The geometry for the brake model is loosely based on the front rotors for a 2005 Ford Mustang. The exact dimensions were unknown so the majority of the dimensions are approximate. The geometry was modeled in Rhinoceros 3D and meshed using Eclectic. The rotor diameter is 316mm, the total thickness is 30mm, and there are 48 vents for cooling. The brake pad and caliper models are based on the geometry of rotor and are generic in shape and size. The physical properties of the brake model geometry are shown in Table 1. Volume and surface area values were obtained using the mass properties function in Rhinoceros.
Table 1. Physical Properties of Brake Rotor Geometry
|
Part |
Part Volume (mm^3) |
Surface Area(mm^2) |
Mass (kg) |
Volume/Surface Area (mm) |
|
Rotor |
1714739 |
326706 |
13.324 |
5.25 |
|
Pad |
71119 |
18095 |
0.200 |
3.9 |
|
Pad Backing Plate |
46056 |
20758 |
0.400 |
2.2 |
|
Caliper |
969042 |
14894 |
2.684 |
6.51 |
Brake Thermal Power Calculations
The rate of energy generation during a single stop at constant deceleration was calculated using equations from Brake Design and Safety by Rudolf Limpert. The following assumptions were made to perform the calculations:
-
Initial velocity of the vehicle is 26.822 m/s or 60mph
-
Vehicle comes to a complete stop (0 m/s)
-
Time between multiple stops is 1.4 min (84 sec)
-
Mass of the vehicle is 1554 kg.
-
Weight is distributed 57% to the front and 43% to the rear
-
Vehicle wheelbase is 2720mm (107.08in.)
-
Vertical center of gravity is 527.56mm (20.77 in. Based on data from 2003 Ford Mustang)
-
Power generated is distributed 50/50 between the right and left front wheels
-
Percentage of the contact surface covered by the pad is 19.7%.
-
Force distribution varies with braking time, but is 65.8% for a 6-second stop
The power generated in the right front corner module during a 6-second stop is shown graphically in Figure 2. The power is applied separately to the rotor and pad contact surfaces; therefore the power is divided between the two, based on the surface area covered by the pad. The pad covers 19.7% of the contact surface, so 19.7% of the total power is applied to that part as shown by the Pad Contact curve in Figure 2. View a PDF Document showing the complete power input calculations performed in MathCAD Software.
The brake model is set up for 10 consecutive stops spanning a total of 20 minutes. Each braking cycle includes the following events:
-
Vehicle is idle for 1.29 minutes
-
Vehicle accelerates to 60mph in 0.1 minutes
-
Once the vehicle reaches 60mph it immediately decelerates to 0mph in 0.1 minutes
-
Cycle repeats
After ten stops the vehicle sits idle for 5 minutes. The vehicle velocity curve is shown in Figure 3. The brake model uses a square wave for power input as shown in Figure 4.
In this approach the sum of the power generated during the 6-second stop is averaged over the six seconds. For this model the average power applied over the six seconds is 27107 Watts for the rotor contact surfaces and 6630 Watts for the pad contact surfaces. Using the square wave, there is less chance for error when running the model.
For example, if a continuous power curve was used as shown in Figure 5, it may be possible to miss the high power tip of the curve if the time steps were set too large. This is shown graphically in Figure 6. To correct this potential error, very small time steps would be required.
Thermal Results
Figure 8 is a radial transect of the temperatures on the hub and rotor assembly. The temperatures climb steadily with each brake application, then begin the exponential decline.
Transient Results
View a Small Animated GIF.
Download a High Resolution Animation. AVI Video Format (12MB download)
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