# Cutting Force and Cutting Quality during Tapered Milling of Glass Magnesium Board
## 3 Results and Discussion
### Range Analysis of Surface Roughness  
Results of the range analysis of the surface roughness are presented in Table 6. By comparing the R value of each factor, it was found that the R\({}_{\rm h}\) value was the largest, and the value of R\({}_{\rm n}\) was the smallest (R\({}_{\rm h}=5.080>\) R\({}_{\lambda}=2.527>\) R\({}_{\rm n}=0.853\)). Thus, this result indicates that the cutting depth had the greatest influence on the surface roughness, followed by the taper angle and the spindle speed. Meanwhile, taking the surface roughness as the evaluation index, according to the value of K\({}_{\rm i}\), the optimal combination of the three factors with the lowest value of surface roughness could be selected. Hence, the combination of \(\lambda_{1}\)n\({}_{3}\)h\({}_{1}\) was adopted as the optimal cutting parameter, in which the taper angle was 15\({}^{\circ}\), spindle speed was 6000 rpm (43.96 m/s cutting speed), and the cutting depth was 0.5 mm.  
Figure 5 shows the influence of the cutting parameters on the surface roughness, which indicates that the surface roughness increased as the taper angle increased. According to Equation (2) and Figure 4a,b, with increasing the taper angle, the radius of gyration became smaller. The chip could not  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Testing Number** & **Taper angle (\(\lambda\))** & **Spindle Speed (n)** & **Cutting Depth (h)** &
\begin{tabular}{c} **Surface** \\ **Roughness (Ra)** \\ \end{tabular} \\ \hline
1 & 15\({}^{\circ}\) & 4000 rpm & 0.5 mm & 6.00 μm \\
2 & 15\({}^{\circ}\) & 5000 rpm & 1.0 mm & 7.42 μm \\
3 & 15\({}^{\circ}\) & 6000 rpm & 1.5 mm & 9.95 μm \\
4 & 25\({}^{\circ}\) & 4000 rpm & 1. mm & 8.06 μm \\
5 & 25\({}^{\circ}\) & 5000 rpm & 1.5 mm & 10.88 μm \\
6 & 25\({}^{\circ}\) & 6000 rpm & 0.5 mm & 6.32 μm \\
7 & 35\({}^{\circ}\) & 4000 rpm & 1.5 mm & 14.15 μm \\
8 & 35\({}^{\circ}\) & 5000 rpm & 0.5 mm & 7.42 μm \\
9 & 35\({}^{\circ}\) & 6000 rpm & 1.0 mm & 9.38 μm \\ \hline K\({}_{\rm 1}\) & 7.790 & 9.403 & 6.580 & \\ K\({}_{\rm 2}\) & 8.420 & 8.573 & 8.287 & \\ K\({}_{\rm 3}\) & 10.317 & 8.550 & 11.660 & \\ \hline R & 2.527 & 0.853 & 5.080 & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Range analysis of surface roughness (Ra).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factors** & **Sum of squares** & **Degrees of freedom** & **F** & **Prominence** \\ \hline Taper angle (\(\lambda\)) & 200.883 & 2 & 60.726 & Significant \\ Spindle speed (n) & 7.153 & 2 & 2.162 & Insignificant \\ Cutting depth (h) & 1697.455 & 2 & 513.136 & Significant \\ Error & 3.31 & 2 & & \\ Total & 1908.801 & 8 & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: ANOVA results of resultant force (F\({}_{\rm R}\)).  
easily be removed from the workpiece by the cutter. Therefore, the surface roughness increased with an increasing taper angle. Similar to the results of [PERSON] et al. [6] and [PERSON] et al. [22], the surface roughness decreased with the increase of spindle speed and increased with an increased cutting depth (Figure 5). As expressed in Equations (5) and (6), the increasing spindle speed and decreasing cutting depth reduced the feed per tooth and the cutting thickness during the milling process, directly lowering the resistance acting on the cutter and improving the cutting stability. Thus, the cutting quality was improved by increasing the spindle speed and decreasing the cutting depth.