Modeling and Validation of Diamagnetic Rotor Levitated by Permanent Magnetics

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.

Dynamic Analysis of Micro-machined Diamagnetic Stable Permanent Magnet Levitation System

A novel micro-machined diamagnetic stable.levitation system （MDSLS） which is composed of a free permanent magnetic rotor, a ring lifting permanent magnet and two diamagnetic stabilizers was presented. The static and dynamic stable characters of MDSLS were analyzed. The coupled non-linear differential equations were used to describe six-degree-of-freedom motion of the levitated rotor, and the equivalent surface current and combined dia- magnetic image current method were utilized to model the interaction forces and torques between the lifting perma- nent magnet and rotor permanent magnet and also between the rotor permanent magnet and diamagnetic sub- strates. Because of difficulty to get analytical solution, the numerical calculation based on Runge-Kutta method was used to solve the dynamic model. The vibration frequencies were identified b~ fast Fourier transform （FFT） analysis. According to their resonance characteristics and parameters, the translational and angular dynamic stiff- ness were also calculated. The results show that the levitation of the rotor in MDSLS is stable, and the MDSLS is potential for the application in levitation inertial sensor.