A modification on velocity terms of Reynolds equation in a spherical coordinate system

The widely-used Reynolds equation to simulate fluid lubrication in hip implants by Goenka and Booker has velocity terms accounting just for the rotational motion of the femoral head. The present study, therefore, hypothesizes that modifying velocity terms being used in Reynolds equation, which capture both translation and rotation of the femoral head, can affect resultant fluid pressure, fluid-film thickness and friction force. To assess such hypothesis, a computational model of a hip implant based on multibody dynamics methodology and Reynold equation is developed. It is illustrated that modifying velocities can cause friction forces to increase, significantly, compared to Goenker and Booker's. Moreover, the minimum film thickness and maximum fluid pressure undergo notable decreases during the swing and stance phases, respectively.