Multi-layer quasi three-dimensional equivalent model of axial-flux permanent magnet synchronous machine

Abstract

Axial-flux permanent magnet synchronous machine (AFPMSM) enjoys the merits of high torque density and high efficiency, which make it one good candidate in the direct-drive application. The AFPMSM is usually analyzed based on the three-dimensional finite element method (3D FEM) due to its three-dimensional magnetic field distribution. However, the 3D FEM suffers large amount of calculation, time-consuming and is not suitable for the optimization of AFPMSM. Addressing this issue, a multi-layer quasi three-dimensional equivalent model of the AFPMSM is investigated in this paper, which could take the end leakage into consideration. Firstly, the multi-layer quasi three-dimensional equivalent model of the AFPMSM with single stator and single rotor is derived in details, including the equivalent processes and conversions of structure dimensions, motion conditions and electromagnetic parameters. Then, to consider the influence of end leakage on the performance, a correction factor is introduced in the multi-layer quasi three-dimensional equivalent model. Finally, the proposed multi-layer quasi three-dimensional equivalent model is verified by the 3D FEM based on an AFPMSM under different structure parameters. It demonstrates that the errors of flux linkage and average torque obtained by the multi-layer quasi three-dimensional equivalent model and 3D FEM are only around 2% although the structure parameters of the AFPMSM are varied. Besides, the computation time of one case based on the multi-layer quasi three-dimensional equivalent model is only 6 min, which is much less than that of the 3D FEM, 1.8 h, under the same conditions. Thus, the proposed multi-layer quasi three-dimensional equivalent model could be used to optimize the AFPMSM and much time could be saved by this method compared with the 3D FEM.

Modified magnetic equivalent circuit of double‐stator single‐rotor axial flux permanent magnet machine considering stator radial‐end flux‐leakage

“…N is the number of the linear machines. The length of each linear machine is equivalent to the circumference of each layer circumferential middle-section of the DSSR-AFPM machine [7],…”

“…The flux-leakage between the adjacent PMs partially reaches the adjacent PMs directly through the airgap, and partially reaches the adjacent PMs through the stator tooth-tips. The latter would provide a model in the following sub-section D. The leakage reluctance between the adjacent PMs R mm can be expressed by Equation (19) [7],…”

“…The unit of axial machine speed is revolutions per minute, while the unit of linear machine speed is metres per second. The rotational speed is expressed as the linear speed by Equation (7),…”

“…Some researchers propose to expand the AFPM machine into a 2‐D linear machine model and solve it by 2‐D FEA. However, this method generally ignores the effect of stator radial‐end flux‐leakage [7] and the average electromagnetic torque error with 3‐D FEA increase as the armature load increases. The MEC method can design special parametric magnetic circuits for a certain type of machine, and its performance can be quickly predicted in the early stage of machine design and optimisation.…”

“…In ref. [7], the 2‐D FEA results of the SSSR‐AFPM machine are corrected by establishing a leakage magnetic circuit model at the end of the PM, however, the SSSR‐AFPM machine has the problem of unbalanced magnetic force. In ref.…”