### Projects (1999 - Spring 2008)

Engineering >> Mechanical Engineering

## by Timothy Davis

Submitted : Fall 2015

The project has to do with the workings of a disc brake in contact with a steel disc bolted to a wheel of an automobile; determining the most efficient diameter of the brake and size of the rotor to maximize braking torque. The diameter of the rotor can be placed in terms Radius inner, the distance from the center of the rotor to the area contacted by the area of the brake, and Radius outer, the distance from the center of the rotor to the outer edge. An equation for total torque can be derived from both radii, the angle alpha they make, the maximum pressure exerted on the disc by the brake, and the coefficient of friction between the disc and brake pad. The equation for contact area is given as dA=rdrd(theta), which shows the solution is found via polar integration. The polar integral is set with respect to total torque, resulting in the problem integral rdrd(theta) multiplied by constants U, r, and Pmax from Ri to Ro and then from 0 to alpha. After solving the integral you are left with an equation for total torque in terms of U, Pmax, Ro and Ri.

The solution to part (b) was found using the equation from part (a) when all variables aside from Ri were considered fixed. The value Ri is found in terms of Ro by deriving the equation with respect to Ri and setting the resulting equation equal to zero, solving for Ri. To solve problem (c), substitution was used in the equations found in part (a) and part (b). The values given in problem (c) were plugged in resulting in a value for Ro.  The diameter was then fond by multiplying the radii by two, as brake pads are contacting both sides of the rotor.

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 Advisors : Arcadii Grinshpan, Mathematics and Statistics Scott Campbell, Chemical & Biomedical Engineering Suggested By : Scott Campbell