Paper Title
Mathematical Study for Misalign Journal Bearing System

Abstract
The bearing when loosely connected may influence bearing performance and its life. The paper describes a theoretical analysis for predicting bearing performance parameters of a loosely fitted hydrodynamic journal bearing system. Such bearing may cause misalignment either on a horizontal or vertical axis or on both axis of the bearing, depending upon the degree of severity of looseness. The study considers either slight tilt in the bearing axis on its axial (vertical) plane or twist on horizontal plane or twist on horizontal plane in terms of misalignment parameters τ and ∆ respectively. The governing Reynolds equation is solved using finite element method (FEM) for the lubricant flow field in the clearance space of the journal bearing system by Galerkin’s approach. The solution considers quadrilateral elements and the system equation is solved after applying a suitable boundary conditions. In the solution, the equilibrium conditions are established using iterative Newton-Rapson method. The paper discusses the effect of misalignment parameters on static performance parameters, which includes maximum pressure, minimum fluid film thickness, eccentricity ratio, attitude angle, frictional coefficient and fluid-film resisting moment caused due to misalignment for a specified range of speed. The result indicates a significant influence on static performance and therefore necessitates in depth further study. Keywords - FEM, hydrodynamic journal bearing, misalignment, Reynolds equation