Revisiting Rotor Rigid Body Modes: Parametric Study of Stability

Abstract

This paper presents an analytical model of a rigid rotor supported in two fluid film bearings with an emphasis on predicting the instability threshold speed. The factors contributing to the stability of the rotor are discussed and presented graphically using root locus plots. The parametric study of the stability starts from the discussion of the rotor/bearing system with “mirror symmetry”. Three basic cases are considered:(i) Rotor with relatively small gyroscopic effect (small polar moment of inertia) and relatively high transverse moment of inertia. It is found that the pivotal mode instability exists, but the lateral mode controls stability. (ii) Highly gyroscopic rotor (relatively large polar moment of inertia) with also relatively low transverse moment of inertia. It is found that the pivotal mode is infinitely stable and the lateral mode controls stability. (iii) Highly gyroscopic rotor with relatively high transverse moment of inertia. It is found that the pivotal mode exists and controls stability. The lateral mode always exists.Both asymmetry in rotor geometry (location of center of mass with respect to the bearings) and fluid bearing parameters (stiffness, damping) are considered. It is shown that, for a given bearing asymmetry parameter, the maximum stability is achieved when the geometric asymmetry parameter is of equal value. The recommendations on the optimal design from the stability standpoint are given.