Development of a 2-D Analytical Model for the Electromagnetic Computation of Axial-Field Magnetic Gears

This paper describes a two-dimensional (2-D) analytical model to predict the magnetic field distribution in axial-field magnetic gears by using the sub-domain method. The sub-domain method consists in solving the partial differential equations linked to the Maxwell's equations in each rectangular region (magnets, air gaps, and slots) by the separation of variables method. The proposed model is based on a two-dimensional approximation for the magnetic field distribution (mean radius model) i.e. the problem is solved in 2-D Cartesian coordinates. One of the main contributions of the paper concerns the analytic solution of the magnetic field in a slot open on the two sides (space between the ferromagnetic pole-pieces). Moreover, it is shown that the analytical model and the 3-D finite elements simulations follow the same trends in the determination of the optimum values for the geometrical parameters. As the analytical model takes less computational time than 3-D numerical model, it can be used as an effective tool for the first step of design optimization.