International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
Review on Disc Brake Squeal
Rushikesh D. Savant *1, S. Y. Gajjal#2, V. G. Patil#3
*1
#2
M.E. Design (Pursuing), NBN Sinhgad School of Engineering, Pune, India.
Professor, Mechanical Department, NBN Sinhgad School of Engineering, Pune, India.
#3
Vaftsy CAE, Pune, India.
Abstract— The braking process in an automobile involves contact
of metallic solids sliding against each other, which sometimes
generates undesirable noise. With extensive research on brake
noise already reported in literature, the focus of this paper is to
provide the review of brake squeal study. Brake squeal causes
discomfort to driver and passengers degrading their perception
of quality of vehicle. It has been under investigation by
automotive manufacturers for decades due to consistent
customer complaints and high warranty costs. With the advance
of computers and laboratory equipments, significant sources
have been devoted to reducing or eliminating disc brake squeal.
Present paper gives general review on types, generation
mechanisms and parametric study of disc brake squeal.
Keywords— Brake squeal, Eigen value, FEM, Stick-slip, Mode
coupling.
I. INTRODUCTION
Brake is a device by means of which artificial frictional
resistance is applied to moving machine member, in order to
stop motion of machine. During this the undesirable noise is
produced called as brake squeal. Physically, squeal noise
occurs when the friction coupling between the rotor and pad
creates a dynamic instability. This leads to vibration of
structure, which radiates a high frequency nose in the range of
1-16 kHz. Brake noise may be sub-divided into Low
frequency squeal (1000-7000Hz) and High frequency squeal
(8000- 16000Hz). Brake squeal, which usually occurs in the
frequency range of 1-16 kHz, has been one of the most
difficult concerns associated with vehicle brake system. It
causes customer dissatisfaction and increases warranty costs.
Although substantial research has been conducted into
predicting and eliminating brake squeal, it is still difficult to
predict its occurrence due to complexity of the mechanisms
that cause brake squeal. Experimental, numerical and
analytical techniques have been developed in order better
understand, predict and prevent the occurrence of brake squeal.
II. BRAKE SQUEAL
Brakes are one of the most important safety and
performance components in automobile. Brake noise is irritant
to consumers who may believe that it is symptomatic of a
defective brake and files a warranty claim, even though the
brake is functioning exactly as designed in all other aspects.
During brake operation friction between pad and disc can
induce a dynamic instability in the system. This
dynamic instability can create noise, commonly
known as brake squeal. One possible explanation for the brake
squeal phenomenon is the coupling of two neighboring
vibration modes. If two modes are close to each other in the
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frequency range and have similar characteristics they may
merge if the coefficient of friction between the pad and disc
increases. When these modes merge at the same frequency
(become coupled), one of them becomes unstable causing
squeal. Squeal, Groan, Chatter, Judder, Moan, Hum and
Squeak are just a few of the names found in literature. Of
these phenomena, the one generally termed squeal is probably
the most prevalent, disturbing to both vehicle passengers and
the environment, and expensive to brake manufacturers. No
precise definition of brake squeal has gained complete
acceptance, but it is generally agreed that brake squeal is a
sustained, high frequency (>1000 Hz) vibration of brake
system components during a braking action resulting a noise
audible to vehicle occupants and passers-by. As shall be seen
later on, this squeal is often sub-divided into low and high
frequency squeal.
A. Low frequency squeal
Low frequency squeal is generally classified as noise
having a narrow frequency bandwidth in the frequency range
above 1000 Hz yet below the first circumferential
(longitudinal) mode of the rotor. The failure mode for this
category of squeal can be associated with frictional excitation
coupled with a phenomenon referred to as “modal locking” of
brake corner components. Modal locking is the coupling of
two or more modes of various structures producing optimum
conditions for brake squeal.
B. High frequency squeal
One of the most troublesome noise issues in the brake
community is high frequency brake squeal. High frequency
brake squeal is defined as noise which is produced by friction
induced excitation imparted on coupled resonances (closely
spaced modes) of the rotor itself as well as other brake corner
components. It typically is classified as squeal occurring at
frequencies above 5 kHz.
III. BRAKE NOISE GENERATION MECHANISMS
Disc brake squeal occurs when system experiences vibrations
with 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
vibrations result from coupling of modes. Both theories,
however, attribute the brake system vibration and the
accompanying audible noise to variable friction forces at the
pad-rotor interface.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
A. Mode coupling theory
Mode coupling is generally acknowledged to be one of the
most important mechanisms leading to self-excited vibration
in relative sliding systems with frictions. If two vibration
modes are close to each other in the frequency range and have
similar characteristic, they may merge if the coefficient of
friction the pad and disc increases. When these modes merge
at the same frequency called couple frequency, one of them
becomes unstable producing noise. This noise is called as
squeal. The variable friction forces caused by variable normal
forces are sources for squeal. Even if the coefficient of friction
is constant, variable friction forces are still possible.
The detection of system’s borderline between stability and
instability can best be seen on mode coupling diagram. The
diagram shows the frequency f over an increasing friction
coefficient .
f (Hz)
Fig.1 Coupling of the modes
1) Separated modes ( =0):
The modes are not coupled to each other through
frictional forces.
Couple region (0< < c):
Due to non-conservative properties of the friction
forces, the frequencies of both modes are approaching
each other. Additionally, a structural coupling in the
stiffness matrix is needed.
2)
3) Unstable region ( ≥ c):
When the modes have the same frequency, the system
becomes unstable. An increasing friction coefficient leads
to increasing frictional forces, and the system is moving
away from the stable region.
B. Stick-slip mechanism
Friction at low sliding velocity often leads to a non-steady
motion. That is, below a certain sliding velocity and given that
the pulling spring is so soft enough, it is often possible to see
that the motion is made up of periods where the bodies hardly
move, and periods where there are sudden motions. This is
called as Stick-slip motion and is caused by the fact that the
friction force does not remain constant as a function of
distance, time or sliding velocity.
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According to this theory disc brake tended to squeal when
either a static coefficient of friction is higher than the dynamic
coefficient or a dynamic coefficient decreases with increase of
speed present in the contact interface. 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.
IV. APPLICATION OF FEM
The finite element is the tool for modelling disc brake
system and providing a new insight into the problem of brake
squeal. FEM allows accurate representation of complex
geometries and boundary condition. The finite element
method has been employed by the researchers in the brake
squeal study. One of the uses of finite element method is to
investigate the modes and the natural frequency of the brake
rotor with complex eigen value. Modal participation method is
used in order to analyse the contribution of each part of the
brake system in generating the squeal.
A. Formulation of problem
The equation of motion for vibrating system is
Mü + Ců + Ku = f
(1)
Where M, C and K are mass, damping and stiffness matrices
and u is the generalised displacement vector. For the friction
induced vibration, it is assumed that the forcing function is
mainly contributed by the friction force fluctuation between
the rotor and lining interface. The friction interface is modeled
as an array of friction. With this simplified interface model,
the force vector is linearized as
f = Kf u
(2)
Where, Kf is friction stiffness matrix. A homogeneous
equation is then obtained by combining (1) and (2) and by
moving the friction term to the left-hand side
Mü + Ců + [K- Kf] u = 0
(3)
Equation (3) is now the equation of motion for a free vibration
system with a pseudo forcing function in the stiffness term.
The friction stiffness acts as a so-called “direct current”
springs that causes the stiffness matrix to be asymmetric. A
complex eigenvalue algorithm is then used to solve this
eigenvalue problem in order to obtain eigenvalue and eigen
vectors in complex values. Eigen values with positive real
parts are identified as unstable modes, which always appear in
complex conjugate pairs. When the damping matrix is
negligible, both roots of complex pair have virtually the same
imaginary values and the real values have opposite signs.
Eigen vectors are also the same except for an opposite sign the
phase angles.
The complementary solution to the homogenous, second order,
matrix differential equation (3) above is in the form of
{u}={Ø}est
(4)
Performing the appropriate differentiations and substituting
into (3) yields the complex eigenvalue problem:
([M]s2 + [C]s + K) {Ø}= {0}
(5)
Non-trivial solutions for the displacement occur only when the
matrix in parenthesis is singular. This matrix is singular only
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International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
for certain values of s (si), called complex eigen values. The
arbitrary scaled solution vectors Ø i 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.
Th eigen values and eigen vectors of (5) may be complex,
consisting of both a real and imaginary part. For under
damped systems the eigen values always occur in complex
conjugate pairs. For a particular mode the eigen value pair is
Si12= σi + jωi
(6)
Where σi is the real part and ωi is the imaginary part for the ith
mode. By examining the real part of the system eigen values
the modes that are unstable and likely to produce squeal are
revealed. Eigen values with positive real parts are identified as
unstable modes, which always appear in complex conjugate
pairs. Complex eigenvalue analysis procedure and its
relationship with corresponding experiments is illustrated in
Fig.2
Create component model
Modal
tests
Component level validation
Create system model
Apply friction stiffness matrix
Complex eigenvalue analysis
Obtain:
 Natural frequencies
 Negative damping values
 Complex mode shapes
Vehicle or
Dynamometer
tests
Identify squeal mode
Parametric design studies
Fig.2 Complex eigenvalue analysis procedure
V. PARAMETRIC STUDY
A. Coefficient of friction
Brake squeal is generally defined as a friction induced
instability phenomenon. Since friction is the main cause of
instability, a complex eigenvalue analysis has been undertaken
to assess the brake stability as the friction coefficient values.
The effect of the friction coefficient of the pad-rotor interface
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is performed. The unstable modes for varying from 0.2 to
0.6 are plotted as real parts versus frequency to illustrate how
the instability increases with friction level. With the low
friction coefficient all of the modes of the system will be
stable. As the coefficient of friction is increased, modes can be
driven closer to one another in frequency. At some critical
friction value, a sudden change occurs (called bifurcation),
and a new mode exists that contains the original modes as a
coupled pair.
Fig.3 Unstable frequencies with variation of friction coefficient
Fig.3 shows results in the form of the real part as a function of
frequency for different friction coefficients. It was observed
that with equal to 0.2, one unstable mode is predicted at
high frequency 9600 Hz. with increasing friction coefficient
values up to 0.6 a numbers of unstable modes are seen to
appear. It was observed that the propensity of squeal increases
with higher coefficients of friction. This is because the higher
coefficient of friction causes the variable frictional forces to
be higher resulting in the tendency to excite greater number of
unstable modes.
B. Temperature
Disc brake systems operate within a wide temperature
range of 100C up to 5000C, under extreme situations. The
dynamic behavior of the brake system is strongly influenced
by the operation temperature, since changes in this parameter
alter the modal behavior of the brake components. An
increase in brake temperature tends to cause a reduction in
the component stiffness, both for the pad and the rotor.
However, the influence is stronger for the pad than for the
rotor, mainly because of the presence of the friction material.
C. Wear
One of the most important parameters to be considered in
a brake system is the pad wear. Wear is directly proportional
to the braking pressure. The effects of wear are not limited to
changes in the dimensions of the brake pad. The wear leads
to several changes in the pad friction material. The effects of
the wear are concerned with changes in the brake pad
dimensions, elastic properties and damping loss factor of the
friction material.
D. Braking pressure
The effect of braking pressure is introduced into the finite
element model through the variation of the contact stiffness
between the rotor and the pads. The use of the stress-strain
relationship method to determine this contact stiffness,
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International Journal of Engineering Trends and Technology (IJETT) – Volume 9 Number 12 - Mar 2014
allows an evaluation of the effect of the braking pressure on
the contact stiffness. Similar evaluations have been carried
out numerically that, increases in braking pressure lead to
high values for contact stiffness.
Contact
Stiffness
(MN/m)
Contact Pressure (bar)
Fig.4 Contact stiffness between rotor and pad as a function of braking
pressure
The braking pressure has an important effect in terms of
defining the main unstable frequency. Basically, increases in
braking pressure lead to linear increase in the main unstable
frequency. In some cases, the braking pressure leads to some
other unstable frequencies, such as a pressure of 75 psi. A
consequence of this result is the conclusion that for a high
braking pressure the frequency where the noise occurs tends
to be higher.
VI. CONCLUSION
It is now generally accepted that brake squeal is caused by
induced vibration. There are two major hypotheses in
explaining the phenomenon: the first is that the squeal is due
to stick-slip phenomenon at the friction interface, while the
second attributes that the squeal is due to the geometric (mode)
coupling of the brake assembly. Complex eigenvalue analysis
is widespread used for low frequency squeal and no doubt
time domain analysis will follow with increase the
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computational power and reductions of the cost. The squeal
can be reduced by increasing the friction coefficient and
decreasing the contact stiffness of the pad- disc system. Brake
temperature affects the brake pad stiffness, altering the
coupling mechanisms between the rotor and pad. Wear is an
operational condition that must be considered in numerical
models, since it has a strong effect on the stability
characteristics. Hence, parametric study is helpful for brake
squeal analysis.
ACKNOWLEDGMENT
The authors would like to thank the anonymous reviewers
for their comments which were very helpful in improving the
quality and presentation of this paper.
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