## 5 Discussion
### The Relationship Between the Height of Extrusion Zone and Cutting Depth
On one hand, the contact area between the tool and the rock (corresponding to the inclined plane size of the extrusion zone in Figure 4) can be monitored through numerical experiments; on the other hand, the extrusion zone height (\(h_{c}\)) can be measured using the morphological evolution diagram of the extrusion zone, which is recorded by high-speed camera technology during laboratory cutting tests. Subsequently, \(GDC\) can be determined  
Figure 18: The relationship between \(k\) and \(h^{-0.5}\). by substituting \(\mathbf{h_{c}}\) and \(\mathbf{h}\) into Equation (15), with the result obtained through this monitoring method denoted as \(\mathbf{GDC_{m}}\). Considering the available parameters, the method based on cutting force and size monitoring to determine \(\mathbf{GDC}\) is feasible in this study. Therefore, using a series of schemes with \(\mathbf{v}=35\) mm/s as an example, the relationship between \(\mathbf{GDC_{f}}\) and \(\mathbf{GDC_{m}}\), as well as the cutting depth, is shown in Figure 19. Under the three inclination angles, \(\mathbf{GDC_{f}}\) and \(\mathbf{GDC_{m}}\) are relatively close, indicating that the rake angle has little effect on \(\mathbf{GDC}\) within the range of 10-20\({}^{\circ}\). When \(\mathbf{h}=0.5\) mm, the \(\mathbf{GDC}\) values based on both methods are near 1.00, suggesting that the height of the extrusion zone is close to the cutting depth when the cutting depth is small. As the cutting depth increases, the \(\mathbf{GDC}\) obtained by the two methods decreases sharply at first and then tends to stabilize. When the cutting depth increases from 0.5 mm to 1.5 mm, \(\mathbf{GDC_{f}}\) and \(\mathbf{GDC_{m}}\) decrease from 1.00 to 0.75 and 0.40, respectively, and then both show a slight reduction with further increases in cutting depth. Additionally, \(\mathbf{GDC_{f}}\) and \(\mathbf{GDC_{m}}\) are similar at a cutting depth of 0.5 mm, with the former being larger than the latter at greater cutting depths. This discrepancy may arise because, in the numerical simulation, the rock element is no longer involved in the calculation after the rock failure, leading to a smaller monitored tool-rock contact area. Although there are differences between the results of the two methods, their trends are similar with increasing cutting depth and are consistent with the nonlinear relationship reflected by Equation (16). Therefore, it can be concluded that the analysis of the dynamic cutting rock-breaking mechanism based on the principle of energy conservation is reasonable. To verify the relationship between \(\mathbf{GDC}\) and \(\mathbf{h}\) obtained in this study, experimental data from previous literature are collected. Based on the measured extrusion zone height (\(\mathbf{h_{c}}\)) obtained through high-speed photography technology [35], the relationship between the experimental \(\mathbf{GDC}\) and cutting depth for the two types of rock is shown in Figure 20. The \(\mathbf{GDC}\) of rock 1 is approximately 1.00 when the cutting depth is 0.5 mm. As the cutting depth increases from 0.5 mm to 2.5 mm, the \(\mathbf{GDC}\) of rock 1 decreases sharply at first and then tends to stabilize when the cutting depth exceeds 1.0 mm. The \(\mathbf{GDC}\) variation in rock 2 follows a similar trend to that of rock 1. The relationship between \(\mathbf{GDC}\) and \(\mathbf{h}\) in the cutting test is consistent with the results of theoretical analysis and numerical simulations presented in this study. Figure 19: The variations in \(\mathbf{GDC_{f}}\) and \(\mathbf{GDC_{m}}\) with cutting depth in the schemes of \(\mathbf{v}=35\) mm/s. The variations in GDC with \(\mathbf{h}\) show the smaller the cutting depth is, the closer \(\mathbf{h}_{c}\) is to \(\mathbf{h}\). However, as the cutting depth increases, the height of the extrusion zone no longer equals the cutting depth but gradually decreases to a stable value less than 1.00.