# Cutting Force and Cutting Quality during Tapered Milling of Glass Magnesium Board
## 2 Materials and Methods  
In this work, up-milling was carried out, which was performed in a machining center (MGK01, Nanxing Machinery Co., Ltd., Guangzhou, China) at a constant feed rate of 15 m/min. Glass MGO board was adopted as the machining object, and its mechanical properties are listed in Table 1. The polycrystalline cemented diamond (PCD) cutters used were made from diamond micro-powder sintered with a metal binder, and their main chemical components were carbon, cobalt, and tungsten carbide. As shown in Figure 1 and Table 2, all PCD cutters had the same material properties: a constant tool radius of 140 mm and a constant tooth number of six, but different taper angles, \(\lambda\).  
Orthogonal experimental design was used in this work, which is a design method of multiple factors at multiple levels [20] that can be used to study the influence of various factors (Table 3) on cutting force and cutting quality based on the orthogonal Latin squares table L\({}_{9}\) (3\({}^{4}\)) [21]. The specific experimental design is shown in Table 4. During each combination of cutting parameters, the cutting force and cutting quality were acquired and averaged from three measurements.  
As shown in Figure 2a-c, the cutting force was measured by use of a Kistler three-component dynamometer and then calculated by using Dynoware specialized data processing software, where \(F_{x}\) is defined as the component force perpendicular to the feeding direction, \(F_{y}\) is the component force parallel to the feeding direction, and \(F_{z}\) stands for the component force parallel to the tool axis. In order to more intuitively investigate how various factors affect cutting force, resultant force, \(F_{R}\) was used as an evaluation index of force, and obtained by Equation (1).  
\[F_{R}=\sqrt{{F_{x}}^{2}+{F_{y}}^{2}+{F_{z}}^{2}} \tag{1}\]  
Surface roughness, Ra, was adopted to evaluate the cutting quality of the finished surface. Ra was measured by the surface profiler, and calculated by ACCTee software (Figure 2a,d,e).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Number** & **Taper Angle (\(\lambda\))** & **Spindle Speed (n)** & **Cutting Depth (h)** & **Resultant Force (FR)** \\ \hline
1 & 15\({}^{\circ}\) & 4000 rpm & 0.5 mm & 39.43 N \\
2 & 15\({}^{\circ}\) & 5000 rpm & 1.0 mm & 55.41 N \\
3 & 15\({}^{\circ}\) & 6000 rpm & 1.5 mm & 72.31 N \\
4 & 25\({}^{\circ}\) & 4000 rpm & 1.0 mm & 62.60 N \\
5 & 25\({}^{\circ}\) & 5000 rpm & 1.5 mm & 77.83 N \\
6 & 25\({}^{\circ}\) & 6000 rpm & 0.5 mm & 42.87 N \\
7 & 35\({}^{\circ}\) & 4000 rpm & 1.5 mm & 84.81 N \\
8 & 35\({}^{\circ}\) & 5000 rpm & 0.5 mm & 51.74 N \\
9 & 35\({}^{\circ}\) & 6000 rpm & 1.0 mm & 65.29 N \\ \hline K\({}_{1}\) & 55.717 & 62.280 & 44.680 & \\ K\({}_{2}\) & 61.100 & 61.660 & 61.100 & \\ K\({}_{3}\) & 67.280 & 60.157 & 78.317 & \\ \hline R & 11.563 & 2.123 & 33.637 & \\ \hline \hline \end{tabular}  
* K\({}_{i}\) in the table represents the average value of the No. (i) of level data of each factor, and R represents the difference between the maximum value and the minimum value of each factor K\({}_{i}\), namely, the range of K\({}_{i}\).  
\end{table}
Table 2: Tool angle and properties of polycrystalline cemented diamond (PCD) cutters.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**PCD** & \multicolumn{3}{c}{**Tool Geometries**} & \multicolumn{3}{c}{**Material Properties**} \\ \cline{2-7}
**Cutters** & **Taper Angle** & **Rake Angle** & **Clearance Angle** & **Modulus of Elasticity** & **Thermal Conductivity** & **Hardness** \\ \hline
1 & 15\({}^{\circ}\) & 10\({}^{\circ}\) & 8\({}^{\circ}\) & & & \\
2 & 25\({}^{\circ}\) & 10\({}^{\circ}\) & 8\({}^{\circ}\) & 800 GPa & 560 W-m\({}^{-1}\)-K\({}^{-1}\) & 8000 HV \\
3 & 35\({}^{\circ}\) & 10\({}^{\circ}\) & 8\({}^{\circ}\) & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Cutting parameters.