## 4 Simulation Experiments and Results
### Optimum Back-Rake Angle  
Based on the discussions presented above, it is evident that the optimal back-rake angle for the rock falls within the range of 15-25\({}^{\circ}\). Therefore, simulation tests are conducted with a gradual increase in the back-rake angle, specifically in increments of 1\({}^{\circ}\) within the 15-25\({}^{\circ}\) range. This allows for a more precise examination of the stress distribution and the cutting tooth contact stress diagram during a single tooth drilling cut. For instance, the stress diagram and the cutting tooth contact stress diagram for a single tooth drilling cut at a 15\({}^{\circ}\) back-rake angle are displayed below:  
During the vibration of the drill cutting core, the core experiences stress that does not meet the fidelity performance requirements. The cutting teeth create localized force concentrations near the contact points during cutting, leading to plastic deformation of the rock, mostly at the point where the cutting teeth are in direct contact with the core, which is consistent with the results of the theoretical model. To enhance core fidelity, it is crucial to identify the area where the maximum stress point is located and minimize the peak value of this stress point, as shown in Figure 9.  
Figure 8: The standard deviation of mean cutting forces and mean cutting forces at the back-rake. By utilizing the post-processing function in ABAQUS 2023, the stresses at the outermost edge of the core were derived for different inclination angles, and the variation of residual stresses with the cutting path for different inclination angles is shown in Figure 10. Different colours represent different cutting angles. As observed in Figure 10, the area of direct contact with the cutting teeth experiences the highest stress levels. Furthermore, the cores obtained after cutting display a concentration of residual stresses at the edges, which consequently impacts the fidelity of the cores [32; 33]. These findings align with the residual stress patterns identified in the theoretical analysis. As observed in Figure 11, the back inclination angle is in the range of \(15^{\circ}\) to \(21^{\circ}\), as the angle increases, the specific work of breaking the rock gradually decreases, and the maximum stress first increases and then decreases. This is because a smaller back inclination angle can produce a greater concentration of stress on the cutting edge and cutting surface, making it easier for the cutting teeth to enter the rock, giving full play to the advantages of shear breaking and improving the breaking efficiency, but also leading to a sharp increase  
Figure 10: Stress variation along the cutting boundary. The cutting back-rake angle was set as \(20^{\circ}\), \(21^{\circ}\), \(22^{\circ}\), \(23^{\circ}\), and \(24^{\circ}\). Figure 9: Abaqus simulation results at \(15^{\circ}\) back-rake angles. in the maximum stress. As the back inclination angle gradually increases from 17\({}^{\circ}\) to 21\({}^{\circ}\), the breaking area of the cutting tooth in contact with the rock slowly increases, and as shown above, the standard deviation of the cutting force gradually decreases at this time. The fluctuation of the cutting force decreases, which improves the stability of drilling and coring, gradually decreases the maximum stress and attains the lowest at the back inclination angle of 21\({}^{\circ}\). Between 21\({}^{\circ}\) and 25\({}^{\circ}\), there is a rapid increase in the MSE and maximum stress. In this case, it is due to the increase in the back inclination angle to the cutting teeth compacting the rock and the increase in friction between the cutting teeth and the rock as the angle increases. The rock-breaking mode transitions from shear crushing to shear-impact crushing. As a result, higher mechanical energy is required to break the rock under the same cutting speed and depth. This leads to increased MSE and a significant fluctuation in cutting force during impact crushing, which is consistent with the conclusions of [PERSON] et al.