## 4 Cooling System Design and Cooling Simulation Based on UG and Moldflow
### Cooling Process Simulation and Analysis
#### 4.3.2 Design of Experiments for Optimized Conformal Cooling Channels  
The experimental design methodology was employed as a guiding framework for the development of conformal cooling channels. The design process encompassed a comprehensive experimental approach, taking into consideration the thin-walled characteristic of the products with wall thicknesses typically ranging from 0 to 2 mm, as well as the diameter of the cooling channels, which was determined based on the specified boundary conditions, falling within the range of 4-6 mm. The initial experimental design of DOE-1 was established based on general rules of thumb for mold designers. In this set of experiments, circular cross-sections were employed for all the cooling products, and the specific details of the DOE parameters can be found in Table 2. The design cases were denoted as 1.1, 1.2, and so forth, in accordance with the experimental design plan.  
We enhanced the experiments conducted on DOE-2, DOE-3, and DOE-4 by incorporating various channel cross-sectional shapes, including trapezoidal, dome, and rectangular, as shown in Table 3. To maintain a consistent cross-sectional area, these shapes were derived from circular cross-sections by keeping the area constant and by recalculating the dimensions. For instance, if the diameter of a circular cross-section is 6 mm, its area would be 28.27 square millimeters. This area can be converted to other shapes, such as a rectangular cross-section with dimensions of 5.3 \(\times\) 5.3 mm, a trapezoidal cross-section with a top width of 4.0 mm, a bottom width of 5.0 mm, and a height of 6.3 mm, or a dome-shaped cross-section with a width of 8.0 mm and a width of 5.0 mm. However, the exact value of the dome-type cross-sectional area is challenging to calculate; thus, an approximate value is used.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Case** & **Diameter** & **Cooling** & **Case** & **Diameter** & **Cooling** \\
**Number** & **(mm)** & **Time (s)** & **Number** & **(mm)** & **Time (s)** \\ \hline
1.1 & 4.0 & 27.89 & 1.12 & 5.1 & 25.77 \\
1.2 & 4.1 & 27.78 & 1.13 & 5.2 & 25.25 \\
1.3 & 4.2 & 27.58 & 1.14 & 5.3 & 25.07 \\
1.4 & 4.3 & 27.42 & 1.15 & 5.4 & 24.93 \\
1.5 & 4.4 & 27.20 & 1.16 & 5.5 & 24.80 \\
1.6 & 4.5 & 27.01 & 1.17 & 5.6 & 24.67 \\
1.7 & 4.6 & 26.79 & 1.18 & 5.7 & 24.53 \\
1.8 & 4.7 & 25.31 & 1.19 & 5.8 & 24.53 \\
1.9 & 4.8 & 25.49 & 1.20 & 5.9 & 24.37 \\
1.10 & 4.9 & 25.76 & 1.21 & 6.0 & 24.19 \\
1.11 & 5.0 & 25.98 & & & \\ \hline \end{tabular}
\end{table}
Table 2: Case setup variables in design of experiments (DOE-1).  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **DOE-2** & \multicolumn{2}{c}{**DOE-3**} & \multicolumn{2}{c}{**DOE-4**} \\ \hline
**Case** & **X-Section** & **Case** & **X-Section** & **Case** & **X-Section** \\
**Number** & **(mm \(\ast\) mm)** & **Number** & **(mm \(\ast\) mm)** & **Number** & **(mm \(\ast\) mm)** \\ \hline
2.1 & (2.7 + 3.3) \(\ast\) 4.2/2 & 3.1 & 5.3 \(\times\) 3.3 & 4.1 & 3.5 \(\times\) 3.5 \\
2.2 & (3.0 + 3.8) \(\ast\) 4.7/2 & 3.2 & 6.0 \(\times\) 3.8 & 4.2 & 4.0 \(\times\) 4.0 \\
2.3 & (3.3 +Based on the classification of cross-sectional shapes, we conducted five sets of experiments with different cross-sectional areas that matched the areas of circular cross-sections with diameters of 4.0, 4.5, 5.0, 5.5, and 6.0 mm. For example, for rectangular cross-sections, we designed cross-sectional areas of 4.1, 4.2, 4.3, 4.4, and 4.5 while maintaining the same area as the corresponding cross-sections of other shapes. Table 4 presents the optimization problem statements for DOE-1, DOE-2, DOE-3, and DOE-4, along with their corresponding conformal cooling channel shapes: circular, trapezoidal, dome-shaped, and rectangular, respectively. Additionally, the table provides an illustration of the design variables and constraints.