Question

The cylindrical carbon brushes in a small electric drill motor are 2 mm in diameter and are spring-loaded against the armature with a force of 1 N. The yield stress of graphite is 40 MPa and the wear coefficient for this tribosystem is k 10-7. If the motor commutator is 10 mm in diameter, and the service speed is 8000rpm, calculate the brush lifetime if 2mm can be worn off the brushes before a loss of electric contact occurs

Answer 1

Let 'T' be brush lifetime before it wears off by 2 mm.

Hence from wear coefficient equation we have:

Volumetric loss)/(Adeformed L As complete 2mm is worn off, volumetric loss volume of the brush Now for wear to occur we need to reach yield stress. 1N/ (Ade formed) 40MPa Adeformed (1/40) 10-2 Also, Adeformed 4mm (Assume 'h' to be longitudinal length of the motor/brush and assuming that brush is fully deformed till it's center) h -Adeformed/4mm(1/160 10m L-T * (8000/60) * (π * 10 * 10-3) .. k = (π * h * (1 * 10-3)2)/(T * (8000/60) * (π * 10 * 10-3) * (1/40) * 10-6) . T = ((1 * 10-3)2)/(10-7 * (8000/60) * (10 * 10-3) * 4 * 10-3) . T (60 10)/(800010 4) 60 1000/32s 31.25min

Hence lifetime of brushes is approx 31.25 minutes.