Prediction of lubricating film thickness in a ball-in-socket model with a soft lining representing human natural and artificial hip joints

A simple ball-in-socket model was adopted in this study to analyse the lubrication problem of both natural hip joints and their artificial replacements. A compliant layered bearing surface was considered to represent articular cartilage as found in the natural synovial joint and also in the artificial hip replacement where an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup was employed. The cup was assumed to be stationary while the ball was assumed to rotate at a steady angular velocity and under a constant load. A successful numerical method developed in a previous study by the present authors was used to solve the Reynolds equation in spherical coordinates, simultaneously in conjunction with the corresponding elasticity equation based upon the constrained column model. Numerical solutions thus obtained enabled general formulae to be fitted for both the minimum film thickness and the central film thickness, based upon the prediction from the equivalent ball-on-plane model and the half-contact angle. These formulae were then applied to predict the lubricating film thickness in both natural hip joints and their artificial replacements.