## 3 Fatigue Life Analysis Based on Load Spectrum
### Calculation and Analysis of Fatigue Life  
Based on the static analysis results and the stress-time load spectrum data [25], combined with the material properties of 20 CrNiMo, the fatigue life of the main reducer gear  
Figure 9: Load spectrum ignoring braking torque. under electromagnetic braking condition and friction braking condition was calculated, respectively. The specific calculation process is shown in Figure 14.  
Figure 11: Contact stress load spectrum of friction braking. Figure 12: Bending stress load spectrum of electromagnetic braking. Figure 10: Contact stress load spectrum of electromagnetic braking. Four nCode SN TimeSeries modules are established and a channel is created with the statics module; the statics results are imported into each of the four modules to calculate the fatigue lives of the main reducer gears under different stress spectra. After importing the static results, nCode will automatically generate various modules for solving. The stress-time history obtained above is imported into TimeSeries input module, and the load spectrum and finite element results are added. In the solver, the material type is set to SN R-ratio multi-curve, and the fatigue curve of the material is the S-N curve [26] of the multi-stress ratio shown in Figure 15. SAE Steel Grade 8620 is found to assign it to all entities, and the Goodman curve is used to correct the mean load. Figure 14: Fatigue life calculation process based on nominal stress method. Figure 13: Load spectrum of friction braking bending stress. After the solver is set up, the fatigue life of the main reducer gears under electromagnetic braking condition and friction braking condition is calculated, respectively, and the results are shown in Figure 16.  
Figure 16: Fatigue life maps of pinion with four load spectrums. (**a**) With contact stress load spectrum of electro-magnetic braking; (**b**) With contact stress load spectrum of friction braking; (**c**) With bending stress load spectrum of electro-magnetic braking; (**d**) With bending stress load spectrum of friction braking. Figure 14.0 20 CrNiMo S-N curve. The fatigue life data of the same dangerous node are extracted, as shown in Figure 14.1 For the main reducer gears, during the normal driving process of the bus, the working face is the concave surface of the pinion, the tooth root of the concave side is tensile stress, and the tooth root of the convex surface is compressive stress. In the case of conventional buses, the stress on the tooth root is also the same during braking, whereas, in the case of battery electric buses with electromagnetic braking, the working face will change to the pinion convex surface during braking, and the compressive stress on the tooth root of this side will also change to tensile stress; the tensile stress on the concave surface will change to compressive stress as well. It can be seen that the stress changes in the pinions are more complex, and the calculations with four load spectrums show that the lowest life spans are all found on the pinions, so that the effects of electromagnetic braking can be analyzed by simply calculating the fatigue life of the pinions. Calculation results showed that the bending fatigue life of pinion concave tooth root under electromagnetic braking condition is 78.9% of that under friction braking condition, while the bending fatigue life of pinion convex tooth roots is 78.5% of that under friction braking condition. The tooth contact fatigue life of pinion working surface under electromagnetic braking condition is 78.2% of that under friction braking condition, which is in line with the engineering practice. This shows that electromagnetic braking does have an influence on the main reducer gears fatigue life.