## 3 Optimization Results  
The design of the FRM before optimization is shown in Figure 3a. The motor in Figure 3a was designed without an optimization algorithm and is described in the article [9]. Figure 3b shows the optimized design. Figure 4 shows the transient values of the torque depending on the rotor position for the modes specified in Table 1. In both modes, the torque waveform of the initial design takes negative values approximately in the middle of the first semi-period, while the optimization eliminates the negative values throughout the period. This is caused mainly by a nonuniform airgap formed by the line segment 1-2 (Figure 1b) in the direction of rotation. The transformation of the shape of the back side of the tooth with the line segment 1\({}^{\prime}\)-2\({}^{\prime}\) (line segment between points 1\({}^{\prime}\) and 2\({}^{\prime}\) in Figure 1b) is not significant. Figures 5 and 6 show the transient values of the current and the voltage, depending on the rotor position for modes specified in Table 1. Forms of currents before and after optimization are almost identical. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Before** & **After** \\ \hline Number of turns per phase & 80 & 91 \\ \hline \(R_{stat,inner}\), mm & 14 & 13.8 \\ \hline \(R_{stat,slot}\), mm & 18 & 17.4 \\ \hline \(R_{stat,bottom}\), mm & 22.5 & 22.463 \\ \hline \(W_{stator1}\), degrees & 8.1 & 15 \\ \hline \(\alpha_{\text{rot}}\), degrees & 35.4 & 17.6 \\ \hline \(w/w_{0}\) & 1 & 2.4119 \\ \hline \(w^{\prime}/w_{0}\) & 1 & 0.56176 \\ \hline Voltage shift, electrical radians & 0.06 & 0.017426 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The FRM parameters varied during the optimization. Additionally, \(R_{stat,middle}=0.5\cdot(R_{stat,slot}+R_{stat,inner})\). Figure 3: Motor design and simultaneous flux density field (T) in the FRM: (**a**) before optimization; (**b**) after. Figure 4: Torque dependencies on the rotor position before and after the optimization: (**a**) mode 1; (**b**) mode 2. Figure 5: Current dependencies on the rotor position before and after the optimization: (**a**) mode 1; (**b**) mode 2. Figure 6: Voltage dependencies on the rotor position before and after optimization. The change in the objective function (2) during optimization is shown in Figure 7. Changing the parameters included in the objective function (2) during the optimization is shown in Figures 8 and 9. Namely, Figure 8 shows the changes in motor efficiency during the optimization for modes specified in Table 1, and Figure 9 shows the change in the motor torque oscillations during the optimization. Figures show that the scattering of the parameters value becomes lower during the optimization that is the optimization converges. Table 4 shows the FRM characteristics before and after the optimization. In Figure 10, the losses for both FRMs in two different modes are presented. Mechanical losses are estimated according to \(5[W]\frac{n}{n_{matd}}+10[W]\Big{(}\frac{n}{n_{matd}}\Big{)}^{3}\), where \(n\)--rotational speed \(n_{matd}\)--rated rotation speed of rotor 18,000 rpm. It can be seen from Table 4 and Figure 4 that PPTTR in the rated mode decreased by 1.6 times, and in the mode with reduced load by 2.6 times. In addition, for FRM before optimization, the torque has sections with negative values, and for FRM after optimization, the torque is positive over the entire period. The objective function \(F\) decreased by 1.9 times. However, FRM losses after optimization increased by 6% in the rated mode. Therefore, optimization (hereinafter referred to as the first optimization) was stopped and a second optimization was launched.