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.

The harmonic current in active magnetic bearing (AMB) system usually results from rotor unbalance and sensor runout. It not only causes considerable harmonic vibration, but also brings about the power saturation and the instability of AMB system especially for the high-speed rotor. Therefore, a novel parallel finite dimension repetitive controller (PFDRC) is proposed to restrain the harmonic current in this paper. Compared with the conventional repetitive controller (RC), PFDRC only introduces the limited imaginary poles, so that the problem that the infinite imaginary poles of RC endanger the stability and instantaneous characteristic of the closed-loop system is solved. In order to realize the harmonic current suppression, the power amplifier system is taken as the controlled object, and the proposed PFDRC is parallel with the original equivalent main controller. Then the root reclus method is adopted to design the parameters and to analyze the closed-loop system stability. Based on the phase-frequency characteristic of the system function, the compensators are introduced to improve the system stability margin. Meanwhile, the low-pass property of power amplifier system is sufficiently taken into consideration in the parameters design. Finally, the simulations and experiments are implemented to validate the effectiveness of the proposed PFDRC, and the results demonstrate that the harmonic current is dramatically restrained by the proposed method.

In order to evaluate the impacts of parameter uncertainty and nonparametric uncertainty on the natural characteristics of a dual-rotor system, a nonparametric probabilistic method based on random matrix theory is proposed. In this paper, a nonparametric Riccati whole transfer model is derived based on the maximum entropy principle and the random matrix theory. It is used to model a dual-rotor system with nonparametric uncertainty, as well as to calculate the natural characteristics of the system. Furthermore, the impacts of parameter uncertainty and nonparametric uncertainty on the natural characteristics at the intermediate support element and at the disk-shaft element are discussed using numerical simulations, and the results are compared with related references. The results show that at the same level of uncertainties, the effect of nonparametric uncertainty is often more significant than that of parameter uncertainty. The effects of uncertainties also increase with the level of uncertainties. The results of this paper provide a theoretical basis for the design of uncertain dual-rotor and multi-rotor systems.