Analysis and Calculation of the Three-Dimensional Air-Gap Magnetic Field and Electromagnetic Torque of a Multishaft Ring-Plate Magnet Gear

A kind of multishaft ring-plate magnet gear (MRMG) structure is proposed. Because an MRMG has the characteristics of an eccentric permanent magnet gear with a small aspect ratio and large magnetic leakage at the end, there is a large deviation when using traditional 2-D FEM or an analytical method to analyze and calculate field and torque values for an MRMG. In this article, a 3-D mathematical analytical model of the MRMG eccentric air-gap magnetic field and electromagnetic torque is established, which is suitable for computer modeling. First, based on the cylindrical coordinate system of the inner and outer permanent magnet rings, the 3-D analytical models of the air-gap magnetic field of the inner and outer permanent magnet rings are established, respectively, by using the vector magnetic potential method. Then, by analyzing the position relationship between the inner and outer permanent magnet rings and their superposition angles, the radial and tangential air-gap magnetic fields of the inner and outer permanent magnet rings are superimposed according to their included angles, and a 3-D analytical model of the air-gap magnetic field and the electromagnetic torque of an MRMG is established. Because all the calculations are magnetic field integrals along the axial length of the MRMG, the magnetic field's end effect is included in the established model, and the calculated results are more accurate than those of a 2-D FEM and analytical method (error >13%). A 3-D FEM and static loading experiment show that the model has a good accuracy (error < 2%) with the measured results and finite-element analysis, but the calculation speed of the model is faster than that of the 3-D FEM, which not only greatly shortens the calculation time but is also suitable for computer programming and is easily used to perform the MRMG analysis and optimization of different MRMG structural parameters.