# Fatigue Damage Assessment of Turbine Runner Blades Considering Sediment Wear
## 4 Fatigue Damage Assessment of Turbine Runner Blades
Figure 9: The von Mises equivalent stress at blade monitoring point Q\({}_{1}\) under various degrees of wear within 1.2 s.  
Combined with the running time under the working conditions in flood season and non-flood season, the total fatigue damage of the monitoring points from Q1 to Q5 before being worn off can be calculated, and the calculation results are as follows. Therefore, the total fatigue damage of monitoring points Q1 to Q5 can be calculated before they are worn out. shown in Table 6. According to the fatigue linear cumulative damage theory, when the cumulative total damage reaches the limit, the value of D equals 1, indicating that the material or part has sustained fatigue damage. Observing the fatigue damage values of each monitoring point reveals that as the wear amount increases, the fatigue damage at each point also increases gradually. A comparison of the total fatigue damage data between Q3 and Q4 shows a consistent pattern: both points are subject to wear due to the internal flow field before fatigue damage to the blade material occurs. In order to compare the changes in the fatigue damage of the runner blades with and without considering wear after working for the same time, the fatigue damage of the runner blades without considering wear at different working times is calculated, respectively. The total fatigue damage of blade danger points at different wear times considering runner blade wear is also compared, as shown in Table 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Monitoring Point**} & \multicolumn{6}{c}{**Fatigue Damage under Different Blade Wear Degrees**} \\ \cline{2-7}  & \(\mathbf{T_{0}}\) & \(\mathbf{T_{1}}\) & \(\mathbf{T_{2}}\) & \(\mathbf{T_{3}}\) & \(\mathbf{T_{4}}\) & \(\mathbf{T_{5}}\) \\ \hline Q1 & 0.00670 & 0.01583 & — & — & — & — \\ Q2 & 0.00463 & 0.00613 & 0.01724 & — & — & — \\ Q3 & 0.00454 & 0.01052 & 0.01562 & 0.02921 & — & — \\ Q4 & 0.00405 & 0.00459 & 0.01316 & 0.0169 & 0.0386 & — \\ Q5 & 0.00246 & 0.00368 & 0.00498 & 0.01305 & 0.02774 & 0.04471 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The total fatigue damage of each monitoring point under different blade wear degrees. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Time (Year)**} & 0 & 0.5 & 0.7 & 1.5 & 1.7 & 2.5 \\ \hline Irrespective of blade wear & & & & & & \\ Fatigue damage & & & & & & \\ Consider blade wear & & & & & & \\ Fatigue damage & & & & & & \\ Damage growth rate & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Total fatigue damage with and without blade wear at the same time. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Stress Cycle Amplitude** (MPa)**} & \multicolumn{2}{c}{**T0**} & \multirow{2}{*}{**Total Damage**} & \multirow{2}{*}{**Stress Cycle**} & \multicolumn{2}{c}{**T1**} \\  & & & & **Amplitude of** & **Amplitude of** & **Amplitude (MPa)** & **Comrection (MPa)** & **Total Damage** \\ \hline
2.64 & 57.64 & & 0.28 & 61.15 & \\
4.73 & 60.37 & & 3.256 & 64.12 & \\
7.12 & 62.76 & 0.00670 & 6.32 & 67.19 & 0.01583 \\
9.16 & 64.80 & & 9.23 & 70.10 & \\
11.54 & 67.18 & & 11.68 & 72.55 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The total fatigue damage of Q1 point of blade running for 2 months under different wear degrees. Figure 11: Operation history of hydraulic turbine in flood season and non-flood season. From the table comparison, it is evident that considering blade wear results in a higher total fatigue damage than when wear is not considered. Additionally, the damage growth rate at the blade's maximum stress point shows an increasing trend with wear. To better understand and compare these changes, a curve illustrating the pressure fatigue damage over time, with and without accounting for wear, was plotted, as seen in Figure 12.  
The fatigue variation curves in Figure 11 reveal that fatigue damage to the blade, when wear is not considered, rises slowly with the runtime of the runner and is unaffected by the flood season conditions.