## 3 Numerical Analysis Conditions  
The variables used in the numerical analysis are shown in Table 3. The analysis included three configurations of windings, three slot opening sizes, three permanent magnet spans, and three permanent magnet thicknesses. Detailed descriptions of Models (1), (2), and (3) used in the numerical analysis are provided below. The power applied to the numerical analysis is a sine wave, Max. Line-Line voltage, rms 36 V, Max line current, rms 13.888 A. (1) Analysis model of turns per coil and slot openings  
The model used to analyze the effect of the number of windings and slot openings is shown in Figure 10. This system was modeled with variables set to reflect windings of 21, 23, and 25 turns. The permanent magnet's thickness was fixed at 3.5 mm, with a span of 23 mm. Slot shape optimization is crucial for comparing performance with different numbers of windings. As the number of windings increases, slot width also increases to accommodate the additional coil space. This necessitates maintaining a consistent fill \begin{table}
\begin{tabular}{c c c} \hline \hline
**Factor** & **Unit** & **Value** \\ \hline Straight part winding temperature & \({}^{\circ}\)C & 120 \\ C.S. end winding temperature & \({}^{\circ}\)C & 120 \\ O.C.S. end winding temperature & \({}^{\circ}\)C & 120 \\ Magnet temperature, T\({}_{\text{mag}}\) & \({}^{\circ}\)C & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Thermal settings used in Altair FluxMotor. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Factor** & **Unit** & **Value** \\ \hline Turns per coil & ea & 21, 23, 25 \\ Slot opening & mm & 2.4, 3.0, 3.6 \\ Magnet span & mm & 23, 25, 27 \\ Magnet thicknesses & mm & 3.5, 4.0, 4.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Variables used in numerical analysis. Figure 9: Winding design in Altair FluxMotor. Figure 11 shows the mechanical output under different winding and slot opening conditions. As the number of windings increased, the maximum torque also increased, but it decreased with a larger slot opening. Conversely, the range of rotation for maximum torque showed the opposite trend. When the number of windings increased from 21 to 25, the maximum torque went up by as much as 18.9%, while the range of maximum torque rotation decreased by up to 38.1%. On the other hand, when the slot opening expanded from 2.4 mm to 3.6 mm, the maximum torque decreased by up to 1.66%, while the range of maximum torque rotation grew by as much as 6.78%. Figure 12 illustrates the variation in cogging torque. The solid line represents a 21 turns, the dashed line a 23 turns, and the dotted line a 25 turns model. The maximum cogging torque and the THD of cogging torque were hardly influenced by changes in the number of turns per coil but were significantly affected by slot opening. When the slot opening was 3.0 mm, the maximum cogging torque reached approximately 0.00295 Nm, while the THD of cogging torque peaked at 2.81%. This effect is likely due to the reduction in the slot opening area that interacts most closely with the permanent magnet. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item** & **Unit** & \multicolumn{3}{c}{**Value**} \\ \hline winding & No. turns & & 21 & \\ slot opening & mm & 2.4 & 3 & 3.6 \\ maximum torque & Nm & 16.36 & 16.24 & 16.09 \\ maximum torque rotation range & rpm & 152.1 & 157.6 & 162.3 \\ maximum cogging torque & peak-peak, Nm & 0.01134 & 0.00295 & 0.00775 \\ THD of cogging torque & \% & 0.978 & 2.81 & 1.03 \\ maximum torque ripple & peak-peak, Nm & 0.1064 & 0.0649 & 0.0595 \\ maximum flux density & T & 0.460 & 0.458 & 0.452 \\ power & W & 261 & 268 & 273 \\ efficiency & \% & 33.5 & 34.1 & 34.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Numerical data of 21-turns-per-coil model.