The air-gap eccentricity will produce unbalanced magnetic pull and cause vibrations and noises in a motor. In this study, the dynamic behavior of a synchronous motorized spindle with inclined eccentricity is investigated. A semi-analytical method is proposed to model the unbalanced magnetic pull and the electromagnetic torque of a rotor with inclined eccentricity, and the semi-analytical method is verified by the finite element method. The dynamic model of a spindle-bearing system is built by taking the centrifugal force and gyroscopic effects into account. Then, the vibration response of dynamic displacement eccentricity, inclined eccentricity including displacement eccentricity and angle eccentricity, rotating speed, and unbalanced mass eccentricity in both time domain and frequency domain are simulated and analyzed. The results show that the eccentricities can lead to fluctuations in amplitudes of the dynamic displacement response and the angle response. The frequency components of the dynamic responses are the combination of rotating frequency, VC frequency, and power frequency. It is indicated that the coupling interactions of bearing forces, unbalanced mass force, and unbalanced magnetic pull have an obvious effect on the spindle-bearing system.
An Extremum Seeking Estimator Design and Its Application to Monitoring Unbalanced Mass Dynamics
