# Distribution and Prediction of Incremental Cutter Flank Wear in High-Efficiency Milling
## 5 Characterization of Distribution State of Wear Depth
After extracting and calculating the instantaneous contact stiffness and incremental wear data of the flank face, the improved grey correlation degree analysis algorithm was used to calculate the correlation between the contact stiffness and the increment in wear [34]. The results are shown in Table 3.  
According to Table 3, the minimum correlation degree is 0.6213 in the correlation degree calculation results, and the remaining correlation degree calculation results are all above 0.65, with all being greater than 0.5 and so belonging to a strong correlation. At the same time, the correlation between the contact stiffness and the increment in wear of the flank is high, indicating that the distribution of the contact stiffness and the incremental wear on the flank have similar variation characteristics with time. In order to study the wear evolution process of the flank, the change in the wear depth \(d_{t}\) of the flank with the cutting stroke \(L_{g}\) was plotted using the color scale diagram. Select 25 wear feature points \(N_{dt}(N_{d1}-N_{d25})\) on the flank along the cutting edge direction as shown in Figure 9, study their wear depth change characteristics when the cutting stroke is 0-0.5 m, and draw the profile of the flank wear depth when the cutting stroke \(L_{g}\) is 0.125 m, 0.25 m, 0.375 m, and 0.5 m.  
In Figure 10, \(L_{g}\) is the cutting stroke of the milling cutter; the value range is [0,0.5], and the unit is m; \(d_{0.5}\) is the wear depth when the cutting stroke is 0.5 m, that is, the wear depth at the end of the cutting stroke; \(d_{r}\) is the wear rate:  
\[d_{r}=\frac{d_{t}^{\text{last}}}{L_{g}^{\text{max}}} \tag{14}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\varphi\)\(\backslash\)\(T\) & \(T_{1}\) & \(T_{2}\) & \(T_{3}\) & \(T_{4}\) & \(T_{5}\) & \(T_{6}\) \\ \hline
15\({}^{\circ}\) & 0.7805 & 0.6894 & 0.6797 & 0.7329 & 0.9012 & 0.9161 \\ \hline
30\({}^{\circ}\) & 0.7873 & 0.6213 & 0.7132 & 0.7851 & 0.7471 & 0.7289 \\ \hline
45\({}^{\circ}\) & 0.6528 & 0.8552 & 0.6644 & 0.88 & 0.6833 & 0.6616 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Grey correlation degree between contact stiffness and incremental wear of the flank at the same time. Figure 9: Feature points of flank wear depth. where \(d_{t}\) last is the wear depth at the end of the cutting stroke; \(L_{g}\) max is the maximum cutting stroke. It can be seen from Figure 10 that the wear depth \(d_{t}\) of different wear feature points varies with the cutting stroke \(L_{g}\). From the overall distribution, although the wear rate is different, the wear depth of all selected points changes with the increase in cutting stroke, indicating that there is no accidental wear at the selected points. Among them, the wear depth of the selected points at both ends is the smallest. When the cutting stroke is 0.5 m, the wear depth of \(N_{d1}\) is \(d_{t}\) = 6.51 \(\times\) 10\({}^{-6}\) mm, and the wear depth of \(N_{d25}\) is \(d_{t}\) = 1.52 \(\times\) 10\({}^{-7}\) mm; The wear rate \(d_{t}\) is 1.08 \(\times\) 10\({}^{-7}\) mm/s and 2.53 \(\times\) 10\({}^{-9}\) mm/s, accounting for only 0.02% and 1.08% of the maximum wear rate. The maximum wear area is between \(N_{d5}\) and \(N_{d15}\), and the wear depth \(d_{t}\) is about 4 \(\times\) 10\({}^{-4}\) mm, which indicates that the main wear area on the flank is relatively concentrated; the maximum wear depth of the flank is \(N_{d11}(N_{4})\), its wear depth \(d_{t}\) = 6.07 \(\times\) 10\({}^{-4}\) mm, followed by \(N_{d8}\) and \(N_{d10}\), and this shows a decreasing trend towards both ends. The position of the feature point \(N_{d11}\) is not near the edge of the cutting area (\(N_{d11}\) and \(N_{d23}\)) nor near the central axis of the flank (\(N_{d17}\)).