Rensselaer Hartford
275 Windsor Street
Hartford, CT 06120
Department of Engineering
MANE 6960 Friction, Wear, and Lubrication of Materials
Spring 2015
Finite Element Analysis of Rotor Surface Roughness
in a Disc Brake System
Report
Submitted to
Professor Ernesto Gutierrez-Miravete
By
Micah Bowen
Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
Bowen, S2015
Abstract
The purpose of this project was to analyze a disc brake system using finite element analysis (FEA) to
determine the effects of different values of rotor surface roughness on the system. This was accomplished
by creating a geometric model of a two blocks representing the disc brake system and varying the heights
of the block surfaces representing different values of surface roughness. The model was meshed, the
material properties for a ceramic brake pad and grey cast iron rotor were applied, and boundary condition
using the FEA software package ANSYS Workbench 14.5. Displacements were applied to one of the
blocks while the other block was fixed representing a brake clamping on the spinning rotor, as shown in
Figure 6. All ANSYS models were isothermal 2D models solve using a static analysis to generate stress
and deflection plots. It was determined that a significant number of test cases, many more than the nine
performed in this report are required to make a conclusion on the impact of surface roughness. Peaks in
the force required to displace the brake pad across the rotor are due to peaks in the rotor surface rather
than the actual roughness average (RA). A summary of the data is found in the results and discussion part
of this report.
Introduction
A vehicle brake disc system is comprised of a caliper, piston, brake pad, and rotor as shown in Figure 1.
When the brake pedal is pressed, a hydraulic piston pushes the brake pad against the brake disc or rotor
attached to the wheel. The friction generated between the brake pad and rotor slows the rotational
velocity of the rotor and attached wheel.
Figure 1: Typical Car Disk Brake Setup [1]
The friction between a brake pad and rotor produces a large amount of heat that is absorbed by the rotor
and cooled by the passing air. The ability to dissipate heat is key the efficiency of the system. If the rotor
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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does not have proper airflow and/or overheats, the rotor can warp. To prevent these thermal issues,
manufactures have developed multiple rotor designs for various vehicle applications as shown in Figure
2. Slotted and drilled rotors designs are used to assist in the removal of heat and gases generated in the
system. However, the downside of these designs is the slots and holes weaken the rotor resulting in
cracking and eventual failure. These designs are suited for applications such as racing where the rotors
undergo high stress and generate a great amount of heat. For daily drivers, a vented rotor is the ideal.
The vented rotor has slotted areas on its edge that increase the heat dissipation in the system without
weakening the rotor.
Figure 2: Vented, Drilled, and Slotted Rotors [3], [4], & [5]
A brake pad consists of a friction material attached to a steel backing that is attached to the caliper-piston
as shown in Figure 3. Attached to the brake pad is a metal clip called a wear indicator that comes into
contact with the rotor surface when the brake pad wears down to the minimum operational thickness. The
contact between the wear indicator and rotor results in a loud squealing sound to notify the operator that
the brake pads need to be replaced.
Figure 3: Brake Pads [2]
In addition to the reduction thickness of the rotor and brake pad, scoring and wear ridges will appear on
the rotor as the system wears as shown in Figure 4. Typically, a rotor lasts through two sets of brake
pads. After the first set of brake pads has worn, it is recommended to resurface the rotor as long as the
thickness of the rotor is greater than the specified original equipment manufacturer (OEM) thickness after
being resurfaced.
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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Figure 4: Brake Disc Wear [10]
The recommended surface finish for a resurfaced rotor is between 30 and 60 RA [9]. Surface roughness
is the measurement of surface irregularities in the surface texture. The RA is the arithmetic average
deviation of the surface valleys and peaks expressed in micro inches [11]. RA is calculated using
Equations 1 and 2 using the variables in Figure 5.
𝑀𝑒𝑎𝑛 𝐿𝑖𝑛𝑒 = ∑𝑖=1
𝑛
𝑅𝐴 = ∑𝑖=1
𝑛
𝑦1 +𝑦2 +𝑦𝑛
𝑛
|ℎ1 |+|ℎ2 |+|ℎ𝑛 |
𝑛
Equation 1
= 𝜇 · 𝑖𝑛
Equation 2
In the previous equations:
yn = measure height from datum to top surface (in)
hn = calculated height from mean line to top surface (in)
n = number of samples
Varied
Surface
h1
h3
hn
Datum
y1
y1
Mean
Line
yn
Figure 5: Diagram of Surface Roughness
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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The rotor material depends on the application, but is commonly made out of grey iron for the automotive
industry. Grey iron is a desirable material for this application based on its metallurgical properties such
as strength, noise, vibration damping capabilities, and wear [6] & [7]. In addition, they are low cost to
produce. Some other rotor materials are stainless steel and aluminum. Stainless steel is used in
applications where weight and preventing rust is important such as bicycles. The downside to stainless
steel is it does not absorb heat (low thermal conductivity) and other material properties leading to much
more wear compared to other metals. Aluminum and layered aluminum/steel rotors are used in
applications such as motorcycles where the combination of lightweight and thermal material properties
such as ability to dissipate heat and thermal expansion are important.
There are three main types of brake pad materials commonly used: semi-metallic, fully metallic, and
ceramic [8]. Semi-metallic brake pads consist of synthetics mixed with flaked metals resulting in a
material that is harder and lasts longer than non-metallic pads. The semi-metallic brake pads are less
expensive compared to other brake pads materials. Fully metallic brake pads are composed of steel and
are ideal for racing applications where significant braking power is required. The downside with fully
metallic brake pads is the increased rotor wear. Ceramic brake pads are constructed from a blend of
ceramic and copper fiber and are desirable over metallic brake pads due to the fact they are quieter, create
less dust, and last longer than metallic brake pads. Ceramic brake pads are not recommended for racing
or heavy duty use due to the fact they do not have a good “bite” for quick braking compared to metallic.
The purpose of this project is to analyze a disc brake system using FEA in ANSYS Workbench 14.5 to
determine the effects of different values of rotor surface roughness on the system. This will be
accomplished by representing the system as two blocks shown in Figure 6. One block will be fixed in all
degrees of freedom (DOF) at the bottom and one side. It will have a varied top surface height
representing the rotor surface roughness. The second block will be aligned horizontally with the first
block at a prescribed height. A displacement will be applied to the block to displace it in the -Y-direction
to the mean line height of the rotor. Once displaced, a second displacement will be applied to the block in
the +X-direction and force probe will be used to determine the amount of force required to displace the
brake pad block. In addition, von Mises stress will be pulled to determine the stresses of both the pad and
rotor. Multiple cases will be run for different surface roughness and compared each other as well as to a
baseline ideal case (rotor surface is flat).
Piston
Displacement
Piston
Displacement
Distance
Mean Line
Height
Y
+
X
Block Representing
Brake Pad
Block Representing
Rotor
Force
Probe
Prescribed
Displacement
Varied Surface
Roughness
Fixed
Surfaces
Figure 6: Block Model Representing Brake Disc System
Figure 7 shows a breakdown of each step in the proposed FEA.
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
Initial Setup
Bowen, S2015
Displacement in
-Y-direction
Block Representing
Brake Pad
Block Representing
Rotor
Y
+
X
Displacement in
X-direction = 0
Displacement in
-Y-direction
Displacement
in +X-direction
Force Probe
Figure 7: FEA Steps
A prescribed displacement in the Y-direction will be used opposed to a force representing the piston force
due to the fact that applying a force in the Y-direction will result in brake pad contacting the varied rotor
surface at the rotor surface peak as shown in Figure 8. The resulting extracted force would not represent a
varied surface, but would represent the force required to drag the brake pad across the rotor surface peak.
Figure 8: Using Force Instead of Displacement for the Brake Pad
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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This project considers a standard vented rotor design and solid brake pad shown in Figure 2 and Figure 3.
The material properties in Table 1 for a grey iron rotor and ceramic brake pad will be used.
Table 1: Rotor and Brake Pad Material Properties
Material
Density
(ρ)
(kg/m3)
Young’s
Modulus
(E)
(GPa)
Tensile
Strength
(σu)
(MPa)
Yield
Strength
(σy)
(MPa)
Poisson’s
Ratio
(ν)
3700
303
193
15,400
0.21
207
172.37
(min)
Aluminum Oxide
AI203 (Ceramic) (1)
SAE(4) J431
G3000
(Grey Cast Iron)(2)
7150
140
Coefficient
of Friction
(μ)
0.3 – 0.5(3)
0.24
Notes:
1. Values for 94% aluminum oxide from [15]. Yield strength from [16].
2. Values from [13]. Yield strength from [14].
3. Values from [17].
4. Society of American Engineers (SAE).
Heat transfer between the brake pad and rotor as well as the heat transfer to the surrounding air is outside
the scope of this project. For this study please see the following reference [12].
Formulation and Solution
Figure 9 shows the dimensions for the blocks representing the brake pad and rotor. These dimensions
were chosen to ensure the extracted von Mises stress distribution would not be impacted by edge effects.
2.00 in
1.00 in
Prescribed
Block Representing Displacement
Brake Pad
Distance
1.00 in Block Representing
Rotor
Mean Line
Height
2.00 in
Figure 9: Block Dimensions
Typical values of surface roughness of the rotor were calculated using excel by splitting the 2.00 in length
of the rotor into 10 segments (0.2 in) and using the random function. Ten segments were selected since it
produced a realistic surface roughness. If too many segments were created, there would be too much
variation in the surface height as shown in Figure 10 and the rotor could not be properly meshed.
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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1.000
Height of Rotor (in)
1.000
1.000
Rotor Height
1,000 Divisions
1.000
Mean Line
1.000
1.000
1.000
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
2.000
Distance Along Rotor (in)
1.000
Height of Rotor (in)
1.000
1.000
Rotor Height
10 Divisions
1.000
Mean Line
1.000
1.000
1.000
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
2.000
Distance Along Rotor (in)
Figure 10: Comparison of 1,000 versus 10 Segment Split Up
The variation in surface height was created by using the RANDOMBETWEEN function in excel and
multiplying by a factor to create the random surface heights. The mean line height and surface roughness
was calculated using Equations 1 and 2. This was done for multiple values of surface roughness from
approximately 15 to 92 RA. Since the surface roughness heights vary on such a small scale (1e-4) in
comparison to the size of the model, the surface height variations were multiplied by 500 in order to get
amplified output from the FEA models.
Using SolidWorks, the geometry from Figure 7 was constructed using the rotor heights from Excel.
These values were imported into SolidWorks as XYZ points in and a spline was used to connect the lines
as shown in Figure 11. In addition, the corner of the brake pad block was rounded to avoid a
concentration point at the corner when in contact with the rotor. Once the dimensions and lines are
defined, the blocks were turned into surfaces and exported to ANSYS Workbench 14.5 as an IGS file.
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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Figure 11: SolidWorks Block Setup
Once in ANSYS Workbench 14.5, a 2D elastic static structural analysis was selected and the material
properties from Table 1 were assigned. Next the IGES file from SolidWorks was imported and the
material properties were assigned. The next step was to setup the contact between the two surfaces as
shown in Figure 12. This was accomplished by setting the brake pad and rotor blocks as contact and
target edges/bodies. A frictional contact with a friction coefficient of 0.4 (average value from Table 1)
was set. A pure penalty method was selected with a pinball region setup to capture both surfaces that will
come into contact.
Figure 12: Contact Setup between Brake Pad and Rotor
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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The contact tool status and initial gaps are shown in Figure 13. The contact tool is used to ensure that the
selected edges that will come into contact are setup correctly.
Figure 13: Contact Tool Checks
Next a mesh was setup as shown in Figure 14. This was accomplished by selecting the edges of the
blocks and setting the number of divisions. A bias type was set in order to have a denser mesh toward the
varied (top) surface of the rotor. Mid-side nodes were kept due to the fact that the varied surface of the
rotor will result in tetrahedral elements along the surface; using mid-side nodes is important when dealing
with tetrahedral elements to properly predict the stress. An element quality check was performed to
ensure proper element shapes. To confirm that accurate results are obtained, a mesh density study for one
of the cases was performed in Appendix B.
Figure 14: Meshing of the Brake Pad and Rotor
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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The next step was to setup the applied displacements and boundary conditions on the rotor and brake pad
as shown in Figure 15. The left side and bottom of the rotor was fixed in all degrees of freedom (Fixed
Support-A). A displacement of 2.0 inches in the X-direction was applied to the right edge of the brake
pad (Displacement 3-C). Another displacement was applied to the top of the brake pad that is equal to
1.10 inches from Figure 11 minus the mean line height (Displacement 4-B).
Figure 15: Applied Displacement, Force, and Fixed Support on the Rotor and Brake Pad
The step times used for the applied force and displacement are shown in Figure 16. For the displacement,
the first five steps (0.5 seconds) was set to displace the brake pad 0.1 inches for this case, which bring it
to the mean line height of the rotor. At 0.5 seconds, the 2.0 inch displacement in the +X-direction was
applied.
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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Figure 16: Step Setups for Force and Displacement
The typical analysis settings are shown in Figure 17. The values for the times varied from case to case
based on the force and displacement step times. Multiple steps were used in order for the problem to
converge. In addition, large deflection was turned on while the weak springs were turned off in the solver
controls.
Figure 17: Setup for Analysis
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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The next step was to set up the solution portion or the FEA. As discussed in the Introduction portion of
this report, the force required to displace the brake pad and von Mises stress plots are required for postprocessing. This was accomplished by selecting a force probe and applying it to the displaced edge of the
brake pad as shown in Figure 18. The equivalent stress (von Mises) plots were selected for all bodies
Figure 18: Force Probe Setup
Once the analysis was completed, the solution information was checked to ensure there were no errors
and that the problem properly converged as shown in Figure 19.
Figure 19: FEA Convergence
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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Results
The post-processing results are tabulated in Table 2 and plotted in Figure 20. An outline of the generated
surfaces is shown in Figure 21 through Figure 27. The post-processing averages the force from the force
probe across all the time steps in order to reduce the impact by outlying peaks in the surface on the force.
Based on the plot in Figure 20, no conclusions can be made from the data due to the fact a significant
number of test cases would be needed. This is due to the peaks in force that result from peaks in the
surface. An example of this is shown in Case 02 which is plotted in Figure 22. Case 02 has a significant
peak at the start and end of the surface which required a significant amount of force to displace the brake
pad. If a significant number of test cases were made and a larger data sample was available, the outlying
peaks could be rules out using a normal distribution curve.
Table 2: Post-processing Data for Cases(2)
Case
Surface Roughness
Value (RA)
Mean Line
Height (in)
Average
Absolute
Force (lbf)
851
1,523
386
1,535
2,724
609
2,749
777
8
1.00000
0.0 (Ideal)(1)
4
1.00001
16.0
3
1.00000
25.8
1
1.00000
37.3
2
1.00000
51.0
5
0.99994
66.3
6
1.00002
77.6
7
1.00001
92.3
Notes:
1. An additional 0.1 inch in displacement was added to generate a force.
2. Tabulated from minimum to maximum surface roughness
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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6
2
4
1
7
8
5
3
Height of Rotor (in)
Figure 20: Average Absolute Force versus Surface Roughness
1.00010
1.00008
1.00006
1.00004
1.00002
1.00000
0.99998
0.99996
0.99994
0.99992
0.99990
0.99988
0.000
Surface
Mean
Line
0.500
1.000
1.500
2.000
Distance Along Rotor (in)
Figure 21: Case 01 Rotor Surface
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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Height of Rotor (in)
1.00010
1.00005
1.00000
Surface
0.99995
Mean
Line
0.99990
0.99985
0.000
0.500
1.000
1.500
2.000
Distance Along Rotor (in)
Figure 22: Case 02 Rotor Surface
1.00008
Height of Rotor (in)
1.00006
1.00004
1.00002
1.00000
Surface
0.99998
0.99996
Mean
Line
0.99994
0.99992
0.99990
0.99988
0.000
0.500
1.000
1.500
2.000
Distance Along Rotor (in)
Figure 23: Case 03 Rotor Surface
1.00005
Height of Rotor (in)
1.00004
1.00003
1.00002
Surface
1.00001
1.00000
Mean
Line
0.99999
0.99998
0.99997
0.99996
0.000
0.500
1.000
1.500
2.000
Distance Along Rotor (in)
Figure 24: Case 04 Rotor Surface
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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Height of Rotor (in)
1.00005
1.00000
0.99995
Surface
0.99990
Mean
Line
0.99985
0.99980
0.000
0.500
1.000
1.500
2.000
Distance Along Rotor (in)
Figure 25: Case 05 Rotor Surface
1.00020
Height of Rotor (in)
1.00015
1.00010
1.00005
Surface
1.00000
0.99995
Mean
Line
0.99990
0.99985
0.99980
0.99975
0.000
0.500
1.000
1.500
2.000
Distance Along Rotor (in)
Figure 26: Case 06 Rotor Surface
1.00025
Height of Rotor (in)
1.00020
1.00015
1.00010
1.00005
Surface
1.00000
0.99995
Mean
Line
0.99990
0.99985
0.99980
0.99975
0.000
0.500
1.000
1.500
2.000
Distance Along Rotor (in)
Figure 27: Case 07 Rotor Surface
Post-processing shows that the contact setup is functioning correctly as shown in the von Mises stress
plot, Figure 28 and the rotor surface is yielding at the surface peaks. These surface peaks lead to the
spikes in force required to displace the brake pad across the surface. In addition, using displacement
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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instead of force on the brake pad allows for contact across multiple surface peaks versus a single peak
shown in Figure 8.
Figure 28: Contact and Yielding in Case 03
Conclusion
The surface roughness of a rotor has a significant impact on the efficiency and wear of a brake system. It
is important to follow the guidelines [9] for rotor surface roughness values when performing maintenance
on a brake system. When modeling a brake system, getting the model to converge when using contact is
extremely difficult and time intensive. If this project was repeated, more test cases would be needed to
make a conclusion. A future recommendation for this project would be to include the thermal effects on
the disc brake system by including the heat generated by friction and by varying the thickness of the rotor
and determining how this impacts the efficiency and wear of the system. In addition to the thermal
effects, analyzing the wear of rotors that have been slotted or drilled, a process used to help dissipate heat,
but make the rotor prove to cracking.
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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References
1. Diskbrake3new-3. Digital image. Olathetoyota. N.p., n.d. Web. 9 Apr. 2015.
<https://parts.olathetoyota.com/images/2014/03/discbrake3new-3.jpg>.
2. Digital image. How Stuff Works. N.p., n.d. Web. 18 Apr. 2015. <http://s.hswstatic.com/gif/brakepads-1.jpg>.
3. Power Stop Slotted Brake Rotors. Digital image. Brake Wearhouse. N.p., n.d. Web. 13 Apr.
2015. <http://www.brakewarehouse.com/images/powerstop/slotted.jpg>.
4. Stainless Steel Cross Drilled Rotors. Digital image. Performance Parts News. N.p., n.d. Web. 13
Apr. 2015. <http://performanceparts.com/News/wp-content/uploads/2012/01/cross-drilledrotor.jpg>.
5. Brake Rotor (10.1" Vented-OEM). Digital image. Techtonics Tuning. N.p., n.d. Web. 13 Apr.
2015. <http://techtonicstuning.com/main/images/615.115.jpg>.
6. Aravind Vadiraj, G.Balachandran, M.Kamaraj, B.Gopalakrishna, D.Venkateshwara Rao, "Wear
behavior of alloyed hypereutectic gray cast iron", Tribology International 43 (2010) 647–653.
7. Aravind Vadiraj, G. Balachandran, M. Kamaraj, B. Gopalakrishna, K. Prabhakara Rao, "Studies
on mechanical and wear properties of alloyed hypereutectic gray cast irons in the as-cast pearlitic
and austempered conditions", Materials and Design 31 (2010) 951–955.
8. "What Are The Best Brake Pads: Ceramic or Semi-Metallic?" What Are The Best Brake Pads?
Ceramic vs. Semi-Metallic. N.p., n.d. Web. 18 Apr. 2015.
<http://www.autoanything.com/brakes/the-best-brake-pads-ceramic-or-metallic.aspx>.
9. "Brake Rotors." Brake Rotors. N.p., n.d. Web. 18 Apr. 2015.
<http://www.aa1car.com/library/brake_rotors.htm>.
10. Digital image. Implass Form. N.p., n.d. Web. 18 Apr. 2015. <http://blog.bavauto.com/wpcontent/uploads/2009/11/fig-71.jpg>.
11. "Surface Roughness (Finish) Review and Equations - Engineers Edge." Surface Roughness
(Finish) Review and Equations - Engineers Edge. N.p., n.d. Web. 19 Apr. 2015.
<http://www.engineersedge.com/surface_finish.htm>.
12. Lipert, R. (1999). Brake Design and Safety (2nd. Ed.). Warrendale, Pa.: Society of Automotive
Engineers.
13. Materials for Engineering: Concepts and Applications, L. H. Van Vlack, Addison-Wesley
Publishing Company, Reading, MA (1982).
14. Iron and Steel Specifications. London: British Steel, Head Office Standards, 1989. Web. 19 Apr.
2015.
15. Porcelain, and Mullite. "8510-1042 Ceramic Material Properties." Coorstek.com. N.p., n.d. Web.
19 Apr. 2015. <http://www.coorstek.com/resource-library/library/85101042_ceramic_material_properties.pdf>.
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Bowen, S2015
16. "Material: Aluminum Oxide (Al2O3), Bulk." Material: Aluminum Oxide (Al2O3), Bulk. N.p.,
n.d. Web. 20 Apr. 2015. <https://www.memsnet.org/material/aluminumoxideal2o3bulk/>.
17. Eltayeb, N., & Liew, K. (2009). On The Dry and Wet Sliding Performance of Potentially New
Frictional Brake Pad Materials For Automotive Industry. Wear, 266 (1-2), 275-287 Melaka,
Malaysia.
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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Appendix A: Excel Code
Figure A-1: Excel Setup for Random Rotor Height
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Finite Element Analysis of Rotor Surface Roughness in a Disc Brake System
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Appendix B: Mesh Study
In the case of contact, mesh density is extremely important to output the correct stress. As discussed in
the Formulation and Solution section of this report, a mesh density study is performed to ensure the
stresses are being properly predicted. Table B tabulates the mesh densities and force required to displace
the brake rotor. Figure B shows the difference in stress plots between the cases. The mesh study was
performed using Case 1 from the Results section of this report.
Table B: Mesh Density Study
Category
Mesh 1(2)
Mesh 2
Mesh 3
Elements
7105
10008
11054
Nodes
7399
11052
12350
-1535
-1580
-1603
N/a
2.9
4.4
Force (lbf)
Percent Difference (%)
(1)
Notes:
1. Percent Difference is calculated as: (MeshX / Mesh1 - 1) × 100.
2. Mesh used in analysis in Results section of this report.
1,600
Absolute Force (lbf)
1,590
1,580
1,570
1,560
1,550
1,540
1,530
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
Nodes
Figure B: von Mises Stress Plots
Table B shows that there is a 5.0% difference in the force; therefore, the use of Mesh 1 is justified. In
addition the plots in Figure B show the von Mises stress does not vary significantly at the peaks of the
varied rotor surface.
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