EXACT SOLUTIONS FOR ROLLING CONTACT BETWEEN VISCOELASTIC CYLINDERS

Abstract

Rolling contact between viscoelastic cylinders, between a viscoelastic cylinder and rigid half-plane, and between a rigid cylinder and viscoelasitic half-plane, is analysed on the assumption of steady rolling and zero shear traction in the contact region, and neglecting inertia effects so that slow rolling in some sense is implied. These problems are reduced to similar singular integral equations for the contact pressure distribution, with the kernels involving both strong and weak singularities and bounded parts. With the viscoelastic behaviour described in terms of a finite spectrum of characteristic times, differential relations between the different parts of the integral are obtained and using this property a method is developed to determine the finite Hilbert transform of the pressure distribution from the integral equation. The contact pressure is then obtained by the standard inversion formula and the resulting Hilbert transforms are expressed in closed form.