Combined effect of spatially fixed and rotating asymmetries on stability of a rotor

In this paper we study the combined effects of bearing and rotor asymmetry on the stability of the classical Laval rotor using analytical techniques. This setting intrinsically features equations of motion with periodic coefficients. We obtain closed form approximations for the stability boundaries which give insights in the interaction of different effects which are elsewhere mostly considered in isolated form. Using a classical two degree of freedom model of a rotor we investigate dissipative and follower force type of forcing in combination with internal and external damping in the presence of both rotating and stationary asymmetries. Since in many technical applications the resulting forces are small compared to the elastic restoring forces of the corresponding symmetric system, the former are treated as perturbations. The results are benchmarked with numerical simulations indicating the range of validity of the approximations. Our model is designed to illustrate the most generic effects originating from the coupling of rotor and bearing asymmetries, which cannot be captured in models with constant coefficients.