## 3 Discrete Element Model for the Interaction between Drilling Device and Soil
### Analysis of Simulation Results of Different Speed and Feed Speed  
#### 3.2.1 Comparative Analysis of Torque at Different Speed  
The simulation model was configured with a maximum soil penetration depth of 80 mm for the drilling device, a linear feed rate of 0.05 m/s for the auger, and a data-saving interval of 0.02 s. Four sets of simulation experiments were conducted. In the data analysis module, experimental result data were exported, focusing on the data recorded between 5 s to 10 s. The variation pattern of the torque experienced by the auger during drilling is illustrated in Figure 10.  
As observed in Figure 10, the variation trends of the torque experienced by the drill shaft in the four experimental sets are essentially consistent. In each case, the torque initially increases from zero to a maximum value, then gradually decreases to a lower level, followed by a repetition of the earlier trend. This alignment corresponds to the contact status between the drilling device and the soil during the drilling process. The helical drilling process can be roughly divided into four stages. In the first stage, before the drill bit penetrates the soil, the torque is nearly zero. As the drill bit drives the helical shaft to longitudinally cut into the soil, the volume of cut soil gradually increases, leading to an increase in torque. Subsequently, the helical blades enter a lateral cutting state, interacting with the soil, causing a sudden increase in torque. With the rotation of the blades, when the first layer of helical blades is fully embedded in the soil, the torque reaches its maximum value. In the second stage, as the first layer of helical blades continues to drill downward, the contact area increases, resulting in a corresponding decrease in torque. In the third stage, when the torque decreases to a certain low value, the next layer of helical blades begins to enter the drilling state. Both the front and rear layers of the blades simultaneously drill into the soil, causing a rapid increase in torque. In the fourth stage, as the contact area between the drill rod and the soil gradually increases, the torque gradually decreases again. This process repeats in a cyclic manner.  
Analyzing the maximum torque values from Figure 10a-d reveals that, as the blade rotation speed increases, the required power consumption for drilling operations also increases. Simultaneously, with higher rotation speeds, the drilling frequency per unit time increases, leading to a shorter interval between peak values, aligning well with practical expectations. Comparing the simulation results with the soil trench experiment results, as shown in Figure 11, the trends in simulated and experimental values are consistent. Torque increases with higher rotation speeds, and the maximum relative error is 7%. The simulation results effectively capture the variation patterns in drilling power consumption and accurately represent torque values. Hence, using the EDEM simulation model developed in this study to assess the working resistance experienced by the spiral blades is reliable. The experimental values for soil tend to be slightly higher than the simulated values, possibly due to additional power consumption caused by environmental factors such as stones in the soil.  
Figure 9: Prototype.  
Figure 11: Comparison of simulation and test results of torque at different speed.