# Analysis of Movement Law and Influencing Factors of Hill-Drop Fertilizer Based on SPH Algorithm
## 2 Methodology
### Fertilizer Motion Simulation
A parametric solid model of cover and opener was established, and a soil model of 1000 mm \(\times\) 400 mm \(\times\) 400 mm also was established in CREO. The model was imported into the preprocessor and meshed. The opener used an automatic meshing method, and the mesh size was 0.05 m; the cover used an automatic meshing method, and the mesh size was 0.03 m; the soil was divided by sweep, and the mesh size was 0.01 m.  
Because the soil is not a homogeneous material, the deviation between simulation results and actual values will be large if the soil is idealized as a continuous medium. In this paper, the material of MAT147 (\"MAT_FHWA_SOIL) was used as a soil model in LS-DYNA, and the Mohr-Coulomb criterion was used to modify it. This model could better simulate the nonlinear stress-strain relationship of the soil, and produce simulation results that are closer to the actual properties. The main model parameter [31] selected according to the actual conditions of the experiment in this paper is shown in Table 1.  
The established soil model was converted into SPH particles, which were generated as solid nodes, and the particle smooth length was defined as 1.2. The contact between the opener and cover was a point-surface erosion contact, \"CONTACT_AUTOMATIC_NODES_TO_SURFACE_ID, and the sliding friction coefficient of the contact surface was 0.4. The X direction was defined as the planter's forward direction, the Y direction was perpendicular to the planter's forward direction, and the Z direction was the vertical direction. The opener restricted the translation of the Y and Z axes and the rotation around the three axes of X, Y, and Z. The cover restricted the translation of the Y and Z axes and the rotation around X and Y axes. The K file was imported into the solver for calculation after the setting was completed. As shown in Figures 2 and 3, in order to study the movement law of fertilizer in the soil under the action of the cover, the fertilizer was distributed in a cube of 40 \(\times\) 60 \(\times\) 100 (length \(\times\) width \(\times\) height) after the experiment. The distance from the upper side of the fertilizer cube to the upper boundary of the soil was 100 mm. In order to simplify the number of particles and the amount of calculations, this article mainly tracked and analyzed 24 points on the four vertical edges of the fertilizer cube in order to study the movement and displacement of the fertilizer. The start time was set when the opener touched the soil, and the simulation ended when it left the soil completely. While the opener and the cover were advancing in the X-axis direction, the cover itself rotated constantly. Fertilizer and soil were disturbed by cover and opener and displaced. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Parameter** & **Value** \\ \hline \multirow{8}{*}{Soil particle} & Bulk modulus (Mpa) & 5.9 \\  & Shear modulus (Mpa) & 2.7 \\  & Density \(\left(\text{kg m}^{-3}\right)\) & 1700 \\  & Moisture content (\%) & 23.57 \\  & Specific gravity & 2.65 \\  & Angle of internal friction (rad) & 0.42 \\  & Cohesion (Kpa) & 12 \\  & Viscoplastic parameter & 1.1 \\  & Water density \(\left(\text{kg m}^{-3}\right)\) & 1000 \\ \hline \multirow{4}{*}{Hill-drop fertilizer device} & Density \(\left(\text{kg m}^{-3}\right)\) & 7850 \\  & Elastic modulus (Pa) & \(2.7\times 10^{11}\) \\ \cline{1-1}  & Possion’s ratio & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model parameter of soil particle and hill-drop fertilizer device. Figure 3: Fertilizer deformation schematic diagram: (**a**) fertilizer state before covering soil; (**b**) fertilizer state after covering soil. Figure 2: Movement process of the hill-drop fertilizer device, (**a**,**d**,**g**) at T = 0.35 s; (**b**,**e**,**h**) at T = 0.60 s; and (**c**,**f**,**i**) at T = 0.85 s.  
When the working speed was set to 1 m/s, the depth of soil of the opener was 250 mm, and the depth of soil of the cover was 100 mm.