## 1 Introduction
The simulation analysis obtained the relationship between the change in cutting angle and the drilling efficiency, and analyzed the influence of cutting speed and drilling speed on the drilling process. A large number of scholars [5; 11; 12; 13] have conducted numerical simulations on rock drilling, and the research results show that impact energy, impact speed, and impact angle have a significant impact on rock fragmentation. As the impact energy increases, the rock fragmentation effect increases. Both the impact angle and impact speed have an optimal value, which can maximize the rock-crushing effect. Cyclic loading will gradually weaken the strength of the rock through multiple loading and unloading processes, leading to fatigue failure, thus affecting the rock-crushing effect. Many scholars have conducted a lot of research on the rock-breaking efficiency of different bit shapes, bit structures and drilling methods [14; 15; 16; 17; 18; 19]. For instance, [PERSON] et al. [14] established a finite element model of the cutting process for PDC drill bits, conducting numerical simulations on the cutting processes of PDC drill bits with varying shapes. The simulation results show that there is no essential difference between cross cutting and straight cutting, the cutting force relationship is oscillatory and non-uniform for all types of tools, and the increase in cutting depth leads to an increase in vibration amplitude. [PERSON] et al. [15] combined experimental investigations with numerical simulations and delved into the rock-fracturing mechanisms of PDC drill bits. They established nonlinear dynamic models for rock units and analyzed stress states within rock units, sliding fracture characteristics, plastic energy dissipation, and stress distribution along cutting edges. In comparison to unidirectional cutting, lateral cutting generates greater tensile stress within rock units. It exhibits lower plastic energy dissipation, and the average stress on the cutting edge is significantly lower than that observed in unidirectional cutting. During the lateral cutting process, rocks undergo not only shear deformation but also brittle fracture. Thisdual mode of failure contributes to an enhancement in the rock's fracturing efficiency. [PERSON] et al. [16] utilized the ABAQUS finite element method to construct a nonlinear dynamic simulation model for the dynamic rock fracturing of both PDC drill bits and roller-cone compound drill bits. Their study delved into the cutting and fracturing mechanisms of these two types of drill bits. It was discovered that, in hard formations, PDC drill bits experience more severe torsional vibration than roller-cone bits, resulting in relatively lower rock-fracturing efficiency. This discrepancy can be attributed to the fact that PDC drill bits rely on a combination of compression and tension for rock fracturing, while roller-cone bits primarily utilize tensile stress for fracturing. Friction and vibration phenomena are present during the drilling process, consequently leading to wear and tear of the drill bit. Therefore, [PERSON] et al. [17] closely integrated the friction between the drill string and the wellbore. They introduced a model to compute the drill string's surface swing response, simulating the redistribution of friction during stick-slip motion caused by swinging and friction. [PERSON] et al. [18] constructed a representative 3D finite element model resembling the microstructure of hard metals. They employed macroscopic devices to conduct macroscopic finite element simulations on the normal and oblique frictional impact of elastic rocks using hard metal spherical tips. Through microstructure analysis, they elucidated that the tensile failure of hard alloy particles on the drill bit is the primary cause of drill bit wear. [PERSON] [19] conducted a comparative study on numerical simulation finite element models, constitutive models, and the accuracy of simulation results for single-tooth and full-bit rock fracturing.