## 4 Simulation Experiments and Results
### Optimum Side-Rake Angle  
Based on the previous findings, the optimal side-rake angle for rock breaking falls within the range of approximately 5-15\({}^{\circ}\). Therefore, simulation tests were conducted with side-rake angles ranging from 5\({}^{\circ}\) to 15\({}^{\circ}\) in increments of 1\({}^{\circ}\). The experimental results are presented in Figure 14.  
In the 5\({}^{\circ}\) to 15\({}^{\circ}\) of the side-rake range, the MSE required to break the rock slightly increases with increasing the side-rake range. Still, the increase is relatively small, and the cutting area tends to grow more slowly, which is broadly consistent with the findings of [PERSON] et al. [24]. on the predicted trend of the effect of lateral dip angle on the specific work of breaking rock. When the side-rake range is between 5\({}^{\circ}\) and 10\({}^{\circ}\), increasing the angle makes it easier for the cutting teeth to penetrate the subsurface rock and exert cutting forces. Furthermore, as the side-rake range increases, it induces shear deformation of the rock in specific areas during the cutting process. This shear deformation reduces the stress  
Figure 14: Maximum stress and MSE values with side-rake angle.  
transfer within the cutting area, resulting in a lower overall stress level within the core. On the other hand, when the side-rake angle exceeds 10\({}^{\circ}\), the contact area between the cutting teeth and the rock gradually increases, causing the rock to transition from pure shear crushing to shear-impact crushing. This results in more direct contact between the rock and the cutting teeth and causes more friction. The increased friction increases the resistance of the cutting teeth in the rock, making it more difficult to break the rock. As a result, the maximum stress in the core increases as the angle increases.  
As shown in Figure 15, the x-axis represents the standard deviation of the cutting force at a side-rack angle of 5-15\({}^{\circ}\), while the y-axis represents the stress at the outermost edge of the core at different dip angles. The z-axis corresponds to various cutting angles' MSE values. These variables are used to create a scatter plot, and a surface is fitted to the data in the XYZ-axis.  
From Figure 15, it is evident that the side-rake angle of the drill has an impact on the maximum stress and MSE, aligning with the findings of the theoretical model. As the side-rake angle increases, the standard deviation of the mean cutting force exhibits a decreasing and then increasing trend. Based on the distribution and aggregation of points, MSE values vary slightly between lateral dips, with adjacent angles often clustered together, and the large differences in maximum stress in the core may be due to a shift in the cutting and crushing method [15]. Based on the simulation results, the optimal back-rack angle is 10\({}^{\circ}\), considering the maximum stress, MSE, and average cutting force. Furthermore, The side-rake angles ranged from 5\({}^{\circ}\) to 15\({}^{\circ}\), with the best side-rake angle of 10\({}^{\circ}\) producing a maximum stress and mechanical specific energy of 0.76 and 0.96 times higher than the highest point, respectively.