CHAPTER 1

INTRODUCTION Brakes are one of the most important safety and performance components in

automobiles. Ever since the advent of the automobile, development of brakes has

focused on increasing braking power and reliability. However, the refinement of

vehicle acoustics and comfort through improvement in other aspects of vehicle design

has dramatically increased the relative contribution of brake noise to these aesthetic

and environmental concerns.

The word “Squeal” means loud noise. Disc brake squeal remains an elusive

problem in the automotive industry. A loud noise or high pitched squeal occurs when

the brakes are applied. The frequency ranges for the low-frequency squeal is 1000–

2000 Hz and for high frequency squeal is 2–15 kHz.

Brake noise is an irritant to consumers who may believe that it is symptomatic

of a defective brake and file a warranty claim, even though the brake is functioning

exactly as designed in all other aspects. Thus, noise generation and suppression have

become prominent considerations in brake part design and manufacture. Indeed, many

makers of materials for brake pads spend up to 50% of their engineering budgets on

noise, vibration and harshness.

1.1 DISC BRAKE MECHANICS

An automotive brake system can be divided into three main parts:

The rotor, as the name is indicating, is rotating with the wheel. It is the

first part in the friction couple.

The brake pad is the second, stationary part of the friction couple. During a

brake application the pad is pressed against the rotor with a hydraulic piston.

The friction forces between the stationary pad and the rotating disc will turn

the kinetic energy of the vehicle into heat. The hydraulic system transfers and

amplifies the brake force from the brake pedal to the hydraulic piston pressing the

linings against the rotor.

1

Figure 1.1 Disc Brake (courtesy www.howstuffworks.com)

The brake pads are the rough friction surface that is pressed against the rotor

to stop the wheel. The rotor is a round plate attached to the hub. The piston presses

one brake pad against the wheel, while the caliper presses the other. The caliper is

“floating” because it moves in a track that allows it to center itself over the rotor. As

the brake fluid fills the cylinder, it pushes the piston to the left; however, it also

pushes the caliper to the right. This allows both brake pads to press against the wheel

simultaneously.

1.2 FINITE ELEMENT MODELS

In recent years, the finite element method has become an indispensable tool

for modeling disc brake systems and providing new insights into the problem of brake

squeal. This method provides a natural and straightforward means for generating

finite dimensional approximations to the governing equations of motion for the

components of the brake system. This is accomplished by admitting polynomial

interpolations of the dependent variables (e.g., displacements, temperature) within

each element subdomain. However, contrary to traditional lumped parameter

techniques, the finite element method allows for accurate representation of complex

geometries and boundary/loading conditions. Also, spatially resolved kinematic and

kinetic quantities, such as strains and stresses, are readily computed as part of the

finite element solution. Furthermore, the accuracy of a finite element model is

typically controlled by the analyst, who may choose to refine the approximation in

order to simulate the response of the brake system with a higher degree of fidelity.

2

The finite element method has been employed by researchers in brake squeal studies

to several ends. One of its earlier uses was to investigate the modes and natural

frequencies of the brake rotor. The most common use is to compute the M and K

matrices in models of disc brakes. Subsequently, a linear eigenvalue analysis is

conducted to determine the system’s frequencies, modes, and stability.

1.3 REASONS FOR BRAKE SQUEAL

Most brake squeal is produced by vibration (resonance instability) of the

brake components, especially the pads and discs (known as force-coupled

excitation).

The callipers and brake pads, which squeeze the brake rotors to make the car

stop, can't get an even grip on a warped rotor hence, vibration.

Cold weather combined with high early-morning humidity (dew) often

worsens brake squeal. Dust on the brakes may also cause squeal.

1.4 PROBLEMS DUE TO SQUEAL

Overall brake squeal can be annoying to the vehicle passengers, passers-by,

pedestrians, etc. especially as vehicle designs become quieter.

Squeaky brakes can panic a driver.

Warranty claims by the customer.

1.5 METHODOLOGY OF WORK FLOW

Figure 1.2 Flowchart of Work flow

3

Literature Survey

Problem Identification

Disc Brake 3D model

Meshing of the

Assembled Drawing

Frequency Analysis

CHAPTER 2

LITERATURE SURVEY2.1 Analysis of brake squeal noise using the finite element method

Roberto Jordan, et al.,[1] This paper summarizes the application of complex

eigenvalue analysis in a finite element model of a commercial brake system. The

effect of the operational parameters (friction coefficient, braking pressure and brake

temperature) and wear on the dynamic stability of the brake system is examined. The

results show that the effect of brake temperature changes the coupling mechanisms

between rotor and pad, which in some cases can be useful in order to reduce the

instabilities and generated noise. Wear is an operational condition that has a strong

effect on the system instability, since stiffness properties of brake pads are influenced

by the changes on geometry and on the friction material, leading to high-frequency

noise generation.

2.2 Analysis of Disc Brake Noise at High and Low Frequency with the Effect of

the Friction

Ammar A. Yousif, et al., [2] This paper is a study on the stick-slip oscillation

of a discrete system with contact interaction as a friction curve. The stick-slip

oscillation with a single degree-of-freedom was examined by means of numerical

time integration , while that with two degrees was by using FEM method. Beam on

rotating disc was used to investigate the effect of friction at low velocity. The

response indicated that the friction ratio was responsible for the separation amplitude

value. The plate on disc was modelled and connected by using matrix27 to investigate

the effect of friction on a high frequency system. The results showed that friction

causes damping at low frequency while at high frequency, it may generate the squeal.

2.3 Linear eigenvalue analysis of the disc-brake squeal problem

Q. Cao1, H. Ouyang1 et al, [3] This paper presents a numerical method to

calculate the unstable frequencies of a car disc brake and suggests a suitable analysis

procedure. The stationary components of the disc brake are modelled using finite

elements and the disc as a thin plate. The separate treatments of the stationary

components and the rotating disc facilitate the modelling of the disc brake squeal as a

4

moving load problem. Some uncertain system parameters of the stationary

components and the disc are tuned to fit experimental results. A linear, complex-

valued, asymmetric eigenvalue formulation is derived for the friction-induced

vibration of the disc brake. Predicted unstable frequencies are compared with

experimentally established squeal frequencies of a real car disc brake.

2.4 Finite Element Analysis of Thermal elastic Instability of Disc Brakes

JW. S Chung et al [4] In this study, the thermoelastic instability (TEI) was

analyzed using the finite element analysis technique. The governing dynamic and heat

equations were described. Three dimensional thermo mechanical analysis model of

the disc brake system were created. An intermediate processor based on the staggered

approached was used to exchange result data: temperature, friction contact power,

nodal displacement and deformation. Disc thickness variation (DTV) and temperature

distribution of the disc were calculated, and the tendency and meaning of each result

were discussed.

2.5 Analysis of disc brake squeal using the Complex Eigenvalue method

P. Liu et al [5]. In this paper, a new functionality of ABAQUS/Standard,

which allows for a nonlinear analysis prior to a complex eigenvalue extraction in

order to study the stability of brake systems, is used to analyse disc brake squeal. An

attempt is made to investigate the effects of system parameters, such as the hydraulic

pressure, the rotational velocity of the disc, the friction coefficient of the contact

interactions between the pads and the disc, the stiffness of the disc, and the stiffness

of the back plates of the pads, on the disc squeal. The simulation results show that

significant pad bending vibration may be responsible for the disc brake squeal.

2.5 CONCLUSION FROM LITERATURE SURVEY

The effect of some operational parameters on the stability characteristics of a

disc brake such as High friction coefficients increases the degree of system instability.

Brake temperature had the effect of reducing the brake pad stiffness, altering the

coupling mechanisms between the rotor and pad. In some cases, this effect can be

useful. An increase in temperature led to an increase in the damping loss factor of the

brake pads. Wear is an operational condition that must be considered in numerical

models, since it has a strong effect on the stability characteristics The effect of a non-

5

conservative (as a friction force) tends to couple the two modes. These effects make

the system able to exchange energy in a way that causes the unstable behaviour of the

brake system to continue. It can be observed that the effects of friction coefficient

enforce the system to generate the squeal at lower frequency from the stable separate

modes. Complex eigenvalue analysis is more useful in finding the unstable frequency

which causes squeal.

2.6 OBJECTIVE

To perform Static analysis for the application of brake pressure.

Static analysis to impose a rotational velocity on the disc.

To extract the natural frequency of the system.

Complex eigenvalue analysis to extract unstable modes and identify the onset

of squeal frequency.

To vary the operational parameters such as friction coefficient, pressure,

contact stiffness and angular velocity and its effect on squeal frequency.

6

CHAPTER 3

BRAKE SQUEAL ANALYSIS

3.1 BRAKE NOISE GENERATION MECHANISM

Disc brake squeal occurs when a system experiences vibrations with a very

large mechanical amplitude. There are two theories that attempt to explain why this

phenomenon occurs. The first theory states that brake squeal is a result of a stick–slip

mechanism . An opposing theory states that high levels of vibration result from

geometric instabilities of the brake system assembly.

An example of stick-slip is a squeaky door hinge. During the stick phase, the

brake lining and cast iron move together, with no slippage at the interface. The stick

time period is variable, depending on speed, load, and system stiffness. When slip

begins, a noise burst occurs, this involves a half-cycle of motion at the rubbing

surface. The sudden energy burst often produces a more sustained audible oscillation.

Figure 3.1 Stick Slip effect

Both theories, however, attribute the brake system vibration and the

accompanying audible noise to variable friction forces at the pad–rotor interface.

According to the first hypothesis, the stick–slip theory, a variable friction coefficient

with respect to sliding velocity between pads and rotor, provides the energy source for

the brake squeal. Several studies based on this theory were conducted when disc

brakes were first used on automobiles. Squeal noise was found to be more likely when

the decreasing relationship between the friction coefficient and the sliding velocity

become pronounced. An increase in the negative slope did not always increase the

7

occurrence of squeal, however, the need for an alternative or accompanying theory

was revealed.

In the case of geometric instability, the second theory, the variable friction

forces are caused by variable normal forces. Even if the coefficient of friction is

constant, variable friction forces are still possible. In this case, two system modes that

are geometrically matched move closer in frequency as the friction coefficient

increases. These two modes eventually couple at the same frequency and become

unstable.

3.2 ANALYSIS OF BRAKE SQUEAL NOISE USING FEM

The stability of the system of equations, according to the geometric stability

hypothesis, reflects the likelihood of squeal for the brake system modelled. Several

techniques for evaluating the stability of a system are available. Approaches

considered were (a) a transient solution of the dynamic equations of motion, (b)

evaluation of the Routh criterion, and (c) an eigenvalue analysis of the system. A

divergent transient solution indicates that instabilities are present in the system.

Likewise, the Routh criterion demonstrates whether or not a system is stable. Such

solutions, however, provide no insight into how the structure could be altered to

remove the instability.

Figure 3.2 Interaction of two masses with friction effect included

8

On the other hand, the complex roots obtained from an eigenvalue analysis

can reveal which system vibration modes are unstable. Knowledge of the unstable

system modes facilitates several control methods: modal frequencies could be moved

by changing components or adding damping, so that the mode in question becomes

stable. Based on the usefulness of the information, complex eigenvalues are used as a

measure of the system stability.

The equation of motion for a vibrating system is

----------------------(1)

where M, C and K are mass, damping and stiffness matrices, respectively, and

u is the generalized displacement vector. For friction induced vibration, it is assumed

that the forcing function F is mainly contributed to by the variable friction force at the

pad–rotor interface. The friction interface is modeled as an array of friction springs as

shown in Fig. 3. With this simplified interface model, the force vector becomes linear.

----------------------(2)

where Kf is the friction stiffness matrix. A homogeneous equation is the

obtained by combining Eqs. (1) and (2) and by moving the friction term to the left-

hand side:

-----------------------(3)

3.3 COMPLEX EIGENVALUE ANALYSIS

The complementary solution to the homogenous, second order, matrix

differential equation above (3) is in the form of

------------------------(4)

Performing the appropriate differentiations and substituting into Eq. (3) yields

the complex eigenvalue problem:

-------------------------(5)

9

Non-trivial solutions for the displacement occur only where the matrix in

parenthesis is singular. This matrix is singular only for certain values of S, called

complex eigenvalues.

The arbitrary scaled solution vectors corresponding to each eigenvalue are the

eigenvectors. They may or may not be complex. These eigenvectors reveal the

relative shape of the oscillatory motion for each solution, or mode, including the

phase relationship between points in the system if they are complex. The eigenvalues

and the eigenvectors of Eq. (5) may be complex, consisting of both a real and

imaginary part. For underdamped systems the eigenvalues always occur in complex

conjugate pairs. For a particular mode the eigenvalue pair is

-------------------------(6)

where is the real part and is the imaginary part for the ith mode. The

motion for each mode can be described in terms of the complex conjugate eigenvalue

and eigenvector:

--------------------------(7)

Thus and are the damping coefficient and damped natural frequency

describing damped sinusoidal motion. If the damping coefficient is negative, decaying

oscillations typical of a stable system result. A positive damping coefficient, however,

causes the amplitude of oscillations to increase with time. Therefore the system is not

stable when the damping coefficient is positive. By examining the real part of the

system eigenvalues the modes that are unstable and likely to produce squeal are

revealed.Variable friction force with variable normal force (interface element) – The

contact stiffness element used in the model describes the interaction between adjacent

nodes of the disc and pads. This is probably the only work which shows, through a

clear and solid based explanation, all the procedures involved in the construction of an

FEM model to analyze disc brake squeal noise.

The friction element must be able to model:

The steady state friction force acting at the interface of the components the

steady state reaction force acting in the normal direction.

10

The varying part of the normal force which is proportional to the stiffness of

the element and the relative displacement of the adjacent nodes and the varying part

of the friction force which is related to the varying normal force according to

Amonton’s law

------------------------(8)

Figure 3.3 A pad coupled to the disc face model with friction elements

Figure 3.4 The effect of normal displacement on the variable normal force

Node 1 represents one of the nodes on the disc face and node 2 is the adjacent node on

the brake pad friction face as shown here in Fig4.3. When perturbed, nodes 1 and 2

move relative to each other, causing a variable force on node 2, which is a function of

11

the relative displacement between the two nodes and the contact stiffness. In the case

where both nodes move further apart.The equation of motion representing the

interaction of nodes 1 and 2 can therefore be used as the basis of the interface

element.

at node 1 (pad friction face):

Fx1 = µkc(y1-y2) …………………..(9)

Fy1 = kc(y1-y2) .…………………(10)

at node 2 (rotor friction face):

Fx2 = -Fx1 ………………….(11)

Fy2 = -Fy1 ………………….(12)

Thus arranging the nodal stiffness relationship in a matrix form:

2.1. COMPLEX EIGENVALUE EXTRACTION

For brake squeal analysis, the most important source of nonlinearity is the

frictional sliding contact between the disc and the pads. ABAQUS allows for a

convenient, but general definition of contact interfaces by specifying the contact

surface and the properties of the interfaces. ABAQUS version 6.10 has developed a

new approach of complex eigenvalue analysis to simulate the disc brake squeal.

Starting from preloading the brake, rotating the disc, and then extracting natural

frequencies and complex eigenvalues, this new approach combines all steps in one

seamless run. The complex eigen problem is solved using the subspace projection

method, thus a natural frequency extraction must be performed first in order to

determine the projection subspace. The governing equation of the system is

----------------------------(13)

12

Where M is the mass matrix, C is the damping matrix, which includes friction-

induced contributions, and K is the stiffness matrix, which is unsymmetric due to

friction. The governing equation can be rewritten as

------------------------------(14)

where μ is the eigenvalue and Φ is the corresponding eigenvector. Both eigenvalues

and eigenvectors may be complex. In order to solve the complex eigen problem, this

system is symmetrized by ignoring the damping matrix C and the unsymmetric

contributions to the stiffness matrix K. Then this symmetric eigenvalue problem is

solved to find the projection subspace. The N eigenvectors obtained from the

symmetric eigenvalue problem are expressed in a matrix as [Φ1, . . . ,ΦN]. Next, the

original matrices are projected onto the subspace of N eigenvectors

---------------(15)

and

-----------------(16)

Then the projected complex eigen problem becomes

------------------------(17)

Finally, the complex eigenvectors of the original system can be obtained by

-----------------------------(18)

If the damping ratio is negative, the system becomes unstable, and vice versa. The

main aim of this analysis is to reduce the damping ratio of the dominant unstable

modes.

13

CHAPTER-4

FINITE ELEMENT MODEL

4.1 SOLID WORK MODELING

The Solid Works Part Design application makes it possible to design precise

3D parts with an intuitive flexible user interface, from sketching in an assembly

context to iterative detailed design. Part Design application will enable you to

accommodate design requirements for parts of various complexities, from simple to

advance.

4.2 DIMENSIONS OF DISC

Figure 4.1 Illustrated disc brake dimensions (all the dimensions in mm)

14

Figure 4.2 3D model disc and pad

Figure 4.3 3D model of disc and pad

4.3 MESHINIG

Hypermesh software highly flexible finite element analysis software. Its important feature is its meshing capability and its flexibility to interact with other geometrical analysis software.

15

Figure 4.4 Meshed Model Disc brake pad

Figure 4.5 Meshed Model of Disc

16

CHAPTER-5

RESULTS AND DISCUSSION

The effects of the system parameters, such as the hydraulic pressure P, the

rotational velocity of the disc W, the friction coefficient of the contact interactions

between the pads and the disc u, the stiffness of the disc, and the stiffness of the back

plates of the pads, on the disc squeal are investigated by the simulation model. The

complex eigenvalue analysis is performed up to 9 kHz which is the range of squeal

occurrence for the present disc model. As mentioned previously, if the damping ratio

is negative, the system becomes unstable, and vice versa; when the disc system is

unstable, the squeal propensity increases with an increased value of the damping

ratio . For clarity, only damping ratio and frequency are plotted. The typical values for

the system parameters used in the simulation are: P = 0.5 MPa, W = 0.5rad/s, u = 0.3,

ED= 210GPa, TD = 5mm, and EP = 210 GPa. Analysis is carried out in Abaqus 6.10,

by changing the values of each parameter while retaining the respective typical values

for the others.

Mode number Real Part

Frequency in hertz

Damping Ratio

1 -5.06 1352 0.0544923082 10.23 1450 -0.102723313 -6.31 1750 0.05249924 -18.12 2256 0.1169446815 -22.98 2487 0.1345351036 0 2985 07 -10.09 2998 0.0490028028 -31.41 3158 0.1448162139 -2.31 3198 0.010517073

10 -1.83 3548 0.00750980811 -4.5 3874 0.01691275212 -0.9 4268 0.00307029113 -100.8 4396 0.33385987314 -3.25 4500 0.01051555615 -0.03 4987 8.75877E-0516 -0.98 5023 0.00284069317 80.37 5896 -0.1984713718 -33.46 6245 0.07801082519 -55.93 6350 0.12824264620 -75.9 6678 0.165484277

Table 5.1 Frequency output17

13521750

24872998

31983874

43964987

58966350

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

friction=0.3

Figure 5.1 Damping ratio vs frequency

The unstable modes are figure 5.3 mode numbers 2,17 with frequency of

1450,5896Hz with negative damping ratio. These frequency causes squeal and

instability to the system.

Figure 5.2 Unstable mode shapes at mode number 2, 17 with frequency 1450,

5896Hz respectively.

5.1 EFFECT OF FRICTION COEFFICIENT

Disc squeal is believed to be caused mainly by friction-induced dynamic

instability. This section presents the effect of the friction coefficient of the contact

interactions between the pads and the disc on the disc squeal, in which the friction

coefficient u varies from 0.3 to 0.8. Fig. 5.2 shows results in the form of the damping

ratio as a function of frequency for different friction coefficients.

18

Frequency Hz

Dam

pin

g R

atio

Stable region

Unstable region

1405

1669

1983

2355

2798

3325

3950

4694

5576

6625

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

friction=0.3friction=0.5friction=0.8

Figure 5.3 Frequency output vs damping ratio for varying friction

coefficient

Figure 5.4 Unstable mode shapes at mode number 6, 20 with frequency

12134,7131Hz respectively when friction coefficient is 0.5

Figure 5.5 Unstable mode shapes at mode number 3,18,19 with frequency 1669,

6078, 6625Hz respectively when friction coefficient is 0.8

19

Dam

pin

g R

atio

Frequency HzUnstable region

It is understandable that with an increase in the friction coefficient, there is an

accompanying increase in the instability of the system, thus an increase in the

damping ratios. This means that the most fundamental method of eliminating brake

squeal is to reduce the friction between the disc and pad. However, this obviously

reduces braking performance and is not a preferable method to employ. The unstable

modes are figure 5.3 mode 2,17 for friction coefficient 0.3, figure 5.4 mode 6,20 for

friction coefficient 0.5 and figure 5.5 mode 3,18,19 for friction coefficient 0.8.The

corresponding mode shapes represents how the disk brake vibration takes place

whether it is in plane or out bound and its frequency are onset of squeal.

5.2 EFFECT OF BRAKE PRESSURE

The effect of the hydraulic pressure P on the squeal propensity is studied by

varying P from 0.5MPa to 1.5MPa. Figure 5.6 shows the change of the damping ratio

with frequency for different hydraulic pressures. The major squeal frequency is

approximately 7 kHz. It can be seen from Figure 5.6 that with an increase in P, the

value of the damping ratio is increased, so the squeal propensity is increased. This is

due to a larger hydraulic pressure inducing more friction between the pads and the

disc. However, the simulation results also show that the effect of the hydraulic

pressure on the disc brake squeal is not significant because the value of the damping

ratio only changes from 0.11 to 0.23 when P increases from 0.5MPa to 1.5MPa.

1405

1689

2022

2420

2896

3466

4148

4965

5943

7113

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

pressure=0.5MPapressure=1.5MPapressure=1.5MPa

Figure 5.6 Frequency output vs damping ratio for varying Brake Pressure

20

Frequency Hz

Dam

ping

ra

tio

Unstable region

Figure 5.7 Unstable mode shapes at mode number 3, 5 with frequency 1632,

1789Hz respectively when brake pressure is 1Mpa.

Figure 5.8 Unstable mode shapes at mode number 1, 3, 18, 19 with frequency

1405, 1689, 6502, 7189Hz respectively when brake pressure is 1.5Mpa.

5.3 EFFECT OF ANGULAR VELOCITY

1419

1838

2379

3080

3988

5164

6688

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

angular velocity=0.5angular velocity=3angular velocity=3

Figure 5.9 Frequency output vs damping ratio for varying angular

velocity

21

Dam

ping

ra

tio

Frequency Hz

Figure 5.9 presents the variation of the damping ratio with the frequency for different

disc angular velocities W (0.5–3.0 rad/s). The dominant squeal frequency is

approximately 6kHz. As the angular velocity increases, the value of the damping ratio

gradually decreases. However, as with the previous case, when changing the hydraulic

pressure, the effect of changing the angular velocity on the squeal propensity is also

not obvious: this can be seen from figure 5.10 which shows the value of the damping

ratio varies with an increase in the rotational velocity of the disc. Here the unstable

modes are mode number 3, 18 for 1.5rad/sec and mode number 3, 19 for 3rad/sec.

The squeal frequency is 1651, 6018 for 1.5ard/sec and 1686, 5689 for 3rad/sec.

5.4 EFFECT OF STIFFNESS OF THE BACK PLATES OF THE PAD

1501

1783

2118

2517

2991

3553

4222

5016

5959

7080

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

back plate youngs modulus=150MPaback plate youngs modulus=180MPaback plate youngs modulus=210MPa

Figure 5.10 Frequency output vs damping ratio for varying back plate

youngs modulus

Brake pads consist of contact plates which are made of a friction material and back

plates. In this study, the effect of Young’s modulus EP the back plates of the pads on

the disc squeal is investigated, in which EP= 150 to 210Mpa the typical value of

Young’s modulus for the back plates of pads. Figure 5.10 shows results of the

damping ratio versus frequency for different Young’s moduli of back plate. It can be

seen that the dominant squeal occurs at a frequency of approximately 6-7kHz. As

Young’s modulus EP, is increased, corresponding to an increase in stiffness of the 22

Dam

ping

ratio

Frequency Hz

Unstable region

back plates of the pads, the value of the damping ratio increases significantly as

shown. This important observation implies that the stiffer back plates of pads cause a

higher squeal propensity. This is so since the friction material connected to the back

plates is very soft compared with the back plate material. Hence the higher the

stiffness of the back plates, the greater the uneven deformation and vibration

magnitude of the pad, and hence the higher the damping ratio. So an effective method

to reduce squeal propensity of disc brake system is to use a damping material for the

back plates of the pads. When youngs modulus of plate at 180GPa there are three

unstable modes at frequency 2376, 5629, 6136Hz and at 210GPa there are four

unstable modes at frequency 1686, 1783, 5016, 7717Hz.Here the damping ratio

increases from 0.10 to 0.42 as modulus increases, thereby increasing squeal

propensity.

Figure 5.11 Unstable mode shapes at mode number 2, 3 with frequency 1686,

1783, 5016, 7717Hz respectively when back plate modulus is 210GPa.

23

Figure 5.12 Unstable mode shapes at mode number 15, 20 with frequency 5016,

7717Hz respectively when back plate modulus is 210GPa.

5.5 UNSTABLE MODES OF DISC BRAKE SYSTEM

The simulation results show that for all the cases owe large damping ratios, the

unstable frequencies are approximately 5-7kHz. There is a significant pad bending

vibration for these cases. Figure 5.13 gives an example of the vibration mode of the

disc brake system at a frequency of 7kHz, where all the system parameters are the

typical values. It can be seen that the disc has only slight out-of-plane modes of

vibration as shown in Figure 5.13, but the pads have serious out-of-plane modes of

vibration which occur mainly at the bottom parts of the pads as shown in Figure 5.13.

This suggests that the brake pads may be the source of the disc brake squeal. So

methods which can reduce the pad bending vibration should be used to eliminate the

disc squeal. One of the methods reported is to use viscoelastic material (damping

material) on the back of the back plates of the pads and another effective method is to

modify the shape of the brake pads to change the coupling between the pads and the

disc . Except the unstable vibration modes which occur at frequency 5-7kHz and are

caused mainly by the pads vibration, the other unstable vibration modes are caused

mainly by the disc vibration. Figure 5.13 give an example of the unstable vibration

mode of the disc brake system at the frequency of 7717Hz, where all the system

parameters are the typical values. It can be seen that the disc has significant out-of-

plane vibration compared with the vibration of pads.

24

Figure 5.13 Vibration mode of the disc brake system at frequency

7717 Hz.

5.6 SQUEAL INDEX

From the eigenvalues analysis, the instability levels and the eigen frequencies

are calculated. The instability level (degree of instability) is defined as the real part of

the eigenvalue α =Re [λ] and the eigen frequency is defined as the imaginary part of

the eigen value ω =Im[λ] Hz. Some authors took the instability level as a squeal

propensity and others do not. In this work the squeal propensity (σ) that is the squeal

index will be taken as

σ = (α2+ ω2)1/2 .sin ( δ/ 2 ) -----------------()

The eigen frequencies will be taken as ω/2π Hz. Where δ is the phase angle.

δ = tan-1(Imaginary part/real part)----------------()

25

1000 2000 3000 4000 5000 6000 7000 8000

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

friction=0.3

friction=0.5

friction=0.8

Figure 5.14. Effect of friction coefficient on brake squeal noise and frequency respectively

Figure 5.14 indicates the effect of friction coefficient on brake squeal noise and

degree of instability. As the friction coefficient increases from 0.3 to 0.8 the squeal

index also increases from 50 to 900. The highest squeal index for 912 for frequency of

7721Hz is obtained for friction coefficient 0.8. In figure 5.15 the modulus of elasticity

of the back plate is increased from 150 to 210GPa. It can be noted from the figure that

as the Young’s modulus back plate increases the squeal index decreases from 75 to

973. The lower value of squeal index of 85 and 89 occurred Young’s modulus of

150GP and 180GPa respectively. The squeal index can be reduced by decreasing the

friction coefficient and youngs modulus of back plate.

26

Sque

al In

dex

Frequency Hz

0 2000 4000 6000 8000 10000

-1500

-1000

-500

0

500

1000

1500

back plate youngs modulus=150GPaback plate youngs modulus=180GPaback plate youngs modulus=210GPa

Figure 5.14. Effect of back plate modulus on brake squeal noise and frequency respectively

The squeal index is more for frequency range of 5-7kHz and when the real part of eigen value is more.

CHAPTER-6

27

Sque

al In

dex

Frequency Hz

CONCLUSION

Friction-induced disc brake squeal is investigated using the new function of

ABAQUS version 6.10, which combines a static analysis and a complex eigenvalue

extraction method. The nonlinear effects can be taken into account in the preloading

steps in order to more accurately model a deformed configuration at which a complex

eigenvalue analysis is performed. The systematic analysis here shows that significant

pad bending vibration may be responsible for causing the disc brake squeal and the

major squeal frequency is approximately 5-7kHz for the present disc brake system.

The effects of the friction between the pads and the disc, the stiffness of the disc, and

the stiffness of the back plates of the pads, on disc squeal, are significant, but the

effects of the hydraulic pressure and the angular velocity of the disc on disc squeal are

not obvious. The squeal can be reduced by decreasing the friction coefficient,

increasing the stiffness of the disc, using damping material on the back of the pads,

and modifying the shape of the brake pads.

SCOPE FOR FUTURE WORK

To include the temperature effect between pad and rotor because an increase

in temperature can sometimes suppress squeal frequency.

To include the piston calliper assembly in finite model and do the frequency

analysis and change the area of contact between pad and disc.

Try to add damping material on back plate so that it can reduce the onset of

squeal frequency.

REFERENCES

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[1] Analysis of brake squeal noise using the finite element method: A parametric

study Ma´rio Tricheˆs Ju´ nior, Samir N.Y. Gerges *, Roberto Jordan Federal Applied

Acoustics 69 (2008) 147–162.

[2] Automotive Drum Brake Squeal Analysis Using Complex Eigenvalue Methods

Ibrahim Ahmed 1, Essam Allam2, Mohamed Khalil2 and Shawki Abouel-

International Journal of Modern Engineering Research Vol.2, Issue.1, pp-179-199,

Jan-Feb 2012 ISSN: 2249-6645.

[3] Automotive disc brake squeal N.M. Kinkaid, O.M. O’Reilly, P. Papadopoulos

Journal of Sound and Vibration 267 (2003) 105–166.

[4] Analysis of Disc Brake Noise at High and Low Frequency with the Effect of the

Friction Ammar A. Yousif and Inzarulfaisham Abd Australian Journal of Basic and

Applied Sciences, 5(3): 209-218, 2011 ISSN 1991-8178.

[5] Analysis of Disc Brake squeal using complex eigen value method P. Liu, H.

Zheng journal on Applied Acoustics 68 (2007) 603–615.

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