## 8 Conclusions  
In response to the problems of thin edges and complex shapes of propeller blades, the surface of the propeller blade is divided into four regions and adopts targeted machining  
Figure 12: Blade roughness curve.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Measurement Target** & **Ideal Size (mm)** & **Measurement 1** & **Measurement 2** & **Measurement 3** & \
\begin{tabular}{c} **Average Size** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **Deviation** \\ **Value (mm)** \\ \end{tabular} \\ \hline Blade radius & 229.36 & 229.69 & 229.62 & 229.64 & 229.65 & 0.29 \\ Section length at 0.2R & 106.89 & 107.32 & 107.28 & 107.29 & 107.30 & 0.41 \\ Section length at 0.5R & 142.18 & 142.80 & 142.83 & 142.88 & 142.84 & 0.66 \\ Section length at 0.95R & 17.17 & 17.22 & 17.28 & 17.20 & 17.23 & 0.06 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Measurement data of blade profile dimensions.  
methods to achieve double-sided collaborative machining, while avoiding the problem of collision between cutters on both sides during the machining process. However, the machining of the tip region still requires auxiliary shoring to decrease deformation and vibration, which urgently needs to be solved.  
1. The spatial curve of the tool path is expressed in the form of parameter equations by fitting the projected curve of the tool path on the Y-X and Y-Z planes. The cutter position points are interpolated on the tool paths of the template surface through double-curve interpolation, and the data alignment from the template surface to the projection surface is completed by calculating the length ratio of the cutter position points in the tool path. This method can quickly obtain the symmetrical-cutter-position-points while ensuring uniformity and smoothness.
2. The interpolation of cutter position points in the variable region was completed by the sigmoid deformation curve, achieving the conversion between double-sided symmetrical machining and double-sided staggered machining. The variable speed stage during the machining process is stable and reliable through experimental verification, suitable for frequent variable speed operations.
3. The feasibility and superiority of the double-sided collaborative machining tool path planning algorithm proposed in this paper for propeller blades have been verified by practical machining experiments. Comparing the integrated data results of double-sided collaborative machining with single-sided machining, the former greatly improves the deformation and vibration in propeller blade machining. By measuring and evaluating the quality of the blades, it can be concluded that it meets the general accuracy requirements, proving that the double-sided collaborative machining method has broad applied foreground and practical value.  
Conceptualization, R.W.; methodology, R.W. and Y.G.; software, X.G. and Y.G.; validation, Y.G.; formal analysis, R.W.; investigation, R.W.; resources, R.W.; data curation, Y.G.; writing--original draft preparation, Y.G.; writing--review and editing, R.W. and X.G.; visualization, Y.G.; supervision, R.W.; project administration, R.W.; funding acquisition, R.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (51975157). Research on the improvement of machining precision on double-cutter & double-surface symmetrical machining for large scale marine propeller.  
Not applicable.  
Data Availability Statement: Data is unavailable due to privacy.  
The authors declare no conflict of interest.