## 1 Introduction
presented the optimization of the hardness of the carbon steel material AISI 1045 under the influence of the input parameters: laser power, scanning speed and focusing distance. They found that the hardness of the hardened surface after laser cutting improved from 200 HV to 660 HV. RSM models are able to interpret hardened width (HW), hardened hardness (MH) and hardness gradient (HG) [17]. [PERSON] et al. showed that when laser cutting thin sapphire sheets with the help of a Bessel beam, a zero taper and a higher roughness were obtained [18]. [PERSON] et al. used a laser beam guided by a water jet to process the nickel alloys used in the aerospace industry, in the technological process of micro-drilling. The improvement consisted of eliminating the burrs of the cut surfaces, reducing the taper and reducing the area affected by the laser heat [19]. [PERSON] et al. optimized the cutting parameters (cutting speed, gas pressure, pulse width, pulse frequency) of two laser sources, solid Nd-YAG and gas CO\({}_{2}\) in pulsed mode. The optimization method is based on several criteria, superiority and inferiority, to identify the most suitable combination, which ensures low R\({}_{\text{a}}\) value, reduced cutting width and slope [20]. [PERSON] et al. presented a low-cost method of manufacturing PMMA (polymethyl methacrylate) nozzles, based on laser cutting and PDMS (polydimethylsiloxane) bonding [21]. [PERSON] et al. experimentally investigated the CO\({}_{2}\) laser cutting of soft steel sheets with a thickness of 15-20 mm. There is a decrease in the quality of the cut edge to thicknesses between 15 and 20 mm [22]. [PERSON] [23], [PERSON] [24] and [PERSON] [25] contributed to the expansion of the CO\({}_{2}\) and Nd-YAG laser application in industrial engineering activities, as well as applications in the production processes of laser cutting, drilling and welding in the manufacture of industrial products. [PERSON] et al. studied the interaction between the cutting parameters and the part parameters depending on the type of chosen material--AlMg3, St37-2 and AISI 304--in order to vary the kerf width. The auxiliary gases used were N\({}_{2}\) and O\({}_{2}\). The results show that the Kerf width increases as the cutting speed decreases, due to the higher accumulated energy [26]. [PERSON] et al. presented the influence of laser parameters on Kerf in the case of SS41 and SUS 304 metal sheets used in engineering applications. The ANOVA method established the most significant parameters used in the experiments: laser power and cutting speed [27]. [PERSON] et al. researched UHSS ultrahard steel in nitrogen and oxygen-assisted laser processing. The results observed after cutting and analysis indicate a better cutting width for nitrogen, and better hardness and perpendicularity of the cut edge when using oxygen as an assistant gas [28]. [PERSON] et al. demonstrated that CO\({}_{2}\) laser technology is advantageous for cutting sheets of Ti-6 Al-4V titanium alloys and pure titanium. For both types of material, the most influential cutting parameter is the laser power in case of cutting width disturbance. Inthis study, Kerf is inversely proportional to the cutting speed [29]. [PERSON] et al. showed laser piercing for Ti6 Al4V alloy in order to obtain quality holes. The analysis of variance indicates that the most influential input parameter is the laser power on the area affected by HAZ heat and the conicity of the processing [30]. [PERSON] et al. presented a mathematical model that describes the influence of laser cutting parameters on the surface roughness, HAZ and the deviation from the rectilinearity of the cut surface. Nomograms are constructed indicating the selection of cutting regimes in case of minimizing the responses for carbon steel sheets with thicknesses of 6, 10 and 14 mm [31]. [PERSON] et al. studied the effect of the input parameters (laser power, gas pressure, cutting speed, nozzle diameter) on the cutting quality for H400 materials.