A Numerical Solution for Layered Solid Contact Problems With Application to Bearings

Presented herein is a method of solution for three dimensional counterformal contact problems involving layered solids. Based on the generalized Boussinesq solution for a layered half space, displacement and stress coefficients are formulated for a uniformly distributed load applied over a rectangular area on the surface of a layered half space. A precise analytical solution has been developed to find the surface pressure, contact area, approach and subsurface stresses for contact of arbitrary surface shapes. Numerical results have been obtained for the indentation of a second order surface with a layered solid for the case the layer to substrate shear modulus ratio equal to 3, which simulates the contact of a steel rolling element with a steel bearing ring supported by aluminum substrate (or housing) in a transmission system.