## 5 Conclusions  
1. An instantaneous cutting model of a high-efficiency milling cutter was developed. Considering the influence of vibration on the overall offset angle and distance of the milling cutter, a simulation model of the machined surface morphology was proposed, a model of the machined surface positional and angular error was developed, and a consistency evaluation model of milling error distribution was proposed.
2. The analysis results of the obvious aboriginality of the factors affecting the consistency of the milling error distribution show that the axial and radial errors of the cutter teeth have the most obvious influences on error distribution. At the same time, the positional and angular errors of the machined surface are sensitive to the spindle speed and the feed per tooth, respectively. The interaction of influencing factors of machined surface error distribution was analyzed by response surface methodology. The maximum indicator of the interaction between spindle speed and milling vibration on the milling surface positional error was 0.36, and the maximum indicator of the interaction between feed per tooth and milling vibration on the milling surface angular error was 0.35. These results show that the interactions caused by process parameters and milling vibration have obvious influences on the distribution consistency of machined surface error, while the interaction of cutter tooth radial and axial errors with process parameters is relatively insensitive.
3. Based on the analysis results of the influence of design variables, a process design model of machined surface error distribution consistency is proposed. The validation results show that the range of positional error of the new process scheme is 17.9% lower than that of the old process scheme, and the range of angular error is reduced by 52.7%, indicating that the error distribution of the new process scheme is relatively concentrated. In addition, through the comparative analysis of the new and old process schemes, the positional error and angular error of the new process scheme are obviously improved compared with those of the old process scheme, proving the efficiency of the proposed design model.  
Conceptualization, P.Z. and Y.J.; methodology, P.Z. and Y.J.; software, Y.J. and C.M.; validation, B.J. and C.M.; investigation, Y.J.; resources, B.J.; data curation, Y.J. and C.M.; writing--original draft preparation, Y.J.; writing--review and editing, Y.J. and B.J.; supervision, B.J. and P.Z.; project administration, B.J.; funding acquisition, B.J. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cutting Depth of**} & \multicolumn{4}{c}{\(\Delta y\)} & \multicolumn{4}{c}{\(\theta\)} \\ \cline{2-9}  & \(M_{amax}\) & \(M_{amin}\) & \(\overline{M}_{a}\) & \(\gamma\) & \(M_{amax}\) & \(M_{amin}\) & \(\overline{M}_{a}\) & \(\gamma\) \\ \hline \(ap=0\) mm & 0.0151 & \(-\)0.0081 & 0.003956 & 0.91 & 0.0273 & \(-\)0.0238 & 0.001672 & 0.87 \\ \(ap=5\) mm & 0.0095 & \(-\)0.007 & 0.00056 & 0.90 & 0.0168 & \(-\)0.0156 & 0.000759 & 0.83 \\ \(ap=10\) mm & 0.0118 & \(-\)0.108 & 0.002193 & 0.85 & 0.0189 & \(-\)0.0318 & \(-\)0.0012 & 0.82 \\ \hline \hline \end{tabular}
\end{table}
Table 9: The consistency of machining error distribution of surface angular error in the new scheme.  
Funding: This research was funded by the National Natural Science Foundation of China, 51875145; the Natural Science Foundation of Heilongjiang Province of China, ZD2020E008; and the National Natural Science Foundation of China, 52105440.