### Determining the Sensitive Stress
Condition 1-Condition 3 account for a high percentage of the entire test cycle, and the supercharger speed is generally not high during the no-load operation. In addition, the test is conducted in one cycle of 10 h, with 35 cycles in total. For a turbine impeller, the alternating stress test is very limited for fatigue performance assessment. Therefore, the test also mainly assesses the endurance performance of a turbine impeller. (2) From the whole test profile, turbine impeller failure is mainly caused by the centrifugal load action associated with the speed of a supercharger. In addition, the material of a turbine impeller is the cast high-temperature alloy K418. The effect of high temperature causes the lasting limit (lasting strength) of the blade root to decrease continuously. From the point of view of material damage principles, this reduction in strength can be quantitatively described by the amount of damage and is monotonic with time. Therefore, the strength damage at the endurance limit or endurance stress can be used as the degradation parameter when analyzing the performance degradation trend of turbine impellers, as well as when evaluating the durability of superchargers. The endurance limit data of K418 at different temperatures and times are shown in Table 2. In this table, the relationship between the temperature, endurance limit, and life (duration) is indicated, and the relationship between the accumulated load, temperature, endurance limit, and life (duration) is implied. From Figure 1, we can see that the main stresses affecting the turbocharger turbine blade roots are the centrifugal and thermal loads. According to Table 2, temperature directly affects the material's endurance limit, while rpm is directly linked to the endurance limit. The endurance limit is the main index for a durability assessment, and so temperature and rpm can be selected as the two sensitive stresses for the assessment test. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sampling**} & \multirow{2}{*}{\(\boldsymbol{\theta}^{c}\)**C**} & \multicolumn{8}{c}{\(\sigma_{\text{100}}\)} & \multirow{2}{*}{\(\sigma_{\text{200}}\)} & \multirow{2}{*}{\(\sigma_{\text{300}}\)} & \multirow{2}{*}{\(\sigma_{\text{500}}\)} & \multirow{2}{*}{\(\sigma_{\text{1000}}\)} & \multirow{2}{*}{\(\sigma_{\text{2000}}\)} & \multirow{2}{*}{\(\sigma_{\text{5000}}\)} & \multirow{2}{*}{\(\sigma_{\text{1000}}\)} \\ \cline{3-3} \cline{8-11}  & & & & & & & & & & & \\ \hline \multirow{11}{*}{Precision cast test rod} & 650 & — & 833 & 820 & 810 & 804 \(\textcircled{1}\) & 774 \(\textcircled{1}\) & — & — & — & — \\  & 700 & 810 & 725 & 720 & 710 & 666 & 627 \(\textcircled{1}\) & 610 \(\textcircled{1}\) & — & — & — \\  & 732 & 710 & 666 & 650 & 630 & 588 & 549 & 530 \(\textcircled{1}\) & 470 \(\textcircled{1}\) & 441 \(\textcircled{1}\) \\  & 750 & 680 & 617 & 610 & 600 & 539 & 510 & 480 & 412 \(\textcircled{1}\) & 372 \(\textcircled{1}\) \\  & 800 & 560 & 480 & 470 & 460 & 412 & 363 & 340 & 294 & 255 \(\textcircled{1}\) \\ \cline{1-1}  & 816 & 540 & 441 & 430 & 400 & 363 & 323 & 300 \(\textcircled{1}\) & 255 \(\textcircled{1}\) & 235 \(\textcircled{1}\) \\ \cline{1-1}  & 850 & 410 & 372 & 350 & 310 & 294 & 265 & 240 \(\textcircled{1}\) & 206 \(\textcircled{1}\) & 167 \(\textcircled{1}\) \\ \cline{1-1}  & 900 & 300 & 274 & 250 & 230 & 216 & 176 & 160 & 137 & 108 \(\textcircled{1}\) \\ \cline{1-1}  & 930 & 250 & 216 & 190 & 180 & 167 \(\textcircled{1}\) & 137 \(\textcircled{1}\) & — & — & — \\ \cline{1-1}  & 950 & 230 & 167 & 155 & 150 & 137 & 118 \(\textcircled{1}\) & 100 \(\textcircled{1}\) & — & — \\ \cline{1-1}  & 982 & 170 & 137 & 125 & 120 & 108 \(\textcircled{1}\) & 88 \(\textcircled{1}\) & — & — & — \\ \cline{1-1}  & 1000 & 140 & 118 & 113 & 110 & 88 \(\textcircled{1}\) & — & — & — & — \\ \hline \hline \end{tabular} \(\textcircled{1}\) Data derived from the integrated curve of thermal intensity parameters.  
\end{table} 
Table 2: Persistence limits of the K418 alloy at different temperatures and times [28].