## 2 Methodology
### BLDC Motor Design  
The initial phase involves the determination of the machine power, speed, pole/slot combination, number of phases, and DC voltage values. Subsequently, machine dimensions are calculated based on Equations (1) and (2), following the determination of the parameters [40, 41, 42]. Initial parameters such as the power, shaft speed, voltage, and pole/slot combination were selected based on referenced UAV configurations and the optimal operating points of components; for example, the power was selected based on the required propulsive power on aircraft, the shaft speed was selected to meet propeller specifications for the maximum rotational speed to connect directly without an additional gearbox, the voltage was selected based on existing batteries on the market and was considered to take current from the battery, and the pole/slot combination was selected to provide a higher winding factor and low harmonics. \[D^{2}l=\frac{P}{C\left(\frac{h}{60}\right)} \tag{1}\]\[X=\sqrt[3]{p}\frac{\pi}{2p} \tag{2}\]  
Following the computation of the machine's diameter, length, and their respective ratios, the air-gap length was determined. The resulting values obtained through calculation and determination are presented in Table 2.  
Using these parameters, the number of turns can be calculated according to Equation (3), where E, kw, \(\tau_{p}\), \(\alpha\), and B are the back emf, winding factor, pole pitch, coefficient, and air-gap magnetic flux density value, respectively. The number of turns affects the air-gap flux density, and according to that, the projected and calculated values could be compared [40]. \[N=\frac{\sqrt{2}E}{\omega k_{w}l\tau_{p}\alpha B} \tag{3}\]  
\[E=0.95V_{d}c \tag{4}\]  
The width of the stator tooth and the calculation of slot dimensions are the next step in the design process. These are calculated using the magnetic flux and current density values, which are determined by the windings. The calculated values are shown in Table 3.  
The thickness of the magnet is another parameter that was calculated, as it affects the creation of the magnetic field on the rotor side. To calculate the thickness of the magnet, Equation (5) was used. The parameters in Equation (5) are presented in Table 4.  
\[d_{m}=\frac{B((\mu_{m})/(\mu_{0}))g_{m}K_{i}K_{r}g}{g_{m}K_{i}B_{r}-B} \tag{5}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Value** \\ \hline Machine Power (P) & 40 [kW] \\ Rated Speed (n) & 2500 [rpm] \\ Machine Constant (C) & 150 [kWs/m\({}^{3}\)] \\ Pole/Slot Combination & 14/15 \\ Number of Phases & 3 \\ DC Voltage & 400 [V] \\ Stator Inner Diameter (D) & 278.3 [mm] \\ Stack Length (l) & 82.6 [mm] \\ Air Gap & 1 [mm] \\ Winding Factor (kw) & 0.95 \\ Integer \(\alpha\) & 2\(\pi\) \\ Air-Gap Flux Density & 0.8 [T] \\ Number of Turns in Phase Winding & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Determined and calculated values of the electric machine. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Value [mm]** \\ \hline Slot Opening Width & 5 \\ Length Between Stator Teeth & 32.38 \\ Stator Tooth Height & 22.74 \\ Stator Yoke & 18.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Stator tooth and slot dimensions. After these calculations, the calculated parameters were imported into ANSYS Maxwell EM Suite 2023 R2 to simulate the designed machine with the FEA method. In Figure 2, the designed machine's 2D model is shown. To run a dynamic simulation, an external circuit was created, and the designed machine was driven with that to observe the speed, current, induced voltage, and torque values. The results are shown in Section 4. To analyze the thermal performance of the designed machine, ANSYS Motor-CAD Version 14.1.5.1 software was used. The designed machine model was created using the parameters calculated in this software, and a thermal model was created. Liquid cooling was used as a cooling system. The thermal model and simulated temperature values are shown in Section 4. The machine, modeled in ANSYS Motor-CAD, is shown in Figure 2.