## 3 Optimization of Cutting Parameters under Optimal MQL Condition
### Results and Discussion  
Table 9 indicates \(S/N\) ratio obtained from Equation (1) and the result of surface roughness (\(R\)a). Three factors were cutting speed (\(v\)), feed rate (\(f\)), depth-of-cut (\(d\)), and workpiece hardness (\(H\)), respectively. Three levels of each factor were represented by \"1\", \"2\", and \"3\". The analytical results were carried out by Minitab software, Version 16. Table 10 shows the mean of the \(S/N\) response for surface roughness of each level of parameters. It shows that the third level of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Level 1** & **Level 2** & **Level 3** \\ \hline \(v\) (m/min) & 40 & 55 & 70 \\ \(f\) (mm/tooth) & 0.01 & 0.02 & 0.03 \\ \(d\) (mm) & 0.2 & 0.4 & 0.6 \\ \(H\) (HRC) & 40 & 45 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameters and levels. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Experiment Number** & \(v\) & \(f\) & \(d\) & \(H\) & Ra (\(\mu\)m) & \(S/N\) **Ratio** \\ \hline  
cutting speed, the first level of feed rate, the first level of depth of cut, and the first level of hardness are highest. Therefore, under the MQL condition, optimal cutting conditions for the experiment will be (3-1-1-1). The ranking means that feed rate is the most influential factor to surface roughness and the second most influential factor is the depth-of-cut. Figure 3 indicated the \(S/N\) response graph for surface roughness. The analytical results of the \(S/N\) response express that, in order to get the best \(R\)a, the optimum cutting parameters are 70 m/min for the cutting speed, 0.01 mm/tooth for the feed rate, 0.2 mm in depth of cut, and 40 HRC for workpiece hardness. Generally, a higher cutting speed, lower feed rate, lower depth of cut, and lower workpiece hardness will lead to good surface roughness under an MQL condition. This result is consistent to the conclusions of [PERSON] _et al._[22] although the study of [PERSON] _et al._ was conducted in dry conditions. An analysis of variance for surface roughness is shown in Table 11. Based on analysis of variance, feed rate and depth-of-cut are the most influential factors regarding surface roughness. They contribute 55.067% and 18.244% to the total effect, respectively. The \(P\) index of feed rate (0.000), the \(P\) index of depth of cut (0.001), and the \(P\) index of workpiece hardness (0.03) less than 0.05 indicate that the effect of these factors has statistical significance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Level** & \(\mathbf{v}\) & \(\mathbf{f}\) & \(\mathbf{d}\) & \(\mathbf{H}\) \\ \hline
1 & 12.28 & 16.03 & 14.74 & 13.95 \\
2 & 12.70 & 12.78 & 12.89 & 13.16 \\
3 & 14.01 & 10.18 & 11.37 & 11.89 \\ Delta & 1.73 & 5.85 & 3.37 & 2.06 \\ Rank & 4 & 1 & 2 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Mean of \(S/N\) response for surface roughness. Figure 3: The effect of cutting parameters on surface roughness. Because optimal MQL conditions for the experiment were determined to be (3-1-1-1) although not present in the experimental process, a verification experiment with optimized MQL parameters was performed to examine the results of the study. The result of surface roughness of the verification test is 0.098 \(\upmu\)m for \(R\)a. The verification experiment is still conducted under MQL conditions. This value is less than the surface roughness of the experiment number 19 (3-1-1-3) that has the smallest value 0.107 shown in Table 9. It proves that the result of the study is of value. According to the analytical procedure employed, the linear regression model for prediction of surface roughness under MQL condition is obtained as follows:  
\[R\text{a-mql}\,=\,-0.2185-0.00106296\upsilon\,+\,7.55556\!f\,+\,0.242778d\,+\,0. 00595556H \tag{2}\]  
where: \(R\)a-mql is surface roughness under MQL conditions. \(\upsilon,f,d\), and \(H\) are cutting speed, feed rate, depth-of-cut, and workpiece hardness, respectively. Table 12 shows an analysis of variance for the linear regression model.