## 3 Results and Discussion
### Effect of Interaction of Process Parameters on the Micro-Hardness of the Coating  
In order to visually observe the effect of the interaction of laser cladding process parameters on the micro-hardness of the coating in the orthogonal experiment, based on the established BPNN-QPSO model, the laser power density is calculated by Equation (17) [40]. By using the controlled variable method, the variation trend and the interaction of micro-hardness with process parameters are plotted in Figures 14 and 15, respectively. It should be noted that the curvature of each contour map in Figure 15 indicates whether the interaction between two independent process parameters is significant. When the contour line tends to be an ellipse, it means that the two process parameters have a strong interaction. When they tend to be circle, the interaction between these two process parameters is small [41].  
\[Q=\frac{4L}{\pi DV} \tag{17}\]  
By controlling the process parameters (\(D\) = 1 mm, \(S\) = (22%, 27%, 35%), \(V\) = 6.33 mm/s), the variation trend of micro-hardness with laser power \(L\) is plotted in Figure 14a. It can be seen that the coating's micro-hardness increased first and then decreased with laser power \(L\). By controlling the process parameters (\(D\) = 1 mm, \(V\) = 6.33 mm/s), the interaction between laser power \(L\) and the overlapping ratio \(S\) was plotted, as shown in Figure 15a. It can be directly seen that it was beneficial to obtain the maximum micro-hardness of coating if the laser power density \(Q_{(L\times S)}\) ranged from 87 W-s-mm\({}^{-2}\) to 92 W-s-mm\({}^{-2}\) and the overlapping ratio \(S\) ranges from 20% to 25% in the interaction between \(L\) and \(S\). In addition, the contour lines of Figure 15a tend to be elliptic, indicating that the interaction between \(L\) and \(S\) was highly significant (\(p\)-value = 0.031).  
By controlling the process parameters (\(L\) = 445.65 W, \(S\) = (22%, 27%, 35%), \(V\) = 6.33 mm/s), the variation trend of micro-hardness with spot diameter \(D\) was plotted in Figure 14b. It can be seen that the micro-hardness of the coating decreased with the increase of spot diameter \(D\). By controlling the process parameters (\(L\) = 445.65 W, \(D\) = 1 mm), the interaction between spot diameter \(D\) and the overlapping ratio \(S\) was plotted, as shown in Figure 15b. It can be observed that it was beneficial to obtain the maximum micro-hardness of the coating when the laser power density \(Q_{(D\times S)}\) ranged from 80 W-s-mm\({}^{-2}\) to 90 W-s-mm\({}^{-2}\) and the overlapping ratio \(S\) ranged from 20% to 25% in the interaction between \(D\) and \(S\). In addition, the contour lines in Figure 15b are approximately elliptic, indicating that the interaction between \(D\) and \(S\) was significant (\(p\)-value = 0.071).  
By controlling the process parameters (\(L\) = 445.65 W, \(D\) = 1 mm, \(V\) = (6 mm/s, 7 mm/s, 8 mm/s)), the variation trend of micro-hardness with overlapping ratio \(S\) is plotted in Figure 14c. It can be known that the micro-hardness decreased with the increase of overlapping ratio \(S\) from 20% to 35%, while micro-hardness of coating increased when overlapping ratio \(S\) increased from 35% to 40%. By controlling the process parameters (\(L\) = 445.65 W, \(D\) = 1 mm), the interaction between the overlapping ratio \(S\) and the scanning velocity \(V\) is plotted as shown in Figure 15c. It can be observed that it was beneficial to obtain the maximum micro-hardness of coating when the laser power density \(Q_{(S\times V)}\) ranged from 70 W-s-mm\({}^{-2}\) to 110 W-s-mm\({}^{-2}\) and the overlapping ratio \(S\) ranged from 20% to 25% in the interaction between \(S\) and \(V\). In addition, the contour lines of Figure 15c tend to be an elliptic, indicating that the interaction between \(S\) and \(V\) was highly significant. (\(p\)-value = 0.009).  
Figure 14: Trend plot of coating micro-hardness: (**a**) laser power; (**b**) spot diameter; (**c**) overlapping ratio.