## 4 Distribution of Instantaneous Cutting Energy Efficiency of Cutter Teeth under Vibration
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Tool Material** & \begin{tabular}{c} **Coating** \\ **Material** \\ \end{tabular} & \begin{tabular}{c} **Thermal** \\ **Conductivity** \(\lambda\) \\ **(w/m-\({}^{\circ}\)C)** \\ \end{tabular} & \begin{tabular}{c} **Rotating** \\ **Speed** \\ **(w/m)** \\ \end{tabular} & \begin{tabular}{c} **Feed Rate** \(v_{f}\) \\ **(mm/min)** \\ \end{tabular} & \begin{tabular}{c} **Cutting Width** \\ **(mm/min)** \\ \end{tabular} & \
\begin{tabular}{c} **Cutting Depth** \\ **(\(a_{e}\) (mm))** \\ \end{tabular} &
\begin{tabular}{c} **Cutting Depth** \\ **(mm)** \\ \end{tabular} \\ \hline WC & Ti-CN & 45 & 1433 & 573 & 0.5 & 10 \\ \hline \end{tabular}
\end{table} 
Table 3: Boundary conditions of finite element simulation. Figure 10: Instantaneous cutting volume of the selected cutting edge point. along the cutting edge direction was obtained using Equation (35). According to Figure 11 and Equations (34) and (35), the shear energy consumption and the tangential force energy consumption were solved. Using Equations (39)-(41), the shear energy efficiency and specific cutting energy of the cutting edge were calculated. We selected the same contact angle in different cycles to study the variation in its instantaneous distribution. The contact angles of the cutter tip were \(162^{\circ}\), \(165.6^{\circ}\), \(169.2^{\circ}\), \(172.8^{\circ}\), \(176.4^{\circ}\), \(180^{\circ}\) and \(183.6^{\circ}\). We took the five cutter teeth in the 470 th cycle as an example when the contact angle was \(172.8^{\circ}\). The distribution of the cutter teeth's instantaneous shear energy efficiency, tangential-force specific energy and specific shear energy along the cutting edge are shown in Figures 12 and 13. In the above figures, \(l\) is the unfolded length of the helical cutting edge of the cutter tooth. It can be seen from Figures 12 and 13 that the instantaneous energy-efficiency distribution and specific cutting energy distribution of the cutting edge without vibration were unstable. This was because in the Deform simulation process, the thermal-stress-coupling field of the milling cutter was constantly changing, which led to the differences in the force at different positions on the cutting edge. This made the volume of material removed different. Therefore, the value of the instantaneous cutting-force energy efficiency along the different heights of same cutting edge without vibration did not remain unchanged. Compared with the instantaneous cutting-force energy=-efficiency distribution of the cutting edge without vibration, milling vibration made the instantaneous shear energy efficiency and specific cutting energy of the cutting edge show more complex spatial distribution. Figure 12: The distribution of instantaneous shear energy efficiency along cutting edge. (**a**) Tooth 1; (**b**) Tooth 2; (**c**) Tooth 3; (**d**) Tooth 4; (**e**) Tooth 5. Identification Method of Variation in Milling Cutter's Cutting Energy-Efficiency Distribution under Vibration  
In order to reveal the dynamic of the instantaneous energy efficiency of the milling cutter under vibration, the cutting edge shear energy efficiency with vibration and without vibration were solved using Equation (39), as shown in Figure 14.  
It can be seen from Figure 14 that at the same time, the distribution of shear energy efficiency along the cutting edge was not consistent. Compared with different times, the shear energy-efficiency values of multiple cutter teeth were obviously different. At the same time, the shear energy efficiency of the cutting edge without milling vibration was significantly higher than that under milling vibration. This means that the milling vibration consumes part of the energy originally used to remove materials during the milling process, thus reducing the shear energy efficiency. Using Equations (40) and (41), the cutting edge specific shear energy and specific tangential-force energy were calculated, as shown in Figures 15 and 16.