Investigation of A Two-Dimensional Model for Cogging Torque Calculation in Homopolar Inductor Machines

Since homopolar inductor machines (HIMs) have a three-dimensional (3-D) magnetic circuit, the researchers usually build a 3-D finite element model (FEM) to accurately predict the HIM cogging torque, which is very time-consuming. To solve this problem, a two-dimensional (2-D) FEM is proposed in this paper. Firstly, the analytical expressions of the HIM cogging torque are derived. Based on the cogging torque expressions, the equivalent principles between 3-D and 2-D FEM are investigated. According to the equivalent principles, the 2-D FEM used for computing the HIM cogging torque can be obtained. To display the 2-D model more vividly, a 48-slot/4-tooth (48 $S\ 4T$) permanent magnet (PM) HIM is exampled and its 2-D FEM is proposed. The 2-D FEM of the 48S4T PM HIM is excited by a field winding. The structure, turn number of field winding and field current amplitude of the 2-D model are illustrated in detail. Furthermore, the differences between the existing 2-D and the proposed 2-D FEM are analyzed. Finally, the cogging torque in the 48 $S\ 4T$ PM HIMs with different rotor tooth-arc to tooth-pitch ratios is computed by their 3-D, existing 2-D and proposed 2-D FEMs, respectively. The results indicate that, compared with the existing 2-D FEM, the proposed 2-D FEM can effectively save the computation time and has the similar computation accuracy as the 3-D FEM. The experimental verification is also carried out on a prototype of the 48 $S\ 4T$ PM HIM. The error between the maximum cogging torque obtained by the proposed 2-D FEM and the experiments is only 2.12%