Flux concentrating multi-tooth splitting poles permanent magnet vernier machine cogging torque optimization and experimental verification

Abstract

Permanent magnet vernier machine (PMVM) based on flux modulation principle has attracted increasing attention in low-speed direct-drive applications due to its high torque capability. A novel flux concentrating multi-tooth splitting poles permanent magnet vernier machine (FCMSP-PMVM) was proposed and designed, which has higher flux density relative to the conventional surface ones. The analytical cogging torque expression of the machine is derived by Maxwell energy method and Fourier series expansion to comprehensively provide insight into the variation of the cogging torque with main parameters. The number of flux modulation pole (FMP) per stator tooth, the circumferential width and radial depth of each FMP, pole arc coefficient, namely $N_{\text{𝐹𝑀𝑃}}$ , $k_d$ , $k_p$ and ${\alpha }_p$ are defined to investigated the relationship between machine unique parameters and its cogging torque. Analysis and computation of the cogging torque characteristic of the proposed flux concentrating PMVM are studied by time-step finite element analysis (FEA). The FEA results demonstrate that $N_{\text{𝐹𝑀𝑃}}$ , $k_d$ and $k_p$ are the key parameters to the cogging torque optimization for the proposed machine. It is also confirmed that the pole arc coefficient has small influence to the cogging torque of the proposed machine compared with the traditional PM machines. Finally, a FCMSP-PMVM prototype is built to verify the above analysis and computation. The measured performance of the constructed prototype machine has confirmed the correctness of finite-element modeling results. Experience gained from this study has led to develop a set of design rules for the concentrated winding PMVM.