Numerical lubrication simulation of metal-on-metal artificial hip joint replacements: Ball-in-socket model and ball-on-plane model

Long-term successful function of artificial hip joint replacements strongly depends on the design parameters of the bearing such as the diameters of femoral head and acetabular cup and the corresponding radial clearance, which determine the lubrication regime experienced in the prostheses. Generally, there are two types of numerical models for elastohydrodynamic lubrication (EHL) analysis of the bearing in the hip joint replacements: ball-in-socket model and effective ball-on-plane model. As the real hip joint is in ball-in-socket configuration, the ball-in-socket lubrication model should be the reasonable approximation to the real bearing. The ball-in-socket model solves a lubrication problem in spherical coordinates, which means all of governing equations, including Reynolds equation, film thickness and load balance equation, should be written in the spherical coordinate forms. In addition, the calculation of the elastic deformation of the bearing surfaces in artificial joints is not a trial problem. Complex spherical geometries in the joint bearing often require employing the finite-element method to determine/extract the displacement influence coefficients at first, and then the deformation is evaluated through using an equivalent discrete spherical convolution model. Fortunately, the fast Fourier transform-based approach is recently developed to speed up the deformation calculation. In comparison with the ball-in-socket model, the effective ball-on-plane model is simple and easy to conduct EHL analysis. The main characteristic of the effective ball-on-plane model is that the elastic deformation was evaluated under an assumption of semi-infinite solid and certainly without the consideration of the curvature effect associated with the ball-in-socket configuration. In the present study, some typical cases of EHL analysis for hip joint replacements were conducted to systematically demonstrate the capability of these two models. It was found that both models were able to provide quite close results in most situations, and the difference may only take place when the head is positioned near the edge of the cup bearing surface.