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

N B Naduvinamani,G K Savitramma

doi:10.1155/2014/690147

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.

Highlights

Synovial joints which are usually globular in appearance are covered with sponge like material called articular cartilage
In hydrodynamic lubrication the thickness of the fluid film is much larger than the height of surface roughness asperities
The main objective of this paper is to investigate the performance characteristics of finite rough poroelastic partial journal bearing system lubricated with couple stress fluids in Synovial fluid Synovial membrane

Summary

Introduction

Synovial joints which are usually globular in appearance are covered with sponge like material called articular cartilage. The joint cavity is filled with sponge like material called synovial fluid. The surfaces of synovial joints have a high degree of geometrical conformity. Their behavior is governed by articular cartilage which is soft glistening tissue with porous properties and synovial fluid which is dialysate of plasma with concentration of hyaluronic molecules, which do not normally pass through cartilage pores. In hydrodynamic lubrication the thickness of the fluid film is much larger than the height of surface roughness asperities. The pressure in the fluid film is generated because of the relative motion of surfaces and wedge action

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