# Fatigue Damage Assessment of Turbine Runner Blades Considering Sediment Wear
## 4 Fatigue Damage Assessment of Turbine Runner Blades  
The von Mises equivalent stress-time history data for each monitoring point on the runner blade, under various degrees of wear, were extracted for a period of 1.2 s. Figure 9 illustrates the stress-time history at monitoring point Q\({}_{1}\) for the same duration under wear degrees T\({}_{0}\) and T\({}_{1}\). As the stress-time history data from blade monitoring points at various wear times, derived from transient dynamics calculations, do not exhibit cyclic symmetry and are thus unsuitable for direct calculation of runner blade fatigue damage, this paper employs the rain-flow counting method to construct a load spectrum from the stress-time history data corresponding to different degrees of wear. This paper classifies the compiled stress amplitude data obtained under various degrees of wear and counts the number of cycles associated with each stress amplitude. Since the statistical stress amplitude is not directly applicable for calculating the fatigue damage of the runner blade across different wear degrees, it requires correction. The material chosen for the turbine runner in this study is ZGOCr13 Ni5 MO. Its yield strength is 495 MPa, and the tensile strength is 735 MPa. The \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{Time} & \multicolumn{6}{c}{Equivalent stress at monitoring point Q\({}_{4}\) (MPa)} \\ \cline{2-7}  & T\({}_{0}\) & T\({}_{1}\) & T\({}_{2}\) & T\({}_{3}\) & T\({}_{4}\) & T\({}_{5}\) \\ \hline
0.02 & 59.50 & 62.52 & 79.50 & 90.24 & 113.27 & — \\
0.04 & 53.81 & 66.77 & 77.38 & 87.20 & 105.08 & — \\
0.06 & 72.50 & 80.97 & 87.67 & 104.08 & 119.48 & — \\
0.08 & 60.83 & 62.03 & 83.08 & 95.96 & 113.05 & — \\
0.10 & 61.44 & 65.75 & 78.91 & 89.9 & 102.16 & — \\
0.12 & 71.71 & 81.21 & 87.03 & 103.17 & 118.44 & — \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{Time} & \multicolumn{6}{c}{Equivalent stress at monitoring point Q\({}_{5}\) (MPa)} \\ \cline{2-7}  & T\({}_{0}\) & T\({}_{1}\) & T\({}_{2}\) & T\({}_{3}\) & T\({}_{4}\) & T\({}_{5}\) \\ \hline
0.02 & 53.56 & 58.41 & 71.58 & 84.41 & 97.32 & 119.78 \\
0.04 & 49.30 & 52.33 & 65.28 & 77.03 & 91.45 & 108.99 \\
0.06 & 71.48 & 75.45 & 81.75 & 91.47 & 99.19 & 127.55 \\
0.08 & 54.62 & 51.62 & 68.09 & 78.91 & 97.56 & 120.16 \\
0.10 & 60.80 & 51.79 & 70.84 & 83.77 & 91.33 & 109.28 \\
0.12 & 69.64 & 74.88 & 81.90 & 91.66 & 99.81 & 127.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._corrected stress amplitude is then compared with the fatigue life curve (S-N curve) of this material [22], as seen in Figure 10. With this comparison, the fatigue cycles for blade monitoring points under different stress amplitudes and two levels of wear can be directly ascertained. Since the wear on runner blades predominantly occurs during the flood season, this study adopts a time scale of 2 months between different wear levels of the blades. Given that the rotation cycle of the runner is 0.12 s, it is possible to determine the total number of cycles and the fatigue damage at each stress amplitude for the blade's monitoring points under various wear conditions through a proportional relationship. Subsequently, the cumulative damage theory was applied to calculate the overall fatigue damage to the blade across different wear conditions, with the findings presented in Table 5.  
The total fatigue damage to the runner blade encompasses the damage accrued under both non-flood and flood season conditions. The unit operates for approximately 300 days annually, with the annual operational time history of the turbine depicted in Figure 11 for both the non-flood and flood seasons. Figure 10: Fatigue life curve of ZG0 Cr13 Ni5 MO material.