Chebyshev Polynomials Fits for Efficient Analysis of Finite Length Squeeze Film Damped Rotors

Abstract

The nonlinear behavior of the hydrodynamic forces generated by squeeze film dampers makes dynamical analyses of rotor-bearing systems incorporating such devices a complex and often long task. When steady-state orbits are to be sought, approximate methods (e.g., harmonic balance method, trigonometric collocation method) can be used in order to save computation cost. However, numerical integration in the time domain cannot be avoided if one wishes to calculate transient responses, or to carry out more meticulous analyses concerning the effects of the damper nonlinear nature on the motion of the system. For finite length squeeze film dampers, neither the short nor the long bearing approximations can be suitably applied, and the fluid pressure field has to be estimated numerically, thus rendering rotordynamics predictions even longer and, for engineering purposes computationally prohibitive. To surmount this problem, the present paper proposes a straightforward procedure to derive polynomial expressions for the squeeze film damper (SFD) forces, for given damper geometry and boundary conditions. This is achieved by applying Chebyshev orthogonal polynomial fits over force data generated by numerically solving the two-dimensional pressure field governing equation. For both transient and steady-state calculations, the use of the SFD forces polynomial expressions is seen to be very efficient and precise.