Coupled bending torsional vibrations of non-ideal energy source rotors going through critical speeds

With the increasing number of rotors working at very high angular velocity, it becomes crucial to understand the dynamic behavior of rotating machineries when going through critical speeds. Models assuming constant velocity speed are not valid in this case of study since crossing the critical speeds implies necessarily non-stationary working conditions. The present work offers a new finite element model for rotors working at non-stationary regime. The rotational speed is introduced to the unknowns of the dynamic problem and six degrees of freedom are considered on each node. A main focus is given to the study of the coupling between the torsional and flexural degrees of freedom. This coupling is introduced by the intrinsic gyroscopic effect as well as the mass unbalance terms. It results in torsional vibrations containing frequency components of twice the excitation frequency of the mass unbalance as well as frequency components reflecting a modulation with the first bending natural frequency. We show that when crossing the critical speed, an additional frequency component of four times the lateral excitaion frequency appears. The coupling is observed through the analytical equations of motion and confirmed by the numerical simulation.