Calibration and Analysis of Seeding Parameters of Soaked Cyperus esculentus L. Seeds

Abstract

The seeds of Cyperus esculentus L. exhibit an uneven surface and irregular shape, which adversely affect precision seeding. Pre-sowing seed soaking treatment not only improves seeding performance, but also enhances the germination capability of C. esculentus seeds. However, the intrinsic parameters of the seeds undergo significant changes after soaking in terms of their physical properties, such as volume, weight, and density. These changes directly influence the fluidity and positioning accuracy of the seeds during the seeding process. Additionally, contact parameters, such as the coefficient of friction and the contact area between the seeds and the seeding apparatus, are altered by soaking. These parameters are crucial for designing efficient seeding devices. Therefore, it is necessary to measure the intrinsic parameters of soaked C. esculentus seeds and their contact parameters with the seeding apparatus to provide parameter support for the precision seeding analysis of pre-soaked C. esculentus. This study focuses on the calibration and experimental investigation of discrete element parameters for soaked C. esculentus seeds. Free-fall collision tests, static friction tests, and rolling friction tests were conducted to calibrate the contact parameters between soaked C. esculentus seeds and between the seeds and steel materials. Using Design-Expert, Plackett–Burman tests, steepest ascent tests, and Box–Behnken response surface tests were designed to obtain the optimal parameter combination for the C. esculentus contact model. The optimal parameters were validated through angle of repose simulation tests and physical experiments. The results indicate that the rolling friction coefficient (F) between seeds, the static friction coefficient (E) between seeds, and the rolling friction coefficient (J) between seeds and steel plates significantly affect the angle of repose. The optimal combination of discrete element parameters is as follows: the static friction coefficient (E) between seeds is 0.675, the rolling friction coefficient (F) between seeds is 0.421, and the rolling friction coefficient (J) between seeds and steel plates is 0.506. Using the calibrated parameters for simulation, the average angle of repose was 32.31°, with a relative error of 1.1% compared to the physical experiments.

1. Introduction

Cyperus esculentus L. is a herbaceous oil seed crop with strong environmental adaptability. It can be planted in barren, marginal, and sandy land, and it has a well-developed root system, offering advantages such as drought resistance, water conservation, windbreak, and sand fixation [1,2]. C. esculentus seeds are nutritionally rich and can be used for various purposes, such as oil extraction, brewing, food, feed, and pharmaceuticals. C. esculentus boasts a high yield, producing 7.5 to 9.0 tons of dried tubers per hectare, with an oil extraction rate reaching up to 24%. The oil yield per unit area exceeds 1800 kg/hm², which is four times that of soybeans and twice that of rapeseed [3].

The “14th Five-Year Plan” for National Planting Industry Development, compiled by the Ministry of Agriculture and Rural Affairs of China, includes C. esculentus as a key variety for the development of oil crops, with its planting area expected to stabilize at about 200,000 mu by 2025 [4]. However, at present, the mechanization technology for C. esculentus planting is still underdeveloped, and there is a shortage of effective C. esculentus machinery, particularly in the area of precision sowing technology, which limits the potential for enhancing both the yield and quality of C. esculentus.

To develop an air-suction-type precision seeder for C. esculentus seeds, it is necessary to measure the characteristic parameters of the seeds and the contact parameters between the seeds and the seeder. However, the uneven and irregular shape of C. esculentus seeds makes it difficult for them to be effectively adsorbed by the seeder, which significantly affects the precision seeding performance. Therefore, soaking the seeds before sowing helps to expand and round their surfaces, improving the seed shape parameters and facilitating effective adsorption during precision seeding. Additionally, soaking activates dormant seeds, enhancing germination rates. However, the characteristic parameters of the seeds change significantly after soaking, making it necessary to accurately measure the intrinsic parameters of soaked C. esculentus seeds and the contact parameters between the seeds and the seeder. This will provide the necessary parameter support for the analysis of the precision seeding of soaked C. esculentus seeds.

The seeder is a core component in the planting of C. esculentus seeds, and the performance of seed filling and discharge is a crucial step in improving efficiency. Traditional optimization processes often fail to account for the contact and motion of C. esculentus seed particles with mechanical components during sowing, making it difficult to achieve the desired optimization goals. The discrete element method, a specialized numerical analysis method for multi-particle systems, has applications across industries such as agriculture and mining. The sowing process of C. esculentus seeds involves classic interactions between particles and mechanical components, making it feasible to conduct calibration simulation experiments using EDEM [5,6,7,8]. A linear function between the zero-level value and the measured value during factor calibration for two key factors—the interspecies static friction factor and the rolling friction factor—of the maize grain bonding model was established, demonstrating that the calibrated contact parameters of the maize discrete elements were plausible [9]. Parameter calibration tests on corn stover–cow dung blends were conducted, using a combination of simulation analysis and physical tests to verify the accuracy of the calibration parameters. The results of the study provide a reference for the discrete element simulation of the compression molding of corn stover–cow dung blends [10]. Parameter calibration tests on potato seeds were also conducted, with the results showing that the simulated particle stacking angle of the calibrated miniature potatoes and the seed distribution matched the real test conditions [11]. The above results demonstrate that using EDEM parameter calibration, the simulation test after the calibration of parameters closely matches the real test population distribution, with no significant differences between the two.

When conducting precision seeding simulation experiments, it is necessary to set the intrinsic parameters of the seeds (density, Poisson’s ratio, shear modulus), as well as the contact parameters between seeds, and between the seeds and seeder materials (static friction coefficient, rolling friction coefficient, restitution coefficient). According to the local standard DB15/T 3454-2024 of the Inner Mongolia Autonomous Region in China, “Technical Regulations for Intercropping of C. esculentus and Soybean”, C. esculentus seeds can be soaked in water at 40 °C to 50 °C or in cold water before sowing [12]. Preliminary experiments have shown that soaking C. esculentus seeds in cold water for 48 h until they are fully swollen results in a very high germination rate and germination potential. After soaking, the seed coat softens, and the granular filling, as well as the geometric characteristics and surface features of the seeds, change significantly. This makes it difficult to achieve the same results in simulation experiments as in actual experiments, necessitating the re-measurement and optimization of the intrinsic characteristics and contact parameters [13,14,15,16,17].

The intrinsic and contact parameters of C. esculentus seeds have been measured by several researchers. These studies solved and calibrated the inter-grain static friction coefficient and inter-grain rolling friction coefficient. The results were verified through seeding simulation experiments, seeder test bench experiments, and field sowing experiments, showing no significant differences between the simulation and real experiments [18,19,20]. However, current research is primarily focused on dry C. esculentus seeds for parameter calibration, without addressing the intrinsic and contact parameters of soaked C. esculentus seeds. Therefore, this study takes soaked C. esculentus seeds as the research object, measures their intrinsic and contact parameters, and constructs a filling model in EDEM. A steel cylinder is used to simulate the angle of accumulation of the seed population. A Plackett–Burman experiment was used to identify the inter-grain rolling friction coefficient, inter-grain static friction coefficient, and the rolling friction coefficient between C. esculentus seeds and the steel plate as significant influencing factors. A steepest ascent experiment was employed to determine the optimal range for these significant factors. Finally, a Box–Behnken response surface experiment was conducted with the goal of minimizing the difference from the actual angle of accumulation of C. esculentus seeds to find the best parameter combination. The results were verified by comparing the simulation and physical experiments, providing parameter support for the analysis of the precision seeding of soaked C. esculentus seeds.

2. Materials and Methods

2.1. Soaking Pre-Treatment of C. esculentus Seeds

Henan Shangqiu Zhongsha No. 2 C. esculentus seeds were selected as the test material. A certain number of seeds were randomly selected, rinsed with water for 10 min, and sterilized with 10% hydrogen peroxide for 30 min, with oscillation and stirring every 10 min. The seeds were then removed and rinsed three times with distilled water, placed in a sterile 500 mL beaker, and immersed in warm water (35 °C). An immersion pre-treatment was set for 48 h, with the water replaced every 12 h, as shown in Figure 1.

2.2. Determination of Physical Parameters of Soaked C. esculentus Seeds

2.2.1. Measurement of Triaxial Dimensions and Density of Soaked C. esculentus Seeds

One hundred soaked C. esculentus seeds were randomly selected, and their length (L), width (W), and thickness (T) were measured using a vernier caliper (accuracy: 0.01 mm). The average values of equivalent diameter (D) and sphericity (Φ) were 12.92 mm and 92%, respectively. The average values for the length (L), width (W), and thickness (T) of the seeds were 14.07 mm, 13.95 mm, and 10.99 mm, respectively. The three-dimensional characteristics of the C. esculentus seeds are shown in Figure 2.

$$D=\sqrt[3]{LWT}$$

(1)

$$\Phi ={\displaystyle \frac{D}{L}}$$

(2)

The triaxial dimensions of C. esculentus seeds after soaking were analyzed using Origin 2024 and were found to be approximately normally distributed, as shown in Figure 3.

Most of the C. esculentus seeds were elliptical. The saturation degree of C. esculentus seeds can be determined by measuring the density, which can also be used as an important parameter for modeling. The DH-300X density measuring instrument was used in the experiment, with measurements repeated in 10 groups. The average density value obtained was 1.185 kg/m³.

2.2.2. Poisson’s Ratio

Poisson’s ratio is the ratio of the corresponding strain perpendicular to the uniaxial strain of the seed in one direction. It is also one of the important parameters for discrete element modeling. In the experimental process, the C. esculentus seeds were loaded in the thickness direction, with the instrument set at a descending speed of 2 mm/min. The loading was stopped when the seed skin appeared to be ruptured, and the thickness was measured using vernier calipers (with an accuracy of 0.01 mm), while the amount of deformation was recorded. In this test, a Beijing Yingsheng Hengtai Technology Co., Ltd., Beijing, China. professional electronic testing machine was used to perform the extrusion test on the soaked C. esculentus seeds, as shown in Figure 4. In total, 10 groups of experiments were conducted. The Poisson’s ratio of the C. esculentus seeds was calculated according to Equation (3).

$$\mathrm{v}={\displaystyle \frac{{\epsilon }_{\mathrm{a}}}{{\epsilon }_b}}={\displaystyle \frac{(w_{\mathrm{b}}-w_a)w_a}{(D_a-D_b)D_a}}$$

(3)

where v is the C. esculentus seed’s Poisson’s ratio; ε_a is a transverse strain of the C. esculentus seed; ε_b is the transverse strain of the C. esculentus seed; ω_a is the initial width of the C. esculentus seed, mm; ω_b is the width of the C. esculentus seed after compression, mm; D_a is the initial thickness of the C. esculentus seed, mm; and D_b is the thickness of the C. esculentus seed after compression, mm.

The mean value of Poisson’s ratio for soaked C. esculentus seeds was measured to be 0.41, based on Equation (3).

2.2.3. Shear Modulus

The magnitude of the shear modulus is a physical quantity that describes the ability of a seed to resist shear deformation [21]. In this paper, an FTC texture meter (TMS-Touch) was used for the extrusion test. During the testing process, soaked C. esculentus seeds were selected and measured using electronic vernier calipers (accuracy of 0.01 mm) to determine their three-axis dimensions. The seeds were placed on the test platform with an initial loading force of 0.3 N and a loading speed of 1.5 mm/min. The computer automatically recorded the pressure change over time during the test. The test was repeated 10 times. The modulus of elasticity of soaked C. esculentus seeds was calculated using Equation (4), and the test setup is shown in Figure 5.

$$E=K_{\mathrm{a}}{\displaystyle \frac{T_C}{A_S}}=K_a{\displaystyle \frac{4T_C}{\pi D^2}}$$

(4)

$$G_{\mathrm{j}}={\displaystyle \frac{E}{2(1+\mu )}}$$

(5)

where E is the modulus of elasticity of the C. esculentus seeds; k_a is the slope of the elastic phase in the curve of pressure with time on the seeds of C. esculentus; T_c is the initial thickness of the extruded C. esculentus seeds, mm; A_s is the equivalent cross-sectional area of the extruded surface of the C. esculentus seeds, mm ²; and G_j is the shear modulus of the C. esculentus seeds.

Combined with the Poisson’s ratio, the shear modulus of the C. esculentus seeds was calculated using Equation (5). The average value of the shear modulus of the C. esculentus seeds was 33 MPa.

2.3. Determination of the Contact Parameters of Soaked C. esculentus Seeds

2.3.1. Static and Dynamic Coefficients of Friction

The coefficient of friction is the nature of the friction between the seed and the contacting surface that produces relative sliding. The determination of the coefficient of friction is one of the important parameters related to the material used to design the seed discharger. The static and dynamic friction coefficients of the test medium for the C. esculentus seeds (steel plates) were determined using a dynamic friction coefficient tester (Xiamen Oriental Instrument Co., Ltd., Xiamen, China, ST-MXZ-1 type). Selected C. esculentus seeds of close size in three axes were peeled, and the skin was tightly fitted on the plate using a strong adhesive. After resting on the seed plate, fitting on the plate took place, resulting in two samples (one on the next). The whole system consisted of the objective stage, control panel, seed plate, drag mechanism, and slider composition. The test device is shown in Figure 6.

One seed plate was placed on the platform of the instrument. Another seed plate was attached to the slider. The moving distance was set at 40 mm, and the instrument was turned on to record the data. The test was repeated 8 times, and the average value was calculated as 0.56 and 0.31 for the static and dynamic friction factors between the seeds of C. esculentus, and 0.57 and 0.4 for the static and dynamic friction factors between the seeds of C. esculentus and the steel plates, respectively.

2.3.2. Collision Recovery Coefficient

The collision recovery coefficient is a parameter concerning the amount of recovery after the collision deformation of the material and the contact panel; it is the ratio of the upward separation velocity after the collision to the vertical downward velocity before the collision [22,23,24]. The contact material panels were selected as C. esculentus seed plates and steel plate materials, and the falling height of the seeds was selected as a fixed height of 30 cm.

Randomly selected C. esculentus seeds free-fall from the drop position; after t1 time of collision with the contact plate (recorded time), the free-fall ends, and the fall speed is V. C. esculentus seeds will produce upward torque after the fall; at this time, the high-speed camera (Phantom T1340) will record the maximum height of seed bouncing (h) and the bouncing speed (V1). The test device is shown in Figure 7.

$$\mathrm{e}={\displaystyle \frac{V_1}{V}}={\displaystyle \frac{\sqrt{2\mathrm{g}h}}{\sqrt{2gH}}}$$

(6)

where e is the collision recovery coefficient; h is the maximum seed bounce height (mm); and H is the seed free-fall height (mm).

The average values of the collision recovery coefficients between the C. esculentus seeds and the seed and steel plates were measured as 0.46 and 0.55, respectively, based on Equation (6).

2.4. Stacking Experiment

Physical Stacking-Angle Measurements

The test was conducted using the bottomless hollow circular steel cylinder lifting method [25,26,27]. The cylindrical cylinder specifications were determined according to the size of the soaked C. esculentus seeds; it had an inner diameter and height of 70 mm and 150 mm, respectively. The lifting speed should not be too fast; through the pre-test, we observed the stacking morphology and comprehensively considered the subsequent simulation to be time-consuming. The experiments were conducted using a lifting speed of 0.04 m/s. In order to ensure that the cylindrical cylinder lifted at a uniform speed, the cylinder was fixed in the texture meter. In order to ensure that the cylindrical cylinder was lifted at a uniform speed, the drum was fixed on the texture apparatus, and the seeds gradually leaked out from the bottom of the drum to form an approximate conical seed pile.

In order to ensure the accuracy of the measurement angle and reduce human error, Matlab 2017 software was utilized for image processing to extract the contour curve of the seed pile. The collective operation steps were as follows: Firstly, we cropped the test image, then took one side of the image at a time for background processing, binarization processing, and extracting the contour curve. Finally, we used the small squares method to fit a straight line to the contour curve, as shown in Figure 8. We repeated five sets of tests to obtain the mean value of the stacking angle, which was 32.68°.

2.5. Simulated Stacking-Angle Test

2.5.1. Discrete Meta-Modeling of Soaked C. esculentus Seeds

C. esculentus seeds are granular materials in Figure 9a. Considering the unevenness of the skin of C. esculentus seeds, in order to accurately establish a discrete elemental model of C. esculentus seeds, inverse general technology was used to establish a three-dimensional model, using a 3D scanner to generate an STL model of the C. esculentus seeds in Figure 9b. This was imported to the EDEM software to consider the efficiency and accuracy of the calibration of the parameters of the discrete elemental simulation and to use the multi-sphere auto-filling modeling approach on the sample model to quickly fill the model with a particle smoothing value of 5. This was combined with 20 small spheres of different particle sizes, and then modified manually in Figure 9c [28,29,30].

2.5.2. Stacking-Angle Instrument Simulation Model and Parameter Setting

The stacking-angle instrument was mapped according to the actual size of the three-dimensional mapping; the drawn three-dimensional model was simplified and imported into the EDEM software. The intrinsic characteristics of the C. esculentus seeds obtained from the test and the contact parameters were entered into the EDEM; the parameters of the steel plate are shown in

Table 1. Steel plate simulation parameters.

Parameters	Numerical Value
Poisson’s ratio of steel plate	0.3
Density of steel plate/(kg·m−3)	7.85 × 103
Shear modulus of steel plate/MPa	7.8 × 104

[31,32]. The particle generation method adopts the normal distribution method, the uniform time in the cylinder to generate 550 seeds, and a precipitation of 0.8 s. All the particles fall into the cylinder, which slowly lifts at a speed of 0.04 m/s. The total length of the simulation is 5 s, which results in the formation of a stable seed pile at the end of the test. An image is collected, and Matlab software is used to determine the population simulation stacking angle and record the tangent value, as shown in Figure 10.

2.6. Test of Stacking Angle

2.6.1. Plackett–Burman Test for Stacking Angle

The Plackett–Burman test was designed by Design-Expert 13 software to take 9 real parameters and 2 virtual parameters, using the angle of stacking of C. esculentus seeds as the response value. The test parameters are shown in

Table 2. Plackett–Burman simulation parameters.

Test Parameters	Encodings
	−1	0	1
Poisson’s ratio of C. esculentus seeds A	0.32	0.41	0.49
Density of C. esculentus seeds B	1.01	1.13	1.23
Shear modulus of C. esculentus seeds C/Mpa	25	33	37
Coefficient of recovery for interspecific collisions in C. esculentus seeds D	0.32	0.46	0.58
Inter-species static friction factor of C. esculentus seeds E	0.42	0.56	0.69
Rolling friction factor between C. esculentus seeds F	0.22	0.31	0.43
C. esculentus seed–steel plate collision recovery coefficient G	0.43	0.55	0.68
C. esculentus seed–steel plate static friction factor H	0.45	0.57	0.69
C. esculentus seed–steel plate rolling friction factor J	0.29	0.40	0.51
Virtual parameter K, L	-	-	-

.

Nine factors, namely Poisson’s ratio, shear modulus, density, interspecies static friction factor, interspecies rolling friction factor, interspecies collision coefficient of recovery of C. esculentus seeds, C. esculentus seed–steel plate static friction factor, C. esculentus seed leaf–steel plate rolling friction factor, and C. esculentus seed–steel plate collision coefficient of recovery, were selected for C. esculentus. The Plackett–Burman test was conducted, and two levels of high and low were set for each parameter based on the actual measurements and the related literature. The test selected three center points, with a total of 15 groups. Each group of tests was simulated after the collection of the corresponding stacking angle image and physical stacking angle. Matlab and Design-Expert 13 were used to measure the simulation of the stacking angle and to undertake the fitting to find the stacking angle.

2.6.2. Maximum Climbing Test Design

The three significant parameters identified through the Plackett–Burman experiment were further tested using the steepest ascent experiment, while other factors were set at their mid-levels. The inter-grain rolling friction coefficient (F), inter-grain static friction coefficient (E), and the rolling friction coefficient between the C. esculentus seeds and the steel plate (J) were taken as the experimental factors, with the angle of accumulation as the response value. The steepest ascent experiment was used to further determine their value ranges, and the design of the steepest ascent experiment is shown in

Table 3. Maximum climbing test design.

Serial Number	Considerations			Stacking Angle θ/°	Relative Error/%
	Interspecies Static Friction Factor (E)	Interspecies Rolling Friction Factor (F)	C. esculentus Seed–Steel Plate Rolling Friction Factor (J)
1	0.40	0.20	0.28	29.81 ± 0.52	8.8
2	0.48	0.26	0.34	30.95 ± 0.69	5.3
3	0.56	0.32	0.4	31.62 ± 0.46	3.2
4	0.64	0.38	0.46	32.15 ± 0.12	1.6
5	0.72	0.44	0.52	33.78 ± 0.33	3.4

.

2.6.3. Box–Behnken Experimental Design

The Box–Behnken experimental design was conducted using Design-Expert 13 software with the experimental parameter design shown in

Table 4. Parameter design of the Box–Behnken test.

Encoding	Experimental Factors
	Interspecies Static Friction Factor (E)	Inter-Species Rolling Friction Factor (F)	C. esculentus Seed–Steel Plate Rolling Friction Factor (J)
−1	0.56	0.32	0.4
0	0.64	0.38	0.46
1	0.72	0.44	0.52

. The inter-grain rolling friction coefficient (F), inter-grain static friction coefficient (E), and the rolling friction coefficient between the C. esculentus seeds and the steel plate (J) were taken as the factors for the response surface experiment. Each factor was set at three levels within its optimal range, and a three-factor, three-level orthogonal experimental design was conducted.

2.6.4. Design of Validation Tests

To study the error between the angle of accumulation obtained from the optimized parameter combination simulation and the angle of accumulation obtained from the experiment, simulations were conducted using the optimized parameter combination for the angle of accumulation. Other non-significant parameters were set at their mid-levels, and the simulation results were compared with the experimental results to verify the reliability of the optimal parameter combination. The verification experiment for the angle of accumulation of the C. esculentus seeds is shown in Figure 11.

3. Results

3.1. Analysis of Plackett–Burman Experiment Results for the Angle of Repose

Variance analysis was conducted on the experimental results, and the model was found to be significant. The factors affecting the experiment were ranked according to their contribution values, as shown in

Table 5. Analysis of simulation parameters in the Plackett–Burman experiment.

Source of Variance	Contribution/%	p-Value	Significance Ranking
Mold	-	0.0078	-
A	1	0.1547	5
B	0.9	0.1735	7
C	1.4	0.1136	4
D	2.8	0.0511	3
E	21	0.0033	2
F	57	0.0008	1
G	0.02	0.7926	8
H	1	0.1565	6
J	6.5	0.0173	3

. Among them, the rolling friction factor (F) between the C. esculentus seeds had the greatest impact on the angle of repose, followed by the static friction factor (E) between the C. esculentus seeds, and finally the rolling friction factor between the C. esculentus seeds and the steel plate.

3.2. Analysis of Steepest Ascent Experiment Results

According to the experimental results, the trend of the angle of repose shows that the relative error first decreases and then increases with the increase in inter-species rolling friction (F), inter-species static friction (E), and the rolling friction factor between the C. esculentus seeds and the steel plate (J). When the inter-species rolling friction (F), inter-species static friction (E), and the rolling friction factor between the C. esculentus seeds and the steel plate (J) are set to 0.64, 0.38, and 0.46, respectively, the relative error between the physical angle of repose and the simulated angle of repose reaches its minimum.

3.3. Analysis of Box–Behnken Experiment Results

The Box–Behnken experiment focuses on several key indicators of the model, including the fitting effect, reliability, lack of fit, and precision. p < 0.01 indicates extremely significant effects, and p < 0.05 indicates significant effects. The overall fitting model has a p-value of 0.0001, indicating a highly significant correlation between the independent and dependent variables. The coefficient of variation (CV) = 0.77% < 10%, indicating the reliability of the experimental basis. The lack of fit term has a p-value of 0.5337 > 0.05, indicating good model fitting with no lack-of-fit phenomenon. The coefficient of determination (R²) of 0.9847 is close to 1 (R²adj = 0.9650, R²pred = 0.8899, R²adj − R²pred < 0.2), indicating the model’s reasonableness. The precision value is 18.19 > 4, indicating good model precision.

The response surface plots of the static friction coefficient (E), rolling friction coefficient (F), and seed–steel plate rolling friction coefficient (J) pairwise interactions with the angle of repose of the C. esculentus seeds are shown in Figure 12. The response surface exhibits a large curvature, indicating that the interactions between the static friction coefficient, rolling friction coefficient, and seed–steel plate collision restitution coefficient significantly affect the angle of repose.

Quadratic regression modeling was performed using Design-Expert 13 software, and the variance analysis of the quadratic polynomial model resulted in the quadratic polynomial regression equation, as shown in Equation (7).

Θ = 4.11 − 0.2738F − 0.4404E + 0.0676J + 0.3027EF + 0.0719EJ + 0.4723EJ − 1.69F² − 1.30E² − 0.8145J²

(7)

3.4. Determining the Optimal Parameter Combination

Using the optimization module of Design-Expert software, the model was optimized with the physical angle of repose of 32.68° as the target. The objective and constraint equations are shown in Equation (8).

$$\left\{\begin{array}{l}\mathrm{Stacking} \mathrm{angle}\left(\mathrm{F},\mathrm{E},\mathrm{J}\right)=32.68\\ \mathrm{s}.\mathrm{t}. \left\{\begin{array}{l} 0.56 \le \mathrm{E} \le 0.72\\ 0.32 \le \mathrm{F} \le 0.44\\ 0.4\le \mathrm{E} \le 0.52\end{array}\right.\end{array}\right.$$

(8)

The optimal combination of parameters was obtained as follows: the static friction coefficient (E) between C. esculentus seeds is 0.675, the rolling friction coefficient (F) is 0.421, and the seed–steel plate rolling friction coefficient (J) is 0.506.

3.5. Verification of Experimental Results Analysis

Simulation was performed using the optimized parameter combinations, and the angle of repose of the C. esculentus seeds was obtained. Three repeated simulation tests were conducted, resulting in an average physical angle of repose of 32.31°, with a relative error of 1.1%. This indicates that the simulation results closely match the physical test values, confirming the reliability of the regression model.

4. Discussion

4.1. Analysis of Seed Parameter Calibration Differences Before and After Soaking

Currently, most researchers primarily focus on dry C. esculentus seeds for parameter calibration. In contrast, this study targets C. esculentus seeds after soaking treatment [17,18,19]. By measuring the intrinsic parameters of soaked C. esculentus seeds and their contact parameters with a seed metering device, we employed the cylindrical lifting method to simulate the bulk angle of repose. Additionally, we utilized free-fall impact tests, static friction tests, and rolling friction tests to calibrate the contact parameters between soaked C. esculentus seeds and between C. esculentus seeds and steel materials.

In the discrete element method (DEM) parameter calibration for C. esculentus seeds after the soaking treatment, it was observed that the soaking treatment significantly affected the physical properties of the seeds. These impact parameters showed consistency compared to dry seeds. Specifically, the rolling friction coefficient, static friction coefficient, and the rolling friction coefficient between the C. esculentus seeds and steel plates had a significant impact on the bulk angle of repose. These impact indicators generally increased after soaking. First, the change in seed shape contour was significant; the seed surface became more regular, and the shape contour became closer to a circular form. This change in shape, combined with the increase in static and rolling friction coefficients, collectively led to an increase in the angle of repose.

4.2. Seed Soaking Pre-Treatment Facilitates Germination

C. esculentus is typically propagated using its tubers as seeds. When dry tubers are used for sowing, the hard outer skin and slow water absorption often result in low germination rates, prolonged germination duration, and weak seedling vigor. These factors subsequently affect the subsequent growth and development of the plants, as well as the final yield establishment. Therefore, soaking C. esculentus tuber seeds before sowing as a pre-treatment can effectively ensure seed germination and improve seedling emergence rate and uniformity [33].

4.3. The Impact of Seed Soaking Pre-Treatment on Cost-Effectiveness in C. esculentus

The surface of C. esculentus seeds is uneven and irregular in shape, which makes it difficult for the seeds to closely adhere to the suction surface of the air-suction seed metering device. This results in suction failure and re-seeding during the sowing process, thereby significantly increasing the rates of seed leakage and re-seeding. Not only does this reduce sowing efficiency, but it can also lead to seed waste and uneven crop growth. To address this issue, this study proposes altering the surface shape of C. esculentus seeds through soaking pre-treatment, making them more conducive to adsorption and discharge by the air-suction seed metering device. The pre-treatment method can effectively improve the contact effect between the seeds and the seed metering device’s suction surface, reducing suction failure and re-seeding phenomena, and thereby lowering the rates of seed leakage and re-seeding.

By optimizing the soaking pre-treatment technology to enhance sowing efficiency, positive impacts are made on environmental sustainability and the cost-effectiveness of precision sowing. Seed waste and the use of pesticides and fertilizers are reduced, and land use efficiency and environmental sustainability are improved.

4.4. Optimization of Sowing for Other Seeds with Irregular Shapes

The irregular shape of seeds presents a significant challenge for seed metering and sowing. Seeds such as corn, peanuts, walnuts, and peas also have irregular surfaces. During mechanized sowing, these irregular shapes often lead to poor compatibility with sowing equipment, thereby affecting sowing efficiency and quality. Through soaking pre-treatment, the seed coat can be softened and the physical properties of the seeds can be improved, making them more conducive to being adsorbed and discharged by sowing equipment, thereby enhancing sowing efficiency.

5. Conclusions

(1) This study takes soaked C. esculentus seeds as the research object. A three-dimensional model was established based on seeds with a high frequency of length, width, and thickness dimensions. A discrete element simulation model of C. esculentus seeds was constructed using particle auto-filling. Combining physical experiments and EDEM simulation experiments, the restitution coefficient, static friction coefficient, and rolling friction coefficient between C. esculentus seeds and steel plates were calibrated through collision rebound tests and static and kinetic friction measurement tests. The experimental results show that the restitution coefficient of C. esculentus seeds against stainless-steel plates is 0.55, and the static and kinetic friction coefficients are 0.57 and 0.4, respectively.

(2) Significant parameter screening and optimization: Through the Plackett–Burman experiment, significant parameters affecting the angle of repose were screened for multiple simulation parameters. The experimental results show that the rolling friction factor (F) and static friction factor (E) between C. esculentus seeds have the most significant impact on the angle of repose, followed by the rolling friction factor (J) between seeds and steel plates. The steepest ascent experiment was used to determine the optimal value range for each significant parameter.

(3) Optimal parameter combination and verification: The Box–Behnken experiment was employed to establish a second-order regression equation for the relative error of the angle of repose. Optimization was performed with the goal of minimizing the relative error of the angle of repose to obtain the best parameter combination: the static friction factor (E) between C. esculentus seeds is 0.675, the rolling friction factor (F) is 0.421, and the rolling friction factor (J) between seeds and steel plates is 0.506. Using this optimal parameter combination for simulation, the average angle of repose obtained is 32.31°. Compared with the results of the physical experiments, the relative error is only 1.1%, indicating that the optimal parameter combination is reasonable. The discrete element simulation parameters calibrated in this study can provide important references for the design and research of precision seeders for C. esculentus seeds.