A theory of vibration in brakes is developed, based on the statistical nature of friction. The conditions under which an incipient vibration can develop are shown to be (i), 4 bm > a2L2 where b = elastic constant of the lining in shear, m = mass per unit area, a = change in coefficient of friction with speed, and L = load force per unit area; and also, (ii), a < 0.
Whether noise will result from the vibration depends on how close the natural frequency of the lining, (4 bm – a2L2)1/2/(4πm), is to a frequency of the drum which can be excited by resonance.
Observations on the relative noisiness of four kinds of lining were correlated with measurements of a and b. When the linings are ranked in order of increasing tendency to noise as predicted by the theory, it is found that the order is the same as that observed in brake tests on road cars.