Analysis of elastohydrodynamic lubrication in McKee-Farrar metal-on-metal hip joint replacement.

An elastohydrodynamic lubrication (EHL) analysis was carried out in this study for a typical McKee-Farrar metal-on-metal hip prosthesis under a simple steady state rotation. The finite element method was used initially to investigate the effect of the cement and bone on the predicted contact pressure distribution between the two articulating surfaces under dry conditions, and subsequently to determine the elastic deformation of both the femoral and the acetabular components required for the lubrication analysis. Both Reynolds equation and the elasticity equation were coupled and solved numerically using the finite difference method. Important features in reducing contact stresses and promoting fluid-film lubrication associated with the McKee-Farrar metal-on-metal hip implant were identified as the large femoral head and the thin acetabular cup. For the typical McKee-Farrar metal-on-metal hip prosthesis considered under typical walking conditions, an increase in the femoral head radius from 14 to 17.4 mm (for a fixed radial clearance of 79 microm) was shown to result in a 25 per cent decrease in the maximum dry contact pressure and a 60 per cent increase in the predicted minimum film thickness. Furthermore, the predicted maximum contact pressure considering both the cement and the bone was found to be decreased by about 80 per cent, while the minimum film thickness was predicted to be increased by 50 per cent. Despite a significant increase in the predicted minimum lubricating film thickness due to the large femoral head and the thin acetabular cup, a mixed lubrication regime was predicted for the McKee-Farrar metal-on-metal hip implant under estimated in vivo steady state walking conditions, depending on the surface roughness of the bearing surfaces. This clearly demonstrated the important influences of the material, design and manufacturing parameters on the tribological performance of these hard-on-hard hip prostheses. Furthermore, in the present contact mechanics analysis, the significant increase in the elasticity due to the relatively thin acetabular cup was not found to cause equatorial contact and gripping of the ball.

Analysis of contact mechanics in McKee-farrar metal-on-metal hip implants.

Contact mechanics analysis for a typical McKee-Farrar metal-on-metal hip implant was carried out in this study. The finite element method was used to predict the contact area and the contact pressure distribution at the bearing surfaces. The study investigated the effects of the cement and underlying bone, the geometrical parameters such as the radial clearance between the acetabular cup and the femoral head, and the acetabular cup thickness, as well as other geometrical features on the acetabular cup such as lip and studs. For all the cases considered, the predicted contact pressure distribution was found to be significantly different from that based upon the classical Hertz contact theory, with the maximum value being away from the centre of the contact region. The lip on the cup was found to have a negligible effect on the predicted contact pressure distribution. The presence of the studs on the outside of the cup caused a significant increase in the local contact pressure distribution, and a slight decrease in the contact region. Reasonably good agreement of the predicted contact pressure distribution was found between a three-dimensional anatomical model and a simple two-dimensional axisymmetric model. The interfacial boundary condition between the acetabular cup and the underlying cement, modelled as perfectly fixed or perfectly unbonded, had a negligible effect on the predicted contact parameters. For a given radial clearance of 0.079 mm, the decrease in the thickness of the acetabular cup from 4.5 to 1.5 mm resulted in an increase in the contact half angle from 15 degrees to 26 degrees, and a decrease in the maximum contact pressure from 55 to 20 MPa. For a given acetabular cup thickness of 1.5 mm, a decrease in the radial clearance from 0.158 to 0.0395 mm led to an increase in the contact half-angle from 20 degrees to 30 degrees, and a decrease in the maximum contact pressure from 30 to 10 MPa. For zero clearance, although the contact pressure was significantly reduced over most of the contact area, the whole acetabular cup came into contact with the femoral head, leading to stress concentration at the edge of the cup. Design optimization of the geometrical parameters, in terms of the acetabular cup thickness and the radial clearance, is important, not only to minimize the contact stress at the bearing surfaces, but also to avoid equatorial and edge contact.

Analysis of elastohydrodynamic lubrication in a novel metal-on-metal hip joint replacement.

Elastohydrodynamic lubrication (EHL) analysis was carried out in this study for a novel metal-on-metal hip prosthesis, which consists of a cobalt-chrome alloy femoral head articulating against a cobalt-chrome alloy acetabular insert connected to a titanium fixation shell through a taper. Finite element models were developed to investigate the effect of the pelvic bone and the load on the predicted contact pressure distribution between the two bearing surfaces under dry conditions. The finite element method was used to develop elasticity models for both the femoral and the acetabular components; it was found that the elastic deformation of the acetabular insert was mainly dependent on the load, rather than the detailed pressure distribution. A modified solution methodology was accordingly developed to couple the elasticity models for both the femoral and the acetabular surfaces with the Reynolds equation and to solve these numerically by the finite difference method. It was found that a load increase from 500 to 2500 N had a negligible effect on the predicted maximum contact pressure and the minimum film thickness, due to the relatively flexible and accommodating structure of the acetabular insert. Furthermore, the predicted minimum film thickness was shown to be significantly greater than the simple estimation based on the assumption of semi-infinite solids (mono-block design) using the Hamrock and Dowson formula. The effects of the viscosity of the lubricant and the radial clearance between the femoral and the acetabular components on the predicted lubricating film thickness were investigated under both in vitro simulator testing and in vivo walking conditions.

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.

Elastohydrodynamic lubrication analysis of metal-on-metal hip prostheses under steady state entraining motion.

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.