Hysteresis and lubricated rubber friction

The effect on the hysteresis coefficient of a scaling down of surface texture is examined theoretically. It is shown that a uniform reduction in scale, where in particular the number of asperities per unit area increases as the square of the scale factor, has no effect on the magnitude of the hysteresis peak although the velocity at which the peak occurs decreases. Temperature is assumed to be unaltered by the scale change. This result indicates a method of deciding whether or not the so-called adhesion component of wet rubber friction is substantially hysteretic in character. The result may also be of use more generally in experimental work since macroscopic surfaces are easier to simulate than microscopic surfaces.Some interesting general formulae are presented for the hysteretic friction coefficient. In particular it is shown that, for rubber on a rigid rough surface at very high pressures, this quantity is given by an integral of the product of the loss modulus of the rubber, the spectral density function for the rigid surface and other trivial factors, or alternatively as an integral over the autocorrelation function for the surface and other factors.