## 3 Results and Discussions
### Laboratory Measurements  
Laboratory measurements were performed on the prototype AFPMSM with the data presented in Table 1. Measurements of the torque size for different loadings were performed as well as the induced voltage measurements at different rotation speeds. Table 7 shows the measured values of induced voltages in individual phases of the machine and average value for all three phases at different rotation speeds. Figure 9: 2D model of the coreless double-sided AFPMSM with dimensions. Table 8 shows the comparison of average measured values of induced voltages and calculated values using the analytical method and developed mathematical model in explicit form. Table 9 shows the comparison of measured values of torque at different electrical current values and comparison with the calculated values, using the analytical method and developed mathematical model in explicit form. Tables 8 and 9 show that the developed mathematical model is accurate, since the matching of the measured values of torque and induced voltage are in good agreement with the calculated results. Some deviation is present in the matching of the results which may be caused by the measuring equipment. For this purpose, we measured the axial component of magnetic flux density in the middle of the distance between PMs on opposite rotor disks. To measure the axial component of magnetic flux density (\(B_{\mathrm{z}}\)) in the middle of the distance between PMs on opposite rotor disks we developed a special tool that enables the PMs to stay in their position and measure the values at exact positions. Two tools were modeled and 3D printed \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(n\) **(min\({}^{-1}\))** & **\(E_{1}\) (V)** & **\(E_{2}\) (V)** & **\(E_{3}\) (V)** & **\(E_{\mathrm{average}}\) (V)** \\ \hline
200 & 11.31 & 11.52 & 11.48 & 11.33 \\
300 & 16.8 & 17.12 & 17.1 & 16.99 \\
400 & 22.5 & 22.88 & 22.67 & 22.65 \\
500 & 28.14 & 28.47 & 28.34 & 28.31 \\
600 & 33.84 & 34.18 & 33.96 & 33.97 \\
700 & 39.44 & 39.83 & 39.6 & 39.62 \\
800 & 45.04 & 45.53 & 45.23 & 45.27 \\
900 & 50.68 & 51.22 & 50.89 & 50.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Induced voltages as different rotation speeds. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(n\) **(min\({}^{-1}\))** & **\(E_{\mathrm{average}}\)** & **\(f\)** & **\(E_{\mathrm{model}}\)** & **\(E_{\mathrm{average}}\)/\(E_{\mathrm{model}}\)** \\
**(min\({}^{-1}\))** & **(V)** & **(Hz)** & **(V)** & **(\%)** \\ \hline
200 & 11.33 & 16.67 & 10.85 & 104.42 \\
300 & 16.99 & 25 & 16.28 & 104.36 \\
400 & 22.65 & 33.33 & 21.7 & 104.38 \\
500 & 28.31 & 41.67 & 27.13 & 104.35 \\
600 & 33.97 & 50 & 32.55 & 104.36 \\
700 & 39.62 & 58.33 & 37.98 & 104.32 \\
800 & 45.27 & 66.67 & 43.41 & 104.28 \\
900 & 50.92 & 75 & 48.83 & 104.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of calculated and measured induced voltages as different rotation speeds. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(I\) & **\(T_{\mathrm{measured}}\)** & **\(T_{\mathrm{model}}\)** & **\(T_{\mathrm{measured}}\)/\(T_{\mathrm{model}}\)** \\
**(A)** & **(Nm)** & **(Nm)** & **(\%)** \\ \hline
10.21 & 16.72 & 15.29 & 109.35 \\
11.00 & 17.97 & 16.48 & 109.04 \\
12.03 & 19.52 & 18.01 & 108.38 \\
13.06 & 21.05 & 19.55 & 107.67 \\
13.98 & 22.41 & 20.93 & 107.07 \\
15.08 & 23.94 & 22.57 & 106.07 \\
16.14 & 25.48 & 24.16 & 105.46 \\
17.18 & 26.91 & 25.72 & 104.63 \\
18.16 & 28.27 & 27.19 & 103.97 \\
19.3 & 29.8 & 28.89 & 103.15 \\
20.19 & 30.97 & 30.22 & 102.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of calculated and measured Torque at different electrical current values. (one 17 mm thick and one 22 mm thick). Figure 9(a) shows the model of the tool with the location of the opening where the measuring probe (Magnetometer KOSHAWA 5 with the magnetic probe) will be inserted and Figure 9(b) shows the printed tool. The measuring probe is inserted into the opening, which is printed to the middle radius of the PMs.