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CHAPTER 3
MODAL ANALYSIS OF DISC BRAKE ASSEMBLY
3.1 INTRODUCTION
Finite element analysis (FEA) is widely used to model the dynamic
response of a structure and has the advantage that complex geometries can be
accurately modeled. But accuracy of the FEA can be questionable and the
reliability of the FE model must be validated by comparing the predicted
results of natural frequencies and mode shapes of the FE model with the
experimental results.
In this chapter, FE models of the disc brake components and
assembly are developed using FE software (ABAQUS 6-8). In order to ensure
that accuracy of the FE model agree with those of the physical components,
two validation stages are used through experimental measurements at both
individual component and at assembly levels. First, FE modal analysis at the
component level is carried out and simulated up to frequencies of 10 kHz.
Then, the mesh sensitivity of the each disc brake components is considered. In
order to correct the predicted frequencies with the experimental results, a FE
updating is used to reduce relative errors between the two sets of results by
tuning the material. Finally, the integrated brake assembly model is corrected
with measured data using proper contact interaction between brake
components. The methodology used for validation of FE model will be
discussed in the following sections, as shown in
Figure 3.1.
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Figure 3.1 Methodology adopted in validation of FE model
3.2 EXPERIMENTAL MODAL ANALYSIS
Experimental modal analysis (EMA) is one of the most useful areas
of structural dynamics testing. It is a technique which has been widely used in
structural engineering for finding the structure's dynamic characteristics under
real mechanical conditions by determining modal parameters, such as natural
frequencies, damping factors and mode shapes of a structure through
experiments, then using them to formulate a mathematical model for its
dynamic behavior. The formulated mathematical model is referred to as the
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modal model of the system and the information on the characteristics is
known as its modal data.
In the last three decades, there have been numerous applications of
modal analysis reported in literature covering wide areas of engineering,
science and technology. One common reason for experimental modal analysis
is the correction of the results of numerical methods. In practice, the accuracy
of FE models is often limited by uncertainties about the actual geometry and
material properties. For disc brake components, it is not possible to specify
their exact material properties or geometry. Uncertainties in material
properties or structural dimensions can be due to manufacturing and assembly
imperfections, or lack of knowledge of material properties and coupling
parameters between subsystems. Hence, experimental modal analysis is
necessary to correlate the measured vibration behaviour of disc brake
components with that predicted by FEA.
3.2.1 Equipment for Experimental Analysis
In this research, impact hammer, accelerometer and dynamic signal
analyzer (DSA) are used to conduct experimental modal analysis, as shown in
Figure 3.2. Frequency response functions (FRFs) are obtained by exciting the
individual disc brake components and assembly using impulse hammer. The
response for the given impulse is captured using an accelerometer. The
natural frequencies and mode shapes are obtained through dynamic signal
analyzer. In the following subsection, equipment used for experiments will be
discussed.
3.2.1.1 Impact hammer
Excitation of the structure is the most critical point of EMA. There
is a large variety of excitation techniques which can be used for obtaining
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structural response in modal testing. The choice of a particular excitation
technique depends on the size, and boundary conditions of the structure, the
excitation signal to be imparted, the required frequency range, the sensing
mechanism and the data analysis procedure (Sujatha 2010).
Figure 3.2 Experimental modal analysis set-up
For the excitation of the disc brake components and assembly, an
impact hammer (Kistler type 9722A) is used to make sure that enough energy
is put into the structural. The impact hammer consists of impact tip, force
sensor, balancing mass and handle. Impact tip is usually made of different
materials (steel, plastic, various rubbers) to satisfy the requirement of
frequencies of interest of the structure under test. The hard tip is selected, as
the solid metal structure like disc brake as all modes have higher frequency
above 200 Hz, by providing sufficient energy for high frequencies. The force
sensor is a piezoelectric transducer that is built into the hammer head to
capture the impact force. This transducer generates a charge which is
converted to a voltage which is used in the DSA.
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3.2.1.2 Accelerometer
For the present experiments, accelerometer (Kistler 8628 B50) with
sensitivity of 10mV/g is used. This accelerometer is attached to the disc brake
components by using beeswax. The mass of accelerometer is small to reduce
the inertia effect of the accelerometer. This accelerometer is used to measured
acceleration of disc brake components, in the form of voltage which is fed
directly to the DSA.
3.2.1.3 Dynamic signal analyzer
The measured signals are analysed by the DSA, where the
excitation and response signals from the hammer and the accelerometer are
acquired through a four-channel analyzer (DEWE-41-T-DSA). The sensitivity
information of the sensors is used to calculate the values for the acceleration
and the force. The DSA also performs the transformations to convert the
measured time domain signals into FRFs.
3.2.2 Experimental Procedure
Generally, the frequency domain of EMA can be classified into
three different types based on the number of FRF’s which are to be included
in the analysis (Ewins 2001). The simplest of the three methods is referred to
as SISO (Single Input, Single Output) which involves measuring a single FRF
for a single input given. A SISO data set is made of a set of FRFs which are
measured individually but sequentially at different points on the structure.
The second test method is referred to as SIMO (Single Input, Multiple
Output). This refers to a set of FRFs measured simultaneously at different
locations for a single input given at a specific location. The third method is
referred to as MIMO (Multiple Input, Multiple Output) in which the FRF’s at
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various points are measured simultaneously while the structure is excited at
several points simultaneously.
In this experimental method, SISO method is adopted to perform
EMA. The modal testing based on SISO method can be performed in two
ways. One is known as the roving hammer technique and the other is roving
accelerometer technique. Both the techniques rely on the principle of
Maxwell’s reciprocity theorem (Roa 2004). The roving hammer technique is
adopted in this research to perform modal test, this means that the
accelerometer location is stationary and the impact location is changed.
3.2.3 Performing Impact Hammer Test
Before starting the test, two issues need to be considered. The first
one is to identify a suitable location for mounting the accelerometer and to
identify various locations on the structure to excite it using the impact
hammer. Choosing a proper location for the accelerometer is a very important
because, if the accelerometer is mounted at a location least disturbed by the
excitation, then it will become difficult to measure FRFs properly. The
location should be at that point of the structure where a high response of the
structure is expected. The location for mounting the accelerometer is decided
by analyzing the mode shapes of the structure obtained through FEA.
The second issue in the modal testing is to determine the tip of the
impact hammer which is used for exciting the structure. The head tip to be
used for exciting the structure should activate as many natural frequencies as
possible. This depends on the time duration of the exciting impulse. If the
time duration of the exciting impulse is too large, then the frequency-
spectrum curve which shows the variation of the exciting impulse with
respect to the frequency will decrease rapidly thereby making the measured
FRF unreliable.
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3.2.4 Extraction of Modal Parameters
In order to extract modal parameters (natural frequency, damping
factor and mode shape) the geometry of the disc brake components is created
in commercial software (DEWE/FRF) to define the various points on which
excitation is given in the experimental and the points at which response is
measured. Once the geometry is created, the measured FRFs are given as
input at the respective points at which they are measured. The extraction of
modal parameters from the measured FRFs is a curve fitting problem. Many
curve fitting methods are available but for the present application, circle
fitting method is adopted to extract the mode shapes and natural frequencies
from the geometry. The modal peak function is calculated by summing
together the real parts, imaginary parts or magnitudes of all transfer functions
in the data block file that is being curve fitted. In this study, the modal peak
function is found to be the most appropriate which can be easily reveal the
natural frequencies of the structures for further study and validate with FE
results.
In experimental modal testing, one of the tools used to ensure the
quality of the acquired signal is coherence (Ewins 2001). Coherence can have
a maximum value of one and a minimum value of zero. Coherence value of
one indicates that the response measured is entirely due to the given input
excitation and value of zero indicates that the measured response is entirely
due to some other excitation than the given excitation. From Figure 3.3, it can
be seen that for the frequency range of interest up to 10 kHz, the coherence
function is one for all the trials conducted. Hence the measured response is
taken as the result of given input excitation.
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Figure 3.3 Overview of DEWE/FRF during EMA
3.2.5 Results of Experimental Modal Analysis
There are two types of experimental measurements which are
conducted. The first is component level measurement using the free-free
boundary condition which allows the structure to vibrate without interference
from other parts, making easier visualization of mode shapes associated with
each natural frequency and validation of corresponding FE model. This is
implemented by placing the components on a sheet of foam insulation during
the testing. The other is assembly level test, using the actual boundary
conditions. This is carried out by exciting the brake assembly under applied
pressure.
3.2.5.1 Experimental modal analysis of brake components
Experimental modal analysis of the rotor, pad, caliper, piston,
anchor bracket and steering knuckle is conducted and analysed individually
with free-free boundary.
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(i) Rotor
The modal analysis of rotor plays an important role in
understanding the disc brake squeal problem. It exhibits different types of
vibration modes, but it can be generally classified as in-plane and out-of-plane
mode. The rotor grid is constructed with 192 points arranged along 24 lines
radiating from the centre of the rotor at an angular spacing of 15°. Each line
contains 7 excited points and one response point, as shown in Figure 3.4.
Measurements are taken at the response point 6 in z (axial)
direction, while the excitation is applied with the impact hammer in the z and
y directions at the other points. As a result, direct measurement of only out-of-
plane and radial in-plane modes is possible. The vibration responses at all the
nodes are measured with accelerometers. The modal parameters are
determined using the software (DEWE/ FRF) and bending modes have the
highest modal peaks. Figure 3.5 shows the experimental FRF of the rotor.
Figure 3.4 Location of excitation and response points of brake rotor
0
2
4
6
8
0 2000 4000 6000 8000 10000
Frequency (Hz)
Am
plitu
de
(m
/s^2
)/N
Figure 3.5 FRF results of the rotor
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(ii) Brake pad
The modal analysis of the pad is carried out on the backing plate of
the pad. The pad grid consisted of 17 points, the accelerometer fixed at
middle point and the excitation in out-of-plane direction is applied to the rest
of points. It is found that only two bending modes are identified over the
frequency range, as shown in Figure 3.6.
0
2
4
6
0 2000 4000 6000 8000 10000
Frequency (Hz)
Am
plitu
de
(m
/s^2
)/N
Figure 3.6 FRF results of brake pad
(iii) Caliper
The caliper grid consisted of 30 points at different position on the
outer surface in all three coordinates. The accelerometer is fixed at the middle
surface of the caliper housing and excitation is conducted on all points to
capture as much of the vibration characteristics as possible. Figure 3.7 shows
the experimental FRF of the caliper.
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0
2
4
6
8
0 2000 4000 6000 8000 10000
Frequency (Hz)
Am
plitu
de
(m
/s^2
)/N
Figure 3.7 FRF results of the caliper
(iv) Anchor bracket
The anchor bracket grid is constructed for 22 points and the
measurement is conducted in all three coordinates on the outer surface of the
bracket. Figure 3.8 shows the experimental FRF of the anchor bracket.
0
2
4
6
8
10
12
0 2000 4000 6000 8000 10000
Frequency (Hz)
Am
plitu
de
(m
/s^2
)/N
Figure 3.8 FRF results of the bracket
(v) Knuckle assembly
Knuckle assembly consists of steering knuckle and wheel hub. The
accelerometer is fixed on wheel hub and excitation is made on the outer
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surface of the assembly. Figure 3.9 shows the experimental FRF of the
knuckle assembly.
0
2
4
6
8
10
12
0 2000 4000 6000 8000 10000
Frequency (Hz)
Am
plitu
de
(m
/s^2
)/N
Figure 3.9 FRF results of the knuckle assembly
(vi) Piston
From the modal analysis of the piston, it is found that only one
natural frequency at 7287 Hz appears within the frequency of interest.
Figure 3.10 shows FRF results of piston.
0
10
20
30
0 2000 4000 6000 8000 10000
Frequency (Hz)
Am
plitu
de
(m
/s^2
)/N
Figure 3.10 FRF results of piston
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3.2.5.2 Experimental modal analysis of disc brake assembly
When the brake system works under applied pressure, the dynamics
of the brake components are changed significantly. In this section, the
individual components are fixed on a brake test rig under applied pressure
using hydraulic pump and pressure gauge as shown in Figure 3.11. Measurements
are confined to the rotor surface. The experimental set-up otherwise is the
same as for the rotor. The excitation is applied with the impact hammer in the
normal direction. Figure 3.12 FRF results of the brake assembly.
Figure 3.11 Experimental modal analysis of disc brake assembly
0
2
4
6
0 2000 4000 6000 8000 10000
Frequency (Hz)
Am
plitu
de
(m
/s^2
)/N
Figure 3.12 FRF results of the brake assembly
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3.3 MODAL ANALYSIS USING FINITE ELEMENT
TECHNIQUE
The key to the success of the prediction of squeal is the correlation
between physical tests and virtual FE modeling, at both component and
assembly level. A three-dimensional FE model of a ventilated disc brake
corner is developed and validated for identifying and fixing brake squeal
problem in the earlier design stages. Figure 3.13 shows the 3-deminsional FE
model of the disc brake corner.
For the purpose of this study, the development of finite element
meshes for each brake components using the software (ABAQUS) is briefly
described. Detailed descriptions about the dynamic characteristics of FE
models validated through experimental modal analysis are also made.
Figure 3.13 Details of the FE model of disc brake corner
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3.3.1 Mesh Sensitivity
The accuracy of the results of FEM is very much dependent on the
mesh size of models. A mesh sensitivity calculation is used to decide the
optimum number of elements in the FE model. Two different mesh sizes are
applied to the same structure, where two modal data sets can be obtained. The
natural frequency differences between the same modes of these two sets can
then be used to determine the convergence frequency range. If the results are
nearly similar, then the coarse mesh is good enough for that particular
geometry, loading and constraints. If the results differ by a large amount
however, it will be necessary to use a finer mesh for further iteration.
The mesh sensitivity is conducted on disc brake components with
three different levels of mesh density, coarse, fine and very fine mesh. The
results in Table 3.1 show that the natural frequency difference between the
same modes when three different meshes are applied in the FE model of the
rotor. It can be seen that the maximum difference in natural frequency, in the
frequency range of interest (0-10 kHz), is less than 5%, which is an
acceptable value.
Table 3.1 Natural frequency difference with different mesh densities
Mode No.
Coarse mesh
1256 element
Fine mesh
2559 element
Very fine mesh
5137 elementDifference ratio
Natural frequency (Hz) Fine- very fine
1,2 1473 1453 1430 1.5%
3,4 3289 3225 3133 2.8%
5,6 5169 5062 4887 3.4%
7,8 7234 7067 6799 3.8%
9,10 9421 9170 8788 4.1%
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3.3.2 FE Model Updating
The aim of FE updating is to reduce maximum relative errors
between the predicted and experimental results. In some cases, it is not
possible to know exact material properties of many dynamic structures due to
a number of factors such as variation in material properties, geometry
dimensions or changes in the excitation over time. Changes in excitations
over time can be caused by wear or fatigue. Uncertainties in material
properties or structural dimensions can be due to manufacturing and assembly
imperfections, or imprecise knowledge of material properties and coupling
parameters between subsystems.
There are a number of researchers used EMA to validate their
models. For example, Kung et al (2000) validated the major brake
components. Maximum difference between experimental and FE modal for
the rotor is 7%, the brake pad is 4% and the caliper is 5 % while other brake
components and assembly were not considered. Abu Baker (2005) conducted
FE modal analysis and compared the predicted result with experimental
results that were given by James (2003). He found that the maximum relative
error for brake assembly is 5.2 % and the rotor is 1% while the other
components were validated by an industry source. Papinniemi (2008) found
that the error between the FE and the experimental values are within 3% for
the bracket except for the mode predicted at 936 Hz is 8.3%, caliper 4.6%,
pad 3.1% and the rotor within 5% except for the mode at 2214 Hz is 10.1%.
Recently, Hassan et al (2009) used a simplified FE model (rotor and brake
pads). He found that the maximum difference between FE and experimental
results of the brake Pad at 5.2 kHz is 7.47% and the rotor at 3.5 kHz is 2.57%.
In this work, due to uncertainties in material properties of the brake
components, FE updating technique based on the tuning material is used. This
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method was used by many researchers to obtain exact material properties of
the brake components (Liles 1989, Richmond et al 1996, Dom et al 2003,
Goto et al 2004, Abu Bakar 2005, Papinniemi 2008, Hassan et al 2009). The
densities are acquired from measurement of the mass and determination
volume of each component from the CAD geometry. The Young’s moduli are
obtained from modal testing results and the Poisson’s ratio is the last variable
to be adjusted, which has a much smaller effect than the density or the
Young’s modulus. The baseline material properties of the disc brake
components after FE updating are listed in Table 3.2.
Table 3.2 Material properties of disc brake component
ComponentsDensity
(kg m-3
)
Young’s modulus
(GPa)
Poisson’s
ratio
Rotor 7155 125 0.23
Friction material 2045 2.6 0.34
Back plate 7850 210 0.3
Caliper 7005 171 0.27
Anchor bracket 7050 166 0.27
Steering knuckle 7625 167 0.29
Wheel hub 7390 168 0.29
Piston 8018 193 0.27
Guide pin 2850 71 0.3
Bolts 7860 210 0.3
3.3.3 FE Modal Results
FE modal analysis of the disc brake components and assembly is
conducted in order to find natural frequencies and corresponding mode shapes.
The results are presented in the form of displacement contour to indicate
maximum (anti-node) and minimum (node) amplitudes, as shown in Figure
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3.14. The node and anti-node should appear in the response frequency
diagram as peak and anti-peak.
Figure 3.14 Vibration mode of brake rotor
3.3.3.1 FE modal analysis of brake components
(i) Rotor
After conducting mesh sensitivity calculation the final FE model of
the rotor consists of 2559 solid elements of type C3D8 with 4988 nodes. With
this FE model modal analysis is carried on the rotor. There are number of
natural frequencies and mode shapes exhibited in the FE results. However,
only nodal diameter (ND) type mode shapes are considered to compare with
experimental results, as illustrated in Figure 3.15.
Rotors are always one of the key factors in brake squeal. Squeal
frequencies are often at or close to rotor’s resonant frequencies. The rotor is
made of cast iron; the Young’s modulus of cast iron depends on carbon
content, and, to a lesser extent, silicon content. The most reliable way to set
the material properties is to tune them to the experimentally determined
modal properties. Based on the tuning process for the rotor properties, the
predicted results are close to the measured as shown in Table 3.3.
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Mode shape at 1453 Hz Mode shape at 3225 Hz
Mode shape at 5062 Hz Mode shape at 7067 Hz
Mode shape at 9170 Hz
Figure 3.15 Rotor brake natural frequencies and mode shapes
(ii) Brake pad
The brake pad consists of two parts: the friction material and a stiff
back plate. The back plate is made of steel and serves to support the friction
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material, which is a complex composite material of about 20 ingredients. In
the FE model, the friction material are assumed to be linear isotropic, as
presented by (Kung et al 2000, Liu et al 2007, Hassan et al 2009).
The finite element model of brake pad consists of 553 solid
elements type C3D8 and 1084 nodes. For validation, the standard values of
steel properties are used for back plate, and tuning material is examined for
friction material. The natural frequencies and corresponding mode shapes
obtained from the FE model are shown in Figure 3.16. The mode shapes for
the brake pad are very similar to bending and twisting modes of beams. A
comparison of the brake pad frequencies from FE model compared to those
found in experimental modal testing are listed in Table 3.3.
First bending mode at 2889 Hz First twisting mode at 4460 Hz
Second bending mode at 6735 Hz Second twisting mode at 8976 Hz
Figure 3.16 Pad brake natural frequencies and mode shapes
(iii) Caliper
The FE model of the caliper consists of 2334 solid elements and
2370 nodes. The caliper is made of ductile cast iron. The modal analysis is
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conducted and the frequencies and shape modes are obtained as shown in
Figure 3.17. Material properties are adjusted to match modal frequencies of
FEA and EMA results by using the same steps used for validation of the rotor.
The results of the predicted results show good agreement with the measured
data as shown in Table 3.3.
Mode shape at 2293 Hz Mode shape at 3964 Hz
Mode shape at 5667 Hz Mode shape at 6587 Hz
Mode shape at 8221 Hz
Figure 3.17 Caliper natural frequencies and mode shapes
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(iv) Anchor bracket
The FE model of anchor bracket consists of 1036 solid elements
and 1644 nodes. Figure 3.18 shows the natural frequencies and mode shapes
of the bracket. A comparison of the anchor bracket frequencies obtained from
FEA is done with those found in experimental modal test is given in Table 3.3.
Mode shape at 880 Hz Mode shape at 1755 Hz
Mode shape at 3164 Hz Mode shape at 4680 Hz
Mode shape at 7533 Hz Mode shape at 9262 Hz
Figure 3.18 Anchor bracket natural frequencies and mode shapes
(v) Knuckle assembly
The FE model of the steering knuckle which consists of 9868 solid
elements and 3585 nodes is created and merged with wheel hub model which
consists of 1654 solid elements types C3D8 and 2786 nodes. The FE modal
73
analysis is conducted on the knuckle assembly and the mode shapes are
plotted in Figure 3.19. Comparison between the FE and experimental modal
analysis is listed in Table 3.3. It is found that there is a good agreement
between the two results.
Mode shape at 1211 Hz Mode shape at 2242 Hz
Mode shape at 4421 Hz Mode shape at 6389 Hz
Mode shape at 7992 Hz Mode shape at 8665 Hz
Figure 3.19 Knuckle assembly natural frequencies and mode shapes
74
(vi) Piston
The FE model of piston consists of 357 solid elements types C3D8
and 576 nodes. Figure 3.20 shows mode shape at frequency of 7392 Hz.
There is only one natural frequency of the piston in the range of interest. The
predicted result from FEA is compared with experimental modal analysis and
it is found that a good agreement with the predicted and measured data.
Figure 3.20 Piston mode shape at 7392 Hz
(vii) Guide-pin and bolts
For this component, only the mesh sensitivity is used to validate the
bolts and guide pin due to difficulty to get acceptable results using
experimental test. From the FE modal analysis, there are two modes found
within the frequency range of interest, as shown in Figure 3.21.
Mode shape at 4709 Hz Mode shape at 9960 Hz
Figure 3.21 Guide-pin and bolts natural frequencies and mode shapes
75
Table 3.3 Comparison between experimental and FE results of brake
components
Components Mode Exp. (Hz) FE (Hz) Error (%)
Rotor
1 1464 1453 -0.7
2 3198 3225 0.8
3 4992 5062 1.4
4 6958 7067 1.5
5 9020 9170 1.6
Anchor bracket
1 878 880 0.2
2 1770 1755 -0.8
3 3341 3164 -5.2
4 4675 4680 0.01
5 7067 7533 6.5
6 9387 9262 -1.3
Caliper
1 2282 2293 -1.7
2 3769 3960 5
3 5651 5667 0.2
4 6909 6587 -4.6
5 8569 8221 -4.0
Brake Pad1 2819 2889 2.4
2 7067 6735 -4.6
piston 1 7287 7392 1.4
Steering knuckle
and wheel hub
1 1232 1211 -1.7
2 2138 2242 4.8
3 4856 4421 -8.9
4 6401 6389 0
5 8214 7995 -2.6
6 8856 8665 -2.2
76
3.3.3.2 FE modal analysis of brake assembly
In this stage of analysis, all the brake components models are
integrated together to form an assembly model and all boundary conditions
and component interfaces are considered. In the FE assembly model, disc
brake components are generally assembled by friction springs through a
number of imaginary linear spring elements, as shown in Figure 3.22(a). In
recent years, an alternative method associated with the direct connection of
brake components have been suggested, thus eliminating the "imaginary
springs", as shown in Figure 3.22(b).
The software used for this study (ABAQUS 6-8) provides three
algorithms to represent interface between contact pairs. They are gap contact
elements, surface-to-surface contact interaction and surface-to-node contact
interaction. Direct contact interaction between disc brake components is
represented by a combination of node-to-surface and surface-to-surface
contact elements. The surface of the rotor is defined as the master surface,
since it has a coarser mesh than the pad and the rotor is a stiffer material. The
pad is consequently selected as the slave surface. For each node on the
“slave” surface software algorithm finds the closest point on the “master”
surface of the contact pair where the master surface's normal passes through
the node on the slave surface, as shown in Figure 3.22(b). Hence a mesh
matching approach is not required for direct contact. A uniform pressure of 1
MPa is applied on the pads’ back plates. FE modal analysis then is conducted
on the assembly model by considering all boundary conditions and
interactions between all components. The natural frequencies and
corresponding mode shapes obtained from the FE model are shown in
Figure 3.23. As shown in Table 3.4 a good agreement is found between the
predicted results and the measured ones.
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(a) Spring contact (b) Direct contact
Figure 3.22 Spring contact and direct contact between disc brake
Mode shape at 1562 Hz Mode shape at 3174 Hz
Mode shape at 5184 Hz Mode shape at 6597 Hz
Mode shape at 9452 Hz
Figure 3.23 Brake assembly natural frequencies and mode shapes
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Table 3.4 Modal results of the brake assembly
Mode Exp. (Hz) FE (Hz) Error (%)
1 1611 1562 -3
2 3222 3174 -1.4
3 5065 5184 2.3
4 6933 6597 -4.8
5 9020 9452 4.7
3.4 CONCLUDING REMARKS
In this chapter, a comprehensive method for conducting modal
analysis on a disc brake by both FE and experimental methods is described.
The natural frequencies and mode shapes extracted from the FE model of the
components and assembly are found to be in good agreement with those
found from the experimental method and hence could be used for further
dynamic simulation studies to investigate brake squeal problems much earlier
in the design cycle.
