Dynamic Modeling of the Anisotropic Non-Ideal Gyroscopic Rotor System

In this paper, the dynamic modeling of the anisotropic non-ideal gyroscopic rotor system is considered. The equations of nonstationary transitions are derived from the motion differential equations, from there the control equation and stationary frequency dependencies, force and energy relations. When the rigidity of the elastic support is anisotropic in orthogonal directions, two critical velocities and, accordingly, two resonance regions are found. Because of the strong interaction of the rotor system with a non-ideal DC motor, slopes of the resonance curves are observed in the regions of critical speeds even in the absence of a non-linear component of the reference stiffness, and loops. It has been proven that the cubic nonlinearity of damping strongly suppresses the resonant amplitudes of the rotor, reduces the size of the loops even more, and strongly attenuates the Sommerfeld effects until they are completely eliminated than linear damping. It is shown that an increase in the magnitude of the cubic nonlinearity of damping greatly facilitates the passage of the resonance region and expands the range of operating speeds. This proves that the amplification of linear damping with cubic nonlinearity of damping is one of the methods for controlling resonant passages and an effective damping model.