## 1 Introduction
They concluded that the minimum Kerf was obtained at a pulse frequency of 25 Hz, while maximum Kerf was obtained at a laser pulse frequency of 20 Hz [32]. [PERSON] et al. showed the influence of the cutting parameters (cutting speed, laser power, frequency, pressure) to identify the responses due to laser cutting (taper, Ra and HAZ) of En-31 molded steel. Mathematical models were developed using the method of response surfaces and it was identified that the best roughness is obtained when selecting process parameters at average values [33]. [PERSON] et al. investigated the effect of laser installation parameters such as laser power, gas pressure, cutting speed and thickness in the case of cutting experiments designed after the Taguchi L27 model on roughness. The statistical analysis was performed using the ANOVA variant. The sensitive parameters identified are the cutting speed and the thickness of the part [34]. [PERSON] et al. used 3-mm-thick Ti sheets to investigate laser cutting. The cutting parameters, laser power, cutting speed and gas pressure ran according to an experimental plan given by [PERSON]'s method in order to analyze the microstructure of the cut edge and optimize the roughness. The conclusion indicated the optimal cutting condition was obtained at laser power P = 3 KW, cutting speed v = 2.400 mm/min and gas pressure \(p\) = 8 bar [35]. [PERSON] et al. studied CO\({}_{2}\) laser cutting on Ti sheet with thickness g = 2 mm. [PERSON]'s method was implemented to minimize roughness and identify optimal cutting parameters. It turned out that the roughness increases when the thermal energy is increased by the laser and decreases at the high cutting speed [36]. [PERSON] et al. studied the laser polishing of S136D die-cast steel using an L16 orthogonal experimental plane. Experiments have shown a tendency for surface roughness to vary with laser energy density using a moving laser heat source [37]. From the above literature it appears that numerous investigations were performed to identify the effects of process parameters on Kerf responses, hardness, roughness and taper [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. In addition, other research included the focusing position, nozzle geometry, stand-off distance on the gas jet, temperature of the cutting area, melting depth, thermal stresses, HAZ [6; 15; 21], and laser fusion deposition technique [11]. Further, some studies methods used modern design and optimization, genetic algorithm, iterative, artificial neural network model, superiority and inferiority criteria [3; 10; 14; 20]. Most research focuses on various metallic materials, alloys, groups of materials with different physical, chemical and thermal properties. The presented studies conducted numerous experimental investigations in order to identify the effects of laser cutting parameters on process responses. At present, there is a diversity of research aimed at finding a suitable combination of the main parameters that affect the quality of cutting. In the previous approaches the most common use of materials in the case of laser heating is found on stainless steel, Ti, mild steel, alloys and reduced on hard and ultra-hard steel. In this study we selected the H400 steel material in the laser manufacturing process due to its extensive capacity for use and exploitation over time, surface conditions and absorbability. H400 is an insufficiently used steel from a technical point of view, and is little used in the laser processing process, which is why it was chosen as a study material. Linear (L) and quadric (Q) prediction models, and regression (L) and (Q) models, respectively, were developed using the response surfaces, which were then compared for adequacy and in the ranking of the cutting factors. A number of physical quantities were calculated that accompany the interaction between radiation and substance as a result of the transformation of light energy into caloric energy.