## 4 Discussion
### Quadratic Predictive Model
The Kerr graph depending on the laser power is steeper and longer compared to the graph representing Kerr depending on the cutting gas pressure which is less deformed, that is a curve less pronounced;
* The damaged values of the cutting width, over 0.38 mm, are obtained at 5100 W laser power and 0.45 bar gas pressure;
* From the spectral analysis of the colors (green to red) corresponding to the cutting width, there is an increase from the set values (average power and pressure) to the extremities;
* Comparing the quadratic model with the prediction given in Figure 9, we find that the minimum cutting width moves from minimum values of gas pressure to average values. The agreement between predictability and the statistical mathematical model for laser power is good, but there are significant differences in gas pressure. The explanation can be attributed to the increase in gas flow that increases the contact  
Figure 10: Graph of the quadric dependence of the cutting width on the laser power and the assist gas pressure. surface so that the cutting width increases. As the cutting gas pressure decreases, the area affected by the gas decreases and the cutting width is minimized. The gas jet is high (length at the outlet of the nozzle) when the pressure increases, the material melts in larger quantities, which leads to an increase in the cutting width, while an average jet of gas affects the steel plate less. The variation of the laser power has as effect the change of temperature and implicitly of the viscosity of the melt. In the case of very narrow cuts, the operation of removing the melt is more difficult. The cutting gas pressure is influenced by the length of the gas flow, which determines a cutting force exerted on the cut surface. Changing the assistant gas flow has effects on Kerf geometry. The low cutting speed causes a significant accumulation of laser energy in the cutting area, which implies a larger cutting width. The cutting width on the top side is larger than the one on the bottom side as it is closer to the laser spot and captures a larger amount of energy. The heat is transmitted inwards with a negative heat gradient. The cutting width on the lower side is larger than on the upper side due to changes in the cutting parameters. There is a pressure gradient towards the outlet, as the amount of heat absorbed increases. Cylindrical cases are rare and depend on the structure of the material. The geometry of the beam changes in the material due to the section variation. The cut in the material is U-shaped due to the decrease of the transmitted energy, so that, at the bottom, the molten material is stationary. As the beam advances in the material it loses energy, so at certain depths the melting time is different.The cutting surface is parabolic, concave and test-tube-bottom shaped. Laser power is a physical quantity that influences the density of energy absorbed by the material. Energy density is closely related to power density and interaction time. If the laser power remains constant, the laser intensity in the material varies with the change of section. Oxygen gas pressure can influence the cutting width due to gas flow, gas flow length and nozzle diameter. The combination of laser power--gas pressure assistant can improve the cutting width. The surface methodology of the Kerf response was developed and influenced by the laser power and the assist gas pressure. Graphs with response areas were obtained for the linear (L) and quadric (Q) models to predict and calculate the global Kerf. Laser power and gas pressure were chosen on the X and Y axes. The Kerf response for the straight profile is made on the Z axis. The prediction graph (L) due to the effects of the interaction between laser power and gas pressure is a curved flat surface. The linear shape of the Kerf answer is given by Equation (10). The graph (L) resulting from the mathematical modeling of the answer is a linear surface indicating the Kerf force. In conditions of average power and average pressure Kerf reaches the value of 0.34 mm.