## 1 Introduction
\begin{table}
\begin{tabular}{c c p{142.3 pt}} \hline \hline
**Number** & **Parameters** & \multicolumn{2}{c}{**Meaning of Parameters**} \\ \hline \multirow{3}{*}{1} & \multirow{3}{*}{\(\sigma_{g}\)-\(x_{g}y_{g}z_{g}\)} & Workpiece coordinate system, where \(\sigma_{g}\) is the origin of the coordinates, which is the vertex behind the bottom of the cutting end of the milling workpiece. The \(x_{g}\) axis is the same as the feed speed direction of the milling cutter, the \(y_{g}\) axis is parallel to the milling width direction, and the \(z_{g}\) axis is parallel to the cutting depth direction. \\ \hline \multirow{3}{*}{2} & \multirow{3}{*}{\(o\)-\(abc\)} & Cutting coordinate system without milling vibration, where \(o\) is the origin of the coordinates, located at the center of the milling cutter bottom. The \(a\) axis is parallel to the feed speed direction, the \(b\) axis is parallel to the cutting width direction, and the \(c\) axis is parallel to the cutting depth direction. \\ \hline \multirow{3}{*}{3} & \multirow{3}{*}{\(o_{v}\)-\(a_{0}b_{v}c_{v}\)} & Cutting coordinate system with milling vibration, where \(o_{v}\) is the coordinate origin, which is the position of the center point of of the bottom surface of the milling cutter under the vibration of the milling cutter. The \(a_{v}\) axis is the milling cutter ideal coordinate system’s \(a\) axis vibration offset state, the \(b_{v}\) axis is the milling cutter ideal coordinate system’s \(b\) axis vibration offset state, and the \(c_{v}\) axis is the milling cutter ideal coordinate system’s \(c_{0}\) axis vibration offset state. \\ \hline \multirow{3}{*}{4} & \multirow{3}{*}{\(o_{i}\)-\(a_{i}b_{i}c_{i}\)} & Cutter tooth coordinate system, where \(o_{i}\) is the knife point. The \(a_{i}\) axis is perpendicular to the cutter tooth’s instantaneous cutting speed direction, and points to the cutter center. The \(b_{i}\) axis is parallel to the instantaneous cutting speed direction of the cutter tooth, and the \(c_{i}\) axis is parallel to the milling cutter spindle. \\ \hline \multirow{3}{*}{5} & \multirow{3}{*}{\(o_{0}\)-\(a_{0}b_{0}c_{0}\)} & Structure coordinate system of the milling cutter, Where \(o_{0}\) is the coordinate origin and is the intersection point of the milling cutter axis and the surface where the minimum point of the cutter tooth is located, where the \(a_{0}\) axis is in the plane where the minimum point of the cutter tip is located, and is perpendicular to the \(b_{0}\) axis, while the \(b_{0}\) axis is in the plane where the minimum point of the cutter tooth is located, and points to the tipping point with the largest outer diameter. \\ \hline \multirow{3}{*}{6} & \(\Delta Z_{i}\) & Milling cutter tooth axial error. \\ \hline \multirow{3}{*}{7} & \(x_{g}\)\({}^{(L)}\) & The value of workpiece length on the \(x_{g}\) axis in the workpiece coordinate system. \\ \hline \multirow{3}{*}{8} & \(y_{g}\)\({}^{(W)}\) & The value of workpiece width on the \(y_{g}\) axis in the workpiece coordinate system. \\ \hline \multirow{3}{*}{9} & \(z_{g}\)\({}^{(H)}\) & The value of workpiece height on \(z_{g}\) axis in the workpiece coordinate system. \\ \hline \multirow{3}{*}{10} & \(m_{i(\text{c1})}\) & Any point on the cutting edge of the milling cutter that participates in the cutting part is the \(i\)th tooth, and the \(c\) axis coordinate of the milling cutter coordinate system is c1. \\ \hline \multirow{3}{*}{11} & \(m_{j(\text{c2})}\) & Any point on the cutting edge of the milling cutter that does not coincide with \(m_{i(\text{c1})}\) in the cutting part is the \(j\)th tooth, and the coordinate of axis \(c\) of the milling cutter coordinate system is c2. \\ \hline \multirow{3}{*}{12} & \(\sum_{1}\) & The plane is parallel to the \(aob\) plane of the milling cutter coordinate system at point \(m_{i(\text{c1})}\). \\ \hline \multirow{3}{*}{13} & \(\sum_{2}\) & Parallel plane of point \(m_{j(\text{c2})}\) and the milling cutter coordinate system’s \(aob\) plane. \\ \hline \multirow{3}{*}{14} & \(V_{f}\) & The milling cutter’s feed rate. \\ \hline \multirow{3}{*}{15} & \multirow{3}{*}{\(\delta\)} & The space angle between the milling cutter spindle and the ideal-state milling cutter spindle under vibration. \\ \hline \multirow{3}{*}{16} & \multirow{3}{*}{\(\varphi si\)} & The angle between the cutter tooth coordinate system of cutter tooth i and the cutter structure coordinate system. \\ \hline \multirow{3}{*}{17} & \multirow{3}{*}{\(\varphi_{q}(l)\)} & The angle between the cutter tooth structure coordinate system and the cutting coordinate system under vibration. \\ \hline \multirow{3}{*}{18} & \multirow{3}{*}{\(\beta\)} & The helix angle of the milling cutter. \\ \hline \hline \end{tabular}
\end{table}