## 4 Second Phase of Experimentation: Results and Discussion  
The industrial BF machine was used according to the previously described method. Each specimen (Figure 4) was extracted and measured by means of roughness measurement. In Figure 8a, the 0\({}^{\circ}\) profile is shown. The initial Ra was more than 15 \(\upmu\)m with a peak-to-valley Rt of about 100 \(\upmu\)m. The profile was symmetrical (the skewness was close to 0) and slightly platykurtic, since the kurtosis was near 2.5. The high value of the root-mean-square slope of the profile, i.e., RAq, indicates a rough surface with a poor reflectivity. If charge 1 was employed and BF parameter set 1 was selected, after 12 h, the profile shown in Figure 8b was obtained. The average roughness Ra was decreased by 41%, as well as the total roughness Rt. A cut of the peaks was observed, suggesting a good BF mechanism; in this condition, the \(Ba\) was about 500 and the employed motion was cascading. As a measure of the profile distribution shape, the skewness was negative, i.e., the profile was mainly made up of valleys, and the kurtosis was 3, as in a Gaussian distribution. After 24 h, the Ra was reduced by an additional 40%, the skewness was \(-\)3, and the profile was markedly leptokurtic (Figure 8c). After 48 h, the original profile was almost deleted; only some scratches were present, probably the deepest original ones (Figure 8d). On the other hand, the employment of charge 3 with the same BF parameters led to a marginal improvement. The original profile of this specimen (Figure 8e) was characterized by almost the same roughness parameters; however, since, in this case, the \(Ba\) was 360, a marginal reduction in Ra was observed with higher peak-to-valley heights, as shown in Figure 8f, for a processing time of 12 h. At 24 h, some differences could be observed in Ra and Rt, but the distribution shape was marginally modified. In fact, in Figure 8g, rounded peaks can be noticed; this is an indication of improper BF surface actions where the particle energy was probably used for local plastic deformation and wear of the profile rather than micro-chipping. This led to a high processing time, as remarked by the profile obtained at 48 h (Figure 8h), which was characterized by negligible variations of all process parameters. Figure 7: Barrel finishing (BF) parameter sets for charge 1 (**a**), charge 2 (**b**), and charge 3 (**c**) within the rolling and cascading regimes. The same poor results were achieved by taking into consideration charge 1 with BF parameter set 3. Here, the _Ba_ was only 250 and, after 24 h, the Ra decreased by only 32% (Figure 9a,b). Charge 1 and BF parameter set 1 appear to be a good combination. These conditions were applied to a surface characterized by different inclinations, where different morphologies were expected. In Figure 9c, the original profile is shown; the initial Ra was about 4 \(\upmu\)m, the total roughness Rt was one-third of the 90\({}^{\circ}\) surface, and the skewness was negative. This was due to the laser scans, which were prominent, giving the profile this behavior. After 24 h, the profile (Figure 9d) was almost deleted; the Ra was markedly reduced, and only some local valleys are observed. When the Inconel718 material was considered, the initial Ra was lower than that of Ti6 Al4V for the same surface orientation of 90\({}^{\circ}\) (Figure 9e). The shape of the profile distribution was almost symmetrical and slightly platykurtic as before. The employment of charge 1 and BF parameter set 1 allowed for good improvement of Ra and Rt after 24 h. The skewness was deeply reduced, and kurtosis was highly leptokurtic, suggesting that proper BF cutting conditions took place. Upon observing the profile (Figure 9f), this mechanism is clear since the peaks were cut away and the valleys were left unaltered. The other BF parameter sets and charges resulted in the same previous observations.