Elastohydrodynamic lubrication analysis of ultra-high molecular weight polyethylene hip joint replacements under squeeze-film motion.

Elastohydrodynamic lubrication was analysed under squeeze-film or normal approach motion for artificial hip joint replacements consisting of an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup and a metallic or ceramic femoral head. A simple ball-in-socket configuration was adopted to represent the hip prosthesis for the lubrication analysis. Both the Reynolds equation and the elasticity equations were solved simultaneously for the lubricant film thickness and hydrodynamic pressure distribution as a function of the squeeze-film time was solved using the Newton-Raphson method. The elastic deformation of the UHMWPE cup was calculated by both the finite element method and a simple equation based upon the constrained column model. Good agreement of the predicted film thickness and pressure distribution was found between these two methods. A simple analytical method based upon the Grubin-Ertel-type approximation developed by Higginson in 1978 [1] was also applied to the present squeeze-film lubrication problem. The predicted squeeze-film thickness from this simple method was found to be remarkably close to that from the full numerical solution. The main design parameters were the femoral head radius, the radial clearance between the femoral head and the acetabular cup, and the thickness and elastic modulus for the UHMWPE cup; the effects of these parameters on the squeeze-film thickness generated in current hip prostheses were investigated.

Prediction of lubricating film thickness in UHMWPE hip joint replacements.

An elastohydrodynamic lubrication model developed for a ball-in-socket configuration in a previous studies by the present authors (Jalali-Vahid et al., Thinning films and tribological interfaces, 26th Leeds-Lyon Symposium on Tribology, 2000, pp. 329-339) was applied to analyse the lubrication problem of a typical artificial hip joint replacement, consisting of an ultra-high molecular weight polyethylene (UHMWPE) acetabular cup against 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 and under a constant load. A wide range of main design parameters were considered. It has been found that the predicted lubricating film thickness increases with a decrease in the radial clearance, an increase in the femoral head radius, an increase in UHMWPE thickness and a decrease in UHMWPE modulus. However, the predicted lubricating film thicknesses are not found to be sufficiently large in relation to the surface roughness of the cup and head to indicate separation of the two articulating surfaces. It should also be noted that if the design features are unable to secure full fluid film lubrication, it may be preferable to select them for minimum wear rather than maximum film thickness. For example, an increase in head radius will enhance the film thickness, but it will also increase the sliding distance and hence wear in mixed or boundary lubrication conditions. Furthermore, it is pointed out that an increase in the predicted lubricant film thickness is usually associated with an increase in the contact area, and this may cause lubricant starvation and stress concentration at the edge of the cup, and adversely affect the tribological performance of the implant. The effect of running-in process on the lubrication in UHMWPE hip joint replacements is also discussed.