Model and experimental verification of a four degrees-of-freedom rotor considering combined eccentricity and electromagnetic effects

In this paper, the combined eccentricity includes the mass eccentricity, static radial eccentricity and angular eccentricity in the rotor of a permanent magnet synchronous motor, and their electromagnetic effects are considered. Approximate analytical expressions of the unbalanced magnetic pull and the additional transverse electromagnetic moment are developed for the combined eccentricity. Moreover, a four degrees-of-freedom rotor system dynamics model is established that describes the influences of these electromagnetic forces and the moments on the rotor with combined eccentricity, when it is not mounted at the midspan of the rotor shaft. The comparisons of the degenerate cases of the four degrees-of-freedom model and Jeffcott rotor model with the radial and angle eccentricities are employed, and the simulation results are in good agreement with one another; further, a critical speed analysis is performed. For experimental validation, the operating mode of the rotor is selected carefully. The rotor of the permanent magnet synchronous motor in an electric vehicle is more compact in the axial direction and hence is considered to be a rigid rotor for which the critical speed is above the operating range of the angular velocity; however, half of the critical speed could be located in this range. Thus, super harmonic resonance occurs, which is discussed based on the combined eccentricity model, and the dynamic response is verified by experiments in which the results agree well in terms of the trajectory shape of the rotor compared with the results of the dynamics model.