chapter 2 research methodology of present study...
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CHAPTER 2
RESEARCH METHODOLOGY OF PRESENT STUDY
2.1 INTRODUCTION
Comprehensive study on brake squeal using experimental approach
is very expensive and time consuming. Furthermore, the results found from
experimental study on a specific brake system may not be applicable to other
type of brake systems. The modern computational and simulation tools using
FE method have matured to a stage where they can provide substantial insight
into prediction and suppression the squeal noise to help improve the design of
disc brake components at early stage. The capabilities of FE models, with a
vast number of degrees of freedom, have enabled the accurate representation
of a brake system. Moreover, the FE method provides much faster and less
cost solutions than experimental methods.
The advantages pointed out above provide a future direction for
finite element method against the experimental methods. However, accuracy
of the FEA can be questionable and some validation tests are usually required
to provide results with most accuracy within available information. In general
the accuracy of the finite element model is very significant issue to correctly
represent the actual of disc brake corner. Liles (1989) used experimental
modal analysis to validate each of disc brake components. This strategy has
been adopted by many other researchers, for example, (Ripin 1995, Lee et al
1998, Liu and Pfeifer 2000, Kung et al 2000). Later, a few of researchers have
validated FE models at some of its individual components and assembly level
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(Dom et al 2003, Goto et al 2004). Out of these work, only few studies
included validation of each disc brake components and brake assembly. In
addition, most of the FE models assumed full contact at the friction lining and
disc interfaces whereas in reality it is not in complete contact.
Various types of analyses have been performed on disc brake
systems through FEA, in an attempt to understand the problem of noise and to
develop a predictive design tool. The most commonly used method is the
complex eigenvalue analysis (CEA) that was used in brake squeal problems
and became the preferred method (Liles 1989, Ripin 1995, Lee et al 1998,
Blaschke et al 2000, Dom et al 2003, Bajer et al 2003, Goto et al 2004, Abu
Bakar and Ouyang 2004, Abu Bakar and Ouyang 2006, Liu et al 2007,
Trichés et al 2008, Dai and Lim 2008). Although the complex eigenvalue
analysis was commonly used in brake squeal problems by many researchers,
the shortcomings of this method are over-predictions and missing unstable
modes in the squeal frequency range (Kung et al 2004). For overcoming on
the limitations of CEA, there are three methods which will be considered in
this research to increase its accuracy.
It can be seen from the previous chapter that earlier FE models of
the disc brake adopted the variation of the geometric details. For example,
many researchers considered a simplified FE model of the disc brake
assembly, that is, a disc and two pads (Liu et al 2007, Trichés et al 2008,
Coudeyras et al 2009). Hassan et al (2009) added the paw fingers and piston
to the FE model. Dai and Lim (2008) developed a FE model consisting of
rotor, caliper, mounting bracket, piston and brake pads to analyze the design
of disc brake pad structure for squeal noise reduction. Some investigators
(Abu Bakar 2005, Papinniemi 2008) used a detailed FE model which consists
of a disc, a piston, a caliper, a bracket, piston and finger pads, two bolts and
two guide pins. Furthermore, it is found that the above finite element models
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were used without steering knuckle or wheel hub which have considerable
influence on squeal occurrence.
The need for development a more realistic finite element model of
disc brake corner by including part of the suspension system which connects
brake assembly with the vehicle chassis, considering its actual boundary
conditions and interaction between components is required to solve the squeal
problem. Furthermore, due to the fact that disc brake squeal depends on a
large number of parameters, using parametric studies by changing one factor
at a time is not enough for evaluation the brake system. Hence, the need of a
new approach to investigate the effects of several factors on squeal generation
and its interactions is very much required to help improve the design of brake
components.
In this research, efforts are focused on the development of an
improved FE model, as an extension of the earlier FE brake models, in which
a 3-dimensional FE model of the disc brake corner that incorporates wheel
hub and steering knuckle is developed and validated at both component and
assembly level. In addition, the real pad surface roughness, negative friction-
velocity slope and friction damping are considered to increase the prediction
accuracy of the complex eigenvalue results. Moreover, the predicted results
are verified by experimental squeal test and compared with dynamic transient
analysis. Hence, the complex eigenvalue results can be used with higher
confidence level for further studies.
Due to the fact that brake squeal is a very complex phenomenon
because of its strong dependence on many parameters including materials and
geometry of brake components, component interaction and many operating
and environmental condition, the need of a new method to find out the
contributions of the material and geometry modifications in reducing the
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squeal propensity and its interactions as well is required. Current research on
brake squeal is integration of the FE simulation with Design of Experiments
(DOE) to assess effectively the contributions of different types of structural
modifications and their interaction for effective reduction of brake squeal.
Based on the literature review and its present status, the following
research methodology is formulated.
1. Development of an improved FE model of the whole disc
brake corner, as an extension to earlier FE disc brake models,
which has an acceptable correlation with experimental modal
analysis results.
2. Prediction of squeal noise for disc brake system using
complex eigenvalue analysis to determine system stability. In
addition usages of experimental squeal test to verify the
predicted results and compare them with dynamic transient
analysis results.
3. Conducting a parametric study to find the effect of different
types of materials used in fabricating disc brake components
for effective reduction of brake squeal.
4. Suppression of the squeal noise using several geometrical
modifications of the disc brake components.
5. Using the techniques of design of experiments (DOE) to find
out the significant contributions of the structural
modifications in reducing the squeal propensity and their
interactions as well.
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6. Using Taguchi method to assess the contributions and their
interaction effects of different types of materials used in
fabricating disc brake components for effective reduction of
brake squeal.
The schematic flow diagram for the proposed methodology is given
Figure 2.1.
Figure 2.1 Overview of research methodology
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2.2 DEVELOPMENT AND VALIDATION OF FE MODEL
2.2.1 Construction of a Disc Brake Corner
A car disc brake corner typically consists of steering knuckle
assembly, wheel hub, and the actual disc brake assembly. The disc brake
assembly consists of a ventilated rotor, a floating caliper with a single piston,
an anchor bracket, two bolts, two guide pins, and two brake pads. The pads
are loosely housed in the caliper and located by the anchor bracket. The brake
pad mounted on the piston is often referred to as the piston-pad, and the pad
on the opposite side is called the finger-pad. The caliper itself is allowed to
slide freely along the two mounting guide pins in a floating caliper design.
The solid model consisting of the whole disc brake corner is shown in
Figure 2.2.
Figure 2.2 A car disc brake corner with floating caliper
The brake corner is connected to the car suspension system through
the steering knuckle, which is mounted on the vehicle chassis. The wheel hub
is connected to the drive line, and the brake cylinder in the caliper is
connected to the hydraulic brake line system, where the piston slides inside
the caliper. Hence, the brake corner can be looked upon as a subsystem
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consisting of a number of components interrelated to each other and to other
sub-systems in the vehicle.
When hydraulic pressure is applied, the piston is pushed forward to
press the inner pad against the disc and simultaneously the outer pad is
pressed by the caliper against the disc. Most of the kinetic energy of the
travelling car is converted to heat through friction between the disc and pads.
Also, a small part of it is converted into sound energy and generates noise.
A detailed 3-dimensional FE model of the complete disc brake
corner is developed using finite element software package (ABAQUS). Figure
2.3 shows the FE model of the commercial disc brake corner. Details of FE
model for each of the components are listed in Table 2.1. FE model uses up to
19,000 solid elements and approximately 78,000 degrees of freedom. The
disc, brake pads, piston, wheel hub, guide pins and bolts are modeled using 8-
node (C3D8) linear brick elements while other components are modeled using
a combination of 8-node (C3D8), 6-node (C3D6) and 4-node (C3D4) linear
brick elements.
Figure 2.3 FE model of disc brake corner
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Table 2.1 Element details of disc brake components
Disc brake componentsTypes of
Element
No. of
Elements
No. of
Nodes
Disc C3D8 2559 4988
Friction
materialC3D8 320 558
Back plate C3D8 233 526
Caliper
C3D8
C3D6
C3D4
2334 2370
Anchor
bracket
C3D8
C3D41036 1644
Steering
knuckle
C3D8
C3D6
C3D4
9868 3585
Wheel hub C3D8 1654 2786
Piston C3D8 357 576
Guide pin C3D8 292 414
Bolt C3D8 58 123
2.2.2 Validation of FE Model
It is well known that brake components possess a wide range of
variations in material properties and sizes. In view of this situation, it is an
important issue to validate FE model with experimental data to ensure that
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accuracy of the dynamical properties of the FE model agree with those of the
physical component. The dynamic testing of structures has become a standard
procedure for FE model validation and updating. Over the past three decades,
modal testing and analysis have become a fast-developing technique for the
experimental evaluation of the dynamic properties of structures (Ewins 2001).
In general, the natural frequencies and mode shapes are important
parameters in the simulation of brake components to study NVH problem.
The FE modal analysis can be used to determine the natural frequencies and
mode shapes of brake components. The eigenvalue and eigenvector must
therefore be solved for mode-frequency analyses. The basic equation of the
classical eigenvalue problem is given by:
0)(2
iiKM (2.1)
where i = Eigenvalue (Natural frequency of mode i)
[M] = Structure mass matrix
[K] = Structure stiffness matrix
[ i] = Eigenvector (Mode shape vector of mode i)
The software used for the above study (ABAQUS 6-8) offers two
algorithms to solve the eigenvalue problem like subspace and Lanczos
method. For a large number of eigenmodes, the Lanczos method works faster
than the subspace method. The subspace method is recommended for analysis
with less than 20 eigenmodes. In the current study, modal analysis contains
many degrees of freedom. Hence, the Lanczos method is used to extract
natural frequencies and mode shapes of a structure.
In this study, two stages are used to validate the FE brake model
using experimental modal analysis, i.e. individual component and assembly
levels.
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2.2.2.1 Validation at component level
In the first stage, experimental modal analysis using the Frequency
Response Function (FRF) measurement is done. FRFs are measured by
exciting each structure with an impact hammer. The acceleration response is
measured with a light accelerometer through dynamic signal analyzer
(DEWE-41-T-DSA). The FRF measurements are recorded for each brake
components. Then, by using DEWE/FRF software, the curve fitting process is
performed on the transfer function spectrums obtained to extract the natural
frequencies, damping ratios and mode shapes.
The disc brake components are modeled in FE software. It is well
known that the accuracy of the results of finite element analysis is very much
dependent on the mesh size of models. In order to decide the proper mesh
size, a convergence study of the initial FE model is executed using mesh
refinement technique. The FE modal analysis of each brake components is
performed. The natural frequencies and mode shapes are extracted using
standard material properties. In order to reduce relative errors between the
predicted frequencies and the experimental results, FE updating (refining
process) is applied through changing material properties of the brake
components (Liles 1989, Richmond et al 1996). Finally, it is found that the
predicted natural frequencies are quite close to the measured values.
2.2.2.2 Validation at assembly level
In the second validation stage, the individual brake components are
assembled together on a brake test rig. Experimental modal test are performed
with brake line pressure of 1 MPa.
In the FE assembly model, the individual disc brake components
are coupled together to form the assembly model using combinations of node-
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to-surface and surface-to-surface contact elements to represent direct contact
interaction between components and all boundary conditions as found in
experimental are considered.
2.3 EVALUATION OF BRAKE SQUEAL
Though much work has been done on the disc brake squeal, it
requires continuous study to refine the prediction accuracy of finite element
models to provide designers appropriate tools to design quiet brakes. There
are two main categories of numerical approaches that are used to study this
problem: complex eigenvalue analysis and transient dynamic analysis.
2.3.1 Complex Eigenvalue Analysis
In this research, the complex eigenvalue analysis has been used to
investigate the stability of brake system modes. One of the earliest researchers
who attempted to incorporate the complex eigenvalue analysis with a large
finite element model using a number of linear spring elements at the friction
interface was Liles (1989). This method later became a standard practice and
widely used in predicting the squeal propensity. The positive real parts of the
complex eigenvalues indicate the degree of instability of the disc brake
assembly and reflect the likelihood of squeal occurrence. To increase the
prediction accuracy of squeal, the real pad surface roughness, negative
damping and positive damping are considered. In order to verify CEA results
experimental squeal test and dynamic transient analysis are performed and
compared with CEA results.
2.3.2 Dynamic Transient Analysis
Dynamic transient analysis based on finite element models
considering transient non-linear behaviors of brake systems were carried out
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by a few of researchers. Nagy et al (1994) were one of the first to perform a
numerical integration in a finite element disc brake. They used
MSC/PATRAN to develop the models of the disc brake components and
MSC/DYNA to conduct the analysis. A major shortcoming of this approach is
that the results do not indicate which mode is responsible for the squeal
problem. Furthermore, the technique is highly computationally intensive
especially for high frequencies.
In this research, dynamic transient analysis that determines the
instability of the system through divergent vibration time response is
performed and compared with the CEA results. The output time domain
information is converted to frequency domain information by using the Fast
Fourier Transform (FFT) technique through MATLAB software.
2.3.3 Experimental Squeal Test
Experimental squeal tests are carried out using a simply brake
dynamometer in order to verify the predicted FE results. The measurement of
squeal noise of the disc brake system is conducted at different operational
conditions. Since squeal is occurring at low speed below 30 km/h and at low
brake pressure below 2 MPa, no large power is required in the drive.
In order to measure squeal noise, bedding-in (warming-up) process
is performed for two hours at low pressure (0.7 MPa) and low disc speed
(50 rpm). Sound pressure level (SPL) measurements are made using
microphone and accelerometer. Output signals from the microphone and
accelerometer are fed to an FFT analyser, and the SPL spectrum is calculated
using special purpose software (DEWEsoft). The recorded data is plotted as
sound pressure level (dB) against frequency (Hz). Experimental results are
used to validate the CEA results.
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2.4 SQUEAL REDUCTION METHODS
Generally, there are a number of techniques that have been used in
order to reduce squeal noise. Structural modifications method is regarded as
one of the most effective ways to reduce squeal.
In this research, several structural modifications are considered to
reduce squeal of the disc brake system. This is accomplished through
reducing or eliminating the positive real parts of complex eigenvalues of the
baseline model. It is convenient to divide such modifications into three
general categories: material modifications, geometric modifications and
adding damping to the brake system through pad shim.
2.4.1 Material Modifications
It is necessary to design the whole brake components such that their
natural frequencies in the audible range are isolated to avoid mode coupling.
There is a traditional method that is used by some researchers by varying the
value of Young’s modulus of disc brake components.
In this study, a newer method is adopted by finding the effects of
different types of material, which are used in fabricating disc brake
components for commonly used vehicles or special types as heavy duty
performance and racing cars.
2.4.2 Geometric Modifications
Geometrical modifications are considered as one of the most
popular ways to suppress or eliminate squeal. In this study, one of the main
used is the modification of geometry of the disc and pads. The disc geometry
modification involves assessment of the influence of the disc neck structure
thickness, number of vanes, hat height, and the disc hat structure thickness on
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squeal generation. The pad geometry modification involves assessment of the
influence of different slots and chamfer configurations on squeal generation.
2.4.3 Damping Shim
The main function of damping shim is to provide additional
damping for the brake system. To simulate the shim, damping is assumed to
be uniformly distributed throughout the shim, and hence the commonly used
Rayleigh damping formulation is used, which is a very convenient way of
accounting for damping with continuous systems.
In the FE model, the shim model is created using a solid element
and modal analysis is validated using experimental modal analysis. Two
damping shims with Rayleigh damping are added onto the back plates of FE
brake assembly and the complex eigenvalue analysis is performed to
investigate their effects on squeal generation.
2.5 DESIGN OF EXPERIMENTS
Design of experiment (DOE) is a more effective way to determine
the effect of two or more factors on a response than a one factor at a time.
Due to the fact that brake squeal noise is a very complex phenomenon which
strong dependence on a huge numbers of parameters, DOE is suggested to
deal with the squeal problem to obtain optimal solution. In general, using the
one at a time plans is discouraged on experimental design and quality
improvement because of more runs are required for the same precision in
effect estimation, some interactions between variables cannot be captured, the
conclusions from the analysis are not general and optimal settings of factors
can be missed.
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In this study, two approaches of DOE are used namely: response
surface methodology to investigate the influencing factors of the brake pad on
the disc brake squeal and Taguchi method to evaluate different types of
materials used for fabricating disc brake components on squeal noise
occurrence.
2.5.1 Taguchi Method
From the previous works, it is understood that different types of
materials are employed for manufacturing brake components. Hence in the
present study, Taguchi method based design of experiment is used to
determine the significant contributions of the material modifications and their
interaction with other design parameters on reducing the squeal propensity.
In the first stage, Taguchi L9 orthogonal array is conducted to
identify the ‘most significant’ variables by ranking with respect to their
relative impact on the squeal occurrence. The L9 orthogonal array consists of
four control parameters at three levels. Then, signal-to-noise ratio (S/N ratio)
is computed using smaller-the-better quality characteristic. Finally,
contribution of material components is computed and plotted.
2.5.2 Response Surface Methodology
The ‘input-output’ relationship between the brake pad geometry
and the brake squeal is constructed for possible prediction of the squeal using
various design parameters of the disc brake.
For finding the most influential variables and their effects, a two
phase strategy is adopted. In the first phase, initial screening of various
variables is taken up. Fractional factorial design (FFD) of experiments is
conducted to identify the most influential variables. Subsequently, in the
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second phase, central composite design (CCD) based response surface
methodology is used to develop a non-linear model for prediction of disc
brake squeal.
2.5.1.1 First Phase: Screening FFD of experiments
In the first phase, initial screening of six variables is investigated. A
total number of eight trials are conducted and the squeal occurrence is
measured for each case. FFD of experiments is conducted to identify the most
influential variables. Pareto chart of the effects is plotted to determine the
magnitude and the importance of the effects.
2.5.1.2 Second Phase: RSM-CCD of Experiments
CCD is one of the most important experimental designs used for
optimizing parameters. Consequent to the first phase, four variables out of the
six variables are selected for the second phase.
A total of twenty five trials are conducted and a set of data is
collected as per the structure of CCD of experiments. A significant test is
conducted to examine the effects of different process parameters and their
interaction on the squeal occurrence.
2.5.1.3 Validation of the model
Statistical significance test and Analysis of Variance (ANOVA) test
is performed on the model using seventeen randomly generated test cases to
check the fitness of the model and to identify the significance of input
variables. Validation of the model and comparison between the simulation
and predicted model is examined.
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2.6 CONCLUDING REMARKS
As per the directions established through the literature survey and
by analysing the needs of the automotive industries, a more refined FE model
has been proposed in this research which includes parts of the suspension
(steering knuckle and wheel hub) to evaluate their influence on squeal
occurrence. In addition, more validation stages are adopted in the present
work. Validation of FE model is conducted using experimental modal
analysis at both individual components and brake assembly. The real pad
surface, negative and positive damping is considered to improve the predicted
results. Moreover, experimental squeal test and dynamic transient analysis is
performed to verify the CEA results.
The contribution of the research also lies in the recommendation of
new structural modifications for disc brake components and modifications of
rotor and pad geometry. Also, effects of pad shim/insulator through FEA and
experimental method on the squeal generation have been brought out in this
research.
The need for a new methodology using integration of the FE
simulation with DOE to better assess the contributions of different types of
structural modifications and its interaction effects for effective reduction of
brake squeal is explained. In the following chapters, application of the
proposed methodology, results of the numerical and experiments methods and
their effectiveness in conducting squeal will be discussed.