## 5 Conclusions  
This paper investigates the process of manufacturing CO\({}_{2}\) laser cutting parts from H400 material. The experimental research was designed according to an experimental plan that was replicated four times to observe the variation of the Kerf mean response. The study investigates the coefficients of controllable parameters to establish the significance and influence of each input factor. The independent parameters selected during the cutting experiments are laser output power, auxiliary gas pressure and cutting speed. Based on the independent experiments, their observations and analysis, the following conclusions were drawn:  
1. An important role in the melting of the material is the heat gradient that influences the cutting, having an unstable role in the upper and lower face of the semi-finished product, which influences the hydrodynamic processes in the melt;
2. The cutting width is dependent on the assisting gas pressure through a quadratic interpolation function;3. The incident laser intensity, the working temperature and the laser intensity at the output of the material are physical quantities analytically determined;
4. The quadratic prediction shows that a cutting width of 0.3 mm is obtained at the laser power inlet level in the range (4980-5020 W) and the cutting gas pressure in the range (0.47-0.51 bar);
5. Contrary to prediction, the square regression response surface model indicates a cutting width <0.32 mm, if the laser power is 5000 W and the assisting gas pressure is 0.5 bar. A relatively good agreement was obtained between the predictive model and the regression mathematical model;
6. The regression graph, indicated by the RSM response area, shows a Kerf value affected as the laser power is 5100 W and the gas pressure in the range (0.46-0.48 bar), but also in the case of laser power of 4900 W and low gas pressure of 0.45 bar, resulting in a Kerf >0.40 mm. It is observed that the edges of the laser power adjustment range at the same time with low gas pressure indicate a negatively affected Kerf;
7. Opposite extreme values, laser power and gas pressure, increase the width of the Kerf;
8. The plane projection shows at quadratic prediction an increase of Kerf according to the Gaussian curve in Figure 9, and in the quadratic regression model after a disk as in Figure 10;
9. The term laser power, in the linear (Equation (10)) and quadric (Equation (11)) polynomials, has the higher effect showing that laser power is the most influential input factor;
10. The prediction linear model of the cutting width is in relative agreement with the calculated polynomial model, the laser power being the most significant parameter in determining the cutting width. The calculated linear model indicates a Kerf of 0.33 mm for the power of 4900 W and the gas pressure of 0.45 bar. The differences between the linear and quadric result are due to the heating of the material during processing;
11. The quadric model is more accurate because it takes into account the interactions between laser power and auxiliary gas pressure, at a constant level at the cutting speed. It also takes into account the combined action of the parameters on Kerf, while the linear model takes into account the independent action of one factor or the other;
12. Pressure is the second significant factor in relations (Equations (10) and (11)). This influences the cutting process through the pressure gradient that eliminates the melt, hot drops and heat transfer through the slot;
13. High power causes an increased power density, which induces a higher amount of heat in the material, resulting in increased Kerf. Response surface models for the evaluation of the Kerf cutting width at the straight profile using the full factorial design L27 were considered appropriate. The empirical data developed are used to predict and calculate the global mean of the Kerf response using the linear (L) and quadric (Q) response area model.