Effect of Surface Roughness on the Squeeze Film Lubrication of Finite Poroelastic Partial Journal Bearings with Couple Stress Fluids: A Special Reference to Hip Joint Lubrication

Abstract

A simplified mathematical model has been developed for understanding the combined effects of surface roughness and couple stresses on the squeeze film behavior of poroelastic bearings in general and that of hip joints in particular. The cartilage is modeled as biphasic poroelastic matrix and synovial fluid is modeled as couple stress fluid. The modified form of averaged Reynolds equation which incorporates the randomized roughness structure as well as elastic nature of articular cartilage with couple stress fluid as lubricant is derived. For the study of rough surfaces, Christensen's stochastic theory is used to study the effect of two types of one-dimensional random roughness, namely, longitudinal roughness pattern and the transverse roughness pattern. The averaged film pressure distribution equations are solved numerically by using the conjugate gradient method. It is observed that the surface roughness effect is dominant and pattern dependent and the influence of couple stresses is to improve the joint performance.