Finite Element Analysis of Disk brake assembly.

Computer Aided Engineering MET-300 Project – Technical Report
Farmingdale State College 04/29/2015
1
Disc Brake Assembly Analysis
INSTRUCTOR: Dr. Gonca Altuger-Genc
MET-300
Mridul Mohta
Pragadeesh Ravichandran
Aditya Kaliappan Velayutham
04/29/2015

2
TABLE OF CONTENTS
1. Abstract……………………………………………………………….3
2. Parameters Involved………………………………………………….5
3. Parts of Braking System……………………………………………...5
4. Geometry of ContactArea…………………………………………...6
5. Objective……………………………………………………………..8
6. Procedure…………………………………………………………….8
7. Selection of Materials……………………………………………….10
8. Mechanical Properties……………………………………………....10
9. Outcomes
1) Analysis Type 1 – Mechanical Event Simulation……………….14
Material A
2) Analysis Type 1 – Mechanical Event Simulation……………….20
Material B
3) Analysis Type 2 – Non-Linear Static Stress Simulation………...24
Material A
4) Analysis Type 2 – Non-Linear Static Stress Simulation………...29
Material B
10.Challenges Faced……………………………………………………34
11.Formulae…………………………………………………………….35
12.Computational Problem……………………………………………..36
13.Design for Manufacturing of Disc Brakes…………………………..38
14.Conclusion…………………………………………………………..39
15.References…………………………………………………………...40

3
Abstract
Disc Brakes are the type of the brakes, which uses the pair of calipers attached
with the brake pads to rub against the disc. This creates friction between the brake pads
and the disc, which in turn reduces the rotatory motion of the axle/wheel or brings it to
stationary. Braking systems rely on friction to bring the vehicle to a halt – hydraulic
pressure pushes brake pads against a cast iron disc. It consists of a disc made up of cast
iron, which is bolted, to the wheel hub and a caliper (stationary mount housing). The
caliper is linked to the vehicle’s stationary part like the axle casing and holding pistons in
each part. In between each piston and the disc there is a friction pad held in position by
retaining pins, spring plates etc. Passages are drilled in the caliper for the fluid to enter or
leave each housing.
Failure of disc brakes - If brake pads are not changed promptly, scarring occurs.
This happens once they reach the end of their service life. Cracking takes place only for
drilled discs that may develop small cracks around edges of holes drilled near the edge of
the disc because of the disc's non-uniform rate of expansion. The discs have a certain
amount of "surface rust". Sometimes when the brakes are applied, a high-pitched squeal
occurs. Most brake squeal is produced by vibration (resonance instability) of the brake
components, especially the pads and discs (known as force-coupled excitation).
The standard disc brake of a 4-wheeler model was done using Autodesk
Mechanical Simulation through which the properties like deflection, heat flux and
temperature of disc brake model were calculated. It is important to understand action
force and friction force on the disc brake new material, how disc brake works more
efficiently, which can help to reduce the accident that may happen at anytime.

4
Figure 1
Figure 2

5
Parameters involved
Clamping Force
Braking Force
Braking Torque
Load torque
Inertia torque
Rubbing speed
Power dissipation
Kinetic energy
Friction torque
Braking time
Maximum disc speed
Deceleration during braking
Delay time for brake signal
External load acting on the brake
Parts of Braking System
 Brake Pedal—force input to system from driver
 Design gives a Mechanical Advantage
 Master Cylinder—converts force to pressure
 Pressure is used to move brake pads into place
 Brake Pads—provide friction force when in contact with rotor
 Works to slow or stop vehicle
 Caliper—holds pads and squeezes them against rotor
 Rotor—spins with wheel

6
 When used in conjunction with brake pads, slows vehicle
 Vents—help provide cooling to brake
► Different materials have different coefficients of friction
► Pad material can be chosen for performance or to create a balance between
performance and durability
Table 1
Geometry of Contact Area
Figure 3
F = Force on pads
θ1, θ2, r1, r0 = Dimensions of brake pad

7
Figure 4
► Step 1: Force is applied to by driver to the master cylinder
► Step 2: Pressure from the master cylinder causes one brake pad to contact rotor
► Step 3: The caliper then self-centers, causing second pad to contact rotor

8
Objective
To develop a technical report by showing the simulation results of the disc brake
assembly for different materials by providing the necessary tables/figures/graphs and to
examine whether the part fails or not based on the safety factor requirements.
The disc brake assembly (Figure 5) on which the analysis has to be done –
Figure 5
Procedure
1. The disc brake assembly file was downloaded as an Autodesk Inventor file.
2. The unnecessary parts of the assembly were removed so as to reduce the
complexity of the project.
3. The entire assembly was cut into half in two different planes. This was done
to reduce the simulation time.
4. The final assembly had three parts – one caliper, brake pad and the rotor.
5. The assembly was then opened in the Autodesk Simulation software.
6. The assembly was meshed by selecting the appropriate 3D Mesh settings and
by clicking “Generate 3D Mesh” command.
7. Once meshing has been done, both the element definition and element type
were defined.
8. The analysis was carried with two different sets of materials for caliper, brake
pad and rotor. (Details mentioned later in this report)

9
9. The analysis was carried with three different simulation types. (Details
mentioned later in this report)
10. The next step was to define the constraints as follows: -
For rotor’s inner side face - fixed constraint,
For calipers – fixed constraint and
For brake pad – fixed except translational in z-axis
Constraints remained the same for Linear and Non - Linear Static Analysis.
In addition, rotation of the rotor along the z-direction was set free for MES
Type.
11. Linear Static Analysis –
 The surface of the brake pad, which faces the rotor, was simulated so
that it moves a certain distance by providing the option of prescribed
displacement.
 This was done by Selecting the surface  Right click, select sub
entities and then the vertices were chosen.
 Then one of the nodes was right clicked and prescribed nodal
displacements were selected.
 The translational motion magnitude was given as 10.666 mm in
negative z - direction and then the load curve was selected for an
addition of the return cycle.
 On the same surface, by following the steps mentioned above, nodal
forces were applied for 1000 N along the same direction as that of the
prescribed displacement.
 The simulation was then made to run.
12. Non – Linear Static Analysis – The same procedures were followed as that
of the Linear Static Analysis. In addition, Surface-to-Surface contact was
defined between the meeting faces of the brake pad and the rotor. Although,
the outcomes were observed to be different.
13. Mechanical Event Simulation type – The same procedures were followed as
that of the Non – Linear Analysis. In addition, two more steps were added i.e.
 Nodal Prescribed Displacement on the rotor - the inner hollow surfaces
of the rotor was selected by drawing a circle over it. In the option
mesh, the joint option was selected to create a joint.
For making the rotation possible, the rotor’s element definition was
changed from truss to beam, which has rotational degree of freedom.
The selection type was changed to rectangle and dragged over the
created joint. The nodes been selected was then right clicked to choose
nodal prescribed displacements and the value of rotation in terms of
number of revolutions was provided.

10
 Capture rate – It analyzes the component in several steps and
increments. More is the value of the capture rate, better is the
simulation result.
Under the parameters section, the capture rate was selected and
defined as 5 for 1-second forward cycle.
So, for a total of 2 seconds, the total time of 10 seconds was made
as a capture rate.
SelectionofMaterials
• The brake disc or rotor is usually made up of cast iron, but in some cases it is
made up of composites such as reinforced carbon–carbon or ceramic matrix
composites.
• We have used two different sets of material type. They are: -
a. Caliper: Aluminum 6061 - O
Brake Pad: ASTM Steel A36
Rotor: Cast Iron ASTM A48 Grade 50
b. Caliper: Aluminum 6061 - O
Brake Pad: Steel AISI 4130
Rotor: Titanium Carbide (TiC)
Mechanical Properties
Aluminum 6061– O [CaliperMaterial]
Metric English
Hardness, Brinell 30 30
Ultimate Tensile Strength 124 MPa 18000 psi
Tensile Yield Strength 55.2 MPa 8000 psi
Elongation at Break 25 % 25 %
Modulus of Elasticity 68.9 GPa 10000 ksi
Ultimate Bearing Strength 228 MPa 33100 psi
Bearing Yield Strength 103 MPa 14900 psi

11
Poisson's Ratio 0.33 0.33
Fatigue Strength 62.1 MPa 9000 psi
Machinability 30 % 30 %
Shear Modulus 26 GPa 3770 ksi
Shear Strength 82.7 MPa 12000 psi
ASTM A36 Steel [Brake Pad Set - 1]
Tensile Strength, Ultimate 400 - 550 MPa 58000 - 79800 psi
Tensile Strength, Yield 250 MPa 36300 psi
Modulus of Elasticity 200 GPa 29000 ksi
Bulk Modulus 160 GPa 23200 ksi
Poisson’s Ratio 0.26 0.26
Shear Modulus 79.3 GPa 11500 ksi
AISI 4130 Steel, normalized at1600°F[BrakePad - Set 2]
Hardness, Brinell 197 197
Hardness, Knoop 219 219
Hardness, Rockwell B 92 92
Hardness, Rockwell C 13 13
Hardness, Vickers 207 207
Tensile Strength, Ultimate 670 MPa 97200 psi
Tensile Strength, Yield 435 MPa 63100 psi

12
Elongation at Break 25.5 % 25.5 %
Reduction of Area 60 % 60 %
Modulus of Elasticity 205 GPa 29700 ksi
Bulk Modulus 140 GPa 20300 ksi
Poisson's Ratio 0.29 0.29
Izod Impact 87 J 64.2 ft-lb
Machinability 70 % 70 %
Shear Modulus 80 GPa 11600 ksi
Gray Cast Iron Grade50 [Rotor Set - 1]
Compressive (Crushing) Strength 1130 MPa (164 x 103 psi)
Density 7.2 g/cm3 (450 lb./ft3)
Elastic (Young's, Tensile) Modulus 130 to 160 GPa (19 to 23 x 106 psi)
Elongation at Break 1 %
Fatigue Strength (Endurance Limit) 148 MPa (21 x 103 psi)
Fracture Toughness 650 MPa-m1/2
Melting Onset (Solidus) 1090 °C (1990 °F)
Shear Strength 503 MPa (73 x 103 psi)
Specific Heat Capacity 450 J/kg-K
Strength to Weight Ratio 48 to 57 kN-m/kg
Tensile Strength: Ultimate (UTS) 345 to 410 MPa (50 to 59 x 103 psi)
Tensile Strength: Yield (Proof) 228 MPa (33 x 103 psi)
Thermal Conductivity 46 W/m-K
Thermal Diffusivity 14

13
Thermal Expansion 10.5 µm/m-K
Titanium Carbide[Rotor Set - 2]
Knoop Micro hardness 2400 2000 – 2400
Hardness, Rockwell A 93 93
Vickers Micro hardness 3200 3200
Tensile Strength, Ultimate 258 MPa 37400 psi
Modulus of Elasticity 448 - 451 GPa 65000 - 65400 ksi
Poisson’s Ratio 0.18 - 0.19 0.18 - 0.19
Shear Modulus 110 - 193 GPa 16000 - 28000 ksi
Shear Strength 89.0MPa
@Temperature 1925 °C
12900psi
@Temperature 3497 °F
The assembly (Figure 6) looked like the following upon meshing–
Figure 6

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Outcomes
1. Analysis Type 1 – Mechanical Event Simulation
Material A - Caliper: Aluminum 6061 - O
Prescribed Displacement – 10.666 mm in the negative z-direction
Force – 1000 N in the negative z-direction
Load Curve - Gradual
Surface-to-Surface Contact – Rotor’s outer surface & brake pad’s inner surface
Capture Rate – 10 seconds
The assembly (Figure 1.1) looked like the following before the analysis was
done-
Figure 1.1

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Maximum Displacement – 10.67 mm
Figure 1.2
Maximum Stress – 3207.31 N/mm2
Figure 1.3

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Maximum Strain – 0.0298476 mm/mm
Figure 1.4
Graph (Figure 1.5) shows maximum stress that the disc brake can handle under
the applied load and the given material conditions -
Figure 1.5

17
Factor of Safety – 0.1142
Figure 1.6
The pictures listed above reveal that when the disc brake assembly is at the 5th
step, the stress induced by the brake pad is more than the disc brake assembly at 10th step
i.e. rotor at 5th step has maximum stress of 3207 N/mm2 than at 10th step. This is because
when the rotor undergoes maximum deflection due to the force applied by the brake pad
(5th step) while being fixed at one end, it bends to the extent, which induces more stress
in it. Thus, at the maximum limit (5th step) stress concentration is higher than when it
reaches the 10th step. This disturbs the original configuration of the rotor and it can never
return back to its initial position after continuous and/or repeated use.

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The picture (Figure 1.7) to show that the load curve is gradual loading –
Figure 1.7
Table 1.1
The brake pad’s material is ASTM A36 Steel, which is a ductile material and the
rotor’s material is Cast Iron ASTM A48 Grade 50, which is also a ductile material.
As it is clearly seen from the safety factor plot that the Factor of Safety (FOS) is
0.1142 < 1.0. This shows that the disc brake fails and cannot bear the stress. Also, it can
be seen from the above table (Table 1.1) that the minimum factor of safety for ductile
material under static load condition is 2.0. So, any value below 2.0 shows that, the disc
brake is not in par with the industrial standards. The failure is unavoidable hence;
it is not safe and unacceptable.
The analysis was also done by providing the load curve as repeated and impact
loading. However, this did not affect the outcome of the analysis and the results were the
same as that of the gradual loading. The factor of safety requirements for ductile material
is more for repeated and impact loading i.e. 8 and 12 respectively.

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Load Curve – Repeated Loading
(Figure 1.8)
Load Curve – Impact Loading
(Figure 1.9)

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2. Analysis Type 1 – Mechanical Event Simulation
Material B - Caliper: Aluminum 6061 - O
Prescribed Displacement – 10.666 mm in the negative z-direction
Load Curve - Gradual
Surface-to-Surface Contact – Rotor’s outer surface & brake pad’s inner surface
Capture Rate – 10 seconds
The assembly (Figure 7) looked like the following before the analysis was done –
(Figure 7)

21
Figure 2.1
Figure 2.2

22
Figure 2.3
Graph (Figure 2.4) shows maximum stress that the disc brake can handle under the
applied load and the given material conditions -
Figure 2.4

23
Factor of safety – 0.245508
Figure 2.5
i.e. rotor at 5th step has maximum stress of 4832.57 N/mm2 than at 10th step. This is
because when the rotor undergoes maximum deflection due to the force applied by the
brake pad (5th step) while being fixed at one end, it bends to the extent, which induces
more stress in it. Thus, at the maximum limit (5th step) stress concentration is higher than
when it reaches the 10th step. This disturbs the original configuration of the rotor and it
can never return back to its initial position after continuous and/or repeated use.

24
Figure 2.6
Table 2.1
The brake pad’s material is Steel AISI 4130, which is a ductile material and the rotor’s
material is Titanium Carbide (TiC), which is also a ductile material.
0.245508 < 1.0. This shows that the disc brake fails and cannot bear the stress. Also, it
can be seen from the above table (Table 2.1) that the minimum factor of safety for ductile
material under static load condition is 2.0. So, any value below 2.0 shows that, the disc
brake is not in par with the industrial standards. The failure is unavoidable hence;
it is not safe and unacceptable.

25
3. Analysis Type 2 – Non-Linear Static Stress Simulation
Material A - Caliper: Aluminum 6061 - O
Load Curve – Gradual
Figure 8
Figure 3.1

26
Figure 3.2
Figure 3.3

27
applied load and the given material conditions –
Figure 3.4
Figure 3.5

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can never return back to its initial position after continuous and/or repeated use.
Figure 3.6
Table 3.1
The brake pad’s material is ASTM A36 Steel, which is a ductile material and the
rotor’s material is Cast Iron ASTM A48 Grade 50, which is also a ductile material.
As it is clearly seen from the safety factor plot that, the Factor of Safety (FOS) is
14.7624 > 1.0. This shows that the disc brake do not fail and can bear the stress. Also, it

29
material under static load condition is 2.0. So, any value above 2.0 shows that, the disc
brake is in par with the industrial standards. The failure is avoidable hence; it is
safe and acceptable.
4. Analysis Type 2 – Non-Linear Static Stress Simulation
Material B - Caliper: Aluminum 6061 - O
Load Curve – Gradual
Figure 9

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Figure 4.1
Figure 4.2

31
Figure 4.3
applied load and the given material conditions –
Figure 4.4

32
Figure 4.5
can never return back to its initial position after continuous and/or use.

33
Figure 4.6
Table 4.1
The brake pad’s material is Steel AISI 4130, which is a ductile material and the rotor’s
material is Titanium Carbide (TiC), which is also a ductile material.
47.5378 > 1.0. This shows that the disc brake do not fail and can bear the stress. Also, it
material under static load condition is 2.0. So, any value above 2.0 shows that, the disc
brake is in par with the industrial standards. The failure is avoidable hence; it is
safe and acceptable.

34
Challenges Faced
 In order to reduce the simulation’s complexity, most of the parts, which play no
and/or less role, were removed from the actual assembly (Figure 10).
Figure 10 - Actual Assembly
 To avoid simulating symmetrical parts and reduce simulation time, the assembly
is further divided into half in two different planes (Figure 11). This helped in
bringing down the size of the actual assembly.
Figure 11 - Assembly after removing the parts
 In spite of providing all the necessary requirements for the simulation, the rotor
was unable to rotate in the desired way.
 Certain analyses under particular conditions were not functioning properly
(Figure 7).

35
Figure 12
 Applying different commands and options like remote force, remote loads and
constraints, which we haven’t been acquainted before was one of the major issues.
Formulae
Stress = Force/Area = F/A
Strain = Change in length/original length = dl/l
Young’s Modulus, E = Stress/Strain
Poisson’s Ratio = Lateral Stain /Longitudinal Strain
Factor of Safety = Ultimate Tensile Strength/ Maximum Stress
Computational Problem
Standard Brake Design
Rotor disc dimension = 240 mm (240×10-3 m)
Rotor disc material = Carbon Ceramic Matrix
Pad brake area = 2000 sq.mm (2000E-6 m)
Pad brake material = Asbestos
Coefficient of friction (Wet Condition) = Ranges between 0.07-0.13
Coefficient of friction (Dry Condition) = Ranges between 0.3-0.5

36
Maximum temperature subjected to = 350°C
Maximum pressure subjected to = 1MPa (E6 Pa)
Forces Acting On Rotor Due To Contact with Brake Pads
Tangential force between pad and rotor (Inner face)
FTRI = µ1.FRI
Where, FTRI = Normal force between pad brake and Rotor (Inner)
µ1 = Coefficient of friction = 0.5
FRI = Pmax / 2 × A pad brake area
So, FTRI = µ1.FRI
FTRI = (0.5)(0.5)(E6 N/sq.m) (2000E6 sq.m)
FTRI = 500 N
Tangential force between pad and rotor (outer face), FTRO.
In this FTRO equal FTRI because same normal force and same material
Brake Torque (TB):
With the assumption of equal coefficients of friction and normal forces FR on the inner
and outer faces:
TB = FT.R
Where TB = Brake torque
µ = Coefficient of friction
FT = Total normal forces on disc brake, [FTRI + FTRO]
FT = 1000 N
R = Radius of rotor disc
So, TB = (1000) (120E-3)
TB = 120 N.m
Brake Distance (x) –
We know that tangential braking force acting at the point of contact of the brake, and
Work done = FT. x (Equation A)
Where FT = FTRI + FTRO
X = Distance travelled (in meter) by the vehicle before it come to rest.
We know kinetic energy of the vehicle.
Kinetic energy = (m.v^2) / 2 (Equation B)
Where m = Mass of vehicle
v = Velocity of vehicle
In order to bring the vehicle to rest, the work done against friction must be equal to
kinetic energy of the vehicle.

37
Therefore equating (Equation A) and (Equation B)
FT. x = (m.v^2) / 2
Assumption v = 100 km/hr = 27.77 m/s
M = 132 kg. (Dry weight of Vehicle)
So we get x = (m.v^2) / 2 FT
x = (132×27.772) / (2×1000) m.
x = 50.89 m
Heat Generated (Q) = M.Cр.ΔT J/s
Flux (q) = Q/A W/m²
Thermal Gradient (K) = q / k K/m
Carbon Ceramic Matrix –
Heat generated Q= m*cp*∆T
Mass of disc = 0.5 kg
Specific Heat Capacity = 800 J/kg°C
Time taken Stopping the Vehicle = 5 sec
Developed Temperature difference = 15°C
Q = 0.5 * 800 * 15= 6000 J
Area of Disc = Π * (R^2 – r^2) = Π * (0.120^2 – 0.055^2) = 0.03573 sq.m
Heat Flux = Heat Generated /Second /area = 6000 / 5 / 0.0357 = 33.585 kw/sq.m
Thermal Gradient = Heat Flux / Thermal Conductivity
= 33.582E3/40
= 839.63 K/m

38
Designfor Manufacturing of Disc Brakes
Figure 13

39
Conclusion
From the results of the simulation and the shown computations, it was found that
the braking force and the number of times the brake has been applied, has a direct
relationship on the life and efficiency of the disc brake assembly.
More is the load applied on the brake pad; more is the force transmitted onto the
rotor and enables it to quickly come to rest. The area where the brake pad rubs the rotor
generates more stress and displacement. As the brake pad is comparatively smaller than
the rotor, it has less factor of safety while being simulated. As the braking force is not
directly applied to the rotor, and passed on through the brake pad in between, it is
essential to know about the amount of force applied on the brake pad rather than knowing
about the rotor’s factor of safety.
Non-Linear Static Stress analysis is preferred over Linear Static Stress analysis
because it is a complex approach, which analyses the stress and strain more quickly and
effectively. It is more accurate than the linear analysis because in linear analysis the basic
assumptions are taken into consideration while the same assumptions are being violated
in the non-linear analysis.
The conditions, which are being taken into account when non-linear analysis is
considered, are dynamic loading or time dependent loading and large deformations of the
component, which give the engineers an efficient way to analyze the part or component
more properly and appropriately than the linear analysis.

40
References
Abhang, Swapnil R., & Bhaskar, D.P. (2014, February). Design and Analysis of Disc
Brake, International Journal of Engineering Trends and Technology (IJETT), Volume 8
Number 4 (ISSN: 2231-5381).
Retrieved from
https://www.ijettjournal.org
Aluminum 6061 – O (n.d.). In ASM Aerospace Specification Metals Inc. online.
Retrieved from
http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA6061O
ASTM Grade 50 (ISO Grade 350, EN-JL 1060) Grey Cast Iron (n.d.). In Makeitfrom.com
online.
Retrieved from
http://www.makeitfrom.com/material-properties/ASTM-Grade-50-ISO-
Grade-350-EN-JL-1060-Grey-Cast-Iron/
Bobo (2013, January 15). Hydraulic Disc Brake. GrabCAD.
Retrieved from
https://grabcad.com/library/hydraulic-disc-brake
Strength of Materials Basics and Equations | Mechanics of Materials Equations (n.d.). In
Engineers Edge online.
Retrieved from
http://www.engineersedge.com/strength_of_materials.htm
Titanium Carbide (TiC) (n.d.). In MATWEB Material Property Data online.
Retrieved from
http://www.matweb.com/search/datasheet.aspx?matguid=058d1b70edbd4b2293f2
98c52bbf9818&ckck=1

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