequency range less than 20 Hz, stiffer tire improves the ride comfort. Also, when the tire’s radial stiffness increases, the suspension mode resonance frequencies decrease while the vehicle body vibration amplitude decreases. Simple mass spring dashpot lumped parameter models, like a 4-degrees-of-freedom model shown in Fig. 6.10, can be used to show how tire properties impact the wheel hop and vehicle body/chassis responses. One example of road to chassis transmissibility estimated using the 4-degrees-of-freedom model is shown in Fig. 6.11. Here the first peak corresponds to body mode while the second peak is the wheel hop mode.

Figure 6.10 Quarter-vehicle suspension model for studying the tire’s low frequency transmissibility.

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Figure 6.11 The road to chassis transmissibility.

Figure 6.12 Mid-frequency transmissibility of a static unloaded tire.

6.4.2 Mid-frequency transmissibility from 30 to 500 Hz Stationary tire has multiple vibration modes between 30 and 500 Hz. Figures 6.12 and 6.13 show two examples of the transmissibility amplitude curves of the static unloaded and loaded tires. It is seen that multiple modes are distributed in this frequency range and can affect the overall tire noise response. These modes are usually grouped into two categories: (1) radial modes and (2) lateral modes. Radial modes have radial distortion patterns where the belt package acts as a ring while the sidewall acts as a spring connecting the ring to the wheel. Fig. 6.14 depicts one of the first

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Figure 6.13 Mid-frequency transmissibility of a static loaded tire.

Figure 6.14 Example of a tire radial mode.

radial modes of the tire. This radial mode is usually seen in the frequency range between 50 and 120 Hz depending on the tire mass, stiffness, and size. Automotive manufacturers are often very interested in this mode as it can impact the vehicle comfort and harshness. Lateral modes have transversal distortion patterns. One example of a tire lateral mode is shown in Fig. 6.15. Crown bending is the main feature of the shown mode and similar lateral modes. These lateral modes are usually observed in the frequency range between 250 and 500 Hz. These lateral modes and their frequencies can be tuned by changing the tire crown stiffness. Depending on the dynamic properties and design parameters of the vehicle suspension and chassis, these modes can greatly impact the vehicle structural borne noise level.

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Figure 6.15 Example of a tire lateral mode.

[c,m] notation is commonly used to categorize these circumferential and lateral tire modes. The first index c represents the number of sinusoidal waves in the circumferential direction. The second index “m” represents the number of waves in the lateral direction at a circumferential location where the shape is at an extreme displacement. At higher frequencies, tire transmissibility is spatial and local and its behavior is governed by waves propagating in the tire. Some of these wave transmission properties were briefly discussed in the previous section when the tire vibrations near the contact patch were reviewed. More indepth studies can be found in many different publications in this area.

6.4.3 Effect of rolling on tire transmissibility A rolling tire exhibits different modal properties from a static tire. There are different dynamic effects causing the rolling tire to exhibit different behavior. Some of these main effects are: 1. Material properties change with the strain amplitude; 2. Pure dynamic effects caused by the centrifugal force, inertia, boundary condition, etc.; 3. Temperature effect caused by the tire heating under rolling condition; 4. Pressure effect caused by the increased inflation pressure due to the dynamic effects and the temperature effect generated by the rotating tire. Experimental studies have shown that, depending on the speed, the measured system resonant frequencies for a stationary tire are less than those for a rolling tire. The system resonant frequencies for a static tire are shifted by approximately 10% when the tire starts rolling. In addition to the frequencies, the mode shapes for a rolling tire are different from

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the ones for a static tire. There are multiple recent studies for predicting the rolling loaded tire transmissibility using the explicit FEA and ALE FEA methods. The readers are referred to these studies for more information [2,3]. In addition to the structural modes and resonances, acoustic resonances can impact and amplify the radiated noise and transmitted vibrations. These acoustic resonances and amplification mechanisms will be discussed in the next section.

6.5 Tire noise and vibration amplification by acoustic resonance In the previous two sections different structural borne and airborne noise generation and transmission mechanisms were studied. Like many acoustic and vibro-acoustic problems, it is important to briefly discuss the amplification mechanisms due to acoustic resonance and structural-fluid coupling which can substantially amplify the generated noise and transmitted vibrations. These acoustic resonance phenomena and amplification mechanisms are discussed in the rest of this chapter.

6.5.1 Tire cavity resonance Tire is a highly damped system due to the large rubber viscoelastic damping effect and the transmitted vibration is affected by this damping effect at structural resonant frequencies. However, due to the coupling between the tire structure and the fluid in the cavity, cavity resonance can adversely impact the transmitted vibrations. Tire cavity is an empty volume in the tire filled with air or some other filling gases such as nitrogen. As the structural vibration propagates in the tire structure, there is a structural-fluid coupling between the cavity air and the tire carcass. The structural vibrations excite air inside the cavity and acoustic waves propagate in the tire cavity. The resultant acoustic pressure variations and fluctuations may induce the fluctuations of the spindle forces that propagate into the suspension and vehicle chassis structure as structural borne noise. Note that the fundamental acoustic cavity resonances consist of two acoustic modes oriented in fore/aft and vertical directions. The cavity has its own natural modes and the air inside the cavity resonates at certain frequency which is a direct function of the acoustic

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wave phase speed and the cavity geometries. For an unloaded tire, the first cavity resonant frequency is approximated as, c f5 2πR where c is the speed of sound in the cavity and R is the average cavity radius. For the passenger vehicle tire sizes, the first cavity resonant frequency stays between 180 and 250 Hz. Based on basic acoustic theory, when the tire starts rolling the air inside the cavity will start moving with the tire. Tire speed will impact the cavity resonance frequency by creating upstream and downstream phase velocities. For an unloaded spinning tire, these frequencies are estimated by: fupstream 5

c1ω 2πR

fdownstream 5

c2ω 2πR

where ω is the tire rolling speed. This will split one tire cavity resonant frequency into two frequencies moving apart from each other as the tire rotating speed is increased. Fig. 6.16 shows the measured vertical spindle force for a rolling tire. The two frequencies associated with the cavity resonance are observed around 200 Hz. Since the cavity has no or the

Figure 6.16 Tire cavity resonance and its frequency split phenomenon.

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minimum acoustic absorption, the acoustic cavity mode resonance can greatly amplify the tire structural borne noise at the cavity resonant frequency. In addition to acoustic cavity resonance, tire has multiple structural resonance frequencies in the vicinity of the cavity resonance frequency which increases the likelihood of the undesired modal coupling. In the past decade several solutions have been developed to address the undesired tire cavity resonance. The developed solutions range from adding an absorbing material like open cell foam to the cavity to narrowband resonators like Helmholtz resonator. Tire cavity resonance and its undesired amplification will be studied in another dedicated chapter later in this book.

6.5.2 Tire pipe resonance Also, most of the airborne noise sources are located close to the footprint/ contact patch. Under certain conditions, some tire features and geometries near the footprint amplify the generated airborne noise. Tire footprint/ contact patch is made of a structure similar to a network of pipes, known as tire grooves and slots, which are filled with air. Since the airborne noise generation sources are very close to the footprint, the cavity resonance of the network of pipes can act as an amplifier. The sound is amplified at the pipe network cavity resonance frequency, which, in most cases, is a direct function of the network cavity geometry. Network length along with the speed of sound can be used to roughly estimate the first tire pipe resonant frequency which is given by, c λ 5 2l and f 5 λ where λ is the wavelength, l is the pipe length (usually equal to the footprint length), c is the speed of sound, and f is the pipe resonant frequency. For a standard passenger vehicle tire, one can expect to see this resonant phenomenon occurring in the frequencies between 800 and 1200 Hz. The simple equation shown here is mostly accurate for a strain pipe. Although the tire grooves act as straight pipes, tire tread pattern has other features, such as cross grooves which can impact the calculated pipe resonant frequency. The actual pipe network resonant frequencies can be experimentally measured or predicted by numerical methods/models such as FEA. An example of application of such numerical methods/models is

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Figure 6.17 Acoustic frequency response function of the tire footprint where the peaks correspond to the groove cavity resonant modes. Blue: ribbed tire; Purple: ribbed tire with additional features.

shown in Fig. 6.17 to illustrate how the pipe resonant frequencies can be impacted by additional features of the tire tread pattern. As it can be seen in Fig. 6.17 that the groove cavity resonant frequencies (there are two distinct pipe lengths), can vary from 5% to 10% of the original values by introducing the features. As the tire starts rolling, the treat impact related to the generated airborne noise increases in a proportional to the tire speed and tire pitch count. At certain tire rotating speeds, the noise frequency can match the groove cavity resonance frequency. Fig. 6.18 shows A-weighted sound pressure data collected at the trailing edge of a rolling tire. Footprint pipe resonance is observed at around 850 Hz. The undesired amplified noise can be perceived in the cabin. The readers are referred to the extensive pipe cavity resonance theory which can be found in any acoustics textbook for further details [4].

6.5.3 Tire horn effect The horn effect is the amplification effect of the air cavity shape formed between the road surface and tire profile surface envelope. This volume or

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Figure 6.18 Measured sound pressure level at footprint trailing edge of a rolling tire. Peaks correspond to the groove cavity resonance modes.

Figure 6.19 The tire cavity volume or geometry formed by the tire and road surfaces in a horn shape.

geometry of the air cavity, formed by the tire tread surface area, road surface, and tire sidewalls is similar to the shape of a horn inspiring the mechanism’s name, as shown in Fig. 6.19. Based on theory of acoustics, this horn shape volume or geometry of the air cavity will resonate when the impedance of the sound source close to the footprint matches with that of the acoustic field. The amplification amplitude is a function of the horn geometry or tire size. For the passenger vehicle sized tires the tire horn effect usually amplifies the noise in the frequencies between 1000 and 2000 Hz.

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The tire horn cavity resonance has the amplification effect with its amplification efficiency increasing with the frequency up to around 1000 Hz which matches the groove resonance frequency and the frequency of the tire tread band impact induced noise and vibrations, as illustrated in Section 6.5.2. The experimental measurement results show that the horn effect is responsible for the noise level increase of about 10 20 dB. Also, it is also shown that the footprint shape and tire width can impact the horn amplification effect.

6.6 Summary In this chapter different tire noise and vibration generation, propagation, and amplification mechanisms are studied. In the first part of the chapter (Section 6.3), different mechanisms contributing to the airborne noise generation were studied. Next (Section 6.4), we reviewed tire’s structural vibrations and transmissibility at different frequencies. Finally (Section 6.5), some mechanisms which amplify the generated structural borne noise and vibrations were discussed. Many of these mechanisms will be further studied in more details in the rest of this book. One main learning outcome of this chapter is to understand that tire is a complicated composite structure. The constructions, material, and geometries of a tire may have different impacts on the overall structural borne noise and airborne noise through these mechanisms. However, neglecting any of the tire parameter variations is naive and may lead to engineering misjudgment.

References [1] Gautam P, Azizi Y, Chandy AJ. An experimental and computational investigation of air-borne noise generation mechanisms in tires. J Vib Control 2019;25(3):529 37. [2] Brinkmeier M, Nackenhorst U, Petersen S, Von Estorff O. A finite element approach for the simulation of tire rolling noise. J Sound Vib 2008;309(2):20 39. [3] Wheeler RL, Dorfi HR, Keum BB. Vibration modes of radial tires: measurement, prediction, and categorization under different boundary and operating conditions. SAE transactions, SAE Technical Paper 2005-01-2523; 2005. p. 2823 37. [4] Fahy FJ. Foundations of engineering acoustics. Elsevier; 2000.

Further reading Campanac P, Duhamel D, Nonami K. Modeling of tire vibrations. In: Proceedings of INTER-NOISE 99, Fort Lauderdale, FL; 1999. p. 113.

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Donavan P, Lodico DM. Tire/pavement noise of test track surfaces designed to replicate California highways. In: Proceedings of INTER-NOISE 09, Ottawa, Canada; 2009. p. 3884. Donavan PR, Oswald LJ. The identification and quantification of truck tire noise sources under on-road operating conditions. In: Proceedings of INTER-NOISE 80, Miami, FL; 1980. p. 253. Dugan EL, Burroughs CB. Measurement of automobile tire tread vibration and radiated noise. In: Proceedings of Noise-Con 03, Cleveland, OH; 2003. p. 168. Eberhardt AC. Development of a transient response model for tire/pavement interaction. In: Proceedings of INTER-NOISE 84, Honolulu, HI; 1984. p. 77. Eberhardt AC. Truck tire vibration sound. In: Proceedings of INTER-NOISE 80, Miami, FL; 1980. p. 281. Fujikawa T, Koike H, Oshino Y, Tachibana H. Road texture for abating truck tire noise generation. In: Proceedings of INTER-NOISE 06, Honolulu, HI; 2006. p. 1191. Gagen MJ. Novel acoustic sources from squeezed cavities in car tires. J Acoust Soc Am 1999;106(2):794. Gautam P, Azizi Y, Chandy A. Developing a statistical model to predict tire noise at different speeds. SAE Int J Veh Dyn Stab NVH 2017;No 1:198 203. Graf RAG, Kuo C-Y, Dowling AP, Graham WR. On the horn effect of a tyre/road interface, Part I: Experiment and computation. J Sound Vib 2002;256(3):417 31. Keltie RF. Analytical model of the truck tire vibration sound mechanism. J Acoust Soc Am 1982;71(2):359. Kim S, Jeong W, Park Y, Lee S. Prediction method for tire air-pumping noise using a hybrid technique. J Acoust Soc Am June 2006;119(6):3799. Leasure WA. Tire-road interaction noise. In: Proceedings of INTER-NOISE 73, Copenhagen, Denmark; 1973. p. 421. Nilsson N, Bennerhult O, Soederqvist S. External tire/road noise: its generation and reduction. In: Proceedings of INTER-NOISE 80, Miami, FL; 1980. p. 245. Plotkin JK, Montroll ML, Fuller WW. The generation of tire noise by air pumping and carcass vibration. In: Proceedings of INTER-NOISE 80, Miami, FL; 1980. p. 273. Ruhala RJ, Burroughs CB. Separation of leading edge, trailing edge, and sidewall noise sources from rolling tires. In: Proceedings of Noise-Con 98, Ypsilanti, MI; 1998. p. 109. Yum K, Bolton JS. Sound radiation modes of a tire on a reflecting surface. In: Proceedings of Noise-Con 04, Baltimore, MD; 2004. p. 161.

CHAPTER 7

Suspension vibration and transfer path analysis Xiandong Liu and Qizhang Feng Beihang University, Beijing, P.R. China

7.1 Introduction The ride comfort of a vehicle is directly affected by noise and vibration levels inside the vehicle when the vehicle is running. Generally, the energy of noise and vibration mainly comes from the powertrain system and contact patches between tires and road surface. Several decades of development on automotive noise and vibration control technology has changed the contribution ranking of various sound sources inside vehicle. For example, in the early stage of vehicle development, the in-cabin noise mainly comes from the powertrain system. But after great advancement in refinement of engine design including combustion, structure, intake system, and exhaust muffler system, the contribution of powertrain noise to the interior noise is significantly reduced, and the contribution of the tire/ road noise is more prominent. Tire/road noise is transmitted to the interior of a vehicle in two ways: airborne noise and structure-borne noise. The specific path of structureborne noise is that, when a tire is rolling on the road, the tread and carcass vibrate due to the excitation arising from the tire/pavement interaction, then the vibration energy propagates through the wheel and the suspension system to the vehicle body, finally radiates into the sound field inside the cabin. Relation between the tire/road noise and the noise inside/outside the vehicle is shown in Fig. 7.1. The vibration frequency of tire body is mainly distributed in the range of tens to hundreds of Hertz. Therefore the structure-borne tire/road noise is the low-medium frequency noise. The interaction between the tire and road is the source of the tire/ road noise. So the interaction characteristics between the tire and road need to be better understood to correctly simulate or model the structureborne tire/road noise. The suspension system is the key component that transmits the structural vibration energy arising from the tire/pavement Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00007-6

© 2020 Elsevier Inc. All rights reserved.

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Figure 7.1 Relation between the tire/road noise and the noise inside/outside a vehicle.

interaction to the vehicle body [1] (as shown in Fig. 7.2). In the transmission process, some vibrations with certain frequencies are greatly attenuated, while some others are significantly enlarged. Therefore this chapter will introduce and discuss the road roughness, the interaction between the tire and road surface, transfer path analysis (TPA) method, the transmission characteristics of vibration and noise energy in the suspension system. References will be provided for the topic being discussed.

7.2 Excitations of suspension system from road and tire When a vehicle is running, the structure-borne noise generated by the tire/road interaction is transmitted through the suspension system, which can be felt inside the vehicle. The tire vibration excited by the road roughness rapidly decreases as the frequency increases. Ideally, the tire and wheel themselves are vibration-damping elements, not vibration sources, but in reality, the tire and wheel attenuate the excitation’s energy from the tire/road interaction and also generate new excitation sources [2,3].

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Figure 7.2 Transfer of energy in the front/rear suspension. (A) Transfer of energy in the front suspension. (B) Transfer of energy in the rear suspension.

7.2.1 Excitation from road roughness The excitation from the tire/pavement interaction is an inherent process where tar strip impact and rough road surface are sources. The tire/pavement interaction mainly consists of two aspects. On one hand, the tire is continuously compressed and released by the road surface, generating vertical excitation force. On the other hand, the tire is continuously circumferentially squeezed and released by the road surface, producing longitudinal excitation force. Intuitively, it can be deducted that the rougher the road surface is, the greater the excitation force generated on the tread is, and the greater the vibration and noise amplitudes generated inside the vehicle are. Sound pressure level (SPL) curves measured at the driver’s right ear are shown in Fig. 7.3 when a vehicle was respectively driven at a constant speed on two different roads with different roughness. It can be seen that, in the frequency range of 50
800 Hz, SPL for the rough road is obviously higher than that for the smooth road. But for the frequency band above about 1000 Hz, the influence of the road surface roughness on the interior noise is very small. The road surface has various characteristics. One of the road surface characteristics of interest is the elevation variation of pavement when a vehicle is driven on the road. Generally, the irregularity of the road surface is normally classified according to the wavelength [3] as undulation for λ $ 50 cm (λ denotes wavelength of road), road roughness for 50 cm $ λ $ 10 cm, macro-texture for 10 cm $ λ $ 0:5 mm, and microtexture for λ # 0:5 mm.

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In-vehicle noise level (dB(A)

80

60

40 Smooth road Rough road 20 50

80 125 200 315 500 800 1250 2000 3150 5000 8000

Frequency (Hz)

Figure 7.3 Noise level measured at driver’s right ear for two different roads with different roughness at a constant speed.

When a vehicle is traveling at a speed v on a road surface of a wavelength λ, the temporal frequency of vertical excitation generated by the road surface is: v f 5 5 nUv (7.1) λ where f is the temporal frequency (Hz); v denotes the vehicle velocity (m/s); n represents the spatial frequency (cycle/m). Considering the ranges of common vehicle speed and temporal frequency of interest, the road roughness is used more often. The roughness of every highway is different, but highway engineers have measured and investigated many roads and obtained their statistical characteristics described by power spectrum density (PSD) in spatial domain. On this basis, ISO/TC108/SC2N67 document suggests that PSD of road roughness is expressed approximately as:
2w n Gq ðnÞ 5 Gq ðn0 Þ (7.2) n0 where n is spatial frequency; n0 is the reference spatial frequency, and n0 5 0:1 m21 ; w is frequency index; Gq ðn0 Þ is the coefficient of the road roughness, also PSD at n 5 n0 . Assuming that the speed of a vehicle is v and frequency index w is 2, based on Eq. (7.2), the expression of the road roughness in temporal frequency domain can be obtained as: v Gq ðf Þ 5 Gq ðn0 Þn20 2 (7.3) f

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Figure 7.4 Roughness of a B-class pavement.

In experimental and simulation study of the road excited vibration and noise inside a vehicle, the excitation signal produced by the road surface in time domain or frequency domain is needed, that is, the model of road roughness is required. The model can be obtained by specific road measurement, and for convenience, it is often obtained by numerical simulation based on the specified PSD of the road roughness. There are some literature [4
6] to investigate the model of the road roughness. For example, the roughness of a B-class pavement with a length of 410 m constructed based on the PSD of the road roughness is shown in Fig. 7.4.

7.2.2 Excitation generated by tire Internal factors of a tire that can produce the excitation are mainly: tire imbalance, tire uniformity, tread pattern, and tire cavity resonance [3]. Tire imbalance results from the nonsymmetrical distribution of mass in a tire, and can generate an excitation force with the tire rotation frequency. Since the tire and wheel work together as an assembly, the socalled tire imbalance is actually the imbalance of tire/wheel assembly. And it can be classified into static imbalance and dynamic imbalance. Static imbalance (or in-plane imbalance) is confined to the wheel plane of the tire. When the tire/wheel assembly is running, a periodic force may be generated acting on the spindle in the vertical and longitudinal directions. Dynamic imbalance (or out-of-plane imbalance) arises from a nonsymmetric mass distribution along the axis of rotation. It may produce a periodic overturning moment about the longitudinal axis and a periodic aligning moment about the vertical axis. These periodic moments serving as excitations will force the tire/wheel assembly to vibrate laterally. Tire nonuniformity is caused by the material or manufacturing anomalies, and can generate varying forces and moments at the axle of tire/wheel

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assembly. The force and moment vary periodically, resulting in much more complex response waveforms than those arising from the tire imbalance. The force and moment signals may be decomposed into a series of harmonic waves with different orders by performing Fourier transform. When the rotating speed of the tire increases, the frequencies of the harmonic waves also increase. Once the frequency of a harmonic wave coincides with a resonant frequency of the wheel-tire-suspension system, the resonance takes place, and the force and moment acting on the spindle will increase dramatically. With the further increase of the tire rotating speed, instead the force and moment decrease. Tire nonuniformity is influenced by lots of factors, and the influencing mechanism is complex. Many investigations of tire nonuniformity have been reported in the literature. When a tire rolls on the road, a series of noises can be generated, such as aerodynamic noise, stick/slip noise, air pumping noise, and so on, which directly affect the ride comfort. For the excitation of suspension system, its energy mainly comes from the impact and vibration of the tread blocks. At the entrance to contact, the tread blocks impact against the road surface, and at the exit from contact, the tread blocks release from the road surface and vibrate. The frequency band of excitations from both of these actions is generally wide, so that it is easy to excite the tread and carcass resonances and generate tire noise. The excitation force generated by the tire/road interaction acts on the tread. The energy of excitation is transmitted to the rim and spoke of the wheel and further to the spindle through two paths, one is the sidewall and the other is the coupling of air cavity inside the tire with the rim. Inner air cavity of a tire is a closed space formed by the tire structure and the rim. Stiffness of the tire and rim is much larger than that of the air inside the tire. Therefore the tire and rim are generally assumed to be rigid in analysis and test. When the tire vibrates, a sound field is generated in the annular air cavity. Tire cavity resonance frequency can be calculated in approximation as [7]: c fi 5 i 3 (7.4) l where i is the order of the cavity resonance; c represents the speed of sound in the acoustic fluid medium; and l is the circumference of the tire at the centroid of the cross-section. It can be seen from Eq. (7.4) that tire cavity resonance frequency is directly related to the size of a tire. Considering the range of the tire’s

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dimension, it can be concluded that the first-order frequency of tire cavity resonance is about 200
250 Hz. Fig. 7.5 shows the acceleration spectrum measured in vertical direction at the spindle arising from the vibration of a loaded tire [2]. In the spectrum, A-peak corresponds to the first-order vibration mode of tire tread. C-peak corresponds to the high-order vibration mode of tire tread. B-peak is not directly caused by the vibration of tire structure, but related with the tire cavity resonance, and its frequency is about 240 Hz. The modal shape of tire cavity resonance is shown in Fig. 7.6. SPL measured at driver’s right ear in the accelerated test of an electric vehicle is shown in Fig. 7.7. First-order cavity resonance frequency of the tire used in the vehicle can be identified as about 225 Hz. It can be seen that the noise energy significantly rises near this frequency. The energy of tire cavity resonance is transmitted to the spindle through the wheel and excites the suspension system, and further causes the vehicle body vibration and interior noise. In recent years, the influence of the tire cavity resonance on the interior noise of a vehicle has been highlighted in the case of continuous reduction of the influence of the powertrain system on the interior noise. Many literature have conducted the in-depth research on the mechanism and suppression methods of the tire cavity resonance, such as the literature [8
11] and so on.

Figure 7.5 Acceleration spectrum measured in vertical direction at the spindle.

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Figure 7.6 Modal shape of a loaded tire cavity resonance.

Figure 7.7 Waterfall spectrum of SPL at driver’s right ear in the acceleration test of an electric vehicle.

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The excitation applied in the suspension system comes from the interaction of the tire and road. When the tire is rolling on road, the excitation’s energy generated by the tire/road interaction is transmitted to the suspension system through the tire, wheel, and spindle. The suspension system has multiple connections with the vehicle body and the subframe, and there are three directions of energy transfer at each connection. So the structure-borne energy arising from the interaction between tire and road propagates to the cabin of vehicle in multiple paths. In order to effectively suppress the transfer of the vibration energy, it is necessary to analyze and rank the contributions of transfer paths to find the paths that contribute majorly or marginally. To this end, TPA method is introduced and used in the following sections.

7.3 Theoretical basis of transfer path analysis method Vehicle is a complex system composed of multiple subsystems connected to each other. The coupled vibration between the subsystems not only increases the vibration and noise level, but also leads to more complicated analysis of NVH problem. The energy of vibration and noise produced by the excitation sources passes through various transfer paths, ultimately causes the tactile, visual, and auditory feelings of the driver and passengers. After decades of development, different TPA methods have been derived, including traditional TPA, fast TPA, multireference TPA, operational transfer path analysis (OTPA), and Operational-X TPA (OPAX). Among these TPA methods, traditional TPA and OTPA are widely used. So these two methods are introduced below.

7.3.1 Traditional transfer path analysis method TPA methods can be used to identify and rank the contributions of various transfer paths of vibration and noise. In traditional TPA method (for simplicity, called as TPA method in the following), the system is assumed to be linear and time-invariant. So the output of the system follows the superposition principle, and the system model is shown in Fig. 7.8. For simplicity, the independent variable f (frequency) is not written in the following equations, and all variables are expressed in frequency

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Figure 7.8 Symbolic block diagram of TPA model.

domain if not specified. In the frequency domain, the output of a linear system can be described as Eq. (7.5) 2 3 H1 6 H2 7 7 (7.5) Y 5 X1 H1 1 X2 H2 1 ? 1 Xn Hn 5 ½X1 X2 ?Xn 6 4 ^ 5 Hn where Y represents the system output signal (vibrational acceleration, sound pressure, etc.); Xi indicates the ith input signal (force, volume velocity, etc.) of the system; Hi denotes the frequency response function (FRF) of the system from the ith input to output. When the system has multiple outputs, Eq. (7.5) can be extended to Eq. (7.6): 3 2 H1;1 H1;2 ? H1;m 6 H2;1 H2;2 ? H2;m 7 7 ½Y1 Y2 ?Ym  5 ½X1 X2 ?Xn 6 (7.6) 4 ^ ^ & ^ 5 Hn;1 Hn;2 ? Hn;m where Yj denotes the jth output signal; Xi indicates the ith input signal; Hij represents the FRF of the system from the ith input to jth output. It can be seen from Eq. (7.6) that the process of TPA involves three key parts: acquisition of the FRF, identification of the structural or acoustic load, and analysis of the contributions. 7.3.1.1 Frequency response function FRFs of a system can be measured by use of impulse hammer or shaker (s) if the structure-borne vibration is considered, or by use of

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loudspeaker(s) or volume velocity source(s) if the airborne noise is studied. It should be noted that in order to reduce the influence of crosstalk between inputs on the measured FRFs, the test needs to be performed under the condition of individual inputs where the system is disassembled. FRF is obtained by: Hi;j 5

Yj Xi

(7.7)

where Xi indicates the input of the hammer test or shaker(s) (in frequency domain) and Yj represents the output (in frequency domain). Ideally, there is no interference signal, and FRF can be directly obtained by Eq. (7.7). However, in practice, there are various noise signal interferences. So FRF is usually estimated by Eq. (7.8) to attenuate the effect of interference signals Hi;j 5

Gyx Gxx

(7.8)

where Gxx indicates auto PSD of the excitation signal Xi , whereas Gyx represents cross PSD between the response signal Yj and the excitation signal Xi .

7.3.1.2 Identification of structural load Identification of structural load refers to determination of the excitation force acting on passive side of the excitation source. The accurate structural load is related to the analysis accuracy of the contribution of each transfer path and the subsequent optimization measures. Load identification usually requires a combination of experiment and theory analysis. The direct method, dynamic stiffness method, and matrix inversion method are often used to identify the structural loads. The direct method is to directly measure the structural working load by the force sensor installed at the passive side of excitation source, which is easy to understand, and the measurement result is intuitive and reliable. However, there are some limitations in practical application since the certain space and the flat support surface are required for installing the force sensor. When there is a damping element between the active side and passive side of the excitation source, the structural load can be described by product of the vibrational displacement difference between the active side and

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passive side of the damping element and the dynamic stiffness. The calculation equation is as follows: aai 2 api Fi 5 Ki U (7.9) 2 ω2 where Fi is the load at the ith degree of freedom of the passive side of the damping element; Ki is the dynamic stiffness corresponding to the ith degree of freedom; aai and api are the vibrational accelerations along the ith degree of freedom at the active side and passive side of the damping element, respectively; ω is the angular frequency. Since the principle of dynamic stiffness method is simple, the method is often used for load identification of the common elastic damping element in a vehicle. It should be noted that, to use this method, the dynamic stiffness needs to be measured in advance. If a damping element has a very large dynamic stiffness, both vibrational accelerations at the active and passive sides are small, which easily produces a large measurement error. The matrix inversion method should then be used. The matrix inversion method is described as follows. First, the reference points are selected, and FRFs from the input points to the reference points are measured and expressed as 3 2 ref ref ref H1;1 H1;2 ? H1;l 6 ref ref ref 7 7 6 Href 5 6 H2;1 H2;2 ? H2;l 7 (7.10) 4 ^ ^ & ^ 5 ref ref ref Hn;1 Hn;2 ? Hn;l ref

where l is the number of outputs at the reference points; Hi;k is FRF ref from the input Xi to the output Yk at the reference point. Then, in test of a vehicle, the real outputs at the reference points are ref ref ref measured, and denoted as Y1 ; Y2 ; . . .; Yl . We have 3 2 ref ref ref H1;1 H1;2 ? H1;l 6 ref h i ref ref 7 7 6 ref ref ref (7.11) Y1 Y2 ?Yl 5 ½X1 X2 ?Xn 6 H2;1 H2;2 ? H2;l 7 4 ^ ^ & ^ 5 ref ref ref Hn;1 Hn;2 ? Hn;l In order to ensure the calculation accuracy, the number of reference outputs is at least 2 times greater than the number of inputs. That is, l $ 2n in Eq. (7.11) is required.

Suspension vibration and transfer path analysis

Finally, the excitation forces of the system can 2 ref ref H1;1 H1;2 h i6 ref ref 6 ½X1 X2 ?Xn  5 Y1ref Y2ref ?Ylref 6 H2;1 H2;2 4 ^ ^ ref ref Hn;1 Hn;2

be obtained as 3 ref 1 ? H1;l ref 7 ? H2;l 7 7 & ^ 5 ref ? Hn;l

127

(7.12)

It should be noted that the second term at right hand side of Eq. (7.12) is a Moore
Penrose (M-P) generalized inverse matrix since l $ 2n, and this matrix can be uniquely determined by using the singular value decomposition (SVD) method. 7.3.1.3 Analysis of transfer path Substituting Eq. (7.12) into Eq. (7.6), the determined as 2 H1;1 6 H2;1 ½Y1 Y2 ?Ym 1 3 m 5 ½X1 X2 ?Xn 1 3 n 6 4 ^ Hn;1

outputs of the system can be H1;2 H2;2 ^ Hn;2

3 ? H1;m ? H2;m 7 7 (7.13) & ^ 5 ? Hn;m n;m

Then, Eq. (7.13) can be simplified as fY g 5 fXgUH

(7.14)

From Eq. (7.13), we may see that the contribution of the ith input to the jth output is: transfer

Yi;j

5 Xi Hi;j

(7.15)

Taking the contributions of all paths into consideration, we have Yj 5

n X

Xi Hi;j

(7.16)

i51

Eqs. (7.15) and (7.16) in the frequency domain are expressed as a quantity and a polynomial in complex number field, respectively, which indicate the magnitude and direction of the contribution of each transfer path to the total response. For a certain frequency, the phase diagram shown in Fig. 7.9 [2] can be obtained based on Eqs. (7.15) and (7.16) where Ai is the magnitude of the complex term XiHi,j (i 5 1,2,3,. . .,n). We may see

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Figure 7.9 Phase diagram of the contributions. (A) Contribution of individual transfer path. (B) Sum of the contributions.

that the reinforcement or weakening effect to the total response may exist due to different phases of these contributions. Therefore to arbitrarily reduce the contribution of a certain transfer path may increase the total response, rather than reduce it. Obviously, TPA provides a way to rank the contribution of each transfer path to the total response for various frequencies, and a guideline for effectively reducing the total response. In practical engineering application, the analysis steps in TPA method are generally: 1. Obtain FRFs of the system: the test is performed by use of impulse hammer or shaker(s) if the structure-borne vibration is considered, or by use of loudspeaker(s) or volume velocity source(s) if the airborne noise is studied. 2. Identify the structural loads: Href is obtained through test, and Yref is measured according to the real operational condition. On the basis, the structural loads or the excitations are identified according to Eq. (7.12). Of course, the direct method or the dynamic stiffness method can also be used to obtain the excitations. 3. Analyze and rank the contributions of transfer paths: the contribution of each transfer path to the total response is calculated according to Eqs. (7.15) and (7.16), and based on the calculation results, the contributions are analyzed and ranked. The above TPA method is introduced for the structure-borne vibration TPA, however, it can also be applied for the airborne noise TPA in

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the similar way where the excitation force is replaced by sound pressure or volume velocity and the acceleration response is replaced by sound pressure or particle velocity. In general, although traditional TPA method is easy to implement, the measured system needs to be disassembled to obtain the FRFs in practice. This not only takes more time, but also changes the boundary conditions of the structure. So the improvement on this method is necessary [12,13].

7.3.2 Operational transfer path analysis In order to overcome the shortcomings of TPA method, an improved TPA method referred to as OTPA method [14
16] was proposed. In OTPA method, the input and output signals in Eq. (7.6) are measured under the actual operational condition without disassembling the system. So the FRF H in Eq. (7.6) is replaced by operational transfer function T , and we have 3 2 T1;1 T1;2 ? T1;m 6 T2;1 T2;2 ? T2;1 7 7 ½Y1 Y2 ?Ym  5 ½X1 X2 ?Xn 6 (7.17) 4 ^ ^ & ^ 5 Tn;1 Tn;2 ? Tn;m where Tij represents the transfer function from ith input to jth output. For a linear time-invariant system, the transfer function T represents its inherent transfer characteristic, and is also a core of OTPA method. In OTPA method, the transfer function T is solved by using matrix inversion method based on a plurality of sets of input and output data measured under different operational conditions. If the test is performed under q different operational conditions, Eq. (7.17) can be written as 3 2 1 Y1 1 Y2 ? 1 Ym 6 2Y 2 Y2 ? 2 Ym 7 7 6 1 7 6 4 ^ ^ & ^ 5 q

Y1 2

q 1

Y2

X1

6 2X 6 1 56 4 ^ q

X1

? q Ym 32 1 T1;1 X2 ? 1 Xn 7 6 2 2 X2 ? Xn 76 T2;1 76 ^ & ^ 54 ^ q

X2

?

q

Xn

Tn;1

T1;2

?

T2;2

?

^ Tn;2

& ?

T1;m

3

T2;l 7 7 7 ^ 5

Tn;m

(7.18)

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where k Xi is the ith input signal obtained from the kth test; k Yj is the jth output signal obtained from the kth test; k 5 1; 2; . . .; q, and q $ n. By comparing Eq. (7.6) with Eq. (7.18), we may see that the expressions of OTPA and TPA are almost identical. But in OTPA method, the transfer function describes transfer characteristic from the vibration responses at the input points to the responses at the output points, whereas in TPA method, the FRF describes the frequency response characteristic from the forces acting on the input points to the responses at the output points. Therefore the peaks or troughs of the transfer function in OTPA method, do not necessarily refer to resonances or antiresonances of the system. For simplicity, Eq. (7.18) can be rewritten as the following matrix form: Y 5 XT

(7.19)

The transfer function in engineering application is usually estimated by Eq. (7.20):  21  H  T 5 XH X X Y 5 G21 (7.20) xx Gxy Where the superscript “H” denotes the conjugate transpose of a matrix; Gxx indicates the auto power spectrum matrix of the input signals, whereas Gxy represents the cross power spectrum matrix between the input signals and the output signals. Both OTPA and multiple input multiple output (MIMO) analysis allow almost fully coherent input signals in the transfer function (TF) matrix estimation from a theoretical point of view. However, in practice the measurement errors will become more and more influential on the TF estimation with the increasing coherence [16]. Therefore the coherence of input signals should be kept below 30%
40% in OTPA or MIMO applications. Otherwise the SVD technique is required for the OTPA method. Matrix X coming from the input signals can be expressed based on SVD theory as below: X 5 UΛVH

(7.21)

where U is a q 3 q unitary matrix, and VH denotes the conjugate transpose of V (a n 3 n unitary matrix); Λ is a q 3 n matrix with nonnegative numbers on the diagonal and zeros off the diagonal, and can be expressed

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as follows

  Λ 5 diag λ1

λ2

...

 λq :0

131

(7.22)

where λ1 ; λ2 . . .λq are the singular values of X, and arranged in nonincreasing fashion, that is, λ1 $ λ2 $ ? $ λq . Usually the smaller singular values of X are mainly caused by the measurement noise and other external disturbances. They are therefore unwanted and should be rejected. Assuming that the singular values such as λp11 $ ? $ λq . 0 are rejected, these values just need to be set as zeros (i.e., λp11 5? 5λq 5 0). Then the singular value matrix Λ can be ~ 5 diag λ1 λ2 . . . λp :0 , and a new input matrix rewritten as Λ can be given by ~ H X0 5 UΛV

(7.23)

The Moore
Penrose generalized inverse matrix (X0 )1 of X0 can be written as  1 H ~ U ðX0 Þ1 5 V Λ (7.24)  1 ~ In Eq. (7.24), Λ is the Moore
Penrose generalized inverse matrix ~ of Λ, and can be obtained as follows 3 2 1 0 ? 0 7 6 λ1 7 6 7 6 1

21  7 6 0  1 . . . 0 0 Λ 7 6 ~ 5 p λ2 (7.25) Λ and Λ21 7 p 56 7 6 0 0 7 6 ^ ^ & ^ 6 17 5 4 0 0 ? λp According to Eq. (7.19), T can be expressed as  1 H 1 ~ U Y T 5 ðX0 Þ Y 5 V Λ

(7.26)

Combining Eq. (7.26) or Eq. (7.20) with Eq. (7.17), the contribution of the input signal Xi to the output signal Yj through the transfer function Ti;j under operational case can be expressed by: transfer

Yi;j

5 Xi Ti;j

(7.27)

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Compared with TPA method, the most prominent advantage of OTPA method is that it can reduce the time cost of modeling since the test of FRFs and disassembly of the system are unnecessary. But OTPA method also has certain limitations. First, OTPA is a TPA method based on transfer function which is different from the FRF in TPA. So OTPA cannot accurately describe the natural modal characteristics of a mechanical system, including modal frequency and modal shape, and so on. Further, if there exists a transfer path where the modal response is not excited, this transfer path will be ignored in OPTA method. Second, the accuracy of OTPA is easily affected by the measuring errors and external interferences, making the analysis accuracy of OTPA lower than that of TPA. In order to overcome above defects, OPAX (Operational-X TPA) method was proposed and studied [17,18]. OPAX method evolves from TPA method, and its modeling accuracy is close to that of TPA method, while its modeling efficiency is almost equivalent to that of OTPA method. For more information about OPAX, readers may consult the corresponding literature.

7.4 Transfer path analysis of suspension vibration The developing trend in automotive industry is toward lightweight design with more powerful engine. In this context, NVH becomes one of crucial performances. The vibration accepted by the passengers inside a vehicle is generally the superposition of multiple vibrations transmitted to the seat in different transfer paths. In running process of a vehicle, the excitation arising from the road roughness is transferred to the suspension through the tire and wheel. Then, through the suspension, the vibration is transmitted to the vehicle body, further to the floor and seat, finally to the human body where the vibration is affected by the characteristics of the suspension and transfer paths. Obviously, the suspension plays important roles in guiding and controlling the relative movement between wheel and vehicle body, mitigating the impact transferred from the road to vehicle body, and damping the vibration of the system, thereby directly affecting the vibration performance of the vehicle. TPA is a widely used methodology to investigate NVH issues. By using this method combining the vehicle test with analysis, the contributions of the transfer paths to the vibration at certain location can be identified and sorted quickly and effectively. This provides a basis for automotive vibration control and improvement of ride comfort.

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The theory of TPA method is not complicated, but it is usually tedious to directly deal with specific engineering problems based on this theory. For this reason, some engineering software is often used to solve the problems. In the process of establishing TPA model, determining FRFs of the system is crucial work with a great cost. The methods for determining FRFs mainly include the method based on test, the method based on simulation calculation, and the method combining the test and simulation. In this section, a passenger car is taken as an example to introduce TPA method identifying the highest ranked contributing path of the suspension. In the road test of the car, the vertical vibration of the floor under driver’s seat is found to be prominent. In fact, the energy of vertical vibration is not only from the road roughness, but also from the powertrain and the transmission system. Only the contribution of road roughness through suspension to the vertical vibration of a certain position (target point) of the floor is discussed here [19]. In test, the car coasts down to eliminate the interference of engine vibration. The car has the double wishbone independent front and E-shaped multilink independent rear suspension systems, respectively, and there are 27 transfer paths between the front/rear suspension systems and car body unilaterally. During the road test, the vertical accelerations at connections between the suspensions and car body and at the floor under driver’s seat are measured. FRFs of transfer paths from the suspensions to car body are measured by use of the impulse hammer test in laboratory. In the end, the transfer paths are analyzed.

7.4.1 Frequency response function of suspension and car body system Acceleration sensors are installed at each connection point between the front/rear suspensions and car body, and the front and rear wheel spindles are respectively tapped with an impulse hammer. By measuring the excitation force signal of the impulse hammer and the acceleration signal at each measuring point, FRF of the suspension can be obtained and expressed as follows: ai;body Hi;susp 5 (7.28) Fwheel where ai;body is the acceleration at the ith connection point between the suspension and car body, and Fwheel is the impact force acting on the

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wheel spindle. It should be noted that all variables in this section are expressed in frequency domain. The acceleration impedance at a connection point between the suspension and car body is equal to the ratio of the excitation force transmitted by the suspension to the acceleration generated by the force. To obtain the impedance of car body, the hammer impact test method can be applied. Before the test, the suspension system is disassembled from the car, and acceleration sensors are installed at connection points in the side of car body. Tap of the impulse hammer is applied near the acceleration sensor, and the excitation and acceleration are recorded to obtain following acceleration impedance of car body: Zi 5

Fi;body ai;body

(7.29)

where Fi;body is the excitation force acting on the connection point at the car body side in the frequency domain. When the connection point is excited, the excitation energy is transmitted to car body, thereby causing vibration at the driver’s seat floor. To obtain the transfer functions of car body, the suspension systems need to be disassembled. By using the hammer test method, the excitation forces (Fi;body ) acting on the connection points at the car body side and the accelerations (aseat ) at the driver’s seat floor for different excitations are acquired. Then, FRF can be obtained as follows: aseat Hi;body 5 (7.30) Fi;body Through the above test, the FRF Hi of transfer path related to the ith connection point from the wheel spindle to the seat floor can be obtained as: Hi 5 Hi;susp UZi UHi;body

(7.31)

In actual test, auto PSDs and cross PSDs of the signals are used to calculate the FRFs and the impedances to reduce the influence of the interference signals.

7.4.2 Identification of load between suspension and car body The loads on path points between the suspensions and car body are generally obtained indirectly by using the matrix inversion method. After selecting appropriate reference points, the accelerations at the reference

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135

points are measured in various operational cases. Next, based on the FRFs between the excitation points and reference points obtained by the test, the loads on path points between the suspensions and car body are determined by using the matrix inversion method. By this way, the wheel-tospindle load can also be obtained. In practical application, the suspension systems need to be disassembled from the car body, and the hammer test method is usually used to obtain the FRFs between the excitation points and reference points.

7.4.3 Transfer path analysis of suspension vibration Taking a passenger car running at a speed of 60 km/h as an example, the contribution of each transfer path to the vertical vibration of the floor under driver’s seat is analyzed in this section. First, the acceleration of the vertical vibration at certain position of the floor is measured, and its frequency spectrum is obtained by using fast Fourier transform (FFT). In the frequency spectrum, there exist four main frequency components (shown in Table 7.1). TPA is performed for one component with frequency of 8.6 Hz as an example. Actually, TPA process for other components is similar. Performing the calculation and analysis of transfer path according to Section 7.3.1, the contribution of each transfer path to the vertical vibration of floor under driver’s seat is obtained. For simplicity, only eight transfer paths with greater contribution are listed and ranked (Table 7.2). With the help of transfer functions calculated by using TPA, a phase diagram (Fig. 7.10) is made for the identified specific frequency (8.6 Hz). The phase diagram shows the individual contribution with phase angle of these eight paths. From Fig. 7.10, we may see that, the transfer path with largest contribution is Y-direction of rear end of lower control arm of front suspension (A), and the contribution is nearly out of phase to those of X-direction of trailing arm of rear suspension (C) and Z-direction of front end of lower control arm of front suspension (H). Therefore the Table 7.1 Frequencies and amplitudes of peaks of vertical vibration at the point of floor. Number of peak

1

2

3

4

Frequency (Hz) Amplitude (9.8 3 1023 m/s2)

1.47 3.53

8.61 2.79

12.61 1.38

17.16 0.90

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Table 7.2 Paths with greater contribution identified by using TPA method. Sequence number

Name

A

Y-direction of rear end of lower control arm of front suspension Z-direction of lower control arm of rear suspension X-direction of trailing arm of rear suspension Y-direction of trailing arm of rear suspension Z-direction of spring connection of rear suspension Z-direction of front end of upper control arm of front suspension Z-direction of damper connection of rear suspension Z-direction of front end of lower control arm of front suspension

B C D E F G H

Figure 7.10 Phase diagram of the contributions of eight paths to vibration at the point of the floor.

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Figure 7.11 Color map of the transfer path contribution.

vibrations from these two paths (C and H) may weaken the contribution of transfer path A. This indicates that when controlling vibration of a system, both magnitude and phase of contribution of each transfer path need to be considered. Obviously, if the vibrations through paths C and H are attenuated, the contribution of transfer path A will grow and the vibration at the point of the floor will also increase. Further, the contributions of all transfer paths and their ranking for each frequency of interest can be obtained by using the TPA method. To clarify the characteristics of each transfer path for different frequencies, the color map similar to Fig. 7.11 can be used. In this figure, horizontal axis represents frequency, and vertical axis describes transfer path, while color represents the magnitude of contribution. Meanwhile, the contributions and rankings are also often various for different running speeds. Therefore it is necessary to comprehensively consider the contributions and rankings for various running speeds and different frequencies in order to accurately grasp the characteristics of each transfer path and effectively control the structural vibration.

7.5 Transfer path analysis of structure-borne tire/road noise The structural and mechanical properties of automotive tire are very complex. When rolling on road, the tire may generate noise and vibration which may be transmitted to the cabin and disturb the ride comfort. These problems are typically referred to as “ride disturbances” [3]. The

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ride disturbances may be excited by the contact between the road and tread or from mechanisms internal to the tire. When the ride disturbances propagate through the air, airborne noise is produced. Airborne noise can travel away from tire and arrive at nearby observers, can also enter the vehicle through openings in the body or by acoustically coupling with the vehicle panels and through the re-radiated effect of the panel vibration inside the vehicle. The ride disturbances can also propagate through the tire, the suspension and other components of the vehicle. The tactile or acoustic signals are produced when the ride disturbances arrive inside the vehicle. The noise inside the vehicle arising from the ride disturbances and transferring through these structures is called as the structure-borne noise of a tire. The emphasis of this section is on the TPA of the structure-borne noise of a tire.

7.5.1 Transfer function of structure-borne noise When testing the transfer function (TF) of structure-borne noise, in addition to the use of the hammer test method, the principle of the reciprocity [20,21] is also applied. For the sake of descriptive integrality, the principle of the reciprocity is introduced for both airborne noise and structure-borne noise here. Airborne noise transfer function may be obtained by using acoustic reciprocity. In Fig. 7.12A, when a volume velocity source Q1 at position 1 works, a sound pressure p2 at position 2 is generated. In the reciprocal experiment (Fig. 7.12B), if a volume velocity Q2 at position 2 works, the sound pressure p1 at position 1 is produced. The reciprocity still remains even though the scattering structures appear in the sound field. At each

Figure 7.12 Acoustic reciprocity in a car body. (A) Direct experiment. (B) Reciprocal experiment.

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Figure 7.13 Vibro-acoustic reciprocity in a car body. (A) Direct experiment. (B) Reciprocal experiment.

position, both source and receiver must have the same directivity. Then, the expression of the acoustic reciprocity may be as follows: p2 p1 (7.32) 5 50 Q Q 50 2 Q1 Q2 1 Furthermore, if the structure-borne noise is investigated and the vibro-acoustic transfer function is required, the vibro-acoustic reciprocity based on fluid
structure interaction can also be used. In Fig. 7.13A, when a point force F1 at position 1 is applied, the structural vibration is excited and the sound pressure p2 at position 2 is generated. For the reciprocal experiment, if a volume source Q2 at position 2 works, the structural vibration is excited and the surface velocity ν 1 on the structure is produced (Fig. 7.13B). Then, the vibro-acoustic reciprocity may be expressed as p2 v1 (7.33) Q2 50 5 F 50 F1 Q2 1

7.5.2 Identification of load on path point and principal component analysis TPA method applies to the situations of both single and multiple excitation sources. TPA of a system with single excitation source is relatively simple, and the process described in Section 7.4.2 can be used to identify load on the path point (the connection point between the suspension and car body) and conduct the corresponding analysis. But the case of tire/ road noise is more complicated since the noise is transmitted to the cabin

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as the interior noise from the multiple independent and mutually uncorrelated excitation inputs when the wheels are rolling on the road. The vibrational energy transmitted from the assemblies of tires and wheels to the car body is mainly determined by dynamic properties of the suspensions and car body. The transfer paths of energy include the shock absorbers and springs, control arms and bushes, stabilizer bars, the tie rods of suspensions, subframe and/or twist beam connection points, and so on [22]. To effectively attenuate the transfer of energy in these paths, the contributions of these transfer paths need to be sorted by analysis. For TPA, the operational vibrations are required. As we know, the excitations from the assemblies of tires and wheels are several mutually incoherent inputs, and act simultaneously on the suspensions. These multiple uncorrelated inputs result in various phase relations which are varying continuously, such as between accelerations, between sound pressures. As a consequence, the single reference correlation studies between wheel center accelerations and interior sound pressures show a globally noncoherent behavior, which means no straightforward vibro-acoustical relation can be obtained. Therefore it is necessary to decompose the operating signals into sets of mathematically independent ones, so-called “virtual” phenomena by using principal component analysis (PCA) [22,23]. The combination of PCA and TPA has also been implemented in commercial software [24]. This methodology can be summarized in Fig. 7.14.

7.5.3 Analysis of interior noise from tire/road interaction based on transfer path analysis Taking a passenger car in development process as an example, TPA method is used to identify the transfer paths from the excitation generated by the interaction between tire and road to the interior noise generated inside the car. In this car, the MacPherson independent front suspension is used, and the rear one is the multilink independent suspension. There are totally 14 connection points which connect these suspensions with the car body and subframe. Considering that three directions (x, y, and z) at each connection point can transfer vibration, there are a total of 42 transfer paths [25]. The excitation from the interaction between tire and road is transferred to the spindle through the assembly of tire and wheel, then transmitted to the car body by the suspension system, finally produces noise inside the car body. The transfer path from the excitation to interior noise is shown in Fig. 7.15.

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Figure 7.14 Analysis process of PCA-TPA.

Figure 7.15 Diagram of tire/road noise transfer path.

7.5.3.1 Transfer path analysis of structure-borne tire/road noise based on test The test includes two parts: one part is performed when the car is running on specified road, including measuring the vibrational accelerations (on the body side) at each connection point between the suspensions and car body or subframe, and measuring the sound pressures at interior measuring points (target points and reference points); the other part is performed in a semianechoic chamber to measure the vibro-acoustic transfer functions from each connection point (path point) of the suspensions to the

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interior measuring points, and the FRFs from each path point to the reference points of structure. In the road test, the microphones need to be fixed near driver’s right ear and rear right passenger’s left ear, and the acceleration sensors need to be installed at 14 connection points between the suspensions and car body or subframe as well as at the wheel spindles and the active ends (close to the spindle) of the springs and shock absorbers. In order to reduce the effects of the engine’s vibration and noise, engine stalling (for manual transmission car) or tip-out (for automatic transmission car) is required for a car taxiing at a speed of 60 km/h on the specified road. When the test is performed in a semianechoic chamber, the suspensions need to be disassembled, but the installation of acceleration sensors and microphones on the car body remains unchanged. By using the hammer test method, the vibro-acoustic transfer functions from each path point to the target points are measured, and the FRFs from each path point to the reference points of the structure can also be obtained to identify the excitation force at the path point. By using the engineering software based on the TPA method, the excitation forces are calculated and the contribution of each transfer path to the noise level at the target point (near the driver’s right ear) is obtained. A color map of the contributions of transfer paths is shown in Fig. 7.16. It indicates that in low-frequency range, there are significant peaks near f1 and f2. By analyzing the contribution of each transfer path, it is concluded that the joint points connecting the left upper rod and right upper rod of rear suspensions with the car body make the greater contributions to the noise at target point.

Figure 7.16 Color map depicting contributions of transfer paths.

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7.5.3.2 Control of structure-borne tire/road noise based on simulation To reduce the contributions of these two transfer paths related to the joint points connecting left/right upper rods of the rear suspensions with the car body, a direct way is to decrease the excitation force at these two joint points. First, the vibration isolation ratio of these two rods in frequency range of interest is analyzed. By test, the root-mean-square values of vibrations in the three directions at the active and passive ends of the rods are obtained. The analysis results indicate that these two rods cannot amplify the vibration in specified frequency range. So the suspect that the greater contribution of the joint point may arise from poor isolation ratio of the rod is excluded. Then, to adjust the bushing’s stiffness and to raise the body panel dynamic stiffness at the installation positions can be conducted to reduce the excitation force at the joint point. In this section, the method to adjust the bushing’s stiffness is discussed. In fact, the bushing’s stiffness is not only related to the transmission of vibration energy, but directly affects the handling stability of a car. Therefore the bushing’s stiffness needs to be optimized by establishing a vibro-acoustic simulation model of the car body to satisfy various performances. Based on the trimmed body (TB) model, an acoustic cavity model is established (shown in Fig. 7.17). On this basis, the vibro-acoustic simulation model can be established. In order to validate the model, the excitation forces at path points identified by test are input into the CAE model, and the sound pressure at target point obtained by simulation is compared with the measured value. After validating the vibro-acoustic simulation

Figure 7.17 Acoustic cavity model of a car body.

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model, a complete model including the suspensions and the vibroacoustic model of car body is established with the excitations acting on the spindles obtained by the test. Based on the complete model, the bushings’ stiffness can be optimized to effectively suppress the vibration energy transmission through the joint points. At last, the handling stability of car with the adjusted bushings is validated. For the passenger car discussed in this section, the simulation results indicate that to reduce the bushings’ stiffness at aforementioned two joint points by about 20% can effectively decrease the contributions to noise level near driver’s right ear, and satisfy the handling stability. Based on the optimization results, the bushings’ stiffness is adjusted, and the road test is carried out again. Compared with the original test results, it can be obtained that the sound pressures near f1 and f2 are significantly reduced by about 5 dB. The goal of attenuating the noise near the driver’s right ear is achieved.

7.6 Summary When a tire is rolling on road, the excitations acting on the tire are produced, including the external excitations (vertical and longitudinal excitations) directly arising from the interaction between tire and road, and the internal excitations (tire imbalance, tire nonuniformity, tire cavity resonance, and so on). The energy of these excitations transmits to the cabin of vehicle through two ways: airborne path and structure-borne one. In this chapter, the structure-borne path is concentrated. In this path, the energy of excitations propagates through the wheel, spindle, suspension system to the vehicle body, then stimulates the sound field and generates the interior noise. In the structure-borne path, the suspension system is key component. The suspension system has multiple connections with the vehicle body and the subframe, and there are three directions of energy transfer at each connection. The common method to analyze the transmission characteristics of suspension system is TPA, mainly including traditional TPA, OTPA, and OPAX. Among these TPA methods, traditional TPA and OTPA are widely used. The process of traditional TPA consists of three key parts: acquisition of FRF, identification of structural load, and contribution analysis. FRFs of a system are measured by use of impulse hammer or shaker(s) tests if structural vibration is considered, or by use of loudspeaker(s) or

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volume velocity source(s) for the airborne noise. Load identification usually requires the combination of test and theory. Through solving the established TPA model, the contribution of each transfer path to the total response can be calculated, and based on the calculation results, the contributions can be analyzed and ranked. OTPA method is similar to traditional TPA method in analysis process. Compared with traditional TPA method, the most prominent advantage of OTPA method is that it can reduce the time cost of modeling since the test of FRFs and disassembly of the system are unnecessary. But OTPA method also has certain limitations. In this chapter, first, the excitation sources of suspension system are introduced and analyzed. Then, the basic principle and operational process of traditional TPA and OTPA are described and discussed. A passenger car is taken as an example to introduce the application of TPA in ranking the contributions of transfer paths of suspension vibration. Finally, another example is introduced to identify the transfer paths of the structure-borne noise of a tire and analyze the control method. The airborne noise TPA can be conducted in the similar way as the structure-borne vibration TPA.

Nomenclatures f temporal frequency (Hz) n spatial frequency (cycle/m) v vehicle velocity; surface velocity G power spectrum density c speed of sound l circumference of the tire at the centroid of the cross-section H frequency response function Y output signal of a system X input signal of a system ω angular frequency K dynamic stiffness T transfer function U unitary matrix V unitary matrix λ singular value a acceleration F force Z mechanical impedance P sound pressure Q volume velocity

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References [1] Lu CH. Test analysis and simulation of vehicle structure-borne road noise. In: 16th international conference on automotive NVH control technology of SAE-China, Changzhou, China; 2019. p. 25
32. [2] Pang J, Chen G, He H. Automotive noise and vibration: principle and application. Beijing: Beijing Institute of Technology Press; 2006. [3] Gent AN, Walter JD. The pneumatic tires. National Highway Traffic Safety Administration; 2005. [4] Liu XD, Wang HX, Shan YC, He T. Construction of road roughness in left and right wheel paths based on PSD and coherence function. Mech Syst Signal Process 2015;60-61:668
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79. [8] Yi JJ, Liu XD, Shan YC, Dong H. Characteristics of sound pressure in the tire cavity arising from acoustic cavity resonance excited by road roughness. Appl Acoust 2019;146:218
26. [9] Mohamed Z, Wang X. A deterministic and statistical energy analysis of tyre cavity resonance noise. Mech Syst Signal Process 2016;70-71:947
57. [10] Tanaka Y, Horikawa S, Murata S. An evaluation method for measuring SPL and mode shape of tire cavity resonance by using multi-microphone system. Appl Acoust 2016;105:171
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72. [13] Sievi A, Martner O, Lutzenberger S. Noise reduction of trains using the operational transfer path analysis-demonstration of the method and evaluation by case study. Tokyo, Japan: Noise and Vibration Mitigation for Rail Transportation Systems; 2012. p. 453
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[21] Fahy FJ. The vibro-acoustic reciprocity principle and applications to noise control. Acta Acust United Acust 1995;81(6):544
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23.

CHAPTER 8

Structure-borne vibration of tire Xiandong Liu and Qizhang Feng Beihang University, Beijing, P.R. China

8.1 Introduction As the only part of a vehicle in contact with road, the tire not only transmits the excitation energy of road to the vehicle body, but also generates vibration and noise by itself. It is well known that reducing vibration and noise can improve the ride comfort of a vehicle. So the vibration and noise of tire need to be attenuated. A lot of researches on the vibration analysis of tire have been performed before. Tielking [1] studied the planar vibration characteristics of a tire by assuming it as a circular shell. Based on basic principle of Tielking’s method, Bohrn [2] studied the static and kinematic characteristics of a tire, and proved the validity of the method by experiment. Potts et al. [3] simulated a tire as a thin ring and studied its natural frequency by considering tire’s mass and geometry. Soedel and Prasad [4] studied the vibration characteristics of a tire under load by using the analytical method, and explained the vibration characteristics of the tire in a free state. Takayama and Yamagishi [5] analyzed tangential and radial forces of a tire when impacting the ground on the assumption of the tire being a rigid ring. Kamitamari and Sakai [6] assumed a tire as an annular beam model and studied the vibration characteristics of the tire. The dynamic characteristic of a tire is the link between the excitation and response. Kropp [7] conducted a deeper research on unloaded and smooth tires with different aspects. In the research, the fixed tire was measured and compared with a two-dimensional ring model, and the phase velocity and damping along the circumference of tire were discussed, and the admittance at radial measuring points was compared with the result of theoretical model. The influence of area on which the force was applied on the admittance was also analyzed. The results showed that “local stiffness” played an important role in the generation of noise. Negrus et al. [8] studied the natural frequency and modal shape of a 175/70R13 tire in analytical and experimental ways. The results indicated Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00008-8

© 2020 Elsevier Inc. All rights reserved.

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that the modal characteristics of a free tire are different from those of a tire with load, and increasing inflation pressure determined growing in natural frequencies for the same mode shape. Ushijima and Takayama [9] investigated the vibrational modes of a rotating tire. They found that the dynamic properties of the rotating tire were obviously different from those of the nonrotating one, and the dynamic characteristics of the rotating tire could be estimated by using the corrected modal parameters. Wei et al. [10] researched the tire dynamic response rolling over an obstacle by using the model of ring on the elastic and viscoelastic foundation, and found that both tire damping and rolling velocity had strong effects on the tire response over a cleat, and the frequency of dynamic load was mainly controlled by the first tire mode. Wave number domain representation of tire vibration has been studied by Bolton et al. [11]. In the paper, a horizontally suspended tire was driven radially at a point on the tread by using a shaker. The research results indicated that the response of a typical passenger car tire at low frequencies was controlled by a small number of relatively slowly propagating flexural modes, while more quickly propagating modes probably associated with extension of tread band appeared at higher frequencies. After that, Bolton et al. published a series of papers on the application of wave number decomposition approach in the analysis of tire vibration. Kim et al. [12] conducted experimental research on the radial natural frequency and damping ratio of tires, and reported the results of different tires (including PCR and TBR tires). The effect of pressure on tire modal parameters was studied by using frequency response function. And by using Tielking’s method [1] based on Hamilton’s principle, the theoretical calculation results of tire vibration were obtained, and showed that the experimental conditions could be considered as the factors to change the natural frequency and damping ratio [12]. It is well known that the modal analysis of a tire is the key of investigating the structure-borne vibration of a tire. Therefore this chapter mainly focuses on the introduction, calculation, and analysis of modal characteristics of tire. First, the modal characteristics of tire and its influencing parameters are introduced, including inflation pressure, tread pattern, tire mass, Young’s modulus of belt cord and belt angle, and so on. Then, the modal testing method of tire is described and analyzed, and the analytical modal models of tire (including 2-D and 3-D ring models) are also discussed. Finally, the finite element model of a tire, its establishment process, and the results of modal simulation are introduced and discussed.

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8.2 Modal characteristics of tire vibration and influencing parameters With the increase of vehicle’s speed, the noise and vibration play more important role in the ride comfort. At present, tire/road noise has become one of the main sources of environmental noise. The characteristics of tire’s natural vibration directly affect the vibration and noise of tire and vehicle. And since tire’s mechanical characteristic is one of the most important properties which influence vehicle’s dynamics behavior, the quantitative analysis of vehicle performance and the design of advanced chassis control systems depend on the research of dynamic models of tire and vehicle.

8.2.1 Modal characteristics of tire vibration The vibration characteristics of a tire directly affect the handling stability, ride comfort, and noise performance of a vehicle. For example, the circumferential first-order mode of a tire is closely related to the slip rate of the vehicle, which in turn affects the control of antilock braking system (ABS). The radial first-order mode is related to the ride comfort, while the higher order mode affects the noise. The steering performance of a vehicle is easily affected by the lateral first-order mode. Generally, the low frequency band of tire mode is related to the ride comfort and the handling stability, while the high frequency band mainly to the noise. Therefore the stiffness and vibration characteristics of tire as important parameters need to be carefully considered in the automotive suspension system design. In the research and development stage, the design of tire needs to be optimized according to the noise, vibration and harshness (NVH) characteristics proposed by auto-maker. The modes of tire are often obtained by the modal test based on the excitation method of hammer impact or vibration shaker (as shown in Fig. 8.1).

8.2.2 Influencing parameters of modal characteristics of tire vibration The influencing parameters mainly include the inflation pressure, tread pattern, tire mass, belt angle, and Young’s moduli of belt cord and tread compound. And they were systematically investigated through a series of tests and simulations in Refs. [13,14].

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Figure 8.1 Modal test of a tire using the vibration shaker.

Figure 8.2 Relation between natural frequency and tire pressure for a smooth tire.

8.2.2.1 Influence of tire pressure The natural frequency of a tire is influenced by the tire pressure which changes the tension of belt ply and the stiffness of tire. The natural frequency increases with the tire pressure. Figs. 8.2 and 8.3 show the relation between the tire pressure and natural frequency [13]. It can be seen from Fig. 8.2 that the higher the order of vibration mode of a tire is, the more susceptible it is to the influence of tire pressure. The tire stiffness increases with the tire pressure, so the natural frequency of the tire increases. Fig. 8.3 indicates that, with the increase of tire pressure, the vibration amplitude corresponding to each order of natural frequency rises since the

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Figure 8.3 Frequency response functions of the tire with different inflation pressures.

radial damping ratio of tire body decreases. Therefore the increase of tire pressure causes the ride comfort of a vehicle to deteriorate. 8.2.2.2 Influence of tread pattern For the purpose of drainage and grip, the tire tread is usually designed with pattern. The tire can be regarded as a vibration system composed of elastic tire body and tread. For a tire with constant tire body parameters, its natural frequency is proportional to the tire stiffness. Fig. 8.4 shows the influence of tread pattern on the natural frequency. Both the tested tires of smooth and patterned tires have the same type of 195/60R14 and the same inflation pressure of 250 kPa. Tread pattern causes the tread mass and stiffness of a patterned tire to be less than those of a smooth tire. It can be seen from Fig. 8.4 that the natural frequencies of smooth tire are lower than those of patterned tire. This indicates that the influence of tread mass on the natural frequencies is greater than that of tread stiffness. Therefore the tread pattern affects the natural frequency, further the vibration and noise performances of a tire. 8.2.2.3 Influence of tire mass Figs. 8.5 and 8.6 show the influence of the tire mass on the natural frequency from two aspects. Both the two tested tires with the same pattern

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Figure 8.4 Influence of tread pattern on the natural frequency.

Figure 8.5 Influence of the tire mass on the natural frequency.

but different mass are from same manufacturer and have the same type of 185/60R14 and the same inflation pressure of 250 kPa. Fig. 8.5 shows that, the lighter-weight tire leads to the lower natural frequency which correspond to the peak frequencies in Fig. 8.6. This means that the effect of tire mass on vibration characteristics is not only on the mass itself, but also on the stiffness of tire body. The effect of

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Figure 8.6 Frequency response functions of tires with different masses.

stiffness on the natural frequency of tire is greater than that of the mass change. According to the vibration theory, the vibration amplitude decreases when the system’s damping increases. The tire can be recognized as a damped vibration system. To meet the demand of light weight and other performances, the thinner sidewall of a tire is generally designed, causing the damping of tire to change. This change may result in lower damping ratio of tire, larger radial vibration of tire, and the deterioration of the ride comfort of a vehicle. But if the match with the suspension system is performed appropriately, the ride comfort may be improved. Therefore the influences of tire mass on tire stiffness, its natural frequency and the ride comfort of vehicle should be considered in the design of tire. 8.2.2.4 Influences of belt angle and Young’s moduli of belt cord and tread compound The influences of inflation pressure and corresponding parameters on the natural frequencies of the vibration modes in the radial and transversal directions are shown in Tables 8.1 and 8.2 [14], where Case 1 represents the original state of a tire, and other cases are obtained by adjusting one parameter based on the previous case. Case 1 has the inflation pressure of 260 kPa, Young’s modulus of the belt cord of 90 GPa, and the belt angle

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Table 8.1 Variation of the natural frequencies of the vibration modes in the radial direction (Hz). Case

Case Case Case Case Case Case

Order

1 2 3 4 5 6

1

2

3

4

5

6

7

8

9

89.27 88.61 88.70 89.68 106.21 107.26

108.5 107.48 107.64 109.55 124.15 125.51

134.05 133.05 133.29 136.13 151.42 152.93

163.18 162.44 162.77 166.49 183.93 186.11

193.86 193.51 193.91 198.46 218.75 222.50

224.97 224.28 225.23 230.66 254.63 260.35

256.66 256.28 256.55 262.92 292.57 299.46

289.76 288.70 288.87 296.19 334.18 341.00

324.61 322.91 323.10 331.19 379.82 385.90

Table 8.2 Variation of the natural frequencies of the vibration modes in the transversal direction (Hz). Case

Case Case Case Case Case Case

Order

1 2 3 4 5 6

1

2

3

4

5

45.25 45.56 45.53 46.20 52.32 54.67

62.05 62.20 62.29 63.08 71.34 73.67

114.39 113.34 113.57 132.49 132.49 134.93

165.15 163.77 164.01 193.05 193.05 195.75

200.31 199.20 199.52 235.62 235.62 238.21

of 22 degrees. Case 2 has the inflation pressure of 260 kPa, Young’s modulus of the belt cord of 90 GPa, but the belt angle of 27 degrees. Case 3 has the inflation pressure of 260 kPa, Young’s modulus of the belt cord of 110 GPa, and the belt angle of 27 degrees. Case 4 has the inflation pressure of 280 kPa, Young’s modulus of the belt cord of 110 GPa, and the belt angle of 27 degrees. Case 5 has Young’s modulus of the tread rubber increased from 10 to 50 MPa, and other parameters are the same as those of Case 4. Case 6 has Young’s modulus of the belt cord increased to 2 times of that of Case 5, and other parameters remain constant. According to the comparison of Case 1 with Case 2, when the belt angle is changed from 22 degrees to 27 degrees, the natural frequencies of the vibration modes along the radial and transversal direction change slightly. The comparison of Case 2 with Case 3 shows that the increase of Young’s modulus of belt cord from 90 to 110 GPa also brings just small change of the natural frequency. Comparing Case 3 with Case 4, we may see that, the growth of inflation pressure from 260 to 280 kPa increases

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the stiffness of tires, so the natural frequencies move to higher values. The comparison of Cases 4 and 5 concludes that, with the increase of Young’s modulus of the tread compound, the natural frequency increases significantly. Comparing Case 5 with Case 6, it is seen that the large Young’s modulus of the belt cord helps to increase the natural frequency as a whole. Overall, there is a greater growth of the higher order natural frequency than that of the lower order natural frequency for the parameter changes in all the cases. Through further comparison and analysis, it can be seen that Young’s modulus of tread compound has a greater influence on the natural frequency of the tire than other parameters.

8.3 Modal test methods of a tire Different from the general mechanical component, tire’s structure is especially complex since multiple materials with great different mechanical properties are included. In modal test of a tire, the suspension or mounting method, the excitation and the sensor locations should be deliberately planed and arranged [15]. Similar to the modal tests of other components, the modal test of a tire is often performed in two mounting boundary conditions: free suspension and rigid mounting of the tire (shown in Fig. 8.7). The theoretical analysis and experimental verification of these two mounting boundary conditions show that, the elastic modes of a tire are mainly composed of the elastic deformation of tire body relative to the wheel center in all the frequency bands of interest since the stiffness of tire body is much smaller than that of the wheel and the tire structure is symmetrical. The test results of these two mounting boundary conditions are basically consistent. Considering that the mounting stiffness of the tire is an uncertain parameter depending on the mounting conditions and the requirement of the mounting parameters in modeling, the free suspension of the tire is recommended. In modal tests, the hammer impact excitation and shaker excitation are widely used. But for a tire, large flexibility of tire body leads to the input frequency of the hammer impact excitation being relatively low. Therefore to obtain higher input frequency, the shaker excitation method is often used in the modal test of a tire. In the selection and installation of force and acceleration sensors, the influences of additional mass, additional stiffness, and other parameters arising from these sensors need to be considered in order to avoid the mode distortion.

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Figure 8.7 Schematic of two mounting boundary conditions in the modal test of a tire. (A) Free suspension. (B) Rigid mounting.

In the tire test, 16 measuring points are arranged along the circumference of a tire, and 7 modes are investigated below 350 Hz [15]. Considering the demand in modeling a tire, the modal tests excited by the radial and tangential forces respectively may be carried out. Due to the coupling effect of the vibration in the three different directions (radial, tangential, and lateral directions), three-dimensional modes appear although the excitation force is just along one direction. According to the engineering demand, the modal shapes in single direction are often extracted. Fig. 8.8 shows the modal shapes of the radial and bias tires in radial direction under radial excitation. All modal shapes of these two kinds of tires are similar except for the first mode (“breathing mode”) of the bias tire. This arises from the structural difference of two kinds of tires. The belt cord of a radial tire arranged along the circumference makes the circumferential stiffness of the tire larger than that of a bias tire. Similar to the vibration of a ring, the natural frequency corresponding to the breathing mode mainly depends on the circumferential stiffness, so it is greater for a radial tire.

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Figure 8.8 Modal shapes of radial and bias tires. (A) Modal shapes of a radial tire. (B) Modal shapes of a bias tire.

This leads that the breathing mode does not appear in the radial tire as the first-order mode. However, for a bias tire, the belt cord arranged in about 45 degrees with the central plane of a tire will produce a lower circumferential stiffness, so the breathing mode may occur at a lower frequency. Tables 8.3 and 8.4 describe the natural frequencies, damping ratios, and modal shapes of the radial and bias tires at different orders under the radial excitation. The first-order natural frequency of the radial tire is significantly lower than that of the bias tire, which coincides with the fact that the vertical stiffness of a radial tire is lower than that of a bias

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Table 8.3 Modal characteristics of the radial tire under radial excitation. Order

1

2

3

4

5

6

7

Frequency (Hz) Modal shape Damping ratio

95.72 Dislocation 0.80%

101.46 Oval 2.11%

114.87 3 petals 1.17%

136.65 4 petals 1.56%

159.87 5 petals 1.62%

184.58 6 petals 1.82%

212.29 7 petals 2.00%

Table 8.4 Modal characteristics of the bias tire under radial excitation. Order

1

2

3

4

5

Frequency (Hz) Modal shape Damping ratio

129.55 Breathing 2.66%

142.28 Dislocation 2.97%

163.59 Oval 3.40%

198.89 3 petals 2.68%

230.25 4 petals 3.02%

tire. The damping ratio of a radial tire is obviously lower than that of a bias tire, which is in agreement with the fact that the rolling resistance coefficient of a radial tire is lower than that of a bias tire.

8.4 Analytical calculation method of tire mode The dynamic performances of a tire affect not only the automotive vibration and noise characteristics and handling stability, but also the fatigue and wear properties of a tire. Therefore the tire modeling and performance prediction are paid much attention to the industry and academia. The ring model of a tire is one of the important tire dynamic models, which is mainly used to study the radial tire. There are some kinds of ring models, such as SWIFT-Tire model based on rigid ring assumption, FTire model based on flexible ring assumption, and RMOD-K tire model. They have been applied in some engineering software to analyze the performances of vehicle. The ring model is first used to study the tire dynamic stiffness, natural frequency, and tire/road contact. In this stage, the sidewall of a tire is expressed by the distributed radial springs, whereas the initial stress in the crown, the rotation effect, the coupling effect between tire and rim, and the tire
suspension
vehicle coupling, are not included. Many scholars have made contributions to the development and application of the ring model, such as Wei et al. [16,17], Liu and Gao [18], and Cao and Bolton [19]. In this section, the establishment and analysis of the two-dimensional and three-dimensional ring models of a tire will be performed.

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8.4.1 Two-dimensional ring model of a tire Generally, two methods may be used to obtain the governing equations of a ring model: one is based on the equilibrium equations, physical equations, and strain
displacement relation in structural mechanics; the other is to use the variation principle. Compared with the bias tire, the radial tire is more popular, whose belt is composed of the high strength cord arranged circumferentially, and the radial body ply cord is arranged at 90 degrees against circumferential direction. Therefore based on its structural feature, a tire may be simplified as a ring model shown in Fig. 8.9 [16]. In the figure, the tire is described as a ring supported on an elastic foundation. The ring represents the crown, and the elastic feature from the sidewall and the air in the tire is simulated by the elastic foundation (expressed by circumferentially distributed radial and tangential springs) which connects the circular ring to the rigid rim. The in-plane dynamic features of a tire can be analyzed by using this model. The governing equations of two-dimensional ring model can be obtained by using Hamilton’s principle: ð t2 δ ðU 2 T 2 W Þdt 5 0 (8.1) t1

Figure 8.9 Two-dimensional ring model of a tire.

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where U is the potential energy, which consists of U1 —bending strain energy stored in the crown and U2 —potential energy stored in the sidewall; T is the kinetic energy of tire crown; W is the work including W1 done by the tire pressure p0 , W2 by the distributed radial force qu acting on the external surface, and W3 by the distributed tangential force qθ and W4 by the distributed moment qβ . The bending strain energy of the tire crown is expressed as  ð 2π ð h  2 1 0 U1 5 b (8.2) σθ εθ 1 σθ εθ rdzdθ 0 22h 2 where σ0θ is the initial stress of the ring; b denotes the width of the crown; r; θ represent the radius and the radius angle of ring’s middle surface, respectively. The potential energy of the tire sidewall is as follows  ð 2π  1 2 1 2 U2 5 (8.3) ku u 1 kv v rdθ 2 2 0 where u and v are the radial and circumferential displacements at the ring’s middle surface, respectively. The kinetic energy of the tire crown is shown as ð 2π 1 _ j2 dθ T5 ρAr j,r (8.4) 2 0 where A is the cross sectional area of the tire crown. The work done by the external forces can be expressed as ~ 2 πr 2 Þ W1 5 p0 ðA W2 5

(8.5)

ð 2π qu urdθ

(8.6)

qθ vrdθ

(8.7)

0

W3 5

ð 2π 0

W4 5

ð 2π 0

qβ βrdθ 5

ð 2π qβ 0

v0 2 u rdθ r

~ is the middle surface area of deformed ring. where A

(8.8)

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163

We may see that correctly obtaining the potential energy and kinetic energy of the tire and the work of external force is crucial for establishing the dynamic equation of tire model. So, the analysis of deformation and force of the ring needs to be performed firstly. Then, the potential energy is described based on the strain and initial stress of ring, and the kinetic energy is expressed by the velocity of particle in the ring, and the external work is obtained by integrating the product of the distributed external force and surface displacement. The derivation of the strain, initial stress, velocity, and work of the external force in the two-dimensional ring model is introduced below. 8.4.1.1 Strain of ring According to the coordinate frame shown in Fig. 8.9, the coordinates of any point at the middle surface of a ring may be expressed as  X 5 rcos θ (8.9) Y 5 rsin θ Considering the deformation of the ring, the coordinates of point at the middle surface is changed to  x 5 rcosθ 2 vsinθ 1 ucosθ (8.10) y 5 rsinθ 1 vcosθ 1 usinθ where u and v are the radial and circumferential displacements of the point. By derivation, the bending strain of the ring can be expressed as [16]     v0 1 u 1 v0 1u 2 1 v2u0 2 z 0 1 εθ 5 1 1 2 ðv 2 uvÞ (8.11) r 2 r 2 r r 0

Generally, v 1r u is a small quantity. If the second-order small quantity v0 1u2 is recognized as small enough to be ignored, we may obtain r   v 0 1 u 1 v2u0 2 z 0 εθ 5 1 2 ðv 2 uvÞ (8.12) 1 r 2 r r where ð Þ0 denotes the partial derivative of ð Þ with respect to θ. For the detailed derivation process, readers may see Refs. [16,20].

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Figure 8.10 Schematic of calculating initial stress in a half ring.

8.4.1.2 Initial stress Assuming that σθ 0 is the initial stress of ring, the relation σθ 0 A 5 T may be easily obtained according to Fig. 8.10. The force equilibrium condition in Y direction may yield ðπ 2T 5 ðρAΩ2 r 1 p0 bÞcosθrdθ (8.13) 0

So, we have σ0θ

1 5 2A

ðπ

  ρAΩ2 r 1 p0 b cosθrdθ

0

p0 br 5 1 ρΩ2 r 2 A

(8.14)

8.4.1.3 Velocity of point at middle surface of ring Differentiating Eq. (8.10) with respect to time, we have x_ 5 ½ 2 ðr 1 uÞsinθ 2 vcosθΩ 2 v_ sinθ 1 u_ cosθ y_ 5 ½ðr 1 uÞcosθ 2 vsinθΩ 1 u_ sinθ 1 v_ cosθ

(8.15)

Then, the radial and tangential velocities of point ðr; θÞ in the ring can be expressed as  ur 5 x_ cosθ 1 y_ sinθ 5 u_ 2 Ωv (8.16) uθ 5 x_ sinθ 1 y_ cosθ 5 v_ 1 ðu 1 rÞΩ

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8.4.1.4 Work of inflation pressure The middle surface area of the deformed ring is expressed as I ~ 5 1 ð 2ydx 1 xdyÞ A 2 ð (8.17)  1 2π  2 0 2 0 0 2 r 1 rv 1 2ru 1 v 2 vu 1 v u 1 u dθ 5 2 0 Ð 2π in which the periodic condition 0 v 0 dθ 5 0 is used. On this basis, the work of inflation pressure is derived as  ð 2π   1 2 0 0 2 W1 5 p0 r u1 (8.18) ν 2 νu 1 ν u 1 u dθ 2r 0 Inserting Eqs. (8.12), (8.14), (8.16) and (8.18) into Eqs. (8.2),
(8.8) and using Hamilton’s principle, the equations of motion of twodimensional ring model are obtained. To get the vibration characteristics of a nonrotating tire, the rotating speed Ω needs to be set to zero. Under this condition, the natural frequency of a tire [16] is obtained as    1=2 1 EI 6 p0 b 4 2 4 2 2 fn 5 ðn 22n 1n Þ1 =2π ðn 2n Þ1ku n 1kv ρAð11n2 Þ r 4 r (8.19) The parameters of two-dimensional ring model of a tire include geometric and physical ones. The geometric parameters include: the cross sectional area A of ring, the equivalent width b, radius r, and thickness h of ring. These parameters can be extracted from the design parameters of tire. The physical parameters include: the equivalent density ρ, the radial spring coefficient ku , the tangential spring coefficient kv , and the equivalent bending stiffness EI. These parameters can be obtained by calculation, experiment, or finite element analysis.

8.4.2 Three-dimensional ring model of tire The two-dimensional ring model can be used to describe the in-plane vibration of a tire, but not the out-of-plane vibration. Three-dimensional ring model of tire which can describe the out-of-plane torsional and bending vibrations was studied by Wei et al. [17], Vu et al. [21], Lu et al. [22,23], Liu and Gao [24], and Yu et al. [25] and applied to perform the

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modal analysis of a tire. In the model, the large deformation and nonlinear strain are considered, and the three-dimensional displacement is adopted. Based on the three-dimensional ring model, the in-plane and out-of-plane equations of motion of a tire can be obtained by using Hamilton’s principle. On this basis, the analytical expressions of the natural frequencies and modal shapes can be achieved by using the modal expansion theorem. Fig. 8.11 indicates the three-dimensional ring model of a tire. Similar to Section 8.4.1, the ring represents the crown of a tire, and the circumferentially distributed radial and tangential springs simulating the elastic features from the tire sidewall and the air in the tire connect the crown to the rigid rim. Additionally, the features of ring along the axial direction need to be included in the model to analyze the out-of-plane vibration of a tire. In Fig. 8.11, the stiffness coefficients of the circumferentially distributed radial and tangential and axial springs are respectively denoted as ku, kv, and kw. The origin of coordinate system is set at the wheel center, and the location of a particle in the tire is described by cylindrical coordinates (r; θ; Z). Meanwhile, the location of a particle in the tire can also be described as (X; Y ; Z) in the fixed coordinate system. 8.4.2.1 Stress and strain of tire crown According to the three-dimensional ring model of a tire (Fig. 8.11), the coordinates of a point in the ring are expressed as 8 > < X 5 rcosθ Y 5 rsinθ (8.20) > : Z 5 Z0 1 w where r is radius; θ is radius angle describing the circumferential location of the point. If the deformation of the tire takes place, the coordinates of a point in the ring are given by 8 > < x 5 rcosθ 2 vsinθ 1 ucosθ y 5 rsinθ 1 vcosθ 1 usinθ (8.21) > : z 5 z0 1 w where u, v, and w are the corresponding radial, circumferential, and axial displacements of the point in the ring, respectively. If the corresponding displacements of the point at ring’s middle surface are respectively denoted as u, v, w and the transverse torsion angle of the ring is expressed by φ, we have

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Figure 8.11 Three-dimensional ring model of a tire. (A) Profile of model. (B) Cross section of model.

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8 u 5 u 1 φzop > > > < w0 v 5 v 1 zin β 2 zop R > > > : w 5 w 1 φzin

(8.22)

where R represents the average radius of ring (or the radius of ring’s mid0 dle surface), and β 5 v 2R u ; zop is Z coordinate of the point; zin 5 R 2 r is the radial relative coordinate of the point in the ring; ð Þ0 denotes the partial derivative of ð Þ with respect to θ. By derivation, the bending strain of the ring can be expressed as [17]     v 0 1 u 1 v0 1u 2 1 v2u0 2 zin 0 wv φ εθ 5 1 1 2 ðv 2 uvÞ 2 2 zop 1 zop 1 r 2 r 2 r r r r (8.23) And the stress is σθ 5 Eεθ

(8.24)

where E is Young’s modulus. Furthermore, the shear strains and stresses are obtained as 8 1 @u @v v > > 1 2 εrθ 5 > > r @θ @r r > > > > < 1 @w @v 1 εθz 5 (8.25) r @θ @z > > > > > > σrθ 5 Gεrθ > > : σθz 5 Gεθz where G is the shear modulus. Performing Taylor expansion to 1r in Eq. (8.25) and omitting the high-order small quantities, the expressions of the shear strains become ! 8 > 1 @φ 1 @w > > > < εrθ 5 R @θ 1 R2 @θ zop ! (8.26) > 1 @φ 1 @w > > > εθz 5 zin 1 2 : R @θ R @θ It should be pointed out that, in above analysis, the shear strains caused by the out-of-plane bend and distortion are included, but ones caused by the inplane deformation are ignored since they are high-order small quantities.

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Figure 8.12 Schematic of tire’s parameters.

8.4.2.2 Equations of motion of three-dimensional ring model Hamilton’s principle is used to obtain the equation of motion of a tire. According to the description of constraint forces and parameters of a tire (Fig. 8.12), and the stress and strain expressions of tire crown, the energy terms in Eq. (8.1) are as follows

U 5b

h ð 2π ð 2 1R 0

1

2

ð 2π " 0

h 1R 2

! 1 1 1 σθ εθ 1 σrθ εrθ 1 σθz εθz 1 σθ 0 εθ rdzdθ 2 2 2

# 1 1 1 1 kw w 2 1 kv v 2 1 ku u2 1 ku ðφbop Þ2 rdθ 2 2 2 2 (8.27)

T5

ð 2π 0

W 5 bp0 r

ð 2π  0

h i  2 1 _ 2 dθ ρAr ðu_ 2ΩvÞ2 1 v_ 1Ωðu1rÞ 1 ðwÞ 2

(8.28)

  ð 2π  1 2 v 2 u0 0 0 2 u 1 ðv 2 vu 1v u 1u Þ dθ 1 qu u 1qv v 1 qβ rdθ 2r r 0 (8.29)

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where σθ 0 is the initial stress in ring, which can be obtained according to the method shown in Section 8.4.1.2; A is the cross sectional area of ring; h is the thickness of tire crown; qu , qv , and qβ are the radial force, tangential force, and moment applied by the contact patch; Ω denotes the angular speed of tire. Inserting Eqs. (8.27),
(8.29) into Eq. (8.1) can yield the governing equations of the three-dimensional ring model of a tire. 8.4.2.3 In-plane free vibration mode of a tire By setting the transverse torsion angle φ and lateral displacement w to be zero, the equations of motion describing the in-plane free vibration of a tire are obtained as follows 8 EIz 4 3 EA 1 > 0 0 0 0 1 > > 4 ðu 2v Þ1σθ A 2 ðu12v 2uvÞ1ku u1 2 ðu1v Þ2p0 b ðu1v Þ1ρA€u 50 >

> > ðu 2vvÞ1σθ 0 A 2 ðv 0 22u0 2vvÞ1kv v 2 2 ðu0 1vvÞ1p0 b ðu0 2vÞ1ρA€v 50 > : r4 r r r (8.30)

where EIz is the in-plane bending stiffness; EA represents the membrane stiffness. The wave functions expressed by the natural vibration modes may be assumed to be 8 N X > > uðθ; tÞ 5 An eiðnθ1ωn tÞ > < n50 (8.31) N X > > iðnθ1ωn tÞ > vðθ; tÞ 5 iB e : n n50

where i is the imaginary unit; An and Bn are the modal amplitudes related to uðθ; tÞ and vðθ; tÞ, respectively. For a nonrotating tire (Ω 5 0), we have the relation σ0θ A 5 p0 br according to Eq. (8.14). Through substituting Eq. (8.31) into Eq. (8.30) and setting the coefficient determinant of equations to be zero, the characteristic equation is expressed as

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p0 bEIz 6 p0 bEA 4 ðn 2 n4 Þ 1 ðn 2 n2 Þ 5 r3 r " # 2 2 2p0 bn2 EAð1 1 n2 Þ 2 EIz n ð1 1 n Þ 2 ρAω 1 1 kv 1 ku 1 r4 r2 r

ðρAω2 Þ2 1

1

kv EIz 4 ku EIz 2 ku EA 2 EIz EA 6 n2 4 2 n 1 n 1 n 1 ðn 2 2n 1 n Þ 1 k p b v 0 r2 r6 r4 r4 r

1 ku p0 b

n2 n4 2 n2 kv EA 1 2 1 ku kv 5 0 1 p0 2 b2 2 r r r (8.32)

Solving Eq. (8.32) yields ρAω 5 2

b6

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 2 4C 2

(8.33)

where b5

C5

EIz n2 ð1 1 n2 Þ 2p0 bn2 EAð1 1 n2 Þ 1 1 1 kv 1 ku r4 r2 r

(8.34)

p0 bEIz 6 p0 bEA 4 EIz EA 6 ðn 2 n4 Þ 1 ðn 2 n2 Þ 1 ðn 2 2n4 1 n2 Þ r3 r6 r5 1

kv EIz 4 ku EIz 2 ku EA 2 n2 n2 n 1 n 1 n 1 k p b p b 1 k v 0 u 0 r2 r4 r4 r r

1 p0 2 b2

n4 2 n2 kv EA 1 2 1 ku kv 2 r r (8.35)

If n 5 0, Eq. (8.33) yields two eigenvalues ω201 and ω202 respectively corresponding to the breathing mode and rotating mode as follows: 8 kv > 2 > > < ω01 5 ρA (8.36) ku 1 EA > 2 > ω 5 > : 02 ρA

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Automotive Tire Noise and Vibrations

8.4.2.4 Out-of-plane free vibration mode of a tire If the out-of-plane vibration mode of a tire is solely considered and no load is applied on the tire (i.e., qu 5 qv 5 qβ 5 0), the potential energy U and kinetic energy T of the tire are expressed as 8 "  2  2  2 # > Ð 0 r > 0 2π b φ φ 2 wv w > > EIr 2 r 2 1 r 1 kw w 1 GIp r 2 1 r U5 0 dθ 1 ku φ 2op > < 2 ð > ρr 2π  2 > 2 > _ > T 5 A w _ 1 I φ dθ p > : 2 0

(8.37) Different from the in-plane vibration modes, there is no coupling between the initial stress of the ring and the out-of-plane vibration. By using Hamilton’s principle, the partial differential equations of the out-ofplane vibration of a tire are obtained as ! ! 8 2 0 0 > 1 @ wv φ 1 @ w φ > EI > 2 kw w 2 ρAw€ 1 GIp 2 50 2 2 1 1 > r 2 > r @θ2 r r r @θ r 2 r < ! ! > 0 0   > 1 @2 wv φ 1 @ w φ > € > > : 2EIr r @θ2 2 r 2 1 r 2 ku φbop 2 ρIp φ 1 GIp r @θ r 2 1 r 5 0 (8.38) The out-of-plane displacement and the transverse torsion angle of the ring expressed by the natural vibration modes can be given by 8 N X > > > wðθ; tÞ 5 Cn eiðnθ1ωn tÞ > < n50 (8.39) N X > > iðnθ1ω tÞ n > > φðθ; tÞ 5 Dn e : n50

By substituting Eq. (8.39) into Eq. (8.38) and using similar method with one in Section 8.4.2.3, the natural frequencies are obtained and given by pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b 6 b2 2 4C 2 ωn 5 (8.40) 2r 2

Structure-borne vibration of tire

173

where

  1 1 n2 n4 2 2 2 GIp 2 1 EIr 2 1 ku r ðGIp n 1 EIr 1 ku bop r Þ 1 (8.41) b5 ρIp ρA r r

C5 1

GIp EIr 2 2 ku bop kw ðGIp n2 1 EIr n4 Þ 1 2 ðGIp r 2 n2 1 EIr r 2 Þ n ðn 21Þ2 1 2 2 2 ρ Ip Ar ρ Ip A ρ Ip A ku kw bop r 4 ρ2 Ip A (8.42)

For the case of n 5 0, Eq. (8.40) yields 8 1 > ðEIr 1 ku bop r 2 Þ ω01 2 5 > > < ρIp r 2 kw > 2 > > : ω02 5 ρA

(8.43)

where ω01 and ω02 are the natural frequencies respectively corresponding to the lateral translational vibration and the out-of-plane torsional vibration.

8.5 Modal analysis of a tire based on finite element method Excitation of a rolling tire mainly comes from the road roughness, the unevenness of tire mass or stiffness, the impact between tread pattern and road surface, and the bending of tread near the contact patch. The vibration of tire is generated by these excitations, and the vibrational energy propagates to the cabin through the wheel, hub, suspension, and body structure. Then the vibration of the body structure and the interior noise are generated. The modal analysis of a tire is the key of investigating the structureborne vibration of a tire. In design stage of a tire, the modal characteristics are generally predicted and analyzed by using finite element method (FEM). Through the modal analysis of three-dimensional tire model based on FEM, the radial, transversal, and circumferential modes of a tire can be obtained. On this basis, various parameters (such as the inflation pressure, the angle of belts, and so on) influencing the vibration characteristics of a

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Automotive Tire Noise and Vibrations

tire can be investigated, and further, the relations of the characteristics with tire operating conditions and material parameters can be obtained. These are helpful to design a high quality tire and match the tire with a vehicle appropriately.

8.5.1 Differential equations of a dynamic system According to the dynamic theory, the differential equations of a dynamic system is expressed as M€a 1 C_a 1 Ka 5 Q

(8.44)

where a€ , a_ , a, and Q are the vectors of acceleration, velocity, displacement, and load, respectively; M, C, and K respectively represent the matrices of mass, damping, and stiffness, which are integrated by the corresponding element matrices as follows P P Ð 8 M 5 e Me 5 e Ve ρNT UNdV > < P P Ð C 5 e Ce 5 e Ve μNT UNdV (8.45) > P e P Ð T : K 5 e K 5 e Ve B UDUBdV where Me , Ce , and Ke are the mass, damping, and stiffness matrices of element e, respectively; ρ is the mass density; N is the matrix of shape function; Ve is the volume of element e; μ denotes the damping coefficient; B is the strain matrix; D indicates the elasticity matrix. When the damping is small enough to be ignored, Eq. (8.44) may be rewritten as M€a 1 Ka 5 Q

(8.46)

For free vibration, Eq. (8.46) is simplified to M€a 1 Ka 5 0

(8.47)

Base on Eq. (8.47), the natural frequencies and modal shapes of a tire can be obtained.

8.5.2 Methods of solving natural frequency and modal shape Actually, obtaining the natural frequencies and modal shapes of a system corresponds to solving the generalized eigenvalue problem of Eq. (8.47) in mathematics. In the finite element analysis, the computational scale is often very great due to the tremendous degrees of freedom. But in practice, only some lower order eigenvalues and corresponding eigenvectors are required for studying the system responses because of the limited

Structure-borne vibration of tire

175

excitation frequency range. Thus some efficient calculation methods with high accuracy and low cost have been developed. The popular methods mainly include the inverse iterative method of matrix, the subspace iteration method, Rayleigh
Ritz method, Lanczos method, Lanczos vector superposition method, and so on. The inverse iterative method of matrix is relatively simple, which is suitable for solving small-scale eigenvalue problem, while the subspace iteration method is the combination of Rayleigh
Ritz method with the inverse iterative method, and suitable for solving large-scale eigenvalue problem. The characteristic of the Lanczos vector superposition method is to directly generate a set of the Lanczos vectors to reduce the number of the equations of motion, and then solve the eigenvalue problem of the reduced equations number. Its calculation efficiency is higher than ones of many other methods.

8.5.3 Establishment of finite element model of a tire The modeling process for the tire modal analysis is generally as such, a two-dimensional axisymmetric model is firstly created, then through the spatial rotation, a three-dimensional model is established. In the engineering software ABAQUS, two types of elements (CGAX4H and CGAX3H) are often used to describe quadrilateral element and triangular element of rubber parts in the two-dimensional axisymmetric tire model. The rotation of the two-dimensional model about the rotation axis to generate a three-dimensional tire model makes these elements (CGAX4H and CGAX3H) change into C3D8H and C3D6H respectively. In addition, the reinforcing components such as belt cords, cap ply cords, carcass cords, and so on are simulated by using rebar elements, whose twodimensional and three-dimensional element types are SFMGAX1 and SFM3D4R, respectively. In modal simulation of a tire, the hyperelastic constitutive models are generally used to describe the rubber materials. The popular models include the Mooney
Rivlin model, the Yeoh model and the NeoHookean model. The Mooney
Rivlin model can be used to describe the tensile deformation behavior with strain less than 100%, but the description for compressive behavior is not accurate enough and the computational stability is not very well. The Yeoh model is suitable for a large deformation, but it does not coincide with the biaxial tensile test results well. The Neo-Hookean model is of the constant shear property and is

176

Automotive Tire Noise and Vibrations

Figure 8.13 Two-dimensional FEM model of a tire.

Figure 8.14 Three-dimensional FEM model of a tire.

generally applicable to the uniaxial tensile deformation with strain less than 40% and the shear deformation with strain less than 90%. The reinforcement components in the belt and carcass of a tire are often described by the rebar element. Cord-rubber composite material is represented by embedding the rebar element into the rubber element. There are three ways to define the rebar element: constant parameter method, angular spacing method, and lift-equation equilibrium method. By using above methods, finite element model of a tire is established. Fig. 8.13 shows the two-dimensional model of a tire (205/55R15), and Fig. 8.14 is the three-dimensional one generated by rotating around the

Structure-borne vibration of tire

177

axis of tire. In the simulation, a standard rim is assembled with the tire, and the inflation pressure is set to be 220 kPa.

8.5.4 Natural frequency and modal shape of a tire In terms of the modal shapes, the vibration modes of a tire can be classified into radial, transversal, and circumferential ones. These three kinds of modes respectively reflect the radial, transversal, and circumferential deformations of a tire at various natural frequencies. The radial mode is highly correlated with the ride comfort of a vehicle. The simulation results are shown in Fig. 8.15. Comparison of the simulation and test results of natural frequencies is shown in Table 8.5 [14]. The transversal modes are related to the shimmy of a tire. The simulation results are shown in Fig. 8.16. Comparison of simulation and measurement results of the natural frequencies of the transversal modes is shown in Table 8.6 [14]. The circumferential mode is related to the slip of a tire relative to road surface. Simulation result of the first-order circumferential mode of a tire is shown in Fig. 8.17. The first-order simulated and measured natural frequencies are 80.48 Hz and 76.3 Hz, respectively, and the relative error is about 5.5%. From the above comparisons of simulation and measurement results of the natural frequencies, we may see that all relative errors are very small except for the third-order natural frequency of transversal vibration mode. In the literature [14], the reason of the large relative error was analyzed and found to be that the excitation force was not great enough and the sensor was not fixed appropriately. After adjusting the excitation force and the fixing of the sensor, the accuracy was improved and satisfying. The modal characteristics of a tire are closely related to the ride comfort of a vehicle and the tire noise. The natural frequency and modal shape mainly depend on the stiffness and mass properties of each material component of the tire. And these properties can be changed by adjusting the distribution and characteristics of the tire materials. Thus the theory and method of adjustment need to be deeply investigated to improve the ride comfort of a vehicle and reduce the tire noise.

Figure 8.15 Simulation results of radial modal shapes of a tire. (A) First-order mode. (B) Second-order mode. (C) Third-order mode. (D) Fourth-order mode. (E) Fifth-order mode. (F) Sixth-order mode. (G) Seventh-order mode. (H) Eighth-order mode. (I) Ninth-order mode.

Table 8.5 Comparison of the simulation and measurement results of the natural frequencies of radial vibration modes. Order

Simulation (Hz) Measurement (Hz) Relative error (%)

1

2

3

4

5

6

7

8

9

89.27 88.3

108.50 114.0

134.05 135.0

163.18 161.0

193.86 190.0

224.97 221.0

256.66 257.0

289.76 295.0

324.61 331.0

1.10

2 4.82

2 0.07

1.35

2.03

1.80

2 0.13

2 1.78

2 1.93

Figure 8.16 Simulation results of the transversal modal shapes of a tire. (A) Firstorder mode. (B) Second-order mode. (C) Third-order mode. (D) Fourth-order mode. (E) Fifth-order mode.

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Automotive Tire Noise and Vibrations

Table 8.6 Comparison of the simulation and measurement results of the natural frequencies of transversal vibration modes. Order

Simulation (Hz) Test (Hz) Relative error (%)

1

2

3

4

5

45.247 47.5 2 4.74

62.046 60.3 2.90

114.390 90.3 26.68

165.150 164.0 0.70

200.310 212.0 2 5.51

Figure 8.17 The first-order circumferential modal shape of a tire.

8.6 Summary Ideally, the assembly of tire and wheel should be a vibration absorber, not an excitation source. However, in actual conditions, due to the interaction of some factors such as the tire rolling, the acoustic cavity resonance inside tire, the vibration of tread and sidewall, a tire may become a new excitation source. The excitation energy generated by the interaction between tire and road propagates through tire and wheel to the spindle, forming the excitation force and torque on the spindle. Then the vibration of suspension system is excited, and the vibrational energy transmits to the vehicle body, causing the vibration of body panels and producing the interior noise. If this excitation is coupled with the tire’s mode, the amplitude of vibration will be magnified greatly, causing the performances of vehicle to deteriorate. Obviously, the structure-borne vibration characteristics of a tire directly affect the vibration and noise performance of a vehicle. And among them,

Structure-borne vibration of tire

181

the modal characteristics of a tire are the core characteristics. The modal characteristics of a tire may be obtained by the modal test, the analytical calculation method, and FEM. The excitation in modal test can be produced generally by the hammer impact method or the shaker excitation method. Since the greater flexibility of the tire body leads to the excitation frequency in the hammer impact method being too low to meet the requirements, the sweep sine wave shaker excitation method is often applied. The experimental results show that the natural frequency of a tire with tread pattern is higher than that of a smooth tire, and Young’s moduli of the belt cord and tread compound, the belt angle and the inflation pressure have influences on the natural frequency of a tire. So in stage of tire structure design, FEM is a common method to predict the modal characteristics of a tire. The ring model is a typical analytical model to investigate the modal characteristics of a tire. At present, there are many forms of the ring model, such as the SWIFT-Tire model, FTire model, and RMOD-K model. They have been applied in some engineering software to analyze the NVH performance, and the ride comfort and handling stability of vehicle. This chapter introduces a two-dimensional tire ring model which describes the in-plane vibration of tire tread and a three-dimensional tire ring model which includes the out-of-plane vibration of the tire. The establishment and solution of equations of motion for these two ring models are described in detail. At last, a finite element model of the tire and its establishment process and the CAE simulation results are introduced and analyzed by using the engineering software.

Nomenclature U T W p0 q σ ε b r θ u v

potential energy kinetic energy stored in the tire crown work tire pressure distributed force or moment stress strain width of tire crown radius of ring’s middle surface in two-dimensional ring model of a tire radius angle of ring’s middle surface radial displacement of a particle in the ring’s middle surface circumferential displacement of a particle in the ring’s middle surface

182 A ~ A Ω h ρ ku kv EI f kw w u v w R E G φ EIz EA ω a Q M C K N V μ B D

Automotive Tire Noise and Vibrations

cross sectional area of tire crown middle surface area of deformed ring angular speed of tire thickness of ring equivalent mass density elastic coefficient of radial spring elastic coefficient of tangential spring equivalent bending stiffness natural frequency of a tire elastic coefficient of axial spring axial displacement of a particle in the ring’s middle surface radial displacement of a point in the ring circumferential displacement of a point in the ring axial displacement of a point in the ring average radius of the ring Young’s modulus Shear modulus transverse torsion angle of the ring in-plane bending stiffness membrane stiffness natural angular frequency vector of displacement vector of load matrix of mass matrix of damping matrix of stiffness matrix of shape function volume damping coefficient strain matrix elasticity matrix

References [1] Tielking JT. Plane vibration characteristics of a pneumatic tire model. SAE Technical Paper 650492; 1965. [2] Bohrn E. Mechanik des Gurtelreifens. Ing Arch 1966;35:82
101. [3] Potts GR, Bell CA, Charek LT, et al. Tire vibrations. Tire Sci Technol 1977;5 (4):202
25. [4] Soedel W, Prasad M. Calculation of natural frequencies and modes of tires in road contact by utilizing eigenvalues of the axisymmetric non-contacting tire. J Sound Vib 1980;70(4):573
84. [5] Takayama M, Yamagishi K. Simulation model of tire vibration. Tire Sci Technol 1983;11(1):38
49. [6] Kamitamari T, Sakai H. A study on radial tire vibration. SAE Technical Paper 852195; 1985. [7] Kropp W. Structure-borne sound on a smooth tyre. Appl Acoust 1989;26(3):181
92.

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[8] Negrus E, Anghelache G, Stanescu A. Finite element analysis and experimental analysis of natural frequencies and mode shapes for a non-rotating tyre. Veh Syst Dyn 1997;27(S1):221
4. [9] Ushijima T, Takayama M. Modal analysis of tire and system simulation. SAE Technical Paper 880585; 1988. [10] Wei YT, Nasdala L, Rothert H. Analysis of tire rolling contact response by REF model. Tire Sci Technol 2004;32(4):214
35. [11] Bolton JS, Song HJ, Kim YK, Kang YJ. Wave number decomposition approach to the analysis of tire vibration. In: Proceedings of the 1998 national conference on noise control, Ypsilanti, Michigan; 1998. 97
102. [12] Kim BS, Chi CH, Lee TK. A study on radial directional natural frequency and damping ratio in a vehicle tire. Appl Acoust 2007;68(5):538
56. [13] Ge JM, Wang WF, Sun SM, Gall R. Tire modal test and its application to tire structure design. Tire Ind 2001;21(4):203
7. [14] Feng XJ, Zheng XG, Wei YT, et al. Finite element analysis on tire vibration and study on its key influencing factors. Tire Ind 2013;33(1):12
20. [15] Guan DH, Wu WD. Experimental modal analysis of tires dynamics. Automot Eng 1995;17(6):328
33. [16] Wei YT, Guan DH, Fan CJ. On the ring model of the tire. Automot Eng 2001;23 (4):217
21. [17] Wei YT, Liu Z, Zhou FQ, Zhao CL. Three-dimensional REF model of tire including the out-of-plane vibration. J Vib Eng 2016;29(5):795
803. [18] Liu Z, Gao Q. In-plane vibration response of time and frequency domain with rigid-elastic coupled tire model with continuous sidewall. Proc Inst Mech Eng K: J Multi-body Dyn 2018;232(4):429
45. [19] Cao R, Bolton JS. A two-dimensional analytical tire cross-sectional model. In: Proceedings of Inter Noise 2017, Hong Kong, China; 2017. p. 97
107. [20] Gong S.R. A study of in-plane dynamics of tires [Ph.D. thesis]. Delft: Delft University of Technology; 1993. [21] Vu TD, Duhamel D, Abbadi Z, et al. A nonlinear circular ring model with rotating effects for tire vibrations. J Sound Vib 2017;388:245
71. [22] Lu T, Tsouvalas A, Metrikine AV. The in-plane free vibration of an elastically supported thin ring rotating at high speeds revisited. J Sound Vib 2017;402:203
18. [23] Lu T, Tsouvalas A, Metrikine AV. A high-order model for in-plane vibrations of rotating rings on elastic foundation. J Sound Vib 2019;455:118
35. [24] Liu ZH, Gao QH. Development of a flexible belt on an elastic multi-stiffness foundation tire model for a heavy load radial tire with a large section ratio. Mech Syst Signal Process 2019;123:43
67. [25] Yu XD, Huang H, Zhang T. A theoretical three-dimensional ring based model for tire high-order bending vibration. J Sound Vib 2019;459:114820.

CHAPTER 9

Structural-acoustic analysis of tire cavity system Zamri Mohamed

Faculty of Mechanical and Automotive Engineering Technology, Universiti Malaysia Pahang, Pekan, Malaysia

9.1 Introduction The design and manufacturing process of tire and wheel has to go through several cycles before they can be ready for production. The process is both time-consuming and expensive. Having an applicable computer modeling during early stages of the development would be cost effective which can be of interest to manufacturers. In automobile industries, the use of finite element (FE) simulation and experimental modal analysis (EMA) methods can be crucial to expedite the processes from design to production. In the aspect of component manufacturing such as tire manufacturing, FE simulation is used to predict the strength and performance of the tires to fulfill the homologation requirement set by the regulating bodies. The same goal is set for the experimental method where its purpose is to verify the design intention and provide evidence that the tires are conforming to the regulations. Tires are subjected to the forces generated by the interaction of the tire tread pattern and the road surface. Over the short to medium time periods, the tire including the tread pattern does not change but this is not the case for the road. The road surface therefore drives the changes in tire vibration, which are reflected by both the spectral content and amplitude as shown in Fig. 9.1 where the same tire is run on two different surfaces laid sequentially. Similarly, the tire cavity noise amplitude is also dependent to the excitation amplitude. The structural and acoustic modes of tire will be excited by road unevenness. Since the tire cavity resonance (TCR) modes are driven by the deflections of the tire’s structure, it will be necessary to investigate the structural-acoustic behavior of tire structure and cavity to understand about the related noise and vibration interaction and mitigation. Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00009-X

© 2020 Elsevier Inc. All rights reserved.

185

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Figure 9.1 Acceleration across a road surface transition [1].

Tire-wheel-cavity structural-acoustic behavior can be investigated by FE simulation either by customized computer codes or using commercial software. The computation scheme of the source can often be integrated to suit one’s need and goal. In this chapter, analytical solution is supported and verified by FE simulation in order to model and simulate tire-wheelcavity structural-acoustic system with emphasis on the coupling mechanism based on the impedance-mobility formulation method.

9.2 Frequency and wave number Two of the most discussed parameters in this chapter are frequency and wave number. These two parameters can be briefly explained and represented in Fig. 9.2. Frequency in Hertz (Hz) is the number of oscillation in 1 s which is multiplied by 2π for conversion to radian/s. Therefore, frequency is a

Structural-acoustic analysis of tire cavity system

187

Figure 9.2 Representation of frequency and wave number.

parameter which is based on time or period. On the other hand, wave number is a parameter based on spatial direction. If frequency is the inverse of the time period, then wave number is the inverse of wavelength. By definition, if frequency unit is in radian/s then the unit for wave number is radian/meter. If frequency deals with how many cycle of waves completed in 1 s, then wave number is defined by how many cycle of waves completed in 1 m distance. Natural frequency is defined by the frequencies at which free resonant vibration can occur. In the structural resonance, if some external excitation approaches the structural natural resonance frequency, the structure will oscillate to its maximum allowable amplitude before breaking (this amplitude will be limited by internal and external damping). Acoustic natural frequency, however, is the free oscillation frequency of the sound wave inside a conduit based on the speed of sound. The excitation can come from the sound source as well as nearby structural vibration. A rectangular box cavity with the following dimension, L 3 W 3 H is shown in Fig. 9.3.

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Automotive Tire Noise and Vibrations

Figure 9.3 Rectangular box cavity.

Figure 9.4 Mode shape in x-direction.

If L is the length of the longest side of the box, the acoustic natural frequency is f 5 ic=L where i is the mode number, i 5 0, 1, 2. . ., and c is the speed of sound. For example, if the first acoustic natural frequency is to be found then f1 5 c=L, whereas if the second acoustic natural frequency is to be found then f2 5 2c=L. Using L as the longest length will enable one to find the lower range acoustic natural frequency as this range is often of interest to practical problems. Sometimes if the higher acoustic natural frequency range becomes the interest, then one can find the acoustic natural frequency by replacing the denominator of the acoustic natural frequency formula with the specific dimension such as W or H. The sound wave representation in x-direction (if L become the denominator) for the rectangular box cavity is shown below. This illustration is called acoustic mode shape, defined by how the acoustic waves are interfering and bouncing between the opposite ends as illustrated in Fig. 9.4.

9.3 Tire cavity resonance The vibration transmitted from the excitation sources of the tire
road interaction and powertrain into the vehicle cabin through the vehicle

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189

structure resides below the frequency range of 500 Hz. In comparison to the many other noise sources, the TCR noise has been identified as the tonal noise that can be clearly heard inside the vehicle cabin which contributes to the increased level of annoyance. The first published work in the area of TCR was [2] where the cavity resonance was defined as an acoustic resonance pressure mode that exists inside the tire cavity. The modal frequency content was found to be dependent to the sound speed of the medium and the tire circumference length at the centroid. Physically, the TCR noise is generated by the acoustic standing wave occurring inside the tire cavity as a result of the tire tread-road excitation. The main adverse effect is the transmission of vibration to the wheel hub which then propagates as tonal noise into the passenger cabin. To quantify the relation of the cavity pressure fluctuations to the force at the hub, it is useful to obtain the acceleration response at the hub analytically where [3] calculated the resultant force and moment at the spindle with and without the acoustic coupling. In his analysis, the calculated point accelerance at the location of the excitation force (on tire tread) was compared to the spindle accelerance from experimental result [4]. The force from the hub would propagate to contribute to the interior noise of vehicle as proven in Ref. [2].

9.4 Tire-cavity-wheel system In simple tire and cavity geometry, the cavity is visualized as toroid shape bounded with the tire tread on the outer layer. Fig. 9.5 illustrates this

Figure 9.5 Simplified tire geometry.

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Automotive Tire Noise and Vibrations

geometry with the appropriate direction coordinates. The wheel rim is usually not modeled as it is regarded as rigid boundary [3,5,6]. As the interaction of sound and structure in the tire cavity system is generally similar to the structural-acoustic interaction with flexible boundary problem in acoustics, the same method can be applied to solve for the pressure at the points inside the cavity and for the velocity at the points on the tire tread surface. A comprehensive theoretical model for coupled response of structuralacoustic system has been well established [7]. The coupled response was obtained from the modal characteristics of the uncoupled system. Later, a so-called impedance-mobility compact matrix (IMCM) method was used to solve the same system [8]. The advantage of this method comes from its formulation simplicity and results in a compact matrix which can be easily solved in numerical computer software. Flexible wall in a structuralacoustic system may exhibit the structural resonances together with the acoustic resonances, therefore requires the use of coupled solution to predict the cavity sound pressure level and the tread point velocity. In conventional structural-acoustic modeling, the most popular form of geometry for finding the differential equation solution of the flexible wall and cavity system is rectangular box. However, solving the tire cavity system requires the use of toroid system. It is impractical to use the exact tire contour in mathematical modeling as the tire profile and sizes differ among different brands. It would be easier to use toroid shape with a rectangular cross section profile (Fig. 9.5) with negligible difference in accuracy. As in Fig. 9.5, the tire and cavity geometry can be constructed from two cylindrical shells with two annular side plates. For simplification, tire sidewall and conjoining wheel rim surface can be regarded as rigid surfaces without sound absorption material boundary.

9.5 Tire cavity resonance frequency Upon excitation, acoustic waves propagate along the toroid cavity from both sides of excitation source in the two opposite directions. These oppositely moving waves interfere with each other and therefore creating standing wave at certain frequencies according to the formula f 5 ic=ðRm θÞ, where i 5 0, 1, 2. . . [2]. This mathematical formula is the simplest form to ascertain the acoustic modal frequencies of an enclosed volume. The denominator is simply the longest boundary distance from the sound source. In the toroid shape, the circumferential length Rm θ is

Structural-acoustic analysis of tire cavity system

191

taken at the middle point, where Rm 5 ðRo 1 Ri Þ=2, Ro , and Ri are the outer and inner radius of the tire cavity, θ is 2Π, and c is the speed of sound. Another way of determining the acoustic natural frequencies is by solving the inhomogeneous wave equation in Eq. (9.1) in cylindrical coordinate. The fluid in the cavity is assumed to be homogenous, inviscid, isotropic, and incompressible. The “sound pressure field” p in the cavity satisfies @2 p 1 @p 1 @2 p @2 p 1 1 1 1 k2 p 5 0 @r 2 r @r r 2 @θ2 @z2

(9.1)

where k 5 ω=c. k is the wave number, ω is the circular frequency in radian/s, and P c is the speed of sound of 343 m/s. Letting pðr; θ; zÞ 5 n an ϕðr; θ; zÞ where an is the acoustic modal amplitude and using separation of variables to the acoustic mode shape function ϕðr; θ; zÞ 5 RðrÞΘðθÞZðzÞ will lead to three differential system equations related to the axial, radial, and azimuthal directions. A general solution representing the acoustic mode shape function ϕðr; θ; zÞ is such that    N X N X N X Umnl Amn Jm ðkmn r Þ 1 Bmn Ym ðkmn r Þ e2imθ 1 d0 eimθ  2ik z  ϕðr; θ; zÞ 5 l 1 c0 eikl z m51 n50 l50 e (9.2) where Jm and Ym are, respectively, the Bessel functions of the first and second kind, both of the order m. Umnl is a normalization factor, while Amn and Bmn depend on the boundary conditions where they are given by Amn 5 Y 0m ðγχÞ and Bmn 5 2 J 0m ðγχÞ for the assumed rigid sidewall boundary. After simplification, Eq. (9.2) becomes   N X N X N X   imθ lπz ϕðr; θ; zÞ 5 Umnl Amn Jm ðkmn r Þ 1 Bmn Ym ðkmn r Þ e cos W m51 n50 l50 (9.3) The second and third sound wave components from Eq. (9.2) are reduced to a single term in Eq. (9.3). In Eq. (9.2), the coefficient d0 of the second sound wave component becomes unity due to the continuity of the tire tread shell in the circumferential direction, while the coefficient c0 for the third sound wave component becomes unity due to the condition Z 0 ð0Þ 5 0. The wave number of kl 5 lπ=W is due to the condition Z 0 ðW Þ 5 0.

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Table 9.1 Roots of Eq. (9.4). m

m51

m52

m53

m54

m55

N

@ first order

@ second order

@ third order

@ fourth order

@ fifth order

1.271

2.532

3.776

4.994

6.183

7.855

8.196

8.740

9.461

10.328

15.417

15.584

15.860

16.240

16.717

23.045

23.156

23.340

23.596

23.921

30.688

30.772

30.910

31.102

31.348

38.339

38.405

38.516

38.670

38.868

n50 @ root n51 @ root n52 @ root n53 @ root n54 @ root n55 @ root

no. 1 no. 2 no. 3 no. 4 no. 5 no. 6

Manipulating the first sound wave component RðrÞ by imposing rigid boundary conditions at the cavity sidewall such that R0 ðRi Þ 5 0 and R0 ðRo Þ 5 0 will produce the characteristic equation denoted in Eq. (9.4). J 0m ðχÞY 0m ðρχÞ 2 Y 0m ðχÞJ 0m ðρχÞ 5 0

(9.4)

where ρ 5 Ri =Ro and kmn 5 χ=Ro . Eq. (9.4) is one of the common Bessel characteristic equation in the physical problem. For this case, it is used for calculation of modal oscillation frequencies of the incompressible liquid in an annulus container. Solving the equation for its roots χ would allow calculation of the cavity natural frequency. The roots χ for m 5 1. . .5, n 5 0. . .5 are listed in Table 9.1. The roots correspond to the first three tire cavity natural frequencies where the roots are, respectively, 1.271, 2.532, and 3.776. The acoustic wave number k in Eq. (9.1) is given by k2 5 k2mn 1 k2l Therefore the tire cavity natural frequency is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2ffi c χ lπ where l 5 0; 1; 2. . . 1 f5 2π Ro W

(9.5)

(9.6)

Structural-acoustic analysis of tire cavity system

193

Table 9.2 First three TCR frequencies. Tire size

Cavity outer radius

Cavity inner radius

f [from Eq. (9.6)]

f 5 ic=ðRm θÞ

FE software

205/65/R15

306

180.5

226.8 452.1 674.4

224.4 448.8 673.2

226.9 452.2 674.5

The first three cavity natural frequencies correspond to m 5 1. . .3, n 5 1, l 5 0 as depicted in Table 9.2. The cavity geometry is generated from the tire size 205/65/R15 (Ro 5 0.306, Ri 5 0.1805, W 5 0.21). The natural frequencies obtained from an FE software is also shown for comparison. However, for the case of Ri . 0:5Ro , the tire cavity natural frequencies can be approximated by Eqs. (9.7) and (9.8) as described by [9]. ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2  2ffi c lπ λmn where m; n; l 5 0; 1; 2. . . (9.7) 1 fmnl 5 2π W Ro  λ2mn



nπRo Ro 2Ri

2



2mRo 1 Ro 1Ri

2 for Ri . 0:5Ro

(9.8)

Apparently, although the formula f 5 ic=ðRm θÞ is much simpler than Eqs. (9.7) and (9.8), where θ 5 2π for m 5 1. . .3, n 5 1, l 5 0, finding the first three cavity natural frequencies by this simplified formula underpredicts the resonance frequencies by up to 1% in comparison to those obtained in Eqs. (9.7) and (9.8) and the FE software. The calculated value of the first tire cavity natural frequency agrees well with the EMA test result measured later with an actual tire. The first cavity frequency measured is at 227 Hz in the modal analysis tests using the impact hammer and sound source excitations. Therefore, it is verified that using the actual tire shape for the cavity would give very similar cavity resonance frequencies to the simplified model in Fig. 9.5. Conclusively, the tire acoustic resonance frequencies are dependent on the centroid circumference length of the cavity. When plotted in time
frequency plot, the TCR will appear as a streak of line on the frequency axis as shown in Fig. 9.6.

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Figure 9.6 Time
frequency plot of a tire shows two cavity modes and one structural mode [1].

9.5.1 Degenerate tire cavity modes Due to the fact that the tire cavity model considered above is symmetrical, the cavity resonance would result in degenerate cavity resonances. Degenerate resonance is defined where two or more resonance modes have the same resonance frequency. For symmetrical objects, it is a consequence of repeated eigenvalues due to the stiffness and mass matrices being the same in all directions. From Eq. (9.3), at arbitrary point in the azimuthal direction the second term is cosðmθ 1 ΦÞ which is equivalent to cosðmθÞcosðΦÞ 1 sinðmθÞsinðΦÞ, where Φ is the phase angle. The above expression really has two modes, sinðmθÞ and cosðmθÞ which are degenerate. This phenomenon is illustrated in the FE simulation outcomes as shown in Fig. 9.7. For example, mode 2 is named as vertical mode and mode 3 as fore-aft mode or vice versa. Mode 2 and mode 3 have the same mode shape contour at the same frequency but differ by 90 degrees phase angle with respect to each other. The same applies for mode 4 and mode 5 and the subsequent symmetrical modes. The acoustic natural frequency for the above mode shapes is listed in Table 9.3. It is seen from Table 9.3 that the two resonance modes have the same resonance frequency. This specific case is named as degenerate mode, a result of the symmetrical structure or object such as the unloaded or undeformed tire cavity structure or geometry used in the analysis. It is a consequence of the repeated eigenvalues due to the stiffness and mass matrices

Structural-acoustic analysis of tire cavity system

195

Figure 9.7 TCR mode shapes for un-deformed tire.

Table 9.3 First 10 TCR frequencies (un-deformed tire)—by FE simulation. Mode

1 2

3

4

5

6

7

8

9

10

Frequency (Hz)

0 226.9 226.9 452.2 452.2 674.5 674.5 902.2 902.2 1076

being the same in all direction. To ensure the degenerate mode shapes have the same frequencies, mesh densities should be increased to the point of convergence. Table 9.3 contains the results obtained using “automesh” feature in an FE software but with increasing mesh size until the frequency value stabilizes. For a beginner in FE simulation, using “automesh” could lead to different frequencies for the degenerate mode shapes. That is, if one simply does “auto-mesh” without sensitivity adjustment, the effect of meshing could distort the frequencies and make the frequency values for mode 2 and mode 3 differs by decimal value (which could misled the interpretation as two distinct modes). Nevertheless, there is one easy way to ensure the two modes have the same exact natural frequency by changing the mesh type from “auto-mesh” to “mapped face mesh.” “Mapped face mesh” will eliminate the effect of mesh nonuniformity from “auto-mesh” in evaluating the resonance frequency. Mode 2 is commonly known as the first TCR mode because mode 1 is essentially the acoustic rigid body mode.

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9.6 Tire tread natural frequency and mode shape Tire tread can be treated as a thin finite cylindrical shell for adopting thin shell theory due to tire tread thickness is less than 10% of the shell radius [9]. There are several shell theories in literatures since Love’s work (1888) but they are different because of the various assumptions on the order and form of small terms in them. The Donnell shell theory is by far the simplest and has been adopted in the other tire case studies for the simply supported conditions [10]. Fig. 9.8 illustrates a cylindrical shell under the coordinate of r; θ; z and the displacements in u; v; w directions. The solution forms for midsurface deformation are ! lπz uz 5 Az cos cosðmθÞcosðωt Þ Ls ! lπz vθ 5 Aθ sin sinðmθÞcosðωt Þ (9.9) Ls ! lπz wr 5 Ar sin cosðmθÞcosðωt Þ; l 5 1; 2; 3. . .; m 5 1; 2; 3:: Ls where Ar ; Aθ ; Az are the coefficients that describe the amplitudes of the deformation and Ls is the shell length. Donnell
Mushtari operator is given by

Figure 9.8 Circular cylindrical shell.

Structural-acoustic analysis of tire cavity system

3

2

@2 ð1 2 νÞ @2 6 @z2 1 2 @θ2 6 6 6 ð1 2 ν 2 ÞR2 @2 6 6 2 ρs 6 E @t 2 6 6 6 6 6 6 6 ð1 1 νÞ @2 6 6 2 @z@θ 6 6 6 6 6 6 6 @ 4ν @z

197

ð1 1 νÞ @2 2 @z@θ

ð1 2 νÞ @2 @2 1 2 @z2 @θ2 2 ρs

7 7 7 7 7 7 7 7 72 3 2 3 7 0 7 uz 74 5 4 5 7 vθ 5 0 @ 7 0 7 wr 7 @θ 7 7 7 7 7 7 2 2 2 7 ð1 2 ν ÞR @ 4 5 1 1 kr 1 ρs E @t 2

@ ν @z

ð1 2 ν 2 ÞR2 @2 E @t 2

@ @θ

@ @ where k 5 h2 =12R2 , r4 5 r2 r2 , r2 5 @z , ρs is the shell density, ν 2 1 @θ2 is Poisson’s ratio, R is the midshell radius, E is the Young’s modulus, h is the shell thickness. Applying the Donnell
Mushtari operator from the matrix above to the shell directional displacement in Eq. (9.9) would result in a system of matrices in Eq. (9.10) whose determinant equals to zero where the dimensionless parameter specifying the cylindrical shell natural frequency Ωf would be solved. Ωf then can be plugged into Eq. (9.11) for the shell natural frequency flm . In the matrix, Ω2f term for the first two diagonal terms is ignored due to retaining only the inertia term associated with radial deformation (wr ) whereas the inertia terms associated with in-plane deformation (uz and vθ ) are neglected [9]. This is also supported by the fact that the tread natural frequencies from 180 Hz to 250 Hz are all those with radial modes [11]. 2

1 1 2 v A i2 6 2λ2 2 @ 6 2 6 6 6 6 11v det6 iλ 6 2 6 6 6 6 4 2vλ 2

2

0

11v iλ 2 0 1 1 2 vA 2 2 2@ λ 2i 2 i

3 vλ 2i 0 h2 2Ω2f 1 1 1 @ 12R2

7 7 7 7 7 7 750 7 7 7 1 7 7 Aðλ2 1i2 Þ2 5 (9.10)

where λ 5 jπR=Ls , ν is Poisson’s ratio, R is midshell radius, Ls is shell length, and i,j are mode order numbers.

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 1=2 Ωf E flm 5 2πR ρs ð12ν 2 Þ

(9.11)

To identify which modes are relevant to the frequency range in this study, modal analysis is performed on the cylindrical shell with R 5 0.3135 m, Ls 5 0.21 m, and h 5 0.015 m. Material specification is taken from the tire tread cut-out tensile test data following the method described in Ref. [12]. The tensile test specimen is taken from Bridgestone RE92 205/65/R15 tire. The measured Young’s modulus is 2.61 3 108 Pa with Poisson’s ratio of 0.45 and density of 1230 kg/m3. The natural frequencies calculated using Eq. (9.11) are compared with those obtained from the FE simulation using commercial software for the uncoupled case and listed in Table 9.4 for the range between 180 and 250 Hz. It is seen that for the lower radial mode numbers, Donnell
Mushtari shell theory gives acceptable results in comparison to the FE simulation results. In order to match the mode numbers from the FE simulation results with those from the analytical method, careful observation is needed because from Eq. (9.11), a number of radial modes may have a lower resonance frequency than that of the lower radial mode number. In FE simulation results, however, the order of the modes is from low to high frequency. So in the FE simulation results, the mode shapes have to be visually inspected to match the modes from Eq. (9.11). For an actual tire which consists of tire tread and sidewall, the structural resonance frequencies would differ from those shown in Table 9.4. However, the vibration modes of an actual tire are very similar to those of the tread-only model as observed in another study [13].

Table 9.4 Tread natural frequencies for 180
250 Hz. Analytical (Hz)

FE simulation (Hz)

Mode (m,l)

192.9 200.2 202.1 219.0 227.7 238.6 266.8 316.7 375.8

178.4 191.2 182.5 215.3 204.1 239.9 240.1 287.4 343.7

(4,1) (3,1) (5,1) (2,1) (6,1) (1,1) (7,1) (8,1) (9,1)

Structural-acoustic analysis of tire cavity system

199

Table 9.5 Normalized plate mode shape coefficients. Bml

pffiffiffiffiffiffiffi 1= πLs pffiffiffi p ffiffiffiffiffiffiffi 2= πLs

m

L

0 1. . .Nθ

1. . .Nz 1. . .Nz

The mode shape functions of a thin circular cylindrical shell with simply supported boundary is defined by   lπz 2 ϕml ðθ; zÞ 5 Bml sin cosðmθÞ (9.12) Ls Bml is the normalized cylindrical shell mode shape coefficient and listed in Table 9.5 where m and l are the modal truncation number in the θ and z directions.

9.7 Structural-acoustic coupling of tire tread and cavity Although solid structures can store energy in compression and shear thus can bear different types of waves such as compressional, flexural, shear, and torsion, fluids can only sustain compressional waves. Therefore, fluid waves could only interact with flexural waves in the adjacent structure. This is also supported by the fact that structural flexural wave particle velocities are perpendicular to the direction of propagation and allows for direct exchange of energy from the fluid particles in compression [14]. Therefore, only the flexural modes of the tire tread were considered in the coupling analysis. For an enclosed cavity volume, pressure fluctuations can be generated by a vibrating elastic structure. The fluctuating pressure on the vibrating surface constitutes radiation loading which may affect the structure motion at the same time. This requires a simultaneous solution on the structure and the fluid as the feedback coupling occurs. In this example, tire tread is considered flexible which takes the excitation from the tire
road interaction as well as fluid loading from the inside cavity. Due to the fluid loading, a strongly coupled solution is needed to describe the structural-acoustic response of the tire cavity system.

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Automotive Tire Noise and Vibrations

9.7.1 Impedance-mobility approach As in Ref. [8] for a single input acoustic system the uncoupled mobility Y and impedance Z are defined as ZA 5 p=Q;

YA 5 Q=p

(9.13)

While for single input structural system they are defined as ZS 5 F=u;

YS 5 u=F

(9.14)

where F is the applied force, u is the resulting velocity, p is the acoustic pressure, and Q is the volume velocity. The coupled mobility ZCA and impedance ZCS are relate to the uncoupled counterparts by ZCA 5 C 2 ZA ;

YCS 5 C 2 YS

(9.15)

C is the coupling factor that relates the structural and acoustic response. The acoustic pressure and structural velocity are related to the source strength and applied force by u5

1 YS ðF 2 SZA QÞ; 1 1 YS ZCA

p5

1 ZA ðQ 1 SYS FÞ 1 1 ZA YCS (9.16)

where S is the tire tread surface area. For a weakly coupled system where the structure or the acoustic response behaves independently of each other, the above equations are given by u 5 YS ðF 2 SZA QÞ;

p 5 ZA ðQ 1 SYS FÞ

(9.17)

The acoustic pressure in the tire cavity at location ðr; θ; zÞ and the flexible wall vibration velocity at location ðθ; zÞ on the shell can be expressed by pðr; θ; z; ωÞ 5

N X

φn ðr; θ; zÞan ðωÞ 5 ϕT Ua

(9.18)

ϕm ðθ; zÞbm ðωÞ 5 φT Ub

(9.19)

n51

uðθ; z; ωÞ 5

M X m51

where a and b are the complex amplitude of the pressure modes and the vibration velocity modes in matrix form; φ is cylinder shell mode shape function, ϕ is acoustic mode shape function, and T is the transpose of a matrix.

Structural-acoustic analysis of tire cavity system

201

For the case whereby the system receives both acoustic and structural excitation the complex amplitudes are given as ! M X ρo c 2 an ðωÞ 5 Cmn bm ðωÞ (9.20) αn ðωÞ qn 1 V m51 ! N X 1 T β ðωÞ gm 2 bm ðωÞ 5 Cmn an ðωÞ (9.21) ρs hS m n51 Ð Ð T where Cmn 5 Cnm ; gm 5 S ϕm ðθ; zÞÞf ðθ; z; ωÞdS and qn 5 V φn ðr; θ; zÞ sðr; θ; z; ωÞdV are, respectively, the generalized modal force and acoustic strength. ρo is the air density, ρs is the tire tread mass density, V is the tire cavity volume, S is the tire tread surface area, and h is the tire tread thickness. The resonance terms αn ðωÞ and β m ðωÞ are given by α1 ðωÞ 5

αn ðωÞ 5

ω2n

1 1=T60 1 iω

2 ω2

β m ðωÞ 5

;

for n 5 1

iω ; 1 j2ηn ωn ω

ω2m

2 ω2

for n 6¼ 1

iω 1 j2ηm ωm ω

(9.22)

(9.23)

(9.24)

T60 is the reverberation time, that is the time taken for the level to decay by 60 dB and η is the damping loss factor. If only one source of excitation is present then either gm or qn is zero. Cmn represents the dimensionless coupling coefficients between the uncoupled structural and acoustic mode shapes over the vibrating structure surface where they are expressed as ð Cmn 5 φn ðr; θ; zÞϕm ðr; θ; zÞdS (9.25) S

Cmn is a measure of spatial match between the tire tread and cavity modes. For a rectangular box-cavity this coupling coefficient can be simplified according to the formula in Ref. [8]. For a cylindrical shell structure, this can be numerically calculated using the software such as Matlab, Eqs. (9.20) and (9.21) can be written in the matrix form as

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Automotive Tire Noise and Vibrations

a 5 Za ðq 1 CbÞ

(9.26)



b 5 Ys g
CT a

(9.27)

The coupled acoustic modal impedance and mobility matrix are written as Zca 5 CT Za C;

Ycs 5 CYs CT

(9.28)

Solving simultaneous matrix equation from Eqs. (9.26) and (9.27) will result in the form of coupled responses for the tire cavity system consisting of a 5 ðI1Za Ycs Þ21 Za ðq 1 CYs gÞ

(9.29)



b 5 ðI1Ya Zca Þ21 Ys q 2 CT Za q

(9.30)

Eqs. (9.29) and (9.30) can be substituted into Eqs. (9.18) and (9.19) to obtain the acoustic pressure in the tire cavity and the structural velocity of the tire tread. The following plots (Figs. 9.9 and 9.10) represent the acoustic pressure inside the tire. The plots are the results of Eqs. (9.18) and (9.19) compared with the FE simulation results. For the same structurally excited tire cavity system, if the tire tread responds as if it was “in vacuo,” then the coupled acoustic impedance has a minor effect on the tire tread vibration where the system is referred as

Figure 9.9 Predicted sound pressure results of analytical and FE simulation (point force excitation).

Structural-acoustic analysis of tire cavity system

203

Figure 9.10 Predicted sound pressure results of analytical and FE simulation (sound source).

weakly coupled. Detailed argument and derivation on this matter can be found in [8]. For the case of weakly coupling, Eqs. (9.29) and (9.30) become a 5 Za ðq 1 CYs gÞ

(9.31)



b 5 Ys q
CT Za q

(9.32)

The degree of coupling between tire structure and tire cavity is dependent on the ratio of the acoustic cavity bulk stiffness to the tire tread mass, the normalized coupling coefficient and the acoustic mode together with the structural mode resonance terms αn , β m [8].

9.8 Finite element simulation of tire structural resonance A full tire FE model as in Fig. 9.11 can be constructed simply by creating a solid structure with the material properties taken from the tire cut-out. The more accurate FE model should be constructed from the tire constituents such as the belt, steel belt, cord, rubber (sidewall and tread) and ply. For finding structural resonance modes, only material properties such as Young’s modulus and Poisson’s ratio together with boundary condition needed to be specified. Internal load can also be assumed because the

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Automotive Tire Noise and Vibrations

Figure 9.11 Tire FE model.

actual tire has internal air pressure which could affect the structural resonance. It is known that the effect of air pressure to cavity resonance is very small and negligible. For the purpose of visualizing the likely structural modes that would couple with the lowest acoustic cavity mode, it is sufficient to model only the tread. However, in order to obtain more accurate results, it will be more meaningful to use the full tire model considering all of the internal constituents of tire structure. In Table 9.6, all three lowest structural modes both using the full tire and tread only models are simulated. The structural modal frequencies of the full tire and tread only models for the mode (1, 1) differ significantly (i.e., 184 and 236 Hz). For the purpose of studying the structural-acoustic coupling of the tire cavity, it will be easier to utilize the tread only model to depict the coupling phenomenon. This is because the structural mode and acoustic cavity mode that could couple with each other are only those that have mode shape resemblance. Since the topic discusses about the structuralacoustic coupling, it will be more beneficial to explain about how that could happen than to find the actual tire that would have that coupling effect. It will be laborious to test every tire that would have (1, 1) and (2, 1) modes very close to its cavity resonance (i.e., 0%
20% frequency proximity). The following section will discuss about how the structural modes could interact with the cavity modes to change the original cavity resonance frequency. The structural and acoustic modes are obtained using the analytical solutions which are verified by the FE simulation and experimental results.

Table 9.6 Comparison structural resonance frequencies between the full tire and tread FE model. Mode

Full tire (fixed bead with 30 psi pressure)

Tire tread model (simply supported, in vacuo)

Tire tread model, (simply supported, 30 psi pressure)

248 Hz

245 Hz

244 Hz

184 Hz

235 Hz

236 Hz

193 Hz

213 Hz

220 Hz

(0,1)

(1,1)

(2,1)

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Automotive Tire Noise and Vibrations

Figure 9.12 (A) FE model point force excitation. (B) Sound source excitation.

9.9 Finite element simulation of structural-acoustic coupling of tire cavity FE model can be utilized to validate the results of the analytical model. Some vibro-acoustic software has the capability to implement the strongly coupled condition between the acoustic and structural subsystems. This feature enables the FE model of the cavity and the structure to be solved simultaneously, resulting in the pressure solution for any point in the cavity and vibration velocity solution for any point on the tread area. In Fig. 9.12, the FE model is shown for both the point force excitation (constant velocity source) and sound source excitation inputs. To apply the sound source excitation, an area on the cavity FE model equivalent to the speaker area needs to be selected whereas to apply volume velocity sound source, a point force on the tread FE model needs to be selected. To achieve simply supported condition at the edges of the model, points at the edges are constrained in circumferential and axial direction but not circumferentially rotational direction. Table 9.6 shows the dimensions of the FE model and the material properties adopted. The FE simulation will enable one to obtain mode contour plot at any specific frequency in three dimensions. The acoustic cavity pressure amplitude peaks at 214 and 255 Hz as found in Fig. 9.9 can be plotted for their mode contours as shown in Fig. 9.13. The structural modes (2, 1) and (1, 1) can be observed at the same frequency respectively. The acoustic pressures amplitude will depend on the strength of the force excitation or sound source excitation input. By observation it can be seen that the cavity mode at 214 Hz can easily couple to the (2, 1) structural mode. The cavity mode at 255 Hz can couple to the (1, 1) structural mode.

Structural-acoustic analysis of tire cavity system

207

Figure 9.13 Mode shape contour plot at (A) 214 and (B) 255 Hz.

The amplitude of coupling can only be observed by the experimental sound and vibration measurement results.

9.10 Experiment using model from FEM From the previous section, it has been discussed that the phenomenon of structural-acoustic coupling in the tire cavity system would be possible if

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Automotive Tire Noise and Vibrations

Table 9.7 Material properties of the FE model. Material

Dimension (m)

Density (kg/m3)

Sound Speed (m/s)

Young’s modulus (N/m2)

Poisson’s ratio

Damping ratio

Tread

R 5 0.306 Thickness 5 0.015 R2 5 0.306, R1 5 0.1805, W 5 0.21

1230




2.61 3 108

0.45

0.01

1.21

343







0.01

Cavity (air)

Figure 9.14 Experiment model.

the structural mode shape and the acoustic mode shape are nearby in frequency values and matching each other in the spatial direction. The spatial direction matching is referring to Eq. (9.25) where if the calculated values are greater than 0, then the coupling could be significant. One can prove this by finding that the modes in Fig. 9.9 can most efficiently couple to the mode (1, 1) in Table 9.7. However, to perform the experiment of structural-acoustic coupling with an actual tire would be difficult due to the presence of tire sidewall with its own damping. In this section we are going to illustrate the coupling between the tire tread and acoustic cavity modes since we have the analytical solution of the coupling in Section 9.4. Therefore, it is best to perform the experiments with only the tread cut out from actual tire with the sidewall replaced with a rigid wall as shown in Fig. 9.14. If we use the full tire model, we could only compare the results between the FE simulation and experiment measurement without being able to compare to analytical solution. Furthermore, one has to selectively find tire brand and size that

Structural-acoustic analysis of tire cavity system

209

Figure 9.15 Cavity sound pressure spectrum measured from experiment model in Fig. 9.10.

would have its structural and acoustic modes meeting the coupling criteria as discussed earlier. Impact hammer force transducer and accelerometer could be used to obtain the frequency response functions of the tire tread. Alternatively, sound loudspeaker and microphone sensor could be used to obtain the sound pressure spectrum and frequency response functions of the cavity. The results of using the second method are illustrated in Fig. 9.15 where the double peaks around 215 and 255 Hz are observed. The double peaks are correlated to the strong coupling phenomenon as identified in the analytical and FE simulation results earlier. One must realize that the acoustic resonance without coupling would be located at 227 Hz as calculated in Table 9.3. So, the presence of coupling actually has altered the acoustic resonance into two frequencies of 215 and 255 Hz. So if an engineer has designed such tire to have its acoustic resonance at 227 Hz then the actual resonance frequency has shifted due to the coupling phenomenon. This change could have adverse effects on design intent of the other components in terms of vibration limit and criteria. One available tire and rim was tested using the impact hammer, force transducer, and microphone. However, there was no coupling sign observed due to the tire and cavity not meeting the coupling criteria discussed previously. However, one can see the case where no coupling is present in both Figs. 9.16 and 9.17. Fig. 9.16 shows the acceleration spectrum collected on

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Automotive Tire Noise and Vibrations

Figure 9.16 Frequency response functions measured using impact hammer.

Figure 9.17 Sound pressure auto-power spectrum density (ref 5 20 3 1026 Pa) under a loudspeaker sound source excitation.

the tire tread while Fig. 9.17 shows the sound pressure spectra from the two microphones at 2 perpendicular locations. It is obvious that only one peak is present around 227 Hz (similar to the calculated TCR frequency without coupling). One thing to note in Fig. 9.17 is that the second plot has a lower amplitude peak around 227 Hz which is caused by the location of the second microphone at the cavity node area.

Structural-acoustic analysis of tire cavity system

211

9.11 Effect of loaded tire In the previous analysis, only the unloaded tire case was presented for simplicity especially from the mathematics point of view. The main purpose of this section is to extend the coupling analysis to loaded tire. Since it is known that tire will be deformed by some amount on the contact patch when vehicle is driven on the road, it is only logical to include the effects of loaded or deformed tire on the TCR noise. On the effects of loaded tire, tire contact patch will be deformed thereby changing the overall tire shape and the boundary condition. In addition, in reality the deflected area will change location continuously as the tire is rolling which complicates the phenomenon. While the analytical study of the deformed toroid shape related to this changing boundary condition was not found in literature, experimental work has been done before by Feng and Gu [15]. The experimental work was made possible by the use of internal wireless microphone sensor inside the tire cavity itself. An accelerometer was placed at the wheel suspension hub to capture the hub acceleration at the vehicle speeds of 48 and 80 km/h. As a result, a phenomenological approach was done to solve the related mathematical equations. In that study, it was shown that the resonance peak for loaded tire split into two different values, ωV and ωH . The peaks will veer away from each other if the rolling speed increases. The split cavity modal frequencies ωV and ωH are related to the unloaded tire cavity mode frequency ωO by q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ωO 5 ω2V 1 ω2H =2 (9.33) About the implementation of IMCM method to the loaded tire case, one has to use both ωV and ωH to replace ωn in Section 9.5 for finding the structural-acoustic response. So there will be two responses, one for ωV and one for ωH . Both the responses can be superposed to obtain a single response. For both the cases of loaded and rolling tire, they would only change the cavity resonance frequency by some amount. For example, for loaded tire, the peak of 227 Hz would be split to approximately 224 and 230 Hz for 20 mm tire patch deformation. When the rolling speed increases for the loaded tire, the peaks at 224 and 230 Hz would be separated further apart. For accuracy, these peaks need to be identified by experiment as was done in Refs. [16] and [5].

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9.12 Road experiment using internal microphone All of the previous studies used external microphone mounted outside the tire carcass (whether in laboratory setting or on the road environment). While the data results obtained were sufficient to be matched with those of the theoretical and FE simulation, it is worthwhile to look at the degree of agreement when the microphone is mounted inside the tire cavity itself while the tire is running. Measuring the tire cavity response while driving on a variety of road surfaces is more difficult to do than in laboratory setting. The challenge faced in making accurate measurements inside the tire was mainly in packaging the instrumentation, where the microphone sensor will be subjected to rough environment inside the tire cavity when the tire rolls and getting the data recorded. Due to the fact of rolling tires, it would be necessary to use slip rings to connect the microphone to the acquisition hardware. Slip rings are liable to inject noise into the signal and become unreliable with age. The realistic alternative was to use wireless link. Due to this demands, in 2004 Bay Systems in conjunction with Cooper Tire set out to investigate all aspects of tire noise and vibration. One of their projects was to develop tire cavity measurement (TCM) modules to resolve the instrumentation issue. The first step was to establish the absolute maximum cavity noise level to be 150 dB and to develop an accurate and robust transducer system that could be fitted to most of wheels in laboratory and on road without making any changes to the wheel. The goal was achieved in 2006. In 2012 Bay Systems found from their measurements that the cavity noise levels varied tremendously for tires of the same size. Also they reported that tire manufacturers were not reliably reducing the cavity noise levels in new designs and in some cases a new tire’s cavity resonance noise was twice as noisy. Fig. 9.18 shows the TCM modules installed on a test wheel and Fig. 9.19 illustrates the noise level of two types of tires with the same size measured with tire cavity microphone (TCM) [1]. The difference in the noise levels clearly shows that much can be done to reduce the tire cavity noise but it must be acknowledged that the noise may not be the first priority.

9.13 Summary This chapter has explored the tire cavity noise by means of analytical, finite element, and experimental methods. The acoustic response inside

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Figure 9.18 TCM on test wheel [1].

Figure 9.19 Cavity noise level for two winter tires of the same size running down on a laboratory rig [1].

tire cavity is described as the source of the structure-born noise found in vehicle cabin. Analytical solution of the coupled tire cavity structuralacoustic system using impedance compact mobility matrix is shown. The result is presented by the sound pressure level inside the tire cavity as well

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as the tread wall vibration velocity. In the analytical solution, the analytical results of the strong coupling showed that the natural frequencies of the uncoupled cavity and structures have been shifted and the sound pressure peak has been split apart into two peaks. The likely tire structural modes that have tendency to couple with the tire cavity mode were identified by the geometric coupling coefficient. The analytical result is verified by the finite element simulation result. Experimental results are measured by the microphone and accelerometer to detect the TCR frequency as well as to show the changes to the peaks once the tire is deformed due to load. In addition, data results from an actual tire cavity analytical model show the double peaks for the deformed tire. The difference/gap between the peak frequencies becomes larger as the rotational speed of the wheel tire increases. Latest tool to measure TCR is briefed where on the road testing will be easier to be performed while improving the data quality.

Nomenclature L Ls c f i Ro Ri Rm θ k ω p an ϕðr; θ; zÞ Jm Ym Umnl m; n; l i; j χ ρs ν E h flm

box cavity length cylinder shell length speed of sound frequency in Hertz integer 1,2,3. . . the outer and inner radius of the tire cavity the outer and inner radius of the tire cavity average outer and inner radius angle in radian acoustic wave number the circular frequency in radian/s sound pressure acoustic modal amplitude acoustic mode shape function the Bessel functions of the first and second kind the Bessel functions of the first and second kind normalization factor order mode order number Bessel’s roots shell density, ν is Poisson’s ratio Poisson’s ratio Young’s modulus shell thickness or tire tread thickness shell natural frequency

Structural-acoustic analysis of tire cavity system

Bml ϕml Y Z F u Q ZCA ZCS C S a b ρo V T60 η Cmn ωH ωV ωO

215

normalized cylindrical shell mode shape coefficient mode shape function uncoupled mobility uncoupled impedance force velocity volume velocity coupled mobility coupled impedance coupling factor tire tread surface area complex amplitude of the pressure modes complex amplitude of the vibration velocity modes air density tire cavity volume reverberation time damping loss factor coupling coefficient horizontal mode tire cavity resonance frequency vertical mode tire cavity resonance frequency unloaded tire cavity resonance frequency

References [1] Bennets A. Re: Tire cavity microphone from Bay Systems Ltd. Message to Zamri Mohamed. 3 Sept 2019. E-mail. [2] Sakata T, Morimura H, Ide H. Effects of tire cavity resonance on vehicle road noise. Tire Sci Technol 1990;18(2):68
79. [3] Molisani LR, Burdisso RA, Tsihlas D. A coupled tire structure/acoustic cavity model. Int J Solids Struct 2003;40:5125
38. [4] Yamauchi H, Akiyoshi Y. Theoretical analysis of tire acoustic cavity noise and proposal of improvement technique. JSAE Rev 2002;23:89
94. [5] Thompson JK. Plane wave resonance in the air cavity as a vehicle interior noise source. Tire Sci Technol 1995;23(1):2
10. [6] Fernandez ET. The influence of tire air cavities on vehicle acoustics [PhD thesis]. KTH University, Stockholm, Sweden; 2006. [7] Dowell EH, Gorman GF. Acoustoelasticity: general theory, acoustic modes and forced response to sinusoidal excitation, including comparisons with experiment. J Sound Vib 1977;52:519
42. [8] Kim SM, Brennan MJ. A compact matrix formulation using the impedance and mobility approach for the analysis of structural-acoustic systems. J Sound Vib 1999;223(1):97
113. [9] Blevins RD. Formulas for natural frequency and mode shape. Florida: Krieger Pub Co.; 1995. [10] Molisani L. A coupled tire structure-acoustic cavity model [PhD thesis]. Virginia Polytechnic Institute & State University, USA; 2004. [11] Wang X, Mohamed Z, Ren H, Liang X, Shu H. A study of tire, cavity and rim coupling resonance induced noise. Int J Veh Noise Vib 2014;10(1/2):25
50. [12] Yang X, Olatunbosun OA, Bolanriwa EO. Material testing for finite element tire model. SAE Int J Mater Manuf 2010;3(1):211
20.

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[13] Mohamed Z, Wang X, Jazar R. Structural-acoustic coupling study of tire-cavity resonance. J Vib Control 2016;22(2):513
29. [14] Norton MP, Karczub DG. Fundamentals of noise and vibration analysis for engineers. Cambridge: Cambridge University Press; 2003. [15] Feng ZC, Gu P. Modeling and experimental verification of vibration and noise caused by the cavity modes of a rolling tire under static loading. SAE paper 201101-1581; 2011. [16] Feng ZC, Gu P, Chen Y, Li Z. Modeling and experimental investigation of tire cavity noise generation mechanisms for a rolling tire. SAE paper 2009-01-2104; 2009.

CHAPTER 10

Computer-aided engineering findings on the physics of tire/road noise Laith Egab

School of Engineering, RMIT University, Melbourne, VIC, Australia

10.1 Introduction The simulation of the tire/road noise has gained remarkable attention in recent years. This is because of the increasing demand for the vehicle performance and intense competition among tire manufacturers. Tires are made from many different components from the softest solid materials to tough and hard materials like textile fibers and steels, which are one of the most complex composites. The prediction of tire performance from simulations is a challenge, not only due to the materials the tires are made from, but also because of the presence of a highly nonlinear structure in the tires, as well as dynamic contact boundary conditions. In order to reduce the product development time, computer-aided engineering (CAE) and simulation tools are already popular for use in tire industries. The simulation of vehicles and their tires has become one of the very important aspects of the tire design and failure analysis for most of tire companies. Simulation technology or capability has been developed in almost all important areas such as the performance prediction, design, optimization, and manufacturing. This means in the areas such as structure design, manufacturing, performance prediction, and optimization. New CAE simulation tools have enabled investigation of the tire/road noise in the early stages of the design process by performing most of the analyses using virtual models. Also, the application of other optimization techniques such as the Genetic Algorithm (GA) technique can help in performing sensitivity analysis and optimization studies by postprocessing the CAE analysis results.

Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00010-6

© 2020 Elsevier Inc. All rights reserved.

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The complexity of the tire models has evolved throughout time. New modeling techniques and more powerful computational tools are continuously being developed and introduced. The simpler models of the tire structure are presented using a lumped parameter approach that discretizes the tire belt into an elastic ring, string, or beam suspended on an elastic/ plastic foundation. These models require tests to identify the equivalent lumped properties of the system. This procedure is highly dependent on the discretization level of the system in addition to the type of the forced elements that are used between the system components. Additionally, these models, due to their simplified approach, lack some of the system informative factors, such as precise local defamation of the contact patch and complete response spectrum of the system (e.g., frequency content of the response). The more detailed are considered in the tire models that incorporate finite element methodology to discretize the tire structure to a higher extent, resulting in more complex models. For parameterizing the FEM tire models, experimental tests need to be conducted to fully define the material properties to be used in the code. Once the material properties are fully defined, the FEM tire models can be used in various design context without the need to characterize the system again, similar to the lumped parameter approaches. All of these activities come at the cost of more tedious modeling efforts and longer computational time. In addition to the aforementioned models, there are also some semianalytical semifinite element models that consider a simplification of the actual problem in order to incorporate the tire experimental data in a way so that the tire mechanics can be fully illustrated with less computational effort. In this chapter, the methodologies, challenges, and perspectives of developing a tire model for the vehicle simulation are discussed. First the CAE methodologies like the finite element method (FEM), the boundary element method (BEM), the waveguide finite element method (WFEM), as well as statistical energy analysis (SEA), energy finite element analysis (EFEA), computational fluid dynamics (CFD), and transfer path analysis (TPA) are presented and discussed. Vehicle suspension corner module is discussed and the mechanisms of the wheel imbalance, wheel force variation, and wheel impact force related friction are described and analyzed. Then the auralization models of tire/road noise and the current trends and challenges in the CAE modeling of tire/road noise are included. Finally, the chapter will conclude with a summary.

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10.2 Computer-aided engineering simulation methodologies This section covers state-of-the-art methodologies in tire/road noise modeling and simulations and outlines different classes of CAE methodologies. Deterministic methods are applied in the low frequencies, energy methods are applied in the high frequencies, and hybrid methods are applied in the mid frequencies.

10.2.1 Deterministic methods at low frequency In the low frequency range, the characteristic length of the system is smaller than or in the same order of magnitude as the dominant physical wavelengths of the dynamic response. The response of the system is determined by well-separated modes and can be predicted by means of deterministic numerical methods. In particular, the FEM and BEM are most commonly applied in the low frequency range. 10.2.1.1 Finite element method The mechanical behavior of the tire depends on many parameters, such as tire geometrical and material property parameters. Identifying these parameters and correlating them to the vehicle performance using empirical models might have limitation due to similar test conditions. On the other hand, using simple physical models for estimating the vehicle performance from the model input parameters might lead to significant errors. One alternative numerical method for analyzing tire dynamics is the FEM. The FEM is an efficient and low-cost numerical method that can be used for complicated tire dynamic analysis. The method represents the geometry of each single component by a set of numerous small sized elements (finite elements). Within these elements, field variables such as structural displacement and acoustic pressure are described in terms of simple, polynomial shape functions [1]. In regard to the structure-borne noise, the most effective approach to reduce the noise is to modify components in the structural transfer path. Thus it is a common practice to develop large detailed computer models of the vehicle components using finite element (FE). Subsequently, the component models are integrated using substructuring techniques for analysis of the assembled system. The tire model is one such substructures, and the tire finite element model has been used since the 1970s. The number of elements was first considered to be only a few hundred. It is

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currently a few million since the inclusion of the three-dimensional (3D) tread patterns and coupling between multiple subsystems/substructures [2,3]. The earliest models started with the 2D (two-dimensional) thin shell element models—axisymmetric and coarsely meshed tire models. These simplifications are adopted due to limited computational resources. The simulation output accuracy of the tire models is enough for the problem of interest. Now the models that inherit a 3D, full FEM, nonlinear fine mesh can capture the dynamic response of the tire with a high fidelity. Typical FE numerical models for prediction of the tire/road noise consist of the wheel
tire
cavity structure model and tire/road contact model. These models can be divided into two categories: low-order analytical models and higher-order analytical models [4]. The low-order analytical models are based on analytical descriptions and physical insights, yielding computationally efficient numerical results that can be evaluated in a fast and efficient manner. However, correlating the parameters of these models to physical tire design parameters, such as reinforcement fiber angles, tire cross-section geometry, and rubber compound properties, is typically not possible. Furthermore, inherent nonlinear behavior of the tire due to, for example, rubber compounds and reinforcement materials, is typically not included in these models. Therefore the use of higherorder numerical tire models, where the models are built in a rigorous, mathematical way analogous to the real physical tire, appears to be more appropriate. These models include physical design parameters, such as rubber compounds and reinforcement fiber angles. They also allow different material properties to be described by dedicated constitutive models, using material test data rather than system-level tire measurement data. The detailed tire geometry can be replicated, given an adequate discretization of the tire cross-section and circumference. Hence, these high-fidelity models can be developed as a numerical predictive approach for tire design. Many tire models are described based on nonlinear FE formulations. These FE formulations allow the inclusion of all sorts of nonlinearities, thereby enable the inclusion of a range of relevant physical effects such as nonlinear large strain behavior, incompressible material behavior, time and/or frequency-dependent viscous material behavior, and embedded reinforcement behavior. Recently a fully nonlinear finite element model was combined with an arbitrary Lagrangian
Eulerian (ALE) formulation to describe both the rolling dynamics as well as the interaction between the tire and coarse

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road surface [4]. In this model, a geometrical constraint approach is used to describe the tire/road interaction, rather than a constitutive approach, in order to keep the proposed method fully predictive and not relying on measurement data. However, the main shortcoming of a geometrical constraint approach is well known to be its large computational costs and simulation times. Therefore the nonlinear Multi-Expansion Modal Reduction/Hyperreduction method is applied to reduce the numerical computation costs and corresponding simulation times. Despite the fast increase of computer performance over recent decades, it is still not possible to simulate the complete nonlinear dynamic behavior of rolling tires and subsequent sound radiation directly. A significant reduction of the computational cost can be achieved by employing a modal superposition technique. This leads to a computational strategy, where the tire/road noise is analyzed in several subsequent steps summarized as the following [5]: • Computation of the nonlinear steady-state rolling analysis using the Modal Arbitrary Lagrangian
Eulerian (M-ALE) approach, which includes the effects of the rotation inertia and inflation pressure loads. • Complex eigenvalue analysis for the steady state of the rolling tire. • Determination of the excitation due to the texture of the road surface. • Computation of the operational vibrations with modal superposition. • Noise radiation analysis. Due to the heterogeneity and nonlinear nature of the tires, the method of finite element analysis seems to be the only tool for reliable modeling of the behavior of such a system. A lot of commercial FE analysis software, such as ABAQUS, ANSYS, MSC, MARC, LS-DYNA, and HYPERWORKS are applicable. 10.2.1.2 Boundary element method The BEM, also known as the boundary integral equation method (BIEM), is an alternative deterministic method which incorporates a mesh that is only located on the boundaries of the domain and hence are attractive for free surface problems. There are two kinds of BEM. The direct one (DBEM) requires a closed boundary so that physical variables (pressure and normal velocity in acoustics) can only be considered on one side of the surface (interior or exterior), while the indirect one (IBEM) can consider both sides of the surface and does not need a closed surface. Both kinds of BEM are based on the direct solution of the Helmholtz equation.

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The BEM has significant advantages over the FEM as there is no need for discretizing the domain under consideration into the elements, and this method only requires the boundary data as inputs. Therefore the meshing effort is limited, and the system matrices are smaller. However, the BEM also has disadvantages over the FEM; the BEM matrices are fully populated, with complex and frequency-dependent coefficients, which deteriorate the efficiency of the solution. Furthermore, singularities may arise in the solution, and these must be prevented [6]. BEMs can predict the sound radiation of a tire from the knowledge of the tire geometry and the surface velocity of the tire. BEMs can use the modal properties from the FE analysis. Therefore the tire geometry is readily identifiable, and the modal properties can be used to determine the velocity at any point on the surface of the tire. And the intensity of the sound radiation can be identified and tracked while design changes are made to the tire. The BEM with nonreflecting boundary conditions and infinite elements is usually used to simulate the sound radiation based on the surface acceleration response of rolling tires [7]. Fig. 10.1 shows the 3D boundary element (BE) model with different filed point locations adapted from [7]. 10.2.1.3 Waveguide finite element method The WFEM is an FE-based approach by which approximate wave solutions are found for such structures or fluids. The method guides the waves in a single direction, such as the circumferential direction of the tire, with

Figure 10.1 BE model with different point locations.

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constant physical properties in that direction [8]. WFEM uses a 2D finite element model over the cross-section of the waveguide and describe the response of the tire in terms of a set of waves in that direction. The response of the nodes in direction X at time t is governed by the following equation:
 @2 @ @ K2 2 1 K1 1 K0 1 M 2 VðX; t Þ 5 FðX; t Þ (10.1) @X @t @X where Ki is the stiffness matrix, M is the mass matrix, FðX; tÞ is a vector originating from the external load, and VðX; t Þ contains all the nodal degrees of freedom (DOF). The WFEM was used to investigate the vibrational behavior of tires. It uses special shell and solid waveguide finite elements to model the tire sidewalls, belt, and tread. The model has successfully been used to calculate the driving and transfer mobility, tire/road noise, and rolling resistance. The main advantage of the WFEM as compared to standard FE formulations is the decreased calculation burden. This stems from the fact that only the cross-section is discretized, reducing the number of DOF introduced to the model. An additional advantage compared to conventional FE is that different wave-types are easy to identify and analyze, allowing for a somewhat deeper physical understanding of the investigated structure [9].

10.2.2 Energy methods at high frequency In the high frequency range, when the dimension of the structure is considerably large with respect to the wavelength, conventional finite element analysis (FEA) requires a very large number of elements in order to properly capture the high frequency characteristics of a given structure. This consequently causes tremendously high computational costs and thus makes displacement-based FEA methods unfeasible [10]. On the other hand, SEA and EFEA can be used for simulating the vibroacoustic response of such large-scale structures at high frequencies within much less time. 10.2.2.1 Statistical energy analysis SEA is an energy-based method for complex vibroacoustic problems at high frequencies. It is typically used for modeling the sound and vibration

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energy dissipations and transmissions in the systems/subsystems such as vehicles, buildings, or industrial devices. It uses a combination of analytical, empirical, and experimental data. Since only local modes of SEA subsystems are required, the method is restricted to high frequency behavior. A complex vibroacoustic system is modeled as an assembly of coupled subsystems. Coupling loss factors are defined as those that relate the energy flow to the subsystem energies. A power balance for each subsystem results in a set of linear algebraic equations that can be solved for the vibratory energy of each subsystem. Structural displacements and acoustic pressures are then computed from the energy results [11,12]. The application of SEA requires an accurate estimation of the parameters such as loss factors, as well as the modal density used in power balance equations because prediction accuracy depends on the estimation accuracy of the parameters. The modal density for a 3D rectangular annular sound field enclosed by rigid walls is given by: nðωÞ 5

ω2 V ωA L 1 1 2π2 c 2 8πc 2 16πc

(10.2)

where V and A are the volume and surface area of the rectangular annular sound field, respectively; L is the total length of the edges of rigid walls. From Langley [13] the model density for cylindrical shell is given by:  θð1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 dθ 2 ΩR 2 cos4 θ

(10.3)

 2  π=2 ð sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k0 SΩR 1 nI 5 dθ 2 2 2π ωR ΩR 2 cos4 θ

(10.4)



k2 SΩR nII 5 0 2 2π ωR

θ0

θ1

where nII is the modal density of type 2 while nI is of type 1. Type 2 refers to waves and modes with a lower value of k2 characterized by waves with motion restricted by in-plane stiffness, while type 1 corresponds to waves and modes with a large value of k1 characterized by waves with motion restricted by flexural stiffness of the cylinder wall. In the SEA model of the tire
cavity, the acoustic radiation loss factor becomes related to the coupling loss factor when the annular acoustic cavity couples with the cylindrical shell. Therefore the coupling loss factor from the cylindrical shell to the annular cavity η12 is given by [14]:

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η12 5

2ρ0 cσ ωρsa

225

(10.5)

where ρ0 is the density of the cavity fluid, c is the speed of sound, σ is the radiation efficiency, ω is the center frequency of a frequency band, and ρsa is the surface mass density. The reciprocity relationship between the two subsystems is given by n1 η12 5 n2 η21

(10.6)

The coupling loss factor from the annular cavity to the cylindrical shell is given by: η21 5

2ρ0 cσn1 ωρsa n2

(10.7)

where n1 is the cylindrical shell modal density and n2 is the annular cavity modal density. It can be seen clearly from Eq. (10.7) that the tire
cavity coupling relationship depends on the accurate evaluation of the radiation efficiency. The radiation efficiency in the whole frequency bands containing some acoustically fast modes is given by [15] as:  3 ΩR 2 f R =fc pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ (10.8) 12ð1 2 v2 Þ 4B B5

nðωÞπhωR L

(10.9)

where fR is the ring frequency while v is the Poisson’s ratio, fc is the critical frequency for the cylindrical shell, L is the cylinder axial width. There are many advantages for using the SEA method, such as a decrease in computation time, but there are also a number of disadvantages. For example, SEA cannot produce a detailed response prediction, and only generates the spatial, frequency, and ensemble average values. It is therefore not possible to use SEA for detailed modal or natural resonant frequency analysis. Also, due to the high modal overlap requirement in SEA, accurate results are often limited to those in higher frequencies. In recent years, variance models for SEA based on a perturbation approach have been implemented. The method has been validated experimentally to be able to provide an accurate prediction of the variance.

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Figure 10.2 SEA model of the tire
cavity.

While SEA generally predicts the mean energy level, which is an important indication of the expected response, the addition of the variance provides a more complete description of the statistical response of the system. A display model of the tire
cavity using AutoSEA [14] is shown in Fig. 10.2. 10.2.2.2 Energy finite element analysis EFEA is a finite element-based computational method for high frequency vibration and acoustic analysis [16]. The EFEA applies finite element discretization to solve the governing differential energy equations. The primary variable in EFEA is defined as the time averaged energy density over a period and space averaged energy density over a wavelength. The EFEA is compatible with low frequency FEM models since it can use an FEM database. This permits modeling flexibility and cost-saving as one FE model can be applied to both low and high frequency analysis. The prediction of a spatially varying energy level within a structural subsystem is available with the EFEA computation. The postprocessing of EFEA results also provides straight-forward visualization of the energy flow in a system, which is convenient for diagnoses and control of noise propagation. EFEA can be applied to model highly damped or nonuniformly damped materials, and to model distributed masses as well as multipoint power input. Due to the utilization of the finite element technique, EFEA also has the other advantages that traditional FEM does not have.

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It can be easily applied to irregular domains and geometries that are composed of different materials or mixed boundary conditions. Although SEA models result in a few of equations which are easy to solve, they cannot be developed from CAD data, local damping cannot be accounted for, and the model development requires specialized knowledge. In contrast, EFEA offers an improved alternative formulation to the SEA for simulating the structural-acoustic behavior of built-up structures. It is based on deriving governing differential equations in terms of energy density variables and employing a finite element approach for solving them numerically. There are several advantages offered by EFEA. These advantages include the generation of the numerical model based on geometry; spatial variation of the damping properties can be considered within a particular structural member; the excitation can be applied at discrete locations on the model, and EFEA can be applied to the high frequency range, which benefits the large community of FEA users. These unique capabilities make the EFEA method a powerful simulation tool for design and analysis.

10.2.3 Hybrid methods in the mid frequency range In between the low frequency application range of the deterministic methods and the high frequency application range of the SEA methods, there still exists the mid frequency range, for which currently mature prediction methods are required [17]. The prediction of the response of a vibroacoustic system in this mid frequency range faces two major difficulties due to a relatively short wavelength. Firstly, many DOF are required to capture the deformation details of the system, and secondly the response of the system can be sensitive to imperfections, so that manufacturing uncertainties can lead to significant variability in the performance of nominally identical items [17]. Recently, SEA is combined with deterministic method to simulate the characteristics of the tire
cavity coupling [18]. While the deterministic method focuses on the cavity pressure response and the complaint wall vibration velocity response at low frequency, SEA focuses on the response at high frequencies. The tire
cavity coupling system is modeled as an annular cylinder, where the side and inner walls are assumed to be rigid, while the tire surface structure is assumed to be flexible. The vibration energy of the tire surface structure E1 is statistically calculated as follows:

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E1 5

Π1 1 ωE2 nn12 ðωÞ ðωÞ η12   ω η1 1 η12

(10.10)

where Π1 is the power input to the tire structure, ω is the angular frequency, η1 and η2 are the damping loss factors of the tire structure and the tire cavity, η12 is the coupling loss factor from the tire surface structure to the tire cavity. The acoustic energy E2 of the tire cavity is given by: ððð ð ω2 2 2 1 1 p ðr; θ; zÞ 2 πW ðR0 2Ri Þ dωdV E2 5 (10.11) V V 2 ω1 ω ρo c 2 where V is the volume of the cavity, ω1 and ω2 are the lower and upper limits of the frequency band, pω is the root mean square time- and spaceaveraged pressure of the cavity obtained from experiment, r, θ, and z are cylindrical coordinates, W is the tire width, R0 and Ri are the outer and inner radii of the tire cavity, respectively, ρo is the air density, and c is the speed of sound in air. Fig. 10.3 shows the cavity energy curve calculated from the analytical SEA method agreed well with those predicted with AutoSEA and measured experimentally [14].

Figure 10.3 Mean cavity energy from the measurement, calculated, and AutoSEA simulation.

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10.3 Other computer-aided engineering simulation methodologies 10.3.1 Computational fluid dynamics CFD is a simulation tool that combines a numerical solution and analytical or mathematics solution to model fluid flow situations. CFD tries to determine the numerical solution of the equations that rule the fluids’ flow, while the analytical or mathematic solution obtains the complete numerical description of the flow field studied in space and time. The CFD of the tire model employs a large eddy simulation (LES) turbulence modeling approach which requires the Naiver
Stokes (N
S) equations to be solved for simple groove geometries with a moving bottom wall that represents the deformation during the tire movement along the road surface. The alternative modeling approach uses the lattice Boltzmann method (LBM) which is a special discretization of the continuum Boltzmann equation in space, time, and velocity and uses the very large eddy simulation (VLES) approach for turbulence modeling. Successful CFD analysis requires the boundary conditions to be defined at the boundaries of the flow domain which enable all the boundary variables to be calculated. It also requires the initial conditions of the solution variables for steady state or transient simulation to be defined. Recently, CFD and the FEM were successfully combined to study the hydroplaning effect on the tire. These studies suggested that a car should travel on wet roads with low to mid speeds less than 65
85 km/h in order to avoid aquaplaning.

10.3.2 Transfer path analysis TPA is a simulation tool used to identify structure-borne and airborne energy transfer routes from the excitation source to a given receiver location in the low-mid frequency range. In principle, TPA is applied to evaluate the contribution along each transfer path from the source to the receiver, so that one can identify the components along that path that need to be modified to solve a specific problem, and perhaps to optimize the design by choosing desirable characteristics for these components. TPA can be applied to solve many vibroacoustic issues in manufacturing industries. Performing TPA on a car engine mounting system helps reduce interior noise, on driving wheel suspension and seating systems helps reduce the system vibration, and thus improve the driver and passenger comfort. Road noise disturbance in a vehicle can be minimized

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using the multi reference TPA technique. Nowadays, TPA is even employed to complement pass-by noise engineering methods so as to reduce the overall vehicle’s pass-by noise. TPA can be combined with hybrid FE/experimental modeling for acoustic optimization of a design. Operational transfer path analysis (OPTA) can be used to analyze the tire/ road noise at a certain receiver location, where an artificial head records the interior noise during this coast-down testing. An entirely different analysis concept is used for TPA. For TPA a vehicle is characterized by its “noise paths” rather than by actual geometry. The principal aim of TPA is to sum up all individual noise paths (individual noise sources multiplied by respective noise transfer function (NTF) or sensitivity) to the full vehicle noise or vibration response. Individual noise sources are typically mount forces, intake and exhaust orifice noise, powertrain noise radiation, high frequency noise, and underhood sound due to powertrain rigid body motion, etc. For the example of a powertrain mount, the respective noise source would be mount displacement multiplied by mount stiffness; the respective noise sensitivity would be p/F (sound pressure (p) per unit excitation force (F)) or NTF. The mathematical requirement for TPA methods itself is significantly lower than for FE or BE methods, but valid TPA models require representative data such as noise sensitivities, for example. If the latter cannot be predicted with high confidence, these TPA methods need to be based on the measured noise sensitivities. Hence these TPA methods will be “exact” only for installations of “new” powertrains into given structures. Noise sources can be determined from measurements or CAE analyses.

10.4 Vehicle suspension corner module simulation The suspension system is the key component that transmits the forces generated at the tire contact patch to the vehicle body. The most important forces are those from the ground that react and balance the weight of the vehicle. These reactions are primarily taken up by the deflections of the suspension springs. However, modern suspensions are highly complex mechanisms comprising various links and joints. These links balance a significant proportion of the total tire forces particularly during cornering and braking, where significant shear stresses are generated at the contact patch.

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The mathematical model of the vehicle which is capable of simulating the ride and handling characteristics of the vehicle has been developed and implemented in ADAMS/Car. MSC ADAMS is a mechanical system dynamics simulation tool widely used by chassis/suspension designers in automotive industry. It is a virtual prototype software which includes various interfaces for modeling, equation solving, optimization, simulation, and visualizing aids. It also enables users to import rigid body models from different CAD software and flexible bodies from packages like MSC Nastran [19]. The dynamic characterization modeling is characterized by various elements in the actual vehicle, such as coil springs, telescopic shock absorbers, and pneumatic wheels. Fig. 10.4 shows the front suspension system modeled as double fishbone per wheel suspension mechanism, also called as the deformable parallelogram arrangement, with elastic elements (coil springs) and dissipative elements (telescopic hydraulic dampers) driven by a bi-articulated rod [19].

Figure 10.4 Front suspension system modeled in ADAMS-Car.

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Although suspension and chassis systems are responsible for ride and handling characteristics of the vehicle, the tire is ultimately responsible for generating the control forces required to operate the vehicle. All these forces acting on the vehicle are either generated by the tire/road interface or by the aerodynamics effects, where at low speeds the aerodynamics effects can be ignored. Therefore the accuracy of the tire model describing the forces on the tire
road interface is thus of exceptional importance. It should ensure that the simulation model accurately represents the status of an actual vehicle. For the simulation of pneumatic tires, the behavior of the tires has been characterized by different tire models which are incorporated in ADAMS/Tire such as PAC2002 Tyre Model, PAC-TMIE Tyre Model, Pacejka ’89 Models’, Pacejka ’94 Models’, and Fiala Model. The Pacejka models also known as the magic formulae is widely used to describe the tire forces in longitudinal and lateral directions [20]. The normal force of the tire is calculated for a tire deflection as: ( )     Fy 2 R0 Fx 2 2 2 qFcx1 2 qFcy1 1 qFcγ1 γ Fz 5 1 5 qv2 jωj V0 Fz0 Fz0 " (10.12)  2 # ρ ρ Fz0 1 Cz ρ_ 1 qFz2 qFz1 R0 R0 where Fz is the normal force, ω is the rotational speed, γ is the camber angle, and qv2 is the tire stiffness verification coefficient with speed, qFcx1 is the tire stiffness interaction with Fx , qFcy1 is the tire stiffness interaction with Fy , qFcγ1 is the tire stiffness interaction with camber, qFz1 is the tire vertical stiffness coefficient (linear), qFz2 is the tire vertical stiffness coefficient (quadratic), R0 is unloaded tire radius, ρ_ is the tire deflection velocity, and Cz is the vertical tire damping coefficient. When a vehicle undertakes a cornering operation, lateral force is developed at the tire
road contact area. This lateral force is dynamic force due to lateral acceleration of the vehicle and called a cornering force. It highly depends on the tire vertical load. As the vertical load of the tire increases under the cornering condition, the cornering force also increases. In addition, the cornering force also depends on the slip angle of the tire. As the slip angle increases under the same vertical load on the tire, the cornering force also increases.

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10.5 Mechanisms of the wheel imbalance induced vibration Tire/wheel imbalance results from the nonsymmetrical distribution of mass in a tire, wheel or other rotating component of the suspension system. Imbalance can be classified either static (in-plane imbalance) or dynamic (out-plane imbalance). Static imbalance is confined to the wheel plane of the tire. It generates a periodic force variation at the axle in the vertical and longitudinal directions of a driven vehicle. Other sources of tire imbalance are large slips, multiple splices near the same circumferential location around the tire or mass rotation in other rotational components. A nonsymmetrical axis of rotation can also cause a static imbalance. The magnitude of the imbalance force is given by the following equation: F 5 mrω2

(10.13)

where F is the imbalance force, m is the imbalance mass, r is the effective radius, and ω is the rotational speed. While dynamic imbalance results from nonsymmetric mass distribution along the axis of rotation, this produces an overturning moment variation about the longitudinal axis and aligning moment variation about the vertical axis. It can cause a vibration of the vehicle steering system.

10.6 Tire
road interaction caused by dynamic force variation induced by a hexagon tire Tire force variation or nonuniformities is caused by material or manufacturing irregularities that can generate varying forces and moments at the axle of the tire/wheel assembly. These nonuniformities forces and moments are usually measured in either low-speed balancing machines for factory/shop or high-speed balancing machines for research. These forces and moments are periodic and if the rotational speed of the tire is known, then the frequency of any harmonic order at any test speed can be determined by the following equation: f 5 N 3 RPS

(10.14)

where f is the frequency, N is harmonic order, and RPS is the number of revolutions per second of the rotating tire. As the speed of the tire increases, the frequencies of the harmonic orders will also increase. At some point the frequency of a harmonic will

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Automotive Tire Noise and Vibrations

coincide with a resonant frequency of the tire, and the level of the vibration amplitude will increase dramatically. Any force and moment variation can potentially cause a ride disturbance, but the experience has shown the vibrations in the radial (vertical) and longitudinal (fore/aft or drag) directions are the most important contributors of the ride disturbance. In addition, the dynamic imbalance induced aligning moment resonance can cause a torsional vibrational disturbance of the steering wheel of the vehicle. The longitudinal force variation is proportional to the radial runout of the tire and the square of the velocity which is given by F ~ V 2 ΔRK

(10.15)

where V is the vehicle velocity, ΔR is the radial runout, and K is constant.

10.7 Tire
road interface impact force and friction forceinduced vibration The friction between the tire and the pavement is a complex phenomenon depending on many factors such as viscoelastic properties of rubber, pavement texture, temperature, vehicle speed, slip ratio, and normal pressure of the contact patch. Experiments have shown that the friction between the tire and the pavement is dependent on the vehicle speed and on the slip ratio during the vehicle maneuvering processes, such as braking, accelerating, or cornering [21]. The analysis of tire
pavement contacts requires not only understanding the material properties of the tire; but also, the knowledge of the vehicle operation and pavement surface condition. It is expected that the development of tangential contact stress is related to the frictional behavior of the contact surfaces. The formulation of slipping/adhesion zones in the contact area would change depending on the allowed maximum friction force before tire slipping. However, obtaining an accurate description of the frictional relationship is difficult when modeling the tire
pavement interaction. Therefore an appropriate friction model is needed to accurately capture the realistic interaction between the tire and pavement at various tire rolling speeds. The development of the friction force between the rubber and rough hard surface depends on two effects that are commonly described as the adhesion and hysteretic deformation, respectively. The adhesion component is the result of the interface shear and is significant for a clean and smooth surface. The magnitude of adhesion component is related to the

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product of the actual contact area and the interface shear strength. The hysteresis component is the result of the rubber damping losses related to energy dissipation which is caused by surface asperities [22]. Hysteric friction is enhanced with a rise in temperature [23]. Pavement friction is defined as the retarding tangential force developed at the tire
pavement interface that resists longitudinal sliding when braking forces are applied to the vehicle tires or sideways sliding when a vehicle steer around a curve. The sliding friction coefficient is calculated by: μ5

Fh Fv

(10.16)

where μ is the sliding friction coefficient, F is the tangential force at the tire
pavement surface, and Fv is the vertical load on tire. There are a number of friction models which have been developed to characterize the tire
pavement friction behavior for vehicle dynamics and stability control. The magic formula is well-known empirical model used in vehicle handling simulations, and given by [24]: F ðsÞ 5 c1 sinðc2 arctanðc3 s 2 c4 ðc3 s 2 arctanðc3 sÞÞÞÞ

(10.17)

where FðsÞ is the friction force due to braking or lateral force or selfaligning torque due to cornering, c1 , c2 , c3 are model parameters, and s is the slip ratio or slip angle. The slip angle is the angle between the actual rolling direction of the tire and the direction toward which it is pointing. The slip ratio is defined by: s5

V 2 ω:r Vs :100% 5 :100% V V

(10.18)

where s is the slip ratio, V is the vehicle travel speed, ω is the angular velocity of the tire, r is the free rolling radius, and Vs is the slip speed. When the tire is free rolling there is no slip, so the slip speed and slip ratio are both zero. When the tire is locked, the slip speed is equal to the vehicle speed and the slip ratio is 100%.

10.8 Finite element modeling of tire
pavement interaction The modeling of the tire
pavement interaction is generally simulated in three steps. First, the axisymmetric tire model was loaded with uniform tire inflation pressure at its inner surface. Second, the 3D tire model was

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Figure 10.5 Tire and road surface contact model in ABAQUS.

generated and placed in contact with the pavement under the applied load. In order to generate the 3D model of the tire, the symmetric model generation function is used in ABAQUS to transform the 2D model into 3D. As a result of this transformation, all axisymmetric elements CGAX4H and CGAX3H are converted into solid elements C3D8H and C3D6H respectively. Finally, the tire was rolled on pavement with different angular velocities and transport velocities. The tire rolling process is usually modeled using steady-state transport analysis in ABAQUS/ Standard as shown in Fig. 10.5. The tire is designed as an axis-symmetric sketch then the sketch revolved around the axis and then it is mirrored about the symmetric plane. Finally, the tire road surface contact is created. The hyperelasticity is initially modeled by Neo-Hookean and Mooney
Rivlin which is based on the rubber strain energy. The stain energy function with first and second strain invariants can be expressed as following [25]:     W 5 C10 I1 2 3 1 C01 I2 2 3 (10.19) where C10 and C01 are the material constants experimentally determined, I1 and I2 are the first and second invariant of the unimodular component of the left Cauchy
Green deformation tensor and can be defined by [25]: 2

2

I1 5 λ1 1 λ2 1 λ3 I2 5 λ1

ð22Þ

1 λ2

ð22Þ

2

1 λ3

(10.20) ð22Þ

(10.21)

The λ1 is the deviatoric stretch and is given by: λ1 5 J 21=3 λi

(10.22)

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237

where J is the total volume ratio and λi is the principal stretch that is expressed as: λi 5 1 1 εi

(10.23)

where εi is the principal strain. It should be noted that in these formulas for incompressible and isothermal materials, J 5 1, and λ1 λ2 λ3 5 1. In ABAQUS, the hyperplastic elements with reduced integration and hourglassing control are chosen for avoiding shear locking and hourglassing in simulation. The rubber reinforcement for carcass and belts are usually modeled using rebar elements which allows meshing the cord section independent of the host element. This independent meshing avoids unwanted meshing problems, such as small element between composite layers. In order to implement rebar layer, the following information should be known a priori: rebar thickness, spacing, orientation, location, and material properties. The contact force between the tire and the pavement surface consists of two components: one normal to the pavement surface and one tangential to the pavement surface. Therefore the ground is considered an analytical rigid surface, and surface to surface contact interface is established between the tire tread and road in order to avoid tire tread mesh penetrate the ground. The zero-gap contact is achieved by modeling the contact problem using a Lagrange multiplier method. The coulomb friction law is used to describe the tangential interaction between two contacting surfaces. The contact status is determined by nonlinear equilibrium (solved through iterative procedures) and governed by the transmission of contact forces (normal and tangential) and the relative separation /sliding between two nodes on the surfaces in contact. There are three possible conditions for the nodes at the interface: stick, slip, and separation (Eqs. 10.24,
10.26).

0:5 Stick condition : g 5 0; p , 0; and τ 1 211 τ 22 ,μ  p (10.24)

0:5 5μ  p Slip condition : g 5 0; p , 0; and τ 1 211 τ 22

(10.25)

Separation condition: g . 0; p 5 0; and τ 5 0

(10.26)

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Figure 10.6 3D tire
pavement contact model.

where p is the normal force or pressure (compression is negative), g is the gap between two contact nodes, τ 1 and τ 2 are tangential forces or shear stress, and μ is the friction coefficient. By using the above methods, Fig. 10.6 shows 3D tire
pavement contact model for a groove tire (175SR14) [7].

10.9 Auralization models of tire/road noise A powerful method in the product sound design process is to take advantage of the strengths of both recordings and simulations and combine them into auralization. Kleiner et al. [26] defined auralization as the process of rendering audible the sound field of a source in a space, by physical or mathematical modeling, in such a way as to simulate the binaural listening experience at a given position in the modeled space. According to Vorländer [27], auralization is the technique for creating audible sound files from numerical (simulation, measured, synthesized) data. Auralization can be seen as a hybrid model resulting in a time domain simulation. The required level of details in auralization depends on the stage in the development process. In an early development stage audible errors and artifacts may be acceptable as long as the main character of the sound is realistic. Auralization of the structure-borne tire noise is created by combining each DOF of the hub forces and moments, with the impulse response of the corresponding DOF of the binaural transfer functions (BTFs). Then the operationally measured or simulated hub forces in six DOFs are

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filtered through experimentally measured BTFs from the hub to an artificial head in the cabin of the car. To accurately simulate the hub forces and moments, a detailed and complex computer model of a wheel is needed. This requires that not only correct material properties of the compounds and layers of the tire, but also correct material properties of the rim are available. The boundary conditions of the rim/hub interface as well as the tire/road interaction including the texture of the road surface should also be included in the simulation. Due to the complexity, the tire models are simplified to various degrees. By changing the transfer functions or tire material properties, the model can be used to auralize and evaluate tire noise in an early design phase.

10.10 Trends and challenges in computer-aided engineering modeling of tire/road noise CAE is widely considered as an essential part of the noise and vibration refinement process in vehicle development. Therefore the current trends in CAE modeling of the tire/road noise are summarized as: • A significant tire/road noise is expected to be audible as the powertrain noise of modern vehicles tends to decrease or become less. • Increasing efforts are currently being made by the tire and automotive industries to accurately model the tire/road noise. The major challenges in the tire/road simulation are: 1. The greatest challenge is to develop a fast and accurate model for understanding and simulating the tire/road interaction problem. 2. Another challenge is to develop better material models for both rubber and reinforcing components. 3. Tire simulation models have to represent stationary forces and moments due to the tire deflection and longitudinal and lateral slips. 4. Tire asymmetries due to the conicity and plysteer effects have to be included in the tire simulation models. 5. Thermal effect aspects of the tire properties become very important to be understood as they are motivated by car racing applications involving extreme safety maneuvers. 6. Efficient modeling of the tread pattern is very important and influences many tire performances such as traction, wear, hydroplaning, noise, and vibration. 7. Tires are modeled by considering the nonisothermal conditions for the prediction of the temperature rise and energy losses in the tire.

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8. Tire simulation models for the contact pavement materials of soil, snow, mud, and other soft materials, and noise generation models should be developed, especially in high frequency ranges.

10.11 Summary There have been significant efforts made to increase the reliance on CAE technology in modeling tire/road interaction induced noise, accompanied by a trend to reduce or eliminate prototype testing time during the early design phase. These CAE models should integrate the parameters describing both the tire and the road surface. The interaction mechanisms between the tire and road surface are complex, which makes it difficult to be modeled through the extremely complicated mathematical expressions or equations. This chapter explains that there are models able to simulate the tire
pavement interaction induced noise either through all the mechanisms, or through just some of the mechanisms. The chapter has discussed a very broad range of tire/road noise simulation models. These models were compared in terms of the frequency spectrum range, applications, parameters, etc. It can be reasonably assumed from the preceding discussion that the FEM is still the most suitable technique for examining the tire/road interaction induced noise. This is primarily due to the fact that FEM can model the complete tire structure and take into account almost all other relevant physical phenomena. In accompanying this, the BEM is successfully applied to model the sound radiation of the tire.

Nomenclature Ki M FðX; t Þ VðX; t Þ nðωÞ V A L nII nI σ ρsa η12

the stiffness matrix the mass matrix vector originating from the external load vector contains all the nodal degrees of freedom the modal density of a 3D rectangular annular sound field enclosed by rigid wall the volume of the rectangular annular sound field the area of the rectangular annular sound field the total length of the edges of rigid walls the modal density of type 2 the modal density of type 1 the radiation efficiency the surface mass density the coupling loss factor from cylindrical shell to the annular cavity

Computer-aided engineering findings on the physics of tire/road noise

η21 fR v fc L E1 ω η1 η2 η12 Π1 E2 V ω1 ω2 pω ρ0 c W Fz ω γ qFz1 qFz2 qv2 qFcx1 qFcy1 qFcγ1 R0 ρ_ Cz F m r N RPS μ Fh Fv FðsÞ s V Vs W I1 I2

241

the coupling loss factor from the annular cavity to the cylindrical shell the ring frequency the Poisson’s ratio the critical frequency of the cylindrical shell the cylindrical axial width the vibration energy of the tire structure the angular frequency damping loss factor of the tire damping loss factor of the acoustic cavity the coupling loss factor from the tire structure to the tire cavity the power input the acoustic energy of the tire cavity the volume of the cavity the lower limits of the frequency the upper limits of the frequency the time- and space-averaged rms pressure of the cavity the density of sound in air the speed of sound in air the tire width the normal force the rotational speed the camber angle the tire vertical stiffness coefficient (linear) the tire vertical stiffness coefficient (quadratic) the tire stiffness verification coefficient with speed the tire stiffness interaction with Fx the tire stiffness interaction with Fy the tire stiffness interaction with camber the unloaded tire radius the tire deflection velocity the vertical tire damping coefficient the imbalance force the imbalance mass the effective mass the harmonic order the revolutions per second of the tire the sliding friction coefficient the tangential force at the tire
pavement surface the vertical load on tire the friction force due to braking or lateral force the slip ratio or slip angle the vehicle travel speed the slip speed the strain energy function the first invariant of the unimodular component of the left Cauchy
Green deformation tensor the second invariant of the unimodular component of the left Cauchy
Green deformation tensor

242 C10 C01 J λi εi

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the the the the the

material constant material constant total volume ratio principal stretch principal strain

References [1] Donders S. Computer-aided engineering methodologies for robust automotive NVH design [Ph.D. thesis]. K.U. Leuven, Department of Mechanical Engineering, Division PMA, Leuven, Belgium; 2008. Available online: ,http://hdl.handle.net/ 1979/1698.. [2] Surendranath H, Dunbar M. Parallel computing for tire simulations. Tire Sci Technol 2011;39(3):193
209. [3] Nakajima Y. Application of computational mechanics to tire design—yesterday, today, and tomorrow. Tire Sci Technol 2011;39(4):223
44. [4] De Gregoriis D, Naets F, Kindt P, Desmet W. Development and validation of a fully predictive high-fidelity simulation approach for predicting coarse road dynamic tire/ road rolling contact forces. J Sound Vib 2019;452:147
68. [5] Brinkmeier M, Nackenhorst U, Petersen S, Von Estorff O. A finite element approach for the simulation of tire rolling noise. J Sound Vib 2008;309:20
39. [6] Katsikadelis JT. Boundary elements theory and applications. Amsterdam: Elsevier; 2002. XIV 1 336, ISBN 978-0-080-44107-8. [7] Wang G, Zhou H. Boundary element analysis of rolling tire noise. In: International conference on transportation mechanical and electrical engineering (TMEE); 2011. [8] Li T, Burdissso R, Sandu C. Literature review of models on tire
pavement interaction noise. J Sound Vib 2018;420:357
455. [9] Fraggstedt M. Power dissipation in car tyres, licentiate thesis. Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology; 2006. Available at: ,http://www.ave.kth.se/publications/mwl/downloads/TRITAAVE_2006-26.pdfS.. [10] Amoroso F, De Fenza A, Linari M, Di Giulio M, Lecce L. Energy finite element analysis (EFEA) approach for fuselage noise prediction. Noise and vibration: emerging methods. Sorrento; April 1
4, 2012. [11] Mace B. Statistical energy analysis, energy distribution models and system modes. J Sound Vib 2003;264(2):391409. [12] Langley R, Shorter P, Cotoni V. A hybrid FE-SEA method for the analysis of complex vibro-acoustic systems. In: Proceedings of the NOVEM 2005 conference, Saint-Raphael, France; 2005. [13] Langley R. The modal density and mode count of thin cylinders and curved panels. J Sound Vib 1994;169(1):43
53. [14] Mohamed Z, A study of tyre cavity resonance noise mechanism and countermeasures using vibroacoustic analysis [Ph.D. thesis]. School of Aerospace, Mechanical & Manufacturing Engineering, RMIT University, Australia; August 2014. [15] Szechenyi E. Modal densities and radiation efficiencies of unstiffened cylinders using statistical methods. J Sound Vib 1971;19:65
81. [16] Zhang W, Wang A, Vlahopoulos N, Wu K. High frequency vibration analysis of thin elastic plates under heavy fluid loading by an energy finite element formulation. J Sound Vib 2003;263:21
46. [17] Desmet W. Mid-frequency vibro-acoustic modelling: challenges and potential solutions. In: Proceedings of ISMA, Leuven, Belgium; 2002. p. 835
62.

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[18] Mohamed Z, Wang X. A deterministic and statistical energy analysis of tyre cavity resonance noise. Mech Syst Signal Process 2016;70
71:947
57. [19] Wideberg J, Bordons C, Luque P, Mantaras DA, Marcos D, Kanchwala H. Development and experimental validation of a dynamic model for electric vehicle within hub motors. Proc Soc Behav Sci 2014;160:84
91. [20] Pacejka HB. Tire and vehicle dynamics. Butterworth-Heinemann; 2002. [21] Henry JJ. Evaluation of pavement friction characteristics, NCHRP synthesis 291, TRB, National Research Council, Washington, DC; 2000. [22] Wang H, Al-Qadi IL, Stanciulescu I. Effect of friction on rolling tire
pavement interaction. In: USDOT Region V Regional University Transportation Center final report; 2010. [23] Yu M, Wu G, Kong L, Tang Y. Tire
pavement friction characteristics with elastic properties of asphalt pavements. Appl Sci 2017;7:1123. [24] Pacejka HB. Tire and vehicle dynamics. 2nd ed. Butterworth-Heinemann; 2006. [25] Yang X. Finite element analysis and experimental investigation of tyre chrematistics developing strain-based intelligent tyre system [Ph.D. thesis]. Mechanical engineering, University of Birmingham, Birmingham, UK, September 2011. [26] Kleiner M, Dalenbäck BI, Svensson P. Auralization—an overview. J Audio Eng Soc 1993;41(11):861
75. [27] Vorländer M. Auralization; fundamentals of acoustics, modelling, simulation, algorithms and acoustic virtual reality. RWTH edition Springer; 2008.

CHAPTER 11

Tire cavity noise mitigation using acoustic absorbent materials Zamri Mohamed1 and Laith Egab2 1

Faculty of Mechanical and Automotive Engineering Technology, University Malaysia Pahang, Pekan, Malaysia 2 School of Engineering, RMIT University, Melbourne, VIC, Australia

11.1 Introduction Acoustic absorbent material is normally used for noise treatment in a room or vehicle. The goal is either to lower the sound pressure level in the room or to stop the sound from transmitting to the outside. There is a wide range of sound absorbent materials in the market made from natural or synthetic materials. One possible way of eliminating tire cavity noise is to use acoustic absorbent material by placing it in the tire. The only hindrance to that is finding the proper method of attaching the material to the inside of the tire so that it would be durable and effective. This can be regarded as an implementation problem which would include the economic viability of the solution. In this chapter, several options such as perforated plates, porous material, and air gap are used to enhance the reduction of tire cavity sound pressure level. These three options are combined and named as multilayer trim where electrical analogy is adopted to estimate the total increase in sound absorption coefficient (SAC). Then, the normal incidence SACs of several sound absorbent materials measured by the impedance tube method will be compared with those calculated by the existing empirical formulas. Subsequently, polyfelt as one of the said sound absorbent material will be applied inside tire cavity to test its effectiveness. In the end, polyfelt will be reviewed as one of the viable sound absorbent materials that are able to reduce the structure-borne noise caused by tire cavity resonance. The inclusion of polyfelt material would increase acoustic damping loss in a given mathematical formula. Experimental results are included in this chapter to show the achievable reduction of sound pressure level inside the tire after the polyfelt is inserted.

Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00011-8

© 2020 Elsevier Inc. All rights reserved.

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11.2 Sound absorption coefficient theory The SAC is a common quantity used to evaluate sound absorption efficiency of materials. It is defined as the ratio of absorbed energy to the incident energy and represented by α. If the acoustic energy can be absorbed entirely, then α 5 1. α5

Ea ET 512 Ei Ei

(11.1)

where Ea is the absorbed energy, Ei is the incident energy, and ET is transmitted energy. The SAC of a material depends on the material properties and the thickness of all the layers applied on the surface (types of absorbing material, air gaps, etc.). SAC varies with different frequencies.

11.2.1 Airflow resistivity The airflow resistivity is the most important physical characteristic of a porous material. The resistivity of a porous material is caused by the viscous interaction of the material in relation to the frequency [1]. It is directly linked to the fibrous material acoustic properties which allows for the noninvasive measurements of the fiber diameter and material density from acoustical data. There are several models in the literature that relates the airflow resistivity to material’s density and fiber’s diameter. Airflow resistivity can be measured using constant flow or variable flow. The experimental methods for determination of the airflow resistivity of the materials is well established and reported in ISO 9053 and in Ref. [2]. The airflow resistivity is defined as the ratio of the pressure drop to the volume flow rate of the air through a unit thickness porous material: σ5

Δp A qv h

(11.2)

where A is the sample area, h is the sample thickness, Δp is the pressure drop across the sample, and qv is the volume airflow rate through the sample. Experimental measurements of airflow resistivity were performed according to the direct airflow method described in the ASTM C522-3 standard (2003). Fig. 11.1 shows the airflow resistivity testing system. The sample holder of the system is comprised of two sections with a 100 mm diameter transparent tube for good visibility to avoid material sample

Tire cavity noise mitigation using acoustic absorbent materials

247

Figure 11.1 Airflow resistivity experimental setup.

being compressed during the test. The upper section of the material holder is a thin plastic screen disk attached to a screw mechanism which can be used to adjust the height of this section to hold the material with a corresponding thickness in place. The bottom section of the material holder consists of a circular honeycomb disk on which the material sample is placed. The circular honeycomb disk also maintains the flow for it to be laminar. An adjustable airflow pump allows the user to control the airflow to avoid the high velocity turbulent flow entering the test tube. Measurements were conducted for ten different airflow rate values with three sequential repeated tests for every sample to get an average airflow resistivity. The measured values of airflow resistivity with combination of different thickness and density are given in Table 11.1.

11.2.2 Empirical models The empirical models are generally used for the estimation of the bulk acoustic properties namely the complex propagation constant and the characteristic impedance using the known material’s physical parameters or properties such as airflow resistivity, porosity, tortuosity, viscous, and thermal characteristic lengths. In the literature, several empirical models have been developed which estimate the sound impedance of the material assuming that the material has a rigid skeleton [3,4]. These models correlate the characteristic impedance and the propagation constant to the airflow resistivity of the material [5]. These models are summarized as follows:

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Table 11.1 Measured flow resistivity values of polyfelt fiber with thickness and bulk density. Material type

Thickness (mm)

Bulk density (kg/m3)

Measured airflow resistivity (Pa s/m2)

Trim Trim Trim Trim Trim Trim Trim Trim Trim Trim Trim Trim Trim Trim

20 3.97 19.18 3.7 5 4.8 19 19.2 12.3 12.2 20 19.2 10.74 11.75

52.31 123.5 58.89 140.7 96.6 94.4 52.75 54.2 130.3 130.9 54.3 52.79 142.8 132.7

33,474.40 183,145.75 33,900.30 180,137.73 147,581.76 148,141.87 37,329.3 37,073.4 54,393.94 58,343.08 35,231.41 35,694.95 66,145.05 60,521.31

1 2 3 4 5 6 7 8 9 10 11 12 13 14


 Zm 5 ρ0 c0 1 1 C1 X 2C2 2 jC3 X 2C4

(11.3)


 km 5 ω=c0 1 1 C5 X 2C6 2 jC7 X 2C8

(11.4)

X5

ρ0 f σ

(11.5)

where Zm is the characteristic impedance of porous material, km is the complex propagation constant, ρ0 and c0 are the density of the material and speed of sound in air, ω is the angular frequency of the sound waves, σ is the airflow resistivity, and j is the imaginary unit and equal to the square root of 21. Values of the constants C1
C8 are given in Table 11.2 for various materials.

11.2.3 Effect of airflow resistivity Many studies in acoustic performance of automotive interior trim package have been conducted for many years. The factors influencing acoustic performance of sound absorption materials have been investigated in order to improve and optimize the acoustic performance of the sound absorption material. These factors include the airflow resistivity, porosity,

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249

Table 11.2 Values of the constants C1
C8 for various materials. Material type reference

C1

C2

C3

C4

C5

C6

C7

C8

Rockwool/ fiberglass, Delany and Bazley [3] Polyester, Garai and Pompoli [6] Polyurethane foam (low flow resistivity), Dunn and Davern [7] Porous plastic foam (medium flow resistivity), Qunli [8]

0.0571

0.745

0.087

0.732

0.0978

0.700

0.189

0.595

0.078

0.623

0.074

0.660

0.159

0.571

0.121

0.530

0.114

0.369

0.0985

0.758

0.168

0.715

0.136

0.491

0.212

0.455

0.105

0.607

0.163

0.592

0.188

0.544

tortuosity, viscous, and thermal characteristic lengths. Among these factors, the airflow resistivity has been recognized as the most important factor or properties of sound absorption materials. According to Ref. [9] one of the most important parameters that influence the sound absorbing characteristics of a porous material is the specific flow resistance per unit thickness of the material. Airflow resistivity is globally the most sensitive parameter for each feature in the whole frequency range [10]. Therefore it is necessary to determine the airflow resistivity of the acoustic material since the airflow resistivity can have a good indication of the acoustic performance of the material. A new empirical model was proposed previously by the authors [11] and used to calculate the airflow resistivity for the 14 polyfelt materials based on the bulk density and thickness of the polyfelt materials. The new empirical equation is given by σm 5 κργm h2d m

(11.6)

where σm is the airflow resistivity of the polyfelt, ρm is the mass density of the polyfelt, hm is the polyfelt thickness, and k, γ, d are the constants based on the least square fitting of the measured airflow resistivity data. These constants are given by k 5 627:057, γ 5 0:004315, and d 5 1:0186. To study the relationship between the airflow resistivity and the sound absorption, Trim 1 from Table 11.1 was selected with the mass density of

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Absorption coefficient

0.20

0.15

0.10

0.05

0.00

AFR_10000NS/m4 AFR_20000NS/m4 AFR_30000NS/m4 AFR_40000NS/m4 0

100

200

300

400

500

Frequency (Hz)

Figure 11.2 Absorption coefficient of Trim 1 sound absorption material for various airflow resistivities (AFRs).

52.31 kg/m3, thickness of 20 mm and the airflow resistivity being changed from 10,000 to 40,000 Ns/m4. It is observed from Fig. 11.2 that when the airflow resistivity increases, the SAC increases. It is also noticed that the airflow resistivity does not have much effect on SAC at low frequencies less than 200 Hz but have a clear effect in the mid-high frequency ranges.

11.2.4 Effect of layer thickness Example of the relationship between the sound absorption properties and the thickness of polyfelt materials is shown in Fig. 11.3. Trim 1 has the airflow resistivity of 35,000 Ns/m4 and the mass density of 52.31 kg/m3 with its thickness varied from 10 to 40 mm. The SACs are shown in Fig. 11.3. The SAC shows a linear relationship with the added thickness. It is also noticed that increasing the thickness will enhance the SAC in the whole frequency range.

11.3 Absorption coefficient measurement methodologies Several techniques or methods have been developed for measuring the SAC values. In this chapter the impedance tube SAC measurements will

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251

0.6 10 mm 20 mm 30 mm 40 mm

Absorption coefficient

0.5 0.4 0.3 0.2 0.1 0.0

0

100

200

300

400

500

Frequency (Hz)

Figure 11.3 Absorption coefficient of Trim 1 sound absorption material for various thicknesses.

be focused according to Ref. [12], and the reverberation chamber (Alpha cabin) SAC measurement will also be illustrated according to Ref. [13].

11.3.1 Impedance tube method With increasing importance of noise-control and sound quality as an important aspect of product design, acoustic material testing has gained significance. Acoustic material testing is a process by which the acoustic characteristics of materials are determined in terms of absorption, reflection, impedance, and admittance and transmission loss. The normal incidence SAC of test samples is a good measure of the material’s acoustic property. Such data is useful for design of acoustic enclosures, “quiet” rooms, or for noise control/mitigation applications. The normal incident SACs of the samples were measured using the impedance tube (e.g., Bruel and Kjaer), following the two-microphone broadband method in accordance with Ref. [12]. This method involves the decomposition of a broadband stationary random signal into its incident and reflected components. The signal is generated by a sound source, while the incident and reflected components are determined from the acoustic pressures measured by microphones at two locations in the tube. The 100 and 29 mm diameter samples were cut, and the measurements were conducted with

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Figure 11.4 Impedance tube experimental setup for measurement of the normal incident sound absorption coefficient.

the large tube setup in the valid frequency range of 50
1.6 kHz, and with the small tube setup in the valid frequency range of 500
6.4 kHz. The microphone and the tube correction factors were considered and compensated throughout the measurements. At least two corelated results were recorded for averaging and combining low and high frequency plots, with the cross-over frequency range of 500
1600 kHz. The experimental setup in Fig. 11.4 consists of: a Bruel and Kjaer impedance tube type 4206, 1/4 in., Bruel and Kjaer 4187 condenser microphone cartridge with a Bruel and Kjaer 2670 preamplifier, a Bruel and Kjaer 2716C power amplifier, Bruel and Kjaer PULSE software, and the multianalyzer system type 3560.

11.3.2 Alpha cabin Sound absorption materials are widely used in many noise control applications. The acoustic behavior of these materials can be measured using the impedance tube with small size samples but in practical, materials used in noise control applications are not small and incident waves on them are not planar waves. In practice, materials in different sizes and shapes are used in noise control applications and acoustic field is diffuse. Therefore the acoustic performance of the materials is routinely measured using a reverberation chamber which requires bigger samples for the measurement in accordance with international standards ISO 354.

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Figure 11.5 Alpha cabin measurement setup for random incident sound absorption coefficient.

The alpha cabin is a small reverberation chamber with nonparallel walls used to measure random SAC of the test sample as shown in Fig. 11.5. The acoustic absorption of the alpha cabin is very low, and this design ensures a high level of sound insulation to maintain the low levels of background noises. The alpha cabin test required a 1 m 3 1 m material specimen. The procedure developed during the alpha cabin tests employed the B&K PULSE setup to measure T60 decay time which is like a reverberation room measurement according to Ref. [13]. The alpha cabin has three 50-W coaxial loudspeakers for the sound sources and three microphones used to monitor the SPL inside the chamber. SAC measured by the Alpha cabin is calculated from the measurement of the reverberation time with and without the test sample using Sabine’s empirical formula given below:   V 1 1 Sα 5 λ 3 55:3 3 3 2 (11.7) c T2 T1 where λ is correction factor, c is the speed of sound (m/s), V is the volume of the cabin, S is the surface area, α is the SAC, T2 is the reverberation time with sample, and T1 is the reverberation time without sample.

11.4 Tire cavity damping loss Foam or other suitable porous materials filled into the tire cavity would be able to reduce the distinct resonant sound pressure amplitude peak at

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the first tire cavity resonance mode [14
19]. By experiment, it is found in Ref. [16] that filling the mineral fibers into the tire cavity could reduce the transmitted energy by more than 20 dB while it is shown in Ref. [18] that placing sound absorbent material with 30
40 cm in thickness inside the tire cavity could reduce the sound pressure amplitude peak level at the tire cavity resonance frequency by up to 11 dB. According to Ref. [18] the inside wall of the tire is hard which would provide very small acoustic damping loss (given by the cavity damping loss factor). Adding sound absorbing material can increase the cavity damping loss factor and therefore reduce the sound pressure magnitude of the tire cavity resonance. Oblique incidence SAC would best describe the tire cavity damping loss factor. However, in any case the oblique incidence SAC would be less than normal incidence SAC. Tire cavity acoustic damping loss factor or η2 is proportional to the SAC α according to Eq. (11.8) according to Ref. [20]: η2 5

cαS 8πfV

(11.8)

  where V 5 π R02 2 Ri2 W is the tire torus cavity volume and  S 5 2πðR0 1 Ri ÞW 1 2π R02 2 Ri2 is the surface area enclosing the torus cavity. If sound absorbent material layer is inserted into the tire cavity, one can calculate the material SAC from the normal acoustic impedance Z according to Ref. [21] which is given by:   Z 2ρ0 c 2  (11.9) α 5 1 2  Z 1ρ0 c 

11.5 Sound absorption with perforated plates, porous materials, and air gaps Acoustic impedance of perforated plates was presented by Attenborough and Vér [21] where the important terms include the thickness, hole pitch, hole radius, and porosity of the perforated plates and the air contained in the holes. The perforated plates are presented to be same as the porous materials where the complex wave propagation constant and characteristic impedance could be described in terms of the air density, frequency, wave number, and flow resistivity. Perforated plates, porous materials, and air gap are commonly combined for enhancing sound absorption. In fact, the use of multilayer

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255

materials such as perforated plates, porous materials, and air spaces was studied as a way to enhance sound absorption effects and reduce the dependency to only one material. The application of several materials could reduce the material quantity needed for porous materials to achieve the same sound absorption effects in the intended frequency range. Analytical acoustic transmission analysis that could deal with several compartments of multilayer acoustic absorber was developed in Ref. [4]. The absorption coefficient of a multilayer absorbent is obtained from Ref. [22] using electro-acoustic analogy. As in Refs. [3,4], the acoustic impedance of the mth perforated plate layer is given as Zmp in Eq. (11.10). 2sffiffiffiffiffi 39 8 ! ! > > p ffiffiffiffiffiffiffiffi ffi t t > ρ0 ωρ0 4 8υ pm pm > > 5> > > 8υω 1 1 1 j 1 t Z 5 1 δ 1 1 mp pm m > > > > ω ε 2a ε 2a > > m m m m > > > > > > < = 2 πam εm 5 2 > > > > bm > > > > > > > > > > > > δ 5 0:85 3 2a 3 θ ð ε Þ m m m m > > > > p ffiffiffiffiffi : ; pffiffiffiffiffi θm ðεm Þ 5 1 2 1:47 εm 1 0:47 ε3m (11.10) where am , bm ; tpm are the hole radius, hole pitch, and thickness of the mth layer of the perforated plates respectively. υ is the kinematic viscosity of air at the room temperature. The characteristic impedance of the nth layer 0 air space in the multilayer material is given by Zna while kna is the wave propagation constant. 0

Zna 5 ρ0 c kna 5 jka

(11.11)

The acoustic impedance of the nth layer air gap backed by rigid wall is given by Zna in Eq. (11.12). Zna 5 2 jρ0 ccothðka tan Þ

(11.12)

where tan is the depth of the nth layer air gap and ka 5 ω=c.

11.6 Application to tire cavity To calculate the acoustic pressure in the tire cavity with the application of sound absorbent material, a similar method from the previous chapter can

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Figure 11.6 Calculated sound pressure level amplitude at the toroid cavity center point of r 5 (Ro 1 Ri)/2, z 5 W/2, θ 5 0 (200
270 Hz).

be implemented by solving Equations (9.18), (9.20), and (9.23). The cavity loss factor ηn is replaced by the new loss factor as that in Eq. (11.8) because of the sound absorbent layer addition. Taking Trim 1 sound absorption material, for example, the difference between the calculated acoustic pressure response for the case without and with Trim 1 is shown in Fig. 11.6. In this simulation, the addition of the Trim 1 onto the inner surface of the tire tread causes the cavity sound pressure amplitude peak to reduce by around 6
10 dB. The amplitude reduction is less than the achievable 20 dB reported by Haverkamp [16] using a very good absorbent mineral fiber. In Ref. [16] the material was used to fill the entire cavity. Nevertheless, a reduction of 10 dB is equivalent to 10 times the power ratio reduction. The inclusion of Trim 1 sound absorption material affected the 215 Hz peak more than the peak at 256 Hz. On the contrary, the tire structure damping loss affected the 256 Hz peak more than the peak at 215 Hz. The acoustic and structural damping does not affect independently the two peaks of the sound pressure amplitude curve as the response is coupled.

11.7 Multilayer configuration design To mitigate the effect of tire cavity noise, it is imperative to have maximum absorption at the frequency between 200 and 250 Hz. Using

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257

Figure 11.7 Example of a multilayer sound absorbent layer arrangement with perforated plate and its analogy of multilayer impedance to electrical impedance.

multilayer sound absorbing materials would reduce tire cavity noise more effectively than using a single-layer. From the experimental data in Ref. [22], there were three types of absorbers tested. The first type was constructed with three layers of perforated panel separated by air gap. Type two was constructed with three layers of perforated panels separated by porous materials while the third one was the combination of the first and second types. The SAC values for all the three types were 0.14
0.17, 0.30
0.40, and 0.70
0.85 respectively in the frequency range of 200
250 Hz. Multilayer absorbers were also tested where a configuration with good SAC was obtained where all three segments (i.e., perforated plate, porous material, and air gap) were incorporated. Providing larger air gap and more porous materials would generally produce higher noise absorption. In regard to the usage of the noise absorbent materials inside the tire, it is preferred that the materials are thin and durable. Therefore the minimum number of layers with the highest absorption coefficient should be sought. In the sound absorbing configuration in this example, two perforated plates and two types of porous material are layered against a rigid wall as shown in Fig. 11.7. The equivalent acoustic impedance Γe1 of the first layer of the perforated plate (Plate_1) and the porous material (Trim_1) backed by rigid wall can be regarded to be equivalent to the series connection addition from electrical analogy. Γe1 5 Γp1 1 Γt1

(11.13)

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where Γp1 and Γt1 are the surface acoustic impedance of the first layer of the perforated plate (Plate_1) and the porous material (Trim_1). Due to the sound pressure continuity, the equivalent acoustic impedance Γe1 can be regarded to be in parallel connection with the surface acoustic impedance of the second layer of porous material (Trim_2). Hence, the equivalent acoustic impedance Γe2 induced by the first layers of perforated plate and porous material together with the second layer of porous material can be expressed as Γe1 5

Γe1 Γt2 Γe1 1 Γt2

(11.14)

where Γt2 is the surface acoustic impedance of the second layer of porous material (Trim_2). The same calculation procedures can be repeated to the next layer of perforated plate and porous materials in analysis. The final equivalent multilayer acoustic impedance can be denoted as Γr once all the layers in consideration have been computed. The acoustic absorption coefficient α of the multilayer acoustic absorber can be obtained as   Γr 2ρ0 c 2   α512 (11.15) Γr 1ρ0 c 

11.8 Analytical simulation of the multilayer sound absorber In order to develop a design configuration to mitigate the tire cavity noise, three cases are studied. The first one used Trim 1 and Trim 2 backed with a rigid wall, the second used Trim 1, Trim 2, and air gap backed with a rigid wall and the third one used perforated plate, Trim 1, Trim 2, and air gap backed with a rigid wall. The addition of air gap to Trim 1 and Trim 2 improved the SAC as shown in Fig. 11.8B. Adding an air gap between the layers and the cavity wall would increase the absorption coefficient compared to the case with only the layers against the cavity wall. Fig. 11.8A shows the SACs for Trim 1 and Trim 2 calculated separately. To investigate on the improvement of adding perforated plate as illustrated in Fig. 11.9, the associated SACs are also calculated but its effect is small for changing hole pitch and plate thickness parameters except by changing the hole radius. Even by varying the hole radius, the absorption coefficient would not get any better than 0.82 at 500 Hz as shown in Fig. 11.10A and B. The kinematic viscosity of air at the room temperature

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259

Figure 11.8 (A) Calculated sound absorption coefficient for the case with Trim 1 only and Trim 2 only. (B) Calculated sound absorption coefficient of Trim 1 and Trim 2 for the case with and without 1 cm air gap.

Figure 11.9 Multilayer configuration with perforated plate, sound absorbent material, and air gap. (A)

(B)

0.9

0.8

0.8

0.7

0.7

0.6

Absorption

0.6

Absorption

0.9

0.5 0.4

0.5 0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

50

100

150

200 250 300 Frequency (Hz)

350

400

450

500

0

0

50

100

150

200 250 300 Frequency (Hz)

350

400

450

500

Figure 11.10 (A) Calculated sound absorption coefficient for (Trim 1 1 Trim 2 1 1 cm Air gap) with perforated plate (hole radius 5 10 mm, hole pitch 5 20 mm, plate thickness 0.1
1 mm by 0.1 mm increment). (B) Calculated sound absorption coefficient for (Trim 1 1 Trim 2 1 1 cm Air gap) with perforated plate (plate thickness 5 0.1 mm, hole radius 5 10 mm, hole pitch 20
50 mm by 5 mm increment).

Automotive Tire Noise and Vibrations

260 (A)

(B)

0.9

0.9 0.8

0.8 0.7

0.7

0.6

Absorption

Absorption

0.6 0.5 0.4

0.5 0.4 0.3

0.3 0.2

0.2

0.1

0.1

0

0

50

100

150

200 250 300 Frequency (Hz)

350

400

450

500

0

0

50

100

150

200

250

300

350

400

450

500

Frequency (Hz)

Figure 11.11 (A) Calculated sound absorption coefficient for (Trim 1 1 Trim 2 1 1 cm Air gap) with perforated plate (plate thickness 5 0.1 mm, hole pitch 5 60 mm, hole radius 5
30 mm by 5 mm increment). (B) Calculated sound absorption coefficient for (Trim 1 1 Trim 2 1 Air gap) with air gap varied from 10 to 100 mm by 10 mm increment.

is taken as 18.6 3 1026 Pa s. To further investigate the effect of varying the air gap thickness, the SAC of the absorber configuration with Trim 1, Trim 2, and air gap is calculated when the air gap varied from 1 to 10 cm. The result is shown in Fig. 11.11 where there is a significant improvement when the air gap is increased by a step of 1 cm for every curve in the 0
300 Hz frequency range.

11.9 Using finite element simulation Finite element simulation can be conducted to quickly determine the effects of several parameters on the sound pressure amplitude peak at the resonance. For example, mean power spectral density (PSD) inside the tire cavity can be obtained from a number of points (the more points the better). In this case, when the Trim 1 thickness is changed from 1 to 7 cm both the peaks at 214 and 255 Hz decreases linearly as shown in Fig. 11.12A. Next, the Trim 1 thickness is to be held constant while Trim 1 mass density and air gap thickness varies. In Fig. 11.12B, both the sound pressure amplitude peaks at 214 and 255 Hz stay constant for Trim 1 mass density from 30 to 150 kg/m3. For the case with the air gap being increased as shown in Fig. 11.13, the sound pressure amplitude peak at 214 Hz does not reduce as much as the sound pressure amplitude peak at 255 Hz when the air gap increases. For the 255 Hz sound pressure amplitude peak, the air gap thickness of 2 cm seems to be sufficient as

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Figure 11.12 (A) The sound pressure PSD amplitude peak values (mean of 16 points inside the tire cavity) at 214 and 255 Hz versus the Trim 1 thickness. (B) The sound pressure PSD amplitude peak values (mean of 16 points inside the tire cavity) at 214 and 255 Hz versus the Trim 1 mass density where the Trim 1 thickness was held constant at 20 mm.

Figure 11.13 The sound pressure PSD amplitude peak values (mean of 16 points inside the tire cavity) at 214 and 255 Hz versus the air gap where the Trim 1 thickness was held constant at 20 mm.

increasing more air gap thickness would not reduce the sound pressure amplitude peaks further.

11.10 Experiments on tires There were studies conducted to realize the tire cavity noise mitigation using absorbent materials [14,16,18]. The materials were either fitted onto the rim or attached onto the tire inner surface. Tire acoustic tests were conducted in static and rolling conditions. In this study, it was found to be difficult to fit a tire onto a rim when the rim was attached with absorbent material (foam). As shown in Fig. 11.14, the material would easily

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Figure 11.14 (A) Foam layer on the rim. (B) Polyfelt layer inside tire.

disintegrate during the fitting process because of the limited space on the rim surface. The depression on the rim surface which is often called the rim drop center is designed to make the mounting and dismounting of the tire easy. Therefore even though it would provide a suitable guide in placing the foam, the fitting process would damage the foam. It was also difficult to know whether the foam would be properly seated after the fitment due to the tire bead movement across the rim drop center. Therefore adding foam onto the rim surface was considered unfeasible in comparison to placing the foam on the tire inner surface. The effect of placement of absorbent materials onto the tire inner surface was studied previously but without any guideline for the attachment method and the detailed parameters of materials [18]. The experiment was conducted for this chapter without checking the conformance to tire manufacturer guideline and specification. So it is not intended to find the best way to reduce the cavity resonance noise but to verify the numerical prediction conducted in the previous sections.

11.11 Experimental modal test (impact hammer test) A roving impact test is performed to get more data to observe the force transmissibility effect to the hub after the application of polyfelt to the inner tire surface. Frequency response functions are measured by B&K 4506B tri-axial accelerometer mounted on the tire-wheel hub with 80 impact locations around the tire. The measured frequency response functions are then exported to MEScope software to calculate the mode shape and display its visualization. The frequency response function amplitude plots are shown in Fig. 11.15 for 0
800 Hz frequency range.

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Figure 11.15 Tire-cavity-rim FRF amplitude curves from the impact test results installed with Trim 1 onto the inner surface of the tire. FRF, Frequency response function.

When the tire inner surface is installed with the Trim 1 layer (polyfelt), the resonance amplitude peaks of the frequency response functions of the tire-wheel are decreased in comparison to those without the layer being installed. The vibration suppression is obvious at 226
228 Hz (no peaks observed). Other peaks seen in Fig. 11.15 between 0 and 150 Hz and around 180, 200, and 250 Hz come from the tire structural resonance modes and steel support stand mode respectively.

11.12 Experimental modal analysis test with a shaker excitation Sometimes, the energy supplied by the impact hammer test may not excite all the structural modes of the tire. According to Ref. [23], better results were obtained at the frequencies above the first tire cavity modal frequency via the use of electrodynamic shaker. For the experiment as shown in Fig. 11.16, more excitation energy is required to be able to demonstrate the difference of the cavity sound pressure peak magnitude before and after addition of the Trim 1. Still, the shaker excitation in this experiment does not resemble the actual tire
road interaction where one can apply a larger shaker table for this purpose. Using the shaker however is sufficient to show the difference of the cavity sound pressure peak magnitude for the case with and without the Trim 1. Therefore Trim 1 is

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Figure 11.16 Shaker excitation setup on the deformed tire.

attached onto the inner surface of the tire for the cases of the unloaded and loaded tire where the tire was loaded with L-block and the tire pressure are set at 30 and 19 psi. Fig. 11.16 shows the experimental setup using the shaker excitation for the case of the loaded or deformed tire. It is seen from Fig. 11.17 that only one cavity sound pressure spectrum amplitude peak occurs around 225 Hz. It is seen from Fig. 11.18 that two cavity sound pressure spectrum amplitude peaks occur at frequencies of 224 and 227 Hz where the vertical mode of 227 Hz has a higher peak frequency than the fore-aft mode of 224 Hz for both the inflation pressures. The cavity sound pressure spectrum amplitude peak shows as distinct peak at 227 Hz. With addition of the Trim 1, the cavity sound pressure resonance peak has been suppressed for both the inflation pressures. Specifically, at 30 psi the hub acceleration was suppressed by approximately 10 dB. While the tire inflation pressure does not affect tire cavity resonance frequency as previously understood, it does contribute to higher peak magnitude at the cavity mode frequency. The rise in the inflation pressure produces a stiffer tire wall structure and therefore more rigid and effective at reflecting the sound wave. This causes the cavity to have more energy as a result of less energy transfer to the tire structure and therefore more energy transfer to the hub. Even with addition of the Trim 1, more hub acceleration was measured around 224 Hz at 30 psi than that at 19 psi.

11.13 Design of experiment (Taguchi) Taguchi method analysis is conducted to rank the effect of the variation in Trim 1 and Trim 2 thickness, Trim 1 and Trim 2 mass density as well

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Figure 11.17 Acceleration frequency response function amplitude curves at the hub for the case with (dash line) and without Trim 1 (solid line) at 19 and 30 psi tire pressure under the condition of the unloaded tire.

as the presence of air gap on the sound pressure PSD amplitude peak values at 214 and 255 Hz. This Taguchi analysis would rank the most critical factor that could reduce the tire cavity resonance sound pressure amplitude peak according to the most and least effective factors. Only two different mass densities and thicknesses are studied for the case with and without the air gap. The values of R represent the severity of the factors to the sound pressure PSD amplitude peak values. The bigger the R value, the more effective that factors in reducing the sound pressure PSD amplitude peak values. Tables 11.3 and 11.4 lists the Taguchi matrixes for study of the effect of the Trim 1 and Trim 2 thickness, Trim 1 and Trim 2 mass density, and air gap on the PSD amplitude peak value at 214 and 255 Hz where five variables are Trim 1 and Trim 2 thickness, Trim 1 and Trim 2 mass

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Figure 11.18 Acceleration frequency response function amplitude curves at the hub for the case with Trim 1 (dash line) and without Trim 1 (solid line) at 19 and 30 psi tire pressure under the condition of the loaded tire. Table 11.3 Taguchi matrix for analysis of the effect of the Trim 1 and Trim 2 thickness, Trim 1 and Trim 2 mass density, and air gap on the PSD amplitude peak value at 214 Hz. Exp. No.

Trim 1 thickness

Trim 2 thickness

Trim 1 density

Trim 2 density

Air gap

PSD (dB) at 214 Hz

1 2 3 4 5 6 7 8 Ave 1 (dB) Ave 2 (dB) R

1 cm 1 cm 1 cm 1 cm 2 cm 2 cm 2 cm 2 cm 71.28 69.38 1.90

1 cm 1 cm 2 cm 2 cm 1 cm 1 cm 2 cm 2 cm 70.49 70.18 0.31

50 kg/m3 50 kg/m3 100 kg/m3 100 kg/m3 100 kg/m3 100 kg/m3 50 kg/m3 50 kg/m3 70.38 70.28 0.10

50 kg/m3 100 kg/m3 50 kg/m3 100 kg/m3 50 kg/m3 100 kg/m3 50 kg/m3 100 kg/m3 71.22 69.44 1.78

0 cm 1 cm 0 cm 1 cm 1 cm 0 cm 1 cm 0 cm 71.19 69.47 1.72

73.4 69.5 72.6 69.5 69.5 69.4 69.3 69.3

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Table 11.4 Taguchi matrix for analysis of the effect of the Trim 1 and Trim 2 thickness, Trim 1 and Trim 2 mass density, and air gap on the PSD amplitude peak value at 255 Hz. Exp. #

Trim 1 thickness

Trim 2 thickness

Trim 1 density

Trim 2 density

Air gap

PSD (dB) at 255 Hz

1 2 3 4 5 6 7 8 Ave 1 (dB) Ave 2 (dB) R

1 cm 1 cm 1 cm 1 cm 2 cm 2 cm 2 cm 2 cm 71.78

1 cm 1 cm 2 cm 2 cm 1 cm 1 cm 2 cm 2 cm 70.74

50 kg/m3 50 kg/m3 100 kg/m3 100 kg/m3 100 kg/m3 100 kg/m3 50 kg/m3 50 kg/m3 70.63

50 kg/m3 100 kg/m3 50 kg/m3 100 kg/m3 50 kg/m3 100 kg/m3 50 kg/m3 100 kg/m3 71.53

0 cm 1 cm 0 cm 1 cm 1 cm 0 cm 1 cm 0 cm 73.21

76.0 68.5 71.2 67.5 67.5 71.0 67.5 70.6

69.14

70.18

70.29

69.39

67.71

2.64

0.56

0.34

2.14

10.51

density, and the air gap thickness in addition to two dummy variables are designed as seven input variables for eight tests in the L8 Taguchi matrix. The output target variable is set as the sound pressure PSD amplitude peak value at 214 or 255 Hz. For the 214 Hz peak, Trim 1 thickness is found to be the most effective parameter to be able to reduce the sound pressure PSD amplitude peak value. This is followed by the Trim 2 mass density and the presence of the air gap. The Trim 1 mass density has the least effect on the sound pressure PSD amplitude peak value at 214 Hz. The best combinations of the parameters are Experiments 7 and 8 where Trim 1 and Trim 2 of 2 cm thickness are used, the mass density of 50 kg/m3 is used for Trim 1; the mass density of either 50 or 100 kg/m3 can be used for Trim 2 and the air gap of either 0 or 1 cm can be used. The best combinations of the parameters lead to the low sound pressure PSD amplitude peak value of 69.3 dB at 214 Hz. For the 255 Hz peak, the air gap has the largest effect on the sound pressure PSD amplitude peak value, followed by the Trim 1 thickness and Trim 2 mass density. The Trim 1 mass density and Trim 2 thickness have the least effect on the sound pressure PSD amplitude peak value at 255 Hz. The best combinations of the parameters are Experiments 4 and 5 where the mass density of 100 kg/m3 and the air gap of 1 cm are used. The mass density of either 50 or 100 kg/m3 can be used for Trim 2. The thickness of either 1 or 2 cm can be used for Trim 1 and Trim 2.

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Alternatively, the best combination of the parameters is in Experiment 7 where the mass density of 50 kg/m3 and the thickness of 2 cm are used for both Trim 1 and Trim 2 with the air gap of 1 cm. The best combinations of the parameters lead to the low sound pressure PSD amplitude peak value of 67.5 dB at 255 Hz.

11.14 Summary In this chapter, the use of acoustic absorbent material to mitigate tire cavity noise is presented by means of theoretical modeling, finite element simulation, and laboratory experiment. The inclusion of a felt layer in the tire cavity is represented by addition of the acoustic damping loss factor into the sound pressure response function. The damping loss factor is calculated by finding the SAC values for specific sound absorbent material. Several felt materials are measured for their normal incidence SAC using the two-microphone impedance tube system. In one of the experiments, with a felt around 20 cm in thickness, the reduction of the sound pressure level at the cavity resonance frequency is found to be around 6
10 dB. Multilayer approach is introduced where the multilayer sound absorption characteristics of felt materials is calculated using electrical analogy empirical model. The effect of varying the trim thickness and mass density as well as adding air gap and perforated plate is shown. Taguchi analysis is performed to rank the effect of changing the trim thickness and mass density as well as the presence of air gap on the sound pressure level peaks at 214 and 255 Hz.

Nomenclature α Ea Ei ET σ A h Δp qv Zm km ρ0 c0

the the the the the the the the the the the the the

sound absorption coefficient absorbed energy incident energy transmitted energy airflow resistivity sample area sample thickness pressure drop across the sample volume airflow rate through the sample characteristic impedance of the porous materials complex propagation constant density of sound in air speed of sound in air

Tire cavity noise mitigation using acoustic absorbent materials

ω j σm ρm hm k γ d λ V S T1 T2 η2 Z Zmp am bm tpm υ 0 Zna kna tan Γe1 Γp1 Γt1 Γe2 Γt2 Γr

the the the the the the the the the the the the the the the the the the the the the the the the the the the the the

269

angular frequency imaginary unit and equal the square root of 21 airflow resistivity of the polyfelt polyfelt density polyfelt thickness constant based on the least square fitting of the measured airflow resistivity constant based on the least square fitting of the measured airflow resistivity constant based on the least square fitting of the measured airflow resistivity correction factor volume of the cabin surface area reverberation time without sample reverberation time with sample tire cavity damping loss factor normal acoustic impedance acoustic impedance of mth perforated plate layer hole radius hole pitch thickness of mth perforated plate layer kinematic viscosity of air at room temperature characteristic impedance of the nth layer air space in the multilayer material wave propagation constant depth of nth layer air gap equivalent acoustic impedance of the first layer of the perforated plate (Plate_1) surface acoustic impedance of the first layer of the perforated plate (Plate_1) surface acoustic impedance of the first layer of the porous materials (Trim_1) equivalent acoustic impedance of the first layer of the perforated plate (Plate_1) surface acoustic impedance of the first layer of the porous materials (Trim_2) final equivalent multilayer acoustic impedance

References [1] Sagartzazu X, Hervella-Nieto L, Pagalday JM. Review in sound absorbing materials. Arch Comput Methods Eng 2008;15:311
42. [2] ASTM C52. Acoustics-materials for acoustical applications-determination of airflow resistance; 1991. [3] Delany ME, Bazley EN. Acoustic properties of fibrous absorbent materials. Appl Acoust 1970;3:105
16. [4] Lee F-C, Chen W-H. Acoustic transmission analysis of multi-layer absorbers. J Sound Vib 2001;248:621
34. [5] Bies DA, Hansen CH. Engineering noise control: theory and practice. 4th Edition Boca Raton, FL: CRC Press; 2009. [6] Garai M, Pompoli F. A simple empirical model of polyester fibre materials for acoustical applications. Appl Acoust 2005;66:1383
98. [7] Dunn IP, Davern WA. Calculation of acoustic impedance of multi-layer absorbers. Appl Acoust 1986;19(5):321
34. [8] Qunli W. Empirical relations between acoustical properties and flow resistivity of porous plastic open-cell foam. Appl Acoust 1988;25(3):141
8.

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[9] Seddeq H. Factors influencing acoustic performance of sound absorptive materials. Aust J Basic Appl Sci 2009;3(4):4610
17. [10] Ouisse M, Ichchou M, Chedly S, Collet M. On the sensitivity analysis of porous material models. J Sound Vib 2012;331:5292
308. [11] Egab L, Wang X, Mazlan SK, Choo ML. Development of empirical models of polyfelt fibrous materials for acoustic applications. Int Rev Mech Eng 2013;7:939
46. [12] ASTM E1050-08. Standard test method for impedance and absorption of acoustical materials using a tube, two microphones and a digital frequency analysis system; 2008. [13] ASTM C423-09a. Standard test method for sound absorption and sound absorption coefficients by the reverberation room method; 2009. [14] Sakata T, Morimura H, Ide H. Effects of tire cavity resonance on vehicle road noise. Tire Sci Technol 1990;18(2):68
79. [15] Richards TL. Finite element analysis of structural-acoustic coupling in tyres. J Sound Vib 1991;149(2):235
43. [16] Haverkamp M. Solving vehicle noise problems by analysis of the transmitted sound energy. In: Proceedings of the 2000 international conference on noise and vibration engineering ISMA25, Leuven; 2000. p. 1339
46. [17] Molisani LR, Burdisso RA, Tsihlas D. A coupled tire structure/acoustic cavity model. Int J Solids Struct 2003;40:5125
38. [18] Fernandez ET. The influence of tire air cavities on vehicle acoustics [Ph.D. thesis]. KTH University, Stockholm, Sweden. [19] Jessop AM, Bolton JS. Tire surface vibration and sound radiation resulting from the tire cavity mode. Tire Sci Technol 2011;39(4):245
55. [20] Chen SM, Wang DF, Zan JM. Interior noise prediction of the automobile based on hybrid FE-SEA method. Math Probl Eng 2011;20. [21] Attenborough K, Vér IL. Sound-absorbing materials and sound absorbers. In: Vér IL, Beranek LL, editors. Noise and vibration control engineering: principles and applications. Second Edition John Wiley & Sons Inc; 2006. [22] Congyun Z, Qibai H. A method for calculating the absorption coefficient of a multi-layer absorbent using the electro-acoustic analogy. Appl Acoust 2005;66:879
87. [23] Chittilla K, Yeola Y, Tiwari A, et al. Effect of excitation methods on experimental modal analysis of passenger car tire. SAE International; 2013.

CHAPTER 12

Statistical energy analysis of tire/road noise Xiandong Liu and Qizhang Feng Beihang University, Beijing, P.R. China

12.1 Introduction Statistical energy analysis (SEA) method was proposed in 1960s to meet the urgent requirement of analyzing the intensive modes generated by broadband excitation (jet noise and aerodynamic noise) of the space launch vehicles. Modal analysis and finite element method (FEM) are suitable to analyze the lower order modes of a structure, but for a complex system, which contains the coupling effect of sound field and solid structure, complex vibration transmission paths and a large number of dense modes, these methods encounter insurmountable difficulties. In SEA method, the energy of vibration and sound is recognized as basic dynamic parameter where the excitation, the characteristic, and dynamic response of a system are all regarded as statistical quantities. The relations of these statistical quantities with geometry, material, and medium characteristics are constructed by means of theoretical analysis. This method provides an effective way for studying high-frequency vibration and analyzing high-order dense modes, and is of significance in the fields of structural vibration and noise control, fault diagnosis, and so on. In 1975 Lyon (one of the main contributors to the development of SEA) [1] systematized the method and published a classic work, which laid a firm foundation for the wide application of SEA method. Later, SEA method was applied in the field of vehicle NVH. DeJong [2] established a SEA model of vehicle, which included powertrain excitation, interaction between tire and road, and action of wind on vehicle. The prediction of noise by this model is in good agreement with the test results. Kompella and Bernhard [3] studied the differences between the frequency response functions of different cars in the low frequency range and the high frequency range, and the results showed that the differences were small in the low frequency range. In the high frequency range, the Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00012-X

© 2020 Elsevier Inc. All rights reserved.

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differences were large and the modal response characteristics were fuzzy. Chen et al. [4] used a hybrid method (including analytical and test-based SEA models) to simulate a light truck. Moeller et al. [5] demonstrated a verification method of the vehicle SEA models over the frequency range of 200
5000 Hz. Dong et al. [6] developed a mathematical model to evaluate design options for control of the road noise transmission into the interior of a passenger car based on SEA method, and the effectiveness of different noise control treatments was simulated and evaluated through experimental tests. The research of automotive higher frequency vibration and noise by using SEA mainly focuses on the vehicle’s body and interior noise, and relatively few focuses are placed on the tire. From public literature on vibration and noise model of a tire, we may see that analytical method and FEM for studying the tire noise and vibration in the low frequency range dominate. Vinesse and Nicollet [7] applied the functional analysis method to investigate a rotating tire. The calculated results are in good agreement with the experimental ones in the range of 60
200 Hz. Kropp [8] used the ring model to simulate an unloaded tire. This model has a satisfactory prediction result below 250 Hz, but cannot predict tire’s dynamic behavior above 250 Hz. These analytical models can provide certain understandings about the tire’s dynamic behavior over the low or intermediate frequency range, however, cannot do well over high frequency range, especially for the tire/road noise from 250 to 5000 Hz. Lee and Ni [9] established a SEA model of a tire for investigating the structure-borne noise, and attempted to made the model capable of analyzing tire’s dynamic behavior in the higher frequency range. And their results are indeed improved relative to ones in previous study. Boulahbal et al. [10] focused on establishment of tire’s SEA model, and used modal power to determine the size of subsystems in the model. The results showed that a large number of SEA subsystems were required due to the larger damping in a tire, which obviously attenuated propagation of vibration energy, and in the frequency range where SEA would be useful, the tire’s vibration response was concentrated around 1/3 of the tire size close to the excitation location. Kameyama et al. [11] studied the applicability of theoretical coupling loss factor in SEA method and conducted experimental evaluation on the coupling loss factor of three kinds of tires. Then the analytical coupling loss factor in the SEA model was compared with the experimental results. The results showed that the analytical SEA model can be established in the low frequency range below about 200 Hz.

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Hybrid deterministic-statistical analysis method of vibro-acoustic systems has also been developed in which various components in complex vibration-acoustic systems can be modeled deterministically or statistically. In this method, the statistical model of structure can be combined with the finite element model of acoustic cavity, or a statistical acoustic cavity. And the coupling loss factor can be found by using the hybrid method [12]. FEM is suitable for low frequency analysis while SEA method generally for the high frequency analysis. For the intermediate frequency range of the acoustic-vibration coupled system, Yan et al. [13] proposed a hybrid FE-SEA method, and tested the analysis results by using Monte Carlo simulation. Wang [14] proposed a new deterministic-statistical analysis approach based on a combination or hybrid of deterministic analysis and SEA. This approach has the potential in place of the time-consuming Monte Carlo simulation. SEA method can be used to investigate the noise and vibration of tire. In this chapter, the basic principle of SEA is introduced, and the modeling process and model parameters in SEA are also explained and discussed. Two kinds of tire SEA models with/without cavity and their simulation results are described and analyzed. At last, the application of SEA method in the tire/road noise modeling and simulation of a passenger car is introduced.

12.2 Basic principle of statistical energy analysis The “statistical” in statistical energy analysis means that the research object is extracted from a system described by stochastic parameters. SEA method cannot predict the exact response at a certain position of a system, but can predict the response level of a system more accurately in the statistical sense. The “energy” in statistical energy analysis means that energy is used to describe the dynamic states of various dynamic subsystems in a system. In SEA method, the relations among the coupling subsystems are depicted by using power balance equations. To define energy as independent dynamic variable may unify the expressions of dynamic behaviors of structure and sound field, and be convenient to describe the coupling problems between structure and sound field. Therefore in SEA, the prediction and analysis of the energy in subsystems are first performed; subsequently, the statistics of vibration or sound field in each subsystem are extracted from the obtained energy [1,15].

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Generally speaking, the first step in SEA method is to decompose the complex coupled system into several subsystems easy to analyze in the statistical sense, then the SEA model capable of clearly expressing the characteristics of the input, storage, loss, and transmission of vibrational or sound energy is established. Through solving the SEA model, the energy and statistical parameters of vibration or sound field in each subsystem can be obtained.

12.2.1 Power balance equation of statistical energy analysis In order to illustrate the basic principle of SEA, a SEA model including two subsystems is taken as an example. The schematic diagram of energy flow for the model is shown in Fig. 12.1 [16]. In Fig. 12.1, P1 and P2 denote the power inputs into Subsystems 1 and 2 from outside, respectively; P12 is the power flowing from Subsystem 1 into Subsystem 2 and vice versa; P1d and P2d are the power dissipations caused by the damping of Subsystems 1 and 2. Then, the steady-state power balance equations for both the subsystems are written as follows:
P1 1 P21 5 P12 1 P1d (12.1) P2 1 P12 5 P21 1 P2d

Figure 12.1 Schematic diagram of power flow.

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Assuming that the power dissipation of a subsystem is proportional to its stored energy, we have:
P1d 5 ωη1d E1 (12.2) P2d 5 ωη2d E2 where ω is the angular frequency; η1d and η2d are the damping loss factors of Subsystems 1 and 2, and they are generally related to the structural damping, the structural acoustic radiation, and the energy loss at connection position; E1 and E2 are the total energy stored in Subsystems 1 and 2, respectively. Additionally, the power flowing between subsystems is also assumed to be proportional to the energy stored in the subsystems; thus we have:
P12 5 ωη12 E1 (12.3) P21 5 ωη21 E2 where η12 is the coupling loss factor from Subsystems 1 to 2 and vice versa. Substituting Eqs. (12.2) and (12.3) into Eq. (12.1) and rearranging Eq. (12.1) in matrix form produces a steady-state power balance matrix equation as follows:       P1 E1 η1d 1 η12  2η21  5ω (12.4) P2 2η12 η2d 1 η21 E2 For a system with n subsystems, Eq. (12.4) can be extended to a generalized expression: 10 1 0 1 0 η11 2η21 ? 2ηn1 E1 P1 C C B P2 C B 2η12 B η ? ^ E 22 CB 2 C B C 5 ωB (12.5) @ ^ A @ ^ ^ ^ A@ ^ A ? ? ηnn 2η1n Pn En and ηii 5 ηid 1

n X j51;j6¼i

ηij

(12.6)

where ηid is the damping loss factor of Subsystem i; ηij is the coupling loss factor between Subsystem i and Subsystem j; i 5 1, 2, . . ., n and j 5 1,2, . . ., n.

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12.2.2 Energy description of subsystem In Section 12.2.1, the analysis of the energy balance is concentrated, but the concept of statistics has not been introduced yet. Therefore Eq. (12.5) is applicable to any coupling system in any frequency band. In this section, the statistical hypothesis in SEA is introduced, and the energy parameters in Eq. (12.5) are represented by the physical parameters of subsystems. For a structural Subsystem i, when considering a specific frequency band, the time and space-averaged vibrational energy of the subsystem is described by Ei 5 Mi hv i 2 i

(12.7)

where Mi is the mass of Subsystem i, whereas hvi 2 i is the time and spaceaveraged squared velocity of Subsystem i. For an acoustic cavity Subsystem j in a specific frequency band, the time and space-averaged sound energy of the subsystem is expressed by Ej 5

hpj 2 i ρc 2

Vj

(12.8)

where Vj is the cavity volume, while hpj 2 i is the time and space-averaged squared sound pressure of Subsystem j, and ρ and c are the air density and sound speed in the air, respectively. Substituting Eqs. (12.7) and (12.8) into Eq. (12.5), if the input power and loss factors of all subsystems are known, the statistical vibration velocity or sound pressure of each subsystem can be obtained for the specific frequency band. In SEA, the required parameters can be divided into three groups, which consist of modal density, damping loss factor, and coupling loss factor. These parameters can be obtained through theoretical calculation or measurement [17]. Modal density of a subsystem is defined as modal number per unit frequency increment in a specified frequency band. Energy is the core of SEA, and the energy corresponding to resonating modes is dominant in the entire energy of a system. So, the greater the number of mode in a specified frequency band is, the more the capturing energy from the outside excitations is, the larger the responses arising from the outside excitations are. From above analysis, we may see that modal density is closely related to the response of subsystem and can describe the capacity of subsystem capturing energy.

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12.2.3 Damping loss factor and coupling loss factor Damping loss factor ηd of a subsystem is mainly composed of the following three components: ηd 5 ηs 1 ηr 1 ηb

(12.9)

where ηs is produced by internal friction of the subsystem material, and generally dominates in damping loss factor; ηr arises from the acoustic radiation loss of subsystem vibration to the environment; ηb is related to the energy loss caused by the boundary connection damping of subsystem. In real engineering structures, plate is one of the most widely used structures. Damping loss factor of a plate can be measured by using the method based on energy attenuation. In the method, the subsystem suspended by a set of soft springs is excited by a shaker. After the vibration is steady, the excitation is interrupted abruptly and the decay time of vibration is measured. Based on the decay time, the damping loss factor of plate can be calculated by the following equation [18,19] ηd 5

2:2 T60 dB Uf

(12.10)

where T60 dB is 60 dB decay time and f is the center frequency in a certain 1/3 octave band. There exist different damping characteristic parameters for different types of subsystems. The relations between damping loss factor and other damping characteristic parameters are shown in Table 12.1 [19,20]. Coupling loss factor describing the coupling effect between subsystems is another one of the important parameters in SEA. However, to measure the coupling loss factor is very difficult since it is at least an order of magnitude less than the damping loss factor. So, the coupling loss factor is generally obtained by theoretical calculation. Line junction between two plates is the most common structure
structure coupling between subsystems for SEA model of a car body. Coupling loss factor of the junction is expressed as η12 5

2cg Lτ 12 πωA1

(12.11)

where cg is the group velocity of wave in Plate 1; L is the length of junction line; τ 12 is the wave transmission coefficient of junction from Plate 1

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Table 12.1 Relations between damping loss factor and other parameters. Dissipation descriptor

Symbol

Loss factor Damping ratio Damping coefficient Quality factor Logarithmic decrement Reverberation time Decay rate Wave attenuation Damping bandwidth (half-power) Imaginary part of modulus ðEr 1 iEi Þ Acoustical absorption coefficient

ηd ζ C Q δ T60 dB RD m WB Ei α

SI units

Relation to ηd



Ns/m
neper/s s dB/s neper/m Hz N/m2


ηd ηd =2 2πf ηd M 1=ηd πf ηd 2:2=f ηd 27:3f ηd πf ηd =cg f ηd Er ηd ð8πfV =cAÞηd

Notes: cg denotes group velocity for system in m/s; M represents the subsystem mass; A is the area of walls; V depicts room volume; c is the speed of sound.

to Plate 2; ω is the center angular frequency of frequency band; A1 is the surface area of Plate 1. If the coupling exists between a plate and a sound cavity, the loss factor arising from acoustic radiation of the plate vibration to the environment serves as the coupling loss factor, so we obtain ρ cσ ηsa 5 a (12.12) ωρs Based on the reciprocity of coupling loss factor, we have ρ cσns ηas 5 a ωρs na

(12.13)

where ρa is the mass density of the air; ρs denotes the mass density of the structure; c represents the sound speed; σ is the acoustic radiation coefficient; ns and na are the modal density of the structure and the acoustic cavity, respectively. The reciprocity of coupling loss factor can be mentioned as follows: For a specified frequency band (Δω), the relation between coupling loss factors and mode counts of two coupling subsystems is expressed as [19] ηij Nj 5 ηji Ni

(12.14)

where Ni and Nj represent the mode counts of Subsystems i and j in the frequency band, respectively. Meanwhile, we have Ni 5 ni UΔω and

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Nj 5 nj UΔω. Obviously, the reciprocity of coupling loss factor can be used to calculate the coupling loss factor of a subsystem if that of the coupling subsystem is known. In SEA, for the subsystem with simple shape and the subsystem whose modal density is difficult to be measured, their modal density in the frequency band is generally obtained by theoretical calculation. But for the subsystem with complex shape, the modal density needs to be measured by test.

12.3 Simulation of tire high-frequency vibration and tire cavity resonance noise As the only part of a vehicle in contact with road, tire produces vibration and noise when rolling on the road. In the design process of a tire, SEA method is adopted by the engineers to improve the performance of the high-frequency vibration and noise of the tire. In this section, SEA method is used to investigate the high-frequency vibration and cavity resonance noise of a tire.

12.3.1 Statistical energy analysis model and simulation of tire structure Three basic steps in SEA method are as follows: partitioning the system into subsystems and establishing SEA model, determining the model parameters and external excitations, calculating vibrational or noise energy of each subsystem, and analyzing the transfer path. 12.3.1.1 Subsystem partition and statistical energy analysis model of a tire Tire is a composite material structure containing many kinds of rubber compounds and some reinforcement materials. In appearance, a tire includes tread, shoulder, sidewall, and bead. On the surface of tread, the complicated tread pattern is designed to provide traction and drainage functions. In the SEA model, the tread and sidewalls may be expressed as plates [9]. Excitation of the tire mainly comes from the contact with road. In order to simulate the responses of different parts of a tire, a tire model composed of the tread and the sidewalls is divided into five parts, as shown in Fig. 12.2. In analysis, the bending of tread and sidewalls and the energy of in-plane wave are considered.

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Figure 12.2 SEA model of a tire divided into five parts.

The first step in SEA is the subsystem partition. The partition is generally performed according to physical boundary, and the positions where the material property, thickness of the structure, or type of the structure change are regarded as the physical boundary of the subsystem. In addition, for some applications, the different types of elastic waves may also be recognized as different subsystems even though they exist in same structure. The partition should ensure that the modal density of a subsystem is large enough in the frequency band of interest. The input points of external energy and its distribution as well as the requirement for the position accuracy of the response point should be considered in the partition of subsystems. For example, if the inputs of external energy are spatially random and irrelevant for a subsystem, they can be regarded as a uniform distribution approximately; if the inputs of external energy are greatly different spatially, the more detailed partition is required. According to Boulahbal et al. [10], an acceptable partition criterion is to divide SEA subsystems until the modal power difference between adjacent subsystems is no more than 3 dB. Kropp’s study [8] indicated that the behavior of a tire tread is similar to that of an unrestrained plate in the high frequency range of 250
2000 Hz. Although the sidewalls are not considered in most analytical models, they can be treated as plates in SEA model. Wave theory can be used to describe vibration characteristics and energy transfer in the tread and sidewalls. In the research, three types of waves need to be included: bending, compression, and shearing. In the low frequency band,

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the bending wave plays the most important role in the energy flow, whereas in the relatively high frequency band, the compression and shear waves can be as important as the bending waves [9,21]. 12.3.1.2 Parameters in statistical energy analysis model of a tire In SEA model of a tire, the tread and sidewalls may be treated as plates [9]. The natural frequencies of a rectangular plate are expressed as  4 EI km;n  2 ωm;n 5 (12.15) ρh where m and n are the numbers of mode in two orthogonal directions; E is the Young’s modulus of the plate; I is the moment of inertia; ρ and h denote the mass density and thickness of the plate, respectively; km;n represents the wavenumber of mode (m, n). For the plate, the wavenumber is calculated as h πi2 h πi2 1=2 km;n 5 ðm2δ1 Þ 1 ðn2δ2 Þ (12.16) a b where a and b are the length and width of a plate; δ1 and δ2 are constants depending on the boundary condition at the edges. For higher frequency band, the wavenumber is not sensitive to the boundary conditions [9]. For a plate, the mode count function in a frequency band can be approximately expressed as NðωÞ 

Aω 4πRcL

(12.17)

where A denotes the area of plate; ω represents the central angular frequency of frequency band; R is the radius of gyration pffiffiffiffiffiffiffiffiof ffi the plate crosssection; cL is the speed of compression wave (cL 5 E=ρ). For the bending wave, the modal density in the frequency band can be approximated as [19] nb ðωÞ 

Aω 2πcΦ cg

(12.18)

where cΦ and cg represent the phase velocity and group velocity of the bending wave (dependent on the geometry and material properties of the plate), respectively.

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In-plane compression and shear modes are usually coupled at the boundary and can be treated as one mode group (in-plane wave). The modal density of in-plane wave in the frequency band can be approximately expressed as   Aω 1 1 ni ðωÞ  (12.19) 1 2 2π cL 2 cS pffiffiffiffiffiffiffiffiffi where cL is the phase velocity of the compression mode (cL 5 E=ρ); cS pffiffiffiffiffiffiffiffiffi is the phase velocity of the shear mode (cS 5 G=ρ), and G is the shear modulus. Damping loss factor is used to describe the energy loss of a subsystem during each cycle. In SEA model including multiple subsystems, the damping loss factor of a subsystem is not readily available. For a tire with composite material structure, to measure the damping loss factor of its subsystem is also a challenging work. There are many literature to describe how to obtain the damping loss factor and coupling loss factor of a subsystem, such as Refs. [6,9,19,22]. The reader may consult these references. 12.3.1.3 Simulation results and analysis For simulating the structure-borne tire noise by using SEA method, Lee and Ni [9] established the SEA model of a tire by means of the commercial software SEAM, and applied a unit force at the contact patch of tire to simulate the excitation. The feasibility of the SEA model was verified by the mobility of excitation point (Fig. 12.3). The comparison of the simulation results with the measurement ones showed that SEA method could characterize the high-frequency dynamic characteristics of a tire structure well. Although the ring model and finite element model of a tire are popular for investigating the dynamic behaviors of the tire, they are not applicable in high frequency range. Fortunately, SEA method can do well for analyzing high-frequency vibration and noise. Lee and Ni’s paper [9] is one of the earliest literature to explore the application of SEA method in analyzing the vibration of tire structure. Although the subsystem partition was a little bit rough, and the tread pattern and the tire cavity were not included, and the error was relatively large, it is of significance to promote the application of SEA method in tire noise and vibration analysis.

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283

Figure 12.3 SEA calculation of driving point mobility at the contact patch.

12.3.2 Statistical energy analysis model and simulation of tire cavity system Tire cavity resonance (TCR) noise is a tonal sound that can be clearly heard inside a car cabin when the car is running on road. This tonal sound increases the level of annoyance while adding up to the structural and aerodynamics noise. TCR noise may cause structure-borne noise and vibration at the first-order TCR frequency (200
300 Hz) [23
25]. To describe the coupling mechanism of the tire structure and tire cavity, and to predict the vibration and sound field precisely, Mohamed and Wang [23] proposed a combination method of deterministic analysis and SEA for the first time. In this method, the deterministic part was obtained by using the impedance compact mobility matrix method and the statistical part was done by using SEA. While the impedance compact mobility matrix method was used to offer a deterministic solution to the cavity pressure response in the low frequency range, SEA method was used to provide a statistical solution of the responses in the high frequency range. But for the midfrequency range, the combination of SEA with deterministic analysis methods was used to obtain the coupling characteristics of tire structure and acoustic cavity. This section will introduce SEA model of a tire with acoustic cavity and its simulation.

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12.3.2.1 Statistical energy analysis model of tire with cavity The tire cavity system is simplified as an annular cavity with sidewalls and inner wall assumed to be rigid and outer shell assumed to be flexible [23], as shown in Fig. 12.4. Since the ratio of the tread thickness to its radius is less than 0.1, the tread can be assumed to be a thin finite cylindrical shell [26]. Fig. 12.5 shows the tread model with u, v, and w displacement directions and r, z, and θ coordinates.

Figure 12.4 Model of tire cavity system.

Figure 12.5 Model of tire tread.

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Figure 12.6 SEA model with two subsystems.

The tire cavity system consists of a tire structure and a tire cavity, so it can be divided into two subsystems (Fig. 12.6): Subsystem 1 is the tire structure; Subsystem 2 is the tire cavity. Obviously, the excitation is only from the tread, and generated by the contact of the tire with road surface. So, the external input power of Subsystem 1 is P1 , while that of Subsystem 2 is zero. The power balance equation for the tire cavity system can be expressed as ωη1 E1 1 ωη12 E1 2 ωη21 E2 5 P1

(12.20)

ωη2 E2 1 ωη21 E2 2 ωη12 E1 5 0

(12.21)

where E1 and E2 represent the average vibrational and acoustic energies of Subsystems 1 and 2, respectively; η1 and η2 denote the damping loss factor of Subsystems 1 and 2; η12 is the coupling loss factor from Subsystem 1 to Subsystem 2 and vice versa. 12.3.2.2 Parameters of statistical energy analysis model and external excitation Modal density is one of the main parameters in the SEA model. For a three-dimensional (3D) rectangular annular sound field enclosed by rigid walls, the modal density is given by nðωÞ 5

ω2 V ωA L 1 1 2 3 2 2π c 8πc 16πc

(12.22)

where V and A are the volume and surface area of the rectangular annular sound field, respectively; L is the total length of the edges of rigid walls.

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Modal density of a cylindrical shell can be obtained from literature [23,27] as follows:  2  ð π=2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k0 SΩ 1 dθ (12.23) nI 5 2 2 2π ωR θ1 Ω 2 cos4 θ 

k0 2 SΩ nII 5 2π2 ωR

 ð θ1 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 dθ 2 Ω 2 cos4 θ θ0

(12.24)

where nI is the modal density of type 1 while nII is the modal density of type 2. Type 1 corresponds to waves and modes with a larger value of k1 characterized by waves restricted in motion by flexural stiffness of the cylinder wall. While, type 2 refers to waves and modes with a lower value of k2 characterized by waves with motion restricted by in-plane stiffness [27]. To sum up the modal density of the modes governed by in-plane elastic forces and the modal density of the modes governed by shell wall shear forces and bending moment produces the total modal density. Assuming that n1 ðωÞ and n2 ðωÞ are the modal densities of Subsystems 1 and 2, according to the reciprocity of the coupling loss factor, we have η12 5

n2 ðωÞ η n1 ðωÞ 21

(12.25)

Substituting Eq. (12.25) into Eq. (12.21) leads to η21 5

η2 E2 n2 ðωÞ E1 2 E2 n1 ðωÞ

(12.26)

For the case with known modal densities and damping loss factor, the coupling loss factors of two subsystems can be obtained according to Eqs. (12.25) and (12.26). E1 and E2 in Eq. (12.26) can be measured experimentally according to Eqs. (12.7) and (12.8). Additionally, the theoretical analysis method can also be used to obtain the coupling loss factors, which is described in detail in Refs. [23,28]. In this method, the acoustic radiation efficiency of the tire structure is needed. The input power of the SEA model of the tire cavity system is from the excitation of road on vibrating tire. Generally, a point force excitation from an electro-dynamic shaker acting at the tire may be used to simulate the excitation. The input power from a point force source is written as

Statistical energy analysis of tire/road noise

P1 5 jF0 j2 ReðY Þ

287

(12.27)

where P1 is the input power; F0 is the amplitude of the point force, and ReðY Þ is the real part of the excitation point mobility. According to Refs. [23,29], there is nn ReðY Þ 5 (12.28) 4ρs cL ht 2 Fl 2 where nn is the normalized modal density (nn 5 ht cL nðωÞ=ðLRm Þ); L pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi denotes the perimeter of the cylindrical shell, and cL 5 E=½ρs ð1 2 v 2 Þ, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fl 5 1 1 2μð2μΩr 2 =βÞ21=5 , β 5 ht 2 =12Rm 2 , μ 5 Rm ρ0 =2ht ρs , while Ωr 5 ωRm =cL . 12.3.2.3 Simulation of tire cavity system using statistical energy analysis Although the principle of SEA is not very complicated and the number of subsystem is not very large, most people tend to use the commercial software on SEA since the commercial software is more convenient and efficient in solving the engineering problem. Based on the obtained model parameters and the input power, the average energy of tire acoustic cavity can be obtained by using the software (Fig. 12.7) [23].

Figure 12.7 SEA results showing the average cavity energy from the measurement and software simulation.

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Fig. 12.7 shows a comparison of SEA results calculated from the software simulation and the measurement of a simplified tire model. In the experiment, the acoustic pressures at 16 points distributing in the cavity are measured. And these acoustic pressures are averaged in the form of auto power spectral density which has to be integrated over 150
500 Hz to produce mean squared pressure values (hp2 i). After substituting hp2 i into Eq. (12.8), the mean energy of cavity from the measurement is obtained. It can be seen that although slight difference exists between the two curves, they are in good agreement on the whole. Mohamed and Wang [23] suggested that the difference was the result of limited number of the measuring points, and in theory, the result from the measurement should be more similar to that from the software when increasing the number.

12.4 Tire/road noise modeling and simulation using statistical energy analysis Noise inside a car cabin has direct influences on the ride comfort and the perceived quality of the car. With the steady advancement in the noise and vibration reduction technology of automotive powertrain system, the contribution of tire/road noise to interior noise of a car becomes prominent. Especially at moderate speeds, the tire/road noise becomes a dominant noise source since the powertrain noise is less noticed at cruise conditions and the wind noise becomes more noticeable just at higher speeds. The tire/road noise has a great frequency range from 50 to 20,000 Hz and can be affected by most subsystems, for instance, tires, suspensions, body structure, interior trim, so the typical methods to simulate the tire/ road noise such as finite element analysis and boundary element analysis often have limitations for the high-frequency components [6]. However, SEA method has a great advantage in estimating the response of complex structures at high frequency band. After DeJong [2] applied SEA method in the noise prediction of a car first, the interest in using SEA has grown continuously, and the effort to build the SEA models of cars has developed, for example, Dong et al. [6], Ye et al. [18], Moeller and Pan [30], Wang et al. [31], Chaudhari et al. [32], and Gur et al. [33]. In this section, how to use SEA method to predict and control the tire/road noise is introduced.

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12.4.1 Generation and propagation of tire/road noise The tire/road noise arises from the interaction between rolling tire and road surface. The energy from the interaction appears mainly in two modes [6]: the acoustic energy radiated by the “air-pumping” mechanism of tire tread and the vibration of tire surface, and the vibrational energy transferring into tire tread and spindle. And the energy propagates in two paths: airborne and structure-borne paths. For the airborne path, the sound fields in wheel wells and undercar excite the vibrations of body panels, door seals, and so on, and propagate through any air leakage paths. For the structure-borne path, the vibrational energy propagates through tires, spindles, suspension structures, the connection joints, shock towers, and chassis structure to the body panels and glass surfaces. Obviously, the energy from both airborne and structure-borne paths can excite the vibration of body panels, further generate the noise inside a car cabin.

12.4.2 Statistical energy analysis model of a car body To simulate the tire/road noise by using SEA method, a SEA model needs to be established. Based on the basic assumptions for SEA model [6,19,20], a SEA model describing a car body [31] is built as Fig. 12.8. The model excludes the powertrain, suspensions and tires, but tens of subsystems made of the flexible beams, flexible plates, sandwich plates, cylindrical shells, and 3D cavities. In this model, the engine compartment, the passenger compartment, and trunk chamber are treated as 3D cavities. The body panels, such as the roof, door panels, windshield glasses, and front panel, are represented as flexible plates. Large frame type structures are described as beams with bending and torsional properties.

12.4.3 Input power in statistical energy analysis model The input power arising from the interaction between rolling tire and road surface is generally obtained through experiment. To reduce data contamination from other noise sources such as powertrain and wind noise, the power inputs need to be measured without powertrain operation through the chassis roll test with a rough drum surface representative of a typical coarse road surface in the hemi-anechoic chamber [6,30].

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Figure 12.8 SEA model of a car body.

To obtain the input power of airborne exterior noise, microphones are located at the wheel wells, the under floor space and outside the car. The input power of a sound field to a shell subsystem can be expressed as [18] Pain 5

2π2 c 2 ns ðωÞ σrad hpa 2 i ω2 ρs

(12.29)

where c is the sound speed; ns ðωÞ, σrad , and ρs denote the modal density, sound radiation coefficient, and surface density of the shell, respectively; hpa 2 i describes the time and space-averaged squared sound pressure of the sound field. The structure-borne tire/road noise propagates to the passenger compartment through tires and wheels, suspensions, and body structure. The load sensors and accelerometers mounted at the connections between suspensions and body structure may measure the input forces and accelerations. Based on these data, the input power from the tire tread subsystem may be calculated and given by 1 Psin 5 UReðFin UVin  Þ 2

(12.30)

where Fin is the input force and Vin is the complex conjugate of input velocity which is calculated from the measured acceleration. And the

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input power can also be obtained by using the calculated input velocity and measured impedance Zin according to the following equation [6]: 1 Psin 5 UVin 2 UReðZin Þ 2

(12.31)

12.4.4 Parameters in statistical energy analysis model To simulate the tire/road noise, the parameters in SEA model, such as the modal density, damping loss factor and coupling loss factor, need to be determined. For the simple subsystems such as flat plates and glass plates, and the subsystems whose modal densities are difficult to be measured, their modal densities are generally obtained by theoretical calculation. However, for some subsystems with complicated shape such as shock towers and doors, their modal densities need to be measured. The roof panel, the front and rear fenders, and all the glass panels can be treated as flat plates approximately, and the modal density of bending vibration is expressed as nðωÞ 5

A 4πRcL

(12.32)

where the meaning of each symbol is the same as that in Eq. (12.17). The modal density of the sound field in 3D cavity enclosed by rigid walls, such as the engine compartment, the passenger compartment, and trunk chamber, can be calculated according to Eq. (12.22). The methods for obtaining the damping loss factor and coupling loss factor of a subsystem have been widely studied, and there are many published literature, such as Refs. [6,19,22], and so on. For detailed information, the reader may consult the corresponding literature.

12.4.5 Simulation of tire/road noise After acquiring all parameters and external input power required by the SEA model, the simulation of interior noise of a car can be performed through substituting these data into the power balance equation (12.5). For an engineering project, most people are used to applying the commercial software to predict the dynamic behavior of a system. At present, the commercial software on SEA mainly includes VAONE, SEA 1 , and ACTRAN.

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The SEA model and its simulation results need to be verified by test results. The test results may be obtained according to the following method: three or more measuring points are arranged to measure the sound pressure around the left and right ears of the driver and codriver; then the time and space-averaged squared sound pressures of the subsystem for the frequency bands of interest are calculated based on these sound pressure signals, and on this basis, the distribution of sound pressure level in the specified frequency range is obtained. Fig. 12.9 shows a comparison of the simulation result of the sound field at front compartment inside a passenger car and the corresponding test result. Some literature show that the simulation result based on SEA in the low frequency band below 200
400 Hz has a larger error than that in the high frequency band, and for the frequency band above 400 Hz, if the parameters in the SEA model established appropriately can be determined correctly, the error of SEA prediction is within 2
3 dB. The main reason for this conclusion is that the modal density of a subsystem is very small in low frequency band. The small modal density leads to few mode counts existing in the analyzed frequency band (one-third octave is widely used in SEA of the interior noise). According to literature [18], for a subsystem in the SEA model of a car, it is necessary that 15 or more modes are included in the analyzed frequency band to obtain effective results, and the calculation accuracy grows with the increases of the analyzed frequency and the mode counts in the frequency band.

Figure 12.9 Simulation result versus test result.

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Once the results are validated, the SEA model for simulating the tire/ road noise is often used further in the following fields: 1. Transfer path analysis of the tire/road noise. The contributions of the structure-borne and airborne sources to the total noise may be, respectively, obtained for any frequency band. So, the dominant transfer path can be identified. Furthermore, by calculating the SEA model, the contribution of the input power at each connection between car body and suspensions, and the contributions from different airborne sources, may also be acquired, respectively. So, a more detailed breakdown of each transfer path is shown. These can provide important information for controlling the tire/road noise. 2. The sensitivity analysis. The SEA model can be used to evaluate the effects of various parameters on the interior noise caused by the interaction between tire and road. For example, when the parameters in coefficient matrix of power balance equation (12.5) are changed, the interior noise may be different. Thus based on the calculation, the sensitivity of the interior noise to various parameters may be obtained and ranked. This can provide information for improving the design to control the tire/road noise. 3. The prediction, analysis, and evaluation of the properties of sound absorption and isolation, and sound package design of a car.

12.5 Summary Although SEA method was proposed in 1960s, its application in automotive industry started in 1980s. Even so, once the application was seen, automotive engineers rapidly paid more attention to SEA method. Thus the application of SEA method in automotive industry develops very quickly. In the early time, the engineers in the Big Three conducted many explorations, published a series of papers, and promoted the application of SEA method in automotive industry. In recent years, since the development tasks of a new vehicle are increasingly undertaken by the automobile component suppliers, the application of SEA method also extends to the component suppliers. These make SEA method one of the most quickly developing methods. After several decades of development in attenuating the noise and vibration of automotive powertrain system, the contribution of the powertrain to interior noise is significantly reduced, and the contribution of the tire/road noise is more prominent. Therefore the research and

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development in the field of tire’s noise and vibration are attracting much attention from the industry and academia. As an excellent method suitable to investigate high-frequency vibration and noise, SEA method has been applied to predict and control tire’s noise and vibration as well as the interior noise of a car arising from the interaction between tire and road. The research results indicate that, if the parameters in the SEA model established appropriately can be determined correctly, the error of simulation result based on SEA in the frequency band above 400 Hz is within 2
3 dB. It should also be noted that the simulation result of SEA in the low frequency band below 200
400 Hz has a larger error than that in the high frequency band. As an analysis method, the applications of SEA method in investigating the tire/road noise mainly include the prediction of tire/road noise, transfer path analysis, the sensitivity analysis, the prediction, analysis, and evaluation of the properties of sound absorption and isolation, and sound package design of a car.

Nomenclature Pi power input into Subsystem i from outside ω angular frequency (radian/s) η damping/coupling loss factor E energy stored in subsystem; Young’s modulus Mi mass of Subsystem i hvi 2 i time and space-averaged squared velocity of Subsystem i hpi 2 i time and space-averaged squared sound pressure of Subsystem i ρ mass density c sound speed in the air cg group velocity of wave t60 dB 60 dB decay time of sound A surface area of plate V volume; velocity spectral amplitude L length F force spectral amplitude ns modal density of a structure na modal density of an acoustic cavity Ni mode count of Subsystem i I moment of inertia k wavenumber Y mechanical mobility, V/F Z mechanical impedance, F/V

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References [1] Lyon RH. Statistic energy analysis of dynamic systems: theory and applications. Cambridge: MIT Press; 1975. [2] DeJong RG. A study of vehicle interior noise using statistical energy analysis. SAE Technical Paper 850960; 1985. [3] Kompella MS, Bernhard RJ. Measurement of the statistical variation of structuralacoustic characteristics of automotive vehicles. SAE Technical Paper 931272; 1993. [4] Chen HY, O'Keefe M, Bremner P. A comparison of test-based and analytic SEA models for vibro-acoustics of a light truck. SAE Technical Paper 951329; 1995. [5] Moeller MJ, Pan J, DeJong RG. A novel approach to statistical energy analysis model validation. SAE Technical Paper 951328; 1995. [6] Dong B, Green M, Voutyras M, et al. Road noise modelling using statistical energy analysis method. SAE Technical Paper 951327; 1995. [7] Vinesse E, Nicollet H. Surface waves on the rotating tyre: an application of functional analysis. J Sound Vib 1988;126(1):85
96. [8] Kropp W. Structure-borne sound on a smooth tyre. Appl Acoust 1989;26 (3):181
92. [9] Lee J, Ni A. Structure-borne tire noise statistical energy analysis model. Tire Sci Technol 1997;25(3):177
86. [10] Boulahbal D, Britton JD, Muthukrishnan M, et al. High frequency tire vibration for SEA model partitioning. SAE Technical Paper 2005-01-2556; 2005. [11] Kameyama Y, Sawada K, Nakamura H, et al. Analytical SEA modeling of smooth tire vibration. Trans Soc Automot Eng Jpn 2018;49(5):986
92. [12] Langley RS, Cordioli JA. Hybrid deterministic-statistical analysis of vibro-acoustic systems with domain couplings on statistical components. J Sound Vib 2009;321(35):893
912. [13] Yan Y, Li P, Lin H. Analysis and experimental validation of the middle-frequency vibro-acoustic coupling property for aircraft structural model based on the wave coupling hybrid FE-SEA method. J Sound Vib 2016;371:227
36. [14] Wang X. Deterministic-statistical analysis of a structural-acoustic system. J Sound Vib 2011;330(20):4827
50. [15] Wang Q, Huang H, Yao D. Configuration coupling dynamics. Beijing: China Astronautic Publishing House; 1999. [16] Pang J, Chen G, He H. Automotive noise and vibration: principle and application. Beijing: Beijing Institute of Technology Press; 2006. [17] Cimerman B, Bharj T, Borello G. Overview of the experimental approach to statistical energy analysis. SAE Technical Paper 971968; 1997. [18] Ye WP, Yi M, Jin XX, et al. Car interior noise simulation using statistical energy analysis method. J Tongji Univ 2001;29(9):1066
71. [19] Lyon RH, DeJong RG. Theory and application of statistical energy analysis. Boston: Butterworth-Heinemann; 1995. [20] Yao DY, Wang QZ. Principle and application of statistical energy analysis. Beijing: Beijing Institute of Technology Press; 1995. [21] Lyon RH. In-plane contribution to structural noise transmission. Noise Control Eng J 1986;26(1):22
7. [22] Fernández M, Chimeno M, Roibás E, et al. Loss factors identification from E-SEA techniques. InterNoise 2019. Madrid, Span; 2019. [23] Mohamed Z, Wang X. A deterministic and statistical energy analysis of tyre cavity resonance noise. Mech Syst Signal Process 2016;70:947
57. [24] Mohamed Z, Wang X, Jazar R. Structural-acoustic coupling study of tyre-cavity resonance. J Vib Control 2016;22(2):513
29.

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[25] Yi JJ, Liu XD, Shan YC, Dong H. Characteristics of sound pressure in the tire cavity arising from acoustic cavity resonance excited by road roughness. Appl Acoust 2019;146:218
26. [26] Blevins RD. Formulas for natural frequency and mode shape. Malabar: Krieger Pub Co; 1995. [27] Langley R. The modal density and mode count of thin cylinders and curved panels. J Sound Vib 1994;169(1):43
53. [28] Norton MP, Karczub DG. Fundamentals of noise and vibration analysis for engineers. Cambridge: Cambridge University Press; 2003. [29] Finnveden S. Formulas for modal density and for input power from mechanical and fluid point sources in fluid filled pipes. J Sound Vib 1997;208(5):705
28. [30] Moeller MJ, Pan J. Statistical energy analysis for road noise simulation. SAE Technical Paper 971972; 1997. [31] Wang DF, Chen SM, Qu W, et al. Car interior noise prediction and experimentation using statistical energy analysis. J Jilin Univ 2009;39(Suppl. 1):68
73. [32] Chaudhari VV, Radhika V, Vijay R. Frontloading approach for sound package design for noise reduction and weight optimization using statistical energy analysis. SAE Int J Veh Dyn Stab NVH 2017;1(1):66
72. [33] Gur Y, Pan J, Wagner D. Sound package development for lightweight vehicle design using statistical energy analysis (SEA). SAE Technical Paper 2015-01-2302; 2015.

CHAPTER 13

Pass-by noise: regulation and measurement Xu Wang

School of Engineering, RMIT University, Melbourne, VIC, Australia

13.1 Introduction As the amount of highway vehicles increases, road traffic noise has become one of the main contributors to environmental noise, which represents a burden to people resulting in annoyance, sleep disturbance, or cardiovascular disease. Traffic noise impacts health and produces difficulty with speech and degrades real estate values. Without a significant strategy for controlling traffic noise, the economic growth will be slowed down due to public resistance to the expanded highway capacity. Hence, legislation is an effective way to reduce the noise level and minimize its impact in order to enhance public health and improve life quality of community. Fig. 13.1 shows the evolution of highway vehicle pass-by noise limits in dB(A) from 1970 to 2019 for passenger cars, buses, and trucks within European Union. It is seen from Fig. 13.1 that the highway vehicle pass-by noise limits are getting down and becoming tightened. In order to study pass-by noise, pass-by noise test will have to be conducted. A vehicle test that refers to a procedure of measuring the noise emission levels on an exterior test track is called pass-by noise test. The pass-by noise test is aimed to reflect the exterior noise emission levels from the vehicle in an urban traffic environment.

13.2 Generation mechanisms and characteristics of the tire/ road pass-by noise Tire/road pass-by noise has not been reduced much since the recent decades ago in comparison with the powertrain and exhaust system pass-by noise. Tire/road pass-by noise remains a significant contributor to the overall pass-by noise. Generation mechanisms and characteristics of the Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00013-1

© 2020 Elsevier Inc. All rights reserved.

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Figure 13.1 Change trend of the pass-by noise limits in dB(A) within European Union [1].

tire/road pass-by noise and the effect of the air temperature on the tire/ road pass-by noise will be studied below.

13.2.1 Generation mechanisms of the tire/road pass-by noise The generation mechanisms for the tire/road pass-by noise are complex but can roughly be divided into structure-borne and airborne related mechanisms. The impact of the road surface pattern on the tire surface, adhesion mechanisms, the stick/slip effect between the tire tread pattern element and the road surface, are all assumed to generate the structureborne noise. Air displacement mechanisms, such as the pumping effect of air in the pockets between the tire tread and the road surface, are believed to generate the airborne noise. The contribution of each mechanism to the overall tire/road noise varies depending upon the tire type and size, the road surface characteristics, pavement construction, and vehicle operating conditions [2]. Although the tire radiates sound, the effect of the road structure must not be neglected. Tire/road pass-by noise is a result of the interaction between the tire and the road. The noise sources, which have major contributions to the overall A-weighted noise level, are located near the tire contact patch at or in the vicinity of the leading and trailing edges [2]. Amplification mechanisms like the horn effect, different acoustical and mechanical impedance effects, and the tire structural and acoustical resonance effects have a large effect on the radiation and transmission of tire/road noise to a receiver [2]. The horn effect is believed to be one of the most influential effects among these mechanisms. Therefore

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the horn effect can have a decisive contribution to the overall pass-by noise level. The horn effects of a single tire resting on the ground and of a tire mounted to a vehicle were analyzed in Refs. [2,3]. The geometrical boundary of the acoustical horn is bounded by the leading or trailing edge of the tire and the road surface. The matching of the acoustic impedance in the “horn” and the ambient acoustic impedance is believed to have provided favorable conditions for the amplification of sound radiation [2]. Conducting the reciprocity measurements of acoustical transfer functions on a single tire with a loudspeaker in line with the tire plane positioned at 1 m distance to the tire and with the microphone in line with the tire plane at a distance of 10 mm off the contact patch trailing edge of the tire and the road where an amplification of sound pressure level up to 23 dB was reported [3]. The conclusions are that the horn effect is greatest at the location closest to the contact patch trailing edge. The effect is greatest in the frequency range from 1 to 5 kHz with the maximum amplification in the frequency range of 2
3 kHz. The analysis of the angular properties of the horn effect concludes that the sound radiation decreases when the receiver microphone is moved away from the in-line plane of the tire to a position perpendicular to the tire plane. If a coast-by situation of the single tire is simulated with respect to the receiver position, which is at a distance of 7.5 m away from the tire and a height of 1.2 m above the ground [3], in addition to that the measured sound pressure values have to be corrected for distance attenuation, the angular acoustic properties should also be considered. The coupling between the distance attenuation and the horn effect leads to a maximum amplification of the measured sound pressure levels between the angles of 45 degrees and 75 degrees off the tire plane in the frequency range around 1000 Hz. This coupling may have a large influence on the overall pass-by noise level, since the pass-by noise level is determined using the frequency A-weighting sound pressure level. If the tire was mounted on a vehicle when the measurement was carried out [3], the overall amplification due to the horn effect at the receiver microphone position with the vehicle body is larger than that without the vehicle body. The maximum amplification occurs again at the angles between 45 degrees and 75 degrees off the tire plane in the low frequency range less than 400 Hz. Thus sound reflections from the vehicle body and the ground contribute to the overall pass-by noise level in a manner, which does not occur in the single tire experiments without the vehicle body. The amplification differs by only 2 dB for the angles between 45 degrees and 90 degrees off

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the tire plane, while the amplification in the tire plane is lower with the vehicle body than that without the vehicle body. This might be caused by the screening effect of the vehicle body. Thus a shorter distance between the noise source and the receiver microphone in conjunction with those angles at which the screening influence of the vehicle body is smallest provides the most favorable conditions for the highest contributions to the overall vehicle pass-by noise [3]. Tire/road noise radiation is not omni-directional, but it demonstrates a certain directivity. The directivity pattern consists of the horizontal and vertical directivity. An example of the horizontal directivity of the tire/road noise is shown in Fig. 13.2 [2]. The one-third-octave band frequency spectrum of a standard tire is shown in Fig. 13.2. The standard tire is tested on a dynamometer where

Figure 13.2 Horizontal directivity of the tire/road noise of a single tire measured on a dynamometer drum at a radius of approximately 0.4 m around the tire [2].

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its outer drum surface is covered with a special replication of a road surface. The sound radiation in the frequencies less than 1000 Hz occurs predominantly at the front of the tire (0 degrees or 360 degrees), whereas the sound radiation in the higher frequencies of 1.5
8 kHz radiates relatively more toward the rear of the tire (180 degrees). In general, sound radiation at the front of the tire is slightly higher than that at the rear of the tire. The sound radiation perpendicular to the tire plane is rather small compared to those in the forward and aft directions of the tire plane. The sound radiation of the tire/road noise is largely affected by the vehicle body in the vertical direction. An indication about the vertical directivity is illustrated in Ref. [4]. Tests were conducted on a public road with an average vehicle speed of 90 km/h. Sound pressure was recorded to the side of the vehicle at different heights above the road. The results indicate a constant level of sound radiation when the angle from the receiver microphone to the contact patch of the tire/road is less than 45 degrees. When the angle from the receiver microphone to the contact patch of the tire/road increases and is larger than 45 degrees, the sound radiation level declines by approximately 3 dB. When the height of the receiver microphone above the ground is reduced to a certain value, the measured sound radiation will reach a constant level. The difference is caused by the screening effect of the vehicle body. Clearly, both the horizontal and vertical directivity of tire/road noise will have an impact on the overall pass-by noise level. During the acceleration process of the pass-by noise test vehicle, the drive wheels experience high acceleration, torque, and slip, which results in extra dynamic loading toward the drive axle leading to higher vertical loads on the drive wheels. The sound intensity level of a tire/road noise rises as the acceleration increases [2]. The increase of the torque results in higher tire/road noise at 30 km/h [5]. An increase in sound pressure level of about 20 dB(A) was observed from measuring the pass-by noise of a summer tire of a trailer on an asphalt concrete road at a speed of 50 km/h, if the slip increased by up to 10%. If the slip was further increased, the noise level remained approximately same [2]. The effect of the vertical dynamic load on tire/ road noise was studied in Ref. [6] where it was found that when the vertical dynamic loads are increased up to 3000 N in the speed range from 50 to 70 km/h, the pass-by noise sound pressure levels also increase. When the vertical dynamic loads are increased up to 5000 N, the pass-by noise sound pressure levels decrease slightly in general. This is because the pass-by noise sound pressure level for the vertical dynamic load of 5000 N

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at 50 km/h reaches the maximum value for the specific speed. Vehicle acceleration can be substituted by vehicle deceleration to generate the extra torque and its contribution to the tire/road noise. It is noted in Ref. [2] that there is no difference in the pass-by noise sound pressure level between an accelerated and braked test. The tire/road pass-by noise can be measured on a decelerating vehicle fitted with different tire types as illustrated in Ref. [7] where it is concluded that the wider is the tire, the higher are the pass-by noise levels and the wider is the dominant excited frequency band. The constant speed cruise pass-by noise tests were conducted for vehicles over a speed range from 40 to 100 km/h according to the statistical pass-by method. The results show a linear relation between the measured sound pressure level and the vehicle speed on a logarithmic scale [2]. The pass-by noise level varies from 69 to 78 dB(A) over a speed range from 50 to 70 km/h. The pass-by noise level of heavy vehicles is higher than that of passenger cars and the noise-speed relation of heavy vehicles is not entirely linear for the lower speed range. The moving frame acoustic holography, acoustic near-field holography, or beam forming method can be applied in order to analyze vehicle tire sound radiation under different pass-by test conditions [8]. The noise source amplitudes are found to vary with the driving conditions. Noise sources are approximately equal in strength for the front and the rear axle in the accelerating condition. For the constant speed condition, the noise source at the front tire is dominant and for the coast-down condition, the noise source at the rear axle has the highest amplitudes. It is concluded that tire/road noise level depends on the driving state, which includes the force transfer in the tire contact patch, tire vibrations, oscillating air cavities, etc. For the constant speed cruise test, high sound pressure levels are found in an area between the front and rear axle. The high sound pressure levels in the area are caused by the interference effects between sound radiation from the front and rear tires [8]. The accelerating pass-by noise test condition exhibits higher sound intensity levels than the constant-speed and coast-down pass-by noise test conditions. The constant-speed pass-by noise level is largely influenced by the interference between the radiated sound from the front and rear tires. A strong directivity of the constant-speed pass-by noise between the axles is developed from the side of the vehicle perpendicularly pointing away due to the interference effect. All the three driving conditions are important for the analysis of the vehicle pass-by noise. This is why the

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accelerating and constant speed cruise test conditions are both implemented in ISO 362-1. The coast-down condition is often used to determine the contribution of tire/road noise to the overall pass-by noise level.

13.2.2 Pass-by noise frequency content Analysis of the frequency content of pass-by noise assists in the understanding of noise source characteristics. However, detailed testing of each major noise source is required in order to identify and reduce critical pass-by noise source contributions. Fig. 13.3 [7] presents three color map diagrams of different pass-by noise tests taken with a compact class vehicle. The evolution of the spectral content with time during a vehicle passby noise test is visualized, which helps to study individual noise source characteristics and contributions. On the left-hand side, Fig. 13.3A shows the result of a vehicle pass-by noise test with the engine being switched off and slick tires in use, thus only the wind noise is measured. In the middle, Fig. 13.3B shows the result of the vehicle equipped with regular tires, but with the engine still being switched off during the pass-by noise test, which results in a combination of wind noise and tire/road noise. There are no specific resonant frequencies, but the increasing amplitude of components in the frequency range between 500 Hz and 2 kHz are caused by the nontread pattern tire/road noise [7] and the noise appears to have random characteristic. On the right-hand side, Fig. 13.3C demonstrates the sound pressure frequency spectrum during the normal ISO 362 test. Compared to the middle part of the contour maps, Fig. 13.3A and B have lower amplitude of components between 500 Hz and 2 kHz than Fig. 13.3C, which may be caused by the increasing vehicle speed or tire rotational speed, respectively. Furthermore, Fig. 13.3C has higher sound pressure levels in the frequency range larger than 2 kHz and less than 500 Hz. The noise in the frequency range less than 500 Hz is dominantly generated by the engine orders, and related to the sound radiation of the engine, intake, and exhaust system [7]. The contribution of each noise source varies according to the vehicle position. When the vehicle has passed the microphone position, the exhaust orifice noise is dominant. The exhaust orifice noise is screened by the vehicle body, when the vehicle approaches the microphone. A similar situation occurs regarding the engine and intake system radiated noise when the vehicle is moving away from the receiver microphone. Since only the measurement time is demonstrated in Fig. 13.3,

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Figure 13.3 Color map plots of different pass-by noise tests: (A) with engine being switched off and with slick tires; (B) with engine being switched off and with standard tires; (C) ISO 362 test [7].

it is impossible to relate the sound pressure spectrum directly to the vehicle position on the test track, which would have given a better understanding of the local radiation characteristic of the noise sources. Analysis of ISO 362 pass-by noise tests reported in Refs. [9,10] concluded that the vehicle pass-by noise sources are significantly influenced by engine speed. The higher the vehicle or engine speed then the higher is the radiated sound pressure level. Therefore the highest sound emission occurs at the highest engine speed. However, the highest engine speed is reached at the end of the acceleration period when the distance between the vehicle pass-by noise sources and the receiver microphone is greatest. In this case, the radiated sound is attenuated through distance, and the recorded sound pressure level at the receiver microphone location is less than the sound pressure level when the receiver microphone is closer to the source. Consequently, the pass-by noise level is dependent on the sound radiation of the noise sources and the distance between the noise sources and the microphone. Thus when the effects of the sound radiation and distance are best combined and most favorable for the overall pass-by noise level, the highest pass-by noise level is achieved. Furthermore, the noise source screening and the angle between the sound source and the receiver microphone have a decisive influence on the recorded pass-by noise sound pressure level.

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13.2.3 The effect of the air temperature on the pass-by noise The pass-by noise level of a passenger car being driven on seven types of road surfaces (DAC, VTAC, PAC, SD8/10, SSD0.8/1.5, PCC, and CC) at 90 km/h was investigated for different temperature conditions where classic tire (Tire A) and winter tire (Tire B) were tested [11]. The road surfaces are defined by the generic name of the technique, and the grading size. Indication is given of the thickness of the surface layer and of the mean texture depth (MTD) measured with a volumetric patch technique. DAC road surface is defined as a dense asphalt concrete (DAC) 0/10 grading, 6.2 cm thick on average, with MTD of 0.86 mm; PAC road surface is defined as a porous asphalt concrete (PAC) 0/10 grading, 4 cm thick on average, with MTD of 1.67 mm; VTAC road surface is defined as a very thin asphalt concrete (VTAC) 0/10 grading, 2.5 cm thick on average, with MTD of 1.49 mm. DAC, PAC, VTAC road surfaces are all used for the asphalt wearing courses. SD road surface is defined as a rough epoxy bound surface dressing (SD) 8/10 grading, with MTD of 4.3 mm; SSD road surface is defined as a thin and smooth epoxy bound surface dressing (SSD) 0.8/1.5 grading, with MTD of 0.70 mm. Both the SD and SSD road surfaces have surface dressings. CC road surface is defined as a cement concrete (CC) textured with burlap, 12 cm thick plates, with 0.8 mm MTD; PCC road surface is defined as a porous cement concrete (PCC), 12 cm thick, with 1.14 mm MTD. Both the CC and PCC road surfaces are used for cement concrete roads. The effect of temperature on pass-by tire/road noise emission was studied on seven different road surfaces. The results are shown in Fig. 13.4. From Fig. 13.4, a linear relationship between noise level and air temperature variations is observed. A very small effect is noticed on the cement concrete road surfaces. The concrete pavements always have a lower temperature effect than asphalt pavements. The very small effect observed may be caused by the relatively smooth texture of the two concrete surfaces tested. The tested concrete surfaces with the surface dressings have more temperature effects on the pass-by tire/road noise level than the pure concrete surfaces. When the ambient temperature increases, tire/road pass-by noise emission level decreases on the bituminous pavements. The variation of temperature coefficient can exceed 0.1 dB(A)/°C where the temperature coefficient is defined as the A-weighting SPL change per unit temperature change by degree Celsius. This effect depends on a combination of tire and road.

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Figure 13.4 Pass-by noise levels at 90 km/h as a function of the air temperature for different road surfaces [11].

It is seen from Fig. 13.5 that the temperature effect is highest in the low and high frequency ranges, which could be explained by the generating mechanisms rather than by the propagation mechanisms. This is because the temperature effect on the pass-by noise spectrum caused by the propagation mechanisms of the tire/road noise could be evenly distributed in the whole frequency range. A clear relation between the pass-by tire/road noise and road pavement (or tire) stiffness is observed in Figs. 13.6 and 13.7, which could justify the temperature effect on low frequency tire/road noise. It is seen from Fig. 13.6 that the DAC road surface has a larger temperature effect on low frequency tire/road noise than the epoxy bound road surfaces (SD and SSD). In the medium frequency range, between 500 Hz and 1.25 kHz, the effect of temperature on pass-by tire/road noise is low in general. In the high frequency range, the pass-by tire/road noise generation is dominated by air pumping, adhesion, and friction mechanisms. The road surface with a thin and SSD has a larger temperature effect on the high frequency tire/ road noise than the DAC road surface and the road surface with a rough epoxy bound surface dressing.

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Figure 13.5 Pass-by noise spectrum at 90 km/h on VTAC road for Tire B, at four different air temperatures [11].

Figure 13.6 One-third-octave band air temperature coefficients for dense asphalt concrete pavements (uncorrelated data are excluded) [11].

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Figure 13.7 One-third-octave band air temperature coefficients for porous asphalt concrete pavements (uncorrelated data are excluded) [11].

It is seen from Fig. 13.7 that when there is some porosity on the bituminous road surface, the effect of temperature on tire/road noise is lower. However, no clear dependence of the temperature coefficient on the roughness or texture of road surfaces is observed. These coefficients in Figs. 13.6 and 13.7 were obtained for two regular passenger car tires, and noise levels evaluated at 90 km/h on relatively smooth and medium rough road surfaces.

13.3 ISO 362-1/ECE R51.03 Vehicle exterior noise emission is quantified in terms of idle noise and pass-by noise with the latter being considered to represent an approximation to typical urban driving behavior. The international standard ISO 362-1/ECE R51.03 represents a guideline for the measurement and calculation of the pass-by noise level for any vehicle class. When the pass-by noise test is studied in this section, the regulation outline is first introduced, followed by methods and instruments in Sections 13.3.1
13.3.4 including acceleration test targets, acceleration test gear selections, acceleration and constant speed cruise tests. Interpretation of test results under ISO 362-1/ECE R51.03 is then demonstrated in Section 13.3.5.

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Figure 13.8 Test site layout and typical microphone locations for the outdoor and indoor pass-by noise tests: (A) outdoor test section layout (ISO 362-1/2); (B) indoor test section layout (ISO 362-3) [1].

The ISO 362-1/ECE R51.03 test simulates actual in-use noise emission through weighted average sound pressure level peak values of the wide open throttle (WOT) and constant speed cruise tests. The estimate of pass-by noise level Lurban (expressed in dB(A)), representative of the external noise level of a vehicle under typical urban traffic conditions, is done under partial load, that is, based on measurements under full load acceleration and at a constant speed of 50 km/h. Acceleration and speed requirements determine gear selection, and acceleration targets are selected based on the ratio of vehicle power over mass, which is performance based. The layout of the test track in the ISO 362-1 test method is shown in Fig. 13.8. From Fig. 13.8A, it is clear that the acceleration zone consists of a square area of 20 m by 20 m. A sound level meter of high precision shall be used. Measurement shall be carried out with a weighting network and a time constant conforming to “curve A” and the “fast response” respectively. The sound level meter shall be calibrated against a standard sound source immediately before and after each series of test runs. If the meter reading obtained from either of these calibrations deviates by more than 1 dB(A) from the corresponding reading taken at the time of the last freefield calibration the test shall be considered invalid. The actual deviation shall be recorded. In order to improve the accuracy of the tests, each type

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of the tests in either of the driving directions should be repeated 2
3 times to collect the measurement data for the average result. The test vehicle approaches the test section in the test gear along the centerline of the test track in a certain speed. As the front of the vehicle enters the test section crossing line A-A, the accelerator pedal is fully depressed as rapidly as practicable and remains fully depressed until the rear of the vehicle crosses the line B-B when the accelerator pedal is fully released as rapidly as possible. The test vehicle speed approaching the entry of the test section should be made so that the test vehicle will reach 50 6 1 km/h at the location of the measurement microphones in the middle of the test section. The test result for each microphone is the maximum noise level (dB(A) Fast) measured while the vehicle is accelerating through the test section. The rotational speed of the engine shall be measured by an independent tachometer whose accuracy is within a variation of 6 3% of the actual speed of rotation. The number of test runs performed in each test gear is defined by the regulation under test. During the test no one shall stay in the measurement area except the observer and the driver. Their presence must have no influence on the meter reading. The surface of the test track used to measure the noise of vehicles in motion shall be such as not to cause excessive tire noise. Measurements shall not be made under poor weather conditions. Any sound pressure level peak, which appears to be unrelated to the characteristics of the general sound pressure level of the vehicle shall be ignored in taking the readings. If a wind guard is used, its influence on the sensitivity and the directional characteristics of the microphone shall be taken into consideration. The test tracks under ISO 362-1/ECE R51.03 is certified according to the ISO10844:2011 standard, which outlines requirements for road surface texture, evenness, acoustic absorption, and road surface material. The road surface texture is measured using a vehicle mounted laser profilemeter and the road surface sound absorption coefficient is measured using an in situ impedance tube. The tracks in ISO10844:2011 are designed to be particularly quiet. Pass-by noise contribution pie charts of powertrain and tire/road noise sources under ISO 362-1/ECE R51.03 are shown in Fig. 13.9. It is seen from Fig. 13.9 that the powertrain noise share is 60%, and the tire/road noise share is 40% in the all gears under the ISO 362-1/ECE R51.03 test conditions as shown in Fig. 13.9.

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Figure 13.9 Pass-by noise contribution of powertrain and tire/road noise sources under ISO 362-1/ECE R51.03 [1].

The reported sound pressure level under the ISO 362-1/ECE R51.03 test condition adopts the weighted average of the pass-by noise levels of the acceleration and constant speed cruise tests where weighting depends on the achieved acceleration. Relevant sound sources of ISO 362-1/ECE R51.03 are powertrain related for acceleration tests, tire/road related and base engine related for constant speed cruise tests. The ISO 362-1/ECE R51.03 test produces lower peak sound pressure level results for most vehicles, but its limits are also tighter. The ISO 362-1/ECE R51.03 test requires vehicles to achieve real world noise emission consistent with the reported regulatory value. Calibration strategies (e.g., “urban mode”) are no longer effective or allowed. Vehicles of low power mass ratios need to pay a close attention to the pass-by noise test as these vehicles run the test at higher engine RPM speed than other vehicles. For ISO 362-1/ECE R51.03, tires become critical for the pass-by noise test in addition to exhaust, engine, and induction. Ambient temperature effects on reportable result have been significantly reduced. Since the acceleration targets, vehicle mass, engine performance, gear ratios, final drive ratios, etc. have important influence on the results of the pass-by noise tests, the pass-by noise issue becomes a balance decision on how to allocate noise sources. The ISO 362-1/ECE R51.03 regulation prohibits on “Test

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Detection” of any kind. No “dB subtraction,” no shaved tires and no allowance for diesel engines are allowed. Off-cycle testing is included that avoids test detection as well as requires “expected” linear behavior under the WOT acceleration test (approximately no more than 5
6 dB/ 1000 rpm) up to a particular engine and road speed range based on the vehicle characteristics. The ISO 362-1/ECE R51.03 pass-by noise limits vary depending on vehicle type. Table 13.1 lists the general and off-road pass-by noise limits against vehicle types where the vehicles can be used for the carriage of passengers and goods with different mass and rated engine power under ISO 362-1/ECE R51.03. It is seen from Table 13.1 that for M1 passenger vehicles on general road with the number of seats less than 9, the pass-by noise limit is 68 dB(A).

13.3.1 ISO 362-1/ECE R51.03 acceleration test targets Based on the measurement and statistical analyses of urban traffic noise, a formula has been developed to calculate the pass-by noise level Lurban. This formula depends on the two noise levels corresponding to the test under full load acceleration and at a constant speed of 50 km/h, as well as power-to-mass ratio of the vehicle: PMR (in kW/ton). The PMR ratio is given by: PMR 5

P 3 1000 ðW=kgÞ M

(13.1)

where P is the vehicle power in kW; M is the vehicle mass in kg. The PMR ratio allows to calculate two accelerations for each type of vehicle—target and reference accelerations. The target acceleration aurban defines the typical acceleration in urban traffic derived from statistical investigations and is a function of the PMR of the vehicle, which is given by aurban 5 0:63 3 log10 ðPMRÞ 2 0:09 ðm=s2 Þ

(13.2)

The reference acceleration for the WOT test awot-ref (in m/s2) is defined as the acceleration required during the full load acceleration test. It is expressed in terms of the PMR of the vehicle:  awot-ref 5 1:59 3 log10 ðPMRÞ 2 1:41 ðm=s2 Þ for PMR $ 25 2 awot-ref 5 aurban 5 0:63 3 log10 ðPMRÞ 2 0:09 ðm=s Þ for PMR , 25 (13.3)

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Table 13.1 Pass-by noise limits of vehicles used for the carriage of passengers and goods under ISO 362-1/ECE R51.03. Vehicle category code

Description of vehicle category

M

Vehicle used for the carriage of passengers Number of seats # 9; power to mass ratio , 150 kW/ton Number of seats # 9; power to mass ratio $ 150 kW/ton Number of seats . 9; mass , 2 tons Number of seats . 9; 2 tons , mass # 3.5 tons Number of seats . 9; 3.5 tons , mass # 5 tons; rated engine power , 150 kW Number of seats . 9; 3.5 tons , mass # 5 tons; rated engine power $ 150 kW Number of seats . 9; mass . 5 tons; rated engine power , 150 kW Number of seats . 9; mass . 5 tons; rated engine power $ 150 kW Vehicles used for the carriage of goods mass , 2 tons 2 tons , mass # 3.5 tons 3.5 tons , mass # 12 tons; rated engine power , 75 kW 3.5 tons , mass # 12 tons; 75 kW # rated engine power , 150 kW 3.5 tons , mass # 12 tons; rated engine power . 150 kW mass . 12 tons; 75 kW # rated engine power , 150 kW mass . 12 tons; rated engine power $ 150 kW

M1

M2

M3

N N1 N2

N3

Limit values expressed in dB(A)

General 68

Offroad 69

69

69

70 71

70 72

72

73

74

76

73

74

75

77

69 70 72

69 71 73

73

74

75

77

75

76

78

80

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The target acceleration is the typical (partial-open-throttle) acceleration in urban traffic, not the WOT acceleration. The reference acceleration is the WOT acceleration. The target acceleration is therefore different from the reference acceleration.

13.3.2 ISO 362-1/ECE R51.03 acceleration test gear selections The gear used for the acceleration test is dependent on the vehicle performance. The gear used is the same for both manual and automatic transmissions. Automatic transmissions should be tested locked in gear in manual mode (Tap Shift/Tiptronic) or by use of other electronic control system. The vehicle is tested in the gear producing acceleration during the test (awot) closest to the reference acceleration awot-ref determined in Eq. (13.3), but not exceeding 3.0 m/s2. If one gear gives an acceleration within 6 5% variation of the reference acceleration awot-ref, the test is run in one gear. If no gears achieve the reference acceleration, then the test is run in two gears (i.e., one gear with higher acceleration (Gear i) and one with lower acceleration (Gear i 1 1)). For vehicles with only one gear (e.g., electric vehicles), the acceleration test is carried out in this gear.

13.3.3 ISO 362-1/ECE R51.03 acceleration test In the ISO 362-1/ECE R51.03, acceleration test, several preparation runs may be required to determine test entry speed and test gear to achieve the reference acceleration awot-ref and 50 km/h at the microphones (line P-P as shown in Fig. 13.8). For the full load acceleration test, the driver must accelerate so that the vehicle speed is at 50 km/h in the middle of the test track P-P (see Fig. 13.8). The noise levels recorded at both the microphones are A-weighted and then converted to an overall noise level value. The noise level values used correspond to the maximum sound pressure level values during the vehicle passage on the track. Four test runs should be performed in each test gear consecutively, all within a variation range of 2 dB(A). The noise levels corresponding to the four runs are then averaged at each microphone. Speeds should be measured at lines A-A, P-P, and B-B.

13.3.4 ISO 362-1/ECE R51.03 constant speed cruise test In the ISO 362-1/ECE R51.03 constant speed cruise test, the test vehicle maintains a constant speed of 50 6 1 km/h along the centerline of the test track throughout the test section in each of the gears used for the constant

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speed cruise test. Four constant speed cruise test runs are performed in each test gear consecutively, all within a variation range of 2 dB(A). The constant speed cruise test is not required for vehicles with the power mass ratio larger than 25. The test result for each microphone is the maximum noise level (dB(A) Fast) measured while the vehicle is driven through the test section. The noise levels corresponding to the four runs are then averaged at each microphone.

13.3.5 Interpretation of test results under ISO 362-1/ECE R51.03 For each set of the acceleration test and constant speed cruise test runs, the average maximum sound pressure level is calculated for each side of the vehicle. The intermediate result is the higher of those two values, giving the following values: Lwot(i) 5 Gear i acceleration test noise result (dB(A)). Lwot(i11) 5 Gear i 1 1 acceleration test noise result (dB(A)) (for vehicles tested in two gears). Lcrs(i) 5 Gear i cruise test noise result (dB(A)). Lcrs(i11) 5 Gear i 1 1 cruise test noise result (dB(A)) (for vehicles tested in two gears). For each of the acceleration test runs, the acceleration through the test section based on the entry (line A-A) and exit (line B-B) speeds giving the following values: awot(i) 5 Gear i acceleration in m/s2. awot(i11) 5 Gear i 1 1 acceleration in m/s2 (for vehicles tested in two gears). For passenger (M1) and light commercial (N1) vehicles tested in one gear, if a specific gear ratio (i) gives an acceleration within a tolerance interval of 6 5% variation of the reference acceleration for the WOT test awot-ref, and not exceeding 2 m/s2, then this gear ratio will be chosen to perform the test. The pass-by noise level Lurban is calculated by performing a linear interpolation between the two recorded sound pressure levels. The reported pass-by noise test result Lurban is calculated by: Lurban 5 LwotðiÞ 2 kp ðLwotðiÞ 2 LcrsðiÞ Þ

(13.4)

where Lwot(i) and Lcrs(i) (expressed in dB(A)) represent respectively the sound pressure levels corresponding to the full load acceleration of the vehicle awot(i) (in m/s2) and at a constant speed of 50 km/h for the gear ratio (i). The partial power factor kp, represents a dimensionless

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numerical quantity. It is used to interpolate the test results under full load acceleration and at constant vehicle speed. This factor kp is given by the following equation: aurban (13.5) kp 5 1 2 awotðiÞ For passenger (M1) and light commercial (N1) vehicles tested in two gears, in most cases, there is no gear ratio to approach the reference acceleration for the WOT test awot-ref. In this case, the acceleration awot-ref is framed by the nearest accelerations of the two gear ratios: awot(i) and awot (i11). The reported pass-by noise test result Lurban is calculated as follows: Lurban 5 Lwot-rep 2 kp ðLwot-rep 2 Lcrs-rep Þ

(13.6)

where Lwot-rep and Lcrs-rep (in dB(A)) correspond respectively to the linear interpolation between the two sound pressure levels of the gear ratios (i) and (i 1 1), under full load acceleration awot-ref and at a constant speed of 50 km/h. In the case of two gear ratios, the partial power factor kp is given by the following equation: aurban (13.7) kp 5 1 2 awot-ref Lwot-rep and Lcrs-rep are then given by the following equation:  Lwot-rep 5 Lwotði11Þ 1 k 3 ðLwotðiÞ 2 Lwotði11Þ Þ Lcrs-rep 5 Lcrsði11Þ 1 k 3 ðLcrsðiÞ 2 Lcrsði11Þ Þ

(13.8)

where k5

awot-ref 2 awotði11Þ awotðiÞ 2 awotði11Þ

(13.9)

While all of the above equations look complex, in practice when the ISO 362-1/ECE R51.03 test procedure is actually run, they can be automated into the data collection software for all of these calculations and do not require manual calculation of vehicle data input.

13.3.6 ISO 362-3 indoor pass-by noise test and simulation development In ISO 362-3, the pass-by noise is measured indoor where a test vehicle is stationary and its wheels are driven to rotate by driving drums of a chassis dynamometer while the speeds of switching on-off of measurement

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channels of microphones are controlled to be close to the test vehicle speeds in the field, which is specified in ISO 362-1/2. Content of ISO 362-3 is based on that of ISO 362-1/2 (same operating conditions, same gears), but special attentions are given to instrumentation, test room requirements, dynamometer requirements, test procedures, and test method. ISO 362-3 requires new tools for better understanding of noise emission physics, which is independent from outdoor climatic conditions. ISO 362-3 improves the test efficiency and reproducibility for manufacturers and approval authorities and provides a basis for a virtual approval test in the future. ISO 362-1/2 and ISO 362-3 should provide identical results. Large semianechoic chambers with chassis dynamometers provide an alternative test environment to traditional outdoor pass-by noise experiments. For any indoor simulation of pass-by noise, it is generally advisable to provide similar test conditions as are required in the standard ISO 3621/2. This decreases systematic measurement errors and approximates the experimental result of the real pass-by noise test more accurately. Instead of measuring the pass-by noise levels outdoor, many automotive OEMs prefer executing part of the measurements indoor. In-room tests offer many advantages. First of all, the test is not influenced by the weather conditions; it can be performed throughout the year. Ambient air temperature can easily be controlled indoor. Second, the vehicle is “driven” in repeatable, controlled conditions, making the measurement sequences much more efficient and effective. Third, no wireless data transfer between vehicle and track is required, which greatly simplifies instrumentation. The experimental setting is simple: the vehicle is positioned on a chassis-dyno in a semianechoic room. Linear arrays of microphones are placed at 7.5 m away from the centerline of the vehicle covering the distance from 210 m to 110 m along the vehicle longitudinal centerline. The pass-by noise levels are estimated by interpolating the noise levels measured at different microphone positions along both the sides of the vehicle. A schematic representation of a classical setup is shown in Fig. 13.8B. The distance between microphones is either constant, for example, 1 m, or varying with a smaller spacing distance where the highest noise levels are expected. The number of microphones depends on the spacing distance and the size of the chamber. Speed and load conditions of a vehicle in the real pass-by test are simulated by means of the chassis dynamometer enabling acceleration or

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constant-speed driving conditions, while sound pressure is recorded by the microphones. The indoor simulation can be run fully automatically and be well controlled to provide good experimental repeatability, which cannot always be achieved by road tests. Since both the microphones and vehicle are not in motion, in order to predict the pass-by noise level for different track position, an inverse approach is used. Basically, the microphones located before the vehicle dominantly measure the pass-by noise when the vehicle “drives into” the test section of the track, while the microphones located after the vehicle dominantly measure the pass-by noise when the vehicle “drives out of” the test track. Estimates of the vehicle speed obtained from the chassis dynamometer combined with engine speed measurements are used to calculate the vehicle position in the test track. The relevant microphone signals are recorded for the different vehicle’s “positions” on the track, their measurement data and results are interpolated between adjacent microphones. The measurement data recordings are then connected in a sequence. The signal transitions between adjacent microphone recording signals are smoothed out to eliminate the leaps and discontinuities of the overall signal trace curve. Coherent and incoherent parts of the signal are separately processed through different algorithms. Finally, a filter is applied to account for the Doppler frequency shift of a translation noise source. The resulting signal is an estimated time dependent pass-by noise signal, which can also be applied for subjective listening test for the purpose of the in-depth jury testing and psychoacoustic analyses. The semianechoic room ensures to have free field conditions in the frequency range of interest; the lower cut-off frequency is dependent on the room dimensions. When large semianechoic chambers are not available, certain correction measures have to be applied to carry out the indoor simulation of the pass-by noise test in smaller rooms. The microphone line array has to be located in acoustic far field of test vehicle, but the distance between the microphones and the centerline of a vehicle can be less than 7.5 m. In order to estimate the sound pressure at 7.5 m, correction has to be applied based on the inverse square law. The essential assumption for this procedure is that the radiated noise source is a point source, which is named as the acoustic center. The acoustic center is assumed to be placed on the ground within the range of the vehicle dimensions and it may be frequency and driving condition dependent.

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The acoustic center is not fixed at one location and movable, therefore the accuracy of the pass-by simulation needs to be corrected. The location of the microphone of the highest sound pressure reading out of the sideline microphones which cover the overall vehicle dimension length determines the position of the acoustic center. Vehicles with their engine mounted in the front tend to have the acoustic center in the middle of the vehicle, since both the exhaust orifice noise and engine noise are major noise contributors. For a rear mounted engine, the acoustic center moves to the rear of the vehicle. The length of certain test chambers may be too small to cover the measurement angle of the microphone line array. The measurement angle is the maximum angle of the line connecting the vehicle entering the test track and the ISO 362-1/2 pass-by microphone with respect to the vertical direction of the test track centerline. Hence, the microphones can be placed outside the line array in order to cover the whole area within the angle. The acoustic center is idealized, as it cannot represent the origin of the sound radiation of all vehicle noise sources. The systematic error resulting from the utilization of the small room can be reduced and corrected following a certain procedure. The accurate replication of tire/road noise on the drum of the chassis dynamometer is related to the road replication material and its surface structure on the drum. The drum curvature has less influence. The nondriven wheels of a vehicle are usually locked, if only one set of chassis dynamometer drums is available. Thus the contribution to the rolling noise of these locked tires is neglected. Slick tires are applied in order to eliminate the effect of the tire/road noise from the indoor pass-by noise of a vehicle in the semianechoic chamber. Tire/road noise measured with a propulsion noise isolated vehicle can then be added to the pass-by noise estimation. The indoor simulated pass-by noise and real pass-by noise are compared against the test track position that the test vehicle is located in the acceleration test. The comparison between the indoor simulated passby noise and real pass-by noise shows a difference of less than 1 dB(A). The high accuracy of the indoor test facility has been verified by the tests. However, the one-third-octave spectra of the indoor pass-by noise simulation show a higher variation of sound pressure levels than those of the real pass-by noise test, which is attributed to different absorption characteristics of the ground. Although the indoor simulated pass-by noise test with microphone arrays cannot be used for the homologation process of the ISO 362-1/2, but it can support the development process from component level to

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vehicle level. The drum surface is ideally covered with a road material meeting the requirements regarding road surface texture and reflection characteristics according to ISO10844:2011 in order to compare the indoor simulated pass-by noise test with the ISO 362-1/2 test. Variations caused by the driver and his driving style can be eliminated by automatic control of the accelerator pedal. Free-field conditions between the vehicle and the microphones are essential for control of the variations of the measured sound pressure level amplitudes within 6 2.5 dB(A) and the lower cut-off frequency down to about 50 Hz. Free-field conditions between the vehicle and the microphones are verified to have the effect within 6 1 dB(A) in the one-third-octave band frequencies greater than 100 Hz. Since ideal free-field conditions do not exist indoors, the deviations from the ideal free-field conditions may make the experimental results inaccurate. The background noise of the chassis dynamometer is not allowed to contribute to the overall radiated noise level. For a vehicle with an equivalent speed of 50 km/h, the measured background noise is less than 40 dB (A) measured from a microphone at a height of 1 m above the ground near the dynamometer. The wind noise of a moving vehicle cannot be replicated, since its contribution to the pass-by noise is small and negligible in the speed range of the pass-by noise test. Discrepancies between indoor simulated and real pass-by noise test results exist regardless of the layout and characteristics of the indoor test facility, the number of microphones adopted and the algorithm applied to calculate the overall sound pressure level. However, vehicles equipped with different components can be tested and their results can be compared under the same conditions. A stationary vehicle in the indoor simulated pass-by noise test is easier for its noise sources to be shielded and to provide more reliable information of the noise source contributions to the overall pass-by noise level than a moving vehicle in the real pass-by noise test. Other noise source identification techniques can be more easily applied in the indoor simulated pass-by noise test than those in the real pass-by noise test such as acoustic near-field holography or beam forming. Beneficially, the trained measurement personnel can conduct a subjective evaluation of the pass-by noise for its characteristics around the vehicle during testing. Finally, as the vehicle is not moving, a more extensive instrumentation of the vehicle is possible and relatively easy. This additional instrumentation will help engineers gaining more insights of the acoustic behavior and contribution of the various subsystem components. Indoor facilities

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Figure 13.10 Contribution subsources of the overall pass-by noise.

also allow for testing prototypes or vehicle mock-ups at an early stage of the design process.

13.4 Source and contribution identification of pass-by noise Pass-by noise research and development requires balancing of all exterior noise sources to achieve overall target levels. Subsystem targets should be set as a starting point for the pass-by noise research and development based on the best-off results or practices of previous similar vehicle tests. Fig. 13.10 shows the contribution subsources of the overall pass-by noise, which consist of the induction and tailpipe noise, tire/road noise, engine and transmission radiated noise, driveline radiated, and exhaust radiated noise. Once test vehicles are available in the mule or early prototype stages, physical tests can be run to determine the overall pass-by noise performance. If the vehicle pass-by noise level exceeds the program targets and/ or legal limits, a contribution study should be carried out to determine and rank the major contributors of the pass-by noise level. A contribution study involves using a windowing technique to isolate each noise source to determine its contribution to the overall pass-by levels. Results are used to identify, which noise sources require a further reduction. For example, Fig. 13.11 shows the contribution study using a windowing technique to isolate intake and exhaust noise sources to determine their contribution to the overall pass-by noise levels where extra-large intake and exhaust mufflers are applied to exclude the contributions of the

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Figure 13.11 Contribution study using a windowing technique to isolate intake and exhaust noise sources to determine their contribution to the overall pass-by levels.

induction and exhaust tailpipe noise in the overall pass-by noise. In addition, shaved or slick tires can be used to partly exclude the contribution or effect of the tire/road noise. The constant speed cruise and coast-down tests using the neural gear can be used to exclude the powertrain noise contributions to the overall pass-by noise, such as the contributions of the engine/transmission radiated noise, the driveline and exhaust radiated noise to the overall pass-by noise. The ranking and contribution study results of a passenger vehicle are given, for example, in Table 13.2. It is seen from Table 13.2 that the tailpipe airborne noise and exhaust radiated overall contribute the largest to the overall pass-by noise level. Each of the tailpipe airborne noise and exhaust radiated overall contributes 25% of the overall pass-by noise level. The tire/road noise contributes the second largest to the overall pass-by noise level, which is 19%. The induction snorkel airborne noise and other noise sources contribute the least to the overall pass-by noise level. Each of them contributes 9% of the overall pass-by noise level. It is noticed that the production clean air duct radiated noise contributes 13% of the overall pass-by noise level, which is the pass-by wind (aerodynamic) noise and easy to be ignored.

13.5 Other pass-by noise research and development In addition to the overall maximum noise level required for certification activities, most pass-by noise data acquisition systems can provide a large amount of additional data that can be useful in the pass-by noise research and development. Information such as road speed, engine RPM speed,

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Table 13.2 Ranking and contribution study results of an example passenger vehicle. Ranking Subsystem

1 2 3 4 5 6

Contribution test estimate (dB(A)) Combined Left Right Combined (Pa)

%

Overall

75.4

75.5 75.3

0.12

100

Tail pipe airborne Exhaust radiated overall Tire/road Production clean Air duct radiated Induction snorkel airborne Other remaining

69.4 69.4 68.2 66.7

68.9 70.2 68.7 68.6

0.06 0.06 0.05 0.04

25.1 25.1 19.1 13.5

64.3 64.1

64.8 64 64.6 64

0.03 0.03

8.7 8.5

69.8 68.3 67.6 62.9

throttle position, and instantaneous noise level can be recorded and plotted versus track position. Frequency spectra can be extracted from the noise measurement data in order to obtain the average, peak hold, or the maximum noise level, to determine problem frequencies/orders for the noise refinement work and to identify the root cause. Fig. 13.12 shows typical measurement data of the pass-by noise where the top chart shows the vehicle speed (km/h) versus the distance from the measurement microphones in the middle of the test section. The second top chart records the engine rotational speed versus the distance from the measurement microphones in the middle of the test section. The third

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Figure 13.12 Typical measurement data of the pass-by noise.

and fourth charts show the total order (black curve) and combustion order (blue curve) (the number of engine cylinder divided by two) spectra of the sound pressure signals recorded on the left and/or right-hand side exterior measurement microphones. At the position of 210 m in the horizontal axis, the frontend of the test vehicle enters the test section (A-A line in Fig. 13.8A). At the position of 0 m in the horizontal axis, the frontend of the test vehicle reaches the middle of the test section or the position of the left and/or right-hand side exterior measurement microphones (P-P line in Fig. 13.8A). At the position of 10 m in the horizontal axis, the frontend of the test vehicle leaves the test section (B-B line in Fig. 13.8A). It is seen from Fig. 13.12 that the maximum total sound pressure levels occur at both the left- and right-hand side exterior measurement microphones. The total order sound pressure spectrum amplitude curves measured at both the left- and right-hand side microphones coincide with each other very well, so do the combustion order sound pressure spectrum amplitude curves. The sound pressure spectrum amplitude curve peaks of the engine combustion order measured at both the

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left- and right-hand side exterior measurement microphones occur when the frontend of the test vehicle reaches the entry line of the test section, which may be related to the engine induction snorkel airborne, clean production air duct radiated, and engine radiated noise. The sound pressure spectrum amplitude curve peaks of the engine combustion order also occur when the frontend of the test vehicle is 0.8 m away before the middle of the test section, which may be related to the engine intake airborne, engine radiated, and overall exhaust radiated noise. The sound pressure spectrum amplitude curve peaks of the engine combustion order also occur when the frontend of the test vehicle is 2.5 m away after the exit of the test section, which may be related to the engine tail pipe airborne and overall exhaust radiated noise. Figs. 13.13 and 13.14 [12] present typical recordings of the A-weighted overall pass-by noise level signals of the left- and right-hand side microphones against the position of the front of a passenger vehicle from the middle of the test section in the second and third gears according

Figure 13.13 Pass-by noise level recordings in the second gear according to ISO 362 [13].

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Figure 13.14 Pass-by noise sound pressure level recording in the third gear according to ISO 362 [13].

to ISO 362 [13]. At the position of 210 m in the horizontal axis, the front bumper of the test vehicle reaches the entry of the test section (A-A line in Fig. 13.8A). At the position of 0 m in the horizontal axis, the front bumper of the test vehicle reaches the middle of the test section (P-P line in Fig. 13.8A). At the position of 10 m in the horizontal axis, the front bumper of the test vehicle reaches the exit of the test section (B-B line in Fig. 13.8A). A scatter band frames the solid curves of the sound pressure signals where the black bold curves are the average pass-by noise sound pressure level curves. The vehicle speed is also plotted. The dot line represents the vehicle speed increases linearly with the distance of the front bumper of the test vehicle away from the entry of the test section. The sound pressure level curve peaks occurring at 6
7 m after the test vehicle passes the middle of the test section are believed to be most related to the tail pipe airborne and exhaust radiated overall noise, as the exhaust tail pipe of the test vehicle faces and is close to the measurement microphones at this position.

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The average and scatter band of the pass-by noise level curves are calculated based on many times of the test results and presented in Figs. 13.13 and 13.14 where the measured sound pressure level curves versus the distance are symmetric for the two opposite driving directions. Pass-by certification and development tests can be carried out at proving ground using a data acquisition system such as the Bruel and Kjaer Pulse data acquisition system. The system consists of two front ends, one in-vehicle and one ground station linked by a wireless connection, logging the following parameters of the sound pressure levels—left and right sides of test section, trigger signals (at the entry and exit of the test section), vehicle speed (measured via the vehicle mounted Laser Profilemeter or the V-box), engine RPM speed (measured via tachometer), and throttle position (measured via throttle position sensor and ECU module). Design of Experiment (DOE) method (Taguchi method), factorial experiment (the orthogonal experiment or test) will be applied to plan the experiments and process the experimental results, from which the subsources of the pass-by noise and their contributions to the overall pass-by noise level can be identified. Fig. 13.15 shows the A-weighted sound pressure level curves versus the distance of the front bumper of the test vehicle away from the entry

Figure 13.15 Pass-by noise signal recordings of the left-hand side microphone in the second and third gear slow acceleration tests of a medium class vehicle according to ISO 362 [14].

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of the test section in the second and third gears. At the position of 0 m in the horizontal axis, the front bumper of the test vehicle reaches the entry of the test section (A-A line in Fig. 13.8A). At the position of 10 m in the horizontal axis, the front bumper of the test vehicle reaches the middle of the test section (P-P line in Fig. 13.8A). At the position of 20 m in the horizontal axis, the front bumper of the test vehicle reaches the exit of the test section (B-B line in Fig. 13.8A). It is seen from Fig. 13.15 that there are two peaks of the A-weighted sound pressure level curves. One occurs when the test vehicle reaches at 0.5 m before the middle of the test section, which may be related to the engine combustion noise including the induction snorkel airborne noise, production clean air duct radiated, and engine radiated noise. The other occurs when the test vehicle is at 7 m away after the middle of the test section, which may be related to the exhaust tail pipe airborne noise, exhaust radiated overall noise, and engine radiated noise. It is seen that the A-weighted sound pressure level in the second gear is higher than that in the third gear. In the second gear, the second peak of the A-weighted sound pressure level curve is dominant, as the peak is related to the exhaust system noise, and the engine noise is dominant in this gear. In the third gear, the first peak of the A-weighted sound pressure level curve is dominant as the peak is related to the induction snorkel airborne noise and production clean air duct radiated noise, and the vehicle has a higher speed in the gear. Fig. 13.16 shows the individual noise source contributions to the overall pass-by noise level for the acceleration test. At the position of 0 m in the horizontal axis, the front bumper of the test vehicle reaches the entry of the test section (A-A line in Fig. 13.8A). At the position of 10 m in the horizontal axis, the front bumper of the test vehicle reaches the middle of the test section (P-P line in Fig. 13.8A). At the position of 20 m in the horizontal axis, the front bumper of the test vehicle reaches the exit of the test section (B-B line in Fig. 13.8A). It is seen from Fig. 13.16 that in the acceleration test of the vehicle, the engine noise contributes the most to the overall passby noise level, the tire/road noise contributes the second most. When the test vehicle is driven before the middle of the test section, the exhaust radiated overall noise contribute the third most, and the exhaust orifice/tail pipe induced noise contributes the least. When the test vehicle passes the middle of the test section, the exhaust orifice/tail pipe induced noise contributes the third most and the exhaust radiated overall noise contribute the least. It is seen from Fig. 13.17 that the sound pressure constant percentage bandwidth (CPB) spectrum amplitude curves of the left- and right-hand

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Figure 13.16 Individual noise source contributions to the overall pass-by noise level for one selected vehicle [14].

Figure 13.17 Constant percentage bandwidth (CPB) spectrum amplitude curves of the measured sound pressure signals of the left- and right-hand side measurement microphones for the constant speed cruise tests.

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side measurement microphones in the constant speed cruise tests coincide with each other very well. There is a peak at 165.48 Hz for both the sound pressure CPB spectrum amplitude curves measured by the left- and right-hand side microphones, which may be related to the tire-pavement interaction noise.

13.6 Summary Regulation testing and analysis methods of the pass-by noise have been studied. The pass-by tire/road noise contribution has been separately discussed for its generation mechanisms, frequency contents, and characteristics. The impact of the road surface pattern on the tire surface, and adhesion mechanisms, the stick/slip effect between the tire tread pattern element and the road surface, are all assumed to generate the structure-borne noise. Tire/ road pass-by noise is a result of the interaction between the tire and the road. The tire/road noise sources which have major contributions to the overall A-weighted noise level, are located near the tire contact patch at or in the vicinity of the leading and trailing edges. Amplification mechanisms like the horn effect, different acoustical and mechanical impedance effects, the tire structural and acoustical resonance effects such as tire width, directivity, and body shield have a large effect on the radiation and transmission of tire/road noise to a receiver. The horn effect and road surface design can have a decisive contribution to the overall pass-by tire/road noise level. ISO 362-1/2/ECE R51.03 includes both the acceleration and constant speed cruise tests, which can better regulate the pass-by tire/road noise emission. ISO 362-3 improves the test efficiency and reproducibility for manufacturers and approval authorities and provides a basis for a virtual approval test in the future. The ranking and contribution study results of a passenger vehicle show that the tailpipe airborne and exhaust radiated overall contribute most while the tire/road noise contributes the second most to the overall pass-by noise level. Induction snorkel airborne contributes the least to the overall pass-by noise level.

Nomenclature awot(i) awot(i11) aurban awot-ref k

Gear i acceleration in m/s2 Gear i 1 1 acceleration in m/s2 (for vehicles tested in two gears) the typical acceleration in urban traffic the reference acceleration for the wide open throttle test the linear interpolation coefficient

Pass-by noise: regulation and measurement

kp Lwot(i) Lwot(i11) Lcrs(i) Lcrs(i11) Lwot-rep Lcrs-rep Lurban M PMR P

331

the partial power factor gear i acceleration test sound pressure level (dB(A)) gear i 1 1 acceleration test sound pressure level (dB(A)) (for vehicles tested in two gears) gear i cruise test sound pressure level (dB(A)) gear i 1 1 cruise test sound pressure level (dB(A)) (for vehicles tested in two gears) the linear interpolation between the two sound pressure levels of the gear ratios (i) and (i 1 1) under full load acceleration awot-ref the linear interpolation between the two sound pressure levels of the gear ratios (i) and (i 1 1) at a constant speed of 50 km/h the external noise level of a vehicle under typical urban traffic conditions or the estimate of the pass-by noise level vehicle mass power mass ratio vehicle power

References [1] Janssens K, Bianciardi F, Britte L, Van de Ponseele P, Van der Auweraer H. Pass-by noise engineering: a review of different transfer path analysis techniques. In: Proceedings of ISMA2014 including USD2014; 2014. [2] Sandberg U, Ejsmont JA. Tire/road noise reference book. Kisa (Sweden): Informex; 2002. [3] Kropp W, Bécot F-X, Barrelet S. On the sound radiation from tires. Acta Acust United Acust 2000;86:769
79. [4] Mori Y, Fukushima A, Uesaka K, Ohnishi H. Noise directivity of vehicles on actual road. Proceedings of inter-noise 1999;1
4. [5] Steven H. Pkw-Reifen/Fahrbahngerausche bei unterschiedlichen Fahrbedingungen (Tire/road noise of passenger vehicles in different driving conditions). Frankfurt/ Main: Forschungsvereinigung Automobiltechnik e.V.; 2000. [6] Iwao K, Yamazaki I. A study on the mechanism of tire/road noise. JSAE Rev 1996;17:139
44. [7] Alt N, Wolff K, Eisele G, Pichot F. Fahrzeugaussengeräuschsimulation (Vehicle exterior noise simulation). Automobiltechnische Z 2006;108:832
6. [8] Park S-H, Kim Y-H. Visualization of pass-by noise by means of moving frame acoustic holography. J Acoust Soc Am 2001;110:2326
39. [9] Phillips AV, Orchard M. Drive-by noise prediction by vehicle system analysis. SAE Technical Paper Series 2001-01-1562; 2001. [10] Genuit K, Guidati S, Sottek R. Progresses in pass-by simulation techniques. SAE Technical Paper Series 2005-01-2262; 2005. [11] Anfosso-Lédée F, Yves Pichaud Y. Temperature effect on tire
road noise. Appl Acoust 2007;68(2007):1
16. [12] VDI-Richtlinien 2563. Geräuschanteile von Straßenfahrzeugen
Meßtechnische Erfassung und Bewertung (Guideline of the Association of German Engineers (VDI): noise components of vehicles; measurement and assessment). Düsseldorf: Verein Deutscher Ingenieure; 1990. [13] Taylor N. Pass-by noise—a brief overview. Presentation held at Loughborough University; 2007. [14] Biermann J-W. Geräuschverhalten von Kraftfahrzeugen (Noise characteristics of vehicles)—lecture notes. Aachen: Institute for vehicles at RWTH Aachen University; 2004.

CHAPTER 14

Pass-by noise: simulation and analysis Xu Wang

School of Engineering, RMIT University, Melbourne, VIC, Australia

14.1 Introduction The aim of predictive methods for the vehicle pass-by noise test is to predict the maximum A-weighted sound pressure level as an indication of whether the ISO 362-1/2 pass-by noise test can be passed. However, a more in-depth analysis of the evolution of exterior noise may be desirable. Certain methods allow contribution analysis of the vehicle noise sources enabling identification of critical noise sources. Predicted pass-by noise can be analyzed against the track position or evaluated in the frequency domain at discrete positions on the test track. Distinctive features of the methods are experimental or numerical, indoor or outdoor, complete vehicle test or system base tests. Predictive methods can combine one or more of these features. To ensure compliance with the pass-by noise test requirement, vehicle manufacturers and suppliers must quantify vehicle noise source characteristics during the design stage of the vehicle. In addition, predictive tools and prediction methods need to be available to investigate the characteristics of different noise sources contributing to the overall pass-by noise level during the product development phase in order to estimate the final pass-by noise level. In this section, the current available methods based on transfer path analysis (TPA) including the pass-by noise synthesis prediction model, sensitivity analysis and uncertainty propagation, substitution monopole technique (SMT), airborne source quantification (ASQ), and transmissibility approach will be introduced.

14.2 Pass-by noise prediction model Prediction model, or synthesis model, is based on a simple SourceTransfer-Receiver model, also known as the TPA method where a source Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00014-3

© 2020 Elsevier Inc. All rights reserved.

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is divided into k subsources assumed to be uncorrelated, and the contribution of each subsource is the product of the acoustic flow multiplied by the acoustic transfer function between this subsource and the microphone which is 7.5 m away from the track centerline axis. This method is used not only to reproduce the level of vehicle pass-by noise, but also to classify subsources and analyze their contribution to total noise level separately. It is thus possible to define a noise level target for each subsource, by acting on the subsource such as modifying the structure, or by acting on the acoustic transfer function such as adding absorbent or insulating treatments. The noise emitted by each subsource is thus calculated at discrete positions over the entire length of the test track and given by: n D D E X E   _ 2i ðωÞ UTFij ðωÞ2 p2j ðωÞ 5 (14.1) Q i51

_ i 5 iωUQi is the volume where h.i is the temporal and spatial average; Q acceleration flow rate corresponding to the subsource i (expressed in m3/ s2) and ω (in rad/s) is the angular velocity. n corresponds to the number of subsources. pj (in Pa) is the sound pressure at the measurement point j, and finally TFij (expressed in Pa 3 s2/m3) represents the transfer function between the subsource i and the measurement point j. For the tire/road pass-by noise, the sound pressure contribution of the tirepavement interaction noise (TPIN) is directly measured at 7.5 m away from the centerline of the test track for several vehicle speeds (from 30 to 80 km/h). A logarithmic regression is then performed to obtain the coefficients Ap and Bp, which depend on the tire, as illustrated in the following empirical equation and given by   V Lpc 5 Ap Ulog (14.2) 1 Bp 50 where Lpc (in dB(A)) represents the overall noise level of the test vehicle where the vehicle propulsion noise is isolated. Ap and Bp are constants that depend on the tire and the vehicle’s position on the track, and V represents the vehicle speed in km/h. The acoustic radiation of the sources as well as the transfer functions are constantly changing during the test. Indeed, the contribution of each noise subsources varies according to the conditions under which the vehicle passes through the test track. The acoustic radiation of the subsources depends mainly on the engine speed, while the acoustic transfer functions

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Figure 14.1 Complete diagram of the synthesis model [1].

depend on the position of the vehicle on the track. This must be taken into account in the model for predicting the level of the pass-by noise. To do this, it is necessary to use the same test run conditions as the regulatory tests and to calculate the vehicle accelerations for each gear ratio during test runs under full load acceleration (the vehicle acceleration is considered constant). It also allows us to choose the gear ratio with its acceleration approaching awot-ref with a variation of 6 5%. In the case, where no gear ratio allows to approach this reference acceleration, the two gear ratios (i) and (i 1 1) are chosen, which allows to frame awot-ref according to Eq. (13.3). Fig. 14.1 represents a complete diagram of the operating principle of the synthesis model. In order to calculate the acceleration of awot(i) that corresponds to a speed of V 5 50 km/h at the measurement microphones, the following equation is developed according to the fundamental principle of dynamics and given by awotðiÞ 5

FdðiÞ 2 Fr mg 1 RJ 2

(14.3)

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where R (in m) is the radius of the tire, J (expressed in kg m2) represents the rotational moment of inertia of the vehicle’s kinematic chain, Fr (in N) designates the resistive force at 50 km/h, Fd(i) (in N) corresponds to the driving force developed by the vehicle at 50 km/h for the gear ratio (i), and finally mg (in kg) represents a total vehicle mass. The resistive force Fr is given by mg Fr 5 Faero 1 Fbearing 1 Fbrake 1 Rr U (14.4) 1000 where Faero (in N) is the aerodynamic force which is proportional to the square of the vehicle speed (the speed here is set at 50 km/h), Rr (in N/ ton) is the rolling resistance force coefficient, Fbearing (in N) is the bearing friction, and Fbrake (in N) is the brake friction. The driving force Fd(i) can be calculated from the engine torque, vehicle speed and transmission efficiency and is given by FdðiÞ 5

3600Uωe ηy U UTor 1000UV 100

(14.5)

where Tor is the engine torque, ηy is the transmission efficiency in percentage (%), ωe is the engine rotation speed in rad/s and given by ωe 5

2πUNe 60

(14.6)

where Ne is the engine rotation speed in (rpm); Eq. (14.5) then becomes FdðiÞ 5

120UπUNe ηy 120Uπ ηy U U UTor 5 UTor VmilleðiÞ 100 1000UV 100

(14.7)

where Vmille(i) (expressed in km/h) represents the vehicle speed when the engine speed Ne 5 1000 rpm. This parameter depends on the gearbox ratio and the circumference of the tire. The parameter Vmille(i) allows us to make the link between the vehicle speed V and the engine rotational speed Ne (expressed in rpm), using the following linear relationship: V5

VmilleðiÞ UNe 1000

(14.8)

Tor is the full load torque which is developed by the engine when the vehicle’s accelerator pedal is fully depressed. This parameter is directly measured as a function of the engine rotation speed.

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The accelerations awot(i) are then calculated from Eqs. (14.3), (14.4), and (14.7). Then we choose the acceleration that approaches awot-ref with a variation of 6 5%. In case no gear ratio allows to approach this reference acceleration, it is framed with awot(i) and awot(i11) according to Eqs. (13.6) (13.9). From the accelerations awot(i) and/or awot(i11), the vehicle speed can be calculated over the entire length of the test track as  2  2  1 Umg U 3600 V 2 V02 5 mg UawotðiÞ UðXv 2 Xv0 Þ 1000 2 (14.9)  2 or V 2 5 2U 1000 awotðiÞ UðXv 2 Xv0 Þ 1 V02 3600 where V0 5 0 km/h corresponding to the vehicle speed at the position Xv0 5 0 m. The vehicle speed V allows to obtain the contribution of the tire/road noise by using Eq. (14.2). For full load acceleration configurations, a measured pass-by noise sound pressure level value related to the effect of wheel torque Ttire (in Nm) is added to the contribution of the tire/road noise at constant speed. The engine speed Ne is obtained from the vehicle speed, using Eq. (14.8). It gives the possibility to obtain the power of the subsources Waci (in Watt) corresponding to the current engine rotational speed for each position of the vehicle on the track Xv. These powers will be transformed into a volume acceleration flow rate _ i , before being multiplied by the appropriate transfer functions TFij to Q obtain the contribution of each subsource (see Eq. 14.1). Thus at the output of the model, we obtain the noise levels for each run: Lcrs(i); Lwot(i); Lcrs (i11); Lwot(i11). The noise level Lurban is obtained from Eqs. (13.6)(13.9) by interpolating these noise levels. The powertrain is modeled here by a single point source. To quantify the volume acceleration flow rate of this source, measurements are made on the powertrain extracted from the vehicle and installed on a test bench. The tests are carried out under the same load conditions as those corresponding to the pass-by noise test. The total acoustic power of the powertrain Wac is obtained by intensity measurements, with the engine running at 3000 rpm. To obtain the acoustic power as a function of the engine speed Ne, microphones are placed at a distance of 1 m in front of each side of the powertrain. Then the total power is extrapolated using the root mean square of the sound pressure levels of all microphones at

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1 m. Therefore the powertrain is assimilated to a single acoustic monopole _ i baffled by the powertrain wall. i with a volume acceleration flow rate Q The acoustic volume acceleration flow rate is obtained from the acoustic power of the powertrain Waci: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi _ i ðωÞ 5 2πc Waci ðωÞ (14.10) Q ρ where c represents the velocity of sound (in m/s) and ρ represents the density of air (in kg/m3). The powertrain is then divided into 21 zones. For each zone, a transfer function TFij is measured by the reciprocal method. For this purpose, a calibrated sound source of a known flow rate is moved away 1 m between two measurement points along a line located 7.5 m from the centerline of the track and 1.2 m high above the ground. Sound pressure levels of the selected zone are measured. The 21 measured acoustic pressure transfers are averaged quadratically to represent the acoustic pressure transfer of the powertrain by a point source. The acoustic flow rate of the sources and the transfer functions can be represented by overall values of the output. Indeed, the value to be analyzed at the output of the model, that is, the level Lurban mentioned in ISO 362-1/ ECE R51.03 is given as an A-weighted overall sound pressure level value. Therefore all the source powers (powertrain, intake, exhaust tail, exhaust line) and their adequate transfer functions of a model will be reduced to the overall sound pressure level values.

14.3 Sensitivity analysis and propagation of uncertainty To perform sensitivity analysis and propagation of uncertainty, it is assumed that the model is sufficiently accurate to predict the behavior of the system (the equations are relevant and the approximations introduced in the model are controlled), and only the parametric uncertainties are focused on. Indeed, calculations are generally made in a deterministic way; however, in reality, the values of the input parameters are not exactly known and are therefore subject to uncertainties. A probabilistic approach is then better adopted by considering the input and output parameters of the model as random variables. These uncertainties can then be propagated in the model using quasi-Monte Carlo methods. Finally, a sensitivity analysis study can be carried out through the Monte Carlo simulations to study the impact of the variability of the input parameters

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on the variability of the output noise levels of the synthesis model. Influential parameters are identified and classified by vehicle family. All the steps in a general framework are summarized for uncertainty studies as below: 1. Specification of the problem: definition of the model(s), input and output variables, quantities of interest as well as the objectives of the study. 2. Quantification of uncertainties related to the input parameters of the model, and attribution of probability distributions, based on available or measured data, literature or expert judgment. 3. Propagation of uncertainties (forward process) in the model and evaluation of the variability of the output induced by the uncertainty of the input data. 4. Sensitivity analysis is the backward process which allows to measure the sensitivity of the variables of interest to the input parameters. 5. Depending on the result obtained, it is sometimes important to redefine the problem and return to the different stages of the study. The main objective of the sensitivity analysis is to study the impact of the variability of each input parameter on the model’s output(s) where the parameters that influence the most, those that do not influence the output, and those that interact within the model can be determined. The sensitivity analysis can simplify the model or even improve its understanding. The sensitivity analysis is an aid to validate a calculation code, to orient research efforts, or to justify the dimensioning or modification of a system in terms of safety. A linear relationship between the inputs and the outputs of the prediction model is expected to be verified. This allows us to define the standardized regression coefficient SRCi, where SRCi2 5 Si represents the sensitivity index that is proportional to the ratio of the variance of input parameter Xi divided by the variance of the output Y. SRCi is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi VarðXi Þ SRCi 5 β i U (14.11) VarðY Þ where Var(Xi) is the variance of input parameter Xi; Var(Y) is the variance of the output Y; β i is the regression coefficient of the input parameter Xi. When performing a linear regression between the output Y and the inputs X, it is important to calculate the correlation coefficient of the model R2. The coefficient represents a quality criterion for model

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prediction, that is, it provides a measure of how the linear regression model _ Y can reproduce the real output vector Y. The coefficient corresponds to the part of the variance of the model output Y explained by the linear regression and is given by N P

VarðY^ Þ j51 R2 5 5 N P VarðY Þ

ð^yðjÞ 2yÞ2 (14.12) ðyðjÞ 2yÞ2

j51

where y represents the mean of the sample {y(1), . . ., y(N)}, y^ ðjÞ represents the prediction of the linear model, and yðjÞ represents the real output. Note that the closer the correlation coefficient R2 is to the unit, the better the performance of the regression model, and that the sum of the square of the SRC indices is R2, and given by k X

SRCi2 5 R2

(14.13)

i51

It should be noticed that if two variables Xi and Xj are dependent, then the sensitivity index Si no longer expresses only the sensitivity measure of Xi to Y but also a part of the influence of the parameter Xj on Y, and is given by Si 5 Sic 1 Siu

(14.14)

where Siu and Sic are, respectively, the uncorrelated and correlated part of the sensitivity index Si. Some input parameters of the synthesis model can be highly correlated (see Fig. 14.1). For example, the acoustic power of the sources Wac depend on the rotational speed of the engine Ne and therefore on the total mass mg, the vehicle speed at 1000 rpm (Vmille) and the engine torque in full loads. The contribution of tire/road noise Lpc is another example, since it depends on the vehicle speed V, and therefore on the three parameters mentioned above. It is then necessary to know how to interpret the sensitivity indices of these correlated input parameters.

14.4 Substitution monopole technique Source strength descriptors are defined for both the airborne and structure-borne sound. Their common basis is that the physical sources

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are modeled in terms of fictitious elementary sources, such as acoustical monopoles. The strength of these equivalent substitution sources is determined indirectly in most cases. One practical advantage concerns the feature that the proposed descriptors are much less affected in strongly different installation environments than the more conventional source strength descriptors. Another practical advantage is that the use of elementary substitution sources as source models facilitates the very convenient application of experimental reciprocity techniques for transmission path ranking. In this subsection, the source models with fictitious monopole sources, which are distributed over the radiating surfaces will be studied. These sources can be either correlated or uncorrelated. Only the airborne sound pressure responses and acoustical monopoles are focused for prediction and analysis of the pass-by noise. The limitation of the SMT method and its validation experiments will be illustrated.

14.4.1 Method of correlated equivalent monopoles In Fig. 14.2A, the velocity distribution over the sound radiating surface is used as a source strength descriptor. The machine’s surface is divided into incremental areas ΔSi with normal velocity vi. Each subarea is seen as an acoustical point source with volume velocity Qi 5 viΔSi. The source velocity vi can be measured on each subarea, for example, with the machine installed on a test bed.

Figure 14.2 Method of correlated monopoles: (A) piston source model and “direct” measurement of transfer functions; (B) reciprocal measurement of transfer functions [2].

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Transfer functions from each point source to the far field receiver position depend on their acoustical surroundings. They need to be experimentally measured with the source in situ. These measurements become practical even for sources in small spaces, like within an enclosure, when the principle of reciprocity is used. In the reciprocal experiment as shown in Fig. 14.2B an omnidirectional source with volume velocity Q0r is placed at the original receiver point and the sound pressures pi are measured on each subarea of the passive structure. The assumption behind this application of reciprocity is that the small fictitious piston sources on the source surface may be replaced by fictitious monopoles directly against this surface. If the mesh size is properly chosen, this is acoustically correct in most situations of real-life practices. The partial contribution to the far field radiated sound due to the airborne sound radiation from the engine or from certain parts of it, is given by:  0 X p pr 5 ðvi UΔSi ÞU i0 (14.15) Qr i If the transmission path is alternated, for example, by changing an enclosure, the source part of Eq. (14.15) remains the same, but the transfer function part has to be measured for the new situation. The method may work well at low frequencies and for simple vibration patterns considering its practicability. For example, for the analysis of interior noise in cars caused by the rather low frequency rigid body vibrations of the car engine, the method is expected to be far superior to the use of a single loudspeaker source as substitution source [3]. This method is also called as “transfer path analysis (TPA)” method. The principle is based on the method proposed by Mason and Fahy [4] and the Cremer’s description of a synthesis method using directional Green’s functions [5]. However, for high frequencies and for complex structural shapes and vibration fields, the large amount of data needed, makes this method unfeasible.

14.4.2 Method of uncorrelated equivalent monopoles The acoustical source using uncorrelated monopoles on the surface of the vibrating structure can be modeled. This method needs fewer measurements than the correlated monopole method. The phase of sound pressure responses can be neglected, while the reciprocal measurements of transfer functions can be retained. The uncorrelated monopole method has a better accuracy than the correlated monopole method at higher

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frequency and for complex vibrating structures. For small acoustical sources or compact radiating structures (i.e., with dimensions small compared to the wavelength of sound) often the radiated sound wave is rather directional. In these cases, the sound pressure phase cannot be neglected without causing the prediction errors, the method of uncorrelated equivalent monopoles is not applicable. The method of correlated equivalent monopoles will have to be applied as illustrated in the above subsection. 14.4.2.1 Source strength definition of uncorrelated monopoles The radiating surface is first divided into m subareas, which are considered as partial sources, see Fig. 14.3A. For truck engines, for example, such partial sources can be valve and distribution covers and oil sumps. It is assumed that on each subarea, the sound radiation of the structure may be replaced by that of n(j) uncorrelated monopole sources each with the same strength. The acoustical source strength of each subarea is defined as the total squared volume velocity of the n(j) monopole sources and given by Q2eq ðjÞ 5 nðjÞUQ2eq;i ðjÞ

(14.16)

whether or not this equivalent source strength is independent of the acoustical surroundings will be illustrated later. The transfer functions

Figure 14.3 Method of uncorrelated monopoles: (A) subdivision in partial source areas Sj; (B) reciprocal measurement of transfer functions [2].

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between the partial sources and a receiver position are first defined and their measurement method is illustrated below. 14.4.2.2 Transfer functions The transfer function between a subarea and a receiver position is defined as the average transfer function over the n(j) monopole positions. Because direct measurement of the transfer functions is difficult, the reciprocity principle is applied in the same way as mentioned for the correlated monopole method and shown in Fig. 14.3B. The average transfer function over the n(j) monopole positions is then given by nðjÞ  1 X p0i 2 Tj;r 5 (14.17) nðjÞ i51 Q0r 2ðjÞ The radiated sound due to the m radiating subareas is then given by p2r 5

m X j51

p2r ðjÞ 5

m X

Tj;r UQ2eq ðjÞ

(14.18)

j51

Eq. (14.18) clearly shows the distinction between the source strengths and transfer system properties. The acoustical strengths of the uncorrelated monopoles can be determined in two different methods as briefly illustrated below. 14.4.2.3 Determination of the source strength of uncorrelated monopoles One method of determining the source strength as illustrated by Eq. (14.16) is from sound intensity measurements [6]. This method is valid when the source radiates about the same power as that in the free field (e.g., on an engine test rig). For each subarea, the radiated sound power can be determined from sound intensity measurements on a measurement plane close to it. Now the equivalent volume velocity can be found from equating the measured sound power with the estimated power radiated by the uncorrelated monopoles. It is assumed that for most of the fictitious point sources, the radiation resistance equals that for a monopole on an acoustically hard baffle radiating into a half-space, the source strengths are then given by Q2eq ðjÞ 5 nðjÞUQ2eq;i ðjÞ  PðjÞU

2UπUc ρUω2

(14.19)

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where c denotes the speed of sound in the air, ρ is the density and ω is the radian frequency. Alternatively, the other method of a local enclosure for determining the equivalent volume velocities can be applied as the sound intensity method is not practical when the sources change rapidly. A vehicle engine on a test rig under fast run-up conditions is an example which is representative for the pass-by noise tests. It is impractical to measure sound intensity from a lot of discrete points for many repeatable run-ups. In the local enclosure method, the partial source S(j) under consideration, radiates sound into a temporarily attached local enclosure, the interior space of which is effectively shielded from the other parts of the engine. The method constitutes three steps. In the first step, when the engine is running, the mean square sound pressure p21;k inside the enclosure is measured at q different positions, as shown in Fig. 14.4A. In the second step, it is

Figure 14.4 Principle of determining the equivalent volume velocity using transfer functions within a locally attached enclosure [2]. (A) Sound pressure measurement with running engine; (B) n(j) uncorrelated monopoles; (C) reciprocal measurement of enclosure transfer function.

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assumed that the real source can be replaced by n(j) uncorrelated monopoles, as shown in Fig. 14.4B. The transfer functions between monopoles and microphones are given by 2 ðjÞ 5 Hi;k

p22;k Q2i ðjÞ

(14.20)

For the sound pressure, the index number 2 for the sound pressure measurements is used to distinguish from the index number 1 with the engine in operation as shown in Fig. 14.4A. The reciprocal transfer function measurement turns out to be practical as shown in Fig. 14.4C. From each of the q microphone responses in Fig. 14.4A, the partial volume velocity can be roughly estimated. Averaging over all q available microphone responses according to Fig. 14.4A would give a smoother estimation of the source strength, which is given by 8 !21 9 q < nðjÞ = X X nðjÞ 2 2 ^ eq ðjÞ 5 U Q (14.21) p21;k U Hi;k ðjÞ ; q k51 : i51 The estimations of the source strength according to both the methods according to Eqs. (14.19) and (14.21) should be consistent. 14.4.2.4 Validation experiments A laboratory experiment on the airborne sound transmission for an internal combustion engine in an automotive test room was studied in Ref. [7]. The purpose of the experiments is to compare measured sound pressure levels with predicted ones from Eq. (14.18). The equivalent source strength is determined using the intensity method and the agreement between the measured and predicted results according to Eq. (14.18) is quite good. This agreement holds for 400 Hz , f , 2000 Hz, even in narrow bands according to Zhenget al. [7], whereas it holds for one-third octave results for 200 Hz , f , 4000 Hz according to Verheij[6]. From these experiments with a combustion engine and with an engine simulator, both installed in relatively large spaces, the uncorrelated monopole method has provided a valid source strength descriptor. The laboratory experiments on an engine simulator without and with enclosures were studied for transmission path quantification in Ref. [2]. The results from an analysis according to Eq. (14.18) imply that the proposed source strength descriptor remains unaltered when the acoustical

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Figure 14.5 Equivalent volume velocity levels (1/3-octaves) of truck engine oil sump at the engine speeds of about 1000 and 1625 rpm determined from three different experiments [2].

surroundings of the engine simulator changes drastically. Fig. 14.5 shows the equivalent source strength levels of the oil sump of the engine simulator, determined from three different experiments. Because of the transient nature, the source strength varies with time. The data shown corresponds with an ensemble average of time segment samples over 1/16 s at apparent engine speeds of about 1000 and 1625 rpm. The results derived from the sound intensity measurements are obtained from the measurements at 32 measurement points rather close to the oil sump. The results obtained from the local enclosure method as shown in Eq. (14.21) are obtained from experiments with two different enclosures. One had a volume of 0.3 m3, the other 1.2 m3. In both the enclosures, four microphones are placed in corners, as shown in Fig. 14.4A. In the reciprocity experiments 22 microphones are positioned against the oil sump, as in Fig. 14.4C. The miniature sound source, which is used for these reciprocal experiments, has been described in Ref. [8]. It is seen from Fig. 14.5 that for 315 Hz , f , 3150 Hz (the most important frequency range for exterior noise from trucks), there are only minor differences in the source strength estimates. The measured and calculated data were also reported for the A-weighted sound pressure levels as a function of running speed in Ref. [8]. The differences of the predicted and measured sound pressure levels stay within 1.5 dB(A) for the apparent speed variation from 1000 to 2250 rpm. Because the sound pressure

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spectrum of the engine simulator was made equal to that of a genuine truck engine, this close agreement has validated the two source strength determination methods. The SMT was limited to machines or machinery components in the frequency range from 200 to 4000 Hz for source characterization. The elegance of the method is to get input quantity for numerical modeling of sound transfer problems. In cases where the phase relationships cannot be ignored (i.e., the correlated monopole method), there is a practical need for further development of measurement methods for volume velocity of vibrating structures. The uncorrelated monopole method is attractive for its relative simplicity, especially for radiators with complex shape and vibration behavior.

14.5 Airborne source quantification method ASQ is applied to separate the airborne noise sources on a vehicle and evaluate their individual contribution to the overall pass-by noise level. The technique is based on a TPA approach. The approach follows a procedure of four steps as outlined in Fig. 14.6. A detailed method description is presented below for an indoor test setup with vehicle on the chassis-dyno and linear arrays of microphones on both sides of the room. A conceptual picture of the approach is shown in Fig. 14.7.

Figure 14.6 Flow diagram of ASQ method [9].

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Figure 14.7 Conceptual picture of ASQ approach [9].

Step 1—Frequency domain ASQ model: two types of ASQ models of (1) a traditional linear phase-based pressure inversion method and (2) a power-based formulation can be developed in the frequency domain. The linear ASQ method tends to discretize the noise radiating components into coherent point sources, respecting a spacing of less than half the acoustic wavelength for the maximum frequency of interest. The summed contribution of the individual point noise sources to each target microphone k can be given by yk ðωÞ 5

k X

Qi ðωÞUNTFki ðωÞ

(14.22)

i51

where yk are the target microphone responses, Qi are the acoustic loads, and NTFki are the noise transfer functions between load i and target k. The acoustic loads can be identified in two ways: (1) by a direct calculation based on operating surface normal velocities and (2) by an indirect identification procedure using a pressure inversion method. The surface normal velocity method is the most suitable for the lower frequency range, while the pressure inversion method is better suited for the mid and higher frequencies and for components where measuring a surface normal velocity is not possible or practical, for example, for the tires and exhaust.

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In the application examples presented below, the acoustic loads are identified using an inverse estimation approach. A set of indicator microphones is uniformly distributed around the noise sources and a local transfer function matrix is measured between the source points and indicators. The operational loads are then identified from the indicator measurement data multiplied by the inverse of the local transfer function matrix and given by

 Qi ðωÞ 5 ½Hji ðωÞ21 Ufuj ðωÞg (14.23) where uj are the operational indicator measurements and [Hji(ω)] is the local transfer function matrix between the source points i and indicators j. The number of indicators j is taken higher than the number of source points i to ensure stability of the matrix inversion. In this case, the least square estimated method has to be applied to identify the operational loads at the source where the least square estimated transfer function matrix is calculated by the square root of the local transfer function matrix multiplied by its transpose in the front. The local transfer function matrix between the source points and indicators and the transfer functions between the source points and the target microphones are measured with a calibrated volume velocity source (VVS). The measurements are usually conducted in a direct way by consecutive excitation tests (one excitation per source point). Note that Eqs. (14.22) and (14.23) represent a complex, linear formulation of the problem, considering amplitude and phase in the load identification and noise contribution analysis. This complex, linear ASQ formulation is suited for closely spaced, correlated noise sources. More recently, a power-based ASQ approach was developed to overcome the limitations of the phase-based approach at high frequencies. When extending the frequency range to several thousand Hertz, the discretization into point sources becomes very dense due to the short wavelengths, and moreover the estimation of the operational loads by matrix inversion becomes very sensitive to phase errors. A power-based approach is more suited in that case. The power-based ASQ model assumes uncorrelated loads and omits the phase information in the formulation. With such an approach, larger surface areas or patches can be created that are represented by an average source strength. The target responses can then be formulated by equation y2k ðωÞ 5

k X i51

Q2i ðωÞUNTFki2 ðωÞ

(14.24)

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where Q2i are the acoustic loads expressed as auto-power spectrum density function; the noise transfer functions in this equation can also be considered as an average transfer from several discrete point sources. Here again, the acoustic loads are identified using a pressure inversion method. This can be expressed as:

2  Qi ðωÞ 5 ½Hji2 ðωÞ21 Ufu2j ðωÞg (14.25) The number of indicator responses should exceed the number of loads to have a well-determined system of equations when calculating the pseudo-inverse. An over determination by a factor 2 is typically taken as a rule-of-thumb. Still, one of the remaining drawbacks of the energetic pressure inversion in Eq. (14.25) is that it can return negative load power estimations, which is physically not realistic. There can be several reasons for this such as measurement noise on the data, missing sources in the analysis, etc. However, this drawback can be overcome by solving the above system equations with a constrained least squares method forcing the load estimates to be positive. The power-based ASQ approach is suited for uncorrelated, broadband type of excitations, allowing an extension of the frequency range up to frequencies well above 1 kHz. Step 2—Time domain synthesis of acoustic loads and partial noise contributions: in the second step of the method, finite impulse response (FIR) filter sets are constructed from the frequency-domain ASQ model. These filters allow a time-domain synthesis of the acoustic loads and their partial contributions to the targets starting from the measured indicator time signals [7]. When using a power-based model, scaling factors are applied to transform the sound pressure of the indicator measurements to acoustic loads. FFT convolution is used to do the required time-domain filtering. This FFT-based implementation makes use of the well-known Overlap-Add method and avoids time-consuming convolutions in the time domain. A proper filter preprocessing (treatment of delays, etc.) is important, making sure that the filters are causal and do not generate artifacts. The advantage of the time-domain synthesis is that streams of time data (loads, partial contributions, summed contributions) become available, enabling a dedicated pass-by noise processing (time and frequency domain) and sound quality analysis (listening and objective metrics). Step 3—Pass-by noise synthesis: In the third step of the approach, the pass-by sounds are generated for the zero position (x 5 0) on the left and right target microphone arrays by mixing the r target microphone responses synthesized in the previous step. The mixing is performed for

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each source contribution. First, the time-delay is removed from every synthesized target response signal. For example, when considering the source contribution of the exhaust, the applied time-delays are the travel times of the exhaust noise to reach the different target microphones. These time-delays can be derived from the phase slope in the NTF’s. By applying the time shifts, the target responses become well aligned in phase, avoiding interference problems when mixing the signals. The shifted signals are then recombined into a pass-by sound by taking into account the speed profile of the vehicle, which is measured from the chassis dyno. The pass-by sound is generated by running through the different targets, from microphone 1 in the front of the vehicle toward microphone r in the back, and meanwhile mixing the sounds of the closest two microphones. In a final stage, the Doppler shift is included by resampling the audio data. This is achieved by applying a nonlinear transformation of time, taking into account the time-varying distance or delay between source and pass-by noise target location. Step 4—Source contribution analysis: the output of the previous three steps allows several interesting analyses like: 1. analysis and ranking of the different source contributions in a pass-by noise test 2. comparison of the summed noise contributions with measurements 3. detailed time-frequency analyses 4. listening and sound quality assessment The ASQ technique can be applied in in-room test environments as well as outdoor. Three innovative techniques of a traditional pressure inversion method (linear ASQ), a power-based approach (energetic ASQ) and a signal processing technique using the transmissibility approach can help engineers better quantify the noise contribution of the different vehicle subsystems to the overall pass-by noise levels and allow them to set accurate targets for the subsystem components.

14.6 Transmissibility approach The ASQ technique is able to accurately separate different airborne noise sources and evaluate their contribution to the overall pass-by noise level. However, the ASQ technique has its limitation when dealing with high frequency harmonic noise sources as those in electric vehicles. In that case, the ASQ technique requires a very fine discretization of the electric

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motor in a large number of coherent point sources to ensure an accurate prediction of the loads. Large instrumentation and measurement efforts (large number of microphones, many FRF excitation tests, etc.) are then required, making the ASQ approach impractical. A new method is therefore proposed for this specific electric vehicle application case. The method is based on a transmissibility approach and appears to perform very well as a source separation technique due to the incoherent nature of the electric motor and tire/road noise sources. The method is based on a MIMO (multiple input multiple output) transmissibility estimation between multiple references indicators placed nearby the engine and tire/ road noise sources (system inputs) and the target microphones along both sides of the vehicle (system outputs). The transmissibility values are estimated from operational input and output measurement data. FRF measurements with calibrated speaker source are not required, which is interesting from a practical point of view. For every target microphone k, the transmissibility model can be formulated as follows: yk ðωÞ 5

n X

Tki ðωÞUri ðωÞ

(14.26)

i51

with ri are the operational references and Tki are the transmissibility values between the references and the kth target microphone. Accelerometers (electric motor) as well as microphones (electric motor, tires) can be used as input references. The transmissibility functions between all inputs and outputs are estimated and given by ½Tki ðωÞ 5 ½Sii ðωÞ21 U½Ski ðωÞ

(14.27)

where [Sii(ω)] is the input auto-power matrix (reference auto- and crosspowers) and [Ski(ω)] the cross-power matrix (cross-powers between all references and targets). A pseudo-inversion of the matrix is applied based on singular value decomposition (SVD). The transmissibility approach is totally different from the ASQ method in concept. When the approach is applied, any possible errors must be minimized to ensure reliable results. For example, (1) the engine and tire references must be uncorrelated to correctly estimate the transmissibility functions and (2) the cross-coupling between these references must be as small as possible. This is the case for the electric vehicle application example. The electric motor and tire/road noise sources are generally incoherent, the former is characterized by sharp, high frequency tonal

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components while the latter is characterized by broadband type of noise. The cross-coupling between engine and tire references is minimized when accelerometers are used as reference for the electric motor (mainly picking up motor noise, almost no tire/road noise leaking in) and the motor harmonics are filtered out from the tire/road noise of the microphone measurements in a preprocessing phase. Similarly, as in the ASQ method, a time domain analysis is performed once a good frequencydomain model is obtained. FIR filters are derived from the estimated transmissibility functions and applied to the reference measurement data to compute the partial noise contributions of the electric motor and each of the tires. Likewise, FFT convolution is applied to perform the required time-domain filtering.

14.7 Numerical prediction methods for the pass-by noise The vehicle pass-by noise can be predicted by means of numerical methods. Such methods can be applied to analyze the pass-by noise characteristics of a vehicle in its early development stage to reduce the experimental efforts. Such methods include the neural networks technique and the boundary element method (BEM). The fast multipole method (FMM) can also be applied to simulate very large BEM models to save the calculation time and to increase analyzable maximum frequency limit.

14.7.1 Neural networks approach A neural network consists of neurons. Neurons are simple processing units and connected to each other to form a network [10]. An output value of a typical artificial neuron is derived from several input values. The input values are multiplied by a weight, summed up, added with a bias and passed on to a transfer function. Advanced neural networks of the “multilayer perceptron” consist of several inputs influencing different layers of neurons. A neural network can be used as a predictive model which is trained from example data. Vehicle design parameters have a significant influence on the pass-by noise, but an exact analytical calculation of the pass-by noise at an early vehicle design stage is not feasible. The neural network method is applied for prediction of the vehicle pass-by noise to offer a feasible alternative [11]. A ranked list of vehicle parameters affecting vehicle pass-by noise is established and applicable to any vehicle where the vehicle parameters should be practical to collect. These parameters are used as input values

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for the neural network model. A sufficiently high number of training examples are required to train the network. The number of the training examples should be in thousands. The training examples are obtained by collecting test data from a large number of predecessor vehicles. Weighting factors have to be defined for further preparation of test data. A neural network for the estimation of vehicle performance, the data of vehicle parameters and test conditions are combined to be used as the input to the neural networks model for prediction of the pass-by noise. The averaged error over all test cases of the predicted pass-by noise level in comparison to the actual pass-by noise level should be just 6 1.4%. However, rather large deviations of 24 dB(A) for the predicted results are shown in a distribution over many data points. Deviations increase when a new, quieter vehicle is studied. The network has to be retrained with the latest vehicle technology in a continuing way otherwise technology leaps in the most recently developed vehicles may generate a possible source of errors. Another disadvantage of the neural network method is requiring the vast amount of test data from previous vehicle models, which could be hard to collect.

14.7.2 Boundary element method The BEM calculates the sound pressure level at a specified location in space which is excited by a medium near a noise source. The source and the receiver locations are modeled by mesh elements. The satisfactory performance of a BEM simulation depends on sufficient computer resources which are important prerequisites. A trade-off between model accuracy and available computer facilities should be made [10,12]. In order to predict vehicle pass-by noise, a highly complex model would have to be set up, which automatically leads to a requirement for high performance computing. In general, six to ten elements are required to accurately represent an acoustical wavelength. The number of elements has an impact on the maximum analyzable frequency range and computation time. If exterior noise propagation is modeled and analyzed for a whole vehicle, the number of elements is enormous. The calculation time increases heavily, resulting in this method not applicable in practice for the frequencies higher than 500 Hz [10]. The frequency resolution is another aspect of concern, which increases the computation time. The transfer function can be estimated from a small number of frequency data points. However, the quality of the estimated transfer function may be

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compromised [10]. A BEM model of the four major noise sources (engine, intake manifold, exhaust tailpipe, tire/road) plus vehicle body was established in Ref. [12] to estimate the pass-by noise at 23 specific frequencies in the frequency range of 19.953162.2 Hz. Each noise source was modeled via a generic source. The generic source should represent an approximated geometry of the real source dimensions. Thus the model is simplified, resulting in computation time being reduced. The sound pressure measurement results in the vicinity of the real noise source during a pass-by noise test can be used to reconstruct the radiated acoustic field of each generic source, so that the excitation velocities on the surface elements of the generic source are obtained. The predicted sound pressure values can be compared with the measured values. Transmission and reflection effects caused by the vehicle body and the ground can be considered in the BEM model where the pass-by noise evaluation points are arranged in a line of field points along both sides of the vehicle model at 7.5 m distance and 1.2 m height. Since the meshed structure consists of openings and multiple connections, the transfer functions between the generic sources and the evaluation points are obtained through the indirect BEM. The surface velocities on the generic sources and the corresponding transfer functions are combined to predict the pass-by noise where all noise sources are assumed to be incoherent. The calculated and measured maximum overall A-weighted sound pressure level of a pass-by noise test in third gear were compared [12] where the computed level value is slightly higher, the deviation of which is only 1.1 dB(A). However, the predicted and measured pass-by noise levels against track position were not compared. Further, this technique requires sound pressure measurements, otherwise the reconstruction of the acoustic field of the noise sources is impossible. After the normal surface velocity distribution is obtained from the existing finite element models, boundary element models are generated in order to simulate sound radiation. The normal surface velocities are used to calculate the sound pressure distribution in the far-field at discrete frequencies. Since the simulations do not include all excitation mechanisms, it is impossible to accurately quantify the sound pressure distribution. However, the directivity characteristics of the radiated sound field of the analyzed components can be qualitatively evaluated. The fast multipole boundary element method (FMBEM) can be applied to overcome the trade-off of the limited maximum frequency _versus excessive computation time of the traditional BEM [10].

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The FMBEM can be applied to solve the BEM problems with millions of degrees of freedom and reduce the number of degrees of freedom from the order of millions to the order of tens of thousands and increase the maximum frequency of analysis up to 2 kHz. The FMBEM can also be applied to calculate the transfer functions between the source and receiver locations in a pass-by noise test configuration. The major noise sources are modeled as point sources where their source strengths are quantified by volume velocity which can be measured or simulated. Sound reflections from the ground are considered in the model. The simulated and measured pass-by noise levels are compared from all transfer paths where an average deviation of up to 4 dB is found. These discrepancies may be related to the poor quality of the modeling of the noise sources inside the engine compartment.

14.8 Summary Simulation, analysis, and numerical prediction methods of the pass-by noise have been studied for source identification and sensitivity analysis based on TPA methods. Prediction synthesis model based on the TPA method can not only reproduce the level of vehicle pass-by noise, but also classify sources and analyze their contribution to total noise level separately. The sensitivity analysis can simplify the model or even improve its understanding. SMT facilitates the very convenient application of experimental reciprocity techniques for transmission path ranking. The SMT was limited to machines or machinery components in the frequency range from 200 to 4000 Hz for source characterization. The ASQ technique can be applied in in-room test environments as well as outdoor and can help engineers better quantify the noise contribution of the different vehicle subsystems to the overall pass-by noise levels. The ASQ technique has its limitation when dealing with high frequency harmonic noise sources as those in electric vehicles which can be overcome by the transmissibility approach. The neural network and BEM can be applied for prediction of the passby noise. However, the neural networks technique needs the vast amount of test data from previous vehicle models and has to be retrained with the latest vehicle technology in a continuing way. BEM is only applicable in the frequencies less than 500 Hz. The FMM can be applied to save the calculation time and to increase analyzable maximum frequency limit.

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Nomenclature awot(i) awot(i11) awot Ap Bp c Faero Fbearing Fbrake Fd(i) Fr [Hji(ω)] 2 Hi;k ðjÞ J Lwot(i) Lwot(i11) Lcrs(i) Lcrs(i11) Lurban Lpc m mg n n(j) Ne NTFki pj PðjÞ p21;k pr p0i p22;k q Qi _i Q Q0r

gear i acceleration in m/s2 gear i 1 1 acceleration in m/s2 (for vehicles tested in two gears) the vehicle acceleration during the wide open throttle (WOT) test runs the constants that depend on the tire and the vehicle’s position on the track, or logarithmic regression coefficients of the constant speed cruise test sound pressure level versus vehicle speed for the slope term the constants that depend on the tire and the vehicle’s position on the track, or logarithmic regression coefficients of the constant speed cruise test sound pressure level versus vehicle speed for the intercept term the velocity of sound (in m/s) the aerodynamic force the bearing friction the brake friction the driving force developed by the vehicle at 50 km/h for the gear ratio (i) the resistive force at 50 km/h the local transfer function matrix between the source points i and indicators j the squared acoustic transfer function the rotational moment of inertia of the vehicle’s kinematic chain gear i acceleration test sound pressure level (dB(A)) gear i 1 1 acceleration test sound pressure level (dB(A)) (for vehicles tested in two gears) gear i cruise test sound pressure level (dB(A)) gear i 1 1 cruise test sound pressure level (dB(A)) (for vehicles tested in two gears) the external noise level of a vehicle under typical urban traffic conditions or the estimate of the pass-by noise level the contribution of the tire/road noise sound pressure level the number of the divided radiating surface area a total vehicle mass the number of subsources the number of uncorrelated monopole sources each with the same strength the engine rotation speed in (rpm) the noise transfer functions between load i and target k the sound pressure at the measurement point j the average sound power over the radiating subdivided area the measured sound pressure square at receiver sound pressure at the receiver point r sound pressure measured at the source point i the measured sound pressure square at source the number of microphone responses the acoustic loads or the volume velocity flow rate corresponding to the subsource i the volume acceleration flow rate corresponding to the subsource i the source strength of a calibrated volume velocity acoustic source at the receiver r

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Q2eq;i ðjÞ Q2eq ðjÞ ri R Rr R2 Si SRCi Siu Sic SðWac ;Lpc Þ u SðW ac ;Lpc Þ

Sðmg ;Vmille ;Tor Þ u Sðm g ;Vmille ;Tor Þ c Sðm g ;Vmille ;Tor Þ S(j) [Sii(ω)] [Ski(ω)] ΔSi Tor Ttire Tj;r Tki TFij uj V V0 vi Vmille(i) Vmille Var(Xi) Var(Y) Waci Wac Xv Xv0 Xi X Y _Y y yðjÞ

359

the acoustical source strength of each subdivided area i the total squared volume velocity of the n(j) monopole sources the operational references the radius of the tire the rolling resistance force the correlation coefficient the sensitivity index the standardized regression coefficient the uncorrelated part of the sensitivity index Si the correlated part of the sensitivity index Si the sensitivity index of the acoustic power of the sources Wac and tire/road noise sound pressure level Lpc the sensitivity index of the uncorrelated acoustic power of the sources Wac and tire/road noise sound pressure level Lpc the sensitivity index of the parameters mg, Vmille, and Tor the sensitivity index of the uncorrelated parameters mg, Vmille, and Tor the sensitivity index of the correlated parameters mg, Vmille, and Tor the partial source S(j) under consideration the auto-power spectrum density matrix of inputs (reference auto- and crosspowers) the cross-power spectrum density matrix (cross power-spectrum density functions between all references and targets) the subdivided area of a subsource the engine torque or the full load torque which is developed by the engine when the vehicle’s accelerator pedal is fully depressed wheel torque the average transfer function over the n(j) monopole positions transmissibility values between the references and the kth target microphone the transfer function between the subsource i and the measurement point j the operational indicator measurements the vehicle speed in km/h the vehicle speed at the position Xv0 5 0 m the normal velocity of the subdivided area of a subsource the vehicle speed in the ith gear when the engine speed Ne 5 1000 rpm the vehicle speed when the engine speed Ne 5 1000 rpm the variance of Xi parameter the variance of the Y output the acoustic power of the subsource i the total acoustic power the position of the vehicle on the track the vehicle location/position in the track the ith input parameter or variable the input parameters or variables the output variable the estimated output variable through the linear regression model the mean of the sample the real output of the jth sample

360 yk y^ ðjÞ ωe ω ηy ρ βi

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the target microphone responses the prediction of the linear model output of the jth sample the engine rotation speed in rad/s angular frequency transmission efficiency in percentage (%) the density of air (in kg/m3) the regression coefficient of the Xi parameter or variable

References [1] Hamdad H, Pézerat C, Gauvreau B, Locqueteau C, Denoual Y. Sensitivity analysis and propagation of uncertainty for the simulation of vehicle pass-by noise. Appl Acoust 2019;149:8598. [2] Verheij JW. Inverse and reciprocity methods for machinery noise, source characterization and sound path quantification, Part 1: Sources. Int J Acoust Vib 1997;2 (1):1120. [3] Verheij JW. Experimental procedures for quantifying sound paths to the interior of road vehicles. In: Proceedings of the 2nd international conference on vehicle comfort, Part 1, Bologna; 1992. p. 48391. [4] Mason JM, Fahy FJ. Application of a reciprocity technique for the determination of the contributions of various regions of a vibrating body to the sound pressure at a receiver point. In: Proceedings of the Institute of Acoustics, vol. 12, Part 1; 1990. p. 46976. [5] Cremer L. The physics of the violin. Cambridge, MA: The MIT Press; 1984. [6] Verheij JW. Reciprocity method for quantification of airborne sound transfer from machinery. In: Proceedings of the second international congress on recent developments in air- and structure-borne sound and vibration, vol. 1, Auburn University, Auburn, AL; 1992. p. 5918. [7] Zheng J, Fahy FJ, Anderton D. Application of a vibroacoustic reciprocity technique to the prediction of sound radiation by a motored IC engine. Appl Acoust 1994;42:33346. [8] Verheij JW. On the characterization of the acoustical source strength of structural components. In: Proceedings ISAAC 6: advanced techniques in applied and numerical acoustics, Leuven; 1995. p. III 124. [9] Janssens K, Bianciardi F, Britte L, Van de Ponseele P, Van der Auweraer H. Pass-by noise engineering: a review of different transfer path analysis techniques. In: Proceedings of ISMA2014 including USD2014; 2014. [10] Huijssen J, Fiala P, Hallez R, Donders S, Desmet W. Numerical evaluation of source receiver transfer functions with the Fast Multipole Boundary Element Method for predicting pass-by noise levels of automotive vehicles. J Sound Vib 2012;331:208096. [11] Fry J, Jennings P, Taylor N, Jackson P. Vehicle drive-by noise prediction: a neural networks approach. SAE Technical Paper Series 1999-01-1740; 1999. [12] Genuit K, Guidati S, Sottek R. Progresses in pass-by simulation techniques. SAE Technical Paper Series 2005-01-2262; 2005.

CHAPTER 15

Summary and future scope Tan Li1,2 1

Maxxis Technology Center, Suwanee, GA, United States Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, United States

2

Tire/road noise or tire pavement interaction noise (TPIN) has been intensively studied since the 1970s, including measurement techniques [1], physical mechanisms [2], influencing parameters [3], modeling methods [4], and reduction approaches [5]. Significant improvements in this area have been observed in the last two decades. The measurement techniques on TPIN have evolved from simple overall SPL tests to more accurate on-board sound intensity (OBSI) tests, and then to sound field holography in the lab. Each technique has advantages and disadvantages. The roadside measurement is very easy and is regulation-oriented; however, it is not accurate or informative, and no steady and precise noise spectrum can be obtained. The lab measurement is very flexible, interesting, and is research-oriented; however, it is typically prohibitive in terms of equipment and sometimes fails to represent the actual driving conditions on the road. The on-board measurement is intermediate between the above two. In summary, the selection of the measurement technique should be based on the equipment available, measurement goals, and test environment. Because each measurement technique has its limitations in some aspects, it is typically suggested that multiple techniques are used to evaluate the TPIN characteristics from different perspectives. For example, coast-by (CB) can be used to measure the far-field exterior noise, close proximity (CPX), or OBSI for near-field exterior noise, in-vehicle for interior noise/vibration/sound quality, and lab drum for transfer path or modal responses. In addition, the on-board exterior noise measurement techniques are more readily accepted as replacements for pass-by noise (PBN) measurement techniques for research and product development purposes, because they are able to obtain noise data for a longer duration and with little environmental influence, which is favorable for the data analysis. As the technology of transducer, data acquisition, and computation advances, narrowband spectrum will be used Automotive Tire Noise and Vibrations DOI: https://doi.org/10.1016/B978-0-12-818409-7.00015-5

© 2020 Elsevier Inc. All rights reserved.

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more frequently for digital signal processing instead of octave, 1/3 octave, or 1/12 octave band; as a result, more precise spectral contents can be analyzed and mechanisms can be better identified. However, in terms of product approval, pass-by measurements and subjective evaluations will still be frequently used due to the unique characteristics of hearing perception, especially when different noise components at different frequencies vary. Jury testing is a statistical approach for subjective evaluations because different persons have different hearing perceptions. The physical mechanisms of TPIN include generation mechanisms, amplification mechanisms, and attenuation mechanisms. Impact (vibrodynamic or vibro-acoustic noise) and air pumping (aerodynamic or aeroacoustic noise) are the most important generation mechanisms and have been extensively investigated and included in most of the TPIN models. As an amplification mechanism, the cavity resonance has also drawn particular attention and interest. However, the dominant frequencies of the cavity resonance are so low that they might only have considerable effect on the vehicle interior noise, rather than the exterior TPIN. Pipe resonance due to the tread longitudinal grooves plays considerable roles in the PBN. The attenuation mechanisms are significantly related to the pavement characteristics and might be the key to reducing TPIN. Categorized by the medium of transmission, structure-borne noise in vehicle interior can be attenuated by vibration isolators such as suspension damper, while airborne noise in vehicle exterior can be reduced by absorption materials such as porous asphalt. It should be pointed out that some of the physical mechanisms in the literature are based on reasonable engineering assumptions, which have not been conclusively verified with solid evidence. The influencing parameters on TPIN can be divided into five categories: driver influence parameters, tire-related parameters, tread pattern parameters, pavement-related parameters, and environmental parameters. In general, on the same pavement and under the same environmental conditions, the most important parameters are speed, longitudinal force/ slip (acceleration), wear/aging, and tread pattern. The tread pattern might not be the most important influencing factor, but it is considered to be the most easily modified property of a tire. The pavement parameters, such as pavement texture and acoustic/mechanical impedance, are usually more important than tread pattern and other tire parameters. However, it should be noted that some studies on the influencing parameters were mostly based on the experimental measurements sometimes without reasonable theoretical explanations. In the future, the theory development

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and experimental validation should be more consolidated to reveal the physical mechanisms and the influencing parameters on TPIN. The trend of TPIN control might focus not only on the reduction of the noise level but also on the tuning of the spectral shape or the sound quality, which potentially will attract more attention. Analogous to psychoacoustics, similar activities have been conducted in vehicle/tire dynamics such as handling and ride to correlate objective vehicle responses with subjective evaluations, which can be called “psycho-dynamics.” In addition, usually noise, vibration, and harshness (NVH) is engineered at a later phase of the vehicle/tire design cycle and not much freedom is available for improvement considering the cost. Therefore more and more vehicle/tire companies involve both NVH group and Vehicle Dynamics group in parallel for product development because the two performances are usually highly correlated. The modeling methods of TPIN can be divided into three categories: deterministic models, statistical models, and hybrid models. The deterministic TPIN models include conventional physics models, finite element and boundary element models, and computational fluid dynamics models. They generally give insight into the noise generation and propagation mechanisms. The influence of each specific parameter on TPIN can be numerically analyzed. The conventional physics models typically use dynamic laws to calculate the tire vibration modes; the finite element and boundary element models are capable of obtaining the structure-borne tire noise under arbitrary excitations; the computational fluid dynamics models are intended for the airborne noise analysis. However, a large number of tire parameters are unavoidably needed for deterministic modeling, which is very difficult in practice. In addition, most of the models were limited to the frequency range of below 500 Hz, and few models went through experimental validation. Therefore the accuracy of these models is in question. The statistical TPIN models include traditional regression models, principal component analysis models, and soft computing models. They generally correlate the noise levels with the influencing parameters using only experimental data without the knowledge of underlying mechanisms. They typically have better accuracy than the deterministic models. The traditional regression analysis, including linear and nonlinear regression, is widely used for models with easy form of equations and having not many variables; the principal component analysis can be used to reduce the number of variables; soft computing such as neural networks has the advantage that no specific form of equations is

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needed for modeling. However, large amounts of data are needed for statistical modeling, especially when the number of variables is large; this results in high labor cost. In addition, most of the current models include only variables related to the pavement; few models have investigated the influence of tire parameters except for some fuzzy logic models. It was also unlikely or impossible to gain insight into the noise generation mechanisms or separate the different mechanisms. The hybrid TPIN models include tire pavement interface models, mechanism separation models, and noise propagation models. They combine the advantage of the deterministic model and statistical model. The hybrid model sheds light on the noise generation mechanism as a deterministic model, and also has good accuracy as a statistical model. The tire pavement interface model gives insight into the interaction and excitation between the tire and pavement; the mechanism separation model investigates the noise source individually; the noise propagation model is capable of predicting the TPIN at arbitrary receiver locations. However, the hybrid model tends to be more complex than the deterministic or statistical model. The careful selection of intermediate parameters is often the key to the success of the subsequent statistical correlation procedure. The deterministic models were dominant before the 2000s, especially for conventional physics models. With the development of computing technology, finite element method (FEM) and computational fluid dynamics (CFD) models are being used frequently thereafter. The use of these models has improved the understanding of TPIN generation mechanisms. Further, partly owing to the computing technology and data techniques, the statistical models have started playing an important role after the 2000s. The application of statistical algorithms to TPIN modeling has been found to be successful, and has led to fairly good prediction accuracy, which is very encouraging. In the 2010s, the hybrid models have become increasingly acceptable among researchers. Due to the pressure from the regulations and customers, the tire/automotive companies and pavement organizations have been endeavoring to reduce the TPIN. Tire industries attempted to optimize the tread pattern and tire construction for quieter tires, including application of pitch sequencing, tire cavity foam/fiber, and tread and rim modifications. Pavement industries attempted to modify the pavement texture, stiffness, and absorption for quieter pavement. In the future, more and more research should be focused on the interaction between tire and pavement, which would lead to a quieter combination rather than quiet tire and

Summary and future scope

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quiet pavement separately. The challenge for both tire and pavement industries is that the acoustic performance of tire and pavement usually conflicts with other performances, such as traction, handling, rolling resistance, hydroplaning, and durability. Therefore a compromise between noise reduction and maintaining other performances should be carefully considered and made. As noise from engine and wind turbulence reduces, TPIN becomes dominant noise source for passenger vehicles above 40 and 70 km/h for trucks. TPIN might become more dominant in the electric vehicles (EV) with internal combustion engine (ICE) removed. In addition, the sound spectral shape of EV is very different from that of ICE vehicles. Usually, EV shows worse sound quality especially at higher frequencies over 1000 Hz due to the electric motor generating tonal noise, which is not masked by the sound of ICE at lower frequencies. The dominant frequency range of TPIN from 800 to 1200 Hz might deteriorate the sound quality of EV. On the other hand, some countries start to put forth regulations on the minimum sound generated from EV at low speed considering the safety of pedestrians. Therefore the TPIN control or reduction in the future might become an art: (1) increasing TPIN at low speed while decreasing at high speed and (2) shifting the spectral contents to lower frequencies that would be more pleasant to humans. The sound quality also has to do with what the drivers/passengers expect from the vehicle under different conditions/maneuvers. For example, the loudness should decrease as vehicle slows down while the opposite trend will probably cause uncomfortable feeling. A dominant low frequency noise at specific engine orders especially during acceleration is preferred by a sports car while a low sound pressure level is usually targeted for a luxury car. Tires are designed to generate appropriate squeal noise during braking as warning signal and also during cornering (or drifting) for racing competitions to highlight the speed [6]. This new research area can be called “emotion acoustics” or “emo-acoustics,” as compared to the conventional “psychoacoustics” on the perception of sound for its physiological effect or and mechanism of “physio-acoustics.” This “emo-acoustics” target may change for different countries, different cultures, and different people. It may also change with time. For example, for some electric vehicles, artificial ICE noise was added to reflect the acceleration and power. In the present author’s opinion, this is analogous to the wagon body when automobile was first transitioned from the horse carriage in 1910s. As electric

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vehicles become prevalent, people may get used to the silent power instead of reflecting power by sound. As shown in Fig. 15.1, TPIN is due to the interaction between pavement surface and tire tread [7]. The tread pattern noise excited by periodic tread pitches is usually tonal and sharp. To some extent, the road noise excited by the pavement texture can mask the tread pattern noise, which is actually favorable to sound quality though the overall noise level increases. Regulators are more focused on vehicle exterior noise (purely airborne), while consumers are more interested in vehicle interior noise where sound quality is more important. More and more studies investigate how tire vibrations and noise transmit into the cabin through the suspension and car body, considering the tire as a component of the vehicle system. Therefore tire/road noise is better considered as vehicle/tire/road noise with tire as the bridge. The advancements of measurement and CAE (Computer-Aided Engineering) simulation capabilities in the last two decades have shed light on the tire noise/vibration mechanisms, such as transfer path analysis (TPA), noise/vibration components separation, statistical energy analysis (SEA), finite element analysis (FEA) and experimental modal analysis, boundary element method (BEM), and fluid structure interaction (FSI).

Figure 15.1 Tire/road noise generation mechanisms.

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For the purpose of improving fuel efficiency, more and more carmakers are switching from using steel body panel to using aluminum alloy or magnesium alloy body panel to reduce vehicle weight, especially for electric vehicles. Because the sound transmission loss is basically dependent on the area mass density (mass per unit surface area) for a panel without sound packaging materials, more sound will be transmitted into vehicle interior, both airborne and structure-borne, if the panel has less weight. Sound packaging materials are more and more commonly used on vehicle body panels and tire inner liners to damp the vibrations and insulate the sound. In summary, tire noise is a perfect integration of nearly all NVH challenges, including the following: • Vibro-acoustics, vibration-induced noise: road texture impacting tread block (analogous to chassis exciting vehicle body panel) • Aero-acoustics, air flow-induced noise: tread groove air pumping (analogous to exhaust pipe) • Rotating machinery (analogous to powertrain) • Cavity resonance (analogous to vehicle cabin) • A combination of periodic and random excitations: tread pattern and road surface • Flexible or nondeterministic boundary conditions: suspension, tire contact patch • Nonlinearity: quiet tire on one road/vehicle does not mean quiet on another road/vehicle • High damping: modes difficult to identify (In acoustics, high damping usually implies no or limited issues, which is not true for tire noise.) • Transfer paths: structure-borne and airborne • Friction noise: stick/slip between tread rubber and road surface • Air pumping generating shock waves (analogous to combustion explosion in engine) • Stick/snap (adhesion) mechanism between tread and pavement; air turbulence due to tire rotation (wind noise); pipe resonance and Helmholtz resonance from tread grooves; horn effect due to tire shape; vibration attenuation and sound absorption in the pavement, etc. Significant progress has been made in some of the areas over recent decades, but there are still a lot of unknowns. Sandberg and Ejsmont concluded “Tyre/Road Noise Reference Book” with a question: “Daybreak or sunset for tyre/road noise?” [8]. As a conclusion for the present book, we are confident to say “automotive tire/road noise is right in the morning.”

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References [1] Li T. A state-of-the-art review of measurement techniques on tire pavement interaction noise. Meas J Int Meas Confed 2018;128:325 51. Available from: https://doi. org/10.1016/j.measurement.2018.06.056. [2] Li T. A review on physical mechanisms of tire pavement interaction noise. SAE Int J Veh Dyn Stab NVH 2019;3. [3] Li T. Influencing parameters on tire pavement interaction noise: review, experiments and design considerations. Designs 2018;2:38. [4] Li T, Burdisso R, Sandu C. Literature review of models on tire pavement interaction noise. J Sound Vib 2018;420:357 445. Available from: https://doi.org/10.1016/j. jsv.2018.01.026. [5] Li T. Literature review of tire pavement interaction noise and reduction approaches. J Vibroeng 2018;20:2424 52. [6] Li T. Tire braking/cornering noise analysis: stick/slip mechanism. In: NoiseCon 2019, August 26 28, 2019, San Diego, CA; 2019. [7] T. Li, Tire pavement interaction noise (TPIN) modeling using artificial neural network (ANN) [PhD dissertation]. Virginia Tech; 2017. [8] U. Sandberg, J.A. Ejsmont, Tyre/road noise reference book. Kisa, Sweden; Harg, Sweden: INFORMEX; 2002.

Index Note: Page numbers followed by “f” and “t” refer to figures and tables, respectively.

A ABAQUS, 237 tire and road surface contact model in, 236f ABS. See Antilock braking system (ABS) Acceleration sensors, 133 134 Acceleration spectrum, 53 Acceleration test, 12, 314 and constant speed cruise test, 315 gear selections, 314 process of pass-by noise, 301 303 targets, 312 314 Accelerometers (electric motor), 209, 211, 352 353 Acoustic absorption material, 245 by alpha cabin, 245, 253 design of experiment (Taguchi), 264 268, 266t, 267t experimental modal test (impact hammer test), 262 263 with shaker excitation, 263 264 experiments on tires, 261 262 measurement methodologies, 250 253 alpha cabin, 252 253, 253f impedance tube method, 251 252, 252f of multilayer absorbent. See Multilayer noise absorbent material sound absorption coefficient. See Sound absorption coefficient (SAC) of materials testing, 251 252 tire cavity damping loss, 253 254 using finite element simulation, 260 261 Acoustic damping loss factor, 253 254 Acoustic impedance, 298 300 Acoustic mode shape function, 188, 191 Acoustic natural frequency, 187 188, 191, 194 Acoustic pressure fluctuations, 91 92

Acoustic reciprocity, 138 139, 138f Acoustics, 1 Acoustic transfer functions, 334 335 ADAMS-Car, 231, 231f Adhesion component, 234 235 Aero-acoustic noise sources, 94 95, 98 AFRs. See Airflow resistivities (AFRs) Airborne noise, 4, 94 96, 115, 137 138 structural borne noise and, 92f, 93 95, 93f transfer function, 138 139 transmission mechanisms, 93 Airborne noise radiation, 82 outdoor objective evaluation, 86 89 Airborne path, 289 Airborne source quantification (ASQ) method, 348 353, 348f, 349f, 357 Air displacement mechanisms, 298 300 Airflow resistivities (AFRs), 246 250 effect of, 248 250 experimental measurements of, 246 247, 247f layer thickness effect, 250 measured flow resistivity values of, 248t Air gap perforated panel separated by, 256 257 sound absorption with, 254 255 Air pumping noise, 28 29, 31, 35 generation mechanism, 97 98, 97f Air-pumping theoretical model, 3 Air volume velocity spectrum, 35 37, 36f ALE formulation. See Arbitrary Lagrangian Eulerian (ALE) formulation Alpha cabin, 252 253, 253f Ambient acoustic impedance, 298 300 Amplification mechanisms, 108 113, 298 300, 362 cavity resonance, 108 110, 109f, 111f, 112f horn effect, 111 113, 112f

369

370

Index

Amplification mechanisms (Continued) pipe resonance, 110 111 Analytical calculation method of tire mode, 160 173 three-dimensional ring model, 165 173 two-dimensional ring model, 161 165 Anechoic chamber, 77 78 Antilock braking system (ABS), 151 Arbitrary Lagrangian Eulerian (ALE) formulation, 220 221 ASQ method. See Airborne source quantification (ASQ) method ASTM C522-3 standard (2003), 246 247 Attenuation mechanisms, 362 Auralization models, of tire/road noise, 238 239 “Automesh,” finite element simulation using, 194 195 Automotive industry, statistical energy analysis method in, 293 Automotive powertrain system, 288, 293 294 A-weighted tire noise, 17, 17t filter, 79, 79f sound pressure levels, 298 300, 327 328, 347 348 of noise components, 17t tread pattern spectra and, 37f, 38f Axisymmetric tire model, 235 236

B Bearing hub/spindle, 75 76 BEM. See Boundary element method (BEM) Bessel functions, 191 BIEM. See Boundary integral equation method (BIEM) Binaural transfer functions (BTFs), 238 239 Boundary element method (BEM), 221 222, 222f, 355 357 neural network and, 357 Boundary integral equation method (BIEM), 221 BTFs. See Binaural transfer functions (BTFs)

C CAE. See Computer-aided engineering (CAE) Car body system, 133 134 acoustic cavity model of, 143f vibro-acoustic reciprocity in, 139, 139f Cavity resonance, tire, 188 189 amplification mechanisms, 108 110, 109f, 111f, 112f frequency, 71, 120 Cement concrete (CC) road surface, 305 CFD. See Computational fluid dynamics (CFD) Circumferential mode, 177 Close-proximity (CPX) method, 3 4, 10 12, 56 Coherent tread profile spectrum, 32 35, 34f Computational fluid dynamics (CFD), 229 Computer-aided engineering (CAE), 217 auralization models of tire/road noise, 238 239 simulation methodologies, 219 228 computational fluid dynamics, 229 deterministic methods, 219 223 energy methods, 223 227 finite element method, 219 221 hybrid methods, 227 228 transfer path analysis, 229 230 simulation tools, 217 tire pavement interaction model, 235 238 tire road interaction force and friction force induced vibration, 234 235 by force variation, 233 234 tire/wheel imbalance induced vibration, 233 trends and challenges in, 239 240 vehicle suspension corner module simulation, 230 232 Constant percentage bandwidth (CPB) spectrum amplitude, 328 330, 329f Constant speed cruise test, 314 315 Constant-speed pass-by noise level, 302 303 Conventional OBSI system, 10 12

Index

Conventional physics models, 363 364 Conventional structural-acoustic modeling, 190 Cornering force, 232 Correlated equivalent monopoles method, 341 342, 341f Coupled response, 190 Coupling loss factor, 224 225, 277 279 reciprocity of, 278 279, 286 CPX method. See Close-proximity (CPX) method CTWIST laser scanning machine, 31 32

D Damping loss factor, 282 of subsystem, 277 279 DBEM. See Direct boundary element method (DBEM) Deformable parallelogram arrangement, 231 Degenerate cavity resonances, 194 Dense asphalt concrete (DAC) road surface, 305 306 Design of Experiment (DOE) method, 327 Detailed tire geometry, 220 Deterministic analysis methods, 219 223 boundary element method, 221 222 finite element method, 219 221 statistical energy analysis method with, 283 waveguide finite element method, 222 223 Deterministic models tire pavement interaction noise, 363 364 tread patterns on tire/road noise, 28 Direct boundary element method (DBEM), 221 Direct method, 125 Displacement spectrum, 53 DOE method. See Design of Experiment (DOE) method Donnell Mushtari operator, 196 198 Donnell shell theory, 196 Dynamic imbalance, 119 Dynamic stiffness method, 126

371

Dynamic system, differential equations of, 174 Dynamic test, tire, 68 70

E EFEA. See Energy finite element analysis (EFEA) EMA methods. See Experimental modal analysis (EMA) methods Emo-acoustics, 365 366 Empirical models, 247 250 Energy finite element analysis (EFEA), 226 227 “Energy” in statistical energy analysis, 273 Energy methods, 223 227 energy finite element analysis, 226 227 statistical energy analysis, 223 226 Engine simulator, laboratory experiments on, 346 347 Excitations of suspension system, 116 123 generated by tire, 119 123 road roughness, 117 119 Exhaust orifice noise, 303 304 Experimental modal analysis (EMA) methods, 185 Experimental modal test (impact hammer test), 208f, 262 263 with shaker excitation, 263 264 Experiments on tires, 261 262 shaker excitation in, 263 264 Taguchi method analysis, 264 268 Exterior TRN, 1 3

F Fast multipole boundary element method (FMBEM), 356 357 FEM. See Finite element method (FEM) Finite element analysis (FEA), 110 111, 223 Finite element method (FEM), 219 221 differential equations of dynamic system, 174 establishment of, 175 177 modal analysis of, 173 179, 271 natural frequency and modal shape methods, 174 175 ring model and, 282

372

Index

Finite element method (FEM) (Continued) three-dimensional model, 175, 176f tire models, 218 two-dimensional model, 175, 176f Finite element model numerical models, 220 of tire pavement interaction, 235 238 Finite element (FE) simulation, 185, 194, 195t, 204f acoustic absorption material using, 260 261 experiment using model in, 207 210, 208f, 209f material properties of, 208t of structural-acoustic coupling of tire cavity, 206 207 of tire structural resonance, 203 205 using “automesh”, 194 195 Finite impulse response (FIR) filter, 351, 353 354 FIR filter. See Finite impulse response (FIR) filter First-order cavity resonance frequency, 121 First-order circumferential modal, 177, 180f FMBEM. See Fast multipole boundary element method (FMBEM) Frequency content of pass-by noise, 303 304 domain ASQ model, 349, 351 and wave number, 186 188, 187f Frequency response functions (FRFs), 123 125, 133, 262 acceleration, 266f with different inflation pressures, 153f with different masses, 155f of suspension and car body system, 133 134 tire-cavity-rim, 263f using impact hammer, 210f FRFs. See Frequency response functions (FRFs) FTire model, 160

G GA technique. See Genetic Algorithm (GA) technique

Generation mechanisms, 2 4, 91 airborne noise, 92f, 93 96 air pumping noise, 97 98, 97f of friction induced noise, 98 100, 99f of pass-by noise, 298 303 stick/slip (friction), 43 stick/snap, 43 structural borne noise, 92f, 93 95 transmission mechanism, 102 108 tire airborne noise, 76 tire noise, 13 and vibration. See Tire noise and vibrations tire/road noise, 32, 363 364, 366f vibration, 95 102 Genetic Algorithm (GA) technique, 217 Geometrical constraint approach, 220 221 Geometric nonuniformity of tire, 100 101, 101f

H Hamilton’s principle, 161 162, 165 Hammer test method, 138 Head Acoustics HMS system, 86 Head measurement system, 86 Helmholtz equation, 221 Helmholtz resonance mechanisms, 44 Hexagon tire, dynamic force variation induced by, 233 234 Higher-order analytical models, 220 Horizontally suspended tire, 150 Horn effect of amplification mechanisms, 111 113, 112f distance attenuation and, 298 300 of single tire resting, 298 300 Hybrid deterministic-statistical analysis method, 273 Hybrid models, tread patterns on tire/road noise, 28 Hybrid TPIN models, 363 364 Hyperelastic constitutive models, 175 176 Hyperelasticity, 236 Hysteresis component, 234 235 Hysteric friction, 234 235

Index

I IBEM. See Indirect boundary element method (IBEM) IMCM method. See Impedance-mobility compact matrix (IMCM) method Impact hammer test, 262 263 Impedance compact mobility matrix method, 283 Impedance-mobility approach, 200 203 Impedance-mobility compact matrix (IMCM) method, 190, 211 Impedance tube method, 251 252, 252f In-cabin tire airborne noise, 82f, 83, 87f, 88f Incoherent tread profile spectrum, 33 35, 34f Indirect boundary element method (IBEM), 221 Indoor airborne noise characterization, 76 82, 78f Indoor testing, 65 82 structural borne noise characterization, 67 76 high frequencies, 74 76 rolling tire impact test, 72 74, 72f, 75f stationary tire, 68 71 Influencing parameters, of vibration modal characteristics, 151 157 belt angle, 155 157 tire mass, 153 155 tire pressure, 152 153 tread pattern, 153 Young’s moduli of belt cord, 155 157 In-plane compression, 282 In-plane free vibration mode, 170 171 Interior noise, 115 Interior TRN, 1 2 Internal microphone, road experiment using, 212 Inverse iterative method of matrix, 174 175 ISO 362-1/ECE R51.03 test, 308 321, 313t acceleration test, 314 gear selections, 314 targets, 312 314

373

constant speed cruise test, 314 315 homologation process of, 319 320 interpretation of test results under, 315 316 off-cycle testing, 311 312 pass-by noise limits, 312 PMR ratio, 312 ISO 362-3 indoor simulation test, 316 321

L Lab drum surface. See Roadwheel surface Lanczos vector superposition method, 175 Lateral force, 232 Lattice Boltzmann method (LBM), 229 LBM. See Lattice Boltzmann method (LBM) Linear ASQ formulation, 350 Linear regression model, 339 340 Linear time-invariant system, 129 130 Load identification, 125 127, 144 145 on path point and principal component analysis, 139 140 suspension and car body, 134 135 Local transfer function matrix, 350 Logarithmic regression, 334 Low-order analytical models, 220

M Macro-texture, 44 Magic formulae, 232 M-ALE approach. See Modal Arbitrary Lagrangian Eulerian (M-ALE) approach Mapped face mesh, 194 195 Mass nonuniformity of tire, 100 Matrix inversion method, 126, 129 130 Mean profile depth (MPD), 3 definition, 53f for pavement, 51 53, 52f Mean texture depth (MTD), 305 Measurement methods of tire/road noise airborne noise radiation, 83 cavity resonance frequency, 71 indoor airborne noise characterization, 76 82, 78f

374

Index

Measurement methods of tire/road noise (Continued) indoor testing methods. See Indoor testing modal force hammer, 68 71, 69f noncontact, 70 on-board sound intensity, 86 87, 88f outdoor testing. See Outdoor testing pass-by noise measurement, 89 sound power, 79 81, 81f sound pressure level, 80f structural borne noise, 85f of tire transmissibility, 69f, 70 Mega-texture, 44 Microphones, 79 Microtexture, 43 44 amplitude, 43 44 MIMO. See Multiple input multiple output (MIMO) Modal analysis test and finite element method, 271 for tire measurement, 69f, 70 Modal Arbitrary Lagrangian Eulerian (MALE) approach, 221 Modal characteristics, 4, 177 of bias tire under radial excitation, 160t of tire vibration, 151 157 influencing parameters, 151 157 Modal density, 285 of bending vibration, 291 in frequency band, 281 of in-plane wave, 282 of subsystem, 276 Modal force hammer, 68 71, 69f Modal/Mode shapes, of tire of bias tires, 158 160, 159f of breathing mode, 158 160 degenerate, 194 195 first-order circumferential, 180f natural frequencies and, 165 166, 174 175, 177 179 of radial tires, 158 160, 159f, 178f tire tread natural frequency and, 196 199 Modal test of hammer impact excitation, 157 of tire method, 157 160, 158f

Monte Carlo simulations, 273, 338 339 Mooney Rivlin model, 175 176 Moore Penrose generalized inverse matrix, 131 MPD. See Mean profile depth (MPD) MTD. See Mean texture depth (MTD) Multilayer acoustic absorber, 254 255 Multilayer noise absorbent material, 257f analytical simulation of, 258 260 configuration design, 256 258 Multiple input multiple output (MIMO), 130, 352 353

N Natural frequency, 165, 187 acoustic, 187 188, 191 first-order, 158 160 and modal/mode shapes, 165 166, 174 175, 177 179 tire tread, 196 199 tire mass on, 153 154, 154f and tire pressure, 152 153, 152f of transversal vibration modes, 180t tread pattern on, 154f variation of vibration modes, 156t Natural vibration of tire, 151, 172 Near-field sound pressure measurement, 77 Neo-Hookean model, 175 176 Noise, 1 inside/outside, 115, 116f spectrograms, 21, 22f and vibration, control technology, 115 Noise separation, 7, 12 19, 47 close proximity measurement, 7 12 and combination, 20 24, 21f generation mechanisms, 13 noise components, 12 14, 13f, 24f order tracking analysis, 14 16 results, 16 19 techniques, 45 46 Noise transfer function (NTF), 230 Noise, vibration and harshness (NVH), 65 66, 151, 362 363 indoor test, 66f. See also Indoor testing outdoor test, 66f. See also Outdoor testing Noncontact measurement methods, 70

Index

Nonlinear finite element model, 220 221 Nontread pattern noise (NTPN), 14, 16f, 17, 19f, 29, 57 58 components, 30f pavement texture velocity spectrum and, 57f road surface texture on, 45 46 on rough and smooth pavement, 48 49, 49f, 49t separation technique, 14 16, 15f sound pressure level, 17t NP on Steel, 21 23 NTF. See Noise transfer function (NTF) NTPN. See Nontread pattern noise (NTPN) Numerical prediction methods for pass-by noise, 354 357 boundary element method, 355 357 neural networks method, 354 355 NVH. See Noise, vibration and harshness (NVH)

O OASPLs. See Overall A-weighted sound pressure levels (OASPLs) OBSI. See On-board sound intensity (OBSI) On-board sound intensity (OBSI) measurement method, 86 87, 88f system, 10 12, 11f tests, 361 362 Operational transfer path analysis (OTPA) method, 129 132, 144 145, 229 230 Optical sensor signal (once-per-revolution signal), 10 12, 14 16 Order synchronous averaging, 14 16 OTPA method. See Operational transfer path analysis (OTPA) method Outdoor testing, 83 89 objective evaluation, 83 89 airborne noise, 86 89 pass-by noise measurement, 89 structural borne noise, 83 85 subjective evaluation, 83 Out-of-plane vibration mode, 96, 172 173

375

Overall A-weighted sound pressure levels (OASPLs) rough and smooth nontread pattern noise on, 48 49, 49t total noise on, 46 47, 47t tread pattern noise on, 47 48, 48t Overlap-Add method, 351

P Pacejka models, 232 Pass-by noise (PBN), 5, 94 95, 333 airborne source quantification method, 348 352 average and scatter band, 327 contribution of powertrain, 310, 311f effect of air temperature on, 305 308 frequency content of, 303 304 generation mechanisms of, 297 308 horizontal directivity of, 300f ISO 362-1/ECE R51.03 test. See ISO 362-1/ECE R51.03 test ISO 362-3 indoor simulation test, 316 321 limits, 297, 298f measurement, 66, 89 data, 323 325, 324f techniques, 361 362 numerical prediction methods, 354 357 boundary element method, 355 357 neural network method, 354 355 outdoor and indoor test, 309f prediction model, 333 338, 335f research and development, 322 330 sensitivity analysis and propagation of uncertainty, 338 340 sound pressure levels, 301 302, 304, 306f, 326f sound radiation, 300 301 source and contribution identification, 321 322, 321f, 322f, 323t standard tire, 300 301 substitution monopole technique, 340 348 correlated equivalent monopoles method, 341 342, 341f

376

Index

Pass-by noise (PBN) (Continued) uncorrelated monopoles method. See Uncorrelated equivalent monopoles method synthesis, 351 352 transmissibility approach, 352 354 vehicle test, 297 Patterned on ISO, 21 23 Patterned on Steel, 21 23 Pavement friction, 235 texture, 43, 51f characterization, 50 55 mean profile depth, 51 53, 52f parameters, 43 rough and smooth, 45 50 shape factor (g-factor) for, 52f and tire/road noise, spectral trend between, 56 58 transfer function and regression model, 58 61 PBN. See Pass-by noise (PBN) PCA. See Principal component analysis (PCA) PCB modal force hammer, 69f Perforated plates, sound absorption with, 254 255, 257 258 Physio-acoustics, 365 366 Pipe resonance, 21 23, 362 amplification mechanisms, 110 111 frequency, 27 28 Polyfelt material, 245, 248 250, 248t Porosity or sound absorption, 43 Porous asphalt concrete (PAC) road surface, 305 Porous materials, 246, 257 258 sound absorption with, 254 255 Power-based ASQ approach/model, 350 351 Power spectrum density (PSD), 118 Power-to-mass ratio (PMR), 312 Powertrain system, 115, 121, 337 338 pass-by noise contribution of, 310, 311f Prediction model, 335f pass-by noise test, 333 338 on transfer path analysis method, 333, 342, 357

using directional Green’s functions, 342 Pressure inversion method, 349 351 Primary parameters, pavement, 43 Principal component analysis (PCA), 140, 141f PSD. See Power spectrum density (PSD) Psycho-dynamics, 362 363

Q Quarter vehicle suspension test, 76f, 104f Quasi-Monte Carlo methods, 338 339

R Radial first-order mode, 151 Radial vibration modes, 177 natural frequencies of, 156t, 179t Radiated sound pressure measurement, 78 Rayleigh Ritz method, 175 Reciprocal transfer function, 346 Reference accelerations, 312 314 Resistive force, 335 336 Reverberant chamber, 78 Ride disturbances, 137 138 Ring models, 160 three-dimensional, 165 173, 167f two-dimensional. See Two-dimensional ring model RMOD-K tire model, 160 Road experiment using internal microphone, 212 Road noise. See Tire/road noise (TRN) Road roughness, 117 119, 132 of B-class pavement, 119f power spectrum density of, 118 Road surfaces, 1, 3 4, 43, 45 46, 78, 83 84, 86, 117, 185 air temperature for, 306f pattern, 298 300 texture, 3, 99 100, 310 transition, 186f types of, 305 Road texture noise, 20 21 Road traffic noise, 2 3 Road wheel drum, 82 Roadwheel surface, 20 21 Rolling tire impact test, 72 74, 72f, 75f Rotating tire, 149 150

Index

Rough and smooth pavement, 45 50 noise components, percent contribution, 50 nontread pattern noise on, 48 49 total noise, 46 47, 46f, 47t tread pattern noise on, 47 48, 47f, 48t 175/70R13 tire, 149 150 Rubber hardness, 9

S SAC of materials. See Sound absorption coefficient (SAC) of materials SD road surface, 305 SEA. See Statistical energy analysis (SEA) Secondary parameters, pavement, 43 Self-excitation frequencies, 102 Semianechoic chamber, 77 78 Sensitivity analysis, 293 and propagation, uncertainty, 338 340 Shaker excitation, 263 264, 264f Shape factor (g-factor), for pavement, 51 53, 52f Signal processing techniques, 70 Singular value decomposition (SVD) method, 127, 130 131 Smooth pavement, 45 50 SMT. See Substitution monopole technique (SMT) Sound absorption coefficient (SAC) of materials, 245, 259f acoustic performance of, 248 250, 250f, 251f measurement methodologies, 250 253 multilayer, analytical simulation of, 258 260 normal incident, 252f oblique incidence, 253 254 with perforated plates, porous materials, and air gaps, 254 255 PSD amplitude peak values, 261f random incident, 253f theory, 246 250 airflow resistivity. See Airflow resistivities (AFRs) empirical models, 247 248 tire cavity with application, 255 256 values of, 249t

377

Sound, enhancement mechanisms, 2 Sound intensity measurements, 77 Sound power measurement, 77, 79 81, 81f Sound pressure levels (SPLs), 3, 80f, 117, 121, 191, 337 338 of noise components, 17t pass-by noise, 301 302 waterfall spectrum of, 122f Sound radiation of tire/road noise, 300 301 Source identification of pass-by noise, 321 322, 321f Source strength, 340 341 acoustical, 343 344 equivalent, 346 estimations, 346 of uncorrelated monopoles, 343 346 Source-Transfer-Receiver model, 333 334. See also Transfer path analysis (TPA) method Spatial direction matching, 207 208 SPLs. See Sound pressure levels (SPLs) SRC. See Standardized regression coefficient (SRC) SSD road surface, 305 Standardized regression coefficient (SRC), 339 Standard tire, of road noise, 298 300 Static imbalance, 119, 233 Static tire impact modal analysis tests, 72 Static tire transmissibility, effect of rolling on, 107 108 Stationary tire, 68 71 Statistical energy analysis (SEA), 223 226, 271, 283f advantages for, 225 applications, 294 in automotive industry, 293 with deterministic analysis methods, 283 modeling, 279 281, 280f of car body, 289, 290f input power in, 289 291 parameters in, 281 282, 285 287, 291 tire cavity system, 284 287, 284f tread, 284f

378

Index

Statistical energy analysis (SEA) (Continued) with two subsystems, 285f principle, 273 279, 287 coupling loss factor, 277 279 damping loss factor, 277 279, 278t energy description of subsystem, 276 power balance equation, 274 275, 274f simulation results and analysis, 282 tire cavity system, 283 288, 284f tire/road noise modeling and, 288 293 vs. test result, 292f statistical hypothesis in, 276 structure-borne tire noise by, 282 subsystem partition and, 279 281 theoretical coupling loss factor in, 272 of tire cavity, 226f tire for investigating, 272 variance models for, 225 226 vibration and noise by, 272 Statistical hypothesis in SEA, 273, 276 Statistical models, tread patterns on tire/ road noise, 28 Statistical TPIN models, 363 364 Statistical vibration velocity, 276 Stick/slip (friction) generation mechanism, 43 Stick/snap generation mechanism, 43 Stiffness nonuniformity of tire, 101 102, 102f Structural-acoustic coupling, 204, 206 207 Structural-acoustic system coupled response of, 190 finite element simulation of, 206 207 flexible wall in, 190 in tire cavity system. See Tire cavity resonance (TCR) noise tire-cavity-wheel, 189 190 Structural borne noise, 85f, 94 and airborne noise, 92f, 93 95, 93f indoor testing methods, 67 76 outdoor testing, 83 85 transmission mechanism, 102 108

low frequency transmissibility, 103 104 vibrations, 92 Structural natural resonance frequency, 187 Structure-borne tire/road noise, 4, 115 116 path, 289 transfer function of, 138 139 transfer path analysis method of, 137 144 on simulation, 143 144 on test, 141 142 Structure-borne vibration, 92 analysis of, 149 analytical calculation method of tire mode, 160 173 three-dimensional ring model. See Three-dimensional ring model two-dimensional ring model. See Two-dimensional ring model dynamic characteristic, 149 finite element method, modal analysis of, 173 179 differential equations of dynamic system, 174 establishment of, 175 177 natural frequency and modal shape, 174 175 two-dimensional model, 175, 176f modal characteristics of, 151 157 influencing parameters. See Influencing parameters, of vibration modal characteristics natural frequency. See Natural frequency Substitution monopole technique (SMT), 340 348, 357 correlated equivalent monopoles method, 341 342, 341f uncorrelated monopoles method. See Uncorrelated equivalent monopoles method Surface normal velocity method, 349 Suspension system, 115 116, 144, 230 and car body system frequency response function, 133 134 identification of load, 134 135

Index

transfer path analysis of suspension vibration, 135 137 excitations, 116 123 generated by tire, 119 123 road roughness, 117 119 front/rear, 133 Suspension vibration, 132 137 SVD method. See Singular value decomposition (SVD) method SWIFT-Tire model, 160 Synthesis model. See Prediction model Systematic error, 319

T Tachometer signal monitoring, 20 21 Taguchi method analysis, 264 268, 266t, 267t. See also Design of Experiment (DOE) method Target acceleration, 312, 314 TB model. See Trimmed body (TB) model TCM. See Tire cavity measurement (TCM)Tire cavity microphone (TCM) TCR noise. See Tire cavity resonance (TCR) noise Tertiary parameters, pavement, 43 Test pavement, 9 10, 10f Test tires sizes, 10t specifications of, 8t tread patterns of, 9f vehicles, 11f Texture, pavement, 43, 51f characterization, 50 55 features, 43 mean profile depth, 51 53, 52f metrics of, 60t shape factor (g-factor) for, 52f spectrum analysis, 44 45 and tire/road noise, spectral trend between, 56 58, 56f velocity spectrum, 53, 56 57, 59f TF. See Transfer function (TF) Theoretical analysis method, 286 Three-dimensional ring model, 165 173, 167f equation of motion, 169 170

379

in-plane free vibration mode, 170 171 stress and strain of tire crown, 166 168 3D tire pavement contact model, 235 236, 238, 238f 3D tread pattern/profile, 31 32 Tielking’s method, 149 150 Time-domain synthesis, 351 Time frequency plot of tire, 194f Tire cavity coupling system, 227 228 Tire cavity, damping loss factor, 253 254, 268 Tire cavity measurement (TCM), 212 on test wheel, 213f Tire cavity microphone (TCM), 212 Tire cavity resonance (TCR) noise, 185, 188 189, 245, 264 265 effect of loaded tire, 211 finite element simulation. See Finite element (FE) simulation frequency, 190 195, 193t, 264 high-frequency vibration and, 279 288 modes, 185 186 degenerate, 194 195 for un-deformed tire, 195f, 195t road experiment using internal microphone, 212 sound pressure magnitude of, 253 254 structural-acoustic coupling, 204, 206 207 tire-cavity-wheel system, 189 190 wave number, 186 188 Tire cavity system, 284f, 286 287 model of, 284f simulation of, 287 288 statistical energy analysis model of, 283 288 Tire-cavity-wheel structural-acoustic system, 189 190 Tire finite element model, 219 220 Tire grooves and slots, 110 111 Tire imbalance, 119 Tire models, 219 220, 232 with cavity system, 284 285, 284f computational fluid dynamics, 229 finite element method, 218 statistical energy analysis, 272, 279 281, 280f

380

Index

Tire models (Continued) parameters in, 281 282 subsystem partition, 279 281 tread, 284f vibration and noise, 272 Tire noise and vibrations, 95 102 air pumping, 97 98 amplification mechanisms. See also Amplification mechanisms cavity resonance, 108 110 horn effect, 111 113 pipe resonance, 110 111 friction induced, 98 100 impact induced, 95 97, 96f low frequency transmissibility, 103 104, 104f mid-frequency transmissibility, 105 107, 105f, 106f transmissibility and propagation path, 103f Tire nonuniformity, 100 102, 101f, 119 120 Tire pavement interaction noise (TPIN), 1 2, 7, 21, 27, 43, 117, 334. See also Tire/road noise (TRN) control/reduction, 365 366 finite element modeling of, 235 238 generation mechanism, 44, 362 influencing parameters on, 362 363 measurement techniques on, 361 362 mechanisms, 21, 31 microtexture amplitude and, 43 44 modeling methods of, 363 364 physical mechanisms of, 362 rough and smooth pavement, 45 50 Tire road interaction noise, 1, 95 96 force and friction force induced vibration, 234 235 by force variation, 233 234 Tire/road noise (TRN), 1, 7, 115 accurate replication of, 319 auralization models of, 238 239 computer-aided engineering. See Computer-aided engineering (CAE) contact model, 220 generation and propagation, 289

generation mechanisms, 32, 366f. See also Air pumping noise; Generation mechanisms measurement methods of. See Measurement methods of tire/ road noise and noise inside/outside, 115, 116f nontread pattern. See Nontread pattern noise (NTPN) pass-by noise. See Pass-by noise (PBN) radiation, 298 300 road surface on, 4 separation. See Noise separation simulation of, 291 293 sound intensity level of, 301 302 sound power measurement, 79 81 sound radiation of, 300 301 spectral trend between pavement texture and, 56 58, 56f statistical energy analysis method. See Statistical energy analysis (SEA) structure-borne, 115 116 transfer path analysis. See Transfer path analysis (TPA) method tread patterns on. See Tread patterns noise (TPN) and vibrations, 67 82 Tires dynamic behavior, 272 experiments on, 261 262 structural and acoustic modes, 185 186 Tire stiffness, 152 153 Tire tread natural frequency, 196 199, 198t structural-acoustic coupling of, 199 203 impedance-mobility approach, 200 203 Tire/tyre, 1 Tire wheel assembly system, 65 67, 119 bearing hub/spindle, 75 76 dynamic test, 68 70 outdoor testing, 83 89 on structural borne noise. See Structural borne noise Total noise, 29, 30f on rough and smooth road sections, 46 47, 46f, 47t

Index

spectrogram, 58f Total tire noise (TTN), 18 19, 19f TPA method. See Transfer path analysis (TPA) method TPIN. See Tire pavement interaction noise (TPIN) TPN. See Tread patterns noise (TPN) Traditional transfer path analysis method, 123 129 analysis of, 127 129 frequency response function, 124 125 identification of structural load, 125 127 Traffic noise, 1 Transfer function (TF), 58 61, 59f, 68, 342, 344 in engineering application, 130 of structure-borne tire/road noise, 138 139 vibro-acoustic, 139, 141 142 Transfer path analysis (TPA) method, 4, 115 116, 141f, 229 230, 333, 342 contribution of, 136t, 137f, 142f operational, 129 132 principal component analysis, 140, 141f of structure-borne tire/road noise, 137 144 on simulation, 143 144 on test, 141 142 of suspension vibration, 132 137. See also Suspension system symbolic block diagram of, 124f theoretical basis of, 123 133 tire/road interaction based on, 140 144, 293 traditional. See Traditional transfer path analysis method Transmissibility approach, 352 354 Transversal vibration modes, 177 natural frequency of, 180t Transverse section profile, 31 32 Treaded tire, 28 29 Tread impact noise, 28 29, 31, 35, 38 mechanism, 32 Tread patterns noise (TPN), 3 4, 13 14, 16f, 17, 19f, 20 21, 27, 29, 366 and A-weighted tire noise, 37f, 38f

381

components, 30f percent contribution, 50, 50t deterministic models, 28 hybrid models, 28 influence of, 153 on natural frequency, 154f for NP on ISO, 24 parameterization, 31 37 air volume velocity spectrum, 35 37 profile spectrum, 32 35, 33f for Patterned on ISO, 23 road surface texture on, 45 46, 45f rough and smooth road sections, 47 48, 47f, 48t separation technique, 14 16, 15f sound pressure level, 17t statistical models, 28 of test tires, 9f and tire noise, correlation between, 37 39 Trimmed body (TB) model, 143 144 TRN. See Tire/road noise (TRN) Turbulence noise, 20 21, 24 Two-dimensional axisymmetric model, 175 Two-dimensional ring model, 149, 161 165, 161f external force in, 163 initial stress, 164 parameters, 165 strain of ring, 163 using Hamilton’s principle, 165 velocities of point, 164 work of inflation pressure, 165 Two-microphone broadband method, 251 252, 268

U Uncertainty, sensitivity analysis and propagation, 338 340 Uncorrelated equivalent monopoles method, 342 348, 343f acoustical strengths of, 344 determination of source strength, 344 346, 345f source strength definition of, 343 344 transfer functions, 344

382

Index

Uncorrelated equivalent monopoles method (Continued) validation experiments, 346 348

V Vehicle indoor testing, 83 Vehicle interior noise spectrum, 57, 57f Vehicle suspension corner module simulation, 230 232 Vehicle test, pass-by noise, 297 Velocity spectrum, 53 texture, 56 57, 59f Very large eddy simulation (VLES) approach, 229 Very thin asphalt concrete (VTAC), 305 Vibration-acoustic systems, 273 Vibrations friction induced, 98 100 generation mechanisms, 95 102 in-cabin noise and, 83 outdoor noise and, 83, 84f propagated, 94 root-mean-square values of, 143 structure-borne. See Structure-borne vibration suppression, 263 tire noise and. See Tire noise and vibrations tire nonuniformity as, 100 102

tire/road noise and, 67 82 transmissibility, 67 Vibroacoustic system, 224, 227 reciprocity, 139, 139f simulation model, 143 transfer function, 139, 141 142 VLES approach. See Very large eddy simulation (VLES) approach Volume velocity source (VVS), 350 VTAC. See Very thin asphalt concrete (VTAC) VVS. See Volume velocity source (VVS)

W Waveguide finite element method (WFEM), 222 223 Wave number, frequency and, 186 188, 187f Wave theory, 280 281 WFEM. See Waveguide finite element method (WFEM) Wheel-tire-suspension system, 119 120

Y Yeoh model, 175 176 Young’s moduli of belt cord, 155 157

Z Zero-gap contact, 237 238