Development and Validation of a Discrete Element Simulation Model for Pressing Holes in Sowing Substrates

Abstract

To conduct DEM simulation research on the collision characteristics between seeds and pressed substrate holes, a discrete element model of mechanically pressed holes in sowing substrates was developed in this study. The geometric DEM models of sowing substrate particles were established based on the sieve test, and the Hertz–Mindlin with JKR contact model was utilized for simulating of the fine, moist, and cohesive substrate particles. The angle of repose measured by the funnel method was served as the target, Plackett–Burman experiments were conducted to screen significant contact mechanical parameters, while steepest ascent and Box–Behnken experiments were employed to define their value ranges. A neural network model for predicting the angle of repose was constructed, and a genetic algorithm was applied to optimize the significant contact mechanical parameters. The cross-sectional profiles of the pressing hole were obtained through image profile feature extraction in simulation and 3D scanning projection methods in the experiment. The calibrated inter-particle dynamic friction coefficient, inter-particle coefficient of restitution, dynamic friction coefficient between particles and stainless steel, and JKR surface energy of the substrate were 0.0349, 0.5448, 0.0233, and 0.4279, respectively. The deviation of the simulated angle of repose utilizing the optimized contact parameters was 0.4°. The shapes of the pressed holes obtained from simulation and experiment showed good consistency. The pressing speed had no significant effect on the mean depth of all sampling points, suggesting that a higher pressing speed should be set to improve the operation efficiency. The pressing depth has a highly significant effect on the mean depth of all sampled points, but no significant effect on the deviation between the simulated and experimental mean depths. The maximum difference in the mean depth deviation between simulated and experimental sampled points is 1.308 mm. It demonstrates that the established discrete element model can efficiently and accurately simulate the deformation of the pressing hole in sowing substrate. It provides an applicable simulation model for fast optimization design of the pressing hole and sowing equipment.

1. Introduction

In precision seeding for plug seedling production, sowing seeds at the center of pressed substrate holes to an optimal depth enhances root development, improves seedling quality, ensures seedling growth uniformity, and facilitates subsequent transplanting operations [1,2]. When seeds are sown into pressed substrate holes with an initial velocity, contact collisions may cause positional deviation from the center of the substrate hole. Due to the extremely short collision duration and minimal rebound displacement of the seed, physical experiments are insufficient to fully characterize collision dynamics. The discrete element method (DEM), a well-established computational approach for analyzing granular material dynamics, has been extensively applied to study interactions between agricultural machinery components and granular substrates [3,4]. To investigate collision mechanics between seeds and pressed substrate holes using DEM, it is essential to first develop a robust DEM simulation model for mechanically pressed holes in sowing substrates [5,6,7].

The geometric modeling of granular particles is a critical factor that significantly influences the efficiency and accuracy of DEM simulations. Current research primarily focuses on seedling substrates, where sieve analysis has been employed to determine the particle size distribution. Subsequently, particle models are constructed using either single-sphere or multi-sphere combination methods. For instance, Du et al. [8] developed a seedling substrate particle model utilizing spheres with a uniform diameter of 1 mm. Hu et al. [9] constructed particle models for peat, perlite, and vermiculite using spheres with diameter ranges of 0.2~0.5 mm, 1.5~3 mm, and 0.4~1 mm, respectively. Wang et al. [10] established a seedling substrate particle model employing spheres with diameters ranging from 0.096 to 1.25 mm. Tian et al. [11] modeled peat, perlite, and vermiculite particles using combinations of 4, 12, and 41 spheres, respectively. The multi-sphere combination method offers enhanced simulation accuracy compared to the single-sphere approach, while it involves more complex calculations of inter-particle contact forces, leading to increased simulation times.

The rational contact mechanics model parameters between particles are essential factors influencing the accuracy of DEM simulations. The contact models investigated for seedling substrates encompass the Hertz–Mindlin with bonding model, which incorporates a bonding radius and fracture criterion to simulate particle cohesion and breakage [8,12]; the elasto-plastic cohesion model (ECM), which employs a piecewise contact mechanics response function to describe the accumulation of plastic deformation during loading–unloading cycles [11,13]; and the Hertz–Mindlin with JKR model, which utilizes the equivalent surface energy parameter to simulate van der Waals forces between moist particles [10]. The contact mechanics parameters between particles are typically calibrated with discrete element simulation and experimental methods [14,15,16,17]. The angle of repose or the static angle of repose were normally used as the response indicator. Parameters such as the static friction coefficient, rolling friction coefficient, restitution coefficient, and JKR surface energy are optimized through Plackett–Burman tests, steepest ascent tests, response surface methodology, and regression analysis [18,19,20]. Previous research demonstrates that the contact mechanics parameters obtained through simulation calibration exhibit high accuracy.

Machine learning and intelligent optimization algorithms exhibit robust nonlinear fitting and parameter optimization capabilities, resulting in their growing application in the parameter calibration of DEM simulations. Ma et al. [21] optimized the contact model parameters of alfalfa particles using the non-dominated sorting genetic algorithm II (NSGA-II). Ding et al. [22] proposed a genetic algorithm-backpropagation neural network-genetic algorithm (GA-BP-GA) method for optimizing the contact parameters of camellia oleifera seeds, which was found to be superior to the response surface methodology in terms of accuracy and efficiency. Long et al. [23] introduced a calibration method for soil elasto-plastic discrete element model parameters based on recurrent neural networks (RNN). Ye et al. [24] developed a calibration method for discrete element model parameters using backpropagation neural networks (BPNN) for simulating dynamic granular flow behavior. Benvenuti et al. [25] proposed a method combining artificial neural networks (ANN) with batch experiments to calibrate contact parameters for granular materials. Klejment [26] proposed a calibration method for discrete element contact parameters based on multiple linear regression (MLR) and RF. Hwang et al. [27] employed ANN to construct predictive models for the relationship between contact parameters and collision behavior of non-spherical particles. Mohajeri et al. [28] calibrated DEM model parameters for ring shear tests within the NSGA-II framework. The above studies demonstrated that machine learning optimization methods achieve higher fitting accuracy and global optimization capabilities compared with traditional regression fitting methods.

An accurate DEM model of the pressing hole in sowing substrates serves as a critical foundation for systematic investigation of seed substrate collision dynamics. While existing DEM models of seedling substrates have primarily been utilized for end-effector optimization in transplanting systems, there remains a notable absence of studies specifically addressing the modeling of the pressed substrate hole. The main purpose of the study was to develop a DEM model specially for simulation study on the pressing hole in sowing substrates. The specific objectives of this study were as follows: (1) construct a geometric and contact mechanical models of the sowing substrate; (2) determine contact mechanical parameters by simulation calibration experiments; and (3) verify the accuracy and effectiveness of the proposed DEM model by experimental comparison.

2. Materials and Methods

2.1. Geometric Models of Sowing Substrate

The sowing substrate is composed of peat, perlite, and vermiculite in a mass ratio of 6:3:1, with a moisture content of 50~60%. Ten grams of peat, perlite, and vermiculite were taken, respectively. Vibrating sieving was performed using screens with mesh sizes of 10 (2 mm), 16 (1.25 mm), 30 (0.6 mm), 60 (0.3 mm), 150 (0.1 mm), and 300 (0.053 mm). The substrates retained on each screen were weighed. The experiment was repeated three times, and the average values were taken to obtain the particle size distribution results for the three types of substrates, as shown in Figure 1.

The particle diameter of peat is predominantly distributed within the range of 0.3 to 1.25 mm, accounting for 76.35% of the total. Perlite particles are mainly found in the diameter range of 0.6 to 2 mm, comprising 81.88% of the sample. Vermiculite particles are primarily distributed between 0.3 and 2 mm in diameter, making up 93.56% of the total distribution.

Considering the complex shapes and small sizes of the sowing substrate particles, and taking into account both simulation efficiency and accuracy, a particle simulation model was established in the EDEM 2021 software using a random multiplication method for sphere diameters. As shown in Figure 2, for the blocky peat and vermiculite, a sphere with a diameter of 0.8 mm was used as the reference, and the simulation models were randomly generated with scaling factors ranging from 0.375 to 1.56 and from 0.375 to 2.5, respectively. In the case of the flaky perlite, a combination of eight spheres, each with a diameter of 1 mm, served as the reference, and the simulation models were randomly generated with scaling factors ranging from 0.6 to 2.

2.2. Contact Mechanics Models of Sowing Substrate

Due to the high moisture content of the sowing substrate, there is a certain degree of adhesion between the substrate particles. Therefore, the Hertz–Mindlin with JKR contact model, which can simulate the adhesion of fine and moist particles, was selected. The surface energy was introduced into the normal elastic force of the substrate particles to characterize the bonding and elastoplasticity among them [29].

In the Hertz–Mindlin with JKR model, the normal elastic contact force and overlap are, respectively, represented in Formulas (1) and (2) [30].

$$F_{JKR}={\displaystyle \frac{4E_{eq}{\alpha }^3}{3R_{eq}}}-4\sqrt{\pi {\alpha }^3\gamma E_{eq}}$$

(1)

$$\delta ={\displaystyle \frac{{\alpha }^2}{R_{\mathrm{eq}}}}-\sqrt{{\displaystyle \frac{4\pi \gamma \alpha }{E_{eq}}}}$$

(2)

where $F_{JKR}$ is the normal contact force, N; $\delta$ is the normal overlap, m; $E_{eq}$ is the equivalent elastic modulus of the two contacting particles, Pa; $R_{eq}$ is the equivalent radius of the two contacting particles, m; $\alpha$ is the contact radius, m; and $\gamma$ is the surface energy, N/m.

The $E_{eq}$ and $R_{eq}$ are defined, respectively, by Formulas (3) and (4).

$${\displaystyle \frac{1}{E_{eq}}}={\displaystyle \frac{(1-{{\upsilon }_1}^2)}{E_1}}+{\displaystyle \frac{(1-{{\upsilon }_2}^2)}{E_2}}$$

(3)

$${\displaystyle \frac{1}{R_{\mathrm{eq}}}}={\displaystyle \frac{1}{R_1}}+{\displaystyle \frac{1}{R_2}}$$

(4)

where $E_1$ is the elastic modulus of particle 1, Pa; ${\nu }_1$ is the Poisson’s ratio of particle 1; $R_1$ is the radius of particle 1, m; $E_2$ is the elastic modulus of particle 2, Pa; ${\nu }_2$ is the Poisson’s ratio of particle 2; and $R_2$ is the radius of particle 2, m.

If the three types of substrate particles are treated with different mechanical properties, a total of 30 contact mechanical parameters need to be determined. This would result in an excessively complicated calibration process for the simulation. To simplify the analysis, the three types of substrate particles are simplified to have the same mechanical properties. Based on preliminary experiments and previous studies [31,32], the substrate particles were characterized by a Poisson’s ratio of 0.4, a shear modulus of 10 MPa, and a density of 0.632 g/cm³.

2.3. Measurement Test for Angle of Repose

The angle of repose of the substrate particles was measured using the funnel method. The substrate particle pile image capture test platform is illustrated in Figure 3. The distance between the outlet of the funnel and the receiving table was 150 mm. The proportionally mixed substrate was poured into the funnel, allowing the substrate to flow smoothly through the outlet and form a conical pile. Once the particles came to be stationary, the frontal images of the substrate pile were captured with the MV-A5051CU545 camera (Huarui Technology Co., Ltd., Haining, China) and the MVviewer 2.3.5 software.

The image of the substrate particle pile was processed with MATLAB R2019b software, including binarization, erosion, noise removal by minimum connected domain, and edge detection using the Canny operator with double thresholds to obtain the coordinate points of the edge contours. The contour coordinate points were then imported into Origin 2017 software to generate a scatter plot. Linear fitting was performed on the contour points on both sides, and the average slope of the fitted lines on both sides was used as the tangent value of the angle of repose. The image processing procedure for the substrate particle pile is shown in Figure 4. The experiment was repeated three times, and the average angle of repose obtained was 32.86° ± 0.85°.

2.4. Parameter Simulation Calibration Experiment

A simulation model for angle of repose was developed based on the test platform as shown in Figure 5. As the mass ratio of peat, perlite and vermiculite was 6:3:1, the number of particles generated for peat, perlite, and vermiculite was set at 7.5 × 10⁴, 2.5 × 10³, and 1.25 × 10⁴, respectively, with a particle generation time of 2.5 s. After the stable substrate particle pile was formed, the front view of the particle pile was captured, and the simulation angle of repose was determined using the same image processing method as in the experimental measurement.

The Plackett–Burman test was designed with Design-Expert 13 software. The test factors include the inter-particle static friction coefficient (A), inter-particle dynamic friction coefficient (B) and inter-particle collision recovery coefficient (C), particle stainless steel static friction coefficient (D), particle stainless steel dynamic friction coefficient (E) and particle stainless steel collision recovery coefficient (F), along with the substrate JKR surface energy (G). Referring to the particle material data in the EDEM software, the value ranges of each factor were determined. For each factor, low and high level were selected within the reference range and represented as −1 and +1, respectively, as shown in

Table 1. Factor level of the Plackett–Burman test.

Factor	Level
	Low Level (−1)	High Level (+1)
A	0.20	1.04
B	0.01	0.10
C	0.15	0.75
D	0.2	0.3
E	0.020	0.035
F	0.12	0.20
G	0.1	3.5

.

The results of the Plackett–Burman experiment were analyzed to identify the parameters that significantly affect the angle of repose. A steepest ascent experiment was designed with the angle of repose as the response variable. During the simulation, non-significant factors were set to the midpoint value between the high and low levels in Table 1. Significant factors were designed with six experimental levels at a certain step size, and the simulation results of the angle of repose at each factor level were analyzed. Then, a Box–Behnken experimental design was conducted, where significant factors were set to three levels corresponding to the smallest relative error of the angle of repose. Results of the Box–Behnken experiment were served as the dataset for optimizing the significant factors.

2.5. Parameter Prediction Optimization Based on BP-GA

A three-layer feedforward neural network was constructed with significant factors as inputs and the angle of repose as the output, as shown in Figure 6.

The neuron number of the hidden layer $s$ is calculated by Formula (5).

$$s=\sqrt{n+l}+c$$

(5)

where $n$ is the number of input variables; $l$ is the number of output variables (here $l$ is taken as 1); and $c$ is a constant (ranging from 1 to 11). The optimal neuron number of the hidden layers $s$ is determined with the trial-and-error method.

All the Box–Behnken experimental result data were randomly divided into training dataset and test dataset with the ratio of 7:3. The input parameters were normalized with following Formula (6):

$$x_{iN}={\displaystyle \frac{x_i-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_i\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left(x_i\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_i\right)}}$$

(6)

where $x_i$ is the original value of the input variable; min ($x_i$) is the minimum value of the input variable $x_i$; max ($x_i$) is the maximum value of the input variable $x_i$; and $x_{iN}$ is the normalized value of the input variable.

Coefficient of determination ($R^2$) and mean squared error (MSE) were used to evaluate the fitting performance of the developed predictive model as given in Formulas (7) and (8). The larger $R^2$ value and the smaller MSE indicate better fitting performance of the developed predictive model.

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}{{\sum }_{i=1}^n{(y_i-\overline{y})}^2}}$$

(7)

$$MSE={\displaystyle \frac{1}{n}}\sum _{i=1}^n{({\widehat{y}}_i-y_i)}^2$$

(8)

where $y_i$ and ${\widehat{y}}_i$ represent the simulation and predicted angle of repose value of the ith output; $\overline{y}$ represents the mean value of the simulation angle of repose; and $n$ represents the total number of the dataset.

The measured angle of repose of 32.86° was regarded as the optimization objective. The backpropagation algorithm was utilized for network training. The learning rate for the training process was set at 0.01, with a maximum of 100 training steps. Input parameters were optimized through selection, crossover, and mutation operations of the GA. The population size for genetic optimization was 20, with a selection coefficient of 0.8, a crossover coefficient of 0.4, and a coefficient of mutation of 0.2.

2.6. Simulation and Experimental Comparison for Pressing Hole in Sowing Substrate

2.6.1. Simulation of Pressing Hole in Sowing Substrate

To verify the optimized contact model parameters, a simulation model for a pressing hole in sowing substrate was constructed. The three-dimensional model of the pressing head and plug tray cell was created with SolidWorks 2019 software and then imported into the EDEM software. The DEM particle models of peat, perlite, and vermiculite were established with a volume ratio of approximately 1:15:1 and a particle number ratio of approximately 30:1:5. As shown in Figure 7, the brown particles represent peat, the white particles represent perlite, and the dark yellow particles represent vermiculite.

As shown in Figure 7, the pressing head compresses the sowing substrate downward at a certain speed. Once a certain pressing depth is reached, the pressing head returns upward to its initial position. Considering the operation efficiency and the conventional pressing depth range of 5 to 15 mm for plug tray seedling cultivation, both three levels of pressing speed and depth were utilized in the simulation, as shown in

Table 2. Simulation factor and level.

Level	Factor
	Pressing Speed/(mm/s)	Pressing Depth/(mm)
1	4	5
2	6	10
3	8	15

.

A thin and transparent slice with a thickness of 2 mm was set in the XOZ plane of the simulation model and the pressing head was set to be invisible. The cross-sectional contour of the sowing substrate with the pressing hole was captured and processed using MATLAB software. Wiener filtering was applied for noise reduction, and morphological opening operations were used to remove noise points. The imcontour function was employed to extract the edge curve of the cross-sectional contour, as shown in Figure 8.

2.6.2. Test of Pressing Hole in Sowing Substrate

A universal tensile testing machine (accuracy of 0.001 N, test force range of 0 to 500 N) was utilized to construct the test platform of a pressing hole in sowing substrate, as shown in Figure 9. The pressing head and the plug tray cell support were fixed on the upper and lower clamps of the testing machine, respectively. To ensure the alignment between the center of the pressing head and the center of the plug tray cell, positioning pins were installed on both sides of the pressing head and the plug tray cell support. The test was conducted by driving the pressing head into the plug tray cell filling with sowing substrate.

A handheld Einstar 3D scanner (Xianlin 3D Technology Co., Ltd., Hangzhou, China), featuring a point distance of 0.1 to 3 mm and a maximum scanning speed of 14 frames per second, was used to collect point cloud data from the surface of the pressed substrate holes, as shown in Figure 10.

The point cloud data of the pressed hole were tracked, spliced, and deleted with the EXStar v1.0.6.0 software, and then projected onto the XOZ plane, as shown in Figure 11a. In the projected section, edge points were retained, and the background was processed to be white. The Matlab software was used to detect and extract the X and Z coordinates of the edge points. By fitting those edge points, the section contour of the pressed hole is obtained, as shown in Figure 11b.

2.6.3. Comparison Method of Simulation and Test

Comparison of the experimental and simulation section contour of the pressed hole is shown in Figure 12. Along the X-axis, sampling points are set with 2 mm intervals on either side of the central origin O. At the sampling point $i$, the Z-axis coordinate values corresponding to the simulated and experimental section contours, denoted as $Z_{iS}$ and $Z_{iE}$, are recorded. The mean simulation depth $Z_S$ and the mean experimental depth $Z_E$ are calculated by Formulas (10) and (11). The deviation between the mean simulation and experimental depth $\Delta z_{SE}$ is defined as shown in Formula (12).

$$z_S={\displaystyle \frac{{\sum }_{i=1}^m{z}_{iS}}{m}}$$

(9)

$$z_E={\displaystyle \frac{{\sum }_{i=1}^m{z}_{iE}}{m}}$$

(10)

$$\Delta z_{SE}=\left|z_S-z_E\right|$$

(11)

where $m$ represents the number of sampling points. For the pressing depths of 5 mm, 10 mm, and 15 mm, $m$ is 5, 11, and 17, respectively.

The smaller ${∆Z}_{SE}$ is, the better the consistency between the simulation and experimental section contours of the pressed hole, and the higher accuracy of the DEM simulation of the pressing hole in sowing substrate can be validated.

3. Results

3.1. Simulation Calibration Test Result

The Plackett–Burman simulation experiments consisting of 12 groups, with each group being simulated three times, were conducted to obtain the average angle of repose as shown in

Table 3. Plackett–Burman design and results.

NO.	A	B	C	D	E	F	G	Angle of Repose/(°)
1	1	1	1	−1	−1	−1	1	62.48
2	−1	−1	−1	−1	−1	−1	−1	9.22
3	1	−1	1	1	−1	1	1	24.75
4	1	1	−1	−1	−1	1	−1	25.21
5	−1	1	1	1	−1	−1	−1	1.95
6	1	1	−1	1	1	1	−1	28.73
7	1	−1	1	1	1	−1	−1	2.33
8	−1	−1	1	−1	1	1	−1	0.83
9	−1	−1	−1	1	−1	1	1	71.48
10	−1	1	−1	1	1	−1	1	83.42
11	1	−1	−1	−1	1	−1	1	52.23
12	−1	1	1	−1	1	1	1	74.13

. Analysis of variance (ANOVA) indicated that the significant influence coefficients of the angle of repose were 0.3464 for the inter-particle static friction coefficient (A), 0.0499 for the inter-particle dynamic friction coefficient (B), 0.0661 for the inter-particle collision recovery coefficient (C), 0.8118 for the particle–stainless steel dynamic friction coefficient (D), 0.3343 for the kinetic friction coefficient between particles and stainless steel (E), 0.7765 for the particle–stainless steel collision recovery coefficient (F), and 0.002 for the substrate JKR surface energy (G). Ranked by their significant influence, the substrate JKR surface energy (G), the inter-particle dynamic friction coefficient (B), the inter-particle collision recovery coefficient (C), and kinetic friction coefficient between particles and stainless steel (E) were selected as the factors for the steepest ascent experiment. The values of the four factors were assigned by equally dividing the parameter range specified in Table 1.

Those factors that have no significant effect on the angle of repose were taken as the middle values between the high and low levels in Table 1. Therefore, the values of the inter-particle static friction coefficient (A), particle–stainless steel static friction coefficient (D), and the particle–stainless steel collision recovery coefficient (F) were assigned as 0.62, 0.25, and 0.16, respectively. Six groups of steepest ascent experiments were designed, and the results are shown in

Table 4. Results of the steepest ascent experiment.

NO.	B	C	E	G	Angle of Repose/(°)
1	0.010	0.75	0.020	0.10	3.13
2	0.028	0.63	0.023	0.78	21.73
3	0.046	0.51	0.026	1.46	60.35
4	0.064	0.39	0.029	2.14	75.35
5	0.082	0.27	0.032	2.82	81.60
6	0.100	0.15	0.035	3.50	84.59

.

In Table 4, the second group of parameters obtained the smallest relative error compared to the measured angle of repose. The adjacent first and third groups of data were selected to conduct a four-factor, three-level Box–Behnken experiment, and the results are shown in

Table 5. Results of Box–Behnken experiment.

NO.	B	C	E	G	Angle of Repose/(°)
1	0.028	0.75	0.023	0.10	2.45
2	0.010	0.63	0.026	0.78	13.01
3	0.028	0.63	0.023	0.78	28.78
4	0.010	0.63	0.023	1.46	30.64
5	0.028	0.75	0.020	0.78	3.14
6	0.028	0.63	0.023	0.78	23.97
7	0.028	0.51	0.020	0.78	39.22
8	0.028	0.51	0.023	0.10	19.49
9	0.010	0.63	0.020	0.78	11.07
10	0.028	0.63	0.026	0.10	6.20
11	0.028	0.63	0.023	0.78	22.73
12	0.028	0.51	0.023	1.46	57.01
13	0.028	0.63	0.026	1.46	39.99
14	0.028	0.63	0.023	0.78	26.81
15	0.010	0.75	0.023	0.78	2.43
16	0.028	0.51	0.026	0.78	38.22
17	0.046	0.63	0.026	0.78	30.53
18	0.046	0.63	0.020	0.78	33.68
19	0.028	0.75	0.023	1.46	7.31
20	0.028	0.75	0.026	0.78	3.28
21	0.028	0.63	0.020	0.10	4.15
22	0.028	0.63	0.020	1.46	41.14
23	0.010	0.51	0.023	0.78	30.68
24	0.010	0.63	0.023	0.10	2.37
25	0.046	0.63	0.023	1.46	43.05
26	0.028	0.63	0.023	0.78	21.44
27	0.046	0.63	0.023	0.10	5.93
28	0.046	0.75	0.023	0.78	2.57
29	0.046	0.51	0.023	0.78	40.85

.

Based on the results of the steepest ascent experiment and the Box–Behnken experiment, the inter-particle dynamic friction coefficient (B), the inter-particle collision recovery coefficient (C), kinetic friction coefficient between particles and stainless steel (E), and the substrate JKR surface energy (G) were determined as the input variables of the neural network shown in Figure 6, and the value range of the four input variables are 0.01~0.046, 0.51~0.75, 0.02~0.026, 0.1~1.46, and 2.37~57.01, respectively. According to Formula (5), the neuron number of the hidden layer ranges from 4 to 14. The optimal neuron number of the hidden layer, which achieved a high prediction accuracy, was determined to be 10 through multiple instances of adjustments.

The scatter plot of comparing predicted and simulated angles of repose is shown in Figure 13. The coefficient of determination $R^2$ of the predictive model on the training and testing dataset were 0.9962 and 0.9735, respectively. This indicates a strong correlation between the predicted and simulated angle of reposes during both training and testing phases. The developed predictive model could at least explain the 97.35% variability of the angle of repose in the testing phase. The MSE values on the training and testing dataset were 0.9284 and 6.5954, respectively. This verified the high predictive accuracy of the developed predictive model.

Through parameters optimization with the genetic algorithm, the inter-particle dynamic friction coefficient (B), the inter-particle collision recovery coefficient (C), kinetic friction coefficient between particles and stainless steel (E), and the substrate JKR surface energy (G) were determined as 0.0349, 0.5448, 0.0233, and 0.4279, respectively. The angle of repose of 32.46° was obtained by simulating with those optimized parameters. The simulation deviation of 0.4° from the measured angle of repose indicates that the proposed parameter calibration method could achieve high fitting accuracy, and the calibrated parameters are applicable.

3.2. Comparison of Simulated and Experimental Results

The simulated and experimental results of pressing hole in the sowing substrate are shown in Figure 14. For different pressing depth and speed, both simulation and experimental results show that pressed conical holes were formed within the sowing substrate, characterized by the maximum depth at the center sampling point and progressively decreasing towards the end sampling points.

At the pressing depth of 5 mm, the simulated and experimental depth ranges for the center sampling point are 4.895~4.982 mm and 3.166~3.491 mm, respectively, while those for the end sampling point are 1.744~2.070 mm and 1.462~1.713 mm, respectively. At the pressing depth of 10 mm, the simulated and experimental depth ranges for the center sampling point are 9.734~9.771 mm and 7.352~7.637 mm, respectively, while those for the end sampling point are 1.365~1.598 mm and 1.290~3.076 mm, respectively. At the pressing depth of 15 mm, the simulated and experimental depth ranges for the center sampling point are 14.103~14.221 mm and 11.611~12.347 mm, respectively, while those for the end sampling point are 0.614~0.966 mm and 1.234~1.582 mm, respectively. This indicates that at a certain pressing depth and different indentation speeds, there is no significant difference in the simulated or experimental depths of each sampling point.

At certain pressing depths of $X_1$ and pressing speeds of $X_2$, the mean simulated depth $Z_S$ and the mean experimental depth $Z_E$ of all sampling points are shown in

Table 6. Mean pressing depth of simulated and experiment.

NO.	X1	X2	ZS	ZE	ΔZSE
1	5	4	3.425	2.412	1.013
2	5	6	3.386	2.365	1.021
3	5	8	3.432	2.354	1.078
4	10	4	5.814	4.696	1.118
5	10	6	5.683	4.804	0.879
6	10	8	5.835	4.527	1.308
7	15	4	7.517	6.349	1.168
8	15	6	7.708	6.639	1.069
9	15	8	7.578	6.303	1.275

X₁, X₂ are pressing depths and pressing speeds. Z_S, Z_E, and ΔZ_SE are the mean simulated depth, the mean experimental depth, and the deviation between the mean simulation and experimental depth.

. It indicates that the mean simulated depth $Z_S$ is greater than the mean experimental depth $Z_E$. The results of the variance analysis indicate that the p-values for pressing speed on the mean simulation and experimental depths were 0.5324 and 0.2257, respectively. It shows that pressing speed has no significant effect on the mean depths obtained from simulation or experiment. Therefore, a higher pressing speed can be utilized to enhance the operation efficiency of the pressing hole.

The p-values for the pressing depth are both less than 0.0001, indicating that pressing depth has a highly significant effect on the mean depths obtained from both simulation and experiment. At a given pressing depth, the mean depth deviation between simulation and experiment (${∆Z}_{SE}$) shows no significant difference. The maximum ${∆Z}_{SE}$ of 1.308 mm indicates that the deformation patterns of the pressing hole in the sowing substrate obtained from simulation and experiments are in good agreement.

4. Discussion

The DEM contact model and parameters for pressing holes in sowing substrate, as determined in this study, were compared with those from prior research, as shown in

Table 7. Comparison of DEM model and parameters with prior research.

Contact Model	This Study	Wang et al. [10]	Cui et al. [7]	Hu et al. [9]
	Hertz–Mindlin with JKR	Hertz–Mindlin with JKR	Hertz–Mindlin with Bonding	Edinburgh Elasto-Plastic Adhesion
Inter-particle static friction coefficient	0.6200	0.5385	0.4270	0.6500
Inter-particle dynamic friction coefficient	0.0349	0.0970	0.0390	0.3450
Inter-particle collision recovery coefficient	0.5448	0.1420	0.1200	0.2000
JKR surface energy/(J·m−2)	0.4279	2.3250	-	3.5000
Normal stiffness/(N·m−1)	-	-	1 × 108	-
Shear stiffness/(N·m−1)	-	-	5 × 107	-
Critical normal stress/(Pa)	-	-	30,000	-
Critical shear stress/(Pa)	-	-	15,000	-
Constant pull-off force/(N)	-	-	-	−0.002
Contact plasticity ratio	-	-	-	0.6
Slope exp	-	-	-	1.5
Tensile exp	-	-	-	1
Tangential stiff multiplier	-	-	-	0.4

. Differences exist among these model parameters, particularly in the JKR surface energy, which reflects the adhesive properties between substrate particles. DEM simulations of pressing holes in the substrate using parameters from prior studies were conducted at a pressing depth of 10 mm and a pressing speed of 6 mm/s. Deviations between simulated and experimental depths ${∆Z}_{SE}$ reported by Wang et al. [10], Cui et al. [7], and Hu et al. [9] were 1.131 mm, 2.706 mm, and 1.247 mm, respectively, all exceeding the 0.879 mm deviation observed in this study. This indicates that the models and parameters developed in this study are better suited for simulating pressing hole dynamics in sowing substrates.

In this simulation study, a certain degree of rebound was observed after the sowing substrate was compressed and deformed, and the experimental rebound was greater compared with that of the simulation. Simplifying the three types of substrate particles as identical mechanical properties in simulation is likely the main reason for the rebound deformation differences. Additionally, the simplification of the geometric shapes and particle quantities of the three substrates in simulation may also contribute to the differences of rebound behavior.

5. Conclusions

A DEM model for simulation of the pressing hole in the sowing substrate was studied. The geometric model of the substrate particles was constructed by scaling the diameter of the spheres within a certain proportional range, and the Hertz–Mindlin with JKR model was utilized as the contact model for the substrate particles. Through simulation calibration experiments and optimization using the BP-GA method, the inter-particle dynamic friction coefficient, the inter-particle collision recovery coefficient, kinetic friction coefficient between particles and stainless steel, and the substrate JKR surface energy were determined as 0.0349, 0.5448, 0.0233, and 0.4279, respectively. The simulation and measurement deviation of 0.4° for angle of repose proved the effectiveness of the substrate particle model and those optimized parameters. The conical holes in the sowing substrate obtained by simulations and experiments demonstrated a high degree of consistency. They revealed that higher pressing speed should be utilized to enhance the operation efficiency of the pressing hole. The maximum mean depth deviation of 1.308 mm between simulation and experiment verified the accuracy and applicable of the developed DEM model.

The DEM of the pressed substrate hole still exhibits certain discrepancies compared to actual physical substrate conditions. For further enhancing accuracy and practicality of the DEM simulation model for the sowing substrate, peat, perlite, and vermiculite would be treated as particles with distinct elastic moduli and Poisson’s ratios. Calibration and optimization for those physic parameters would be conducted in a future study. Additionally, the DEM simulation model of the sowing substrate would be used in exploring the collision and interaction mechanisms between seeds and the surface of the pressed sowing substrate holes. It is expected to provide a microscopic research method for seeds precisely falling in the plug tray cell.