Analytical Modeling and Analysis of High-Torque-Density Three-Segment Halbach Array PM Machine by Considering Leakage Flux

Conventional finite element method (FEM) has a complex model and a long optimization time for Halbach array PM machines. This paper proposes a hybrid analytical method that combines the subdomain method (SM) and the magnetic circuit method (MEC) for analyzing a high-torque-density, three-segment Halbach array rotor permanent magnet (PM) machine, accounting for Halbach array magnetization and end leakage flux. Firstly, to address the challenge posed by complex PM shapes in the Halbach array PM machine, a novel subdivision equivalence method is conducted. Then, the magnetic equivalent circuit (MEC) of the stator and rotor is established, and the axial leakage flux and nonlinearity of the iron core are taken into account. In addition, electromagnetic performance, such as air gap flux density, cogging torque, electromagnetic torque, and back electromotive force (back-EMF), is obtained based on the proposed hybrid analytical model. The analytical results are verified by using the finite element method (FEM), and the results show that the error is less than 2%. Finally, a 15 kW prototype PM machine with a Halbach array PM rotor is manufactured and tested, and the results validate the accuracy and efficiency of the analytical method.