Simulation of wear in a rolling–sliding contact by a semi-Winkler model and the Archard’s wear law

The purpose of this work is to develop a method of controlling the friction and wear affecting the contact pair in rolling–sliding contact. The scope is in small-scale tribology by which mechanism of wear would be clarified on first hand by Archard’s law. The prerequisite for using Archard’s wear law in a simulation is proper piecewise linear modelling of contact at the substructural level, including prediction of deformations and relative motions for every part of the contact. The deformation level at the real contact depends on such parameters as normal forces, relative motions, geometry, surface tractions, etc. There is a need for a simulation tool that explains the role of these parameters. The present work simulates the well-known disc-on-disc test for dry wear. The deformation field due to normal load is solved by the Winkler mattress method. The tangential stress field is subsequently calculated knowing the normal pressure field, the penetration and the general rigid body movement for every subregion. The influence functions from potential theory are used to model the tangential traction and displacement field in the contact. The special computing excludes the need for the creep constants that depend on the Poisson’s ratio and the result is not dependent on the shape of the contact area. Every rectangular cell is tested whether it is subject to sliding. The sliding distance is calculated by subtracting elastic displacements from the relative motion of the rigid body. The elastic deflections are reversible and exist both under the sticking region in contact and also in the sliding region. A comparison of the results of a simulation and a disc-on-disc test is presented. Good agreement was found for both wear and rolling friction at different load and creep levels.