A pad-disk brake system was selected for a 300 kg motorcycle. The brake pads were made of carbon graphite reinforced cast iron, measuring 52 mm x 127 mm x 12.6 mm thick. When sliding against the iron disk, the pads had a friction coefficient of 0.3 and wear coefficient of 3 x 10^-6. The brake caliper applies 300 N of force to press the pads against the disk. The problem is to determine how many stops the motorcycle can make from 150 kph to a complete stop before the pads wear away.

1. A pad-disk brake system with cast Iron disk and carbon graphite metal reinforced brake pads of
approximate dimensions 52 mm width x 127 mm length x 12.6 mm thickness with hardness H =
200 MPa was selected for a 300 kg motorcycle. When running against the iron disk, a pad
exhibits friction coefficient 0.3 and wear coefficient 3 x 10^-6. The brake caliper visible in the
first two figures presses two brake pads with 300 N normal force against the iron brake disk,
sandwiched between the pads. Friction sliding of two pads against a brake disk on each
motorcycle wheel converts the motorcycle's kinetic energy to heat. Assume the brakes
decelerate the motorcycle from 150 kph to a complete stop. How many of these stops can be
expected from this brake system, before the pads wear away? Hint: Pad-disk sliding at the brakes
consumes the motorcycle's energy. From pad sliding distance get wear volume, then compare to
pad volume
Solution
Here the normal force is F , friction force = uN where u is coefficient of friction , N is Normal
reaction.
Now we will take the moment about the centre of the wheel.
And calcualte the net torque.
Now we have to apply the Uniform wear condition
According to uniform wear condition
T = uFRm ---(1) where T is net torque , F is force and Rm is mean radius.
And we calculate the total energy dissipiation from change in kinetic energy.
As it is mentioned that the initial velocity is 150kph and finally it stops. = 1/2MV2 ----- (2)
where M is mass and V is velocity.
Therefore we have total energy and energy dissipiation in one stop i.e from torque calculations.
Now we will divide the equation (2) by (1).
Hence we can find out that how many of the stop it will take to wear away the pad.