Dynamic Modeling of the Anisotropic Non-Ideal Weakly Gyroscopic Rotor System

In this paper, the dynamic modeling of the anisotropic non-ideal weakly gyroscopic rotor system is considered. Equations of nonstationary transitions are derived from motion differential equations; then, the control equation, stationary frequency dependencies, and force and energy relations are obtained. 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 nonlinear component of the reference stiffness, and loops are also recorded. It is proven that, compared with linear damping, 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. 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 is an effective method for controlling resonant passages and an effective damping model.