The dependence of friction on surface roughness

The variation of the coefficient of friction (0.57 to 0.88) with surface roughness is investigated experimentally in the case of emery paper sliding on various grades of emery paper. It is established that the main variable part of the friction is a function of the ratio of the radii of the emery particles in the two surfaces, and is a minimum when the radii are equal. Theoretically it is shown that the work done in the repeated up-and-down motion of the smaller particles against the elastic backing, as they slide over the larger particles in the opposing sheet, accounts well for the form and magnitude of this friction component, the fraction of the energy lost in the hysteresis being 0.6. The remaining practically constant part of the friction is then 0.42, which is appreciably larger than the friction of sapphire on sapphire, 0.2, but is not far from the value 0.36 determined experimentally for a chip of mineral emery sliding on a smoothed surface prepared on a fresh fracture of the mineral.