Finite element analysis of elastohydrodynamic lubrication in an artificial hip joint under squeeze film motion using fluid–structure interaction method

Abstract

Classical approach for elastohydrodynamic lubrication problems contains solution of Reynolds and elasticity equations simultaneously, where elasticity equation was derived based on semi-infinite solid assumption. Fluid–structure interaction method which uses finite element formulation is another alternative approach for elastohydrodynamic lubrication problems. Present study contains two sections: first finite element method was used to evaluate accuracy of semi-infinite assumption for deformation in an artificial joint cup for a verity of material and geometrical properties. Then fluid–structure interaction method was used to simulate an artificial hip joint lubrication under squeeze film motion and efficiency and accuracy of this method was speculated by comparing the results to a previously done work. In the first section, deformation of a cup under Hertzian contact was calculated by finite element software ADINA. Various combinations of cup thickness, material properties, and dimensions of contact ellipse were modeled and results compared to the answer of semi-infinite assumption and column method for the same problem. Then a ball-in socket configuration for an artificial hip joint was modeled by an ultra-high-molecular-weight polyethylene cup and a Stainless Steel ball in the same software. Fluid film pressure and thickness were extracted from the results and compared to a previous study. Results for deformation of cup show that semi-infinite assumption and column method do not lead to acceptable accuracy for geometrical conditions of artificial hip joint. For fluid–structure interaction analysis of squeeze film motion, at first time steps, pressure distribution shows differences with the previous work, but at last time steps, fluid film pressure matches the previous study. For all time steps, film thickness of fluid–structure interaction method is higher than what was reported by previous work. The main reason is that no mesh independency check was performed for previous work, while for this study mesh independency of answers was analyzed by creating two other models.