## 2 Materials and Methods
### Study 1: Identification of Main Influencing Variables and Interactions
#### 2.2.1 Design of Experiments
\begin{table}
\begin{tabular}{c c} \hline
**Setting** & **Value** \\ \hline Material & Sintratec PA12 (black) \\ Mixing ratio & 60\% Fresh powder/40\% used powder \\ Number of initial layers in sintering phase & 20 \\ Sintering temperature, \(\mathrm{T_{O}}\) & 175 \({}^{\circ}\)C \\ Laser spot diameter & \(\approx\)0.1 mm \\ Laser output & 1.6 W \\ Hatch distance & 0.1 mm \\ Scan speed & 650 mm/s \\ Layer thickness & 0.1 mm \\ Energy density per unit area, \(\mathrm{E_{F}}\) & 0.025 J/mm\({}^{2}\) \\ Inert gas & - \\ Process chamber temperature & Uncontrollable (\(\approx\)110 \({}^{\circ}\)C) \\ Difference between hot spot and cold spot in & \(\Delta\)7 K \\ the stable built area (105 mm \(\times\) 105 mm) & 90 min \\ Heating up time & 10 h (overnight) \\ Cooling down time & 170 \({}^{\circ}\)C \\ Platform heater & \(\approx\)0.9 \\ Powder emissivity, \(\epsilon_{\mathrm{P}}\) & \(\approx\)0.9 \\ Fibre nozzle emissivity, \(\epsilon_{\mathrm{D}}\) & \(\approx\)0.9 (graphite lacquer) \\ Emissivity of the surface of the additional heat & \(\approx\)0.9 (graphite lacquer) \\ source (metal plate), \(\epsilon_{\mathrm{HM3}}\) & \\ \hline \end{tabular}
\end{table} 
Table 4: Process and material parameters of the developed LS system selected for the investigations. \begin{table}
\begin{tabular}{c c c c c} \hline
**Abbreviation** & **Factor** & \(-\mathbf{1}\) & \(\mathbf{1}\) & **Change** \\ \hline A & \(\kappa\) & Planar & Convex & Before printing \\ B & \(\mathrm{d_{D,o}}\) & 4 & 2 & Before printing \\ C & \(\mathrm{h_{D}}\) & 0.8 & 0.4 & Before printing \\ D & \(\mathrm{T_{D}}\) & 280 & 310 & Simply via PLC \\ E & \(\mathrm{v_{D}}\) & 30 & 60 & Simply via PLC \\ F & \(\mathrm{T_{HM3}}\) & 190 & 200 & Simply via PLC \\ \hline \end{tabular}
\end{table} 
Table 3: Investigated influencing factors with abbreviations, factor levels and adjustability. heating and cooling down times of the LS machine, only one print per day is realistic. Performing 64 individual prints, therefore, requires 64 working days. For each repetition of all factor level combinations, the effort increases. In addition, the available build volume of the developed LS machine was not optimally used with one specimen per run. This results in the highly inefficient use of build space and the associated high powder consumption. Although unsintered powder can be reused, it does not have the same properties as fresh powder [27; 28; 29]. This study uses a full factorial SPD with eight main units and eight subunits to determine the significance of the factors in Table 3. Implementing an SPD allows the \(2^{3}=8\) factor level combinations of the simple modifiable factors (D, E and F) specimens to be produced simultaneously in one print run (subunit). The three factors that are difficult to change (A, B and C) are kept constant (main unit). In this way, the effort required to produce the 64 specimens is reduced to eight print runs instead of 64. In addition to time savings, material and energy costs can also be reduced. Further information on the design and evaluation of SPD can be found in [30]. To estimate the required number of experiments, a trade-off must be made between the size of the detectable effect and the experimental effort. The effort should be as great as necessary and as small as possible to prevent waste of resources. The number of individual experiments depends on the required resolution of the detectable effects, \(\Delta\mu\), and the standard deviation, \(\sigma\), of the individual values. The required number of individual experiments can be estimated by the following Equation (4) and is based on [25]. \[\mathrm{N}=2\times\mathrm{n}=60\times\left(\frac{\sigma}{\Delta\mu}\right)^{2} \tag{4}\]  
Since the standard deviation of the tests is unknown, it was estimated by further preliminary tests [26]. The standard deviation for the width \(\mathrm{b}_{\mathrm{HAZ}}\) is 211 \(\upmu\)m and 77 \(\upmu\)m for the depth \(\mathrm{t}_{\mathrm{HAZ}}\).