# Evaluation of Non-Planar Tool Interaction in Milling of Shaped Surfaces Using a Copy Milling Cutter
## 3 Results
### Evaluation of Surface Deviations by the 3D Scanning Method  
The position of the scanned points corresponded to the applied deviation range as shown in Figure 19.  
Nine points of contact between the tool and the machined surface were identified and selected, where the 3D dimensional deviations of the selected 3D scan points were plotted in the X, Y, and Z coordinate system. These control points are shown in Figure 20. Based on the set deviation and the colour coding of the measured points, it was possible to identify the points that characterize the uncut or undercut points to the final dimension. The measured surface deviations by the scanning method are shown in Table 6.  
Figure 19: Comparison of the face scan with the original 3D model.  
Figure 18: Comparison of the angle engagement size with the extracted area and volume data.  
Analysis of the deviations of the surface showed that the places defined the undercut in the machining process, which are characterized by negative deviations compared to the initial 3D model. The maximum negative deviation was reached at position no. 2 (value \(-\)0.146 mm) and the smallest negative at position no. 3 (value \(-\)0.002 mm). The highest positive deviation was measured at position no. 5 (value 0.114 mm) and the smallest positive at position no. 6. (value 0.028 mm). The negative deviations obtained by the scanning method were achieved due to machining near the centre of the tool, which was affected by the changing effective diameter of the tool for a given position due to the curvature of the surface. As a result, this has been shown to adversely affect production accuracy. The highest negative deviations for position no. 4 (\(-\)0.139 mm), position no. 8 (\(-\)0.102 mm), position no. 9 (\(-\)0.127 mm) corresponded to the maximum and minimum values of the Deff parameter compared to positive deviations for tool position no. 5 (0.114 mm) and for position no. 6 (0.028 mm). A graphical comparison between the obtained surface deviations given in Table 6 and the values of the effective diameter parameter Deff max and Deff min (Table 3), for specific positions of the tool with respect to the curvature of the surface is shown in Figure 21.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Position 1** & **Position 2** & **Position 3** & **Position 4** & **Position 5** & **Position 6** & **Position 7** & **Position 8** & **Position 9** \\ \hline \(-\)0.036 & \(-\)0.146 & \(-\)0.002 & \(-\)0.139 & 0.114 & 0.028 & \(-\)0.075 & \(-\)0.102 & \(-\)0.127 \\ \hline \end{tabular}
\end{table}
Table 6: Measured surface deviations for specific tool positions with respect to surface curvature.  
Figure 21: Comparison of surface deviations with Deff max and Deff min values.  
Figure 20: Focus of the facial scan control points relative to the original 3D model.  
It can be concluded that the negative deviations obtained by the scanning method were due to machining near the tool centre, which was affected by the changing effective tool diameter for that position with respect to the curvature of the surface. As a result, an adverse effect on production accuracy was demonstrated. The highest negative deviations for position 4 (\(-\)0.139 mm), position 8 (\(-\)0.102 mm), and position 9 (\(-\)0.127 mm) corresponded to the maximum and minimum values of the Deff parameter compared to the positive deviations for tool position 5 (0.114 mm) and for position 6 (0.028 mm).