## 4 Results and Discussions  
After the regression equation determining for the \(\mathrm{R_{a}}\), the results were predicted at any area of the experimental domain, based on the determined regression models. Thus, the \(\mathrm{R_{a}}\) values of the surface profile were determined using the obtained regression equations. The \(\mathrm{R_{a}}\) calculated values results afferent to the \(\mathrm{R_{a}}\) measured values are shown in Table 10.  
Starting with these calculations, the comparative graphical representations were made between the experimentally determined measurements and the calculated values using the regression equation determined by the [PERSON] method and the central composite design (Figure 9). Figure 10 compares the relative errors obtained in these two situations. In the graphs in Figures 9 and 10, the evolution of the \(\mathrm{R_{a}}\) values was presented, depending on the cutting speed, which is the most important factor in the surface roughness. Based on the graph analysis, it was found that the calculated arithmetic means deviations of the surface profile based on the regression equations approximate the experimental values with a total average error of 22% for the [PERSON]'s method and 27% for the central composite design. Divided by cutting speed intervals, this error accumulates the averages of the following errors presented in Table 11.  
Figure 10: Comparison between the relative errors obtained ([PERSON]’s method versus central composite design). Figure 9: Comparison between the \(\mathrm{R_{a}}\) measured versus \(\mathrm{R_{a}}\) calculated using [PERSON]’s method and central composite design. The error problem is generated by the values of 570 m/min and 610 m/min. At these cutting speeds, the average roughness of the area, measured by experiments, registers the critical distribution. The roughness value increasing was generated by the vibrations as a result of the machining. It was found that the poorest quality results at 570 m/min and 610 m/min cutting speed. The values of the surface roughness recorded at these speeds are quite high compared to those at lower speeds and upper speeds, respectively. Vibration events lead to a rough surface. This vibration is the effect of a resonance phenomenon given by tool (piece) materials used. The vibration has not been measured during the experiment, but the statement is based on the fact that all other experiment conditions were respected on all combinations: the same CNC machine, the same setup, the same type of material (certified material by lab tests, mechanical and chemical test). The causes, consequences and production process have to be studied further. Several papers dealing with this subject have been identified in the literature. For example, [34] in his paper presents the effects of the spindle attributed forced vibrations on the processing characteristics of the vertical milling process. The effects of three spindle levels attributed to forced vibrations together with feed rate and axial cutting depth are evaluated on surface roughness, dimensional accuracy and tool wear under constant conditions of radial cutting depth and cutting speed. He found that the vibration amplitude of machine tools and the axial cutting depth are statistically significant at a 95% confidence level for surface roughness, the vibration amplitude being the most important factor followed by the axial cutting depth. It is found that higher values of vibration amplitude and feed speed result in excessive tool wear, with the vibration amplitude combined with the feed rate and axial depth, resulting in a catastrophic damage to the tool. Another research belongs to [35], who found that the profile milling processes are very sensitive to vibrations caused by the cutter leakage, especially when it comes to operations in which the diameter of the cut varies on a scale of a few millimeters.