Simple analytical description of contact pressure and wear evolution in non-conformal contacts

The present study proposes an analytical approach to describe contact pressure and wear evolution in line and point contacts. Starting from the unworn condition, described by Hertz theory, modifications of geometry and pressure distribution due to wear are included. Under the basic assumption of parabolic wear and pressure profiles, derived from Finite Element simulations, simple equations governing the phenomenon are derived, where the maximum wear depth evolution is described by a first order differential equation which can be easily solved. Interestingly, the maximum pressure remains dependent on the radius of curvature at the nominal contact point according to Hertz theory, but pressure is not null at the extremes of the contact region. The contact width can be derived from equilibrium conditions and wear law. The reliability of the procedure is proved by the perfect agreement with Finite Element simulations.