Vibration analysis of hydrostatic gas bearing spindle considering the elastic deformation of rotor

Abstract

In this study, we present the vibration analysis procedure of a hydrostatic gas bearing spindle considering the stiffness and damping of a gas film and the effect of elastic deformation of the components of a rotor. An equation of motion for the elastic vibration of the rotor is formulated using the finite element method and then combined with the rigid-body equation of motion of the housing and the gas film stiffness and damping calculated from the frequency domain analysis of the perturbed Reynolds equation. Since the gas film stiffness and damping are functions of frequency and mode shape, the natural frequency and the damping ratio of each vibration mode are calculated iteratively until both the eigenvalue analysis and gas film analysis are satisfied. The calculated natural frequencies of the gas bearing spindle are found to be in good agreement with the experimental ones. The calculated damping ratios qualitatively agree with the experimental ones with quantitative discrepancy of 30% for the same mode.