## 2 Experimental Procedure
### Influence of Time-Averaged Cavity Pressure on Part Warpage  
For the second phase of injection molding experiments, a full-factorial experiment design was used to vary the melt temperature, packing pressure, and packing time, and the process conditions are shown in Table 3. The contribution of each parameter and the influence of cross-interactions were analyzed. The time-averaged cavity pressure was first calculated from the pressure profile integral using the following equation, and a case illustration is shown in Figure 6. Figure 6 depicts the pressure evolution during various stages of the injection phase. The pressure starts to rise when the melt front arrives at the sensor location. Once the melt is filled with the cavity, pressure quickly rises to the target packing pressure and holds this value for some time (depending on packing time) in the packing phase. After the end of the packing process, the pressure continues to drop until it reaches atmospheric pressure or when the part is ejected. Once the mold cavity is filled, melt crystallization starts (\(t_{1}\)). When crystallization is over (\(t_{2}\)), the melt is assumed to be solidified, and packing becomes noneffective. The time-averaged packing pressure, \(P_{Surg}\), is defined as  
\[P_{Surg}=\frac{1}{\Delta t}\int_{t_{1}}^{t_{2}}\overline{p}(t)dt \tag{2}\]  
where \(t_{1}\) and \(t_{2}\) represent the packing starting and crystallization completion time, respectively. \(\Delta t\) is the time interval between \(t_{1}\) and \(t_{2}\). The mean pressure value was then averaged at three measured locations (near the gate, designated as NG; in the middle, designated as MID; and far away from the gate, designated as FG) and correlated with the measured part shrinkage. A linear regression model was constructed to correlate the time-averaged cavity pressure and measured shrinkage using first-, second-, and third-order functions, as shown in Equations (3)-(6):  
\[S_{V}=\frac{L_{0}-L}{L_{0}}\times 100\% \tag{3}\]  
where \(S_{V}\) is the measured shrinkage, \(L_{0}\) is the original length of the cavity, and \(L\) is the molded part length. The correlation between the time-averaged solidification pressure, \(P_{Sav}\), and part shrinkage, \(S_{V}\), can be represented by  
\[S_{V}=\text{A1}-\text{B1}\times P_{Surg} \tag{4}\]  
\[S_{V}=\text{A2}-\text{B2}\times P_{Surg}+\text{C2}\times P_{Surg2} \tag{5}\]  
\[S_{V}=\text{A3}-\text{B3}\times P_{Surg}+\text{C3}\times P_{Surg2}+D3\times P _{Surg3} \tag{6}\]  
where Ai, Bi, Ci, and Di (i = 1, 2, 3) are constants to be determined from the relevant data. The appropriate function was confirmed using residual analysis [27; 28]. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Fixed Process Parameters**} \\ \hline Injection speed & (mm/s) & 20 \\ Velocity/pressure switch position & (mm) & 4 \\ Packing pressure & (bar) & 800 \\ Packing time & (s) & 9 \\ Melt temperature & (\({}^{\circ}\)C) & 235 \\ Mold temperature & (\({}^{\circ}\)C) & 50 \\ Cooling time & (s) & 5, 7.5, 10, 12.5, 15, 17.5, 22.5, 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Molding experimental parameters to determine part warpage with varying cooling times. Figure 6: Illustration of pressure integral calculation from which the time-averaged solidification pressure can be evaluated. Evolution of pressure profile at various stages of processing are noted.