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

Abstract

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.

Friction of total hip replacements with different bearings and loading conditions

“…2,4,15 An in vitro study of novel differential hardness ceramic-on-metal (CoM) implants have shown reduced wear rates compared with MoM bearings. 16 Theoretical lubrication studies have proposed that MoP bearings operate towards the boundary end of the mixed lubricating regime, 17 suggesting that the load is primarily carried by solid asperity contact. Further studies examining MoM and CoC bearings have shown that both operate towards the fluid film lubrication end of the mixed lubricating regime, where the bearing surfaces are mostly separated by the lubricant.…”

Transient viscoelastic lubrication analyses of UHMWPE hip replacements

“…In all the previous studies [3,[24][25][26][27][28][29] that investigated the time-dependent lubrication performance of UHMWPE hip replacements, only the Reynolds equation considered the effects of the previous time instant on the present instant. The deformation at a given instant was determined by the hydrodynamic pressure of that single instant.…”

“…The reason for employing the simple constrained column model was mainly because there were no full-field analytical solutions for the mechanical deformation of the ball-in-socket geometry. This limitation was overcome by Jagatia and Jin [3,4] using the finite element method (FEM) to calculate the elastic influence coefficients. However, the calculation process was complex and time consuming.…”

Theoretical studies of elastohydrodynamic lubrication of artificial hip joints

“…Under certain conditions, the transient lubrication analysis can be decoupled into a steady-state entraining (section 4.2) and a time-dependent squeeze-film problem. An elastohydrodynamic squeeze-film lubrication analysis has recently been carried out by Jagatia et al [43] for UHMWPE-onmetal hip implants, following on the earlier studies by Mabuchi and Sasada [44] and Wang et al [45]. Such a simplified analysis can be particularly useful for examining the lubrication of hip joints during the stance phase, as the speed encountered is usually very low, and under microseparation condition between the femoral head and the cup [46].…”