A Stability Analysis Method for High-Speed Magnetically Suspended Rotors Based on Tensor Product Model Transformation

Abstract

The stability of whirling modes of high-speed magnetically suspended rotors due to strong gyroscope effects varies with the speed, which is the main factor affecting the stability of the system. In this article, a speed-dependent linear parameter-varying (LPV) model of an active magnetic bearing (AMB) rotor system is derived. Then, an improved tensor product model transformation (TPMT) method is introduced to transform the dynamic model into a tensor product model form on a bounded parameter domain, in which the decomposed vertex systems are further remapped to analyze the stability easily. Moreover, a stability criterion based on dual-frequency Bode diagrams is developed. By analyzing the whirling stability characteristics of each vertex system, the stability judgment and stability margin calculation of the high-speed AMB rotor in the whole speed range can be realized, which effectively reduces the complexity of the radial rotation stability analysis of high-speed magnetically suspended rotors. The results show that this method is a feasible solution to analyze the stability of the parameter-dependent time-varying AMB model.