# On the Impact of Additive Manufacturing Processes Complexity on Modelling
## 3 Implementation and Primary Results  
The goal of this section is to apply the aforementioned numerically on AM process groups and classify them with respect to their complexity. To this end, the data used here are taken from relevant literature and are applied on the framework that was described above. All the values are summarized in Tables 2 and 3. Therefore, as mentioned in the previous section, regarding the choice of discrete values for the aforementioned variables, one needs to set criteria on their discretization taking into account their values range. To this end, what follows is a justification of selection of three characteristics for each one of them: (a) minimum value, (b) maximum value and (c) the largest possible step they can obtain, which is defined as \"Important Step\" herein. This is not a straightforward task, however, one requires previous knowledge, either from theoretical models, or from experimental works, since the procedure of discretizing the variables is not a heuristic method. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Process** & **Material** & **Process Parameters** & **Min** & **Max** & \begin{tabular}{c} **Important** \\ **Step** \\ \end{tabular} & \
\begin{tabular}{c} **Alternatives** \\ **(Max – Min + 1)/Step** \\ \end{tabular} \\ \hline SLM [26] & Steel & Laser Power (kW) & 1 & 10 & 0.1 & 100 \\ FDM [67] & PLA & Heat Power (W) & 150 & 300 & 10 & 16 \\ SLA [66] & Resin & Laser Power (mW) & 30 & 80 & 10 & 6 \\ Cement-based &
\begin{tabular}{c} Extrusion/Head \\ \end{tabular} & 0.55 & 2.5 & 0.5 & 6 \\ AM [18] & Cement & Speed ratio & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Indicative quality-affecting process parameters per process, along with minimum, maximum, and important-step values and alternatives calculation. Figure 8: Process variables implicated in the complexity estimation. For SLM, laser power has been selected as the process parameter because it is the most important in terms of defining the quality of a part due to the nature of the thermal-based process mechanism. The important step has been set to 0.1 kW, the minimum value to 1 kW, and the maximum to 10 kW, leading to a total of 100 alternatives. For FDM, heating power has been selected as the process parameter because it is the most defining parameter of the heating-based process mechanism. Following the same procedure, 16 alternatives have been defined in FDM. In SLA, owing to the nature of the process mechanism (photopolymerization), the laser-power values are relatively low compared with the power values of the thermal AM process groups. In addition, it is noted that the difference between the minimum (30 mW) and maximum (80 mW) indicative values is not considerable in comparison to the important step. Finally, in concrete AM, the speed ratio of the head speed and the extrusion speed is the most important process parameter in terms of defining part quality. This decision is derived from the fact that if, according to the literature [21], one utilizes this ratio and the extrusion speed as two process parameters, instead of utilizing the two speeds, then the quality and the time as criteria are decoupled. Thus, the extrusion speed can be used as a tool for selecting the process time and the aforementioned ratio can be used as a control for quality. The important step is quite difficult to find, as by reviewing previous works it can be seen that the partitions in corresponding the ratio scale are non-linear [21]. For the sake of simplicity, though, an average value of 0.5 is adopted. In general, the process-parameter selection for the aforementioned processes, as well as the minimum and maximum values are supported by the extensive literature review that has been presented in a previous work by the present authors [18]. This is also the case for the important step, however, additional knowledge is needed, such as input from control performance [82].