## 4 Discussion  
### Linear Predictive Model  
The linear predictive model shown in Figure 8a shows that, during the cutting of the parts, the laser power was progressively changed to the values of 4900 W, 5000 W and 5100 W. A set value of the laser power outside the range of 4900-5100 W, indicates an increase in cutting width. The simultaneous variation of two parameters of influence (laser power, auxiliary gas pressure) on the cutting width, determines the most appropriate influence of the predictive factors if the level of the cutting speed is maintained at a constant value. The linear prediction graph rendered by the RSM method shows a 2D surface with the interaction between the laser power and the assistant gas pressure. The cutting width can be evaluated, following the interaction between two influencing factors, as follows:  
* When the laser power has values in the range 4980-5040 W while the assist gas pressure is in the range 0.45-0.48 bar, a cutting width of less than 0.3 mm results;
* The minimum gas pressure of 0.45 bar at the same time as the maximum power of 5100 W, has a cutting width <0.34 mm;
* The assist gas pressure at the average level, at the same time as maximum values of the laser power, shows a cutting width >0.38 mm. The same result is obtained when the laser power is maintained at the minimum value of 4880 W, at the same time as the oxygen gas pressure is located at the maximum value of 0.55 bar;
* If the laser power is the minimum of 4900 W and the assisting gas pressure is in the range 0.45-0.53 bar a cutting width <0.34 mm results;
* The change of the cutting gas pressure values compared to the values within the range 0.44-0.48 bar, at the same time as that of the laser power located in the range 4980-5040 W, determines a significant increase of the Kerf parameter;
* The laser power 5000 W, at the same time with the cutting gas pressure 0.45 bar ensures the best Kerf below 0.3 mm. Figure 8: (**a**) Linear predictive model of influence factors; (**b**) Linear dependence of cutting width as a function of laser power and gas pressure. The linear prediction graph anticipates that the best results of the cutting width are obtained at low values of the assist gas pressure (0.45-0.48 bar) with values of the laser power in the range (4980-5040 W). The average value of the laser power leads to a better absorbability of the laser energy by the material, small amount of molten material, optimal heat distribution efficiency and low processing cost. A low value of the laser power negatively influences the melting process. The linear mathematical model (Figure 8b) for the cutting width is given by the regression calculation in case of the interaction between the laser power (P) and the assistant gas pressure (p) by the relation:  
\[\text{Kerf}=0.2574+2.7778\cdot\text{E}-5\cdot\text{P}-0.1111\cdot\text{p}, \tag{10}\]  
In the ANOVA linear regression function, the interaction effect of the laser power term is higher than that of the assisting gas pressure (0.1111). It means that the most significant factor in determining the cutting width is the laser power. The positive sign indicates in the linear equation that the laser power is an influencing factor that determines the increase of the cutting width and the minus sign shows that the gas pressure acts in the direction of decreasing Kerf. The interaction of laser power and cutting gas pressure will change the geometry produced in the slit; the two independent factors optimized validate the quality of Kerf. Regression analysis studies the effect of each controllable factor on the Kerf response during laser cutting. This demonstrates that the laser parameters used in cutting have an influential effect on the results of the experiment.