# Sustainable Manufacturing Decisions through the Optimization of Printing Parameters in 3D Printing
## 2 Materials and Methods
### Methods for Single-Objective and Multiobjective Optimization  
As requirements change, the dimensions of product manufacturing considerations change quantitatively. In this study, the product quality, carbon emissions, and cost that are emphasized in sustainable manufacturing are regarded as single-objective and multi-objective optimization goals. The single objectives are W, OW, OL, T, carbon dioxide emissions, material cost, labor cost, and electricity cost. The aim of the single-objective optimization in this study is to investigate the impact of the printing parameters on the FFF-3D printer using the Taguchi method. This method helps determine the significance and impact of different factors. The experimental matrix is referred to as an orthogonal array. The experiments were designed using the Taguchi method to help evaluate the impact of the five factors, namely the fan rate, print speed, nozzle temperature, build plate temperature, and layer thickness, on five important outputs, namely the dimensional accuracy, carbon dioxide emissions, electricity cost, material cost, and labor cost. Each factor consists of either two or three levels and was repeated three times to reduce the overall experimental errors (Table 2). To avoid the dependence of factors in the orthogonal array L18, we filled the factors only in lines 1, 3, 4, 5, and 6, as shown in Table 3.  
To choose appropriate factors and characterize their impacts, eight single-objective properties were investigated in terms of the signal-to-noise ratio (SNR). The SNR characteristics of these eight single objects (the lower the SNR, the better the performance characteristics) were calculated using Equations (5) and (6), and the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factor** & **Printing Parameter** & **Degree of Freedom** & **Level 1** & **Level 2** & **Level 3** \\ \hline A & Fan rate (\%) & 2 & 100 & 50 & - \\ \hline B & Print speed (mm/s) & 3 & 30 & 25 & 20 \\ \hline C & Nozzle temperature (\({}^{\circ}\)C) & 3 & 210 & 200 & 190 \\ \hline D & Build plate temperature (\({}^{\circ}\)C) & 3 & 60 & 30 & 15 \\ \hline E & Layer thickness (mm) & 3 & 0.3 & 0.2 & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Level of each factor. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Num. ** & **1** & **3** & **4** & **5** & **6** \\ \cline{2-5}  & **A** & **B** & **C** & **D** & **E**  
using the mean and standard deviations. The significance of the factors on all targets was then presented using the main effects plot. Finally, the contribution ratio of each factor could be obtained from the analysis of variance (ANOVA). ANOVA was used to interpret a series of experimental results to assess the significance of individual factors. The sum of squares and percentage contribution of each factor were denoted as \(SS_{j}\) and \(P_{j}\), respectively, and their values could be obtained using Equations (6) and (7), respectively. In Equations (7) and (8), \(j\) is the individual parameter, and the total sum of squares is the SNR minus the correction factor. \[S=\sqrt{\frac{\sum_{i=1}^{n}(y_{i}-\overline{y})^{2}}{n}} \tag{5}\]  
\[\text{SNR}=-10\cdot\log(\overline{y}^{2}+S^{2}) \tag{6}\]  
\[SS_{j}=\frac{1}{n_{P_{j}}}\sum_{j=1}^{k}\Bigl{(}SNR_{P_{j}}\Bigr{)}^{2}-\frac{ T^{2}}{n},\;T=\sum_{i=1}^{n}SNR_{i} \tag{7}\]  
\[\rho_{P_{j}}=\left(\frac{SS_{j}}{SS_{T}}\right)\times 100\% \tag{8}\]  
\(S\): standard deviation of \(y\);  
\(y\): observed data of the three single objectives;  
\(\overline{y}\): average of the observed data;  
\(n\): number of experiments. Although the optimal printing parameters of the eight single objects can be obtained using the Taguchi method, it can be inferred that the optimal parameters of a single objective are different from the rest of the responses. A decision-making method that can simultaneously solve all the responses of the requirements must be incorporated to attain sustainable manufacturing.