Numerical solutions for the elastic deformation of spherical bearing surfaces of metal-on-metal hip joint implants

On the elastohydrodynamic lubrication analysis, one of the most time-consuming issues is the calculation of surface deformation. Two methods are usually adopted to fasten the calculation: the multi-level multi-integration (MLMI) and the fast Fourier transform (FFT). However, in spherical models such as for hip joint replacements, the finite-element method has to be employed instead of analytical formulations to determine the influence coefficients. It limits the coarsest grid to 60 x 60 points to ensure numerical accuracy. This limitation prevents the MLMI to achieve high performance. Therefore, a combined MLMI and FFT method is proposed. The basic idea is to replace the direct summation on the coarse grids in the MLMI by the FFT algorithm. The combined method is validated by comparing to the individual MLMI and FFT. The combined method is found to perform fastest. In solving a quasi-static elastohydrodynamic lubrication solution, approximately 65 per cent less CPU time is required on grid 512 x 512, and the accuracy is not affected. For the usual semi-infinite plane models, sometimes a large number of levels can cause a lot of additional operations and storage space when translating data between the levels. The combined MLMI and FFT method can be an alternative way to choose the coarse grid more flexibly, reduce the number of grid levels, and optimize the computing performance.