XVII Encontro de Modelagem Computacional
V Encontro de Ciência e Engenharia de Materiais
Universidade Católica de Petrópolis (UCP), Petrópolis/RJ, Brasil. 15-17 out. 2014
METHODOLOGY TO ESTABLISH TEMPERATURE DISTRIBUTION IN DRUM
BRAKE'S FRICTION MATERIAL
Carlos Abílio Passos Travaglia – [email protected]
Master Student
Luiz Carlos Rolim Lopes, M.Sc., D.Sc. – [email protected]
Associate Professor
Programa de Pós-graduação em Engenharia Metalúrgica - PPGEM, Universidade Federal
Fluminense – Volta Redonda, RJ – Brazil
Abstract. Once a numerical model for brake assembly is available, it is possible to
understand the effects of successive brake applications on the temperature distribution in
drum brake’s friction materials. This is a fundamental aspect to determine, for instance, the
thermal stress distribution which is related to the warming and cooling of the brakes. In this
work, an analytically obtained stabilization temperature was used to establish a heat flux
through the friction material in a numerical model applying finite element analysis. The
numerical solution for temperature distribution was compared with experimental data for
validation of the methodology.
Key words: Brake Drum, Friction material, Temperature, Stabilization, Finite Element Model
1.
INTRODUCTION
Numerical models are been used more frequently during development of new
components specially, on the automotive industry. On the other hand, sometimes simulation
of real events can be very complex and take a long time of computation.
In this work, a simple methodology to determine the temperature distribution in friction
material of S cam type drum brake is proposed. Successive brake events, that induce
accumulation of energy in brake linings are replaced, in the model, by just one step that
causes the material to reach the thermal equilibrium.
This methodology is extremely useful because during real vehicle's application, the brake
components are approximately in steady state. In other words, almost the totality of the
energy generated during the brakes is dissipated to the environment due to convection on the
drum brake's external surface.
2.
THEORY AND ANALYTICAL CALCULATION
2.1 Prediction of the stabilization temperature in repeated braking
According to Limpert (1999), the stabilization temperature can be predicted by the
average temperature variation, external surface area, At, thermal proprieties of the brake drum
and its density, ρR. In addition, the convective coefficient, h, cooling time between brake
events, tr and temperature of the air around the brake assembly, T∞, must be available,
according to eq. (01).
TS = {ΔTR} / {1 – exp[([(– h At tr) / (ρR cR vR)]} + T∞
(01)
XVII Encontro de Modelagem Computacional
V Encontro de Ciência e Engenharia de Materiais
Universidade Católica de Petrópolis (UCP), Petrópolis/RJ, Brasil. 15-17 out. 2014
The average temperature variation of the drum, ΔTR, can be determined, since thermal
proprieties of the drum, the average brake torque, ΔT, angular velocity of the vehicle’s wheels
during the braking cycles, Δω, braking time, t and the quantity of energy absorbed by the
drum, PR are known.
In order to estimate the quantity of energy absorbed by the drum, the conservation of the
mechanical energy principle and the relationship between friction material and brake drum
thermal resistances must be applied.
The temperature variation of the drum during one braking cycle can be calculated by
equation described below:
ΔTR = (PR ΔT Δω t) / (ρR cR vR)
(02)
Where the average of brake torque in S cam brakes, ΔT is function of the average
pneumatic pressure inside the brake actuator, Δpa and design geometrical characteristics of the
brake, like actuator sectional area, Aa, lever length, L, S cam effective radius, rS, brake radius,
rf, mechanical efficiency, η and the empirical coefficients KA and KT, function respectively of
brake lever movement and temperature. The relationship between these parameters is
expressed according to:
ΔT = (Δpa – p0) Aa L [1 / (2 rS)] BF rf η KA KT
(03)
Where p0 is the pressure necessary to put brake lining and drum in contact (threshold
pressure) and BF is the brake factor (relationship between friction force between lining and
drum and the force that pulls brake shoes against the drum).
2.2 Calculation of stabilization temperature based on real brake cycles
For accomplishing this work, a commercial vehicle has traveled on road and some
experimental data have been measured at some specific locations of one of the S cam front
brakes, until stabilization of the temperature, after several brake applications. Figure 1 shows
a schematic and a picture of the brake. The load on the vehicle was 17,000.00 Kg.
Fig. 1 – Tested Front Brakes and Vehicle Instrumentation – Man Latin America
Figure 2 shows evolution of the temperature in the friction material, during the test, in
three different locations. Also, in this figure it is plotted the pneumatic pressure inside brake
actuator.
XVII Encontro de Modelagem Computacional
V Encontro de Ciência e Engenharia de Materiais
Universidade Católica de Petrópolis (UCP), Petrópolis/RJ, Brasil. 15-17 out. 2014
Fig. 2 – Temperature Evolution during Stabilization Temperature Test in Friction Material
and Actuator Pressure during Brake Events – Man Latin America
The data acquired during the road test are presented in table 01.
Table 1 – Measurement Data – Man Latin America
Data
Average pressure inside brake actuator – Δpa
Cooling average time – tr
Braking average time – t
Average vehicle’s velocity at route – Δv
Average wheel's angular velocity – Δω
Temperature of air around the brake at beginning of the cycles – T∞
Environment temperature – T∞’
Unit
Value
[Pa] 324358.42
[s]
56.63
[s]
5.26
[m/s]
11.11
[s-1]
22.68
[K]
336.00
[K]
295.00
The front brake design data are described in table 2.
Table 2 – Brake’s Characteristics – Man Latin America
Characteristics
Unit
Threshold pressure – p0
[Pa]
Mechanical actuator inside area – Aa
[m2]
Brake lever lenght – L
[m]
S cam effective radius – rS
[m]
Brake factor – BF
–
Brake radius – rf
[m]
Brake's mechanical efficiency – η
–
KA coefficient
–
KT coefficient
–
Drum’s density – ρR
[Kg/m3]
Drum’s volume – vR
[m3]
External surface area – At
[m2]
Specific heat – cR
[J/KgK]
Value
0.32 x 105
0.0155
0.1524
0.0127
1.21
0.205
0.80
0.98
1.00
7150.00
0.80 x 10-2
3.83 x 10-1
535.00
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Universidade Católica de Petrópolis (UCP), Petrópolis/RJ, Brasil. 15-17 out. 2014
After applying equations (01), (02) and (03), the analytical stabilization temperature of
the front brake could be determined.
The table 03 below shows calculated data.
Table 3 – Calculation of Brake Thermal Energy
Data
Unit
Quantity of energy absorbed by the drum – PR
–
Average brake torque – ΔT
[Nm]
[W]
Average heat flux through brake drum – Δ R
Temperature variation of brake drum – ΔTR
[K]
Coefficient of empirical convective coefficient equation – β* [Nms/hKm3]
Convective coefficient – h*
[Nms/hKm]
[K]
Stabilization temperature – TS
[ºC]
Value
0.91
5287.54
109108.01
18.75
0.70
488943.25
540.29
267.30
*According to Limpert, et al. (1999), convective coefficient can be obtained once known
the vehicle's velocity and coefficient β. β is equivalent to 0.7 Nms/hKm3 (1.94 x 10-4 J/Km3)
when referring to front brakes and 0.3 Nms/hKm3 (0.83 x 10-4 J/Km3), when referred to rear
brakes.
A comparison between experimental and analytically predicted stabilization temperature
shows that they are in good agreement. The stabilization temperatures were respectively
280ºC (553 K) and 267.30ºC (540.30 K), representing an error of 4.54%. Both curves are
represented on figure 3.
Fig. 3 – Comparison between Experimental and Analytical Stabilization Curves
XVII Encontro de Modelagem Computacional
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Universidade Católica de Petrópolis (UCP), Petrópolis/RJ, Brasil. 15-17 out. 2014
3. NUMERICAL SIMULATION
3.1 Methodology for determination of temperature distribution in friction materials
Considering that the contact between friction material and brake drum is perfect during
brake applications and the heat change by radiation can be neglected, it’s possible to
substitute all the brake cycles by one thermal load in order to predict the temperature
distribution on friction material.
Once the stabilization temperature is analytically determined by equation (01), it is
possible to obtain the temperature distribution in the friction material by creating a hypothetic
heat flux on the surface in contact with the brake drum.
Assuming the hypothesis that temperature of brake drum does not vary along its thickness
direction (between internal and external surface), it is possible to create this flux, by setting
friction film temperature as stabilization temperature and setting all the other model’s
elements temperature as environment. This heat flux must persist until the transient state is
overtaken and steady state of the model is attained.
3.2 The model and boundary conditions
In order to simulate the warming of the friction material, the applicative Abaqus vs. 6.12
was used.
Before performing simulation, it was necessary to define material proprieties of the
assembly (rivet, isotropic: SAE 1020, brake shoe, isotropic: EN-GJS-500-7 and friction
material, orthotropic). Besides of that, material orientation, reference coordinate system,
convection surfaces and interface areas were also input.
The convective coefficient between air and friction material, hi, corresponds to the natural
convection. The anchor points of the model were compatible with the motion of the assembly,
allowing increase of its volume due to thermal expansion, according shown on figure 4.
Fig. 4 – Mechanical and Thermal Model for Numerical Analysis
XVII Encontro de Modelagem Computacional
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Universidade Católica de Petrópolis (UCP), Petrópolis/RJ, Brasil. 15-17 out. 2014
The riveting pressure load, pp, was determined in conformity with the real process, in
partnership with the friction material and brake manufacturer.
It was assumed for this simulation that the friction material was orthotropic with isotropy
on the plans orthogonal to the manufacturing process compression axle, in accordance to
Casaril, Gomes, Soares, Fredel, Al-Qureshi (2007). This particularity allows relating the
directional proprieties of the composite.
Table 4 presents some proprieties of the friction material. Some of them were obtained by
friction material manufacturer and other calculated considering the above mentioned
hypothesis, in accordance to Gay, Hoa and Tsai (2003) and Daniel and Ishai (1994).
Table 4 – Proprieties of Friction Material – Manufacturer of Friction Material
Characteristics
Unit
Value
Fibers relative volume – Glass E-type
[%]
40%
Matrix relative volume – Phenolic Resin + other compounds
[%]
60%
Poisson coefficient between fibers and compression directions – νLt
–
0.28
Poisson coefficient between compression and fibers directions – νtL
–
0.12
Poisson coefficient on the isotropic plan – νz
–
0.20
Young modulus at fibers direction – EL
[GPa]
4.08
Young modulus at compression direction – Et
[GPa]
1.82
Shear modulus between fibers and compression directions – GLt
[GPa]
2.31
-1
Thermal expansion coefficient at fibers direction – αL
[K ] 5.90 x 10-6
Thermal expansion coefficient at compression direction – αt
[K-1] 1.20 x 10-5
The total time of simulation was 3000s.
4.
RESULTS
After simulation, temperature distribution in the friction material was obtained. Figure 5
shows numerical temperature distribution after 3000s of thermal equilibrium. The lowest
temperatures were found in the region near to the S cam, as can be observed in the figure.
Fig. 5 – Temperature Distribution on Friction Material after Thermal Equilibrium
XVII Encontro de Modelagem Computacional
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Universidade Católica de Petrópolis (UCP), Petrópolis/RJ, Brasil. 15-17 out. 2014
In addition, it was also evaluated de displacement of the assembly due to thermal
expansion. In figure 6, is possible to verify that the area with higher displacement is also near
to the S cam. The maximum displacement was 1.10 mm.
Fig. 6 – Resultant Displacement due to Thermal Expansion of the Model
5.
VALIDATION
5.1 Comparison between numerical and experimental thermal equilibrium
In order to validate the methodology proposed in this work, the temperature distribution
obtained after numerical analysis was compared to the experimental temperatures measured
during data acquisition described in section 2 (see figure 2). For this measurement, three
thermo-couples, T1, T2 and T3, positioned in different places inside friction material, were
used, as shown in figure 7. The position of each thermo-couple is described in table 5.
XVII Encontro de Modelagem Computacional
V Encontro de Ciência e Engenharia de Materiais
Universidade Católica de Petrópolis (UCP), Petrópolis/RJ, Brasil. 15-17 out. 2014
Fig. 7 – Instrumentation Points on Brake Assembly – Man Latin America
Table 5 – Position of Thermo-couples – Man Latin America
Thermo-couples
Radial Position [r]
Angular Position [Ω]
T1
T2
T3
195 mm
205 mm
200 mm
70º
90º
98º
Figure 8 shows a comparison between the numerical and experimental temperatures
obtained after thermal equilibrium. In both cases the positions of the compared temperatures
are according to the table 5. The higher error observed was 4.23%, related to thermo-couple
T1.
Fig. 8 – Temperature Distribution on Friction Material: Experimental x Numerical
XVII Encontro de Modelagem Computacional
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Universidade Católica de Petrópolis (UCP), Petrópolis/RJ, Brasil. 15-17 out. 2014
6.
CONCLUSIONS
a. The stabilization temperature can be obtained once the brake design data is available.
On the other hand, vehicular speed, average pneumatic pressure in brake actuator, braking and
cooling time can estimated by brake engineer based on his product development experience.
b. Analytical stabilization temperature of friction film has shown very good agreement
with experimental (4.54%). It seems that this analytical solution can be used by engineers
during new projects development steps, without necessity of directly instrument the brakes
and acquire data from field.
c. Maximum error of 4.23% between experimental and numerical model stabilization
temperatures ensures that methodology of substituting successive brake applications for one
thermal load can be applied successfully in order to predict the temperature distribution on
friction material, helping engineers to understand the effects of the temperature on it.
d. Determination of the friction material temperature distribution during steady state is
the first step for predicting the thermal stress distribution on it. Adding to the model, for
instance, the braking mechanical loads, the thermal stresses can be associated to the
mechanical resulting on a more accurate finite element analysis.
Acknowledgments
The authors are grateful to the following institutions:
MAN LATIN AMERICA for the availability of prototype vehicle and time for project
development.
SMART-TECH for its cooperation during development of the numerical model in the Abaqus
application.
CAPES for the financial support to the PPGEM/UFF.
REFERENCES
Casaril, Alexandre; Gomes, Eduardo R., Soares, Marcos R., Fredel, Márcio C., Al-Qureshi, Hazin Ali; Análise
Micro-mecânica dos Compósitos com Fibras Curtas e Partículas; Revista Matéria; v.12, n.2, pp 408- 419;
2007
Daniel, Isaac M., Ishai, Ori; Engineering Mechanics of Composite Materials; Oxford, New York; Oxford
University Press, 1994
Gay, D., Hoa, Suong G., Tsai, Stephen W.; Composite Materials: Design and Applications; CRC Press LLC;
2003
Limpert, Rudolf; Brake Design and Safety; 2nd Edition; SAE International; 1999