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Abstract As an innovative, low-power consuming, and low-stiffness suspension approach, the diamagnetic levitation technique has attracted considerable interest because of its potential applicability in miniaturized mechanical systems. The foundation of a diamagnetic levitation system is mathematical modeling, which is essential for operating performance optimization and stability prediction. However, few studies on systematic mathematical modeling have been reported. In this study, a systematic mathematical model for a disc-shaped diamagnetically levitated rotor on a permanent magnet array is proposed. Based on the proposed model, the magnetic field distribution characteristics, diamagnetic levitation force characteristics (i.e., levitation height and stiffness), and optimized theoretical conditions for realizing stable levitation are determined. Experiments are conducted to verify the feasibility of the proposed mathematical model. Theoretical predictions and experimental results indicate that increasing the levitation height enlarges the stable region. Moreover, with a further increase in the rotor radius, the stable regions of the rotor gradually diminish and even vanish. Thus, when the levitation height is fixed, a moderate rotor radius permits stable levitation. This study proposes a mathematical modeling method for a diamagnetic levitation system that has potential applications in miniaturized mechanical systems.
Xu et al. (Mon,) studied this question.