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A Vibro-Acoustic Study of Vehicle Suspension Systems:Experimental and Mathematical Component Approaches

Eskil Lindberg

Doctoral Thesis

Stockholm 2013Material and Structural Acoustics Group

The Marcus Wallenberg Laboratory for Sound and Vibration ResearchDepartment of Aeronautical and Vehicle Engineering

Postal address Visiting address ContactRoyal Institute of Technology Teknikringen 8 Tel: +46 8 733643650MWL/AVE Stockholm Email: [email protected] 44 StockholmSweden

Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stock-holm framläggs till offentlig granskning för avläggande av teknologie doktorexamenonsdag den 22 maj 2013, 13:15 i sal F3, Lindstedtsvägen 26, KTH, Stockholm.

TRITA-AVE-2013:17ISSN-1651-7660ISBN-978-91-7501-732-7

c© Eskil Lindberg, 2013

A Vibro-Acoustic Study of Vehicle Suspension Systems: Experimental and Math-ematical Component ApproachesEskil Lindberg

Material and Structural Acoustics GroupThe Marcus Wallenberg Laboratory for Sound and Vibration ResearchDepartment of Aeronautical and Vehicle EngineeringRoyal Institute of Technology

AbstractThe objective of the present work is to study the vehicle suspension as a vibro-acousticsystem of high complexity, consisting of many sub-systems with fundamentally dif-ferent acoustical properties. In a parallel numerical and experimental modelling ef-fort, important contributions to the understanding of its behaviour have been achieved.These findings are based on a balance between component investigations and globalmodelling of the complete system; they have been formulated for the transmission ofboth tyre-road excitation and friction-induced vibrations in the brake system.

Initially an experimental study was conducted on a full vehicle test rig studying thebroadband interior brake noise problem of, here named, roughness noise. The purposeof the study was twofold: first, to determine if the transmission from the source tothe interior of the vehicle was structure-borne; second, to study the complexity of thesuspension as a vibro-acoustic system. Parameters affecting the vibro-acoustic sourcewere varied to gain understanding of the source mechanisms. This experimental studylaid the foundation of the first part of this thesis (paper A) and provided the directionsfor the second part, the development of a mathematical modelling approach (paper Band C). In these two papers, methods for analysing the complex vibro-acoustic transferof structure-borne sound in a vehicle suspension system were developed. The last partwas then focussed on the wheel rim influence on the vibro-acoustic behaviour (paperD) of the suspension system. As a whole, the work clearly demonstrates that it is pos-sible to conduct component studies of subsystems in the vehicle suspension system;and from these component studies it is possible draw conclusions that very well mayavoid severe degradations in the interior noise of future vehicle generations.Keywords: Acoustics; Vehicle suspension; Disc brake; Wheel rim Roughness noise;Interior tyre-road noise Component mode synthesis; Undeformed coupling interface;

Dissertation

The work presented in this doctoral thesis was carried out at the Department of Aero-nautical and Vehicle Engineering, the Royal Institute of Technology (KTH) in Stock-holm, Sweden.

This thesis consists of two parts. The first part gives an overview of the research witha summary of the performed work. The second part collects the following scientificarticles:

Paper A. E. Lindberg, N.-E. Hörlin and P. Göransson. ”An Experimental Study ofInterior Vehicle Roughness Noise from Disc Brake Systems”. Applied Acoustics; 201374(3) , pp. 396-406.

Paper B. E. Lindberg, N.-E. Hörlin and P. Göransson. ”Component Mode Synthe-sis Using Undeformed Interface Coupling Modes to Connect Soft and Stiff Substruc-tures”. Shock and Vibration; 2013 20(1) , pp. 157-170.

Paper C. E. Lindberg, M. Östberg, N.-E. Hörlin and P. Göransson. ”A Vibro-Acoustic Reduced Order Model Using Undeformed Coupling Interface Substructuring– With Application to Rubber Bushing Isolation in Vehicle Suspension Systems”.Submitted to Applied Acoustics

Paper D. E. Lindberg. ”Tyre-Road Noise – Experimental Component Investigationof the Structural Dynamic Behaviour of the Rim”. Report, ISBN 978-91-7501-752-5.

v

The following papers are not included in this thesis due its content being out of thescope of this thesis.

* E. Lindberg, P. B. U. Andersson. ”Experimental Investigation of Sound PowerRadiation From Partly Open Enclosure With Numerous Interior Objects”. 19th Inter-national Congress on Acoustics, 2007, Madrid.

* P. B. U. Andersson and E. Lindberg. ”Boundary element method for intensity po-tential approach: Predicting the radiated sound power from partially enclosed noisesources”. Acta Acustica united with Acustica; 2012 98(4) , pp. 588-599

Some of the results have been presented in conferences.

* E. Lindberg, N.-E. Hörlin, P. Göransson. ”Experimental Study of Wire BrushBrake Noise on a Personal Car”. SAE Brake Colloquium and Exhibition 2009, Tampa,FL. (Oral only)

* E. Lindberg. ”Tyre-Road Noise – Experimental Component Investigation of theStructural Dynamic Behaviour of the Rim”. AIA-DAGA Conference on Acoustics2013, Merano.

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Acknowledgements

First of all I would like to thank my supervisors Nils-Erik Hörlin and Peter Göranssonfor your support and guidance. Nisse, you have challenged me and have given me newview on things, thank you! Peter, thank you for being there when I needed you!!

Martin Östberg thank you for the good cooperation with paper C.

A big thanks goes to Kent Lindgren for his devotion and expertise in the lab!

The industrial partners of this work are acknowledged: SAAB automobile, Opel andDaimler AG. People that deserve extra credit are: Anders Sköld, Maurice Claessens,Daniel Sachse, Ralf Lehmann, Otto Gartmeier and Eric Bauer.

To my fellow PhD-students, thank you all for your support and friendship. Specialthanks goes to Eleonora Nordgren and Mathias Barbagallo!

Finally to my family, mamma, pappa and Ida, thank you!

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Contents

I Overview and Summary 1

1 Introduction 31.1 Societal motivation of thesis . . . . . . . . . . . . . . . . . . . . . . 31.2 Industrial motivation of this thesis . . . . . . . . . . . . . . . . . . . 41.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Brake noise and friction-induced sound and vibrations 92.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Friction-induced noise . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Brake noise classification . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Roughness noise theory . . . . . . . . . . . . . . . . . . . . 11

3 Interior brake roughness noise 133.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2.1 Brake pressure . . . . . . . . . . . . . . . . . . . . . . . . . 143.2.2 System loading . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.3 Vehicle speed . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Conclusions and findings . . . . . . . . . . . . . . . . . . . . . . . . 243.3.1 Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4 Component mode synthesis approach 274.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

ix

4.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2.1 General problem . . . . . . . . . . . . . . . . . . . . . . . . 294.2.2 Change of basis . . . . . . . . . . . . . . . . . . . . . . . . . 304.2.3 Local modes . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . 334.3.1 Test structure . . . . . . . . . . . . . . . . . . . . . . . . . . 344.3.2 Vibro-acoustic response . . . . . . . . . . . . . . . . . . . . 344.3.3 Evaluation of the approach . . . . . . . . . . . . . . . . . . . 35

4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5 UCI as a framework 375.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Local substruture models and global assembly . . . . . . . . . . . . 38

5.2.1 Global model description . . . . . . . . . . . . . . . . . . . . 395.2.2 Results – total transmitted power . . . . . . . . . . . . . . . . 405.2.3 Transmission path . . . . . . . . . . . . . . . . . . . . . . . 425.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6 Wheel rim influence on interior noise 476.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.2 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.2.1 Interior noise and rim parmeter correlations . . . . . . . . . . 496.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7 Outlook 53

II Appended Papers 61

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Part I

Overview and Summary

1

CHAPTER 1

Introduction

This chapter summarises the overall objectives for the research that is discussed in thisthesis. After a brief introduction of the scope of the work the aims are briefly addressedending with the outline of the thesis.

1.1 Societal motivation of thesisThis is an applied study where structure-borne noise in vehicle suspension systemsis investigated. The societal motivation was to build competence and knowledge thatcould be used in the development of vehicles with reduced negative impact on theenvironment. Two environmental concerns, i.e. reducing noise pollution and energyconsumption, prevail. The functional aspect tying these problems together is the struc-tural mass. Both structure-borne sound and energy consumption can be argued to becorrelated to the structural mass of the vehicle. Generally speaking, high structuralmass leads to both less structure-borne noise and higher energy/fuel consumption ofthe vehicle and vice versa. Hence, in vehicles there must be a trade-off between en-ergy consumption and structural borne noise. Fortunately, problems of structure-bornenoise are not only governed by the structural mass: In addition, damping and iso-lation treatments can be designed together with optimisation of the stiffness and themass properties to open up profound possibilities. However, the minimisation of thestructural mass for a given noise problem requires a deep understanding of the vibro-acoustic system and the dominant source mechanisms, is required. This is where thisthesis intends to contribute to advance in the current state-of-the-art.

3

4 1 Introduction

1.2 Industrial motivation of this thesis

From an industrial/vehicle manufacturers, point of view the objective is to producevehicles which are attractive for customers, in other words meeting their demands;e.g. on the interior acoustic environment, and on the fuel consumptions of the vehicle.In this sense, the commercial and societal goals coincide well, thus underlining therelevance of the topic as such. For the present research, the industrial motivation asset by SAAB Automobile AB, the initial industrial partner in the project, was to gainknowledge and understanding of brake noise in general. This was in anticipation ofan increasing importance for this noise source as the weight of the cars of tomorrowcould be be expected to be substantially reduced compared to the present fleet.

The initial focus of the research was set on a particular source of interior noise, i.e. abrake noise problem usually referred to as moan noise, but gradually changed into amore general study of the complete vehicle suspension system and of a broadbandnoise phenomenon related to brake pad-disc interaction in general. This was driven bythe first results, which opened up for a more general investigation of the suspensionsystem as such, reducing the emphasis on the actual source mechanism in favour of astudy of the broadband transfer of vibro-acoustic power through the suspension as awhole.

1.3 Background

Research is the search for new and novel knowledge, where the scientific study is theactive, systematic and methodical process of accumulating this knowledge. The meth-ods used in the scientific study can be many e.g. cartography, case study, classification,experience, experiment, interview, mathematical model, simulation, statistical analy-sis and ethnography. The findings that are discussed in this work are mainly basedon two of these methods i.e., experiments and mathematical models. They are com-municated as this thesis which is a collation of papers that is summarised in a generalintroduction. The introduction is written with the purpose of giving a shorter and lesstechnical summary of the papers, and of providing a motivation to the thesis. Thisthesis consists of four appended papers A to D; in paper A and D experimental studieswere conducted and in paper B and C a mathematical approach was developed.

Often a distinction between basic- and applied- research is made. Basic research is

1.4 Overview 5

the scientific study, which is said to be driven by the curiosity of the researcher withthe primary goal of extending the human knowledge and theoretical understanding ofour existence. Applied research on the other hand is goal oriented, the goals can becommercial or social, set by e.g. companies, states or unions.

In the onset of this thesis work the goals were formulated by SAAB Automobile ABtogether with Vinnova and KTH. Even though the scientific work in this thesis wouldnot have started if it was not for the industrial need, the actual end result is not differentfrom any basic research work.

In the end, the most significant impact of the knowledge gained may very well be themodelling of the vehicle suspension as a vibro-acoustic system as such. This standsin contrast to a detailed investigation of a specific phenomenon, for instance frictioninduced vibrations.

1.4 Overview

The common denominator for the parts of the current work is the vehicle suspensionsystem itself. It was concluded from an early stage of the research performed in thisproject (paper A), that the vehicle suspension as a vibro-acoustic system is too com-plicated to be fully understood from purely global analyses, such as the full vehicleexperimental studies in paper A. The questions generated by that part of the workcould be summarised as: i) what is governing the friction source, which parametersare affecting the generation of vibrations in the contact? ii) how is the brake systemassembly (calliper, pads, disc etc.) affecting the final interior noise? iii) how do vi-brations generated in the disc-pad interaction transfer from the brake system in to thevehicle?

The vehicle industry has seen a tremendous development since the early introductionof the mass-produced cars. It is a well-known fact that vehicles make noise, howeverthe attitudes related to it have continuously shifted over the years. There are severalreasons for this: some are attributed to the overall performance of the vehicles them-selves, such as higher speeds (noisier) and more powerful engines (noisier); others areattributed to advances in technologies related to improved noise encapsulations andvehicle cabin isolation of air-borne noise. However, with increasing environmentalconcerns related to transport, there is a growing trend towards lightweight body struc-

6 1 Introduction

tures, potentially leading to lower fuel consumption and lower CO2 emissions. Thishas two sides, as seen from the perspectives of the present research. On one hand,the contradictory relation between structural mass and noise gives reasons for someconcern; this concern may partially be addressed with encapsulation and isolation ad-vances for air-borne noise and, in addition, with the results discussed and obtained inthis thesis. With the gain in the understanding of the interior noise associated withthe transfer of vibro-acoustic energy through the suspension system, the potential forimprovements is substantial.

In retrospect, it is clear that in order to understand how the components interact and in-fluence the vibro-acoustics, a mathematical modelling approach had to be developed.What was not as obvious, was which type of modelling would in the end facilitatethe analysis of complex geometries, such as the vehicle suspension system. The finiteelement method (FEM) is well-known for its flexibility and versatility, however, withincreasing geometrical complexity the method tends to involve increasing model sizesand corresponding computational challenges. Furthermore, to investigate the vehiclesuspension system, materials with very different stiffness and non proportional fre-quency dependence (i.e. rubber) have to be considered, such as rubber bushings andsteel arms: this is a problem. Finally the large number of components in the vehiclesuspension system as a whole, forms a computational and modelling problem in itself.To summarise the research had to adress a modelling problem with three main issues:i) system complexity (the number of components), ii) geometrical complexity and iii)material complexity.

The method in this thesis addresses all these modelling issues (however it is not saidthat it is the only way to come to a solution). In simple words it could be explainedin the following. In paper B a substructuring approach is suggested. Substructuring issimply a method where the local, in this case, dynamic behaviour of a component isseparately described together with coupling conditions for the specific coupling inter-faces. The local component may be described with a reduced set of equations in theglobal formulation. The idea is that the global modelling size may be reduced withthis approach, hence making it possible to solve with the computer resources of to-day. In paper B the local components were reduced using normal mode superposition,overcoming some of the geometrical complexity, where a reduced set of these modesare used in the global formulation. In its classical version, component mode synthesis(CMS) does not reduce the the modelling size of the coupling interfaces, a limitationwhich could be a potential problem in the current context. In paper B this problem is

1.5 Outline 7

suggested to be overcome by using to an advantage the material complexity mentionedabove. Typically, the rubber steel mismatch in structural stiffness is large for rubberbushings connected to steel arms, and in paper B it is shown that if a stiffness ratiobetween interacting bodies for a given geometry is large then it is enough to modelthe coupling interfaces as undeformable (for a given acceptable error). This reduceseach coupling interface to only 6 degrees of freedom (DOF) from whatever number ofDOFs (often in the order of several thousands). The suggested method of undeformedcoupling interfaces (UCI) was further explored in paper C where the simplicity of thecoupling conditions was further utilised. Here, the UCI-method was suggested as afundament of a reduced order model (ROM) of a subsystem of a vehicle suspensionsystem consisting of one link arm connected to a vehicle body through two rubberbushings.

There is one component of the vehicle suspension system which frequently is ne-glected, namely the wheel rim. As a further step in demonstrating the importanceof adequate tools for dealing with structural-borne noise in the suspension system, anexperimental component investigation of the relative influence of this particular partwas performed (paper D). In this investigation it was shown that the interior noise ina vehicle using two different sets of rims could have in the order of 5 dB differencefor the same nominal driving conditions. In this work it was shown that this differencecould, contrary to common knowledge, be associated with the stiffness of the rim.

In summary, the subject of structure-borne noise in vehicle suspension system willcontinue to be a challenge for researchers and vehicle industry for many years to come.With the results discussed in this thesis, a point of view on how this challenge may betackled is given, that possibly could alleviate some of these problems.

1.5 Outline

In the next chapters a summary of the research discussed in papers A to D is found.

• Chapter 2 gives an overview of the related research in the field of friction-induced noise and vibrations, and disc brake noise in general.

• Chapter 3 presents an overview of the experimental study on the disc brakeroughness noise.

8 1 Introduction

• Chapter 4 presents an overview of the mathematical modelling approach of com-ponent mode synthesis using undeformed coupling interfaces.

• Chapter 5 presents an overview of the reduced order modeling approach sug-gested for vibro-acoustic modelling of the vehicle suspension system.

• Chapter 6 presents an overview of a component investigation of the wheel rim.

• Chapter 7 gives an outlook for future research.

• Appended papers A to D give the complete results of the thesis.

CHAPTER 2

Brake noise and friction-inducedsound and vibrations

The first part of this thesis consists of an experimental investigation of the interiorbroadband vehicle brake noise phenomenon referred to as wire brush noise, roughnessnoise or rubbing noise. This chapter aims at giving a background into the theory of therelated friction-induced noise and vibration problem. It serves as a starting point forbuilding the understanding of the suspension system influence to the problem.

2.1 BackgroundThe subject of friction-induced sound and vibrations is truly multidisciplinary and havemany applications e.g. music acoustics (bow instruments), seismology and railwaynoise (curve squeal). The common factor of all of these is that an unstable frictionforce creates a dynamic excitation of the interacting bodies. A friction force is a non-conservative entity and is governed by the tangential stresses created by the relativemotion of two bodies Shpenkov (1995). Friction forces may, from a micro-structuralviewpoint, be explained as adhesive junctions formed by asperities in contact, and theshear force needed to cause breakaway Sheng (2008). When asperities break loose,they release stored elastic energy, resulting in a vibro-acoustic response. In addition,the ploughing effects of abrasion wear Wriggers (2006) can also be a mechanism inthe vibro-acoustic source. The exact type of excitation is highly dependent on theproperties of the contact, such as the surface roughness, the sliding speed, and thecontact pressure Persson (2000). Various types of noise phenomena with different

9

10 2 Brake noise and friction-induced sound and vibrations

spectral frequency contents are associated with friction, such as tonal and broadbandnoise, either due to feedback of structural resonances or surfaces roughness. In 1979,Yokoi and Nakai (1979) made a classification of friction-induced noise to be eitherrubbing or squealing. According to this work, rubbing is a broadband phenomenonwhere a large frequency range is excited, whereas squealing is a high pitch tonal noisewhere only a narrow frequency band is excited.

2.2 Friction-induced noiseIn the literature, a vast amount of knowledge can be found on the acoustic behaviour ofsome of the important local contact parameters, primarily from different experimentalstudies. For instance, Yokoi and Nakai (1979, 1980, 1981a,b, 1982) have shown ex-perimentally in a series of papers that noise levels (sound recorded close to the contactand vibrations of one of the contact bodies) have strong correlation with both surfaceroughness and sliding speed. Furthermore, these results have been confirmed by othersand further studied on similar effects for various types of materials and setups, Othmanand Elkholy (1990); Othman et al. (1990); Stoimenov et al. (2007); Ben Abdelouniset al. (2010); Zahouani et al. (2009); Jibiki et al. (2001). However, most publicationsconcerning friction-induced noise focus understandably on the squealing noise, per-haps due to its perceived annoyance. This type of noise is mostly associated with astick-slip phenomenon, a concept sometimes used loosely but in general stems froma variation in the friction force. It can originate from the difference of dynamic andstatic friction coefficient or varying normal force caused by for example resonances,and can occur on many different length scales. Therefore the source mechanism maybe seen as a local or global phenomenon of the surface in contact. For further dis-cussion of stick-slip phenomena see for instance Akay (2002); Sheng (2008); Persson(2000); Chen et al. (2005).

2.3 Brake noise classificationDespite the multitude of brake noise phenomena, it may be argued that all of themcan be classified as belonging either to squealing and/or roughness friction-inducednoise. However, it is also common to classify brake noise according to where in thefrequency spectra the noise phenomenon can be expected. For instance, Akay (2002)uses this kind of classification which serves as a good tool to find a common name ofthe phenomenon and thus, the appropriate literature on the subject. In fact, there are

2.3 Brake noise classification 11

many different names of brake noises, sometimes without a clear and unique corre-spondence. Most attention concerning brake noise has been focused on the high-pitchtonal-noise phenomenon, such as, the disc brake squeal, (DBS) phenomenon (out ofthousands see Chen et al. (2005); Papinniemi et al. (2002); Kinkaid et al. (2003); Hoff-mann and Gaul (2008)). Another, scarcely studied, tonal brake noise problem is themoan phenomenon (to the knowledge of the author the core of the literature is Nackand Joshi (1995); Gugino et al. (2000); Wang et al. (2003); Kim et al. (2005); Kimand Park (2006); Hoffmann and Gaul (2008)). Common for these tonal brake noiseproblems are that they are considered to have a strong dynamic coupling to the sup-porting structure. This coupling is known to be a non-linear feedback between struc-tural dynamics and unsteady surface contact, Sheng (2008); Chen et al. (2005), wherestructural resonances create an unstable friction force that feeds energy back into theresonance. For instance, DBS occurs when a circumferential mode of the disc is trig-gered, and a dynamic force is created at the same frequency as the mode, resulting inan unstable system. In addition, there are many other brake noise phenomena whichmay not arise from an unstable non-linear feedback phenomenon, which has to someextent been studied in literature, for example (hot and cold) judder and roughnessnoise (wire brush). Judder occurs when the disc exhibits non-uniform behaviour inthe circumferential direction, e.g. disc thickness variations Sheng (2008); Hoffmannand Gaul (2008). However, the roughness brake noise problem seems not to havebeen studied much in the literature. The source may be described as a broadband“rubbing/roughness/scratch” noise. Its broadband nature, compared to the tonal natureof for instance DBS, suggests a fundamental difference of the generating mechanisms.Perhaps the most prominent is that the roughness phenomenon does not exhibit a stronglink between structural resonances and the source mechanism itself. A supporting il-lustration comes from flow acoustics, where steady mean flow whistle noise, such asthe tones from a flute, are by necessity considered as non-linear feedback mechanisms.In contrast, noise sources of broadband character, are often considered to have a weaklink between system resonances and sound generating mechanism, e.g. the broadbandpart of a turbulent sound generated by a fan Carley and Fitzpatrick (2000); Powell(1961).

2.3.1 Roughness noise theory

The surface roughness and the sliding speed are two very important parameters whencharacterising roughness noise. How the surface roughness of the interacting bodiesaffects noise generation has been studied for quite some time. For instance, Yokoi and

12 2 Brake noise and friction-induced sound and vibrations

Nakai (1982) used a so called pin-on-rim setup where they pressed a steel rod onto anunlubricated rotating disc. The surface roughness of the disc was varied between mea-surements, and they concluded that there is a correlation between increasing surfaceroughness and an increase in sound pressure and vibration levels in the system. Theyfound that the noise could be predicted with the simple formula, Eq. (2.1):

∆Lp (dB) = 20 log10( HHref

)m, (2.1)

where H is a statistical value of the surface roughness, and m = 0.8 for the overallvalue of the sound pressure level, (SPL) and m = 1.2 for the peak SPL for the rod res-onance frequencies. They showed that there is a strong correlation between increasedsliding speed and the sound and vibration levels observed in the system. The relativesound pressure level change due to increasing speed could then be approximated bythe relation:

∆Lp (dB) = 20 log10( VVref

)n, (2.2)

where V is the sliding speed and n is a value that can range between 0.6 and 1.1.The correlation between surface roughness and noise has also been confirmed Oth-man and Elkholy (1990) and Ben Abdelounis et al. (2010). Furthermore, Othman andElkholy (1990) also stated that the correlation is independent of the contact sample sizeand material. As a matter of fact, also the correlation between speed and noise statedby Yokoi and Nakai (1982) has been confirmed by Smyth and Rice (2009); Ben Abde-lounis et al. (2010). Moreover, Smyth and Rice (2009) showed that the sliding speedhad no effect on the frequency content of the roughness noise, and Ben Abdelouniset al. (2010) showed that the noise dependency on the surface roughness and the slid-ing speed could be separated. They found that the problem may be modelled using thesame variables as Yokoi and Nakai (1982), but using 0.8 ≤m≤ 1.16 and 0.7 ≤n≤ 0.96,as

∆Lp (dB) = 20 log10(( VVref

)n ( HHref

)m). (2.3)

In addition, Othman et al. (1990) have stated that “The magnitude SPL is sensitive tovariation in contact load; increasing the contact load tends to increase the SPL and viceversa”. In that paper a spring stylus was run over a rough surface and the roughnesswas estimated from the sound generated.

CHAPTER 3

Interior brake roughness noise

This chapter presents an experimental study of interior brake roughness noise. Theexperiments were conducted in a laboratory environment, the test object was a smallpassenger car with disc brakes. The study showed that the problem of interior rough-ness noise can be viewed as a structural-borne noise problem well correlated to boththe vehicle speed and the brake pressure.

3.1 Experimental setup

The experiments discussed here were performed under laboratory conditions, where asmall passenger car was put on rollers (see Fig. 3.1). The test object was selected for itssize and weight, based on the hypothesis that roughness noise is more prominent for alightweight vehicle. The main part of this study consisted of several noise and vibrationrecordings, for different vehicle speeds and brake forces. In each measurement thebrake force and vehicle speed were kept constant through the recording, and all noiseand vibration signals were acquired simultaneously. The sound pressure was recordedboth inside the passenger cabin and close to the brake system. The accelerations wererecorded at numerous locations in the brake system. For the sake of conciseness theresults herein are from measurements conducted while driving only the left front wheelof vehicle. Detailed explanation of the setup and the measurements can be found inpaper A, together with a discussion of sources of errors in the measurements.

13

14 3 Interior brake roughness noise

Figure 3.1: Photograph of the full vehicle experimental rig.

3.2 Results and discussion

3.2.1 Brake pressure

It is clear from the observations made in the experimental study that the interior rough-ness noise may be considered as a broadband phenomenon (see paper A). The mea-surements show that increased brake pressure leads to a broadband increase of theinterior SPL. This may also be observed concerning the vibration levels of the brakepad (see paper A).

In Fig. 3.2 the normalised total (0.1-1 kHz) levels of the acceleration of the calliper(X-,Y- and Z-directions) and interior SPL are plotted as a function of brake pressure,the corresponding vehicle speed is 2.9 km/h and all curves are normalised to the accel-eration level of the calliper in Y-direction for a brake pressure of 1/2 bar and speed of2.9 km/h. Two visualisation lines are added, the dashed line shows the corresponding3 dB per doubling of brake pressure slopes i.e. linearly proportional brake pressure(P), and the dashdotted line shows the slope that is proportional to the brake pressure

3.2 Results and discussion 15

0.5 1 2 4 80

5

10

15

20

25

Brake pressure (log10

scale) [bar]

Nor

mal

ised

Lev

el0.

1−1k

Hz [d

B]

Visualisation line ∝P

Visualisation line ∝P 2/3

Interior SPLCalliper

x

Callipery

Calliperz

Figure 3.2: Total normalised Levels between 0.1-1kHz , Function of brake pressure. InteriorSPL, calliper acceleration levels, circles interior SPL, calliper acceleration in Z-,Y-,X-direction, crosses, stars and triangles respectively, with the correspondingvehicle speed of 2.9 km/h, normalised with the acceleration level of the calliper Y-direction for a brake pressure of 1/2 bar and speed of 2.9 km/h. Two visualisationline are added, the dashed line show a 3 dB per doubling of brake pressure slopei.e. linearly proportional to the brake pressure (P), the dashdotted line slope isproportional to the brake pressure as ∝ P2/3.

as ∝ P2/3. Note that in Fig. 3.2 the brake pressure is plotted in a logarithmic scale.

As discussed in the previous chapter, increasing the brake pressure while keeping thesliding speed constant will result in an increase of the interior noise in the vehicle andthe vibrations of the brake system.

Based on the assumption that the vibro-acoustic frictional source is proportional tothe stored elastic energy released in the breakaway when the asperities break loose,it could be argued that the source level should be linearly proportional to the contactpressure and hence increased by 3 dB per doubling of the contact pressure. Indeed,as may be seen in Fig. 3.2, the total (0.1-1 kHz) acceleration level of the calliper inthe vertical (Z-) direction follows this quite well. On the other hand, the slopes of theinterior SPL and the calliper acceleration in the X- and Y-directions appear to haveslopes that are proportional to the brake pressure as ∝ P2/3. Keep in mind that the con-


tact plane of disk and pad is the XZ-plane and the sliding direction is in the Z-direction.

In an attempt to describe the vibro-acoustic source, one could argue that the vibrationslevels generated in the contact zone should be proportional to the stiffness (or to theresistance in motion). The broadband character of this source may then be explainedas local stiffness variations in the contact zone, where the overall level is consideredto be proportional to the ”DC” component of the stiffness. Assuming that the ”DC”component of the stiffness in the normal direction could be represented by Hertz con-tact theory and the tangential resistance to motion by an elasto-plastic analogy of theCoulomb’s friction law, then, for Hertz contact theory the normal elastic contact stiff-ness is proportional to the contact force (Johnson (1985)) as Kn ∝ F2/3

n , where Kn is thenormal contact stiffness and Fn is the normal force. From the elasto-plastic analogy ofthe Coulomb’s friction law one could then argue that the friction force can be viewedas a plastic ”stiffness” as Kplastic

t ∝ Fnµ where µ is the friction coefficient. From thisthe following vibration level relation could then be formed,

∆La (dB) = 10 log10( PαPαref

), (3.1)

where Pref is an arbitrary reference contact pressure, and α = 2/3 for the levels in thenormal direction to the contact zone and α = 1 in the tangential (or sliding direction).

If the contact between pads and disc could be described by Hertz theory and Coulomb’sfriction law then it is interesting to see that there seems to be a link between the normalcontact stiffness (Hertz theory) and the interior SPL. It should also be noted that theinterior SPL has a slope very similar to both the calliper accelerations in X- and Y-direction. Possible explanations for these behaviours, see Fig. 3.2, might be: i) most ofthe vibro-acoustic energy is realised when asperity break loose in the sliding directionin the frictional contact, and due to the orientation (sliding direction coincides fairlywell with the vertical direction) of the brake system the vertical direction is mostly ex-cited, ii) the vibration levels of X- and Y-directions are not uniquely dependent on thenormal contact stiffness, instead they might be dependent on the plastic frictional con-tact stiffness, iii) the interior SPL is more related to calliper vibration levels in the X-and Y-directions than in the Z-direction . Possibly the suspension with shock absorberisolates and absorbs these vibrations more efficiently. Based on the type of brake-disc-pad assembly, on the suspension system (transfer path) and on the hypothesis fromEq. (3.1), a relation for the interior SPL may be written as,


∆Lp (dB) = 10 log10( P2/3+ γPP2/3

ref + γPref), (3.2)

where γ = Ht/Hn is a constant that gives a measure of the relative influence of eachexcitation direction to the interior noise Ht = Psound/Fexci

t and Hn = Psound/Fexcin . This

constant γ could be experimentally determined. From the shaker measurements dis-cussed in paper A the constant was determined as,

γ =

√√√√∫ 1000

100|Ht( f )|2 d f∫ 1000

100|Hn( f )|2 d f

(3.3)

where f is the frequency in Hz and Hn and Ht is the measured transfer functions ofsound pressure over excitation force in Y- and Z-direction respectively. In the currentinvestigation γ was found to be 0.10. In Fig. 3.3 the interior SPL is plotted togetherwith three visualisation lines from Eq. (3.1) with α = 2/3, α = 1 and Eq. (3.2) usingthe experimental γ = 0.10. These data are recorded for the brake pressure rangeof 2.5-5 bar since this was the range in which the best agreement for the SPL couldbe found in Fig. 3.2. A clear correlation for the interior SPL may be observed inFig. 3.3 with the combined model. It should be noted that the extreme values, a zeroγ or an infinite γ, correspond to a model proportional to only P2/3 or P respectively.In the current investigation the experimental γ was found to be small and hence theinterior SPL had a slope close to the curve for P2/3. However, having said that, for adifferent design of the brake and suspensions system a different γ would most likelyhave been found. Thus, from the combined Hertz contact theory and a Coulomb’sstiffness analogy model of the interior SPL, it is suggested that the orientation of thebrake and suspension system is an important design parameter for the reduction ofinterior roughness noise.

3.2.2 System loadingYet another operational parameter having a significant influence on both the interiornoise and acceleration levels of the brake system, is the applied brake pressure. This isquite obvious from the clear trend that can be seen with increased brake pressure anda corresponding increased acoustical response (see Fig. 9 paper A). This dependencebetween interior noise and the contact pressure has to the knowledge of the author notbeen extensively investigated before. Thus, the strong link between the brake pressureand the interior noise is a new and original result arising out of this work.


2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

Brake pressure [bar]

Nor

mal

ised

Lev

el0.

1−1k

Hz [d

B]

Visualisation line ∝PInterior SPL

Visualisation line ∝P 2/3+P 0.1

Visualisation line ∝P 2/3

Figure 3.3: Total normalised Levels between 0.1-1kHz , Function of brake pressure. InteriorSPL, with the corresponding vehicle speed of 2.9 km/h, normalised SPL for abrake pressure of 2.5 bar and speed of 2.9 km/h. Three visualisation line are added,the dashed line show a 3 dB per doubling of brake pressure slope i.e. linearlyproportional to the brake pressure (P), the dashdotted line slope is proportionalto the brake pressure as ∝ P2/3 and the solid line show the combined model inEq. (3.2).

Observing the shifting in the frequency of the peaks in Fig. 9(b), paper A, togetherwith the amplification in the different frequency bands, see Fig. 9(a), paper A, indi-cates that there might also be a process where the vibro-acoustic system is affectedby the brake pressure. Hence, not only the source mechanisms are affected by thecontact pressure but also the actual transmission paths between the source and the in-terior SPL. One possible reason for this behaviour shown in Fig. 9, paper A, could bethe coupling conditions in the contact zone itself, that is, the increased brake pressureleads to stronger coupling and hence the vibro-acoustic system is changed. Anotherhypothesis might be that an increased brake pressure will also lead to an increasedbrake force, and this force must be carried by the calliper. This may pre-load the bush-ings and result in geometrical non-linearities when different connectors change relativeposition, thus also changing the vibro-acoustic system.

In Fig. 3.4 the acceleration levels of the outer brake pad are shown, with Fig. 3.4(a)


showing a zoom of the three highest peaks that could be seen in Fig. 9(b), paper A, forthe three different non-zero brake pressures. In Fig. 3.4(b) the acceleration levels aredrawn for three different situations, the thick black and the dashed lines are for the twomeasurements with a shaker excitation. The thick black line is for the case of a 110 kgexternal load and was used to simulate the brake force at high brake pressure. Thedashed line is for the case when no external load was used, for the same amplitude ofelectric signal to the shaker. In both cases the brake pressure was kept at 5 bar. Sincean adaptor was necessary to enable shaker excitation, the thin solid line in Fig. 3.4(b)is included to show that the system still is fairly intact, despite the external load. Thethin solid line shows the results from similar measurements as in Fig. 3.4(a), exceptthat the adaptor was used, when 5 bar brake pressure was used for a vehicle speed of1.9 km/h. For further information on the adaptor setup see paper A.

Interestingly enough, when comparing the curves in Fig. 3.4, there is a shift upwardsof the two highest (in frequency) peaks with the load (Fig. 3.4(b)) and this shift seemsto be of the same order of magnitude as may be observed in Fig. 3.4(a). Hence, thehypothesis that the static brake force loading may change the vibro-acoustic systemproperties appears to be valid.

The static loading influence on the interior noise is highly dependent on the vibro-acoustic transfer path properties, thus governing how much noise is transferred intothe vehicle compartment for a given excitation. The effect of the static loading fromthe brake force is modelled using measured transfer functions (see Eq. (3.4)). Thesewere measured (calliper acceleration to interior sound pressure) with and without the110 kg load and an estimate of the interior noise was made from the acceleration ofthe calliper. Three different transfer functions were measured separately with a shaker,exciting the calliper in the three coordinate directions and simultaneously measuringthe acceleration, in the direction of the excitation force, in the excitation point andthe interior sound pressure. The interior noise was estimated by using acceleration(all three coordinate directions) measured on the calliper for the case of 5 bar brakepressure and 1.3 km/h vehicle speed. The total level was estimated by treating eachcoordinate directions as being uncorrelated. In Fig. 3.5 the total level of the transferfunction estimation with and without the external load is shown together with the di-rectly measured interior SPL. The plot is zoomed in at the frequency region between500-700 Hz since it is the region where the strongest amplification of interior SPL canbe observed for increased brake pressure (see Fig. 9(a) paper A). The interior noise


550 600 650 700 75060

62

64

66

68

70

72

74

76

78

80

Frequency [Hz]

Leve

l [dB

re.

1 μ

m/s

2 ]

5.0 [bar]3.3 [bar]1.8 [bar]

(a) Acceleration levels of the outer pad in the disc rotationalaxis direction, when applying external pressure to the brakeliquid. dashed line 1.8 bar, thin line 3.3 bar and thick line5 bar. Vehicle speed 1.3 km/h. No adaptor, (Zoomin fromFig. 9(b) paper A, 5 Hz resolution

550 600 650 700 75070

72

74

76

78

80

82

84

86

88

90

Frequency [Hz]

Leve

l [dB

re.

1 μ

m/s

2 ]

Shaker, 0 [kg]Shaker, 110 [kg]Roller, 0 [kg]

(b) Acceleration levels of the outer pad in the disc rotationalaxis direction. Dashed line shaker excitation of brake calliperin disc rotational axis direction no external load, no rotation,5 bar pressure. Thick line shaker excitation of brake calliperin the disc rotational axis direction a 110 kg external load, norotation, 5 bar pressure. Thin line roller excitation, 5 bar. Allusing an adaptor, 5 Hz resolution

Figure 3.4: Graph comparing the frequency shifts, effect of an external force and the brakeforce, for the pad acceleration in normal direction to disc.


was then estimated using

|pest|2 =

∣∣∣arolx

∣∣∣2 ∣∣∣Hshap, ax

∣∣∣2 +∣∣∣arol

y

∣∣∣2 ∣∣∣∣Hshap, ay

∣∣∣∣2 +∣∣∣arol

z

∣∣∣2 ∣∣∣Hshap, az

∣∣∣2 (3.4)

where pest is the estimated interior sound pressure and arol is the acceleration measuredin X, Y or Z direction when braking with the roller. Hsha

p, a is a transfer function betweeninterior sound pressure and driving point acceleration (X, Y or Z direction) either withstatic loading or with out loading, measured with a shaker. The estimated interior noisefor the two cases is compared with the measured interior noise from the same measure-ment as when arol was recorded in (see Fig. 3.5).

There are of course limitations with this procedure of estimating the interior noise andthe assumptions made. The first assumption implies that the brake system (calliper,disc and pad assemble) could be treated as a rigid body suggesting that the movementof the system could be described using six degrees of freedom (DOF), the three spatialdirections and the three rotations around the corresponding axis. These DOFs couldideally be represented using six independent shaker measurements of the brake sys-tem. Here, only three independent shaker measurements were used. Secondly, assum-ing that the different shaker measurements could be conducted separately, also impliesthat all measured directions could be treated as being uncorrelated. These assumptionsmay appear very crude, since there will of course be correlation between the differentDOFs, and a three DOF representation of the motion of the brake system may be acrude approximation. But, interestingly enough the results presented in Fig. 3.5 givesa good representation of the interior noise despite these simplifications. Furthermore,it appears that the model using the loaded transfer functions have a better representa-tion of the directly measured results. Hence, it could be argued that the system loadingeffect discussed above has an influence on the transfer path problem. Moreover, it hasalso been demonstrated that there is a clear link between vibrations in the calliper andthe noise inside the vehicle.

3.2.3 Vehicle speedTo investigate the influence of the vehicle speed, Fig. 3.6 shows the sound pressure,inside the vehicle (a), and acceleration levels, of the brake pad (b), respectively when5 bar pressure is applied to the brake liquid for the three speeds 1.3, 1.9 and 2.9 km/h.The plotted pad vibration was measured in the Y-direction (inward disc rotational axisdirection). What can be noted in Fig. 3.6(a) is that changing the vehicle speed es-sentially corresponds to a broadband increase of the overall SPL inside the plotted


500 550 600 650 70015

20

25

30

35

40

45

50

55

60

65

70

Frequency [Hz]

SP

L [d

B r

e. 2

0 μP

a]

MeasurementEstimation without loadEstimation with load

Figure 3.5: Measured and estimated SPL for 5 bar brake pressure and 1.3 km/h using the adap-tor. Thick line, direct measurement. Thin line, estimation using “unload” transferfunction. Dashed line, estimation using “load” transfer function.

frequency range. Consequently, no frequency band seems to be affected more thananother, as was the case in Fig. 3.4 for different brake pressures. It is futhermore clearfrom Fig. 3.6(b) that the peaks in the frequency response do not shift with increasingspeed.

Roughness noise is probably present in all vehicles with solid material friction brakes.However, it is mostly masked by other noise sources. To the knowledge of the authormost of the cases where wire brush (roughness) noise is reported as a problem arefor low vehicle speed when background levels are lower, so the effects of tyre-roadand other sources are of course important in how the noise event is perceived. In thisinvestigation the masking effects were minimised to allow for a better picture of thegeneration of the excitation itself.

One of the goals of the present work was to see how the interior roughness brakenoise in the vehicle correlates to the sliding speed. Furthermore, it gave a possibilityto study how results from experimental studies of simplified setups such as the pin-on-rim setup by Yokoi and Nakai (1982), may be related to the problem of an entirebrake system including the vibro-acoustic transfer path problem. In the literature itmay be found that statistical values describing the surface roughness are important pa-


100 200 300 400 500 600 700 80025

30

35

40

45

50

55

60

65

70

Frequency [Hz]

SP

L [d

B r

e. 2

0 μP

a]

2.9 [km/h]1.9 [km/h]1.3 [km/h]

(a) Sound pressure levels

100 200 300 400 500 600 700 80068

70

72

74

76

78

80

82

84

86

88

90

Frequency [Hz]

Leve

l [dB

re.

1 μ

m/s

2 ]

2.9 [km/h]1.9 [km/h]1.3 [km/h]

(b) Acceleration levels of brake pad,Y-direction

Figure 3.6: Levels for different speeds. Thick black line 1.3 km/h, dashed line 1.9 km/h andthick gray line 2.9 km/h. Brake pressure in all cases 5 bar.


rameters that govern the frictional noise source mechanism, but measurement results inliterature have also suggested that surface roughness parameters and sliding speed pa-rameters may be independently studied, Ben Abdelounis et al. (2010). In other words,sliding speed as a noise generating parameter may be studied without knowledge ofthe parameters describing the surface roughness. In addition, the size of the contactpairs should not affect the behaviour. It may be seen in Fig. 3.6 that there is indeeda broadband increase of both interior noise levels and brake system vibrations. Asstated by Smyth and Rice (2009), the noise dependence on sliding speed should notaffect the frequency content, but only increasing the overall level of the noise, which isverified for the current problem see Fig. 3.6. It may also be argued that sliding speeddependence of the noise problem is simpler to model than the brake pressure effect,as there seems to be little system altering effect associated with change of the speed.In Fig. 3.7 the interior total (0.1-1 kHz) normalised SPL is shown as a function ofthe vehicle speed for the brake pressure 1.3 and 5 bar respectively, the normalisationchosen as the total SPL from the lowest speed using the same brake individual brakepressure. The limits from the two equations Eq. (2.2) (Yokoi and Nakai (1982)) andEq. (2.3) (Ben Abdelounis et al. (2010)) are also included in the graph. In fact, it canbe seen that even though these formulas were derived from simplified measurementsand the results from this study is for a much more complex setup, the results correlatesurprisingly well.

3.3 Conclusions and findingsThe main results from measurements performed on a full vehicle laboratory test rigare presented. The test rig was designed by the author for the purpose of full vehiclein-situ measurements of brake noise. Evidently it is possible to reproduce the effectsof friction-induced noise in a vehicle using this test rig.

3.3.1 Findings

The vibro-acoustic excitation of the roughness noise vibrations may be divided intotwo components. That is, i) vibro-acoustic excitation in the sliding direction, in thesemeasurements a linear proportionality to the brake-pressure was found, ii) the vibro-acoustic excitation in normal direction of the contact plane, in these measurements anon-linear proportionality to the brake-pressure was found (the brake pressure to thepower of 2/3 is proportional to the acceleration levels). The proportionalities in both

3.3 Conclusions and findings 25

1 2 3 4 5 6 70

2

4

6

8

10

12

14

16

18

Roller speed [km/h]

Nor

mal

ised

SP

L 0.1−

1kH

z [dB

]

Ben Abdelounis et al.Yokoi and Nakai1.3 [bar]5.0 [bar]

Figure 3.7: Total normalised SPL between 0.1-1 kHz as a function of roller speed. Crosses,interior noise for a brake pressure of 1.3 bar. Circles, interior noise for a brakepressure of 5 bar. Dashed line, limits from Eq. (2.3). Dotted line, limits fromEq. (2.2). Normalisation total SPL of individual signal and 1.3 km/h.

cases can be argued to be linked to the stiffness, where the resisting force (stiffness) inthe sliding direction is directly proportional to the brake pressure which is consistentwith Coulomb’s friction law. The contact stiffness in the normal direction is propor-tional to the contact pressure to the power of 2/3, according to the Hertz contact theory.

Combined models of the Hertz contact theory and the Coulomb’s friction law maythen be used to predict the relative total interior SPL change due to a change in brakepressure.

3.3.2 ConclusionsIt is concluded that the vehicle phenomenon of interior disc brake roughness noise(wire brush) is a purely structure-borne noise problem, hence not air-borne (see paperA). Moreover, the noise phenomenon is dependent on the brake pressure and the ve-hicle speed. Both interior SPL and brake system vibrations increase with increasingbrake pressure and sliding speed. Furthermore, increased brake pressure may lead tosystem altering effects, and this loading of the system has to be included in order toaccurately model the problem.

CHAPTER 4

Component mode synthesis approach

This chapter introduces a component mode synthesis approach where the undeformableattribute of an interface between a soft and a stiff connector is directly enabled in theformulation of the coupling condition. It is based on the assumption of undeformedcoupling interfaces and on the classic Craig-Bampton method. It is shown that thecomputational cost can be greatly reduced using the undeformed coupling interfacesapproach compared both to a direct finite element solution as well as to the classicCraig-Bampton method. For a system built of components of the same properties asthe rubber bushing/ linking arm assembly, the accuracy is shown to be very good froman engineering perspective (less than 1% error).

4.1 BackgroundFrom the experimental study (in previous chapter) it was concluded that disc brakeroughness noise may be viewed as structure-borne noise phenomenon. Furthermore,system altering effects of the brake force were observed for the transfer path system.These two findings lead to the conclusion that a deeper knowledge of the vibro-acousticsystem characteristics of the vehicle suspension was needed. This part of the thesisintroduces an approach to model multifaceted systems using a finite element approach;the number of degrees of freedom is reduced to a small number of local normal modesand a set of six undeformed interface coupling modes per coupling interfaces. Anexample of such a multifaced systems is the suspension system of a vehicle, with thisapproach problems associated with the rubber bushings and complex geometries arehandled. This is shown to lead to computationally fast and accurate modelling of sucha system.

27

28 4 Component mode synthesis approach

4.1.1 Introduction

Herein, a reduction technique for modelling of suspension systems is suggested, hav-ing the potential of overcoming the problem of an unnecessary large number of DOFsin the mathematical description of the vibro-acoustic field.

Reduction methods in structural dynamics (vibro-acoustics) often use the concept ofmodes: a set of normal modes (eigenmodes) are generated from an eigenvalue prob-lem. The theory of modal superposition states that a reduced set eigenmodes can beused to span an approximate solution of the original problem. The choice of the set ofincluded modes in the approximated solution may come from a physical motivation.The normal choice is only to include modes with eigenfrequencies below a particularupper frequency limit. The theory of how reduced subsystems can be coupled togetheris commonly referred to as component mode synthesis (CMS). CMS can be describedas a method where the local behaviour of individual substructures is described by aset of reduced local eigenmodes. Force and displacement continuity between the sub-structures are enforced by a set of coupling functions (constraint modes).

There exists several different versions of the CMS method, which are distinguishedby the use of local eigenmodes: fixed interface, Craig and Bampton (1968); free in-terfaces, (Rixen (2004); hybrid, MacNeal (1971)). Common to all is that continuitybetween substructures is ensured by a static condensation. The static solution of theinner DOFs is computed by successively prescribing either a unit displacement or unitforce (fixed and free interfaces respectively) at the coupling interface one DOF at atime. This procedure generates a solution vector for each interface DOF and thesevectors may be seen as coupling modes. Together with the local eigenmodes, the so-lution of the fully coupled problem may now be spanned. For a deeper descriptionof the different formulations, the reader is referred to the review paper of De Klerket al. (2008). A limitation of classic CMS methods such as the Craig-Bampton (C&B)method is that the reduction order is limited by the size of the coupling interface, hencethis method is only appropriate for systems with small coupling interfaces, Junge et al.(2009); Tran (2009); Balmes (1996). Furthermore, non-conforming meshes betweendifferent components may appear e.g. because different components are developed bydifferent groups of engineers, Farhat and Geradin (1992). The problem with non-conforming mesh interfaces is usually dealt with by introducing additional constraintsin the form of so called Lagrange multipliers (see for instance rix (1998); Farhat andGeradin (1992)).

4.2 Theory 29

Research on the interface reduction is a research area which attracted considerableinterest, for instance, Tran (2001, 2009); Balmes (1996); Herrmann et al. (2010). Mostof the methods use static condensations of the inner modes on the global problem.Thus, the new system only comprises interface DOFs, that may be used to generateyet another set of basis function by solving the new eigenvalue problem. However, aphysically motivated truncation criterion based on the eigenfrequency cannot be usedto choose a reduced set of interface DOFs eigenmodes basis function. Instead, themethod is limited to criteria as e.g. evaluation of the strain energy of each mode, ger(2000) or singular value decomposition Balmes (2005); Herrmann et al. (2010).

In this thesis a physically motivated technique of interface reduction is presented. Thetechnique is proposed for coupling between soft and stiff parts, such as the connectionto rubber bushings in the vehicle suspension system. The physical reasoning is basedon the assumption that an interface between a soft and a stiff part will have an approx-imately undeformed interface shape. Hence, the displacement of the interface can bedescribed by the six rigid ”body” motions (three orthogonal spatial directions and thethree rotations around these axes), van der Valk (2010).

This method also allows for a substantial reduction of the original problem and com-pletely eliminates the problem of non-conforming meshes: only a conforming coordi-nate system is needed when generating the undeformed interface displacement func-tions.

4.2 Theory

4.2.1 General problem

In Fig. 4.1 the system used in this section is defined to give an basic understanding ofthe theory behind the modelling approach. The vibro-acoustic displacement field u(x)is defined in the domain Ω which is entirely enclosed by the boundary ∂Ω. The bound-ary is subdivided into a coupling interface boundary Σ and the remaining boundary Γ.Λ is the union of boundary Γ and the domain Ω.

The continuum mechanical displacement field u(x) may be written in a FE discretizedrepresentation. The displacement DOF vector may also be subdivided into UΣ and


Figure 4.1: The vibro-acoustic displacement u(x) and the body force g(x) in the domain Ω

where Σ = ∂Ω \ Γ, and Λ = Ω ∪ Γ. x = [x1; x2; x3] is the position in space

UΛ, where UΣ corresponds to the nodal displacement vector belonging to the couplingboundary Σ and UΛ is the nodal displacement vector belonging to Λ. The correspond-ing matrix representation of the problem may be written as[ (

KΣΣ KΣΛ

KTΣΛ

KΛΛ

)− ω2

(MΣΣ MΣΛ

MTΣΛ

MΛΛ

)] (UΣ

UΛ

)=

(FΣ

FΛ

), (4.1)

where K and M are the stiffness and mass matrices respectively, U and F are thedisplacement and force vectors respectively.

4.2.2 Change of basisThis section explains how to generate the (nodal) displacement vector representationof the basis functions used in the change basis CMS approach. The Classical C&Bsubstructuring method uses one set of basis function to span the local DOF of eachsubstructure, and another set of functions for the coupling of the structures. The twosets of functions will be herein referred to as local modes and coupling modes.

4.2.3 Local modesThe local modes are generated by a constrained eigenvalue problem. On the couplinginterface Σ a homogeneous (zero) Dirichlet condition is imposed as UΣ = 0. Together

4.2 Theory 31

with a zero force conditions on Γ. Hence, the eigenvalue problem may be written as(KΛΛ − ω

2MΛΛ

)UΛ = 0 (4.2)

The solution of Eq. (4.2) gives the eigenvalues ω2n and eigenvectors φn. The total dis-

placement vectors of the constrained eigenvalue problem, including the constrainedcoupling interface DOFs as zeroes, is written as in Eq. (4.3) where each column corre-sponds to a displacement eigenvector:

Φ =

[0

φΛ,(1) · · ·φΛ,(n)

]=

[0ΦΛ

](4.3)

This is the first set of basis functions used in the projection from local DOFs to gener-alised DOFs.

Coupling modes

To allow for a kinematic coupling to an adjacent substructure, basis functions which arenon-zero on Σ are needed. These are constructed by static solutions of Mcoup different,linearly independent boundary value problems having different non-zero prescribeddisplacement conditions on Σ. These boundary constraints are imposed via the FE dis-placement vector UΣ = ψΣ,(m) where FΣ = 0 and FΛ = 0. Denoting the correspondingsolution of UΛ of the remaining displacement DOFs by UΛ = ψΛ,(m), the mth solutionis obtained by solving the static problem(

KΣΣ KΣΛ

KTΣΛ

KΛΛ

) (ψΣ,(m)ψΛ,(m)

)=

(00

)(4.4)

hence,ψΛ,(m) = −K−1

ΛΛKTΣΛψΣ,(m). (4.5)

The Mcoup solutions of Eq. (4.5) may be organised as shown in Eq. (4.6) where eachcolumn corresponds to the displacement vector (or ”mode”) for a given imposed dis-placement vector ψΣ,(m):

Ψ =

[ΨΣ

ΨΛ

]=

[ψΣ,(1) · · · ψΣ,(m)ψΛ,(1) · · · ψΛ,(m)

](4.6)

This is the second set of basic function used in the projection from local DOFs togeneralised DOFs.


Modal projection

If the two projection basis functions of the local and the coupling modes are assembledthe total projection basis Θ reads

Θ = [Ψ,Φ] =

[ΨΣ 0ΨΛ ΦΛ

]. (4.7)

The projection of each component may then be written as

S = ΘTKΘ, W = ΘTMΘ, (4.8)

andG = ΘTF, Umodal = ΘQ, (4.9)

with the following transformed system of generalised coordinates[ (SΣΣ 00 SΛΛ

)− ω2

(WΣΣ WΣΛ

WTΣΛ

WΛΛ

)] (QΣ

QΛ

)=

(GΣ

GΛ

). (4.10)

If the eigenvectors φΛ in the projection basis are mass normalised then WΛΛ is an diag-onal matrix with only ones in the diagonal, SΛΛ is a diagonal matrix with the eigenval-ues ω2

n in the diagonal. The mass and the stiffness submatrices of the interface DOFs ,WΣΣ and SΣΣ are full matrices, the coupling (interface or inner DOFs) mass submatrix(WΣΛ) is also full. Hence, also the global mass matrix W is full. However, the fastsolution properties of the diagonal matrix WΛΛ can still be utilised by condensing thesolution to the interface DOFs.

Classic Craig-Bampton

In Eq. (4.10) the general form of the classic C&B method is formulated. For the specialcase when ΨΣ is chosen as the identity matrix I then Eq. (4.10) corresponds exactly tothe classic C&B method, which is based on the calculation of the inner response (onΛ) for the case of successive unit displacement of each DOF (on Σ), while keepingall other DOFs on the interface fixed. This procedure of repeating the calculation ofEq. (4.5) as many times as there are DOFs on Σ, is equivalent to replacing ΨΣ with theunit matrix. Hence, no reduction of interface (Σ) DOFs is made, since multiplying bya square unit matrix will not change the dimension of the resulting matrix.


Rigid interfaces six DOFs

So far only a general form of the classic C&B CMS has been presented. In the pre-sented theory, the possibility of using any function that can be described on Σ has beenshown for the calculation of the static coupling modes ψ. As stated before in the clas-sic formulation of the C&B CMS, an unreduced interface formulation is used. Here,a different set of displacement conditions are constructed to generate a different set ofstatic coupling modes using Eq. (4.5). This approach allows for a truncation of thecoupling interface.

At this point the UCI approach is introduced. The deformations of an interface be-tween two connected bodies could be argued to be governed (among other parameters)by the relative stiffness of the bodies. If there is a large relative difference of the stiff-ness, then the coupling interface may translate and rotate, but keeping its original shapealmost undeformed. The stiffer body interfaces behave almost as a free boundary andthe softer body interfaces behave similar to a spatially prescribed translation and rota-tion, that is, identical to the stiffer body translation and rotation.

These assumptions of undeformed coupling interfaces allow for a restriction of cou-pling modes to represent six different rigid motions of the interface, e.g. three trans-lations and three rotations around a common rotation point. In all other aspects thesecoupling modes correspond to the classic C&B coupling modes. The main advantageof this approach is that the number of coupling modes is reduced from the number ofFE DOFs associated to the coupling boundary Σ, to six. Another important feature isthat mesh compatibility is not required, only the translation directions, rotation axesand rotation point have to be compatible. Formally, not even the geometry has to becompatible.

For a deeper description of the CMS UCI approach see paper B.

4.3 Results and discussion

In order to evaluate the usefulness of the proposed approach, a test structure is imple-mented. The question is whether the approach with the UCI may be used for vibro-acoustic modelling of built up substructures of fundamentally different stiffness.


Figure 4.2: The test structure used in this thesis consisting of seven substructures. Boundaryconditions are indicated by R (Rigid or Fixed) or F (unit surface force condition inall the spatial directions).

4.3.1 Test structure

The test structure herein used is shown in Fig. 4.2, the properties of which are chosento resemble the vibro-acoustic problem of a triangular linking arm in a vehicle suspen-sion system, the linking arm often being connected to the stiff vehicle body in threepositions via rubber bushings. It consists of a cross (substructure 3 in Fig. 4.2) in orderto resemble the linking arm. The rubber bushings are included as blocks (substructures2, 4 and 6 in Fig. 4.2) and three connecting parts are included (substructures 1, 5 and 7in Fig. 4.2) to mimic the stiffness of the vehicle body. A more detailed description ofthe test object can be found in the appended paper B.

4.3.2 Vibro-acoustic response

From Figs. 5 and 6 in paper B, three different frequency regions may be recognised.These are defined as low (0-100 Hz), mid (100-600 Hz) and high (600-1000 Hz),mainly for evaluation purposes. In the low frequency range there are rigid body res-onances behaviours of substructure 3. At mid frequencies the behaviour is mostlygoverned by the mass law, and at high frequencies there are three elastic modes of thecross that governs the response. In Fig. 4.3 the solution (spatial root mean squaredvalue (RMS) of the displacement magnitude of substructure 3) is shown for differ-ent Young’s modulus of the ”soft” connectors. When the relative Young’s modulusmoves closer to unity, then the first rigid body resonances moves up in frequency


1 10 100 10000

20

40

60

80

100

120

Frequency [Hz]

Dis

plac

emen

t [dB

re.

1 p

m]

Erel

= 10−6

Erel

= 10−4

Erel

= 10−2

Erel

= 1

Figure 4.3: The vibro-acoustic response, integral of the total displacement of substructure 3for four different Young’s module of the soft connectors, presented as the relativeYoung’s modulus.

(see Fig. 4.3).

4.3.3 Evaluation of the approachRelative Young’s modulus

In Fig. 4.4 the overall relative difference, in the defined frequency ranges (low, mid andhigh), is shown for a changing stiffness of the ”soft” connectors. In other words, allmaterial properties are kept constant except the Young’s modulus of the substructures2, 4 and 6. What may be seen in Fig. 4.4 is that all the results for C&B and UCI haveresults that may be considered as accurate results from an engineering point of view,with a deviation less than 1%, for the relative Young’s modulus Erel less than 10−3 (rel-ative Young’s modulus is defined as, Erel = Esoft/Estiff). As expected, the displacementsat higher frequencies are the hardest to predict with the UCI approach. This is proba-bly due to the fact that at high frequencies, the size of the interfaces become significantin comparison to the wave length. In this test case, a fairly large interface was used.In real vehicle suspension systems, the interfaces between structures and bushings areusually smaller. Note that the test case evaluated here should be viewed as a proof ofconcept, verifying the possibility of modelling built up structures with softer and stifferparts, such as the vehicle suspensions. So far, results have only been shown including


all modes for the C&B and the UCI approach, which highlight the consequences of theUCI approach compared to the C&B method. It should be noted that the C&B methodwithout any inner reduction should give exactly the same result as the direct FE sinceonly a projection is made.

10−6

10−5

10−4

10−3

10−2

10−1

100

10−14

10−12

10−10

10−8

10−6

10−4

10−2

100

Rel

ativ

e di

ffere

nce

[−]

Relative Young’s modulus [−]

C&BLow

UCILow

C&BHigh

UCIHigh

C&BMid

UCIMid

Figure 4.4: The total relative difference between the modal solutions and the direct solutionfor the three frequency bands, using all inner modes. Function of the stiffness ofthe ”soft” contactors (function of relative stiffness). C&B method (dashed lines)UCI approach (solid lines).

4.4 ConclusionsA component mode synthesis approach that uses undeformed coupling interfaces isproposed. The approach enables a significant reduction of the original problems, whereclassic CMSs are limited to reduction of DOFs not associated with the coupling inter-faces. The approach also overcomes any problem of non-conforming mesh of differ-ent components. It is demonstrated that specific systems may be modelled using thesuggested approach, giving results that from an engineering point of view are quiteacceptable. For the approach itself to be valid, the stiffness of the connecting bodiesmust be fundamentally different, such as, for the rubber bushing connected to a steellinking arm in a vehicle suspension system.

CHAPTER 5

UCI as a framework

This chapter outlines the reduced order model (ROM) built using the UCI as proposedin this thesis. The method may be used to reduce the order of a global problem: this isdone by subdividing the global system to substructures interacting through a suitablenumber of UCIs. The local dynamic behaviour of each substructure may then be mod-elled with a, for that particular problem, best suited description. The feasibility of themethod is demonstrated by a sensitivity analysis of the vibro-acoustic power isolationin a vehicle suspension system, comprised of a link arm connected to a vehicle carbody through two rubber bushings.

5.1 BackgroundAs shown in the previous chapter, the use of an UCI-approach may be a powerful toolin the establishment of a reduced order model (ROM). In this chapter a more generalapproach to the use of an UCI modelling is formulated. The potential in this methodis demonstrated in a parametric analysis on subsystem level, allowing for an analysisof the flow of vibro-acoustic energy through a hypothetical suspension system into avehicle car body.

A hypothetical vehicle suspension system, with a link arm connected to a car body viarubber bushings, is modelled using the UCI-approach. The link arm is modelled by theC&B-UCI-approach, where the inner degrees of freedom (DOF)s are tranformed bya normal mode superposition, using a reduced set of the calculated inner modes. Therubber in the bushings is described by a realistic and frequency dependent visco-elastic

37

38 5 UCI as a framework

material model. The model has non-proportional damping, which effectively prohibitsthe direct use of a modal approach. In order to reduce the size of the bushing models,the rotational symmetry of the bushings is used in a reduction of the spatial dimensionof the resulting problem, allowing for a computationally efficient two-dimensional fi-nite element modelling Östberg et al. (2010). Furthermore, the UCI enables a straight-forward connection between the suspension system and an interface dynamic stiffnessmatrix of the car body. In this case this dynamic stiffness matrix components werecalculated and supplied by a car manufacturer from a full body-in-white FEM.

In order to assess the importance of the orientation of the rubber bushings, in the actualinstallation, and to illustrate the potential of optimising the vibro-acoustic properties ofthe vehicle with respect to these, a parameter study is undertaken where the mountingorientations of the bushings are varied. The results show that the global vibro-acousticproperties can vary by several orders of magnitude.

5.2 Local substruture models and global assembly

∑ i 2

∑ i 1

Λ i

F i 2

F i 1

U i 1

U i 2

Figure 5.1: Principal sketch of a substructure Λi with two interfaces Σi1 and Σi

2.

The proposed substructuring methodology relies on the assumption of undeformedcoupling interfaces, allowing for a dynamic description of each interface in terms ofsix generalised forces and displacements (of which three are rotational forces mo-ments and three rotational displacements angles). The two interfaces 1 and 2 of

5.2 Local substruture models and global assembly 39

the substructure i, (Fig. 5.1) are described in terms of dynamic stiffness matrices, re-lating the generalised forces for interface m, Fi

m = [F ix|m, F

iy|m, F

iz|m,M

ix|m,M

iy|m,M

iz|m]T,

to the generalised displacements, Uim = [U i

x|m,Uiy|m,U

iz|m,Φ

ix|m,Φ

iy|m,Φ

iz|m]T, (T denotes

transpose) by [Fi

1Fi

2

]=

[Di

11 Di12

Di21 Di

22

] [Ui

1Ui

2

]+

[Ti

1Ti

2

]. (5.1)

The first three components of the generalised force vector are the corresponding Carte-sian components and the other three are the moment vector Cartesian components.Similarly, the generalised displacement vector has three displacement Cartesian com-ponents and three rotational Cartesian components, while Ti

m accounts for the localforce contributions internal to substructures. Furthermore, the interface dynamic stiff-ness matrix,

Di ≡

[Di

11 Di12

Di21 Di

22

](5.2)

is defined, where Di12 = (Di

21)T. An assembly of the dynamic stiffness components isreadily performed, details may be found in paper C, resulting in the global dynamicstiffness matrix for the idealised vehicle suspension system.

5.2.1 Global model description

A schematic representation of the global assembly of the substrucures can be seen inFig. 5.2 where; the car geometry is represented by a block, the bushings are representedby the 3D equivalents of the bushing models, and the link is represented by the actualgeometry used in the substructure model described below. Bushings 1 and 2 are con-nected to the car at interfaces 1 and 2 respectively. The axial direction of bushing 1 isaligned with the z-axis, while bushing 2 is aligned with the x-axis. In order to demon-strate the UCI modelling, three different types of sub-models are used to construct theglobal model. The link arm is modelled using the CMS-UCI explained in the previ-ous chapter. The two rubber bushings are modelled using a UCI-ROM derived froma 2D axisymmetric model using a frequency dependent visco-elastic material model.Finally the car body model is a frequency dependent UCI-ROM from a full car bodyfinite element model. A more thorough explanation of the different models may befound in paper C.

One key advantage of any ROM in general and the proposed method in particular


Figure 5.2: Principal sketch of the assembled system, where the light green Λ1,(Arm) part repre-sents the link arm, the dark green parts Λ2,(Bush1) and Λ3,(Bush2) the rubber bushingsand the brown part the car body Λ4,(Car). The red surface on the far left of the linkarm indicates the external force location.

is that parameter studies are easily conducted on a substructure level. As an illustra-tion of the potential in the usage of the UCI-ROM, a study is undertaken in which theorientations of the rubber bushings, which are used to connect the link arm to the carbody, are varied.

5.2.2 Results – total transmitted powerThe vibro-acoustic power transmitted into the generic car structure is evaluated. Thepurpose is to investigate the sensitivity of the vibration isolation provided by the sus-pension system and its dependence on the rubber bushing configuration. Thus, in thefollowing all discussion referring to transmitted power means the net flow of energyinto the car substructure. As excitation, distributed unit traction forces are applieduniformly at one surface (surface indicated with red in Fig. 5.2). The power (Pi

n) iscalculated from the interface displacements (Ui

n) and traction forces (Fin) vectors for

each substructure and coupling interface n = 1, 2 using

Pin =

12R( Fi

n iωUi∗n ), (5.3)

where ∗ denote the complex conjugate and R the real part.


0 100 200 300 400 500

10−12

10−11

10−10

10−9

10−8

Powerinto

car[W

]

Frequency [Hz]

Ω1x

Ω1y

Ω2y

Ω2y

(a) Force excitation in x-direction

0 100 200 300 400 500

10−12

10−11

10−10

10−9

10−8

Powerinto

car[W

]

Frequency [Hz]

Ω1x

Ω1y

Ω2y

Ω2y

(b) Force excitation in y-direction

Figure 5.3: Total power into the car substructure. Four different bushing rotations are shown;range 1-180 deg for each 3 deg. Rotations around x (blue) and y (green) respec-tively of bushing 1, rotations around y (grey) and z (red) respectively of bushing2. Black dashed line shows the original orientation while the solid black line isincluded to show the individual frequency response (of one of the responses withhigh power).

In Figs. 5.3 the total vibro-acoustic power transmitted into the car structure, and itsdependence on the bushing (tilting) orientation angles, are illustrated. The bushingsare rotated around their local x′ and y′ axes separately (hence not rotating around theaxial direction of the bushing z′ see Fig. 3 paper C). This corresponds to rotations withan angle Ω1

x around the global x-axis and angle Ω1y around the global y-axis, respec-

tively, for bushing 1. For bushing 2, Ω2y and Ω2

z rotations around the global y- andz-axis, respectively, are used. The excitation is applied in either the global x-direction(Fig. 5.3(a)) or in the y-direction (Fig. 5.3(b)).

It is apparent that the effect of rotating the bushings is most significant for frequen-cies above ∼ 200 Hz; for rotations around Ω1

x and Ω2z for which the variations of the

power relative to the original configurations are of orders of magnitudes. The solidblack lines in Fig. 5.3 is included to visualise the individual frequency response of oneof the configurations giving a high response.

To further emphasize the potential of reorienting the bushings and to illustrate therobustness of the achieved results, the most influential rotation angles for each load


0

20

40

60

80

100

120

140

160

180

Ω1 x[deg]

Ω1x of max

Ω1x of min

0 100 200 300 400 5000

5

10

15

20

25

30

35

40

45

Ratio

max

min

[-]

Frequency [Hz]

Ratio

(a) Force excitation in x-direction, angularparmeter Ω1

x

0

20

40

60

80

100

120

140

160

180

Ω2 z[deg]

Ω2z of max

Ω2z of min

0 100 200 300 400 5000

5

10

15

20

25

30

Ratio

max

min

[-]

Frequency [Hz]

Ratio

(b) Force excitation in y-direction, angularparmeter Ω2

z

Figure 5.4: Ratio of the angular configuration giving the maximum of transmitted power, foreach frequency, and the one giving the minimum (red curve NB y-axis right side),and at what angles the maxima and minima are found (blue and black curve re-spectively NB! y-axis left side).

case (Ω1x for x-excitation and Ω2

z for y-excitation) are studied more closely in Fig. 5.4.Here the angles for which a minimum and maximum of transmitted power occurs isshown, this for each frequency (1 Hz frequency resolution) together with the powerratio between these extremal angles (right y-axis red line NB two y-axis in the graph).

5.2.3 Transmission path

Considering the complexity of the vehicle suspension system, it is evident that a deeperknowledge of the system at hand would be needed to establish efficient design strate-gies. If, for example, an optimisation with respect to isolation is required, the mostimportant factors determining the total energy flow would represent an interesting eval-uation criteria. Analysing the different energy transmission paths, the results in Fig. 5.5are obtained for the two load cases separately. Here the percentage of the total power(summed over the frequency band 400-500 Hz) going through each bushing is shown,each subsubfigure is plotted as a function of angular orientation of the bushings withtwo vertical lines added indicating the angle at which the maximum and minimum oftotal transmitted power occur.


0

20

40

60

80

100

Ω1x[deg] Ω

1y[deg]

0 45 90 135 180

0

20

40

60

80

100

Ω2y[deg]

Ratiopower[%

]

0 45 90 135 180

Ω2z[deg]

Bush 1

Bush 2

MaxMin

(a) Force excitation in x-direction

0

20

40

60

80

100

Ω1x[deg] Ω

1y[deg]

0 45 90 135 180

0

20

40

60

80

100

Ω2y[deg]

Ratiopower[%

]

0 45 90 135 180

Ω2z[deg]

Bush 1

Bush 2

MaxMin

(b) Force excitation in y-direction

Figure 5.5: Portion of power transmitted through each bushing as a function of angular param-eter change (total power in the 400-500 Hz frequency range). Red lines: bushing1, Blue lines: bushing 2. Vertical lines indicate the angle for the maximum (blackdashed line) and minimum (green dashed-dotted line) of total energy flow into thegeneric car.

10−15

10−10

x y z ωx ωy ωz

0 100 200 300 400 500

−10−10

−10−15

Powercar[W

]

Frequency [Hz]

(a) Bushing 1

10−15

10−10

x y z ωx ωy ωz

0 100 200 300 400 500

−10−10

−10−15

Powercar[W

]

Frequency [Hz]

(b) Bushing 2

Figure 5.6: Power transmitted into and out of the generic car for each DOF as a function ofangular parameter change of Ω2

z , for x-direction excitation. ω indicate rotationalDOFs. NB logarithmic y-axis for both for negative and positive power, cut ofabsolute powers less the 10−19.


To further illustrate the complexity of the energy flow in the system, the energy flow inand out of the of the generic car structure of each individual DOFs is plotted (Fig. 5.6)for the angular parameter Ω2

z , the results are for an excitation force in x-direction. Thetwo subfigures Figs. 5.6(a) and 5.6(b) are respectively showing the power for bushings1 and 2.

The total power going into the car structure in this idealised test case must have posi-tive power, since no power is injected into the car structure itself. Having said that, itmay be observed that individual DOFs may have negative signs since the system is aclosed circuit for the power transmission.

5.2.4 Discussion

It is evident from Fig. 5.4 that; i) in the higher frequency range studied, the potentialfor optimisation is great, with a maximum power ratio of ∼ 40 and ii) the differencebetween max and min angles is quite stable (at least above 100 Hz) and large. Thissuggests that the results may be considered robust with respect to imperfection of thehardware implementation.

In Fig. 5.5 it should be noted that i) the ratio between the powers passing throughbushings 1 and 2 may be significantly altered by changing the angular orientations ofthe bushings, ii) for the two different excitation directions the resulting power ratiosshow totally different behaviour, hence a study of the isolation effects of the rubberbushings must include the appropriate excitation of the problem at hand iii) the powerratio between bushings 1 and 2 can vary much, even though the total power is stillfairly constant (e.g. compare Figs. 5.3(b) and 5.5(b) for parameter Ω1

y).

It may be seen in Fig. 5.6 that, not only the total power transmitted into the car ischanged when varying the angular parameter, but also the ratios of the different DOFsare highly affected by the change of angle. Rotating the bushings, with the corre-sponding change in their stiffness parameters (see Fig. 6 paper C), significantly altersthe energy flow. This adds a further argument for the current UCI-ROM approach asthe bushings cannot be modeled using a spring stiffness representation.

5.3 Conclusions 45

5.3 ConclusionsThe substructuring methodology presented, where an undeformed coupling interfaceformalism is used to model a vehicle suspension system, has been found to be a pow-erful tool for investigating the complex mechanisms associated with structure-bornesound in vehicles. Using appropriate models for each substructure, a study of theinfluence of the rubber bushings used to connect the link arm to the car body is under-taken. It is found that, by rotating the bushings, the power transferred to the car bodycan be altered by orders of magnitude. On one hand, this opens up for radically de-creasing the disturbances transmitted through the suspension system, but on the otherhand as well identifying the possible sensitivity of the system to imperfections in theactual physical hardware installation, hence giving robust result. Finally, it should bestressed that the method discussed here is itself general, but to ease the understandingit is here illustrated for an idealised model.

CHAPTER 6

Wheel rim influence on interior noise

This chapter discusses a study of the correlation of component properties to the interiornoise. The component is the wheel rim, which is a crucial part in the transfer of acous-tic power from tyre-road excitation to interior noise. For low frequencies this transfercan often be explained as a structure-borne noise problem. Often this component isignored when its comes to is influence to the tyre-road noise; however, the results fromthis work show that the rim may have large influence on the interior noise.

6.1 BackgroundSo far in this thesis a component investigation of the brake system and the associatedstructural transfer of acoustic power have been discussed. Furthermore, a substruc-turing approach using undeformed coupling interfaces as a framework for connectingcomponents in a vehicle suspension model has been introduced. There is one addi-tional component involved in the acoustic power transfer in the vehicle suspensionsystem that is of principal interest, the wheel rim. This study is of experimental naturewhere the system properties of the rim are correlated to the interior noise from thetyre-road interaction.

When it comes to tyre-road noise, the interior noise field is not as well covered inthe literature as the exterior noise. It may typically be subdivided into either structure-borne or air-borne noise transmission Bekke et al. (2010), where low frequency prob-lems are commonly considered as predominantly structure-borne, Molisani et al. (2003);Sakata et al. (1990) and vice versa. As an example, Sakata et al. (1990) showed it waspossible to in a study correlating the interior noise and the measured spindle forces

47

48 6 Wheel rim influence on interior noise

below 400 Hz.

The rim itself as a subject of research in relation to interior and exterior tyre-roadnoise sees an increasing interest, partially fuelled by differences in interior noise lev-els that have been reported for different rims Sandberg and Ejsmont (2002); Curà andCurti (2004); Kindt et al. (2009); Kido and Ueyama (2005); Feng et al. (2009). Fur-thermore, the simplifying assumption of a rigid rim is not shared by all researchers inthe field; for instance Yam et al. (2000) reports that the rim modes have an influenceon the characteristics of tyre modes, and Hayashi (2007) has shown that for the tyrecavity mode the vibration levels in the suspension system may be altered significantlywhen changing numerically the out-of-plane torsional stiffness of the rim. Kindt et al.(2009) showed that, from mobility calculations of a tyre wheel assembly model, theresults in the low frequency range differed substantially if a rigid wheel was used in-stead of a flexible one. In that paper it is also stated that different wheels can produceperceptibly different vehicle interior noise, in the frequency range 200-350 Hz up to 5dB differences were found when comparing a steel and an aluminium wheel.

This latter observation forms the starting point for the current study, where a statis-tical approach to correlate structure-borne interior tyre-road noise to rim system pa-rameters is used. The basis for the study was road noise measurements combined withcomponent vibration measurements and corresponding analysis, for different rims.

6.2 Approach

The work discussed in this study takes as a starting point a measurement data base builtduring several years at a vehicle manufacturer. These measurement data were collectedfrom a wide range of measurement types such as modal measurements performed oncomponents and subsystems, road measurements and rolling road rig measurements.The result in this chapter is based on two of these, namely the road measurements andcomponent mode measurements. The modal measurements have been post-processedin order to get the dynamic stiffness values of the rim, and these measured stiffness val-ues have been used to validate calculated finite element stiffness results. An overviewof the measurement and the calculations in this chapter can be found in paper D.

6.2 Approach 49

ID Rim 1 Rim 2 Rim 3 Rim 4 Rim 5Spokes no spokes 7 spokes 7 spokes 7 × 2 spokes 10 spokes

Material Steel Alu. Alu. Alu. Alu.Weight 8 kg 7.5 kg 10.3 kg 9.3 kg 7.4 kg

Dimensions 16” 7” 16” 7” 16” 7” 16” 7” 16” 7”Static stiffness 1379 kN/m 3619 kN/m 6866 kN/m 5430 kN/m 5007 kN/m

Table 6.1: Summary of rim properties, static stiffness is the 0 Hz component of the out-of-plane torsional stiffness of the disc of the rim as predefined.

6.2.1 Interior noise and rim parmeter correlations

In this subsection results from rim parameter correlations are presented, where thecorrelations have been made for the rims listed in Table 6.1, where the most importantparametric data for each rim are shown. These are in summary: rim identifier, numberof spokes, material, mass, dimensions and static axial stiffness (calculated as discussedin paper D).

Figure 6.1: Interior sound pressure levels (bottom lines, right y-axis) and calculated dynamicout-of-plane torsional stiffness of rim disc. SPL, four aluminium rims (Rim 2-5)different runs 60 km/h changing only the front rims. Stiffness calculations per-formed for the corresponding rims (Rim 2-5)

.


Fig.6.1 shows the A-weighted interior SPL in the front seat of the vehicle for roadmeasurements using the four different aluminium rims in Table 6.1 NB right y-axis.The calculated axial dynamic stiffnesses are also shown for the aluminium rims used,NB left y-axis. It may be seen that there is a clear tendency between a high SPL and alow rim stiffness and vice versa, for all investigated rims. This is particularly noticablein the frequency range ∼100-230 Hz, with the exception for the peak at around 170 Hzwhere Rim 5 gives the highest SPL.

To further illustrate the correlation between rim stiffness and interior noise, Fig.6.2also includes results for a steel rim, confirming the previously observed link betweenlow frequency interior noise and rim stiffness. To investigate in some more detail the

Figure 6.2: Interior sound pressure levels (bottom lines, right y-axis) and calculated dynamicout-of-plane torsional stiffness of rim disc. SPL, two aluminium rims (Rim 3 & 5)and the steel rim (Rim 1) different runs 60 km/h changing the front rims. Stiffnesscalculations performed for the corresponding rims (Rim 1, 3 & 5).

correlation of rim parameters to the interior SPL in Fig.6.3, the interior SPL is shownas a scatter plot for all the five studied rims as a function of static axial stiffness andmass, where the static stiffness was used since the dynamic stiffness does not varymuch in the low frequency range (with an exception for the steel rim). Three prede-fined problematic frequency ranges were used where for each the maximum SPL in thisparticular frequency range is shown (the ranges are: 105-120, 125-145 and 215-225Hz). To study the correlation, a logarithmic measure was used (dB values),

6.3 Discussion 51

(a) SPL as function of calculated static stiff-ness

(b) SPL as function total mass of rim

Figure 6.3: Mass and stiffness as a function of interior SPL for the five rims, three interiornoise values, peak values in pre defined low frequency problem areas, blue 105-120 Hz, violet 125-145 Hz and yellow 215-220 Hz.

R2 =

∑(v1 − v1)(v2 − v2)√∑

(v1 − v1)2 ∑(v2 − v2)2

, (6.1)

where v1 and v2 are the two sets of values of comparison the original values and thetrend line values, and v1 and v2 are the sample mean values.This was fitted to the 3 different noise ranges, as shown together with the correspond-ing R2 value in Fig.6.3, which simply gives a measure of how good the fit is (rangingfrom 0 to 1 where 1 is a perfect fit). It may be seen that the correlation values (R2) arewell above 0.75 for the static stiffness correlation while the correlation values obtainedwith respect to the mass are low.

6.3 DiscussionFrom Figs. 6.1 and 6.2 it may be seen that there is a broad band qualitative correlationof the interior SPL with the dynamic stiffness values. Comparing the interior noisecurves to the total rim mass in Table 6.1, it is quite clear that there is no correlation,it is quite clear that there is no correlation, even though the heaviest rim is one of therims with lowest interior SPL; this does not hold for all rims. Thus, including the


correlation results for the peak values in Fig. 6.3 it is clear that mass is not the mainparameter influencing the interior noise for the low frequency tyre-road problem beinginvestigated. In fact using the same material, for a given rim design it is likely thata heavier rim is stiffer than a lighter rim, if not designed/optimised for stiffness. Theresults suggest that there should be room for optimisation of low frequency interiorSPL by changing the rim’s torsional stiffness of the disc, and that this may be achievedwithout added mass.

6.4 ConclusionA systematic approach is presented for studying the influence of components in thevehicle suspension system, in particular when structure-borne noise problems are ofinterest in the vehicle.

In this thesis the influence of the rim dynamics on interior tyre-road noise has beensystematically shown together with its structure-borne character. Furthermore it hasbeen shown that there is a strong qualitative correlation of the broad band low fre-quency interior tyre-road noise to the dynamic and static stiffness of the rim disc. Theresults found suggest that the mass of the rim has a negligible effect on the interiornoise.

CHAPTER 7

Outlook

This chapter gives en overview of the outcome of this thesis and tries to in the light ofthe results look into the future of vehicle suspension research.

There are several different steps and subprojects that may be done to continue theprogress towards the overall objectives set up for this thesis.

Thanks to this study it is now known that:• The interior brake noise studied in this thesis is a structural-borne phenomenon

where broadband vibrations are generated in the disc-pad interaction. (paper A,section 4.1)

• Vehicle speed and brake pressure are well correlated with the interior noise andvibration levels. (paper A, section 4.2 and 4.4)

• The vibrations in the sliding direction and in the normal direction of the contactsurfaces have different relations to the brake pressure. (paper A section 4.2)

• The brake force generated when applying a brake pressure can affect the sys-tem properties and hence the vibro-acoustic transfer path from the brakes to theinterior noise. (paper A, section 4.2.1)

• There is a substantial computational efficiency gain from modelling the vehi-cle suspension systems transfer path, using a Craig and Bampton componentmode synthesis technique using undeformed coupling modes (that is, the UCIapproach). (paper B, section 3.3.3)

53

54 7 Outlook

• A UCI approach can be used as a framework for connecting submodels of dif-ferent components in the vehicle suspension system. (paper C)

• The UCI approach is well suited for acoustic component sensitivity and optimi-sation studies, such as the orientation of rubber bushings.(paper C)

• The wheel rim can have strong influence on the low frequency interior tyre-road noise; the stiffness of the rim for a given dimension of the rim is the mainparameter. (paper D)

There are vast possibilities to research into structure-borne noise in the vehicle suspen-sion system, with numerous open questions remaining to be answered. The modellingaspects of the this thesis could be further developed, by including more sub-models ofcomponents such as the rim, tyre, shock absorber and coil-spring. Some of these com-ponents may be suited for an analytical model some may be easier to include throughexperimental models. The development of new coupling conditions is an interestingfuture study for the cases where the undeformable attribute is not applicable. The cou-pling may be between components of relatively the same stiffness where deformationof the coupling interfaces is of impotence but also ball joints coupling where rotationmay be neglected is interesting.

The main open questions concerning the disc brake roughness noise may be sum-marised as:

• To increase the understanding of the directional aspects (sliding- and normal tocontact plane direction) of the broadband vibro-acoustic friction source. Whenmay Hertz contact models be used and when is Coulomb’s friction law appro-priate? For which contact pressures/sliding speed/surface roughness are theyvalid?

• A deeper understanding of the brake disc assembly influence on the interiornoise. How do brake systems move? Which DOFs (rigid body, elastic) areneeded to sufficiently describe the global motion of the brake system assembly?

• Systematic studies of the vibro-acoustic transfer path of the suspension systemin order to better understand the possible loading effects. Why does the transferpath change, is it mainly geometrical non-linearity or is it the preloading of thebushings which is the most important.

References

G. P. Shpenkov, Friction Surface Phenomena, Elsevier Science B.V., 1995.

G. Sheng, Friction-Induced Vibration and Sound; principles and applications, CRCpress, 2008.

P. Wriggers, Computational Contact Mechanics, Springer-Verlag, 2006.

B. N. J. Persson, Sliding Friction: Physical Principles and Applications, Springer,second edition, 2000.

M. Yokoi, M. Nakai, A fundamental study on frictional noise (1st report, the generatingmechanism of rubbing noise and squeal noise)., Bulletin of JSME 22 (1979) 1665–1671.

M. Yokoi, M. Nakai, A fundamental study on frictional noise (2nd report. the gen-erating mechanism of squeal noise of higher modes.), Bulletin of JSME 23 (1980)2118–2124.

M. Yokoi, M. Nakai, A fundamental study on frictional noise (3rd report. the influenceof periodic surface roughness on frictional noise.), Bulletin of JSME 24 (1981a)1470–1476.

M. Yokoi, M. Nakai, A fundamental study on frictional noise (4th report . the influenceof angle of inclination of the rod on frictional noise.), Bulletin of JSME 24 (1981b)1477–1483.

M. Yokoi, M. Nakai, A fundamental study on frictional noise (5th report. the influenceof random surface roughness on frictional noise.), Bulletin of JSME 25 (1982) 827–833.

55

56 REFERENCES

M. O. Othman, A. H. Elkholy, Surface-roughness measurement using dry frictionnoise, Exp Mech 30 (1990) 309–312.

M. O. Othman, A. H. Elkholy, A. A. Seireg, Experimental investigation of frictionalnoise and surface-roughness characteristics, Experimental Mechanics 30 (1990)328–331.

B. L. Stoimenov, S. Maruyama, K. Adachi, K. Kato, The roughness effect on thefrequency of frictional sound, Tribology International 40 (2007) 659–664.

H. Ben Abdelounis, A. Le Bot, J. Perret-Liaudet, H. Zahouani, An experimental studyon roughness noise of dry rough flat surfaces, Wear 268 (2010) 335 – 345.

H. Zahouani, R. Vargiolu, G. Boyer, C. Pailler-Mattei, L. Laquièze, A. Mavon, Frictionnoise of human skin in vivo, Wear 267 (2009) 1274–1280.

T. Jibiki, M. Shima, H. Akita, M. Tamura, A basic study of friction noise caused byfretting, Wear 250-251 (2001) 1492–1503.

A. Akay, Acoustics of friction, J. Acoust. Soc. Am. 111 (2002) 1525–1548.

F. Chen, C. A. Tan, R. L. Quaglia, Disc Brake Squeal Mechanism, Analysis, Evalua-tion, and Reduction/Prevention, SAE International, 2005.

A. Papinniemi, J. C. S. Lai, J. Zhao, L. Loader, Brake squeal: A literature review,Appl. Acoust. 63 (2002) 391–400.

N. M. Kinkaid, O. M. O’Reilly, P. Papadopoulos, Automotive disc brake squeal, J.Sound Vibrat. 267 (2003) 105–166.

N. P. Hoffmann, L. Gaul, Friction induced vibrations of brakes: Research fields andactivities, in: SAE Technical Paper series, No. 2008-01-2579.

W. V. Nack, A. M. Joshi, Friction induced vibration: Brake moan, in: SAE TechnicalPaper series, No. 95095, SAE.

A. Gugino, J. Janevic, L. Fecske, Brake moan simulation using flexible methods inmultibody dynamics, in: SAE Technical Paper series, No. 2000-01-2769.

A. Wang, L. Zhang, N. Jaber, J. R. R. B. Corp., On brake moan mechanism from themodeling perspective, in: SAE Technical Paper series, No. 2003-01-0681.

REFERENCES 57

C.-J. Kim, B.-H. Lee, C.-Y. Lee, H.-I. Jeong, Analysis on the induced brake moannoise in the coupled torsional beam axle suspension module, in: SAE TechnicalPaper series, No. 2005-01-3920.

J.-Y. Kim, K.-H. Park, Brake moan simulation using complex eigenvalue analysis, in:Abaqus Users Conference.

M. Carley, J. A. Fitzpatrick, Spectral conditioning of propeller noise from broadbandsources, J. Sound Vibrat. 238 (2000) 31–49.

A. Powell, On the edgetone, J. Acoust. Soc. Am. 33 (1961) 395–409.

S. Smyth, H. J. Rice, Measurement of dry sliding friction rubbing noise using nearfieldacoustic holography, Acta Acust United Ac 95 (2009) 247–258.

P. B. U. Andersson, W. Kropp, Rapid tyre/road separation: An experimental study ofadherence forces and noise generation, Wear 266 (2009) 129 – 138.

K. L. Johnson, Contact mechanics, Cambridge University Press, 1985.

R. Craig, M. Bampton, Coupling of substructures for dynamic analyses, AIAA Journal6 (7) (1968) 1313–1319.

D. Rixen, A dual Craig-Bampton method for dynamic substructuring, Journal ofComputational and Applied Mathematics 168 (2004) 383–391.

R. MacNeal, A hybrid method of component mode synthesis, Computers and Struc-tures 1 (1971) 581–601.

D. De Klerk, D. Rixen, S. Voormeeren, General framework for dynamic substruc-turing: History, review, and classification of techniques, AIAA Journal 46 (2008)1169–1181.

M. Junge, D. Brunner, J. Becker, L. Gaul, Interface-reduction for the Craig-Bamptonand Rubin method applied to FE-BE coupling with a large fluid-structure interface,International Journal for Numerical Methods in Engineering 77 (2009) 1731–1752.

D.-M. Tran, Component mode synthesis methods using partial interface modes: Ap-plication to tuned and mistuned structures with cyclic symmetry, Computers andStructures 87 (2009) 1141–1153.

58 REFERENCES

E. Balmes, Use of generalized interface degrees of freedom in component mode syn-thesis, in: Proceedings of the 14th International Modal Analysis Conference, vol-ume 1, pp. 204–210.

C. Farhat, M. Geradin, A hybrid formulation of a component mode synthesis method,in: AIAA-92-2383.

A two-step, two-field hybrid method for the static and dynamic analysis of substructureproblems with conforming and non-conforming interfaces, Computer Methods inApplied Mechanics and Engineering 154 (1998) 229–264.

D.-M. Tran, Component mode synthesis methods using interface modes. applicationto structures with cyclic symmetry, Computers and Structures 79 (2001) 209–222.

J. Herrmann, M. Maess, L. Gaul, Substructuring including interface reduction forthe efficient vibro-acoustic simulation of fluid-filled piping systems, MechanicalSystems and Signal Processing 24 (2010) 153–163.

Model reduction for efficient FEM/BEM coupling, in: Proceedings of ISMA 25 Leu-ven, Belgium.

E. Balmes, Modes and regular shapes. how to extend component mode synthesis the-ory, in: Proceedings of the XI DINAME.

P. van der Valk, Model Reduction and interface modeling in dynamic substructuring,Master’s thesis, Delft University of Technology, 2010.

M. Magalhaes, N. Ferguson, Acoustic-structural interaction analysis using the compo-nent mode synthesis method, Applied Acoustics 64 (2003) 1049–1067.

L. Hinke, F. Dohnal, B. Mace, T. Waters, N. Ferguson, Component mode synthesis asa framework for uncertainty analysis, Journal of Sound and Vibration 324 (2009)161–178.

S.-K. Hong, B. Epureanu, M. Castanier, D. Gorsich, Parametric reduced-order modelsfor predicting the vibration response of complex structures with component damageand uncertainties, Journal of Sound and Vibration 330 (2011) 1091–1110.

L. Ji, B. Mace, R. Pinnington, A mode-based approach for the mid-frequency vibrationanalysis of coupled long- and short-wavelength structures, Journal of Sound andVibration 289 (2006) 148–170.

REFERENCES 59

J. Lin, B. Mace, An interface decomposition technique for reducing the size of con-ventional component mode synthesis models, Advances in Vibration Engineering11 (2012) 337–348.

S. Donders, B. Pluymers, P. Ragnarsson, R. Hadjit, W. Desmet, The wave-based sub-structuring approach for the efficient description of interface dynamics in substruc-turing, Journal of Sound and Vibration 329 (2010) 1062–1080.

A. Maressa, D. Mundo, S. Donders, W. Desmet, A wave-based substructuring ap-proach for concept modeling of vehicle joints, Computers and Structures 89 (2011)2369–2376.

D. D. Klerk, D. Rixen, Solving the rdof problem in experimental dynamic substructur-ing, in: Proceedings of the Twenty Sixth International Modal Analysis Conference,Orlando, FL.

E. Lindberg, N.-E. Hörlin, P. Göransson, Component mode synthesis using unde-formed interface coupling modes to connect soft and stiff substructures, Shock andVibration 20 (2013) 157–170.

M. Östberg, N.-E. Hörlin, P. Göransson, Weak formulation of biot’s equations incylindrical coordinates with harmonic expansion in the circumferential direction,International journal for numerical methods in engineering 81 (2010) 1439–1454.

A. Kuijpers, G. van Blokland, Tyre/road noise models in the last two decades: a criticalevaluation, in: Inter noise The 2001 International Congress and Exhibition on NoiseControl Engineering The Hague, The Netherlands.

W. Kropp, Structure-borne sound on a smooth tyre, Applied Acoustics 26 (1989)181–192.

K. Larsson, W. Kropp, A high-frequency three-dimensional tyre model based on twocoupled elastic layers, Journal of Sound and Vibration 253 (2002) 889–908.

I. Lopez, R. Blom, N. Roozen, H. Nijmeijer, Modelling vibrations on deformed rollingtyres-a modal approach, Journal of Sound and Vibration 307 (2007) 481–494.

U. Sandberg, J. A. Ejsmont, Tyre/road noise reference book, Informex Ejsmont andSandberg Handelsbolag, first edition, 2002.

60 REFERENCES

S. Fong, Tyre noise predictions from computed road surface texture induced contactpressure, in: Inter.Noise 98, Christchurch, New Zealand, 1998.

D. A. Bekke, Y. H. Wijnant, A. de Boer, Experimental review on interior tire-roadnoise models, in: International Conference on Noise and Vibration Engineering,ISMA 2010, 20-22 September, 2010, Leuven, Belgium.

L. Molisani, R. Burdisso, D. Tsihlas, A coupled tire structure/acoustic cavity model,International Journal of Solids and Structures 40 (2003) 5125–5138.

T. Sakata, H. Morimura, H. Ide, Effects of tire cavity resonance on vehicle road noise,Tire Science and Technology 18 (1990) 68–79.

F. Curà, G. Curti, Dynamic and acoustic characterisation of automotive wheels, Shockand Vibration 11 (2004) 493–504.

P. Kindt, P. Sas, W. Desmet, Development and validation of a three-dimensional ring-based structural tyre model, Journal of Sound and Vibration 326 (2009) 852–869.

I. Kido, S. Ueyama, Coupled vibration analysis of tire and wheel for road noise im-provement, in: SAE 2005-01-2525 SAE 2005-01-2525 SAE 2005-01-2525.

Z. C. Feng, P. Gu, Y. Chen, Z. Li, Modeling and experimental investigation of tirecavity noise generation mechanisms for a rolling tire, in: SAE 2009-01-2104.

L. H. Yam, D. H. Guan, A. Q. Zhang, Three-dimensional mode shapes of a tire usingexperimental modal analysis, Experimental Mechanics 40 (2000) 369–375.

I. Hayashi, Experimental analysis of acoustic coupling vibration of wheel and suspen-sion vibration on tire cavity resonance, in: SAE 2007-01-2345.

Part II

Appended Papers

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