## 3 Simulation Results and Analysis
### Results and Discussion: Safety Factors (Maximum Stress and Temperature Rise)  
When low-coercivity magnets are used in the IPMSM, there is a risk that the permanent magnets will irreversibly demagnetize due to the application of the flux-weakening control. The demagnetization can easily occur due to the thinner permanent magnets used in the optimized structure under the same current conditions. Therefore, it is necessary to determine that there is no irreversible demagnetization that occurs within the normal operating range of the motor, especially in the extreme condition. Figure 12: Torque–speed and power–speed characteristic curves: (**a**) torque–speed curve; and (**b**) power–speed curve. Figure 13: The Efficiency maps for the two structures under rated operating conditions: (**a**) the efficiency map for original structure; and (**b**) the efficiency map for optimized structure. The permanent magnets used in the optimized structure are the same as in the original one; the material is called N38 UH. Using the B-H curve as a reference, the simulation with three different temperatures is carried out under a 250 A current and at a speed of 10,000 rpm. The results shown in Figure 14 reveal that in the normal operating range, the \"\(\
abla\)-type\" permanent magnets' demagnetization is severer in the inner V-shape part. The demagnetization parameters are listed in Table 7 and show that the demagnetization is not irreversible. The mechanical structure strength of the rotor is a key factor when analyzing the safety of the motor when the motor is running at high speed. So, the stress distribution of the rotor is simulated by the 3-D model at the speed of 10,000 rpm, and the established 3-D models of the two different structures are shown in Figure 15. The setup of the rotor materials is listed in Table 8.  
The stress distributions of the two schemes are simulated at the speed of 10,000 rpm, and Figure 16 shows parts of the rotor nephogram of the stress. As the figure shows, the maximum value of stress is near 150 MPa in both structures, and the max points are both mainly distributed at the radial and circumferential magnetic bridge connections. However, the limited stress of the traditional steel type B35 AV1900 is around 300-400 MPa; hence, the mechanical structure strength of the optimized structure satisfies the safety request. If the motor shell and cooling methods of the optimized structure are different from the original structure, the production costs and manufacturing difficulty should be reassessed, and the comparison complexity will increase. So, the simulation of the temperature rise of the optimized structure is carried out with the same motor shell and cooling methods. Firstly, the equivalent cooling model is built using the Motor-CAD (ver. 11.1.5.1) software as shown in Figure 17. And then, the validation of this model is verified through comparing the temperature rise of the original to the real motor test temperature rise data. A thermal network method is adopted during the temperature rise calculation for fast computation speed and accuracy because the heat transfer phenomena are complex. The discrete data and simulation results with varied output power are illustrated in Figure 18, and all the data of different power values are obtained with a rated speed of 3000 rpm. (It should be noted that in the real limited condition, the motor should only operate at a rated speed and output power of 60 kW for 3 min under a 180 \({}^{\circ}\)C temperature limit, so the 60 kW temperature simulation only needs to use the temperature value at 3 min, but not the one at stable status, as a reference.) Figure 16: The rotor nephogram of stress: (**a**) original scheme; and (**b**) optimized scheme. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Rotor Core** & **Permanent Magnet** \\ \hline Density & 7650 kg/m\({}^{3}\) & 7500 kg/m\({}^{3}\) \\ [PERSON]’s modulus & \(2\times 10^{11}\) Pa & \(1.8\times 10^{11}\) Pa \\ [PERSON]’s ratio & 0.3 & 0.3 \\ \hline \end{tabular}
\end{table}