A simple ball-in-socket configuration was considered in this analysis of the lubrication of a typical artificial hip joint replacement, consisting of an UHMWPE acetabular cup and a metallic or ceramic femoral head. The cup was assumed to be stationary whilst the ball was assumed to rotate at a steady angular velocity under a constant load. The Reynolds equation was solved in spherical coordinates, simultaneously in conjunction with the corresponding elasticity equation based upon the constrained column model, using the Newton-Raphson method. The prediction of the film thickness and pressure distribution has been performed for a typical example of UHMWPE total hip joint replacements under average kinetic conditions during walking. An equivalent ball-on-plane model using an effective radius was also used to predict the minimum film thickness and make comparisons with the ball-in-socket model for this particular example. The numerical method has been found to be quite successful under realistic conditions experienced in current ultra high molecular weight polyethylene (UHMWPE) total hip joint replacements. The predicted minimum film thickness for the example chosen is about 15% smaller than that based upon the corresponding ball-on-plane model, due to the higher-pressure distribution around the cup in order to balance the applied load ad consequently the smaller film thickness for the ball-in-socket model. The results obtained in this study show that a significant increase in the minimum film thickness is achieved along with a corresponding fall in pressure when the elastic deformation of the UHMWPE bearing surface is considered. However, the predicted lubricant film thickness is not greater than the surface roughness of the UHMWPE bearing surface and hence asperity contact, though reduced by an improved fluid film, will still exist.
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