On the Choice of Shape Functions of Unsymmetrical Elastic Rotors

Abstract

In this paper the effects of rotordynamics under the aspect of the choice of shape functions are discussed. For this purpose a rotor system which consists of a slim shaft and two rigid disks is modeled using theProjection Equation. The shaft is assumed as an elasticEuler-Bernoullibeam, supported by two bearings modeled as radial spring systems. The rotor is driven by a permanent-magnet synchronous motor whose torque is transmitted with a spur gear pair next to one of the bearings. ARitzapproach is used to separate the elastic displacements in position and time, thereby different shape functions are evaluated. Approximated eigenfunctions are computed and used as shape functions as well. For validation, the eigenfrequencies are compared with semi-analytical ones, calculated with theTransfer-Matrix-Methodand experimental results. The insights obtained from this work should make it easier to choose the appropriate shape functions for such problems.