University of Puerto Rico

Mayaguez Campus

Department of Mechanical Engineering

Design of a Brake Disc

Tania M. Ortiz Menéndez

Liza M. Cardona Gonzalez

Ramón Torres

Objectives

Design of the rotor component for a disc brake system using load analysis, stress

analysis and fracture analysis system approach.

Description

A caliper disc brake is the most common type of disc brakes used in modern cars. It is

compound of a piston, a caliper, the brake pads, the rotor and the hub. The single compound

that we will be designing on is the rotor. The rotor is the compound that receives the force

applied by the brake pads when the brake pedal is pressed and the piston is activated

producing the caliper to close.

Design Details

We must first understand what are its function and the parameters that are important

in its use. We need to know all of these things in order to make a good design. What do braking

systems really do? The brakes of your car convert the energy of motion into heat. In other

words the brakes in your car are responsible for converting kinetic energy into thermal energy.

One important thing to take into consideration for our design is that small changes in the speed

have a huge impact on the brake temperatures. This is an index that will have to watch very

carefully when we take into consideration our design. There are many forces that can stop our

car. An example of this can be wind or gravity. We need brakes to assist us in the process of

stopping the car. The Brake system is composed of many parts. The most important are the

Brake Pedal, The Master Cylinder, Calipers, The Pads and the Rotor. We will briefly analyze the

role of each of these parts and their role in the process of stopping our car.

We will first start off with an analysis of the brake pedal. The purpose is to harness and

multiply the force exerted by the driver's foot. For the analysis of the Pedal we assumed an

input driver force of 90lb a pedal ratio of 4:1. We then multiplied the force by the ratio. The

resulting force gave us a value 360 lbf. The brake pedal itself cannot take the car to a complete

stop. The rest of the components are very important. The only modification that we can make

to the brake pedal is to change the pedal ratio. For our project we assumed a pedal ratio of 4:1.

Another important component in the design of our brake disk is the master cylinder.

The master cylinder is responsible for converting the amplified force from the brake pedal into

hydraulic pressure. It consists of a cylinder, a piston, break pedal output rod on one side and

brake fluid on the other side of the cylinder. As the pedal assembly output rod pushes on the

piston, the piston moves within the cylinder and pushes against the fluid, creating hydraulic

pressure. We calculate the pressure generated by the master cylinder by dividing the force

created by the pedal divided by its area. For the master cylinder we used dimension of 0.7

inches of diameter. The area of the pedal was . And the force of the pedal as

mentioned before was 360 lbf. The calculation gave us a value of 935.44psi. This component is

also very important. But this alone does not stop the car. There are some things that we can

change in our master cylinder in order to obtain the performance that we want. If we increase

its diameter it will decrease the amount of pressure generated. Even the smallest change in

diameter makes a big difference in the performance of the cylinder.

Our third component is the calipers of the car. The caliper is very similar to a piston with

pressurized fluid on one side. The caliper uses hydraulic force on the input to create mechanical

work. The caliper does a squeezing or clamping force of the brake disk. We calculated this

clamping force by multiplying the pressure of the cylinder by the area of the cylinder. This

calculation gives us 5877.6 lb. The clamping force of the caliper is very sensitive to changes in

the diameter of the caliper.

The fourth component that we will analyze is the brake pad. It is a big misconception

that changing brake pad material will magically decrease your stopping distances. There is

actually no relationship between each other. The brake pads squeeze the rotor with the force

that is generated by the calipers. To analyze the brake pads we needed a friction coefficient.

We took the value of .

And last but not least the Rotor. The rotor also assists in the process of stopping the car,

but it does not stop it. The rotor plays 2 important roles. It acts like a frictional interface for the

brake pads. It reacts to the output by absorbing the torque created. For the analysis we

assumed a value of 2644.9 ft-lb. The rotor must also serve the purpose of absorbing the heat

that is generated by the rubbing of the brake pads against the rotors face.

For our analysis we used the values of and an internal diameter of

we then used an equation to calculate the torque that is generated in the rotor. The

calculation of gave us about 32,796 ft-in. the calculation of J (polar inertial moment)

gave us 6613.4 . In SI units the calculation of gave us a value of 30.75 psi.

For our design material we have two choices a ceramic material and gray cast iron. We

choose gray cast iron as the appropriate material for it wear resistance and hardness. Also it

absorbs and dissipates heat well to cool the brakes. (Refer to Appendix B).

After the material is selected a fracture analysis can be done. For the design the fracture

analysis was performed for the static and dynamic aspects. For the static aspect we assumed a

value of 2.5 for the stress concentration factor. The calculated value for the safety factor using

the Internal Friction Theory for a brittle material and the ultimate tensile and compressive

strength for the material properties (Refer to Appendix C) is 30.81. Also a value of 2.2 was

assumed for the stress concentration factor on the dynamic aspect. We used the alternating

forces exerted in the disc. The forces fluctuate from 0 to 437289.8 lb. The τ(amplitude) of

437289.8 lb and the τ(mean) of 218644.9 lb were corrected with the dynamic stress

concentration factor. With the corrected values the principal stresses were calculated. The

values for σ1(amplitude) and σ1(mean) were used to calculate the safety factor with the

Modified-Goodman equation. The calculated value for the dynamic safety factor is 5.896 .

Conclusions

With this project we achieved a safe, durable and viable design for a rotor component in

a disc brake system taking in consideration the forces exerted for all the components in the

brake system. In our fracture analysis for the static and the dynamic approach we found that

our safety factor numbers are elevated. With this we demonstrate that disc brakes do not

fracture. That is because the force exerted in the disc is a compressive force. That’s why the

materials used for the manufacturing of brake disc are brittle. Also for that reason we calculate

a big endurance limit.

Appendix A

Calculations:

Pedal

Input driver force=100lb

Ratio 6:1

Master Cylinder

Calipers

4 pistons

Pads

=

Rotor

Material: Gray Cast Iron

Assumed:

Internal Friction Theory (IFT)

Fracture Analysis Dynamic

Endurance Limit

Appendix B

Graph for the material Selection

Graph Representing the Alternating Forces

Appendix C

Subcategory: Ferrous Metal; Gray Cast Iron; Metal

Key Words: Grey Cast Iron, ASTM A 48 Class 40, cast irons

Component    Wt. %

C 3.25 - 3.5  Cr 0.05 - 0.45  Cu 0.15 - 0.4  

Component    Wt. %

Mn 0.5 - 0.9  Mo 0.05 - 0.1  Ni 0.05 - 0.2  

Component    Wt. %

P Max 0.12  S Max 0.15  Si 1.8 - 2.3  

Material Notes: Carbon listed in the composition above is the total carbon. Can be oil quench hardened from 860°C to attain a Rockwell C 50 minimum surface hardness. Data provided by the manufacturer, Siltin Industries, Inc

Physical Properties Metric English Comments

Density 7.15 g/cc 0.258 lb/in³  Typical for Gray Cast Iron

Mechanical Properties

Hardness, Brinell 183 - 234 183 - 234  Hardness, Knoop 258 258  Converted from Brinell hardness.Hardness, Rockwell B 97 97  Converted from Brinell hardness.Hardness, Rockwell C 20 20  Converted from Brinell hardness.Hardness, Vickers 246 246  Converted from Brinell hardness.Tensile Strength, Ultimate Min 276 MPa Min 40000 psi  Ultimate Compressive Strength

Min 1034 MPa

Min 150000 psi

 

Machinability 0 % 0 %  Very good machinability. No numerical rating available.