# A New Multi-Axial Flux Pm Motor-Generator System for Flywheel Energy Storage
## 3 Results
### Experimental Results  
#### 3.2.1 No-Load Operation  
The number of slots per phase (n\({}_{\text{s}}\)) in the 2-pole and 12-pole AFPM machine winding designed for FESS is calculated from Equation (5) [28]. In Equation (5), x and m are the number of slots and number of phases, respectively. \[\text{n}_{\text{s}}=\frac{\text{x}}{\text{m}} \tag{5}\]  
In Equations (6)-(9), y\({}_{\text{x}}\), c, \(\alpha\), f, and n are the number of steps, color number (slot number of phase under a pole), and the electrical angle (\(\alpha\)), frequency, revolution per minute (rpm), respectively [27; 28]. \[\text{y}_{\text{x}}=\frac{\text{x}}{\text{2p}} \tag{6}\]  
\[\text{c}=\frac{\text{x}}{\text{2p.m}} \tag{7}\]  
\[\alpha=\frac{\text{180.2p}}{\text{x}} \tag{8}\]  
\[\text{f}=\frac{\text{n.2p}}{\text{120}} \tag{9}\]  
The winding values of the designed AFPM machines are calculated from Equations (5)-(8) and given in Table 3.  
Figure 6: Maxwell model of the 2p = 12 pole AFPM motor–generator. An experimental setup of Flywheel was given in Figure 7. The experimental setup consists of two main components: a flywheel and an AFPM motor-generator. Other parts in the experimental setup are as follows: drive motor, oscilloscope, computer, loads, and current clamp. The loads shown in Figure 7 simulate the coil magnetic launcher. Consequently, the stage settings applied to the loads ensured that the flywheel was discharged with maximum current. The electro-motor voltage values corresponding to the rpm of the 2p = 2 pole AFPM motor winding are given in Figure 8. When the values of Figure 8 are examined, 17.9 V at 586 rpm and 45.3 V at 1482 rpm are obtained. The values shown in Figure 8 represent the phase-neutral voltage (V\({}_{\text{pn}}\)) obtained during the generator mode (idle operation) of the axial flux machine. An oscilloscope was utilized in the experimental study to measure these V\({}_{\text{pn}}\) values. Additionally, the motor rpm values indicate the operating frequency. The frequency values corresponding to the V\({}_{\text{pn}}\)-rpm pairs of 586.2-17.9, 885.6-27.6, 1182-35.9, and 1482-45.3 (V\({}_{\text{pn}}\)-rpm), as shown in the graph, are 9.77, 14.76, 19.7, and 24.7 (Hz), respectively, according to Equation (9). \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **2p = 2 Pole** & \multicolumn{3}{c}{**2p = 12 Pole**} \\  & & **A** & **B** & **C** \\ \hline Number of Slots (x) & 36 & 36 & 36 & 36 \\ Number of single poles (2p) & 2 & 12 & 12 & 12 \\ Number of phases (m) & 3 & 3 & 3 & 3 \\ Electrical angle (\(\alpha\)) & 10 & 60 & 60 & 60 \\ Number of slots per phase (ns) & 12 & 12 & 12 & 12 \\ Color number (c) & 6 & 1 & 1 & 1 \\ The number of step (y\({}_{\text{x}}\)) & (1–16) & (1–4) & (1–4) & (1–4) \\ Number of turns (turn/slot) & 80 & 40 & 40 & 5 \\ Conductor diameter (mm) & 0.5 & 0.5 & 0.5 & 8 \(\times\) 0.5 \\ Winding type & Toroidal & & Trapezoidal & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The winding (A–B–C) values of the designed AFPM machines. Figure 7: Test setup for flywheel (1—Flyheell, 2—Drive motor, 3—Driver, 4—Oscilloscope, 5—Computer, 6—Loads, 7—Current clamp, 8—AFPM motor–generator). The electro-motor force (emf) values obtained from the 2p = 12 poles of AFPM motor-generator windings are given in Figure 9. As seen in Figure 9a, the A and B windings of the 2p = 12 pole AFPM motor-generator are identical. Since the C winding in Figure 9b, designed for CML, consists of 8-conductor winding; the emf is approximately 1/8 for the same revolution numbers. The Vpn values obtained from the oscilloscope are shown in Figure 9a,b. Figure 9a presents the frequency values for winding A as follows: 12.53 Hz at 125.3-24.9 Vpn-rpm, 19.7 Hz at 197-39.1 Vpn-rpm, 29.67 Hz at 296.7-59.9 Vpn-rpm, 35.92 Hz at 359.2-72.3 Vpn-rpm, 42.33 Hz at 423.3-84.2 Vpn-rpm, and 45.92 Hz at 459.2-91 Vpn-rpm, calculated using Equation (9). Figure 8: 2p = 2 Pole AFPM motor Vpn-rpm characteristic. Figure 9: 2p = 12 Pole AFPM motor Vpn-rpm characteristic **(a)** A–B windings and **(b)** C winding.