Lubrication Model of an Artificial Hip Joint: Pressure Profile Versus Inclination Angle of the Acetabular Cup

Abstract

Formulation of a three-dimensional, quasi-static lubrication model of an artificial hip joint is proposed which includes the inclination angle of the acetabular cup. This is performed by deriving a transformed Reynolds equation accounting for this cup tilt angle. The numerical simulation also addresses mass conservation at the location of film rupture. A 3-D spherical representation of the articulating surfaces of the hip prosthesis is mapped onto a cartesian coordinate system of the entire geometry of the “ball and socket” joint. Results include the lubricating fluid pressure distributions for various inclination angles of the acetabular cup demonstrating that the greatest pressures occur for large eccentricities in the upward vertical direction.