# Characterization of Dolomite Stone Broken Under Axial Impact
## 2 Numerical Simulation of Single-Cutter Rock Breaking Under Axial Impacts
### Results and Discussion of Numerical Simulation
#### 2.4.2 Characteristics of Cutting Analysis  
The cutting force referred to the transverse force exerted on an individual cutter during the cutting process, which was associated with the torque necessary for rock fragmentation. The contact area served as an indicator of the intrusion effect of the PDC cutter. When subjected to axial impact, the intrusion effect of the cutter was amplified, leading to an increase in the contact area between the cutter and the rock. As illustrated in Figure 7a,b, the cutting force and contact area exhibited three distinct phases. In the initial phase (0-0.05 s), the cutting force demonstrated a general upward trend, suggesting that under axial pressure, the PDC cutter progressively penetrated the rock, which aligned with the increasing trend of the contact area. In the second phase (0.05-0.08 s), the cutting force remained relatively stable overall, yet exhibited sharp fluctuations in response to the cutting action. Similarly, the contact area displayed a stepped increase, indicating that the cutting action was progressively enhanced by the impact force. Following 0.08 s, the cutting action of the PDC cutter concluded, and the cutter subsequently transported the tail rock away from the main rock mass. As depicted in Figure 7c, both the average cutting force and average contact area increased with the amplitude of the impact, demonstrating a more pronounced linear relationship. Specifically, under an impact amplitude of 1.5, the cutting force increased by 46.7%, and the average contact area expanded by 27.7% compared with the conventional scenario with no impact at an amplitude of 1.0. The frictional dynamics and the total energy input during the rock fragmentation process utilizing PDC cutters were critical for comprehending their rock-breaking characteristics under axial impact, as illustrated in Figure 8. Figure 8a,b depict the frictional force and the work associated with friction at varying impact amplitudes. It was evident that the influence of friction became more pronounced with an increase in impact amplitude; however, the variation in friction work during the intrusion phase was minimal. In contrast, there was a significant increase in friction work during the stable cutting phase, with the rate of increase becoming steeper as the impact amplitude rose. Figure 8c presents the energy input, which exhibited a similar trend to that of the friction work, suggesting that  
Figure 6: Response of Mises stress (**a**) and maximum principal stress response (**b**) at different axial impact frequencies. augmenting the axial impact amplitude necessitated a corresponding increase in the overall energy required for the operation of a single PDC cutter. Consequently, in the context of axial impact tool design, it was imperative to prioritize the identification of an effective source of impact energy and to explore methods for augmenting this energy source to enhance the amplitude of the impact. Nevertheless, it was essential to recognize that an increase in energy input during the process may result in adverse effects, such as the generation of friction energy. Thus, the efficiency of energy transfer emerged as a critical consideration in the design of impact tools [42; 43]. Figure 9 illustrates the response patterns of each parameter in relation to variations in axial impact frequency. An increase in the impact frequency corresponded to a decrease in the average cutting force, which diminished by 10.6% when comparing 80 Hz with 10 Hz. The impact frequency exerted minimal influence on the contact area curve, which exhibited a consistent trend. Additionally, the average contact area demonstrated a slight decreasing gradient as the impact frequency rose, remaining approximately constant at around 1.25. Figure 7: Response of cutting force (**a**), contact area (**b**), and average (**c**) for different axial impact amplitudes. Figure 8: Response of friction (**a**), frictional energy (**b**), and total input energy (**c**) for different axial impact amplitudes.