Analytical Modeling and Optimization of Dual-Layer Segmented Halbach Permanent-Magnet Machines

In this article, two kinds of dual-layer segmented Halbach arrays have been proposed for permanent-magnet (PM) brushless machines. The analytical expressions of magnetic fields due to the inner-/outer-layer Halbach magnets have been separately obtained. For the maximal flux density in the air gap, the optimal magnet segment radian ratios or magnetization angles for each dual-layer Halbach array have been analytically determined separately. The induced back electromotive force and electromagnetic torque have been analytically obtained. The prediction results show that the optimized electromagnetic performances for each double-layer segmented Halbach array with different slot and pole combinations are better than those for the corresponding single-layer one. The proposed analytical model can also be applied for optimizing the multi-layer segmented Halbach array. The analytical prediction results of a PM machine with the double-layer segmented Halbach array have been compared with those obtained by a finite-element method.