## 2 Specification and Experiment of Basic WFSM  
A typical WFSM has a saliency ratio (\(L_{q}/L_{d}\)), and this ratio contributes to the generation of reluctance torque (\(T_{r}\)). The output torque (\(T\)) of the motor comprises two main components: magnetic torque (\(T_{m}\)) and reluctance torque. The former arises from the alignment of the magnetic flux generated by the stator winding with that produced by the rotor winding. On the other hand, reluctance torque is a result of the disparity between \(L_{d}\) and \(L_{q}\) of the rotor. This phenomenon is fundamental in understanding the torque equation of the conventional WFSM. In Equation (1), \(p\) is the number of pole pairs, \(\Psi_{f}\) is the field flux, \(i_{a}\) is the peak value of the stator current, and \(\beta\) is the current phase angle [17]. \[T=T_{r}+T_{m}=1.5p\{\Psi_{f}\mathrm{a}\mathrm{cos}\beta+0.5(L_{q}-L_{d})i_{a} ^{2}\mathrm{sin}2\beta\} \tag{1}\]  
To calculate the inductance using the torque equation, the magnetic equivalent circuit is represented as shown in Figure 3. The magnetic resistance can be calculated as follows:  
\[R_{m}=\ \frac{l}{\mu A} \tag{2}\]  
where \(l\) is the length, \(\mu\) is the permeability, and \(A\) is the cross-sectional area of the magnetic flux path. The relative permeability of air and copper is significantly smaller compared with that of the core, indicating that the magnetic resistance of the d axis is smaller than  
Figure 2: Structure of machines: (**a**) basic WFSM; (**b**) PMa-WFSM. that of the q axis, as expressed in the equation. With the magnetic resistance determined, the inductance can be calculated as follows:  
\[L_{d}=\frac{NF_{d}}{i_{d}}=\frac{N^{2}}{R_{gd}+R_{sd}+R_{rd}}\,\ L_{q}=\frac{ NF_{q}}{i_{q}}=\frac{N^{2}}{R_{gq}+R_{sq}+R_{rq}} \tag{3}\]  
where \(F_{d}\), \(i_{d}\), \(R_{gd}\), \(R_{sd}\), and \(R_{rd}\) are components of the d axis, which includes the magnetic flux, current, air-gap reluctance, stator magnetic resistance, and rotor magnetic resistance; \(F_{q}\), \(i_{q}\), \(R_{gq}\), \(R_{sq}\), and \(R_{rq}\) are components of the q axis, which includes the magnetic flux, current, air-gap magnetic resistance, stator magnetic resistance, and rotor magnetic resistance. \(N\) represents a turn of the winding coil. The specifications of the basic WFSM are shown in Table 1. To achieve rated torque, the rated stator current was selected to be 13.5 A\({}_{\text{rms}}\), and the rotor current was chosen to be 5 A\({}_{\text{dc}}\). Additionally, considering the current density to be below 4 A/mm\({}^{2}\) and manufacturing constraints, a slot fill factor of 0.35 was adopted, with the number of turns for the stator being set to six turns, while for the rotor, it was set to six turns. The winding method for the stator used distributed winding to reduce harmonics, while the rotor was wound with concentrated windings. The number of poles per phase is three. After selecting the specifications, the design process was initiated, and a 5 kW WFSM was manufactured. The experimental setup was configured as shown in Figure 4a. The average torque value was extracted using a servo motor. The difference between the experimental values and FEM analysis results in output performance was compared through the no-load EMF peak, no-load EMF plot, and average torque. \begin{table}
\begin{tabular}{c c} \hline \hline
**Specification** & **Value** \\ \hline Output power & 5 kW \\ Rated torque/speed & 31.91 Nm/1500 rpm \\ Rated stator peak current & 19.09 A \\ Rated rotor current & 5 A\({}_{\text{dc}}\) \\ Number of poles/slots & 16 pole/72 slot \\ Stator/rotor outer diameter & 236 mm/170 mm \\ Coil space factor & 0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specification of basic WFSM. Figure 3: The magnetic equivalent circuit of the basic WFSM. The output performance of a WFSM is significantly influenced by the field current.