Research on a Vibrationally Tuned Directional Seed Supply Method Based on ADAMS-EDEM Coupling and the Optimization of System Parameters

Abstract

We have combined the theory of bulk dynamics and the agronomic requirements of precision sowing with the aim of resolving the technical problems of poor seed mobility and the difficulty in controlling suction posture, which leads to an increase in the leakage rate and a reduction in seed qualification index scores. In this study, a vibrationally tuned directional seed supply method and system are proposed. We carried out a force analysis of seeds, constructed kinematic equations for seeds and seed boxes to specify the state of the seed motion, and determined the structural parameters and the range of structural parameters that affect the seed suction posture. In addition, we coupled the ADAMS-EDEM simulation of the motion process of the seed and seed boxes and analyzed the vibrational tuning process of the seeds and the angle of inclination of the bottom surface of the seed box. The speed of the eccentric wheel and the eccentric distance were used as test factors. Three-factor and three-level Box–Behnken central combination testing with a single-grain rate, multiple-grain rate, and cavity rate were used as response indicators. Mathematical models were obtained between the experimental factors and the response indicators. Multi-objective optimization of mathematical regression models was carried out with Design-Expert 10.0.4 software. The optimal parameter combination obtained was a tilt angle of 14.27°, an eccentric wheel speed of 4.48 rad/s, and an eccentricity of 1.94 mm. The rate of single grains was 90.75%, the rate of multiple grains was 3.63%, and the rate of cavities was 5.62%. In bench performance tests, using an angle of inclination of 14°, the speed of the eccentric wheel was 4.50 rad/s and the eccentricity was 2 mm. The mean value of the single-grain rate was 89.28%, the mean value of the multiple-grain rate was 3.89%, and the mean value of the cavity rate was 6.83%. The test error was within permissible limits, and reliable results were achieved for parameter optimization. The results met the technical requirements for precision sowing. The results of the study can provide academic references for theoretical research on the methodology of posturing and directional seed supply. They can also provide ideas for the design and development of seed supply systems for precision sowing machinery.

1. Introduction

Seedling transplanting is the main mode of the efficient cultivation of vegetable crops such as dried peppers and processed tomatoes. Compared to the live field model, it has the advantages of protection from natural disasters, high growth intensity, improved crop quality, and higher yields [1,2,3,4].

The hole tray seeder is a key piece of equipment for seedling transplants [5,6]. The most common type of seed sowing machine used at home and abroad is the air-suction seed tray. This machine is classified, according to its principle of construction, as either a flat [7,8,9], roller [10,11,12], or needle [13,14,15] machine. In operation, it uses the negative pressure of airflow to absorb seeds, quantitatively clean them, carry them, and drop them without air. It has the advantages of high productivity and seed adaptability [16,17]. However, the existing air-absorbent seed discharger has a high leakage rate and a low seed pick-up pass rate when faced with irregular small-grained seeds without pelletization [18,19,20]. The reasons for this are as follows: the vacuum negative pressure seed extraction method and structure of the air-absorbent seed discharger make it difficult to regulate the seed suction posture, as well as having poor mobility, resulting in a decline in the accuracy of technical problems related to seed discharge. This inability to consistently and reliably guarantee the “one hole, one seed” precision sowing technology requirement is a direct constraint on the application and promotion of air-suction seed dischargers in the factory nursery of irregular small-grain vegetable seeds.

In recent years, scholars at home and abroad have conducted a great deal of research on the methods and theories of adjusting the seed suction posture and improving seed mobility. In terms of postural adjustments, Zhang et al. [21] designed a hole–slot combination-type hole and clarified the variation rule of rice seed positioning with time, and Chen et al. [22] designed an air-aspirated seed discharger with an inclined convex seed extraction structure. The results showed that the single-grain adsorption rate of the convex disk was better than that of the grooved disk and the flat disk. He et al. [23] designed a positive and negative pressure-type wheat precision seed discharger to limit the seed filling position. The addition of curved auxiliary seed filling plates and seed stirring disks improved single-seed filling performance. Li et al. [24] designed a type-hole insert for grading maize seed. The results showed that seed grading affects the sowing performance. Zhao et al. [25] designed a structure-assisted stabilized suction posture-based air-aspirated precision seeding device for sunflower seeds. The results showed that the parameter combinations for optimal seeding performance were a suction hole width of 10.5 mm and a depth of 3 mm. For improving seed mobility, a discrete element simulation of a hybrid rice vibratory seed homogenizing device was designed by Lu et al. [26]. The results show that when the vibration frequency of the vibrating disk is 57–59 Hz, the seed population is evenly distributed in the vibrating disk, and the sowing effect is better. Liu et al. [27] designed a piezoelectric vibration-type seed leveling device. The results show that the interaction of the vibration direction angle and steering groove angle has a significant effect on the test results. Miao et al. [28] simulated the camphor pine seed population distribution in a vibrating disk using the Hertz–Mindlin no-slip contact model. The results show that when the frequency is 20 Hz and the amplitude is 5 mm, the distribution of the seed population is optimal and the effect of seed absorption is the best. He et al. [29] designed an electromagnetic vibrating single-bud sugarcane seeding device. The results showed that the primary and secondary factors affecting the quality index of the row of seeds were the amplitude, frequency, and helix angle. In summary, the researchers all achieved some results in this field. However, the various machines developed are either complicated by a great number of mechanisms or complicated in structure. This may be due to an adjustment of the seed suction posture that is not organically combined with high mobility. The result is that existing seed dischargers are not effective when faced with small, irregular particles of seeds that have not been pelletized. The problem of their high leakage rate and low seed-take rate has not been effectively addressed.

For these reasons, in this study, a vibratory position-directed seed supply method and system is proposed. This method combines the theory of bulk dynamics and the agronomic requirements of precision sowing. Force analysis of seeds is carried out to construct the kinematic equations of the seed and the seed box, to clarify the state of the seed motion, and to determine the structural parameters and ranges affecting the suction posture of the seed. The ADAMS-EDEM coupled simulation of the motion process of the seed and the seed box is performed to analyze the vibration tuning process of the seed. Using the inclination angle of the bottom surface of the seed box, the rotational speed of the eccentric wheel, and the eccentric distance as test factors, and using the single-grain rate, the multigrain rate, and the cavity rate as response indices, a three-factor and three-level Box–Behnken central combination test was carried out to optimally solve the optimal parameter combinations of the key components. The aim was to provide insights for theoretical research on the method of position-directed seed supply and to provide ideas for the design and development of a seed supply system of precision sowing machinery.

2. Vibratory Position Directional Seed Supply System and Working Principle

2.1. Vibratory Position Directional Seed Supply System

As shown in Figure 1, the vibratory position directional seed supply system mainly consists of a first-order height-limiting partition, a second-order height-limiting partition, a Y-type guide groove, a position-adjusting inclined surface, a seed standing support surface, a U-shaped fork, an eccentric wheel, etc. In this case, the eccentric wheel, the U-fork, the support seat, and the seed box constitute the vibration system. The eccentric wheel rotates periodically which, in turn, drives the seed box to vibrate periodically around the outer surface of the seed discharge drum.

2.2. Working Principle of Vibratory Position Directional Seed Supply

During operation, the eccentric wheel drives the posturing seed box to vibrate periodically around the outer surface of the drum. The cyclic vibration of the position-controlled seed box “boils” the seeds inside. The seed is subjected to an inertial force Fg. The horizontal component of the inertial force Fgx causes the seed to move along the Y-shaped guide groove towards the hole in the surface of the seed discharge drum, as shown in Figure 2e. The Y-type guide groove transition with this arc connection prevents seed collisions at transitions, as shown in Figure 2d. The vertical component of the inertial force Fgy makes the seeds “boil”, preventing seed-to-seed and seed layer-to-seed layer interaction forces from constraining seed movement. This results in an improvement in seed mobility, as shown in Figure 2e. After the seed has moved along the inclined bottom surface to the attuned inclined surface, seeds “glide” along the position-adjusted inclined plane. Seeds are constantly adjusting their position as they glide along. The seed assumes a “standing” position after sliding over the stance ramp, as shown in Figure 2a, matching the holes in the drum surface and lying flat. Seeds are stably adsorbed by the surface pores of the drum, rotating the seed discharge drum through the seed carrying area to the seed feeding area. In the seed drop zone, the seed is dropped by its own gravity and repulsive force into the hole tray to complete the sowing before the next cycle of seeding is performed.

The height H₁ of the first-order height-limiting partition from the bottom surface of the seed box is greater than the maximum value of the vertical height of two seeds lying flat and less than the minimum value of the vertical height of three seeds lying flat. Only two layers of seeds are allowed to pass sideways underneath the first-order height-restricted partition, controlling seed layer thickness between the two-order height-limiting partitions, as shown in Figure 2c. The height H₂ of the second-order height-limiting partition from the bottom of the seed box is greater than the maximum value of the lateral height of a single seed and less than the minimum value of the lateral height of two seeds. The passage under the second-order height-restricted bulkhead is limited to a single layer of seeds standing on their sides, as shown in Figure 2b. First- and second-order height-limiting bulkheads are curved. The distance between the height-limiting partition and the inclined bottom surface of the seed box decreases gradually, allowing progressive control of the seed layer thickness and preventing seed congestion that leads to increased seeder leakage.

3. Characterization of Seed Vibration Attunement Motion

3.1. Analysis of Cyclic Vibration Law of Seed Box

The vibratory posturing seed box consists of U-forks and support brackets mounted on the surface of the seed discharge drum and frame. When working, the eccentric wheel rotates as the master motion, and the seed box vibrates periodically as the slave motion. The eccentric wheel rotates at a constant speed to drive the posturing seed box to vibrate periodically around the surface of the seed discharge drum.

Assuming that the speed of the eccentric wheel is r, rad·s⁻¹; the rotation time of the eccentric wheel during one vibration cycle is t, s; and the angle of rotation of the eccentric wheel is θ, the following will hold true:

$$\theta =2\mathsf{\pi }tr$$

(1)

It should be assumed that the inclined base of the seed box is AB. The inclined bottom surface of the seed box should not be restricted by the center of the rotation; it should be free to flatten. As shown in Figure 3, P is the geometric center of the eccentric wheel, O is the center of rotation of the eccentric wheel, R is the geometric radius of the eccentric wheel (mm), r is the radius of the base circle of the eccentric wheel (mm), d is the eccentricity distance (mm), the projection of the eccentricity d on the line PM is PQ, and S is the translational displacement of the inclined base of the seed box (mm), the endpoints of the displacement S are M and N, as shown in the following equation:

$$S=R-r-d\cos 2\mathsf{\pi }tr$$

(2)

Considering the motion limitation of the seed box’s center of rotation on the inclined bottom surface of the box, the inclined bottom surface of the seed box rotates around the center of the seed discharge roller, as shown in Figure 4. Assuming that the geometrical center of the cross-section of the seed discharge drum is E, the distance between the geometric center of the cross-section of the seed discharge roller and the tangent of the inclined bottom surface of the seed box and the eccentric wheel in the initial state is L (mm), and the angle of rotation of the inclined base of the seed box is α, the following equation will hold true:

$$\alpha =\arctan \frac{R-r-d\cos 2\mathsf{\pi }tr}{L}$$

(3)

It is assumed that the distance between the seed on the inclined bottom surface of the seed box and the geometric center of the cross-section of the seed discharge roller is D, mm, and the displacement of the seed under the driving action of the eccentric wheel is X, mm. This is based on the principle of similarity. As a result, the following equation will hold true:

$$\frac{X}{S}=\frac{D}{L}$$

(4)

If we substitute Equation (3) into Equation (4), the following equation will apply:

$$X=\frac{D}{L}\left(R-r-d\cos 2\mathsf{\pi }tr\right)$$

(5)

During the push–stroke movement of the eccentric wheel, which results in the gradual increase in the vertical distance between the center of rotation of the eccentric wheel and the inclined bottom surface of the seed box from (R − d) cm to (R + d) cm, the seed box and the seed move synchronously. During the return movement of the eccentric wheel, the vertical distance between the center of rotation of the eccentric wheel and the inclined bottom surface of the seed box decreases gradually. Due to the tension of the support spring, the inclined bottom surface of the seed box accelerates the return journey against the eccentric wheel. Assuming that the coefficient of strength of the support spring is K (N/m), the shape variable of the support spring is ∆x (mm), and the spring force of a single support spring is F (N), the following equation will apply:

$$F=4K\Delta x$$

(6)

If we assume that the acceleration during the return journey of the seed box is a_b (m·s⁻²), the mass of the seed box is M (kg), g is the acceleration of gravity (m·s⁻²), and G is the gravity of the seed box (N), the following equation will apply:

$$\{\begin{array}{l}M{a}_b=4K\Delta x+G\cos \alpha \\ G=Mg\end{array}$$

(7)

From Equation (7), we can observe that, during the return movement of the seed box, the acceleration of the seed box in the direction of the axis of the support spring is greater than the acceleration of gravity in the direction of the axis of the support spring. Therefore, the seed box will be separated from the seed during the return journey. Due to inertia, the seed will move in a parabolic motion under the acceleration of gravity. Assuming that the seed mass is m (kg), the partial acceleration of the seed perpendicular to the direction of the inclined base of the seed box is a_sx (m·s⁻²), and the partial acceleration of the seed in the direction parallel to the inclined base of the seed box is a_sy (m·s⁻²), the following equation will apply:

$$\{\begin{array}{l}{a}_{sy}=g\cos \alpha \\ a_{sx}=g\sin \alpha \end{array}$$

(8)

3.2. Analysis of the Law of Motion of Seeds That are “Boiling”

At the moment of separation of the seed box from the seed, we can assume that the common velocity of the seed box and the seed is v, m·s⁻¹, based on the law of conservation of energy. As a result, the following equation will hold true:

$$\frac{1}{2}\left(M+m\right)v^2+\left(M+m\right)g\Delta x+4\times \frac{1}{2}K{\delta }^2=Es$$

(9)

The following will also hold true:

$$Es=4\times \frac{1}{2}K{\left(\Delta x+\delta \right)}^2$$

(10)

If we substitute (10) into (9), we will achieve the following result:

$$v=\sqrt{\frac{4K\Delta x^2\left(\Delta x+2\delta \right)}{M+m}-2g\Delta x}$$

(11)

The seed box will be separated from the seed. Due to the inertial force, the seeds are in a free upward motion. Assuming that the height of the seed during its free upward motion is h_s, mm, the following will be true:

$$v^2=2g{h}_s$$

(12)

This can also be expressed as follows:

$$h_s=\frac{2K\Delta x\left(\Delta x+\delta \right)}{g\left(M+m\right)}-\Delta x$$

(13)

From Equation (13), we can see that the free upthrow height of the seed is related to the stiffness coefficient of the support spring K, the deformation caused by the eccentric wheel Δx, the mass of the seed box M, and the mass of the seed m. After the seeds and seed boxes are separated, the seed box is subjected to the combined action of the supporting spring tension and its gravity. As seed boxes begin their return movement, and the acceleration gradually increases in the return motion, the upward height of the seed box is assumed to be h_b, mm, based on the law of conservation of energy. As a result, the following will be true:

$${K{h}_b}^2+2Mg{h}_b-M{v}^2+2Mg\delta -4K{\delta }^2=0$$

(14)

This can also be expressed as follows:

$$h_b=\sqrt{\frac{M{v}^2+4K{\delta }^2-2Mg\delta }{K}}-\frac{Mg}{K}$$

(15)

The mass of the seed box M is 2.5 kg. In the seed supply performance test, Nongkang Dried Pepper King was selected as the test subject, and its thousand-grain weight was 5.7064 g. Based on Equations (11), (13) and (15), we can obtain the following: when the eccentric wheel eccentricity is 2 mm, the upward distance h_b of the seed box is 4 mm, the distance h_s of the upward movement of the seeds is 10.68 mm, and the upthrow height of dried chili seeds after separation from the inclined bottom of the seed box is 6.68 mm. Therefore, the height of the second-order height-limiting spacer from the inclined bottom surface of the seed box should be not less than 6.68 mm.

3.3. Analysis of the Mechanism of Seed Precision-Guided Movement

During operation, the eccentric wheels drive the posturing seed box to vibrate periodically around the outer surface of the drum. The cyclic vibration of the position-controlled seed box “boils” the seeds inside. The seed is subjected to an inertial force Fg. The horizontal component of the inertial force Fgx causes the seed to move along the Y-shaped guide groove towards the hole in the surface of the seed discharge drum. The width of the Y-type guide groove is gradually reduced. Only single-listed dried chili seeds are allowed to pass through, eventually. As shown in Figure 5a, the Y-type guide groove transition with the arc connection prevents seed collisions at transitions, and the vertical component of the inertial force Fgy makes the seeds “boil”. This prevents inter-seed and inter-seed layer interaction forces constraining seed movement and improves the mobility of seeds and seed layers.

The height H₁ of the first-order height-limiting partition from the bottom surface of the seed box is greater than the maximum value of the vertical height of two seeds lying flat and less than the minimum value of the vertical height of three seeds lying flat. Only two layers of seeds are allowed to pass sideways underneath the first-order height-restricted partition, controlling the seed layer thickness between the second-order height-limiting partitions. The height H₂ of the second-order height-limiting partition from the bottom of the seed box is greater than the maximum value of the lateral height of a single seed and less than the minimum value of the lateral height of two seeds. Passage under the second-order height-restricted bulkhead is limited to a single layer of seeds standing on their sides. First- and second-order height-limiting bulkheads are curved. The distance between the height-limiting partition and the inclined bottom surface of the seed box decreases gradually, allowing progressive control of seed layer thickness and preventing seed congestion. This leads to a lower seeding pass rate for planters, as shown in Figure 5b.

3.4. Analysis of Seed Vibration Position Adjustment Mechanism

After the seed has moved along the inclined bottom surface to the attuned inclined surface, the seeds “glide” along the position-adjusted inclined plane, constantly adjusting their position during the glide. As shown in Figure 6, for seed position adjustment states 2, 4, 5, and 6, the seed assumes a “standing” position after sliding over the stance ramp. As shown in the second seed position adjustment state, in Figure 6, the holes in the drum surface can be matched for the seeds to lie flat. Seeds are stably adsorbed by the surface pores of the drum. By rotating the seed discharge drum through the seed carrying area to the seed feeding area, in the seed drop zone, the seed is dropped by its own gravity and repulsive force into the hole tray to complete the sowing. Subsequently, the next cycle of seeding can be performed.

4. ADAMS-EDEM Coupled Simulation Test

4.1. Design of Experiments for Coupled ADAMS-EDEM Simulation

4.1.1. Construction of a Physical Model of the Seed Box

For simulation purposes, the simplification and physical modeling of the seed supply system structures were carried out. The seed supply system consists of a seed discharge roller, a seed box, an eccentric wheel, a left support seat, a right support seat, and a spring, as shown in Figure 7a. The seed discharge roller had a diameter of 100 mm, a length of 246 mm, a hole diameter of 8 mm, and a hole spacing of 32 mm. The length of the seed box was 200 mm, the width of the seed stand support surface was 1 mm, the position incline was a circular arc with a radius of 2 mm, and the inclined base was 33 mm. The second-order height-limiting spacer was 12.39 mm from the stance ramp (three times the width of the seed) and the first-order height-limiting spacer was 20.65 mm from the stance ramp. The first- and second-order height-limiting partitions were curved, with a radius of 8.26 mm. The height of the first-order height-limiting partition was 38.26 mm and the height of the second-order height-limiting partition was 8.26 mm. The width of the Y-type guide groove was gradually reduced from 32 mm to 4.5 mm until a single column of seeds was allowed to pass. The seed box support base consisted of four stepped columns for mounting the springs to the frame. The first-order stepped cylinders were 16 mm in diameter and 5 mm thick. The second-order stepped cylinders were 12 mm in diameter and 5 mm in thickness. The distance between the centers of the two adjacent stepped cylinders was 38.24 mm. The eccentric wheel had a diameter of 10 mm, an eccentricity of 2 mm, a thickness of 3 mm, and a rotational speed of 1080 °/s. The eccentric wheel had a diameter of 10 mm, an eccentricity of 2 mm, and a thickness of 3 mm.

4.1.2. Multi-Body Dynamics Modeling and Parameter Setting

The seed box physical model was imported into ADAMS. The assembly consisted of the following five parts: the seed discharge roller, the seed box, the eccentric wheel, the left support seat, and the right support seat. The component materials were added, including the seed discharge roller, seed box, eccentric wheel, left support seat, and right support seat. The following settings were used in STEEL: Poisson’s ratio was set to 0.29, density was set to 7801 kg/m³, and Young’s modulus was set to 2.07 × 10¹¹ Pa. Then, we added connectors and a fixed joint for the seed roller, left support, and right support. We revolved the joint for the eccentric wheel, added motions, revolved the joint of the eccentric wheel again, and added rotational joint motion. Then, we added the following forces: two for each of the left and right supports, creating a translational spring damper. The spring-damping coefficient was set to 0.06 N/(m/s) and the spring stiffness coefficient was set to 150 N/mm. We added contact and contact force between the seed box and drum, using contact force of the solid-to-solid type. Then, we added contact force between the seed box and the eccentric wheel, using contact force of the solid-to-solid type. Subsequently, we added a general force vector to the seed discharge roller, seed box, eccentric wheel, left support seat, and right support seat, as shown in Figure 7b.

4.1.3. Discrete element Model Building and Parameter Setting

We imported the seed box physical models into EDEM with the control-type minimum size option set to 0.1. The assembly consisted of the following five parts: the seed discharge roller, the seed box, the eccentric wheel, the left support seat, and the right support seat. We added material properties, using the same material property settings as in ADAMS. Each component was made of steel. Poisson’s ratio was set to 0.29, density was set to 7801 kg/m³, and Young’s modulus was set to 2.07 × 10¹¹ Pa. We used the steel property parameters specified in the ADAMS Software (2020, HEXAGON, Chantilly, VA, USA). The coefficient of recovery between the seed box and the seed granular material was 0.6, the coefficient of static friction was 0.3, and the coefficient of rolling friction was 0.12 [30]. The drop zone was located above the seed box; the drop zone length was 180 mm and the drop zone width was 25 mm, as shown in Figure 7c.

4.2. Seed Supply Performance Simulation Test Program

Nongkang Dried Pepper King was selected as the test object, its three-axis dimensions were measured, and a physical model was constructed. The state of motion of the seeds in the seed box can be deconstructed into two parts. One of these is the movement along the Y-type guide groove on the bottom surface of the seed box to the hole on the surface of the seed discharge drum. During movement, the seed is subjected to friction from the bottom surface of the seed box, which is related to the angle of inclination of the seed box. The second part is the vertical component of the inertial force Fgy, which causes the seeds to “boil”. Under- or overboiling of the seed will result in the seed not being able to pass through the height-limiting partition, which directly affects the eligibility index of the discharged seed. The seed’s boiling state is related to the eccentric wheel speed and eccentric distance. Therefore, a three-factor, three-level Box–Behnken central combination design experiment was used with a single-grain rate, multiple-grain rate, and voiding rate as the main performance indicators. The trial was divided into 17 groups according to the design requirements of the Box–Behnken central combination design trial. The range of values for the factors affecting seed supply performance was determined based on previous trials. The bottom of the seed box was inclined at an angle of 10–20°, the speed of the eccentric wheel was 3–5 rad/s, and the eccentric distance was 1–3 mm. Each group of tests was repeated three times, and the average value was used as the result of that group of tests. Data were processed using Design Expert 10.0.4. Fitted regression equations were established between each test factor and the response indicator. The optimal combination of parameters for the angle of inclination of the bottom surface of the seed box was determined using the speed of the eccentric wheel and the eccentric distance. This provided a basis for the optimal design of the structural parameters of the seed box. The coding of the experimental factors is shown in

Table 1. Coding table of test factors.

Coded Value	Considerations
	Tilt Angle X1/°	Eccentric Wheel Speed X2/rad·s−1	Eccentricity X3/mm
−1	10	3	1
0	15	4	2
1	20	5	3

.

4.3. Test Results and Analyses

The orthogonal test protocol and results are shown in

Table 2. Orthogonal test scheme and results.

Serial Number	X1/ °	X2/ rad·s−1	X3/ mm	A /%	D /%	M /%
1	10	3	2	79.78	6.29	13.93
2	20	3	2	86.61	6.95	6.44
3	10	5	2	87.83	4.32	7.85
4	20	5	2	83.32	8.77	7.91
5	10	4	1	85.48	4.37	10.15
6	20	4	1	84.55	8.18	7.27
7	10	4	3	83.56	5.61	10.83
8	20	4	3	85.86	8.21	5.93
9	15	3	1	86.43	4.74	8.83
10	15	5	1	89.19	5.14	5.67
11	15	3	3	86.62	4.66	8.72
12	15	5	3	89.68	5.27	5.05
13	15	4	2	89.72	3.84	6.44
14	15	4	2	90.11	4.28	5.61
15	15	4	2	90.46	3.11	6.43
16	15	4	2	90.81	3.48	5.71
17	15	4	2	92.13	2.86	5.01

, and the ANOVA is shown in

Table 3. Analysis of variance of orthogonal experiment results.

Source	Percentage of Seeds Per Kernel				Multiplicity				Cavitation Rate
	Sum of Squares	df	F	p	Sum of Squares	df	F	p	Sum of Squares	df	F	p
Model	165.83	9	33.33	<0.0001	50.56	9	21.25	0.0003	89.14	9	33.03	<0.0001
X1	1.70	1	3.08	0.1228	16.59	1	62.75	<0.0001	28.92	1	96.45	<0.0001
X2	13.99	1	25.31	0.0015	0.0924	1	0.3497	0.5729	16.36	1	54.56	0.0002
X3	0.0006	1	0.0011	0.9744	0.2178	1	0.8238	0.3942	0.2415	1	0.8055	0.3993
X1X2	32.15	1	58.15	0.0001	3.59	1	13.58	0.0078	14.25	1	47.53	0.0002
X1X3	2.61	1	4.72	0.0664	0.3660	1	1.38	0.2778	1.02	1	3.40	0.1076
X2X3	0.0225	1	0.0407	0.8459	0.0110	1	0.0417	0.8440	0.0650	1	0.2169	0.6556
X12	92.59	1	167.48	<0.0001	23.34	1	88.27	<0.0001	22.96	1	76.57	<0.0001
X22	10.40	1	18.82	0.0034	2.15	1	8.12	0.0247	3.10	1	10.33	0.0148
X32	5.04	1	9.12	0.0194	2.21	1	8.35	0.0233	0.5764	1	1.92	0.2081
Residual	3.87	7			1.85	7			2.10	7
Lack of fit	0.4613	3	0.1804	0.9045	0.5655	3	0.5867	0.6551	0.6320	3	0.5745	0.6615
Pure error	3.41	4			1.29	4			1.47	4
Cor total	169.70	16			52.41	16			91.24	16

. Data were processed using the Design Expert 10.0.4 software. The fitted regression equations between the angle of inclination of the bottom surface of the seed box X₁, the rotational speed of the eccentric wheel X₂, and the eccentric distance X_3, on the one hand, and the rates of single grains A, multiple grains D, and cavitation M, on the other hand, were established as follows:

$$\begin{gathered} \begin{array}{l}A=-16.349+7.664X_1+22.252X_2+1.663X_3-0.567X_1{X}_2+0.162X_1{X}_3+0.075X_2{X}_3\\ \hspace{1em}\hspace{1em}-0.188X_1^2-1.572X_2^2-1.094X_3^2\end{array} \\ \begin{array}{l}D=43.922-3.174X_1-8.554X_2-2.035X_3+0.190X_1{X}_2-0.061X_1{X}_3+0.053X_2{X}_3\\ \hspace{1em}\hspace{1em}+0.094X_1^2+0.714X_2^2+0.724X_3^2\end{array} \\ \begin{array}{l}M=72.426-4.490X_1-13.698X_2+0.371X_3+0.378X_1{X}_2-0.101X_1{X}_3-0.128X_2{X}_3\\ \hspace{1em}\hspace{1em}+0.093X_1^2+0.858X_2^2+0.370X_3^2\end{array} \end{gathered}$$

(16)

Significance analysis of the regression models was carried out. From the ANOVA table, it can be observed that the models for the experimental indicators’ row seeding eligibility, reseeding, and leakage indices were highly significant (p < 0.01), the misfit terms were not significant (p > 0.05), and the regression equations were not misfit. Upon removing the insignificant terms from the regression model, the following fitted regression equation was obtained:

$$\begin{gathered} A=-16.349+7.664X_1+22.252X_2-0.567X_1{X}_2-0.188X_1^2-1.572X_2^2-1.094X_3^2 \\ D=43.922-3.174X_1+0.190X_1{X}_2+0.094X_1^2+0.714X_2^2+0.724X_3^2 \\ M=72.426-4.490X_1-13.698X_2+0.378X_1{X}_2+0.093X_1^2+0.858X_2^2 \end{gathered}$$

(17)

The regression model fitting coefficient of determination R² was 0.9772, 0.9647, and 0.9770, indicating that the regression model predicted a value with a high correlation with the actual value. The p-values of the misfit terms were 0.9045, 0.6551, and 0.6615, respectively, which were all greater than 0.05, indicating that the regression equations were well fitted. This equation can be used to optimize the structural parameters of the vibrationally tuned seed box.

Based on Table 3, the ANOVA of the orthogonal test results showed that the order of influence of the test factors on the evaluation indices of the seed supply performance was the eccentric wheel speed, eccentric distance, and tilting angle of the bottom surface of the seed box. The interaction term X₁X₂ of the angle of inclination of the seed box bottom and the speed of the eccentric wheel had a significant effect on the rate of single grains, multiple grains, and cavitation.

Response surface plots of the effect of the interaction of the angle of inclination of the bottom surface of the seed box and the rotational speed of the eccentric wheel on the rate of single grains, multiple grains, and cavitation were obtained by using Design Expert V 10.0.4 software, as shown in Figure 8.

Based on Figure 8a, when the rotational speed of the eccentric wheel was 4 rad/s and the angle of inclination of the bottom surface of the seed box gradually increased, the single-grain rate showed an increasing and then decreasing trend of change. There was a gradual increase in the percentage of single grains when the angle of inclination of the bottom of the seed box was increased from 10° to 15.24°. The percentage of single grains decreased gradually when the angle of inclination of the bottom of the seed box was increased from 15.24° to 20°. The maximum value of 90.66% was obtained when the bottom of the seed box was inclined at an angle of about 15.24°, when the angle of inclination of the bottom of the seed box was 15°, and the speed of the eccentric wheel was gradually increased. The single-grain rate showed an increasing and then decreasing trend of change. With an increase in the eccentric wheel speed from 3 rad/s to 4.42 rad/s, the single-grain rate gradually increased. As the speed of the eccentric wheel was increased from 4.42 rad/s to 5 rad/s, the rate of single grains gradually decreased. At an eccentric wheel speed of about 4.42 rad/s, the single-grain rate showed a maximum value of 90.92%.

Based on Figure 8b, when the rotational speed of the eccentric wheel was 4 rad/s and the angle of inclination of the bottom surface of the seed box gradually increased, the multigrain rate showed a decreasing and then increasing trend of change. The multigrain rate decreased as the angle of inclination of the bottom of the seed box increased from 10° to 13.47°. There was a gradual increase in the multigrain rate when the angle of inclination of the bottom of the seed box was increased from 13.47° to 20°. The multigrain rate had a minimum value, of 3.29%, when the angle of inclination of the bottom of the seed box was about 13.47°. When the angle of inclination of the bottom of the seed box was 15°, and the speed of the eccentric wheel was gradually increased, the multigrain rate showed a decreasing and then increasing trend of change. The multigrain rate decreased gradually as the eccentric wheel speed increased from 3 rad/s to 3.93 rad/s. The multigrain rate gradually increased as the eccentric wheel speed increased from 3.93 rad/s to 5 rad/s. The multigrain rate had a minimum value, of 3.51%, at an eccentric wheel speed of approximately 3.93 rad/s.

Based on Figure 8c, when the rotational speed of the eccentric wheel was 4 rad/s, the angle of inclination of the bottom surface of the seed box gradually increased. The cavitation rate showed a trend of decreasing and then increasing. With an increase in the angle of inclination of the bottom of the seed box from 10° to 17.04°, the rate of voiding decreased gradually. With an increase of 20° from 17.04° in the angle of inclination of the bottom of the seed box, there was a gradual increase in the rate of cavitation. The cavity rate had a minimum value, of 5.45%, when the bottom of the seed box was inclined at an angle of approximately 17.04°. When the angle of inclination of the bottom of the seed box was 15°, the speed of the eccentric wheel gradually increased, and the cavitation rate showed a trend of decreasing and then increasing. With an increase in eccentric wheel speed from 3 rad/s to 4.83 rad/s, the cavitation rate gradually decreased. With an increase in eccentric wheel speed from 4.83 rad/s to 5 rad/s, the cavitation rate gradually increased. The cavitation rate had a minimum value of 5.24% at an eccentric wheel speed of about 4.83 rad/s.

Analyzing the causes shows that, when the rotational speed of the eccentric wheel is certain, the angle of inclination of the bottom surface of the seed box increases, producing a gradual increase in the mobility of seeds and decreasing seed-to-seed and seed layer-to-seed layer interaction forces. Seeds can quickly pass through two layers of height-restricted partitions and move along the Y-type guide groove toward the hole in the surface of the seed discharge drum, increasing the rate of single grains and decreasing the rate of cavities. When the angle of inclination of the bottom of the seed box is too great, the inertial force Fg on the seed is greater. When the vertical component of the inertial force Fgy is high, the seeds in the seed box “boil” excessively. The distance between the two steps of the height-limiting partition and the bottom of the seed box is short, making it difficult for excessively “boiled” seeds to pass through. This results in a decrease in the rate of single grains and an increase in the rate of cavities. When the bottom of the seed box is inclined at a certain angle, the speed of the eccentric wheel increases, producing a gradual increase in the mobility of seeds and decreasing seed-to-seed and seed layer-to-seed layer interaction forces. Seeds can quickly pass through two layers of height-restricted partitions and move along the Y-type guide groove toward the hole in the surface of the seed discharge drum, increasing the rate of single grains and decreasing the rate of cavities. When the angle of inclination of the bottom of the seed box is too great, the inertial force Fg on the seed is greater. The vertical component of the inertial force Fgy is high and the seeds in the seed box “boil” excessively. The distance between the two steps of the height-limiting partition and the bottom of the seed box is short, making it difficult for excessively “boiled” seeds to pass through. This results in a decrease in the rate of single grains and an increase in the rate of cavities.

4.4. Parameter Optimization

To obtain the optimal combination of operating parameters for the vibratory postural seed box, we used the maximum single-grain rate, multiple-grain rate, and minimum single-grain rate as the objective function. Combined with the boundary conditions of each experimental factor, a regression model of seed supply performance evaluation indices was designed for multi-objective optimization. The optimization objective function and constraints were as follows:

$$\{\begin{array}{l}{10}^{°}\le X1\le {20}^{°}\\ 3 rad/s\le X2\le 5 rad/s\\ 1 mm\le X3\le 3 mm\\ maximize A(X_1,X2,X3)\\ minimize D(X_1,X2,X3)\\ minimize M(X_1,X2,X3)\end{array}$$

(18)

Substituting the objective function and constraints into Design-Expert 10.0.4 yields the following optimal parameter combination for the test: a seed box bottom inclination angle of 14.27°, an eccentric wheel speed of 4.48 rad/s, and an eccentric distance of 1.94 mm. The vibrationally adjusted seed box had 90.95% single grains, 3.49% multiple grains, and 5.56% cavities.

To verify reliability, simulation verification tests of the seed supply performance were conducted. In the simulation test, the bottom of the seed box was tilted at an angle of 14.27°, the speed of the eccentric wheel was 4.48 rad/s, and the eccentricity was 1.94 mm. The test was repeated three times, and the average value was used as the test result. The following results were obtained: 90.75% of the total were single grains, 3.63% were multiple grains, and 5.62% were cavities in the vibrationally adjusted seed box. Seed supply performance simulation validation tests in the vibratory position seed box showed a decrease of 0.20% in the single-grain rate, an increase of 0.14% in the multiple-grain rate, and an increase of 0.06% in the cavitation rate compared to the optimized results. The maximum error between simulation verification tests and optimization results for seed supply performance was 0.30%. The test errors fell within permissible limits, and reliable parameter optimization results were achieved. We concluded that, due to the stochastic nature of seed generation from pellet plants in simulation experiments, the spatial location and position of the generated seeds varied during each trial, resulting in different results for each simulation test with minor errors. However, the test error was within the permissible limits.

4.5. Seed Supply Performance Bench Tests and Results

To verify the feasibility of the vibratory position seed supply method and the reliability of the parameter optimization, seed supply performance bench tests were carried out. Nongkang Dried Pepper King was selected as the test subject; its thousand-grain weight was 5.7018 g and the water content of the seeds was 6% ± 0.5%. The experiment was carried out in the precision sowing laboratory of Shihezi University. To facilitate processing, the bottom of the seed box was tilted at an angle of 14°, the speed of the eccentric wheel was 4.50 rad/s, and the eccentric distance was 2 mm. During the test, the vibratory position adjustment seed box was installed on the air-suction seeder (GD-1200), and the test setup is shown in Figure 9. The test was repeated three times, and the average value was used as the result of the test.

The seed supply performance bench test produced the following results: 89.28% of the total were single grains, 3.89% were multiple grains, and 6.83% were cavities in the vibrationally adjusted seed box. In the seed supply performance bench test, the single-grain rate of the vibratory position seed box decreased by 1.47%, the multigrain rate increased by 0.26%, and the cavity rate increased by 1.21% compared with the simulation validation test. The maximum error between simulation verification tests and optimization results for seed supply performance was 1.47%. The test’s error was within the permissible range. Therefore, the vibratory position supply method was deemed to be feasible, and the parameter optimization was reliable. The following conclusions were reached: Firstly, to facilitate processing, in the seed supply performance bench test, some key structural parameters were different from the seed supply performance simulation and verification test, resulting in errors in the test results. Secondly, in the seed supply performance bench test, the vibration of the test device affects the seed supply performance, leading to errors in the test results.

5. Discussion

In the simulation tests, the vibration attunement structure was modified for simulation purposes. Only five holes were retained on the surface of the seed discharge drum during the simulation. The simulation test only considered the seed supply performance of the vibrationally tuned seed box. Therefore, the simulation test results are plausible.

Aiming to resolve the technical problems of poor seed mobility and difficulty in controlling the suction posture increasing the rate of leakage and decreasing the index of seed qualification, in this study, a vibrationally tuned directional seed supply method and system were proposed. In the seed supply performance simulation verification test, the vibratory position seed box had a 90.75% single-grain rate, 3.63% multiple-grain rate, and 5.62% cavity rate. Of the total amount of grains, 89.28% were single grains, 3.89% were multiple grains, and 6.83% were cavities in the vibratory conditioning seed boxes in the seed supply performance bench tests. In accordance with the JB/T10293-2013 technical conditions for single-grain (precision) seeders, we aimed for a pass index greater than or equal to 80%, a mass index less than or equal to 8% of the requirements, and a replay index less than or equal to 15%. Simulation tests and bench tests all met the above indices. It can be assumed that the difficulties with poor seed mobility and the regulation of the suction posture have been solved. The structure of this vibratory seed box is mainly adapted to roller seeders. In the future, the vibratory seed box structure will be developed for flat planters and needle planters, further increasing the application scope of vibratory posturing seed boxes.

SolidWorks was used for modeling and the ADAMS-EDEM was used for the coupled simulation; the latter is a traditional method widely used for the simulation of seeding machinery, ore transport machinery, and mixing machinery [31]. To facilitate the simulation, only the vibration between the seed discharge roller, the vibration-adjusted seed box, and the support spring were considered in the simulation process. The support base was connected to the frame and was set to be fixed during the simulation. The effect of rack vibration on seed supply performance was not considered, and the simulation test was inadequate. In subsequent work, the research team will minimize the rack vibration to make the bench test more similar to the seed supply performance simulation test.

Based on the results of the seed supply performance simulation test, it can be seen that the interaction term X₁X₂ of the angle of inclination of the seed box bottom and the speed of the eccentric wheel had a significant effect on the rate of single grains, multiple grains, and cavitation. When the rotational speed of the eccentric wheel was certain, the angle of inclination of the bottom surface of the seed box increased. This gradual increase in the mobility of seeds produced a decreasing seed-to-seed and seed layer-to-seed layer interaction force. Seeds were able to quickly pass through two layers of height-restricted partitions and move along the Y-type guide groove toward the hole in the surface of the seed discharge drum, producing an increase in the rate of single grains and a decrease in the rate of cavities. When the angle of inclination of the bottom of the seed box was too great, the inertial force Fg on the seed was greater, the vertical component of the inertial force Fgy was high, and the seeds in the seed box “boiled” excessively. The distance between the two steps of the height-limiting partition and the bottom of the seed box is short, making it difficult for excessively “boiled” seeds to pass through. This results in a decrease in the rate of single grains and an increase in the rate of cavities. When the bottom of the seed box is inclined at a certain angle, as the speed of the eccentric wheel increases, a gradual increase in the mobility of seeds occurs. This decreases seed-to-seed and seed layer-to-seed layer interaction forces. Seeds can quickly pass through two layers of height-restricted partitions and move along the Y-type guide groove toward the hole in the surface of the seed discharge drum, producing an increase in the rate of single grains and a decrease in the rate of cavities. When the angle of inclination of the bottom of the seed box is too great, the inertial force Fg on the seed is greater. When the vertical component of the inertial force Fgy is high, the seeds in the seed box “boil” excessively. The distance between the two steps of the height-limiting partition and the bottom of the seed box is short, making it difficult for excessively “boiled” seeds to pass through, resulting in a decrease in the rate of single grains and an increase in the rate of cavities.

In the seed supply performance simulation validation test, the vibratory position seed box produced a 0.20% decrease in the single-grain rate, a 0.14% increase in the multiple-grain rate, and a 0.06% increase in the cavitation rate compared to the optimized results. The maximum error between simulation verification tests and optimization results for the seed supply performance is 0.30%. This led us to conclude that, due to the random nature of seed generation from the particle plant in the simulation trials, the spatial location and position of the generated seeds varied during each trial, resulting in different results and minor errors in each simulation test. However, the test error was within the permissible range. In subsequent work, the research team will investigate the effect of the initial spatial position and the position of seeds on the seed supply performance of vibrationally tuned seed boxes using a single seed as an object.

6. Conclusions

Based on the analysis of variance (ANOVA) of the results of the seed supply performance simulation test, the following conclusions were reached: The main performance evaluation indicators of the vibration-conditioned seed box, in order of predominance, are the speed of the eccentric wheel, the eccentric distance, and the angle of inclination of the bottom surface of the box. The interaction term X₁X₂ of the angle of inclination of the bottom of the seed box and the speed of the eccentric wheel have a significant effect on the rate of single grains, multiple grains, and cavitation.

Seed supply performance simulation test results (when the angle of inclination of the bottom surface of the seed box is 14.27°, the speed of the eccentric wheel is 4.48 rad/s, and the eccentric distance is 1.94 mm, resulting in 90.75% single grains, 3.63% multiple grains, and 5.62% cavities in the vibrationally adjusted seed box) and bench test results (when the angle of inclination of the bottom surface of the seed box is 14°, the speed of the eccentric wheel is 4.50 rad/s, and the eccentric distance is 2 mm, resulting in a mean value of single-kernel rate of 89.28%, a mean value of the multiple kernel rate of 3.89%, and a mean value of the cavity rate of 6.83% for the vibrationally conditioned seed boxes) are better than JB/T10293-2013 “single-grain (precision) seeder technical conditions” because the qualified index is greater than or equal to 80%, the leakage index is less than or equal to 8% of the requirements, and the reseeding index is less than or equal to 15% of the technical requirements. Thus, it can be seen that the vibration position adjustment method for seed supply is feasible and can improve the problems of the increased leakage rate and decreased quality index of seed discharge due to the poor fluidity of the seed and the difficulty in adjusting the suction posture of the seed sowing machine. The results of this study provide insights for theoretical research on the method of tuning and directional seed supply. It also offers ideas for the design and development of seed supply systems for precision planting machinery.

7. Patents

The work reported in this manuscript is the subject of an application for a national patent for an invention entitled “A Precision-Directed Posture Seed Supply Mechanism and Method, Application No.: 2023112105408, Bulletin Publication No.: CN 117158162 A”, and the case status is as follows: awaiting proposal for substantial examination.