## 6 Response Analysis and Experimental Verification of Milling Cutter's Cutting Energy Efficiency
### Experimental Verification of Instantaneous Cutting Energy Efficiency of Milling Cutter  
In order to verify the correctness of the calculation of the instantaneous tangential-force energy efficiency of the milling cutter under vibration, the calculation results and the measured results of the tangential-force energy efficiency were compared. Among them, the input energy of the milling vibration of the calculation result and measured result of the milling cutter input energy were both measured via experiments. According to Figures 6 and 19 and Equation (42), the input energy of milling cutter vibration was obtained, as shown in Figure 23.  
\[P_{v}(t)\ =\ F_{a}(t)\cdot v_{v}(t)\ =\ m\cdot a(t)\cdot v_{v}(t) \tag{42}\]  
Comparing (a) and (b) in Figure 23, it can be seen that reducing the spindle speed, increasing the feed rate per tooth, and changing the distribution of the cutter tooth error resulted in changes in the vibration acceleration signal. This caused significant differences in the vibration input energy of the milling cutter. Among them, the vibration input energy of the milling cutter in scheme 1 was concentrated in the middle cutting section, which indicated that the input energy of the milling cutter fluctuated in the middle cutting section. The input energy of milling vibration in scheme 2 was relatively high during the cut-in section, representing that the input energy of the milling cutter was relatively unstable during the cut-in section. Using Equation (17), the solved results and measured results of the tangential-force energy efficiency of scheme 1 and scheme 2 were obtained. We took the 470 th cycle results as an example, as shown in Figure 24.  
As seen from Figure 24, the distribution curve of the tangential-force energy efficiency of the milling cutter was close to the measured result. The relative error range between the tangential-force energy-efficiency calculation and the measured results in scheme 1 was 5.8%-18.4%. The relative error range between the tangential-force energy-efficiency calculation and the measured results in scheme 2 was 5.1%-19.3%. In order to further verify the accuracy of the distribution of the milling cutter tangential-force energy-efficiency  
Figure 23: Input energy of milling vibration of scheme 1 and scheme 2. (a) scheme 1; (b) scheme 2. Figure 24: The solved and measured results of tangential-force energy efficiency of milling cutter. (a) scheme 1; (b) scheme 2.  
calculation results, the improved grey relative correlation analysis algorithm was used. The tangential-force energy-efficiency solution result was the comparison sequence, and the measured tangential-force energy efficiency result was the reference sequence. The correlation degree of scheme 1 was 0.87, and the correlation degree of scheme 2 was 0.89. The above results showed that the overall level and variation in the calculation results of milling cutter tangential-force energy efficiency were in good agreement with the measured results. In order to verify the correctness of the calculation model of the instantaneous cutting-force specific energy of the milling cutter, the experimental results and calculation results of the tangential-force specific energy were compared. According to the machined surface topography measured via white-light interferometer (model: Talysurf CCI MP, produced by [PERSON]), the measured results of the instantaneous cutting volume of the milling cutter were obtained, as shown in Figure 25 and Equations (43)-(46). Using Figure 25, the cutting volume was calculated using the structure of the milling cutter and the instantaneous posture of the cutter teeth, as shown in Equations (43)-(46).