A Numerical Procedure for Designing Profiled Rolling Elements

Abstract

A numerical procedure is developed for studying the pressure and stress distributions resulting from the contact of two elastic bodies. The pressure distribution is obtained by a quadratic programming method such that the resulting displacements satisfy the geometric constraints of the contact problem, and the bodies are in a state of minimum potential energy. The potential method is used to calculate the subsurface stresses due to a constant pressure over a rectangular element. The stresses due to the contact pressure are then obtained by superposition of the contributions of all the elements in the contact area. A small number of elements (5 × 5) provides pressure and stress solutions within two percent of the closed-form solution for quadratic surfaces. For surfaces with abrupt changes in geometry, more elements are required. This procedure can be used to locate an optimum profile for rolling element bearings.