Analysis of armature magnetic field of slotless permanent magnet machine with arbitrary-phase equidirectional toroidal winding

For permanent magnet (PM) machines, analysis of armature magnetic field (AMF) plays an essential role in the qualitative analysis of machine operation principle, quantitative calculation of machine electromagnetic performance, further optimization or innovation of the machine, and so on. The winding configuration determines the primitive armature magnetomotive force (MMF), which greatly influences the AMF. In this paper, the AMF analytical model of slotless PM machines with arbitrary-phase equidirectional toroidal winding (EDTW) is derived, and the harmonic characteristics of the AMF are analyzed. Firstly, the expression of the arbitrary-phase EDTW primitive armature MMF is derived, and the band factor is introduced to represent the influence of coil bandwidth on the MMF. Secondly, the AMF analytical model is derived by introducing the concept of ideal air-gap permeability density, and the harmonic characteristics of the AMF are analyzed. Finally, taking 3, 4, 5, and 6-phase EDTW as examples, the relevant conclusions obtained by the analytical method (AM) are compared with those obtained by the finite element method (FEM). The comparison results show good consistency, confirming the accuracy and effectiveness of the AM. The relevant conclusions of this paper can provide a reference for the further research and application of the EDTW. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).