Squeeze film dampers supporting high-speed rotors: Fluid inertia effects

Abstract

This work represents closed-form analytical expressions for the operating parameters for short-length open-ended squeeze film dampers, including the lubricant velocity profiles, hydrodynamic pressure distribution, and lubricant reaction forces. The proposed closed-form expressions provide an accelerated calculation of the squeeze film damper parameters, specifically for rotordynamics applications. In order to determine the analytical solutions for the squeeze film damper parameters, the thin film equations for lubricant are introduced in the presence of the influence of lubricant inertia. Subsequently, two different analytical techniques, namely the momentum approximation method, and the perturbation method are applied to the thin film equations. Moreover, the solution for the lubricant flow equations are analytically determined to represent closed-form expressions for the hydrodynamic pressure distribution and the velocity component profiles in squeeze film dampers. Additionally, the expressions for the hydrodynamic pressure distribution are integrated over the journal surface, either numerically or analytically by using Booker’s integrals, to develop expressions for the fluid film reaction forces. Lastly, the developed squeeze film damper models are incorporated into simulation models in Matlab and Simulink®, and the results are compared against a well-established force coefficient model to verify the accuracy of the calculations. The results of the simulations verify the effect of the lubricant inertia components, namely the convective and temporal (i.e., unsteady) inertia components on the squeeze film damper dynamics, including hydrodynamic pressure distribution and fluid film reaction forces. Additionally, the simulation results suggest a close agreement between the proposed models and the results in the literature.