# 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  
Regarding the study of rock-breaking mechanisms under ultra-high speed, we primarily focused on stress S and equivalent plastic strain (PEEQ) as our key parameters [6; 18; 19; 21; 22]. Simplifying the microscopic process of diamond rock-breaking as micro-cutting, based on bit rock cutting analysis experience, we divide the bottom of the rock-breaking pit into two areas, as shown in Figure 8. The part of the rock in contact with the area in front of the diamond after penetration is termed the \"front tool face\". The region in contact with the rock in front of the bit is the \"back tool face\" [15; 16]. The rock-crushing area on the front face is the effective crushing area, where the rock undergoes crushing due to the bit's extrusion and cutting actions. The resulting equivalent plastic strain and damage in this area are termed effective strain and damage. Conversely, the area on the rear cutter face is deemed the ineffective plastic strain and damage area. The 3D diamond rock crushing process takes into account both the vertical feed and cutting width of the diamond. Variations in diamond cutting width have a significant impact on the volume of the rock-crushing pit. Understanding how diamond width changes with different drilling speeds is crucial. Using the stress cloud map at 12 m/s as an example, we segment the diamond's one-revolution behavior into distinct points (Figure 9). According to Equation (8), the equivalent plastic strain of the rock unit is eliminated when  
Figure 6: (a) MSE change curve with speed; (b) torque curve of weight on bit with speed. Figure 7: Curve of cutting depth per revolution with speed. it matches the equivalent plastic strain at the moment of rock crushing. The diamond's cutting process per revolution is divided into nine stages. Initially, the diamond penetrates the rock by 0.1 mm, causing no surface damage, and a crushing crater forms due to stress concentration. The rock transitions from elastic to plastic deformation, accumulating plastic strain until it matches the equivalent plastic strain unit, at which point it breaks. As the diamond progresses from point 2 to point 8, the stress cloud diagram shows significant stress concentration on both the front and back blade surfaces, diffusing stress waves and expanding the rock's crushing pit. The pit size gradually increases with rotation until, at point 9, the stress value dramatically drops, forming a complete ring-shaped crushing pit (Figure 9). Considering the notable MSE reduction in Stage II (Figure 6a), the next section explores the energy expended by the diamond to crush a unit volume of rock per revolution and the mechanics of rock crushing to illuminate this phenomenon. Figure 10 illustrates the variation in the contact width between the diamond and rock, represented as the rock crater width, at different rotational speeds. Initially, at point 1, the contact width is 0.2 mm. As drilling continues, the contact width increases rapidly, and this rate of increase diminishes as the rotational speed rises. Between 5 m/s and 10 m/s, the crater width remains relatively stable, with differences within a range of 0.002 mm. As the ROP remains constant, the depth of cut per revolution of the drill tooth decreases with increasing rotational speed, as depicted in Figure 7. The relationship between the volume of rock crushed per revolution of the diamond and the MSE serves as a critical basis for optimizing drill bit design. Given that different volumes of rock are crushed within the same drilling time at various RPM values, evaluating drill bit rock-crushing efficiency solely based on the volume of diamond crushed per revolution is insufficient. Figure 8: Schematic diagram of rock-breaking process of micro-cutting with ID bits. Figure 9: _Cont._  
By considering the curves of diamond width and cutting depth at different RPM values, the quantity of rock broken per revolution can be computed.