## 3 Electromagnetic Characteristic Analysis
### Loss Analysis  
The loss of the motor is the direct cause of its temperature rise. The temperature rise will affect the motor's operational performance. The loss of the axial flux permanent magnet motor must be analyzed. In reference [24], losses were calculated using simplified empirical formulas and two-dimensional models. To achieve more precise loss calculations, this paper employs the Maxwell tensor method in combination with the three-dimensional finite element method and more accurate loss formulas for a detailed analysis. In this paper, the motor loss is calculated when the rated output power is 0.3 kW to verify that its efficiency is within a reasonable range. The stator core of the motor adopts the soft magnetic alloy material of 1J22, and the core loss will occur under the excitation of the sinusoidal alternating magnetic field of the winding. Core loss mainly includes hysteresis loss, eddy current loss, and additional loss. The basic formula of core loss, proposed by [PERSON], is as follows:  
\[P_{\text{Fe}}=P_{\text{h}}+P_{\text{c}}+P_{\text{e}} \tag{7}\]  
\[P_{\text{h}}=k_{\text{h}}\cdot f\cdot B_{\text{m}}^{\alpha} \tag{8}\]  
\[P_{\text{c}}=k_{\text{c}}\cdot f^{2}\cdot B_{\text{m}}^{2} \tag{9}\]  
\[P_{\text{e}}=k_{\text{e}}\cdot f^{1.5}\cdot B_{\text{m}}^{1.5} \tag{10}\]  
where \(P_{\text{Fe}}\) is the total core loss and \(P_{\text{h}}\), \(P_{\text{c}}\), and \(P_{\text{e}}\) represent the hysteresis, eddy current, and additional losses, respectively. The coefficients \(k_{\text{h}}\), \(k_{\text{c}}\), and \(k_{\text{e}}\) denote the respective loss coefficients; \(f\) is the frequency; \(B_{\text{m}}\) is the maximum magnetic flux density; and \(\alpha\) is the core flux density coefficient. Among them, the coefficients \(k_{\text{h}}\), \(k_{\text{c}}\), \(k_{\text{e}}\), and \(\alpha\) are obtained by referring to the data of the 1J22 soft magnetic alloy material provided by the material supplier. Coefficients \(k_{\text{h}}\) and \(\alpha\) are variables related to the magnetic induction intensity. The parameters of 1J22 soft magnetic alloy material are input into the software for calculation, and the core loss curve can be obtained. As shown in Figure 20, the stator core loss of the motor is about 630 mW. The motor adopts a double-stator three-phase winding structure, so the winding loss is generated by the three-phase windings of the upper and lower stators. Due to the low speed of the axial flux permanent magnet motor, the high frequency magnetic field has little effect on the winding loss, and the additional winding loss caused by the skin effect can be ignored. The winding loss of the axial flux permanent magnet motor is as follows:  
\[P_{\text{C}_{\text{H}}}=mI^{2}R_{AC} \tag{11}\]  
Figure 20: Motor stator core loss. where \(P_{Cu}\) is the winding loss, \(m\) is the number of winding phases, \(I\) is the RMS current, and \(R_{AC}\) is the AC resistance of a single-phase winding. The AC resistance is given by the following:  
\[R_{AC}=k_{\rm R}.\frac{Nl_{\rm av}}{\sigma S_{\rm C}} \tag{12}\]  
\[m_{\rm Cu}=\rho Nl_{\rm av}S_{\rm C} \tag{13}\]  
where \(k_{\rm R}\) is the resistance coefficient (it is a correction coefficient considering various factors, which can make up for the deviation of resistance calculation based on basic physical parameters to a certain extent), \(N\) is the number of turns of single-phase winding, \(l_{\rm av}\) is the average length of single turn, \(\sigma\) is the conductivity of the conductor, \(S_{\rm C}\) is the cross-sectional area of conductor, \(m_{\rm Cu}\) is the mass of conductor, and \(\rho\) is the density of conductor. The calculation formula of the winding loss of axial flux permanent magnet motor is obtained by introducing Equations (12) and (13) into Equation (11):  
\[P_{\rm Cu}=mI^{2}\frac{k_{\rm R}m_{\rm Cu}}{\sigma\rho S_{\rm C}^{2}}=mI^{2} \frac{k_{\rm R}m_{\rm Cu}}{\sigma\rho} \tag{14}\]  
where \(J\) is the conductor current density, \(J=I/S_{\rm C}\).