## 4 Validation of Proposed Method  
### Three-Dimensional Model and Proposed Two-Dimensional Model  
To verify the effectiveness of the aforementioned methods, the electromagnetic performance of an axial flux permanent magnet synchronous motor with a 10-pole, 12-slot double-sided stator and a single rotor in series magnetic circuit form is calculated using the three-dimensional finite element method and the two-dimensional equivalent finite element method proposed in this paper. The size parameters of the corresponding model are shown in Table 1.  
Figure 10: Differences between two simplified equivalent methods for axial flux permanent magnet synchronous motors: (**a**) original method; (**b**) proposed method.  
Here, taking the nine-segment division method as an example, a two-dimensional equivalent linear motor model of the motor is established, where the average radius and scaling coefficient corresponding to each layer are shown in Table 2.  
According to the above dimensions and materials, the three-dimensional model and two-dimensional model of the axial flux permanent magnet synchronous motor are, respectively, established. Because the motor has symmetry, in order to reduce the time of three-dimensional calculation, the complete motor model is simplified into a quarter model according to the symmetry relationship and is halved along the axial direction and tangential direction of the motor. The simplified 3D motor model and meshing situation are shown in Figure 11, with a mesh element number of 1,366,668 and a node number of 307,790, respectively. According to the two-dimensional equivalent method described in the previous chapter, a two-dimensional linear motor equivalent model of the motor is established, as shown in Figure 12. Due to the fast calculation speed of two-dimensional, in order to simplify it symmetrically, if it is necessary to further improve the calculation speed, the model can be treated similarly with reference to three-dimensional symmetry. The mesh element number and node number of the linear motor model in the middle layer shown in Figure 12 are 282,786 and 149,043, respectively. Here, the maximum edge length for both 3D and 2D sections is maintained to be 0.5 mm.  
\begin{table}
\begin{tabular}{c c} \hline
**Size Parameter** & **Parameter Value** \\ \hline Inner radius of stator core (mm) & 50 \\ Outer radius of stator core (mm) & 100 \\ Permanent magnet thickness (mm) & 10 \\ Air gap length (mm) & 1 \\ Width of stator slot (mm) & 20 \\ Stator slot depth (mm) & 15 \\ Single stator axial length (mm) & 25 \\ Permanent magnet material & NdFeB42 \\ Number of turns (turns) & 76 \\ Rated speed (r/min) & 600 \\ Polar arc coefficient & 0.83 \\ Number of poles & 10 \\ Number of slots & 12 \\ Inner radius of permanent magnet (mm) & 50 \\ \hline \end{tabular}
\end{table}
Table 1: Size parameters of axial flux permanent magnet synchronous motor.  
\begin{table}
\begin{tabular}{c c c} \hline
**Layered Serial Number** & **Average Radius** & **Scaling Coefficient** \\ \hline
1 st & 52.77778 & 0.7037 \\
2 nd & 58.33333 & 0.77778 \\
3 rd & 63.88889 & 0.85185 \\
4 th & 69.44444 & 0.92593 \\
5 th & 75 & 1 \\
6 th & 80.55556 & 1.07407 \\
7 th & 86.11111 & 1.14815 \\
8 th & 91.66667 & 1.22222 \\
9 th & 97.22222 & 1.2963 \\ \hline \end{tabular}
\end{table}
Table 2: Average radius and scaling coefficient.