2-D and 3-D Analytical Calculation of the Magnetic Field and Levitation Force Between Two Halbach Permanent Magnet Arrays

As we know, the analytical calculation of magnetic field and magnetic force has important guiding significance for the optimal design of the size and structure of a magnet. At present, the magnetic field and magnetic force between two permanent magnet (PM) monomers have been described by effective analytical models. However, the magnetic field strength and magnetic force generated by two PM monomers are limited and cannot meet the requirements of a PM levitation system with high magnetic field strength and large levitation force. To this end, this article establishes analytical calculation models of magnetic field and levitation force between two Halbach PM arrays. First, on the basis of Ampere molecular circulation hypothesis, the 2-D analytical model of magnetic field was established based on the surface current method; on the basis of magnetic charge theory, the 3-D analytical model of magnetic field was established based on the magnetic charge method. Second, based on the analytical models of magnetic field, the 2-D and 3-D analytic models of levitation force were derived by virtual work method, respectively. Numerically, the results of two analytical models of magnetic field and two analytical models of levitation force have been compared to verify the accuracy of the models. At the same time, the 2-D and 3-D finite element simulation models of magnetic field and levitation force were established, respectively, and the accuracy of the analytical models were verified again. The results show that the analytical models established in this article is effective and can be used to guide the design and optimization of the magnet composed of two Halbach arrays.