Ae0301 095 102
Ae0301 095 102
Ae0301 095 102
Keywords: railway transport, brake disc, finite element method (FEM), thermal and
stress analysis
1 INTRODUCTION
The main problem of braking and stopping a heavy train system is the great input of
heat flux into the disc in a very short time. Because of high temperature difference the
material is exposed to high stress. The result is a heat shock. The problem can be
solved only by applying a non stationary and numerical calculation. The analysis is
carried out for two models of the disc (Fig. 1) (the disc is supposed to be symmetrical)
and for two modes of load. The material of the brake disc is rounded graphite defined
under the standard SIST EN 1563:1998(en) [2] with a characteristic EN-GJS-500-7
(EN-JS 1050). The disc is screwed on the hub, which is upset upon the axle of the train
wagon. During the analysis only one part of the working cycle is considered, and that
is warming up and cooling down.
The paper work Stress analysis of a brake disc considering centrifugal and thermal load
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2 NUMERICAL MODEL
2.1 Modeling and preparing the 3D model
In this analysis two models of the disc are considered:
brake disc without wear (Fig. 2);
worn out brake disc with a 7 mm wear on each side.
tb
Fig. 3. Stop braking load
t [s]
P=const.
Qpr [J]
t [s]
The goal is to find out how the temperature is distributed on the whole construction
of the disc by braking on a flat track to a standstill (Fig. 3). The deceleration factor is
1.4 m/s2. The part of the braking energy that transfers on the surrounding air is not
considered. The reason for that is the high braking power which causes the dominant
effect of the heat flux. An assumption is made that the heat flux uses the convection
with a heat transfer coefficient of 10 W/m2K.
Because of a constant heat flux into the disc, braking on a hill (Fig. 4) is a bigger
disadvantage, than braking on a flat track. An assumption is made that the heat transfer
coefficient of the forced convection is 100 W/m2K. The goal is to determine how the
temperatures and stress rise if the disc reaches the maximum working temperature of
350C.
In both cases the effect of the humidity in the air and the heat transfer with
radiation is not considered.
2.3 Determination of the physical model
Braking on the flat track derives from the physical model for determination of the heat
transfer in dependency from the braking time. Beside that the weight distribution of the
vehicle is considered. The weight arrangement is 60/40 [3] in the favor of the front part
of the carriage. This means that the front part of the carriage takes 60% of the whole
load. In our case only 10 % of the whole brake force is applied to one disc from the
forward part of the carriage.
Because of the mentioned weight distribution, only the front part of the carriage is
analyzed. Every carriage is consistent of for axles with three brake discs attached to
each axle. The kinetic energy [3] for one wheel considering constant deceleration is:
t
z
z
1
0,1 M v02 = P(t )dt =2 Fdisc vdisc (t )dt ,
2
0
0
(1)
The change of energy is equal to the heat flux on the surface of the disc. This ratio
is used to calculate the thermal load on the brake disc. Other data used for the analysis
are listed in table 1.
Mass of the vehicle M [kg]
Start velocity v0 [m/s]
Deceleration a [m/s2]
Braking time tb [s]
Effective radius of the braking disc rd [m]
Radius of the wheel rw [m]
Incline of the track []
Friction coefficient disc/pad [/]
Surface of the braking pad Ac [mm2]
70 000
70
1,4
50
0,247
0,460
11
0,4
20000
1
M v02
2
=
= 9125 ,5 [ N ]
r
1
2 d v0 t z a t z2
rw
2
0 ,1
Fdisc
(2)
Instant heats flux entering one side of the braking disc [3]:
r
Q (t ) = Fdisc vdisc (t ) = Fdisc d (v0 a t ) = 343000 6860 t [ W ] .
rw
(3)
In the case of braking on a flat track 26 time steps, each step 2 seconds long, are
considered.
In the case of braking on a hill, a physical model is used to determine the heat flux
in dependency of the potential energy. The vehicle is maintaining a constant speed of
250 km/h. Consequently the heat flux is constant. The energy is considered to be
equally divided between the 12 discs of the vehicle. The energy balance is:
M g h = 12 Q tb ,
(4)
With the consideration of trigonometry and constant speed, the brake power for
one disc is:
M g v0 sin
= 43711 [ W ] ,
Q =
12
In this case 52 time steps with a constant heat flux are used.
(5)
p=
Fdisc
= 1,14 [MPa ] .
Ac
(6)
Q rw
= 233 [ N ] .
2 v0 rd
(7)
p=
233
= 0,03 [MPa ] .
20000 0,4
(8)
Q
fixing spot
Fig. 5. The meshed disc section with the load and fixing spot
To perform the analysis the material properties from the table 2 are used.
Heat conductivity [W/mK]
Density [kg/m3]
Specific heat cp [J/kgK]
Module of elasticity E [MPa]
Poisson number [/]
35,2
7100
515
169000
0,275
[C]
a)
[C]
b)
Fig. 6. Temperature fields for the new disc a) and the worn out disc b) braking on a flat track
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For the worn out disc with the same load, the maximum temperatures of 211C are
achieved after 38 s. They appear on areas where the wreath of the disk and the cooling
ribs are not connected. In this case the ribs are heavier exposed to the heat flux because
the disc wreaths are thinner. The temperatures are from 30 40 C higher. After a time
period of 52 s the temperature of the disc reaches 195C (Fig. 6, b).
For the worn out disc on an inclined track the temperature after 104 s reach 240C.
The highest values are on the contact surface between the brake disc and brake pad.
Because of the high traveling speed, the temperature of the cooling ribs first fall from
150C to 125C. After a while the temperature rise back to 140C (Fig 7, a).
[C]
a)
[C]
b)
Fig. 7. Temperature fields for the new disc a) and the worn out disc
b) braking on an inclined track
The temperature for a worn out disc after 104 s are 258C. The hottest areas appear
on the same spots as they do in the first test flat track. Beside that, at first the
temperature of the cooling ribs fall from 150C to 130C. After a while they rise back
to 147C (Fig. 7, b).
The area directly beneath the braking pad carries the main burden. This is also the
place where the highest temperatures are achieved. The figures show how the
temperatures toward the hub fall. This information is needed to determine the influence
of the heat flux on the disc.
3.2 Analysis of the stress
Thermal stresses in the disc appear because the temperatures rise. Beside the thermal
stress, the centrifugal load and the holding force of the brake caliper is also considered.
The goal of this analysis is to determine the influence of the centrifugal load in
comparison with the thermal load. The comparison stress is given on von Mises.
In the case of a flat track and considering the centrifugal load, the stresses are
185 MPa. On spots where the thermal stresses are the highest, the value is 110 MPa
(Fig. 8, a).
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[MPa]
[MPa]
a)
b)
Fig. 8. Stress field for the new disc a) and the worn out disc b) braking on a flat track
In case of the worn out disc with the same load, the maximum value is 174 MPa.
The maximum values appear on the passage of the holding teeth (Fig. 8, b).
In the case of braking on an inclined track the stress for the new disc reach up to
162 MPa (Fig.9, a).
[MPa]
[MPa]
a)
b)
Fig. 9. Stress field for the new disc a) and the worn out disc b) braking on an inclined track
In the last case of the analyzed worn out disc the stress are 148 MPa (Fig. 9, b).
The maximum values appear on the passage of the holding teeth.
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We achieved the highest difference in values by braking on a flat track. The reason
why - there is a greater temperature difference in the first case as it was in the second.
5 CONCLUSIONS
Temperatures and stress in discs under different loads are very high. Although they are
fulfilling the buyers requirements for safety, we did not considered shearing forces,
residual stress and the cyclic loads during brake discs lifespan. The results need to be
compared with experimental results, which is also our suggestion for future work.
References:
[1]
[2]
[3]
[4]
[5]
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