Three-Dimensional Analytical Modeling of Axial-Flux Permanent Magnet Drivers

In this paper, the axial-flux permanent magnet driver is modeled and analyzed in a simple and novel way under three-dimensional cylindrical coordinates. The inherent three-dimensional characteristics of the device are comprehensively considered, and the governing equations are solved by simplifying the boundary conditions. The axial magnetization of the sector-shaped permanent magnets is accurately described in an algebraic form by the parameters, which makes the physical meaning more explicit than the purely mathematical expression in general series forms. The parameters of the Bessel function are determined simply and the magnetic field distribution of permanent magnets and the air-gap is solved. Furthermore, the field solutions are completely analytical, which provides convenience and satisfactory accuracy for modeling a series of electromagnetic performance parameters, such as the axial electromagnetic force density, axial electromagnetic force, and electromagnetic torque. The correctness and accuracy of the analytical models are fully verified by three-dimensional finite element simulations and a 15 kW prototype and the results of calculations, simulations, and experiments under three methods are highly consistent. The influence of several design parameters on magnetic field distribution and performance is studied and discussed. The results indicate that the modeling method proposed in this paper can calculate the magnetic field distribution and performance accurately and rapidly, which affords an important reference for the design and optimization of axial-flux permanent magnet drivers.