## 3 Discrete Element Model for the Interaction between Drilling Device and Soil
### Analysis of Simulation Results of Different Speed and Feed Speed
#### 3.2.3 Analysis of Three-Way Working Resistance  
1. Force analysis As illustrated in Figure 13, selecting the spiral blades as the objects for force analysis, the directions of the three-dimensional working resistances are defined as follows: along the rotation direction of the spiral main axis is the positive horizontal resistance (F\({}_{x}\)), downward from the soil surface is the positive vertical resistance (F\({}_{y}\)), and inward from the vertical blade is the positive lateral resistance (F\({}_{z}\)). 2. The influence of speed on three-way resistance With a fixed tillage depth of 80 mm, a feed rate of 0.05 m/s, and rotational speeds of 100 r\(\cdot\)min\({}^{-1}\), 200 r\(\cdot\)min\({}^{-1}\), 300 r\(\cdot\)min\({}^{-1}\), and 400 r\(\cdot\)min\({}^{-1}\), four sets of simulation experiments were conducted. The variation in the maximum three-dimensional resistances experienced by the spiral blades with respect to rotational speed is depicted in Figure 14. The maximum resistance encountered by the spiral blades in the vertical direction surpasses that encountered in the horizontal and lateral directions, with vertical resistance being the primary factor influencing drilling power consumption. The maximum values of horizontal and lateral resistances are roughly similar. As the rotational speed increases, the maximum vertical resistance continues to rise, while horizontal and lateral resistances show a declining trend. When the speed exceeds 200 r\(\cdot\)min\({}^{-1}\), the decline in horizontal and lateral resistances becomes gradual. However, when the speed exceeds 300 r\(\cdot\)min\({}^{-1}\), both resistances in these directions experience a sudden increase. This phenomenon is attributed to the surrounding soil resisting the downward rotational motion of the spiral blades during drilling operations, exerting compressive forces on the blades. As the speed increases, the compressive force also intensifies, offsetting some of the forces in the horizontal and lateral directions, resulting in a decreasing trend for these two forces. Simultaneously, with higher speeds, the drilling volume of the spiral blades per unit time increases, leading to a greater force in the vertical direction. However, the relative change in the resultant force on the spiral blades is not significant. The variations in vertical and lateral resistances directly impact the torque experienced by the spiral blades. Soil trench experiments indicate that the torque on the spiral blades also increases with higher rotational speeds, and when the speed exceeds 300 r\(\cdot\)min\({}^{-1}\) the torque increases more rapidly. Figure 13: Direction of three-axis working resistance. Note: F\({}_{x}\) is the horizontal resistance, F\({}_{y}\) is the vertical resistance under the vertical soil face, F\({}_{z}\) is the inward lateral resistance of the vertical spiral blade, N, v is the downward feed speed of the tool, m/s, n is the rotational speed of the spiral blade, r\(\cdot\)min\({}^{-1}\). 3. Influence of feed speed on three-directional resistance  
With a fixed tillage depth of 80 mm, a rotational speed of 200 r\(\cdot\)min\({}^{-1}\), and feed rates of 0.03 m/s, 0.05 m/s, and 0.07 m/s, three sets of simulation experiments were conducted. The variation in the maximum three-dimensional resistances experienced by the spiral blades with respect to the feed rate is depicted in Figure 15. Vertical resistance is the primary factor influencing drilling power consumption, and the maximum lateral resistance is slightly greater than the maximum parallel resistance. As the feed rate increases, the maximum resistances in all three directions also increase. When the feed rate exceeds 0.05 m/s, the maximum lateral resistance sharply increases, while the growth rates of the maximum vertical and horizontal resistances remain relatively constant. Soil trench experiments indicate that the torque on the spiral blades increases with faster feed rates, albeit at a relatively moderate rate.