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

Abstract

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%. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.