# Numerical Simulation on Dynamic Response of Drilling Parameters in Loaded Rock Mass
## 3 Establishment of Numerical Model
### Analysis of Drilling Parameters Under Different Revolution Speed Conditions  
In order to deeply explore the characteristic variation law of drilling parameters under different rotational speed conditions, this study carried out drilling simulation experiments on coal, mudstone, sandy mudstone, and siltstone. In the simulation process, the thrust of the drill bit is fixed at 5000 N. By changing the revolution speed of the drill bit, the time-drilling depth, time-drilling rate, and time-torque relationship curves of coal, mudstone, sandy mudstone, and sandstone under different revolution speeds are obtained, as well as the curves of torque and drilling rate with revolution speed, as shown in Figures 9-13. Figure 9: Variation curves of drilling parameters of coal under different revolution speeds with thrust of 5000 N. (**a**) Time–drilling depth variation curve; (**b**) time–drilling rate variation curve; (**c**) time–torque variation curve. In Figure 9b, Figure 10b, Figure 11b, and Figure 12b, it can be seen that under a thrust of 5000 N, the drilling rate fluctuates greatly with time, and the higher the speed, the more violent the fluctuation. At 60 r/min, the drilling rates of coal, mudstone, sandy mudstone, and siltstone are 51.28 mm/s, 24.25 mm/s, 22.21 mm/s, and 15.01 mm/s, respectively. The drilling rate is at a low level for most of the time, and the fluctuation frequency is low. When the revolution speed is increased to 120 r/min, the drilling rates of coal, mudstone, sandy mudstone, and siltstone are 99.83 mm/s, 48.21 mm/s, 41.49 mm/s, and 28.20 mm/s, respectively. There will be relatively stable and strong cutting force, which can continuously break the rock and promote the stable drilling of the drill bit. Although there are still fluctuations in the follow-up, the fluctuation range is significantly reduced compared with the low revolution speed condition. This is because after the revolution speed increases, the continuity of the drill bit cutting will not be stuck or reversely pushed  
Figure 11: Variation curves of drilling parameters of sandy mudstone under different revolution speeds with thrust of 5000 N. (**a**) Time-drilling depth variation curve; (**b**) time-drilling rate variation curve; curve; (**c**) time–torque variation curve. Figure 12: Variation curves of drilling parameters of siltstone under different revolution speeds with thrust of 5000 N. (**a**) Time-drilling depth variation curve; (**b**) time–drilling rate variation curve; (**c**) time–torque variation curve. Figure 10: Variation curves of drilling parameters of mudstone under different revolution speeds with thrust of 5000 N. (**a**) Time-drilling depth variation curve; (**b**) time–drilling rate variation curve; (**c**) time–torque variation curve. as at low of a revolution speed. The stable cutting frequency and relatively sufficient cutting force brought by the higher revolution speed make the drilling rate maintain a relatively stable fluctuation range. When the revolution speed is increased to 240 r/min, the drilling rates of coal, mudstone, sandy mudstone, and siltstone are 197.37 mm/s, 96.46 mm/s, 85.71 mm/s, and 46.15 mm/s, respectively. The fluctuation in the drilling rate is the most severe; not only is the fluctuation range large but also the fluctuation frequency is high. The friction between the drill bit and rock increases sharply at a high revolution speed. According to the relationship between friction and speed, this has a great interference on the drilling rate. Although it can reach a high positive peak at multiple time points, it shows high drilling efficiency at a high revolution speed. However, unstable fluctuations also mean that there are risks in the drilling process. Through the analysis of the time-drilling depth change curves of Figure 9a, Figure 10a, Figure 11a, and Figure 12a, it can be seen that the slope increases with the increase in the revolution speed.