## 3 Results
### Dynamic Rock Breaking Analysis of Impregnated Diamond Bit  
The PDC diamond core bit gradually comes into contact with the rock surface under the influence of drilling speed and rotation speed. It fractures the surface rock units in contact, exposing the next layer of rock units as a new rock surface. Due to the continuous effect of drilling speed and rotational speed, the drill bit and the rock surface form a new contact relationship again. The drill bit and the surface rock unit undergo a repeated cycle of contact-destruction-re-contact, and finally form a wellbore. As shown in Figure 2a during drilling at 0.1 s, the drill bit just comes into contact with the rock surface, and an indentation is formed on the rock surface; as time increases, the contact area between the drill bit and the rock increases, eventually forming a ring with the same inner and outer diameter as the drill bit. The drilling process is shown in Figure 2a-h. Among them, the maximum stress value appears at the part where the drill bit contacts the rock, mainly distributed at the bottom of the hole and around the hole. When the arc edge of the drill bit penetrates the rock completely, the stress value distribution is basically stable. Figure 3 is the cloud diagram of the major and minor principal stresses of the rock during the drilling process, and the principal stress value is specified to follow the principle of positive tension and negative pressure. At the contact point between the drill bit and the rock, there are tensile stress and compressive stress at the bottom of the hole and the rock units around the bottom of the drill hole, and the areas of tensile stress and compressive stress appear crosswise, but the failure is dominated by tensile stress. Due to the constraints of boundary conditions, the rock units are all under compression in the range far from the borehole. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Density** \\ \(\rho\)/(kg\(\cdot\)m\({}^{-3}\)) \\ \end{tabular} & \begin{tabular}{c} **Deformation** \\ **Modulus** \\ **E/GPa** \\ \end{tabular} & \begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ **c/MPa** \\ \end{tabular} & \begin{tabular}{c} **Cohesion** \\ **c/MPa** \\ \end{tabular} & \
\begin{tabular}{c} **Internal Friction** \\ **Angle** \\ **\(\varphi\)/(\({}^{\circ}\))** \\ \end{tabular} &
\begin{tabular}{c} **Compressive** \\ **Strength** \\ **Rc/MPa** \\ \end{tabular} \\ \hline
2750 & 33 & 0.2 & 2.1 & 60 & 90 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical and mechanical parameters of rock. Figure 2: Borehole formation process under the action of the impregnated diamond bit. (**a**) 0.1 s (**b**) 0.2 s (**c**) 0.5 s (**d**) 1.0 s (**e**) 2.0 s (**f**) 3.0 s (**g**) 4.0 s (**h**) 5.0 s.  
Figure 4 shows the counter thrust force and counter torque of the rock on the drill bit during the drilling process. The increase in thrust and torque over time is divided into two stages, namely the unstable stage and the stable stage. During the unstable stage, thrust force and torque increase rapidly. This can be explained by the fact that when the drill bit comes into contact with the rock surface, a large impact pressure will be generated, so the torque and thrust will increase rapidly in a short period of time. When the time reaches 0.2 s, the thrust and torque are in a stable fluctuating state. The thrust fluctuates at 10,000 N and the torque fluctuates at 400 N\(\cdot\)m. At this time, drilling is in a stable stage. This is because the drill bit gradually invades the rock, and the resistance of the rock to the drill bit remains stable. This is consistent with the research results of previous scholars [43]. During the phase of stable oscillations in thrust force and torque, if the combined effect of drilling speed and rotation speed is insufficient to break the rock, the drill bit is compelled to halt its advancement. Meanwhile, the drill string continues to twist and accumulate energy under the influence of the current drilling speed and rotation speed.