chapter 4 development and validation of fe modelarahim/chapter4.pdf · chapter 4 development and...

Chapter 4 Development and Validation of FE Model 70

Chapter 4

Development and Validation of FE Model

4.1 Introduction

An essential stage in studying disc brake squeal using finite element (FE) method is

the development and validation of the disc brake FE model. It has been thought that

an accurate representation of a disc brake (geometry and material properties) and

validated FE model would later produce reliable and accurate results. In current

practice in developing an FE model most researchers make simplifications and

assume that the pad and disc interface is a perfect plane surface. However, it is

already known that most contact interfaces have rough and irregular surfaces.

Although this simplification may ease the model development and reduce modelling

time, it perhaps can reduce the accuracy of predicted results, particularly in the

contact analysis and subsequently complex eigenvalue analysis. Development of the

FE model that takes into account a real surface topography of friction material is

explained in this chapter.

It is a standard practice that the FE model must be validated before further analysis is

made. Up to this point, most FE models are validated either at the component level

alone or combination of component and assembly levels. In the present chapter, the

developed FE model will be validated at the component level and the assembly level,

and a confirmation with the brake pad contact pressure distribution is also made. It is

thought that through the proposed three-stage methodology, prediction of squeal

occurrence can be improved compared with the previous methodology and it, in turn,

will make the complex eigenvalue analysis a predictive rather than diagnosis tool.

In summary, this chapter presents development and validation of a 3-dimensional

finite element model of a real disc brake. Modal analysis and contact analysis are

performed to obtain correlation between predicted and experimental results. The

natural frequencies and mode shapes of disc brake components and assembly models

are compared with the experimental results of James (2003). In the meantime


predicted brake pad contact pressure distributions are compared with analysed

images obtained through the contact tests.

4.2 Finite Element Model of Disc Brake

4.2.1 Development of FE Model

All the disc brake components are modelled carefully in order to achieve as accurate

representation as possible of a real disc brake. Most of the critical geometries of the

components are taken into account except for some very small local features such as

chamfers in all the components, tiny grooves in the brake pad and the calliper, and

brake fluid transfer hole. Even though these geometries are not included in the

model, by adjusting appropriate density or Young’s modulus, identical masses are

obtained between FE model and the real disc components. There are also other

components that not present in the current model, namely a rubber seal and two

rubber washers. It is thought that these two components are not significant to squeal

occurrence. The damping shims are not modelled because they have also been

removed in the squeal experiments.

As explained in the previous chapter, friction material should be modelled in a

realistic manner by considering a real surface topography. Measurements on the real

surface of friction material are made for several brake pads. This includes worn and

brand new brake pads. Since only a pair of brake pads have been extensively used in

the experiments and thus classified as worn pads, the brand new brake pads are

thought to be necessary for validation purposes. This can be used to check validity of

the proposed methodology and to enhance confidence with the current work i.e., to

validate contact pressure distribution between predicted and measured data. All

surface topographies that are measured using a linear gauge are shown in figure 4.0.

Details of measurement process are given in Chapter 3. It can be seen that for new

brake pads, the surface topographies are all quite different. Although it can be argued

that it may be due to defects during manufacturing process and the brake pads have

not undergone a bedding-in process, with the current surface topographies, it seems

that differences in surface profile remain even after various braking applications. If

this is true, it may lead to different contact pressure distributions that may

significantly influence squeal generation.


a) Pad 1 (Worn)

b) Pad 2 (New)

c) Pad 3 (New)

Figure 4.0: Surface topography at the piston pad (left) and finger pad (right)

After all of the component models are completed, they must be brought together to

form an assembly model. Attempts have been made to employ surface-surface

contact elements for all the contacted surfaces in the brake assembly. However,

convergence has been an issue and such a solution has never been achieved.

Therefore, combination of linear spring elements and surface-to-surface contact

elements (only at the disc/pad interface) are used to represent contact interaction

between disc brake components. The assembly model is rigidly constrained at the

boltholes of the disc and of the carrier bracket and is used throughout all the

analyses. This has been a common practice in the brake research community. Kung

et al. (2000) included steering knuckle in their FE model and numerical results

suggested that this inclusion would influence squeal occurrence.


4.2.2 FE Modal Analysis of Disc Brake Components

In order to obtain dynamic characteristics of disc brake components or assembly, it is

common practice to perform modal analysis from which natural frequencies and its

graphical mode shapes can be captured easily. In this section, all the components are

firstly simulated in free-free boundary condition and there are no constraints imposed

on the components. Natural frequencies up to 9 kHz are considered since this study

takes into account squeal frequencies between 1~ 8 kHz. In this work, the finite

element model of the disc is validated by the researcher himself and compared with

the experimental data while the material data of the other components were validated

and provided by an industry source. It is always desirable to validate all the

components at once. This has not been done by the researcher due to limitation in the

equipment and tools available in the laboratory. It is thought that laser vibrometers

can capture natural frequencies and mode shapes more accurately, as no contact with

the components is needed. This can reduce errors in measuring dynamic behaviour of

the components compared with the accelerometers, which need to be attached to the

components.

The first stage of the proposed methodology is to correlate between predicted and

experimental results of the disc brake components. In this section predicted natural

frequencies and mode shapes are listed and shown respectively for each of the disc

brake components.

4.2.2.1 Disc

For the free-free boundary condition of the brake disc, a number of modes for up to

frequencies of 9 kHz are extracted and captured. There are various mode shapes

exhibited in the numerical results. However, only nodal diameter type mode shapes

are considered because they are the dominant ones in the squeal events. The

calculated natural frequencies and mode shapes are given in figure 4.1, which

includes 2ND up to 7ND (nodal diameters). The number of nodal diameters based on

a number of nodes and anti-nodes appearing on the rubbing surfaces of the disc.

Using standard material properties for cast iron the predicted frequencies are not well

correlated with the experimental results. Hence tuning of the density and Young’s

modulus is necessary to reduce relative errors between the two sets of results. Having


tuned the material properties the maximum relative error is – 0.5 % and are shown in

Table 4.0. These results are based on the material properties given in Table 4.1.

a) 2 nodal diameter at 932 Hz b) 3 nodal diameter at 1814 Hz

c) 4 nodal diameter at 2940 Hz d) 5 nodal diameter at 4369 Hz

e) 6 nodal diameter at 6070 Hz f) 7 nodal diameter at 7979 Hz

Figure 4.1: Mode shapes of the disc at free-free boundary condition

Table 4.0: Modal results of the disc at free-free boundary condition

MODE 2ND

3ND 4ND 5ND 6ND 7ND

Test (Hz) 937 1809 2942 4371 6064 7961

FE (Hz) 932 1814 2940 4369 6070 7979

Error (%) -0.5 0.3 -0.1 0.0 0.1 0.2


Table 4.1: Material data of disc brake components

DIS

C

BA

CK

PL

AT

E

PIS

TO

N

CA

LL

IPE

R

CA

RR

IER

GU

IDE

PIN

BO

LT

FR

ICT

ION

MA

TE

RIA

L

Density

(kgm-3

) 7107.6 7850.0 7918.0 7545.0 6997.0 7850.0 9720.0 2798.0

Young’s

modulus

(GPa)

105.3 210.0 210.0 210.0 157.3 700.0 52.0 Orthotropic

Poisson’s

ratio 0.211 0.3 0.3 0.3 0.3 0.3 0.3 -

4.2.2.2 Brake pad

FE modal analysis of the brake pad, which is composed of two parts, namely back

plate and friction material, is simulated based on the material data given in Tables

4.1 and 4.2. The friction material is an orthotropic material which has nine

independent elastic constants in its stiffness matrix as given in Table 4.2. Matrix D in

the stress-strain relationship, Dεσ = for this orthotropic material is given as follows:

2323

0 1313

0 0 1212

0 0 0 3333

0 0 0 2233

2222

0 0 0 1133

1122

1111

D

Dsym

D

D

DD

DDD

(4.0)


where

1332212

1331322321121

1

,232323

,131313

,121212

,)311232

(22233

,)322131

(11133

,)233121

(11122

,)2112

1(33333

,)3113

1(22222

,)3223

1(11111

ννννννννν

ννν

ννν

ννν

νν

νν

νν

−−−−=Υ

=

=

=

Υ+=

Υ+=

Υ+=

Υ−=

Υ−=

Υ−=

GD

GD

GD

ED

ED

ED

ED

ED

ED

GvE and , are the Young’s modulus , Poisson’s ratio and shear modulus respectively

that associated with the material’s principal direction.

The eigenvalue analysis of the brake pad model predicted a total of 4 modes within

frequency range 3~9 kHz. From the results the first mode occurs at a frequency of

3107 Hz, which is the first bending type as illustrated in figure 4.2a. It is clearly seen

that anti-node appears at the centre of the pad and two nodes at equal distance from

the centre showing the maximum displacement.

The second mode occurs at a frequency of 4557 Hz is of the first twisting mode type.

The displacement contour plot indicates two nodal lines running diagonally across

the pad from abutments and curving to the pad centre. The mode shape shown in

figure 4.2b could be more properly described as a twisting mode.

The third mode is also the bending type mode as clearly shown in figure 4.2c, which

is generated at a frequency 7043 Hz. From the equal displacement contour plot, there

are 3 nodes appear on the displaced pad; one of the nodes is located at the centreline

of the pad and the other two at either end of the pad. This mode shape is known as

the second bending mode.


The fourth mode at a frequency of 8857 Hz and is shown in figure 4.2d is of a similar

twisting type to the one shown in figure 4.2b but of a different order. There are three

node lines, one running across the central part of the pad and one running across the

lower quarter of each half of the pad. This mode shape is termed the second twisting

mode.

a) First bending mode at 3107 Hz b) First twisting mode at 4557 Hz

c) Second bending mode at 7043 Hz d) Second twisting mode at 8857 Hz

Figure 4.2: Mode shapes of the brake pad

Table 4.2: Orthotropic material of the friction material (in Pascal)

D1111 D1122 D2222 D1133 D2233

8.746E+9 1.938E+9 8.746E+9 3.160E+8 3.160E+8

D3333 D1212 D1313 D2323

2.432E+9 3.404E+9 1.631E+9 1.631E+9

4.2.2.3 Calliper

There are about 13 modes generated from the simulated modal analysis ranging from

2 ~ 9 kHz. All the extracted natural frequencies are given in Table 4.3. In this section

only the modes that are close to the natural frequencies of the disc are shown. There

are three such modes. The first mode is obtained at a frequency of 2799 Hz in which

the fingers of the calliper are moving towards each other. This is clearly shown in

figure 4.3a where the red arrows indicate directions of the fingers movement.


The second mode of the calliper is found at a frequency of 6080 Hz. The two red

arrows are indicating that the two fingers move in opposite directions as shown in

figure 4.3b. Meanwhile the third such mode is generated at a frequency of 7818 Hz.

The maximum displacement is no longer appearing at the fingers rather it appears at

the calliper arms. Figure 4.3c shows that the arms are experiencing bending

displacement as indicated by the two red arrows.

Table 4.3: Simulated natural frequencies of the calliper

Mode No. Frequency (Hz) Mode No. Frequency (Hz)

1 2347 8 6945

2 2799 9 7317

3 3650 10 7598

4 5080 11 7818

5 5683 12 8943

6 6080 13 8991

7 6616


3-D View 2-D View (Bottom)

a) Mode shape1 at a frequency of 2799 Hz


b) Mode shape 2 at a frequency of 6080 Hz


c) Mode shape 3 at a frequency of 7818 Hz

Figure 4.3: Mode shapes of the calliper


4.2.2.4 Carrier

There are about 16 modes generated within the frequency range of interest. The

simulated natural frequencies found in the analysis are given in Table 4.4. Similar to

the calliper, only the modes whose frequencies are close to those of the disc are

illustrated and described. It is found that there are four such modes.

The first closest mode is found at a frequency of 1788 Hz as shown in figure 4.4a.

The displacement plot shows that the carrier bridge is experiencing maximum

bending at the centre (front view). While the bridge is not much distorted by looking

at the top view torque members are seen move away from each other.

The second closest mode is generated at a frequency of 3007 Hz where once again

the carrier bridge is experiencing maximum displacement at the centre but in the

different direction. The bending mode of the bridge appears in the normal direction

as shown in figure 4.4b. From the front view, the bridge is stretching a bit. The

torque members are moving towards each other.

The third closest mode is obtained at a frequency of 6144 Hz and is of the bridge

bending mode. This type of mode is similar to the one found in figure 4.4b but in

different order of bending mode. There are three nodes and two anti-nodes appear on

the bridge. This mode is termed as second bending mode of the bridge. However, the

torque members remain unchanged. This mode shape is illustrated in figure 4.4c.

The last closest mode is again related to the carrier bridge and it appears at a

frequency of 7994 Hz as shown in figure 4.4d. This mode is not the bending type

rather the centre of the bridge is bulging from its original shape. The torque

members’ position remains the same.


Top View Front View

a) 1788 Hz b) 3007 Hz

c) 6144 Hz d) 7994 Hz

Figure 4.4: Mode shapes of the carrier

Table 4.4: Simulated natural frequencies of the carrier

Mode No. Frequency (Hz) Mode No. Frequency (Hz)

1 1362 9 5250

2 1788 10 6144

3 1930 11 6410

4 2557 12 6876

5 2579 13 7082

6 3007 14 7569

7 3454 15 7994

8 4851 16 8226

Bridge

Torque

member


4.2.2.5 Piston

From the simulated modal analysis, it is found that only one mode appears within the

frequency of interest. This mode is generated at a frequency 7317 Hz and its contour

plot is given in figure 4.5. From the displacement plot, there appear four nodes. This

type of shape is termed as 2-diametric mode.

2-D View 3-D View

Figure 4.5: Second diametric mode of the piston at a frequency of 7317 Hz

4.2.2.6 Guide pin and bolt

It is convenient to analyse the guide pin and bolt together. This is because the two

components are attached together where the bolts are screwing into guide pins holes.

From the simulated modal analysis, there are two modes found within the frequency

range of interest. The first mode is occurring at a frequency of 6360 Hz and is of the

bending type mode. This is clearly seen from the contour plot, as shown in figure

4.6a, that the bolt is displacing away from the guide pin. The second mode is found

at a frequency of 7198 Hz and is shown in figure 4.6b. From the figure, it shows that

the bolt is twisted at where it screws to the guide pin. This mode shape is known as

twisting type mode.

a) First bending mode at 6360 Hz b) First twisting mode at 7198 Hz

Figure 4.6: Mode shapes of guide pin and bolt assembly


4.2.3 FE Modal Analysis of Disc Brake Assembly

The second stage of the methodology is to capture dynamic characteristics of the

assembled model. The previous separated disc brake components must be now

coupled together to form the assembly model. As discussed earlier in this chapter, a

combination of linear spring elements and surface-to-surface contact elements are

used to represent contact interaction between disc brake components and disc/pad

interface respectively. Table 4.5 shows details of disc brake couplings that are

employed in the FE assembly model.

In the experimental modal analysis, a brake-line pressure of 1 MPa is imposed to the

stationary disc brake assembly. A similar condition is also applied to the FE brake

assembly model. In this validation, measurements are taken on the disc as it has a

more regular shape than the other components. For the FE assembly model, spring

stiffness values are tuned systematically as follows:

• Any components that allow to slide between them the spring value is set to a

very low stiffness e.g. around 0.5 N/m. Example of this is between the guide

pin and the carrier as given in Table 4.5

• Any components that restrict movement at any directions e.g. between bolt

and calliper arm, the spring value is set a very high stiffness e.g. around

1E+10 N/m.

• Any components that may experience to vibrate e.g. back plate, the spring

stiffness is set around 1E+6 N/m.

Once those spring values are set, modal analysis is performed to obtain natural

frequencies of the disc and their associated mode shapes. A comparison is made

between predicted and experimental results of the disc. If there are large relative

errors, the spring stiffness values for linking two components need to be adjusted or

updated. This updating process is continued until the relative errors are reduced to an

acceptable level. Since the process is performed based on the trails and errors

process, it takes a lot of time and requires engineering intuition to identify more

influential springs and pick up appropriate spring constants.

After a number of attempts, good agreement between predicted and experimental

results was achieved. Correlation between the two frequencies that include 2ND up

to 7ND of the disc is given in Table 4.6. From the table, it is found that the maximum


relative error is - 5.2 %. These predicted results are based on the spring stiffness

values that are given in Table 4.5. Mode shapes of the FE assembly are described in

figure 4.7. The simulated FE modal analysis is able to predict two frequencies at 3-

nodal diameter as obtained in the experiments, which are generated at 1730.1 Hz and

2151.1 Hz. While in the experiments these frequencies are found at 1750.7 Hz and

2154.9 Hz. The highest relative error is found on 6-nodal diameter, for which the

predicted frequency is 5837.1 Hz while the experimental frequency is 6159.0 Hz.

The lower relative error is about – 0.1 % on the second 3-nodal diameter, for which

the frequencies are 2151.1 Hz and 2154.9 Hz in theory and in experiments

respectively. In this validation process, static friction coefficient (at pads/disc

interface) is also play an important role to reduce the relative errors. It is found that

static friction coefficient of 7.0=µ give better correlation in assembly model as

describe in Table 4.6.

Table 4.5: Disc brake assembly model couplings

No Connections DOF Coordinate

System

No. of

Spring

Stiffness

(N/m)

1 Piston wall-Calliper housing 1 Local 66 1.00E+9

2 Piston- Back plate 1 Global 38 2.80E+6



5 Calliper finger- Back plate 1 Global 104 1.02E+6



8 Leading abutment- Carrier 1 Global 24 0.50E+0

9 Leading abutment- Carrier 2 Global 24 1.00E+9

10 Trailing abutment- Carrier 1 Global 24 1.00E+9

11 Trailing abutment- Carrier 2 Global 24 1.00E+9

12 Leading bolt- Calliper arm 1 Local 16 3.00E+10



15 Trailing bolt- Calliper arm 1 Local 16 3.00E+10



18 Leading guide pin- Carrier 1 Local 18 1.00E+9

19 Leading guide pin- Carrier 3 Local 18 0.50E+0

20 Trailing guide pin- Carrier 1 Local 18 1.00E+9

21 Trailing guide pin- Carrier 3 Local 18 0.50E+0


a) 2ND at 1246.9 Hz b) 3ND at 1730.1 Hz

c) 3ND at 2151.1 Hz d) 4ND at 2966.2 Hz

e) 5ND at 4445.7 Hz f) 6ND at 5837.1 Hz

g) 7ND at 8045.2 Hz

Figure 4.7: Mode shapes of the assembly model


Table 4.6: Modal results of the assembly measured on the disc

MODE 2ND

3ND 3ND 4ND 5ND 6ND 7ND

Test (Hz) 1287.2 1750.7 2154.9 2980.4 4543.7 6159.0 7970.0

FE (Hz) 1246.9 1730.1 2151.1 2966.2 4445.7 5837.1 8045.2

Error (%) -3.1 -1.1 -0.1 -0.4 -2.1 -5.2 0.9

4.3 Contact Analysis

The third and final stage of the proposed methodology is to conduct experiment and

simulation of contact pressure distribution under stationary application of the disc

brake (that is, application of brake with no torque or rotation of the disc).The

experimental results will be used to confirm contact pressure distribution predicted in

the FE model. In this section, brake pad models with real surface topography that

illustrate in figures 4.0a ~ 4.0c are employed. The brand new pads are used in order

to confirm the measurements taken from the linear gauge and also to show accuracy

and reliability of the available tool.

4.3.1 Contact Tests

In this work, Pressurex® Super Low (SL) pressure-indicating film, which can

accommodate contact pressure in the range of between 0.5 ~ 2.8 MPa, is selected.

The films are tested under certain brake-line pressures for 30 second and then

removed from the disc/pad interfaces. Figure 4.8 shows example of pressure-

indicating film before and after the contact testing. From the figure, the tested film

only provides stress marks without revealing its magnitude. Therefore it is necessary

to obtain both qualitative and quantitative of the contact pressure distribution. In

doing so Topaq

Pressure Analysis system that can interpret the stress marks is used.

Configurations of the tested pads are given in Table 4.7.


Figure 4.8: Pressure-indicating films before (left) and after (right) the static

contact pressure testing

Table 4.7: Configurations of tested pad

Identification Pad

conditions Damping shim

Brake-line

pressure (MPa)

Pad 1 Worn No 2.5

Pad 2 New No 2.5

Pad 3a New No 2.5

Pad 3b New No 1.5

It is shown that contact pressure distributions for the worn pad (Pad 1) seem to be

concentrated (red colour) at the outer border region of the pads, while zero pressure

at the inner border region of the pads. It is suggested that wear takes place more at

the inner border than the outer border. It is also shown that contact pressure

distributions are asymmetric for the piston and finger pads. This might due to

irregularities in the surface topography of the friction material. The red colour shows

the highest contact pressure. Contact pressure distributions of the worn pad are

shown in figure 4.9a. Areas in contact for both the piston and finger pads are 1.436e-

3m2

and 1.484e-3m2 respectively.

For the brand new pads, i.e. Pad 2 and Pad 3a that come from the same box and the

same manufacturer, it is seen that they have different contact pressure distributions

both at the piston and finger pads as shown in figures 4.9b and 4.9c. These variations

are due to its surface topography as shown in figure 4.0. It is seen from figure 4.9b

that contact pressures are distributed more even than Pad 3a. There are areas of

contact at the trailing edge for Pad 2. But there seems to be separation in that region

for Pad 3a. The areas of contact for the piston and the finger pads are 1.361e-3 m2

and 1.069e-3 m2 respectively. From figure 4.9c, contact pressure seems to be zero at

the centre of the pads. Most of the highest contact pressures appear at the outer


border of the pads. Areas in contact for Pad 3a are 8.090e-4m3 and 9.230e-4m

2 for

the piston and the finger pads respectively.

By applying different levels of brake-line pressure, the higher the pressure the more

the contact areas should be generated. This is proved in figure 4.9d where compared

to figure 4.9c, it is seen that the areas of highest pressure are reduced significantly. It

is also confirmed that the areas of contact for the piston and the finger pads are

reduced to 6.370e-4 m2 and 6.857e-4 m

2 respectively. This gives to reduction of

about 21% and 26% for the piston and the finger pads respectively.

a) Pad 1 b) Pad 2

c) Pad 3a d) Pad 3b

Figure 4.9: Analysed images of the tested pads: piston pad (left) and finger pad

(right). Top of the images are the leading edge.


4.3.2 FE Contact Analysis

In the FE contact analysis, the brake pad models are similar to those used in the

contact tests. Now the real surface profile of the brake pads will be considered in the

sense that the surface profile information is incorporated in the FE model of the

brake pad surface by adjusting its surface coordinates in the normal direction. Similar

configurations of the test are also adopted in order to make comparison between the

two results, predicted versus experimental.

The first contact simulation is performed on the worn pad or Pad 1 at a brake-line

pressure of 2.5 MPa. It can be seen in figure 4.10a that the areas in contact are almost

the same with those found in the experiment. Predicted contact areas in the contact

analysis are 1.441e-3m2 and 1.784e-3m

2 for the piston and the finger pads

respectively. The results suggest that there are fairly good agreements between the

two as described in figure 4.11. The contact area of the piston pad seems closer to the

experimental one, compared with the finger pad.

The second contact simulation is done for Pad 2, which is subjected a brake-line

pressure of 2.5 MPa. From figure 4.10b contact pressure seems to be biased towards

the outer radius of the pads. These patterns are most likely to be the same for those

obtained in figure 4.9b. In the simulation it is found that the contact areas for the

piston pad is 8.476e-4m2 and for the finger pad is 8.131e-4 m

2. These contact areas

are less than those measured in the experiments. However, it still produces quite

reasonable correlations against the experimental results especially at the finger pad as

described in figure 4.11.

The third contact analysis is simulated for Pad 3a, in which a brake-line pressure of

2.5 MPa is applied to the disc brake assembly model. Predicted areas of the highest

contact pressure are in good agreements with the experimental results. Contact

pressure distribution of Pad 3a is illustrated in figure 4.10c. For Pad 3a, predicted

contact areas are 1.046e-3 m2 and 1.020e-3 m

2 for the piston and the finger pads

respectively. It can be seen from figure 4.11 that the difference in the finger pad is

small while there is a quite large difference at the piston pad. However, overall, fairly

good agreement is achieved between predicted and experimental results.


The last contact analysis is similar to the third except for a different brake-line

pressure of 1.5 MPa applied to the assembly model. The predicted areas in contact

should be less than those predicted in third analysis and showed in figure 4.9d. Once

again, good correlations are achieved between predicted and experimental results in

terms of areas of the highest contact pressure. The locations of the contact pressure

distribution are almost identical to the experimental one. In the contact simulation, it

is predicted that the contact areas of the piston pad are 5.943e-4 m2 and of the finger

pad is 6.860e-4 m2. These contact areas are nearly the same as those measured in the

experiment. Figure 4.11 shows that there are small differences in the contact area for

both the piston and the finger pads.

a) Pad 1

b) Pad 2

Figure 4.10: Predicted contact pressure distribution: piston pad (left) and finger

pad (right). Top of the diagrams are the leading edge


c) Pad 3a

d) Pad 3b

Figure 4.10 (cont’d): Predicted contact pressure distribution: piston pad (left) and

finger pad (right). Top of the diagrams are the leading edge


Figure 4.11: Comparison between experiment and FE analysis in the contact area

4.4 Summary

This section describes in details development and validation of the FE model. The

researcher proposes a three-stage methodology as follows:

• Validation of disc brake components using modal analysis

• Validation of a disc brake assembly using modal analysis

• Confirmation of contact pressure distribution considering a real surface

topography of brake pads

From the modal analysis, it is shown that good agreement is achieved for both

components and assembly levels. This can only be done after tuning or updating


process in which material properties of the components and spring stiffness value are

adjusted at each level. It is also found that there are a number of close natural

frequencies among brake components. It has been hypothesised in the past that this

closeness could lead to the generation of squeal. This hypothesis will be investigated

further in the next chapter.

Previous studies using the finite element method assume the presence of perfect

plane surface at the disc and pads interface. The current FE model includes a real

surface topography of the brake pad interface. Measurements pad surface profiles are

taken using a linear gauge. It is found that current tools are able to produce good

measurements and subsequently producing more realistic and predicted contact

pressure distribution. It is also shown that current meshes of individual FE model,

particularly of the brake pads, are sufficiently dense to produce realistic prediction of

contact pressure distributions and also to capture mode shapes of natural frequencies

up to 9 kHz. However, current predicted results can be improved by using better

mesh quality. Given an accurate representation of disc brake components and

assembly, subsequent simulation is able to produce much better predicted results.

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