Flexible spinning and precessing rotor–stability analysis based on different analytical and finite element models

Abstract

This study analyzes the elastic vibration of a simultaneously spinning and precessing cantilevered rotor for its stability margin and whirl frequency. The governing equations suggest that the stability is largely governed by two counteracting effects – the centrifugal stiffening and the precession softening. The concentrated mass and inertia of the disc as well as the distributed mass of the shaft contribute to both of these effects. A finite element formulation shows that along with the standard matrices for conventional rotor dynamic analysis, two completely new ones are obtained to account for the effect of precession. Two- and four-degrees-of-freedom models indicate that the rotor is always stable irrespective of its precession speed. But, interestingly, results from the converged finite element model show that the rotor will be unstable beyond a moderately high value of precession speed. The reason for this can be attributed to the shape of deformation of the rotor during its motion. This shape is only approximate in two- and four-degrees-of-freedom models. The Campbell diagrams computed using the four-degrees-of-freedom model and the finite element model are compared and presented.