# Additive Manufacturing of Ceramic Reference Spheres by Stereolithography (SLA)
## 4 Results and Discussion
Additionally, analyzing the residuals obtained from the point clouds captured by contact with the SP25M (Renishaw, Gloucestershire, UK) on the 18 available spheres, it can be noted that all of them exhibit some ovalization error in the horizontal plane (OXY) and some flattening in the vertical direction (Z) across all possible combinations of design variables and positions. As an example, Figure 13 shows the magnified residuals of three evaluated artifacts. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Tray Location**} & **Artifact Code** & **Form Error** & **Artifact Code** & **Form Error** & **Artifact Code** & **Form Error** \\  & **(Bullet Shape,** & & **(Mushroom** & & **(Mushroom** & **(mm)** \\  & **with Inner** & & **Shape, without** & & **Shape, with** & \\  & **Support, Pole** & **(mm)** & **Inner Support,** & & **Inner Support,** & \\  & **Upwards)** & & **Pole Upwards)** & & **Pole Upwards)** & \\ \hline Rear & B_F_U_20\(1\)1 & 0.125 & M_E_U_20\(1\)1 & 0.123 & M_F_U_20\(1\)1 & 0.132 \\ Center & B_F_U_20\(1\)2 & 0.096 & M_E_U_20\(1\)2 & 0.075 & M_F_U_20\(1\)2 & 0.112 \\ Front & B_F_U_20\(1\)3 & 0.125 & M_E_U_20\(1\)3 & 0.094 & M_F_U_20\(1\)3 & 0.142 \\ \hline Rear & B_F_U_20\(2\)1 & 0.085 & M_E_U_20\(2\)1 & 0.089 & M_F_U_20\(2\)1 & 0.096 \\ Center & B_F_U_20\(2\)2 & 0.077 & M_E_U_20\(2\)2 & 0.075 & M_F_U_20\(2\)2 & 0.071 \\ Front & B_F_U_20\(2\)3 & 0.083 & M_E_U_20\(2\)3 & 0.088 & M_F_U_20\(2\)3 & 0.086 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Form errors of the spheres. Figure 12: Geometrical quality chart of the different spheres. Figure 13: _Cont._  
Based on the above observations, it was decided to analyze the influence of process parameters on the quality indicators of the spheres, i.e., to determine whether using a sphere with different shape, infill, thickness, orientation, or position on the printing may could yield a geometry closer to the nominal (with less diameter deviation and/or less form error). Ultimately, this analysis aimed to identify if a specific combination of design parameters could achieve a sphere with less deformation. The following correlations between design parameters and deviations (DesvD or DesvF) are highlighted from this analysis:  
DesvD (Diameter Deviation): There is a correlation between the position in which the spheres are manufactured and the diameter deviation they exhibit. Spheres manufactured in positions 1 or 3 are better, followed by those made in position 2, which in all cases resulted in a smaller average size (Figure 14a). DesvF (Form Error): (1) There is a correlation between wall thickness and observed form error, being smaller in spheres with a 2 mm thickness than in those with 1 mm (Figure 14b). (2) There is a correlation between infill and form error, with empty spheres (E) performing slightly better than filled ones (F) (Figure 14c). (3) There is some correlation,  
Figure 13: Examples of residuals with graphical magnification of deviations for different artifacts: (**a**) Bullet & Filled & Upwards B_F_U_20\(1\)1, (**b**) Mushroom & Empty & Upwards M_E_U_20\(1\)1 y (**c**) Mushroom & Filled & Upwards M_F_U_20\(1\)1.  
though inconclusive, between position and form error, with the best spheres being those in position 2, followed by positions 1 and 3 (Figure 14d). Figure 14: Different correlations between design variables and deviations of diameter and form error. (**a**) Correlation between the position and diameter deviations, (**b**) Correlation between wall thick-ness and form error deviations, (**c**) Correlation between infill and form error deviations, (**d**) Correlation between position and form error deviations.