A universal dynamic model and solution scheme for the electrical rotor system with wide range of eccentricity

Different eccentricities of the electrical rotor have been extensively studied, whereas the application scope of air-gap modeling is ignored and appropriate solution method is unclear. This paper aims to propose a universal dynamic model and solution scheme for the electrical rotor system with wide range of eccentricity. A unified and concise air-gap length model considering both the static and dynamic eccentricities is proposed. The analytical and numerical calculation methods are explored to obtain the magnetic pull force. The boundary of large and small relative eccentricity is defined and the corresponding calculation approaches are determined. A universal and complete dynamic model of the rotor system considering the magnetic pull force, magnetic suspension force and rubbing force are established. The dynamic model for small eccentricity is further normalized and handled with the multi-scale analytical method. Effects of different parameters on the dynamic responses for the large eccentricity cases are investigated. The frequency response relationship and stability criterion are obtained through the analytical derivation for the small eccentricity cases. Response amplitudes with different dimensionless parameters are studied and verified by the numerical method. Results indicate that the analytical method for magnetic pull force is just suitable for small eccentricity and the numerical approach is necessary for large eccentricity. The static eccentricity and unbalanced mass etc. will enlarge the displacement amplitude. An appropriate equivalent stiffness of magnetic suspension force is needed. The multi-scale perturbation method can be adopted to obtain the analytical results of the rotor system for small eccentricity cases with good accuracy. This paper can be a systematic benchmark for further research of the electrical rotor with different eccentricities.