Linear Complementarity Framework for 3D Steady-State Rolling Contact Problems Including Creepages with Isotropic and Anisotropic Friction for Circular Hertzian Contact

In this article, the problem of 3D steady-state rolling contacts with dry friction for circular Hertzian contacts is formulated mathematically as a linear complementarity problem (LCP). The complementarity variables are the traction and the relative slip of contact regions, in which a polyhedral friction law is employed. The present work uses the general expressions describing the surface deformations due to uniform traction over a rectangular area on an elastic half-space to derive the influence coefficient matrix for rolling contact problems. Three possible creepage types-that is, longitudinal, lateral, and spin creepage-are considered in this work. Firstly, the numerical results are verified against the existing numerical solutions and good agreement has been found. Secondly, the anisotropic friction is studied by the verified approach. Some numerical examples are provided to illustrate the current LCP method for both isotropic and anisotropic friction in which the combined effects of the three kinds of creepage on the traction distribution are shown.