## 4 Distribution of Instantaneous Cutting Energy Efficiency of Cutter Teeth under Vibration
According to Figure 15, the distribution of the specific shear energy of the cutting edges with different cutter teeth was obviously different. At the same time, the specific shear energy of the cutting edge with milling vibration was higher than that without milling vibration. This means that in the process of milling, the existence of milling vibration reduced the useful energy consumption, causing a reduction in the volume of material removed, ultimately leading to an increase in the specific shear energy. Figure 13: The distribution of instantaneous specific cutting energy along cutting edge. (**a**) Tooth 1, (**b**) Tooth 2; (**c**) Tooth 3; (**d**) Tooth 4; (**e**) Tooth 5. Figure 14: The distributive variation in instantaneous shear energy efficiency of cutting edge with and without vibration. (**a**) Without milling vibration; (**b**) with milling vibration. Figure 15: The distributive variation in instantaneous specific shear energy of cutting edge with and without vibration. (**a**) Without milling vibration; (**b**) with milling vibration. It can be seen from Figure 16 that milling vibration reduced the specific tangential-force energy of the cutting edge and increased the complexity of its distribution. Compared with Figures 15 and 16, the specific tangential-force energy was significantly higher than the specific shear energy. This was because the energy consumption of tangential force also included the energy consumption of cutter tooth friction and heat loss. Therefore, if the same workpiece material volume was removed in a unit of time, the energy consumption of tangential force would be greater than that of shearing. According to Equations (17) and (19), the cutting energy efficiency of the milling cutter was obtained, as shown in Figure 17.  
Figure 16: The distributive variation in instantaneous specific tangential-force energy of cutting edge with and without vibration. (**a**) Without milling vibration; (**b**) with milling vibration. Figure 17: Cutting energy efficiency of milling cutter. We can see from Figure 17 that, influenced by milling vibration, the cutting energy efficiency of the milling cutter was variable during the process of cutting in and out of the workpiece. The overall level of specific tangential-force energy of the milling cutter was higher than the specific shear energy, but the effective utilization of energy was reflected in the material removal volume. Compared with the energy consumption of the tangential force, the energy consumption of shearing could directly affect the volume of removed materials. Therefore, the specific shear energy was more suitable for evaluating the cutting performance of milling cutter than the specific tangential-force energy. According to the above model and results, the identification method of distributive variation in instantaneous cutting energy efficiency under milling vibration was proposed, as shown in Figure 10:0  
The method used the relationship between the instantaneous cutting behavior of the cutter teeth under milling vibration and cutter tooth error, obtaining the finite element thermal-stress-coupling field of any position on the effective cutting edge of the milling cutter. The distributions of the instantaneous tangential force and shearing force along the cutting edge were quantitatively characterized. Additionally, changes in the instantaneous tangential-force energy consumption and shear energy consumption of the milling cutter were further revealed. The distribution and its variation in the milling cutter's energy efficiency and specific cutting energy along the cutting edge were revealed using the calculation method of the milling cutter's instantaneous cutting energy efficiency. The method was verified using the relative and grey relative correlation degrees, as shown in Figure 10:1  
When the type of milling cutter and the cutting parameters changed, according to the above method, the structural parameters, the pose parameters of the milling cutter and cutter teeth, and the cutting parameters were changed accordingly.