Whirling modes stability criterion for a magnetically suspended flywheel rotor with significant gyroscopic effects and bending modes

To intuitively analyze the absolute and relative stability of the forward and backward whirling modes of the high-speed magnetically suspended flywheel rotor with significant gyroscopic effects and bending modes, this paper presents a whirling modes stability criterion based on complex coefficient frequency characteristics method. Through variable reconstruction, the multiple-input multiple-output magnetically suspended rotor system is converted into a single-input single-output (SISO) system with complex coefficients. The stability equivalence of the systems before and after variable reconstruction has been proven. Based on this, the inherent relationships between the distribution of the closed-loop poles of the complex coefficient SISO system and the whirling modes stability are revealed, and the Nyquist stability criterion is further extended by applying the argument principle. All of these lay the foundation for the whirling modes stability theorem, and then, their stability criterion is further developed. Simulation and experimental results prove the effectiveness and correctness of the presented criterion.