Analytical Calculation and Experiment of 3-D Electromagnetic Force of Permanent Magnet Electrodynamic Suspension System

The electromagnetic module is essential for the stability of the permanent magnet (PM) electrodynamic suspension (EDS) system, and the accurate calculation of the electromagnetic force is the premise of studying the dynamic performance of the Halbach array. To establish an accurate and effective dynamic model of the PM EDS, considering the translational and vertical motions of the magnet, an analytical model (AM) of the linear Halbach array is established in this research. According to the Biot-Savart law and the surface current method, the 3-D magnetic flux density expression is derived. When the linear Halbach array translationally and vertically moves, the magnetic vector potential equations are formulated using the Fourier transform and are solved using truncated region eigenfunction expansion. Then, compared with the 3-D finite element model in steady state, the average errors of lift force and drag force only are 0.87% and 3.96%, respectively. The accuracy of the AM satisfies the requirements of dynamic modeling and analysis of the PM EDS system. Furthermore, considering the translational and vertical motions, the validity of the AM is verified by comparing the analytic calculations with the dynamic experiment data on the high-speed rotating experiment platform.