## 4 Geometrical Analysis
### Microgometrical Deviations  
Figure 10 presents the results obtained for the areal surface roughness parameters _Sa_ and _Sz_, measured on the machined specimens under different combinations of \(v_{c}\), \(f\), and \(D\). These parameters provide a three-dimensional characterization of the surface texture, where _Sa_ represents the arithmetic mean height of the surface and _Sz_ denotes the maximum height difference between the highest peak and the lowest valley within the measured area.  
The analysis of the machined specimens shows a clear influence of both cutting parameters. A \(v_{c}\) increase from 50 to 200 m/min generally results in higher _Sa_ values, particularly at low \(f\) values. This is attributed to the thermal effects, which soften the surface and cause localized marking or material creep, potentially increasing surface roughness. These effects are more evident under conditions of prolonged interaction between tool and workpiece, such as low \(f\).  
The \(f\) variation exhibits the most significant influence on both _Sa_ and _Sz_. As feed increases from 0.05 mm/rev to 0.2 mm/rev, there is a noticeable rise in the roughness values. This is explained by the larger uncut chip thickness, which results in more prominent tool marks and surface undulations. Higher \(f\) reduces the overlap between successive tool passes, producing a coarser surface profile. This trend is consistent across different diameters and \(v_{c}\).  
Figure 10: Surface roughness obtained in turned samples as a function of \(v_{c}\), \(f\) and \(D\), and printed samples by FFF as a function of layer thickness: (**a**) _Sa_; (**b**) _Sz_.  
In contrast, the specimen diameter appears to have a secondary influence. Although larger diameters tend to show slightly lower \(Sa\) values under identical cutting conditions, this effect is related to higher structural stiffness, which minimizes vibrations and helps to maintain a more stable cutting path.  
For comparison, \(Sa\) and \(Sz\) have also been evaluated on reference specimens manufactured solely by FFF (Figure 11). The high-resolution specimen, printed with a layer thickness of 0.05 mm, exhibited a relatively smooth surface, with \(Sa\) values in the range of those obtained through low \(f\) values. However, the roughness values were still higher than the best machined results, particularly in terms of \(Sz\), where peak-to-valley differences were accentuated by the layered fabrication.  
The low-resolution FFF specimen, printed with a 0.30 mm layer thickness, shows significantly worse surface quality, with both \(Sa\) and \(Sz\) values exceeding those observed in any of the machined cases. The pronounced ridges and valleys inherent to the additive process at coarse layer heights highlight the limitations of FFF in achieving fine surface finishes without post-processing.  
Overall, these results demonstrate that machining significantly improves surface quality compared with additive manufacturing alone. This is particularly evident in the reduction in extreme topographical features (\(Sz\)). Furthermore, the strong dependence of surface roughness on feed rate aligns with trends well documented in the machining of metallic materials, where roughness is primarily governed by the feed per revolution [57]. In addition, the absolute roughness values recorded in PLA-CF are generally higher than  
Figure 11: Surface topography obtained in machined and printed samples.  
those typically observed in metals such as aluminum or titanium alloys [58; 59]. This suggests that, despite the differences in material behavior, feed remains the dominant parameter in controlling surface finish for both polymers and metals.