Analytical magnetic circuit design optimization of electrical machines with air gap winding using a Halbach array

This paper aims to analyze the influence of a Halbach array by using a semi analytical design optimization approach on a novel electrical machine design with slotless air gap winding. The useable magnetic flux density caused by the Halbach array magnetization is studied and compared to conventional radial magnetization systems. First, several discrete magnetic flux densities are analyzed for an infinitesimal wire size in an air gap range from 0.1 mm to 5 mm by the finite element method in Ansys Maxwell. Fourier analysis is used to approximate continuous functions for each magnetic flux density characteristic for each air gap height. Then, using a six-step commutation control, the magnetic flux acting on a certain phase geometry is considered for a parametric machine model. The design optimization approach utilizes the design freedom of the magnetic flux density shape in air gap as well as the heights and depths of all magnetic circuit components, which are stator and rotor cores, permanent magnets, air gap, and air gap winding. Use of a nonlinear optimization formulation, allows for fast and precise analytical calculation of objective function. In this way the influence of both magnetizations on Pareto optimal machine design sets, when mass and efficiency are weighted, are compared. Other design requirements, such as torque, current, air gap and wire height, are considered via constraints on this optimization. Finally, an optimal motor design study for the Halbach array magnetization pattern is compared to the conventional radial magnetization. As a reference design, an existing 15-inch rim wheel-hub motor with air gap winding is used.