Establishment of the Interaction Simulation Model between Plug Seedlings and Soil

Abstract

Currently, the simulation parameters for the model of the interaction between the transplanter, the plug seedlings, the soil, and the pot damage mechanism still need to be clarified. The optimization design of the planters and the improvement of planting quality are still urgent issues that need to be solved. In this paper, the simulation parameters of the pot and the soil were calibrated based on the pressure distribution measurement technology. With the actual collision impact force and matrix loss rate as the targets, a four-factor, three-level orthogonal test was designed to obtain the optimal parameters. Through the optimization analysis of the experimental results, it could be concluded that the pot–soil restitution coefficient, the pot–soil static friction coefficient, the pot–soil rolling friction coefficient, and the surface energy were 0.31, 0.88, 0.35, and 1.07 J/m², respectively. The experimental verification of the optimal parameter combination showed that the relative error of the collision impact force was 1.65% and that the relative error of the matrix loss rate was 2.32%, which verified the model’s reliability. Based on the optimal parameters, the movement law of the hole tray seedlings was studied at different positions during the transplanting process. The plug seedlings collided not only with the planter but also with the soil, which led to the breakage and looseness of the pot structure. The relative error between the matrix loss rate of the transplanter inserting soil, the matrix loss rate of the transplanter that did not enter the soil, and the simulated matrix loss rate was less than 10%, which further proved the accuracy of the simulation model.

1. Introduction

Plug seedling pots are mainly composed of peat, vermiculite, perlite, and other agricultural materials in proportion. The seedling’s root system is coiled within the seedling substrate to form a pot with a particular strength and elasticity. Mechanized transplanting can carry out the processes of picking up, feeding, carrying, and planting seedlings [1,2,3,4,5]. The plug seedlings will certainly brush against the planter, soil, etc., and come into contact with them. When it comes to transplanting, pot damage represents a fairly intricate system.

It is challenging to explain pot damage and the variations in plug seedling movements using traditional techniques. Discrete element simulation is a valuable tool in problem solving, especially with the advancement of computer simulation capabilities. When researching the mechanism of the harm caused by marijuana, it is especially appropriate [6,7]. In recent years, scholars have used the discrete element method to study plug seedlings’ pot damage and matrix loss. Tian et al. [8] established a matrix model of different particles based on the discrete element method to study the interaction between steel needles and the matrix. Hu et al. [9] carried out a discrete element model for pot particles and conducted an EDEM–RecurDyn coupling simulation for the removal of seedling claws; they explicitly analyzed the effects of the insertion depth of the removal of the seedling claws and the initial clamping depth of the removal of the seedling claws on the removal effect. Cui et al. [10] analyzed the process of the picking up of seedling pots by the seedling picker via an EDEM–RecurDyn coupling simulation; they obtained better working parameters of the seedling picker and carried out a seedling-picking test verification. The seedling matrix model was developed by Gao et al. using the discrete element approach; thus, the interaction of the steel needle and the seedling matrix was investigated [11]. An EDEM–RecurDyn coupling simulation was used to study the force exerted on the pot during seedling separation. The influence of the planting frequency and the angle of the seedling dropping point on the deflection and fragmentation of the pot was obtained through the response surface method [12]. The discrete element method was used to simulate and analyze the process of the pot seedling lifting, and the mechanism of the matrix loss of the pot and the law of the displacement change of the pot were obtained [13]. A discrete element simulation of the clamping of three different shapes of harvesting manipulators was carried out with the integrity rate of the pot as an index, and it was found that, when the seedling-picking acceleration was 0.3 m/s², the hexagonal finger shovel was the best [14]. Existing studies mainly focus on the mutual movement law between the pot and the seedling claw at the seedling-picking stage. More research is necessary on the interaction law between the transplanter, the plug seedlings, and the soil. Therefore, it is necessary to determine the simulation parameters of the plug seedlings and the soil using physical experiments and to explore the movement law of the plug seedlings and the change law for pot damage.

In this study, the simulation parameters of the pot and the soil were calibrated based on pressure distribution measurement technology. With the actual collision impact force and matrix loss rate as the target, a four-factor, three-level orthogonal test was designed to obtain the optimal parameters. Based on the optimal parameters, the movement law of the plug seedlings during the transplanting process was conducted. Using the matrix loss rate during the transplanting process as the experimental indicator, a soil bin experiment was compared with the simulation to verify the accuracy of the model. This study aims to provide a foundation for the improvement of the planting quality and the optimization of the planting design.

2. Materials and Methods

2.1. Test Material

Inner Mongolia Heyuan Agricultural Technology Co., Ltd. (Hohhot, Inner Mongolia Autonomous Region, China) cultivates oil sunflower plug seedlings with 72 specifications. With a mass ratio of 3:1:1, the seedling matrix consisted of vermiculite, grass carbon, and pearlstone [15]. The age of the seedlings was 30 d. The percentage of moisture content obtained via the oven-drying method was 58.78–62.47%. The growth of the plug seedlings was as expected, and there were no diseases or pests, as shown in Figure 1. In order to simplify the calculation, the mass of the 72 plug seedlings was approximated as the mass of the pot. The upper-surface dimension × bottom surface dimension × height of the 72-plug-seedling pot was 40 mm × 20 mm × 45 mm. The pot volume was 42 cm³ and the density was 357 kg/m³.

2.2. Free-Drop Impact Test

2.2.1. Physical Test of the Free-Drop Impact

The critical components of the free-drop impact examination of the plug seedling, as well as the soil, were the handle, test soil bin, Tekscan pressure distribution measurement device (Tekscan Inc., Boston, MA, USA) [16,17,18], and seedling gripper, as illustrated in Figure 2. There was a 14.52% moisture content in the sandy loam soil. The soil compaction was 90~100 N/cm². The height and width of the soil in the soil bin were 160 mm and 370 mm, respectively. The soil surface was wrapped with a plastic film. To safeguard the sensor and guarantee the buffer performance, it was placed on the plastic wrap surface and covered with a small layer of dirt. Before the experiment, the soil was compacted manually, and the soil compactness was measured using a firmness tester. After each free-drop impact test, the residual matrix on the surface cleaners and the sensor zeroed. This test was mainly conducted as follows: (1) The plastic film was laid on the soil surface, and the 5250 flexible-film-network tactile pressure sensor was deployed to conduct the drop impact test of the plug seedlings at different drop heights. (2) In order to make it possible for the seedling gripper to grasp the pot, the pot’s collision with the earth kept the 20 mm stem below the pot. Various heights of the pots were used to perform the drop impact test. A distribution cloud map was produced that complied with the data obtained from the pressure distribution measurement equipment during testing, including the contact stress, contact area, and peak contact stress [19,20]. After each free-drop impact test, the matrix loss rate and collision impact force were measured. Each group performed the same process several times. Then, the average was obtained at the end. The red block diagram in Figure 2 indicates that some of the sensors were exposed outside, while the rest were located below the surface soil. Its dimensions were 245.9 × 245.9 mm. The degree of spatial resolution was 3.2/cm². The imaging rate was 0~100 Hz and the stress detection limit was 0~0.179 MPa.

2.2.2. Pot Damage Measurement Method

It was vital to examine the matrix loss both prior to and following the free-drop effect of the plug seedlings in order to investigate the law of pot damage. There was more pot damage when the plug seedlings’ matrix loss was higher. Conversely, a decrease in the matrix loss of the plug seedlings resulted in a reduction in pot damage. The matrix loss rate (P₁) represents the percentage of the mass of the seedlings after the free drop and the mass of the matrix before the free drop [21], as shown in Formula (1). After repeated experiments, the matrix loss rate of the plug seedlings was 5.02%.

$$P_1=\frac{M-M_1}{M} \times 100\%$$

(1)

Here, $P_1$ is the matrix loss rate, %; M is the mass of the plug seedlings before the free-drop impact, g; M₁ is the mass of the plug seedlings after the free-drop impact, g.

2.3. Determination of the Contact Parameters of the Pot

2.3.1. Determination of the Restitution Coefficient

The method of free fall is used to determine the restitution coefficient between the pot and the soil [22]. The formula for calculating the collision restitution coefficient is shown in Formula (2):

$$e=v_1/v_2$$

(2)

where $v_1$ is the velocity of the pot before the collision, m/s; $v_2$ is the velocity of the pot after the collision, m/s.

It is assumed that the pot is affected by gravity during the falling process, and the normal velocity of the pot before the collision is obtained by the kinetic energy theorem.

$$v_1=\sqrt{2g{h}_1}$$

(3)

The normal velocity after the collision:

$$v_2=\sqrt{2g{h}_2}$$

(4)

Thus,

$$e=\frac{\left|v_2\right|}{\left|v_1\right|}=\sqrt{\frac{h_2}{h_1}}$$

(5)

where $h_1$ is the drop height of the pot before the collision, mm; $h_2$ is the highest point at which the bounce rises following a collision, mm.

The markers of the pot with better root wrapping were selected and the recovery coefficient was measured. The test surface was 2000 mm away from the high-speed camera lens. The pot’s designated tip rebounded back after falling freely into the test soil bin from a height of 350 mm. The PCO.dimax S4 high-speed camera (PCO Company, Göttingen, Germany) was used to film the pot’s collision process. According to the picture postprocessing program TEMA 3.4, the displacement in the vertical plane was 700 mm and the distance in the horizontal plane was 400 mm. The vertical displacement curve is shown in Figure 3. The final value was determined by repeating each group many times and averaging the results. Therefore, the pot–soil restitution coefficient was 0.24~0.36.

2.3.2. Static Friction Coefficient Test

The process of creating the cylindrical soil block involves filling the cylindrical container with dirt, as seen in Figure 4. The test plane of the inclinometer was fastened to the cylindrical container’s bottom. The spinning was stopped as soon as the pot began to slip, and the angle at that moment was noted. The static friction coefficient between the soil and the pot was calculated using Formula (6). The final value was determined by repeating each group many times and averaging the results. Thus, the pot–soil static friction coefficient was 0.63~0.81.

$$\mu =\tan \phi$$

(6)

Here, $\mu$ is the static friction coefficient; $\phi$ is the angle indicated at which the pot slides within the testing plane, (°).

2.4. Determination of the Contact Model

The EDEM 2018 has many in-built contact models. Mainly, these include the Hertz–Mindlin (no-slip) contact model, the Hertz–Mindlin with bonding contact model, the Hertz–Mindlin with JKR contact model, and the linear-spring contact model. In discrete element simulation, the contact mechanics model directly affects the contact force and torque between particles and has a significant impact on particle bonding collisions. The mechanical model shown in Figure 5 is a spring-damping model that can clearly represent the characteristics of both the elastic and the inelastic contact forces between bonded particles [23,24].

In the process of transplanting, the plug seedling soil has a certain amount of water; so, there is the phenomenon of adhesion between particles. Using the ordinary contact model, it is complex to accurately simulate the mechanical behavior of the plug seedlings after they have been planted in the soil. The Hertz–Mindlin and JKR contact model was chosen; this model introduces surface energy into the interaction between particles and better demonstrates the interaction between the planter and the soil. The tangential elastic force, normal dissipative force, and tangential dissipative force are consistent with the Hertz–Mindlin (no-slip) contact model. The normal elastic force is based on the Johnson–Kendall–Roberts (JKR) theory. The normal force depends on the overlap and the interaction parameter, the surface energy, in the following way [25,26,27]:

$$F_{\mathrm{JKR}}=-4\sqrt{\pi \times \gamma \times E^{\ast }}{\alpha }^{\frac{3}{2}}+\frac{4E^{*}}{3R^{\ast }}{\alpha }^3$$

(7)

$$\delta =\frac{{\alpha }^2}{R^{*}}-\sqrt{\frac{4\pi \times \gamma \times \alpha }{E^{*}}}$$

(8)

where $F_{\mathrm{JKR}}$ is the typical elasticity, N; $\alpha$ is the particles’ contact radius, m; $\delta$ is the overlap between two particles, m; $\gamma$ is the surface energy, J/m²; $E^{*}$ is the corresponding elastic modulus, Pa; $R^{*}$ is the comparable contact radius, m.

The definitions of the equivalent contact radius and the equivalent modulus of elasticity are as follows:

$$\frac{1}{E^{*}}=\frac{1-v_1^2}{E_1}-\frac{1-v_2^2}{E_2}$$

(9)

$$\frac{1}{R^{*}}=\frac{1}{R_1}-\frac{1}{R_2}$$

(10)

where $E_1,E_2$ is the elastic modulus of two contact particles, Pa; $v_1,v_2$ is the Poisson ratio of two contact particles; $R_1,R_2$ is the contact radius of two contact particles, m.

For $\gamma =0$, the Johnson–Kendall–Roberts (JKR) normal elastic force is equal to the Hertz–Mindlin normal force:

$$F_{\mathrm{JKR}}=F_{\mathrm{Hertz}}=\frac{4E^{*}}{3}\sqrt{R^{*}}{\delta }^{\frac{3}{2}}$$

(11)

This model provides attractive cohesion forces even if the particles are not in physical contact. The maximum gap between particles with nonzero force is given by the following:

$${\delta }_{\mathrm{c}}=\frac{{\alpha }_c^2}{R^{*}}-\sqrt{\frac{4\pi \times \gamma \times {\alpha }_c}{E^{*}}}$$

(12)

$${\alpha }_{\mathrm{c}}={\left[\frac{9\pi \gamma R^{*2}}{2E^{*}}-\left(\frac{3}{4}-\frac{1}{\sqrt{2}}\right)\right]}^{\frac{1}{3}}$$

(13)

where ${\alpha }_{\mathrm{c}}$ is the maximum normal clearance between particles with nonzero cohesion, m; ${\alpha }_{\mathrm{c}}$ is the maximum normal clearance between particles with nonzero cohesion, m.

For $\delta >{\delta }_{\mathrm{c}}$, the cohesion force between particles becomes 0. The maximum value of the cohesion force occurs when particles are not in physical contact and the separation gap is less than ${\delta }_{\mathrm{c}}$. The value of the maximum cohesion force, called the pull-out force, is given by the following:

$$F_{\mathrm{cohesion}}=-\frac{3}{2}\pi \gamma R^{*}$$

(14)

2.5. Establishment of the Drop Impact Model between the Pot and the Soil

When the external force on the particles is greater than the bonding force between the particles, the bonding bonds between the particles break down, resulting in the deformation of the pot and matrix loss. Consequently, the model selected to examine the forces between the pot particles and the pot damage processes was the Hertz–Mindlin with bonding model [28,29]. The fundamental particles of the model used for this work were spherical. There were 2587 particles overall, with a particle radius of 1.3 mm. Figure 6 displays the pot’s physical model and its simulation model.

The actual size of the physical test was simplified to improve the simulation efficiency and calculation time. A discrete element model was established for the drop impact between the pot and the soil block (length × width × height was 245.9 × 245.9 × 60 mm) when the drop height was 350 mm. The soil model was the Hertz–Mindlin with bonding. The soil particles were elemental spherical particles with a particle radius of 3 mm, and the total number of particles was 31,239. The simulation parameters of the soil particles have been calibrated through the probe model of the soil, and the compaction meter has been established [30,31] (Figure 7), as shown in

Table 1. Basic parameters of the soil model.

Simulation Parameters	Value
Soil density/(kg/m3)	1452
Poisson’s ratio of soil	0.42
Shear modulus of soil/Pa	1 × 106
Soil–soil restitution coefficient	0.45
Soil–soil static friction coefficient	0.4
Soil–soil rolling friction coefficient	0.3
The normal stiffness coefficient/(N/m3)	24,000,000
The tangential stiffness coefficient/(N/m3)	17,000,000
The critical normal stress/Pa	235,000
The tangential critical stress/Pa	186,000
The particle bonding radius/mm	3.5

. There is a copy of the pot particle coordinates in the particle factory data file called “Particle_Cluster_Data.txt”. Primary data regarding the pot particles are recorded in “Particle Replacement prefs.txt”. The API file “Particlereplacement_v2_x64.dll” with the particle factory was imported into EDEM 2018. The data storage interval was 0.0001 s, while the time step (Rayleigh) was 1%. The grid size was set to 3 times the minimum particle radius. The total movement time was 1.6 s, and the particles’ replacement and bonding time was 1.13 s. The discrete element model of the drop impact between the pot and the soil is shown in Figure 8.

2.6. Simulation Test Design of the Pot–Soil Parameter Calibration

The simulation parameters of the pot model were calibrated between the pot and the steel plate [32]. The pot–soil restitution coefficient, the pot–soil static friction coefficient, the pot–soil rolling friction coefficient, and the surface energy were used as test factors. With the actual collision impact force and matrix loss rate as the target, a 4-factor, 3-level orthogonal test was designed. The test factors and levels of the simulation test are shown in

Table 2. Factors and levels of the simulation test for the collision impact force.

Variable	Factors	Low Level (−1)	Middle Level (0)	High Level (+1)
A	Pot–soil restitution coefficient	0.26	0.37	0.48
B	Pot–soil static friction coefficient	0.75	0.84	0.92
C	Pot–soil rolling friction coefficient	0.35	0.39	0.43
D	Surface energy/(J/m2)	1	1.5	2

. Each group had numerous repeats of the 29 tests, the results of which were averaged. The experimental design and results are shown in

Table 3. Experimental design and results.

No.	Factors				Collision Impact Force/N	Matrix Loss Rate/%
	A	B	C	D
1	−1	−1	0	0	7.01	4.98
2	1	−1	0	0	5.53	3.5
3	−1	1	0	0	5.43	3.43
4	1	1	0	0	4.28	2.65
5	0	0	−1	−1	8.23	5.82
6	0	0	1	−1	7.15	5.12
7	0	0	−1	1	2.93	0.9
8	0	0	1	1	4.75	2.72
9	−1	0	0	−1	11.63	6.6
10	1	0	0	−1	7.31	5.28
11	−1	0	0	1	3.98	2.95
12	1	0	0	1	5.98	3.95
13	0	−1	−1	0	6.27	4.24
14	0	1	−1	0	2.84	0.91
15	0	−1	1	0	5.11	3.08
16	0	1	1	0	4.86	2.83
17	−1	0	−1	0	4.81	2.68
18	1	0	−1	0	5.74	3.71
19	−1	0	1	0	7.32	5.29
20	1	0	1	0	3.79	2.36
21	0	−1	0	−1	9.71	7.68
22	0	1	0	−1	7.06	5.43
23	0	−1	0	1	5.19	3.76
24	0	1	0	1	4.46	2.43
25	0	0	0	0	4.59	3.16
26	0	0	0	0	4.23	2.59
27	0	0	0	0	4.67	2.64
28	0	0	0	0	4.54	2.56
29	0	0	0	0	5.62	2.59

.

2.7. Comparative Analysis of the Pot Damage during the Transplanting Process

Before the test, pretreatments, such as the adjustment of the moisture content, the rotary tillage, and compaction, were needed [33,34]. In the test, the mechanical vibration and the sliding action of the land wheel were not considered, the forward speed of the soil tanker was equal to that of the transplanter, and the influence of the fine soil particles attached to the surface of the hole tray seedling pot was not considered. As shown in Figure 9, this experiment mainly includes the facilitation of the determination of the pot damage of each hole tray seedling. Label paper was tightly attached to the stem of the hole tray seedling. After the transplantation experiment, it was manually excavated from the hole and weighed. A rectangular tunnel was dug in the duckbill drilling and transplanting area, and the soil compactness was adjusted artificially according to the experimental requirements. After the transplanting test, the hole tray seedlings were weighed using an electronic balance. The matrix loss rate of the hole tray seedlings in each group was calculated by Formula (15). Thirty groups were determined in each group and the average value was taken as the final value.

$$K_1=\frac{Q_0-Q_1}{Q_0}\times 100\%$$

(15)

Here, $K_1$ is the matrix loss rate of the hole tray seedling, %; $Q_0$ is the mass of the plug seedlings before transplanting, g; $Q_1$ is the mass of the plug seedlings after transplanting, g.

3. Results and Analysis

3.1. Result and Analysis of the Contact Stress Distribution

Tests for the drop impact on the soil and plug seedlings, as well as on the pot and soil, should be performed at several heights. As seen in Figure 10, the contact stresses and their distribution law were determined using the pressure distribution measuring method. There was minimal tension in the dark-blue area and considerable stress in the red area. The locus of high stress was found approximately in the central region, with the stress levels showing a decreasing pattern from the center of the region to the outside. As the drop height increased, the low-stress distribution decreased significantly.

Table 4. Comparison of the collision impact forces.

Type	Dropping Height/mm
	50 mm	150 mm	250 mm	350 mm
Collision impact force of the whole seedlings/N	5.08	6.08	7.41	8.99
Collision impact force of the pots/N	4.37	5.30	6.52	7.87
Relative error/%	13.98	12.83	12.01	12.46

shows that there was a less than 15% relative inaccuracy between the collision impact force of the pot and the collision impact force of the whole plug seedling. Thus, the pot can replace the collision mechanical characteristics of the whole plug seedling.

3.2. Simulation Parameter Regression Model Establishment and Variance Analysis

Table 5. Analysis of variance (ANOVA) of the collision impact force.

Source	Equation of Squares	Degrees of Freedom	Mean Square	F-Value	p-Value
Model	101.57	14	7.26	44.35	<0.0001 **
A	4.75	1	4.75	29.04	<0.0001 **
B	8.15	1	8.15	49.82	<0.0001 **
C	0.39	1	0.39	2.38	0.1455
D	47.20	1	47.20	288.53	<0.0001 **
AB	0.03	1	0.03	0.17	0.6895
AC	4.97	1	4.97	30.40	<0.0001 **
AD	9.99	1	9.99	61.04	<0.0001 **
BC	2.53	1	2.53	15.45	0.0015 **
BD	0.92	1	0.92	5.63	0.0325 *
CD	2.10	1	2.10	12.85	0.003 **
A2	4.64	1	4.64	28.37	0.0001 **
B2	0.30	1	0.30	1.80	0.2005
C2	0.51	1	0.51	3.12	0.0992
D2	15.43	1	15.43	94.29	<0.0001 **
Residual	2.29	14	0.16
Lack-of-Fit	1.19	10	0.12	0.43	0.8717
Pure Error	1.10	4	0.28
Cor Total	103.86	28
R2	0.9779

Notes: * indicates significant (p < 0.05); ** indicates highly significant (p < 0.01).

displays the analysis of variance (ANOVA) for the aforementioned quadratic regression model of the collision impact force. The regression model had a value of p < 0.0001, which indicated that the factors and the relationship between the response values in this model were significant. It was evident from the lack-of-fit (p = 0.8717 > 0.05) that the regression equation fit perfectly. The coefficient of determination, R², was 0.9779, indicating that 97.79% of the experimental differences could be explained by the model, and the fitting degree with the actual data was relatively high. The correction determination coefficient of this equation, Adj-R² = 0.9559, was very close to 1, which indicated that the regression equation had a high reliability and could be used for further analysis. Excluding insignificant items, the regression model for the collision impact force was obtained as shown in Formula (16):

$$\begin{array}{l}F=4.69-0.63\times A-0.82\times B-1.98\times D-1.12\times AC+1.58\times AD\\ + 0.79\times BC+0.48\times BD+0.73\times CD+0.86\times A^2+1.55D^2\end{array}$$

(16)

where $F$ is the collision impact force, N; $A$, $B$, $C$, and $D$ are the pot–soil restitution coefficient, the pot–soil static friction coefficient, the pot–soil rolling friction coefficient, and the surface energy (J/m²), respectively.

Table 6. Analysis of variance (ANOVA) of the matrix loss rate.

Source	Equation of Squares	Degrees of Freedom	Mean Square	F-Value	p-Value
Model	66.72	14	4.77	21.43	<0.0001 **
A	1.67	1	1.67	7.52	0.0159 *
B	7.62	1	7.62	34.24	<0.0001 **
C	0.82	1	0.82	3.69	0.0752
D	30.78	1	30.78	138.41	<0.0001 **
AB	0.12	1	0.12	0.55	0.4703
AC	3.92	1	3.92	17.63	0.0009 **
AD	1.35	1	1.35	6.05	0.0275 *
BC	2.37	1	2.37	10.66	0.0056 **
BD	0.21	1	0.21	0.95	0.3459
CD	1.59	1	1.59	7.14	0.0182 *
A2	3.39	1	3.39	15.23	0.0016 **
B2	1.12	1	1.12	5.03	0.0417 *
C2	0.38	1	0.38	1.71	0.2117
D2	12.36	1	12.36	55.55	<0.0001 **
Residual	3.11	14	0.22
Lack-of-Fit	2.86	10	0.29	4.41	0.0826
Pure Error	0.26	4	0.065
Cor Total	69.83	28
R2	0.9554

Notes: * indicates significant (p < 0.05); ** indicates highly significant (p < 0.01).

displays the analysis of variance (ANOVA) for the matrix loss rate quadratic regression model mentioned previously. The regression model had a value of p < 0.0001, which indicated that the factors and the relationship between the response values in this model were significant. It was evident from the lack-of-fit (p = 0.0826 > 0.05) that the regression equation fit perfectly. The coefficient of determination, R², was 0.9554, indicating that 95.54% of the experimental differences could be explained by the model, and the fitting degree with the actual data was relatively high. The correction determination coefficient of this equation, Adj-R² = 0.9108, was very close to 1, which indicated that the regression equation had high reliability and could be used for further analysis. Excluding insignificant items, the regression model for the matrix loss rate was obtained as shown in Formula (17):

$$\begin{array}{l}{P}_1=2.55-0.37\times A-0.80\times B-1.60\times D-0.99\times AC+0.58\times AD\\ + 0.77\times BC+0.63\times CD+0.77\times A^2+0.46B^2+1.43D^2\end{array}$$

(17)

where $P_1$ is the matrix loss rate, N; $A$, $B$, $C$, and $D$ are the pot–soil restitution coefficient, the pot–soil static friction coefficient, the pot–soil rolling friction coefficient, and the surface energy (J/m²), respectively.

3.3. Parameter Optimization and Test Verification

Taking the actual collision impact force (F = 7.87 N) and matrix loss rate (P₁ = 5.02%) between the pot and soil with the drop height of 350 mm as the target, the influence parameters were optimized. The optimal parameter combination was obtained as follows: the pot–soil restitution coefficient was 0.31; the pot–soil static friction coefficient was 0.88; the pot–soil rolling friction coefficient was 0.35; the surface energy was 1.07 J/m². The experimental verification of the optimal parameter combination showed that the relative error of the collision impact force was 1.65% and that the relative error of the matrix loss rate was 2.32%, which verified the model’s reliability.

3.4. Analysis of the Movement Process of the Plug Seedlings

During the field transplanting process, the transplanting object was a soft plug seedling, and by using the discrete element method for the simulation analysis, it was possible to obtain microscopic data that could not be obtained from the actual physical experiments. Taking the forward speed of the transplanter as v = 1.25 km/h and the planting depth as h = 80 mm, for example, the simulation was carried out. The simulation parameters of the hole tray seedling and steel plate were obtained from the references. Figure 11 shows the variation pattern of the vertical drop of the plug seedlings. A simulated soil model was formed 5.0 s before the simulation, but the plug seedlings were not generated. The planting device started to move from 5.0 s, and when the planting device reached the designated position, the seedlings began to generate and fall vertically. As can be seen from Figure 11a,b, the plug seedlings moved downward under the influence of gravity and finally fell to the bottom of the planter. Figure 11c shows the movement of the plug seedlings when the planter reached the lowest point. Figure 11d shows that the transplanting device was opened to the maximum and that the plug seedlings fell into the holes. In the process of transplanting, the plug seedlings not only collided with the planter, but also collided with the soil, which led to the breakage and looseness of the pot structure.

3.5. Experimental Study on the Pot Damage during Transplantation

When the forward speed of the transplanter was 1.25 km/h, the planting depth was 80 mm, the soil compactness was 90~100 N/cm², and the hole tray seedlings with 72 specifications were cultivated with the same growth and good root-wrapping degree. Taking the matrix loss rate as the test index, the pot damage experiments of the hole tray seedlings were carried out, and the results were compared with the discrete element simulation. The test results are shown in

Table 7. Comparative analysis of the matrix loss rate during transplanting.

Type	Matrix Loss Rate of the Planter Inserting the Hole	Matrix Loss Rate of the Planter Not Entering the Hole
Test value (%)	14.87	13.86
Simulation value (%)	14.08	12.91
Relative error (%)	5.31	6.85

; it can be seen that the relative error between the matrix loss rate of the transplanter inserting soil, the matrix loss rate of the transplanter that did not enter the soil, and the simulated matrix loss rate was less than 10%, which proved the accuracy of the simulation model.

4. Conclusions

(1)

The simulation parameters of the pot and soil were calibrated based on the pressure distribution measurement technology. With the actual collision impact force and matrix loss rate as the target, a four-factor, three-level orthogonal test was designed to obtain the optimal parameters. Through the optimization analysis of the experimental results, it could be concluded that the pot–soil restitution coefficient, the pot–soil static friction coefficient, the pot–soil rolling friction coefficient, and the surface energy were 0.31, 0.88, 0.35, and 1.07 J/m², respectively. The experimental verification of the optimal parameter combination showed that the relative error of the collision impact force was 1.65% and that the relative error of the matrix loss rate was 2.32%, which verified the model’s reliability.

(2)

Based on the optimal parameters, the movement law of the hole tray seedlings was studied at different positions during the transplanting process. The plug seedlings collided not only with the planter but also with the soil, which led to the breakage and looseness of the pot structure. The relative error between the matrix loss rate of the transplanter inserting soil, the matrix loss rate of the transplanter that did not enter the soil, and the simulated matrix loss rate was less than 10%, which further proved the accuracy of the simulation model.

Based on the preliminary experimental results, this article ultimately determined the interaction parameters between the plug seedlings, planter, and soil. In the next step, we will focus on studying the displacement changes in the plug seedlings during the process of entering and exiting the soil, obtaining the displacement changes in the plug seedlings in the X, Y, and Z directions, and exploring the interaction mechanism between the hole tray seedlings, planters, and soil.