## 2 Methodology and Model Establishment
### Finite Element Model for Dynamic Rock Fragmentation by Drill Bit
#### 2.3.1 Establishing the Contact Model between the Drill Bit and the Rock  
Taking into account the energy consumption of the drilling rig, the stiffness and toughness of the drill pipe, and the accuracy of the results, it can be seen from the geometric analysis that the drill bit model adopts a 75\(\#\) impregnated diamond core drill bit with an outer diameter of 75 mm and an inner diameter of 59 mm, which can meet 80\(\%\) of the demand. It is equipped with 7 evenly distributed waterways. To better align with real-world drilling conditions, the drill bit model is designed with an edge-worn shape, featuring a curved profile. During the rock drilling process, considering the drill bit's significantly higher strength compared to the rock, the drill bit is defined as a rigid body. This implies that no deformation occurs during drilling. In addition, set a reference point RP to bind with the drill. The drilling and rotation of the drill bit are controlled by controlling the movement of the reference point. The rock model is a disc with a thickness of 20 mm and a diameter of 150 mm (twice the outer diameter of the drill bit), as shown in Figure 1. The diameter of 150 mm was chosen to ensure that the rock model was large enough to simulate conditions in actual drilling and to provide sufficient surface area for drilling operations. The rock thickness of 20 mm was chosen to use thinner rock samples in the simulations to simplify the experiments and reduce material costs. The mesh division of the contact part between the drill bit and the rock is denser, and the division of the edge part is looser, which can ensure the calculation accuracy and better simulate the exfoliation process of cuttings. Hence, a structured meshing method is employed for the rock, utilizing 8-node linear hexahedral reduced-integration elements with hourglass control (C3D8R). The mesh size in the contact region between the drill bit and the rock is approximately 1.5 mm, while around the edges, it is about 8 mm. The mesh size along the thickness direction is approximately 0.5 mm. The diamond-impregnated core bit is suitable for the grid division method of free, and the tetrahedron unit (C3D10M) is used to divide the grid, and the overall grid size is about 4 mm. In this model, the surface-to-surface method is employed to establish the contact interaction between the impregnated diamond core bit and the rock. The contact interaction between the impregnated diamond core bit and the rock comprises mainly two aspects: first, the normal interaction between the two; and second, the direct tangential interaction between them. (1)  
Normal contact model between drill bit and rock:  
The normal contact relationship between the drill bit and the rock is relatively clear. Only when the drill bit comes into contact with the rock can the two contacting surfaces transmit loads to each other in a compressed state. This type of contact behavior is referred to as hard contact. Under the influence of normal load, the drill bit gradually compresses the rock, leading to an increasing deformation of the rock in the normal direction. However, this contact does not result in penetration through the rock; it merely compresses the rock material. (2)  
Tangential contact model between drill bit and rock:  
Under the influence of normal loading, the drill bit comes into close contact with the rock. As the drill bit rotates around the axis of the drill rod, frictional forces arise at the contact surface between them. When this frictional force falls below a specific critical threshold, the drill bit remains in an adhering state with the contact surface, and the drill bit does not initiate rotation. Nevertheless, upon surpassing this critical threshold, the contact surface initiates relative sliding, indicating that the drill bit is in a sliding state.