## 3 Results and Discussion
### Surface Roughness  
When looking at the regression prediction model for surface roughness (\(R_{a}\)) across the X-Y plane traversed in the X direction (see Equation (5) and Figure 11), it was noticeable that the surface inclination angle had the most significant influence on the obtainable roughness, followed by layer thickness, which is supported by the results obtained using ANOVA, which identified the three most significant parameters, such as first, surface inclination angle (\(p\)-value = 0.0031), second, layer thickness (\(p\)-value = 0.0051), and third, printing speed (\(p\)-value = 0.4316). \[ \begin{array}{l}R_{a_{X}}=34.062-0.06*x_{1}+10.233*x_{2}+1.924*x_{3}+1.008*x_{4 }+9.633*x_{5}-0.864*\\ x_{1}x_{2}+0.415*x_{1}x_{3}-1.053*x_{1}x_{4}+1.276*x_{1}x_{5}+3.702*x_{2}x_{3}+ 3.768*x_{2}x_{5}+1.374*\\ x_{3}x_{4}+1.667*x_{3}x_{5}+0.227*x_{4}x_{5}-2.971*x_{2}{}^{2}+1.24*x_{3}{}^{2 }+0.976*x_{4}{}^{2}-19.403*x_{52}\end{array}  \tag{5}\]  
where \"\(x_{1}\)\" is the normalized value for infill percentage, \"\(x_{2}\)\" refers to the normalized value of layer thickness, \"\(x_{3}\)\" denotes the normalized value of printing speed, \"\(x_{4}\)\" is the normalized value for printing temperature, and \"\(x_{5}\)\" represents the normalized value for the surface inclination angle. Although printing speed came third in this list, it is much less significant for generating surface roughness than surface inclination and layer thickness. This can be explained by the staircase effect. When printing with thicker layers, the staircase becomes more distinct, since there are fewer, but higher steps. If the surface inclination angle is close to 90\({}^{\circ}\), the staircase changes to the layer profile. Because of that the surface roughness decreases but does not disappear. A higher printing speed and printing temperature slightly increase roughness, while the infill percentage has no influence. Note that surface roughness in the Y direction was found to have same trends to that obtained in the X direction. Figure 12 illustrates some interaction effects. Again, the staircase effect can be observed, when looking at the interaction of surface inclination angle and layer thickness. With rising angle and layer thickness, the surface roughness increases. In addition, the gap between the graphs shows that thick layers combined with angles between 45\({}^{\circ}\) and 90\({}^{\circ}\) enhance the staircase effect and hence, the roughness. In addition, the printing temperature, printing speed, and layer thickness appear to affect surface roughness. Thin layers and slow speeds paired with a high temperature decreases the roughness, since the filament is less viscous, not under tension, and is able to spread out and connect with previous layers. The opposite is observed at low temperatures, thin layers, and slow speeds, because the filament creates blobs due to its high viscosity, the slow speed does not stretch the filament, and thin layers cool rapidly. Figure 11: Predicted effects of changes in process parameters on the error\(\%\) for surface roughness in the X direction. The investigations of [PERSON] et al. [27], [PERSON] et al. [28], [PERSON] et al. [32], and [PERSON] et al. [33] confirm the results of this study that layer thickness greatly influences the surface quality. [PERSON] et al. [29] also ascribe this result to the staircase effect. Moreover, both [PERSON] et al. [29] and [PERSON] et al. [33] support the observation that the part/build orientation, which is comparable to the surface inclination angle, is having a significant impact on surface roughness. Agreement is also found concerning the impact of printing speed, which was low in the investigation of [PERSON] et al. [28] agreeing with the ANOVA result obtained in this study. [PERSON] et al. [32] and [PERSON] et al. [28] confirmed the low impact of printing temperature, if it is considered independently from the other parameters. [PERSON] et al.