Three-Dimensional Electromagnetic Analytical Model of 6-DOF Maglev Planar Motor With Passive Halbach PM Mover

The magnetic charge method (MCM) is usually used for analyzing the passive permanent magnet (PM) mover of maglev planar motor (MPM). However, this method cannot characterize the 3-D magnetic field of this mover type due to its lack of ability to model the magnetic field at the longitudinal end of the mover. In this article, a general 3-D electromagnetic analytical model based on the equivalent surface current method (SCM) is proposed, which can accurately characterize the 3-D magnetic field of this type of mover for future optimization. First, a single-degree-of-freedom (DOF) 3-D analytical model of a single-set Halbach PM array is established by the equivalent SCM, and an analytical algorithm based on 3-D spatial transformation and magnetic vector mapping is proposed to extend the single-DOF to 6-DOF model. Then, the 6-DOF 3-D electromagnetic analytical model of the passive Halbach PM mover of the MPM is obtained by using the principle of magnetic field superposition. Furthermore, in order to verify the accuracy of this model, a 3-D finite element analysis (FEAs) of the Halbach PM array and the mover of MPM are implemented and compared with the analytical method. Besides, in order to verify the generality of this improved analytical model, another passive Halbach PM mover type with triangular array was also analyzed and compared. Finally, a test platform is built to measure the magnetic field of the mover of MPM and experimental results were compared with the SCM and finite element method (FEM). The results indicate that this improved analytical model can be used to characterize the 3-D magnetic field of the Halbach PMs and the movers of MPM accurately, which can provide a basis for the study of the end effect of PM array and the design optimization of the mover structure. Most importantly, the 3-D magnetic field analytical model presented in this article plays a crucial role in the detection of the mover’s pose in MPM.