## 3 Mechanical-Electromagnetic Performance Analysis
### Mechanical and Rotor Dynamics Performance Analysis  
#### 3.2.1 Mechanical Stress Analysis  
After electromagnetic design, mechanical design is examined. However, this process is not suitable for designing a HS machine due to the existence of a large centrifugal force. The PM contributes much less to rotor rigidity than the shaft does. Therefore, in order to obtain a more robust rotor, the shaft diameter needs to be maximized when the rotor outer diameter is fixed. Furthermore, a sleeve is employed to protect the PM from interference or shrink fit. The mechanical design of HSPMSMs was investigated, focusing on obtaining optimal sleeve design. In this section, mechanical performance is optimized and compared in terms of stress and dynamics under the same output power. In order to ensure that the rotor could run in an HS state, the following mechanical constraints need to be considered:  
1. maximal stresses in the sleeve cannot exceed their permissible safety stress;
2. contact force between PM and sleeve is high enough to meet torque transfer;
3. rate rotor speed is below the first critical speed, and its difference needs to be more than 15% at least.  
Because sleeve stress changes with rotation speed and working temperature, the worst condition, with the rotor at 160 kpm and 120 \({}^{\circ}\)C, is considered in this section. In the integrated rotor, mechanical stress in each part of the rotor needs to be lower than the permitted stress value. Mechanical stress is calculated by using 3D FEM. The material properties of the retained sleeve were obtained from the material suppliers and are shown in Table 2. As M1 was a cylindrical PM structure, a Ti6 Al4V was used as the sleeve to enhance rotor rigidity. The permitted stress of CFC and Ti6 Al4V is 1000 and 1300 Mpa along the tangential direction, which was adopted in M1 and M2, respectively. The permitted stress of silicon sheet 10 JNEX900 is only 700 Mpa, which is used as the M3 and M4. The calculated mechanical stress distribution and total deformation on the sleeve at the rated operation conditions are shown in Figures 4 and 5. All rotor parts could meet the material requirements, and M1 presented the lowest stress due to its smaller rotor diameter and solid cylindrical structure. For M3 and M4, the maximal stress of the sleeve occurred at the flux bridge, while it was less than 90% of the permitted stress of the adopted material, as shown in Figure 4c,d. The total deformation of M3 was the highest, but this kind of deformation was still within the permitted elastic deformation, as shown in Figure 5c. When the maximal stress was within the permitted range, the sleeve-free M3 and M4 had more advantages, while M1 and M2 had higher stress limitations due to their use of a sleeve.  
Figure 3: HSPMSM torque with different rotors at no-load. (**a**) Waveforms; (**b**) spectral analysis.  
Figure 4: Mechanical stress distribution in the rotor at rated operation conditions (160 krpm). (**a**) M1; (**b**) M2; (**c**) M3; (**d**) M4.  
Figure 5: Total deformation distribution in the rotor at rated operation conditions (160 krpm). (**a**) M1; (**b**) M2; (**c**) M3; (**d**) M4.