thermal deformation analysis of automotive disc brake squeal
DESCRIPTION
Thermal Deformation Analysis of Automotive Disc Brake SquealTRANSCRIPT
Thermal Deformation Analysis of Automotive Disc Brake
Squeal
BY
Muhammad Zahir Hassan
Submitted in accordance with the requirements for the degree of
Doctor of Philosophy
The University of Leeds
School of Mechanical Engineering
July 2009
The candidate confirms that the work submitted is his own and that appropriate
credit has been given where reference has been made to the work of others
This copy has been supplied on the understanding that it is copyright material and that
no quotation from the thesis may be published without proper acknowledgement
Abstract -
Automotive disc brake squeal has been a major concern in warranty issues and a
challenging problem for many years. A variety of tools have been developed which
include both experimental studies and numerical modelling technique to tackle the
problem. The aim of this project is to develop a validated thermo-mechanical finite
element model considering both the mechanical structural compliance and thermal
effects in the dynamic instability of a disc brake system leading to squeal. A key issue
in the process is to investigate the structural deformation of the brake components due
to the combined effect of thermal expansion and contact loading between pad and disc
when subjected to temperature change during a typical braking cycle. A new
methodology is introduced whereby a fully coupled transient thermo-mechanical
analysis is carried out to provide the temperature and contact distributions within the
brake before executing an instability analysis using the complex eigenvalue method. A
case study is carried out based on a typical passenger car brake as it undergoes a partial
simulation of the SAE J2521 drag braking noise test. The actuation pressure, coefficient
of friction and vehicle travelling speed are all considered to derive the temperature
dependent contact pressure distributions making allowance for the "rotating heat
source" effect. An experimental investigation using a brake dynamometer is also carried
out to measuring the squealing noise and thermal deformation which leads to a
validation of the results predicted by the numerical modelling. It is demonstrated that
the fully coupled thermo-mechanical FE model enhances understanding of the time
dependent non-linear contact behaviour at the friction interface. This, in turn,
demonstrates the fugitive nature of brake squeal through the system eigenvalues that
appear and disappear as a function of temperature throughout the braking period.
Parametric studies on the geometrical effect and materials of brake components
determine the contribution of each of these factors to brake squeal. The approach
therefore can be use as a predictive tool to evaluate disc brake squeal using finite
element method.
CHAPTER ONE
Introduction
1.1 Overview
Disc brake squeal still continues to be a major concern for the automotive industry
despite the efforts to reduce its occurrence during the past decades. It has been the
subject of both experimental and numerical modelling since 1930s (Jarvis and Mills,
1963). The continuously evolving expectations related to vehicle performance have
resulted in the car manufacturer having to strive to provide not only a competitive and
efficient braking system, but also a 'quiet' braking system (Mohd Ripin, 1995).
The elimination of brake squeal noise is very important as it causes discomfort of the
vehicle occupants as well as any pedestrians. Squeal problems may cause the car
manufacturer substantial revenue loss from warranty claims associated with the quality
of noise produced by the brake despite the fact that the brake remains fully functional
and safe (Lang and Smales, 1983).
The trade-offs involved in this process continue to challenge engineers to understand
and control brake noise and vibration phenomena. From a theoretical perspective, disc
brake squeal can be classified as a form of friction-induced vibration (North, 1972).
The characteristic and the understanding of this problem are complicated by the fact
that it is a transient phenomenon. The disc rotor, while acting like a speaker, is a
rotating component and the assembled brake combines many components with
complex interfaces (Limpert, 1999).
There are three general categories of noise associated with automotive disc brakes.
These categories are classified according to the frequency range in which the noise
occurs. Low frequency disc brake noise typically occurs in the frequency range
between 100 and 1000 Hz (Kinkaid et al.,2003). The noise types-in this category are
known as grunt, groan, grind and moan (Millner, 1978; Papinniemi et al., 2002).
Squeal is defined as brake noise occurs above 1000 Hz. For the frequency bandwidth
1000 Hz to 5 kHz, the noise generated is classified as low frequency squeal (Dunlap et
al., 1999). High frequency squeal is classified as squeal occurring above 5 kHz (Crolla
and Lang, 1991). Low frequency squeal is distinct from low frequency noise since the
squeal noise is strongly related to the elastic vibration of the brake rotor and its
associated natural frequencies (Lang and Smales, 1983).
1.2 Research Background
In recent years, finite element analyses (FEA) have become a standard and favourable
methodology through which to study brake squeal (Kinkaid et al., 2003). This is
because the finite element analysis is able to rapidly simulate brake squeal events for
any changes made in the design of the brake components compared to experimental
work (Papinniemi et al., 2002). Experimental programmes increase the cost as well as
the duration of the design and development process (Yumoto and Okarnura, 2006).
The moving contact interfaces underneath the disc-pad challenge engineers to extend
the brake squeal modelling with the incorporation of both thermal and structural
effects (Hassan et al., 2008). Up to now, most researchers have omitted to include the
effect of structural deformation and temperature dependent material properties when
studying brake squeal. This is due to the complexity as well as the computing load
involved in the inclusion of the thermal effects in brake instability studies (Ouyang et
al., 2005). Most of the studies related to thermal effects focus on low frequency
vibration, i.e. brake judder (Kubota et al., 1998).
To address the problem, a validated fully coupled FE model with respect to brake
squeal analysis is required. The FE model should improved the existing FE modelling
approach through integrated studies of time dependent thermo-mechanical effects
within a non-linear contact analysis followed by brake instability analysis using the
most common numerical prediction technique, namely the complex eigenvalue
method. Computational and experimental methods must be combined to correlate and
validate the results obtained from the models (Ouyang et al., 2005). Good correlation 2
between the finite element modelling and experimental results through dynamometer
testing will deliver positive outcomes towards the research targets. (Ioannidis et al.,
2005).
1.3 Aim and Objective of Research
1.3.1 Aim
The overall aim of this research is to develop a fully coupled thermo-mechanical FE
model to investigate brake system stability that includes the structural deformation of
the brake components when subject to thermal effects. The SAE J2521 drag brake test
considers different stages of brake instability particularly in relation to the temperature
distribution including both heating and cooling effects. The development of a fully
coupled thermo-mechanical model will also take account of the so-called "rotating heat
source" effect in order to predict the non-axisymmetric rotor temperature distributions
that occur in practice. This will lead to a representative FE model in which instability
is predicted throughout the braking period.
The study will consider four major aspects in the modelling of the brake squeal
phenomenon. These are the development of validated 3-dimensional FE models
through free-free modal analysis, non-linear thermo-mechanical contact pressure
analysis, instability prediction thorough complex eigenvalue analysis and parametric
studies based on the brake design. Experimental work using a brake dynamometer
which measure the thermal characteristics and squeal is required for the comparison
and validation of the numerical modelling results.
1.3.2 Objectives
The objectives of the research are as follows:
1. To develop a validated 3-dimensional finite element model of a typical
brake assembly by conducting free-free modal analysis in order to validate
the finite element models by correlation of natural frequency data extracted
from the finite element model with the results from experimental modal
analysis (EMA). 3
. . 11. To simulate the thermo-mechanical contact pressure distribution at the disc
and pad interface with frictional contact conditions under'the dynamic drag
braking define by SAE 52521 test schedule.
iii. To conduct instability analysis of the disc brake system using complex
eigenvalue analysis (CEA).
iv. To simulate the effects of material properties and geometrical changes of
the brake components on the occurrence of squeal noise.
v. To correlate the predictions of the finite element model with the results of
experimental investigations carried out using the Leeds Brake
Dynamometer.
1.4 Organisation of Thesis
The remainder of this thesis is compromised of eight further chapters as summarised
below.
Chapter 2: A review of literature relevant to the present study comprising brake
system fundamentals, brake noise in general and in particular squeal noise.
Chapter 3: The new methodology, proposed through the integrated FE approach is
described. This uses a fully coupled thermo-mechanical instability simulation
technique to study the dynamic behaviour of a typical automotive brake system during
different periods within a braking event.
Chapter 4: Experimental free-free modal analysis of the brake system components.
This determines the individual brake component's free vibration behaviour and these
results are used to develop appropriate FE models.
Chapter 5: This experimental section discusses the laboratory based brake
dynamometer test facility and data acquisition system that is used to carried out the
drag brake test. The experimental work evaluates the brake system performance by
measuring the temperature, disc distortion and squeal noise.
Chapter 6: A non-linear thermo-mechanical contact analysis investigates the disc-pad
non-linear transient thermal and contact pressure distribution under specific drag
braking operating conditions. The effect of contact pressure distribution under heating
and cooling conditions is reported for different contact interface properties. The results
(for example, contact condition) are presented as a function of time. This chapter also
discusses the effect of disc deformation during the heating-up process. A thorough
study gives an insight into the extent of disc coning during the braking process. A
correlation between the FE model prediction and experimental results is presented.
Chapter 7: Squeal prediction through complex eigenvalue analysis is presented as a
function of time during the braking cycle. The unstable complex modes and
frequencies are extracted throughout the braking period. These results lead to better
understanding of the fugitive nature of the squeal problem.
Chapter 8: Parametric studies of brake component geometry and material properties
establish the importance of these parameters with respect to squeal events. This section
discusses the relationship between brake operating conditions, brake geometry,
material properties and squeal noise generation or propensity.
Chapter 9: Conclusions are drawn from the overall findings of the research along with
recommendations for future work.
CHAPTER TWO
Literature Review
2.1 Introduction
The subject of brake squeal has generated a considerable volume of literature which
includes a number of theories that have been formulated to explain the mechanisms of
brake squeal. Studies on disc brake squeal involve two major areas of study: disc-pad
interaction and friction-induced vibration.
This chapter begins with an introduction to the automotive disc brake system, to give
an overview of disc brake components and their function. The distinct categories of
automotive brake noise are presented according to the frequency range in which they
occur. A review of brake squeal literature is then presented that explains the disc brake
squeal phenomenon. The scientific findings are categorised into theoretical, finite
element (FE) and experimental approaches to tackle and analyse brake squeal
problems. In the FE section, a review on disc-pad contact pressure distribution, which
has become essential feature of brake squeal study, is presented. A review of brake
thermal analysis and brake instability analysis is also described. The subsequent
section discusses experimental investigations that have been employed to tackle squeal
problems followed by research reviews publication related to the area of brake noise.
Finally, summary of the existing approaches are provided together with their
limitations for tackling real brake noise issues. The structure of the chapter is shown in
Figure 2-1.
Introduction to Automotive Braking System
I Description of Automotive Brake Noise I
v Low Frequency Low Frequency High Frequency
Brake Noise Brake Squeal Brake Squeal i L
Research Work b Approach 4
Theoretical Experimental Finite Element Research Work Analysis
I I I Brake Noise Research Reviews x
Summary
Figure 2- 1 : Overview of Literature Review
2.2 Automotive Disc Brake System
2.2.1 Historical Background
Elmer Ambrose Sperry pioneered the development of the clutch type disc brake in
1898 as cited in Hughes (1971). The design featured an electromagnetically actuated
disc where braking torque is generated when the brake magnet disc is pressed into
contact with another disc known as the brake disc.
The first patented model of disc brake was registered by Frederick William Lanchester
in 1902 (Cited in Newcomb and Spurr, 1967). The disc brake, consisting of a sheet
metal rotor connected to one of the rear wheels of a vehicle and is pinched at the wheel
edges in order to slow down the vehicle. This invention predates the early type of
sports car disc brake system design in the early 1950s which traces its developments to
Dunlop, Girling and the Lockheed Corporation (Newcomb and Spun, 1967). The
sport-type design of brake disc is similar to the present type of disc brake which can be
found on most road vehicles (Harper, 1998). The biggest problem that Lanchester
encountered was noise as metal-to-metal contact between the copper linings and metal
disc caused an intense screech that sent chills through anyone within earshot. Since
then, the materials and actuation method used in this early brake have been greatly
modified and improved.
The most important contribution towards the widespread used of brake discs is due to
enhanced safety regulations throughout the world. For instance, most cars in the
United States are equipped with front brake discs due to Federal Motor Vehicle Safety
Standards (FMVSS) 105 regulations, which require all cars to meet standard stopping
distance and brake fade requirements (Oppenheimer, 1977). This is because disc
brakes satisfy the braking power specification with superior water resistance and fade
performance compared to drum brakes.
2.2.2 Brake Components and Functions
A disc brake system usually consists of a brake disc rotor, two brake pads and a
calliper (SAE International, 2007). The combination of these components allows the
rotating wheel to experience severe braking in a short stopping distance. The braking
surface is the area on which the braking action of the friction material takes place
(Limpert, 1999).
Figure 2-2 illustrates the disc brake system components on a passenger vehicle. The
centre part of the brake disc has a circular aperture, which is locates on the wheel hub
(SAE International, 2007). It is surrounded by a number of holes for the wheel bolts.
The brake disc rotates along with the wheel. The normal load, produced when the
brake is actuated result in the generation of an in-plane friction force at the disc-pad
interface. This in turn produces a brake torque about the centre of rotation of the wheel
as shown in Figure 2-3. The reaction to the brake torque is seen in the brake force,
between the tyre and ground, that slow the vehicle.
Figure 2-2: Brake system components: 1) Piston 2) Calliper 3) Pad 4) Brake Disc
Retainer 5) Rotor Disc 6) Wheel Hub (Flickr, 2008)
Brake Torque Disc
gular locity -
Direction of
transmitted to the Motion
vehicle
Axle load
Braking force -,
Brake f Force ryre-Road Normal Reaction
Figure 2-3: Schematic diagram of forces and moment acting on wheel
9
The ventilated brake rotor is a one-piece casting with cooling fins between the two
braking surfaces. This enables air to circulate between the braking surfaces, making
them less sensitive to heat build-up and more resistant to fade. Dirt and water do not
generally affect the braking action since contaminants are thrown off by the centrifugal
action of the brake disc or scraped off by the pads. In addition, the equal clamping
action of the two brake pads tends to ensure uniform, straight-line stops (SAE
International, 2007).
The two main functions of the brake rotor are the transmission of mechanical force and
the dissipation of heat, produced when functioning at both medium and high
temperature (Limpert, 1999). This means that the materials used for brake discs must
be able to support high temperatures (Grieve et al., 1998). The rotor material must be
cost effective, allowing for potential reductions in weight as well as for the stability of
the components (Ioannidis et al., 2005).
A solid disc brake consists of a rubbing surface and a top hat section (Bae and Wicket,
2000). The section that connects these two parts is known as the neck (Yumoto and
Okamura, 2006). The rubbing surface section is the area where a tangential friction
force is generated when the disc interacts with a stationary pad to stop the moving
vehicle. The disc rubbing surface area is sometimes known as the cheek (Grieve et al.,
1998; Koetniyom, 2000). A top hat section is connected to the disc rubbing surface and
mounted to the vehicle wheel hub.
A disc brake which has separate inboard and outboard rubbing surfaces with cooling
vanes or fins in between is known as a ventilated rotor. These vanes allow the air to
flow through the structure and cool the rubbing surfaces during and after all braking
events. There are two types of ventilated disc: front-vented and back-vented.
Figure 2-4(a) shows the front-vented type of disc brake, where the top hat section is
connected by the neck to the outboard rubbing surface. On the other hand, a neck that
connects the inboard rubbing surface with the top hat section as shown in Figure 2-4(b)
creates what is known as a back-vented disc (SAE International, 2007).
Rubbing
I Neck
(a) Front-Vented Disc (b) Back-Vented Disc
Figure 2-4: Typical front and back-vented disc (Koetniyom, 2000)
The friction between the pad and disc plays a decisive role in defining the amount of
pedal force required to obtain a given rate of deceleration (Papinniemi et al., 2002).
This factor is also important in designing brakes for the balanced operation of a vehicle
as brake imbalance can lead to a yaw torque about the vertical that could compromise
the vehicle stability. The additional task for the brake disc is to induce air movement,
as air moving over the rubbing surface of the disc reduces the heats build up (Valvano
and Lee, 2000).
The brake pad is designed to rub against the disc surface leading to diminution of
vehicle speed, thereby converting mechanical work into thermal energy. The structure
of the pads can be very complex (Nicholson, 1995). They can consist of different
materials or numerous parallel layers as shown in Figure 2-5. There are many different
types of friction material on the market which can be classified into the following
categories: semi-metallic (SM), non-asbestos organic (NAO) and sintered metal
(Anderson, 1992). A friction material is mounted to a rigid metal backplate using
adhesive. A substrate material is sometimes located in between the friction material
and backplate. The main function of the substrate material is to act as a thermal
insulator that will prevent an excessive flow of heat towards the piston and brake fluid
as well as damping vibration. The backplate distributes the force exerted by the piston
over the pad contact surface (Lee et al., 2003a). An anti noise layer or shim located
behind the backing plate minimises the transmission of vibrations produced during
braking action.
Friction Material
Backplate
Anti-noise layer
Figure 2-5: Brake pad construction (Nicholson, 1995)
The calliper, which contains one or more pistons, holds the two brake pads on either
side of the rotor. The movement of the pistons is controlled by a hydraulic system
(SAE International, 2007). When hydraulic pressure is applied by pressing the brake
pedal, the piston is pushed forward to press the inner pad against the rotor while the
housing is pushed in the opposite direction to press the outer pad against the rotor,
hence generating a hydraulic clamp around the rotor. For the fixed (non-floating)
calliper type of disc brake system, each piston presses the brake pad against its
respective side of the brake rubbing surface, as shown in Figure 2-6(a). Meanwhile the
floating calliper housing, which is designed to slide on its support, reacts by shifting
and pushing the pads against both sides of the disc as shown in Figure 2-6(b) (SAE
International, 2007).
Figure 2-6: Brake system components (SAE International, 2007)
(a) Cross sectional view of Brake System: Fixed Calliper
(b) Cross sectional view of Brake System: Floating Calliper
2.3 Description of Automotive Disc Brake System Noise
There are three general categories of noise associated with the automotive brake disc.
These categories are classified according to the frequency range in which they occur
(Dunlap et al., 1999).
i. Low Frequency Noise ( Less than 1000 Hz )
ii. Low Frequency Squeal ( 1000 Hz to 5000 Hz )
iii. High Frequency Squeal ( Greater than 5000 Hz )
2.3.1 Low Frequency Brake Noise
Low frequency disc brake noise typically occurs in the frequency range between 100
and 1000 Hz (Lang and Smales, 1983). Low frequency vibration has been attributed to
variation of coefficient of friction with sliding velocity. This type of noise is caused by
friction material excitation at the brake rotor and lining interface where the energy is
transmitted as a vibration within the wheel comer which couples with other chassis
components punlap et al., 1999). The noise types in this category are known as
judder, groan and hum.
Groan is defined as a semi-resonant vibration with frequency typically less than 100
Hz. Groan as well as hum may i~-~volve the rigid body rotational modes of the calliper
and local suspension parts. The typical frequency range for hum noise is between 200
and 400 Hz. Judder generally occurs at frequencies below 150 Hz but high-speed
judder exists in the frequency range of between 150 to 250 HZ (Kubota et al., 1998).
The judder phenomenon, which is felt rather than heard, is characterised by vehicle
body and steering system vibrations. Cyclic variations in brake torque resulting from
disc circumferential thickness variation cause this very low frequency non-resonant
vibration.
2.3.2 Low Frequency Brake Squeal
For the frequency bandwidth 1000 Hz to 5000 Hz, the noise generated is classified as
low frequency squeal (Fosberr~ and Holubecki, 1955; Lang and Smales, 1983;
Kinkaid et al., 2003). Squeal is related to vibration involving transverse motion of the
disc and a bending or twisting motion of the brake pad. The disc mode order is often
such that the wavelength of the mode is less than the arc length of the pad. The noise
generation can be associated with frictional excitation coupled with a phenomenon
known as modal 'locking' (Dunlap et al., 1999). The friction force at the interface
couples these modes and produces an instability known as 'binary flutter' due to its
similarity to aircraft wing flutter (Crolla and Lang, 1991).
2.3.3 High Frequency Brake Squeal
High frequency squeal is classified as squeal occurring above 5 kHz (Dunlap et al.,
1999). The noise is produced by friction induced excitation causing coupled resonance
of the rotor and other brake components. Higher frequency squeal is sometimes
referred to as squeak (Lang and Smales, 1983).
2.4 Theoretical and Multi-body Methods Approach
The first description of brake squeal noise by Mills (1938) as cited in Kinkaid et al.
(2003) shows how a simple model of an elastic rubbing system can be used to
demonstrate the instability of a brake system. This simplified model shows a fragment
of pad material rubbing against the disc connected to the calliper by means of a visco-
elastic system, comprising a parallel combination of spring and a linear damper. This
model assumes that the friction coefficient is not fixed and varies in a linear manner
with the rotational speed of the disc relative to the pad as shown in Figure 2-7.
Linear damper
Figure 2-7: A model of non-linear stick-slip vibration (Mills (1938) as cited in Kinkaid
et al. (2003))
From the simple rubbing surface model shown in Figure 2-7, the coefficient of friction
is assumed to be:
where p, : is static friction coefficient,
A : is magnitude of the slope of the friction speed curve,
V : is conveyer speed,
x : is instantaneous velocity of mass.
The equation of motion of the rubbing block with mass M and applied normal force N
can be presented as:
Substituting equation 2-1 into equation 2-2 generates the following equation:
Re-arranging the previous two equations generates:
Since h is always positive, equation 2-4 gives a negative damping term, which makes
the system become unstable as illustrated in Figure 2-8. As a result, the negative slope
of the friction curve is the main mechanism for the system to generate instability.
Kinetic Friction Coefficient ,us
b v
Sliding Speed
Figure 2-8: Kinetic friction coefficient as a linear function of sliding speed with
negative slope
Spurr (1961) introduced the sprag-slip model since the experimental investigations
following Mills's model description showed that the negative slope of the friction
versus speed curve could not alone explain all the phenomena associated with brake
squeal. Spurr came up with mechanism that includes a geometrically induced
instability arising from the friction coefficient. The main difference between the Spurr
and Mills model is that the sprag-slip mechanism does not require the negative slope of
the friction versus curve model and also explains why the out-of-plane modes are
excited by the in-plane friction force. However the Spurr model still could not explain
real brake system squeal noise generation.
In 1963, Jarvis and Mills adapted the Spurr model to produce a further mathematical
model of brake squeal. Their work shows that the instability of coupling between the
two members (disc and pad) produces brake squeal by idealising the brake system as a
simplified model of a cantilever-disc system. The cantilever is subjected to both
normal force and friction force. Increase in normal force will increases the friction
force which pushes the cantilever away. By using the Lagrange method, Jarvis and
Mills proved that the cause of instability is not due solely to variation in the coefficient
of friction. They proposed a complete model of the brake system, which included the
calliper. The mathematical model proposed by Jarvis and Mills was validated by pin
on disc experiment, which has become widely adapted equipment for the study of
squeal characteristics as shown in Figure 2-9.
Figure 2-9: Jarvis and Mills cantilever-disc system model (Jarvis and Mills, 1963)
A better model developed by North (1972) can be regarded as an 8 degree of freedom
model for the brake assembly with four major components; two brake pads, a disc and
calliper as shown in Figure 2-10. These components were allowed to move in the
transverse direction and also rotate.
In contrast to the North model, Millner (1978) developed a squeal model based on a
fixed calliper disc brake. The main feature of this model is that it can examine the
effect of centre of pressure between the piston and brake pad. Millner concluded that,
as well as the geometry, instability could be excited in almost any contact
configuration when the coefficient of friction is sufficiently high. He further
demonstrated that the propensity for brake squeal can be reduced by moving the centre
of pressure towards the trailing edge of the brake pad.
Rudolph and Popp (2001) published a 14 degree of freedom multi body brake
assembly model as shown in Figure 2-1 1 in which there are 18 coupling elements
between the rigid bodies. The force and moment coupling depends on the relative
displacement and velocity between the two connected rigid bodies. An important
feature of this model is that the coefficient of friction is assumed to depend on the
brake line pressure at the initial temperature of the disc. The model was verified by the
experimental data.
I Pad
Y 1
Disc
11111
Pad + ;Lo;
Figure 2-10: %degrees of freedom brake assembly model (North, 1972)
10 8
Outer Pad 7 + 2 1 )
Disc
4 13
Inner Pad
11 12
Figure 2-1 1: 14-Degrees of freedom brake assembly model (Rudolph and Popp 2001)
- -
2.5 Modelling Approach: Finite Element Analysis
Free Canier Supporting Carrier b
18
15 Calliper
- -
The finite element (FE) method is the most popular of approaches used to simulate the
performance of a brake system design (Liles, 1989; Lee et al., 2003a). The vast
number of degree of freedom and high fidelity of an FE model has enabled the FEA to
deliver a detailed representation of the brake system performance (Ouyang et al.,
2005). There are several types of analysis that have been used by researchers to
evaluate a given design with a view to producing an early predictive tool with which to
evaluate problems (Kinkaid et al., 2003). The following section presents the FE
techniques used to tackle brake design issues which include thermal, contact pressure
and instability analyses. The latter have used the complex eigenvalue and transient
dynamic approaches.
16
1
2.5.1 Thermal Analysis
During braking, the kinetic energy of the moving vehicle is converted into thermal
energy through friction at the disc and pad interface. Frictional heat is generated at the
rubbing surface due to the interactions between the pad and disc. The disc absorbs up
19
to 90% of the generated heat energy by means of conduction away from the friction
interface between disc and pad (Limpert, 1975). The energy is quickly dissipated to the
surrounding air. Radiation also helps to dissipate the heat energy stored within the
rotor when the temperature is high.
Prediction of the surface temperature of a disc brake as well as that of the pad is
complicated (Thuresson, 2000). This difficulty is due to the complex interactions
between the thermal and mechanical behaviour of the brake components (Ouyang et
al., 2005). The finite element method (FEM) is the most popular and widely used tool
to simulate the influence of temperature in brake system design and performance. Bolt
(1989) defined several numerical procedures for thermal analysis using the FE method
to investigate disc brake performance. He revealed that FEA is the fastest and most
accurate way to study the influence of temperature at the early design stage of a brake
system.
There are three main categories of FE thermal modelling discussed in the following
subsections: heat transfer analysis, thermal stress analysis and coupled thermo-
mechanical analysis.
2.5.1.1 Heat Transfer Analysis
The non-uniform heat flux input to the disc brake is calculated from the non-uniform
pressure distribution, friction coefficient and sliding velocity along the disc-pad
interface. The amount of heat flux that flow into each component depends on the disc
and pad material (Thuresson, 2004). The value of calculated heat flux is applied to the
FE model to examine the resulting temperature distributions (Koetniyom, 2000).
Limpert (1975) studied the thermal performance of a solid disc brake during braking.
The heat flux for the disc was derived from the coefficient of friction and heat
proportioning between the rotor and pad under uniform pressure loading. Experimental
work was carried out to supported the results obtained from the theoretical
calculations. During a series of brake applications, the results obtained from the
experimental work and the theoretical calculations were well correlated.
Sheridan et al. (1988) studied different techniques for the thermal modelling of a disc
brake ranging from a simple axisymmetric FE model to a complex 3-dimensional FE
model. The paper also reviewed methods to calculate the thermal boundary conditions
of the model. The effect of energy input and output as well as the material properties,
such as thermal conductivity and specific heat, had a significant influence on the
temperature response. Their findings suggested that 90% of the heat generated during
braking is transferred by convection to the ambient air.
Huang and Chen (2006) constructed a 3-dimensional FE model of a disc brake to
investigate its cooling performance in terms of the design parameters and boundary
conditions. Each surface of the rotor was subjected to different values of convection
heat transfer coefficient obtained from theoretical calculations. The neck fillet radius,
which connects the rubbing plate to the top hat, was modified to study its influence on
the cooling process during braking. The simulation shows that the highest temperature
appeared at the mean radius location of the rubbing surface for both outboard and
inboard side and this magnitude significantly depended on the fillet radius of the neck.
Sun (2006) developed a thermal model of disc brake system using ABAQUS by
combining this with computational fluid dynamics (CFD) and a FORTRAN user
subroutine to study the brake equilibrium temperature rise. The thermal model was
correlated to physical test data during braking under mountain test schedules to study
the effect of rotor, dust shield, wheel, wheel cover and air deflector on the brake
performance. The simulation indicated that the modifications made to the rotor, dust
shield and wheel geometry greatly improved the brake cooling performance when the
brake temperature rise was between 370°C to 480°C. The results also showed that the
number of vanes and the air deflector design also influenced the brake equilibrium
temperature rise.
2.5.1.2 Thermal Stress Analysis
A thermal stress analysis of a brake disc uses the temperatures predicted in the
preceding heat transfer analysis (Koetniyom, 2000). The nodal temperatures derived
from the heat transfer analysis provide temperature variation input to the structural
model to carry out the thermal stress analysis.
Timtner (1979) investigated the effect of changes in the geometry of a solid brake disc;
looked at the top hat section depth and thickness as well as the undercut depth, which
influence the disc brake coning, using a linear elastic FE model. ~ i r ~ t l y , he carried out
the heat transfer analysis to obtain the nodal temperatures of the disc brake and then
transferred these temperatures to the structural model to conduct the thermal stress
analysis. The numerical results show that the degree of brake disc coning is reduced
when the top hat section depth, thickness and undercut depth fire increased. He
concluded that the greatest influence on brake disc coning was the value of hat
thickness.
Fukano and Matsui (1986) used the same technique as Timtner (1979) to conduct an
elastic thermal stress analysis of an automotive disc brake. The material properties of
the disc, made out of cast iron, were temperature dependent. The outcome of their
investigation predicted cracking in the top hat section of the disc, which was close to
high stress concentrations around the bolt holes. This is due to fgct that maximum
tensile stress in the disc exceeded the tensile strength of the cast iron. Experimental
work showed good agreement with predicted cracking obtained from the ~umerical
modelling results.
Valvano and Lee (2000) utilized an ABAQUS program to investigate the thermal
distortion of a brake rotor. The program is able to calculate thermal parameters based
on measured data, using a brake dynamometer, for use in FE modelling. These
parameter inputs were transported directly into ABAQUS and an alysed using both
transient and steady-state conditions to calculate the temperature distribution and
thermal stresses. The finite element analysis is divided into two categories: initial heat
transfer analysis followed by the uncoupled thermal analysis th-at determines the
thermal stresses and distortion of the brake rotor. This approach allaws the heat input
and output of the heating and cooling process for a given brake system to be compared
with the measured temperature and distortion data based on ex~edmental work. The
method can also be a viable tool in the early stages of brake design t o reduce unwanted
thermal distortion in the disc brake system.
Koetniyom (2000) investigated the thermal response of a cast i r o ~ disc brake using
FEA. He generated a complex thermo-mechanical model based on ulniaxial cyclic tests
from samples cut from a Rover 200 ventilated disc. By using tlhe user developed
material subroutine in ABAQUS, the thermal responses of back and front-vented disc
designs are compared and validated with the uniaxial cyclic test dat8. The results show
that the back-vented disc suffers lower thermal distortion but with higher plastic strain
accumulation at the vanes and neck section. This indicates that the back-vented disc is
subjected to high temperature and plastic stresses that are most likely to cause thermal
cracking under repeated thermal cycling.
Phan and Kondyles (2003) combined the computational fluid dynamics (CFD)
technique with heat transfer analysis for the brake rotor development process. They
carried out a thermal modelling technique to optimise the rotor design considering
thermal film coefficient, rotor coning, temperature and thermal stress distribution.
They found that the combined technique provided accurate thermal data to predict
rotor thermal distortion so that the coning problems can be reduced at the early design
stage.
Yumoto and Okamura (2006) constructed a disc brake system development program
using computer aided engineering (CAE). The study of brake performance can be
carried out by manipulating pull down menus in a graphical user interference (GUI) to
conduct parametric design studies and FEA modelling. The methodology of the
program satisfies the requirement of the brake performance analysis: thermal
modelling, judder and squeal analysis. The program is divided into two main steps, the
finite element stage followed by the design optimisation step. The pre-processor allows
the user to define the geometry of the disc brake model, carry out the thermal analysis
followed by the complex eigenvalue analysis. In the post processor stage, the program
will automatically simulate the results. The program helps to reduce the time taken to
design the brake system as well as improving the quality of the brake design.
2.5.1.3 Coupled Thermo-Mechanical Analysis
Coupled thermo-mechanical problems have recently become one of the important
research areas in brake performance. The coupled model predicts the temperatures as a
function of time and derives a new contact pressure distribution when the disc and pad
come into contact at the start of each time step (Hassan et al., 2008).
Brooks et al. (1994) investigated thermal judder using a fully coupled thermal
structural model. The FE thermal model predicted the temperature as a function of
time during the presence of heat flux. The temperature field was then transferred to the
structural model to derive the contact pressure distribution. The change in contact
pressure underneath the contact surface was then used to derive a new heat flux
distribution to feed back to the thermal model and therefore the model was considered
to be fully coupled. A parametric study was camed out to investigate the effect of
friction material properties. The results show that friction material stiffness should be
low as this generates a more uniform contact distribution for both temperature and
contact pressure. A high thermal conductivity and a low coefficient of expansion also
promote a uniform pressure distribution.
Yi et al. (2001) used a fully-coupled model to determine the critical speed using an
eigenvalue formulation to study the thermo-elastic instability (TEI). The eigenvalue
method predicts the critical speeds for the disc brake TEI by identifying the minor
design changes related to the critical vehicle speed. An accompanying experiment is
carried using an infrared detector where the results are used to validate the critical
speed derived by the FE model. They concluded that fully coupled FE model is one of
the best numerical approaches for TEI studies.
Thuresson (2002) camed out an investigation into the contact problem between two
bodies in high speed sliding contact using quasi-static analysis. A thermo-mechanical
wear model was developed to obtain the interface pressure and temperature
distribution. The thermal analysis was camed out using the boundary element method
and solved using a Newton-type method to investigate contact geometry subject to
change in interface friction. He found that temperature and wear effects have a large
impact on the disc-pad contact interface pressure distributions. At a low coefficient of
wear, thermal expansion dominated the pressure distribution. In contrast, when the
coefficient of wear is high, thermal expansion tends to have less effect on the
distribution of contact pressure. Thuresson concluded that the model gave promising
results and both temperature and pressure distributions are accurately determined by
considering the effect of wear.
Recent studies by Zhu et al. (2008) simulate the SAE 52521 drag braking squeal test
sequence using a sequentially coupled thermal structural FE model based on the Leeds