Thermal Analysis of a Brake Rotor with Various Brake Pad
Materials
MANE-6960: Friction and Wear of Materials
Prof. Ernesto Guitierrez-Miravete
12/17/12
By: Hrant Khatchadourian
Introduction:
An interesting topic everyone can relate to that involves friction and wear of materials is
the operation of a braking system on a modern day automobile. A typical disc brake system on
a car uses a brake rotor (or disc) fixed to the axles of the car so that it rotates respectively with
the cars wheels. Also part of the braking system is a stationary brake caliper fixed to the
steering knuckle which floats around the rotor. Each brake caliper has a brake pad on each side
that applies a clamping pressure (force) on the contacting surfaces of the rotor in motion to
gradually slow the car down. This type of interaction uses friction (force) between the brake
pads and brake rotor to slow down the rotation of the wheels. Wear is also generated on the
brake pad every time the brake pedal is applied. This research project will consist of analyzing
the friction force and heat generation due to the friction of the brake pads onto the rotor using
an ideal braking condition. Some other things that will be analyzed are different types of brake
pad materials and how they affect the friction and surface temperatures of the brakes.
In this paper a hard braking scenario will be used to formulate results. During hard
braking, extreme temperatures can be generated onto the brake rotors causing material
degradation and performance due to thermoelastic deformation. If the sliding speed of the
rotor is high, then the thermoelastic deformation of the material can cause non-uniform
contact pressures which in turn cause localized hot spots on the brake rotor/pad contact
surfaces. These localized hot spots are accompanied with high localized stresses that can lead
to material degradation of the brake rotor. One can relate to this scenario by experiencing
brake vibrations in the steering wheel caused by the localized stresses thermomechanically
deforming the brake rotor (brake warping). This paper will show the temperature profile of the
brake rotor during the braking period and also show results of temperature distribution along
the radial length of the brake pad.
Some assumptions that were implemented to simplify the analysis were that only half
the brake rotor and subsequently 1 pad was modeled. This may not accurately replicate total
heat distributions throughout the rotor, but the bulk of heat distribution is primarily on the
contact surface. The interior core of the brake rotor was also not modeled, which normally has
slotted vents (not visible on the outer faces of the rotor) that help with cooling and heat
distribution during excessive use. Wear resulting from the friction between the brake pad and
rotor is assumed to be small and has been neglected. The wear rate would be useful in further
analysis of the brake pad during extended life testing. It is also assumed that the vehicle is
traveling on a flat surface with no drag forces or no external losses imposed on the vehicle
besides actual braking from the brake pads. Finally, only the convective heat dissipated from
the rotor to ambient air has been modeled, no heat dissipation due to radiation was
considered.
Theory:
In this analysis the vehicle is defined by having characteristics based on a 2006 Subaru
WRX STI, which has a vehicle mass of around 3,300 lbs. (m ≈ 1500 kg), a wheel radius of 12
inches (rwheel ≈ 0.3048 m) and has a brake pad surface area of around 7 in2 (Apad ≈ 0.0045161
m2). The hard braking scenario that was used in this analysis is defined by an initial vehicle
speed of 80 mph (V0 ≈ 35.763 m/s) while braking with a vehicle deceleration of -25 mph/s (α ≈ 11.176 m/s2) for a duration of 2 seconds. A 1 second cool down period has also been
implemented into the model to analyze the cooling effects with the different brake pad
materials. The brake rotor that is used in this analysis is a typical Grey Cast Iron BS grade 180
brake rotor. Four different brake pads were analyzed which are the typical Semi-Metallic
Aluminum alloy pad, an Organic White Asbestos pad, Organic non-asbestos Kevlar 29 Aramid
Fiber pad and a Ceramic Fiber Al2O3 pad. Material properties for the brake rotor and brake
pads are given in Table (1).
Brake Rotor
Gray Cast Iron BS grade 180
Brake Pads
Aluminum alloy
White Asbestos
Kevlar 29 Aramid Fiber
Ceramic Al2O3
Thermal
Modulus of Coeff. of Thermal
Conductivity
Density
Heat Capacity Poissons ratio Elasticity
Expansion
k [W/m*K] ρ [kg/m^3] Cp [J/kg*K]
ν
E [Gpa]
α [1/K]
52
7150
423
0.24
140
1.10E-05
140
4
0.25
30
2700
2500
1440
3800
840
1060
1440
700
0.33
0.28
0.36
0.22
69
165
71
325
2.32E-05
4.25E-06
-3.30E-06
8.40E-06
Table 1 – Brake Rotor and Pad Material Properties
While assuming no potential energy losses or drag forces, the kinetic energy of the car
can be calculated using equation (1). While braking, the change in the kinetic energy of the car
is taken up by the braking system. The work input needed by all eight brake pads (2 pads per
brake) is found by taking the time derivative of the change in kinetic energy as shown in
equation (2). While substituting in the terms for velocity and acceleration into equation (2) it
can be rewritten in the form shown in equation (3). Knowing the angular speed, angular
acceleration and radius of the vehicles wheels, the total power needed to slow the vehicle
down can be calculated.
𝐸=
1
2
𝑚(𝑉𝑓2 − 𝑉𝑖2 )
[𝐽]
(1)
2
𝑚𝑉
𝑃 = − 𝑑⁄𝑑𝑡 ( 2 )
𝐽
[ 𝑠 = 𝑊]
𝑃 = − 𝑚 ∗ 𝑉 ∗ 𝑑𝑣⁄𝑑𝑡
𝜔𝑐𝑎𝑟 =
𝑎 = 𝑑𝑣⁄𝑑𝑡
→
𝑉𝑐𝑎𝑟
𝑟𝑤ℎ𝑒𝑒𝑙
(2)
[𝑊]
→ 𝑉𝑐𝑎𝑟 = 𝜔𝑟𝑤ℎ𝑒𝑒𝑙
𝛼𝑐𝑎𝑟 =
𝑎𝑇
→
𝑟𝑤ℎ𝑒𝑒𝑙
𝑃 = − 𝑚 ∗ 𝜔𝑟𝑤ℎ𝑒𝑒𝑙 ∗ 𝛼𝑟𝑤ℎ𝑒𝑒𝑙
2
𝑃𝑐𝑎𝑟 = − 𝑚 ∗ 𝑟𝑤ℎ𝑒𝑒𝑙
∗ 𝜔(𝑡) ∗ 𝛼
𝑎 = 𝛼𝑟𝑤ℎ𝑒𝑒𝑙
[𝑊]
[𝑊]
(3)
The work done per unit time caused by friction between the brake pad and rotor can be
expressed using equation (4). Substituting in force for mass and acceleration the equation can
be rewritten in the form of friction force required by the brake pad. Knowing the angular speed
of the wheel and the mean radius of the brake pad the power equation is written in the form
shown in equation (5).
𝑃 = 𝑚∗𝑉∗𝑎
𝐹 = 𝑚𝑎
𝑃 = 𝐹∗𝑉
[𝑊]
[𝑁]
[𝑊]
(4)
𝑉𝑝𝑎𝑑 = 𝜔𝑟𝑝𝑎𝑑
𝑃𝑏𝑟𝑎𝑘𝑒 = 𝐹𝑝𝑎𝑑 ∗ 𝜔(𝑡) 𝑟𝑝𝑎𝑑
[𝑊]
(5)
If the power required to slow the vehicle down in equation (3) is set equal to the power
in terms of the friction force required by a single brake pad in equation (5), the friction force
can then be solved for as shown in equation (6). Keep in mind that the power of slowing the
car down is divided by eight to acquire it in terms of a single brake pad.
𝑠𝑒𝑡: 𝑃𝑐𝑎𝑟 = 𝑃𝑏𝑟𝑎𝑘𝑒
2
− 𝑚 ∗ 𝑟𝑤ℎ𝑒𝑒𝑙
∗ 𝜔(𝑡) ∗ 𝛼 = 𝐹𝑝𝑎𝑑 ∗ 𝜔(𝑡) 𝑟𝑝𝑎𝑑
2
− 𝑚 ∗ 𝑟𝑤ℎ𝑒𝑒𝑙
∗ 𝜔(𝑡) ∗ 𝛼
= 𝐹𝑝𝑎𝑑 ∗ 𝜔(𝑡) 𝑟𝑝𝑎𝑑
8
𝐹𝑝𝑎𝑑 =
2
−𝑚𝑐𝑎𝑟 ∗𝑟𝑤ℎ𝑒𝑒𝑙
∗𝛼𝑐𝑎𝑟
8∗𝑟𝑝𝑎𝑑
1
[𝑁] → [
𝑘𝑔∗𝑚2 ∗ 2
𝑠
𝑚
=
𝑘𝑔∗𝑚
𝑠2
= 𝑁]
(6)
Knowing the amount of power generated during the particular braking period that was
used in this analysis, equation (5) is used to transform that energy into heat (power) input on
the contact surface of the brake pad as shown in equation (7). When this heat source is
dividing by the surface area of the brake pad, the heat flux for a single brake pad can be
calculated as shown in equation (8). Now that the heat input into the brake system has been
accounted for, the heat dissipation into the air by convection also needs to be accounted for so
that there is no excessive temperature build up in the brake rotors.
𝑞𝑝𝑟𝑜𝑑 = 𝐹𝑝𝑎𝑑 ∗ 𝜔(𝑡) 𝑟𝑝𝑎𝑑 [𝑊]
𝑞 ′′ 𝑝𝑟𝑜𝑑 =
𝑞𝑝𝑟𝑜𝑑
𝐴𝑝𝑎𝑑
𝑊
[𝑚2 ]
(7)
(8)
Using Newton’s law of cooling, the convective heat transfer equation for the dissipation
of heat from the brake rotor and brake pads to the ambient air is given as equation (9). Using
the respective surface areas and heat transfer coefficients of the brake rotor and brake pads,
the heat flux dissipation can be model. Equation (10) shows how to solve for the convective
heat transfer coefficient (h) using the Nusselt number (Nu), thermal conductivity (k) and the
effective diameter of either brake rotor or pad. The Nusselt number is a dimensionless ratio of
convective to conductive heat transfer coefficients of a given material. Expressing the Nusselt
number for a forced air convection scenario similar to Dittus-Boelter equation (for turbulent
flow) is given in equation (11). Equation (12) shows the heat transfer coefficient substituting in
terms for the dimensionless quantities of the Reynolds number and Prandtl number. The
Reynolds number gives a measure of the ratio of inertial forces to viscous forces while the
Prandtl number gives the ratio of momentum diffusivity (kinematic viscosity) to thermal
diffusivity.
𝑄 = 𝐴 ∗ ℎ ∗ (𝑇1 − 𝑇2 ) [𝑊]
ℎ =
𝑁𝑢∗𝑘
𝑑
[
𝑊
𝑚2 ∗𝐾
(9)
]
(10)
𝑁𝑢 = 0.037𝑅𝑒 0.8 𝑃𝑟 0.33
𝑅𝑒 =
𝜌∗𝑉∗𝑑
𝜇
𝑃𝑟 =
ℎ =
0.037∗𝑘
𝑑
∗(
𝐶𝑝 ∗ 𝜇
𝑘
𝜌∗𝑉∗𝑑 0.8
𝜇
(11)
)
𝐶𝑝 ∗𝜇 0.33
∗(
𝑘
)
[
𝑊
𝑚2 ∗𝐾
]
(12)
Results:
The model geometry used in COMSOL to represent a brake rotor and pad similar to one
that would be found on a 2006 Subaru Impreza WRX STI can be seen in Figure (1). The transient
vehicle braking profile that governed the COMSOL model was carried out from a 0 to 3 second
time interval using a time step of 0.1 seconds. As defined in the theory of this report, the
vehicle speed profile is shown in Figure (2) and subsequently the friction force on a single brake
pad, as defined by equation (6), is shown in Figure (3). It can be seen from the figures that the
vehicle was initially traveling at a speed of around 36 [m/s] and slowing down to a speed of
under 14 [m/s] within the 2 seconds of braking due to the deceleration rate of -11.176 [m/s^2].
During the 1 second cool down the vehicle continued traveling at around 14 m/s until the
simulation was stopped. It can be seen in Figure (3) that a constant Friction Force of 5250 [N]
was applied by the brake pad during the braking period of the simulation.
Figure 1 – Model Geometry
Figure 2 – Vehicle Speed Profile
Figure 3 – Friction Force of a Brake Pad vs. Time
Using COMSOL, the temperature distribution of the brake rotor and pad at different
time steps (0.1s, 0.5s, 1.0s, 1.5s, 2.0s and 3.0s) have been captured for analysis, as shown in
Figure (4) for an Aluminum alloy brake pad. It can be seen that the temperature of the brake
rotor reaches 450°F within 0.5 seconds of the brake being applied and that the maximum
temperature of 563°F is reached at around 1.6 seconds. From looking at Figure (5) of the
temperature profile on the top point and bottom point of the front side of the brake pad, it can
be seen that the top of the brake pad does get hotter than the bottom (over 100°F) most likely
due to the local velocity of the rotor being faster towards the top than on the bottom of the
pad. This uneven temperature profile can give clues as to how the face of the rotor undergoes
thermal stress and how it could relate to warping of the brake rotor. Looking more closely at
the radial temperature profile of the front side of the brake pad at a particular time step can
help show how this warping could occur. Figure (6) shows this radial profile of the Aluminum
alloy brake pad at a time step of 1.6 seconds where the maximum temperature of the pad is
reached. Semi-metallic brake pads such as this are considered very durable but in turn cause
more wear on the brake rotor surface. Softer organic type brake pads pose less wear on brake
rotors.
Figure 4 – Surface Temperature Distribution of Aluminum Alloy Brake Pads at various time steps
(0.1s, 0.5s, 1s, 1.5s, 2s and 3s)
Figure 5 – Temperature Profile of the top and bottom points on the front face of the Aluminum
Brake Pad
Figure 6 – Radial Temperature of front side of Aluminum Alloy Brake Pad @ t=1.6s
By analyzing the same set of results for a White Asbestos organic brake pad, as shown in
Figures (7-9), it can be seen that the temperature of the brake rotor reaches 485°F within 0.5
seconds of the brake being applied and that the maximum temperature of 595°F is reached at
around 1.4 seconds. Compared to the Aluminum alloy brake pad, the White Asbestos type
brake pads get hotter in temperature and heat up quicker during the same braking profile.
Although the Aluminum alloy brake pads perform slightly better, these organic type brake pads
are less expensive compared to the metallic type pads. The metallic brake pads are also slightly
heavier than the organic brake pads which could slightly affect the gas mileage of the vehicle.
Since the organic pads get hotter and have a quicker change in thermal energy, they
subsequently wear faster.
Figure 7 - Surface Temperature Distribution of White Asbestos Brake Pads at various time steps
(0.1s, 0.5s, 1s, 1.5s, 2s and 3s)
Figure 8 - Temperature Profile of the top and bottom points on the front face of the White
Asbestos Brake Pad
Figure 9 - Radial Temperature of front side of White Asbestos Alloy Brake Pad @ t=1.4s
Next a Kevlar 29 Aramid Fiber brake pad was analyzed. This is an organic non-asbestos
type brake pad. The results shown in Figures (10-12) are for the Kevlar Fiber brake pad and it
can be seen that the temperature of the brake rotor reaches 493°F within 0.5 seconds of the
brake being applied and that the maximum temperature of 607°F is reached at around 1.6
seconds. Compared to the Aluminum alloy and White Asbestos type brake pads, the Kevlar
Fiber pad reaches the highest temperatures. Although the metallic and organic asbestos pads
do not absorb as much heat as the Kevlar pad, these organic non-asbestos type brake pads are
a newer higher performing organic type pad. One good trait about this pad is that at the end of
the 1 second cool down, the Kevlar pad was the coolest despite also being the hottest during
the braking period. The low thermal conductivity of the Kevlar Fiber pad helps keep the bulk
temperature of the pad low which is helpful during excessive use (or cyclical usage) of the pad.
Figure 10 - Surface Temperature Distribution of Kevlar Aramid Fiber Brake Pads at various time
steps (0.1s, 0.5s, 1s, 1.5s, 2s and 3s)
Figure 11 - Temperature Profile of the top and bottom points on the front face of the Kevlar
Aramid Fiber Brake Pad
Figure 12 - Radial Temperature of front side of Kevlar Aramid Fiber Brake Pad @ t=1.4s
Finally a Ceramic Al2O3 (Aluminum Oxide Ceramic) brake pad was analyzed. The results
shown in Figures (13-15) are for the Ceramic fiber brake pad and it can be seen that the
temperature of the brake rotor reaches 465°F within 0.5 seconds of the brake being applied
and that the maximum temperature of 576°F is reached at around 1.4 seconds. Although these
Ceramic pads are more expensive than other types of pads, they offer cleaner operation (less
brake dust) and provide excellent braking while producing less wear on the brake rotor.
Although the Ceramic pads stay cooler than the other organic type pads, the Aluminum alloy
pad still stay the coolest under the same braking conditions.
Figure 13 - Surface Temperature Distribution of Ceramic Al2O3 Brake Pads at various time steps
(0.1s, 0.5s, 1s, 1.5s, 2s and 3s)
Figure 14 - Temperature Profile of the top and bottom points on the front face of the Ceramic
Al2O3 Brake Pad
Figure 15 - Radial Temperature of front side of Ceramic Al2O3 Brake Pad @ t=1.4s
Conclusion:
In conclusion COMSOL Multiphsyics was used to gather useful insight on the
temperature distribution and effects of various brake pads on a brake rotor during a hard
braking scenario. Four different types of brake pads were analyzed to see how each would
compare. As expected the semi-metallic pad and the ceramic aluminum oxide pad showed the
best results as far as temperature rise and subsequent distribution. This information can be
used when determining what type of brake pad material one should select for their driving
habits. Using the results found in this analysis and other readily accessible common knowledge
of different types of brake pads such as price, self-wear rate and rotor wear rate, the
appropriate brake pads can be chosen.
Further analysis would include adding radiant heat dissipation, modeling a full brake
rotor with 2 pads, adding in slotted vents internal to the rotor and possibly considering slotted
or cross-drilled surfaces on the rotor. These additions would make the analysis more accurate
and in depth but the basic idea of heat generation and distribution due to kinetic energy
consumption in the brake system with various brake pad materials has been studied.