Establishment of a Discrete-Element Model and Verification of a Seeder Bench Experiment for Sesbania Seeds

Abstract

In light of the absence of discrete-element simulation characteristic parameters for the precision-seeding simulation process associated with Sesbania, this study investigated the physical properties of “CAS Sesbania No. 6” Sesbania seeds and measured the characteristic parameters of the Sesbania seeds in order to build a discrete-element model. The inter-seed contact parameters were calibrated to improve the seed model’s accuracy through stacking experiments and Box–Behnken response surface methodology. The stacking angle of Sesbania seeds was determined to be 34.5°; this was used as the evaluation index when simulating the stacking experiments. The results indicated that the coefficient of collision recovery, static friction, and rolling friction (inter-seed) were 0.168, 0.339, and 0.083, respectively. Substituting the calibrated parameters into the model, the simulation yielded a simulated stacking angle of 34.9°. The simulation results and bench experiment outcomes were compared to validate the applicability of the Sesbania seed discrete-element model in the context of seeder-simulation experiments. The results indicated that the percentage errors for the replay-seeding rate and missed-seeding rate between the simulation experiment and the bench experiment were 5.90% and 5.84%, respectively. All test results satisfied the technical requirements, confirming the calibration results’ reliability and providing a theoretical basis for the optimization of the design and simulation of Sesbania precision-seeding devices.

1. Introduction

The total area of saline–alkali land in China is approximately 99.13 million hectares, accounting for roughly one-tenth of the country’s total land area. The extensive scale, wide distribution, severe degree, and complex soil salinization and alkalinization types have become major abiotic stress factors affecting China’s ecological environmental security and sustainable ecological development. These issues severely constrain ecological construction, agricultural production, and land development and utilization. Biological improvement refers to the process of ameliorating saline–alkali soil through the life activities of organisms [1,2]. This approach is considered one of the most ecologically sustainable and economically advantageous technical measures for soil remediation. Sesbania, a herbaceous plant of the legume family, exhibits strong nitrogen fixation capabilities and is commonly utilized as a pioneer crop for saline–alkali land improvement. China has achieved a series of positive advancements in using Sesbania for saline–alkali land treatment. Sesbania planting has been widely promoted as a biological improvement technology across various regions. The “CAS Sesbania No. 6” Sesbania seed has been successfully trial-planted in multiple saline–alkali land regions, achieving satisfactory results. It is presently undergoing trial planting at the experimental base in Guangxi, China.

With the increasing labor costs in agriculture, mechanical sowing has become an approach critical to enhancing the efficiency of Sesbania planting. Compared with other leguminous plants, Sesbania seeds have a smaller diameter and weigh less. The number of seeds per hole should be restricted to three to five to ensure an adequate germination rate and appropriate sowing density. However, most precision seeders for tiny seeds are tailored for single-seed precision sowing. In contrast, spoon-type seeders for multi-seed sowing are typically suited for medium-sized seeds. This inability to meet the requirements of mechanical precision sowing associated with Sesbania seeds significantly hinders the mechanization of Sesbania planting.

The discrete-element method [3], as a numerical analysis technique specifically tailored for multi-particle systems, has been extensively utilized in the optimization analysis of seeding machinery [4,5,6,7]. When conducting simulation studies on seeders using the discrete-element method, defining the characteristic parameters of the simulation model is essential. Consequently, calibrating the discrete-element model parameters of seeds becomes necessary.

Scholars have measured discrete-element simulation parameters for seeds of significant food and economic crops such as wheat and vegetables [8,9,10,11]. Regarding leguminous plants, Liu et al. [12] measured the parameters of adzuki bean seeds. Xu et al. [13] performed size analysis and modeling for soybeans, providing valuable references for the structural optimization of seeding devices. However, research on seed material properties and discrete-element simulation parameters relative to the “CAS Sesbania No. 6” Sesbania seed remains scarce, which significantly constrains the development of mechanical precision seeding for Sesbania.

Against this background, the characteristic parameters of the Sesbania seeds were measured and the discrete-element simulation model for the “CAS Sesbania No. 6” seed was built. The sowing process was simulated using EDEM, which is discrete-element simulation software, and the sowing performance was evaluated through bench experiments to validate the fidelity of the model and simulation parameters. The discrete-element model of Sesbania seed in this paper has now been applied to the design optimization of precision seeders to solve the problem of mechanical sowing of Sesbania.

2. Materials and Methods

2.1. Materials

The “CAS Sesbania No. 6” Sesbania seed was selected as the research object. Certain materials come into direct contact with the seeds during the seed’s operation. These materials include plastic polylactic acid (PLA), polymethyl methacrylate (PMMA), SAE 304 stainless steel, and 6061 aluminum alloy. All tests were conducted in the Intelligent Agricultural Machinery Laboratory at Guangxi University under controlled environmental conditions, with an indoor temperature of (24 ± 2) °C and relative humidity of 76%.

2.2. Physical Parameters

It is essential to determine the seeds’ fundamental material properties before constructing a discrete-element model of Sesbania seeds using the EDEM. These include physical properties (triaxial size, thousand-seed weight, density, and moisture content) and mechanical properties (Poisson’s ratio and elastic modulus). It is also necessary to measure the contact-related characteristics for the seeder material and the seeds, including the coefficient of restitution, coefficient of static friction, and coefficient of rolling friction.

2.2.1. Basic Physical Parameters of Sesbania Seeds

One hundred seeds of Sesbania were randomly selected. An electronic caliper (accuracy: 0.01 mm) was used to measure the Sesbania seeds’ triaxial size (length × width × height). The average triaxial size was 4.09 mm × 2.26 mm × 1.98 mm. Since Sesbania seeds are ellipsoid-like in shape, their volume was calculated using the ellipsoid volume formula, Formula (1). The results indicated that the three-dimensional volumes of the seeds followed a nearly normal distribution (Figure 1), with an average volume of 9.811 mm³ and a standard deviation of 2.999 mm³.

$$V={\displaystyle \frac{1}{6}}\pi LBT$$

(1)

where $V$ is the volume of an individual seed (in mm³); $L$ is the length of an individual seed (in mm); $B$ is the width of an individual seed (in mm); and $T$ is the height of an individual seed (in mm).

The thousand-seed weight of the Sesbania seed was determined using the thousand-grain method. The weight of one thousand seeds was measured using an electronic scale (accuracy: 0.01 g), and a total of five groups of data were collected. The weight difference between each group was less than 5%, ensuring measurement consistency. The average thousand-seed weight was determined to be 15.25 g. The density of five groups of Sesbania seed samples was determined using the liquid displacement method [14], providing precise measurements for further analysis. The average density of Sesbania seeds was determined to be 1.154 × 10³ kg/m³.

Five additional groups of seeds were selected, and the water content of the Sesbania seeds was determined using the constant-temperature drying method. A vacuum drying oven (model: BoXun BZF-50) was set to a constant temperature of 103 ± 2 °C, and the seeds were dried for 8 h. The weight of the seeds was measured both before and after the drying process, and the water content of the Sesbania seeds was determined to be 13%.

2.2.2. Poisson’s Ratio and Elastic Modulus of Sesbania Seeds

The Poisson’s ratio of the seeds describes a material property that characterizes the ratio of lateral normal strain to axial normal strain when seeds are subjected to external forces [15]. The elastic modulus of the seeds quantifies the material’s capacity to deform and withstand deformation under external forces. Specifically, it is defined as the ratio of stress to strain when the material is subjected to axial loading [16].

Given Sesbania seeds’ small size and ellipsoidal shape, applying axial loads poses significant challenges. Therefore, the width and height of the Sesbania seeds were measured after the load was applied along the height direction. During the compression test, the Sesbania seed was horizontally positioned on the testing platform of the universal compressing machine (model: INSTRON 6800), as illustrated in Figure 2. The pressure was incrementally applied until seed fracture occurred. The universal compressing machine recorded both the applied pressure and the displacement, in the height direction, of the seeds. The variation in seed width was measured using an electronic caliper. Eleven sets of valid experimental data were collected. The Poisson’s ratio was calculated using Formula (2), yielding an average value of 0.449. The elastic modulus was determined using Formula (3), resulting in an average value of 5.577 × 10⁷ Pa.

$$\mu ={\displaystyle \frac{\left|b\right|}{t}}={\displaystyle \frac{|b_1-b_2|}{t_1-t_2}}$$

(2)

$$E={\displaystyle \frac{\sigma }{\epsilon }}$$

(3)

where $\mu$ is the Poisson’s ratio; $b$ is the variation in seed width (in mm); $t$ is the variation in seed height (in mm); $b_1$ is the seed width before compression (in mm); $b_2$ is the seed width after compression (in mm); $t_1$ is the seed height before compression (in mm); $t_2$ is the seed height after compression (in mm). $E$ is the elastic modulus (in Pa); $\sigma$ is the compressive stress (in Pa); and $\epsilon$ is the linear strain.

2.2.3. Coefficient of Restitution

The coefficient of restitution is a physical parameter that quantifies the ratio of the relative velocities of two objects after a collision relative to that same ratio before the collision. In agricultural applications, the particle coefficient of restitution is typically defined as the ratio of a particle’s velocities before and after impact. This parameter is essential for understanding the motion-related behavior of particles following a collision and is primarily used for calibrating simulation parameters to model particle dynamics accurately [17].

The coefficient of restitution was determined by testing the seeds’ free fall and rebound. The experimental setup consisted of material plates for testing (PMMA, SAE 304 stainless steel, PLA, and 6061 aluminum alloy), grid coordinate paper, digital camera (model: Canon EOS 200DII), tweezers, and LED lighting. The coordinate paper was affixed to the wall perpendicular to the tested material plate, with the camera lens aligned directly toward it. The LED lighting was adjusted to ensure that the camera could capture the trajectory of the seed’s fall, as illustrated in Figure 3. Given the small size of Sesbania seeds, the initial height was set to 100 mm to record the seed’s rebound process fully.

During the experiment, a single Sesbania seed was carefully positioned 100 mm above the material’s surface in order to be tested using forceps, with one side of the forceps aligned closely with the coordinate paper. The seed was released to allow it to fall freely under gravity. Simultaneously, the digital camera recorded the entire process in full HD at 60 frames per second to capture the trajectory of the seed’s motion in order to measure its rebound height after its collision with the material. Subsequently, the video file was imported into the video processing software and played in slow motion to analyze the collision and rebound trajectory. The coordinates of the seed at its highest rebound point were recorded to determine the maximum rebound height. Ten groups of valid rebound height data were collected for each of the four materials tested (PMMA, SAE 304 stainless steel, PLA, and 6061 aluminum alloy). Neglecting the velocity change of the test material plate after the collision [18], the coefficient of restitution was determined by applying Formula (4).

$$e={\displaystyle \frac{|v_1^{\prime }-v_2^{\prime }|}{|v_1-v_2|}}={\displaystyle \frac{\left|v_1^{\prime }\right|}{\left|v_1\right|}}={\displaystyle \frac{\sqrt{2gh}}{\sqrt{2gH}}}=\sqrt{{\displaystyle \frac{h}{H}}}$$

(4)

where $e$ is the coefficient of restitution; $v_1$ is the velocity of the seed before collision (in m/s); $v_1^{\prime }$ is the velocity of the seed after collision (in m/s); $v_2$ is the velocity of the material plate before collision (in m/s); $v_2^{\prime }$ is the velocity of the material plate after collision (in m/s); $H$ is the initial falling height of the seed (in mm); and $h$ is the maximum rebound height of the seed (in mm).

The coefficient of restitution between Sesbania seeds was also determined using free fall and collision rebound tests. Before the measurement, Sesbania seeds with similar diameters were carefully arranged in close contact, and attached to a paper surface using tweezers, forming a seed material plate (Figure 4). To enhance the visibility of the rebound height after collision, during the experiment, the Sesbania seeds were positioned at a height of 250 mm, directly above the seed material plate, and then allowed to fall freely under gravity. Ten groups of valid rebound height data were collected, and their average value was calculated.

The coefficients of restitution between Sesbania seeds and PMMA, SAE 304 stainless steel, PLA, and 6061 aluminum alloy were calculated to be 0.376, 0.474, 0.431, and 0.544, respectively. The coefficient of restitution for Sesbania seeds was calculated to be 0.161.

2.2.4. Coefficient of Static Friction

The coefficient of static friction is defined as the ratio of the maximum frictional force and the normal force exerted between the material and its contact surface before sliding. This parameter reflects the frictional characteristics of the contact surfaces between materials. Typically, the sliding friction angle is employed to characterize the frictional behavior when granular materials undergo relative sliding on a contact surface, with its tangent value corresponding to the coefficient of static friction [19]. The coefficient of static friction plays a critical role in the design of agricultural machinery, particularly seeding equipment, as it directly influences seed flow properties and the smoothness of seed dispensing.

The coefficient of static friction was measured using the inclined plane method. When the angle of the inclined plane was smaller than the sliding friction angle, the Sesbania seeds remained relatively stationary on the inclined plane. When the inclination angle exceeded the sliding friction angle, the seeds began to slide down. The test setup consisted of the material plate for testing, a digital inclinometer (accuracy: 0.01°), and a self-made inclined plane lifting platform, as illustrated in Figure 5. The material plate was securely fastened to the inclined plane, and the handle adjusted the inclination angle.

During the experiment, tweezers were used to position the Sesbania seeds along the longitudinal axis of the test material plate. As the slope angle increased progressively, seeds began to slide on the test material plate once the slope angle exceeded the sliding friction angle. The slope was fixed at this point, and the inclination angle was measured using an inclinometer to determine the sliding friction angle. Test values showing a tendency to roll were excluded, and only results corresponding to pure sliding motion were considered valid. Ten groups of valid data were collected for each type of test material plate (PMMA, SAE 304 stainless steel, PLA, and 6061 aluminum alloy) and the material plate of Sesbania seeds. The coefficient of static friction was calculated using Formula (5).

$$f_s=\mathrm{t}\mathrm{a}\mathrm{n}\phi$$

(5)

where $f_s$ is the coefficient of static friction; $\phi$ is the sliding friction angle (in °).

The coefficients of static friction between the Sesbania seeds and PMMA, SAE 304 stainless steel, PLA, and 6061 aluminum alloy, as well as between the seeds themselves, were determined to be 0.601, 0.466, 0.498, 0.448, and 0.677, respectively.

2.2.5. Coefficient of Rolling Friction

The coefficient of rolling friction is determined by the ratio of the frictional force experienced by the material while rolling on the contact surface to the normal force applied perpendicularly to the contact surface. Typically, the rolling friction angle represents the rolling friction characteristics between single-grain columnar, spherical, or quasi-spherical materials and the contact surface [19].

The coefficient of rolling friction was also measured using the inclined plane method. Seeds with similar widths and heights were carefully selected, to ensure the seeds remained rolling during the experiment. During the test, a single Sesbania seed was horizontally positioned on the test material plate using tweezers, enabling it to roll along the inclined plane. When the inclination angle exceeded the sliding friction angle, the seed began to roll on the test material plate. At this point, the inclined plane was fixed, and the inclination angle was measured with an inclinometer to determine the rolling friction angle. Ten groups of valid data were collected for each type of test material plate (PMMA, SAE 304 stainless steel, PLA, and 6061 aluminum alloy) and the seed material plate. The coefficient of rolling friction was calculated using Formula (6).

$$f_k={\displaystyle \frac{\delta }{R}}=\mathrm{t}\mathrm{a}\mathrm{n}\theta$$

(6)

where $f_k$ is the coefficient of rolling friction; $\delta$ is the dimensional value of the rolling friction coefficient (in mm); $R$ is the rolling radius (in mm); and $\theta$ is the rolling friction angle (in °).

The coefficients of rolling friction between the Sesbania seeds and PMMA, SAE 304 stainless steel, PLA, and 6061 aluminum alloy, as well as between the seeds themselves, were determined to be 0.211, 0.222, 0.209, 0.207, and 0.242, respectively.

2.3. Stacking Test

The stacking test is a method used to evaluate the stacking characteristics of granular materials. The stacking angle indicates the flowability and frictional behavior of granular materials. A simulation analysis of the stacking process investigates the impact of the granular material model on simulation accuracy. In light of these results, the parameters of the simulation model are calibrated [5,20,21].

2.3.1. Physical Stacking Angle

For convenience of observation and the recording of the stacking angle of the Sesbania seeds, a box was fabricated, using PMMA plate, to function as a physical stacking angle measurement device. The box had internal dimensions of 100 mm × 100 mm × 150 mm. During the experiment, 0.3 kg of Sesbania seeds was placed into the box. One side of the box was slowly raised, allowing the seeds to slide toward the opening under the influence of gravity, forming a stable slope, as illustrated in Figure 6. The physical stacking angle was measured using a digital inclinometer. The experiment was repeated 10 times, yielding an average value of 34.5°.

2.3.2. DEM Model of Sesbania Seed

Based on the shape and average dimensions of the Sesbania seed, a three-dimensional model was constructed and loaded into EDEM. The imported contour model was filled with spherical particles. A higher degree of fidelity in the particle model requires more spherical particles for filling and a smaller particle radius, which increases the demand for simulation time and computational resources. However, using an insufficient number of spherical particles during modeling can lead to increased model error and introduce significant inaccuracies in the inter-particle contact parameter settings during the simulation analysis.

Through pre-simulation experiments, particles with a minimum radius between 0.5 and 1.5 mm were used for automatic filling and adjustment. The models were subjected to a free-fall simulation at a height of 100 mm onto a base plate made of 304 stainless steel. A comparison was made between the simulated rebound heights and the actual rebound heights in terms of their relative disparity. The results indicate that when the minimum radius of the filling particles exceeds 1.1 mm, simulation accuracy decreases. When the minimum radius is below 0.9 mm, there is no significant improvement in simulation accuracy, and when the minimum radius is less than 0.6 mm, a minor Rayleigh time step must be set to ensure stable simulation performance. The time step in the EDEM simulation must be set within the Rayleigh time step. The Rayleigh time step is determined by the shear modulus, density, radius, and Poisson’s ratio of the granular material. If the time step is excessively large, phenomena such as particle explosion or penetration may occur, compromising the accuracy of the simulation results. Ultimately, it was determined that the discrete-element model for the Sesbania seed should consist of spherical particles with radii varying between 0.9 and 1.15 mm, as illustrated in Figure 7. This model exhibits relatively low computational costs and high simulation accuracy, achieving a maximum simulated rebound height of 22.5 mm. This corresponds to a percentage error of 0.22%, in comparison with the mean rebound height of 22.45 mm.

The seed model’s volume distribution was set as a normal distribution. By integrating the measured material characteristic parameters presented in this study with data from References [19,22,23,24,25], the parameters relevant to the stacking simulation were ascertained and subsequently input into the EDEM, as summarized in

Table 1. Material parameters for the simulation.

Material	Parameters	Numerical Value
Sesbania seed	Density (kg/m3)	1.154 × 103
	Poisson’s ratio	0.449
	Elastic modulus (Pa)	5.577 × 107
PMMA	Density (kg/m3)	1.18 × 103
	Poisson’s ratio	0.33
	Shear modulus (Pa)	1.77 × 108
304 Stainless steel	Density (kg/m3)	7.93 × 103
	Poisson’s ratio	0.3
	Shear modulus (Pa)	1.7 × 1011
PLA	Density (kg/m3)	1.11 × 103
	Poisson’s ratio	0.3
	Shear modulus (Pa)	2.2 × 108
6061 Aluminum alloy	Density (kg/m3)	2.7 × 103
	Poisson’s ratio	0.33
	Shear modulus (Pa)	2.7 × 109
Sesbania seed–PMMA	Coefficient of restitution	0.376
	Coefficient of static friction	0.601
	Coefficient of rolling friction	0.211
Sesbania seed–304 Stainless steel	Coefficient of restitution	0.474
	Coefficient of static friction	0.466
	Coefficient of rolling friction	0.222
Sesbania seed–PLA	Coefficient of restitution	0.431
	Coefficient of static friction	0.498
	Coefficient of rolling friction	0.209
Sesbania seed–6061 Aluminum alloy	Coefficient of restitution	0.544
	Coefficient of static friction	0.448
	Coefficient of rolling friction	0.207
Sesbania seeds	Coefficient of restitution	0.161
	Coefficient of static friction	0.677
	Coefficient of rolling friction	0.242

.

2.3.3. Simulated Stacking Angle

The box for the stacking test was three-dimensionally modeled and loaded into EDEM. During the simulation, the total weight of the Sesbania seed model was set to 0.3 kg, and the simulation duration was 3 s. The resulting simulated stacking angle was 47.64°; this corresponds to a percentage error of 38.09%, in contrast to the physical stacking angle of 34.5°. This discrepancy arises because the state of the particle pile is determined by both sliding friction and rolling friction [26], and the contact characteristic parameters of the Sesbania seeds in the model do not perfectly match the actual values. Specifically, the gaps between the spherical particles in the seed model increase the contact area during simulation, leading to deviations. Additionally, the surface of the seed plate used for measuring the contact parameters is relatively uneven, further contributing to errors relative to the measured results and the actual values. Therefore, the relative disparity between the measured and simulated stacking angles should be employed as an indicator when calibrating the contact characteristic parameters of the Sesbania seeds.

2.4. Calibration of Contact Parameters Between Sesbania Seeds

With the contact characteristic parameters of Sesbania seed as experimental factors, the simulated stacking angle as the experimental variable, and the actual stacking angle as the target, a three-factor and three-level Box–Behnken response surface methodology (RSM) experiment was designed. Drawing on the measured contact characteristic parameters and relevant references [27,28], the experimental factors and levels were determined, as presented in

Table 2. Factors and levels for the parameter calibration experiment.

Levels	Factors
	Coefficient of Recovery A	Coefficient of Static Friction B	Coefficient of Rolling Friction C
−1	0.10	0.10	0.01
0	0.30	0.42	0.15
1	0.50	0.74	0.29

. The range of all factors includes the measured values and refers to the parameters of legume seeds in the references. The experimental scheme and outcomes are summarized in

Table 3. Scheme and outcomes of the parameter calibration experiment.

Test Group	A	B	C	Simulated Stacking Angle (°)
1	0	−1	−1	17.41
2	1	1	0	44.19
3	−1	1	0	45.00
4	0	0	0	43.03
5	0	0	0	42.65
6	0	0	0	41.91
7	−1	0	−1	30.26
8	−1	−1	0	22.98
9	0	1	−1	31.74
10	0	0	0	40.49
11	1	−1	0	23.14
12	1	0	1	45.83
13	1	0	−1	29.33
14	0	0	0	40.60
15	0	1	1	53.39
16	−1	0	1	48.93
17	0	−1	1	24.44

.

The quadratic polynomial regression model used to determine the relative disparity between the measured and simulated stacking angles was established by analyzing the experimental data in Table 3 using the Design-Expert 10 software.

$$Y=41.74-0.59A+10.8B+7.98C-0.24AB-0.54AC+3.65BC-0.53A^2-7.38B^2-2.62C^2$$

(7)

where Y is the simulated stacking angle (in °).

The variance analysis of the test data in Table 3 is summarized in

Table 4. Variance analysis of the regression model.

Source of Variance	Mean Square	Freedom	Sum of Squares	p	Significance
Model	1771.78	9	196.86	<0.0001	**
A	2.74	1	2.74	0.2480
B	932.26	1	932.26	<0.0001	**
C	509.76	1	509.76	<0.0001	**
AB	0.24	1	0.24	0.7227
AC	1.18	1	1.18	0.4358
BC	53.36	1	53.36	0.0008	**
A2	1.19	1	1.19	0.4334
B2	229.12	1	229.12	<0.0001	**
C2	28.83	1	28.83	0.0046	**
Residual	12.07	7	1.72
Lack of fit	6.68	3	2.23	0.3120
Pure error	5.38	4	1.35
Sum	1783.85	16

Note: “**” denotes that the item is highly significant (p < 0.01), “*” denotes that the item is significant (p < 0.05).

. In light of the results of the analysis, the simulated stacking angle Y exhibits a highly significant correlation with the coefficient of static friction B, the coefficient of rolling friction C, the interaction term BC, and B² and C². Among these factors, the coefficient of static friction B exerts the most substantial influence on the research outcomes. The p-value for the lack-of-fit term is 0.312, which exceeds 0.05, indicating that the lack-of-fit of the regression model is not significant. This suggests that the regression model demonstrates high fit and the quadratic polynomial simulation is reliable. The coefficient of determination (R²) of the model is 0.9932, and the adjusted coefficient of determination (Adj R²) is 0.9845, both of which are nearly identical to 1. Additionally, the coefficient of variation (C.V.) is 3.57%, and the precision value is 37.296, which exceeds 4, further confirming that the regression model has high credibility and accuracy.

With the physical stacking angle as the target value, the Design-Expert software optimizes and solves the regression model. The objective function and constraint conditions are presented in Formula (8).

$$\left\{\begin{array}{c}Y\left(A, B,C\right)=34.5\\ 0.10\le A\le 0.50\\ 0.10\le B\le 0.74\\ 0.01\le C\le 0.29\end{array}\right.$$

(8)

The calibrated values of the coefficient of restitution, coefficient of static friction, and coefficient of rolling friction between the Sesbania seeds were determined to be 0.168, 0.339, and 0.083, respectively.

3. Results and Discussion

3.1. Verification of Stacking Simulation

The calibrated parameters were substituted for the original seed-model parameters, and the stacking simulation was conducted a second time for verification. After model calibration and vectorization, it was concluded that the simulated stacking angle was 34.90° (Figure 8), with a percentage error of 1.16% relative to the physical stacking angle of 34.5°. These results indicate a minimal discrepancy between the simulation and the actual experimental data. Consequently, subsequent simulation analyses adopted the three calibrated values as the contact parameters for Sesbania seeds.

3.2. Verification of Sowing

To verify whether the discrete-element model of Sesbania seed can be utilized in the optimization analysis of the seeder, a sowing experiment was conducted using the improved spoon-type seeder. The replay-seeding and missed-seeding indexes obtained from the sowing simulation and seeder bench experiments were compared. This comparison further validates the accuracy of the calibrated simulation parameters for Sesbania seed.

3.2.1. Device of Verification

The seeder used in the actual test was a spoon-type seeder with a self-designed spoon plate. The seeder primarily comprises a seed-filling shell, a seed-sowing spoon plate, a seed isolation board, a seed warehouse, an outer shell, and a seed-clearing brush. The seed-filling shell was constructed from PMMA, the spoon plate was fabricated using PLA, the seed isolation board was made of SAE 304 stainless steel, and the seed warehouse was composed of 6061 aluminum alloy. To enhance the simulation efficiency, the seeder structure was simplified by excluding components that would not come into contact with the seeds. The simplified model is presented in Figure 9.

During the seeder’s operation, seeds are transferred from the seed-filling shell into the seeder. As the seed-sowing spoon plate rotates, the spoons’ mouths carry the seeds to the top of the seeder. Impacted by the dual factors of gravity and the seed-clearing brush, the seeds in each spoon’s mouth pass through the seed isolation board and fall into their corresponding seed warehouses. The seed warehouses rotate synchronously, and ultimately, the seeds are discharged through the opening of the outer shell, thereby achieving mechanical seeding.

3.2.2. Sowing Simulation Experiment

During the sowing simulation experiment, the materials of the simulation model were identical to those of the actual device. The simplified three-dimensional model of the seeder was loaded into EDEM, and the material parameters of the seeder components were configured according to Table 1. The total weight of the simulated Sesbania seed model was set to 0.2 kg. The simulation duration comprised 15 s at the low rotational speed (9.26 r/min) and 10 s at the high rotational speed (47.62 r/min). After the simulation, a grid block was added below the seed outlet in the EDEM post-processing module, in which the number of seeds falling was recorded every 0.01 s, as illustrated in Figure 10.

The simulation was conducted three times. The replay-seeding and missed-seeding rates were calculated using Formulas (9) and (10), and the average values were subsequently determined. The final test results indicated a replay-seeding rate of 11.81% and a missed-seeding rate of 7.09%.

$$D={\displaystyle \frac{n_1}{N}}\times 100\%$$

(9)

$$M={\displaystyle \frac{n_2}{N}}\times 100\%$$

(10)

where $D$ is the replay-seeding rate; $M$ is the missed-seeding rate; $n_1$ is the number of instances where the number of dropped seeds exceeds 5; $n_2$ is the number of instances where the number of dropped seeds is fewer than 3; and $N$ is the total number of dropped seeds.

3.2.3. Seeder Bench Experiment

The seeder bench experiment was performed on the computer vision-based seeder test bench in the Intelligent Agricultural Machinery Laboratory at Guangxi University, as illustrated in Figure 11. The test bench parameters were calibrated to align with those of the simulation experiment. The conveyor belt speed was set to 5 km/h, and the seeder rotational speed alternated between 9.26 r/min and 47.62 r/min. A weight of seeds of 0.2 kg was used for testing. The data collection durations were 5 s for low-speed and 3 s for high-speed tests, with 13 datasets processed. After image screening, datasets containing broken seeds or foreign matter were excluded, and only valid data were retained for analysis, to ensure the accuracy of the bench experiment data. The bench experiment results were compared with the simulation test results, as summarized in

Table 5. Comparison between bench experiment and simulation experiment.

Experiment Indices	Simulation Values	Experiment Values	Relative Error
Replay-seeding rate/%	11.81	12.55	5.90
Missed-seeding rate/%	7.09	7.53	5.84

. The replay-seeding rate from the bench experiment was 12.55%, resulting in a percentage error of 5.90% relative to the simulation experiment. The missed-seeding rate from the bench experiment was 7.53%, leading to a percentage error of 5.84% relative to the simulation experiment. Both percentage errors were below 10%. These results confirm the reliability of the Sesbania simulation parameter calibration and validate the applicability of the established discrete-element model for Sesbania seeds used in the seeder simulation experiment.

4. Conclusions

Physical experiments enable the measurement of the material property parameters associated with Sesbania seeds. These parameters encompass the triaxial size, thousand-seed weight, density, Poisson’s ratio, and elastic modulus of the seeds, as well as the coefficients of restitution, static friction, and rolling friction between the seeds and materials such as PMMA, SAE 304 stainless steel, PLA, and 6061 aluminum alloy. Based on these material property parameters of Sesbania seeds, the DEM of the seeds can be constructed.

With the physical stacking angle as the target, the Box–Behnken experimental method, with three factors and three levels, was employed to perform the stacking simulation experiment. This process facilitated the calibration of the contact characteristic parameters between Sesbania seeds. After calibration, the coefficient of restitution, coefficient of static friction, and coefficient of rolling friction between the seeds were determined to be 0.168, 0.339, and 0.083, respectively. The calibrated simulation stacking angle was 34.9°, exhibiting a percentage error of only 1.16% relative to the physical stacking angle.

With the replay-seeding and missed-seeding rates as test indicators, the sowing simulation test results were compared against the bench experiment results. The results indicate that the replay-seeding and missed-seeding rates in the simulation test were 11.81% and 7.09%, respectively, whereas the corresponding rates in the bench experiment were 12.55% and 7.53%. The discrepancies in relative terms between the simulation outcomes and the results from the seeder bench experiments were minor. These results met the technical requirements, confirming that the calibrated simulation parameters for Sesbania seeds can be applied in the seeder simulation experiment.

Through the parameter measurement of Sesbania seeds, it was found that, when compared with the Vigna and Glycine genera, the coefficients of restitution between Sesbania seeds are lower. In contrast, the coefficient of friction is higher. This suggests that Sesbania seeds exhibit weaker fluidity. These considerations provide valuable references for the simulation and optimization of the Sesbania precision seeder. In addition to fulfilling the agronomic requirements for Sesbania sowing, the design of the seeder must also account for seed damage resulting from the operation of its parts and the influence of seed stacking during the seed-carrying process. Seeds can be categorized based on their damage status, and discrete-element modeling can be performed for each category, following the methodologies established for intact seeds [29]. However, this study did not investigate the question of damaged seeds. Future research could involve the statistical analysis of the proportions of various types of damaged seeds within Sesbania seeds and incorporate corresponding discrete-element models into EDEM, in proportion, to enhance the optimization of the seeder design. Additionally, the damage mechanisms relevant to seeds under the forces applied could be investigated, allowing for further refinement of the seeder structure through force simulations conducted in EDEM’s post-processing module [30].