Rolling contact between dissimilar viscoelastic cylinders

This paper treats the plane problem of rolling contact between linear viscoelastic cylinders with different radii and different quantitative mechanical response. The analysis is an extension of that previously given for the simpler problem of rolling contact between two identical cylinders (or equivalently one cylinder and a rigid half-plane), for which a singular integral equation was derived connecting pressure and normal displacement in the contact region. The present problem is shown to lead to an integral equation of identical form but containing further parameters which reflect the difference in the properties of the two cylinders. A neater construction of the closed form solution of the integral equation is presented and the final formulae are expressed in terms of tabulated functions. An illustration is given for a viscoelastic model with two characteristic times.