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EB2013-MS-007
THERMOMECHANICAL SIMULATION OF WEAR AND HOT BANDSIN A DISC BRAKE
BY ADOPTING AN EULERIAN APPROACHRashid, Asim*, Strömberg,
NiclasDepartment of Mechanical Engineering, Jönköping University,
Sweden.
Keywords: Eulerian framework, frictional heat, hot band, wear
history, pad wear, repeated braking
Abstract: In this paper frictional heating of a disc brake is
simulated while taking wear into account. By
performingthermomechanical finite element analysis, it is studied
how the wear history will influence the development of hotbands.
The frictional heat analysis is based on an Eulerian formulation of
the disc, which requires significantlylower computational time as
compared to a standard Lagrangian approach. A real disc-pad system
to a heavytruck is considered, where complete three-dimensional
geometries of the ventilated disc and pad are used in
thesimulations. A sequential approach is adopted, where the contact
forces are computed at each time step taking thewear and thermal
deformations of the mating parts into account. After each brake
cycle, the wear profile of the padis updated and used in subsequent
analysis. The results show that when wear is considered, different
distributionsof the temperature on disc are obtained for each new
brake cycle. After a few braking cycles two hot bands appearon the
disc surface instead of only one. These results are in agreement
with experimental observations.
1. INTRODUCTION
Disc brakes are used to adjust the speed of a vehicle by
pressing a set of pads against a rotating disc. It converts
thekinetic energy of the moving vehicle mainly into heat. This heat
causes the disc and the pad surface temperatureto rise in a short
period of time. Due to relative sliding, both the pad and disc
wear, which affects the behavior ofdisc-pad system over time. Since
the pad material is softer as compared to the brake disc, the wear
of the pad isdominant [1]. Higher temperature of the pad surface
during braking also affects life of the pad negatively due
toincreased wear rate.
Tribological contact in disc brakes has been studied both by
physical experiments and numerical simulations. Bothtechniques have
their own roles and importance to understand the disc-pad system
fully. Lee and Barber [2] per-formed an experimental investigation
of thermoelastic instability in disc brakes. They observed that
temperatureinitially rises faster at the inner and outer radii of
the pad after many repeated test runs. They attributed this
behaviorto the concentrated wear at the center of the pad during
previous runs. Eriksson et al. [3] provided a comprehensiveoverview
of different processes, both at micro and macro scale, causing the
contact surface variations. Panier etal. [4] performed an
experimental investigation of railway disc brakes and proposed a
classification of hot spotsobserved on a brake disc surface based
on thermographs. They also studied the influence of pad stiffness
and padcontact length on hot spots development. Österle et al. [5]
performed a pin-on-disc test and showed that a thirdbody with a
different structure and composition from the first bodies was
trapped in a gap between the pin and thedisc. The pin was cut from
a commercial brake pad and the disc material was cast iron. Hong et
al. [6] comparedthe friction and wear characteristics of three
friction materials with different binder resins. In their study,
the wearrate below a critical temperature showed a slow increase,
but above it the wear rate increased rapidly. Furthermorebelow the
critical temperature binder played a minor role in the wear
resistance of the friction material, but above itthe wear rate was
strongly influenced by the thermal decomposition of the resin.
Contact pressure distribution is an important parameter for
disc-pad systems. For the experimental study of the dis-tribution
of contact pressure, pressure sensitive films [1] have been used.
These methods can only be used for staticanalysis. Due to wear and
other thermomechanical changes, contact pressure distribution does
not stay constant dur-ing braking operation so numerical
simulations become an obvious choice to determine the evolution of
the contactpressure. Many researchers have used numerical
simulations to enhance the understanding of the disc-pad
system.Dufrénoy and Weichert [7] implemented a two-dimensional (2D)
fully coupled thermomechanical algorithm takingwear into account.
Kao et al. [8] developed a three-dimensional (3D) FE model capable
of performing fully coupledthermomechanical analysis. They took the
effect of wear on contact pressure distribution into consideration.
Theyused this model to study hot judder in a disc brake. Koetniyom
et al. [9] performed sequentially coupled thermo-mechanical finite
element analysis of disc brakes under repeated braking conditions.
They considered only a smallsegment of the disc taking the cyclic
symmetry into account and assumed a uniform heat flux. In [10],
Dufrénoyand Weichert developed an uncoupled 3D FE model. They
simulated only one-twelfth of the disc by considering theaxial and
rotational symmetries of the disc and used temperature dependent
material data. Gao et al. [11] developeda fully coupled 3D
thermomechanical FE model to investigate the fatigue fracture in
disc brakes. They assumedthat thermal properties of the materials
for disc and pad are invariant with temperature. Abubakar and
Ouyang [1]performed wear simulation of a brake pad by using a
commercial FEA software and compared their results with
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physical tests. They considered the real surface topography of
the pad while building the finite element model bymeasuring height
distributions with a gauge. Söderberg and Andersson [12] performed
a simulation of wear andcontact pressure distributions of the brake
pad using a general purpose finite element analysis software.
Vernerssonand Lundén [13] studied the behavior of brakes
numerically for repeated brake cycles. They used a 2D fully
coupledFE model while considering the coefficient of friction as
being constant and a temperature dependency of the wearrate. They
found out that wear of the pad strongly depends on the stiffness of
the friction material and its mounting.
Today, the prevalent way to simulate frictional heating of disc
brakes in commercial softwares is to use the La-grangian approach
in which the finite element mesh of a disc rotates relative to a
brake pad. Although this approachworks well, it is not feasible due
to extremely long computational times. Particularly, for simulating
repeated brak-ing this approach is of little importance for
practical use. Sometimes two-dimensional FE models are used to
reducethe computational time but this approach is not sufficient to
model complex behavior. The rotational symmetryof the disc makes it
possible to model it using an Eulerian approach, in which the
finite element mesh of the discdoes not rotate relative to the
brake pad but the material flows through the mesh. This requires
significantly lowercomputational time as compared to the Lagrangian
approach. Nguyen et al. [14] developed an Eulerian algorithmfor
sequentially coupled thermal mechanical analysis of a solid disc
brake. First they performed a 3D contact cal-culation to determine
the distribution of the pressure. Then a sequentially coupled
analysis is implemented by firstperforming a transient heat
transfer Eulerian analysis followed by a steady-state mechanical
analysis. Recently,Strömberg [15] developed a finite element
approach using an Eulerian framework for simulation of frictional
heat-ing in sliding contacts. In his approach, the fully coupled
problem is decoupled in one mechanical contact problemand a
frictional heat problem. For each time step the thermoelastic
contact problem is first solved for the temperaturefield from the
previous time step. Then, the heat transfer problem is solved for
the corresponding frictional power.In another paper [16] this
approach was implemented for simulating frictional heating in
disc-pad systems.
In this work, frictional heating of a disc brake, while taking
the wear into account, is simulated by implementing anEulerian
approach. A toolbox developed by Strömberg, which is based and
described in his earlier work [16] butnow extended to include wear
of the pad, is used to perform the frictional heat analysis. In
this Eulerian approachthe contact pressure is not constant, but
varies at each time step taking into account the wear and
thermomechanicaldeformations of the disc and the pad. This updated
contact pressure information is used to compute wear, and
heatgeneration and its flow to the contacting bodies at each time
step. In such manner, the wear and nodal temperaturesare updated
accurately and their history is recorded at each time step. Then a
Python script is used to write the wearand temperature history to
an output file for subsequent use. The disc-pad system is simulated
for several brakecycles. After each brake cycle pad geometry
reflects the material removed by accumulated wear and this
updatedgeometry of the pad is used in subsequent brake cycles.
Because the finite element mesh of the disc does not rotaterelative
to the pad, the contact region is always well defined and a
node-to-node based approach can be adopted.This allows the mesh to
be refined only in the region where the brake pad is in contact
with the disc, which results inlower computational time. The output
file with temperature history can be used e.g. in a sequentially
coupled stressanalysis.
The results show the appearance of two hot bands on the disc
surface after several brake cycles which cannot bepredicted when
wear is ignored. The Eulerian approach has proved tremendously
cheap in terms of computationaltime when compared to a fully
coupled Lagrangian approach. This is demonstrated by presenting
numerical results.
2. FRICTIONAL HEAT ANALYSIS
The workflow of the approach used for frictional heat analysis
is shown in Fig. 1. An input file, which contains themeshed
geometry with appropriate boundary conditions and loads is required
for the frictional heat analysis. Duringthis analysis linear
thermo-elasticity is adopted and the problem is decoupled in two
parts. In the first part, for a
Input file
In-house software
ODB file
Figure 1: Workflow of sequential approach.
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Specify initial temperatures of
disc and pad.
Thermoelastic contact problem
is solved while taking the wear
into account and contact pressure
distribution is determined.
Wear gaps are updated.
Heat transfer problem is solved
and new nodal temperatures are
determined.
Figure 2: Sequential approach used during frictional heat
analysis to determine temperature history.
Table 1: Material properties for frictional heat analysis.
Disc Pad PlateThermal conductivity [W/mK] 47 0.5 46Young’s
modulus [GPa] 92.9 2.2 210Poisson’s ratio [-] 0.26 0.25 0.3Thermal
expansion coefficient [10−5/K] 1.55 1 1.15Density [kg/m3] 7200 1550
7800Heat capacity [J/kgK] 507 1200 460
given temperature distribution the contact problem is solved
while taking the wear of the pad into account to obtainthe nodal
displacements and contact pressure distribution. The new contact
pressure distribution is used to updatethe wear gaps. In the second
part, for the obtained contact pressure distribution the energy
balance is solved and newnodal temperatures are determined. These
equation systems are then solved sequentially and, wear and
temperaturehistories are developed. The nodal temperatures
determined at a time step are taken into account in the next
timestep to update the deformed geometry of the disc and pad. This
is shown schematically in Fig. 2. The wear andnodal temperature
history is then written in an output file (called ODB file) by
using a Python script. Details aboutthe governing equations can be
found in [16].
Three parts are considered for the frictional heat analysis.
Materials assumed for the disc and the back plate are castiron and
steel, respectively. Friction material used as brake pad is a
composite. Temperature independent materialproperties used for
these parts are listed in Table 1.
3. NUMERICAL RESULTS
The assembly of the disc-pad system considered in this paper is
shown in Fig. 3. This is an assembly of a disc-pad system of a
heavy Volvo truck. The outer diameter and thickness of the disc are
434 [mm] and 45 [mm],respectively. The ventilated disc is
geometrically symmetric about a plane normal to the z-axis. It is
assumedthat thermomechanical loads applied to the system are
symmetric so only half of this assembly is considered forthe
simulation and symmetry constraints are applied on the nodes lying
on the symmetry plane. Some detailedgeometry at the inner radius
has been removed to simplify the model as that is not important for
this analysis. Thedisplacements along x and y directions of the
nodes located at the inner radius of the disc are set to zero. All
thesurfaces of the disc, except the one lying on the the symmetry
plane are considered to lose heat by convection.
The brake pad is supported by a steel plate at the back side as
shown in Fig. 4. Some detailed geometry of the backplate which is
not necessary for the simulation has been removed. Two cylindrical
pins apply a normal force on theback surface of the back plate
which transmits it to the pad. Displacements at the back surface of
the back plate,other than along the force direction, are fixed.
Furthermore temperature is set to zero on the back surface.
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The disc is meshed such that it has smaller elements where it
contacts the pad as shown in Fig. 5 (only a smallportion of the
disc is shown). This is an advantage of the Eulerian approach
because the finite element mesh of thedisc does not rotate relative
to the brake pad but the material flows through the mesh. The heat
flux generated at theinterface of the stationary pad and the disc
is considered with convective heat transfer in the disc. In a
Lagrangianapproach a fine mesh should be applied on the complete
surface of the disc because the finite element mesh of thedisc
rotates relative to the brake pad or some adaptive strategy should
have to be applied. All the parts consideredfor the simulation are
meshed with 4-node linear tetrahedron elements in HyperMesh
(HyperWorks 10.0). Thesemeshed parts are then used to prepare input
file with boundary conditions and loads in Abaqus/CAE. The
discassembly is meshed with 269438 elements that has 64957 nodes
and 185697 degrees of freedom.
Now the results of frictional heat simulations will be described
for two different cases. In the first case, a brakeapplication is
simulated for one cycle and wear is not considered. Figure 6 shows
the surface temperature as afunction of time and disc radius for
this case. The nodes of the disc chosen for this plot are located
at 180◦ awayfrom the middle of the pad. A brake force of 24.5 [kN]
is applied for 45 [s] on the back surface of back plate. Theangular
velocity of the disc is 45 [rad/s] and held constant throughout the
simulation. This loadcase corresponds to atruck moving downhill
with a constant speed. The force is ramped up by using a
log-sigmoid function during 20 timeincrements and then held
constant for next 70 increments with time step = 0.5 [s]. The
friction coefficient is µ = 0.3,contact conductance coefficient is
ϕ = 0.1 [W/NK] and convection coefficient is set to 50 [W/m2K]. The
brakeforce generates an average brake moment of 1240 [Nm] after the
ramping up. The total CPU time is 4272 [s] on aworkstation with
Intel Xeon X5672 3.20 GHz processor. In the graph it can be seen
that temperature is not uniformlydistributed over the disc instead
a narrow band with relatively higher temperature appears in
approximately middleof the disc surface.
In the second case, brake application is simulated for several
cycles and material removed due to wear in each cycleis considered
in subsequent braking operations. During each brake cycle, the wear
coefficient is set to 10−10 [m2/N]and rest of the parameters are
same as for the first case. The total CPU time for a single cycle
is 4289 [s] on aworkstation with Intel Xeon X5672 3.20 GHz
processor. Each brake cycle requires almost the same CPU time
foreach simulation. In Fig. 7, temperature of the disc surface is
shown at the end of brake operation for first cycle.A ring of high
temperatures, called a hot band, is evident in the middle of the
disc. Figure 8a shows the surfacetemperature as a function of time
and disc radius for the first cycle of brake application. The nodes
of the discchosen for this plot are located at 180◦ away from the
middle of the pad. In the graph it can be seen that during thecycle
there is only one hot band on the disc surface.
By intuition it can be thought that the high temperature ring
should form near the outer radius of the disc. Butthe ring appeared
approximately in the middle of the disc surface. It might be
understood by studying the contactpressure plots at different time
steps as shown in Fig. 10. In Fig. 10a the contact pressure plot
for the first timeincrement or at the moment when the pad comes
into contact with the disc is shown. It can be seen that the
contactpressure is not the highest at the outer radius of the pad.
The region where contact pressure is higher generates moreheat and
causes further expansion of the disc and the pad material near this
area which in turn causes higher contactpressure. In the meantime
convex bending caused by thermal deformation of the pad and the
back plate, as shownin Fig. 9, also plays a major role in
concentration of contact pressure towards the middle of the pad
surface. This
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Figure 3: An assembly of the disc-pad system, also showing the
cylindrical pins used to push the back plate.
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Back Plate Brake Pad
Figure 4: Brake pad with back plate.
convex bending can be explained by the expansion of the pad
surface material due to the increase in temperatures.The frictional
heat causes the pad surface temperature to rise in a short period
of time as compared to the innerregion of the pad and the back
plate as shown in Fig. 9. Consequently, the surface expands more
than the innerregion of the pad and the back plate which results in
the convex bending. These phenomena combined with theramping up of
brake force in later increments, causes the higher contact pressure
in an area which is away from theouter radius of disc as shown in
Fig. 10d.
In Fig. 11 contact pressure plots are shown for further time
steps when the brake force is held constant for the firstcycle and
Fig. 12 shows the wear on the pad for corresponding time steps. It
can be seen that the contact pressurekeeps on concentrating towards
the middle of the pad with increasing time increments. It can also
be observed thatwear is higher in the areas where contact pressure
is higher.
Figure 8b shows the surface temperature as a function of time
and disc radius for the 41st cycle of brake application.It can be
seen that in the beginning there are two hot bands which converge
to one as the temperature increases withtime. In Figure 13 which
shows temperature of the disc surface at 13th time increment for
the 41st cycle of brakeapplication, two hot bands can be seen. In
Fig. 14, temperature of the disc surface is shown at the end of
brakeoperation for the 41st cycle of brake application. By
comparing with Fig. 7, it can be concluded that after 41
brakecycles the maximum temperature has decreased and the hot band
becomes wider at the end of brake operation. Theappearance of two
bands can be explained by the shifting of high contact pressure
areas. Due to the concentratedwear in the middle of the pad during
repeated brakings, a depression appears when the pad cools down and
returnsto its undeformed state at the end of a brake operation. So
during next brake cycle, the high contact pressure firstbuilds on
the outer regions of the pad surface. In Fig. 15 accumulated wear
of the pad is shown at the end of the40th brake cycle. Fig. 16
shows the distribution of contact pressure during the 41st cycle.
It can be seen that contactpressure first builds on the outer
regions which are less worn out and then due to thermomechanical
deformations ofthe pad, as discussed before, moves to the middle of
the pad surface with increasing time increments. By comparingthe
results of the first case with those obtained for the first brake
cycle of the second case, it can be concluded thatfor a pad without
wear history there is no noticeable influence during braking due to
wear. But accumulated weardoes have a significant influence on the
distribution of temperature after some brake cycles.
4. DISCUSSION
The temperatures predicted by the in-house software have been
compared with the temperatures recorded by athermal imaging camera
during a physical test and found to be relatively higher. Moreover,
two hot bands predictedafter repeated brake cycles are not as
distinct as observed in the thermographs. These differences could
be dueto temperature independent material data, friction
coefficient, and wear coefficient used during the frictional
heatanalysis. For more realistic results, temperature dependent
material data should be used. Furthermore, the friction
Step: Step−1Increment 44: Step Time = 22.00
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Figure 5: Mesh of the disc.
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100120140160
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Time [s]Radius [mm]
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Figure 6: Temperature as a function of time and disc radius
obtained by frictional heat simulation.
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440 496 553 610 667 723 780 837 894 950100710641121
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Figure 7: After the brake application at the first cycle, a ring
of high temperature develops on the disc surface.
coefficient of a brake pad is generally dependent on
temperature, velocity and contact pressure [17] but in this workit
is assumed to be constant at µ = 0.3 to represent an average
behavior. Similarly, the wear coefficient is generallydependent on
temperature and velocity [6, 18] but in this work it is assumed to
be constant at 10−10 [m2/N]. Ina very near future, we will extend
this work such that a temperature dependent behavior of the
friction and wearcoefficients is included in the proposed method.
At present the in-house software assumes constant angular
velocityof the disc that corresponds to a vehicle moving downhill
with a constant speed but in the future it could also beextended to
non-constant angular velocities.
5. CONCLUDING REMARKS
In this work frictional heat analysis of a disc brake has been
performed taking into account wear of a pad. Thisanalysis is
performed in an in-house software based on the Eulerian approach.
It has been shown that brakinghistory affects the evolution of
temperature distribution during a brake cycle. The analysis
predicts concentratedwear in the middle of the pad which results in
the appearance of two hot bands after repeated brake cycles.
It has been shown that other than the local factors e.g. thermal
expansion, convex bending of the pad and the backplate also plays a
major role in the contact surface evolution. Phenomenon of convex
bending has been describedin other works [2, 3], to the best of our
knowledge, but no experimental observation or numerical simulation
resultshave been presented to support it. In this paper it has been
shown with numerical simulations that convex bendingplays a major
role in the concentration of contact pressure to the middle of
pad.
This method has proved tremendously cheap in terms of
computational time when compared to the Lagrangianapproach. In the
future this approach can be used to study the influence of
different geometries of the pad and thedisc on the maximum
temperature with a reasonable simulation time. It can be very
useful when studying newdesigns for real disc brake systems.
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(b) Cycle =41
Figure 8: Temperature as a function of time and disc radius with
the consideration of wear.
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0 56112167223279335390446502558614669
Figure 9: Thermally induced deformations of the pad and back
plate during brake operation shown in differentprojections. The
deformation is exaggerated for visual clarity.
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0.0000.0050.0100.0140.0190.0240.0290.0330.0380.0430.0480.0520.057
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Figure 10: Nodal contact forces represented as pressure plots on
the pad surface shown at different time steps forthe first cycle
during ramping up of the brake force. The legend is given in
[N].
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Figure 11: Nodal contact forces represented as pressure plots on
the pad surface shown at different time steps forthe first cycle
while the force is held constant. The legend is given in [N].
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YZ
(b) t = 25 sNT11
+0.0e+00+5.8e−07+1.2e−06+1.8e−06+2.3e−06+2.9e−06+3.5e−06+4.1e−06+4.7e−06+5.3e−06+5.8e−06+6.4e−06+7.0e−06
Step: heat, Step with own NT11 dataIncrement 70: Step Time =
0.777777777778Primary Var: NT11Deformed Var: not set Deformation
Scale Factor: not set
ODB: Brake3P_WEAR.odb Abaqus/Standard 6.9−EF1 Mon Jan 30
15:12:00 W. Europe Standard Time 2012
X
YZ
(c) t = 35 s
NT11
+0.0e+00+8.3e−07+1.7e−06+2.5e−06+3.3e−06+4.2e−06+5.0e−06+5.8e−06+6.7e−06+7.5e−06+8.3e−06+9.2e−06+1.0e−05
Step: heat, Step with own NT11 dataIncrement 90: Step Time =
1.0Primary Var: NT11Deformed Var: not set Deformation Scale Factor:
not set
ODB: Brake3P_WEAR.odb Abaqus/Standard 6.9−EF1 Mon Jan 30
15:12:00 W. Europe Standard Time 2012
X
YZ
(d) t = 45 s
Figure 12: Wear on the pad surface, shown in [m], at different
time steps for the first cycle.
Viewport: 1 ODB:
E:/DiscBrakes/Results/No_..._Simulation_1/Brake3P.odb
NT11
439 497 554 612 669 726 784 841 899 956101410711129
Step: heat, Step with own NT11 dataIncrement 90: Step Time =
0.989010989011Primary Var: NT11Deformed Var: not set Deformation
Scale Factor: not set
ODB: Brake3P.odb Abaqus/Standard 6.9−EF1 Thu Jan 26 08:56:30 W.
Europe Standard Time 2012
X
Y
Z
NT11
0 18 35 53 71 88106124142159177195212
Step: heat, Step with own NT11 dataIncrement 13: Step Time =
0.142857142857Primary Var: NT11Deformed Var: not set Deformation
Scale Factor: not set
ODB: Brake3P.odb Abaqus/Standard 6.9−EF1 Wed Feb 01 14:29:11 W.
Europe Standard Time 2012
X
Y
Z
Figure 13: Two bands of high temperatures on the disc surface at
t = 6.5 [s] during the 41st cycle of brake application.
8
-
Viewport: 1 ODB:
E:/DiscBrakes/Results/No_..._Simulation_1/Brake3P.odb
NT11
439 497 554 612 669 726 784 841 899 956101410711129
Step: heat, Step with own NT11 dataIncrement 90: Step Time =
0.989010989011Primary Var: NT11Deformed Var: not set Deformation
Scale Factor: not set
ODB: Brake3P.odb Abaqus/Standard 6.9−EF1 Thu Jan 26 08:56:30 W.
Europe Standard Time 2012
X
Y
Z
NT11
432 480 528 577 625 673 721 770 818 866 914 9631011
Step: heat, Step with own NT11 dataIncrement 90: Step Time =
0.989010989011Primary Var: NT11Deformed Var: not set Deformation
Scale Factor: not set
ODB: Brake3P.odb Abaqus/Standard 6.9−EF1 Wed Feb 01 14:29:11 W.
Europe Standard Time 2012
X
Y
Z
Figure 14: After the brake application at the 41st cycle, a ring
of high temperatures develops on the disc surface.
NT11
0E+00 14E−06 28E−06 42E−06 56E−06 70E−06 85E−06
99E−06113E−06127E−06141E−06155E−06169E−06
Step: heat, Step with own NT11 dataIncrement 1: Step Time =
0.0111111111111Primary Var: NT11Deformed Var: not set Deformation
Scale Factor: not set
ODB: Brake3P_WEAR.odb Abaqus/Standard 6.9−EF1 Wed Feb 01
14:19:08 W. Europe Standard Time 2012
X
YZ
Figure 15: Accumulated wear on the pad surface, shown in [m], at
the end of the 40th cycle.
NT11
0.000 1.813 3.627 5.440 7.253
9.06610.88012.69314.50616.32018.13319.94621.759
Step: heat, Step with own NT11 dataIncrement 10: Step Time =
0.111111111111Primary Var: NT11Deformed Var: not set Deformation
Scale Factor: not set
ODB: Brake3P_PN.odb Abaqus/Standard 6.9−EF1 Wed Feb 01 14:15:36
W. Europe Standard Time 2012
X
YZ
(a) t = 5 s
NT11
0.000
5.10610.21115.31720.42325.52930.63435.74040.84645.95251.05756.16361.269
Step: heat, Step with own NT11 dataIncrement 30: Step Time =
0.333333333333Primary Var: NT11Deformed Var: not set Deformation
Scale Factor: not set
ODB: Brake3P_PN.odb Abaqus/Standard 6.9−EF1 Wed Feb 01 14:15:36
W. Europe Standard Time 2012
X
YZ
(b) t = 15 s
NT11
0.000
6.43112.86119.29225.72232.15338.58345.01451.44457.87564.30570.73677.166
Step: heat, Step with own NT11 dataIncrement 60: Step Time =
0.666666666667Primary Var: NT11Deformed Var: not set Deformation
Scale Factor: not set
ODB: Brake3P_PN.odb Abaqus/Standard 6.9−EF1 Wed Feb 01 14:15:36
W. Europe Standard Time 2012
X
YZ
(c) t = 30 s
NT11
0.000 12.129 24.258 36.386 48.515 60.644 72.773 84.902
97.030109.159121.288133.417145.546
Step: heat, Step with own NT11 dataIncrement 90: Step Time =
1.0Primary Var: NT11Deformed Var: not set Deformation Scale Factor:
not set
ODB: Brake3P_PN.odb Abaqus/Standard 6.9−EF1 Wed Feb 01 14:15:36
W. Europe Standard Time 2012
X
YZ
(d) t = 45 s
Figure 16: Nodal contact forces represented as pressure plots on
the pad surface shown at different time steps forthe 41st cycle.
The legend is given in [N].
9
-
6. ACKNOWLEDGEMENT
This project was financed by Vinnova (FFI-Strategic Vehicle
Research and Innovation) and Volvo 3P.
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