Analysis of a Rigid Cylinder Rolling over a Linear Elastic Half-space in the Full-slip Regime

Abstract

This paper provides an analytical solution for the deformation of an elastic half-space caused by a cylindrical roller. The roller is considered rigid, and is forced into the half space and rolls across its surface, with contact modelled by Coulomb friction. In general, portions of the surface of the roller in contact with the half space may slip across the surface of the half space, or may stick to it. In this paper, we consider only the regime where all of the rollers contact surface is slipping. This results in a mixed boundary value problem, which is formulated as a $2\times 2$ matrix Wiener-Hopf problem. The exponential factors in the Wiener-Hopf matrix allows a solution by following the iterative method of Priddin, Kisil, and Ayton (Phil. Trans. Roy. Soc. A 378, p. 20190241, 2020) which is implemented numerically by computing Cauchy transforms using a spectral method following Slevinsky and Olver (J. Comput. Phys. 332, pp. 290-315, 2017). The limits of the contact region are located a posteriori by applying an optimisation method. The solution is illustrated with several examples, and numerical code to compute the solutions in general is included in the supplementary material.