Effects of The Christensen’s Theory on Performance Characteristics of Three-lobe bearings Lubricated with Micro-polar Fluids

It has been generally assumed that bearing surfaces can be represented as mathematically smooth planes. However, it seems too unrealistic when the characterization of the topography of solid surfaces is of interest in the study of a number of interfacial phenomena such as friction and wear, and mechanical contact resistance. In this paper, attention is focused by considering rough three-lobe bearings, which are lubricated with non-Newtonian micro-polar fluids. Equations of lubrication, constitutive equations, and, boundary conditions are derived for micro-polar fluids. These fluids respond to micro-rotational motions and spin inertia. Therefore, it can support couple stress anddistributed body couples. The generalized average Reynolds-type equation is derived for the rough three-lobe bearings and stochastic Christensen’s model has been applied in order to model such rough surfaces. A stochastic finite element model of three-lobe hydrodynamic bearings with rough surfaces (longitudinal and transverse roughness), considering lubricant film thickness as a stochastic variable was formulated. The performance of the rough three- lobe beatings is compared with corresponding smooth three-lobe bearings. The expressions for the load carrying capacity, frictional force, and the coefficient of friction are studied. The numerical computations, finite element method, of the results show that the surface roughness has not generally a profound effect on pressure distributions and performance characteristics. So, this model would be recommended to be use in modeling roughness surfaces with high frequencies.