Approximating fluid bearing characteristics using polynomials for the nonlinear dynamics of rotating machines

Modeling the nonlinear dynamics of rotors supported by finite length journal bearings is of great importance in various engineering applications. In this study, four-dimensional polynomial functions are evaluated to represent the nonlinear hydrodynamic force based on a previously evaluated database. These functions are then used to model the dynamics of flexible rotor/bearing systems. The quasi statics and dynamics of rotor-bearing systems are investigated, and the results are compared with the numerical solution obtained by solving the Reynolds equation at each timestep. The findings indicate that the current analysis yields favorable agreement with the direct solution of Reynolds equation in both perturbation analysis from the equilibrium position and dynamic analysis. Moreover, the analysis reveals that the computational time required to solve the dynamics of rotor-bearing systems is significantly lower than that of solving Reynolds equation at each timestep to acquire the bearing forces.