# Numerical Simulation of Rock-Breaking Mechanism by Spherical Tooth Impact in Granite Formation
They constructed a mechanical impact-thermal coupling physical model to examine the effects of this coupling on impact stress wave propagation, energy transfer efficiency, and rock damage. [PERSON] et al. [19] conducted impact drilling experiments to investigate the influence of impact parameters on rock-breaking efficiency. Using an orthogonal experimental method and regression analysis, they studied the effects of operational parameters on rock drilling efficiency. Their results showed that impact power has the greatest influence on drilling efficiency. The optimal parameter combination was determined to be an impact power of 6.4 kW, a rotational speed of 240 r/min, a thrust force of 3800 N, and a 7-button drill bit. Additionally, [PERSON] et al. [20], [PERSON] et al. [14], and [PERSON] et al. [21] revealed the significant role of waveform characteristics in the energy transfer efficiency of impact drilling. Their findings provide critical insights into the optimization of impact drilling systems for enhanced performance. In addition to focusing on rock-breaking efficiency and methods, the propagation and extension of internal cracks during rock impact remain a key area of research for scholars. [PERSON] et al. [22] and [PERSON] [23] used numerical methods to study the effect of confining pressure on rock-breaking behavior. Their findings revealed that confining pressure reduces rock penetration rates and suppresses crack propagation. [PERSON] et al. [24; 25] further investigated the mechanisms of lateral crack development during rock compression through numerical simulations. They discovered that the lateral cracks within the crushed zone are caused by a combination of tensile and shear failure, while those outside the crushed zone primarily result from tensile failure. In addition, they designed bi-axial indentation experiments to study rock-breaking behavior under different stress conditions, highlighting the decisive role of surface and internal cracks in the rock-breaking process. [PERSON] et al. [26] explored the influence of pre-existing or structural cracks on rock-breaking efficiency. Their results demonstrated that such cracks facilitate the rock-breaking process by providing pathways for stress concentration and crack propagation. Meanwhile, [PERSON] et al. [27] studied the fracture patterns of rocks under dynamic indentation loading. Their research uncovered the key mechanisms of internal crack propagation under dynamic impact, providing valuable insights for improving rock-breaking techniques. To analyze the physical characteristics and microstructures of rocks during indentation experiments, [PERSON] et al. [28] conducted double-indentation tests on granite, limestone, and sandstone. They determined the optimal spacing between indentations to achieve overlapping crack regions, thereby enhancing rock fragmentation efficiency. These studies offer important theoretical and practical guidance for the design and optimization of impact drilling and rock-breaking technologies. While previous studies, including our own work [29], focused on optimizing single-diameter button arrangements under static or quasi-static conditions, the current research advances the field through three key innovations. First, we expand the parameter scope by systematically comparing 16 mm and 22 mm button diameters under varied impact energies (20-40 J) and drilling pressures (1-1.8 kN), addressing a critical gap in understanding diameter-dependent performance trade-offs. Second, we propose a novel stress overlap analysis framework to optimize circumferential and radial button spacing, which maximizes stress superposition effects while minimizing button count. These methodological and analytical advancements bridge the gap between single-button experiments and practical multi-button drill bit design, offering actionable insights for enhancing ROP and tool longevity in complex granite formations.