A general elastohydrodynamic lubrication analysis of artificial hip joints employing a compliant layered socket under steady state rotation

A general numerical methodology was developed in the present study to analyse the elastohydrodynamic lubrication problem of a compliant layered socket against a rigid ball under steady state rotation representing flexion and extension during walking, with particular reference to artificial hip joint replacements. The general numerical methodology consisted of using the Newton-Raphson method to solve the Reynolds equation, simultaneously with the full elasticity equation using the finite element method in combination with the fast Fourier transform technique. Two specific types of acetabular cup were considered, one with ultra-high molecular weight polyethylene used in current total hip joint replacements, and one with polyurethane proposed for compliant layered 'cushion form bearings' for future developments. The film thickness and the pressure distribution for both cups were obtained under a wide range of operating conditions. The predicted central or average film thicknesses within the contact conjunction were compared with those estimated from various simplified theories available in the literature. A simple analytical methodology was consequently established to estimate the lubricating film thickness in a compliant layered socket, based on the corresponding ball-on-plane model and the consideration of the curvature effect.