## 5 Correlation Analysis between the Tool Flank Wear and Friction Wear Energy Density  
The validity of above the model and method should be verified. The experimental results of the milling tool flank wear for scheme 1 and scheme 2 were detected by white light interferometer, as shown in Figures 13 and 14.  
From Figures 13 and 14, the accumulated wear depths at different locations on the flank of the cutter teeth are obtained; Equations (12) and (13) are used to solve the mean, maximum and minimum values of friction wear energy density and total friction energy at the corresponding position of each tool tooth during the process of milling the workpiece. These results of the comparative analysis of the accumulated wear depth and friction wear energy density for the two experimental schemes are shown in Figures 15 and 16. Where, the greater the inverse of the mean and maximum values of friction wear energy density, the lower the wear resistance of the point and the more intense the degree of friction wear.  
Figure 14: Experimental results of the wear profile of three blades of scheme 2: (**a**) tooth 1; (**b**) tooth 2; (**c**) tooth 3.  
Figure 13: Experimental results of the wear profile of three blades of scheme 1: (**a**) tooth 1; (**b**) tooth 2; (**c**) tooth 3.  
To further verify the correctness of the friction and wear energy density solution model and the identification method of variation, the results of the friction and wear energy density solution on the flank face in Figures 15 and 16 were used as the comparison sequence, and the accumulated wear depth measured results were used as the reference sequence, and an improved gray relative correlation analysis algorithm was used to analyze the accumulated wear depth and friction wear energy density obtained from the two experimental schemes, respectively; the results are shown in Table 4.  
In Table 4, the correlation of the accumulated wear depth between the two experiments are bigger than 0.860, and the correlation of the inverse maximum and mean value of the friction wear energy density between the two experiments are bigger than 0.790 and 0.740, respectively. It is shown that the friction and wear intensity of the flank face identified by using the solution results of the instantaneous friction and wear energy density model on the flank under different cutting conditions is in good agreement with the actual measured wear depth.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cutter Tooth** & \multicolumn{3}{c}{**Scheme 1**} & \multicolumn{3}{c}{**Scheme 2**} \\ \cline{2-7}
**Number** & \(\sum E_{i}\) & \(e_{i\text{max}}\)\({}^{-1}\) & \(\overline{e_{i}}\)\({}^{-1}\) & \(\sum E_{i}\) & \(e_{i\text{max}}\)\({}^{-1}\) & \(\overline{e_{i}}\)\({}^{-1}\) \\ \hline \multirow{2}{*}{Tooth 1} & 0.968 & 0.930 & 0.869 & 0.955 & 0.907 & 0.877 \\  & 0.886 & 0.831 & 0.771 & 0.889 & 0.824 & 0.786 \\  & 0.956 & 0.922 & 0.841 & 0.869 & 0.794 & 0.745 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Correlation between cumulative wear depth and friction wear energy density.  
Figure 16: Wear depth and friction wear energy density of three blades of scheme 2 (\(y_{i}\) = 6.700 mm): (a) tooth 1; (b) tooth 2; (c) tooth 3.  
Figure 15: Wear depth and friction wear energy density of three blades of scheme 1 (\(y_{i}\) = 6.700 mm): (a) tooth 1; (b) tooth 2; (c) tooth 3.  
From the above results, the proposed model and method could realize the correct solution and identification of the response of the dynamic relationship between friction energy and flank wear under different process scheme conditions, and the influence of the friction wear process on the flank face by the milling parameters, cutter tooth error, and milling vibration could be effectively revealed.