Non-stationary Resonance Transition of the Gyroscopic Rigid Rotor with Nonlinear Damping and Non-ideal Energy Source

Abstract

The article constructs differential equations of motion of a gyroscopic rigid unbalanced rotor with nonlinear cubic damping and nonlinear stiffness, taking into account the anisotropy of the linear stiffness of the elastic support material and interaction with a non-ideal DC motor with a linear characteristic, and the dynamics of the rotor is studied by a numerical method. Two jumping nonlinear effects are observed during the accelerated resonant transition from a large amplitude to a smaller one, accompanied by Sommerfeld effects, during the resonant transition with the decelerated motor from a smaller amplitude of oscillations to a larger one, corresponding to two critical speeds. Nonlinear cubic damping suppresses the maximum amplitudes in the regions of critical velocity and amplitude after similar resonant increasing and damping beats oscillations. At sufficiently close critical velocities, exit from the resonance at a lower critical velocity can lead to capture at another resonance at a higher critical velocity, the severity of the Sommerfeld effect on each of the resonant regions becomes comparable. Therefore, the evaluation of the response of the dynamics of resonant transients is of paramount importance for the correct design of the vibration insulation of the rotor machine.