## 4 Discussion
### Quadratic Predictive Model  
The 3D diagram in Figure 9 provides a clear picture of how the prediction factors, laser power and gas pressure affect the cutting width of Hardox 400 steel parts. It is observed that the smallest values of cutting width are obtained when the laser power is 5000 W, and the assist gas pressure has a low value located in the range 0.45-0.46 bar. The values increase with the distance (somewhat circular, semi-elliptical) from the area characterized by average power values and low pressure values. The highest values of the cutting width (over 0.38 mm) are obtained, on the one hand, for small values of the laser power, 4900 W, at the same time with increased values of the cutting gas pressure of about 0.55 bar, and on the other hand, at high laser power values 5100 W and gas pressure value of 0.50 bar. Specifically, the best cutting width (0.30 mm) is obtained for laser power 5000 W and auxiliary gas pressure 0.46 bar. For the response confidence interval of \(\pm\)1 mm (width = 0.26-0.28 mm), the graph shows values of the laser power between 4980 and 5020 W, at the same time as the gas pressure between 0.45 and 0.48 bar. The response surface combines the shape of a classical paraboloid (in the centre) with a hyperbolic paraboloid (at the extremes) and shows that the cutting width has a variation of the shape of the Gaussian bell, with the tip on the average axis of laser power. If the laser power is maintained at average values and the gas pressure increases, the bell rises, which means that the cutting width increases. The predicted graph indicates a significant influence of the input parameters (power and pressure) on the cutting width using the RSM model. The estimated square model of the cutting width, depending on the laser power and the assist gas pressure, using the regression technique is represented by the polynomial in Figure 10  
\[\mathrm{Kerf}=89.5315-0.0357\cdot\mathrm{x}-0.03889\cdot\mathrm{y}+3.6111\cdot \mathrm{E}-6\cdot\mathrm{x}\cdot\mathrm{x}-0.0008\cdot\mathrm{x}\cdot\mathrm{y }+4.4444\cdot\mathrm{y}\cdot\mathrm{y}, \tag{11}\]  
Figure 9: Prediction of the dependence of the cutting width on the laser power and the assist gas pressure. The term of the square laser power effect is greater than the term of the assistant gas pressure effect with the experimentally used data. It results that the significant factor is the laser power. The term containing the square of the laser power is positive, which means that the dominant effect of the laser power is to increase the value of the Kerr response, while the positive sign of the term containing the square of the pressure shows that the dominant effect of the second influencing factor, gas pressure, is of Kerr increasing. Furthermore, it can be seen that the important factors that interact with each other affect Kerr. From this identification it is found that the most influential factor on the kerf is the laser power, and the second significant factor is the assist gas pressure. The coefficient of the model is 89.5315, the correlation coefficient of the interaction between laser power and pressure is 0.0008, which indicates an effect conjugated with a Kerr reduction influence, and the linear correlation coefficients of laser power and gas pressure are low which shows a decrease Kerr take together with the level of independent factors. By analysing Figure 9 the following aspects were deduced:  
* The cutting width is a quadratic surface, resulting from the interaction between laser power and auxiliary gas pressure;
* The low value of the cutting width, below 0.32 mm, is obtained when the cutting gas pressure is 0.50 bar, and the gas pressure 5000 W;
* The shape of the Kerr variation in the RSM model is a paraboloid representing a quadratic surface that indicates a more pronounced influence of the laser power than the gas pressure.