## 5 Conclusions  
In this work, a six-phase distributed single-winding BPMSM with 12 slots and 2 poles (six-phase DSW-12/2-BPMSM) was proposed and investigated, utilizing the performance advantages of the distributed winding structure. First, the structure of the six-phase DSW-12/2-BPMSM was introduced, as well as its electromagnetic torque and magnetic levitation force control principle. Then, by fully considering the influence of the relative permeability parameter of permanent magnets (i.e., including the relative permeability parameter in the calculation formula of the average equivalent air gap length, \(g_{0}\)), accurate modeling of the electromagnetic torque and the radial magnetic levitation force was conducted. This was based on the distribution function method, coordinate transformations, and the principle of imaginary displacement. Finally, FEM validation and analysis of the established mathematical models was carried out using Ansys Maxwell software, and a detailed comparative analysis of the electromagnetic characteristics was performed with the commonly used six-phase CSW-6/2-BPMSM structure. The research conclusions are as follows:  
(1) In the case of an unsaturated magnetic circuit of the six-phase DSW-12/2-BPMSM, the electromagnetic torque and controllable magnetic levitation force are proportional to the torque current and levitation current, respectively. (2) For the six-phase DSW-12/2-BPMSM, the established electromagnetic torque and controllable magnetic levitation force models are effective and have high calculation accuracy. Under the setting conditions of the motor structure parameter in this work, the maximum calculation error of the torque model did not exceed 6.86%, while the maximum calculation errors of the controllable magnetic levitation force model and the eccentric magnetic pull force model did not exceed 0.25% and 6.4%, respectively. The maximum calculation errors were all within the acceptable range. The reasons for the errors include the following: firstly, in terms of material properties, the influences of magnetic circuit nonlinearity and the harmonic magnetic field were not sufficiently considered; secondly, although the main geometrical structure was considered in the modeling, the simplified treatment of some details will lead to errors. In order to improve the model's accuracy, the material properties and nonlinear modeling will be further optimized subsequently. (3) The six-phase DSW-12/2-BPMSM is a single-winding BPMSM structure well suited for low-power applications. Compared to the traditional six-phase CSW-6/2-BPMSM structure with centralized windings, the steady-state magnetic levitation force control stiffness of the researched six-phase DSW-12/2-BPMSM is slightly lower. However, the six-phase DSW-12/2-BPMSM adopts a distributed single-winding structure, which is able to reduce the influence of harmonics, allowing it to obtain better control characteristics in terms of torque and levitation force. The six-phase DSW-12/2-BPMSM has relatively large \begin{table}
\begin{tabular}{c c c} \hline \hline
**Characteristics/** & **Six-Phase** & **Six-Phase** \\
**Performance** & **CSW-6/2-BPMSM** & **DSW-12/2-BPMSM** \\ \hline Mechanical structure & Simple & Moderate \\ Harmonic content & High & Low \\ Torque stiffness & Moderate & High \\ Suspension force stiffness & Moderate & Moderate \\ Torque pulsation & Moderate & Small \\ Suspension force pulsation & Large & Moderate \\ Coupling & Moderate & Low \\ Efficiency & Moderate & Higher \\ Noise & Obvious & Moderate \\ Field of application & Low power & Low power \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparative summary of characteristics between the two BPMSM structures. torque control stiffness, and its dynamic torque waveform over time is relatively smooth; moreover, the peak-to-peak pulsation rate of its magnetic levitation force waveform and its coupling effect of torque current with the radial magnetic levitation force are both acceptable.