## 4 Results and Analysis
### Vibration Response Analysis of Shafting under Different Blade Wear Degrees
In addition, the peak value also appears at two or three times the frequency of the turbine runner system's vibration response, but the value is small. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Wear Thickness** & **0 mm** & **3.209 mm** & **9.626 mm** & **16.043 mm** & **22.461 mm** \\ \hline \(x_{\text{2p-p}}\) (\(\mu\)m) & 20.55 & 27.09 & 32.02 & 36.42 & 41.37 \\ \(y_{\text{2p-p}}\) (\(\mu\)m) & 22.20 & 27.31 & 31.63 & 36.15 & 41.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The peak-peak value of the turbine runner system in x and y directions for different wear degrees. Figure 11: Time-domain comparison of radial displacement response of turbine runner system with different wear degrees: (**a**) x direction, (**b**) y direction. Figure 14: Frequency-domain comparison diagram of displacement response of turbine runner in x direction with different wear degrees. Figure 12: Frequency-domain diagram of vibration response of generator system in x direction: (**a**) unworn, (**b**) wear 22.461 mm. Figure 13: Frequency-domain diagram of vibration response of turbine runner system in x direction: (**a**) unworn, (**b**) wear 22.461 mm. Figures 15 and 16 show the axis-locus diagram of the spindle system when the runner blades are in two wear states at the rated speed. It can be seen from the figure that the shape of the axis-locus diagram of the generator rotor and the turbine runner tends to be circular and has good sealing properties. When the wear degree of the runner blade increases, the axis locus of the generator rotor has almost no trend of increasing, and the neutrality is good. However, the axis locus of the turbine runner system is not located at the origin of the coordinates, because the mean value of the radial fluid excitation force is not zero, which leads to a certain degree of deviation in the vibration response of the turbine runner system. Figure 17 shows the comparison of the axis locus of the turbine runner system with no blade wear and four wear degrees. It can be seen from the figure that with the increasing wear thickness of runner blades, the range of the axis locus of the turbine runner system also expands. The distance between the axis-locus coordinates and the origin of coordinates during the movement of the turbine runner system is calculated, as shown in Table 7. It can be seen that the maximum deviation distance of the axis locus changes from the initial 16.48 \(\upmu\)m to 21.70 \(\upmu\)m, with an increase of about 31.67%. Figure 16: Comparison of axis locus of the turbine runner system with unworn blades and worn blades of 22.461 mm. Figure 15: Comparison of axis locus of generator system with unworn blades and worn blades of 22.461 mm. Figure 20 shows the phase trajectory of the turbine runner under different blade wear degrees. As can be seen from the figure, with an increase in the degree of wear, the phase trajectory circle continues to expand, but the degree of fluctuation is relatively reduced. This is because the axis locus increases continuously under the influence of the rotating frequency excited force, while the disturbance amplitude of the blade frequency fluid excited force does not increase significantly. When the turbine runner moves in the x direction, its maximum speed increases from 0.57 mm/s to 0.72 mm/s, an increase of about 26.32%, indicating that the kinetic energy of the turbine runner system increases significantly during this process. If it continues to increase according to this trend, there is a greater risk of accidents when the turbine runner system collides with a larger kinetic energy.