## 4 Results and Discussion
### Analysis of the S/N Ratio and Variance  
The surface particles are extracted and the coordinates of particles are obtained to calculate the surface roughness of the simulation model. Table 7 shows the simulation results of the surface roughness value and _S/N_ ratio for surface roughness. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Speed** & **Cutting Force (Relative Error \%)** & **Thrust Force (Relative Error \%)** \\ \hline
75 & \(-7.49\%\) & \(-11.03\%\) \\
94 & \(-3.87\%\) & \(16.34\%\) \\
116 & \(-7.24\%\) & \(-11.39\%\) \\
150 & \(-10.26\%\) & \(9.42\%\) \\
188 & \(-8.67\%\) & \(-7.83\%\) \\
233 & \(-7.73\%\) & \(8.64\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of errors in the simulation and experimental data for cutting force and feed force values. Figure 16: Average cutting force under different cutting speeds. Figure 17: Average thrust force under different cutting speeds. Table 8 is the \(S\)/\(N\) response table for surface roughness; it gives each level a mean \(S\)/\(N\) ratio and the total mean \(S\)/\(N\) ratio. In addition, the different values of the \(S\)/\(N\) ratio between maximum and minimum are also given in Table 8. It can be seen that the feed and rake angle have the highest difference value, 10.3221 and 10.4239 respectively. According to the Taguchi method, the larger the difference between the values of the \(S\)/\(N\) ratio are, the more effect there will be on surface roughness. Therefore, changing the feed and rake angle will change the value of surface roughness of the simulation model significantly. Figure 18 shows the \(S\)/\(N\) response graph for surface roughness. As mentioned in Equation (25) and Equation (26), a greater value of the \(S\)/\(N\) ratio will have a smaller variance of surface roughness (the smaller the better). The variance analysis (ANOVA) is also a helpful and efficient tool for testing and determining which cutting parameter have an obvious effect on surface roughness. As shown in Table 9, it shows the rake angle and feed have an obvious effect on the surface roughness, while the cutting speed compared \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Experiment Number**} & \multicolumn{4}{c}{**Cutting Parameter Level**} & \multirow{2}{*}{**Model Surface**} & \multirow{2}{*}{**\(S\)/\(N\) Ratios for**} \\ \cline{2-2} \cline{4-6}  & **A** & & & & **A**oughness (10\({}^{-1}\)\(\mu\)m) & **Surface Roughness** \\ \hline
1 & \(0^{\circ}\) & 240 m/s & 0.07 mm/rev & 2.251 & \(-\)7.048 \\
2 & \(0^{\circ}\) & 120 m/s & 0.1 mm/rev & 6.136 & \(-\)15.758 \\
3 & \(0^{\circ}\) & 60 m/s & 0.13 mm/rev & 12.256 & \(-\)21.67 \\
4 & \(3^{\circ}\) & 240 m/s & 0.13 mm/rev & 3.191 & \(-\)10.079 \\
5 & \(3^{\circ}\) & 120 m/s & 0.07 mm/rev & 5.341 & \(-\)14.553 \\
6 & \(3^{\circ}\) & 60 m/s & 0.1 mm/rev & 2.086 & \(-\)6.387 \\
7 & \(7^{\circ}\) & 240 m/s & 0.1 mm/rev & 2.693 & \(-\)8.605 \\
8 & \(7^{\circ}\) & 120 m/s & 0.13 mm/rev & 1.020 & \(-\)0.172 \\
9 & \(7^{\circ}\) & 60 m/s & 0.07 mm/rev & 1.753 & \(-\)4.876 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Simulation results for surface roughness and \(S\)/\(N\) ratio. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Symbol**} & \multirow{2}{*}{**Cutting Parameter**} & \multicolumn{4}{c}{**Mean \(S\)/\(N\) Ratio**} \\ \cline{3-5}  & & **Level 1** & **Level 2** & **Level 3** & **Max-min** \\ \hline A & Rake angle & \(-14.8574\) & \(-8.5769\) & \(-4.5353\) & 10.3221 \\ B & Cutting speed & \(-9.3391\) & \(-10.1607\) & \(-10.2373\) & 0.8982 \\ C & Feed & \(-4.5508\) & \(-11.0096\) & \(-14.9747\) & 10.4239 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: \(S\)/\(N\) ratio response table. Figure 18: Cutting parameters of \(S\)/\(N\) response graph (A-Rake angle; B- Cutting speed; C- Feed). to other parameters has little effect on surface roughness, since their contributions in percentage are 45.602, 46.721 and 1.0407 respectively. In addition, if we only consider these three parameters for lowering the surface roughness in cutting processing.