Analysis of a Viscoelastic Spinning and Precessing Rotor - A Comparative Study using Two and Four Degree of Freedom Models and Finite Elements

The present work analyzes the visco-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 have contributions to both of the above effects. A finite element formulation shows that along with the standard matrices for conventional rotor dynamic analysis, one obtains two completely new ones to account for the effect of precession. Two degree and four degree of freedom models indicate that the rotor becomes ultimately stable with an increase in precession speed. However, interestingly, results from a converged finite element model shows that the rotor will become unstable again 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 degree of freedom models. The Campbell diagrams computed using four-degree of freedom model and finite element model are compared and presented.