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

Because the magnetic circuits of homopolar inductor machines (HIMs) are three-dimensional (3-D), a 3-D finite element model (FEM) is usually built to accurately compute the cogging torque in HIMs, but the drawback is very time-consuming in modeling and computing. Therefore, a two-dimensional (2-D) FEM of HIMs is needed to simplify the computation of the 3-D FEM. However, the existing odd harmonic 2-D FEM cannot accurately predict the cogging torque in HIMs. To address this problem, this paper proposes a full-order harmonic 2-D FEM. First, the analytical expressions of HIM cogging torque are derived by the combination of energy method and air-gap field modulation principle. Based on the obtained analytical expressions, the equivalent principles between the 3-D and 2-D FEMs are analyzed. According to the above equivalent principles and taking a 48-slot/4-tooth (48S4T) permanent magnet (PM) HIM as an example, a full-order harmonic 2-D FEM of the example machine excited by a field winding is proposed. The structure of the full-order harmonic 2-D FEM is described in detail. The turn number of field winding and field current amplitude of the proposed 2-D FEM are investigated. The differences between the odd harmonic 2-D and full-order harmonic 2-D FEMs are also analyzed. Finally, the cogging torque in the 48S4T PM HIM with distinct rotor tooth-arc to tooth-pitch ratios is computed by 3-D, odd harmonic 2-D and full-order harmonic 2-D FEMs of the machine, respectively. The results illustrate that compared with the odd harmonic 2-D FEM, the full-order harmonic 2-D FEM can shorten the calculation time and has the similar computation accuracy as the 3-D FEM. Moreover, the experimental validation is performed on a prototype of the 48S4T PM HIM. The error between the maximum cogging torque obtained by the full-order harmonic 2-D FEM and experiments is only 2.12%. (c) 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.