## 2 Experiments and Analysis
### Experimental Results and Range Analysis
#### 2.2.2 Effect of Test Factors on Erosion Depth
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(q\) & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \(d\) & 0.71 & 0.52 & 0.45 & 0.4 & 0.37 & 0.35 & 0.34 & 0.32 & 0.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correction coefficients for different levels. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Values**} & \multicolumn{4}{c}{**Factors**} \\ \cline{2-5}  & \(p\) **(MPa)** & \(\alpha\) (\({}^{\circ}\)) & \(t\) **(s)** & **s (mm)** \\ \hline \(K_{1}\) & 0.923 & 3.517 & 3.361 & 8.207 \\ \(K_{2}\) & 2.368 & 4.326 & 3.762 & 7.728 \\ \(K_{3}\) & 4.860 & 4.414 & 4.138 & \\ \(K_{4}\) & 7.784 & 3.678 & 4.674 & \\ \(k_{1}\) & 0.231 & 0.879 & 0.840 & 1.026 \\ \(k_{2}\) & 0.592 & 1.082 & 0.941 & 0.966 \\ \(k_{3}\) & 1.215 & 1.104 & 1.035 & \\ \(k_{4}\) & 1.946 & 0.920 & 1.169 & \\ \hline \(R\) & 1.715 & 0.224 & 0.32 small, in which the effect of impact time is greater than the jet angle. The correction range of standoff distance is the smallest, so its change has the least influence on the test index. The factor and index chart can further analyze the influence of various factors in the test ranges on the index of erosion depth, as shown in Figure 5. The trend chart of the factors and indexes are based on the levels of each factor as the abscissa, and the average value \(k_{i}\) of the test indexes in Table 3 is used as the ordinate. It can more intuitively show the change trend of the test index with the change of the factor level. For the jet pressure factor, the average value of the test index corresponding to the fourth level \(k_{4}\) is the largest, so 8 MPa is the optimal level for this factor. Similarly, the optimal levels of impact time, jet angle and standoff distance are 80 s, 60\({}^{\circ}\), and 10 mm, respectively, so the optimal level combination in this orthogonal test design is (_p_,\(a\),\(t\),_s_)\({}^{**}\) = (_p_4_,\(a\),_3\(t\),_4\(s\),_1_). Since this combination is not in the test list, a supplementary verification test is required. Under this condition, the erosion depth is 2.238 cm, which is indeed larger than the maximum index value of 2.108 cm on the fourteenth test in Table 2. This shows that the optimal working condition by range analysis is effective. In addition, Figure 5a reflects that when jet pressure is in the range of 2-8 MPa, erosion depth increases significantly with the increase of jet pressure. In Figure 5b, with the increase of jet angle, the optimal jet angle is around 60\({}^{\circ}\), which is consistent with the experimental result of [PERSON] et al. [41]. Figure 5c describes that erosion depth is increasing with the increase of impact time in the range below 80 s. In Figure 5d, standoff distance is within the test range of 10-15 mm, and the erosion depth decreases as the standoff distance increases. This is because the distance for energy exchange between water jet and the surrounding medium has become longer, and the entrainment effect of the boundary layer causes more low-speed surrounding media to be mixed into water jet, which can reduce the erosion ability of water jet. This is in accordance with the results of [PERSON] et al. [42]. Figure 5: Trend chart of the average indexes \(k_{i}\) of erosion depth. (**a**) Jet pressure, (**b**) jet angle, (**c**) impact time, (**d**) standoff distance.