## 3 Experimental Results and Discussion
### Effect of Process Parameters on Surface Roughness
#### 3.2.1 ANOVA Results for Surface Roughness
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Ra\_L1**} & \multicolumn{2}{c}{**Ra\_L2**} & \multicolumn{2}{c}{**Ra\_L3**} \\ \hline
**Control Factor** & **F-Value** & \(p\)**-Value** & **F-Value** & \(p\)**-Value** & **F-Value** & \(p\)**-Value** \\ \hline M & 3.44 & **0.044** & 24.41 & **0.000** & 17.54 & **0.000** \\ t & 3.33 & **0.048** & 11.25 & **0.000** & 2.66 & 0.088 \\ Cs (\%) & 1.08 & 0.307 & 6.76 & **0.015** & 0.34 & 0.564 \\ P (\%) & 1.11 & 0.300 & 1.21 & 0.282 & 0.00 & 0.980 \\ M*Cs (\%) & 12.91 & **0.000** & 43.67 & **0.000** & 14.82 & **0.000** \\ M*P (\%) & 2.09 & 0.139 & 1.67 & 0.207 & 1.45 & 0.252 \\ t*Cs (\%) & 0.15 & 0.864 & 0.40 & 0.676 & 0.14 & 0.872 \\ t*P (\%) & 1.47 & 0.246 & 1.74 & 0.195 & 2.27 & 0.123 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: ANOVA results for arithmetic mean surface roughness, computed F-value and \(p\)-value. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**RSm\_L1**} & \multicolumn{2}{c}{**RSm\_L2**} & \multicolumn{2}{c}{**RSm\_L3**} \\ \hline
**Control Factor** & **F-Value** & \(p\)**-Value** & **F-Value** & \(p\)**-Value** & **F-Value** & \(p\)**-Value** \\ \hline M & 22.10 & **0.000** & 157.89 & **0.000** & 66.06 & **0.000** \\ t & 6.76 & **0.003** & 14.99 & **0.000** & 7.65 & **0.002** \\ Cs (\%) & 0.82 & 0.371 & 5.96 & **0.022** & 6.19 & **0.019** \\ P (\%) & 1.65 & 0.208 & 13.18 & **0.001** & 4.69 & **0.039** \\ M*Cs (\%) & 1.76 & 0.188 & 2.08 & 0.144 & 10.15 & **0.001** \\ M*P (\%) & 1.22 & 0.308 & 0.62 & 0.548 & 0.07 & 0.937 \\ t*Cs (\%) & 1.02 & 0.372 & 2.15 & 0.136 & 0.48 & 0.627 \\ t*P (\%) & 1.64 & 0.209 & 9.80 & 0.001 & 2.74 & 0.082 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: ANOVA results for mean width of profile elements, computed F-value and \(p\)-value. to be insensitive to changes in cutting speed (\(\sim\)1.63 \(\upmu\)m). It is useful to note that this interaction is also found to be significant for geometrical variables. For extensive analysis of the cutting surface morphology, the spacing parameter RSm was selected. From the statistical analysis, RSm_L1 was only affected by workpiece parameters (i.e., material and thickness), whereas RSm_L2 and RSm_L3 were influenced by all the main effects. The only two significant interactions were t*P (%) and M*Cs (%) for RSm_L2 and for RSm_L3, respectively. As shown in Figure 15, laser cutting of AlMg3 provided the lowest value of RSm, followed by  
Figure 14: Interaction plot for arithmetic surface roughness. Figure 13: Main effects plot for arithmetic surface roughness (upper, middle and lower workpiece surface). laser cutting of AISI 304, whereas laser cutting of St37-2 resulted in the highest. Moreover, unlike the amplitude parameters, RSm_L2 and RSm_L3 increased when increasing cutting speed. More specifically, this result mainly occurred in laser cutting of AISI 304, as shown in Figure 16. In addition, the mean width of profile elements slightly increased when cutting AlMg3, indicating a small irregularity in the drag lines due to the light-reflectivity and heat-conductivity of this material, in line with Ref [16]. In laser cutting of St37-2, similar to Ra and Rz, RSm also increased from 0.27 to 0.29 mm as the cutting speed decreased. According to the cycling side burning theory, side burning occurs at cutting speeds smaller than the reaction front speed, resulting in the formation of periodic patterns [29]. Furthermore, it was found that RSm decreased with thickness. As for the gas pressure, t\({}^{\text{e}}\)P (%) was found to be significant. The interaction plot for RSm_L2 showed that, in laser cutting of thin sections, the spacing parameter decreased at lower gas pressure (from 0.24 to 0.18 mm). The adequacy of fit for the regression models of roughness parameters was in the range of 66.96-96.65%. Figure 16: Interaction plot for RSm. Figure 15: Main effects plot for mean width of profile elements (upper, middle and lower workpiece surface).