## 3 Results
The functional relationship between the cutting width and the laser power is approximated by the polynomial:  
\[\text{Kerf}=5.0\cdot\text{E}-0.6\cdot\text{x}^{2}-0.0498\cdot\text{x}+124.4667. \tag{2}\]  
The best dimensions of the slot width are obtained at average values of laser power equal to 5000 W and cutting gas pressure of 0.50 bar. The speed between values of 1800 and 1900 mm/min ensures a better quality of the cut surface, smaller cutting width, if we consider an average laser power level 5000 W, and an average pressure of 0.50 bar. If the pressure is increased to 0.55 bar the results become unsatisfactory. Series 1 was chosen for all minimum levels of the independent parameters (4900 W; 0.45 bar; 1700 mm/min), at the average levels of the cutting parameters (5000 W; 0.50 bar; 1800 mm/min) and at the level of maximum input parameters (5100 W; 0.55 bar; 1900 mm/min). With the help of the Graph 4 program, the dependence of the cutting width was obtained depending on the assistant gas pressure and the functional relationship between them (Figure 5). The minimum pressure is obtained using [PERSON]'s theorem and is equal to 0.508 bar. The Karl-Pearson coefficient is equal to 1 which indicates that there is a strong link between the cutting width and the assist gas pressure. The parts manufactured by laser processing are geometrically characterized by a minimum width of 0.30, under the conditions of setting the input parameters at 5000 W, 0.50 bar and 1800 mm/min. Figure 4: Influence of laser power on cutting width. Series 2 was obtained under the following experimental conditions: (5000 W; 1900 mm/min; 0.45 bar), (5000 W; 1900 mm/min; 0.50 bar) and (5000 W; 1900 mm/min; 0.50 bar). Very good cutting widths were obtained for the pressure range (0.47-0.48 bar). The minimum of the function is 0.479 bar characterized by a cutting width of 0.31 mm. The optimal cutting conditions are described by the variation of the cutting width as a function of the auxiliary gas pressure for H400 using the polynomial:  
\[\mathrm{Kerf}=10\cdot\mathrm{x}^{2}-9.5\cdot\mathrm{x}+2.55, \tag{3}\]  
For series 1 (laser power 4900 W), the measurements made on the cutting width highlighted three pieces with 0.30 mm, three pieces with 0.35 mm and three pieces with 0.40 mm. It is observed that under conditions of minimum gas pressure, laser power and speed, a maximum cutting width is obtained, and for the combination of minimum power, maximum pressure and speed a minimum cutting width (0.30 mm) results. Series 2 with pieces numbered from 10 to 18, has six pieces with minimum values of cutting width (0.30 mm), due to preheating of the sheet. Series 3 with parts 19 to 27 has a single piece with a cutting width equal to 0.30 mm (piece 25), because the sheet was heated during previous processing. We therefore conclude that the parameters used in series 1 and 2 are indicated as a priority in the technological process of cutting in order to have a minimum cutting width, material savings, low energy consumption and implicitly low processing costs. The input data needed to determine the cost of the laser manufacturing process were centralized in Table 4, with the prices being of the manufacturers. The study aims to determine the cost of the manufacturing process, which is of interest to manufacturers of such facilities, but especially to users. The first column of the table contains the cost elements identified in the processing. The second column indicates the calculation relationship. All costs were expressed in Euro/hour. Figure 5: Influence of auxiliary gas pressure on cutting width. The range of variation of the cutting width allows the evolution of the processing cost between certain limits. The consumptions in the table are specific to the installation used for laser processing. The analysis of the experiment shows a good arrangement of the block of parts. An important parameter used in cutting is the assist gas pressure.