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CHAPTER 2

RESEARCH METHODOLOGY OF PRESENT STUDY

2.1 INTRODUCTION

Comprehensive study on brake squeal using experimental approach

is very expensive and time consuming. Furthermore, the results found from

experimental study on a specific brake system may not be applicable to other

type of brake systems. The modern computational and simulation tools using

FE method have matured to a stage where they can provide substantial insight

into prediction and suppression the squeal noise to help improve the design of

disc brake components at early stage. The capabilities of FE models, with a

vast number of degrees of freedom, have enabled the accurate representation

of a brake system. Moreover, the FE method provides much faster and less

cost solutions than experimental methods.

The advantages pointed out above provide a future direction for

finite element method against the experimental methods. However, accuracy

of the FEA can be questionable and some validation tests are usually required

to provide results with most accuracy within available information. In general

the accuracy of the finite element model is very significant issue to correctly

represent the actual of disc brake corner. Liles (1989) used experimental

modal analysis to validate each of disc brake components. This strategy has

been adopted by many other researchers, for example, (Ripin 1995, Lee et al

1998, Liu and Pfeifer 2000, Kung et al 2000). Later, a few of researchers have

validated FE models at some of its individual components and assembly level

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(Dom et al 2003, Goto et al 2004). Out of these work, only few studies

included validation of each disc brake components and brake assembly. In

addition, most of the FE models assumed full contact at the friction lining and

disc interfaces whereas in reality it is not in complete contact.

Various types of analyses have been performed on disc brake

systems through FEA, in an attempt to understand the problem of noise and to

develop a predictive design tool. The most commonly used method is the

complex eigenvalue analysis (CEA) that was used in brake squeal problems

and became the preferred method (Liles 1989, Ripin 1995, Lee et al 1998,

Blaschke et al 2000, Dom et al 2003, Bajer et al 2003, Goto et al 2004, Abu

Bakar and Ouyang 2004, Abu Bakar and Ouyang 2006, Liu et al 2007,

Trichés et al 2008, Dai and Lim 2008). Although the complex eigenvalue

analysis was commonly used in brake squeal problems by many researchers,

the shortcomings of this method are over-predictions and missing unstable

modes in the squeal frequency range (Kung et al 2004). For overcoming on

the limitations of CEA, there are three methods which will be considered in

this research to increase its accuracy.

It can be seen from the previous chapter that earlier FE models of

the disc brake adopted the variation of the geometric details. For example,

many researchers considered a simplified FE model of the disc brake

assembly, that is, a disc and two pads (Liu et al 2007, Trichés et al 2008,

Coudeyras et al 2009). Hassan et al (2009) added the paw fingers and piston

to the FE model. Dai and Lim (2008) developed a FE model consisting of

rotor, caliper, mounting bracket, piston and brake pads to analyze the design

of disc brake pad structure for squeal noise reduction. Some investigators

(Abu Bakar 2005, Papinniemi 2008) used a detailed FE model which consists

of a disc, a piston, a caliper, a bracket, piston and finger pads, two bolts and

two guide pins. Furthermore, it is found that the above finite element models

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were used without steering knuckle or wheel hub which have considerable

influence on squeal occurrence.

The need for development a more realistic finite element model of

disc brake corner by including part of the suspension system which connects

brake assembly with the vehicle chassis, considering its actual boundary

conditions and interaction between components is required to solve the squeal

problem. Furthermore, due to the fact that disc brake squeal depends on a

large number of parameters, using parametric studies by changing one factor

at a time is not enough for evaluation the brake system. Hence, the need of a

new approach to investigate the effects of several factors on squeal generation

and its interactions is very much required to help improve the design of brake

components.

In this research, efforts are focused on the development of an

improved FE model, as an extension of the earlier FE brake models, in which

a 3-dimensional FE model of the disc brake corner that incorporates wheel

hub and steering knuckle is developed and validated at both component and

assembly level. In addition, the real pad surface roughness, negative friction-

velocity slope and friction damping are considered to increase the prediction

accuracy of the complex eigenvalue results. Moreover, the predicted results

are verified by experimental squeal test and compared with dynamic transient

analysis. Hence, the complex eigenvalue results can be used with higher

confidence level for further studies.

Due to the fact that brake squeal is a very complex phenomenon

because of its strong dependence on many parameters including materials and

geometry of brake components, component interaction and many operating

and environmental condition, the need of a new method to find out the

contributions of the material and geometry modifications in reducing the

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squeal propensity and its interactions as well is required. Current research on

brake squeal is integration of the FE simulation with Design of Experiments

(DOE) to assess effectively the contributions of different types of structural

modifications and their interaction for effective reduction of brake squeal.

Based on the literature review and its present status, the following

research methodology is formulated.

1. Development of an improved FE model of the whole disc

brake corner, as an extension to earlier FE disc brake models,

which has an acceptable correlation with experimental modal

analysis results.

2. Prediction of squeal noise for disc brake system using

complex eigenvalue analysis to determine system stability. In

addition usages of experimental squeal test to verify the

predicted results and compare them with dynamic transient

analysis results.

3. Conducting a parametric study to find the effect of different

types of materials used in fabricating disc brake components

for effective reduction of brake squeal.

4. Suppression of the squeal noise using several geometrical

modifications of the disc brake components.

5. Using the techniques of design of experiments (DOE) to find

out the significant contributions of the structural

modifications in reducing the squeal propensity and their

interactions as well.

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6. Using Taguchi method to assess the contributions and their

interaction effects of different types of materials used in

fabricating disc brake components for effective reduction of

brake squeal.

The schematic flow diagram for the proposed methodology is given

Figure 2.1.

Figure 2.1 Overview of research methodology

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2.2 DEVELOPMENT AND VALIDATION OF FE MODEL

2.2.1 Construction of a Disc Brake Corner

A car disc brake corner typically consists of steering knuckle

assembly, wheel hub, and the actual disc brake assembly. The disc brake

assembly consists of a ventilated rotor, a floating caliper with a single piston,

an anchor bracket, two bolts, two guide pins, and two brake pads. The pads

are loosely housed in the caliper and located by the anchor bracket. The brake

pad mounted on the piston is often referred to as the piston-pad, and the pad

on the opposite side is called the finger-pad. The caliper itself is allowed to

slide freely along the two mounting guide pins in a floating caliper design.

The solid model consisting of the whole disc brake corner is shown in

Figure 2.2.

Figure 2.2 A car disc brake corner with floating caliper

The brake corner is connected to the car suspension system through

the steering knuckle, which is mounted on the vehicle chassis. The wheel hub

is connected to the drive line, and the brake cylinder in the caliper is

connected to the hydraulic brake line system, where the piston slides inside

the caliper. Hence, the brake corner can be looked upon as a subsystem

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consisting of a number of components interrelated to each other and to other

sub-systems in the vehicle.

When hydraulic pressure is applied, the piston is pushed forward to

press the inner pad against the disc and simultaneously the outer pad is

pressed by the caliper against the disc. Most of the kinetic energy of the

travelling car is converted to heat through friction between the disc and pads.

Also, a small part of it is converted into sound energy and generates noise.

A detailed 3-dimensional FE model of the complete disc brake

corner is developed using finite element software package (ABAQUS). Figure

2.3 shows the FE model of the commercial disc brake corner. Details of FE

model for each of the components are listed in Table 2.1. FE model uses up to

19,000 solid elements and approximately 78,000 degrees of freedom. The

disc, brake pads, piston, wheel hub, guide pins and bolts are modeled using 8-

node (C3D8) linear brick elements while other components are modeled using

a combination of 8-node (C3D8), 6-node (C3D6) and 4-node (C3D4) linear

brick elements.

Figure 2.3 FE model of disc brake corner

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Table 2.1 Element details of disc brake components

Disc brake componentsTypes of

Element

No. of

Elements

No. of

Nodes

Disc C3D8 2559 4988

Friction

materialC3D8 320 558

Back plate C3D8 233 526

Caliper

C3D8

C3D6

C3D4

2334 2370

Anchor

bracket

C3D8

C3D41036 1644

Steering

knuckle

C3D8

C3D6

C3D4

9868 3585

Wheel hub C3D8 1654 2786

Piston C3D8 357 576

Guide pin C3D8 292 414

Bolt C3D8 58 123

2.2.2 Validation of FE Model

It is well known that brake components possess a wide range of

variations in material properties and sizes. In view of this situation, it is an

important issue to validate FE model with experimental data to ensure that

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accuracy of the dynamical properties of the FE model agree with those of the

physical component. The dynamic testing of structures has become a standard

procedure for FE model validation and updating. Over the past three decades,

modal testing and analysis have become a fast-developing technique for the

experimental evaluation of the dynamic properties of structures (Ewins 2001).

In general, the natural frequencies and mode shapes are important

parameters in the simulation of brake components to study NVH problem.

The FE modal analysis can be used to determine the natural frequencies and

mode shapes of brake components. The eigenvalue and eigenvector must

therefore be solved for mode-frequency analyses. The basic equation of the

classical eigenvalue problem is given by:

0)(2

iiKM (2.1)

where i = Eigenvalue (Natural frequency of mode i)

[M] = Structure mass matrix

[K] = Structure stiffness matrix

[ i] = Eigenvector (Mode shape vector of mode i)

The software used for the above study (ABAQUS 6-8) offers two

algorithms to solve the eigenvalue problem like subspace and Lanczos

method. For a large number of eigenmodes, the Lanczos method works faster

than the subspace method. The subspace method is recommended for analysis

with less than 20 eigenmodes. In the current study, modal analysis contains

many degrees of freedom. Hence, the Lanczos method is used to extract

natural frequencies and mode shapes of a structure.

In this study, two stages are used to validate the FE brake model

using experimental modal analysis, i.e. individual component and assembly

levels.

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2.2.2.1 Validation at component level

In the first stage, experimental modal analysis using the Frequency

Response Function (FRF) measurement is done. FRFs are measured by

exciting each structure with an impact hammer. The acceleration response is

measured with a light accelerometer through dynamic signal analyzer

(DEWE-41-T-DSA). The FRF measurements are recorded for each brake

components. Then, by using DEWE/FRF software, the curve fitting process is

performed on the transfer function spectrums obtained to extract the natural

frequencies, damping ratios and mode shapes.

The disc brake components are modeled in FE software. It is well

known that the accuracy of the results of finite element analysis is very much

dependent on the mesh size of models. In order to decide the proper mesh

size, a convergence study of the initial FE model is executed using mesh

refinement technique. The FE modal analysis of each brake components is

performed. The natural frequencies and mode shapes are extracted using

standard material properties. In order to reduce relative errors between the

predicted frequencies and the experimental results, FE updating (refining

process) is applied through changing material properties of the brake

components (Liles 1989, Richmond et al 1996). Finally, it is found that the

predicted natural frequencies are quite close to the measured values.

2.2.2.2 Validation at assembly level

In the second validation stage, the individual brake components are

assembled together on a brake test rig. Experimental modal test are performed

with brake line pressure of 1 MPa.

In the FE assembly model, the individual disc brake components

are coupled together to form the assembly model using combinations of node-

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to-surface and surface-to-surface contact elements to represent direct contact

interaction between components and all boundary conditions as found in

experimental are considered.

2.3 EVALUATION OF BRAKE SQUEAL

Though much work has been done on the disc brake squeal, it

requires continuous study to refine the prediction accuracy of finite element

models to provide designers appropriate tools to design quiet brakes. There

are two main categories of numerical approaches that are used to study this

problem: complex eigenvalue analysis and transient dynamic analysis.

2.3.1 Complex Eigenvalue Analysis

In this research, the complex eigenvalue analysis has been used to

investigate the stability of brake system modes. One of the earliest researchers

who attempted to incorporate the complex eigenvalue analysis with a large

finite element model using a number of linear spring elements at the friction

interface was Liles (1989). This method later became a standard practice and

widely used in predicting the squeal propensity. The positive real parts of the

complex eigenvalues indicate the degree of instability of the disc brake

assembly and reflect the likelihood of squeal occurrence. To increase the

prediction accuracy of squeal, the real pad surface roughness, negative

damping and positive damping are considered. In order to verify CEA results

experimental squeal test and dynamic transient analysis are performed and

compared with CEA results.

2.3.2 Dynamic Transient Analysis

Dynamic transient analysis based on finite element models

considering transient non-linear behaviors of brake systems were carried out

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by a few of researchers. Nagy et al (1994) were one of the first to perform a

numerical integration in a finite element disc brake. They used

MSC/PATRAN to develop the models of the disc brake components and

MSC/DYNA to conduct the analysis. A major shortcoming of this approach is

that the results do not indicate which mode is responsible for the squeal

problem. Furthermore, the technique is highly computationally intensive

especially for high frequencies.

In this research, dynamic transient analysis that determines the

instability of the system through divergent vibration time response is

performed and compared with the CEA results. The output time domain

information is converted to frequency domain information by using the Fast

Fourier Transform (FFT) technique through MATLAB software.

2.3.3 Experimental Squeal Test

Experimental squeal tests are carried out using a simply brake

dynamometer in order to verify the predicted FE results. The measurement of

squeal noise of the disc brake system is conducted at different operational

conditions. Since squeal is occurring at low speed below 30 km/h and at low

brake pressure below 2 MPa, no large power is required in the drive.

In order to measure squeal noise, bedding-in (warming-up) process

is performed for two hours at low pressure (0.7 MPa) and low disc speed

(50 rpm). Sound pressure level (SPL) measurements are made using

microphone and accelerometer. Output signals from the microphone and

accelerometer are fed to an FFT analyser, and the SPL spectrum is calculated

using special purpose software (DEWEsoft). The recorded data is plotted as

sound pressure level (dB) against frequency (Hz). Experimental results are

used to validate the CEA results.

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2.4 SQUEAL REDUCTION METHODS

Generally, there are a number of techniques that have been used in

order to reduce squeal noise. Structural modifications method is regarded as

one of the most effective ways to reduce squeal.

In this research, several structural modifications are considered to

reduce squeal of the disc brake system. This is accomplished through

reducing or eliminating the positive real parts of complex eigenvalues of the

baseline model. It is convenient to divide such modifications into three

general categories: material modifications, geometric modifications and

adding damping to the brake system through pad shim.

2.4.1 Material Modifications

It is necessary to design the whole brake components such that their

natural frequencies in the audible range are isolated to avoid mode coupling.

There is a traditional method that is used by some researchers by varying the

value of Young’s modulus of disc brake components.

In this study, a newer method is adopted by finding the effects of

different types of material, which are used in fabricating disc brake

components for commonly used vehicles or special types as heavy duty

performance and racing cars.

2.4.2 Geometric Modifications

Geometrical modifications are considered as one of the most

popular ways to suppress or eliminate squeal. In this study, one of the main

used is the modification of geometry of the disc and pads. The disc geometry

modification involves assessment of the influence of the disc neck structure

thickness, number of vanes, hat height, and the disc hat structure thickness on

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squeal generation. The pad geometry modification involves assessment of the

influence of different slots and chamfer configurations on squeal generation.

2.4.3 Damping Shim

The main function of damping shim is to provide additional

damping for the brake system. To simulate the shim, damping is assumed to

be uniformly distributed throughout the shim, and hence the commonly used

Rayleigh damping formulation is used, which is a very convenient way of

accounting for damping with continuous systems.

In the FE model, the shim model is created using a solid element

and modal analysis is validated using experimental modal analysis. Two

damping shims with Rayleigh damping are added onto the back plates of FE

brake assembly and the complex eigenvalue analysis is performed to

investigate their effects on squeal generation.

2.5 DESIGN OF EXPERIMENTS

Design of experiment (DOE) is a more effective way to determine

the effect of two or more factors on a response than a one factor at a time.

Due to the fact that brake squeal noise is a very complex phenomenon which

strong dependence on a huge numbers of parameters, DOE is suggested to

deal with the squeal problem to obtain optimal solution. In general, using the

one at a time plans is discouraged on experimental design and quality

improvement because of more runs are required for the same precision in

effect estimation, some interactions between variables cannot be captured, the

conclusions from the analysis are not general and optimal settings of factors

can be missed.

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In this study, two approaches of DOE are used namely: response

surface methodology to investigate the influencing factors of the brake pad on

the disc brake squeal and Taguchi method to evaluate different types of

materials used for fabricating disc brake components on squeal noise

occurrence.

2.5.1 Taguchi Method

From the previous works, it is understood that different types of

materials are employed for manufacturing brake components. Hence in the

present study, Taguchi method based design of experiment is used to

determine the significant contributions of the material modifications and their

interaction with other design parameters on reducing the squeal propensity.

In the first stage, Taguchi L9 orthogonal array is conducted to

identify the ‘most significant’ variables by ranking with respect to their

relative impact on the squeal occurrence. The L9 orthogonal array consists of

four control parameters at three levels. Then, signal-to-noise ratio (S/N ratio)

is computed using smaller-the-better quality characteristic. Finally,

contribution of material components is computed and plotted.

2.5.2 Response Surface Methodology

The ‘input-output’ relationship between the brake pad geometry

and the brake squeal is constructed for possible prediction of the squeal using

various design parameters of the disc brake.

For finding the most influential variables and their effects, a two

phase strategy is adopted. In the first phase, initial screening of various

variables is taken up. Fractional factorial design (FFD) of experiments is

conducted to identify the most influential variables. Subsequently, in the

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second phase, central composite design (CCD) based response surface

methodology is used to develop a non-linear model for prediction of disc

brake squeal.

2.5.1.1 First Phase: Screening FFD of experiments

In the first phase, initial screening of six variables is investigated. A

total number of eight trials are conducted and the squeal occurrence is

measured for each case. FFD of experiments is conducted to identify the most

influential variables. Pareto chart of the effects is plotted to determine the

magnitude and the importance of the effects.

2.5.1.2 Second Phase: RSM-CCD of Experiments

CCD is one of the most important experimental designs used for

optimizing parameters. Consequent to the first phase, four variables out of the

six variables are selected for the second phase.

A total of twenty five trials are conducted and a set of data is

collected as per the structure of CCD of experiments. A significant test is

conducted to examine the effects of different process parameters and their

interaction on the squeal occurrence.

2.5.1.3 Validation of the model

Statistical significance test and Analysis of Variance (ANOVA) test

is performed on the model using seventeen randomly generated test cases to

check the fitness of the model and to identify the significance of input

variables. Validation of the model and comparison between the simulation

and predicted model is examined.

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2.6 CONCLUDING REMARKS

As per the directions established through the literature survey and

by analysing the needs of the automotive industries, a more refined FE model

has been proposed in this research which includes parts of the suspension

(steering knuckle and wheel hub) to evaluate their influence on squeal

occurrence. In addition, more validation stages are adopted in the present

work. Validation of FE model is conducted using experimental modal

analysis at both individual components and brake assembly. The real pad

surface, negative and positive damping is considered to improve the predicted

results. Moreover, experimental squeal test and dynamic transient analysis is

performed to verify the CEA results.

The contribution of the research also lies in the recommendation of

new structural modifications for disc brake components and modifications of

rotor and pad geometry. Also, effects of pad shim/insulator through FEA and

experimental method on the squeal generation have been brought out in this

research.

The need for a new methodology using integration of the FE

simulation with DOE to better assess the contributions of different types of

structural modifications and its interaction effects for effective reduction of

brake squeal is explained. In the following chapters, application of the

proposed methodology, results of the numerical and experiments methods and

their effectiveness in conducting squeal will be discussed.