## 2 Experiments
### Quantification of Volumetric Shrinkage and Surface Roughness
#### 2.3.2 Surface Roughness Quantification  
Every manufacturing process has a unique surface finish known as the \"fingerprint.\" This unique surface finish is in fact the surface topography of the finished product [38]. Peaks and valleys make up every material's surface when observed at the microscopic scale. Variations in the dimensions of these \"peaks and valleys\", as well as the spacing between them, dictate the surface topography's variety.  
A number of different methods can be used to describe the surface properties of materials. These include contact and non-contact approaches. More details of these techniques can be found in [39]. In this study, surface roughness is assessed utilizing a 3D optical profiling system, specifically the Contour GT-K1-3D Optical Microscope, manufactured by Bruker in Billerica, MA, USA, as illustrated in Figure 3. Three-dimensional optical profilometers have been utilized in the scientific and industrial fields to evaluate the performance and surface quality of materials [40]. The profiling system makes use of a method that has an easy-to-use interface. It uses interferometry with white and green light. With sub-nanoscale resolution, the profiling system can quickly measure three-dimensional surfaces at scales ranging from millimeters to nanometers. The Contour GT-K1 can conduct 3D surface metrology because of its quick data gathering abilities, simple measurement setup, and small fingerprint [41]. Moreover, the arithmetic mean of the absolute value (\(Ra\)) (ISO 4287 [42]), as defined by Equation (2) [43; 44], was employed to quantify the roughness  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Injection Molding** & **Symbol** & **Lower Bound** & **Upper Bound** & **Units** \\ \hline Injection pressure & \(I_{P}\) & 450 & 800 & bar \\ Packing pressure & \(P_{P}\) & 100 & 400 & bar \\ Packing time & \(P_{t}\) & 3 & 9 & s \\ Cooling time & \(C_{t}\) & 10 & 30 & s \\ Injection speed & \(I_{S}\) & 15 & 60 & mm/s \\ Melt temperature & \(M_{T}\) & 200 & 250 & \({}^{\circ}\)C \\ Mold temperature & \(M\sigma_{T}\) & 15 & 45 & \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table}
Table 3: The lower and upper limits of the concerned process parameters.  
parameter for a specified sample length of the finished surface across various experimental configurations. In Equation (2), \(L\) represents the profile length, and \(Z\) denotes the absolute value of the roughness profile, as depicted in Figure 4.  
\[R_{a}=\frac{1}{L}\int\limits_{0}^{L}|Z(x)|dx. \tag{2}\]  
The selection of the \(Ra\) parameter was primarily because \(Ra\) is one of the most commonly used parameters for evaluating surface roughness in both academic research and industrial practice, especially in the context of injection molding. Its widespread adoption is due to its simplicity, ease of measurement, and straightforward interpretation, making it a standard reference in many surface quality studies [45; 46]. \(Ra\) serves as a significant parameter in evaluating the surface quality of polymeric components, particularly in injection molding. While \(Ra\) does not encompass all nuances of surface texture, its correlation with visual appearance and functional properties such as friction and wear has been documented in various studies. Experimental research indicates that improved surface quality, represented by reduced \(Ra\) values, enhances appearance characteristics; specifically, parts with lower roughness often exhibit better gloss and est  
Figure 4: A graphical illustration of the average surface roughness (Ra) definition.  
Figure 3: Three-dimensional optical profilometer (Contour GT-K1-3D Optical Microscope).