## 3 Numerical Analysis Conditions
### Analysis Results by Magnet Span and Thickness  
As shown in Tables 9-11, numerical analysis was conducted to assess the impact of the span and thickness of the permanent magnet. The number of windings was set to 25, and slot opening size was set to 3.0 mm. Figure 14: Mechanical power and efficiency by turns per coil and slot opening. (**a**) Power; (**b**) efficiency. Figure 13: Torque ripple variation for each turns per coil and slot opening condition. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item** & **Unit** & \multicolumn{3}{c}{**Value**} \\ \hline span & mm & \multicolumn{3}{c}{25} \\ thickness & mm & 3.5 & 4 & 4.5 \\ maximum torque & Nm & 19.77 & 20.5 & 21.0 \\ maximum torque rotation range & rpm & 96.0 & 94.9 & 94.0 \\ maximum cogging torque & peak-peak, Nm & 0.001390 & 0.001440 & 0.001460 \\ THD of cogging torque & \% & 7.52 & 7.88 & 8.32 \\ maximum torque ripple & peak-peak, Nm & 0.1669 & 0.1647 & 0.1663 \\ maximum flux density & T & 0.518 & 0.534 & 0.546 \\ power & W & 198.8 & 203 & 207 \\ efficiency & \% & 24.6 & 25.0 & 25.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Numerical data of 25 mm span model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Unit** & \multicolumn{3}{c}{**Value**} \\ \hline span & mm & \multicolumn{3}{c}{27} \\ thickness & mm & 3.5 & 4 & 4.5 \\ maximum torque & Nm & 19.99 & 20.7 & 21.3 \\ maximum torque rotation range & rpm & 95.2 & 94.1 & 93.2 \\ maximum cogging torque & peak-peak, Nm & 0.00251 & 0.00258 & 0.00254 \\ THD of cogging torque & \% & 8.76 & 9.22 & 9.75 \\ maximum torque ripple & peak-peak, Nm & 0.223 & 0.219 & 0.215 \\ maximum flux density & T & 0.520 & 0.536 & 0.549 \\ power & W & 199.3 & 204 & 207 \\ efficiency & \% & 24.6 & 25.1 & 25.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Numerical data of 27 mm span model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item** & **Unit** & \multicolumn{3}{c}{**Value**} \\ \hline span & mm & \multicolumn{3}{c}{23} \\ thickness & mm & 3.5 & 4 & 4.5 \\ maximum torque & Nm & 19.31 & 19.98 & 20.5 \\ maximum torque rotation range & rpm & 97.6 & 96.5 & 95.7 \\ maximum cogging torque & peak-peak, Nm & 0.00296 & 0.00306 & 0.00308 \\ THD of cogging torque & \% & 2.80 & 2.77 & 2.86 \\ maximum torque ripple & peak-peak, Nm & 0.0838 & 0.0843 & 0.0819 \\ maximum flux density & T & 0.512 & 0.528 & 0.540 \\ power & W & 197.3 & 202 & 206 \\ efficiency & \% & 24.4 & 24.9 & 25.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Numerical data of 23 mm span model. Figure 16 illustrates the variation in cogging torque. The solid line represents a 23 mm span, the dashed line a 25 mm, and the dotted line a 27 mm model. When the thickness increases from 3.5 mm to 4.5 mm, maximum cogging torque increases by up to 5.47%, and the THD of cogging torque increases by up to 11.4%. When the magnet span increases, the maximum cogging torque decreases by up to 17.6%, while the THD of cogging torque increases by up to 241%. Particularly, when the span increases from 25 mm to 27 mm, the THD of cogging torque increases by a maximum of 17.20%. However, when the span increases from 23 mm to 25 mm, there is a significant increase of up to 223.8% in the THD of cogging torque. Figure 17 demonstrates the variation in torque ripple. The solid line represents a 23 mm span, the dashed line a 25 mm, and the dotted line a 27 mm model. When the span increases from 23 mm to 27 mm, the maximum torque ripple increases by up to 165.5%. Figure 16: Cogging torque variation for each span and thickness condition. Figure 15: Result of various magnet span and thickness models. However, when the thickness increases from 3.5 mm to 4.5 mm for spans of 23 mm and 27 mm, the maximum torque ripple decreases by 2.30% and 3.59%, respectively. For a span of 25 mm, there is a decrease of 0.359% in maximum torque ripple.