## 3 Results and Discussion
### Cut Kerf Angle  
Table 7 summarizes the results of the analysis of variance conducted on the cut kerf angle. The study revealed that both the linear effect of the laser power (LP) and the cutting speed (CS) had a significant impact on the response. Moreover, the interaction between the laser power and the cutting speed was also a significant term. Using the Design Expert software 12v, a regression equation (Equation (5)) was developed to establish the relationship between the cut kerf angle and the various process parameters.  
\[\text{Cut kerf angle}=-13.72+0.27\times\text{LP}+1.49\times\text{CS}-0.02 \times\text{LP}\times\text{CS} \tag{5}\]  
Figure 10 illustrates the response surface plots for the cut kerf angle based on the process parameters. Consistent with the ANOVA in Table 6, Figure 10a demonstrates that the focal plane position (FPP) has a negligible impact on the cut kerf angle, while the cutting speed has a significant and direct proportional influence. By utilizing the regression equation (Equation (5)), the behavior of the cutting speed and laser power in Figure 10b can be explained. The maximum cut kerf angle occurs at the minimum laser power and at the maximum cutting speed. In this situation, the heat input decreases, as shown in Equation (5), and less laser energy interacts with the material. Conversely, when the laser power is high and the cutting speed low, the cut kerf angle decreases. The trend for the correlation between the laser power and the focal plane position is similar to Figure 10a: the focal plane position is insignificant, and the laser power in all conditions has a similar effect.  
The correlation between the cut kerf angle and the heat input can be analyzed using a scatter plot and by calculating the correlation coefficient. The correlation coefficient  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Source of Variation** & **Degree of Freedom** & **Sum of Squares** & **Mean Squares** & **F Value** & \(p\) **Value** \\ \hline Model & 2.82 & 3 & 0.94 & 4.03 & 0.0314 \\ A-LP & 0.028 & 1 & 0.028 & 0.12 & 0.7347 \\ B-CS & 1.39 & 1 & 1.39 & 5.94 & 0.0300 \\ AB & 1.41 & 1 & 1.41 & 6.03 & 0.0290 \\ Residual & 3.04 & 13 & 0.23 & & \\ Lack of Fit & 2.82 & 11 & 0.26 & 2.32 & 0.3393 \\ Pure Error & 0.22 & 2 & 0.11 & & \\ Total & 5.86 & 16 & & & \\ \hline R-Sq = \% 48.17 & & & R-Sq (adj) = \% 36.21 & & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Revised analysis of variance of the cut kerf angle.  
Figure 10: Response surfaces of the cut kerf angle in terms of (**a**) FPP and CS, and (**b**) LP and CS.  
between the cut kerr angle and the heat input is approximately \(-0.2\), indicating a weak negative correlation. This suggests that, as the heat input increases, the cut kerr angle decreases slightly.  
The surface morphologies before laser cutting significantly influence the kerr quality in the laser cutting processes. These morphologies impact factors like light absorption, heat distribution, and material removal, shaping the interaction between the laser beam and the material. Understanding the initial surface conditions is crucial, affecting the consistency of the laser-material interaction and the subsequent results. Variations in surface morphologies, such as roughness or impurities, may lead to heterogeneous energy absorption during laser cutting, causing non-uniformities in the kerr geometry. Surface irregularities can also affect heat dissipation and material ejection dynamics.