# Study of the Critical Speed of Ultra-High-Speed Diamond Drilling Technology in Marble
## 3 Simulation and Discussion
### Effect of Rock Breaking Mechanism by Ultra-High Speed
Ultimately, at the interface of compressive and tensile stress in the diamond-rock contact area, rock failure occurs, forming the pit. The stress cloud diagram reveals that the pit area is mainly under tensile stress, while the tooth's leading and trailing faces are under compressive stress. At 7 m/s and 9 m/s, the rock pit is mainly under tensile stress, with continued cutting increasing tensile and compressive stress values around the pit. At the junction, a new rock fracture zone forms, and the pit  
Figure 11: PEEQ and rock-breaking specific work per revolution change curve with speed. continues to expand. After a single rotation, the entire rock layer is fragmented, revealing a new rock at the well's bottom. The equivalent plastic strain cloud diagram demonstrates that the rock surrounding the crushing pit has undergone residual plastic deformation (Figure 13). The equivalent plastic strain map of the rock at the bottom of the borehole is extracted from the critical speeds of stages I and II. At 9 m/s, the maximum value of equivalent plastic strain at the drill bit's face is reduced by 12.4% compared to that at 2 m/s. Although the distribution of the residual equivalent plastic strain at the bottom of the borehole remains consistent, the residual equivalent plastic strain of the rock generally decreases in the same distribution area. By considering Figure 11 and Equation (8), we analyzed the region of equivalent plastic strain generated by the rock at the bottom of the borehole during the diamond-breaking process. The decrease in the value and distribution ratio of the residual equivalent plastic strain in the rock at the bottom of the borehole further suggests that the increase in rotational speed altered the rock's crushing mechanism. In summary, during the high-speed diamond rock-crushing process, the rock initially experiences elastic deformation when subjected to cutting forces beneath the diamond. Once the stress surpasses the yield stress, it enters a plastic deformation stage. With continued drilling, the equivalent plastic strain in the rock exceeds a critical value, resulting in rock fracturing (as per Equation (8)), and some rock is removed, forming debris. The newly exposed rock forms the bottom of the borehole and undergoes further diamond cutting. In the diamond-cut area and adjacent areas of the rock, compressive and tensile stress regions intersect, with tensile stress being the primary mode of rock damage. In contrast, areas farther from the diamond in the rock model remain in a compressive stress state and do not fracture [28,29]. The rock-breaking situation, concerning the diamond-cutting depth per revolution, is analyzed from the perspective of the efficiency of breaking the same volume of rock per unit time. As depicted in Figure 11, the rock-breaking specific work performed by the diamond to break the same volume of rock per unit time exhibits a decreasing trend with increasing  
Figure 12: Fracture pit-induced rock stress cloud in varied-speed diamond rock breaking: (**a**) 2 m/s; (**b**) 7 m/s; (**c**) 9 m/s; (**d**) 12 m/s. rotational speed, eventually stabilizing after reaching 7 m/s. With increasing speed, the depth of cut per revolution of the diamond decreases due to the diamond consistently maintaining a drilling speed of 0.05 m/s. Consequently, the horizontal coordinates in Figure 11 can also represent the change in the depth of cut per revolution of the diamond. The increase in speed implies a reduction in the volume of rock fragmented per revolution of the diamond. While the volume of rock crushed per revolution decreases, the energy consumption per unit volume of rock crushed by the teeth diminishes significantly, and the crushing efficiency remains undiminished. This further underscores that increasing the rotational speed effectively enhances crushing efficiency, with the mechanism shifting when the rotational speed reaches 7 m/s. The application of ultra-high rotational speed can, thus, significantly improve crushing efficiency.