# Study of the Critical Speed of Ultra-High-Speed Diamond Drilling Technology in Marble
## 3 Simulation and Discussion
### Effect of Varied Rotational Speed on Energy  
Figure 16 provides a comprehensive summary and comparison of vertical stress versus time curves for diamond at different speed intervals [30]. Initially, during the onset of cutting, the stress experiences a relatively modest increase, primarily attributable to the deformation caused by the face's extrusion. However, as drilling advances, the diamond stress undergoes pronounced and periodic fluctuations. This fluctuation is spurred by the expanding depth and width of the diamond as it penetrates the rock, leading to a rapid surge in diamond stress. The process of the diamond crushing the rock goes hand-in-hand with stress-strain accumulation within the rock unit, persisting until the unit is ultimately eliminated. Consequently, the contact area between the diamond and the rock diminishes, precipitating a rapid drop in stress values. Subsequently, as drilling persists, the diamond face re-establishes contact with the rock surface, causing stress values to once again ascend. This cyclical process of stress fluctuation exhibits periodicity. The peak of the cutting force increases as the speed increases and the distance between adjacent peaks decreases. The cycle time for the diamond to finish cutting and crushing the rock becomes shorter. From the previous analysis of the results of diamond drilling at  
Figure 14: Equivalent plastic strain of rock under ultra-high rotational speed and conventional rotational speed. Figure 15: Node number of broken area. high speeds, the increase in speed leads to a decrease in the depth of cut per revolution of the diamond. According to the existing research, the lower the cutting depth, the lower the plastic deformation of the rock, which leads to the plastic deformation of the rock and reduces the efficiency of rock crushing. However, Figure 8 shows that after the rotational speed reaches 7 m/s, the diamond-cutting depth per revolution is basically stable, but the residual equivalent plastic strain value of the rock appears to be greatly reduced. This shows that the depth of cut is not the only evaluation index that affects the transformation of the elastic-plastic crushing mechanism of the rock, but that the change in rotational speed also has a great influence. In conclusion, according to the simulation results, the optimum speed range is 7 m/s-9 m/s, taking into account the diamond-cutting force, the MSE and the equivalent plastic strain value of the rock. For a more comprehensive analysis of energy consumption in rock crushing and the distribution of different energies across various speed intervals, this paper examines the internal energy of the entire rock-crushing model and the energy consumed by drilling teeth during rock crushing from two distinct perspectives. Rock, as a complex elastic-plastic material, undergoes fractures that result from the combined influence of dissipative energy and releasable energy. Dissipative energy predominantly leads to damage and the plastic deformation of rock units, serving as the primary driving force behind the creation of new surfaces during rock fracturing. Elastic strain, on the other hand, causes elastic deformation within the rock, and energy is subsequently released when the rock is unloaded. Upon subjecting the rock to loading, two key changes occur: the formation of new surfaces and the development of internal plastic strain and damage. For the entire diamond rock crushing model, the total energy involved in the rock crushing process can be categorized into three components: the kinetic energy exerted by the drill bit (ALLKE), the internal energy of the rock (ALLIE), and the external work performed (ALLWK). To gain a deeper understanding of the energy distribution within the rock during the entire process, from stress-strain accumulation to reaching the damage value unit due to the action of the drill teeth, it is essential to elucidate the study of energy distribution.