# On the Impact of Additive Manufacturing Processes Complexity on Modelling
## 2 Framework
In view of addressing the plethora of different AM processes, the aspects that are finally kept in this metamodeling approach are the process mechanism and its process parameters, as well as the motion of the head related to the part. Also, the quality is the manufacturing attribute [1] that is of interest, implicating a whole family of related key performance indicators. As explained further below, these indicators have to be defined in the next step, based on the process category and the manufacturer's interests. Therefore, one characteristic process of each process group has been selected; SLM has been chosen  
Figure 4: The current meta modelling framework. from the metal-based AM processes, FDM was chosen from the plastic-based and SLA from the resin-based ones. Regarding cement-based AM, the process chosen has been that of concrete printing, instead of contour crafting, due to lack of mold [74]. Concerning the temperature of these processes, the process mechanism of the metal-based AM (PBF) demonstrates the highest temperature, followed by that of the plastic-based AM (FDM). Thus, a chart occurs (Figure 5) implicating these concepts through a graph and separating the interlinking entities in four different categories, as below:  
1. [noitemsep]
2. Software, including a form of input to the process. 3. Hardware, specifying what is being affected directly by the corresponding software. 4. The process characteristic, which mainly consists of motion and bonding; the latter is depending on the process that this procedure is applied on, so candidates underlying mechanisms may be solidification (i.e., in SLM) and polymerization (i.e., in SLM). 5. Manufacturing, containing the corresponding KPIs (that is quality, in the context of the current work). However, this is still an abstract scheme, so it needs to be elaborated and possibly simplified. Thus, the corresponding abstract entities (indicated by the word \"software\" in Figure 5, implying some sort of control), ought to be transformed into regulated variables, potentially towards quantification. In the meantime, output variables, specifically quality-related ones as mentioned in Figure 5, are analyzed into output (Quality) related variable(s), per manufacturing process. Next, the two categories \"Hardware\" and \"Process\" are substituted by key variables, also per manufacturing process. This is not a straightforward choice, however, there are more than one aspects that contribute towards justifying the choices in Figure 6, such as literature aspects in modelling and control. As indicated in literature, temperature can be considered such a variable for metals, since it guarantees the solidification (enthalpy is overlooked deliberately for reasons of simplification), while temperature gradient is responsible for stresses formation [22] and temperature's temporal derivative causes defects creation (this may also cover the melt-pool effect on defects, due to enthalpy rate) [75]. As far as the other manufacturing processes are concerned, plastics are signed once more by temperature [76], resins operate on a power-exposure time basis, so cure depth can be used to simplify that [77] and cement-based additive manufacturing relies on additives for a sufficiently good combination of printability and settling time [21]. Figure 5: Abstractive metamodeling in AM. The quality of each process is also different, spanning from simple dimensional inaccuracies to all four indicators of Figure 6. Thus, the impact of the process parameters can be measured based on the variance of the performance indicators (\(Q\)), as per Equation (1), adopted from literature [78], with \(V\) denoting a bonding key variable and \(S\) a motion variable. \[I=\frac{\partial Q}{\partial V}\Delta V+\frac{\partial Q}{\partial S}\Delta S, \tag{1}\]  
All in all, this metric can be used to quantify the impact of the variances of process parameters on the quality indicator.