Influence of Unbalanced Magnetic Pull on Free Vibration Characteristics of Motor Rotor Based on Multi-scale Method

For the perfectly balanced rotor, the mass eccentricity can be neglected. However, for the permanent magnet synchronous motor used in vehicles, the radial disturbances such as shift process, road roughness and engine excitation, result in the free whirl of the rotor and hence the dynamic eccentricity. Therefore, unbalanced magnetic pull influences the free whirl. In this paper, according to the stiffness characteristic of the system, the coefficient of the nonlinear term in the motion equation is discussed to determine the application condition of multi-scale method. Based on this method, the analytical solutions of the free vibration are obtained and the vibration characteristics are investigated. The results show that both the complex amplitudes of the forward whirl and the backward whirl are time varying due to the nonlinearity of the unbalanced magnetic pull. The magnitudes of the two complex amplitudes remain unchanged. However, the corresponding phases are linear functions with respect to the time, and the change rates depend on the two magnitudes while the frequencies of the two whirls decrease. When the magnitudes of the amplitudes are equal to each other and nonzero, the two frequencies are also equal to each other and the whirl orbit of the rotor is a line. When one of the amplitudes is zero, the orbit is a circle. The general case is that the magnitudes of the amplitudes are nonzero and are not equal to each other. The two whirls are coupled and the frequencies are no longer equal to each other while the orbit is a rotating approximate ellipse. The amplitude modulation phenomena of the radial displacement components appear because the time varying phases cause the different forward and backward whirl frequencies. The analytical solutions by multi-scale method are in good agreement with the numerical results for the small amplitude.