Energy transformation at the friction interface of a brake
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Energy transformation at thefriction interface of a brake
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LOUGHBOROUGH UNIVERSITY OF TECHNOLOGY
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ENERGY TRANSFORMATION AT THE
FRICTION INTERFACE OF A BRAKE
by A. J. DAY
A DOCTORAL THESIS
Submitted in partial fulfilment of the requirements for the award of Ph.D.
of the Loughborough University of Technology, September, 1983.
Supervisors: Dr. T. P. Newcomb Department of Transport Technology.
P. R. J. Harding Mintex Limited.
~ by A. J. Day, 1983.
i·
ABSTRACT
Energy transformation at the friction interface of a brake has been studied in
a system where resin bonded composite friction material is applied to a metal
mating body. A time-step simulation of braking friction was developed using
finite element techniques, based upon the PAFEC 75 program, combining
calculations of interface contact, pressure and friction force distributions
with transient temperature analysis. Only compressive normal forces and
tangential friction forces are transmitted across the interface, and these were
assumed to be related by Amontons' Laws; the coefficient of friction so
defined being considered constant for the purposes of the analyses presented.
The work done against friction was computed from local interface pressure and
velocity, and assumed to be wholly converted into heat which was transferred by
conduction from the interface. A study of alternative mechanisms of energy
interchange identified no significant contribution to frictional energy
transformation from thermal degradation of the friction material. Used
friction material and its thermophysical properties were described by 3 phases;
Virgin material, Reaction zone, and a Char layer. A fourth phase represented
interfacial wear debris or surface coating effects and a fifth phase described
the metal mating body. Friction material wear was incorporated utilizing
empirically derived wear criteria based upon local interface pressure and
temperature.
Analyses were completed using finite element meshes designed to model the rotor
and stator components of an annular disc brake and a leading/trailing shoe drum
brake in 2-D axisymmetric and 2-D plane configurations respectively. Frictional
heat was assumed to be generated at nodes on the lining friction surface and
conducted both into the friction material and across the interface into the
mating material. Contact resistance was modelled by the conductivity of
interface elements and in this way artificial heat partitioning was avoided. A
special technique for the dynamic simulation of interfacial heat transfer was
developed for the 2-D plane configuration, where frictional heat generation
varied in the direction of brake drum rotation.
Braking torque, pressure, temperature and wear distributions were calculated,
without the limitations imposed by assumptions inherent in conventional
analyses, which showed good correlation with observed and measured experimental
results from an annular brake rig. The validity of the analysis method was further confirmed by comparison of measured drum brake performance data with
calculated results. The work thus makes a significant contribution towards a
better understanding of friction and wear in brakes, and also represents a
considerable advance in their analysis.
ii
ACKNOWLEDGEMENTS
The author would like to thank the Procurement Executive, Ministry of Defence,
and the Directors of Mintex Ltd., for their support and permission to publish
this thesis. He is particularly grateful to Mr. M. P. Thomas, Technical
Director, Mintex Ltd., for his continuing interest in the project.
Special thanks are due to Mr. P. R. J. Harding and Dr. T. P. Newcomb for their
enthusiastic and invaluable encouragement, advice and criticism throughout.
Thanks are also extended to colleagues at Mintex Ltd., for their specialist
advice and assistance, in particular;
Mr. J. W. Longley and Mr.R. Whitaker, General Research - Materials
Development,
Mr. L. Johnson and Mr. M. R. Goldthorpe (now of Sheffield University),
Research and Development Computer Section,
/
Mr. G. Butterworth, Materials Development,
Mr. H. Parker, Production and Process Development Engineering,
Mr. D. Scrutton, Mr. B. Oram and staff, Dynamometer Engineering,
Mr. R. N. Carr and Mr. R. G. McLellan, Commercial Vehicle Brakes
Engineering.
Finally, the author would like to express his gratitude to Mrs. M. Currer for
her expert typing and utmost patience.
Andrew Day,
August, 1983
Abstract
Acknowledgements
Nomenclature
Chapter 1
Chapter. 2
2.1
2.2
2.3
2.4
Chapter 3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
Chapter 4
4.1
4.2
4.3
4.4
4.5
Chapter 5
5.1
5.2
5.3
5.4
5.5
5.6
iii
INTRODUCTION
LITERATURE STUDY
Friction and Wear
CONTENTS
Frictional Heat Generation and Temperature Calculation
Non-Uniform Frictional Heat Generation
Summary
SIMULATION OF BRAKING FRICTION
The Combined Thermal, Thermo-Elastic and Wear Analysis
The Finite Element Method
The Stress Transfer Method for "No-Tension" Analysis
The Gap Force Method for "No-Tension" Analysis
Rigid Boundary "No-Tension" Simulation
Thermal Calculations
Discussion
FRICTION MATERIALS
Chemical Nature of Friction Materials
Material Properties
Wear of Friction Materials
Coefficient of Friction
Discussion
FINITE ELEMENT SIMULATION OF BRAKING FRICTION IN
AN ANNULAR DISC BRAKE
Finite Element Idealization
Test Analyses
Trial Simulations using the CST Method
Analysis of Brake Applications using the CST Method
Analysis of Brake Applications using the Gap Force
Method
Discussion of Results
PAGE
i
ii
v
1
4
4
7
10
15
17
17
20
23
30
36
37
40
42
42
53
57
65
66
68
68
74
81
86
104
114
Chapter 6
6.1
6.2
6.3
6.4
6.5
6.6
Chapter 7
7.1
7.2
Chapter 8
8. 1
8.2
8.3
Appendix 1
Appendix 2
Appendix 3
Appendix 4
Appendix 5
iv
FINITE ELEMENT SIMULATION OF BRAKING FRICTION IN A
DRUM BRAKE 122
Finite Element Idealization 122
Trial Simulation with the Combined Shoe and Drum Model 133
The Effects of Temperature and Wear on the Drum Brake
Simulation
The Effects of Lining Thermal Expansion on the Drum
Brake Simulation
Full Drum Brake Simulation
Discussion of Results
EXPERIMENTAL CORRELATION OF RESULTS
Annular Disc Brake
Cam Operated Drum Brake
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
Summary
Conclusions
Recommendations for Future Work
REFERENCES
APPENDICES
Incorporation of the 5 phase friction material and mating body model
Interface pressure, temperature and wear distributions calculated in annular disc brake trial simulations
Theory of S-cam actuation
Lining surface pressure, temperature and wear distributions calculated in drum brake trial simulations
Test procedure - Annular brake rig
145
162
164
178
185
185
221
230
230
232
236
236
241
242
244
269
271
279
A
A(
a
a" etc. ,
B [B), [B1], [B2] b
b" etc. , bc
C [C) Cp c [c)
[D)
d d'
do
E e Suffix "en
F ..oF {F}
{AFG} fo f( ), f1( ), f2( )
[G) g
[H) h
I
i,j
v
NOMENCLATURE
area (m') polynomial function (area) constant deflection coefficients
constant constant matrices constant deflection coefficients convective part of cooling rate coefficient (s-1)
constant constant matrix Specific Heat (constant pressure) (J/kgK) constant deflection coefficient matrix
constant matrix relating stress and strain in a
fini te element; {G'"}e = [D) {t:.} e dimension (m) effective diameter of air-flow path distance between an heat source node and the adjacent node in the predominant direction of heat
flow
Young's Modulus (N/m') constant (2.71828) refers to element
force (N) force increment nodal force matrix gap force matrix Fourier number = St¥/do' polynomial functions
constant matrix 9.81 m/s'
constant matrix surface heat transfer coefficient (W/m')
rotational inertia (kgm')
counters
k
L
L
M [M] m
Dlo mr
N Nu [N] n
nc
P {p} Pr p
Pi p
{p} p( )
Q
Qa • Q • Qav qi Q1,
R
R
Re r
s [S]
{s}
Q2
vi
Thermal Conductivity (W/mK)
length dimension (m) number
constant, M = 1/ts (s-1) constant matrix mass (kg) initial mass
rtAid .. e. mass ~auring reaction.
initial frictional heat flux, Q = N(1-Mt) (W/m') Nusselt number, Nu = hd' Ik constant matrix number number of in-contact interface nodes or node pairs
applied normal force (N) external force matrix Prandtl number, Pr = Cp?/k interface pressure (N/m') pressure at node i average interface pressure pressure loading matrix polynomial function (pressure)
heat energy (J)
Arrhenius activation energy heat flux (W/m') average heat flux nodal heat energy frictional heat friction material respectively
reaction force (N)
flux (or
(Q = Qi+Q2) applied to slider) and mating body
universal gas constant, R = 8.3143 kJ/kmolK Reynold's number, Re = vadp I") radius dimension (m) camshaft bearing radius camshaft base circle radius mean radius polynomial function (radius)
surface stiffness matrix
,
surface displacement matrix
T AT
Tc Ts { }T t ~t
$t
ts
U ux , uy {u} u( )
v v
va
"W Ws , Wc
w, w
wi Aw fw
x, y, z
Z
Q(
vii
torque (Nm) torque increment camshaft torque specific torque (Ts = T!Tc) matrix transpose time (s) simulation time-step time-step (for transient temperature calculations) duration of brake application
internal energy (J)
relative displacement (in x, y directions) displacement matrix polynomial displacement function
volume (m3) sliding velocity (m!s) air flow velocity
external work done (J)
virtual work due to stress and equivalent nodal loads respectively. wear, average wear calculated wear at node i wear increment (weight loss per unit area) wear increment (thickness loss per unit area)
Cartesian coordinates
rate of reaction
coefficient of thermal expansion (K-')
constants
thermal diffusivity (b" = k!fCp) (m'/s)
displacement (m) nodal displacement matrix displacement increment relative gap node displacement increment matrix
strain
initial strain nodal strain due to applied forces
~
ry
B
A
Il
Ilc
" S
7f
P
C>
{cs-} cr-( )
1:
V t/>
x: j, r c.> w
viii
transformed "z" axis dynamic viscosity (kg/sm)
temperature (K)
dynamic friction coefficient (Ils static) camshaft/bush friction coefficient Poisson's ratio
transformed "x" axis
constant ('11" = 3. 14159)
density (kg/m3)
direct stress (N/ml) stress matrix stress polynomial function
shear stress (N/ml)
heat partition ratio
angle (degrees)
transformed "y" axis
functions
angular velocity (rad/s)
angular acceleration (rad/s l )
Suffix 1 or 2 applied to thermo-physical properties refers to the friction material (or slider) and the mating body respectively, e.g. 1(" ¥2.
Suffix 1 or 2 applied to parameters refers to initial or final, (minimum or maximum) values, unless otherwise specified.
1
1 • INTRODUCTION
Frictional energy transformation describes the processes by which kinetic
energy is dissipated via friction at the interface between two bodies in
sliding contact. Friction forces are primarily generated by physical
interaction, on a microscopic scale, of surface asperities, and the work
done against the relative motion of contacting asperities by abrasion,
elastic or plastic deformation, shearing of junctions, etc., produces heat
energy in the surface layers of the rubbing pair. Transient changes in
temperature are produced as this heat is transferred away from the
interface, affecting the physical conditions of asperity contact so that
friction, and wear, characteristics are generally found to be temperature
dependent.
The actual temperatures produced depend upon how effectively the frictional
heat generated can be dissipated from the interface and therefore energy
transformation is of fundamental importance to the design and operation of
all types of friction brake. These brakes are widely used to provide an
inexpensive, consistent and reliable means of retardation over the complete
speed range of operation, and can conveniently generate large frictional
forces to give high rates of deceleration. Large quantities of heat can
therefore be involved, creating a severe thermal environment at the
friction interface, and special friction materials have been developed over
a period of many years to withstand high temperatures while providing
adequate and consistent friction and wear performance over the full range
of operating conditions. Such materials are mainly resin bonded fibre
composites of complex physical and chemical structure.
The factors which influence energy transformation at the friction interface
of a brake are:-
1. The amount of frictional heat generated which is transferred by
conduction from the interface into the bulk of the friction material,
the mating body and eventually dissipated to the surroundings, as
distinct from other mechanisms of heat absorption or dissipation.
2. The thermophysical properties of the materials which comprise the
friction components of the brake.
2.
3. The proportion of frictional heat generated which flows into each part
of the friction pair.
4. The distribution of frictional heat generation over the friction
interface.
5. Macroscopic surface effects such as material wear, localized interface
pressure distributions and localized thermal expansion, and their
effects upon the distribution of frictional heat generation.
The retarding force generated by a friction brake ultimately depends upon
these factors which in turn are largely controlled by the mechanical design
of the brake assembly and the actual materials used. An accurate analysis
of the performance of any brake is therefore not possible unless all these
factors concerning frictional energy transformation are taken into account.
Conventional analysis of brakes has considered each of these factors in
isolation so that the effects of their interdependence on all aspects of
brake operation has not been studied, and it is only with the availability
of considerable computational power that it has been possible to
investigate the combined problem.
The finite element method is a powerful technique for the solution of many
engineering problems, and has been extensively used for stress or thermal
analysis applied to brake components. The first step forward in the
specific use of the technique for the study of frictional effects under
high energy sliding contact conditions was made by Kennedy and Ling (Ref.
1) who simulated thermo-elastic instablli.ty and transient contact changes
at the interface of an aircraft-type annular disc brake using sintered
metal friction material. This approach has been used as a basis and
extended for the present study of the little known effects of energy
transformation at the friction interface. of a brake, incorporating the
thermophysical, friction and wear properties of resin bonded composite
friction materials, together with the ~ffects of brake performance arising
from the geometry and mechanical design of brakes and brake components. A
number of techniques for Simulating the characteristics of a friction
interface in finite element analysis have been investigated, and the
combined simulation techniques have been applied to two different
configurations of friction brake, viz., an annular disc brake and a
leading/trailing shoe drum brake assembly. Interfacial pressure
distributions and frictional drag forces are an essential part of the
3.
simulation method and therefore the work also represents a sophisticated
method of brake performance calculation which is not limited by the
assumptions inherent in conventional methods.
Analyses are described in which frictional heat generation and dissipation,
together with the flexure of rotational and stationary components, are
shown to produce variations in contact conditions at the interface with
time during individual brake applications, starting from conditions of full
interface contact. Calculated distributions of temperature, interface
pressure and wear in the brake friction pair, together with calculated
from an brake performance, are compared with experimental data obtained
annular brake test rig, and also from drum brake test results.
of the literature concerning friction braking ·shows that
A survey
the work
represents not only a considerable advance in the analysis of friction
brakes, but also makes a significant contribution towards a better
understanding of the basic mechanisms of friction and wear involved in
automotive brake technology.
4.
2. LITERATURE STUDY
2.1 FRICTION AND WEAR
2.1.1 Classical theories of friction, in particular adhesion and abrasion,
are based upon some mechanism of surface interaction usually applied to
a rubbing pair which is made up of similar materials, most frequently
metals, under carefully controlled conditions of sliding. The
characterisation of asperities in terms of the surface topography was
first discussed by Bowden and Tabor (Ref. 2) in 1938, and since then
the study of interface mechanics and surface topography has been an
important part of research into the fundamentals of friction and wear.
Contact between two nominally flat surfaces occurs at microscopic peaks
or asperi ties on the surfaces and over the area associa ted with each
asperity, contact stresses may be high so that the resulting
deformation can be elastic, elastoplastic or plastic. Archard (Ref.
3) found that for static elastic contact, simple Hertzian theory
applied to a successively refined surface topography idealization gave
a relationship between area of contact and' the normal force which
tended towards direct proportionality. Utilizing this surface
topography idealization for sliding contact between highly elastic
materials such as metals, a mechanism of friction based upon asperity
interaction produced results which were generally consistent with
Amontons' Laws, since the relationship between normal force and
tangential friction force can be seen to hold if the tangential force
between two contacting asperities is also directly proportional to the
real area of contact. Kraghelsky (Ref. 4) found that Amontons' Laws
were valid under conditions of ideal plasticity, and the combination of
elastic and plastic deformation of asperities has since provided the
basis for calculations of the macroscopic friction coeffiCient, e.g.
Halling (Ref. 5).
The basic mechanism of dry friction is considered to include two main
factors; adhesion and deformation, of which the latter, which is
related to ploughing and grooving, and may involve abrasion, is
predominantly responsible for any departure from Amontons' Laws. One of
the major constituents of composite friction materials is a polymeric
resin and in relating theory to practice in polymer friction Lancaster
(Ref. 6) observed that Amontons' Laws do not always hold for
2.1.2
2.1.3
5·
polymer/polymer and polymer/metal combina tions because of the
significant contribution of the deformation component to the friction
force generated.
The wear of polymers can be categorized into 3 main types (Ref.6) viz.
abrasive, fatigue and adhesive. Abrasive wear requires the presence
of hard asperities on the mating surface, or hard particles between the
surfaces (third body abrasion) since the polymer alone will not cause
mechanical damage (Ref. 7). This type of wear may therefore be
initiated by other constituents of composite friction materials which
are generally abrasive in nature towards the metal mating surface,
Lancaster (Ref. 8) found that for polymer-based bearing materials,
fillers play a major role in friction and wear processes, altering the
friction and wear properties by modifying the topography of the mating
surface. Mildly abrasive components, e.g. silica or asbestos, can
have a beneficial effect on wear by producing. smoother surfaces, while
those which make the mating surface rougher as rubbing proceeds can be
responsible for an increase in the wear rate (Ref. 6).
Interactions between the various constituents of composite friction
materials can be extremely complex in terms of their effect upon
friction and wear. Smoothing of the mating surface by abrasion
encourages the forma tion of transfer films (Ref. 6), which can cause
increased wear with brittle polymers, or reduced wear with the more
ductile polymers. The formation of transfer films, mainly as a result
of adhesion, is however very sensitive to contamination, either from
external sources or from the constituents, thereby preventing any
transfer to the mating surface.
Polymer friction and wear have been found to be highly temperature
dependent, mainly because of the marked reduction in elastic modulus
with increased temperature. The relatively low thermal conductivity
of most polymers makes interface thermal effects important, and
carefully controlled low speed test conditions are necessary to
minimize any associated temperature rise (Ref. 6) so that the effects
of certain parameters, e.g. load, can be isolated from those of thermal
softening. Fibre reinforcement enables the strength as well as the
friction and wear properties of polymers to be improved and Lancaster
(Ref .8) noted that levels of friction and' wear independent of the
polymeric binder could be achieved under dry sliding condi t ions. This
1
2.1.4
2.1.5
6.
forms the basis of resin bonded composite friction material technology,
where heat resistant fibres are used to reinforce a polymeric binder
resin so that much greater levels of frictional heating can be
tolerated, and under normal conditions of use, the frictional behaviour
of such materials is consistent with Amontons' Laws.
Interactions between the constituents of composite friction materials
which affect the physical nature of friction and wear are further
complicated by chemical reactions within the material (Ref. 9),
primarily thermal degradation or pyrolysis of the various organic
components caused by frictional heat generation. The polymeric resin
used in friction materials is usually a phenolic type, for which the
thermal degradation follows an Arrhenius rate law, Le. the rate of
reaction is described by the relationship (Ref. 10)
-Z = Bexp(-Qa/R8) (2. 1 )
Bark et al (Ref. 11) found that the degradation produced under high
temperature sliding conditions was not as severe as would be expected
from simple pyrolysis at the same temperature for the same length of
time, supporting the existence of an ablation type mechanism, providing
sacrificial protection to the subsurface material. The ablation of
phenolic resin has been extensively studied in relation to heat shields
(Ref. 12, 13); the major difference from aerodynamic ablation is the
removal of the sacrificial char layer by wear rather than erosion by
the airflow.
Physical and chemical interactions between the constituents of the
friction material and their effect upon the complex thermal environment
at the brake friction interface effectively prevent the description of
either the frictional or wear properties of the resin bonded composite
material in simple terins of basic material properties (Ref. 14), and
the wear of resin bonded composite friction material has been most
usefully described by empirical wear correlations, Hhee and Liu (Hef.
15, 16) showed that the wear of fibre reinforced friction materials
could be divided into two temperature regimes: , , , ,
6w =,6 pavbtc
and Aw = ,6pavbtexp(-Qa/R8)
below 232°C
above 232°C
(2.2)
(2.3)
7.
The exponential term clearly demonstrates the influence of an energy
acttva ted pyrolysis mechanism in the high temperature wear regime and
highlights the effect of temperature on the observed wear rate of resin
bonded composite friction materials.
Although this type of wear correlation can be an effective idealization
under most circumstances, there are many other factors which contribute
to the friction and wear characteristics of resin bonded composite
friction material. Mating surface finish and topography, which plays
such an important part in fundamental theories of friction and wear has
been shown to affect the friction force generated in brakes (Ref. 17).
Trace elements such as titanium and vanadium in the mating body have
been found to have a considerable effect upon both the friction and
wear of certain types of resin bonded composite friction material as
well as wear of the mating surface itself, implying some definite
interaction between the two parts of the friction pair which, at
present, is not fully understood (Ref. 18).
2.2 FRICTIONAL HEAT GENERATION AND TEMPERATURE CALCULATION
2.2.1 The work done against frictional forces at the interface is generally
assumed to be wholly converted into heat energy so that for the
purposes of analysis, frictional contact can be idealized as a moving
heat source on an infinite body. Blok (Ref. 19) produced an
analytical solution for a square heat source of side length 2L moving
on a large body, of the form:
a z (411"1)1 (Q1L) 00 vL1\" kl
(2.4)
for high velocity, and
&, Z (~)(Q1L) DO 'lf1 kl
(2.5)
for low velocity, where in each case 0", represents the steady state
temperature. These calculations relied upon satisfactory
determination of the proportion of generated heat transferred to each
part of the friction pair. for a single small region of stationary
contact between two large bodies, the heat partition was determined to
give equal surface temperatures;
(2.6)
\,
2.2.2
8.
For high speed sliding conditions Blok (Ref. 19) averaged the surface
temperatures YsiFl! 8EtY8'isR (eh') to give an approximation to the
actual interface temperature rise. Jaeger (Ref. 20) found that the ,on
heat partition determined by this approximately depended upon the
conditions of sliding, and also observed that the partition described
by;
(2.7)
was necessary for instantaneous heat generation at an infinite sliding
friction interface.
In experiments on a thermocouple tip sliding against metal discs of
different thermal conductivity, Spurr (Ref. 21) found that interface
temperatures calculated using Jaeger's analysis applied to the disc did
not agree with measured values. These results indicated that the
analysis did not correctly describe the heat partition between the two
surfaces for the system under consideration, and became progressively
more inaccurate with decreased disc thermal conductivity.
Ling and Pu (Ref. 22) suggested that the average macroscopic
temperature of two surfaces in frictional contact would not be the same
because of thermal resistance at the friction interface. Measurement of
the average heat transfer coefficients showed similar values to static
interface values, ranging from approximately 1000 W/mzK to 25000 W/mzK
at average normal pressures of less than 1000 kN/m'. The effect of
surface layers in the analysis of temperatures generated by moving
composite bodies was studied by Ling and Yang (Ref. 23) whose examples
showed that a thin layer had a considerable effect upon the surface
temperatures, as predicted by Jaeger (Ref. 20).
From moving heat source analysis, "flash" temperatures which are
considerably higher than the average surface temperature can be
calculated for individual asperity contacts (Ref. 24). Penetration of
heat into the surfaces from these contacts is, in most cases, very
small (Ref. 20), and thermal expansion of the surface layer on a
microscopic scale is therefore an important factor in determining the
positions of actual asperity contact at any time during sliding. The
influence of local thermal expansion on thermo-elastic instability at
2.2.3
9.
the friction interface was verified by Barber (Ref. 25) using a
three-pin slider with which contact varied from pin to pin dul'ing a
cyc le of expansion and wear. Dow and Burton (Ref. 26) showed tha t
this type of mechanism operated even in the absence of wear.
A major complication in the calculation of temperature distributions in
a friction pair is therefore not only that the moving heat source
analysis refers to contacting asperities, whose position and number
must be determined, but also that these parameters vary with time. Ling
(Ref. 27) presented a stochastic approach to the problem where both the
distribution of individual contacting areas over a larger region of
frictional contact, and their variation with time, were assumed to be
random.
The calculation of temperatures in the friction components of brakes
and clutches has been extensively studied by Newcomb. The most
practical (and now most widely used) method was considered (Ref. 28,
29) as a problem of one-dimensional heat flow from the interface,
giving the solution for friction surface temperature at short times
into the brake application as:
kB 2tl 2 t
N IS! = (1 - -)
"Id 3 ts (2.8)
where Q = N(l-Mt) describes the frictional heat input.
The distribution of heat between the two bodies is determined from the
heat partition equation which takes into account the different surface
areas of brake drums and linings (or brake discs and pads) to give
equal average surface temperatures for each body;
(2.9)
A further investigation (Ref. 30) showed that for typical drum brake
and annular clutch or brake designs the problem of frictional sliding
contact could be reduced to one of stationary heat source analysis in
which the whole friction surface was considered as a continuous heat
source. For small areas of friction material operating against a
rotating disc or drum the problem reverted to that of a moving heat
source for which the analysis of Blok (Ref. 19) or Jaeger (Ref. 20) was
necessary. Temperatures in automotive disc brakes were calculated
10.
assuming that the effective rate of heat generation at any point on the
disc was the average over the disc surface for which negligible
circumferential temperature variation was assumed, using a similar
one-dimensional analysis as presented for the drum brake. Newcomb also
presented the solution for the flow of heat from the friction interface
of a disc brake without prior heat partition, with the assumption of
zero contact resistance at the interface.
2.3 NON-UNIFORM FRICTIONAL HEAT GENERATION
2.3.1 The assumption of one-dimensional heat flow and corresponding uniform
frictional heat energy input to the friction pair implies uniform
2.3.2
interface contact and pressure distribution. On a microscopic scale
this assumption is clearly incompatible with considerations of asperity
contact and thermo-elastic instability, while on the macroscopic scale
the distribution of pressure over the friction surface is seldom
uniform. Pressure variation at a brake friction interface results in
local variations in frictional work done, non-uniform heat generation
and uneven temperature distributions, and Wetenkamp and Kipp (Ref. 31)
noted that although the contact surfaces may be carefully machined and
prepared to minimize initial contact pressure variation, slight
differences in pressure cannot be prevented. Once uneven temperatures
have been generated non-uniform thermal expansion of the surfaces
exaggerates interface pressure variations. Santini and Kennedy (Ref.
32) monitored temperatures in disc brake pads, confirming the existence
of non-uniform pad/disc contact constantly shifting in position with
time. Calculation of the interface pressure distribution is therefore
an important pre-requisite for the study of the effects of non-uniform
frictional heat generation.
For both disc and drum brakes, Parker and Newcomb (Ref. 33) observed
that the static distribution of interface pressure was altered by the
application of tangential friction forces under dynamic conditions. The
dynamic pressure distribution in a drum
assumed to be determined by the geometry of
brake has generally been
the brake (Ref. 34, 35, 36,
37) and drum brake analysis based upon graphical techniques makes the
fundamental assumptions of a rigid brake shoe and drum, and a lining
material which is linear elastic in compression. With these
assumptions, pressure distribution is constrained to be dependent upon
the virtual displacement of the brake shoe, generating a sinusoidal
2.3.4
11 •
form (see figure 2.1), although the analysis could be modified to allow
for an assumed uniform pressure distribution as generated by a brake
shoe possessing a certain amount of flexi bility (Hef. 35) • Newcomb
(Ref. 28) investigated the effect of a sinusoidal pressure distribution
over a drum brake lining on calculated transient temperatures using the
summation of Fourier series, showing a significant alteration in
friction surface temperatures.
The limitations of the assumptions inherent in conventional geometric
drum brake analysis concerning the form of the pressure distribution
were recognised by Millner and Parsons (Ref. 38) who idealized the
brake shoe as a thin, curved elastic strip, and the brake drum as a
thin proof ring. The analysis (Ref. 38, 39) used experimentally
determined influence coefficients in a computer program to calculate
the pressure distribution, from which the results demonstrated an
improvement on the conventional analysis. Flexure of component parts of
the brake assembly was also shown to have a considerable effect upon
the braking torque generated and Wintle (Ref. 40) furthered the study
of torque variations of drum brakes by finite element analysis of a
flexible brake shoe operating against a rigid brake drum. An
automatic procedure for the application of tangential friction forces
in the finite element model presented by Day, Harding and Newcomb (Ref.
41) enabled all the advantages of the finite element method, in
particular the ability to model different designs of brake shoe quickly
and easily, to be employed in a new method of brake analysis.
Calculated brake performance showed good agreement with experimental
data, confirming that the flexible shoe, rigid drum approach was an
improvement on geometric analyses, while the calculated pressure
distributions were significantly different from the conventional
sinusoidal form as shown in figure 2.1 and comparable with those
calculated by Millner and Parsons, (Ref. 38). In all these analyses
axial pressure variation was assumed to be negligible.
The dynamic distribution of pressure at the interface between brake pad
and disc was studied by Harding and Wintle (Hef. 42) in an
investigation of flexural effects in disc brake pads. A 2-D finite
element analysis of a brake pad, incorporating tangential friction drag
forces at a rigid boundary showed that thermal distortions and
mechanical deflections could lead to pressure variation and partial
contact at the friction interface in the circumferential direction as
r Z Z CJ
--0 JJ rn (Jl (Jl
6
§3t. rn
:s: z --3
N
2
0
Drum Brake Lining Pressure Distributions (Ref. 41)
FLEXIBLE SHOE & FLEXIBLE LINING
- -- RIGID SHOE & FLEXIBLE LINING
----- ------- ------ --., -Cl . t-.) 60 0 60 . ~
trailing end LINING ARC LENGTH (degrees) leading end
2.3.5
2.3.6
13·
shown in figure 2.2. Even with the assumption of a rigid disc, radial
pressure variations may arise from differential work effects as
described by Chichinadze (Ref. 43) for an annular disc brake, and in
practice such effects may be exacerbated by "coning" or thermal
distortion of the disc (Ref. 44).
A number of analyses have been presented which investigate the effect
of non-uniform frictional heat generation on calculated brake
temperatures, using pre-defined distributions of contact and pressure.
El-Sherbiny and Newcomb (Ref. 45) used finite difference methods for
the investigation of band contact in an annular dry clutch which showed
that peak temperatures during engagement could be higher or lower than
those calculated for full contact depending upon the type of contact
chosen. Ashworth, El-Sherbiny and Newcomb (Ref. 46) investigated the
effects of band contact of drum brake linings using a finite difference
method for temperature calculation, and a finite element method for the
subsequent calculation of thermal distortions. The frictional heat
energy was assumed to enter the drum alone and the two analyses were
otherwise unconnected, with neither thermal nor physical interaction
between the lining and drum.
Kennedy and Ling (Ref. 1) recognized the importance of the
inter-dependence of interface pressure, temperature and wear in braking
friction and presented a combined thermal, thermo-elastic and wear
simulation of the high energy sliding conditions in a disc brake, using
finite element techniques. The analysis, described in detail by
Kennedy (Ref. 47), was based upon one friction interface from a
multiplate aircraft brake comprising annular sintered metal friction
discs and steel mating discs, and could be approximated to cover single
pad or "spot" type disc brakes used in automotive applications. Each
brake application was divided into a number of time-steps, over each of
which the interface contact and pressure distributions were assumed to
remain constant, and the wear occurring during the time-step was
calculated using a criterion based upon the strain energy in small
"source" elements at the surface of the friction material. The
frictional energy was assumed to be all converted to hea t for the
transient temperature calculation and the heat flow into each part of
the friction pair was defined by their thermophysical properties so
that artificial heat partitioning was not required.
Disc Broke Pad Pressure Distributions (Ref. 42)
I '" I
'" /
/
" /"
.--
DYNAMIC
STATIC
"'.".,--------- ---
PI2
-"-
"-"-
P/2
"-" , " "-
\
,., c;) .
15.
Friction interface contact was modelled using the "Stress Transfer"
technique to allow compression-only behaviour, and loss of interface
contact, to be taken into account in the interface pressure
distribution calculation and the subsequent determination of the
non-uniform frictional heat flux input. Calculated transient changes in
interface contact positions and areas were in agreement with observed
effects, and interface temperatures were found to be dependent upon the
contact geometry and the material properties of the friction
components. Investigations into the effect of thermal parameters on
interface temperatures showed that the distribution of frictional heat
flux between the friction pair depended upon the thermal diffusivity
and the volume of the two bodies, while for the type of brake studied,
temperatures were affected by the conductivity, volume and heat
capacity of the friction components.
2.4 SUMMARY
The generation of heat during braking, part of the frictional energy
transformation process, produces high interface temperatures and a severe
thermal environment affecting both the frictional and wear characteristics
of the mating surfaces. When considered in conjunction with the physical
and chemical interactions which occur in resin bonded composite friction
materials during use, the basic mechanisms of friction and wear at a
sliding interface become extremely complex. Furthermore, interface
pressure and temperature are interdependent, contributing to the process
of thermo-elastic instability through localized thermal expansion effects
which, together with material wear on a microscopic scale, cause changes
in the distribution of asperity contact with time. On a larger scale,
the macroscopic pressure distribution over the full friction surface area
shows a similar interdependence with temperature and wear so that
distributions of interface temperature and pressure vary with time and are
seldom, if ever, completely uniform.
Conventional methods of brake performance calculation are limited by
assumptions concerning the distribution of interface pressure whilst
interdependent thermal and wear effects associated with brake operation
have not normally been covered in any such analyses. Assumptions
concerning interface pressure distributions lead to assumptions of
frict ional heat generation, and calculated interface temperature
distributions are then further limited by the artificial partitioning of
16.
heat between the two rubbing surfaces. An
understanding of frictional energy transformation
improvement in
and the effects
the
of
pressure, temperature and wear at the friction interface of a brake can
only be achieved by the use of more sophisticated analysis techniques
combining the mechanical aspects of brake operation with temperature
related effects arising from frictional heat generation. Although the
braking friction process can be simplified by basing the friction
characteristics upon Amontons' Laws, and incorporating empirical wear
correlations, a realistic simulation of braking is a complex problem for
which computer methods represent the only practical solution.
The combination of finite element techniques for friction interface
simulation and a time-step idealization, represents a useful application
of modern methods to the analysis of friction brakes. Several different
examples of friction interface simulation, including that used by Kennedy
and Ling, have been identified in the literature study and are described
in Chapter 3.
17.
3. SIMULATION OF BRAKING FRICTION
3.1 THE COMBINED THERMAL, THERMO-ELASTIC AND WEAR ANALYSIS
3.1.1 Characteristics of the Friction Interface
Any interface represents a discontinuity between two different bodies
or parts of the same body, where, unless a physical bond exists between
the two, only compressive normal forces can be transmitted. In
principle, therefore, the two bodies behave independently unless
compressive forces are applied to keep them together at the interface.
Because contact between any pair of touching bodies occurs at a number
of asperities on the surfaces, there are regions where contact is not
made. In these regions compressi ve forces are not transmi t ted, and
frictional forces are not genera ted, even though external compressi ve
forces are being applied. Furthermore, due to bulk deflection, such
as mechanical flexure of one or both of the bodies under external
loading, certain areas may physically bend away from each other,
modifying the extent of the friction interface, so that any assumption
of constant, uniform pressure distribution across the apparent area of
contact at a brake friction interface is unrealistic.
Mechanisms of friction between two surfaces in sliding contact were
discussed in Chapter 2, where it was observed that avoiding extreme
effects of temperature or thermal decomposition (de-naturing) of the
surface layers, the frictional characteristics of resin bonded
composi te friction material were consistent with Amontons' Laws. In
this case, normal applied force and the generated frictional force are
directly proportional, with the constant of proportionality defined as
the macroscopic frictio~_ coefficient, independent of _yal"iations in
interface pressure or temperature;
F = !-IP (3.1)
and the frictional force opposes the direction of relative motion
between the contacting surfaces. Equation (3.1) has been taken as the
basic premise for the simulation of the brake friction interface;
contact over any region of the friction interface produces a local
friction force of a magni tude determined from the local normal force
18.
(the product of interface pressure and area), and the macroscopic
friction coefficient. The total friction force generated is then the
sum of all the individual friction forces developed over the friction
interface.
It is generally assumed that all of the energy dissipated in a friction
brake is converted to heat as a result of the work done by the
frictional forces at the interface between the two bodies in sliding
contact. With a friction interface simulation it is possible to
examine this assumption and also other mechanisms of heat dissipation
or absorption, distinct from conduction, through the friction pair. In
particular the known effects of heat and temperature on the resin
bonded composite friction material are to cause chemical changes in the
material which may be exothermic or endothermic, and to introduce an
ablation type mechanism resulting from char formation and wear at the
friction interface.
The exact mechanism by which frictional heat is generated is not fully
understood, but it has been noted (Ref. 22) that some heat is generated
within the surface layers of the two bodies, implying that heat may be
generated as a result of deformation of the surface layers. The rate at
which this heat can be removed from the interface determines the
subsequent temperature distribution; Ling and Pu (Ref .22) found that
the assumption of equal temperatures either side of the interface
(equation (2.8» could not be confirmed for high speed sliding, and
referred to a "macroscopic jump" between the temperature of each
friction surface. This temperature difference was suggested to be due
to thermal resistance at the interface, resulting from contact
resistance over regions of non-intimate contact, and the observed
presence of wear debris at the interface of a friction brake offered
further supporting evidence. Localised high surface temperatures or
"flash" temperatures are also frequently observed as "strip" braking,
"fire banding" or "hot spots" on the friction surface of the metal
mating body, indicating that thermal conditions at the friction
interface are not only far from being constant, but can be
exceptionally severe.
In the case of prolonged sliding contact under conditions of high
normal load, the microscopic scale of asperity interaction at a brake
friction interface is affected by the generation of heat and the
3.1.2
19.
process of wear of both contacting surfaces. Work is done in the
deformation, abrasion or shearing of individual asperity contacts, and
since the nature of the surface topography causes the points of actual
contact to be non-uniformly distributed, the interface pressure
distributions and the generation of heat are irregular over the rubbing
surfaces. Distortion of the surface profile is exaggerated by
localized thermal expansion;
reach high temperatures and
the regions of high interface pressure
have the greatest localized thermal
expansion. This is an unstable process, known as thermo-elastic
instabili ty which causes transfer of the interface loading to those
regions which are already regions of high interface pressure. The
process is, however, modified by wear, which is dependent upon both
temperature and pressure, so those regions of greatest pressure and
temperature will also have the greatest wear. Where the rate of wear
exceeds the rate of expansion at the friction surface, the interface
pressure is reduced, leading to lower heat generation, temperatures and
thermal expansion so the interface loading is transferred to other
regions where the same process continues. This type of mechanism can
be simulated on a macroscopic scale by considering such effects over
small (but not microscopic) areas of the friction interface such as may
be defined by a finite element mesh.
The Simulation Method
The brake application is first divided into a number of simulation
time-steps over each of which the friction process involves the
determination of interface contact and pressure distributions together
with frictional drag forces (the thermo-elastic analysis) and the
calculation of transient temperature distributions (the thermal
analysis), which both employ finite element solution techniques.
Interface contact and pressure distributions are assumed to remain
constant over the duration of each time-step so that the simulation
proceeds in a sequence of consecutive calculations. Frictional heat
flux at the start of each time-step is computed as described in Section
3.6 and wear of the friction material is computed from nodal interface
pressures and temperatures as described in Chapter 4. Thermal
calculations utilize the standard PAFEC 75 analysis, but for the
interface contact and pressure distribution calculations, special
techniques were required to cater for "no-tension" behaviour at the
friction interface, and the generation and application of tangential
20.
friction forces. The finite element method is briefly described in
Section 3.2 before details of methods for "no-tension" friction
interface analysis are discussed in Sections 3.3, 3.~ and 3.5.
3.2 THE FINITE ELEMENT METHOD
3.2.1 A brief description of the Finite Element Method
Matrix methods of analysis based upon force/displacement relationships
for individual structural elements have been widely used for the
solution of framework or network problems. In simplest form, elastic
stress/strain relationships are applied to individual elements (bars,
beams or plates) which are interconnected at specific points on their
boundaries, termed nodal points, to transmit forces between elements.
For any such element
{F} = (3.2 ) e
{a} = e
and the characteristic relationship between nodal forces and nodal
displacements for the element can be represented by
= (3.4)
By analogy with Hooke's Law, the matrix [S]e is known as the element
stiffness matrix, while {FEo} e is the vector of initial strains, e.g.
thermal expansion. Idealization of the entire structure is completed
by the process of "assembly" in which the equations (3.4) for each
element are brought together in a system force/displacement matrix
relationship. Since the structure is represented by an assembly of
similar elements interconnected at the nodal pOints, displacement
compatibility between the elements is ensured, and for structural
equilibrium the nodal equilibrium forces at the nodes can be
calculated, from which stresses and strains in individual elements are
easily evaluated.
21.
When concerned with an elastic continuum, an infinite number of
elements and nodes would theoretically be required, so the fini te
element method seeks to produce a realistic idealization of a continuum
by a finite number of elements (and nodes) of a much more sophisticated
type. A finite element defines a small area or volume within the body
over which the stress/strain constitutive relationship is known. An
assembly of such elements, interconnected at nodal points, can then
represent the elastic continuum provided that displacement
compatibility exists over the length of each element boundary. The
state of displacement within each finite element must be uniquely
defined by a set of "displacement functions" from the displacement of
the nodal points so that the calculated displacement along the boundary
between two adjacent elements is, as near as possible, identical, and
gaps between the elements along their boundaries do not occur in the
strained state. Because the displacement functions can only
approximate to this inter-element continuity, the effectiveness of this
approximation is fundamental to the success of the finite element
idealization.
The shape of the finite element is not limited to regular,
straight-sided polygons, and one great advantage of the finite element
method is its ability to provide an accurate idealization of the actual
shape of the continuum. The "iso-parametric" family of finite
elements use a polynomial transformation from the (x, y, z) domain to
the (5')('S) domain where the element takes the form of a unit square
centred at the origin.
The solution of the finite element idealization follows through
consideration of continuity and overall equilibrium for an elastic
continuum, and is equivalent to the minimization of total Potential
Energy in a displaced sy-stem.
d (U+W)
d(Eo) = 0
U = l [{fc}T [DJ {to} d(V) (strain energy)
-! [{~o? [DJ {~o} d(V) (initial strain energy)
+ (internal virtual work)
(3.5)
<3.6 )
and
+
+
= {cS} T {p)
! {s} T {p}d(V)
! {s} T {g)d(S)
22.
(external nodal forces)
(external pressure)
(external distributed loading)
Minimization of the Potential Energy function is a special case of
Variational Calculus, which, used in the finite element solution,
enables the method to be used for general field theory. The concept
of Variational Calculus can be described by considering a problem for
which the solution requires the minimization of some "functional" over
a certain field, which is an integral function of some unknown
function, e.g.
• •••• ) d(V)
••••• ) d(S) (3.8)
The minimization of the functional ~ is, by Euler's theorem of
variational calculus, directly equivalent to the solution of one or
more corresponding differential equations (known as the Euler
equations), and so the special case for stress analysis of an elastic
continuum gives:
where both f, ({'/'» and f2({ of}) are quadratics in {..p). ~ gives
(3.8a)
Minimization of
Provided that the finite element discretization holds, i.e.
If({~})d(V) = L r<{f}e) (3. '0)
J'P then <J{'I') = 0 corresponds to equation (3.5) summed over the entire
continuum, and the terms f, ({'/'}) and f2({'/'}) correspond to U and 1J respectively (equations (3.6) and (3.7». Because the variational
statement for this case can be obtained from physical principles
applied to the elastic continuum, it is not necessary to define the
Euler equations to enable the solution to be found by minimization of
the Potential Energy.
3.2.2
23·
In the case of heat transfer and temperature calculation, derivation
through physical analogy is not possible; instead, the Euler equations
are known, being the governing differential equations, from which the
variational formulation can be found. For steady state heat
conduction, for example, Laplace's equation
= '\]''1'= o (3.11)
represents the Euler equation and the functional (equation (3.8» can
be shown to be
j= (3.12)
The procedure is similar for transient temperature solution, with the
addition of a further iterative or time-step solution for the
determination of temperature variation with time. Heat flux input and
all types of boundary conditions can be included to facilitate the
solution of the most complex heat transfer problems.
The PAFEC 75 Program
Finite element programs for the solution of engineering problems are
widely available and one such program is PAFEC 75 (Ref. 48) on which
the analysis work presented here is based. The program has been
extended and modified in a number of ways to deal with the non-linear
tempera tu re and contact effects at a friction interface, enabling
advantage to be taken of this tried and tested commercially available
finite element program.
3.3 THE STRESS TRANSFER METHOD FOR "NO TENSION" ANALYSIS
3.3.1 The Stress Transfer Concept
The simple approach to the "compression-only" requirement of interface
forces is to analyse the body as a continuous fully elastic structure
and inspect the interface region for tensile stresses. The elements of
the finite element mesh where these occur are then removed from the
analysis which is repeated until no tensile stresses are computed. For
the structural analysis of materials which can only carry compressive
stress, such as soil or rock, the simple approach was found to be
unsatisfactory as it did not always reach convergence and the solution
24.
where a no-tension interface developed was found to bear no
relationship to the development of physical crack patterns in the
structure. The "Stress Transfer" method of Zienkiewicz et al (Ref.
49) was specifically developed as a solution to this problem and the
essential steps of the method are as follows:
Stage Calculate principal stresses from a fully elastic analysis.
Stage 2 Eliminate any tensile principal stresses without allowing any
further displacement within the structure by applying equilibrium
restraining forces.
Stage 3 Null the effect of these forces by applying equal and
opposi te nodal forces. Re-analyse the structure for the effect of
such forces and superimpose the resulting stress distribution upon that
produced in Stage 2.
Stage 4
produced.
Repeat stages 2 and 3 until negligible tensile stresses are
This was the method on which Kennedy's work was based (Ref. 47) and in
his finite element program an incremental loading technique was used,
providing a means of applying a desired actuation force while being
limited to displacement loading. By modifying the elastic constants
for out-of-contact elements the no-tension state could be achieved
quickly for each load increment.
Implementation of the Stress Transfer Method
The Stress Transfer method was first implemented in the PAFEC program
for trial purposes, for the 2-D axisymmetric configuration in which th~
elements defining the friction interface were designated "friction
interface source" (fis) elements, since the same finite element mesh
was conveniently used for thermal calculations where heat flux input
was applied at nodes on these same elements.
defined so that the element x axis was
The element topology was
normal to the friction
interface, and the requirement for compression-only behaviour at the
interface was therefore
o (3.13)
25·
The first stage of the Stress Transfer process involved a full analysis
of the finite element model of the \ brake friction pair. The second
stage was quite straightforward because the "no-tension" stresses were
those normal to the friction interface, and their position, magnitude
and direction were defined. To calculate the nodal forces equivalent
·to the tensile normal stresses along the interface, it was assumed that
they followed a quadratic power law:
(3.14 )
where 1.- defines the transformed element axis parallel to the friction
interface. The displacement function associated with the fis elements
is also quadratic:
u(x..) = b1 + b2 (X) + b3(X,)' (3.15 )
or u(X) = [8] [)(.] (3.15a)
and for the element
{ u} = [C) ['X-] (3.15b)
The PAFEC system for computing equivalent nodal loads equates the
virtual work done by each loading system, so that
Ws = WF
where Ws = ) u ()(.)er():,) d ()(.) o
and
Substituting for {u}e and [8] in equation (3.16) gives
1 = 1 [8] [C]-l6"(X-)d():,)
o
(3.16)
(3.17)
(3.18)
(3.19 )
Substituting for ~(~), multiplying out and integrating equation (3.19)
gives
{E'} = [
~ 1~ -~] {;~} 30 -1 2 4 0-3
(3.19a)
along the interface of the fis element, so that {E'} is the vector of
equilibrium restraining forces for Stage 2. Stages 3 and 4 were
further solutions which required no modifications to the eXisting
system matrices.
3.3.4
26.
Stress/Strain Relationships for fis Elements
The relationship between stress and strain in a fis element is given by
= 0.20)
and altering [DJ for out-of-contact fis elements was found by Kennedy
to speed up convergence. For the general 2-D axisymmetric case,
[ ,-" -V "] [DJ = E 1-v 0 v ")/ 0.21 ) (1+"\1)( 1-2-.;1) 0 0 l-v 0
-V ")/ o 1-v
and since neither shear stress parallel to the interface cr yz) nor
stress normal to the interface (.s-x) are carried by an out-of -contact
fis element, the coefficients can be changed to give
[DJ 1 = E (1+)))( 1-2))) [l
o 0 1-"" 0 o 0
,v 0
0.22 )
This modification was incorporated into the program by setting up and
storing both [DJ and [DJ1 for each fis element and a contact criterion
determined which was used for the assembly of the system stiffness
matrix. The most consistent results (see Chapter 5) were given by the
average stress over the element interface nodes; when found to be
tensile, the element was considered to have lost contact. A further
check on the contact state of out-of-contact fis elements was made by
computing the nodal stresses using both [DJ and [DJ1 and applying the
criterion to each. Where an
a state of compression using
iteration continued.
out-of-contact element was found to be in
[DJ1, it was returned to contact and the
The Combined Stress Transfer Method
Calculations by the Stress Transfer method were found to be slow, and
it was observed that while the method represented a powerful technique
for the analysis of no-tension materials, the 2-D axisymmetric
simulation of the friction interface was a much simpler problem in
comparison, since the posi tion of the interface and the direction of
no-tension behaviour are defined. Only a small number of elements in
the fini te element model, viz. the fis elements, were required to act
in compression only, and any change from [DJ to [DJl could be
27.
accommodated by a partial re-merge of the system stiffness matrix [S]
instead of a full re-solution. In the Stress Transfer method as
programmed into the PAFEC system, both [D) and [D]1 were computed and
stored in the initial stages of the solution, and [S] was assembled
using [D) or [D) 1 as determined by the contact criterion, which was
basically similar to the simple approach described in Section 3.3.1.
Parts of the Stress Transfer programming were therefore combined with
the simple i tera ti ve approach, using the contact criterion to assess
the state of·stress within the fis elements, and repeating the analysis
with a modified system stiffness matrix. A flow chart for this
procedure is shown in figure 3.1, and the method was found to involve
considerably less extra programming than the Stress Transfer method.
The PAFEC program operates in a sequence of well-defined stages in the
finite element analysis, and the principal modifications refer to the
PAFEC Phase 6 (element and system matrix generation) and Phase 7
(solution of the primary unknowns), as follows (Ref. 50):
1. An extra data module containing friction interface information is
included in the PAFEC module library.
2. In Phase 6, both [D) and [D) 1 are set up and stored; all fis
3.
elements are assumed to be in contact for the first iteration
unless specified otherwise in the data. For subsequent iterations
the contact criterion determines which is to be used, and the
elements in [S] are modified accordingly.
The element stressing routines, PAFEC Phase 9, are
calculate the stresses in the fis elements for
required to
the contact
criterion, and are therefore brought forward into PAFEC Phase 7 so
the iterations operate only between PAFEC Phases 6 and.7.· Each fis
element is stressed using both [D) and [D]1 to assess the contact
state of the element, and the interface pressure distribution is
determined from the nodal stresses on the friction surface of each
fis element as described in Section 5.2.
4. When the iterations are complete, the analysis proceeds as normal
to a full stress calculation, if required. The simulation
requires information regarding the final contact state of the fis
elements for one time-step to be stored for the initial iteration
rw
28.
COMBINED STRESS TRANSFER METHOD - FLOW CHART
Define fis elements and friction interface parameters in Data
Read Data and Store
Form Stiffness Matrices
NO __ o__-.(
form {Se} as normal
NO
as~emble fsJ us~ng [Se i
fis?
another
>-----j_- YES
form and
element:)-_f>_-YES __ ...... __ ...J
displacements
FIG. 3.1
YES Change relevant coefficients in {S} to use {sj or {sJ " whichever was previously not used
state
c; has
)-~-YF.S-------------~------------~ another fis element
'V
~---->-- NO J~~:~~~~~YIO:' --------<e---------------------------------' ~ont"cV
state? V
ITERATION COMPLETE
3.3.5
29.
of the next which is achieved by writing the information to Backing
Store (8.S.), a file accessed by the program at the beginning of
each time-step.
Application of Wear
In the context of the finite element analysis, the effect of wear at
the friction interface is to reduce the compressive strain in the
in-contact fis elements, at the same time increasing the compressi ve
strain in the out-of-contact fis elements, encouraging them to return
to contact. The overall effect on the finite element mesh should be
zero so that no pre-stress or prescribed displacements are introduced
artificially , while the wear modifies the relative strain states of
each fis element, thereby contributing to contact variation and changes
in the interface pressure distribution. This required effect was
achieved by applying the difference between the nodal wear and the
average interface wear to each node in the interface as follows:
Calculated wear = at node i
Considering this as an additional strain at the node,
= (3.23)
and the strain at node i is therefore
0.24 )
For those fis elements in-contact
(3.25)
For those fis elements out-of-contact
= o <3. 25a)
To avoid the necessity of applying an external prescribed displacement,
as a first approximation, the additional compressive strain applied due
to wear at each node in the interface is,
<3.26 )
30.
E wear = 1 nc
Lt 6 wear. nc i= 1 1
<3.27 )
where nc is the number of in-contact interface nodes.
Summing equation (3.26) over the friction interface gives:
n
n _
= ~ .L: t. wear _ n i= 1
and the overall effect is zero.
The strain at interface nodes is therefore
{t} =
<3.28)
<3.29 )
For the purposes of the simulation the wear of the metal mating surface
was assumed to be zero, and wear in the fis elements, which represented
the surface layers of the friction material, was determined from the
wear characteristics of the friction material as discussed in Section
4.3. The calculated wear in each time-step was added to previous
values to give the cumulative wear over the duration of the simulation.
3.4 THE GAP FORCE METHOD FOR "NO-TENSION" ANALYSIS
3.4.1 The Gap Force Concept
The Combined Stress Transfer method enabled a sliding friction pair to
be modelled by a finite element mesh containing an interface defined by
special no-tension (fis) elements. An alternative approach was to
model each part of the friction pair by a separate finite element mesh,
connec ted together at the friction surfaces by nodal "Gap Forces",
which have the characteristics associa ted wi th the forces transmi t ted
across the friction interface, viz. compression-only. The method has
been extensively used for structural analysis where members which may
be initially separated can come into contact under load (Ref. 51, 52,
53). In such an event tangential frictional forces may be developed as
well as normal compressive forces transmitted, and problems of
shrink-fit and bonding have been studied using this method. The
slippage which may occur when the relative tangential force exceeds the
bond strength has definite parallels in problems of static and dynamic
frictional contact.
3.4.2
31.
Development of the Gap Force Method
Figure 3.2 represents a section of a friction interface between two
contacting compressible bodies, in which the surface node pairs 1, 2
and 3 are separated by initial gaps of .61, .62 , 063 respectively. Upon
application of an external compressive load, the relative displacement
of node pair 1 in the direction normal to the interface is 611, and the
necessary condition is for
~11 (3.30 )
Contact is produced between the two surfaces at node pair 1 when;
~11 (3.30a)
in which case normal forces are transmitted between the bodies and
friction forces are exerted in the tangential direction at the nodes.
If
611 < ..0.1 (3.30b)
contact is not achieved and no transmission of forces occurs at node
pair 1. By Amontons' Laws, the normal forces (F" for node pair 1)
and the tangential friction forces (F12) are related by
(3.31)
for dynamic friction, and
(3.32 )
for static friction. The direction of the frictional force opposes
the direction of relative motion for sliding friction, while for static
friction the magnitude and direction is sufficient (up to the limit) to
prevent relative tangential displacement of the nodes. If the
limiting value (~sF11) is reached, the node pair are permitted to slip
relative to each other in the tangential direction opposite to the
applied friction force.
Calculation of the equal and opposite Gap Forces applied to the
interface node pairs is based upon the method of Deflection
Coefficients. The total relative displacement of any node pair in the
32. FIG. 3.2
Gap Force Interface Simulation
body /
~"" node "'" pai r 1 pair 2 """ ,," " "-
node "" "" "".~ pair 3 "" "" elastic "- "" body '\
(0) INITIAL GAPS, BEFORE LOADING " "-
F12
"'~'" node pair 1
in-contact
~2 F3~ "'-
node pair 2 . nod~ "" out of pair 3 contact, in-contact
no transmitted forces
( b) DURING THE APPLICATION OF LOADING
33. interface is the sum of the relative displacements at that particular
node pair resulting from the Gap Forces applied at every node pair in
the interface. In the direction normal to the interface the relative
displacement at node pair 1 produced by a normal Gap Force increment
~Fi1 at node i is
(3.33 )
The full relative displacement of node pair 1 due to all the applied
interface Gap Force increments {dF} is
n
A .)11 = L Uxli = allAFll + a12AF21 + •••• + a1o"Fn1 i=l
and, with tangential forces related to normal forces by equation (3.31)
or (3.32), in the tangential or in-plane direction:
n
Ll~12 = L, uyli = b".~F12 + b1~F22 + ••• + b1 n.oFn1 i=l
0.35 )
The relative displacements of the interface node pairs may therefore be
represented by the matrix equation
0] {AFll} b AFi2
or [cl (3.36a)
where the values of the coefficients in [cl are determined from the
solution of the unit force load cases for each node pair.
Solving equation (3.36a) for {LlFG} provides Gap Force values to be
incorporated in the nodal force vector {F}
equation (3.4) which is then solved for {S}. the relative interface nodal displacements in
of the governing system
The difference between
{I} and{4da} determines
the nodal displacements required for the calculation of the Gap Force
increments for the next iteration. The Gap Force distribution is
built up by superposition and the process continues until a stable Gap
Force distribution is reached with no gap overclosure. At all stages
during the analysis the system is linear, and therefore no element
matrix re-assembly, or re-merging of the system stiffness matrix is
necessary.
34.
The Gap Force method was developed for the PAFEC 75 program by
Goldthorpe (Ref. 54) for both dynamic and static friction interface
simulation for 2-D plane or axisymmetric analysis, and a flow chart for
the solution program is shown in figure 3.3. Friction interfaces are
defined by the position of interface node pairs which must be
positioned close enough together to avoid any significant loss of
stiffness across the interface. The actual gap sizes are specified
separately, along with the properties of the friction interfaces
(coefficient of friction, static or dynamic, etc.) as additional data
input to the program.
Under the application of an external load, there is no initial
restraint on the amount of relative movement of the nodes in each pair,
and the iteration proceeds by calculating the gap forces which are
required to reduce the relative movement to the size of the gap
concerned from equation (3.36). Where tensile forces are calculated,
the gap has obviously "underclosed", and contact has not occurred, so
zero gap force is applied at these node pairs. The iteration
continues with further gap force increments until all the gap forces
are compressive, when tangential sliding friction forces, or the static
friction criteria are applied. The full solution for nodal
displacements is achieved by superposition of the final solution of the
system load cases and the initial solution of the external load case.
The whole process is repeated with friction forces applied until
successive iterations converge to give a compatible gap force and
friction force distribution.
The interface pressure distribution can be calculated without using the
PAFEC Phase 9 stressing routines (unless the full stress distribution
in the finite element model is required) by assuming the form of the
pressure distribution. Average interface pressure over one face of an
element adjacent to the interface may be calculated from;
{ ;:: 1 1
{ ::1 6 0 0
2 = 0 - 0 (3.37)
3 1
0 0 6 31
where P1 = P2 = P3 = Pi
35.
GAP FORCE METHOD - FLOW CHART
Define interface node pairs, gap dimensions and friction interface parameters in data
t I Read data and Store
t p'orm Stiffness Matrixl
t IGenerate System Load Casesl
t Solve for displacements '/
(System and Applied Load Cases)
t Evaluate deflection coefficients
matrices [A] and [B] t I
Calculate gap closure for each node pair [gap closure = current displacement - previous gap]
t Calculate gap force increments to give required closure
from {Fill = [A]-l {ASi11 etc.
t add Fil to previous Fil to give total gap force
r--NO ~ total for5e~YES----positive
...."
Set force increment equal and opposite to
last total force
~ current· total NO forces within YES
Calculate interface node displacements from superposition of system load case solutions for total gap forces and initial solution of applied load case. Back substitute and complete solution.
FIG. 3.3
36.
alternatively a quadratic form may be assumed, utilising equation
(3.19a).
Application of Wear
In the Gap Force method the actual dimension of the gap between the two
friction surfaces is determined by the specified gap value, not by the
dimensions of the finite element mesh, so wear of the friction material
can therefore be easily incorporated into the simulation by increasing
the gap size by the amount of wear which has occurred at each node
pair. The wear criterion used for the calculation of wear is
described in Section 4.3. The cumulative wear is carried over to the
next time-step by updating the sizes of the gaps in the data module in
Backing Store.
3.5 RIGID BOUNDARY "NO-TENSION" SIMULATION
3.5.1 Description
A simple technique for the application of friction forces to a 2-D
finite element model is the computation of tangential friction forces
from calculated normal reactions on a rigidly constrained boundary, and
the subsequent iteration to a compatible normal force and tangential
friction drag system. This method was used by Wintle (Ref. 40) who
modelled a brake shoe and lining so that the friction surface of the
lining was the rigidly constrained boundary, and the iterations were
completed manually to an acceptably converged solution. With the
assistance of an automatic iteration program, (see fig. 3.4) the method
was extended for drum brake analysis by Day, Harding and Newcomb, (Ref.
41) and was shown to yield good results for drum brake torque output
calculations.
The method is quick and effective but is unsuitable for a thermal and
thermo-elastic simulation of the brake friction interface because only
one part of the friction pair is modelled, and displacement, flexure
and distortion of the mating body, due to thermal or mechanical
loading, cannot be included. However, extensive use of the technique
has confirmed its validity and it has therefore been used for the
purposes of comparison between the Combined Stress Trans fer and Gap
force friction interface simulation techniques. The results from
YES
37. RIGID BOUNDARY METHOD - FLOW CHART
Define friction surface by rigid boundary constraint of the finite element mesh.
Define friction interface parameters in Data.
NO
Read Data and Store
Form Stiffness Matrices and commence solution
Complete solution to the calculation of REACTIONS
is current REACTION
comprcssive >---YES
FIG. 3.4
Release Constraint at this boundary node
Apply frictional fore'" F = ~R as external load on this boundary node
NO r--'-NO YES
is
L----Er---~--NN~e~xtt--~--~~JL~NO iteration
total riction drag
wi thin 1 % )--t=-- YES of previous
?
Iteration Complete
38. simple test analyses, shown later in Section 5.2, are similar,
confirming the satisfactory operation, while also illustrating the
limitations, of each technique.
3.6 THERMAL CALCULATIONS
3.6.1 Thermal aspects of the friction interface simulation
3.6.2
A combined thermal and thermo-elastic analysis is essential for the
simulation of a brake friction interface, and the time-step approach,
as used by Kennedy (Ref. 47) was adopted. Over the duration of each
time-step the interface contact and pressure distributions are assumed
to remain unchanged, and transient temperatures are calculated based
upon a heat flux distribution computed from the pressure distribution.
This represented a practicable approach to the combined analysis of
interface contact, pressure, and temperature distributions and the
length of time-step used was necessarily a compromise between accuracy
and cost.
In the PAFEC system, the same finite element mesh can be used for both
thermal and stress analysis, provided that the correct boundary
conditions are applied. This has been found to be convenient for the
2-D axisymmetric, but not for the 2-D plane analysis, and the design of
the finite element mesh is discussed in Chapters 5 and 6 for
particular configurations of brake to which the friction interface
simulation has been applied.
Frictional Work
The braking torque generated in a friction brake is calculated from:
x2 T = ~ ~r(x)p(x)A(x)dx
xl
(3.38 )
where a pressure distribution p(x) exists over a friction surface xl to
For a 2-D axisymmetric idealization of an annular disc brake
configuration, this simplifies to
r2
T = I ~21T r'p(r)dr r,
<3.39 )
39·
The friction surface in the finite element mesh is divided into "nodal
areas" associated with each node in the friction interface, and over
each such nodal area the pressure distribution may be assumed constant;
From equation (3.39) the contribution of each nodal area to the total
torque generated is
T =
= ri1 + ri2 for small nodal areas 2
and the total torque generated is therefore n
T ~L.4. T = E IlPi[2fr rm' (ri2-r i 1) 1 i=1
(3.40 )
(3. 40a)
(3.41)
For a 2-D drum brake configuration, x is measured along the lining
surface in terms of q" the angle subtended at the centre of the lining
arc, so that equation (3.38) becomes:
and for the finite element idealization:
n
T = L:.6 T = 2::::: Ilr2pi ~i i=1
The instantaneous power dissipation during braking is
A. Q = .4. T Go:)
and the total energy dissipated over the time-step is
Q =
c.J is constant for constant torque, therefore
T - At = I
•
(3.42 )
(3.43)
(3.44 )
(3.45 )
(3.46 )
40. Assuming that 100% of the work done by the brake is converted to heat
energy, and generated at nodes in the friction interface, heat flux is
applied and transient temperature distributions are calculated using
the standard PAFEC 75 analysis. The heat flux input to each interface
node is calculated from equation (3.44) using the relevant value of~T,
and applied as a ramp change over the time-step Llt from ""1 to ""2.
3.7 DISCUSSION
Simulation of the braking friction process by a time-step idealization
enables the combined effects of pressure, temperature and wear at the
friction interface to be investigated using finite element analysis
techniques. Methods for the analysis of the characteristic "no-tension"
behaviour at the interface have been developed for incorporation into the
PAFEC 75 program utilizing either special elements at the friction
interface (fis elements) or Gap Forces connecting the two parts of the
friction pair. The effects of wear at the surface of the friction
material may also be included.
The Combined Stress Transfer (CST) method was found to be more convenient
to use than the Stress Transfer method and is suitable for use in the 2-D
axisymroetric configuration where the generated friction forces are in the
circumferential (out of plane) direction. These do not affect the
interface contact or pressure distribution calculations since the only
relevant friction forces are those arising from the relative displacement
of the friction components in the radial direction which introduces shear
into the fis elements. Such displacement must be small to minimize
unrealistic effects at the friction interface, and therefore extension
of the CST method to include dynamic friction forces has not been pursued.
The Gap Force method enables friction forces, static or dynamic, to be
realistically incorporated according to -Amontons' Laws, and fs therefore
eminently suitable for either 2-D axisymroetric or 2-D plane configurations
and could easily be extended for 3-D analysis purposes. Comparison of
the different methods of interface simulation together with the Rigid
Boundary technique (previously used for drum brake analysis (Ref. 41» is
described in Chapter 5.
The work done against friction has so far been assumed to be all converted
to heat, calculated from nodal values of interface pressure and applied
to nodes on the surface of the friction material. Heat generation and
dissipation, and consequent temperature rise, are known to affect the
/
41. resin bonded composite friction material and it is necessary to determine
whether there are any mechanisms of frictional heat absorption or
dissipation which contribute to the process of frictional energy
transformation. Detailed study of the friction material is also
necessary so that thermophysical properties appertaining to its use can be
applied to the finite element idealization with some confidence. Changes
in these properties, not only with temperature, but also with thermal
degradation of the friction material, may have a significant effect upon
the idealization. The physical and chemical aspects of resin bonded
composite friction materials are studied in detail in Chapter 4.
42.
4. FRICTION MATERIAL
4.1 CHEMICAL NATURE OF FRICTION MATERIALS
4.1.1 Formulation
Modern friction materials are specially formulated from many
constituents to give good frictional and wear performance under the
sliding contact conditions of braking. The basis of such formulation
is usually a polymeric binder (resin) and a fibrous matrix which
provides most of the mechanical strength necessary to withstand the
generated frictional forces. Recent trends have been away from
asbestos fibre, once almost universally used, towards alternative heat
resistant fibrous materials with fewer known environmental
disadvantages, and the use of such materials has tended to highlight
thermal problems in braking and the importance of the processes of
frictional energy
etc., which are
transforma tion. The fillers,
added are intended to tailor
friction modifiers,
it to give the
characteristics as required, and it is often found that a trace of one
particular component is all that is necessary to achieve the desired
result. It is not possible as yet to relate the frictional, or wear,
performance to any material parameter based upon the bulk physical
properties, which are largely determined by the basic components of the
formulation.
4.1.2. Chemical Reactions in the Friction Material
Chemical reactions of the organic components exert a major influence
upon the behaviour of the friction material, and since the generation
of heat is _ an essential part of the brake friction proces_s, _ chemical
reactions, which are generally temperature controlled, can range from
minor reactions to full scale pyrolysis yielding a char residue. The
polymeric binder is most commonly based on a phenolic resin, and may
include phenol, cresol, xylenol and other related organic compounds. A
knowledge of the kinetics of thermal decomposition is
investigate the energy interchange which may occur
chemical reactions and to give a physical insight
essential to
during these
into possible
mechanisms which govern the tribological behaviour at the interface.
43·
Information on the degradation mass losses of resin bonded friction
material has been provided by Whitaker (Ref. 55) using Thermo-
Gravimetric Analysis (TGA) methods. The thermal decomposition of the
phenolic resin has been shown to be an energy activated process
following an Arrhenius rate law where
Reaction Rate Z = Bexp(-Qa/RS) (4.1)
in the chemical kinetic equation
(4.2)
Small (lg) block samples, which were found to give the most consistent
results, were analysed for a range of heating rates, and values of the
coefficients Band
(4.2) (see Table
Qa in
4.1) •
equation (4.1)
The value of n
were estimated from equation
was consistently found to be
unity, so that the rate of degradation is directly, proportional to the
amount of undegraded material present at any stage during the analysis.
This is particularly useful when using the TGA technique because the
weight loss can be directly related to the degraded material.
TABLE 4.1. REACTION RATE COEFFICIENTS
MATERIAL HEATING B Qa NUMBER RATE
(OC/min) (min- 1 ) (kJ/mol)
1 8 5.6 x 109 140 6 1.7 x 10 10 145 4 2.9 x 108 130
---------------- --------------- -------------1-------------2 6 4.4 x 108 120
4 4.9 x 109 140 ---------------- --------------- -------------r--------------
3 6 1.8 x 10 12 160 4 1.2 x 10 10 140
The heating rates used were very much lower than those existing in a
brake friction interface, but such rates are impossible to achieve in
practice, while still permitting an analysis. The results shown in
Table 4.1 were obtained using air, but similar values for Qa were
obtained in an inert atmosphere of Nitrogen which is generally
considered to be more representative of the oxygen-starved conditions
at the friction interface. The variation in the estimated values of B
was part ially due to sampling errors, but as can be seen from the
typical results obtained by Whitaker (Figures 4.1 and 4.2) the
o C")
<Jl <Jl o -l
<Jl <Jl <{ ::E:
o N
200
44.
TGA RESULTS
HEATING RATE 6 DEGREES PER MINUTE
4-
""
FIG. 4.1
---~ "--"
If) If)
0 ...J
If) If)
« ::E
o
45.
TGA RESULTS
HEATING RATE 6 DEGREES PER MINUTE
FIG.4.2
o ("')
r . o
moss loss +'
-~--~----------- ~ 'E-~
0 N . 0
o . o
. ------ - -- "]"--,----,-- -r ----r-T 6bo 800
TEMPERATURE °C
46.
polynomial curve fit to the data does not always coincide at the
observed start of reaction, affecting B accordingly. Figure 4.1
shows measured percentage mass loss with temperature (together with the
polynomial curve fit) and in Figure 4.2, the same measured percentage
resin loss and the calculated rate dm/dt are shown. A general
characteristic of the results from TGA of organic friction materials
is the number of peaks in the reaction rate (dm/dt) of which two define
the major pyrolysis reactions. The first may occur between 200°C and
400°C depending upon the particular material, and is generally assigned
to the thermal degradation of a second major organic component of the
friction material (usually a friction modifier), while the second
occurs between 550°C and 600°C, representing the thermal degradation of
the phenolic binder. These results compare well with other published
work on phenolic resin decomposition, e.g •. Nelson (Ref. 56) where a
typical value of Qa is quoted as 140 kJ/mol and the major reaction peak
occurs at approximately 580°C.
4.1.3. Breakdown Products of Friction Material
The products of thermal degradation of resin bonded composite friction
material include solid, liquid and gaseous components, representing the
char residue (solids) and mass loss during the reaction (liq uids and
gases). The production of volatile components at the interface is
considered to affect frictional performance; brake fade, for example,
is thought to result from gaseous or liquid fractions released at the
interface, (Ref. 57) because of the high pressures. Volatile products
usually associated with thermal degradation of phenolic resins have
been identified using Pyrolysis-Gas Chromatography and Mass
Spectrometry techniques, and good correlation between these two meth~ds
was found. One of them, the P.G.C. technique (Ref. 58) has been used
within Mintex Ltd. for the identification of evolved species (Ref. 59):
Hydrogen, Carbon monoxide and dioxide, Methane, Ethane, Ethylene,
Acetylene, Water and Formaldehyde were all detected using thermal
conductivity techniques, Aromatic Hydrocarbons and Phenols were
detected using flame ionization detection, and gaseous species were
identified using Infra-Red Spectroscopy techniques. Reactions in the
range 350°C to 600°C as identified in TGA (Section 4.1.2) were
investigated under different gases and the results showed that while as
much as 30 cm3 of gaseous product could be produced in Nitrogen (inert
atmosphere) from 0.5 cm3 of solid friction material, in air some
4.1. 4
47.
condensation occurred reducing the final volume of gaseous product.
These experiments encountered great difficulty in achieving accurate
measurements but some idea of the relative concentrations of evolved
gases under inert atmosphere conditions is shown in Table 4.2.
TABLE 4.2 MEASURED GASEOUS CONCENTRATION - MOULDED DISC BRAKE PAD MATERIAL (NO. 1).
TEMPERATURE METHANE CARBON : I ETHYLENE I ETHANE I AMMONIA CARBON DIOXIDE MONOXIDE
(OC) volume parts ~er million
400 1900 8200 600 1500 - -450 2700 5500 1100 1600 - -500 4600 7200 2300 3400 - -
Degradation Profiles in Used Friction Material
The nature and extent of the thermally induced chemical reactions in
used friction material can be assessed by analysing layers of material
through its thickness. If the friction material has been subjected to
quasi-steady usage, progressive degradation can be considered to have
produced thermal equilibrium at each layer.
A number of disc brake pads which had been subjected to a steady duty
level under dynamometer test conditions were examined by Whitaker (Ref.
60) • The layers were removed in thicknesses of 0.5 mm using a slow
speed milling cutter, and the samples thus collected were analysed for
organic content by Thermogravimetric analysis. The total volatile
content of each layer of a model friction material (Material number 2;
65% asbestos, 20% inert filler and 15% Phenolic resin by weight) was
found to range from 16.3% (virgin) to 11.5% (surface layer char) as
shown in figure 4.3. The elemental carbon content of each layer was
also determined and found to increase from' 611. of the organic content
in the virgin condition to 741. in the surface layer, results which were
in general agreement with those of Bark et al (Ref. 11) who found a
0.125 mm surface layer of a similar model compound to have over 901.
carbon in the organiC content. Commercial friction material
formulations which contain additional organic components as friction
modifiers have been found to produce a degradation profile similar to
that also shown in figure 4.3, indicating reduced penetration of
Degradation Profile through Disc Brake Pad Material
17
o ::0 Cl }> Z n
n o Z -i fTl Z -i
10
-----=:=------- .......... '--~
"" '\ \
-- MATERIAL No. 1 \ - - - TYPICAL COMMERCIAL MATERIAL \
\ \ \ \ \
\
6 4 2 0 DEPTH BELOW FRICTION SURFACE (mm)
"T'\
Cl . .l>-. w
4.1. 5
49.
thermal degradation with a more pronounced char layer. Similar
effects have been shown for drum brake linings by Jacko and Du Charme
(Ref. 61).
Further evidence of the nature of thermal degrada tion in the surface
layers of the material was found by examining each layer using PGC
techniques. From the breakdown products identified, the oxygenated
organic species (phenol, cresol, xylenol) which predominate in the
virgin friction material were absent in the surface layer, where the
de-oxygena ted species (benzene, toluene and xylene) formed the major
part of the organic content. Selecting Phenol as an example of the
oxygenated species it was shown (figure 4.4) that over 30% phenol
content in virgin material was reduced to zero at the surface layer,
while the Benzene content, an example of the de-oxygenated species,
increased from 2% to over 14% (figure 4.5).
Energy of Degradation of Friction Material
The energy of a chemical reaction may be
Differential Thermal Analysis (DTA) technique,
determined using the
where the total hea t
content of a sample of material is compared with that of an inert
material heated through the same temperature range in the same
environment. Using this technique Sykes (Ref. 62) showed that in an
inert atmosphere of helium, the energy absorbed during complete
degradation of Phenolic Resin was 293 kJ/kg over the temperature range
350·C to 850·C, and found the char produced to consist mainly of
carbon (93%). In a study of ablation mechanisms, Beecher and
Rosensweig (Ref. 63) demonstrated that the heat of decomposition of a
glass reinforced phenolic resin, 375 kJ per kg of resin, represented
only 4% of the total energy required to heat the material through the
prescribed temperature range.
Material from the surface layer of the used friction material described
previously (Section 4.1.4) was examined by OTA, and the results showed
that in an oxidising atmosphere (air) the reactions were exothermic,
while in an inert atmosphere (nitrogen) the reactions were endothermic.
The process of friction material degradation has already been shown to
result in de-oxygenation of the organic species and therefore the
reactions at the interface are considered to occur in inert atmosphere
condi t ions, orA of other layers from the used friction material
Phenol Content of Used Disc Brake Pad
~--.....
................
"-~ 30 '-------.. 0
"--u
'" :r: rn '\ z \. 0
\ r
"T] \ ::lJ \ 0
3:: • \ \Jl
20 400 C 0
-u \ • G) -- -- 450 C \ n
\ \ \ \ \
10 \ \ \ \ \ .,., \ -
Cl . -I>-.
0 , , , -I>-
6 4 2 0 DEPTH BELOW FRICTION SURFACE (mm)
Benzene Content of Used Disc Broke Pad
25
/ /
~ 20 / 0 / OJ / m
/ z • N 1.00 C / m / V1
~
Z • I . ---- I. 50 C m 15 / " / JJ 0 / :s:
/ lJ 10 I Q n /
/ /'
.. / --//
5 ./
../ ----..----
.." -Cl .
0 • • • • ...
6 I. 2 0 Ul
DEPTH BELOW FRICTION SURFACE (mm)
4.1.6
52.
showed that different amounts of energy were required to degrade each
layer, most for the virgin material and least for the surface layer.
The amount of energy required to degrade virgin material to char was
estimated to be 45 kJ per kg of friction material.
Idealization of the breakdown products of Friction Material - the 5
phase Model
The foregoing investigation of the degradation profile of resin bonded
composite friction material used under high energy braking conditions
has shown that thermally induced chemical reactions cause changes in
phase of the friction material. Although such changes are continuous
through the thickness of the material, an approximation of the
important characteristics of the phase changes has been made by an
idealization of the material in 3 phases of degradation. Referring to
the degradation profile shown in figure 4.3, the idealization
represents a layer which is predominantly char, a phase in which some
degradation is apparent and a third phase of unreacted or virgin
material. Based upon the chemical analysis of used friction material,
these phases are described as follows:
PHASE 1 Virgin friction material exists in a relatively unchanged state from ambient temperature to about 180·c.
PHASE 2 The Reaction Zone or Transpiration state is the phase in which degradation occurs, in the temperature range 180·c to 400·C.
PHASE 3 The surface layer of Char is the residue from the Reaction Zone, and exists within the temperature range 400·C to 1000·C.
The idealization of the materials comprising the rubbing pair is completed by:
PHASE 4 Wear debris, which descri bes the products in the spaces between the two surfaces at the interface, may also include any material transfer to the mating surface. This phase consists mainly of inorganic material and, once sliding is initiated and wear has occurred, can be present right through the temperature range, from ambient to 1000·C.
PHASE 5 Metal mating body, which for the purposes of the finite element idealization (Chapter 3) is assumed to be perfectly smooth and elastiC, and unaffected by wear. Grade 14 or 17 grey Cast Iron (BS1452) is commonly used for automotive brake drums or discs, high carbon steels are frequently used in mu1tip1ate annular disc brakes, and non-ferrous metals, e.g. copper may be used in specialist applica tions.
, (
53.
4.2 MATERIAL PROPERTIES
4.2.1 Measurement of Properties
The measurement of simple mechanical parameters of resin bonded
composite friction material demonstrates the anisotropic nature of the
material by producing, for example, three different values for tensile
strength in each orthogonal direction. Although anisotropic materials
can be modelled by finite element analysis, the amount of detailed
study of both the techniques involved and the material itself is beyond
the scope of this work. In attempting to measure the thermophysical
properties of friction material, the following assumptions have been
made:
1. The material is linear elastic in tension and compression,
2. The property measured in the direction of interest also applies to the other orthogonal directions,
3. The properties are constant with time.
It has been found that generalised values are required for properties
in finite element analysis since, e.g. compressive effects in the
direction normal to the interface are equally important to the analysis
as flexural effects in the transverse direction.
Young's Modulus (E) for the material has been estimated from the
compressibility characteristics of the material (compressive pressure :
compressive strain) in the direction normal to the ,interface, and also
from the characteristics obtained during tensile testing, which uses a
specimen cut in the transverse direction.
Poisson's Ratio (~) is a difficult parameter to measure for polymeric
materials because classical isotropic behaviour iSe not always found and
can only be assumed for the purposes of model simplification. This
may, however, be justified since friction ma terial is almost always
used in a configuration where the thickness is small in comparison with
the other dimensions, and bonding or riveting to a backing plate or
brake shoe reduces the lateral strains introduced by compressive
applied forces. High surface friction also produces a lateral
stiffening effect even where friction drag creates tangential tensile
forces. Al though conventional measurement techniques using "right
cylinder" shaped specimens may yield values of V as high as 0.5 (Which
4.2.2
54.
is theoretically inadmissible for isotropic elastic materials)
experience of brake analysis has shown that good correlation can be
achieved using a value of similar to that of the backing plate or shoe,
viz. 0.25.
Density (f) can be accurately determined and the comparison between
measured density (measured by the displacement method) and theoretical
density (calculated from the material formulation) enables the voids
ratio of the material to be determined if required.
Thermal Expansion (~) was measured using small (6 mm diameter by 4 mm
thick) specimens in the direction normal to the friction interface,
over a temperature range from ambient to 375°C, for a heating rate of
20 o C/min. (See Section 4.2.3).
Thermal Conductivity (k) was investigated using "Lee's Disc" type of
apparatus.
Specific Heat (Cp ) was actually calculated from the material
formulation and this technique has been found to correlate well with
measured values from 2 methods of determination, viz. Newton's Cooling
method and a method based upon DTA.
Variation of Material Properties with Temperature
All thermophysical properties are temperature dependent to some extent
and, with resin bonded composite friction material, matters are
further complicated by chemical reactions within the material. The
idealization of friction material into 3 phases, viz. Virgin material,
Reaction Zone and Char (see Section 4.1.6) required thermophysical
properties throughout the temperature range of each phase in order to
be incorporated into the finite element analysis, ~ as described~~ in
Appendix 1. Typical property values for each phase are shown in Tables
4.3 and 4.4 for a moulded disc brake pad material and a heavy duty
moulded drum brake lining material. Where measured values were not
available, estimates were made either from published work on friction
materials or literature values for similar chemical compounds. The
measurements published by Lagedrost et al (Rer. 64) for composi te
railway brake blocks were determined by advanced techniques utilising a
TABLE 4.3
MATERIAL TRANSITION TEMPERATURES LOWER HIGHER
(formation) (degradation)
VIRGIN - 200·C DRUM BRAKE MATERIAL
REACTION 200·C 400·C ZONE DRUM BRAKE MATL
CHAR LAYER 400·C 1000·C
WEAR DEBRIS - -
x MOULDED DISC BRAKE PAD MATERIAL
PROPERTY VALUE OF PROPERTY AT TEMPERATURE
50 100 150 200 250 300 350 400
E(N/mm2) 300 280 260 240 f(kg/m3) 2250 •
-6 -6 -6 -6 ~(K-l ) 14xl0 23xl0 32xl0 78xl0 k(W/mK) 0.9 .. Cp(J/kgK) 1200 .. E(N/mm") 300 280 260 240 220 .. f(kg/m3 ) .. 2250 •
-6 -6 -6 -6 -6 -6 lS'(K-l) 14Xl0 23xl0 32xl0 57xl0 81xl0 85xl0 k(W/mK) • 0.9 • Cp(J/kgK) • 1000 , .. E(N/mm") -f(kg/m3 ) .. 1500 tcK-l ) -k(W/mK) .. 0.2 Cp(J/kgK) .. 700
Mechanical Strength Negligible (E, f ,'t "'" zero) k(W/mK) 0.07 Cp(J/kgK) 1000
(·C)
500 600 700
•
• .. .. ..
V1 V1
TABLE 4.4
MATERIAL TRANSITION TEMPERATURES LOWER HIGHER
(formation) (de.o:radation)
VIRGIN - 200°C DRUM BRAKE MATERIAL
REACTION 200°C 400°C ZONE DRUM BRAKE MATL
CHAR LAYER 400°C 1000 0 C
WEAR DEBRIS - -
HEAVY DUTY MOULDED DRUM BRAKE LINING MATERIAL
PROPERTY VALUE OF PROPERTY AT TEMPERATURE
50 100 150 200 250 300 350 400
E(N/mm2) 372 330 290 250 P (kg/m3) 1550 ..
-6 -6 -6 -6 If(K-l) 12xl0 20xl0 35xl0 47xl0 k(W/mK) 0.5 .. Cp(J/kgK) 1235 • E(N/mm~) 372 330 290 250 220 200 • f(kg/m 3 ) 1550 ..
-6 -6 -6 -6 -6 -6 '6(K-l) 10Xl0 10xl0 16xl0 20xl0 25xl0 • 15xl0 k(W/mK) • 0.5 .. Cp(J/kgK) .. 1200 .. E(N/mm~) -f(kg/m 3 ) .. 1500 ~(K-l ) -k(W/mK) • 0.2 Cp(J/kgK) .. 700
Mechanical Strength Negligible (E'f''!; ~ zero) ~
k(W/mK), 0.07 Cp(J/kgK) 1000
(OC)
500 600 700
.. .. •
.. ..
V1
'"
57.
pulsed laser and a differential scanning calorimeter, and these are in
general agreement with values measured for automotive friction
materials.
Determination of the Coefficient of Thermal Expansion of Heavy Duty
Moulded Drum Brake Lining Material
Specimens of friction material for the measurement of the coefficient
of thermal expansion were cut from full size pads or linings. The
thermal expansion of the material in the virgin condition was found to
be greater, and to have a different characteristic with temperature,
than that measured on repeat tests on the same sample. These repeat
tests were considered to represent material in the "Reaction Zone"
phase, and the effect was investigated by taking 5 consecutive
measurements on 3 samples of the drum brake lining material.
The maximum thermal expansion coefficient of a virgin material was
found to be approximately 80 x 10-6 K-1 over the temperature range
200°C-250°C as shown in figure 4.6. Above 300°C approximately, the
sample appeared to contract, indicating that the material was changing
phase from the virgin state. This was confirmed by the second
measurements shown 1n figure 4.7, and subsequent measurements (figure
4.8) showed little further change; therefore the coefficients of
thermal expansion of the drum brake lining material in the Reaction
Zone phase, over the temperature range 0-375°C, were estimated from
figure 4.8.
4.3 WEAR OF FRICTION MATERIALS
4.3.1 Idealized Wear Relationships
The energy activated process of thermal decomposition of the phenolic
resin, which follows an Arrhenius rate law (equation (4.1», was found
by Rhee and Liu (Ref. 16) to be a major factor in the high temperature
wear of resin bonded composite friction materials.
described by the two relationships:
I I ' Below 232°C ~w = f3 pa vb t
Above 232°C .6.w = ,Bpavbtexp(-Qa/Re)
The wear rate was
(4.3)
(4.4)
58. FIG. 4.6
T her m al EXR..:::a:..:..:n:.::::s;..::i o:.:....n~o::...:f~M;..::o:..::u:..:.:ld::.:e:....:d==--::::.D.:....:r u:::..:m~::::.B.:....:ra~k~e
100 )(10-6
z o
Lining Material
(a) Virgin
V>
~ IT ~ I ~ ot-~~~~~~~~--~~~~~~~~~~:-~~ 0::: 100 200 300 !.OO W TEMPERATURE (·C) I f-
Z ...JO <{-
2:~ o:::<{ WQ IX I-W
Z ...JO <{-2:Lf) o:::Z W~ IX I- W
o
o
59· FIG. 4.7
Thermal Expansion of Moulded Drum Brake Lining Material
( b) Non -virgin
o 100 200 300
o
TEMPERATURE ('Cl
FIG. 4.8
Thermal EXRansion of Moulded Drum Brake Lining Material
(c) Reaction Zone
100 :2 00 300 l.u i TEMPERATURE ('Cl
60.
The effect of sliding velocity was not investigated, but in the finite
element simulation where each brake application is divided into a
number of time-steps of short duration (Chapter 3) over which the
change in sliding speed is small, the effect on wear could be safely
assumed to be negligible. Velocity can be considered to be included
in the exponential term of equation (4.4) since the velocity component
provides the energy for higher temperature weal' at incl'eased sliding
speeds. Below 232°C, where the contribution of the energy controlled
mechanism is negligible (equation (4.3», it is usually assumed that
both a' and b' are unity and wear is linearly related to work done.
Rhee and Liu (Ref. 16) presented Arrhenius plots (loge( Llw/t) vs lIB)
fol' a number of commel'cial brake lining materials which demonstrated a
linear relationship enabling values of -Qa/R (slope) and 10ge(,B pa)
(intercept) to be determined. The values of activation energy (Qa)
obtained, between 16 and 40 kJ/mol could be compal'ed with activation
energies obtained from TGA analysis for the thermal decomposi ticn of
friction material (Section 4.1.2, Table 4.1) and from published results
for the decomposition of phenolic resin alone, both of which gave
values in the region of 140 kJ/mol. Thus, although the Arrhenius
plots provided evidence for an energy activated wear process, thermal
decomposition of the phenolic resin alone does not appear to define
completely the material wear rate. A possible explanation for the
difference, however, lies in the different heating rates, with the high
energy sliding conditions producing much higher heating rates than is
possible in TGA methods.
Empirical Determination of Wear Rates
The approach used by Rhee and Liu (Ref. 16) was considel'ed to be the
best method for the examination of friction material wear, and so an
empil'ical wear criterion of the fOl'm;
(4.5)
was used, based upon equation (4.4). Numerical values for the
constants in this equation were determined using data fl'om friction
matel'ial weal' tests on the F. M. T. or "Chase" machine. This is a
standard machine for friction and wear assessment in the U.S.A. (where
it was developed), in the U.K. (B.S. AU 142) and other European
61.
countries, and consists of a dead weight loaded 25 mm (1 inch) square
specimen rubbing against a 280 mm (11 inch) diameter brake drum. Test
data were obtained using a Company-developed wear assessment schedule
designed to give test wear comparable with the wear occurring in
practice for similar pressure and duty levels. Details of this
schedule, for which the rubbing speed is maintained constant at 6.34
mls during the prescribed number of cycles, are shown in Table 4.5.
TABLE 4.5. CHASE WEAR ASSESSMENT SCHEDULE
Number of Initial Drum Rubbing Total Cycle Applications Temperature Time Time
(OC) (s) (s)
20 100 10 30 200 100 10 30 200 200 10 30 50 300 10 20 20 400 10 20 20 100 10 30
The wear of the specimen was measured both in terms of thickness loss
and weight loss at the end of each temperature step, providing a check
for non-uniform wear which can occur as a result of thickness
distortion (swell) or particle drop-out. Table 4.6 shows the
comparison between weight loss and thickness loss for a moulded disc
brake pad material. There was only a small difference between the two
methods and the weight loss results were used in preference since they
were considered to be more accurate.
TABLE 4.6 COMPARISON OF WEIGHT LOSS AND THICKNESS LOSS FOR A MOULDED DISC BRAKE PAD MATERIAL
Temp. Pressure Thickness Weight Loss Measured Weight Loss Loss
J w(mm) L\w x 104
°C (MN/m') (kg) Aw x 104 (kg)
100 1.38 0.193 2.478 2.515 0.69 0.094 1.207 1.324 1.38 0.266 3.415 3.295
200 1.38 0.137 1.759 1.827 0.69 0.131 1.682 1. 700 1.38 0.172 2.209 2.110
300 1.38 0.298 3.827 4.078 0.69 0.230 2.945 3.096 1.38 0.380 4.879 5.565
400 1.38 0.278 3.570 4.138 0.69 0.081 1. 040 1.448 1. 38 0.230 2.953 3.291
-
62.
Wear test data for a moulded disc brake pad material and a heavy duty
drum brake lining ma terial are shown in Tables 4.7 and 4.8
respectively.
Writing equation (4.5) in logarithmic form,
(4.6)
least squares fits to an Arrhenius plot (loge(A wit) vs 1161) of the
data in Table 4.7, shown in figure 4.9, yielded the relationships for
the disc brake pad material;
(at 1.38 MN/m') loge(~w/t) = -2.75 - 2311/&
(at 0.69 MN/m') loge(~w/t) = -3.47 - 2237/&
(4.7)
(4.8)
from which the value of the index "a" in equation (4.6) was found to be
approximately unity.
TABLE 4.7 MOULDED DISC BRAKE PAD MATERIAL WEAR MEASUREMENTS
Temp. Pressure Wear .bw Time ~w ...lxl03 loge (g/in') t t B ~w
(OC) (MN/m') (s) (g/m's) (K-l) t
100 1.38 0.2515 2000 0.195 2.68 -8.54 200 1.38 0.1827 2000 0.142 2.11 -8.86 300 1.38 0.4078 500 1.264 1.75 -6.67 400 1.38 0.4138 200 3.207 1.49 -5.74
100 0.69 0.1324 2000 0.103 2.68 -9.18 200 0.69 0.1700 2000 0.132 2.11 -8.93 300 0.69 0.3096 500 0.960 1.75 -6.95 400 0.69 0.1448 200 1.122 1. 49 -6.79
100 1.38 0.3295 2000 0.255 2.68 -8.27 200 1.38 0.2110 2000 0.164 2. 11 -8.72 300 1.38 0.5565 500 1.725 1.75 -6.36 400 1.38 0.3291 200 2.551 1.49 -5.97
63. FIG. 4.9
Moulded Disc Broke Pad Material Wear
-5
-10+---~--...,---~--~-~~-~ 3·0 1/8 x 103 1-0 2-0
Moulded Drum Broke Lining Material Wear FIG.4.10
-5
\ \
\ \ \/ \~ ~ ~
\
-10t----~ HI 2n
\ \
\
:lO 1/8 xio J
TABLE-4~8--MOULDED HEAVY DUTY DRUM BRAKE LINING MATERIAL WEAR MEASUREMENTS
Temp. Pressure WearAw Time Aw ...1x103 Loge (g/in') t t B 4w
(OC) (MN/m') (s) (p:/m's) (K-1 ) t
100 1.38 0.229 2000 0.177 2.68 -8.64 200 1.38 0.374 2000 0.290 2. 11 -8.15 300 1.38 0.270 500 0.836 1. 75 -7.09 400 1.38 0.777 200 6.027 1.49 -5.11
100 1.38 0.152 2000 0.118 2.68 -9.04 200 1.38 0.360 2000 0.279 2. 11 -8.18 300 1.38 0.339 500 1.050 1.75 -6.86 400 1.38 0.549 200 4.255 1.49 -5.46
100 1.38 0.139 2000 0.108 2.68 -9.13 200 1. 38 0.498 2000 0.386 2. 11 -7.86 300 1.38 0.312 500 0.969 1.75 -6.94 400 1.38 0.810 200 6.279 1.49 -5.07
100 1.38 0.152 2000 0.118 2.68 -9.04 200 1.38 0.360 2000 0.279 2. 11 -8.18 300 1.38 0.187 500 0.580 1. 75 -7.45 400 1.38 0.602 200 4.664 1.49 -5.37
100 1.38 0.102 2000 0.079 2.68 -9.45 200 1.38 0.259 2000 0.201 2.11 -8.51 300 1.38 0.162 500 0.502 1.75 -7.60 400 1.38 0.341 200 2.640 1.49 -5.94
100 1.38 0.127 2000 0.098 2.68 -9.23 200 1.38 0.249 2000 0.193 2. 11 -8.55 300 1.38 0.220 500 0.682 1. 75 -7.29 400 1.38 0.471 200 3.650 1.49 -5.61
100 1.38 0.121 2000 0.094 2.68 -9.27 200 1.38 0.259 2000 0.201 2. 11 -8.51 300 1.38 0.201 500 0.625 1.75 -7.38 400 1.38 0.416 200 3.225 1.49 -5.74
From these results, the value of Qa/R was taken to be 2250 K and
independent of operating pressure. Similar analysis of the data in
Table 4.8 (figure 4. 10) yielded a value of Qa/R of 2900 K and the
following equations for wear were derived for each of the two materials
studied:
Disc Brake Pad Material
dw/t = AW/ft = 1.5 x 1O- 11 p exp(-2250/6/) m/s (4.9)
Heavy Duty Drum Brake Lining Material
[wit = .dw/ft = 4.73 x 1O- 12p exp(-290018) m/s (4.10)
Equations (4.9) and (4.10) were used in the finite element analysis for
the calculation of wear at the surface of the friction material, using
nodal pressure and temperature values.
Equations (4.9) and (4.10) showed that the activation energy
controlling the wear rate of the heavy duty drum brake lining material,
24kJ/mol, was higher than that of the disc brake pad material,
19kJ/mol. Together with the values measured by Rhee and Liu (Ref.16),
from 16kJ/mol to 40kJ/mol, these results demonstrated the wide range of
activation energies of different types of friction material using
various polymeric binder resins. Where the Arrhenius type mechanism is
applicable, different activation energies associated with the thermal
degradation of polymeric resins appear to provide some indication of
the relative wear resistance of different friction materials.
4.4 COEFFICIENT OF FRICTION
4.4.1 Measurement of Friction Coefficient
4.4.2
The coefficient of friction of any resin bonded composite friction
material varies with a number of parameters, e.g. temperature, time,
sliding speed, and also depends upon the mating material. Cast iron,
used for automotive brake drums or discs, is generally utilized as the
mating material for the measurement of friction coefficient by
performance assessment either on small sample test machines (e.g. the
F.M.T. or Chase Machine) or on actual brake assemblies. Each has its
shortcomings;
while the
the former introduces artificial operating conditions
latter introduces complicating effects of the brake
performance, usually due either to self-energising or de-energising
mechanisms inherent in the, brake geometry - see Chapter 6.
Values of Friction Coefficient
Although frictional energy transformation is affected by changes in the
coefficient of friction, the objectives of this work were to study the
effects of frictional energy transformation on all aspects of brake
66.
performance independent of friction variation (Chapter 1). Single
representative values of friction level were therefore assessed from a
wide range of material performance data under "average" duty level
operating conditions.
Taking into account the effect of an EN8a mating surface and full face
contact in the annular configuration a coefficient of friction for the
moulded disc brake pad material of 0.3 was used in the 2-D axisymmetric
disc brake analysis (Chapter 5).
For the heavy duty moulded drum brake lining material a coefficient of
friction of 0.38 was used in the plane 2-D drum brake analysis
(Chapter 6).
4.5 DISCUSSION
Thermal and physical changes occur in resin bonded composite friction
material during braking which may be represented by 3 phases of material,
viz. Virgin zone, Reaction zone and a Char layer. A fourth layer of wear
debris at the interface and a fifth phase describing the metal mating body
complete the 5 phase idealization of the brake friction pair. An
attempt has been made to assess the significance of the energy interchange
involved in friction material phase changes by studying the thermal
degradation of Phenolic resin. The energy required to degrade virgin
friction material containing 15% Phenolic resin to char amounted to an
estimated 45 kJ per kg of material. The amount of frictional energy
which could therefore be assigned to the charring of each fis element of
the finite element model (Chapter 5) would be 55J, which compared with the
total energy dissipation over 3.5s at 600 kW/m' average power dissipation,
represents about 2% of the frictional energy dissipated over each fis
element. In the finite element simulation this phase change would occur
only when the transi tion temperature (average element temperature) was
reached, and, being irreversible, would only occur once during the
simulation. The relatively large size of the finite elements would also
make the change unrealistic in comparison with the continuous nature of
the wear/char formation mechanism; the amount of char which would form
during one 3.5s brake application would be much less than the thickness of
the fis elements since the char layer, once formed, would probably remain
at a relatively constant thickness, with new char forming to replace that
worn away. It may therefore be concluded that the energy interchange
involved in the thermal degradation of resin bonded composite friction
material does not make a significant contribution to the process of
frictional energy transformation.
Material properties have been presented for use in the finite element
analysis, but because of the complex nature of both the friction material
and the friction process, generalizations have been necessary. Some
effects of temperature variation on thermophysical properties have been
investigated and the coefficient of thermal expansion was found to be
particularly sensitive, especially in the virgin condition, and values
representing the Reaction Zone have been found to be the most consistent.
Although the wear of friction materials is not wholly governed by an
Arrhenius type of reaction, it represents a convenient empirical
description which yields a useful wear criterion. Frictional
characteristics have been assumed to be consistent with Amontons' Laws and
unaffected by temperature or pressure. Using this information concerning
the resin bonded composite friction material, and the finite element
methods described in Chapter 3, the dissipation of frictional heat energy
from the friction interface of an annular disc brake and a drum brake is
studied in Chapters 5 and 6.
68.
5. FINITE ELEMENT SIMULATION OF BRAKING FRICTION
IN AN ANNULAR DISC BRAKE
5.1 FINITE ELEMENT IDEALIZATION
5.1.1 2-D Axisymmetric Idealization
As previously described (Chapter 3) the finite element analysis method
has been developed using a 2-D axisymmetric idealization to represent
the annular discs of a multi-plate brake. A section through one
friction pair from the middle of a typical annular disc brake is shown
in figure 5.1, and by assuming the stack to be infinitely long, end
effects may be ignored so the rotor and stator are symmetrical about
their centre planes across which no heat therefore flows.
The 2-D axisymmetric finite element model represents a 3-D solid of
revolution provided that there is no circumferential variation in the
geometrical section so that contact, pressure, temperature and wear
distributions at the friction surface represent bands or annular rings
around a complete 360· of revolution. Although in practice, these
effects may be observed at the annular brake friction interface both as
"banding" and as localised "spotting", only the former can be
considered in this idealization.
5.1.2. Mesh Design
The finite element mesh used for the analysis was a model of the
friction pair from an annular brake test rig to be used for
experimental correlation of the results. The annular friction
surfaces were specifically designed to be 0.362 m 0.0. and 0.321 m
1.0., giving a narrow rubbing width of approximately 20 mm at a mean
radius of 0.17075 m. The mesh design was developed so that the same
basic form could be conveniently used for both the thermo-elastic and
thermal analyses of each time-step.
Transient temperature calculation in the PAFEC 75 system utilizes a
time-marching procedure for which a time-step value must be specified
(distinct from the time-step used in the simulation of the braking
process). To avoid oscillation and to obtain the most consistent
results, the time-step duration 6t must satisfy the criterion:-
69. ANNULAR FRICTION PAIR CONFIGURATION.
FIG. 5.1
Applied=---_.... t-t-H-f<ltttftl7!-l Force
'O;~ir---.:.R.:.::ec.:::act ion
FINITE ELEMENT MESH
I I I
--AXIS OF ROTATION-----
I I I ." " I I
" ", \
\ " " "
\ \
" "
, "
70.
0.5 "fo< 2 (5.1)
where fo = (5.2)
Since the cost is inversely proportional to the time-step duration, a
compromise between accuracy and cost was essential, and a time-step of
O.ls required do for the friction material to be 0.25 mm to give fo = 0.5. The mesh was designed with 3 layers of elements corresponding to
this dimension either side of the interface to cater for the expected
steep temperature gradients, while further away from the friction
interface the element size was increased as any effect of thermal shock
would be reduced. The number of elements at the friction interface
was determined by the minimum required to enable contact effects to be
realistically simulated. For the Combined Stress Transfer (CST)
method of interface simulation, the friction interface was defined by
"friction interface source" (fis) elements, mostly 1 mm long by 0.5 mm
thick, to give 20 elements and 42 nodes along the width of the rubbing
interface.
Frictional heat generation was assumed to occur at nodes on the face of
each fis element common to both the friction material and the fis
element, to simulate the generation of heat within the surface layers
as noted by Ling and Pu (Ref. 22) and discussed in Section 3.1.1. The
thermal properties of the interface elements therefore controlled the
contact resistance across the friction interface and were assumed to
be the properties of wear debris for out-of-contact elements and
friction material for in-contact elements (see Tables 4.3 and 4.4)
either of which could include other effects such as surface coating.
A diagram of the finite element mesh for CST analysis is shown in
figure 5.2 and the number and types of elements used are summarized in
Table 5.1.
TABLE 5.1 ELEMENT DETAILS
ELEMENT TYPE AND DESCRIPTION NUMBER ANALYSIS TYPE
36210 8 Node Quadrilateral 110 STRESS 36110 6 Node Triangle 60 STRESS 39210 8 Node Quadrilateral 110 THERMAL 39110 6 Node Triangle 60 THERMAL 39310 6 Node Boundary 26 THERMAL
71.
Finite Element Mesh
2-D Axisymmetric Configuration
181
179
-177 E E
III => 175 o « a:::
173
171
169
167
165
o
FRICTION ~ STATOR BACKING PLATE. MATERIAL. ~
3 5 7 8 9 THICKNESS (mm)
FIG. 5.2
y(radial)
L---':::;"x (axial)
ROTOR.
12 13 145
5.1. 3
5.1.4
72.
When used with the other friction interface simulation methods viz. the
Gap Force method and the Rigid Boundary method, the finite element
model required slight modification from its original form developed for
the CST Method. For the Gap Force method, elements 112 - 131 were
deleted for the stress analysis and the gap node pairs (see Section
3.4) were defined either side of the gap thus created, i.e., node pairs
86 and 107, 359 and 400, 87 and 108, etc. No change was necessary to
the finite element model for thermal calculations. The Rigid Boundary
method, only used for test comparison purposes, modelled the mating
body as a rigid boundary and required the boundary restraint on the
radial (y) plane defined through node 107 in the axial (x) direction.
Only the friction material and backing plate part of the finite element
model as shown in figure 5.2 was therefore used.
Thermo-elastic Analysis - Loading and Constraints
A multiplate annular disc brake is actuated by an axial force applied
at one end of the stack and is reacted at the other end. In the
finite element idealization the mid planes of the stator and rotor
plates (the outer faces of the finite element model) were constrained
to remain plane while taking the actuation and reaction forces
respectively. The actuaticn force loading was applied as a single
point load, equal to the total applied force, to node 595, and all the
other nodes in this plane were constrained to the same displacement by
means of the PAFEC REPEATED.FREEDOMS facility (this duplicates all the
constraint and freedom information for all nodes so defined). Nodes
along the midplane of the rotor were constrained as a rigid boundary.
This method of loading and constraint proved to function
satisfactorily, with the only disadvantage that bulk distortion
effects, in particular disc coning, could not be investigated, and had
to be accepted as a limitation of the idealization.
Thermal Analysis - Boundary Conditions
In order to minimize cost, only the rotor and stator components were
included in the finite element model, and the effects of heat transfer
from the circumferential edges of the annular discs were modelled using
the PAFEC surface heat transfer elements. The heat transfer
coefficient from the edge of the rotor was estimated using a number of
different methods. For an annular clutch El-Sherbiny and Newcomb
73.
(Ref. 45) assumed a constant value of 41 W/m'K over all exposed annular
surfaces which was derived by using a modified version of Nusselt's
equation (Ref. 65):
Nu = 0.055 (Re) 0.75 (Pr)0.4 (5.3)
for air flowing parallel to a smooth plane surface where PrO. 4 :::::- 1.
Cooling measurements from motor vehicle disc brakes have been
correlated by Newcomb and Millner (Ref. 66) using the relationship:
Nu = 0.015 (Re)0.8 (5.4 )
for turbulent flow around a disc. Using. equations (5.3) and (5.4) the
calculated surface heat transfer coefficients are shown in Table 5.2
for r = 0.181 m and &Jr = 7.0 m/so
TABLE 5.2 CALCULATED SURFACE HEAT TRANSFER COEFFICIENTS
Air I' 1 Re k h h temper- (kg/m3) (W/mK) (eqn 5.3) (eqn 5.4) ature(OC) (kg/ms) (W/m'K) (W/m'K)
0 1.294 17x10-6 606000 0.024 158 84 100 0.946 22x10-6 342000 0.032 138 71 200 0.746 26x10-6 228000 0.039 124 62 300 0.616 30x10-6 163000 0.045 111 55
The actual values of heat transfer coefficient from the free surfaces
of rotor and stator are dependent upon the design of the brake and the
amount of convection cooling which may be applied. Kennedy (Ref. 1)
assumed that all external surfaces were insulated, an assumption which
is acceptable for short duration transient temperature calculations.
Pearce (Ref. 67) carried out a comprehensive study of thermal boundary
qonditions for a commercially available air-cooled annular disc brake,
from which the relationship
h = 0.027 (601ol/21T) 1. 6 + 400 W/m' K (5.5)
was derived for the heat transfer coefficient from the edge of the
rotor disc. The high value given by this formula reflects the
SUbstantial ventilation cooling of that particular design of brake.
74.
Further detailed study of thermal boundary conditions was not pursued,
and an estimate of 100 W/m'K for the heat transfer coefficient from
free rotating surfaces (rotor) was made. This value was also
considered suitable for stationary free surfaces (stator), for which
cooling was provided by air flow produced by the rotating components,
(together with, on the experimental rig, a small flow of air necessary
for dust extraction through the casing) and for the heat flow between
contacting surfaces at the splines.
5.2 TEST ANALYSES
5.2.1 Test Load Cases
Two simple load cases were set up to validate the model for interface
contact determination and thermo-elastic analysis purposes. These were
run using each of the 3 techniques for friction interface simulation;
the Rigid Boundary method, the CST method, and the Gap Force method
(Chapter 3), to provide a comparison of the resul ts obtained, and to
check the satisfactory performance of each. Each method had been
developed using simple test models so that the principles of operation
were known to be correct.
Test Load Case 1 (Figure 5.3)
Compressive pOint load of 500N applied to node 593, radius 0.171 m.
Reactions taken at the centre plane of the rotor (restrained in the
axial (global x) direction).
Test Load Case 2 (Figure 5.4)
Tensile load of 500N evenly distributed over nodes 583, 584, 585 of
element 222.
Compressive load of 1667N evenly distributed over nodes 593 - 599 of
elements 227, 228, 229.
Reaction taken at the centre plane of the rotor (restrained as in test
load case 1).
75. FIG. 5.3
Test Load Case 1 y
'-----7X
W I-« .....J .....J
node 593 0.. ,«
SOON 0::: ~ W Z 1-' 0::: « 0 ~ '2: I-u 0 « 0::: m z .....J
O. .....J
W I- W W U W I- 0::: I-CJ) LL CJ)
node node 11 127
Test Load Case 2 FIG. 5.4
500 N {<t!'--I . \
W I-« .....J .....J 0.. - «
- --, , 0:::
~ .W 0:::
1 z ~ 0 ~ I-
1667 N u 2: 0
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0 .....J
W I- W W U W I- 0::: I-CJ) LL Vl
/ node' node
11 127
5.2.2
5.2.3
76. The elements in the finite element model were assigned the properties
of virgin friction material (Table 4.3) or of the steel mating body or
backing plate (see Table 5.3) as shown in figures 5.3 and 5.4.
TABLE 5.3 THERMOPHYSICAL PROPERTIES OF STEEL
E k Cp (N/mm' ) (kg/m') (K-1) (W/mK) (J/kgK)
209x103 7800 11 x10-6 48 452
Results from Test Load Case 1
The interface pressure distributions calculated using each analysis
method are shown in figure- 5.5: the computation of interface
pressures for the Gap Force method was described in Section 3.4 and for
the CST method the pressures were computed from the average value of
stress at each fis element node. A smooth pressure distribution was
produced by both the Gap Force and the Rigid Boundary methods, but
variability was observed, particularly over the friction surface of the
free edge elements (nos. 112 and 131), in the pressures calculated
using the CST method. These resulted from edge effects in the finite
element idealization where excessive distortion of edge elements
(demonstrated by the "bulging" of the edge fis elements in the
displaced shape plot in figure 5.6) affected the calculated stresses.
The other two methods were not affected in the same way because the
pressure distribution was computed from surface forces and not from the
element stresses. This variability would normally be discounted in
fitting a smooth curve to the pressure distribution and in the full
thermal and thermo-elastic analysis the average pressure over the fis
element friction surface was used to define the interface pressure
distribution in histogram form.
Results from Test Load Case 2
This load case was designed to test the "compression-only" function of
the CST and the Gap Force methods of interface simulation technique
compared with the Rigid Boundary method. The interface contact and
pressure distributions are shown in figure 5.7 and again the Rigid
Boundary Method and the Gap Force method were in close agreement, with
all elements from the outer radius to element 122 (0.170 m radius) out
of contact under the applied loading. This indicated that modelling
Z -i rn :;0
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Test Load Case 1
r:/ •
,
, , I
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Interface Pressure Distributions
Combined Stress Transfer Method
+-+- + Gap Force Method
0-0-0 Rigid Boundary Method
1605 mm Inner radius RUBBIN G PATH WI DTH
, , , , , q1
Outer radius 151mm
-Cl
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78.
Test Load Case 1 - C S T method
Q§Rlaced Shap...£
. -------
, 1/ ~ , 1"-I 1/ ~ i I", I
, , 1/ ~ I
1""-
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I" ~I :/ ~ I",
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Distorted mesh Undistorted mesh
FIG. 5.6
Z -1 rTJ
250
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v ::0
~ 150 (j1 c ::0 rTJ
~ 100 z -3 t'-l
50
o
Test Load Case 2 Interface Pressure Distributions
Combined Stress Transfer Method
Gap Force Method
00 0 Rigid Boundary Method
01 I . 1605mm Inner radius RUBBING PATH WIDTH Outer radius 181 mrr
,1-' . '\ 17 l \ ~ \ ~~Yl ' 1"-
! \ ',' }, 17 : ' \ ,..;. I Y ". " I'-.
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-----
GAP FORCE METHOD
___ --I", III '\ -I
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-' ~17 ~ ~ '> ~
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COMBINED STRESS TRANSFER METHOD
Test Load Case 2 Displaced Shapes
CD o
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5.2.4
81.
the rotor as a rigid boundary gives a good approximation to the
behaviour of the friction pair where the rotor is significantly stiffer
than the low modulus friction material, and in the absence of any
thermal or wear effects. The CST method predicted lost contact
extending from the outer radius to element 119 (0.173 m radius) and
again showed slight oscillation in the calculated pressures over the
free edge elements, 120 and 131.
The difference between the CST method and the other two methods is
ascribed to the different behaviour of the interface simulation. Those
fis elements which are in-contact possess a radial stiffness which
affects the radial strains accordingly, spreading the interface load
over a larger area in this test case. Comparison of the displaced
shape plots for all 3 methods under test load case 2 (figure 5.8) shows
that radial displacements at the interface were reduced for the CST
method.
Further testing of the Simulation Methods
Both the CST and the Gap Force method have been shown to function
satisfactorily in the simulation of compression-only interface contact,
but the full thermal, thermo-elastic and wear simulation could only be
tested by trial analyses. The results from such trial simulations are
presented in the Section 5.3 for the CST method which was the first to
be developed.
5.3 TRIAL SIMULATIONS USING THE CST METHOD
5.3.1 Simulation Parameters
A total of three trial simulations were completed, covering the
following types and-duty levels of brake applications;
1. Constant Speed Drag Braking, 2. High Energy Braking, 3. Low Energy Braking,
which enabled the convergence and stability of each part of the
analysis to be studied, so that refinements could be made where
appropriate.
82.
The maximum sliding speed was set at 6.5 m/s, approximately the same
as the sliding speed at which the wear data were obtained (Section
This corresponded to a maximum rotational speed of 38 rad/s
(370 rev /min), which was therefore used as the initial speed in the
brake . applications to rest, while for the constant speed drag
simulation a speed of 19 rad/s was used so that the average speed of
rotation in each case was the same. For a friction coefficient of 0.3
the average power dissipation level for each simulation was as shown in
Table 5.4. The method of loading and constraint of the finite element
model were described in Section 5.1.3 and are shown in figure 5.9.
TABLE 5.4 POWER DISSIPATION LEVELS
Simulation Average Power Dissipation Actuation Force (kW/m') (bhJl/in' ) (kN)
1 570 0.49 12.8 2 2450 2.1 55.4 3 120 0.1 2.8
Details of the Finite Element Analysis
Elements 112 - 131 were designated fis elements
work done, assumed to be wholly converted into heat
as heat flux input to nodes 86-106 on the friction
and the frictional
energy, was applied
surface. These
trial simulations were isolated from complicating factors arising from
the substantial difference between the thermophysical properties of the
friction material and the backing plate or mating body by assigning the
properties of virgin friction material to all elements in the sta tor
part of the finite element model as shown in figure 5.9, to remove
effects of backing plate flexure (Ref. 42). The friction material
properties were extended 1.5 mm into the mating body part of the
finite element mesh- to show up any instability or oscillation iil-th-e
transient temperature calculation which might have arisen from large
heat flux input to low conductivity materials, so the results were not
intended to be directly comparable with actual practice at this stage.
The duration of the simulation time-step was a compromise between cost
and realistic step-wise approximation and for the constant speed drag
braking analysis a time-step of 1s was used. This was later reduced
to 0.5s to cater for the high initial rates of frictional heat input
during brake applications to rest.
83. FIG. 5.9
Trial Simulation - Loading and Constraint
y
583
Friction Interface
Nodes along this face I constrained by PROPERTIES OF I
repeated freedoms --FRICTION MATERIAL-with node 593 I
12·83 kN -++593
Icj I~ I~ 1°
V)
I~ I~ I~ ID-
L-________ J-____ D--L~/
603 Node Numbers 127 169 191
'----~x
Nodes along this face restrained in axial (x) direction
5.3.3
84.
Results
Interface pressure, temperature and wear distributions for each
time-step of the 3 simulations are shown in Appendix 2 (figures A2.1
-A2.21l. The interface pressures were averaged over the friction
surface of each fis element, according to the formula:
(5.6)
where P1 and P3 represent the pressure at corner nodes and P2 the
pressure at the midside node (for constant pressure element face
loading is apportioned in the ratio 1 : 4 : 1).
also averaged over each fis element:
Interface wear was
(5.71
The results from these trial simulations showed that great variation in
interface pressure, temperature and wear could be produced by different
operating conditions at different duty levels. The interdependence of
pressure, temperature and wear was evident over each time-step such
that high temperature and wear were generated over regions of high
interface pressure. Stress variability over free edge fis elements,
resulting from excessive element distortion was responsible for
pressure, and corresponding temperature, peaks at the edges of contact
regions which could be 2 or 3 times as high as the general interface
temperature level over the contact region. These calculated temperature
peaks reached maximum values of 1300·C (constant speed drag braking),
3000·C (high energy braking) and 500·C (low energy braking) and were
considered to represent effects arising from the simulation method
which were exaggerated by the low thermal conductivity of the material
either side of the friction interface. Even at these high interface
temperatures, the stability of the transient temperature calculation
was amply demonstrated by the absence of oscillation in the axial
temperature profiles (figures A2.21-A2.24).
Interface pressure variability also affected the convergence of the eST
interface contact determination which during these early analyses used
a contact criterion based upon the average normal stresses on the nodes
of the fis element. Although Quick convergence was achieved (within 3
iterations) at the start of each trial simulation, in later time-steps
85.
one or more fis elements at the edge of the in-contact regions
oscillated between contact states so that the limit of 8 iterations was
reached without a stable solution. The high energy trial simulation
only converged up to 1.5s out of the full 3.5s compared with 2s for the
low energy trial simulation, which suggested that high temperatures
contributed to large thermal strains in the fis elements and could
increase the variability of interface stresses, particularly in edge
elements, to an unmanageable level. The differences between the
interface pressure distributions in consecutive iterations were small
(Table 5.5), and in order to enable the simulation to continue, any
oscillating fis elements were assumed to have lost contact.
TABLE 5.5 EXAMPLE OF INTERFACE PRESSURE IN SUCCESSIVE NON-CONVERGED
ITERATIONS, HIGH ENERGY TRIAL SIMULATION
fis element Time-step 4 (1.5 - 2.0 sec) number Average interface pressure
iteration 7 iteration 8
90 0 0 91 0 170 92 0 17 93 0 0 94 0 0 95 2870 480 96 3080 2000 97 2710 3010 98 3550 3790 99 4170 4390 100 4680 4830 101 5210 5270 102 5620 5680 103 5690 5870 104 5360 6580 105 5300 7190 106 1020 1010 107 1180 0 108 0 0 109 0 0
Although these effects of interface pressure variability could have
been reduced by refinement of the finite element mesh in the region of
the interface, a cost penalty would have been incurred. The most
effecti ve means of improving the convergence of the CST analysis was
found to be a modification to the contact criterion (See Section
5.4.2).
86.
5.4 ANALYSIS OF BRAKE APPLICATIONS USING THE CST METHOD
5.4.1 Low Energy Braking
The same low energy frictional sliding conditions as in the trial
simulation 3 (Section 5.3) were used as the subject of an analysis of a
low energy brake application from an initial speed of 38 rad/s to a
final speed of zero in a time of 3.5 s at an average power dissipation
of 510 kW/m'.
The friction interface was defined by the fis elements (112-113), which
were assigned the properties of friction material, with the surface of
the friction material positioned along the line of nodes 86-106. Nodes
101-121 again defined the plane of the idealized rotor surface, and the
rotor and backing plate elements were assigned the properties of steel.
Calculated interface pressure, temperature and wear distributions are
shown in figures 5.10 - 5.16 and again reflected the interdependence of
these three parameters. Initial high pressure regions at the inner
and outer edges of the rubbing path, exaggerated by edge effects, and
corresponding temperature peaks of 300·C compared with approximately
10·C over the central contact region, produced high wear so that
contact at the edges of the rubbing path was lost by the end of the
brake application. Oscillation between contact states of fis elements
at the edges of contact again prevented satisfactory convergence of the
CST interface contact determination from the 5th time-step on, so the
same assumption as used in the previous trial simulation (Section
5.3.3) was necessary to enable the simulation to continue.
As anticipated, the interface temperatures calculated in this
simulation were lower than the ,results from the low energy trial
simulation where the heat transfer from the interface was reduced by
1.5 mm of low conductivity friction material between the friction
interface and the rotor instead of the 0.5 mm thickness of the fis
elements. Typical axial temperature profiles (figure 5.11) showed
that rotor temperatures reached a maximum of about 45·C. Maximum wear
of 0.84 ~ was predicted over element 131 at the inner radius of the
rubbing path, while the average wear was 0.12 ~m. This represents a
microscopic amount over the 3.5s brake application but can provide some
idea of the transient effects of friction material wear during the
s imula tion.
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N
I i -7 " .•• ; .. T:H· tTH din': HH· ~rl;H f'[·H· ·• .. i .. "1--.:,. '1 . '~':'L ;.:; .. "'j i. __ ~.::.- .-::. __ ,100
0.. ................... : .. :: ...... ::.'... ; 181 mm
-+---'--'-1'----::-~..:, ...... -~.-. i-----,--'--. -~-r__ ..... _..: ... OUT ER RADIUS I I I' I 1 ~ : t . • .• I ' .
Ln .
::E .. m
p ::D
/, - ,
z --; m ::D
1000
TJ' . - ._ .... p n m·
"D ::D m V1
~·500 . ::D m
.C
• '··,·,,·y·· .. ·• ..... II .. ··•··· .... ·, : .... :. . . ..... I'· .. _, -'-,. ,
! ..• ' .•. , .. : •. : I..·· I· .• ' . I:" ....... :. ... .. .. ····:··1.'···' " . _~ i .~ ~
;!·~·'I·; . .• ~ .. \.. .. j .... , ........ . L" I' .: I·' .. .: ...... i ............ ~ i. !
_,. 1 . . >,. ..: " . : ..• : ' I.,.: .... ~ . _c .. _ ... : L .. ' •.• • :
.. , ._ ... 1"1 "I"! ' .~ . . ,
·'--·-+=~-...:.~~·~S¥~f4~:c)·~·7···r-··"·-[J· ',' -~ , ... 'I ... .'i lE.. ,"':'" <C·· . ,...:.'-,...:. .. I !
, ·-5OQ. ..
..200· i I
o . 0 . "'IR~itR .'" •.•.. ~IHF:I'··:···'~:·'~·i'I~::" ...... 1.OL ER: RADIUS 1.5C':~~~I.. ......., , .... ! ........ ! .... • _:Y'J' , I <IS.. . :. , . IN\Jf='R iRMi1 LJS. ': "":.. . ,. •.. i ! ' .. , ',-. i' I ... ..
, ~
150
W 0::: 100 ::::> '<i: 0::: W 0..' ::E w I-
50
94. FIG. 5.17
Axial Temperature Profiles - Low Energy 8raking_
TemReralures 01 Radius 179mm
STATOR
2.55----
0'55 ----i".1 1· 0 5 ---+-111
3,Os-------Hl1 2 ·Os,---~1l:.;· 5~sc=:=tIJ~\
3· 5s-----H:J:t+.
<lJ L> o -'-(j) ~
c ROTOR
o ~~~~~~~~~--~~--~~~~~--~~ o 5 10 1L.'5
THICKNESS (mm)
5.4.2
95.
Medium Energy Braking
Medium energy braking conditions for the annular brake configuration
were devised to give an average power dissipation of 600 kW/m' (0.5
bhp/in') as follows:
Initial rotational speed~l = 38 rad/s Final rotational speed ""2 = 0 Duration of brake application ts = 3.5s Friction coefficient ~ = 0.3 Actuation force P = 13 kN
Boundary conditions, restraints and element material properties were
the same as for the previous simulation (Section 5.4.1). Convergence of
the CST interface contact determination was much improved by modifying
the contact criterion to the average stress over the fis element
interface nodes as described in Section 5.3.3.
The results from this analysis were presented by Day and Newcomb (Ref.
68) and the interface pressure, temperature and wear distributions for
each time-step are reproduced in figures 5.18 -5.24. At the start of
the brake application (fig. 5.18) a fairly uniform interface pressure
distribution gave rise to little radial variation in temperature and
wear at the end of the first time-step. After 2 seconds a band of
lost contact occurred (fig. 5.21) at the outer edge of the rubbing path
while at the inner edge higher pressure resulted in higher temperatures
and greater wear. At the instant when
greatest wear had occurred at the inner
the brake had come to rest,
radius (2.6 ~ over element
131) and interface contact had been lost at both the inner and outer
edges of the rubbing path (figure 5.24). Peak interface temperatures of
400·C 500·C were reached in the early stages of the brake
application, with some variation resulting from the pressure variation
across the friction surface of fis elements. Final interface
temperatures over the in-contact region of the rubbing surfaces were
around 200·C, and the axial temperature profiles (figure 5.25) showed
the bulk rotor temperature to have reached 105°C by the end of the
brake application.
The amount of friction material wear which occurs during a single brake
application is very small and the calculated wear for this analysis,
averaged over the rubbing surface, was approximately 1 ~. This was
Interface Pr~ssu.re,j T.~rhP~tdH0t~:-I&ffiJCl[~J.!~tiW~~!w76fl---:--:--- .:-- __ .. 0 --
2.~Q AX i~_~rfi~et~ic---I-c51nti~L1rc tl~k-:---~E aicen:---\;:oE -rq~--t31Qkihg~: __ ~_n_- -: : :1 -io:---- - -: - ---- ,: -li~' - I ,1- I i I .
:>
rn ;;:)
;; :;] c-:
i :-n. 1 i = 1
3 I -,j
: i ,
1000
---TIME---8--{}-5-5ee. .': >.F c!-!.&~-AiA(3~1IS); I i : ------
. _____ ~.:I· -- . .-:--- ·:1-: .JJ,--i-J, ... r I.. ]' - :.' . ___ . ____ _ ... " ... : ..... ,1. •. , I ~ . , ..... ,.. .. ...... "- ------ .. ----........ -.... --- .. - ... . .", I· 1 - • -I- . :
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'I ... .. . r . : ,.., .. I
. '. ',' ... , .. --,. ..- .... ;_ -'RRSS(j~-Ei . ___ I . "'1: .1,1 "'i -----:------+---+---'-1 r . . f-'---------,-.. ----- -- -500 • i ' . . ::"f' ::;- , .~.c;<-:'i:'i'i'-:· M-' . 'rl; ....... -.. -.-.-__ '-__ . __ ---L '. ......1 .. ... :fiEr PEr ATU~E .... i . I ______ ~ _____ . __ ___ .
--\ fll
_. :,:.1:
. :s:: 400=U
fll ::0 l> -! C ::0
300fll
ex>
2, I I ;
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m ! :> I ~ ! ~~
!
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I
J
Z -1 rn AJ T] l> Cl in
1000
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'" " ':.-I: jF ,: i tu '-!>.· I, I" " ''.''' , ::. ''I'' '--,--',_11 '
'.' I::. ':: I,::. ' •• :' ,. 'e:" __ ',' .... "'--' .'::'" .. __ , •• : "1':: '.:1':. :: .. '1"":: ,,,'.'." .:1,""",' .'.,,:,: '.;:1 :','" :--,:,,:-:.,,+, ,
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\ : ! 1,,/I,,;.;.I'V ,.....-',~--:-;-! ',- ... ~~: -'\ --, ,\.., . .,"-' '" /:--i-~'~":.:" , " ::1' I .,' ",' '" .<, "." ',' ~ \ 11
'." 1-/ ' li I i I .' i, .------1--·< , , . "'.-.,'.::' : - __ 11 ·+1'."'1, ' "'- '
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I
I '
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L.OO-:u m JJ p, -i C JJ 300-m
-200 . , I ---, ----- -----,--, -, ,
i '" ___ , :-_--:-:~:iF ••.. ....:.:_ .. L1
•• :, , •••••••• :-,:: ,: " r--'--, __
~c "'- ~':_J . '··'""':,..:'-"Co c -,c;"- '''---~!''+H' e'i ' ... 0
~-100
, , " , , + I T' ,.--,----O 1_ i ,"." ' '2, " , ::1 .,' ' ,-:' '.--.:: , ' 0-
lW5 mrfJ . ,,' .,' ,/Rl!JB BIN ,. THYv' pt[H , ',,;' , " .,",., ,,! 181 mm INNER RADIUS' ,-' -- ,1 --'---:--- - """'- " OUTER RADIUS
! ,,',' i
Cl . U1 .
.--_ ..... -. ,
" '.. .., .,.~! .uti.,><, .! i .• ,.,.
. .. "'; " . . :'. ,,; .. . " . ; . , ! .'.' ..•.. •.•••. ......... ... .... , .. 1 .;.
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. I·' ,. r'········:·· . .• . .. _+_..... . .. !.. ••.••• ~ .•..
\ ·1· \·,1,11::· ,...; ..: J;;k /1\ J ./:\ ' .; .. ! .' h. .. / ",;(1'\:;1'\/ v'\.7'+'\;.;, ". \ .i J, ·~i····
I I("t~/i y ~' .••• , •. ' .. 'I···:·· . ..•. .. . 1 .... 1 n I· .j..... . / ' ., ... :._... .· .. 11~+'i
I :. I ·.i·" .',..! .. ,. I· .... '... . ... ;. . ., I!. ; \ ' . , i .. , . ;: .. , ,,::.,. : ., .; .. .. T ': I.
1000 21 I i Z
-1
~I ~ "'i }> I' ;;: :;J n
I. fTl :J U :3 j pg
1 .
I :. it I" I,· ., ••.•.. '1/ . •. 'V· ... +.: .. I-~-- ~.~ . ." , .. :: .... : ..... '
.. : I . t., ........ '., .. ,.,. •..•• ,: •. T , ••. ' •• , .• ;.~ ... '.' .• , .... '.: . " .".,.1 .... ' .... 1 "
-, ~ ~500 j m
................. _._*,1 _:--t---e'f-:'-f ·'-j9jSS"r'· ·+'f··'B'·f-· '+1"-·2"··k~·~·"'F-~-f·-'-cfTj~~i~:·-;-·T······ .. ~, .. .... . .....: I. • •....•.. :j, .• ·11. ,. ·.I_J~, ___ .:~- LLI.::L.: . -'~.~ .... , ,1 __ , -.
, .' • .,,":" ':-~"'':"~"" : ::.,'''.... .".' .... ' ... , ,. ,. i . ;. ... -~:~." ...•.. ':.., ••. " •• ' ••• '.... . . .' . ' .. 1. ".,; .• ' 'i· ,: ..• : .
I I ~
~
3 N 1-- --
·500
-; fTl ~
400 v fTl ::0 ):> -; C ::0
300fTl
200·· 1
lOG-·
.... '····:·······;--·--'=r=i--; • ....,.,+,:~".d.:.,.::.·.·.·*';j·l· i:.: ... + .. "'-' .. 8"s,,;',,+-.. c" ..• ~. +1.8"-,.""-,,,.4, c"f,!,,,ci, ,...;..+~f,i:.:" •• ,4...,"c.d.~ .. ". l:.. +-'--1-····" i-
D· ~5m~ . j" ,,::, RI~r:;r"WI~T~i,' . .. .. •..•.• .., 181mg ..... INNER-.RAQ·· 1.l....OUTER RADIUS
'" CD
"
. l::?
2
:E :T"i }> :;J
-, J , I
I
, , ,. . ..,
Interface :pr~S?L,He;,:p'II!il~:0.(, ••. " 8l'b)rtll!lqnvg /"t::bt I ...
z --',
fTl ::0 T) }> n fTl
2D .. AxiSVtTl;llell,>(.,K~'IJJ.(itiJ6 I ...,>1., >, ...... I",. \ --.-.-.----.
TIME ... 1
" :-,,,:~" ··,·· ... H .. ·i ··i ..... ' · ••• ,'1· I .... ·· ....... 1'--.. -
, : : .. "._::!.<' .• ~'. ..: .. <'' •. , .... ,. . i i
. :; i .. , .," '1 •• ' , .. ':'. ," •••.. ,. I.' • '., ·· •.••. 'l" ••.. :",., . ..:; . I
'.... .. ""::1'.::"""'" "., . . "' .... 1 .. : .• ,'.' '... .i. I'.'. ., '. " •. :,',.""':.'" j::"':" : .. ,. i:
-:-. -. ·-···~·-·-t-I'---'---'-· ;f; '7r::i: f:: 'ti :~:: 'f' '4't "':,, ::-r~-f :1-,;'-",'" .-1-' -'-'-·'l r,' l_" ·-·t· '-' '-;-.: "..,'+r'" ;~>"-,, 't:I'-"" -,----':- -1" ':-,-, .. '-" "+'.' .-.. : .• II.-.I--.y" r-H--.'· I : ,I" : .: ..... i" ... - .. - ....
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, I' ., I i.,. " 1>1; ., •• :;. , ----- .. '\ .1: :.,' , ,-::'j .' ' .. ··1··' . ··:.:·',·1······:· ....•..
, . ,',: , "L ' . . ... -J---
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I
500
. -; fTl'-D ::s:'-D
400;:g ::0 l:> -; c
300~
, , ,', 'I, •••. '818·' 11 •• ":. : .• ':, :.'i.: ' •• ",' ',.' ,\\' .-: '·'28.-0'j' ,~ : !.'" ,r.· ," ' .. : i' I.: i .• , "":'::": , •. .. ,:.J<, .. !.:. >: ..... ,. "',"
i· .,. I" :':. ' ,... , ... 'i'::' "",.·::.,::"1"'-'\:",,:;,::::,,, .. " ·l·-·'···' ....... ' . . ~._ _: .,.i: 'i i.' .. ':' 'i'':;;':'; ';"::':·f".J:.q;':':!;';<.i, i .• :i-.. . , ~ ~ , ... :. 'f--';" .' • .' ['.'" 'i<::-, lLJI::cl,."";~ ", ,"--' . - .1 ' .':. ",' ......... ,',: :.',L,·' ::,,1'.' ':,i.,"".'·' 'i -~ -~""._ 31',) ... '" . :-'L .; ., .•• : ,.".,. I " ,", •.• '",;,:1 .• ,;. 1 ,--·····100
; ,1:""'1 ...., i>'" '·:~~:'H'---·:::': 'j'! L- __
• ..." "".,' ,.,:1 .' •. " , ' . . ........ ". ,. :: ...... ::""1,::"--::::",--·, .... : ... I""" i' o I',:: . :.:'[:::1::/,,1.: ....•. :: "'j .. ' .. i .'.' ,
15CSmm , . .· ... IRIIP ~rr. .• ~rn VVI··· f·.f' .', ; INNER-iRAOIU5 I . . ••• .' • -r--.-.:- .
... 1 .. · .. ·1 .. ··,· .. ," ",' ,
o 181mm
OUTER RADIUS
21 I I
~ ,
I '" :> , ~-' i ,
I ::; I
3 I ' . .:
:J
~
iJ '" VI
2500 . :::0 fT'
500
-i me; 3: 0
L.OO;:g ::0 l> -i C
300-~
ri'
··200- , ,
21 , , i
:El :"7""i
>i ::01
I !
~ , i :3 j ,
; i
."\ V
I
;. i
:1"',
V JJ iTl 'J)
-'--'-""""";--~~-T--c';-T--;'7;:+-C-"-':"--"---'- - -. "
Interface Pr";~~I~r"'. '1t:'IIHJ::lrn1U .·,.,I~ IlrnJI:.-'l.:i'-'if·/l;-,r ;----T .. ----'---________ ~.;....::.....:::,::,::..,' \..if.H~ '="+-"~ ".'·,~'.';;'· .. :.;,·cr;l=,..,~'~"g""~,=+::...:.:.:-. ~lJ\C1 .H.UU~f:::'IVft::',ul i 2 ~O .. 6xisv,i'~ile lC- ,Gc[)fi( 1~IUll ) ;'.: ....•..... ; ..• : ; .... ;, .......... ~ :::.....:..=:::.....~~=:::}==:;==*==F9=:#?~~#=f~~rl~+rl:c7:--1,--·+~I........;--f---c-1·-- -.--.-.......
1000
T IM re ~ '" ~" :: ....... '...:.. •.••• .: .••• ., , ;.; ... ; "'1 ...... ; .. ; ... . . ...•.. !. . L. .;;, . :,:cf;; "'.;.' .;. 1:,':;,;
;
__ --l ... ___ .. _. ! ;, .' .";' '; .' •••..... . 'ji' '....,:, .. ;r:I·.····,··: ,., ....••. . ..... ... ..1. ..... ,...... .' -.. -.
1 .. ·; .. --·--'· .. -·-t+---;-+--'--c't--.--ri~~~+-';-;'-+-"7-_I_c".::--,I...,.:..;.c_,_f_.;-.;..._+__7_+-:-+-.,._f_..--I--··-....... : .1 . ...., .. ;. ' .. TI: ..•• · ••• ·:··..1' :... .1·'·, . LI·:· ... ,; ..
-I .: .,.
l---"':·'L· , .. : t"! ·· .. ·1 ... ; ....... ; I,
--'.: j,,:.;; "., k' .••..•••..•. ! ...... ... ..... .... ;-·f··· .. ·
,_.-- . ,. ; .; '1' •• "" ..•• ; ';1 .. i .:
"'1"';' "I;;" ,.c;.' ;+c.:.;;i~.c ~',I _______ ' ~;; ';' ;;.c"'.., ••• 1...,.:..;.·,.... .... ·+. '...,.",,',. ',-' ·rl.;-:.-ccr-,::--,·+I-'".,..;'-''' b".,-· ":"'_1'._ .. _.,. __ .. ; __ .....
',~, 'I'j !.::' .';" ,:,T7 ;;".:' .'.' .-,)- .. ;; .. ' r· ; .. c.· ... I'" .
: /\ ... ' .. ~~ I' ;... 1'" . ,< ; ·-'-'cc--J.·....,.··-I-....c·+- .... -t--· .;. - .......
,. it· \ ,. ; .. , .;. ;; .
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." . ~''-'-~=-l';'' I i , .. ;
2500 JJ
...... ,- I,: 'J.' ... 1'.; ,., :1.;'11 .. L ... ; •.•• I •••••• : •• ;; ......... r. ., / ";1 '/:/ .. ~ .. ' ... .: .;" "."-,,,, ".) ".. ; IV ; i(; v./ .>:~. I\::/.<.? '''V I'V ..... !\V .... .. .. I·'· '. , .... , I ...... ·.l ":. ';;":. '.. -:. ',: .. ... , 1; .. \ (. I . . iT!
T. Z -3
N
.... -i+.,.. i' .. : .... ::: .. ;;" ;',;. ; .. i.;· ,,:, r..;",·,
/ '.' -.:~!~ .. ~~~IJhl;~j·;.;:~":+'HJl'+8W-8···ill,··'D···*S '1"" __ ;;··fIT.· i P;4·· ;.}.i:;j·'·'·f;· '.l •.• {L~ .• ~~'~I.l" '1' ~"+!=~~l ..: ..•• ' ••.•..• ..,. ·;i ....... ;.; .;" " ... ,"_'-- : ......... ~_, __ L;. . .. " .;;. . .. ,...
... - . ...... -"::__'--1' Hl---.--+-:-.f--..,.,;-'--i-·'; ; ..... +-,'+", •• ';.c,i'--!" f;c.·;.'-;···:"".··+·.·c;= '.",. ':+:'",,::":,-' ".4' '-.;···-.;.T.;_. •• ·+I'cc.:.;.[[+'· ;",,"'cc '.' 4··-.;.···· •• .;;,·· ••• -+'-'-7--;;"_+ .... _. ", _ .... ;_ .. , ....... _.+.1:-...... .,. ..... '_ .. , ...... '1__ .. .- 1 ;.. ;. ...:.;; ..... ;. '. ,.;.; ;: ;., , .. ' ; .'.: • -.
i ...... ;... !;";""" ...... i .... · .. ,; ..... '.;·· "'; ., •. :. ;.. 1.... __ _
._ .. , .......
1\
, , , .. .;.
-50Q
ri'
·aJO· I
.1QQ
o , , .: '·1·,", ·t",.'IT'< . .., ...... ...... ; ....
1C:n'c: ' ; I' IRlilPPIK,r ;.c.:; ;,<'-.:,:.o', .•.. ; ; :. luui.Jmm : ; ·'i,··"~,-,,,,~I· .r'Af' o'YIUI.,H.; .1.. ! .. i·;··· I ""e R. .RAr.ilnlJ!, /C:'ch.i .... - •... ;.---t-...... ;-;--'-';-.. +.---.... . .. ..... ........ .. .... ; ..... ,",.'-, ,~ i' ,
Q 181mm
OUTER RADIUS :. .:!
Cl
. Ul .. . N W
2
'-'
::J i 3, I
, < , I
nJ 'J
100e,
Z -i m )J
;;; n en
U ::0, m Vl Lt) cSOO ::0 m
~
r, z -3
N
I 0
-500
-1 me) 3:: '"
400~ . ::0 J> -1 C
300 ;:g
n'
200
iOO ..., Cl
400
300
oU
w 200 0:: ~
~ 0:: W 0.... 2: w I-
100
o
103. FIG. 5.25
Axial TemRerature Profiles - Medium Energy Braking.
(eST Anal~sis) 1-55--
TemRerotures at Radius 179 mm
1-05
0-55
2-05
\ 2-55
~, 3-05 3·55
~ j
'--.
- "----
~ "---~'----0 -'-
STATOR (]J
ROTOR c
o 5 10 11.5 THICKNESS (mm)
104.
about 10 times greater than that predicted for the low energy braking,
giving an indication of the temperature sensitivity of the wear of
these materials determined from the wear criterion (equation (4.9».
5.5 ANALYSIS OF BRAKE APPLICATIONS USING THE GAP FORCE METHOD
5.5.1 Finite Element Analysis Details
5.5.2
The Gap Force method, as described in Section 3.4, did not require fis
elements 112 - 131 for the calculation of interface pressure and
contact distribution. Deleting these elements for the thermo-elastic
analysis therefore divided the finite element model into two
independent parts which were then connected by Gap Forces between the
corresponding node pairs across the interface as shown in figure 5.26.
The gap or separating distance between the nodes of each pair was
determined by the wear at that point in the interface. Material
properties were assigned as also shown in figure 5.26 and the actuation
force boundary conditions and restraints were applied in exactly the
same way as in previous analyses.
A major difference between the Gap Force and the CST methods is that in
the former the interface nodes are free to move in the plane of the
friction interface, being restrained only by friction forces. The
tangential forces provide the braking torque for which a dynamic 1.1 of
0.3 was defined, but the in-plane radial friction forces must also be
included, for which a realistic static 1.1 value of 0.5 was used.
Medium Energy Braking
The same operating conditions as described in Section 5.4.2 for the
medium energy~ braking_ analysis using~ the CST method were adopted for
this analysis using the Gap Force method:
Initial rotation speed ~1 Final rotational speed lJ2 Duration of brake application ts Friction coefficient 1.1 Actuation force P
= = = = =
38 rad/s 0 3.5s 0.3 13 kN
The analysis proceeded in a sequence of 0.5s time-steps as before and
the calculated interface pressure, temperature and wear distributions
are shown in figures 5.27 - 5.33. After o. 5s (fig. 5.27) the
distributions were similar to those predicted by the CST method with
105· FIG. 5.26
Gap Force Anal~sis - Loading and Constraint
13kN
Interface Node Fbirs
5f=8.::..3 ____ -.-_~86-107t__-~
w ~ -l -l a.. « ~ 0:: ... 593 z w w .. ~ '<i: u u it « 2: 0:: co 0:: a
z w b 0:: a I-a I- z 0::
~ U I- 0:: <Jl LL
603 Node Numbers 1 6 -12~-""'1~(
y
'---~X
---"-',
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OUTER RADIUS -' !..
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-' --'
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i i , I
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. "'1-- --.------ --,-- -.--.,----- -: .. --.----- .. -: -.. - -.----.-- -.-
Interface Pressure,! T~~p'~roture:&iC~m0loti~e We:ar : I: 1 • I .. i 1 !
2 -00<ui$y-mbJ~tht ___ : Cdh'fi~UrCntibm u __ :i __ u ___ '-) __ : __ i : I ! t ! !'! I
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.1 .. 1' 1- • I
---...."...---
I I 0 !RUBBING' PATH WIDTH : ! I !! --j--_._--
01 181 mm w
OUTER RADIUS W
150,5mm INNER RADIUS
113· FIG. 5.34
Axial TemRerature Profiles - Medium Energy Braking:..
400
300
,u
w 200 a::: ::::)
~ a::: w Q...
L w f-
100
o o
(Gap Force Analysis)
Temperatures at Radius 179mm
1·05
1·55
0·55
2·05 1\
2·55 111\ 3·05 1,\ 3·55
r--
~ I----~ ~I---0 ~
L ClJ
STATOR ~ ROTOR c
5 10 14·5 THICKNESS (mm)
114.
interface temperature generally rising slightly towards the outer edge
of the rubbing path. This reflected the work differential between
inner and outer radial positions because of the slight change in
relative sliding speed. Interface pressure at the inner and outer
radii was slightly greater than over the central region, but after 1s
(fig. 5.28) the pressure at these positions was reduced by wear, and
contact was lost over 1mm at both edges after 1.5s (fig. 5.29).
Interface pressure distributions showed negligible variability between
adjacent nodes in the interface and no problems with convergence were
encountered. At the end of the analysis (after 3.5s) figure 5.33
shows loss of contact predicted over 3mm at the outer, and 2mm at the
inner radii, While interface temperatures ranged from about 100·C at
the edges to about 230·C elsewhere. Maximum wear (1 ~m) occurred over
the region between nodes 90 and 94 (radius 0.173 m - 0.177 m) while the
average wear over the rubbing surface was approximately 0.7 ~m.
The axial temperature profiles (figure 5.34) sho.wed steep temperature
gradients through the friction material, while bulk rotor temperatures
reached approximately 120·C by the end of the brake application.
5.6 DISCUSSION OF RESULTS
5.6.1 Convergence
2-D axisymmetric interface simulation using the CST method produced
variability in the calculated interface pressures between adjacent
nodes which led to corresponding variation of nodal temperature and
wear calculated in the combined analysis. Such variability was
particularly severe over fis elements at the edges of contact regions,
at the inner or outer radius of the full rubbing path width or adjacent
to an out-of-contact fis element, and was exacerbated by the inclusion
of thermal expansion in the analysis. The excessive distortion. of
free edge elements is a well-known effect in finite element analysis,
but the effects upon stress distribution can usually be minimized by
refining the mesh over the region in question, and using a smooth curve
to define the distribution, ignoring any edge effects. Further
refinement of the finite element mesh for this analysis was limited by
cost considerations and although the pressure distribution could be
adequately described by a smooth curve through the calculated values
5.6.2
115.
such a distribution could not be used for the computation of energy
input without producing serious
temperature distribution.
variability in the transient
These problems of interface pressure variability affected the
convergence of the eST analysis to stable contact conditions. Large
calculated pressure variation across the friction surface of each fis
element could cause the original contact cri terion (which determined
the contact state of each fis element by the average normal stress) to
oscillate between in-contact and out-of-contact states so that
convergence was not reached (see Section 5.3.3). Problems of
convergence were much reduced by adopting an alternative contact
criterion (see Section 5.4.2). Test analyses of all three types of
interface simulation technique (Section 5.2) showed that neither the
Rigid Boundary method nor the Gap Force method suffered from problems
of pressure variability or convergence in the determination of stable
interface contact conditions. These latter methods computed interface
pressure from surface normal forces, and the contact criterion was
applied to each interface node or node pair individually, and not to an
entire fis element. Thus the Gap Force method was considered to be
superior to the eST method in this respect.
Interface Pressure Distribution
The Rigid Boundary and the Gap Force methods for interface simulation
showed close, agreement in the pressure distributions calculated for
test load cases 1 and 2. In test load case 1 (figure 5.5) the
pressure distribution calculated using the eST method was within 3% of
the other two distributions over the central region, but deviated over
the elements at inner and outer edges. In test load case 2 (figure
5.7) the eST method predicted a different contact area which affected
the pressure distribution, and again, edge effects were~apparent.
The results from the trial simulations with the eST method (Section
5.3) demonstrated how interface contact could vary during braking; over
the duration of each brake application it was observed that lost
contact resulted in frictional heat only being generated over less than
50% of the total surface area: In the full thermal, thermo-elast ic
and wear simulations, the eST method produced smooth pressure
distributions over the first time-step, but subsequently showed more
variabili ty.
5.6.3
116.
The initial pressure distribution calculated by the Gap Force method
for the medium energy application showed a pressure rise effect at both
the inner and outer edges of the rubbing path which was small enough to
be neutralized by wear in subsequent time-steps. The corresponding
eST analysis showed slightly less variation in pressure across the
rubbing path width. Over subsequent time-steps in the Gap Force
analysis the pressure distributions were generally smooth, showing a
slight increase towards the outer radius which would correspond with
increased temperature and thermal expansion resulting from the
differential work rate. over the rubbing path width. These were
considered to be more satisfactory than the more variable eST pressure
distributions (See figure 5.35).
By the end of the medium energy braking simulation the regions of lost
contact predicted by each method were similar; 3 mm at the outer
radius and 1 mm at the inner radius for the eST analysis, compared with
3 mm at the outer radius and 2 mm at the inner radius for the Gap Force
analysis.
Temperature Distribution
Temperature variability calculated in the trial analyses was generally
evident in the Gap Force analyses, and was considered to be an effect
of the eST analysis resulting from pressure variability in the fis
elements rather than having any great practical significance. In all
cases, however, the behaviour of the simulation was shown to be in
keeping with the nature of the mechanism of thermo-elastic instability
with interdependence of the interface pressure, temperature and wear
effects.
Ignoring temperature peaks where edge effects or pressure variability
were evident, the general level of interface temperature over
in-contact regions showed the highest in-stop interface temperature to
occur at about 1.5s into the 3.5s brake application. This compares
which has been with half-way through the brake application to rest,
calculated for a disc for which >- )1.21 (Ref. 69), and
(eST method), approximately 75°e for the low energy simulation
were
and
350°C or 375°e for the medium energy simulations (eST or Gap Force
methods respectively). The combined effects of lost contact at inner
ComRarison of Calculated Interface Pressures
Medium Energy Braking_ Time 1·5 - 2·05
I
I 2000 \ - , I Gap Force Method z
\ ~ ~ ~ rn .---. eST Method ~
:z: --J
'T1
\ I \ .
1> n fTl
\ I \ L! ::kJ rn I I \ Lf1 I \ 2e 1000
I
\ I \ /'
;::; , \ rr \ -
\ I ")';" \ z -3 \ I N
~ "T1 -Cl . U'l
0 . RUBBING PATH WIDTH 181mm w 1605mm U'l
I NNER RADIUS OUTER RADIUS
5.6.4
118.
and outer edges of the rubbing path, with little or no frictional heat
generation and radial heat flow, were observed to produce low
temperatures over these regions.
The axial temperature profiles through the thickness of the friction
ma terial, backing plate and rotor showed that for in-contact regions,
the highes t tempera tu re a t any given radius was produced at the
position of heat source, i.e. the node at which heat flux is input.
Where interface contact was lost, however, a "temperature inversion"
could arise, so that the highest temperature is produced at a position
below the rubbing surface of the friction material. The effects of
thermal expansion within the friction material could thus be more
complicated than is generally assumed.
Calculated rotor temperatures increased with time and steady state
temperatures were not reached by the end of each simulation. The
effect of increased thermal resistance between the interface and the
rotor could be demonstrated by comparing the trial simulations (Section
5.3) with the results in Section 5.4 and 5.5; in the low duty analysis
interface temperature rises were increased by as much as 100% while
rotor temperatures showed little change. Detailed study of the effects
of different interface conductance using combined thermal,
thermo-elastic and wear simulation techniques is therefore essential to
enable the actual values of friction material surface temperatures to
be predicted. The lower friction surface temperatures calculated
towards the inner and outer edges of the rubbing path indicated heat
flow from the edges of the rotor and stator. This effect was evident
in surface temperatures measured by Ingram (Ref. 10) on a large (0.2 m
disc outer radius) caliper disc brake with a 16 mm rubbing path width,
although the effect is less pronounced for the narrow rubbing path
annular disc brake.
Interface Wear Distributions
The interface pressure oscillations and temperature peaks produced by
the CST method over the edge ris elements comb ined to produce regions
of high wear which were not predicted in the Gap Force analysis. For
example, the highest wear in the CST analysis occurred at the inner
radius over elements 131 and 130 which corresponded to the regions of
the greatest pressure var iab i 1 i. ty t where;;J.s Ln the Gap Force ana lysis
greatest wear occurred over elements 116 - 118. The latter is in
5.6.5
119.
better agreement with the effects of a constant pressure distribution
where the greatest wear occurs towards the outer radius corresponding
to maximum sliding speed and consequent work done. The analyses have
shown the interdependent processes affecting interface pressure,
temperature and wear, to be generally convergent; any high localised
pressure produces local temperature peaks and greater wear so that the
interface loading is redistributed elsewhere in preference. Obviously
any variability which can be directly attributed to the analysis method
is undesirable, and for this reason the Gap Force method is preferable
to the CST method although in both cases the levelling effect of wear
exerts a strong controlling influence.
Comparison with Conventional Calculations
Newcomb (Ref. 29) showed that the axial temperature distribution in a
rotor or stator disc of semi-thickness d could be calculated from,
1>0
= 2tl L n=o
00
1 [ierfc(n +
2 -x)' (1 _x)' " + ierfc n + - + ,/\
2d 2 2d
1. 5 '""' 3 -BMt ~ [i erfc(n 1
+ - -2
x, 3 1 _X)'] _)A + i erfc(n + -2 + ~ 2d 2d
n=o
.
]
(5.B)
where Q = N( 1 - Mt) describes the frictional hea t flux, apportioned
between the rotor and stator in the ratio
Y1 -Y2
= =
0.107
0.B93
(friction material)
(rotor)
calculated using the heat partition formula, equation (2.9).
Although equation (5.8) may be used to calculate temperature
distributions in the steel rotor, a simplified version (Ref. 69) can be
used since >'2 < 1.21;
[) = t - -)
2ts (5.9)
The axial temperature profile through the friction material and the
rotor surface tempera tllre were calcu la ted using equa tions (5.8) and
(5.9) respectively at the end (t = 3.5s) of the medium energy brake
applications <lnalysed in Sections 5.~.2 and S.5.2, "nd are shown In Tab le 5.6 compared with the temperil. tures calcula ted from the fin l te
120.
element analysis (Section 5.5.2) at the centre of the rubbing path
width.
width;
These temperatures are not constant across the rubbing path
friction material surface temperatures vary from less than
100·C at the inner and outer radii to a maximum of 220·C over the
TABLE 5.6 COMPARISON OF CALCULATED TEMPERATURES
FINITE FINITE ELEMENT TEMPERATURES CALCULATED USING ELEMENT TEMPERATURES AT USING EQUATIONS (5.8) OR (5.9) NODE NO. (·C) (·C)
96 220 83 75 221 76 54 177 62 33 125 49
248 83 38 17 54 32
207 37 29 6 26 28
Rotor 127 175 surface
central region, while rotor surface temperatures were found to vary
from 108°C at the outer radius and 102°C at the inner radius to a
maximum of 128°C over the central region.
Estimated average surface temperatures from the finite element
calculations are approximately 190°C for the friction material and
120°C for the rotor. It is evident from both the surface temperatures
and the temperature profile through the thickness of the friction
material that the heat partition used in equations (5.8) and (5.9) in
this case assigns more heat to the rotor and less to the stator
compared with the finite element calculations. The artificial
partitioning of heat, equation (2.9) assumes equal surface temperatures
(implying no cont-act resistance ~ffects) under stea-dyO state conditions.
For transient braking, therefore, the heat partition may be inaccurate
but since, in the majority of cases, only a small proportion of the
frictional heat generated enters the brake linings, the effect upon the
calculated rotor temperatures is small. In practice, rotor temperatures
under repeated braking conditions are largely ()ontrolled by the
boundary heat transfer conditions, and the partition of heat may often
be ignored completely for rotor temperature calculation purposes with
no serious loss of accuracy. The calculation of tempera tu re
distributions within the friction material is, however, a completely
rii ffprpnt. mrioU-.pr hpC'rl.tl~p it.~ low thermal condu~tivitv means that the
5.6.6
121.
temperatures produced are very sensitive to the applied heat flux. The
use of the finite element analysis method, which avoids artificial heat
partitioning, is therefore a major improvement in the calculation of
temperatures in friction brake components and is essential for the
study of frictional energy transformation.
Computer Usage
Both the CST and the Gap Force methods are iterative and therefore
considerable computer usage is necessary for the interface contact and
pressure determination. The PAFEC transient temperature solution
program is also time-consuming so the total cost in terms of computer
usage for each time-step is not insignificant. Typical requirements
for each time-step for the computer on which this work was carried out
were as follows:
CST METHOD
Thermo-elastic Calculation Transient Temperature Calculation
GAP FORCE METHOD
Thermo-elastic Calculation Transient Temperature Calculation
Run time Core requirement (hours) (Kwords)
0.17 - 0.32 0.2
0.5 - 0.55 0.2
46 48
76 48
The figures, demonstrate that the superiority of the Gap Force method
over the CST method is achieved only at the expense of greater computer
usage requirements.
122.
6. FINITE ELEMENT SIMULATION OF BRAKING FRICTION
IN A DRUM BRAI{E
6.1 FINITE ELEMENT IDEALIZATION
6.1.1 2-Dimensional Simulation
6.1.2
The Gap Force method for inter face simulation (Section 3.4) was used
for the combined thermal, thermo-elastic and wear analysis of a
conventional drum brake in a 2-dimensional finite element model
incorporating 2 flexible brake shoes and linings, and a brake drum.
Variations across the width of the rubbing surface, which are known to
occur in practice, e.g. "bell-mouthing" or "barrelling" of brake drums,
were not covered; cost considera tions made the 2-D idealization much
more attractive than any 3-D analysis, although the simulation method
is perfectly capable of being extended for use in 3-D.
The analysis was based upon a cam operated fixed anchor (Le. pivoted
shoe) leading/trailing brake assembly, of 0.2095 m rubbing radius, and
0.178 m width (figure 6.1) for which some test data were available,
presented as part of an investigation into the performance variation of
cam operated drum brakes (Ref. 71). The operation of the drum brake
was divided into a number of time-steps of 0.5 s duration, each of
which consisted firstly of a calculation to determine the contact
pattern and the pressure distribution between each lining and the drum,
assumed to remain constant over the time-step, and secondly a transient
temperature calculation based on the frictional energy generated over
that time-step. Separa te fini te element meshes were required to
minimise the cost of each calculation.
The Finite Element Mesh for Interface Contact and Pressure
Distribution Calculation (Thermo-elastic analysis)
Brake Shoe and Lining.
Each brake shoe was modelled by a single row of elements as shown in
figure 6.2 (a) 0.178 m wide by 0.034 m deep, designed to provide the
same flexural rigidity as the original twin web design. A second row
of elements modelled the 110· arc length by 0.178 m wide friction
material lining so that the finite element mesh for the shoe and lining
TYPICAL CAM OPERATED DRUM BRAKE ASSEMBLY
~~~~& ....... .,..---- Broke drum
Actuating
Corn rollers
• Cam Anchor block
124. FIG. 6.2(0)
Finite Element Mesh (Thermo-elastic Analysis) .
(a) Brake Shoes and Linings
Friction Material
JCoo
ANCHOR
B '1 \0 \( 12 13
Leading Shoe
24-8
125· FIG. 6.2(b)
Finite Element Mesh (Thermo-elastic Analysis)
( b) Broke Drum
129
:Zb2 z.~o
D.o.R.
131
2SB Leading 1\6 position
111 Anchor position
Cam 121
position
III Trailing Shoe 290
position 292 1:14
I~S
NODE NUMBERS
6.1.3
126.
comprised only 27 elements and 114 nodes. This equtva-lent-sectton--
modelling technique was found to
analysis· by the finite element
economical 2-D idealization.
Brake Drum
be very effective for drum brake
method (Ref. 41), providing an
The brake drum was idealized as an annular ring of 0.2097 m I.D., 0.238
m 0.0., and 0.178 m wide, comprising a single row of 36 elements with a
total of 180 nodes as shown in figure 6.2 (b).
Combined Shoe and Drum.
The full finite element mesh thus comprised a total of 90 isoparametric
elements, mainly 8-noded quadrilateral but with a small number of
6-noded triangular elements, and a total of 408 nodes. The friction
interface was positioned at the rubbing surfaces of the linings and the
drum, and corresponding node pairs were defined for the purposes of the
Gap Force method of interface simulation.
The Finite Element Mesh for Temperature Calculation (Thermal analysis)
Brake Shoe and Lining
A simple design of mesh utilizing large elements was inadequate for
thermal calculations because of the stability criterion (equation
(5.1), and a large number of small elements were necessary to model
the friction material lining as shown in figure 6.3(a) giving
do = 0.25 mm. In order to minimize the size of the finite element,
mesh the amount of heat transfer through the lining was assumed to be
negligible for transient braking of short duration and only the
friction material was modelled, using 110 isoparametric elements with a
total of 385 nodes.
Brake Drum
The thermophysical properties of the cast iron brake drum enabled the
stability criterion (equation (5.1) to be satisfied using 16 large
elements in 2 layers of an annular ring 0.2097 m 1.0., 0.238 m 0.0. and
0.178 ID w.ide, as shown in figure 6.3(b).
Finite Element Mesh (Thermal Analysis)
(0) Friction Linin9_
ANCHOR
Leading Shoe Lining o 146 n 147 12 148 13 1~9
14'" I
:;0 o 0-~.
o q 0 N
~ 'CS 0 (j\ CP to
~ 3 3
Surface Nodes I~ ISO 15
/5/
CAM
..., Cl . 0-.
128.
Finite Element Mesh (Thermal Analxsisl
( b 1 Broke Drum
17>1
11')
1'29
123
135
FIG. 6.3(b)
6.1.4 Simulation of Frictional Heat Transfer from the Friction Interface
In the 2-D drum brake simulation, circumferential variation in
lining/drum pressure and contact was inherent in the brake performance
calculations unlike the annular brake (Chapter 5) in which the pressure
distribution was assumed to be constant in the circumferential
direction. Assuming frictional heat to be generated near. the friction
surface (Section 3.1.1), it was therefore not sufficient to provide a
heat transfer path by connecting nodes on the lining surface with
corresponding nodes on the drum inner surface via "fis type" elements,
as described in Section 5.1.2. For each complete revolution of the
brake drum, each point on the drum inner surface passed each point on
the lining friction surface once, and therefore while the. lining
surface temperature might vary according to the pressure distribution,
the drum surface temperature would be, approximately, some
time-averaged constant value around the inner circumference.
The calculation of transient temperatures when the lining pressure
distribution is non-uniform was considered by Newcomb (Ref. 28) for a
sinusoidal pressure distribution. The summation of Fourier components
in that analysis suggested a simpler technique to simulate frictional
heat energy transfer between the lining and drum in which the PAFEC
surface heat transfer elements were used to connect each node on the
lining friction surface to each node on the drum inner surface as shown
schematically in figure 6.4. The frictional work done was assumed to
be all converted to heat, calculated from interface nodal forces as
described in Section 3.6.2 so that:
frictional heat generated at node i on the lining surface = qi and
n
the total frictional heat energy Q = L. qi i=1
(6.1)
The amount of heat flow into the lining and the drum was assumed to be
dependent upon the thermal properties of the drum and lining material,
the interface contact resistance between them, and the boundary heat
transfer conditions, so that over the period of one simulation
time-step
= qO,i + (6.2)
130. FIG. 6.4
Simulation of Frictional Heat Transfer
from the Friction Interface
Node 1
Heat Transferred to N d . - 1 o e J - - qo . L ,I
Node L
~--~--~~~~~~~~~--~~~--Orum
Friction Surface
~--------L Inlng node i Friction Surface Frictional Heat
generated at node i = q
Heat Flow into Lining = qL·
,I
(nodes 1- n )
6.1.5
131.
Since the heat generated at node i is effectively transferred to all L nodes on the drum inner surface, the amount of heat transferred from
node i on the lining surface to node j on the drum surface is
= and the total heat transferred to node j is
n
qO,j = Lqj,i i= 1
=
(6.3)
(6.4)
In this way a uniform heat flux qo, j can be applied to each node j on
the drum inner surface while the heat flux input to the friction lining
is determined by the lining surface pressure distribution over the
simulation time-step.
This method, new in its application to brake analysis, was successfully
used to simulate frictional energy transformation by the generation of
frictional heat at the friction material surface, and the transfer of
heat to the brake drum without artificial partitioning. Contact
resistance across the friction interface, which was observed by Ling
and Pu (Ref. 22) to be responsible for a macroscopic jump between the
temperature of each friction surface, was simulated by the effective
heat transfer coefficient specified for the PAFEC surface heat transfer
elements connecting the linings to the drum. Effects of wear debris,
surface coating, etc., which had been simulated in the annular brake •
analysis (Chapter 5) by the thermophysical properties of the fis
elements, were also found by Ling and Pu to be equivalent to average
interface heat transfer coefficients ranging from 1000 W/m'K to 25000
For the purposes of this analysis the lowest value, 1000 W/m'K
was specified, simulating the maximum realistic effect of interface
contact resistance.
Thermo-elastic Analysis - Loading and Constraints
The drum brake under consideration was, in practice, actuated by a
twin-lobed cam, which when rotated, provided actuation force and lift
to each brake shoe. (A description of the operation of this type of
cam, given by Oay and Harding (Ref. 71) is included in Appendix 3).
The cam centre was assumed to be rigidly fixed to allow rotation only,
so that both shoes were given an equal amount of lift per degree of cam
6.1.6
132.
rotation and the actuation was applied to the finite element model as a
prescribed displacement of nodes 192 and 248 at the tips of the leading
and trailing shoes respectively.
Nodes 160 and 216, which were positioned at the centres of the anchor
pins of the leading and trailing shoes were constrained to allow only
rotational degrees of freedom, simulating a pivoted abutment. It was
necessary to constrain the drum part of the model without affecting the
different distortions produced by the friction drag and radial pressure
of each shoe, whilst maintaining the centre of the drum coincident with
the central axis of the brake as defined by the positioning of the two
brake shoes. The most realistic method of achieving this was found to
be the restraint of 4 nodes spaced gO· apart, on the outer
circumference of the drum ring (nodes 129, 131, 133, 135) so that only
radial displacements were permitted.
The initial contact between lining and drum affects the interface
pressure distribution and the calculation of drum brake performance.
Therefore unless otherwise specified, all interface node pairs were
assumed to be initially in contact, equivalent to conditions of perfect
initial contact between lining and drum, so that the friction surfaces
had exactly the same rubbing radius and were perfectly concentric. The
practical interpretation of this would be fully bedded-in linings under
actuation forces approaching zero.
Thermal Analysis - Boundary Conditions
The inner surface of the friction material lining, adjacent to the shoe
platform, was, as previously described, (Section 6.1.3) assumed to be
insulated for transient temperature calculations of short duration.
Surfa£e he~t tran~fer from the_Xr~e ends of the linings was simulated
using the PAFEC surface heat transfer elements and a surface
coefficient of 5 W/m'K was considered to be representative of heat
transfer from a surface with no significant contribution from forced
convection.
Heat transfer from the outer surface of brake drums is generally
considered to be dependent upon vehicle speed, but is restricted by the
close proximity of the wheel hub and rim, especially in commercial
vehicles. Newcomb and Millner (Ref. 66) derived an expression for the
convective part of the cooling rate of brake drums and discs:
6.1.7
133.
0.0127 A (v )0.8 (6.5)
m
from which a surface heat transfer coefficient of approximately 80W/m'K
was calculated for a vehicle speed of 80 km/h (50 mile/hour). For
braking from this initial speed to zero, an average surface heat
transfer coefficient of 40 W/m'K throughout the brake application was
considered suitable.
Material Properties
The elements of both finite element meshes were assigned the relevant
thermophysical properties of heavy duty moulded drum brake material
(see Table 4.4) for the lining elements, cast iron for the drum
elements, and mild steel for the brake shoe elements.
6.1).
(See Table
TABLE 6.1. THERMOPHYSICAL PROPERTIES OF CAST IRON & MILD STEEL
Young's Poisson's Density Coefficient Thermal Specific Modulus Ratio of thermal conduc- Heat
E " f expansion tivity. 'l5 k Cp
(N/mm') (kp;/m3) (K-l ) (W/mK) (J/ki>:K)
Cast Iron 125 x 103 0.25 7100 12 x 10-6 54 586
Mild Steel 209 x 103 0.3 7800 11 x 10-6 , 48 452
6.2 TRIAL SIMULATION WITH THE COMBINED SHOE AND DRUM MODEL
6.2.1 Simulation Parameters
A test case was completed for the analysis of braking friction in a
drum brake under typical operating conditions, equivalent to a vehicle
deceleration of approximately 14% g (1.39 m/s') from 50 km/h to rest
in 10s. For a typical wheel rolling radius of 540 mm, this
represented an angular deceleration of 25.5 rad/s' from an initial
rubbing speed of 5.5 m/s, similar to the sliding speed at which the
wear criterion was derived (Section 4.3).
6.2.2
134.
A time-step of 0.5s, which had been found to be satisfactory in the
annular brake analysis, was again used, and the low deceleration
ensured that the change in speed over each time-step was relatively
small. For the transient temperature calculation a time-step value of
0.05s was found to produce minimal oscillation in the calculated
temperature gradients.
The friction lining was assumed to have constant thermophysical
properties corresponding to those of virgin friction material and as an
additional simplification the coefficient of thermal expansion of both
the lining and drum materials were set to zero, although temperature
distributions were calculated during each simulation time-step from an
initial (ambient) temperature of 10·C. In this way the brake torque
and shoe factors for each· time-step were comparable with those
calculated using the Rigid Boundary method for drum brake analysis,
where temperature effects are not included.
Actuation Force and Effective Cam Lift
The prescribed displacement actuation applied to the finite element
mesh required some prior knowledge of the relationship between shoe tip
actuation force and shoe tip displacement (effective cam lift). This
relationship was investigated by comparing the results obtained from
brake analysis using two different designs of finite element mesh with
the Rigid Boundary method for friction interface simulation. The
results, summarized in Table 6.2, showed that although a detailed
finite element model of the brake shoe predicted a lower braking torque
for a given prescribed displacement, this was balanced by a lower
actuation force and there was no difference in the calculated shoe
factor.
TABLE 6.2 RELATIONSHIP BETWEEN EFFECTIVE CAM LIFT AND SHOE TIP FORCE FOR TWO-DESIGNS OF FINITE ELEMENT MESH
Effective Lining Shoe Friction Cam Lift friction actua- Drag
coeff- tion force icient force
(mm) 11 (kN) (kN)
Equivalent (Leading Shoe 0.25 0.38 35.1 57.9 Section (
f "e.model (Trailing Shoe 0.25 0.38 75.9 37.8
Detailed (Leading Shoe 0.25 0.38 26.3 43.3 (
f.e.model (Trailing Shoe 0.25 0.38 61.1 30.5
Shoe Fac-tor
1.65
0.50
1.65
0.50
6.2.3
135·
The relationship between shoe tip actuation force and the shoe tip
prescribed displacement was different again for the combined shoe and
drum finite element model because of the introduction of the flexible
drum, and a prescribed displacement of 0.25 mm was found to produce a
total initial brake torque of 8930 Nm. For the initial
therefore, the operating conditions described in Section
time-step,
6.2.1 were
equi valent to a wheel load of 11800 kg (ignoring rotational inertia)
and an average specific power dissipation of 0.79 MW/m' (0.69
bhp/in l).
Initial Pressure Distribution
The difference in shoe factor between the rigid drum and flexible drum
analyses (Table 6.3) can be explained by comparison of the lining/drum
interface pressure distributions for leading and trailing shoes shown
in figures 6.5 and 6.6 respectively. The effect of the flexible drum
is to increase the pressure at both ends of the linings, giving a "heel
and toe" type of pressure distribution (cosinusoidal about the lining
ends) consistent with increased shoe factor.
TABLE 6.3 COMPARISON OF CALCULATED SHOE FACTORS
Shoe factor, Gap Shoe Factor, Rigid Force Method Boundary Method
(Flexible Drum) (Rip:id Drum)
Leading Shoe 1.97 1.65
Trailing ShOe 0.58 0.50
6.2.4 Results
The simulation was continued until 3. 5s of the 10s brake application
had been completed. _ -From the pressure distribution calculated for
each time-step, assumed to remain constant over the time-step, the
frictional heat generated at each node on the lining surface was
calculated (See Section 3.6.2) and applied as nodal heat flux input as
described in Section 6.1.4. (It was necessary to subdivide the
calculated heat flux at each node on the lining surface for application
to the thermal finite element mesh, which had twice as many elements in
the lining surface). Typical examples of the lining friction surface
temperature rise over the first O. 5s are shown in figure 6.7. and
although some oscillation occurred over the early part of the
-Z -i rn JJ3 "ll
f; I rn
~2 rn Vl Vl C JJ 1nl 3: z -3 ~O
""-
Lining Pressure Distribution - Comp-orison of Rigid and Flexible Drum Analyses
Leading Shoe./!- =0-38. Cam Lift = 0-25mm
Rigid Drum
Flexible Drum
"- / '\.
, 55 ANCHOR
" /' " / '\. /'
" /' , //
'- ---........ --------- ----- - ---o
LINING ARC (Degrees) 55
CAM
..., Cl .
Z --I rn :::0
;:; 3 n rn
u pg 2 iJl iJl C :::0 rn
1
\ \ \
\ '\
i
55 ANCHOR
"-
Lining Pressure Distribution - ComRorison of Rigid and Flexible Drum Anolyses
Trailing Shoe, p = 0-38, Cam Lift = 0-25 mm
--Rigid Drum
---- Flexible Drum
"-"
'-:- "'-. ---- --i i I I
o LINING ARC (Degrees)
./' .,./ --~
,/ /'
/ /
,/
./ /'
55 CAM
."
C) .
u o
138. FIG. 6.7
Cam or~eroted Drum Broke Trial Simu lotion - temRerot ure rise at lining surface over first 0-55
1000
w 800 0::
~ ___ ·node 1 1\ . .-.~.-. (trailing end)
1 \ ""'./
:::> I-<t: 0:: W a.. ~ w I-
600
400
200
\ + -+ __ t---"'- - ..... node 81 I \ / ",,- /--v- (trailing end) I \ / t-/
i \ / \ . /
I \, I I I I I
1 I
+
--. Leading Shoe
+--+ Trailing Shoe
._-_.node 12 ~-.-
.~./--.-.- (centre)
t--+--+ __ +- - +-- i-node 70
_.L.. _ _ +-- --t---+-- ,.-
O~----~----~----~--~~--~ o 01 0-2 03 Of. O-S
TIME (s)
139.
temperature rise, stable values were reached by the end. The lining
surface temperature distributions at 0.5s showed some variability
between temperatures on adjacent nodes but generally followed the
pressure distributions as shown for the leading shoe in figure 6.8. The
corresponding drum inner surface temperature distribution at 0.5s
showed only a minor variation from 50 0 C at corner nodes to 52.3 0 C at
midside nodes, confirming that the method for the simulation of
frictional energy transfer from the friction interface was functioning
as required. From these interface pressure and temperature
distributions the wear over each simulation time-step was calculated
using equation (4.10). Greatest wear occurred over the regions of
highest interface pressure and temperature, at the ends of the linings
for the initial simulation time-step.
Temperature profiles through the thickness of the lining and drum
showed very little heat penetration into the friction material during
the initial 0.5s with no evidence of oscillation in the temperature
gradients (fig. 6.9). Lining surface pressure, temperature and wear
distributions for the simulation are included in Appendix 4, figures
A4.1 to A4.7, and showed how the pressure and temperature distributions
changed during the simulation. An example of the variation of lining
and drum surface temperatures is shown for selected surface nodes in
figure 6.10.
TABLE 6.4 CALCULATED BRAKING TORQUE AND SHOE FACTORS
Time into brake Leading Trailing Braking application Shoe factor Shoe factor Torque
(s) (Nm)
0.5 1.97 0.58 8931 1.0 1.97 0.58 8909 1.5 1.97 0.58 8885 2.0 1.97 0.58 8860-2.5 1~96 0.58 8398 3.0 1.96 0.58 8828 3.5 1.96 0.58 8804
In the absence of thermal expansion, (a simplifying assumption for this
trial simulation) the braking torque generated by the brake for the
prescribed displacement actuation and the calculated shoe factors were
affected only by friction material wear, producing a reduction in brake
torque output during the simulation time as summarized in Table 6.4.
The calculated cumulative wear after 3.5s (as shown in figure A4.6) is deta iled in Table 6.5, and can be seen to be very small, as expected
U ::0 m ~2 c ::v m
3:1 z 3
o
Leading Shoe Lining Surface Temperature & Pressure Distributions
(Trial simulation) hO'5s
, 55 ANCHOR
+--+ Pressure
,-, , -
o LINING ARC (Degrees)
1" .
, 55
CAM
--i m 3:
800 ;:g ::0
~ C ::0
600 m
n
400
200
0
•
,., Cl . 0-. <Xl
-i rn :s:
700
Cl 600 rn JJ
~ C
~ 500 - .
400
300
200
100
o
TemReroture Profiles
(Trial simulation, t=O·Ss)
LINING
through L.S. Lining
Trailing end of Leading Shoe
Middle of Leading Shoe
i
0·2095 DRUM
&. Drum
, 0·238
RADIUS (m)
142. FIG. 6.10
Surface TemRerature Variation during Braking_
(Trial simulation - Drum Brake)
800 .----."'"
.u
W 0:: ::::> f<X: 0:: 600 w Q..
:::E w f-
400
200
o o
-to, I" I '+--+ I \ I \ I \\
.~
.~.~. L.S. node 1
I \ I \
+-. I ~+~ ...... + ......
I I I I I I I I I
..... -toT.Snode81
. ____ .-.-.-.-. L.S node 12 ....--. . __ • __ +T.S. node 70
_ --+--. UM ....... -
2 3 35 TIME (5)
6.2.5
143·
for a single brake application. Consequently the effect. of wear on
the brake performance during this simulation is very slight, evidenced
only by a reduction in leading shoe factor from 1.91 to 1.96.
The distorted shape of the drum (e.g. figure 6.11) was almost
symmetrical, confirming that the applied restraints were preventing any
displacement of the drum centre from the central axis of the brake. The
maximum radial displacement was approximately -0.11 mm inwards, while
the maximum outward displacement was +0.13 mm at a position on the drum
close to the centre of the leading shoe lining.
TABLE 6.5 CUMULATIVE LINING WEAR AT 3.5s
Leading Shoe Wear Trailing Shoe Wear node no. (um) node no. (um)
1 3.64 59 4.56 2 3.90 60 0.80 3 1. 15 61 0.25 4 0.52 62 0.05 5 0.15 63 0.01 6 0.06 64 -8 0.02 65 -9 0.01 61 -10 - 68 -11 - 69 -12 - 10 -13 - 11 -14 0.01 12 -15 0.01 13 -16 0.02 14 -11 0.03 15 -18 0.05 76 0.03 19 0.11 17 0.10 20 0.24 18 0.41 21 0.69 19 0.19 22 1.20 80 2.91 23 6.11 81 1.11
Convergence
Convergence of the interface contact calculation, using the Gap Force
method was generally achieved within 8 iterations. The slight
variability in interface pressure distributions, observed particularly
as edge effects at the ends of the linings, was evidence that the
finite element mesh design would benefit from refinement. Because of
the associated extra cost of such refinement, however, these results
were accepted as being within the required limits of stability and
accuracy_ It was also observed that, as in the previous annular brake
simulation, the calculated interface temperatures were sensitive to the
+0"
::0 l> 0 -l> , 0
~O 3:
0 Vl -i 0 ::0 -i
0 Z
-0·'
Drum Distortion (Trial simulation, t = 0-5 s)
-90 0 90 1BO
• Leading Shoe
• Trailing Shoe
Lining Arc Lining Arc
-90 DEGREES
145·
accurate calculation of nodal heat flux, and calculated temperature
variability was reduced by using gap forces rather than axial interface
pressure for the computation of frictional heat generation.
6.3 THE EFFECTS OF TEMPERATURE AND WEAR ON THE DRUM BRAKE SIMULATION
6.3.1 Simulation Parameters
The very low wear rate of the heavy duty friction material used on this
type of commercial vehicle brake was demonstrated in the trial
simulation (Section 6.2) to make only a small contribution to changes
in brake torque generated during a single brake application. In order
to generate greater amounts of wear without increasing the number of
simulation time-steps, the wear criterion (equation (4.10» was
increased by a factor of 10 to enable some effects of lining wear to be
demonstrated:
.Aw = 4.73 x 10-11 p exp(-2900/B) m/s (6.6) ft
Thermal expansion of the friction material was again set to zero, but
the thermal expansion of the brake drum and all other material
thermophysical properties were as described in Section 6.1.7. Initial
temperature conditions were chosen to simulate the operation of a brake
in the "warmed up" condition, i.e. at a drum bulk temperature of 100·C,
and because of the low thermal diffusivity of the friction material a
temperature gradient through the thickness was specified; from 100·C
at the friction surface to ambient (20·C) on the back face of the
lining. The temperatures (estimated from a 1-D finite difference
calculation for the temperature distribution between two faces of a
body, one at 100·C, the other insulated and at 20 0 C) are shown in Table
6.6.
The radial expansion resulting from the bulk drum temperature rise of
100·C was approximately 0.22 mm, to compensate for which a slight
increase in the prescribed displacement actuation was required and for
the initial time-step a value of 0.7 mm was found to produce a braking
torque of 5487 Nm. This was sufficient to brake a wheel load of 2570
kg from 80 km/h to zero at 40~ g (neglecting rotational inertia) over
a time of 5.66 s, equivalent to an initial specific power dissipation I over the entire lining friction surface of 1.55 MW/m' (1.34 bhp/in').
146.
TABLE 6.6 INITIAL TEMPERATURE GRADIENT THROUGH LINING THICKNESS
Node No. Radius Depth below friction Temperature surface
(mm) (mm) (OC)
1 209.50 0 100.0 159 209.25 0.25 96.8 182 209.00 0.50 94.0 227 208.50 1.00 88.3 250 208.00 1.50 83.0 295 207.25 2.25 75.4 318 206.50 3.00 68.0 363 205.25 4.25 60.6
24 204.00 5.50 46.0 416 203.25 6.25 24.0
36 202.50 7.00 20.0
Pressure Distribution
Calculated lining friction surface pressure, temperature and wear
distributions are shown in figures 6.12 - 6.19. Over the first time
step both leading and trailing shoes showed the highest pressure to
occur at the cam end of the lining, while loss of contact between the
lining and· drum was predicted at the leading end of the trailing shoe.
For the second time-step the combined effect of lining wear and drum
thermal expansion was found to be sufficient to reduce the generated
braking torque by 23%, and in order to maintain the brake duty level
the prescribed displacement actuation was increased from 0.7 mm to 0.85
mm. This increase produced a definite cosinusoidal pressure
distribution demonstrating a form of non-linearity known to be
associated with drum brake operation: the braking torque generated may
be increased not only because the actuation force is increased, but
also because the pressure distribution may adopt an increased tendency
towards "heel and toe" due to flexure of the brake shoe and drum.
As the analysis progressed the pressure distributions clearly showed
that the effect of lining wear is to reduce the pressure peaks on the
lining surface so that the distribution tends towards that of uniform
pressure along the lining arc length. Even with the exaggerated rate of
wear used in this simulation a completely uniform pressure distribution
was not produced by the end of the simulation, and lining pressure
varied from approximately 2000 kN/m' over the ends of the linings to
approximately 500 kN/m' over the central region.
pressure were evident at the ends of the linings.
Some edge effects on
147.
100
Cl
Lining Surface, Pressure. Temperature & Wear FIG.6.12 i i : '
Drum Broke Simulation, Time = 0- OS sec N'
5S • LEADING SHOE ~ z ::8 -,.
o t-+-~: ' : '-,SS Anc'hnr
o r ) PC'
1000
•
r---F--, , 0
55 o 1
.u
14B. Lining
Drum
100
I • I ' . 1-: I '
o
Surface PresstJre. ,Temperature;& Wear FiG.6.13 ! ~ i
8roI-<Je Simulation: Time::: OS+lO:sec
, o S~;
, ' I ) "'n 1 ,
149. Lining
Drum Surface Pressure. Temperature & .Wear FIG.6.14
: !
. Bro~e Simulation: Time::: 1·0::,.5 sec _. 100 • LEADING SHOE 1000
!' , , I
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, W 1
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! I I~-··~F~-~~~-'--~' o 55
(' r"n
o
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150. Lining Surface: Pressure, ,Tempewture i& iWebr FIG.6.15 I i I .' ;! I i i '
. I. ;; I, 1 '
DrurrL.8roke Simulation! Tirn~.::;15 ~ 2·0 sec -=. 1 ",'" NEI,.. • \;IV' 1 ':::; 5
.: 1. , "11, !.. .. .. u
, ~,,'-~'.~I -~'" i'~'-' .. :.... !"I" I .• .. ... • ...... ".~ . ,'''''; I jv : ..•. ., . p , ··1 .. ·· 1- .. 1· .. ·, ,1.[ ..•. !:- ... ,.... . ...... .,- '." .: . ....;~.
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. .
SS Corn
o
ij
'1 I
151. Lining Surface, Pressure. Ternper:ature ,& :Wear FIG.6.16 I • " 1 !
Drum Broke Simulation! Time =2·0+2:5 sec "" :
100 55 ----Z i 2J '
.-51 .~ .. ~ .~
,--' .!J) .: .. ·;.w -+ + ........... . . !.~I .J ·~f· ' .. +. j .~ .. g ........... .
"';':' .: ...... ,<. •. :. ' .•... . i·l ····1 .•
i I ,,::1, :: " ! .~ ._.L... ..1. ....... '+-7~ ,
• I. :
.' • ·1.
. j , j
.... "I'Jr:X, ••
.1
j .. !
-~.-: I ,
I . I • I·: I :
1 00 ~
ss
LEADING SHOE 1000
i . T" ..... , ..• ~
i i ",'-' i-I .. ~
, ! , .... i D , .... ,,, .... . ._c .. _._ "", ... ; .. _f.= ...
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• ••••
... :.. :
. :.::. . .. : . '::'. ';";"":: ";:':.':::" :;.: . +::: ",. I'.: •.• :: . • .. ',' .... 1.. ,. ....... " '::'
,-._, "". I :. ;/.: ~ •.... "::'..'-":-,-'.''''':', ... ::.: ,·:_,-'"'"0',·: .. -:"T ( . ::..... • .• -,- _'," ,,:,...c,:. •. I:: .. ,
, ~ -r:-" -' ,-- ,
0 , ' ,
,-I
,-------, 55
0
152.
100
Lining
Drum Surface Pressure,Temperature .&Weor FIG.6.17
. ..
. Broke. Simulation. Time.:::2S::iJ:O sec
LEADING SHOE 1000
J.._. iL ......lI.... . r.' ... . '. ·.NI G""-A'·· (De .,inb. 1 ... .
~. __ .~:!">H .. :k!-u,,di .·1 ! :1.1">' ::"i j: .... .. . .... .. .. ... ........ . ................ 1 ..
. .. .. .
. l- ';"-Ef-- .. ::: +-... -j- ... _1 .. _. +- ._,_._ .. .1-_+ ... _+ -:-+: " l ~ .
.i ... !-.. ~ .... I .. -·~·-·J·: .. J·J ... ) ... .1 ... 1.. ... j .. J .. -i .. -... -----,-:... .I-"-~. I '0:: : ,a ! ' ! I j ! : " I It. 0:
'<l: I I: v ,., I I tu ·w:·i .. ·'~ .... T .1.., . . . .. L ....+-!._:--:.o.:: ~ i i 0::1 i ' i ,! L
i Q..I ' I' I 'w I : I : I : I .
o
~; . ····il···l
j
···· ·~oo· ~ .0. ! ,
,. ·LL<tJ.·· ;:... ; .:.:"... . " / : # 0::: • '1
·w·· ,/ ~ / I Le, /
I / -' ._. _ , _ ...... ' - • - • --. -. - ,. - r _ • _ r ~. --,
A 11(" hi \1 , " p, I
o
153.
100
I . I I : .
I
Cl
Lining
Drum
Surface, Pressure. Temperature & Wear FIG.6.18
Brake Simulation. Time = 3-0 -,-3-5 sec
iLEA,OING SHOE.
. , 1 ' f), ., 1
1000
....... ·· .. ·u
o ('n I
.,
~ 1 :1 1
54. Lihing Surface; Pressl'Jre, ,TeroperatJre ,& :We'or FhG.6.19 ; : i : . .; i I I I I
o i • B ' j c- . i t' . t· : 3 5 : L. 0 ; rum .. roKle.D.lmulo IOn, Ime=.·.;.. .. :.i . sec. i j
N 'f LE40lNG SHOE _.1Iinn '., l~O- ~5 : , , - "!UU '_
i i· ... ~·f !..... ij ....-:~c) ! ! -1·W! i i 1 : -
I ···~I·· I~: . ····1-·:· ... i . .1. ... ··I·-j--·" . .~. I--=I-+'.~· 1·---:--- :--,-1·------, . • ••••. ~.
_J__.~ .0: , .. , . I ,. !:! ~ ..• : .,.,.,. fj
!~:.41 ,,"~ ··'1 .". < -- .... ... ... . ; .. , .. :;,> ...•••.•.• , ".', ..•....... :,-.. .'. >u· " .,'-:. .. i.C " ;......, . ..; ! ,.. ',,, " .• ... .'~ :'.' •.• sp .•... ~I ., ' . T\ .. , ,..... .•..•... .... ,...",j ~1 .
. . ... ,.: ':::7C : .. ,,;,..-1-., . " ,., .• '....:.. ·'._I __ !_I'~': I , '" ,'" .:::: ",I.... " ",·1>'," , ... ,. ".> "". ,,, .. ".'" ·,,·,'T , .. , "L" E" •. ; • . ,.. .., ... , .. ". ,.. . •.. , .,} ·'··':+1")
.• . .... ' .• ""1\ ,:, .. 1':··CI·-> -; > I. .. . .•. , .••• :,~l;,.J;.;r .' . • •. ':'
":f,-'-, ... :'::".,-"1' • .":-"." .. '~'/'I--f:l··· "" .... ' ••... ,' ..' ·:'_LU <T~ U ,:~ .'. ':::'''_ •. •• ' .' .. ". >,.E ". ., " .. ,-:, ":.; ", T ' ••• : ••• ' j ... :~ .,:. '..". ,,'.' ., •••• , ·'·R
..•....••• ~ .. ,....~ ............• ,,·····'·1 I ., .. ·'r. , ,.:;: cc <, ;:;: : .. " .•. ". .• .... ..,. • :'HU
l·....·~ .... :' .. 1 •.•..•.. -> ,','.' I; .: ••••. ;.:g 'ty. - .: .. - .. :-:-.: I ... ::'; .
. ,~. ".~ ! ! I '1 + .....• ,.'._' .. "~_ i '~,. 'V: i - ! .; i·: • :? -- .:. :~ ,~,. 'r-"":" ---'r:"'-! .~.--I:--f-·-ci""~---:r1:--.t\. w~··
'-I"~ , . 'r' . ·1 ·1 ~'"'. 'j ..
:'l·~ ! ' : I i ; : , .. 1-, ..... -.. <tj ..,-.: i·!·' . ,. " -. .1. , r , , Lu " ,I
0::: ',:1' .~ i ~:. • .'1 r- _ ...... L-..-· Z: ."..-
r --:
I 00 .r-+-t 1 I --+- , ,
')5 0 , ,
_or
r= '(' r- - , I
, , ,_--l
,
.
, 5:)
r ,
0
6.3.3
6.3.4
155.
Brake Torque Output
The reduction in both torque and shoe factor shown in Table 6.7,
resulting from lining wear and drum thermal expansion, meant that
although the braking torque was assumed to be constant over each 0.5s
time-step, the deceleration was not constant from one time-step to the
next. The increase in actuation prescribed displacement caused the
vehicle speed to be reduced from 80 km/h to 18.9km/h in 4s, instead
of the original 5.66s, calculated for a constant 40% g deceleration, in
spite of the reduction of braking torque calculated during the
simulation. In-stop braking torque fluctuation is frequently observed
in practice, particularly in drum brakes, and although actuator travel
may be changed to compensate for clearance variation, further
investigation, using this analysis technique, would be of interest.
TABLE 6.7 CALCULATED BRAKING TORQUE
Time Time Shoe tip L.S. L.S T.S. T .5. Braking Step Displace- friction factor friction factor Torque No. ment drag drag
(s) (mm) (kN) (kN) (kNm)
1 0-0.5 0.7 15.9 1.86 10.3 0.49 5.5 2 0.5-1.0 0.85 26.5 1.89 17.3 0.51 9.2 3 1.0:-1.5 0.85 21.1 1.85 13.4 0.50 7.2 4 1.5-2.0 0.85 18.5 1.83 11.7 0.49 6.3 5 2.0-2.5 0.85 16.0 1.80 10.3 0.48 5.5 6 2.5-3.0 0.85 14.2 1.78 9.5 0.48 5.0 7 3.0-3.5 0.85 13.0 1.76 9.0 0.47 4.6 8 3.5-4.0 0.85 12.4 1.74 8.7 0.47 4.4
Lining Temperature Distribution
The lining surface temperature distributions closely followed the
pressure distributions, with high temperatures at the positions of high
pressure. Tnese temperatures were~ affected by edge effe~cts, and values
of temperature and pressure at the ends of the linings were considered
to be more realistically estimated from continuing a smooth curve drawn
through the pressure or temperature values at nodes on the other
elements in the lining friction surface. High surface temperatures of
800·C-900·C were predicted during the early stages of the analysis, at
the high pressure regions near the ends of the linings, whilst over the
central region of the linings the temperatures ranged from 200·C-300·C.
In this analysis the leading shoe generated greater frictional drag so
that the surface temperatures predicted were generally higher than on
the trailing shoe.
Towards the end of the brake application the combination of a more
uniform pressure distribution and reduced frictional heat generation
produced a more uniform lining surface temperature distribution as
shown in figure 6.19, around 200·C for both shoes. Typical
temperature profiles through the thickness of the leading shoe friction
material lining at 4.0s are shown in figure 6.20 and can be compared
with the initial gradient defined in Table 6.6, indicating that heat
penetration into the friction material during the analysis occurred to
a depth of approximately 5 mm. A small temperature inversion effect
can be observed at the trailing end, where lining/drum contact has been
lost and the highest temperature occurs about 0.5 mm below the surface.
Examples of variations in calculated lining surface temperature through
the simulation are shown in figure 6.21.
6.3.5. Drum Temperature Distributions
6.3.6
There was negligible circumferential variation in the calculated drum
temperature which, over the 4s duration, increased from 100·C to 160·c
at the drum inner surface as shown in figure 6.21. The temperature
profile through the drum thickness after 4s is shown in figure 6.20,
demonstrating that only a very small temperature rise at the outer drum
surface occurred.
Drum Distortion
Drum distortion, measured by the radial displacement of nodes on the
inner surface of the brake drum, is shown in figure 6.22 for the
initial (0-0.5s) and "final (3.5s-4.0s) time~steps. Maximum and
minimum displacements occurred at positions adjacent to the centre of
the leading shoe lining arc length and adjacent to the centre of the
actuating cam respectively; the greatest radial expansion was +0.508
mm and the least was -0.023 mm, both over the second time-step (figure
6.23). Drum distortion was almost symmetrical over leading and
trailing shoes, again confirming the satisfactory behaviour of the
constraints system, and was modified by lining wear as well as by
thermal expansion. While the maximum radial drum displacement
decreased only slightly over the total simulation period, after the
-i rn :s:: IJ rn )J
~ c )J rn
() •
400
200
o
TemReraiure Profiles through L.s. Lining & Drum
Drum Broke Simulation t = 4·0 s
Middle of~
Lead;ng Shoe 7 ~~-_____________ _ _ ~ __ '--:;:::;/----~-Trailing end of Leading Shoe
i
LINING 0-2095 DRUM 0-238 RADIUS ··(rn) .
. '" . IV o
--~-- --~~--~-
158. FIG.6.21
Surface TemRerature Variation during Braking
Drum Broke Simulation
800
.u
W 0: ::::> I-::
~ 600 w 0... :L w f-
400
200
o
+ /\ I \ / \ / \
/ \ I '\ I , I , t , I \ I of, I ' I "
/ \ \
I ' . \-
I ~.s. " 11 node 12 ~ +, I V·~. "+ T. S. node 81 I .____..~ . I . \:____.
I ;~~~~+-_~ __ ·----·--.LSnode 1
I +/ DRUM I /,/
, , • i , o 1 2 3 t.
TIME (s)
JJ :l> o :l> r +0·5 o JJ C ~
o (fl
d JJ ~
o z
3 3
o
Drum Distortion (Drum Brake Simulation)
-- -
-90
/
/ /
/
/
/ /
/
/ /
/
/' /
~
/ -1=0·55
i
o
.. Leading Shoe
Lining arc
'- , ',_t=45
\ , ,
,
, \ ,
i
90
/
, I
/
•
... --- ...
/
/
/ /
Trailing
Lining
lea
"
"
Shoe
arc
, " , ,
" , \ , ,
..
, ,
-90 DEGREES
C"l . 0-.
160. FIG.6.23
Maximum & Minimum Drum Inner Surface
Radio! Distortion during Braking.
(Drum Broke Simulation)
0·5 J Maximum Radial Distortion
E (node 119. adjacent to centre E of leading shoe)
z 0 I-a: ~ If)
0
L ::::> a: 0
..J Minimum <l: Radial Distortion 0
<l: (node 121, adjacent to cam a: position)
0 0 2 3 t.
TIME (s)
161.
first time-step, the minimum radial displacement increased by 0.140 mm
to +0.117mm (outward) at the final time-step (0.355 - 0.40s), as
indicated in figure 6.23.
6.3.7 Wear
6.3.8
TABLE 6.8 CUMULATIVE LINING WEAR AT 4.0s
Leading Shoe Wear Trailing Shoe Wear node no. (!lm) node no. (!lm)
1 2.42 59 0.33 2 6.44 60 0.14 3 4.96 61 0.16 4 3.78 62 0.15 5 2.70 63 0.17 6 1.94 64 0.15 7 1.36 65 0.12 8 1.02 66 0.10 9 0.80 67 0.08
10 0.66 68 0.06 11 0.52 69 0.04 12 0.45 70 0.03 13 0.41 71 0.02 14 0.43 72 0.05 15 0.53 73 0.10 16 0.73 74 0.28 17 1. 14 75 0.66 18 1.73 76 1.80 19 3.01 77 4.11 20 5.15 78 10.13 21 9.54 79 16.69 22 12.73 80 36.29 23 44.92 81 12.68
The greatest calculated cumulative wear after 4s (Table 6.8) occurred
at the ends of the linings, demonstrating the tendency towards uniform
distriblltion of pressllre as a result of wear. Compared with the
calculated wear values shown in Table 6.5 for the previous simulation,
the values shown in Table 6.8 are greater only because the wear
criterion has been exaggerated by a factor of 10. The effect of wear
on the calculated brake performance would appear to be small compared
with the effects of drum thermal expansion.
Convergence
Convergence of the lining/drum contact and friction drag calculations
generally required about 20 iterations for each time-step, an increase
over the previous simulation which resulted from the extension of the
\~ ,
162.
analysis to include drum thermal stress and expansion effects which
affected the calculation of gap forces and nodal strains. The change in
either run time or computer usage was negligible.
6.4 THE EFFECTS OF LINING THERMAL EXPANSION ON THE DRUM BRAKE SIMULATION
6.4.1 Thermal Expansion of Friction Material
6.4.2
The surface layers of the lining material, normally considered to be
the Char or Reaction Zone phases, were not modelled in this 2-D drum
brake idealization because of the large size of the lining elements
used. In practice most of the thickness of the lining friction
material is affected by heat during use, and as shown in Section 4.2.3,
the thermal expansion characteristics of used (i.e. non-virgin) lining
material as measured from repeat testing of the same sample, are
different from those of virgin (i.e. unaffected by heat) material. In
this case the "used" friction material properties were considered to
represent the properties of the Reaction Zone for which the values of
the coefficient of thermal expansion were lower and more stable with
temperature as shown in Table 4.4. For the purposes of this
simulation the friction lining material was assigned the values of
coefficient of thermal expansiC?n of Reaction Zone material, using the
Variable Properties program modification described in Appendix 1.
Simulation Parameters
Apart from the lining thermal expansion, all thermophysical properties
of the friction linings, brake shoes and brake drum were the same as
used in the previous simulation (Section 6.3.1), and the exaggerated
wear criterion (equation (6.6» was also applied to the lining wear in
this analysis. The initial bulk drum temperature was again set at
100·C, and the temperature distribution through the lining was the same
as detailed in Table 6.6.
An actuation prescribed displacement (effective cam lift) of 0.9 mm on
each shoe tip produced an initial braking torque of 13230' Nm. This
was sufficient to decelerate a wheel load of 4000 kg at a rate of 62~ g
(6.1 m/s'), and from an initial vehicle speed of 80 km/h the duration
of the brake operation would be 3.65s, (neglecting rotational inertia).
These conditions represented heavy duty braking at an ini t ial power
dissipation of 3.8 MW/m' 0.3 bhp/in').
6.4.3
6.4.4
Pressure Distribution
The lining surface pressure distributions for the first time-step are
shown in figure 6.24; at the ambient temperature of 20°C there were no
effects of thermal expansion. These distributions (together with the
calculated temperature and wear over the first time-step) showed the
characteristic cosinusoidal shape which was more pronounced than in the
previous analysis (Section 6.3) because of the higher aotuation foroes.
The lining/drum contact and pressure distributions over the seoond
time-step (O.5s-1.0s) were calculated twice, using values of the
coefficient of thermal expansion for friction material in the Virgin
phase and the Reaction Zone phase for comparison purposes. The
pressure distributions (both shown in figure 6.25) were similar, with
the greatest difference occurring in the high pressure regions at the
ends of the linings. The higher temperatures calculated over these
regions in the first time-step affected the value of the coefficient of
thermal expansion, which is temperature dependent, and the differences
in pressure mainly reflected the differences between the thermal
expansion characteristics of friction material in the Virgin and
Reaction Zone phases at the higher temperatures. No other significant
differences between the two pressure distributions were observed.
Brake Torque Output
The effect of lining thermal expansion on the brake performance is
summarized in Table 6.9. The difference in the pressure distributions
showed up in terms of brake performance only as a small change in the
leading shoe factor, but greater thermal expansion of the virgin
friction material produced a significant increase in the generated
braking torque for the same applied prescribed displacement. Shoe
factors were relatively~ unaffected ~and therefore any extra brake torque
would be obtained only by an increase in actuation force, indicating an
increase in the effectiveness of the applied prescribed displacement.
High values of the coefficient of thermal expansion also tended to
exaggerate the edge effects and therefore values associated with
friction material in the Reaction Zone phase, (Section 6.4.1) were
considered to be better suited to this drum brake simulation.
164.
TABLE 6.9 EFFECT OF LINING THERMAL EXPANSION ON BRAKE PERFORMANCE
Lining Leading Trailing Total Shoe Factors Material Shoe Shoe Brake Leading Trailing Proper- Torque Torque Torque ties (Nm) (Nm) (Nm)
Virgin 9089 6264 15353 1.91 0.54
Reaction Zone 8085 5569 13654 1.89 0.54
6.5 FULL DRUM BRAKE SIMULATION
6.5.1 Simulation Parameters
6.5.2
6.5.3
The analysis which was commenced to investigate the effect of lining
thermal expansion (Section 6.4) was continued as a full thermal,
thermo-elastic and wear simulation of the operation of a drum brake
under the same operating conditions.
duration, were completed.
Pressure Distribution
6 time-steps, each of o. 5s
The lining surface pressure, temperature and wear distributions for
each time-step are shown in figures 6.24-6.29, over which the pressure
distribution varied to show regions of lost contact at the anchor ends
of both leading and trailing shoes over the final time-step. On the
trailing shoe, the pressure was concentrated over the part of the
lining at the cam end of the shoe.
Calculated lining pressure varied from approximately 3000kN/m l at the
ends, and 500 kN/m l over the central region of the leading shoe lining
during the second time-step, to approximately 1000kN/m l and 300kN/m l
respectively over the final time-step. Some variability was evident
in the pressure distribution which suggested that- as well as edge
effects, step changes in the coefficient of thermal expansion of
adjacent elements could also cause some pressure variability.
Brake Torque Output.
The calculated braking torque during each time-step in this simulation
is summarized in Table 6.10. These values can be compared with those
'from the previous analysis, shown in Table 6.7, in which the· shoe
L" . S fP' '1i t' &'W' FIG. ~65. • Ihlng lJr Glee i . reSSlUre, empefiQ ure: i: ebr .: 6.24 i ' : ! I I I I i ! I :
Drum .Brol:<Je5imulntioni Tim~::;b~([)5if,~c ~ ~ \i ' . I • , ' , ! •
1()O "Eis , il,.tA,QJNGS,MQ~ if, ",,/ '" '1000 --.: . ': I ill z , ,
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.<:( . • .. ". 'J' '" ,.,: • .. : . I .. : . ..j-·--:----f---+H·i--\----- i---' ' ---- .. .' . . ~ . \ . '1/' .... '1:1 ,. )".~" i .~~ ...• ~::.-\ li ci + 1-'. : .' '~8; -.-':-Ll--· !.~- '-1\ 1\-----1---L ..• - .•. ! i ";--' ". : .":i
[ I 'ffi- ,!\J. ',' ' i . '.':'I.!" !.... ... :j : 1--''''. , i! ~ .- . r-l -: .-~-.-!-.-.;.-./:
I I r--, I
o o ~-~I~-=::~~~~~~~~~~I--~~: 0 55 0: ~ Ancln LINING Af~C (Deg) Cam
~66. Lihing SLJddce i Pr~SSlUre. iTempe~ature & iWebr ~~~5; ; ; I' - ~ . I • ! 1 ," 'I r--, " ,!. I 1 ' ,
OrulTL . BcoKleSiml.Jlation! Time.::: (j)·5i-UD sec
:
-=. ~s . i/l. ~-. i iL~4o'N~ . SrfOE: ... 1600 2 I!\\, ' /"
.. i. '- J ....!... I.· ; .. . I·· ,L.', ... : .... ,-.. ~. _ ..... , .. (0.
: "'- U /: i r-..: I , i. I. I .. . -+-"'1'" .. , .... , , E.~ .. :".~- :\ I\! .... '...;.... ' ........ : ... / . .,.. .. 1 .. i; ... ·tlu .. ; = \ .. '1 ... . .,. 0::: .;~. ; g .. ...... . ;< / D
; )9;;1.' :1f •.• :. ':j .... \' I" .:.+-;.. ../ ... ' I;: r,e ':T' 5 I ~. iliJ .,': '.' I, .,,,. ,; U . k ~.'" ' "', .. . ... , .~
.. i> .• ; !-:'i{f+>:') ." • . X!';· ., 'il/·.; .:' '..... ". ,Lw . • ·';;k .. ,;",. ; V \: ,. TL'b ;.. ,:: .. '; I .. ;·;. '.,'. :,.,., ••.. V,·, . .. ; .•.• , •. : ~ "",. '.' ~ '\{IX: . I. ..,' il
',1'.', ." . "'Ii ; .. '''I',,' .' : : : . ... , ,
'---I .. l't-'q'
0 .0 ' L o 55 o SS Anchor _______ .....lill.C1lQ[~ ___ .bLII'IN~IN,G Af<C( Deq) Cam
Lihing Surface: Pressure"TenilpeliOture i& iWebr.; F6
1G26
" . I 1 g i ' , , I ; . I "! ' .-"-. . ,I It. .! 'i!'
0" '1) C··[ t" I r·.l 10 15 . . rum, COf"<Je.DlmLJ a lon,lmt::'=: : .. -:L.·. lsec ---' Ni i I
" ,0 ¥5 "L i Lc 40lNQ SHOE,.....' ';i'OOO"
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170. , Llnina Surface i Pr~SSlUre, ;Terr!l!J~uture i& iWeor~9
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6.5.4
171.
factors and braking torque varied through the duration of the brake
operation in a similar way. Again the reduction in braking torque
throughout the application meant that the deceleration was not constant
from one time-step to the next. The initial vehicle speed of 80 km/h
was actually retarded to 28.9 km/h in the 3s of brake operation,
equivalent to a change in rotational speed from 40.85 rad/s to 14.71
rad/s. The slight increase in brake torque over the 2nd time-step was
a result of thermal expansion of the lining which in subsequent
time-steps appeared to be balanced by drum thermal expansion.
TABLE 6.10 CALCULATED BRAKING TORQUE
Time Time Shoetip L.S. L.S. T.S. T.S. Braking Step Displace- friction factor friction factor Torque No. (s) ment drag drag
(mm) (kN) (kN) (kNm)
1 0-0.5 0.9 37.8 1.92 25.4 0.54 13.2 2 0.5-1.0 0.9 38.6 1.89 26.6 0.54 13.7 3 1.0-1.5 0.9 38.2 1.89 20.2 0.53 12.2 4 1.5-2.0 0.9 31.7 1.87 16.8 0.51 10.2 5 2.0-2.5 0.9 23.4 1.82 11.4 0.48 7.3 6 2.5-3.0 0.9 15.9 1.73 8.7 0.47 5.2
Temperature Distribution
The interdependence between interface pressure and temperature was
again evident with calculated high lining surface temperature
corresponding to high interface pressure. At the ends of the linings,
calculated surface temperatures of 900·C or more were attained over the
initial time-step, compared with 300-400·C over the central region.
Afterwards these temperature peaks were reduced, leading to surface
temperature distributions which were generally more uniform, between
200·C and 400·C. Examples of surface temperature variation through
the brake application, shown in figure 6.30, indicated that highest
lining surface temperatures were reached early in the simulation.
The calculated drum inner surface temperatures were sensibly uniform in
the circumferential direction and were similar to the lowest lining
surface temperatures, reaching about 225·C at 1.5s. At the outer
surface a temperature rise of only 2·C was calculated, indicating that
steady state thermal conditions in the drum had not been reached.
172. FIG.6.30
Surface Temperature Variation during Braking_
. Drum Brake Simulation
1000
.u - 800 w 0:: ::::> ~ 0:: W CL ~-
W ~ 600
400
200
o I
o
+ I
I \
\ \ \ \
\~ \ L.S. node 1
\ ,
• '-.... \ ...... + tS. node 81 .~. --+/
",.
ls.n~~ 70 _"\::::"L5. node 12 /,~
6 "DRUM
I • • 1 2 3
TIME (5)
173.
Typical temperature profiles through the lining and drum at 3.0s are
shown in figure 6. 31 • High surface temperatures were invariably
associated with very steep temperature gradients, indicating. very
little heat penetration into the material. There was zero calculated
temperature rise at the back face of the friction material, confirming
that the lining-only finite element model for the thermal analysis was
a realistic assumption for transient braking conditions. The
temperature inversion effect occurred as a result of lost lining/drum
contact at the trailing end of the leading shoe, where heat flowed away
from that region without any frictional heat generation.
6.5.5 Drum Distortion
The distorted shape of the finite element mesh at 0.5s is shown in
figure 6.32, and as illustrated in figure 6.33 in terms of the radial
displacement of inner surface nodes, drum distortion altered over the
3s braking duration due to the combined effects of lining wear and
thermal expansion. Maximum radial displacement, adjacent to the
centre of the leading shoe lining arc length, showed little variation,
while the minimum displacement changed from -0.109 mm to +0.095 mm as
shown in figure 6.34.
6.5.6 Wear
TABLE 6.11 CUMULATIVE LINING WEAR AT 3.0s
Leaal.ng Shoe l!ear node no. (J.UD)
-rral..Ll.ng Snoe l!ear node no. ( !lDI)
1 15.21 59 10.91 2 64.57 60 7.49 3 32.98 61 2.08 4 26.81 62 0.94 5 13.79 63 0.38 6 8.70 64 0.14 7 3.60 65 0.15 8 1.74 66 - - 0.16 9 1.68 67 0.05
10 1.62 68 0.01 11 1.24 69 0.01 12 0.87 70 -13 0.84 71 -14 0.75 72 0.01 15 0.93 73 0.03 16 1. 19 74 0.12 17 2.76 75 0.79 18 7.21 76 9.14 19 12.32 77 16.53 20 25.71 78 34.78 21 35.08 79 62.55 22 62.79 80 131 .84 23 72.69 81 10.90
~ rn 3:: Ll rn ::0
~ C ::0 rn
[,00
200
o
TemReruture Profiles through L.S. Lining & Drum
Drum Brake Simulation t = 3 ·Os
roiling end of lead ing shoe
Middle of leading shoe ---.f.-J
LINING 0-2095 DRUM 0·238 RAbIUS(m)
175. FIG.6.32
Finite Element Mesh Di?Rloced ShoRe
t = 0'5s (Full Drum Broke Simulqtion)
D.OR ...:.. ~
ANCHOR CAM
'.
"" - --. - -, - - __ 1 __ -'
mesh
Drum Distortion (Full Drum Broke Simulation)
::0 l> 0 l>
~
--J r ---, '" " ---, ' ,
0-5 / , , "-0 / ,
"-::0 / , , C I \ ,
I -...- 3-05 :s:: , \ ,
\ 0 \
, (Jl " -I \
, 0 / ,
/ " ::0 / /
, , -I -- / , / "-
~
0 0-55 , /
Z ,- --
0 3 3 0 100 -90
-0-1 DEGREES ."
Cl
Leading Shoe Trailing Shoe . 0-
0 • • . Lining arc Lining~ arc w
w
177 . FIG.6.34
Maximum & Minimum Drum Inner Surface
Radial Distortion during Broking_
(FULL DRUM BRAKE SIMULATION)
Maximum Radial Distortion
E 0-5 (node 119. adjacent to centre E of leading shoe)
z 0 f-0:: 0 f-III 0
:E :::> 0:: 0
-l <t: 0 <{ 0:: J .Minimum
-Radial Distortion (node 121. adjacent to cam
0 position)
0 1 I 2 3 TIME ( s)
-0·1 J
The calculated cumulative wear after 3s shown in Table 6.11 can be
compared with that obtained in the previous analysis, Table 6.8, at the
same exaggerated wear rate. As a result of the higher pressures and
temperatures generated under heavy duty operating conditions, much
greater wear of the lining occurred. Although calculated lining
surface temperatures were little higher than those calculated in the
previous analysis (Section 6.3) the average wear increased from 4.67 ~
to 9.38 ~ on the leading shoe, and from 3.67 ~ to 12.57 ~ on the
trailing shoe.
6.6 DISCUSSION OF RESULTS
6.6.1 The Finite Element Model
The results from the analyses described demonstrated that many of the
performance characteristics associated with the drum brake could be
simulated using a simple finite element mesh and the Gap Force method
for frictional interface simulation. The technique devised for the
transfer of frictional energy from the friction interface was effective
in providing a dynamic simulation of heat dissipation in the model,
avoiding the assumption of heat partition which has previously been a
limitation of the calculation of temperatures in brake components.
Variability in calculated interface pressure distributions led to
corresponding effects in calculated surface temperatures and wear,
which were most evident in the early time-steps of each analysis. This
variability had two main causes; edge effects in the lining pressure
distribution calculation, and the high surface temperatures and steep
temperature gradients which exaggerated thermal expansion effects in
the lining elemen ts. Both these effects could have been reduced by
the· use of a more .refined fin! te element mesh for interface. pressure
calculations, with the penalty of increased cost, but the results were
considered to be within the required limits of accuracy and
consistency.
The thermal finite element model proved to be satisfactory, with
variability in calculated temperatures, particularly at the lining
friction surface, minimized by the accurate computation of frictional
6.6.2
179· heat flux input from nodal friction forces. Very close agreement
between the total work done calculated from the total friction drag and
the sum of individual nodal heat flux values was achieved.
Pressure Distributions
The interface pressure distributions calculated for both the leading
and trailing shoes during the initial stages of each Gap Force
(flexible drum) analysis were cosinusoidal in form ("U" shaped), and
were more exaggerated than those calculated from Rigid Boundary (rigid
drum) analysis. This corresponded with the distorted shape of the
flexible drum which increased the pressure at the ends of the linings,
and the magnitude of the variation within each pressure distribution
depended upon the force applied by the prescribed displacement
actuation. The effect of increased pressure at the ends of the lining
is to increase the shoe factor which was evident in the results
produced under the different actuation forces used in each analysis.
The effect of lining wear alone on the pressure distribution during a
single brake application was found to be very small; an insignificant
reduction in leading shoe factor over 3.5s was calculated. With a
wear rate exaggerated by a factor of 10, and including the effects of
drum thermal expansion, a reduction of 8~ in leading shoe factor was
calculated over a 4s brake application, reflecting a considerable
change in the co sinusoidal pressure distribution. The applied force
and total braking torque which were reduced by approximately 50~,
probably had more influence on the changes in pressure distribution
than either wear or drum thermal expansion.
When lining thermal expansion was included in the simulation a
reduction in braking torque generated during a 3s brake application was
still evident, associated with lower shoe factors and lower pressure
variation~ over the lining surface. Therefore, although the combined
effects of drum and lining thermal expansion and wear could not be
assessed under constant torque conditions as might be applied in
practice, the relationship between pressure distribution and brake
performance as defined by shoe factor was clearly illustrated.
6.6.3
180.
Temperature Distribution
The frictional heat energy generated at any point on the lining surface
was determined by the local pressure, the sliding speed and the
coefficient of friction. Since the sliding speed was the same for all
nodes on the lining surface, and the coefficient of friction was
assumed constant, the nodal heat flux was directly proportional to the
interface pressure distribution for each time-step. The temperature
distributions calculated were then dependent upon the thermophysical
properties of both the friction material and the mating body, together
with the interface contact resistance and heat transfer boundary
conditions. Surface temperatures over each lining corresponded to the
shape of the pressure distribution and were generally higher than
calculated drum inner surface temperatures at any stage during the
analyses. Typical lining surface temperatures in the full simulation
(Section 6.5) ranged from approximately gOO'C over high pressure
regions at the ends of the linings to approximately 200'C over low
pressure regions, compared with a maximum drum inner surface
temperature during the simulation of 225'C. These differences in
surface temperature were controlled by the interface contact
resistance, and the value of 1000 W/m'K which was used, although high
by convective surface heat transfer standards, was at the low end of
the range of values presented by Ling and Pu (Ref. 22). The magnitude
of the calculated interface temperature differences suggests that this
effect is very important in the thermal analysis of high energy
frictional contact conditions.
The temperature inversion effect observed over regions of lost
lining/drum contact, where the peak temperature occurred slightly below
the friction surface, was a result of heat transfer away from that
particular region, without any frictional heat generation. Lateral heat
flow to or from a(ljacent elements affects calculated temperatures, but
the inversion effect was considered to be mainly due to the transfer of
heat from the surface layers of the lining to the drum, which may have
represented a preferred heat flow path than the friction material.
This implied that good thermal conductance existed across the wear
debris or gap separating the two surfaces which were out-of-contact.
Further investigation of this effect is necessary and could be combined
with a study of the effects of interface contact resistance on
temperature distributions by completing further analyses.
6.6.4
181.
Circumferential variation of drum temperatures was minimal, confirming
the satisfactory performance of the interface frictional heat transfer
simulation, but suggesting that there would be a lower limit to the
rotational speed. Below this speed surface heat transfer effects
would cause significant cyclical temperature variation and this method
of simulation of dynamic braking thermal conditions would be
unrealistic.
Temperature profiles through the friction material confirmed that the
assumption of zero heat flow from the back face of the linings was
realistic for transient braking conditions. Heat penetration did not
exceed 7 mm into the linings, which being tapered, were a minimum of 9
mm in thickness. Temperature gradients were generally very steep, but
there was no problem of oscillation in the PAFEC transient temperature
calculation. Drum temperature profiles indicated that steady state
conditions were not reached, and at the outer surface temperature rises
of 1°C or 2°C only were calculated. The fini te element mesh was
therefore considered to be adequate for the analysis of thermal effects
in the drum brake simulation.
Wear
The interdependence of interface pressure, surface temperature and wear
was such that greatest wear occurred over the regions of highest
temperature and pressure. Maximum cumulative wear therefore occurred
at the ends of the linings so that the interface pressure distribution
tended towards a uniform level which, however, was not achieved during
a single brake application, although the magnitude of the wear effect
was obscured to some extent by thermal expansion effects in the
analyses.
The large size of the elements in the finite element mesh for interface
pressure calculations were designed to direct the emphasis towards the
geometric effects of wear on lining/drum contact and interface pressure
distributions, rather than a simulation of thermo-elastic instability
as in the annular brake analysis (Chapter 5). This was mainly due to
limitations both in terms of computer usage and cost on the size of the
idealization , but the same concepts of localized temperature, thermal
expansion and wear, were applied. In the short term, the very small
amounts of wear which occur during a single brake application are likely to have a negligible effect upon brake performance, but in the
6.6.5
6.6.6
182.
long term, cumulative wear will promote a tendency towards uniform
pressure from which the actual pressure distribution during any brake
application will show transient departures depending upon the operating
conditions.
Drum Distortion
Under simulated dynamic braking conditions, the drum distorted into an
oval form, and maximum outward radial deflection occurred at a
posi tion adjacent to the centre of the leading shoe lining arc length
corresponding with that calculated by Millner (Ref. 39). Measurements
by Fensel (Ref. 72) showed the maximum radial drum deflections to occur
at positions displaced towards the trailing ends of the linings, but,
being taken at very low rotational speeds, these were not truly
representative of dynamic braking conditions. Maximum and minimum
deflections were also affected, and were greater than.those calculated
in Section 6.5 for similar braking torque levels. Although this could
represent different designs of drum, Ashworth et al (Ref. 46)
calculated that thermal distortion alone, resulting from band contact
across the drum width, could account for as much as 0.7 mm in a C.V.
drum of radius 0.212 m.
Check Calculations
The temperature rise of a brake drum or a brake lining during a single
brake application may be calculated assuming the flow of heat to be
one-dimensional. From equation (5.8) the temperature rise at the drum
inner surface (the friction surface) is given by:
kB 2d GO Ob 2
= -(1- -Mt) + 4d L,ierfc2nA - 16Mt1.5 L i3er fc2n>, (6.71 N b'! "1ri 3 n=1 n=1
and for large values of A (where the drum can be considered to be
infinite in thickness and the brake applications are of relatively
short duration) , only the first term of equation (6.7) need be
evaluated:
kB 2d 2 = ( 1 - -Mt) (6.8)
N~! 1Y! 3
The maximum value of temperature occurs half-way through the brake
183.
application and is given by (Ref. 69):
t9 max = 0.53N (1~t)l
k (6.9)
For calculations using these formulae it is necessary to partition the
frictional heat energy that which flows into the lining and into the
drum, using equation (2.8). For the drum brake being analysed;
= 0.96 (drum)
= 0.04 (friction material)
For the trial simulation (Section 6.2) the energy input is described by
Q = 1.58 x 106(1- O.lt) W/m' (6.10)
and the maximum friction interface temperature rise was found to be
177°C. This compares with the drum inner surface temperature rise
shown in figure 6.10 of about 90°C. The results from similar
calculations for the other drum brake simulation analyses are shown in
Table 6.12, together with comparisons with the maximum and minimum
lining surface temperatures.
TABLE 6.12 COMPARISON OF CALCULATED TEMPERATURES
Simulation Calculated Maximum Maximum Drum Lining surface Drum inner surface surface temp- temperature rise temperature rise erature rise (f.e. analysis) (equation (8» (f.e.analysis) high low
(OC) (OC) (OC) (OC)
Trial simu-lation 170 90 700 120 (sect.6.2)
Medium duty simulation 166 75 470 150 (sect.6.3) (at 2.0s)
High duty simulation 228 125 800 220 (sect.6.5) (at 1.5s)
True comparison is difficult because the deceleration is not constant
over each brake application, but again the indications are that the
conventional method of apportioning the frictional heat flux to give
6.6.7
184.
equal average friction surface temperatures over-estimates drum
temperatures and under-estimates lining temperatures and does not
include the effects of interface contact resistance.
Newcomb (Ref. 28) calculated a ~12% change in interface temperature at
the trailing and leading ends respectively of a brake lining with a
sinusoidal pressure distribution. No comparable pressure distribution
was produced by the finite element analysis; the trailing ends of both
leading and trailing shoes were generally regions of high temperature,
reflecting the cosinusoidal shape of the predicted pressure
distributions.
computer Usage
The Gap Force method used for friction interface contact simulation,
presented a considerable computer requirement, due mainly to the large
core necessary for the storage of the system load case coefficient
matrices. The finite element mesh design was kept as Simple as
possible, but it was found that the cost of the number of iterations
required to reach
wi th the overall
a steady contact condition was small in comparison
computer costs. The PAFEC transient temperature
solution program was also made more expensive to run because of the
large number of surface heat transfer elements used in the simUlation
of frictional heat transfer, although again the finite element mesh was
kept as simple as possible. Typical computer requirements for each
simulation time-step were as follows:-
Interface contact/pressure/friction drag calculation.
Transient temperature calculation
Run time (hours)
0.37
0.52
Max Core Requirement
(Kwords)
80
49
185.
7. EXPERIMENTAL CORRELATION OF RESULTS
7.1 ANNULAR DISC BRAKE
7.1.1 Annular Brake Test Rig
A brake rig was designed to validate the 2-D axisymmetric finite
element model analysed in Chapter 5, incorporating the following
important design requirements:
1. Annular configuration of friction components.
2. Minimum axial heat flow from the friction interface through the stator plates.
3. Rigid construction to reduce component flexure during operation.
4. Small rubbing path width and large radius to minimize the velocity differential across the friction interface.
5. Ease of instrumentation.
6. Fully enclosed friction interfaces with dust extraction facility to avoid hazardous dust emission during test.
7. Capable of being fitted to, and tested on, a conventional brake test inertia dynamometer.
8. Fast response, non-servo, actuation mechanism, providing a range of interface pressures.
An item of experimental test equipment, which consisted of a
substantial machined steel casing fitted with a splined hub, shaft and
bearings, formed the basis of the rig. A single rotor plate (figure
1.1) and two sta tor plates (figure 7.2) were designed to provide two
friction interfaces of 0.321 m LD. and 0.362 m O.D. from which axial
heat flow was restricted by the low thermal conductivity of the 3.5 mm
thick friction material bonded to the stator backing plates. The
stationary friction material readily enabled thermocouples to be
inserted for the measurement of temperature.
Part of the cross section of the rig wi th the rotor and sta tor plates
in position is shown in figure 7.3. The rotor mated with the splined
hub, and lugs were provided on the outer periphery of the stator
backing plates to transmit the torque reaction to the casing. These
plates were designed to be of sufficient thickness to resist thermal
and mechanical distortion and were made of an EN8a grade steel since
the EN42 grade which is commonly used in multiplate brake assemblies
186. FIG.7.1
Annular Brake Test Rig - ROTOR ,-.. III
'" -2-Ul
~
L 1I 11
I !
oil) ~ozo£ I . I \1" Via • j •
via ,(OSo7:T J j;o LIE .. •
~a (Lt6.V1)HL' • I ..
a"
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w ...J <C t w c.!)
n: \ <C .J \ :I: t--
\ ~ w I-
'" t 0 l-x f-w w l-n: <C w c.!)
i I , ,
101-1 (3'980) LC?O IU,:,,! ll)
52 (203) •
\./
~. 3-~ "'t~L /' \(0 . ..., -------
~I%'· .. ,// "I-l~
'~-'II .--- J:Zll - .
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"'~ --... -.. ~~,. ~ • ..J
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""~
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"-1-'
--6 OIA (0· 15)
';;'1 ro-' 01 <il' 'i(;i 0, c-JI
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I
.-L. \.tt-._-
PLATE. TO 8E PARALLEL WITHIN 0'05 (O·OOl) & FLAT WITHIN 0'13 (0·005)
.. FRICTION MATERIAL
I ,
t~ ! . , .
» ::J ::J C 0 , CD , 0 A ro
~ (j) ........
::0 '-. lO
(Jl
~ ~ o ;0
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CD -J ,
.,., G)
...... ~
ANNULAR PISIDN
188.
Annular Brake Test Rig.
FIG.7.3
CROSS SECTION OF TEST RIG RUBBING SURFACES
189.
was not readily available in the sizes required. Al though
mechanically these high carbon' steels are very suitable for spl1ned
plates, the material itself is far from ideal as a dry friction mating
surface and careful design of the test schedule and operation of the
rig was essential to avoid surface thermal problems such as "blue
spotting".
The friction discs bonded to the stator backing plates were moulded as
complete annuli and carefully machined to size to avoid any
discontinuities in the surface, arising, for example from any joints
between segments, which would affect the frictional performance of the
material and the circumferential symmetry of the friction interface. A
minor modification to the friction material formulation, which was a
conventional resin bonded asbestos based material, was found to be
necessary to overcome initial problems of scoring arising from
frictional incompatibility, with a steel mating surface but the
thermophysical properties, as detailed in Table 4.3, were not altered.
Asbestos was present in the wear debris produced during test, and
although evidence suggests that the asbestos structure would have been
reduced from the characteristic chrysotile to non-hazardous forsterite,
or an amorphous state (Ref. 73), care was taken to avoid dust emission
from the rig. The standard laboratory dust extraction facility was
connected to a large hole in the bottom of the casing so that air was
drawn in through a number of small holes in the casing, over the
friction components and extracted together with any wear debris. This
flow of air also provided some cooling of the rig internal components.
The hydraulic actuation system for the rig utilized proprietary vehicle
brake components compatible with the equipment fitted to the inertia
dynamometer. Three slave cylinders, each of effective diameter 41.3
mm, were mounted on_ the (ront casing so that equal forces could be
applied through 3 spreader bars to the six actuation rods connected to
the annular piston (see figure 7.3), while return coil springs were
fitted to the actuation rods to ensure positive retraction. Average
interface pressure was directly proportional to the line pressure;
p = (line pressure-threshold pressure [bar]) x 401.4
7.1.2
190.
since all force was applied in the axial direction and no servo action
was involved. Free travel was minimized by the use of clearance
shims. The actuation system can be clearly seen in the photograph of
the rig mounted on the inertia dynamometer (figure 7.4), and proved to
operate most satisfactorily during test.
Instrumentation
Pressure Measurement
The average operating interface pressure was determined from the
actuation line pressure (equation (7.1» which was measured by a strain
gauge pressure transducer, with a separate Bourdon tube gauge providing
a useful check. No satisfactory method of measuring actual friction
surface pressures could be devised, although frequent inspection of the
rubbing surfaces was able to provide an indication of high or low
pressure regions (see Section 7.1.4).
Brake Torque Measurement
The standard torque measuring equipment installed on the inertia
dynamometer consisted of a torque arm and force transducer.
Rotor Temperature Measurement
Rotor temperature was measured using a rubbing thermocouple on the
rotor periphery. Good preparation of the rubbing track, and careful
adjustment of the rubbing pressure, minimized frictional heating
effects and enabled reliable measurements of rotor temperatures to be
made.
Line pressure, brake torque and rotor temperature measurements were
recorded on a continuous chart recorder.
Speed Measurement
The standard tachometer fitted to the dynamometer was supplemented by
an electronic revolution counter and speed indicator.
Details of all the instrumentation used are included with the
calibration procedure in Appendix 5.
191.
FIG. 7.4
ANNULAR BRAKE TEST RIG - ACTUATION SYSTEM
192.
Wear Measurement
Friction material wear was measured using a micrometer in terms of
thickness loss at 3 different radial positions in 4 different
circumferential locations at the end of each stage in the test
schedule. Rotor thickness was also measured in 12 equivalent
positions and the partial dismantling of the rig for frequent
measurement provided opportunity for visual inspection of the rubbing
surfaces.
Friction Material Temperature Measurement
Techniques for measuring temperatures within the friction material and
monitoring friction surface temperatures were investigated: although
sophisticated techniques such as optical pyrometry have been widely
used for surface temperature measurement, their use in friction
interface temperature measurement is restricted because of the need to
view the surfaces concerned. This would have necessitated the
provision of a hole (or a number of holes) in the stator and/or rotor,
which would have been an undesirable modification affecting both the
frictional performance and the surface temperatures. Embedded
temperature sensors have been successfully used for the measurement of
temperatures within friction components (both rotor and stator)
although the accuracy of the measurements is limited by the physical
size of the sensor, local heat transfer (heat sink) effects, and
response time. In the case of low conductivity friction material,
accurat.e positioning of the sensor is also vital. However, this
method offered the most straightforward approach and therefore a number
of fine thermocouples were fitted to the friction material of the outer
stator to measure both surface ~emperature distributions and axial
temperature profiles (through the thickness of the friction material)
as accurately as possible.
Eleven thermocouples fitted at different depths and positions in the
friction material on the outer stator plate as shown in figure 7.5 were
used to measure lining temperature distributions. Each thermocouple
was made of 0.1 mm diameter chromel and alumel wires, twisted together
and brazed to form a junction which was then trimmed back to give a
length between 1 mm and 2 mm. The two wires of each thermocouple were passed through 2 adjacent 0.1 mm diameter holes drilled through the
193· FIG.7.S
STATOR THERMOCOUPLE POSITIONS
10+ +2 +1 6+ ~-l8 +7 +4 +3 11+ +5
THERMOCOUPLE NUMBER THERMOCOUPLE POSITION
1
2
3
4
5
6
7
8
9
10
11
5 mm in from outer radius, surface
7.5 mm in from outer radius, surface
Centre of rubbing path, surface
7 mm in from inner radius, surface
3 mm in from inner radius, surface
Centre, backplate
Centre, 1 mm deep
Centre, 1.5 mm deep
Centre, 2 mm deep
5 mm in from outer radius, surface
3.5 mm in from inner radius, surface
194.
friction material in the required position and the junction was pushed
into a slot, cut to the required depth, which joined the two holes at
the friction surface. The precise depth of each thermocouple in the
friction material was measured after installation was complete as the
distance from the friction surface to the thermocouple junction. The
positional accuracy of the thermocouple tips was estimated to be
:1:0.5 mm. Each pair of wires came through a large (3.5 mm) diameter
hole drilled in the backing plate and then passed along radial grooves
filed in the backing plate to emerge at the outer radius. Araldite
epoxy resin in the hole and groove encased the wires, providing both
insulation and a firm attachment, and care was taken to maintain a
flush. surface on the back of the stator plate to prevent uneven contact
affecting the operation of the brake.
A diagram of the installation of each thermocouple is shown in figure
7.6 and a photograph of the thermocouples in position is shown in
figure 7.7. The wires were protected by PTFE sleeving before being
passed through a 12 mm hole in the reaction plate and a corresponding
hole in the rear casing to connect to terminal blocks fixed to the
outside. A twelfth thermocouple was used to measure casing
temperature and all thermocouple channels were provided with cold
junction compensation and individually calibrated prior to testing. The
temperatures measured by these 12 stator thermocouples were recorded, 6
on a continuous 6 channel chart recorder, and 6 on a magnetic tape
recorder for playback through the chart recorder. The equipment can
be seen in the general view of the rig, dynamometer and instrumentation
shown in figure 7.8.
calibration
Each item of instrumentation was individually calibrated as described
in Appendix 5. Under running conditions the temperature indicated by
the rotor rubbing thermocouple was approximately 20·C above ambient at
200 rev/min, due mainly to frictional heating of the thermocouple tip.
Although this error was speed dependent, there was no noticeable
increase from 200 rev/min to 370 rev/min and the indicated rotor
temperature was taken as being approximately 20·C high at 370 rev/min.
195. FIG.7.6
THERMOCOUPLE INSTALLATION
araldite
.. ;. " . -. .' ." "
thermocouple wires
insulating leeving
acking plate
'. -:::-'::': . .-: : : friction .:: ..... ~'. : .. ::: .. :.:; .: : ' .. : material
thermocouple junction
196 .
ANNULAR BRAKE TEST RIG - THERMOCOUPLES IN POSITION
IN FRICTION MATERIAL ON STATOR
FIG. 7 . 7
197 .
ANNULAR BRAKE TEST RIG - GENERAL VIEW INCLUDING
DYNAMOHETER AND INSTRUMENTATION
FIG . 7.8
198.
Test Procedure
The rig was mounted on an inertia dynamometer using adaptors to attach
the rear casing to the tailstock, and the rotor shaft to the
dynamometer flywheels, as shown in figure 7.9. Satisfactory
performance was established by initial trials, at which stage it was
found necessary to make an alteration to the formulation of the
friction material to prevent scoring of the mating surfaces.
The test procedure was designed to reproduce the conditions of medium
duty operation studied in the finite element analysis (Sections 5.4.2
and 5.5.2), but since it was necessary to follow a careful warming-up
procedure (see Section 7. 1 .1)
condi tions could not be achieved.
identical operating temperature
The test schedule is detailed in
Appendix 5, and commenced with low duty bedding to promote good initial
contact over as much of the friction interface as possible, and avoid
early surface damage as a result of uneven contact. After
satisfactory bedding had been achieved, the test continued with a
sequence of brake applications at the operating conditions summarized
in Table 7.1, leading up to the medium duty operating level at 30 bar
line pressure, from 370 rev/min to 50 rev/min. All brake applications
were made from the specified initial speed %10 rev/min to a non-zero
final speed (of 50 rev/min %10 rev/min) to avoid the effects of
reaction torque and backlash in the torque arm when coming to rest. The
operating conditions shown in Table 7.1 were calculated for ~ = 0.37, a
threshold pressure of 2.5 bar, and a total rotational inertia of 123
kgm'. Seven test cycles were completed, each amounting to one stage
in the test procedure.
TABLE 7.1 TEST OPERATING CONDITIONS
Speed Line Braki'lg Time Mean Average Range Pressure Torque Power Interface
Dissipation Pressure (rev/min) (Bar) (Nm) (s) (MW/m') (kN/m')
200-50 5.0 127 15.2 0.04 46 200-50 10.0 380 5. 1 0.11 137 370-65 7.5 254 15.5 0.13 91 370-50 30.0 1395 3.0 0.69 502
Stage of the test procedure included a single 30 bar brake
application. immediately prior to inspection and measurement of the
rotor and stator plates. The number of 30 bar applications was
-- ------------------------
199.
FIG. 7.9
ANNULAR BRAKE TEST RIG -INSTALLATION
7.1.4
200.
increased to 5 for stage 2 and 10 for subsequent stages so that the
repeatability of measurements made at this duty level could be checked,
at the same time producing adequate wear for measurement. Rotor
temperature, line pressure and braking torque were monitored during
every brake application, and friction material temperatures were
continuously recorded, at each stage. The rotor and outer
(thermocoupled) stator plate were measured during the inspection at the
end of each stage, and the inner stator was measured after Stage 5.
Results
During bedding-in the average braking torque plotted against line
pressure indicated friction levels (calculated assuming a friction
radius of 0.17075 m) which settled down from an initial high value of
0.47 to approximately 0.40. Typical torque vs time traces under test
conditions are shown in figure 7.10 in which a certain amount of
in-stop torque variation is evident. The average torque was fairly
consistent and the performance lines in figure 7.11 showed a steady
bedded friction level of approximately 0.37 with a threshold pressure
(required to overcome hydraulic seal friction, retractor springs, etc.)
of 2.5 bar.
Interface Pressure Distribution
Although friction interface pressure cannot be measured directly under
dynamic conditions the distribution of measured temperature and wear,
together with examination of the mating surfaces have all been found to
provide some evidence of the form of pressure distributions that occur
in practice. Inspection of the rotor and stator plates after
bedding-in showed that the friction material surfaces were smooth and
uniform, but at the inspection after Stage 1, the outer half of the
annular friction surface of both stators showed a darker appearance,
indicating a region of high pressure contact where the higher rate of
frictional energy transformation had produced an increased amount of
thermal degradation of the surface layers. This appearance was
carefully highlighted for the photograph of the friction surface of the
outer stator plate shown in figure 7.12. A region of high interface
pressure towards the outer edge of the rubbing path was also confirmed
by high measured temperatures and greater wear over the same region. On
the same inspection (Stage 1) the rotor surface showed a patchy appearance which on subsequent inspections was seen to be due to the
201. F'G.7.10
Annular Brake Test Rig Torgue: Time
1--'--r .\ ... r '-1 \.
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, ... /'" --=::-.f~ L .. _ ':),-:::;:~J- . __ /..~ ~.: :~fl ~:: .:::..Ic[·It- __ -~: ::- .. ~ :.:..: 1 it '1:/ j"J. rr--U;'~'17, l: :I~:' L :' iC~::')'fj ["-=-'. I --t-"-'-I' .-I-lt.,.".-!-n----j-~ -=+-=-1
I i I ! 1· irI71~I~f i~:r-'-T -- t--I I . I i n _ . ...1 i
202.
Annular Brake Test Rig_
Torgue : Actuation Line Pressure
o w a: w l':> l':>L. ~a l/).D
o ~
l/)
w>zen
FIG.7.ll"
El .D
w a: :::> l/) l/) w a: CL
w z ::J
z o ~ :::> fu « o (")
o N .
~----~----~----~----~----~ __ ----~----40 o o N 8 ~
cO
TORQUE (Nm)
o o ~
o
203 .
ANNULAR BRAKE TEST RIG - THERKOCOUPLED STATOR
RUBBING SURFACE AFTER OPERATION
FIG.7. 12
204.
formation of "blue spots", which were displaced from the centre of the
rubbing path towards the outer radius, again providing further evidence
of a region of high interface pressure.
Greater wear over regions of high interface pressure encourages the
removal of high pressure areas and the eventual establishment of a
uniform pressure distribution under steady state conditions. Such a
trend was indicated in the observed surface appearance at subsequent
stages in the test schedule when the darker region was observed to
spread inwards and become less clearly defined until more than 75% of
the width of the rubbing path showed a uniform appearance over which
any evidence of pressure variation was impossible to define.
Temperature
The very low thermal mass embedded thermocouples produced a fast
temperature response to the heat generated, limited only by the
response time of the chart recorder. Typical temperature traces for
30 bar brake applications from 370 rev/m in are shown in figure 7.13,
for which a summary of the "start of stop" temperatures, and the peak
in-stop temperatures recorded, ls shown in Table 7.2.
TABLE 7.2 SUMMARY OF MEASURED TEMPERATURES - 30 BAR, 370 REV/MIN, (STAGE 6)
Thermocouple Start Temperature Peak Temperature Temperature Rise No. (DC) (DC) (DC)
1 186 344 158 2 180 295 115 3 182 249 67 4 179 220 41 5 171 212 41 6 126 128 2 7 181 234 53
- 8 177 202 25 9 148 167 19
10 192 333 141 11 175 203 28
Rotor 165 218 53 (indicated)
Casing 47 47 0
W 0::: :::> f<{ 0::: W 0... ~ W f-
205. FIG.7.13
Annular Brake Test Ri9_
JYQical TemReratures recorded at
~3..:::.0-==b:..:::a:.:...-r --.:I:..:..:..i n..:...::e=- R ressu re, 370 - 5 0 rev / mi n .
,
CD i - 0 ..•
3(.4 C •
THERMOCOUPLE . NO.
M\. \£/ . ®: ·· .. ®6·:~·@8 • .
- . . .- : . .. . . ~
-0" .... _- '0' .. -.1 '~'-'-'-'.'-~'- ---,'-_ .. -.'-~ .. ,,..-, ..
295C .. _:249:C __ 220C .J28C.:.:.: .... 210.G... _.l._~_.
i .:/:_.: i
.: . -. - - ; , • .. _. .. . . T' . . - i
1'- .: ' i
--.!
•
TItv1E < ... _ ... ·305. -..
206.
Comparison of the surface temperatures measured at similar radial
positions but different circumferential locations (thermocouples 1 and
10, 5 and 11) showed good correspondence both in start temperature and
temperature rise, a result which confirmed consistent temperature
measurement with no significant circumferential variation.
Radial distributions of friction material surface temperature at 30 bar
actuation line pressure, 370 - 50 rev/min are shown in Table 7.3, and
indicated an increase in start temperature during each stage from
approximately 160·C to' 180·c (after Stage 1). Start temperature
showed little variation over the rubbing path width, but peak in-stop
temperatures indicated a higher temperature rise near the outer radius
than near the inner radius as shown in figure 7.14, which corresponded
to observed evidence of higher duty operation over the outer regions of
the rubbing surfaces. Small changes in peak temperatures from Stage 2
to Stage 7 of the test schedule confirmed changes in the distribution
of generated heat which corresponded to slight reductions in local
interface pressure caused by greater wear over high pressure regions.
The axial temperature profiles as shown in figure 7.15 for the centre
of the rubbing path indicated a steep temperature gradient over the
region of thermocouples 7, 8 and 9, which, if continued to the friction
interface implied a higher surface temperature than actually measured.
This discrepancy was considered to be due to the heat sink effect
resulting from metal-to-metal contact between the thermocouple tip and
the rotor surface, which was evident in the bright, polished appearance
of the surface thermocouples. The negligible in-stop temperature rise
at the back of the friction material (thermocouple 6) demonstrated
minimal axial heat flow through the stator plate.
The large thermal inertia and slow response of the rubbing thermo
couple introduced a time lag effect which made the in-stop rotor
temperature rise difficult to determine, so the peak indicated rotor
temperatures in Tables 7.2 and 7.3 included some effects of heat soak
and temperature stabilization after the end of the brake application.
Being measured at a low speed of rotation, peak rotor temperatures were
considered to be true values (see Section 7.1.2) and were comparable
wi th the lowest friction material peak in-stop surface temperatures,
taking account of the time lag effects. The rotor start temperatures,
measured at 370 rev/min, were approximately 20·C too high and corrected
values were consistently lower than the corresponding measured friction
material surface temperatures.
207. FIG.7.14
Annular Brake Test Rig
Measured Surface Temperature Distributions
- 500 oU
30bar LINE PRESSURE. 370-50 rev/min
W et:: ::J t:{ et:: W CL L: w f-
o 500
o 500
STAGE 1 no.1
.....-+Peak + -+ of-+ • ____ 0 ____ • ___ .---.Start
• 160'5mm RADIUS
i
STAGE 3 nO.10
+ __ -T~ --+ ..----+
0 __ --.. --- ________ •
160·5 mm
STAGE 5 nO.l0
..--+ ~~
+-_ ...... + .----.------.----
o
lBOmm
lBOmm
o ~i----------------------------~O 160'5mm l80mm
500
STAGE 7 nO.l0
,+-+ +~ -+--... --0 ___ 0_ ---.---#-- __
o l60-5mm RADIUS 180mm
208. FIG.7.1S
Annular Brake Test Rig_
Measured Axial TemQerature Profiles
30bar LINE PRESSURE. 370 - 50 rev/min
.0
w Cl: => ~ Cl: W CL ~ W I-
500
0
500
o 500
o 500
o
STAGE 1 no.1
..A---t-'" Peak ~--+ .----. + ~=--'- 'Start
FRICTION ROTOR -MATERIAL-- .... ---
STAGE 3 no. 10
STAGE 5 no.10
•
STAGE 7 no.10
.. -of ,./"
/ _. "t ----+/.-.--i"'~-~
i •
-35mm-
209.
TABLE 7.3 MEASURED SURFACE TEMPERATURES - 30 BAR, 370-50 REV/MIN
Stage
1
2
3
4
5
6
7
No. of Temperature (OC) at Thermocouple Number Applic-ations 1 2 3 4 5 ROTOR
(indicated) Start Peak Start Peak Start Peak Start Peak Start Peak Start Peak
1 88 177 88 136 88 124 88 115 84 115 71 117
1 180 266 173 218 175 203 172 190 166 183 135 180 5 185 293 179 251 180 226 176 199 168 188 145 175
1 161 266 155 221 158 194 155 168 151 171 150 197 5 173 301 167 262 170 235 167 197 166 186 165 195
10 180 304 173 274 176 248 173 213 172 196 168 201
1 160 265 156 237 158 196 155 179 154 177 175 211 5 179 322 172 281 174 236 171 199 171 195 200 229
10 184 303 179 280 180 248 178 221 178 204 203 230
1 154 302 151 235 151 189 150 175 146 171 155 200 5 176 319 170 284 171 234 170 200 169 192 180 220
10 185 320 179 288 180 250 178 218 177 202 188 224
1 181 376 175 270 177 222 175 201 174 196 170 213 5 182 321 176 293 178 251 175 218 172 199 162 210
10 186 344 180 295 182 249 179 220 177 202 165 218
1 172 330 171 252 173 214 171 197 170 191 170 218 5 176 297 175 280 178 249 175 214 173 200 175 218
10 180 319 180 300 182 256 180 221 177 205 182 218
Friction Material Wear
The cumulative measured wear of the friction material was found to be
approximately linearly related to the total energy dissipation as shown
in figure 7.16, and the circumferential variation indicated that any
initial unevenness was quickly removed to give uniform circumferential
wear over each stage.
The average cumulative circumferential wear for each radial position is
shown in Table 7.4 for the outer (thermocQupled) and inner stators.
Greatest wear on both occurred near the outer radius, which was
consistent with observations of higher pressure and higher interface
temperatures over this region of the rubbing surface. Over the
complete test schedule the average wear of the friction material was
125 Ilm over the outer stator and 73 ~ over the inner stator. From
160
E ~
120 0:: « w 3: w > f« -.J
~80 ::::> u
40
o
210. FIG.7.16
Annular Brake Test Ri9_
Measured Cumulative Wear
+-+
0-0
o
o
Inner radius
Mean radius
Outer radius
--.-
4 5 6 7 STAGE TOTAL ENERGY DISSIPATION (MJ) 12
211.
these values the wear per unit of energy dissipated was a mean of 8.6
J.IIII/MJ over each surface, corresponding to an overall wear rate of
approximately 190 mm3/MJ.
TABLE 7.4 FRICTION MATERIAL WEAR
Average Cumulative Wear (J.IIII) : Total Energy Stator Inner Centre Outer dissipation per
Radius Radius friction interface Stage (MJ)
OUTER 22 31 30 1 1.3 27 43 49 2 3.2 30 58 67 3 5.2 46 79 96 4 7.3 69 104 117 5 9.3 77 117 136 6 11.3 95 130 151 7 13.3
INNER 61 75 82 5 9.3
7.1.5 Comparison and Discussion of Results
The medium duty test operating conditions defined by the 30 bar line
pressure brake applications from 370 rev/min are compared with the
analysis simulation conditions in Table 7.5.
TABLE 7.5 COMPARISON OF TEST AND SIMULATED OPERATING CONDITIONS
Parameter Test Simulated
Applied Force (kN) p 11.0 13.0 Friction Coefficient !.L 0.37 0.30 Initial Speed All 38.75 radls 38.00 radls
(370 rev/min) (363 rev/min) Final Speed "'2 5.24 radls 5.42 radls
(50 rev/min) 52 rev/min) Total Braking Torque (Nm) T 1395 1332
(2 friction interfaces) ~
Duration of Brake Application {i)Ts 3.0 3.0 Deceleration (rad/s') W 11. 34 10.86 Total Energy Dissipation (kJ) Q 90.6 86.8
(2 friction interfaces) Mean Power Density (MW/m') 0.69 0.66
Although most of these parameters were arranged to be closely
comparable, it was not possible to match all the operating conditions
exactly. The measured friction was higher than the level anticipated
for the analysis so that in order to match the braking torque generated
and the total energy dissipation, different values of applied force.
. ·.i ."'-.... ;;j. 212.
were required. Because of the warming-up procedure required, the same
initial temperature conditions for both test and analysis could not be
achieved, and therefore differences due to initial temperature
conditions had to be taken into account in the comparison of results.
Interface Pressure Distribution
The interface pressure distributions calculated using the Gap Force
method for friction interface simulation (Section 5.5) indicated a
definite correspondence between interface pressure, temperature and
wear which was consistent with much of the experimental evidence.
Calculated interface pressure showed an increase towards the outer
radius, starting from uniform initial contact conditions, which was in
agreement with the estimated form of the experimental pressure
variation. The fini te element model constraints did not permit
"coning" distortion of the rotor and stator plates; a small amount of
which would affect the interface pressure distribution. The rig was
designed to minimize such distortion but the experimental results could
not be guaranteed to be completely free from very slight coning
effects. However, the rubbing surfaces were checked with a straight
edge during each inspection and showed no measurable coning distortion,
either warm or cold, and the similarity of the appearance of the
friction surface of each stator was further evidence that the pressure
distribution was not affected by gross distortion of the friction
components.
The calculated results were primarily related to the friction material,
and the rotor was assumed to be a stable mating body, on which no wear
of the rubbing surface occurred. However, the effects observed on the
rotor friction surface were examined in more detail to identify any
contribution to the measured results. A small change in the rotor
--thickness during the test procedure was measured (Table 7.6) which was
investigated further by measuring the rotor surface profile across the
TABLE 7.6 ROTOR THICKNESS MEASUREMENTS
Radial Reduction in Measured Rotor Thickness (;un) Position 1 2 3 4
Inner 15 29 22 24 Centre 11 17 5 7 Outer 4 4 -5 3
213.
rubbing path, using a Talysurf 10 profilometer. Measurements at a
number of different circumferential locations all showed a change in
the surface topography from the original ground surface, and the
measurements presented in Table 7.6 were confirmed by the traces
displayed in figure 7.17. Al though of very small magnitude, such
effects would have contributed to the region of high interface pressure
observed. These measurements corresponded with the effects of
blue-spotting of the rotor surface, where localized phase changes of
the rotor material produced variation in surface hardness and a
localized expansion resulting from an increase in specific volume.
Tangential measurement of the surface profile confirmed the presence of
"spots" rather than bands, but further investigation of such effects
was beyond the scope of the 2-D axisymmetric finite element analysis
which assumed circumferential symmetry.
Temperature Distribu'tion
Comparison of measured temperatures with calculated values showed good
agreement in the shape of the radial distribution of surface
temperatures, as shown in figure 7.18 for surface temperatures measured
in the 10th 30 bar application of stage 7, and the distribution
calculated for medium duty braking at 3.0s (Section 5.5.2, figure
5.32). Actual temperature values were not directly comparable because
of the difference between the measured start temperature used in the
calculations, viz. 25°C. Measured temperature rises were also less
than those calculated for two reasons associated with the use of
thermocouple sensors:
a) heat sink effects as described in Section 7.1.4.
b) the physical size of the thermocoup~e junction which measured a
mean temperature over a small volume.
The temperature gradients measured by thermocouples 6, 7, 8 and 9 were
similar to the calculated gradients, but at a higher temperature level
because of the difference in the start-of-stop temperatures.
Straightforward superposition of the calculated temperature profiles
over the measured values, as shown in figure 7.19, indicated that
measured and calculated temperature gradients at depths of 1.5 mm and
2 mm below the friction surface (thermocouples 8 and 9) were similar.
This suggested that, following the calculated profile from start
----_.- -----I --, T
i .' I . ; • , I' , 2 5 -:- :r.--r-
TALYSURF TRACES rotor outer face positions 1 & 2 -------.....,----,-,.-:-:--:--:--~-..,.,...----:---------------------------.-.
:·lAf.E 1'1 l'lGI \N:.. Al'l' 'j;' 1 f""j f{' -, :--; -j Ij i-: . ,'- .-'!' Ll C j-; r-
--1 rn ~ -u
500
gj 400 ~ C JJ rn
o· 300
200
100
Annular Brake Test Ri9_
Comr:?orison of Measured & Calculated Surface Temf2eratures
Measured (PEAK) + ._ ---=~A--===~-::::':=-:" -_.-'"--".
Calculated (at 3s) ...... -.-.-._.- \
I·-· ...... ·-·-·-·-·-·~+ • ----_ ...... -+
j:------- .------.-----.-----. \ / Measured (START) " . .' . . / ,
• .---./ .. ""'-0 .. __
Initial (Calculated)
o ri----------~~~------------~--------------------------~I 160-5mm INNER RADIUS RUBBING PATH WIDTH OUTER RADIUS 181mm_
~OO
- 300 u . W 0: ~
~ 0: W CL L w f- 200
100
25
o
216. FIG.7.19
Annular Brake Test Rig_
Comparison of measured & calculated axial temperature profiles
Peak ~
Start
I
I I
I I I I --Calculated I + Peak] Slar t Measured temps. • I I I
profiles super posed d tures
upon measure J start tempera
/1 I --- -I -------
I I + Indicated peak I + rotor temp. + I +-I I • Start
I -l-fUtorTemp. - • I~ .+'0
I 15. I • Q
I E Calculaled backplate temp. /
/ .:!! .w- rotor t(>mp. • "0
backplate temp. .:!! Cl> u
.Q .2 :J ij; jJ
8 c
c 0
.;! ~
LL -
10'5mm 3·5mm 0 ~mm
51(>(>1 backing plal(> Friction malerial SI(>el rolor
217 •.
temperatures of about 100·C,
been in the region of 350·C.
actual surface temperatures could have
Similarly, superposition of calculated
rotor temperature rise over measured rotor start temperature suggested
that measured peak rotor temperatures of 213·C could be compared with
estimated peak rotor temperatures of approximately 235·C.
Although straightforward superposition of calculated temperature rises
over different initial temperature levels is not strictly correct since
the boundary heat transfer would be affected, further evidence of
higher interface temperatures than those actually measured was provided
by examination of the rotor rubbing surface. The formation of
"blue-spots" on the rotor indicated the existence. of high interface
temperature (and pressure) regions towards the outer edge or the
rubbing path as shown in the photographs of the rotor rubbing surfaces
in figures 7.20 and 7.21, and in the close-up of the outer surface in
figure 7.22. Referring to this latter photograph, an estimate of the
maximum surface temperature from the colour of the oxide coating gave
280·C at the edge of a blue-spot (purple colour), 260·c at the outer
edge of the rotor (brown-yellow colour) and 250·C at the inner edge of
the rotor (straw-yellow colour).
Friction Material Wear
The amount of friction material wear which occurs during a single brake
application is practically immeasurable as a thickness loss, but since.
the cumulative wear was found to be approximately linearly related to
total energy dissipation, a comparison could be made in terms of the
wear per unit of energy dissipated. The calculated wear rate over
3.0s was approximately 18 !lID/MJ, compared with the measured wear rate
of approximately 9 ~/MJ, which was taken over the full test procedure
in which at least half the total energy was dissipated at low levels of
.p!'e;1sure and Je!!li>eraturE!.
Referring back to the empirical
(4.4), Section 4.3.1) describing
relationships
the wear
(equations (4.3) and
rate of resin bonded
composite friction materials, a linear wear rate would correspond to
low temperature wear. Since the effect of high temperature on the
wear of the friction material over the medium duty operating conditions
was to make a substantial contribution to the overall wear, these two
values,
between which were both of the same order, represented good correlation measured and calculated wear rates. At the same time, because
218 .
ANNULAR BRAKE TEST RIG -ROTOR OUTER FRICTION
SURFACE AFTER OPERATION
" ,
w c; -~ a
'. I """"
FIG.7. 20
I
219 ·
ANNULAR BRAKE TEST RIG - ROTOR INNER FRICTION
SURFACE AFTER OPERATION
I,
'"
w q -~ -
"""
FIG . 7 • 2'
220 .
FIG. 7.22
ANNULAR BRAKE TEST RIG - CLOSE-UP OF ROTOR FRICTION
SURFACE SHOWING "BLUE SPOTS·
221.
the wear was calculated from the wear criterion (equation 4.9»
involving both calculated pressure and temperature, this result
provided substantial verification of the simulation technique overall.
The wear measurements shown in Table 7.4 indicated that greatest wear
occurred over the outer region of the rubbing path, in agreement with
the calculated distribution of wear. The diameter of the micrometer
anvil prevented more detailed measurement of the wear distribution so
the comparison could not be investigated further.
7.2 CAM OPERATED DRUM BRAKE
7.2.1 Introduction
7.2.2
It has previously been established that the distribution of interface
contact and pressure along the arc length of the friction linings of a
drum brake is of prime interest in the calculation of drum brake
performance in terms of shoe factors or brake factor. Having
investigated the correlation between interface pressure, temperature
and wear distributions in the experiments wi th the annular brake test
rig (Section 7.1), the drum brake experimental work was directed
towards validating the predictions of pressure distribution presented
in Chapter 6 by comparison of calculated and measured performance of an
S-cam brake of the type described in Section 6.1.1 which is widely used
in Commercial Vehicle applications.
Analysis of the experimental results obtained indicated that
performance was very sensitive to certain aspects of design,
manufacture and operation of the brake. In particular, the
calculation of the overall Brake Factor (Specific Torque) was found to
be not straightforward because of the action of the cam in apportioning
the work and applied force between the two brake shoes. It was
therefore necessary to take all these effects into account and a
detailed investigation into the performance variation of cam operated
drum brakes, based upon these experimental data, was presented by Day
and Harding (Ref. 71).
Test Procedure
A fixed anchor, leading/trailing shoe S-cam brake assembly, 0.2095 m
rubbing radius and 0.178 m width, fitted to a brake test dynamometer
was operated by an air diaphragm actuator through a lever arm on the
222.
end of the cam shaft. Brake torque, rotational speed and actuation
air line pressure were measured using the standard dynamometer
instrumentation equipment, and drum temperature was monitored using a
spring loaded rubbing thermocouple on the inner surface, carefully
adjusted to minimize frictional heating effects.
The friction linings were carefully ground before commencing the test
procedure, giving a slight "crown" contact to overcome drum runout and
avoid initial operating problems. The first 800 brake applications
provided initial bedding-in, which was assisted by frequent examination
of the lining surfaces and the careful removal of any high spots with
abrasive paper. Although there was no perceptible crown contact on
either shoe after this, only the leading shoe showed signs of complete
lining/drum contact over its full area.
A total of 3800 applications of the brake were completed at a line
pressure of 3.1 bar, from an initial rotational speed of 22 rad/s (210
rev/min) to zero. The test inertia was set at 1420 kgm' to represent
a wheel load of -5.5 tonnes at a rolling radius of 0.51 m so that each
application was equivalent to a 17%g (1.67 m/s') vehicle deceleration
from 40 km/h. At intervals during the test schedule the brake
performance was monitored by measuring the braking torque at line
pressure increments up to a maximum of 6.2 _ bar. Operating drum
temperatures were kept within the limits of a minimum start temperature
of 80·C and a maximum temperature of 150·C.
Test Results
Performance lines of braking torque vs actuation line pressure are
shown in figure 7.23 and these demonstrated definite variations in the
performance characteristics of the brake during the test schedule which
could not be wholly accounted for by progressive changes in the
lining/drum contact and pressure distributions. In particular, the
unusual dual slope characteristic of the early performance lines was
traced (Ref. 74) to inaccuracy in the S-cam profile. Over the initial
cam rotation, which waS utilized only with full thickness (new) linings
fi tted to the brake, measurement showed that the cam profile was
uneven, leading to reduced actuation effectiveness and hence lower
Specific Torque. Reasons for the occurrence of such cam profi le
inaccuracy were discussed by Myers (Ref. 75) but these results
demonstrated that careful manufacture is essential if consistent brake
CD Xl l> A rn·
--i 10 o Xl o c rn
" z 3
5
Corn ORerated Drum Broke - Measured Performance
0 0 100 200 300 400 500 600 700 AIR ACTUATION LINE PRESSURE (kN/m2)
'" '" '-" ·
"T1
Cl · '.J ·
224
performance is to be achieved.
"~".~ ',;y. . . Taking these effects into account,
the brake performance as defined by Specific Torque varied during the
test schedule as shown in Table 7.7.
Specific Torque (Ts) = Brake Torque (T)
Applied Camshaft Torque (Tc)
TABLE 7.7 MEASURED BRAKE PERFORMANCE
Number of Specific Torque Brake Applications Ts
870 7.9 1~00 8.7 2~20 11.5 2~30 10.8 2505 12.0 2515 10.8 3755 9.9 3820 9.7
The combination· of a small amount of initial crown contact, lower
unbedded friction levels, and initial cam profile inaccuracy effects
was responsible for the low Specific Torque values measured in the
early stages of the test schedule. These were gradually overcome, as
indicated by the increase in Specific Torque, between 870 and 2400
applications. The subsequent decrease in Specific Torque between 2500
and 3800 applications confirmed the predicted transition from a partial
"floating cam" mode to the "equal work" mode of operation, where each
brake shoe provided 50~ of the total braking torque (Ref. 71). This
is the mode in which the S-cam brake is designed to operate, and
settling down to this level of brake performance indicated that towards
the end of the test procedure, after some 3800 applications, the
bedding-in was almost complete.
At the end of the tests inspection showed that full contact over the
leading shoe lining arc length had been achieved, but the trailing shoe
showed evidence of rubbing contact only over approximately 60~ of the
lining surface, measured from the trailing (cam) end. Therefore,
although the brake performance appeared to have stabilized, much more
operation would have been required before full arc contact over the
trailing shoe lining was be achieved. Even at an average number of
brake applications of 2 per mile, this indicates the magnitude of
bedding mileage which is to be expected, and during which brake performance is variable.
7.2.4
225.
Comparison and Discussion of Experimental and Calculated Drum Brake
Performance
The calculation of Specific Torque from individual shoe factors depends
upon a number of factors which influence the action of the S-cam, and
for small values of cam rotation and cam lift, the following
relationship was derived for the S-cam force system shown in figure
7.24 as shown in Appendix 3.
Ts :
where
Ilcr a(Pl-P2)
:1:(1 + Ilc')l
(Pl - P2)
:I: (1 + Ilc')l ~ 0 (7.4)
The values of Specific Torque calculated from the finite element
analysis (Section 6.5, Table 6.10) are shown in Table 7.8 for a
camshaft/bush friction coefficient of 0.1, which was found (Ref. 71) to
be applicable to the brake assembly under test, and can be compared
with the experimental data shown in Table 7.7.
TABLE 7.8 CALCULATED SPECIFIC TORQUE (REF. SECTION 6.5)
Time Shoe Tip Total Percentage of Work Specific (s) Displacement Brake done by: Torque
(mm) Torque Leading Trailing Ts (kNm) Shoe Shoe (1l,,:0.1)
0-0.5 0.9 13.2 60% 40% 14.2 0.5-1.0 0.9 13.7 59% 41~ 14.0 1.0-1.5 0.9 12.2 65% 35% 15.3 1.5-2.0 0.9 10.2 65% 35% 14.9 2.0-2.5 0.9 7.3 67% 33% 14.6 2.5-3.0 0.9 5.2 65% 35~ 13.5
These higher calculated values were attributed to two principal
effects; the form of the pressure distributions (Section 7.2.5) and the
apportioning of work between the two shoes. Brake performance
calculations using the Rigid Boundary method for friction interface
simulation (Ref. 71) showed that for conditions of perfect initial
contact, if the leading shoe provided 65~ of the total braking force,
then the Specific Torque would be increased by approximately 25~ from
the equal work value as shown in figure 7.25. The final ... ,",," -
Cam O[:)erated Drum Brake - S-cam Force S~stem
trailing shoe cam roller
I
I I
Iw ,Z
w W 0: ::<::,1-<t:IZ 0: W en u
d
camshaf t rotated through angle ~
leading shoe com rolier
camshaft bearing. radius ra
base circle. radius rb
I\) I\)
'"
w :::> o 0::
~
20
u 15 LL u ~ If)
227.
Cam Operated Drum Brake
Performance Variation - Ref. 71
PERFECT INITIAL CONTACT
Pc = 0'1
10+-------- ----+-
F IG.7 .25
5~-~-~-~-r----+-~--~-~-~--~ 100 6 PROPORTION OF TOTAL
50 BRAKING FORCE PROVIDED
LEADING SHOE BY (%1
o
7.2.5
228.
Specific Torque of approximately 10, considered to be under equal work
conditions, could therefore be increased to approximately 12.5 for the
purposes of comparison with Table 7.8
Comparison and Discussion of Experimental and Calculated Lining
Pressure Distributions
The friction linings were carefully prepared to try and achieve the
"perfect initial contact" conditions as specified in the finite element
analysis, without wearing to the increased radius of a thermally
expanded drum. These initial contact conditions referred to the
contact between the linings and the drum at ambient temperatures, which
also applied to the test contact conditions where the linings were
radius ground at the start of the test, and subsequently checked, at
ambient temperature.
The changes in calculated pressure distribution over the duration of
the simulation were exaggerated by the increased wear rate and a
corresponding reduction in brake torque generated for the same
effective cam lift. However the full arc contact predicted over the
leading shoe lining, and the concentration of pressure over the part of
the lining at the cam end of the trailing shoe together with low
pressure or lost contact over other regions towards the anchor end of
the trailing shoe were confirmed by observed contact patterns. The
trailing shoe pressure distribution was less affected by lining wear
than the leading shoe, indicating that, even at the higher duty level
of brake operation and the increased wear rate of the simulation,
wearing-in to give full arc contact over the trailing shoe would be a
lengthy process. This was in agreement with the experimental result
of incomplete trailing shoe lining/drum contact at the end of the test
procedure.
Over those parts of the lining surfaces which were in rubbing contact
with the drum, it was not possible to identify any distribution of
pressure. Although repeated brake applications under the same
operating conditions, as specified in the test procedure, were designed
to produce a stable, uniform pressure distribution, the cosinusoidal
form of the calculated pressure distributions was considered to be
partially responsible for the higher Specific Torque values shown in
Table 1.8. The effects of different forms of lining pressure
distribution (Ref. 11) showed that a small amount of heel' and toe
229.
contact equivalent to only 0.2 mm radius difference could increase the
leading shoe factor by 13%, and trailing shoe factor by 7%. Comparison
of these results has therefore highlighted the importance of the
pressure distribution in the calculation of drum brake performance, in
which the action of the cam (in this particular design of brake) in
apportioning the applied actuation force between the two brake shoes
has also been shown to be relevant. The practical significance of
pressure distribution variation lies not only in the effect upon brake
performance, but also in the effects of localized frictional heat
generation in the energy transformation process, corresponding to
regions of high interface pressure. Problems of drum or lining
surface thermal damage may therefore persist until bedding is completed
and full rubbing contact between linings and drum is achieved. Since
lining wear and interface pressure have been shown to be
interdependent, complete bedding-in of the mating surfaces implies the
uniform distribution of interface pressure which, because of
interdependent thermal expansion effects, together with practical
considerations of dynamic distortions, drum run-out, bearing
clearances, etc., may never actually be achieved during operation.
230.
8. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
8.1 SUMMARY
The dissipation of kinetic energy via friction at the interface between
two bodies in sliding contact has been studied for the general case of
friction brakes where a resin bonded composite friction material is
applied to a steel or cast iron mating body. This is a complex problem
and sophisticated finite element techniques have been employed in a
simulation of the friction process by a time-step analysis. Consecutive
calculations of interface contact and pressure distributions between two
flexible bodies in frictional contact (thermo-elastic analyses), were
combined with transient temperature calculations (thermal analyses). This
method was used for the analysis of two types of friction brake, viz., an
annular disc brake and a two-shoe drum brake, taking into account the
effects of non-uniform interface pressure distribution and frictional heat
generation.
Two methods for the idealization of the characteristics of a friction
interface were developed in a 2-D axisymmetric configuration, one of
which, the Gap Force method, was found to be more satisfactory, enabling
relative radial motion between the friction components, e.g. resulting
from differential thermal expansion, to be realistically included. Only
normal compressive forces and tangential friction forces may be transmit
ted across a friction interface and these were assumed to be related by
Amontons' Laws; the coefficient of friction so defined being considered
constant for analysis purposes. The Gap Force method was applied to
analyses in the 2-D plane configuration, thereby extending earlier work on
rigid boundary friction interface simulation for drum brake analysis.
Tangential friction drag forces were calculated from local values of
interface pressure, over the lining surface, and their sum gave the total
friction drag and hence the braking torque generated. Wear of the
friction material was incorporated utilizing empirically derived wear
criteria based upon local interface pressure and temperature values.
The work done against friction during each time-step was computed from
local interface pressure and velocity, and assumed to be wholly converted
into heat energy which was transferred by conduction from the interface,
eventually to be dissipated from external free surfaces. A study of
alternative mechanisms of energy interchange identified no significant
contribution to frictional energy transformation from thermal degradation
231.
of the friction material. It was confirmed that used friction material
can be described in 3 phases, viz. Virgin material, Reaction zone and a
Char layer at the working surface, with a fourth phase defined as wear
debris (which may also include polymeric or metallic surface coating
effects) between the rotor and stator friction surfaces. Thermophysical
properties of each phase and their variation with temperature were
investigated for two principal types of resin bonded friction material. A
fifth phase of steel or cast iron described the metal mating body.
Thermo-elastic and thermal finite element analyses present different mesh
design requirements, and although these could-- be accommodated in the
annular brake analysis, thereby allowing the same mesh to be used for
both, cost considerations dictated the use of two different designs of
mesh for the drum brake analysis. In this latter case greater refinement
in the interface region was needed for thermal calculations.
Frictional heat was assumed to be generated at nodes on the friction
material surface and elements connecting these with nodes on the mating
surface enabled the effects of interface contact resistance to be
included. A special method for the dynamic simulation of heat transfer
across the interface of the drum brake model was devised to cater for the
variation of frictional heat generation in the direction of rotation. The
transfer of heat away from the friction interface was therefore controlled
by interface contact resistance and the thermal properties of the mating
materials, without the artificial partitioning of heat used in conven
tional thermal analysis.
Trial analyses were completed to confirm the satisfactory performance of
the simulation technique, after which interface pressure, wear and
temperatures were calculated for applications of the annular disc brake at
various levels of braking duty. The results were compared with
experimental data obtained from a specially designed annular brake test
rig, and the measured tempera ture profiles were found to correspond in
form with those calculated. Pressure distributions could not be measured
directly under dynamic conditions, but observed effects, particularly
concerning the interdependence of interface pressure, temperature and
wear, were found to confirm the predicted results. Wear of the friction
material over the test schedule also showed good correlation with
calculated wear rates, indicating that under normal operating conditions
friction material wear may be adequately described in terms of interface
pressure and temperature by experimental wear criteria.
232.
Analysis of a leading/trailing shoe cam operated drum brake showed that
the dynamic simulation of frictional heat transfer produced a sensibly
constant circumferential temperature distribution around the drum, and
lining temperature distributions which corresponded to the form of their
pressure distributions. The calculated braking torque was comparable
with experimental data obtained from an actual brake on a test dynamo
meter, provided that all contributory factors including those of the cam
actuation mechanism, were taken into account. The effects of drum
flexibility upon the pressure distribution and the interdependence of
interface pressure, temperature and wear were evident in the progressive
changes observed in the lining/drum contact distributions. Changes in
calculated braking torque during a single application were found to be
predominantly a result of drum thermal expansion, although a small overall
effect of lining thermal expansion was also evident. By comparison, the
amount and effects of wear of the friction material over individual brake
applications were small, and such performance variation is, of course,
independent of changes in the dynamic friction coefficient which has been
assumed constant for all calculations.
The work presented has shown that the powerful technique of finite element
modelling can be applied to the complex problems of energy transformation
in friction braking, and the realistic idealization enables calculations
to be made with a minimum of limiting assumptions. A significant advance
in brake analysis has been achieved, together with a better understanding
of the basic mechanisms of friction and wear in brakes. Specific
findings and results have been discussed in context, but general
conclusions are drawn in Section 8.2, referring to all the aspects of
frictional energy transformation which have been covered in this thesis.
8.2 CONCLUSIONS
8.2.1 The energy interchange involved in thermal degradation of resin bonded
composite friction material does not make a significant contribution to
the process of friction energy transformation under the conditions
studied. The most important contributory factors to the successful
operation of such friction materials appear to be low thermal
conducti vity together with the ability to degrade thermally to char
which, in a thin surface layer, retains some physical strength and low
8.2.2
8.2.3
8.2.4
233.
conductivity, and is unaffected by further exposure to high tempera
tures. The surface layers then operate in a continuous cycle of
removal by wear and replacement by newly degraded material.
The generation of frictional heat at the friction material surface is
proportional to the rate of work done (as defined by local interface
pressure, sliding velocity and coefficient of friction) and therefore
its distribution over the interface corresponds to the form of the
pressure distribution. Under dynamic braking conditions interface
pressure is seldom uniform and varies with time, being continuously
modified by a combination of;
a) thermal strains arising from frictional heat generation,
b) mechanical strains arising from changes in the applied actuation force,
c) wear of the friction material.
These effects can cause localized loss of interface contact at any
stage during braking, with a consequent increase in both pressure and
work rate over the remaining in-contact regions.
Friction material and mating body surface temperatures are not
necessarily equal at adjacent posi tions because of the influence of
contact resistance upon the transfer of frictional heat from the
interface. Actual surface temperatures depend upon the distribution
of frictional heat generation, the thermophysical properties of the
mating materials and the interface contact resistance, while boundary
conditions only become important for repeated brake applications or
those of longer duration. Under the conditions studied, lining
surface temperatures have been found to be generally higher than rotor
disc or drum surface temperatures by amounts ranging from a few degrees
to a few hundred degrees.
Temperature distributions on the friction material surface are similar
in form to the corresponding interface pressure distributions although
any direct dependence may be reduced adjacent to the free edges by
lateral heat transfer. In annular disc brakes, the form of the
temperature distribution on the mating surface corresponds to the
pressure distribution in the radial direction modelled, while for drum
brakes, mating surface temperature distributions in the circumferential
direction are uniform within the limits of the idealization.
8.2.5
8.2.6
8.2.7
234.
The wear rate of resin bonded composite friction material may be
realistically considered as being directly proportional to interface
pressure and exponentially related to temperature. A small change in
local interface pressure may thus generate only a small change in
temperature but a substantial change in wear rate, so that wear is
greatest over regions of highest pressure, and continuously modifies
the interface contact conditions, promoting a trend towards uniform
pressure distribution. However, even under heavy duty braking
conditions, the amount of friction material wear which occurs during
individual brake applications is very small so that the eventual
generation of a relatively stable and uniform pressure distribution is
a lengthy process. In practice this condition may never be reached
because of transient changes during operation as described in Section
8.2.2, although the "bedding-in" period is generally considered
complete when evidence of full contact can be observed on the lining
friction surface.
Under experimental conditions where flexure of annular disc brake
components is minimized, wear and thermal expansion of the friction
material are primarily responsible for interface pressure variations
during individual brake applications. The amount of in-stop interface
pressure variation depends upon the duty level of the brake applica
tion; at medium duty levels (0.6 MW/m' average power dissipation) a
reduction in annular contact area of approximately 20% over 3.5s can be
compared with 10% and 50% at 0.1 MW/m' and 2.5 MW/m' respectively.
Where the rubbing path is narrow, as was specifically designed for the
annular brake test rig, torque variations arising from changes in the
effective radius defined by the pressure distribution, are negligible.
During individual drum brake applications, thermal expansion of the
drum appears to be the principal cause of variation in pressure
distribution. No significant in-stop change in lining/drum contact
could be attributed to thermal expansion and wear of the friction
material which were small in comparison with the mechanical and thermal
deflections of the brake drum and shoe components. The form of the
interface pressure distribution is an important factor in the
calculation of drum brake performance and, commencing from perfect
ini tial contact condi tions, a cosinusoidal (U-shaped) pressure
distribution with a correspondingly high shoe factor will be produced
235.
on both leading and trailing shoes. Any consistent change from such
an initial pressure distribution will result from wear over successive
brake applications. (See Section 8.2.5).
8.2.8 The cyclic stress loading generated by the distorted stationary form
imposed upon the rotating brake drum can make a significant contribu
tion to drum loading under dynamic braking conditions.
8.2.9 The Gap Force method for friction interface simulation, where contact
conditions are determined for individual node pairs, provides better
convergence characteristics then alternative methods where interface
contact is related to complete interface elements. Relative displace
ment of the friction surfaces in directions other than that of dynamic
friction drag is an important aspect of brake friction interface
simulation and can be realistically modelled by static friction
considerations. The accuracy of calculated pressure distributions
could be improved, especially where edge effects are evident, by
refining the finite element mesh in these regions.
8.3 RECOMMENDATIONS FOR FUTURE WORK
The use of finite element techniques for the simulation of braking
friction has opened up new possibilities for the detailed analysis of
brakes and braking problems. The effects of wear and temperature on
interface contact and pressure distributions, and consequent brake
performance, under repeated brake application conditions covering both the
"bedding-in" period and the subsequent wear life period, is a particularly
important area for further research. Detailed study of the effects of
contact resistance on interfacial heat transfer and temperature distribu
tions is also required before interfacial temperatures can be accurately
predicted. The interdependence of interface pressure and friction
material surface temperature could provide a key to the _solution _ of the
problem of measuring pressure distributions under dynamic operating
conditions. Finally, although 2-D analysis has provided much insight into
frictional energy transformation and associated effects, circumferential
or axial variations can be significant and therefore extension of the
analysis to 3-D would be most worthwhile.
236.
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241.
\
APPENDICES
242.
APPENDIX 1.
INCORPORATION OF THE 5 PHASE FRICTION MATERIAL AND MATING BODY MODEL
A1.1 Material Phase Change
The 5 phase model for the friction material and mating body was discussed in Section 4.1.6. The friction material may change phase:
Phase 1 (virgin friction material) ~ Phase 2 (Reaction Zone) and Phase 2 ____ Phase 3 (Char),
and these phase changes are of interest in the simulation of braking friction firstly because of the change in thermophysical properties and secondly because of the energy interchange involved in the transition from one phase to the other.
Phase 4, wear debris, is a direct result of wear during sliding contact and Phase 5 represents the metal mating body.
A1.2 Variable Material Properties Program
Additional programming to the PAFEC program has been developed to deal specifically with phase changes in resin bonded composite friction material. The properties of each element are updated in the PAFEC Phase 6 element matrix generation stage of both the transient temperature calculation, and the stress calculation, according to the initial average temperature of that element. A flow chart describing the program is shown in figure A1.1.
A1.3 Effects of Variable Material Properties
The exact effect of the different thermophysical properties of each Phase of friction material is difficult to assess unless accurate material property data is available. Those shown in Tables 4.3 and 4.4 represent typical, approximate values, derived by measurement and from literature values. It was therefore considered that a parametric survey of the effects of thermophysical property variation would be necessary, representing a large volume of work using this finite element simulation technique together with the variable material properties addition for future investigation.
243.
Fig. ALl
VARIABLE MATERIAL PROPERTIES FLOW CHART
no
Variable properties
do not apply to
rotor or backing
plate materiaL
is
the current
element in the yes >---..:-----, friction
material
Retrieve element
material properties.
Continue
Determine average
initial nodal
temperature over
element.
Find property number
which corresponds to this
average temperature and
change property number
accordingly. ,
244.
APPENDIX 2.
INTERFACE PRESSURE, TEMPERATURE AND WEAR DISTRIBUTIONS
CALCULATED IN ANNULAR DISC BRAKE TRIAL SIMULATIONS
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r-~ : .!~:~ii-~· . : -COol: C ___ ., _______ -'- __ --.:---t--: __ __ .~+-.;:;:~-,-;-=--~.~!--- ...... __ .f-I ___ -.. ....,
o t:i· I· j.l~J~! J r--' 1S0-Smm : R8BE3n~i~ PATH WIDT1H-i ! INNER RADIUS . ·-···,-·-t-. -j----! ...... :. .
o 181mm
OUTER RADIUS
2
< : .
o
Z --i rn ::D :;; n fT1
U ::D rn 'J)
.... : •. -- ... --~- ... , .. _\... ... _._ .!. ____ ...• .l.... . .......... " ... _ .... _._ ... ~ ... __ ._. ___ ..
Interface Pressure, i T~rT)p'~ratute:& C~rh0Iati~e iWebr lCJrial ,Simulation) : : I: I : I': I "!' I . I . J I . I I :
2 -0 Axis mmethtH!HCbnfi"U( tiOth --i .!--:L6Wtitie'h---:--!--Brakih ... --- -- y -- - - - Qj QillQ!i ---+---__ .J _____ J _ ~gyJ---.. -g . __ . .: i H'·····'·.·: 1:1·:·: • : !.: .-. T I M E 2-5-:3-G--Sec---'--- ... -r----r-----:r---,-l--------L-------'----- --!·-··----:------r----L---- ____ _
.-:--l---r .I.J-+--i-~+ LT~ L!_ m •
--- -~--+---I----I--'--l----:---+--'-::I--I----- ;--!--+-:--- --. : !. I :' . -! . i r ! I , 1" . ~
--:----t----t------+----t--- -+------j--+--,--j----:----:-I I I I I: :,.._
- ! -- --\--j---- ---l-----i-- - -i---i.- : - t- - i - ~---- i----: . : . , I" ' I ' I . i : .
--- H __ : ___ h __ ;___ i :! i __ +h +--+-. ---)- --- -f-- +---1---+--------'---- -. i II,:!" i '1" I I . .----:----r-.. r----r--dL--:--!---:-i --;----- :------ ------ . -----:---+----LL . ---1----1-- _.1___, ___ ; ______ +____ -- ----r--=i
L • I··! :... !, t , I,: . I j i 1 .......... -- ······:----:··-·t-··---···~-·-:---·j·-· . ..... -_ .. _;.. . .... ""--"--r'---""'" ..... -. -- .. • 1 .. . .1. i .
100 500
--i rn :s:
1.00 u rn ::D » --i c
300 ~
~500 I : i ! ·------f-------t--+----I- "'--i"'---"':" .... -.. ; ...... L ___ . . .. r-
I ::D rn
TZ -3
o
--l . i I . , : ' : I
I .. -- i----f----t-----+---+--,--:---r ---i; ---,---I : i j i I : I
I . _ ......... _L ____ l-. __ .... _L_. __ .. _;_ ........... -..... _ . ____ ._... /' ..... :\-~ _._. ! I I, I ,_.
'--l~\ .:; ,i , - -I - - ,-----t-· .. ----'· '---------i-- -- ... ~-, --- ---- ,.. .-t--. ----- -;- - /
I ; " ..... - ._.' . . / ~r"'- J" I: . _ ......... ;-.-~-.-.-. -- _~-=-t=-=-~._. _____ 1 _____ )_· ___ ~_·"'_~-:;;-;-'::-;':':;-'~"·-IL.-...,
,. ,I ' r ;.--' I _ I L J
150-~ mm . RI!JB~INGJPATH Wlo-nH 1 INNERRADIUS:-----.+-. -t---'-t-"'--I- )-:--1··
~ .. : .
o 181 mm
OUT ER RADIUS
n'
200 . I
100
N
'" -I>-
. 1:5
2
o
.. . . '.. ---t--:--r--.-'----i.- ":'-'-j _, ... __ L._ .:.---1-.-..;-.:.. .
Interface Pressure, . Te.rt)p~rature:&l C0rn0loti~e iWebt I(Triol iSimu lotion) . I c ' . I . c ! ' i' I I ,. i : .
2. -.. 0.. Axis mmethtCbM"fi":UrGiti6m i i'" L6wBnek'iBrakin . -'-'--'-"----'-= ... -=-=y-. .. -- --. gj W·-··-r·--L.-l _~gY-l. __ 9 ....
100
z -;' fll ;;:]
;;: () rTl
j5 fll IJ) V1 cSOO ::0 fll
A Z -3
N
. -, I' 1 ., , 1 I i I,' , 1 i -- • ····c·· . i' il!, 1
TIME 3·0 -·3·5Sec-:i--·- . ...L..-!---: .... --'- .. -l...-.-.L_·-f··_··_I·_ -. .. . - - , I' I . 1 ' ! 1 . : I !! 1 ! I' , 1 1 1 • 1 • ·-i-··----·l-"-t.--r-· .. !- ~ "1 --.f-. '--1-- .,-. ...--~
.-~.- +-' l-··-·-l .. -J ..... ~-.--J.---.L--J----- -L- .. ~.- - ~.---. ~ ! i ' t I i 1 : : i
.·_j._e-._I_···_! . J. ... _'- __ :_.:._ .. _:._~- .. !.-.
. .1. 1 ,
"'~""4··~t-~--!·-····-· -1 -.. ~~ ... -l--..... -! ........ + ....... 1 .. ···_-t· .. __ .. -1-" . "T' .. --'T-" _ •. _-:-
..... _ .. L ...... L--L .. J __ .l .. ! i .... '. _ ... _L..._.._. : I ! !: I: t : .!. : ; ! !" 1 •••. ~_. __ ~ __ • ___ •• ; •• _____ ~. __ '. • ...... _. __ ,_, ..••••. _. _ ••.•••• L __ ...
i .j...:.; I ! ... -t-.----+.-.-~-~- .. --j.-, .. ";"---"'!" ..... : -"-'1"--- .. , ....
1 -1 1 1I . -, -- ·1·· -- r -- -1-' ·--i 'i ..... ,-.• -...-.
. . ... J_-t-·L.-.. i-.. l ... -1. .... ..1.._._'--_1.._ .. , .... --. . r ----1·· -;.-.--~-. i:--j.-----!---·~·- "'-':--j' .. -! .-- -; .. -~-..! ;
I ".]'_.' 1 __ l"-:_.-i,._ .. L_. __ L:._: __ ._ .. _: _ .. .i_.-.i ___ .J ___ :l ___ . ' .. f::_J ·1·· " ...... -------.j---.. ------t-. . I I· I I I :
L ' I I I I I .. / ...... -- ,"~ ., ...•..... i' .. - ...... +-1 i'" i . L '-'-'-. • -.' '. ". -' -:.:.:~--. '-I --r-j _F--,--f------- .~__:::.- :-.= ~I-~-" -1-+-·t--··~ --; "-"L---,
......... ' i - 6- -.-.-.- .-- :...... " • I
, I I .. .... .. . ... I. ... !. . .
500
-; fll :s:
400 Cl fll ::0 l> -; c
300 ~
()'
200
. I
100
o 1-'" . i~'--r---=~'j -,-c-. :---. i- ....... ;: ... -:-:. - ... --'1'- -- ~.. ~- ;::!- .--(~ - ~::.- j
L.;.....,! I. 'L i i I! 150:5 mm INNERPAD-IUS., .... -
. RYSBiN9PATH yvIDTiH. 1 • • 1I . I P--T , __ !--u_ .1. .. -+._, ... : ..... --... , ... -----:---.-,---.-.-_ ..
o 181mm
OUTER RADIUS
I\)
a--Vi
66 A2.22 2 .
2 D Axisymmetric Configuration
Constant Speed Drag Braking (Trial Simulation)
Axial Temperature Profiles (at 179mm rod.)
~ 600 .u
w er: :::> ~ er: w 0.. ~ 400 w f-
200
5
15--
10 THICKNESS (mm)
1L.5
2000
.u
W 0::: =:l f<t: 0::: W 0.. ::E w f-
1000
267. A2.23
2-D Axisymmetric Configuration
High Energ~ Braking (Trial Simulation)
Axial TemRerature Profiles (at 179mm rad.)
0·55 --
f.·Os -~
STATOR THICKNESS (mm) ROTOR
200
.u
w 150 0::: ~ I-<t: 0::: W CL L w I-
100
50
268. A2.24
2-D Axis)'mmetric Configuration
Low Energy Braking (Trial Simulation)
Axial TemQerature Profiles (at 179mm rod)
STATOR
J5s --
0·55 --+---r
<l! U o ~
'(J) ~
c
ROTOR
o ~~~--~~~--~~--~~~~~~----~ o 5 10 11.5 THICKNESS (mm)
APPENDIX 3.
THEORY OF S-CAH ACTUATION
A convenient measure of S-cam brake performance is Specific Torque (Ts) in which the camshaft actuation torque (Tc) is simply calculated from the product of actuation line pressure, actuator effective area, and efficiency, and lever arm length. The relationship between Tc and the shoe tip forces produced by the cam must be defined to allow the total braking torque to be calculated from the friction drag generated by each shoe.
As shown in figure 7.24, the centres of the cam roller and the cam ideally lie on one straight line, and each shoe tip force (Pl or P2) passes through the point of contact between cam and roller, normal to both surfaces. Each force therefore acts through the centre of the cam roller, and is tangential to the base circle of radius rb, so that,
cam lift = rb x camshaft rotation (~) (A3.1 )
This relationship is only approximate in practice because the shoe tips move in an arc about the shoe pivots, and not in a straight line, but is adequate for small displacements. It is also affected by' inaccuracies in the cam profile or roller location (Ref. 75), or by clearance in the camshaft bushes.
The direction of Pl and P2 is dependent upon the angular position of the cam, and is defined by fp, where;
where d
(A3.2 )
(A3.3)
In th; analysis a value of fp = 18°, corresponding to an initial cam rotation of 30 , was used.
Pl and P2 are only equal under ideal "floating cam" conditions, and when these do not apply, there is a reaction force (R) on the camshaft bearing and the effects of camshaft/bush friction must be included in the calculation of Pl and P2. Again referring to figure 7.24;
Pl - P2 R = (A3.4)
( 1 + ,",c·)i
R acts at an angle fR, given by;
tan fR ,",csin~p + cosrfp
= sin~ - ,",ccosfp
(A3.5)
The camshaft torque Tc is given by
(A3.6)
Hence = + (A3.7)
270.
% (1 + !lc')! ~ 0 (A3.8) where
Typical design values of ra and rb are 20 mm and 13.1 mm respectively, and comparison of measured and calculated results presented by Day and Harding (Ref. 71) indicated values of !lc in the region of 0.05 - 0.1
271.
APPENDIX 4.
LINING SURFACE PRESSURE, TEMPERATURE AND WEAR DISTRIBUTIONS
CALCULATED IN DRUM BRAKE TRIAL SIMULATIONS
272.
I I
100
I . I
o
Lining
Drum N
E5 --z Z
w u. <t LL 0:::' W fZ
I o
Surface Pressure, Temperature &
Brake Trial Simulation LEADING SHOE
•
/
55 Anchor
\ , ". '-.
~. -._,-.-.-.
o
-' _. /
/
LINING Af<C ( Deq)
•
/
Wear
55 Corn
A4.1
1000
o
u "
.0
I
I I
273· Lining Surface Pressure, Temperature & Wear A4.2
Drum . Brake Trial Simulation
100 . LEADING SHOE 1000
u .. -i w • . E; . .0::: '\ W .~ .~ . • §5
--I- -w~II-·:·I!::'·. ~- -:,:,' ~ -I,:,'. i ... : '. I,· : I • g I --I \\ .,' "'1-' --to ... ~ . '-r .' T--- T'" "'?-I 3: i'~ !, '\! i .• i ; LI I i. rrD
+-'--l--'--r-i'---I--'~ -' '-:- i--+ ·.i-:--+------i-~- ..1--- !---..,·i-----I~·: +-- -~QO·-!-I' i: " ... : .... ; : .. ! . I . i . i i· • i . ·1··· i·
, l' " • I ' , . ~ I . ;1 ;1 1-;- ---r~- -;----1--'\1--'--;------:-.+-- . ---t'-:-:-l-' 'r --I·----ii
I ! I" .~ .. ; '. I . ; . . I" ·1 ........ ," +--.. + ___ L.._ .-1-, ~ _ .J...- ~ . ___ .1,, __ .'___ " , __ ", ___ L~_ .. L--..i ___ J/ _ ._! ____ •. ___ ~~ : I.r! ::. i\·,i. " /" \::
"'1 .• -.• -t-----~ ;-- -.. ; .. -----j ··--····---1,·~··-~·· ..... : -- .. ->- .. --+./.--.-~.-- ..... - .. -._--.... ! I' ~ i ! ! .-!-.-~.- . ..;.+-~-+--~/ i .!
: -'··--r ---+-- ---!- --"--1-- -)-- ---T--'--- ' .. - -+~ .--.-~---... -.~.----.-: -~-----t-·--i-· .--~-... -:.- .. , I, .. ", -i :
,--j --!--, ;- -1 • ~ 1 ... I~ 7-:=1 . 0:- __ m~ m
j . i .! I.!· 55 ! ,I·· J .•. , • !O : . !. .'.... T . ~5. : , : l--;--j-.-.J--'-.L......J._'-AAGhOr..c.--f--· ._' -. -k.J.NlliJG:-ARCJ(.De-g)---., ... -.. -,: Cam-:,--;--.---~-
f-I~J--- i-~Je- ~.Ul'Olsd-+-' .. j ..• +!rf-ri ; ___ +_ .. -1_' -; -~ • i-fHi' .' H .. ,... , .• +-:--+-: -i----. j---!'-:"+---+---:-+-;--T
.. ! ·"'1····· Y'T ;! .. ·1 ..ITH.RH4ILiN& ··s-i!.iO"·E i .. : "1' t· ..... + ! .T·,r • ! -----'-18e- • IS' -l----.;-+----!.-.....i--..i..j. . m· fil . '--. :.......:,_.i......:...... ... '. ~88-i- ... , : ·r· · j N:",.'; I' ;. , : 1 • I'· :! • I. I :.. ..•• I' .... : • . ; •. I . . , ........... -,~J ....... 1 . , .............. / .. '. " I. . .•... ,....,.
---,---1-- ··4 _, ___ j ___ L. __ I_: +-:..,---J-. + __ L. ____ L_.· ... j--' .~-.• P--· ! 1 I:Zj : r 1 ! I ,t . I : I'" 1·..:......
-- . ..i.-E! .+- ·~.--j----.-j---.i.. : ' ' .. ---·i----+--- J ..... ~1:--~~ . ~. i -w i I !. ! .=>
~. .: .. :~. ',., '~,.'. ! .... ~:g W :·-i··ID-- Cl: 3:' 0: L
I .
I
o
Q W
t3 \ 500~ <{'
~ \ : • z \
I o r--,
55 Anchor
'. / '~ ,~
.. -.-._.-.-.-.-.- .....
o LINING Af(C (DeaJ
•
SS Com
o
....• -.1-,
274.
100
. 5 ~: -:\
····1-: . I
. 1 : --1-; --
0
Lining
Drum N
55 --z L
1 0
Surface Pressure. Temperature & Wear A4.3
Broke Trial Simulation
LEADING SHOE
"-" "- "_._-_.-.- _.
55 0 Anchor LINING ARC
/ -55
( Dea) Cam
1000
0
u ' .
.-I
I I
275.
100
er: . <1:1 W: 3:;
L .:._(.; __ _ I: 1 ; I:
Lining Surface Pressure. Temperature & Wear
Drum Brake Trial Simulation N
E5 -- LEADING SHOE z L
W
A4.4
1000
u .. er ill => 7 er ~ => .~ • .-' I ... ~ .~ er
OJ,: ~ I •. 1 ._,'," ···1- - t- .... . ... ~ ... ill i :, i I ! L
.,-~.- .... !.._.L ...... i.. i ·-.. 1· .. ! ..... j-_ •. -j- -§OG-~ .~ i i\ i;, "1:/ i ! i·
.. ·cw .. -.. .. f . ,: ........ , ... _._.:- - .. ·i" .. :"" ',:' ''';, . J,_ . -1!-. I' ":1-- -11!,' :8 ! !. , !.. /1 : ... _L .. 2l ... .L ~ 1 : 1 ; . i ... ' :"_ ... .1._ J/-. ! __ ', J.--.l!-; I' I - f\:-"i'-'-!""--" : ./" I,;!
: .. . .
i" c- ! .. "i-- ~ .. ~ .. , i.~~::.-;=~·~~~~-L '~j~ ·;;(··j··_·t- --(-(
···.~··.····~-~~r:':- :-~~ .:-, TTt.LI , :. I . 55., : ,.;..;.0 i . : .. I . I , ... 55:· :
....... -...... -, .. -.... : .. _._L.:..-~chbr .. --i-.-.L._. LINING-ARC.J(De.g)--.j ... _ .. ..Lcarh-L-:_ ... -L-: : i ! I • • ].:' ';! .' . : . i' , ",'1 '
..... -.. - ........... +'-'-j-Ti -';'-'1 ;S'''':k-'-O-,'S''-:---: ...c.-i ... ,-: ...... , ._+ .. "',"" -.+ ... --~-t-... ;··Ime·i-z,.· .... ea·:· : : i.'...! I:'·,
'-. ..;_.-+._, .. : .r-: ;.: ! • j' •. , .• i .+-.-~-.. i-~'r' .--~-: I . : .. -j-
-,-!de · •.. i---.!5'LL_'--jfltINilJ! .. S~bE .. i • 1 __ : ' .... J .··/4hee..!. ... . ! ·1 ··i N } :·1 . .li :! : .: "',' .! :1 : ! • I . :FP, :.':.~.:
... _.J ___ .,_ .. _.1.. .. ~. '-t-_+ ... L: .. _L .. '-_t-'--i- .. ..L-'.+ .. ~-+-+.~ '''r-~''''':..c_+-:-.p.
~j . .=.i.. ....: .... !.: '_;....J .. +....c __ ~. '\ .. ~. .L.. . .... ~
er « W 3:
o
~ er ~ w: ~.
ill . ..~
er ~ Q ill
500· f-ill U .« LL er ill fZ
f o
\ . \
55 Anchor
\ "
...... / •
----·-~_6_._._._.-·~
o LINING AfW (r)pn I
•
55 rnrn
o
, , ,
276.
100
E_
~
.. '.': I 1 '
-1-:--
o
Lining
Drum N
E5 ~ z Z
w U <f LL 0::: W fZ
1 o
Surface Pressure, Temperature & _.Weor
Brake Trial Simulation
LEADING SHOE
•
\ • \.. , ./
., .' 1- • _ .. _ .. _ ,,_ .. _ • _ .. _ .. _
.< r----..------.---~-=*=t=""=>t=O='1-=I=:~-_r_-~-_F:.=_=;
ne J_' Ar)Cilor-
o LINING Af·:C ( Ol'Cj )
55 Corn
1000
o
M.5
u .
--I
I I
277.
100
..... : , I'
. I , .
iO
o
Lining
Drum N
E5 --z L
W 0::: => If) If)
W 0::: CL:
w .0::, . => If) If)
W 0:::: (L-
w u ~ 0:lLJ f-Z
I o
Surface Pressure, Temperature & Wear ~~~~~--~~~
A4.6
Brake Trial Simulation
LEADING SHOE
, .. - .... -'"
•
-1- 1
•
• \
• \,
j-
; :. I -1-1;' ---1'--. .
j /, •
..... ---=-... . - .
I I ....... -1'--
j" i I I -- --:-:-l-i--
1000
.u
W 0::: ::> f-<:t 0::: W H_
I L I ru
~GO--f--
I :---[i i. • •
- .! ~-
... - -i -0. • i';
I 55 . i
-,- Cam------.-,. -- ..... ! 'f' :
.. _ ... __ .L. !
i i , , _ •. _._ ••• ~ _.,. __ ... '·0-"""'---·---"'-
i . i i I ! .
,-.---- --i---+---i-· -1800·: : I ! ! ' • I I . -: i; ! U .. : ..... ~., ...... _;-- '.- _! __ .v .. :. - "'0; ••
~! -, ___ ... w
0:: ::> f-<:t 0:: lLJ CL L w
500 f--
=~~~="=' / - --~. ---r------,- ~~-r' -~' ... --_;,c...:....:::..c..:,' o '-I:' 0 <:;5 :.U ~
AI1Chor Uf\JING Af\C (U,_'q) Cum
278.
100
,-, 5; ~
Lining
Drum N'
55 -z L
w . 0:::
~ (J)
'ill :0::; Q..! -I' :w ,0.
--IT~<O-
Surface
. Broke
Pressurg Temperature & Wear A4.7
Trial Simulation
LEADING SHOE 1000
u .
,j
i
.: i ! .~. i • 'j -I) .:~- -t- ... ' . ':/ -T' --'. r,-:I
I i' Z; : • d , ,_ + ' +' .~L._ .. _ ...• 6 •. -···-r---;-- .. - --- --,-- .. ." .... ~
.. .. i... .1.'.. i . .....,/ __ .... ! ___ ~ ....... -.-.-- _..:. __ ~ •. J..
i ..... __ i' • _. i
! .-.-.- ._.- .---
. ----;---------)" ,
..... -.... ;--~ -,---' 10 .. ' :-----.;g r-, -C-;==-=;--;.---:---i--'-ir-r-, -;---;--i--'--i"i-~-;-~'
••.
:
:,' .. _. "'i,' ...•• · .•• ! •. ,_ .. _._J,'.'._ .. - t! 5. ;", •. 1-. .0:' r __ .':... .... ..... liNIN' GO A'RC :( D' j) : : C' ~5 . . _ I -""·'61·' ,. .--G- . ,. .. . :. e·g· ---.. : .. , ... L.am· i , '
1----···--i--·:---·:------: -.-, -+---7---:-'--'!'--"-'-i---'~'+ -'·'-1 • : •• :Tinne~·O-~·SiSeC1. :
••• + •• ----:---·---:-·-------~-.-~----·-:_--·----t--~f__-~-· \ . : --. ~ . - .;. . . . -j. . . . 1· ;. \ .. , ..... ] . . .. ':
.. ,...j --'-1 do- --1-----~5 _.L~_+ -. __ i; I!36j!~LN-r , J.! .0Jl: .. 1 .. 1 :,: I : . : i, C::;. I ' '
I !. Cl , _.1 .-.. --~-- ---T-'--~- -T---_I '~
E ""'-'\ -:
0::: « w 3:
W o:::! =>' (J) Lf) ill 0:::: CL
o
.. --. _ ....
I· ,
, ' 1 ' " . .. -- --r---- -- --j------ -1--- -- ---+-~-: 1 ' I : , I i
/ /'
. --1-- .. ____ L_ ,
• /
•
Se .)
900-j -
--
500
()
279.
APPENDIX 5.
TEST PROCEDURE - ANNULAR BRAKE RIG
1. Calibration
Before commencing the test programme, all transducers and instrumentation were adjusted and calibrated according to this detailed procedure. Instrumentation checks were carried out at intervals during the test programme, but no adjustments were made without repeating the relevant part of the calibration procedure.
For those measurements which were recorded on the Chessell 320 chart recorder (torque, line pressure and rotor temperature) the zero was set 25 mm (1 inch) from the base line of the chart to allow for any zero drift in the negative direction.
The temperature channels in the stator plates could not be calibrated initially because thermocouples were fitted after the plates were bedded. It was therefore necessary to calibrate these at a later stage in the test programme.
The calibration procedure was commenced only when the instrumentation had been switched on and allowed to stabilise for a period of not less than 1 hour.
TORQUE MEASUREMENT:
Brake torque was measured by torque arm utilizing a Sangamo type D95 force transducer recording on a Chessell 320 chart recorder.
Procedure:
Attach balanced lever arm and apply dead weight loading at 1.219 m (4 ft.) centre.
a) With zero loading, adjust the zero on recorder to 25 mm (1 inch) above the chart base line.
b) Apply dead weight load of 83.62 kg (184.35 lb) and adjust span until recorder indicates 1000 Nm torque.
Note:
If the weight of 83.62 kg exactly is not available, the nearest to this value should be used, and the recorder reading should be set to the corresponding torque value, calculated from:
Torque reading = 1.219 x 9.81 x Wkg.
c) Check zero and repeat (a) and (b) if necessary until zero and span are set correctly.
d) Record torque readings at 5 intervals between 0 and 1000 Nm in both increasing load and decreasing load directions.
e) Plot calibration curve (recorded torque : actual torque), date and sign. (Figure A5.1).
280.
ACTUATION LINE PRESSURE
Actuation line pressure was measured with an Intersonde type XP17 0-3000 psi pressure transducer, recording on the Chessell 320 chart recorder. A Helicoid 0-160 bar pressure gauge was also fitted.
Procedure:
The pressure transducer, serial number 23639, is calibrated using a Smiths Industries Dead-weight Tester, type 5340/6.
a) Remove the Intersonde pressure transducer from the actuation line and fit to the Smiths Deadweight Tester.
b) With zero pressure on the transducer adjust zero on the recorder to 25 mm (1 inch) above the basic line of the chart.
c) Apply 100 bar pressure to the transducer and adjust span until the recorder indicates 100 bar pressure.
d) Check zero and repeat (b) and (c) if necessary until both zero and span are set correctly.
e) Record pressure readings at 10 bar intervals from 0 to 100 to 0 bar.
f) Plot the calibration curve (recorded pressure : actual pressure) date and sign. (Figure A5. 2) •
g) The Helicoid pressure gauge should also be calibrated using the deadweight tester, recording pressure readings from 0 to 160 to 0 bar in 10 bar increments. Plot the calibration curve (indicated pressure: actual pressure), date and sign (Figure A5.3).
TEMPERATURE
All temperatures were measured by thermocouples with a Chromel/Alumel junction, each reading through a cold junction compensated thermocouple amplifier.
Procedure
The thermocouple instrumentation is to be calibrated to BS 1927 using a thermocouple potentiometer, Croydon Precision Instrument Co., type P4, serial number 12478. The calibration characteristic for each temperature channel must be plotted, dated and signed. (Figures A5.4 and A5.5).
ROTATIONAL SPEED
Rotational speed was measured in rev/min using an Orbit Controls TIC meter, number 75C50 113, serial number 271. The transducer resolution allowed the speed to be measured to within ±0.25 rev/min.
2. Bedding-in Schedule
MEASUREMENTS TO BE RECORDED
Torque Line Pressure Rotor Temperature.
281.
INERTIA
123 kgm2 (90.6 Ibfts2)
PREPARATION
1) Ensure that splines are clean and free from dust, oil, grease, etc. Clean all dust out of casing.
2) Fit new stator and rotor plates, ensuring that the outer periphery of rotor is prepared, smooth and clean with fine grit paper for the rubbing thermocouple track. Check that rotor slides freely on splines.
3) Re-assemble rig.
4) Check rotation by hand, check static actuation and adjust clearance shims if necessary.
5) Ensure dust extraction pipe is fitted.
PROCEDURE
1) Run dynamometer at 310 rev/min, disconnect motor and drive and allow to free-wheel. Check frictional drag and temperature. If excessive frictional drag is present, indicated by the rig coming to rest in less than 60 seconds, with an associated temperature rise indicated, the clearance in the actuation mechanism should be checked. If this is satisfactory, the rig must be dismantled and checked for internal problems, e.g. sticking on the splines.
2) Run dynamometer at 310 rev/min for 5 minutes. Monitor temperature and check for correct functioning of rubbing thermocouple. Adjust thermocouple tip rubbing pressure if necessary.
3) Apply one 5 bar check, 200 rev/min to 50 rev/min, monitoring temperature, torque and line pressure.
4) If the actuation and performance are satisfactory, apply bedding checks on the following schedule:
Initial speed 200 rev/min. Final speed 50 rev/min
Pressure Number of Recording (bar) Applications
-------- ------------ ---------5 1 1st n 10 1st and 10th
10 50 Every 10, starting at 1st n 10 1st and 10th
10 50 Every 10, starting at 1st
Maximum start temperature 100°C, minimum cycle time 1 minute.
5) Stop dynamometer and open rig for inspection.
6) If plates show no problem of scoring, warping or blue-spotting, clear. dust from inside of rig and re-assemble.
282.
7) Repeat item (4) twice.
8) Stop dynamometer and open rig for inspection.
9) If plates are bedded satisfactorily, remove rotor and stator plates and repeat items (1) to (8) with the next set of plates. If not satisfactorily bedded, re-assemble and repeat items (4) (5) and (6) until satisfactory bedding is achieved.
3. Test Schedule
MEASUREMENTS TO BE RECORDED.
Torque Line pre ss ure Rotor temperature Rotational speed Casing surface temperature Friction material and stator temperatures.
INERTIA
12.3 kgm 2 (90.6 lbfts')
PREPARATION
1) Clean rotor surface with a dry cloth to remove surface dust.
2) Measure rotor thickness at 3 different radii in 4 circumferential positions. These positions are to be ·noted for subsequent measurement.
3) Measure stator thickness at 3 different radii in 4 circumferential positions. These positions can be marked by drill "spots" on the back face of the stator plate.
4) Fit rotor and thermocouples stator plates and check functioning of all thermocouples before assembling rig.
PROCEDURE
1) Check running of rig as in the bedding schedule and check functioning of all thermocouples.
2) Warm up rig with 50 x 10 bar checks, 200 to 50 rev/min, at 60s intervals.
3) Apply 1 x 30 bar applica tion, 370 to 50 rev /min start telQpera ture 100·C.
4) Stop dynamometer and open rig for inspection, removing dust with air suction equipment.
5) Measure rotor and stator thicknesses.
6) Re-assemble rig, repeat items (1) and (2)
7l Apply 5 x 30 bar applications, 370 to 50 rev/min, start temperature 100·C.
283·
8) Stop dynamometer, and open rig for inspection as in (4).
9) Measure rotor and stator as in (5)
10) Re-assemble rig, repeat items (1) and (2).
11) Apply 20 x 7! bar checks, 200 to 50 rev/min, at 60s intervals.
12) Apply 20 x 30 bar applications, 370 to 50 rev/min start temperature 100°C.
13) Stop dynamometer and open rig for inspection as in (4).
14) Measure rotor and stator as in (5).
15) Repeat (10) - (14) four times.
16) Remove this set of rotor and stator plates. set and repeat bedding and test schedules. with a 3rd set of plates.
CALIBRATION CHECK
1) Check all instrumentation.
POST TEST INSPECTION
Replace with a second If necessary, repeat
1) Remove rig from dynamometer, clean and inspect for wear, damage and bearing adjustment.
2) Measure rotor surface finish and profile using Talysurf 10 profilometer.
A-Oo
o
284.
ANNULAR BRAKE TEST RIG
TORQUE CALIBRATION - SANGAMO D95 TRANSDUCER
~-+, INCREASING 7b/{Ci'UE
- - - DEeR-CAS INe, TOR.<;>UE
J/ /
./
/ /'
.;
/ /
// /
./
200 400
/
/ /
/
1000
FIG. A5.1
285· FIG.A5.2
ANNULAR BRAKE TEST RIG
PRESSURE CALIBRATION - INTERSONDE XP17 TRANSDUCER
~f40 " <;,(
/
't ~fJo
UJ 120 ,. ~ fto tI) tI) ~ too ~
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Cfo
286. FIG. A5.3
ANNULAR BRAKE TEST RIG
HELICOID PRESSURE GAUGE CALIBRATION
+----+1 INCREASING PRessuRe.
.--0 DE.C.~ II\IG PRE.SSf.JR.e
/50
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~ !o '( (j 10 Q '< 6e/ -...
50
40
30
10
{a
o L-__________________________________________ _
o fO 20 .10 4D So (Po ~ &0 '10 100 If 0 120 /J:) Irm
7'fcnlA-L P~ESSL/RE (.8.4-'<)
"" J Q
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r ,uJ
J j 300
b "':t::
200
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o o
287.
ANNULAR BRAKE TEST RIG
TEMPERATURE CALIBRATION (CHART RECORDER)
(all channel 5)
FIG. A5.4
loo '200 .3cx:> L{.q) 5CO
\1J.b\CA-TED -, EH':> eC)
500
200
fCO
288.
ANNULAR BRAKE TEST RIG
TEMPERATURE CALIBRATION (TAPE RECORDER)
+ CH"tJ'-I&L t CHAN r-lE.L 2.
( C4tAN NEL. 2-A CtfAN N"'- 4 o CHANNE.L. 5
Q CHANN&L. cO
FIG. AS.S
O~~----~-------.------~-------.------~ o 100 200 300 400
