## 4 Topology of the Permanent Magnet Synchronous Motor
The specific size was successively set to 2, 3, 4, and 5, which resulted in the number of turns per phase being 24, 36, 48, and 60 respectively. Subsequently, applying the physical constraints governing sizes D and L, a large number of topologies emerged. In each case, the electrical and geometric characteristics of the motor were calculated with the help of the Matlab2023a software, the 2D representation of the topology was performed, and the operation of the motor was simulated with the help of the specialized Maxwell 2023R1 software of Ansys. For each topology, the dimensions of the inner diameter of stator D, the outer diameter of stator D\({}_{\text{o}}\), and the axial length of motor L were extracted, as well as efficiency \(\eta\), as calculated and having previously determined the individual forms of losses. Figure 9 shows the variation of the engine performance as a function of the D/L ratio for each of the four considered cases. Based on the shape of the curves and the processing of the set of results, we concluded the following:  
* As the D/L ratio increased, engine efficiency decreased. This reduction was more evident for cases where 24 and 36 turns per phase were used. For N\({}_{\text{s}}\) = 60, the performance remained almost constant throughout the examined range of variation of the specific ratio. * The decrease in efficiency with the increase of the diameter in relation to the effective length of the motor could be explained by the simultaneous increase of the mechanical losses and the losses in the magnets. Conversely, as the length of the motor became longer, the copper losses increased. As far as the core losses were concerned, they showed relatively little change. However, again, the greater axial length for the engine favored their reduction in the majority of cases. * Topologies with N\({}_{\text{s}}\) = 24 and N\({}_{\text{s}}\) = 36 were rejected because they presented an obviously inferior performance compared to the other two considered cases (N\({}_{\text{s}}\) = 48 and N\({}_{\text{s}}\) = 60). The rejection of these topologies was justified by observing the curves in Figure 8, where the non-linear relationship between magnet mass and the diameter-to-length (D/L) ratio is illustrated. As D/L increased, the required magnet mass grew exponentially, highlighting a key design trade-off between torque production and material cost in PMSM design. A higher axial flux concentration could improve torque density but significantly increased material cost and thermal stress. Although the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Quantity** & **Symbol** & **Value** \\ \hline Number of Poles & \(2p\) & 38–**60**–100 \\ Number of Slots & \(Q_{s}\) & 42–**72**–108 \\ Fundamental Winding & \(k_{w}\) & 0.925–**0.933**–0.954 \\ Factor & \(f\) & 158.33–**250**–375 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimized Structural Variables for PMSM Design. topologies showed a lower performance for N\({}_{\rm s}\) = 24 and N\({}_{\rm s}\) = 36, the mass of the magnets was considerably larger. * Topologies with N\({}_{\rm s}\) = 60 seemed to be the most appropriate choice, as they combined the highest efficiency with the smallest mass of magnets. This characteristic also had a direct impact on the cost of the motor implementation due to the high cost of the magnets. So, the engines that belonged to this particular group of results were deemed to be the most economical option. Among the topologies with N\({}_{\rm s}\) = 60, it was decided to study further the one presenting a value for the D/L ratio equal to 0.91. This particular choice was made considering the higher efficiency combined with the lower values in the eddy current loss density in the magnets presented by this configuration. The losses of the magnets had to remain within acceptable limits Otherwise, the intense circulation of eddy currents within their mass would have led to a significant increase in temperature during the operation of the motor and may have eventually caused their temporary or even permanent demagnetization.