INVESTIGATION OF THE STABILITY AND STEADY STATE RESPONSE OF ASYMMETRIC ROTORS, USING FINITE ELEMENT FORMULATION

The motion of a rotor of which both the bearings and the shaft cross-section are asymmetric is generally governed by ordinary differential equations with periodic coefficients. In this paper, modifications are made to incorporate the effect of shaft asymmetry into an existing finite element procedure developed for rotors with symmetric shaft. The model for the elastic asymmetric shaft takes into account rotary inertia and gyroscopic inertia. In addition, this paper describes an existing method of investigating the stability of a general system of differential equations with periodic coefficients, and evaluates its efficiency when applied to asymmetric rotors. The method described is based on Floquetʹs theory and involves the computation of a transfer matrix over one period of motion. The detailed presentation of the equations of motion, both in a rotating frame of reference and in a fixed one, is accompanied by an analysis of specific cases. The equations of motion for a simpler model are obtained by modal expansion. Numerical examples are given in order to show the finite element formulation and the transfer matrix method as applied to asymmetric rotors. Due to the use of linear equations, the results shown in this paper have limited practical utility, but they are useful tools in analyzing the behavior of periodic systems with weak non-linearities.