A General Theory of the Surface Friction of Solids

Abstract

The theory of the surface friction of solids which is developed is based on the assumptions that the adhesion theory of friction is valid and that the asperities, at which contact occurs, deform according to the law stress is proportional to(strain)x. A roughness model is postulated in which the asperities (either spherical or cylindrical) (a) are uniformly distributed over the surface, (b) have the same radius of curvature and (c) all protrude from the surface by the same amount. The analysis leads to the equation F= CLβ relating the frictional force F to the normal load L, an equation which has been found empirically by several investigators. The parameter C is shown to be dependent on the physical properties of the sliding materials, on the degree of surface roughness and on the apparent area of contact, and hence, on the geometrical arrangement of the sliding surfaces, while the parameter β is dependent on the physical properties of the sliding materials only. Amontons' laws of friction (the particular case of the above equation when β is unity) are shown to be interdependent, and when these are obeyed the frictional force is shown to be independent of the degree of surface roughness provided this is not excessive. The influence of surface roughness on the frictional force, found experimentally, is shown to be in accordance with deductions based on the adhesion theory of friction and opposed to deductions based on the Coulomb theory of friction.