## 4 Discussion
### Quadratic Predictive Model
The statistical table reduced after the comparison \(p\) > t, to establish the significance of each influencing factor and the interactions between them, shows that the input parameters randomly influence the cutting process. In Table 8 the project has no interaction with significant influence on the Kerf response. The experimental data are adequate for the regression model. The correlation model was used to determine the most influential input parameter on Kerf. In this study the linear and quadratic regression model is the most appropriate. The graphs show the effect of the interaction between the influencing factors, the laser power and the cutting gas pressure in establ \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters with Limit Levels** & **Influence (Mm)** & \(p\) (Error Probability) > T** \\ \hline Laser power (L) (4900 W; 5100 W) & \(-\)0.022 & 0.442 \\ Laser power (Q) (4900 W; 5100 W) & \(-\)0.022 & 0.378 \\ Gas pressure (L) (0.45 bar; 0.55 bar) & \(-\)0.033 & 0.324 \\ Gas pressure (Q) (0.45 bar; 0.55 bar) & \(-\)0.022 & 0.4429 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Influence of laser power and assisting gas pressure at CO\({}_{2}\) laser cutting. The novelty of the paper consists in the use of a material for which in the specialized literature there were no references related to the cutting width for CO\({}_{2}\) laser processing. In addition, the influence of incident intensity and material temperature on Kerf was established. In addition to the technical aspects presented, the study presents the determination of the processing cost for laser cutting. The results complete other research on other steel grades [25]. The study is more deepened if we take into account the energy of the laser beam. The melting efficiency which takes into account Kerf is mathematically expressed [40]:  
\[\sigma_{\text{melt}}=\sigma_{\text{cut}}\cdot\text{Kerf}, \tag{12}\]  
where \(\sigma_{\text{cut}}\) is the cutting efficiency (how many mm\({}^{2}\) are cut with 1 Joule) (mm\({}^{2}\)/J); \(\sigma_{\text{melt}}\) is the melting efficiency (mm\({}^{3}\)/J). The mathematical modeling of the laser thermal manufacturing is based on the following reasoning: at the interaction of laser radiation with the part material the light energy is instantly transformed into thermal energy, strongly heating a volume V forming the melt [23]. The amount of heat required for heating is Q, and the elementary variation dQ:  
\[\text{dQ}=\rho\cdot\text{V}\cdot\text{c}\cdot\left(\frac{\vartheta\text{T}}{ \vartheta\text{t}}\right)_{\text{z}}\text{dt}, \tag{13}\]  
The absorbed heat flux q entering the elementary surface is in a Gaussian relation with the characteristics of the laser beam by the relation. \[\text{q}=\text{q}_{0}\cdot\text{e}^{-\frac{2\pi^{2}}{\tau_{0}^{2}}}, \tag{14}\]  
The heat in the melt is achieved by decreasing the temperature along the Oz axis, the temperature gradient during t period is:  
\[\frac{\vartheta\text{T}}{\vartheta\text{t}}=\frac{\text{q}_{0}\cdot\text{e}^{ -\frac{2\pi^{2}}{\tau_{0}^{2}}}}{\rho\cdot\text{z}_{\text{m}}\cdot\text{c}} \tag{15}\]  
The radial coordinate r can be calculated by the mathematical relation:  
\[r^{2}=\frac{r_{0}^{2}}{2\ln\left[\left(\frac{\rho\cdot\text{z}_{\text{m}}\cdot \text{c}}{\text{q}_{0}}\right)\cdot\frac{\vartheta\text{T}}{\vartheta\text{t }}\right]} \tag{16}\]  
where q\({}_{0}\) is the heat flux absorbed in the center of the circular region (W/cm\({}^{2}\)); r\({}_{0}\) is the laser beam radius on the material (mm); c is the specific heat (J/kgxK); z\({}_{\text{m}}\) is the melting heat (\(\mu\)m); \(\rho\) is the material density (kg/m\({}^{3}\)).