## 3 Results
The cutting width decreases as the temperature in the material and the incident intensity decrease. If the laser power increases, the cutting width is disturbed due to the energy density. The situation leads to a longer interaction time between the laser radiation and the substance, and the slit increases due to thermal erosion. Specifically, the cutting efficiency of the laser beam decreases with the increase of energy received from the laser, due to losses through thermal conduction. Kerf was evaluated, and the results show a section of the slit as a V-profile, almost straight edges, parallel or A-shaped. In most cases, the top width is larger compared to its size at the bottom edge. Moreover, a sufficient amount of laser energy is absorbed more intensely at the upper edge of the Kerf profile. This energy is transformed into heat, thermal energy that melts a very small portion of the material locally, strongly heats the cut surfaces by changing the metallographic structure of the surfaces, the local change of the material characteristics. The local heat generated in the material, in the area affected by the laser, can trigger chemical reactions very quickly. As a result of the thermal action of the laser and the chemical reaction under the influence of an oxygen jet, changes in the size of the cutting width occur, so that at the lower edge of the material, an increased Kerf results due to burning and melting of cut material. In the process of interaction of laser radiation with the substance there is a temperature gradient through the cut that determines the heat in the slot. The diffusion of heat through the sheet is based on the fact that, under the influence of the laser pulse, the optical energy is instantly transformed into heat. The incident intensity of the laser beam decreases as it enters the material. The gradient of laser radiation intensity can be explained by the fact that the material is resistant, the layers of molten material have different temperatures and the accumulated heat is removed from the slit more difficultly. The temperature difference between the two surfaces of the plate explains that the melt loses mass as it discharges to the bottom edge. The range of variation of the radiation intensity has a higher temperature of the molten area on the surface of the material, and a lower temperature on the lower surface of the steel plate, resulting in a smaller melting area. In this study, the cutting width was determined as a function of laser power, gas pressure, material temperature and the incident intensity of laser radiation. The measured results are represented graphically in Figures 3 and 4 showing a low Kerf at values close to 5000 W and gas pressures in the range of 0.47-0.48 bar. As can be seen from Figures 5 and 6, in the case of the assisting gas pressure of 0.55 bar and a speed of 1900 mm/min, Kerf is the lowest. The same result happens at a temperature of 6.25 \(\times\) 10\({}^{4}\) K and a minimum incident intensity of 15.931 \(\times\) 10\({}^{6}\) W/cm\({}^{2}\). The Kerf cutting width compared to the laser power, the assisting gas pressure, the working temperature and the incident intensity for the H400 sheet with a thickness of 8 mm has a square shape. These curves have a maximum for Kerf processing at oxygen gas pressures and cutting speed under maximizing conditions and a minimum that was reached at selected cutting pressures and inputs at average values. The average cost is for the CO\({}_{2}\) laser installation applied to the 8 mm sheet for H400 at the value of 13.245 Euro/h. The function of approximating the cutting width according to the important cutting parameter, the low pressure of the assistant gas, run at three levels used in the experiment (0.45, 0.50, 0.55) bar is a Lagrange polynomial of quadratic order.