Tirovic1991

137
Disc brake interface Dressure distributions
M Tirovic, MSc, Dipl-Ing
Faculty of Mechanical Engineering, Belgrade University,Belgrade,Yugoslavia
A J Day, MA, PhD, CEng, MIMechE, MPRI
Department ofMechanical and Manufacturing Engineering, University of Bradford
The nature of the contact and pressure at the interface between thefriction material pad and the disc rotor of a ‘spot’-typedisc brake
affects the performance of a brake in terms of torque, temperature distributions and wear. Interface contact and pressure distributions
have been predicted for a particular design offloating caliper passenger car disc brake, using three-dimensional finite element analysis
under static and dynamic brake actuation conditions.
The influence of friction material compressibility, pad backplate thickness, co&cient of friction, caliper flexure, disc stiflness and
actuating piston contact with the piston bore on the interface pressure distribution is examined. The eflect upon brake performance is
discussed in terms of ‘centre of pressure’ and corresponding braking torque, and in terms of observed eflects such as temperature and
wear distribution. The results confirm that in order to ensure consistent disc brake pe$ormance the interface pressure distribution
should be carefully controlled by designing in mechanical rigidity, compliant friction materials and minimum compliance during brake
operation.
NOTATION
b pad width (mm)
D disc diameter (mm)
E’ friction material Young modulus (N/mm2)
f friction material thickness (mm)
h backplate thickness (mm)
I pad length (mm)
rN nominal mean rubbing radius (mm)
p coefficientof friction
v friction material Poisson ratio
1 INTRODUCTION
Disc brakes operate by generating a frictional retarding
force between a frictional material stator, in the form of
a pad or annulus, and a rotor in the form of an annular
disc. Contact between the friction material and the
rotor is generally considered to occur over the full
surface area of the stator, for example the friction
surface of a disc pad, but in practice incompletecontact
may be observed. Even if full contact is achieved, the
interface pressure between the stator and rotor is not
necessarily uniform, and the distribution of interface
pressure is known to be important in the successful
design and operation of all types of friction brake. This
has become even more important recently with the
interest in larger, heavier duty disc brakes for road and
rail use.
The subject of interface pressure distributions in
brakes has been studied for several years. Much of the
associated research has covered drum brakes (1-3), but
the first published research investigating pressure dis-
tributions in a disc brake was by Harding and Wintle
(4). They studied flexural effects in the brake pad
assembly both theoretically and experimentally, using
the theory of beams on elastic foundations and the finite
element method, applied to two-dimensional models.
Tirovic (5) investigated the influence of mechanical and
The MS was received on 21 March 1990 and was acceptedfor publication on 24
April 1991.
DO0890 Q IMechE 1991 0954-4070,
thermal loads on pad deflection, considering a two-
dimensional model of a disc brake pad for a passenger
car. Tirovic and Todorovic (6)presented an analysis of
pad distortions and pressure distributions for a large
brake pad from an air actuated CV disc brake. This was
a three-dimensional analysis with mechanical and
thermal loads, which confirmed earlier two-dimensional
results and the importance of the brake and actuator
design in determining the interface pressure distribu-
tion.
From these considerations (and others) it has been
proposed (7)that pressure and contact at the brake fric-
tion interface can be considered at three levels. The first
relates to large-scale pressure variation over the full
rubbing surface, and is induced by bulk deformation
(usually flexural) effects in the application of actuation
forces. The second relates to ‘macroscopic’ interface
pressure variation, that is finite sized but localized
variations in contact and pressure, arising from local-
ized deformation or distortion of the rubbing surfaces.
The third represents frictional contact on the micro-
scopic scale and is fundamental to the study of friction
and wear. The two first levels are within the control of
the brake designer, while the third is constrained by the
basic tribological characteristics of the chosen friction
pair. In many cases large-scale pressure variation effects
(first level) actively cause macroscopic pressure varia-
tion (second level), but the mechanism by which such
variations are generated and promoted is based upon
the principles of thermoelasticinstability(8).
There is no experimental method available for the
direct measurement of dynamic interface pressure dis-
tribution in brakes, but static pressure distributions
have been measured in disc brakes. Dubensky (9)used
pressure-sensitive paper and Tumbrink (10) used the
ball pressure method; both gave indications of large-
scale pressure variation and confirmed predicted results
elsewhere.
This paper summarizes recent research work related
to the distribution of contact and pressure at the fric-
tion interface of disc brakes and is the second of a series
of three papers emanating from the first brakes work-
191 $2.00 +.05 Proc Instn Mech Engrs Vol 205
at University of Bath - The Library on July 1, 2015pid.sagepub.comDownloaded from

138 M TIROVIC AND A J DAY
Fig. 1 Disc brake caliper assembly
shop held at the University of Bradford in November
1989. Bulk deformation in the disc brake assembly
occurs by (a) flexural effects in the pad assembly, (b)
flexure of the disc and (c) flexure of the caliper, and
these have been studied using finite element analysis as
described next. The results presented are mainly based
upon a floating type of caliper disc brake for a pass-
enger car, as shown in Fig. 1and detailed in Table 1.
2 EFFECT OF FRICTION MATERIAL
COMPRESSIBILITY
21 Background
The compressibilityof the friction material is one of the
major factors influencing the pressure distribution at
the friction interface of any brake. In general, a softer
(lower compression modulus) friction material is prefer-
able, but the lining has to satisfy many other demands
as well, viz. high coefficient of friction, fade resistance
and wear resistance, and compromises are necessary.
According to Harding and Wintle (4) the compress-
ibility of friction materials used in disc brake pads can
vary from E = 500 to nearly loo00 N/mm2, but the
most commonly used disc pad materials for passenger
cars lie in the region of E = 1500N/mm2. Day et al. (3)
give a lower value of E' = 300 N/mm2 for a drum brake
lining. Friction material properties are notoriously difi-
cult to measure and categorize, but it is generally
accepted that linear elastic behaviour can safely be
assumed for small compressive strains (less than 5 per
cent). The importance of temperature dependence of
friction material properties was investigated by Day (2).
22 Method ofanalysis
The effect of friction material compressibility on the
interface pressure distribution has been examined by
finite element analysis of the model shown in Fig. 2.
Table 1 Disc brake assembly details
Disc diameter D
Nominal mean rubbing radius rN
Pad length I
Pad width (maximum) b
Backplatethickness h
Friction material thickness f
Friction material Young modulus E'
Friction material Poisson ratio v
Coefficient of friction p
Part D: Journal of Automobile Engineering
221 mm
94 mm
91 mm
31 mm
5 mm
12 mm
1500 N/mm2
0.25
0.38
Fig. 2 Pad/pistonFE model
This model of a complete pad and backplate
used 233 solid elements (eight-noded brick
assembly
and six-
noded wedge), a total of 408 nodes. Actuating forces
were applied through a separate finite element model of
the caliper piston, the detailed contact conditions
between the piston and backplate being modelled using
'spar' elements. The force applied to the pad was
reacted by the disc which was considered to have infin-
ite stiffness (rigid).The static pressure distribution (that
is with no dynamicfriction drag on the pad surface)was
calculated allowing only compressive forces to be trans-
mitted at the friction interface.
2.3 Results ofanalysis
An hydraulic actuating pressure of 80 bar was applied
to the piston; this would be roughly equivalent to a
vehicle deceleration of 7 m/s2.The distorted pad model
for the standard pad characteristicsis shown in Fig. 3.
The interfacepressure distributionsfor three values of
lining compressibility (see Table 2) are shown in Fig. 4
Fig. 3 Pad distortion under 80 bar hydraulic actuationpres-
sure
@ IMechE 1991

DISC BRAKE INTERFACE PRESSURE DISTRIBUTIONS 139
Table 2 Friction material compressibility
Figure 4a 3 and4b 4c
Friction material
Young modulus E (N/mm2) 300 1500 loo00
Backplate thickness h (mm) 5 5 5
(the model is symmetrical about the pad centre-line).
The results for the static case are linear; that is halving
the actuating force halves the interface pressure at any
point on the friction surface.
Referring to Fig. 4, it can be seen that the length of
friction material in contact with the disc depends upon
the friction material compressibility. Ideally the full
length of the pad will be in contact, and this is best
achieved with the most compressible friction material.
For the standard friction material only 75 per cent of
the pad surface area is in contact, and for a stiff friction
material this is reduced to 60 per cent. These results are
in agreement with the ‘beam on elastic foundation’
analysis (4), and the interface contact area size is not
affected by the actuation force.
3 EFFECT OF BACKPLATE STIFFNESS
3.1 Background
Automotive pad backplates are usually made of mild
steel with the Young modulus in the region of
2.1 x lo5N/mm2. A stiffer backplate, usually achieved
by increasing backplate thickness, is known to give a
more uniform pressure distribution, but thinner back-
plates are preferred because of lower mass and cost of
the pad assembly.
3.2 Results of analysis
The finite element model described in Section 2.2 was
used to calculate the static interface pressure distribu-
tions for different backplate stiffnesses,using backplates
of different thicknesses and friction material Young
modulus as shown in Table 3. The results are presented
in Figure 5.
Fig. 4 Static interface pressure distributions for different
compressibility backplatethickness
Fig. 5 Static interface pressure distributions for different
Proc lnstn Me& Engrs Vol 205Q IMechE 1991

Table 3 Pad backplate thickness
Figure 5a 5b 5c
Friction material
YoungrnodulusE’(N/mm*) 300 1500 IOOOO
Backplatethickness h (mm) 4 4 6
Comparison of Fig. 5a and b shows that, for the same
backplate thickness, the length of contact between the
pad and disc is reduced by about 30 per cent. This is for
the inboard brake pad (actuated by the 45 mm diameter
caliper piston) and assumeslinear elastic behaviour and
perfect initial contact. This is taken to mean that the
friction surfaces of the pad and disc are perfectly aligned
when they are just brought together (7); subsequent
actuation pressure causesinterface contact and pressure
distributions to vary (4). Obviously this contact will be
affected by wear, and this is discussed later in Section
7.4. Figure 5c illustrates that for a sixfold increase in
friction material stiffness (1500-10 OOO N/mm2) the
backplate thickness must be increased by 50 per cent
(4-6 mm) to maintain the length of contact the same as
in Fig. 5b. Although 10000N/mm2 is the maximum
stiffness expected in practical (resin-bonded composite)
friction material (4), these results confirm the impor-
tance of matching backplate stiffness (thickness) to the
frictionmaterial stiffness.A full treatment of the effect of
contact length can be found in the original work of
Harding and Wintle (4).
4 EFFECT OF FRICTION COEFFICIENT
4.1 Background
So far the analyses have dealt with the static case only,
but the dynamic pressure distribution has also been
analysed. The finite element model (Fig. 2) was used
with friction forces introduced at the pad/disc interface
by multiplying the nodal reaction forces at the interface
by the coefficient of friction. Appropriate constraints at
the pad backplate abutments were used to ensure realis-
tic backplate/caliper contact.
4 2 Results
The dynamic contact and pressure distributions have
been predicted for the p values shown in Table 4, and
some results are shown in Fig. 6. These indicate that the
leading part of the pad maintains contact while the
trailing part loses contact over the last 20 per cent of its
length (p= 0.38). The peak lining pressure has increased
from 9 to 12 MN/m’, at a position on the trailing part
of the pad adjacent to the slot. In the radial direction
the position of the ‘centre of pressure’ (for constant
dynamic friction) was unchanged, giving a mean
rubbing radius of 94.7 mm in all three cases (Fig. 6).
Table4 Friction coefficient
Figure 6a 6b 6c
Friction material
YoungrnodulusE’(N/mmz) 1500 1500
Backplate thickness h (mm) 5 5 5
Coefficient of frictionp 0.30 0.38 0.46
(assumed contact)
5 EFFECT OF CALIPER FLEXURE
5.1 Background
So far only bulk deformation effects in the disc brake
pad assembly have been considered. Large-scale inter-
face pressure variations may also occur due to caliper
distortion and deflection under operational loads. The
finite element model has been extended to include the
caliper and the pad assembly on the (non-piston)side of
the floating caliper. A further complication is compli-
ance and clearance in the mounting frame, sliding and
actuation components,which have not been included in
the analysis.
5.2 The finite element model
The finite element model used for this part of the
analysis is illustrated in Fig. 7, and consists of the
caliper, piston and both pads. The floating part of the
caliper is made of aluminium alloy (E = 8 x lo4N/
mm’) and transmits actuating forces only; braking
torque is reacted from the caliper mountings. The
piston part of the mesh was redefined to the exact
geometry of the actuating piston. Contact between the
piston and the ‘inboard‘pad backplate and between the
caliper and the ‘outboard’ pad backplate was modelled
using ‘spar’ elements (which allow only compressive
forces to be transmitted across the contact). Contact
between the piston and the piston bore in the caliper
was modelled using ‘gap’elements to simulate clearance
in the bore.
Only static actuation of the brake was considered in
the analysis (no brake torque generated), which thus
required, by symmetry, only half of the brake assembly
to be modelled. An hydraulic actuating pressure of
80 bar was applied to the piston and reacted on the
floating part of the caliper. The friction material and
backplate properties were the standard values shown in
Tables 2 and 3. The brake disc was assumed to have
infinite stiffness.
5.3 Results
5.3.1 Pressure distributions
The interface pressure distributions for an hydraulic
actuation pressure of 80 bar are shown in Fig. 8a and b
for the inboard (piston side) brake pad and the out-
board brake pad. The inboard pad pressure distribution
may be compared with that of a brake pad under an
actuating force independent of the caliper by comparing
Fig. 8a with Fig. 4b. The pressure distribution is similar
in size, but the contact area is slightly reduced in the
caliper model (Fig. 8a). The maximum pressure is
9.0 MN/m2 in each case, but in the caliper model the
centre of pressure is moved outwards by 0.8-95.6 mm
radius. The outboard pad pressure distribution (Fig. 8b)
has a maximum value of 7.0 MN/m2 and the centre of
pressureis at a radius of 98.5 mm.
5.3.2 Caliper displacement
In actuating the brake, large caliper displacements were
obtained due to compression of the relatively soft fric-
tion material. This particular brake caliper is not well
constrained, and also opens out under actuation load.
@ IMechE 1991

Fig. 6 Dynamic interfacepressure distributions
The most significant effect is in the position of the
maximum interface pressure on the outboard pad; this
occurs at the outer periphery of the rubbing path. In
spite of the ‘opening out’ of the caliper, no contact
between the piston and its bore was predicted. This is
supported by the authors’ experience that the piston/
bore contact arises after some operation time, when pad
taper wear has occurred. ‘Opening-out’ distortion is a
well-known problem with such designs of disc brake
caliper; however, the outboard pad here remains in
Fig. 7 Caliper FE model
Q IMcchE 1991 Proc Instn Mech Engrs Vol 205

Fig. 8 Staticinterfacepressure distributionsfor standardcaliper position
almost full contact with the disc, and the better distrib-
uted backplate loading helps achieve a more uniform
pressure distribution.
5.3.3 Pistonlbore contact
The standard piston/bore clearance of 0.2 mm
(diameter)was reduced to 0.1 mm and the pressure dis-
tributions shown in Fig. 8c and d were calculated.
Contact and pressure distribution were more non-
uniform, and the predicted position of the centre of
pressure increased to a radius of 96.8 mm for the
inboard pad and 99.6 m for the outboard pad. In this
case contact between the piston and the caliper bore
due to piston ‘cockling’occurred.
5.3.4 Caliper position
The caliper was moved from its standard position
(piston bore centre at a radial distance of 94.5 mm from
the disc axis) by 4 mm onwards, while the pads were
unchanged in position. In this configuration, piston
‘cockling’, giving contact between the piston and the
bore, was predicted for a piston/bore clearance of
0.1 mm (diameter), and the interface pressure distribu-
tions are shown in Fig. 9a and b. These are similar to
those for the standard caliper position (Fig. 8c and d),
but with slightly increased contact area and a slightly
more uniform pressure distribution. The predicted posi-
tion of the centre of pressure was reduced to 96.0 and
98.5 mm for the inboard and outboard pads respec-
tively.
For a piston/bore clearance of 0.2 mm (diameter)the
piston cockling still gave piston/bore contact, but when
the piston/bore clearance was further increased to
0.3 mm, no piston bore contact was predicted. In this
last case the interface pressure distributions, shown in
Fig. 9c and d, showed further changes: the outboard
pad remained in full contact with the disc, with a peak
pressure of 7.2 MN/m2, while the inboard pad contact
area was further increased, with a peak pressure of
9.5 MN/m2. The predicted positions of the centre of
pressure for each pad were substantially reduced to 92.0
and 94.8 mm for inboard and outboard pads respec-
tively.
6 EFFECT OF DISC STIFFNESS
6.1 Method of analysis
In all the analyses so far presented here the disc has
been assumed to be of infinite stiffness-an assumption
that will now be examined. A finiteelement model com-
bining two pads, caliper and piston with standard
pistonlbore clearance of 0.2 mm, and brake disc (Fig.
10) was used for a static analysis. This combined model
was necessarily simpler than the previous individual
models, and symmetry allowed only half of the brake
assembly to be modelled.
Static loading was introduced by pressure (80 bar) on
the inside face of the caliper piston bore, and the actu-
ating forces were transmitted to the disc through the
caliper and the disc brake pads. The disc was fixed in
the axial direction to simulate the clamping action of
the wheel and hub.
Q IMechE 1991

Fig. 9 Static interface pressure distributions for non-standard caliper posi-
tion
6.2 Results
The deflected shape of the finite element model is illus-
trated in Fig. 10, which indicates the same type of
caliper deflection predicted in Section 5. The disc
deflected shape is detailed in Fig. 11, indicating a
maximum deformation of 21 pm. Pad interface pressure
(Fig. 12a and b) shows a maximum of 8.5 MN/mZ on
the inboard (non-piston) and 6.5 MN/m2 on the out-
board (non-piston) pads. There is no substantial differ-
ence from the rigid disc pressure distributions (Fig. 8a
and b), although the introduction of disc flexure appears
to make the pressure distribution more uniform. No
contact between the actuating piston and the piston
bore in the caliper was predicted under these conditions
of analysis.
7 DISCUSSION
7.1 General discussion on disc brake pad interface
The results of the analysis presented confirm the results
of two-dimensional finite element analysis (4) and
experimental measurements of static disc brake pad
contact and pressure (9, 10). The static pressure dis-
tributions demonstrate that both friction material com-
pressibility and backplate stiffness are important to
achieve a uniform pressure distribution. Equally impor-
tant is the geometry of the actuation mechanism; a
single piston at the centre of the backplate is less effec-
tive than application forces spread over the length of
the backplate as, for example, in the outer pad of a
slidingcaliper brake.
pressuredistribution
Q IMechE 1991
7.2 Effect of friction drag forces
The introduction of friction drag forces to generate a
‘dynamic’ braking friction analysis causes a significant
change in the interface pressure distribution. Full
contact over the pad surface under static conditions can
be reduced considerably, at the trailing edge during
actual braking operation. There is also evidence that, in
the case of a pad with a transverse slot, the two halves
of the pad behave somewhat independently. Peak inter-
face pressure on the leading half moves towards the
leading end, while the highest pressure over the whole
pad surface occurs at the leading edge (that is adjacent
to the slot) of the trailing half. This suggests that careful
design of pad backplate/actuation geometry is even
more important in a slotted pad assembly. A further
implication of this change in the position of maximum
interface pressure is the effect on noise propensity. The
‘sprag’ mechanism for noise generation (11) depends
upon a critical positioning of frictional contact forces,
which may be reflected in the position of peak pressures
in the pad friction interface. Flexure of the caliper
affects the static pressure distribution; in this case the
caliper ‘opens’ under actuation forces. The resulting
effect on the interface pressure distribution depends
upon the caliper constraints. This caliper, which is free
to float about the slides, is predicted to increase inter-
face pressure towards the outer periphery of the rubbing
path, as observed in practice. Caliper position, relative
to the disc axis, and the presence of contact between the
piston and the piston bore in the caliper are also very
important in the determination of interface pressure dis-
Proc Instn Mech Engrs Vol 205

144 M TIROVIC A N D A J DAY
Fig. 10a Full brake half-model showing resultant displacement of brake
parts
Fig. 10b Caliper displacement in Y direction
Fig. 1Oc Caliper displacement in Z direction
Part D:Journal of Automobile Engineering Q IMechE 1991

DISC BRAKE INTERFACE PRESSURE DISTRIBUTIONS 14s
Fig. 11 Disc displacement in Z direction
tributions. Piston/bore contact will modify the pressure
distribution, causing different wear patterns and
increasingnoise propensity.
7.3 Effect of padldisc frictioninterfacecontact
All the results presented here are for initial conditions
of perfect contact between the friction material and the
disc, that is on brake application the pad makes perfect
contact with the disc. In practice this will not happen,
and, as with drum brakes, the combined effects of bulk
geometry deformation friction material wear and
thermal effects will combine to alter the initial condi-
tions of contact. This will obviously affect the interface
pressure distributions, and those shown here are a guide
to pressure conditions under ideal conditions only.
However, there are some considerations that are worth
highlighting as follows. Perfect initial contact under
static or dynamic conditions produces pad/disc contact
which is unaltered by the actuation force magnitude if
all the brake components are rigid. The pressure dis-
tribution is scaled, but unchanged in form. Non-
linearity is introduced by imperfect padldisc initial
contact, which means that the pressure distribution
varies with actuation force magnitudes. The abutment
also affects the initial contact; a high friction abutment
may prevent free movement and consequent imprecise
initial contact. In some designs of disc brake the pad is
not well constrained and initial contact effects can be
significant.
7.4 EfAEct of frictionmaterialwear
No account has so far been taken of wear of the friction
material at the frictioninterface. Wear invariably occurs
in braking friction, which modifies the pressure distribu-
tion. Wear has been shown to be temperature and pres-
sure dependent, and therefore regions of high interface
pressure are expected to wear away faster than other
low-pressure regions, modifying the pressure distribu-
Q IMechE 1991
Fig. 12 Staticinterfacepressure distributionsincludingdisc distortion
Proc Instn Mech Engrs Val 205

tion accordingly. As with drum brakes, the trend is
expected to be always towards a uniform pressure dis-
tribution, modified by the kinematic constraints on the
brake pad assembly and the operational duty, in terms
of both mechanical and thermal loading.
7 5 Tbermaleffects
Most serious problems in disc brake performance can
be traced to thermal effects. At the level of large-scale
effects causing interface pressure variation, thermal dis-
tortion and expansion in the pads and caliper can
noticeably affect brake performance. However, such
effects lead on to macroscopic pressure variation and
consequent longer-term and more serious problems.
High peaks of interface pressure cause high rates of
local frictional heat flux generation which initiate
macroscopic pressure variation, in particular heat spot-
ting, banding and ultimate cracking, crazing and failure.
Temperatures in the pad can cause more thermal
expansion in the central regions of the pad, thus provo-
king higher interface pressure. More wear may occur
over this region which then causes edge contact after
cooling. This is a well-known effect analogous to the
generation of heel and toe contact in drum brakes, but
is instrumental in causing localized high-pressure and
consequent disc damage. The implication is perhaps
that the thermophysical properties of disc brake pads
should be carefully controlled to minimize these effects.
Temperatures in other parts of the brake assembly, for
example the disc, can affect the pressure distribution, for
example disc coning under thermal loading. The
analysis (Section 6)suggests that disc deflection due to
mechanical loading alone is small compared with
thermal loading; this is considered further by the
authors in another paper (8).
8 CONCLUSIONS
1. In order to ensure consistent disc brake performance
under all conditions, the interface pressure distribu-
tion must be carefully controlled to be maintained as
uniform as possible. Design recommendations
include mechanical rigidity, compliant friction
materials and minimal slack or compliance in the
actuation loading- Caliper displacement, as well as
caliper stiffness,is important.
2. In the finite element analysis of disc brakes, the inter-
face pressure distribution is relatively unaffected by
disc flexure, and a rigid disc is an acceptable assump-
tion. However, actuation geometry requires careful
consideration.
3. Although large-scale interface pressure variation
arising from bulk deformation of brake components
is found in all disc brakes, in-service performance
variation which is directly attributable to these
effects are relatively minor. Macroscopic interface
pressure variation (which may follow on from large-
scale effects)is much more serious in terms of poten-
tial damage to, or failure of, the disc rotor. Disc
brakes appear to be less susceptible to performance
variation induced by bulk geometry effects (first
level) than drum brakes. The problems with disc
brakes, especially under heavy duty, are more subtle,
and require carefulexamination.
4. In order to progress further the analysis of disc brake
interface pressure distributions needs to be more
closely linked to thermal effects.
ACKNOWLEDGEMENTS
The work presented in this paper was completed during
a joint programme of research between the University
of Bradford, United Kingdom, and the University of
Belgrade, Yugoslavia, and the authors are grateful to
both Universities for their support. The work was dis-
cussed during the First Brakes Workshop at the Uni-
versity of Bradford on 29 November 1989 and the
authors gratefully acknowledge the contributions of the
participants, especially those from Industry.
REFERENCES
1 Day, A. J., Harding, P. R. J. and Newcomb, T. P. A finite element
approach to drum brake analysis. Proc. lnstn Mech. Engrs, 1979,
193,401406.
2 Day, A. J. Energy transformation at the friction interface of a
brake. PhD thesis, 1983, Loughborough University of Technology.
3 Day, A. J., Harding, P. R. J. and Newcomb, T. P. Combined
thermal and mechanical analysis of drum brakes. Proc. lnstn
Mech. Engrs, Part D, 1984,198,287-294.
4 Harding, P. R. J. and Wintle, J. B. Flexural effects in disc brake
pads. Proc. lnstn Mech. Engrs, 1978,192, 1-7.
5 Tirovic, M. Theoreticakxperimental analyses of deformations of
disc brake pads due to mechanical and thermal loads (in Serbo-
Croat). MSc thesis, 1982, Faculty of Mechanical Engineering, Bel-
grade University.
6 Tirovic, M. and Todoronc, J. Flextural effects in commercial
vehicle disc brake pads. Conference on Disc brakesfor commercial
vehicles, London, 1988, paper C455/88, pp. 47-52 (Institution of
Mechanical Engineers, London).
7 Day, A. J., Newcomb, T. P. and Tirovic, M. Drum brake interface
pressure distributions. Proc. lmtn Mech. Engrs, Part D, 1991, 205
8 Newcomb, T. P., Day, A. J. and Tirovic, M. Thermal effects and
pressure distributions in brakes. Proc. lnstn Mech. Engrs, Part D,
1991,uH(D3).
9 Dubensky, R. C. Experimental techniques for rotor performance
measurements. SAE paper 850078, 1985.
10 Tumbrink, H. J. Measurement of load distribution on disc brake
pads and optimization of disc brakes using the ball pressure
method. SAE paper 890863,1989.
(D2), 127-136.
11 Spurr, R. T. Brake squeal. Proc. lnstn Mech. Engrs, 1971, C95/71.
Part D: Journalof Automobile Engineering Q IMechE 1991

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