A contribution to the theory of friction

The nature of the interaction between a rigid spherical asperity and an asperity governed by the stress/strain law $\text{?}\text{gs = B}\text{?}\text{ge}{}^{\mathrm{n}}$ is studied. The interfacial shear stress is defined by fτ_max where $\text{0 <!-- ? </ 1</mtext-->}$, τ_max being the maximum allowable shear stress at the contact. By integrating the total effect of a population of such surface asperities expressions for the total frictional forces and the total load are derived. The value of the coefficient of friction is thus obtained and the special conditions for perfectly plastic and elastic behaviour are considered. In both cases the friction coefficient is seen to contain a term defined by the deformation and dependent on surface roughness and a term totally defined by ?.