VP2-01 An Improved Equivalent Magnetic Network for Performance Prediction of Yokeless and Segmented Armature Axial Flux Permanent Magnet Motor
Creators: Chao Wang and Bing Peng
Publisher: name: IEEE
Year: 2025

The existing quasi-3D equivalent magnetic network (EMN) all prioritize the YASA-AFPM’s magnetic field in the air gap but ignore that in the slot [1-3], which may result in errors in predicting synchronous inductance Ls and related performance, such as power factor and maximum torque. An improved quasi-3D EMN, based on [4], is proposed for the YASA-AFPM, whose main novelty is that both magnetic field in the air gap and slot can be accurately predicted. The improved EMN is composed of rectangular permeance element, magnetomotive force (MMF) source and boundary condition, as shown in Fig. 1. There are four crossing permeances per element, and there are multiple elements covering all regions of the motor, especially the air gap and slot region. The PM MMF sources are located in elements at PM region. The winding MMF sources, generated by a single coil, are located both in elements at stator tooth, where the coil is wound, and the slot region, where the coil is occupied. The values of winding MMF sources are calculated by Ampere’s law. The MMF at stator tooth is generated by the whole coil, while that at slot region is generated by the portion of coil surrounding the element. Moreover, the periodic or anti-periodic, and symmetry boundary conditions are employed here to reduce computation time. The nodal analysis, based on Kirchhoff’s law, is employed to solve the EMN, thereby obtaining the distributions of magnetic density, which, in turn, are used to calculate the flux linkage and magnetic energy. The no-load back-EMF is the derivative of no-load flux linkage with respect to time. The inductance can be obtained by utilizing its relationship with current and the stored magnetic energy in the air gap and slot. With id=0, the torque and phase voltage of a 167 r/min YASA-AFPM are shown in Fig. 2. When the phase voltage reaches its maximum, the phase current is 35.2A, and the torque predicted by the EMN is 728.09 Nm, which is 3.75% smaller than 756.43 Nm obtained by the 3D-FEA. Moreover, the influence of Ls on maximum torque cannot be ignored. Ignoring Ls, the calculated phase voltage with 35.2A is 164.4V, which is 21.71% smaller than the actual 210V.References: [1] Y. Huang, T. Zhou, J. Dong, et al., IEEE Trans. Magn., vol. 50, pp. 1-4(2014). [2] X. Sun, L. Wang, X. Fan, et al., Proc. IEEE Trans. Electrific. Conf. Expo, pp. 1-6 (2022). [3] A. Hemeida，A. Lehikoinen, P. Rasilo, et al., IEEE Trans. Ind. Electron., vol. 66, pp. 8318-8333 (2019). [4] S. Yang, S. Asfirane, S. Hlioui, et al., CES Trans. Elect. Machines Syst., vol. 5, pp. 152-162（2021）.
The existing quasi-3D equivalent magnetic network (EMN) all prioritize the YASA-AFPM’s magnetic field in the air gap but ignore that in the slot [1-3], which may result in errors in predicting synchronous inductance Ls and related performance, such as power factor and maximum torque. An improved quasi-3D EMN, based on [4], is proposed for the YASA-AFPM, whose main novelty is that both magnetic field in the air gap and slot can be accurately predicted. The improved EMN is composed of rectangular permeance element, magnetomotive force (MMF) source and boundary condition, as shown in Fig. 1. There are four crossing permeances per element, and there are multiple elements covering all regions of the motor, especially the air gap and slot region. The PM MMF sources are located in elements at PM region. The winding MMF sources, generated by a single coil, are located both in elements at stator tooth, where the coil is wound, and the slot region, where the coil is occupied. The values of winding MMF sources are calculated by Ampere’s law. The MMF at stator tooth is generated by the whole coil, while that at slot region is generated by the portion of coil surrounding the element. Moreover, the periodic or anti-periodic, and symmetry boundary conditions are employed here to reduce computation time. The nodal analysis, based on Kirchhoff’s law, is employed to solve the EMN, thereby obtaining the distributions of magnetic density, which, in turn, are used to calculate the flux linkage and magnetic energy. The no-load back-EMF is the derivative of no-load flux linkage with respect to time. The inductance can be obtained by utilizing its relationship with current and the stored magnetic energy in the air gap and slot. With id=0, the torque and phase voltage of a 167 r/min YASA-AFPM are shown in Fig. 2. When the phase voltage reaches its maximum, the phase current is 35.2A, and the torque predicted by the EMN is 728.09 Nm, which is 3.75% smaller than 756.43 Nm obtained by the 3D-FEA. Moreover, the influence of Ls on maximum torque cannot be ignored. Ignoring Ls, the calculated phase voltage with 35.2A is 164.4V, which is 21.71% smaller than the actual 210V.References: [1] Y. Huang, T. Zhou, J. Dong, et al., IEEE Trans. Magn., vol. 50, pp. 1-4(2014). [2] X. Sun, L. Wang, X. Fan, et al., Proc. IEEE Trans. Electrific. Conf. Expo, pp. 1-6 (2022). [3] A. Hemeida，A. Lehikoinen, P. Rasilo, et al., IEEE Trans. Ind. Electron., vol. 66, pp. 8318-8333 (2019). [4] S. Yang, S. Asfirane, S. Hlioui, et al., CES Trans. Elect. Machines Syst., vol. 5, pp. 152-162（2021）.