## 2 Materials and Methods
### Cutting Force of Direct-Drive Turntable  
This paper analyzes the turning and milling conditions. In turning, the direct-drive turntable drives the workpiece to rotate, and the turning cutter makes the feed movement. When milling, the milling cutter rotates rapidly, driven by the motorized spindle as the main motion, and the tool translation motion is the feed motion. This should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn. Calculation of Milling force  
The milling force is supposed to be one force, but we decompose the force into the X, Y, and Z directions for easy calculation. The applied position of the milling force and the decomposition of the force are shown in Figure 2.  
The spiral milling cutter is used in milling. The workpiece material is HT250, the power of the motorized spindle is 7.5 kW, the rated speed is 1500 rad/min, the tool diameter \(d_{0}\) is 50 mm, and the number of teeth Z is 6. The milling adopts symmetric end-milling. The empirical ratios of each milling force during end-milling are listed in Table 2, and the milling force calculation can be expressed by the following Formula (1). \[F_{r}=513\alpha_{p}^{0.9}\alpha_{f}^{0.74}\alpha_{e}^{1.0}Zd_{0}^{-1.0}K_{Fz} \tag{1}\]  
In the formula, \(\alpha_{p}\) is the milling depth, \(\alpha_{f}\) is the feed per tooth, \(\alpha_{e}\) is the milling width, \(Z\) is the number of cutter teeth, \(d_{0}\) is the milling diameter, and \(K_{Fz}\) is the correction coefficient. The milling width is \(\alpha_{e}\) = 0.6\(d_{0}\) = 30 mm; the milling depth \(\alpha_{P}\) is 2 mm, and the amount of feed per tooth \(\alpha_{f}\) = 0.15 mm/z. By substituting the parameters into Formula (1), \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**Cutting Condition**} & \multirow{2}{*}{**Ratio**} & \multirow{2}{*}{**Symmetric Milling**} & \multicolumn{2}{c}{**Asymmetric Milling**} \\ \cline{3-5}  & & & **Up-Cut-Milling** & **Climb-Milling** \\ \hline End-milling & \(F_{r}/F_{z}\) & 0.85–0.95 & 0.45–0.70 & 0.90–1.00 \\ \(\alpha_{e}\) = (0.4–0.8)\(d_{0}\) & \(F_{e}/F_{z}\) & 0.30–0.40 & 0.60–0.90 & 0.15–0.30 \\ \(\alpha_{f}\) = (0.1–0.2) mm/z & \(F_{c}/F_{z}\) & 0.50–0.55 & 0.50–0.55 & 0.50–0.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The empirical ratios of each milling force in end-milling. Figure 2: Decomposition of milling force. \(F_{r}=846.55\) N. The milling force in each direction is: \(F_{x}=0.9\), \(F_{r}=761.895\) N, \(F_{y}=0.35\), \(F_{r}=296.29\) N, \(F_{z}=-0.52\), and \(F_{r}=-440.20\) N.
2. Calculation of Turning Force The turning force is divided into three forces: the main cutting force \(F_{z}\), the feeding force \(F_{y}\), and the back force \(F_{x}\). According to the data determined in the cutting experiment, the main angle of deflection of the cutting tool is \(K_{r}=45^{\circ}\), the tool cutting-edge inclination is \(\lambda_{s}=0^{\circ}\), and the rake angle is \(\gamma_{0}=10^{\circ}\). The three calculation formulas of turning force are, respectively: \[ \begin{cases}F_{x}=9.81C_{Fx}\cdot\alpha_{p}x_{Fx}\cdot f^{y_{Fx}}\cdot v_{c} ^{n_{Fx}}\cdot K_{Fx}\\ F_{y}=9.81C_{Fy}\cdot\alpha_{p}x_{Fy}\cdot f^{y_{F}}\cdot v_{c}^{n_{Fy}}\cdot K _{Fy}\\ F_{z}=9.81C_{Fz}\cdot\alpha_{p}x_{Fz}\cdot f^{y_{Fz}}\cdot\
u_{c}x_{Fz}\cdot K _{Fz}\end{cases} \] (2)  
In the formula, \(C_{Fx}\), \(C_{Fy}\), and \(C_{Fz}\) depend on the cutting metals and cutting conditions; \(x_{Fx}\), \(y_{Fx}\), \(n_{Fx}\), \(x_{Fy}\), \(y_{Fy}\), \(n_{Fy}\), \(x_{Fz}\), \(y_{Fz}\), and \(n_{Fz}\) are indices of the amount of feed, cutting depth and cutting velocity in the three component forces; \(K_{Fx}\), \(K_{Fy}\), and \(K_{Fz}\) are correction coefficients.