## 6 Response Analysis and Experimental Verification of Milling Cutter's Cutting Energy Efficiency
### Experimental Verification of Instantaneous Cutting Energy Efficiency of Milling Cutter
\[\left[x_{i}^{m_{0}}(t)\quad y_{i}^{m_{0}}(t)\quad z_{i}^{m_{0}}(t)\quad 1 \right]^{T}\ =\ (A_{3}A_{2}T_{3}T_{2}A_{1}T_{1})^{-1}\cdot\left[x^{m_{0}}(t)y^{m_{0}}(t)z^{ m_{0}}(t)\ 1\right]^{T} \tag{43}\]  
\[\left[0\quad 0\quad z_{i}^{m_{k}}(t)\quad 1\right]^{T}\ =\ (A_{3}A_{2}T_{3}T_{2}A_{1}T_{1})^{-1}\cdot\left[0\ 0z^{m_{k}}(t)\ 1 \right]^{T} \tag{44}\]  
\[\xi_{i}(t)\ =\ |z_{i}^{m_{k}}(t)-z_{i}^{m_{0}}(t)|/2\cdot\pi\cdot r_{i}\cdot\cot\beta \tag{45}\]  
\[V^{\prime}\ =\ \int_{m_{0}}^{m_{k}}f_{z}\cdot\sin(\varphi_{i}(t)-\xi_{i}(t)) \cdot(v_{c}\cdot dt)\cdot dz_{i} \tag{46}\]  
According to Equations (43)-(46), the measured results of the instantaneous cutting volume of the milling cutter were obtained. Combined with the measured results of tangential force, the measured results of specific tangential-force energy were calculated. We compared them with the calculation results of the specific tangential-force energy, as shown in Figure 26. When the contact angle of the cutter tip of each cutter tooth was 172.8\({}^{\circ}\), the instantaneous cutting boundary range of the cutter tooth was close to the maximum and the energy consumption of tangential force was high. Therefore, the time corresponding to 172.8\({}^{\circ}\) was selected as the reference value for calculating the cutting-force specific energy in different cutting cycles. It can be seen from Figure 26 that the instantaneous specific tangential force of the milling cutter changed significantly after changing the spindle speed and cutter tooth error distribution. This indicated that the calculation model of the instantaneous tangential-force energy of the milling cutter was sensitive. At the same time, it can be seen that the overall level of the solution results of scheme 1 and scheme 2 was greater than the measured results. In the process of calculating the instantaneous specific tangential-force energy of milling cutter, the value of the unit cutting force was too large, which was the main reason for the above differences. \[P_{v}(t)\ =\ F_{a}(t)\cdot v_{v}(t)\ =\ m\cdot a(t)\cdot v_{v}(t) \tag{42}\]0 Experimental solution of cutting volume. In order to verify the correctness of the calculation of the milling cutter's specific tangential-force energy, the relative error between the measured and the calculated results of the milling cutter's instantaneous specific tangential-force energy in Figure 25 was calculated. The relative error range of scheme 1 was 12.2%-19.3%. The relative error range in scheme 2 was 10.9%-19.0%. In order to further verify the accuracy of specific tangential-force energy distribution, the improved grey relative correlation analysis algorithm was used. The specific tangential-force energy solution result was the comparison sequence and the specific tangential-force energy measured result was the reference sequence. The correlation degree of scheme 1 was 0.84, and the correlation degree of scheme 2 was 0.81. The above results showed that the calculation results of the instantaneous specific tangential-force energy of the milling cutter were highly similar to the measured results. This indicated that the mapping relationship between the cutting energy consumption and the material removal rate can be identified using the instantaneous specific tangential-force energy model of the milling cutter. It would achieve the purpose of evaluating the energy-efficiency level of the milling cutter.