Dynamic analysis of rotors supported on journal bearings by solving reynolds equation using pseudospectral method

Abstract

In the dynamic analysis of rotors supported on journal bearings, Reynolds equation is solved at each time step. In the present work, Reynolds equation is solved using pseudospectral method to estimate fluid film forces. Fluid pressure is approximated by a finite number of Chebyshev polynomials along the bearing length and Fourier series along the bearing circumference. Fluid domain is reduced to a finite set of algebraic equations with pressure at specific grid points as variables using collocation method. Unlike in finite element method (FEM), spectral method uses higher order global basis functions which guarantee high accuracy and lower computational time. A comparison study of fluid film forces for a bearing geometry with an L/D ratio of 0.25 with short bearing theory, solution of Reynolds equation using FEM and pseudospectral method (PSM) is presented. Two different elements are studied in FEM: 3 node triangular element and 9 node quadrilateral element. Computational time taken for one time pressure calculation is also compared. Pseudospectral method is found to be efficient than FEM for a converged solution.