Stability and Unbalance Analysis of Rigid Rotors Supported by Spiral Groove Bearings: Comparison of Different Approaches

Abstract

The dynamic behavior of spiral-grooved gas bearing supported four degrees-of-freedom (DOF) rotors is investigated by means of linearized bearing force coefficients and full time-integrated transient analysis. The transient method consists of a state-space representation, which couples the equations of motion with the compressible thin-film fluid equation. The linearized method is based on the perturbation analysis around a given eccentric shaft position ε, allowing to compute the static and linear dynamic bearing force coefficients at different excitation frequencies. The two methods are compared for a variation of test rotors and bearing geometries in a given compressibility number interval of Λ=[0,40]. The limitations and weaknesses of the linearized model are presented. It is shown that shafts with two symmetric herringbone-grooved journal bearings (HGJBs) have their maximum stability and load capacity if the center of gravity lays in the middle of the two bearings. For symmetric rotors (la/lb=1), the two rigid modes, cylindrical and conical, are present and are influenced by the mass and transverse moment of inertia independently. For asymmetric rotors (la/lb<1), the stability region decreases, and the modes have a mixed shape. It is no longer possible to clearly distinguish between pure cylindrical and pure conical mode shapes. The two methods predict the critical mass and critical transverse moment of inertias within a difference of <7%. A quasi-linear unbalance module for rigid gas bearing supported rotors is presented, which considers eccentricity-dependent bearing force coefficients, allowing to speed up the unbalance response analysis by 4 orders of magnitude. The unbalance module is compared with the full transient orbital analysis, suggesting that the quasi-linear module predicts the nonlinear unbalance response with <6% deviation for amplitudes up to ε<0.5 within the complete compressibility number range.