# Analysis of Powertrain Loading Dynamic Characteristics and the Effects on Fatigue Damage
## 4 Fatigue Damage Analysis  
The above research has proved that the powertrain loading profiles are mainly related to the mean and harmonic engine torque, the harmonic engine torque, and the vibration properties of the powertrain system. In order to investigate the influences of the three factors on fatigue damage of the powertrain system components, three strategies were used to simulate the loading histories of PG testing:  
* Case 1: with the mean engine torque taking into account, the powertrain system was considered as rigid.
* Case 2: with the mean engine torque taking into account, the spring-damper components in the powertrain system were considered.
* Case 3: both the mean and harmonic engine torque was took into account, and the spring-damper components in the powertrain system was considered.  
The simulated results of the three cases are shown in Figure 10. Figure 10a,b show the simulated torque on the engine and the transmission output shafts in shifting process, respectively. Figure 10c,d show a partial enlarged view of the simulated data in acceleration process.  
Figure 9: Comparison of simulation and test data in shifting process. (**a**) Torque on the engine output shaft; (**b**) torque on the transmission output shaft.  
Table 2 shows the statistical results of the three simulation strategies.  
The simulation results of the three strategies will be compared by evaluating component fatigue damage with a pseudo-\(S\)-\(N\) curve, which is applicable in two conditions: one is that the real \(S\)-\(N\) curve of the material or the component is unknown, and the other is that the calculated fatigue damage is zero when the interests are infinite-life designed. If the pseudo-\(S\)-\(N\) curve has the same slope as the real one, the calculated pseudo-damage value can evaluate the intensity of the loading on the components concerned relatively [20]. In this paper, the estimated pseudo-\(S\)-\(N\) curve is set as slope factor \(k=5.23\), referring to the recommended method in reference [21].  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Channel** & **Minimum** & **Maximum** & **Mean** & **MAX RANGE** & **Std Deviation** & **RMS** \\ \hline \multirow{3}{*}{Engine} & Case 1 & \(-\)596.518 & 3201.51 & 1344.351 & 3798.028 & 1371.193 & 1920.273 \\  & Case 2 & \(-\)1848.1 & 3581.597 & 1344.412 & 5429.697 & 1376.596 & 1924.177 \\  & Case 3 & \(-\)2351.01 & 3947.91 & 1344.412 & 6298.921 & 1382.514 & 1928.416 \\ \hline \multirow{3}{*}{Transmission} & Case 1 & \(-\)1697.73 & 6748.207 & 1064.202 & 8445.938 & 1264.079 & 1652.398 \\  & Case 2 & \(-\)3540.17 & 9208.032 & 1064.249 & 12748.2 & 1275.829 & 1661.435 \\ \cline{1-1}  & Case 3 & \(-\)3666.31 & 9522.35 & 1064.249 & 13188.66 & 1276.794 & 1662.175 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistical results of the three simulation strategies (unit: Nm).  
Figure 10: Results of the three simulation strategies: (**a**) engine torque in shifting process; (**b**) transmission torque in shifting process; (**c**) partial enlarged view of engine torque; (**d**) partial enlarged view of transmission torque.