An analysis of rough poroelastic bearings with reference to lubrication mechanism of synovial joints

A simplified mathematical model has been developed for understanding combined effects of surface roughness and couple stresses on the squeeze film behaviour of poroelastic bearings in general and that of synovial joints in particular. The cartilage is modeled as poroelastic matrix and synovial fluid as couple-stress fluid. The modified form of Reynolds equation which incorporates the randomized roughness structure as well as elastic nature of articular cartilage is derived using Christensen stochastic theory by assuming roughness asperity heights are small compared to the film thickness. Finite difference based multigrid method is used for the solution of governing equation. A major advantage of this approach is that errors are minimized as the grid size tends to zero. Also, multigrid method has significant savings in computation and achieves results which have higher accuracy compared to traditional methods. It is observed that the effects of surface roughness are considerably pronounced for the poroelastic bearings with couple-stress fluid as lubricant compared to classical case.