A new approach to finite element modelling of flexible rotors

Abstract

A 3‐dimensional formalism adapted to critical speed and stability analysis of rotating machinery is presented. Gyroscopic effects are properly taken into account in the expression of the kinetic energy through a proper kinematic description which takes account of the local changes of angular velocity induced by the deformation. Two approaches are suggested according to the respective stiffness and geometric properties of the rotating and fixed parts: the rotating frame approach and the inertial frame approach. In both cases, an axisymmetric finite element modelling of the rotor is proposed which takes into account the 3‐dimensional nature of the system while keeping the number of degrees of freedom to a reasonable level. In order to perform the stability analysis, a preliminary reduction of the system is achieved using the component mode method. Critical speeds are calculated next either by the classical sweeping procedure or by a direct method when the restrictive conditions of its applicability are met. The concepts proposed are then applied to an example in order to demonstrate their adequacy.