## 4 Fatigue Analysis and Life Modeling  
### Fatigue Testing  
The rotor studied in this paper is a multi-layer punch-laminated PMSM rotor. The central magnetic bridge of the rotor is a location prone to stress concentration and represents a weak point for rotor strength and fatigue design. To perform a fatigue analysis of the motor rotor, it is necessary to obtain an S-N curve for the rotor material. The material  
Figure 19: The failure diagram of the rotor. Figure 18: Damage contribution ratio under different stress loads. used for the rotor laminations is a non-oriented electrical steel plate produced by Baosteel, with a thickness of 0.3 mm, a silicon content of approximately 3.1%, and a width of 3 mm for its central magnetic spacer bridge. In this study, fatigue specimens of the same size were selected for testing to approximate the actual component and reduce the effect of the structure on its life, as shown in Figure 20.  
All fatigue tests were performed on a 100 kN RUMUL electromagnetic resonance fatigue tester [21], as illustrated in Figure 21. The stress ratio R was set to 0.1, the test frequency was approximately 40 Hz, and tests were conducted using secondary stress levels with maximum stresses of 450 MPa and 350 MPa. Fatigue tests were conducted at both 20 \({}^{\circ}\)C and 150 \({}^{\circ}\)C, as the S-N curve of the rotor laminations also varies at different temperatures, allowing for further consideration of the effect of temperature on rotor life. The fatigue test results of the standard specimen are shown in Figure 22:  
Figure 21: Fatigue specimen test diagram. Figure 20: B30 AVH1500 standard fatigue specimen (**a**) and rotor fatigue specimens (**b**) (unit: mm). The S-N curve obtained by fitting at 22 \({}^{\circ}\)C is as follows:  
\[\text{S}_{a}=1037.55307-110.87374\text{lg}N_{f} \tag{7}\]  
The S-N curve obtained by fitting at 150 \({}^{\circ}\)C is as follows:  
\[\text{S}_{a}=900.2793-118.5052\text{lg}N_{f} \tag{8}\]  
The S-N curve is fitted using a logarithmic coordinate system, where the horizontal axis represents stress levels and the vertical axis represents the logarithmic value of the number of cycles. Under this form, the S-N curve typically presents a linear shape, where the slope k and intercept C of the straight line are both material parameters. By extracting the values of the slope k and intercept C of the material's S-N curve under ambient and high-temperature conditions, the S-N curve under other temperature conditions can be extrapolated using linear interpolation. The resulting graph is shown in Figure 23 below:  
Figure 23: Distribution of S-N slope and intercept at different temperatures. Figure 18:0 Standard fatigue specimen life curve. When conducting fatigue tests on rotor blades, the fatigue specimens need to simulate the centrifugal force load of the rotor under high-speed rotation. As shown in Figure 24, the centrifugal force is simulated by applying tensile loads on the test machine. Three typical operating conditions are selected for loading during the test process: 400 N, 500 N, and 600 N. Figure 24 shows the stress distribution of the motor rotor laminations under a tensile load of 600 N, and the presence of the clamping plate above the rotor facilitates the addition of tensile loads in the finite element setting. The analysis results show that the maximum stress occurs at the center inter-pole bridge, with a magnitude of 462 MPa. The stress levels corresponding to the weak positions under 500 N and 400 N are 425 MPa and 388 MPa, respectively. The experimental results of the fatigue specimens with rotor structural features are presented in Figure 25, with lifetimes of approximately 10\({}^{5}\), 2.2 \(\times\) 10\({}^{5}\) and 6\(\times\)10\({}^{5}\) cycles under the loading conditions of 600 N, 500 N, and 400 N, respectively.