# 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
This approach allows the calculation of the energy expended by the diamond to break a unit volume of rock over one revolution. Figure 11 displays the variation in the energy consumed by the diamond to crush a unit volume of rock per revolution at different speeds. It is evident that the specific energy of rock crushing follows a similar trend to the variation in cutting depth per revolution. Within the range of 7 m/s to 12 m/s, the specific energy of rock crushing remains relatively stable. This implies that, from the perspective of rock-crushing specific energy, further increasing the speed beyond 7 m/s may not significantly enhance rock-crushing efficiency. To comprehensively explore the optimal speed range, we conducted an analysis of the rock's equivalent plastic strain [18]. Figure 11 depicts the evolving curve of equivalent plastic deformation at different speeds. In the initial phase, the values of the rock's equivalent plastic strain exhibit stable fluctuations, with minimal impact from speed increases. However, in the subsequent stage, speeds exceeding 7 m/s lead to a sharp decrease in equivalent plastic strain values, resembling the MSE trend. Reduced values of equivalent plastic strain (PEEQ) imply less plastic deformation during rock breaking, indicating a shift in the rock fragmentation mechanism. In practical drilling, achieving more brittle fracture in rocks is typically preferred. During brittle failure, rocks not only undergo plastic deformation but also experience crack propagation. The inevitability of plastic  
Figure 10: Width of crushing pit at different points per revolution. Figure 9: Schematic diagram of cutting process points. fragmentation throughout the entire rock-breaking process implies that greater energy consumption in plastic fragmentation results in lower rock-breaking efficiency. Hence, the PEEQ variation curve suggests that ultra-high-speed diamond drilling can diminish the plastic fragmentation of rocks within a specific range, offering theoretical support for optimizing drilling parameters and rock-breaking methods. Figures 6 and 11 identify a distortion point between 7 m/s and 12 m/s. Beyond 9 m/s, Mean Square Error (MSE) rises, stabilizing after 12 m/s. The PEEQ within the 9 m/s to 12 m/s curve starts climbing, reaching 0.0273 by 12 m/s. Although PEEQ increases from 7 m/s to 9 m/s, it remains significantly lower than the plastic strain values induced by conventional speed-induced rock fragmentation. In summary, the drilling process can be divided into three stages based on the MSE and PEEQ curves. In the range of 7 m/s to 9 m/s, MSE declines, deviating from conventional drilling speeds. The MSE in Stage I (1 m/s to 7 m/s) mirrors conventional speed drilling, peaking at 7 m/s. Increased speed in conventional drilling does not enhance the efficiency of drill teeth but raises energy consumption. However, in Stage II, post 7 m/s, MSE significantly drops, consistent with high-speed metal-processing research. This supports the'speed valley' concept, where surpassing conventional drilling limits causes MSE to decline, directing more energy to rock fragmentation. Defining the optimal speed range is crucial for widespread ultra-high-speed diamond drilling using various particle types for diverse rock cutting. For the three speed intervals, stress cloud diagrams for diamond rotations at 2 m/s, 7 m/s, 9 m/s, and 12 m/s are chosen. Figure 12 illustrates the variation in maximum principal stress in rock fragmentation pits at different diamond rotation speeds. From the rock center to the outer part of the pit, speed influences the maximum principal stress, showing diverse stress states. At 2 m/s diamond rotation, the pit area is mainly under compressive stress. In Stage II, at 7 m/s, the trailing face's contact area is predominantly under compressive stress, transitioning the rock from elastic to elastoplastic stages. Ongoing cutting expands the tensile stress area in the diamond-rock contact region, causing rock damage and plastic deformation.