## 3 Results
The interpolation method establishes a functional link between the interpolation support consisting of the assisting gas pressure data set and the cutting width. The estimation error calculated as the difference between the actual function and the Lagrange function is 4.25%. To calculate the external parameters of the laser beam, it is important to know the radiation strength, spot diameter and optical properties of the material. The physical phenomena that take place following the laser-material interaction are based on the transformation of laser energy into thermal energy. The increase in local temperature and the distribution of laser-induced heat change the thermal state of the metal by heating-melting-vaporization. The intensity of the incident radiation at the moment of penetration in the material is given by the relation:  
\[\mathrm{I_{0}}=\frac{4\cdot\mathrm{P}}{\pi\cdot\mathrm{d}^{2}}, \tag{6}\]  
The intensity of incident radiation entering the material at depth x follows the relation [35]:  
\[\mathrm{I}=\mathrm{I_{0}}\cdot(1-\mathrm{R})\cdot\mathrm{e}^{-\mathrm{A}\cdot x}, \tag{7}\]  
where R is the coefficient of reflexion; A is the absorption coefficient. The temperature inside the material developed by the absorption of laser radiation is a parameter that indicates the heat input required for heating with phase transformations of the target until melting. The absorption coefficient for metals is 10-15% for the CO\({}_{2}\) laser wavelength of 10.6 \(\upmu\)m [32]. The reflection coefficient depends on the wavelength; in the case of the CO\({}_{2}\) laser it is 0.9. [PERSON] et al. indicated that at 0.2% C, the thermal conductivity is 39 W/m*K [33]. Thus, we obtain the values of the physical quantities studied given in Table 6.  
The dimensions of the target are larger in relation to the radius of the laser spot which generates a constant flow of energy while creating cuts of material, delimiting the slot. The cutting width dependence on the temperature and the incident intensity, under conditions of maximizing oxygen gas pressure and cutting speed, for the three levels of laser power used in the experiment are shown in Figures 6 and 7. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol (u.m.)** & **Value** & \\ \hline Laser power & P (W) & 4900 & 5000 & 5100 \\ Incident intensity & I\({}_{0}\) (W/cm\({}^{2}\)) & 159.31 \(\times\) 10\({}^{5}\) & 162.5 \(\times\) 10\({}^{5}\) & 165. \(\times\) 10\({}^{5}\) \\ Laser temperature in the material & T (K) & 6.25 \(\times\) 10\({}^{4}\) & 6.37 \(\times\) 10\({}^{4}\) & 6.5 \(\times\) 10\({}^{4}\) \\ Laser intensity at the output of the material & I (W/cm\({}^{2}\)) & 7.0 \(\times\) 10\({}^{5}\) & 7.15 \(\times\) 10\({}^{5}\) & 7.29 \(\times\) 10\({}^{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values of intensity and temperature depending on the laser output power. The quadratic regression model of the cutting width as a function of the temperature produced by the laser in the material has the form:  
\[\text{Kerf}=1.6667\cdot\text{E}-0.8\cdot\text{T}^{2}+0.0021\cdot\text{T}-68.6583, \tag{8}\]  
The quadratic regression model of the cutting width as a function of the incident intensity produced by the laser radiation at the entrance to the material has the expression:  
\[\text{Kerf}=0.2434\cdot\text{I}_{0}^{2}+7.9891\cdot\text{I}_{0}-65.2042, \tag{9}\]  
Figure 6: Dependence of cutting width as a function of temperature. Figure 7: Dependence of cutting width depending on the incident laser intensity. The second-order model of quadratic regression was developed for the cutting width by accessing data from independent experiments. The coefficient of determination R\({}^{2}\) was calculated to verify that the data anticipated by the regression model are appropriate. When using the Graph program, the coefficient of determination is 1, which means that the mathematical accuracy of the regression is the most appropriate. When the temperature and power density increase, an increase in the cutting width is observed.