## 4 Analysis and Discussions  
### Temperature Field Distribution of TPMLG  
The steady heat transfer and fluid equations under previous assumptions were solved by software Fluent with boundary conditions and material properties. The temperature field distribution and variation rules were obtained. Firstly steady-state temperature results under the natural air-cooling condition are presented. Figure 8 depicts the temperature field contour of the TPMLG at the middle longitudinal section. The TPMLG temperature gradient can be clearly seen declining from the inside to the outside. Particularly in the axial direction, the temperatures of the windings and the permanent magnets decrease from the axially central position to both ends cooled by ambient air directly. The temperature at the top of the windings' central position is the highest, reaching 127.8 \({}^{\circ}\)C, as shown in Figure 8. The insulation causes a noticeable temperature difference between the windings and the stator, contributing to the high temperature increment of the stator winding and the slot insulation. There is a temperature difference of approximately 10-20 degrees between the upper and the bottom surfaces, due to the heat conduction between the bottom surface of the LG and the base. A certain amount of heat is transferred to the base, affecting the surrounding temperature and may bring heat load to other equipment of the FPEG system. The temperature contour of the windings is presented in Figure 9. The temperature at the top of the windings is higher than that of the bottom, and the temperature in the middle of the windings is higher than those at both ends. The highest temperature of the windings is located at the top of the central position. This is because it is not exposed to the air. Heat is transferred from the top of the central position to ambient air through insulation,  
Figure 8: Temperature contour of the TPMLG at the middle longitudinal section (in \({}^{\circ}\)C). Figure 7: Electromagnetic–thermal coupling module connection diagram. the stator, and the casing, hence the heat transfer resistance is higher than other parts of the windings. Therefore, it is the part with the worst heat-dissipation condition. The temperature of every part in the windings is lower than the maximum allowable working temperature for the standard of class F insulation. Therefore, the temperature distribution of the windings is relatively reasonable. The temperature contour of the permanent magnets embedded in the mover is depicted in Figure 10. In comparison with the windings, the overall temperature field of permanent magnets is lower, because the eddy current loss of the permanent magnets is much smaller than the copper loss of the windings. Similarly, the temperature of the permanent magnets shows a downward trend from the axial center to both ends along the axial direction. Due to the long length of the mover, temperature differs significantly between external air and the air gap, resulting in different heat-dissipation conditions. Conversely, the temperature field of the PMs is more homogeneous than that of the windings in the circumferential direction owing to more uniform heat dissipation conditions and the lower height. Although the eddy current loss in the permanent magnets is relatively small, the fluctuation in temperature of the PMs extends over a range of 27.5 \({}^{\circ}\)C, indicating poor heat dissipation conditions for internal permanent magnets. The top temperature of the PMs reaches 109.2 \({}^{\circ}\)C. Though the temperature is lower than the limited operating temperature, there is still a potential risk of demagnetization in case the TPMLG is placed in an enclosed structure with poor heat dissipation. The only two paths for the PMs to dissipate heat are through convective heat exchange with air and heat conduction with connecting rods, so air gap heat dissipation is crucial for suppressing the temperature rise of the permanent  
Figure 10: Temperature contour of the permanent magnets (in \({}^{\circ}\)C).