## 4 Orthogonal Test Design
### Design Table of Orthogonal Test Plan
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Index** & & \(A\) & \(B\) & \(C\) & \(D\) \\ \hline \multirow{5}{*}{Section taper/\({}^{\circ}\)} & \(\overline{K}_{\parallel 1}\) & 5.025 & 10.342 & 6.285 & 5.682 \\  & \(\overline{K}_{\parallel 2}\) & 6.647 & 4.258 & 6.707 & 4.640 \\  & \(\overline{K}_{\parallel 3}\) & 6.200 & 3.710 & 3.162 & 7.717 \\  & \(\overline{K}_{\parallel 4}\) & 3.752 & 3.315 & 5.470 & 3.585 \\  & \(R_{j}\) & 2.895 & 7.027 & 3.545 & 4.132 \\ \hline \multirow{5}{*}{Section depth/mm} & \(\overline{K}_{\parallel 1}\) & 1.455 & 0.900 & 1.238 & 1.513 \\  & \(\overline{K}_{\parallel 2}\) & 1.480 & 1.288 & 1.433 & 1.355 \\ \cline{1-1}  & \(\overline{K}_{\parallel 3}\) & 1.300 & 1.690 & 1.525 & 1.400 \\ \cline{1-1}  & \(\overline{K}_{\parallel 4}\) & 1.458 & 1.815 & 1.497 & 1.425 \\ \cline{1-1}  & \(R_{j}\) & 0.180 & 0.915 & 0.287 & 0.158 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Range calculation values of orthogonal test results. Figure 10: Experimental values of orthogonal tests 1–16. (**a**) Taper value; (**b**) Depth value. Figure 11: Effect of water-jet velocity on (**a**) cross-section taper and (**b**) cross-section depth. Figure 12: Effect of laser pulse width on (**a**) cross-section taper and (**b**) cross-section depth. Figure 13: Effect of laser repetition frequency on (**a**) cross-section taper and (**b**) cross-section depth. The range analysis results given in Table 5 demonstrate that the section taper was most influenced by factor \(B\), followed by factors \(D\), \(C\), and \(A\). In addition, the actual processing requires that a smaller section taper will result in a larger section depth. The primary and secondary factors, optimal level, and optimal combination (i.e., the optimal solution) were obtained (Table 6) by combining the range calculation results given in Table 4 with the relationships between evaluation indicators and factors shown in Figures 11-14. As shown in Table 6, the optimal process that minimizes the cross-section taper combines a 1.1-ms laser pulse width, 40-Hz frequency, and 180-A current with the 28-m/s water-jet velocity. Under this condition, the cross-section taper after composite processing was 0.3\({}^{\circ}\) (Figure 15a). The optimum process that maximizes the tank depth combines a 1.1-ms laser pulse width, 40-Hz frequency, and 150-A input current with the 20-m/s water-jet velocity. With this configuration, the etched tank had a depth of 2.05 mm but was shaped like a teardrop with a non-ideal taper (Figure 15b). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Evaluation Index**} & **Actual** & **Excellent** & **Water-Jet** & **Pulse** & **Repeat** & \multirow{2}{*}{**Current/A**} \\  & **Requirements** & **Solution** & **Velocity/m/s** & **Width/ms** & **Frequency/Hz** & \\ \hline Section taper/\({}^{\circ}\) & Smaller and better & \(B_{4}D_{4}C_{3}A_{4}\) & 28 & 1.1 & 40 & 180 \\ Section depth/mm & Bigger and better & \(B_{4}C_{3}A_{2}D_{1}\) & 20 & 1.1 & 40 & 150 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Processing parameters in optimized schemes of each evaluation index. Figure 14: Effect of current on (**a**) cross-section taper and (**b**) cross-section depth. Based on the above analysis, the final combination of optimal processing parameters was determined to be \(B_{4}A_{3}C_{3}D_{4}\). The combination of processing parameters that optimized the cross-section taper and cross-section depth of the etched tank were as follows: jet velocity of 24 m/s, laser pulse width of 1.1 m/s, laser frequency of 40 Hz, and input current of 180 A. The cross-section and surface topography of the groove after composite processing under these conditions are shown in Figure 16. As can be seen, the surface of the groove body is free of splitting and slagging defects and has no recast layer. Here, the taper and depth of the groove were 1.2\({}^{\circ}\) and 1.88 mm, respectively.