# Dimensional Errors Due to Overhanging Features in Laser Powder Bed Fusion Parts Made of Ti-6 Al-4V
## 2 Methodology  
### Experimental Design  
Since this paper focusses on investigating down-facing surfaces, a simple design with a 45\({}^{\circ}\) inclined down-facing surface was used as the test piece. Although the printing of surfaces below 45\({}^{\circ}\) is generally possible, 45\({}^{\circ}\) is conventionally considered the limit for printing high-quality down-facing surfaces without support structures [31; 32; 33]. For surfaces below 45\({}^{\circ}\), large dimensional deviations and deteriorating surface textures are exhibited. Therefore, achieving minimal errors at an angle of 45\({}^{\circ}\) without support structures would represent an improvement compared to the state-of-the-art approaches. The different process parameters and their levels chosen to investigate the effect on the dimensional accuracy are listed in Table 1. All test pieces were built using a commercial laser-based powder bed fusion system manufactured by 3 DSystems, the ProX(r) DMP 320 (3 DSystems, Rock Hill, USA), and the Ti-6 Al-4V metal powder used was also supplied by 3 DSystems under the brand name Laserform Ti Gr23(A) (3 DSystems, Rock Hill, USA).  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Levels** \\ \hline Laser Power (W) & 50, 90, 150, 210, 250 \\ Scan Speed (mm/s) & 200, 465, 850, 1235, 1500 \\ Scan Spacing (\(\upmu\)m) & 50, 60, 75, 90, 100 \\ Scan Pattern & Stripes, rectangular cells, hexagonal cells \\ Layer Thickness (\(\upmu\)m) & 60, 90 \\ \hline \end{tabular}
\end{table}
Table 1: Process parameters and levels.  
An inscribed central composite (CCI) experimental design was used and the Design of Experiments (DoE) is shown in Table 2. A central composite design is a type of fractional factorial design of an experiment where all levels and all combinations of process parameters are not tested during the experimentation phase. Fractional factorial designs provide detailed insights into a process while still keeping the number of trials as low as possible [34]. Such a design was therefore chosen to reduce the number of experimental trials and expenditure of time and resources, without losing any insight into the process.  
The parameters presented in Table 2 were used to print the samples for each of the various scan patterns (as seen in Figure 2) and layer thicknesses, resulting in six unique tables and a total of 144 test pieces for analysis. Trials 15 to 24 represent parts printed with the same parameters, while the test pieces were arranged in the build platform following no particular order in order to improve the randomization.  
In the unique methodology followed within this research, the process parameters were only varied within the down-facing area of the part (depicted with light gray in Figure 1), while the rest of the parts were printed with the same standard printing parameters as recommended by the manufacturer for all test pieces, as seen in the image (depicted with darker gray in Figure 1). The down-facing area in this research is a flat surface and does not include any curvature in the surface.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment Nr.** & **Laser Power (W)** & **Scan Speed (mm/s)** & **Scan Spacing (\(\upmu\)m)** \\ \hline
1 & 90 & 465 & 60 \\
2 & 90 & 465 & 90 \\
3 & 90 & 1235 & 60 \\
4 & 90 & 1235 & 90 \\
5 & 210 & 465 & 60 \\
6 & 210 & 465 & 90 \\
7 & 210 & 1235 & 60 \\
8 & 210 & 1235 & 90 \\
9 & 50 & 850 & 75 \\
10 & 250 & 850 & 75 \\
11 & 150 & 200 & 75 \\
12 & 150 & 1500 & 75 \\
13 & 150 & 850 & 50 \\
14 & 150 & 850 & 100 \\
15–24 & 150 & 850 & 75 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Design of Experiments (DoE) for experimental trials.  
Figure 2: The three different scan patterns used in the study were (**a**) stripes, (**b**) rectangular cells, and (**c**) hexagonal cells.