## 2 Instantaneous Posture of the Milling Cutter and the Minor Cutting Edge
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Serial Numbers** & **Parameters** & **Parameters Explanation** \\ \hline \(1\) & \(r_{max}\) & Maximum radius of gyration at the tip of the cutter tooth. \\ \hline \(2\) & \(r_{l}\) & The rotation radius of the \(i\)th cutter tooth. \\ \hline \(3\) & \(D\) & The diameter of the milling cutter. \\ \hline \(4\) & \(\Delta r_{i}\) & The radial error of the \(i\)th cutter tooth. \\ \hline \(5\) & \(\Delta Z_{i}\) & The axial error of \(i\)th cutter tooth. \\ \hline \(6\) & \(l_{i}\) & Distance from the lowest point of the \(i\)th cutter tooth to the end face of the milling cutter. \\ \hline \(7\) & \(l_{1}\) & The total length of the milling cutter. \\ \hline \(8\) & \(\eta_{ii+1}\) & The angle between the \(i\)th cutter tooth and the \((i+1)\)th cutter tooth. \\ \hline \(9\) & \(O_{i}\)-\(X_{i}Y_{i}Z_{i}\) & The cutter tooth coordinate system: \(O_{i}\) is the tip point of the \(i\)th cutter tooth; \(X_{i}\) passes the minor cutting edge and points to the center of the milling cutter; \(Y_{i}\) is perpendicular to the instantaneous cutting speed direction; \(Z_{i}\) is perpendicular to the \(X_{i}\) axis and \(Y_{i}\) axis. \\ \hline \(10\) & \(O_{0}\)-\(X_{0}Y_{0}Z_{0}\) & The milling cutter structure coordinate system: \(O_{0}\) is the center of rotation of the lowest cutter tip in the axial direction; \(X_{0}\) is over \(O_{0}\) and perpendicular to \(Y_{0}\); \(Y_{0}\) crosses the center point \(O_{0}\) and points to the tool tip point of the maximum outer diameter circle; \(Z_{0}\) is perpendicular to the \(X_{0}\) axis and \(Y_{0}\) axis. \\ \hline \(11\) & \(ds\) & Surface element. \\ \hline \(12\) & \(dX_{i}\), \(dX_{i}\) & The length of the surface element in \(X_{i}\) axis and \(Y_{i}\) axis directions. \\ \hline \(13\) & \(l_{X1}\), \(l_{X2}\), \(l_{X3}\) & Length of three segments of the minor cutting edge. \\ \hline \(14\) & \(l_{\gamma}\) & Direction vector of the surface element. \\ \hline \(18\) & \(p_{s}\) & Cutting plane. \\ \hline \(19\) & \(\lambda_{s}^{\prime}\) & End of the dip angle of the blade. \\ \hline \(20\) & \(k_{r}^{\prime}\) & End of the cutting edge angle \\ \hline \(21\) & \(a_{0}^{\prime}\) & End of the relief angle. \\ \hline \(22\) & \(l_{Y_{1}}\) & The intersecting line of the perpendicularity plane and the cutting plane. \\ \hline \(23\) & \(A_{i}(X_{i}Y_{i},Z_{i})\) & Minor flank. \\ \hline \(24\) & _o-xyz_ & Workpiece coordinate. \(x\), \(y\), \(z\) are the length, width, height direction of the workpiece. \\ \hline \(25\) & \(o_{0}\)-uvw & \
\begin{tabular}{c} Milling cutter cutting coordinate without vibration. \(u\), \(v\), \(w\) parallel to the length, width and height direction of the workpiece, respectively \\ \end{tabular} \\ \hline \(26\) & \(O_{c}\)-U\(V\)W &
\begin{tabular}{c} Milling cutter cutting coordinate with vibration. \(U\), \(V\), \(W\) parallel to \(X\), \(Y\), \(Z\) axis in the initial state, rotate around the coordinate system \(O\)s-XYZ when milling. \\ \end{tabular} \\ \hline \(27\) & \(a_{p}\) & The cutting depth of the milling cutter. \\ \hline \(28\) & \(a_{e}\) & The cutting width of the milling cutter. \\ \hline \(29\) & \(n\) & The rotation speed of the milling cutter. \\ \hline \(30\) & \(v_{f}\) & The nominal feed speed of the milling cutter. \\ \hline \(31\) & \(\theta\)(t) & Instantaneous attitude angle of the milling cutter under vibration. \\ \hline \(32\) & \(\varphi_{i}\) & The instantaneous position angle of the cutter teeth in the cutting period determined by the milling cutter speed \\ \hline \(33\) & \(\varphi_{3}\)(t\({}_{0}\)) & The initial cutting angle of the milling cutter. \\ \hline \(34\) & \(\varphi_{q}\)(t\({}_{0}\)) & The angle between structural coordinate system of the cutter and the cutting motion coordinate system under vibration at time \(t_{0}\). \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Explanation of the cutting behavior of the cutter under vibration.