Comparison of numerical methods for elastohydrodynamic lubrication analysis of metal-on-metal hip implants: Multi-grid verses Newton-Raphson

Abstract

Elastohydrodynamic lubrication (EHL) of a metal-on-metal hip implant was investigated under quasi-static operating conditions. Various numerical methods, such as Newton-Raphson (N-R), multi-grid (MG), multi-level multi-integration, and fast Fourier transform technique (FFT), were considered and compared in terms of the convergence and accuracy of the numerical solution. It was found that the numerical convergence for the MG method was much faster, and consequently the computational time required was significantly lower than the N-R method. This feature was particularly evident, when a tighter tolerance was specified on the pressure iteration and a high load or low viscosity was considered. Furthermore, the multi-integration method was found to be more effective, only when four-level grids were considered and compared with the FFT technique. It was concluded that the MG method has the potential to be applied efficiently and effectively for modelling realistic EHL problems of artificial hip joints such as under transient conditions of walking and when the surface topography is considered.