The elastohydrodynamic lubrication problem of metal-on-metal hip joint replacements was considered in this study. A simple ball-in-socket configuration was used to represent the hip prosthesis. The Reynolds equation in a spherical coordinate was adopted for the fluid-film lubrication analysis, to account for the ball-in-socket geometry. The corresponding elastic deformation was calculated by means of the finite element method in order to consider the complex ball-in-socket geometry as well as the backing materials underneath the acetabular cup. Both the Reynolds and the elasticity equations were solved simultaneously using the Newton-Raphson finite difference method. The general methodology developed was then applied to a recent experimental prototype metal-on-metal hip implant. It was shown that the backing materials underneath the acetabular cup had little influence on the predicted contact pressure and the elastic deformation at the bearing surfaces for this particular example. Both the film thickness and the hydrodynamic pressure distributions were obtained under various loads up to 2500 N. The predicted minimum lubricating film thickness from the present study was compared with a simple estimation using the Hamrock and Dowson formulae based upon an equivalent ball-on-plane model and excellent agreement was found. However, it was pointed out that for some forms of metal-on-metal hip prostheses with a thin acetabular cup, a polyethylene inlay underneath a metallic bearing insert or a taper connection between a bearing insert and a fixation shell, the general methodology developed in the present study should be used and this will be considered in future studies.
A numerical study of non-Newtonian transient elastohydrodynamic lubrication of metal-on-metal hip prostheses
