# Optimization Parameters for PLA Through Additive Manufacturing: Taking Mixed Shapes as an Example
## 3 Results and Discussion
### Rsm
#### 3.3.1 RSM of Dimensional Accuracy  
The three factors with the highest F values in the above variation analysis results are used as the design variables of the response surface method. These are A (Nozzle gap height (X1)), B (Extruder temperature (X2)), and C (Bed temperature (X3)). The parameters of the levels are shown in Table 13. The levels of the factors are performed by the Central Composite Design. The levels of the factors are converted into 20 orthogonal arrays. After printing the model, use a caliper to measure the dimensions and record the data. In addition, the experiment was repeated three times and the average was taken. The results are shown in Table 14. The model of Minitab17 is used for analysis. A second-order regression model of the dimensional accuracy score is built. The regression model coefficients are shown in Table 15. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Factor** & **SS** & **DOF** & **Variance** & **F statistic (F)** & \(\rho\%\) & **Confidence** & **Significant** \\ \hline A. & 4.173 & 3 & 1.391 & 17.210 & 19.60\% & 97.90\% & Yes \\ \hline B. & 2.661 & 3 & 0.887 & 10.980 & 12.50\% & 96.00\% & Yes \\ \hline C. & 13.395 & 3 & 4.465 & 55.250 & 62.93\% & 99.60\% & Yes \\ \hline D. & & & & Pooled & & \\ \hline E. & 1.058 & 3 & 0.352 & 1.360 & 4.97\% & 87.10\% & No \\ \hline Error & 0.242 & 3 & 0.081 & & & \\ \hline Total & 21.286 & 15 & 7.095 & & & \\ \hline \end{tabular}
\end{table} 
Table 12: The Second S/N ratio variation analysis (Tensile strength). \begin{table}
\begin{tabular}{c c c c} \hline
**Factor** & **SS** & **DOF** & **Variance** \\ \hline A. Nozzle gap height (mm) & 4.173 & 3 & 1.391 \\ \hline B. Fill spacing (mm) & 2.661 & 3 & 0.887 \\ \hline C. Infill pattern & 13.395 & 3 & 4.465 \\ \hline D. Infill print head velocity (mm/s) & 0.242 & 3 & 0.081 \\ \hline E. Extruder temperature (\({}^{\circ}\)C) & 1.058 & 3 & 0.352 \\ \hline Other & 4.173 & 3 & 1.391 \\ \hline Total & 2.661 & 3 & 0.887 \\ \hline \end{tabular}
\end{table} 
Table 11: The first S/N ratio variation analysis (Tensile strength). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Experiment Factor** & **Unit** & \(-\)**1** & **0** & **+1** \\ \hline X1 (Nozzle gap height) & mm & 0.05 & 0.1 & 0.15 \\ \hline X2 (Extruder temperature) & \({}^{\circ}\)C & 225 & 230 & 235 \\ \hline X3 (Bed temperature) & \({}^{\circ}\)C & 73 & 75 & 77 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Response Surface Method (RSM) Level Parameter Design (Dimensional accuracy). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item** & **Effect** & **Coefficient** & **Coefficient Standard Deviation** & **T Value** & _p Value_ \\ \hline Constant & & 2.819 & 0.188 & 14.99 & 0 \\ \hline X1 & \(-\)0.781 & \(-\)0.391 & 0.210 & \(-\)1.860 & 0.000 \\ \hline X2 & \(-\)0.030 & \(-\)0.015 & 0.210 & \(-\)0.070 & 0.000 \\ \hline X3 & \(-\)0.972 & \(-\)0.486 & 0.210 & \(-\)2.320 & 0.003 \\ \hline X1 \(\times\) X1 & \(-\)1.007 & \(-\)0.503 & 0.344 & \(-\)1.460 & 0.174 \\ \hline X2 \(\times\) X2 & \(-\)0.282 & \(-\)0.141 & 0.344 & \(-\)0.410 & 0.090 \\ \hline X3 \(\times\) X3 & \(-\)1.457 & \(-\)0.728 & 0.344 & \(-\)2.120 & 0.060 \\ \hline X1 \(\times\) X2 & 1.008 & 0.504 & 0.461 & 1.090 & 0.300 \\ \hline X1 \(\times\) X3 & \(-\)0.301 & \(-\)0.150 & 0.461 & \(-\)0.330 & 0.004 \\ \hline X2 \(\times\) X3 & \(-\)1.008 & \(-\)0.504 & 0.461 & \(-\)1.090 & 0.300 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Design results of Response Surface Method (Dimensional accuracy). The regression coefficients are shown in the second line of Table 15. The multinomial regression equation can be obtained by adding the variable and cross terms, expressed as Equation (3):  
\[ \begin{array}{c}\text{Y}=-663+5\;X_{1}+1.86\;X_{2}+5.24\;X_{3}-71.2\;X_{1}{}^{2 }-0.00199\;X_{2}{}^{2}-0.01030\;X_{3}{}^{2}+\\ 0.713\;X_{1}\times X_{2}-0.212\;X_{1}\times X_{3}-0.00713\;X\times X_{3}\end{array}