Table of Contents
ISRN Tribology
Volume 2014 (2014), Article ID 690147, 13 pages
http://dx.doi.org/10.1155/2014/690147
Research Article

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

Department of Mathematics, Gulbarga University, Gulbarga 585106, India

Received 4 November 2013; Accepted 2 January 2014; Published 15 April 2014

Academic Editors: B. A. Akash and D. Eyheramendy

Copyright © 2014 N. B. Naduvinamani and G. K. Savitramma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.