In: New Research on Acoustics ISBN 978-1-60456-403-7
Editor: Benjamin N. Weiss, pp.159-198 © 2008 Nova Science Publishers, Inc.
RECENT STUDIES OF CAR DISC BRAKE SQUEAL
Abd Rahim Abu-Bakar
Department of Automotive Engineering, Faculty of Mechanical Engineering
Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia
Department of Engineering, University of Liverpool
Brownlow Street, Liverpool L69 3GH, U.K.
Friction-induced vibration and noise emanating from car disc brakes is a source of
considerable discomfort and leads to customer dissatisfaction. The high frequency noise above
1 kHz, known as squeal, is very annoying and very difficult to eliminate. There are typically
two methods available to study car disc brake squeal, namely complex eigenvalue analysis
and dynamic transient analysis. Although complex eigenvalue analysis is the standard
methodology used in the brake research community, transient analysis is gradually gaining
popularity. In contrast with complex eigenvalues analysis for assessing only the stability of a
system, transient analysis is capable of determining the vibration level and in theory may
cover the influence of the temperature distribution due to heat transfer between brake
components and into the environment, and other time-variant physical processes, and
nonlinearities. Wear is another distinct aspect of a brake system that influences squeal
generation and itself is affected by the surface roughness of the components in sliding contact.
This chapter reports recent research into car disc brake squeal conducted at the University of
Liverpool. The detailed and refined finite element model of a real disc brake considers the
surface roughness of brake pads and allows the investigation into the contact pressure
distribution affected by the surface roughness and wear. It also includes transient analysis of
heat transfer and its influence on the contact pressure distribution. Finally transient analysis of
the vibration of the brake with the thermal effect is presented. These studies represent recent
advances in the numerical studies of car brake squeal.
Abd Rahim Abu-Bakar and Huajiang Ouyang 2
Passenger cars are one main means of transportations for people travelling from one place to
another. Indeed, vehicle quietness and passenger comfort issues are a major concern. One of
the vehicle components that occasionally generate unwanted vibration and unpleasant noise is
the brake system. As a result, carmakers, brake and friction material suppliers face
challenging tasks to reduce high warranty payouts. Akay (2002) estimated that the warranty
claims due to the noise, vibration and harshness (NVH) issues including brake squeal in
North America alone were up to one billion US dollars a year. Similarly, Abendroth and
Wernitz (2000) noted that many friction material suppliers had to spend up to 50 percent of
their engineering budgets on NVH issues.
In a recent review, Kinkaid et al (2003) listed a wide array of brake noise and vibration
phenomena. Squeal, creep-groan, moan, chatter, judder, hum, and squeak are among the
names that can be found in the open literature. Of these noises, squeal is the most troublesome
and irritant one to both car passengers and the environment, and is expensive to the brakes
and car manufacturers in terms of warranty costs (Crolla and Lang, 1991). It is well accepted
that brakes squeal is due to friction-induced vibration or self-excited vibration via a rotating
disc (Chen et al, 2003a). Brake squeal frequently occurs at frequency above 1 kHz (Lang and
Smales, 1983) and is described as sound pressure level above 78 dB (Eriksson, 2000) or
usually at least 20dB above ambient noise level in the automotive industry.
Brake squeal has been studied since 1930’s by many researchers through experimental,
analytical and numerical methods in an attempt to understand, predict and prevent squeal
occurrence. Although experiments used to be the more credible way of studying disc brake
squeal (Nishiwaki et al, 1990; Yang and Gibson, 1997), there has been a great advancement
in the numerical analysis methodology in recent years. More specifically, the finite element
(FE) method is the preferred method in studying brake squeal. The popularity of finite
element analysis (FEA) is due to the inadequacy of experimental methods in predicting squeal
at early stage in the design process. Moreover, FEA can potentially simulate any changes
made on the disc brake components much faster and easier than experimental methods. A
recent review (Ouyang et al, 2005) stated that experimental methods are expensive due to
hardware costs and long turnaround time for design iterations. In addition, discoveries made
on a particular type of brake are not always transferable to other types of brake and quite
often product developments are based on a trial-and-error basis. Furthermore, a stability
margin is frequently not found experimentally.
With the refinements on the methodology and analysis of the disc brake squeal using the
finite element method being progressively reported in the open literature, it is thought that
refinement in the disc brake model should also be made in parallel. This can be seen from the
previous works of Liles (1989); Ripin (1995) and Lee et al (1998) where a number of linear
spring elements are employed at the friction interface. The introduction of a number of spring
elements at the disc/pads interface is necessary to generate friction-coupling terms
(asymmetric stiffness matrix) that lead to the complex eigenvalues, i.e., unstable behaviour in
which the positive real parts indicate the likelihood of the squeal occurrence. With the
contributions of many researchers (for example, Yuan, 1996, Blaschke et al, 2000) and the
initiative of a finite element software company (ABAQUS, Inc., 2003), linear spring elements
are no longer required as friction-coupling terms can now be directly implemented into the
Recent Studies of Car Disc Brake Squeal 3
stiffness matrix. As a result the effect of non-uniform contact pressure and residual stresses
can be incorporated in the complex eigenvalue analysis (Bajer et al, 2003, Kung et al, 2003).
Another advantage of the current approach is that the surfaces in contact do not need to have
matching meshes and essentially it can reduce data-preparation time. In contrast, the former
approach required nodes on the two contacting surfaces to coincide and hence similar meshes.
Some previous studies assumed full contact at the pads and disc interfaces (Liles, 1989,
Ouyang et al, 2000). Other works (Samie and Sheridan, 1990; Tirovic and Day, 1991;
Ghesquiere and Castel, 1992; Ripin, 1995; Lee et al, 1998; Hohmann et al, 1999; Tamari et
al, 2000, Ioannidis et al, 2003; Abu-Bakar and Ouyang, 2004 and Abu-Bakar et al, 2005b)
have shown that the contact pressure distributions at the disc/pads interfaces are not uniform
and there exists partial contact over the disc surfaces. Traditionally, contact at the disc/pads
interface was simulated using either linear spring elements (Nack, 2000) or non-linear node-
to-node gap elements (Samie and Sheridan, 1990; Tirovic and Day, 1991; Ripin, 1995; Lee et
al, 1998, Tamari et al, 2000). Recent contact analyses (Hohmann et al, 1999; Ouyang et al,
2003a, Ioannidis et al, 2003) no longer use such elements, where a surface based element can
provide more realistic and accurate representation of contact pressure distribution (Bajer et al,
2003, Kung et al, 2003). Incidentally, the contact pressure distribution is believed to be very
influential on squeal generation. Fieldhouse (2000) experimentally and Abu-Bakar et al
(2005a) numerically demonstrated that different pressure contact distributions could promote
or inhibit squeal occurrence.
When developing a finite element model, it is important to validate it in order for the
model to correctly represent the actual structure in terms of the geometry and its material
properties. A validated model should be able to predict squeal sufficiently accurately. Liles
(1989) was the first researcher who conducted and expounded the complex eigenvalue
analysis with a large finite element model and used modal analysis to compare natural
frequencies and the mode shapes for each of disc brake components. This component
validation later became a standard practice (Ripin, 1995; Lee et al, 1998; Guan and Jiang,
1998; Liu and Pfeifer, 2000; Kung et al, 2000, Ioannidis et al, 2003). Even though precise
representations of brake components are possible, results obtained by the complex eigenvalue
analysis did not always correspond to the experimental squeal results. Realising this
shortcoming Richmond et al (1996), Dom et al (2003), Ouyang et al (2003a) and Goto et al
(2004) used a systematic procedure to correlate and update the FE model at both the
component and assembly levels. A tuning process was performed to reduce relative errors in
natural frequencies between predicted and experimental results whereby material properties
and spring stiffness were adjusted in the tuning process.
As progressive refinements on the methodology and analysis stated above are made, it is
thought that a more realistic finite element model should be developed or, in other words,
refinement on the modelling aspects of disc brakes should be made. It is already known that
contact geometry between the disc and friction material interface has a significant
contribution towards squeal generation (Tarter, 1983; Ripin, 1995; Eriksson et al, 1999;
Ibrahim et al, 2000; Soom et al, 2003; Sherif, 2004; Hammerström & Jacobson 2006; Trichěs
et al, 2008; Fieldhouse et al, 2008). They believed that squeal could be generated at particular
conditions of pads topography. Another fact is that the friction material is more prone to
wear. Furthermore, friction material has a much more irregular or corrugated surface than the
disc. It was found that none of the existing finite element models considered friction material
Abd Rahim Abu-Bakar and Huajiang Ouyang 4
surface topography. All of the models assumed that the friction material had a smooth and flat
interface whereas in reality it was rough.
The complex eigenvalue analysis was the method preferred by the industry to study their
squeal noise issues. This method is largely dependent on the results of contact analysis, which
can determine instability in the disc brake assembly. Determination of dynamic contact
pressure through experimental methods remains impossible. However there are methods to
obtain static contact pressure, when the disc is stationary. It is believed that static contact
pressure distribution and its magnitude can be used as a validation tool where correlation
between calculated and measured results can be made. This validation level can enhance
one’s confidence in the developed model as well as provide better prediction of squeal
occurrence. Although complex eigenvalue analysis is the standard methodology used in the
brake research community, transient analysis is gradually gaining popularity. In contrast with
complex eigenvalues analysis for assessing only the stability of the system, transient analysis
is capable of determining the vibration level and in theory may cover the influence of time-
variant physical processes and nonlinearities.
This chapter reports recent advances in the numerical studies of car brake squeal
conducted at the University of Liverpool. The major contributions are a more realistic model
of the disc and pads interface (including surface roughness and wear), inclusion of the
thermal effect on the interfacial pressure distribution and implementation of transient analysis
of the vibration of the brake with the above thermal effect. Results have been drawn from the
PhD thesis of the first author, an MPhil thesis (Li, 2007) and most importantly a number of
recently published papers of the authors and their colleagues in the University of Liverpool.
For the recent advances in the studies of disc brake squeal worldwide, refer to a book written
by some established experts working in this area (Chen et al, 2005)
Recent Numerical Methodology
As mentioned before, most of the FE models of disc brakes are either validated at only
component level or a combination of the components and assembly levels. In the open
literature, it was found that the complex eigenvalue analysis and dynamic transient analysis
were typically employed by the brake research community to study their squeal noise issues.
These two methods require the results of the contact pressure for the subsequent analysis.
Therefore, it would be worthwhile to verify the static pressure distributions between
measured data and simulated results. These three validation stages (Abu-Bakar and Ouyang,
2008) have formed an improved methodology recently developed by the authors. Figure 1
shows the authors’ recent numerical methodology to study car disc brake squeal.
Recent Studies of Car Disc Brake Squeal 5
Finite Element Model
• Guide pins
• Brake pad
Disc Brake Assembly
Surface-based contact at disc/pad
- Pressure indicating film
Figure 1. Overall simulation scheme.
Development and Validation Process of an FE Model
This section will describe in detail the development and validation process of a disc brake
model throughout this research. The first validation stage is using modal analysis, in which
the natural frequencies and mode shapes will be compared with the experimental results. It
has two levels of validation, namely, components and assembly. The second validation stage
uses contact analysis in which static contact pressure distributions at piston and finger pads,
between simulated and measured are compared. There are a number of considerations that
should be taken into account in order to model disc brake components and assembly, and
simulate contact. These considerations are given in the subsequent sections. Chen et al
(2003b) put forward a systematic way of carrying out testing and validation from an
experimentalist’s point of view.
Abd Rahim Abu-Bakar and Huajiang Ouyang 6
Construction of a Disc Brake Model
Two commercial software packages are employed in order to generate the disc brake model
and to simulate different mechanical behaviour. A software package called MSC PATRAN
R2001 is utilised to generate elements and nodes of the disc brake. The advantages of using
this software include the ease of changing one element type to another, e.g., a linear 8-node
solid element (C3D8) to a quadratic 20-node solid element (C3D20), specifying contact
surfaces between the disc and pads, connecting components at interfaces with spring
elements, and simplifying geometry modifications. The software is also capable of generating
an input file that is compatible with ABAQUS v6.4, which will then be used to perform
subsequent analyses such as modal analysis, contact analysis and the complex eigenvalue
A detailed 3-dimensional finite element (FE) model of a Mercedes solid disc brake
assembly is developed. Figure 2(a) and 2(b) show the Liverpool rig of a real disc brake of
floating calliper design and its FE model respectively. The FE model consists of a disc, a
piston, a calliper, a carrier, piston and finger pads, two bolts and two guide pins. A rubber seal
(attached to the piston) and two rubber washers (attached to the guide pins) are not included
in the FE model. Damping shims are also not present since they have also been removed in
the squeal experiments. The FE model uses up to 8350 solid elements and approximately
37,100 degrees of freedom (DOFs). This figure excludes the spring elements that have been
used to connect disc brake components other than between the disc and pads.
The disc, brake pads, piston, guide pins and bolts are developed using a combination of
8-node (C3D8) and 6-node (C3D6) linear solid elements while the other components are
developed using a combination of 8-node (C3D8), 6-node (C3D6) and 4-node (C3D4) linear
solid elements. Element types in the brackets show the notation in ABAQUS nomenclature.
Details for each of the components are given in Table 1.
Figure 2. Disc brake assembly; (a) an actual disc brake (b) FE model.
Recent Studies of Car Disc Brake Squeal 7
Since the contact between the disc and the friction material surfaces is crucial, realistic
representation of those interfaces should be made. The friction material has a rougher surface
and is low in Young’s modulus than the disc, which has quite a smooth and flat surface, and
is less prone to wear. Therefore in this work, actual surfaces at macroscopic scale of piston
and finger pads are considered and measured. A Mitutoyo linear gauge LG-1030E and digital
scale indicator are used to measure and provide reading of the surface respectively as shown
in Figure 3. The linear gauge is able to measure surface height distribution ranging from
0.01mm up to 12 mm.
Table 1. Description of disc brake components
ELEMENT NO. OF
ELEMENTS NO. OF
C3D6 3090 4791
C3D6 416 744
Back plate C3D8
C3D6 2094 2716
Guide pin C3D8
C3D6 388 336
C3D6 80 110
Abd Rahim Abu-Bakar and Huajiang Ouyang 8
Figure 3. Arrangement of tools for surface measurement.
Prior to the measurement, the back plate must be flat and level. This can be confirmed by
taking four measurement points at both pad abutments and the indicator should show similar
height position. Node mapping, as shown in Figure 3, is required so that surface measurement
can be made at particular positions, which are nodes of the FE model. By doing this,
information that is obtained in the measurement can be used to adjust the coordinates of the
piston and finger pad nodes in the brake pad interface model. There are about 227 nodes at
the piston pad interface and 229 nodes at the finger pad interface. Since measurement is taken
manually, it takes about two and half hours to complete this for a single pad. In this work,
three pairs of brake pads (6 pieces) are measured, in which one pair of them are worn while
the rest are new and unworn. All the brake pads are from the same manufacturer. Thus, it is
assumed that the global geometry and material properties of the brake pad are the same. Upon
completion of the modelling, all the disc brake components must be brought together to form
an assembly model. Contact interaction between disc brake components is represented by
linear spring elements (SPRING 2 in the ABAQUS nomenclature) except for the disc/pads
interface where surface-to-surface contact elements are employed. This selection is due to the
fact that contact pressure distributions at the disc/pad interface are more significant than at the
contact interfaces of other components.
Figure 4 shows a schematic diagram of contact interaction that has been used in the disc
brake assembly model. A rigid boundary condition is imposed at the boltholes of the disc and
of the carrier bracket, where all six degrees of freedom are rigidly constrained in the rig.
Recent Studies of Car Disc Brake Squeal 9
Figure 4. Schematic diagram of contact interaction in a disc brake assembly.
The experimental study of structural vibration has made significant contributions to better
understanding of vibration phenomenon and for providing countermeasures in controlling
such phenomenon in practice. Typically, experimental observations always have two-fold
objectives (Ewins, 1984):
• Determining the nature and vibration response levels
• Verifying theoretical models and predictions
The first objective is referred to as a test where vibration forces or responses are
measured during a structure’s normal service or operation while the second is a test where the
structure or component is vibrated with a known excitation. The second test is much more
closely carried out under controlled conditions and this type of test is nowadays known as
modal testing or experimental modal analysis (EMA). There are two different methods of
comparison available to verify a theoretical model over EMA. They are a comparison in
terms of response properties and modal properties. Although response properties of a tested
structure can directly be produced in EMA, it is less convenient for some finite element
software packages when it comes to generate frequency response function (FRF) plots.
Furthermore, comparisons of modal properties are perhaps most common and convenient in
the current practice where natural frequencies and mode shapes (either graphical or
numerical) are used to obtain correlation between predicted and EMA results.
In this work, experimental modal analysis that was conducted by James (2003) was
utilised to verify the developed FE model. Natural frequencies and graphical mode shapes
obtained in the experiments are used to compare with the finite element results. Comparisons
are made at two levels, namely, models of disc brake components and an assembly model.
Firstly, FE modal analysis is performed at components level where the dynamic behaviour of
disc brake components in the free-free boundary condition is captured. The second stage is to
perform FE modal analysis on the disc brake assembly where the disc and the carrier are
mounted to the knuckle. A certain level of brake-line pressure is applied to the stationary disc
Abd Rahim Abu-Bakar and Huajiang Ouyang 10
brake. During the analysis a tuning process (also known as model updating) is required in
order to reduce relative errors between the predicted and experimental results. Normally,
material properties, such as density and spring stiffness, are tuned or adjusted for disc brake
components and assembly models respectively in order to bring closer predicted natural
frequencies to the experimental data.
All the components are firstly simulated in free-free boundary condition and there are no
constraints imposed on the components. Natural frequencies up to 9 kHz are considered since
this study takes into account squeal frequencies between 1~ 8 kHz. The finite element model
of the disc is validated by the authors and compared with the experimental data while the
material data of the other components were validated and provided by an industry source. It is
always desirable to validate all the components at once. This has not been done due to
limitation in the equipment and tools available in the laboratory. It is thought that laser
vibrometers can capture natural frequencies and mode shapes more accurately, as no contact
with the components is needed. This can reduce errors in measuring dynamic behaviour of the
components, compared with using accelerometers, which need to be attached to the
For the free-free boundary condition of the brake disc, a number of modes for up to
frequencies of 9 kHz are extracted and captured. There are various mode shapes exhibited in
the numerical results. However, only nodal diameter type mode shapes are considered
because they were found to be the dominant ones in the observed squeal events of this
particular disc brake. The calculated natural frequencies and mode shapes are given in Figure
5, which includes 2ND up to 7ND (nodal diameters). The number of nodal diameters is based
on the number of nodes and anti-nodes appearing on the rubbing surfaces of the disc. Using
standard material properties for cast iron the predicted frequencies are not well correlated
with the experimental results. Hence tuning of the density and Young’s modulus is necessary
to reduce relative errors between the two sets of results. Having tuned the material properties
the relative errors are shown in Table 2 and the maximum relative error is – 0.5%. The new
material properties after tuning are given in Table 3.
a) 2 nodal diameter mode at 932 Hz b) 3 nodal diameter mode at 1814 Hz
c) 4 nodal diameter mode at 2940 Hz d) 5 nodal diameter mode at 4369 Hz
Recent Studies of Car Disc Brake Squeal 11
e) 6 nodal diameter mode at 6070 Hz f) 7 nodal diameter mode at 7979 Hz
Figure 5. Mode shapes of the disc at free-free boundary condition.
Table 2. Modal results of the disc at free-free boundary condition
MODE 2ND 3ND 4ND 5ND 6ND 7ND
Test (Hz) 937 1809 2942 4371 6064 7961
FE (Hz) 932 1814 2940 4369 6070 7979
Error (%) -0.5 0.3 -0.1 0.0 0.1 0.2
Table 3. Material data of disc brake components
(kgm-3) 7107.6 7850.0 7918.0 7545.0 6997.0 7850.0 9720.0 2798.0
105.3 210.0 210.0 210.0 157.3 700.0 52.0 Orthotropic
ratio 0.211 0.3 0.3 0.3 0.3 0.3 0.3 -
The second stage of the methodology is to capture dynamic characteristics of the
assembled model. The previous separated disc brake components must be now coupled
together to form the assembly model. As discussed earlier in this chapter, a combination of
linear spring elements and surface-to-surface contact elements are used to represent contact
interaction between disc brake components and disc/pad interface, respectively. Table 4
shows details of disc brake couplings that are employed in the FE assembly model.
In the experimental modal analysis, a brake-line pressure of 1 MPa is imposed to the
stationary disc brake assembly. A similar condition is also applied to the FE brake assembly
Abd Rahim Abu-Bakar and Huajiang Ouyang 12
model. In this validation, measurements are taken on the disc as it has a more regular shape
than the other components. For the FE assembly model, spring stiffness values are tuned
systematically as follows:
• At the interface of any two components that allow sliding between them the
tangential spring constant is set at a very low stiffness, e.g., around 0.5 N/m.
Example of this is between the guide pin and the carrier as given in Table 4.
• At the interface of any two components that restrict movement in any directions, e.g.,
between the bolt and the calliper arm, the spring constant is set a very high stiffness,
e.g., around 1E+10 N/m.
• Any two interacting components that experience intermittent contact, e.g., the back
plate and the piston, the spring stiffness is set around 1E+6 N/m.
Table 4. Disc brake assembly model couplings
No Connections DOF Coordinate
1 Piston wall-Calliper housing 1 Local 66 1.00E+9
2 Piston- Back plate 1 Global 38 2.80E+6
3 Piston- Back plate 2 Global 38 2.80E+6
4 Piston- Back plate 3 Global 38 4.00E+6
5 Calliper finger- Back plate 1 Global 104 1.02E+6
6 Calliper finger- Back plate 2 Global 104 1.02E+6
7 Calliper finger- Back plate 3 Global 104 1.46E+6
8 Leading abutment- Carrier 1 Global 24 0.50E+0
9 Leading abutment- Carrier 2 Global 24 1.00E+9
10 Trailing abutment- Carrier 1 Global 24 1.00E+9
11 Trailing abutment- Carrier 2 Global 24 1.00E+9
12 Leading bolt- Calliper arm 1 Local 16 3.00E+10
13 Leading bolt- Calliper arm 2 Local 16 3.00E+10
14 Leading bolt- Calliper arm 3 Local 16 3.00E+10
15 Trailing bolt- Calliper arm 1 Local 16 3.00E+10
16 Trailing bolt- Calliper arm 2 Local 16 3.00E+10
17 Trailing bolt- Calliper arm 3 Local 16 3.00E+10
18 Leading guide pin- Carrier 1 Local 18 1.00E+9
19 Leading guide pin- Carrier 3 Local 18 0.50E+0
20 Trailing guide pin- Carrier 1 Local 18 1.00E+9
21 Trailing guide pin- Carrier 3 Local 18 0.50E+0
Recent Studies of Car Disc Brake Squeal 13
Once those spring constants are set, modal analysis is performed to obtain natural
frequencies of the disc and their associated mode shapes. A comparison is made between
predicted and experimental results of the disc. If there are large relative errors, the spring
stiffness values for linking two components need to be adjusted or updated. This updating
process is continued until the relative errors are reduced to an acceptable level. Since the
process is performed based on the trail-and-error process, it takes a lot of time and requires
engineering intuition to identify more influential springs and pick up appropriate spring
After a number of attempts, good agreements between predicted and experimental results
are achieved. Correlation between the two sets of frequencies that include 2ND up to 7ND of
the disc is given in Table 5. From the table, it is found that the maximum relative error is -
5.2%. These predicted results are based on the spring stiffness values given in Table 4. Mode
shapes of the FE assembly are described in Figure 6. The simulated FE modal analysis is able
to predict two frequencies at 3-nodal diameter as obtained in the experiments, which are
generated at 1730.1 Hz and 2151.1 Hz. While in the experiments these frequencies are found
at 1750.7 Hz and 2154.9 Hz. The highest relative error is found on a 6-nodal diameter mode,
for which the predicted frequency is 5837.1 Hz while the experimental frequency is 6159.0
Hz. The lower relative error is about – 0.1 % on the second 3-nodal diameter mode, for which
the frequencies are 2151.1 Hz and 2154.9 Hz in theory and in experiments respectively. In
this validation process, static friction coefficient (at pads/disc interface) also plays an
important role to reduce the relative errors. It is found that static friction coefficient of
give better correlation in the assembly model as described in Table 5.
a) 2ND at 1246.9 Hz b) 3ND at 1730.1 Hz
c) 3ND at 2151.1 Hz d) 4ND at 2966.2 Hz
Abd Rahim Abu-Bakar and Huajiang Ouyang 14
e) 5ND at 4445.7 Hz f) 6ND at 5837.1 Hz
g) 7ND at 8045.2 Hz
Figure 6. Mode shapes of the assembly model.
The third and final stage of the proposed methodology is to conduct experiments and
simulations of contact pressure distributions under static application of the disc brake (that is,
application of brake with no torque to or rotation of the disc). The experimental results will be
used to confirm contact pressure distribution predicted in the FE model. In this section, brake
pad models with real surface topography illustrated in Figures 7(a) ~ 7(c) are employed. The
new and unworn pad pairs are used in order to confirm the measurements taken from the
linear gauge and also to show the accuracy and reliability of the available tool.
Table 5. Modal results of the assembly measured on the disc
MODE 2ND 3ND 3ND 4ND 5ND 6ND 7ND
Test (Hz) 1287.2 1750.7 2154.9 2980.4 4543.7 6159.0 7970.0
FE (Hz) 1246.9 1730.1 2151.1 2966.2 4445.7 5837.1 8045.2
Error (%) -3.1 -1.1 -0.1 -0.4 -2.1 -5.2 0.9
Recent Studies of Car Disc Brake Squeal 15
Pad pair 1 (Worn)
Pad pair 2 (New)
c) Pad pair 3 (New)
Figure 7. Surface topography at the piston pad (left) and finger pad (right).
In order to capture static contact pressure (stationary disc), Pressurex® Super Low (SL)
pressure-indicating film, which can accommodate contact pressure in the range of between
0.5 ~ 2.8 MPa, is used. Pressure-indicating film is widely used to measure contact pressure
distribution or surface roughness in the automotive industry. Tests conducted before and after
a brake application often showed a noticeable difference between the measured pressure
distribution at the disc and pads interface (Chen et al, 2003b).
In the current investigation, the films are tested under certain brake-line pressures for 30
seconds and then removed from the disc/pad interfaces. Figure 8 shows an example of
pressure-indicating film before and after the contact testing. From the figure, the tested film
only provides stress marks without revealing its magnitude. Topaq® Pressure Analysis system
that can interpret the stress marks is then used. Configurations of the tested pad pairs are
given in Table 6.
Figure 8. Pressure-indicating films before (left) and after (right) the static contact pressure testing.
Abd Rahim Abu-Bakar and Huajiang Ouyang 16
Table 6. Configurations of tested pad
Identification Pad conditions Damping shim Brake-line pressure (MPa)
Pad pair 1 Worn No 2.5
Pad pair 2 New No 2.5
Pad pair 3a New No 2.5
Pad pair 3b New No 1.5
It is shown that contact pressure distributions for the worn pad (Pad pair 1) seem to be
concentrated (red colour) at the outer border region of the pads, while zero pressure exists at
the inner border region of the pads. It is also shown that contact pressure distributions of both
the piston and finger pads are asymmetric. This might be due to irregularities in the surface
topography of the friction material. Contact pressure distributions of the worn pad are shown
in Figure 9(a). The red colour shows the highest contact pressure. Areas in contact for the
piston and finger pads are 1.436e-3m2 and 1.484e-3m2 respectively.
For the new and unworn pads, i.e., Pad pair 2 and Pad pair 3a that come from the same
box and the same manufacturer, it is seen that they have different contact pressure
distributions both at the piston and finger pad surfaces as shown in Figures 9(b) and 9(c).
These variations are due to the surface topography as shown in Figure 7. It is also seen from
figure 9(b) that contact pressures of Pad pair 2 are distributed more evenly than Pad pair 3a.
There is contact at the trailing edge for Pad pair 2. But there seems to be a loss of contact in
that region for Pad pair 3a. The areas of contact for the piston and the finger pads are 1.361e-
3 m2 and 1.069e-3 m2 respectively. From Figure 9(c), the contact pressure seems to be zero at
the centre of the pads. Most of the highest contact pressures appear at the outer border of the
pads. Areas in contact for Pad pair 3a are 8.090e-4m3 and 9.230e-4m2 for the piston and the
finger pads respectively.
By applying different levels of brake-line pressure, the higher the pressure the bigger the
contact areas should be generated. This is illustrated in Figure 9(d) where the areas of highest
pressure are reduced significantly in comparison with Figure 9(c). It is also confirmed that the
areas of contact for the piston and the finger pads are reduced to 6.370e-4 m2 and 6.857e-4 m2
respectively. This means a reduction of about 21% and 26% for the piston and the finger pads
a) Pad pair 1 b) Pad pair 2
Recent Studies of Car Disc Brake Squeal 17
c) Pad pair 3a d) Pad pair 3b
Figure 9. Analysed images of the tested pads: piston pad (left) and finger pad (right) in MPa. Top of the
images are the leading edge.
In the FE contact analysis, the brake pad models are similar to those used in the contact
tests. Now the real surface profile of the brake pads are considered in the sense that the
surface profile information is incorporated in the FE model of the brake pad surface by
adjusting its surface coordinates in the normal direction. Similar configurations of the test are
also adopted in order to make comparison between the two sets of results, predicted versus
The first contact simulation is performed on the worn pad or Pad pair 1 at a brake-line
pressure of 2.5 MPa. It can be seen in Figure 10(a) that the areas in contact are almost the
same as those found in the experiment. Predicted contact areas in the contact analysis are
1.441e-3m2 and 1.784e-3m2 for the piston and the finger pads respectively. The results
suggest that there is fairly good agreement between the two as illustrated in Figure 11. The
contact area of the piston pad seems closer to the experimental one, compared with the finger
The second contact simulation is done for Pad pair 2, which is subjected to the same
brake-line pressure. From Figure 10(b) the contact pressure seems to be biased towards the
outer radius of the pads. These patterns are most likely to be the same for those obtained in
Figure 9(b). In the simulation it is found that the contact areas for the piston pad are 8.476e-
4m2 and for the finger pad is 8.131e-4 m2. These contact areas are smaller than those
measured in the experiments. However, quite reasonable correlations against the experimental
results are obtained especially at the finger pad as described in Figure 11.
The third contact analysis is simulated for Pad pair 3a, subjected to the same brake-line
pressure. Predicted areas of the highest contact pressure are in good agreement with the
experimental results. Contact pressure distribution of Pad pair 3a is illustrated in Figure 10(c).
For Pad pair 3a, predicted contact areas are 1.046e-3 m2 and 1.020e-3 m2 for the piston and
the finger pads respectively. It can be seen from Figure 11 that the difference in the finger pad
is small while there is a quite large difference at the piston pad. However, overall, fairly good
agreement is achieved between predicted and experimental results.
The last contact analysis is similar to the third except under a different brake-line
pressure of 1.5 MPa applied to the assembly model. The predicted areas in contact should be
smaller than those predicted in the third analysis and are shown in Figure 10(d). Once again,
good correlations are achieved between predicted and experimental results in terms of areas
Abd Rahim Abu-Bakar and Huajiang Ouyang 18
of the highest contact pressure. The locations of different levels of the contact pressure
distribution are almost identical to the experimental one. In the contact simulation, it is
predicted that the contact areas of the piston pad and the finger pad are 5.943e-4 m2 and
6.860e-4 m2. These values are nearly the same as those measured in the experiment. Figure 11
shows that there are small differences in the contact area for both the piston and the finger
a) Pad pair 1 b) Pad pair 2
c) Pad pair 3a d) Pad pair 3b
Figure 10. Predicted contact pressure distribution: piston pad (left) and finger pad (right) in Pascal. Top
of the diagrams are the leading edge.
Figure 11. Comparison between experiment and FE analysis in the contact area.
Recent Studies of Car Disc Brake Squeal 19
Contact Pressure Distributions
At the contact interface of disc and brake pads, friction induces wear and heat during braking
applications. Wear is one of the distinct aspects of brake systems that influence the contact
pressure distribution, and itself is affected by the surface roughness of the components in
sliding contact. Temperature is another distinct aspect and it normally rises up at some local
area and thermal deformation of these areas occurs. Due to thermal deformation, the pressure
distribution is also affected. Thermal and mechanical deformations affect each other strongly
and simultaneously. This section looks into the effects of wear and temperature on contact
When two solid bodies are rubbed together they experience material removal, i.e., wear. In
engineering applications the wear depth is a function of normal pressure, sliding distance and
specific wear coefficient and other factors. Rhee (1970) in his study showed that the wear rate
of most friction materials could be given as follows:
cba tvkFW =∆ (1)
where W∆ is the wear volume, F is the contact force, v is the sliding speed, t is the time and
k is the wear constant which is a function of the material and temperature. a, b and c are
constants that should be determined experimentally and c is usually close to unity. This
original formula however cannot be used in the present investigation. Since mass loss due to
wear is directly related to the displacements that occur on the rubbing surface in the normal
direction, Rhee’s wear formula is then modified as:
atΩrkPh =∆ (2)
where h∆ is the wear displacement, P is the normal contact pressure,
is the rotational disc
speed (rad/s), r is the pad mean radius (m) and a, b and c are all constants which remain to be
determined. In incorporating wear into the FE model, the methodology that was proposes by
Podra et al (1999) and Kim et al (2005) is adopted in this work. Bajer et al (2004) also
performed wear simulation particularly for a disc brake. They used ABAQUS v6.5 and
adopted a very simple wear model, i.e., a function of wear rate coefficient and contact
pressure. On the other hand, Abu-Bakar et al (2005a) simulated wear progress over time
using Equation (2) and assumed all constants were unity. In simulating wear, contact analysis
is firstly performed in order to determine the normal contact pressure generated at the piston
and the finger pads interface. Using Equation (2), wear displacements/depths are calculated
based on the following parameters:
1. Predicted contact pressure generated in the contact analysis, P
2. Sliding time, t
3. Specific wear rate coefficient, k
Abd Rahim Abu-Bakar and Huajiang Ouyang 20
4. Pad effective mean radius, r
5. Rotational speed,
Figure 12. Flow chart of proposed wear simulation.
As a case study, Pad pair 2 in Table 6 is used to observe wear evolution on the brake pad
interface. In the wear analysis, a rotational speed is maintained at 6 rad/s and the total braking
Recent Studies of Car Disc Brake Squeal 21
time is set to 4800s (8 minutes). The seemingly short duration of wear tests is due to a
numerical consideration. In the wear formula of Equation (2), the duration of wear, t, must be
specified. The longer the duration of wear, the more the dimensional loss and the greater
change of the contact pressure. However, if t is too big, there will be numerical difficulties in
an ABAQUS run. It has been found through trial-and-error that t = 200 s gives reasonably
good results and good efficiency. Consequently a simulation of 80-minute wear means
twenty-four ABAQUS runs. In line with this numerical consideration, wear tests have not
lasted for numerous hours as normally done in a proper wear test or a squeal test. In theory,
however, numerical simulations of wear may cover an arbitrary length of time. A constant
specific wear rate coefficient is assumed for all braking applications and is set to k = 1.78e-
13m3/Nm (Jang et al, 2004) and the effective pad radius is r = 0.11m. Then, based on the
calculated wear displacements at steady state, a new surface profile for the piston and the
finger pads is created. Figure 12 shows the overall procedure of wear simulation that has been
used by the authors.
During this wear calculation all constants in Equation (2) need to be determined. Having
simulated for various values of constants a, b and c, it is found that the wear formula below
gives reasonably good results.
In Equation (3),
′ is the maximum allowable braking pressure (8MPa for a passenger
car) and Nm/m109.2 37
×=k. Figures 13 and 14 show measured and predicted static
contact pressure distributions at the piston and finger pads, respectively. It can be seen that
most locations of the highest contact pressure (in red colour) predicted are at the outer region
of the brake pads and these are almost identical to the measured data shown in Figure 13. It is
also seen that areas in contact increase as braking duration approaches 80 minutes described
in Figure 15. From the figure, the initial contact areas are predicted as about 7.0e-4 m2 for
both pads and then are predicted as much as 2.9e-3 m2 in the final stage of braking duration.
This is an increase by more than four folds.
Due to wear progress, it is found from the FE analysis that the surface profile of the brake
pads becomes smoother after 80 minutes of wear, as shown in Figures 16(a) and 16(b). As a
result, greater areas of the brake pads come into contact with the disc surface, as also
illustrated in Figures 13 and 14. Graphs in Figure 16 are axial coordinates of the nodes that
form the circumferential centre lines of the pads. It is shown that at the early stage of braking
application, i.e., within 10 – 20 minutes, the axial coordinates change slightly overall in
comparison with the new (unworn) brake pads. Having completed 80 minutes of braking
application the surface height seems to level off and hence implies that some initial rough
patches have been worn out to form smoother ones.
Abd Rahim Abu-Bakar and Huajiang Ouyang 22
New After 10minutes
After 20 minutes After 80 minutes
After 20 minutes After 80 minutes
Figure 13. Measured contact pressure distribution: piston pad (left) and finger pad (right) in MPa. Top
of the diagrams are the leading edge.
New After 10 minutes
Recent Studies of Car Disc Brake Squeal 23
After 20 minutes After 80 minutes
Figure 14. Predicted contact pressure distribution: piston pad (left) and finger pad (right) in Pascal. Top
of the diagrams are the leading edge.
Figure 15. Predicted contact area for different braking application.
Abd Rahim Abu-Bakar and Huajiang Ouyang 24
a) Piston pad
b) Finger pad.
Figure 16. Predicted surface profile due to wear.
In a disc brake system, the brake pads are pressed against the disc in order to generate friction
and therefore to slow down the vehicle. Once friction occurs, it induces a large amount of
Recent Studies of Car Disc Brake Squeal 25
heat in the system. Therefore, thermal effects should be one of the most important aspects,
which is likely to affect squeal generation in a disc brake system. Due to the complex
phenomenon of heat transfer and the difficulty of numerical modelling, thermal effects have
largely been ignored in the past research into disc brake squeal. However, there were a few
researchers who studied thermal characteristics in brakes for purposes other than studying
brake squeal in the past. Day and Newcomb (1984) investigated the friction-generated heat
energy dissipated from the contact interface. Brooks et al (1993) looked into the brake judder
phenomena by using thermo-mechanical finite element model. Kao et al (1994) studied
thermo-elastic instability of disc brake system. Qi et al (2004) investigated temperature
distributions at the friction interface. Recently, Trichěs et al (2008) and Hassan et al (2008)
incorporated thermal effects in complex eigenvalue analysis to investigate instability of the
disc brake assembly.
There are two aspects of thermal effects, namely, thermal deformation and temperature
dependence of material properties. Take contact as an example. If thermal deformation is
considered, then the contact area changes and pressure distribution also becomes different. As
mentioned before, thermal deformation effects are considered in the present work and thermal
analysis is implemented in the baseline model. Therefore, it requires the use of elements with
both temperature and displacement degrees of freedom. The elements of disc and brake pads
are meshed with C3D6 (solid 3-dimensional 6-nodes element) and C3D8 (solid 3-dimensional
8-nodes element) in the baseline disc brake finite element model. These elements are now
replaced by C3D6T and C3D8T, which include the temperature degree of freedom. However,
there is a limitation of ABAQUS software package regarding the element types. Specifically
C3D8T is not available in ABAQUS/Standard version but is available in ABAQUS/Explicit
version. There are two ways to deal with this problem: either creating a new FE model using
those elements available in an ABAQUS/Standard version that allows thermal analysis or
using ABAQUS/Explicit version instead. The former approach is considered a very difficult
task and time-consuming. On the other hand, heat transfer is a transient process and as a result
temperature varies with time. Therefore, dynamic transient analysis in ABAQUS/Explicit
version is considered a more suitable analysis method to simulate the squeal generation under
thermal loading and therefore the latter approach is adopted.
In order to determine the temperature distribution in a medium, it is necessary to solve
the appropriate form of heat transfer equation. However, such a solution depends on the
physical conditions existing at the boundaries of the medium and on conditions existing in the
medium at some initial time. To express the heat transfer in the disc brake model, several
thermal boundary conditions and initial condition need to be defined. As shown in Figure 17,
at the interface between the disc and brake pads heat is generated due to sliding friction,
which is shown in blue colour. In this work, it is assumed that all the mechanical energy is
converted into thermal energy. Al-Bahkali and Barber (2006) noted that the heat flux due to
friction could be expressed as
is the friction coefficient, V is the sliding velocity of the disc and p represents the
contact pressure at the interface.
Abd Rahim Abu-Bakar and Huajiang Ouyang 26
For the exposed region of the disc and brake pads, it is assumed that heat is exchanged
with the environment through convection. Therefore, convection surface boundary condition
is applied there (shown in red colour in Figure17). This can be expressed as
where h is convection heat transfer coefficient, k is thermal conductivity, and ∞
atmosphere temperature and T(0,t) is the temperature at that boundary denoted by 0=x.
Finally, at the surface of the back plate, adiabatic or insulated surface boundary condition
is used and shown in black colour in Figure 17. This can be expressed as
Figure 17. Boundary Condition of Thermal Analysis.
which means there is no heat transfer through the back plate into other disc brake
components. This simplification removes the need to define the convection surface boundary
condition of the exposed regions of the other components and is mainly a numerical
consideration. Lin (2001) and Al-Bahkali and Barber (2006) used the same boundary
conditions in their models. This simplification should be sufficient for short braking
application where heat can hardly propagate far when squeal may occur already. It should
also be noted that Equations (5) and (6) describe one-dimensional heat transfer for the sake of
explanations and three-dimensional heat transfer is actually simulated in the authors’
research. The initial condition of the model is 20oC at every node of the disc and brake pads.
The atmosphere temperature is also 20oC all the time.
Table 7 lists the thermal properties of the disc and brake pads and all these data are from
Lin (2001). However, it turns out that using those appropriate values of thermal properties
leads to exceedingly long computing time. A typical example of thermal analysis of the disc
brake system takes a few weeks to finish. To overcome this problem, Choi and Lee (2003)
used a value of specific heat that is much lower than the realistic value and found that much
Recent Studies of Car Disc Brake Squeal 27
faster convergence to the steady state in the transient thermo elastic analysis could be
achieved. Therefore, a much smaller value of specific heat capacity (20 J/kg K) is also
adopted here instead.
A comparison is made between the contact pressure distributions with and without
thermal effects. Figure 18 is the results of the contact pressure distribution with thermal
effects. Figure 19 shows the contact pressure distribution without thermal effects. These
results are obtained at Ω = 100 rad/s and P = 1 MPa. Comparing these two figures, the
pressure distribution is different. The FE model with thermal effects shows that the contact
pressure at the piston pad is spreading towards the leading edge, compared with the trailing
edge for the FE model without thermal effects. For the finger pad, it shows that a larger
contact area is established at the trailing edge with the thermal effects, compared with the FE
model without thermal effects. The contact pressure is also higher in the model with thermal
effects, which is 10.67 MPa, than the model without thermal effects, which is 6.83 MPa.
Figures 20 and 21 are another example with Ω = 50 rad/s and P = 1 MPa. These two figures
also show that the contact pressure at the piston and the finger pad is higher with the inclusion
of thermal effects than the model without thermal effects. Distributions of contact pressure
are also seen significantly different between the two models.
Table 7. Material thermal properties data of disc and brake pads
Disc Brake pad
Thermal Conductivity (W/m K) 46.73 2.06
Specific Heat (J/kg K) 690.8 749
Thermal Expansion Coefficient 10-6 (1/K) m2 6.6 14.3
Figure 18. Pressure distribution with thermal effects in 100 rad/s and 1 MPa.
Abd Rahim Abu-Bakar and Huajiang Ouyang 28
Figure 19. Pressure distribution without thermal effects in 100 rad/s and 1 MPa.
There are two major numerical methods used in the studies of brake noise by researchers,
namely, complex eigenvalue analysis and dynamic transient analysis. The advantages and
limitations of both methods were commented by Mahajan et al (1999) and Ouyang et al
(2005). In recent years, the dynamic transient analysis is gradually gaining popularity. A
number of researchers pioneered this approach in their studies of squeal behaviour (Chargin
et al, 1997, Hu and Nagy, 1997, Hu et al, 1999, Mahajan et al, 1999). Massi and Baillet
(2005), Abu-Bakar and Ouyang (2006), Massi et al (2007) and Abu-Bakar et al (2007)
furthered this approach. However, none of them considered thermal effects. Dynamic
transient analysis in ABAQUS v6.4 is the approach used in this investigation into the
vibration of the finite element disc brake model. ABAQUS uses central difference integration
rule together with the diagonal lumped mass matrices. The following finite element equation
of motion is solved:
)( ffxM tt
At the beginning of the increment, accelerations are computed as follows:
)( ffMx tt
&& is the acceleration vector, M the diagonal lumped mass matrix, ex
f the applied load
vector and in
f the internal force vector. The superscript t refers to the time increment.
Recent Studies of Car Disc Brake Squeal 29
Figure 20. Pressure distribution with thermal effects in 50 rad/s and 1 MPa.
Figure 21. Pressure distribution without thermal effects in 50 rad/s and 1 MPa.
Abd Rahim Abu-Bakar and Huajiang Ouyang 30
Time step, t
Time step, t
Figure 22. Time history of brake-line pressure and rotational speed.
The velocity and displacement of the body are given in the following equations:
tttt tt xxx &&& ∆+∆
)5.0()()()( ttttttt t∆+∆+∆+ ∆+= xxx & (10)
where the superscripts )5.0( tt ∆− and )5.0( tt
refer to mid-increment values. Since the
central difference operator is not self-starting because of the mid-increment velocity, the
initial values at time t = 0 for velocity and acceleration need to be defined. In this case, both
values are set to zero as the disc is stationary at time t = 0.
The time history of the brake-line pressure and rotational speed are used for describing
operating conditions of the disc brake model, as shown in Figure 22. At the first stage, a brake
pressure is applied gradually until it reaches t1 and then it becomes constant. The disc starts to
rotate at t1 and gradually increases up to t2. Then the rotational speed becomes constant too.
As a case study, two different operating conditions are considered in order to observe
squeal behaviour in the disc brake assembly. The objective of this investigation is to reveal
how thermal aspects affect squeal behaviour. Thus, a comparison between the disc brake
model with and without thermal effects is made in this section. Figures 23 and 24 show the
results of disc brake model with thermal effects at Ω = 50 rad/s and P = 1 MPa. Figure 25 and
Figure 26 show the results from the model without thermal effects. From these figures, it is
found that the vibration amplitude for the model with thermal effects is higher than the model
without thermal effects. Moreover, the patterns of vibration of both examples are also
different. However, the highest frequency components in these examples both are around
1200 Hz. Other examples are shown in Figures 27, 28, 29 and 30. The operational conditions
are Ω = 50 rad/s and P = 0.5 MPa. The vibration amplitude also increases in the model with
thermal effects compared with the results from the model without thermal effects. The highest
frequency components both are around 1400 Hz this time. All these examples indicate that
Recent Studies of Car Disc Brake Squeal 31
thermal effects do affect the vibration level of disc brake system and therefore are very likely
to affect the squeal generation. Therefore, it would be worthwhile to include thermal effects
in the prediction of disc brake squeal.
Figure 23. Time history of acceleration at a particular node with thermal effects (50 rad/s and 1 MPa).
Figure 24. Frequencies after converting from time domain with thermal effects (50 rad/s and 1 MPa).
Abd Rahim Abu-Bakar and Huajiang Ouyang 32
Figure 25. Time history of acceleration at a particular node without thermal effects (50 rad/s and 1
Figure 26. Frequencies after converting from time domain without thermal effects (50 rad/s and 1
Recent Studies of Car Disc Brake Squeal 33
Figure 27. Time history of acceleration at a particular node with thermal effects (50 rad/s and 0.5 MPa).
Figure 28. Frequencies after converting from time domain with thermal effects (50 rad/s and 0.5 MPa).
Abd Rahim Abu-Bakar and Huajiang Ouyang 34
Figure 29. Time history of acceleration at a particular node without thermal effects (50 rad/s and 0.5
Figure 30. Frequencies after converting from time domain without thermal effects (50 rad/s and 0.5
Recent Studies of Car Disc Brake Squeal 35
This chapter outlines recent studies into car disc brake squeal conducted at the University of
Liverpool since 2004. The focus is on the numerical analysis using the finite element method.
The simulation results are supported with measured data in order to verify predictions. An
improved numerical methodology is presented by considering three-validation stages,
namely, modal analysis at component and assembly levels and verification of contact
analysis. Prior to that, a realistic surface roughness of the brake pad at macroscopic level is
considered in the finite element model instead of assuming a smooth and perfect surface that
has been largely adopted by most previous researchers. These two aspects have brought about
significant improvement to the validation as well as analysis. Wear and thermal effects are
other distinct aspects of disc brakes that influence contact pressure distributions and squeal
generation in a disc brake assembly and they are also included in the current investigation.
Transient analysis of disc brake vibration using a large FE model that includes thermal effects
is carried out for the first time.
Some of the work reported in this chapter has been financially supported by TRW
Automotive, Sensor Products LLC and Universiti Teknologi Malaysia. A number of people
have helped this work at Liverpool, notably Dr S. James, Dr Q. Cao and Dr H. Tuah. Their
contributions are gratefully acknowledged. Dr Tie Li of Ford at Basildon and Dr Frank Chen
of Ford at Dearborn have kindly provided some papers.
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