Design and Testing of Soybean Double-Row Seed-Metering Device with Double-Beveled Seed Guide Groove

Abstract

During the operation of a shaped hole seed-metering device, poor seed-filling quality and inconsistent seed-casting points lead to poor seed spacing uniformity, especially in a one-chamber double-row seed-metering device. To solve this problem, a soybean double-row seed-metering device with double-beveled seed guide groove was designed to ensure a high single-seed rate and seed-casting point consistency. Through the theoretical analysis of the working process of the seed-metering device, dynamic and kinematic models of the seeds were established, and the main structural parameters of the seed discharge ring, triage convex ridge, shaped hole, and seed guide groove were determined. The main factors affecting the seeding performance were obtained as the following: the inclination angle of the triage convex ridge, the radius of the shaped hole, and the depth of the seed guide groove. A single-factor test was carried out by discrete element simulation to obtain the inclination angle of the triage convex ridge α₃ = 29°, the radius of the shaped hole r₁ = 4.16–4.5 mm, and the depth of the seed guide groove l₁ = 0.49–1.89 mm. A two-factor, five-level, second-order, orthogonal rotation combination test was conducted to further optimize the structural parameters of the seed-metering device. The two test factors were the radius of the shaped hole and the depth of the seed guide groove, and the evaluation indices were the qualified rate, replay rate, and missed seeding rate. The results showed that the optimal combinations of the structural parameters were the radius of the shaped hole r₁ = 4.33 mm and the depth of the seed guide groove l₁ = 1.20 mm. Subsequent bench testing demonstrated that the seed discharge’s qualified rate was above 94% at operating speeds of 6–10 km/h, and the seeding performance was stable. The final results of the soil trench test showed that the seed-metering device exhibited a qualified rate of 93.31%, replay rate of 2.04%, and missed seeding rate of 4.65% at an operating speed of 8 km/h. This research outcome may serve as a valuable reference and source of inspiration for the innovative design of precision seed-metering devices.

1. Introduction

Precision seeding represents a pivotal developmental trajectory and prevailing trend within the realm of contemporary seeding technology, embodying a commitment to enhancing agricultural efficiency. A seed-metering device is the core component of a precision seeding system, directly influencing the seeding quality and working efficiency [1,2]. Precision seed-metering devices are categorized into mechanical and pneumatic types based on the principle of operation [3]. A mechanical seed-metering device features a simple structure, an ease of maintenance, and low processing costs, making it widely utilized in China.

Researchers have extensively researched on how different filling ways and shaped hole structures affect the filling effect of seed-metering devices [4,5,6,7,8,9]. Zhang et al. [10] aimed to improve the probability of seeds entering the holes of disc seeders, addressing the issue of empty planting by designing a height difference at the edges of the holes. Meng et al. [11] developed a fixed disturbance ring to enhance the activity of seed populations, which subsequently facilitated the design of a fixed disturbance-assisted soybean seeder. To identify the pivotal parameters of a seed-metering device, Li et al. [12] analyzed the movement process and state of the seeds. Li et al. [13] adopted a centrifugal cone disc-pushing seed-filling method to improve the stability of seeding quality, adjusting the seed orientation through friction and vibration. Zhang et al. [14] developed a pneumatic, mechanical, combination single-disc double-row seeder that minimizes seed damage while simultaneously reducing production costs. Li et al. [15] investigated the structure of a seed disc and seed-cleaning device, leading to the design of a double-row pneumatic disc seeder that significantly enhanced the seed-filling rate. Guo et al. [16] improved seeding quality by utilizing a seed guide groove and an auxiliary air-assisted seed-filling shaped hole structure. Chen et al. [17] employed discrete element simulation software to dissect the factors and their combinations influencing seeding performance, ultimately guiding the design of a convex scoop seed-metering device. Dun et al. [18] studied a shaped hole structure. Huang et al. [19] improved the filling force and seeding stability by altering the structure of a seed-filling shaped hole. Their study provided a reference for the design of shaped hole structures. Foreign researchers designed a secondary seed-casting device based on the principle of orderly seeding, with seeds discharged from the same position [20,21,22,23]. Maschio Company (Campodarsego, Italy) uses airflow to ensure uniform plant spacing when seed-casting [24]. Researchers in China have also been researching the uniformity of seed-casting. A seed-guiding mechanism designed by Dong et al. [25] significantly enhanced the seed-casting performance of a seed-metering device under high-speed operating conditions. Chen et al. [26] designed a belt-type seed delivery device aimed at improving the uniformity of the seed-casting process. Li et al. [27,28] designed a linear seed-pushing mechanism for an air-aspirated seed-metering device. This mechanism served to prevent the seed from changing position due to colliding with the seed tube’s interior. Their proposed end toggle mechanism to disengage the seed and the straight-line seed-casting method were effective in resolving lateral seed displacement from the seed-casting effect. The above research directions mainly focused on two aspects of realizing orderly seed-filling and precise seed-casting. These studies effectively improved the performance of seed-metering devices. The problems of the above seed-metering devices mainly include the following: (1) the seed is in an unconstrained state before it enters the shaped hole, and the stability of seed-filling is poor and (2) by solely relying on its own gravity to disperse the seed, the device leads to irregular seed-casting points, thereby impacting the uniformity of spacing among the sown seeds.

Therefore, a soybean double-row seed-metering device with double-beveled seed guide groove was designed. The precision seed-metering device enables the systematic and orderly introduction of seeds into individual holes, thus ensuring the singular presence of one seed per hole. Furthermore, the seeding wheel guarantees the achievement of a consistent seed-casting point.

2. Materials and Methods

2.1. Overall Structure and Working Principle of the Seed-Metering Device

2.1.1. Overall Structure

Figure 1 illustrates the design of a soybean double-row seed-metering device, featuring a double-beveled seed guide groove. It consists of a front cover, front seed chamber, seed discharge ring, rear seed chamber, drive disc, seed guard, rear shell, drive shaft, and other components.

The drive shaft initiates the rotation of the drive disc, which in turn propels the seed discharge ring into circular motion for the purpose of sowing. Simultaneously, the brush wheel, powered by the drive disc, rotates to execute seed-clearing operations. The teeth of the seeding wheel are strategically positioned within the contoured holes of the seed discharge ring, which, upon being rotated by the latter, performs the crucial task of seed-casting. Except for the above three sets of rotating parts, all other parts are non-rotating fixed parts. The triage convex ridge on the seed discharge ring has the capacity to divide the seed population into two distinct portions, which can then be filled independently, which improves the seed-filling efficiency. The seed guide grooves on the triage convex ridge effectively guide the seeds into the shaped holes using the restraining effect of the grooves on the seeds to enhance the seed-filling rate. The teeth of the seeding wheel push the seed to reach the seed-casting point out of the shaped hole, keeping the seed-casting point consistent.

2.1.2. Working Principle

The working process of the seed-metering device is mainly divided into four areas: seed-filling area I, seed-clearing area II, seed transport area III, and seed-casting area IV. The working process is shown in Figure 2.

When the seed-metering device operates, the seed falls into seed-filling area I. The connection between seed-filling area I and seed-casting area IV is divided by a partition on the front and rear seed discharge chambers. The partition serves to prevent the seed from entering seed-casting area IV directly from seed-filling area I. The seeds within the population traverse along the seed guide groove toward the shaped holes. The constraints and propulsion provided by the seed guide groove facilitate a smoother entry of the seeds into the shaped holes, thereby enabling effective guidance. This mechanism results in a significant increase in the seed-filling rate compared to seed-metering devices that rely solely on the seeds’ gravity for filling. The seeds in the shaped holes follow the seed discharge ring as it rotates counterclockwise. When the seed reaches seed-clearing area II, the excess seed falls back to seed-filling area I under the action of the brush wheel and gravity. Afterward, the seeds waiting to be discharged follow the movement of the seed-discharging ring and pass through seed transport area III to seed-casting area IV. The teeth of the seeding wheel extend into the shaped holes on the seed discharge ring. When the seeds reach the seed-casting point, the teeth of the seed discharge ring immediately push the seeds out of the shaped holes, completing the seed-casting operation. Since the position of the seeding wheel remains fixed, the location of the seed-casting point also remains constant, ensuring consistency in the seed-casting point.

2.2. Key Component Design and Related Parameter Analysis

2.2.1. Overall Structure of the Seed Discharge Ring

The seed discharge ring, as depicted in Figure 3, constitutes the core functional element of the seed-metering device, playing a pivotal role in its operation. The seed discharge ring structure comprises a triage convex ridge, seed guide groove, shaped hole, and limiting convex ridge. Triage convex ridges, seed guide grooves, and shaped holes form the seed-filling structure. Double rows of seed guide grooves are staggered on both sides of the triage convex ridge of the seed discharge ring. The shaped holes are designed with rounded corners where they come into contact with the inner circle of the seed discharge ring. This not only effectively reduces seed damage but also facilitates the removal of excess seed from the shaped holes by the brush wheel. The seed discharge ring was designed with a limiting convex ridge on one side, fitting into a slot on the edge of the drive disc to form a whole.

2.2.2. Analysis of the Force Acting on Soybean Seeds

During the seed-filling process, the origin is defined by the center of mass of the seed, with the x-axis aligned to the tangent direction of the seed discharge ring’s rotation, the y-axis to its normal direction, and the z-axis perpendicular to the plane of the seed discharge ring. The three-dimensional coordinate system oxyz is shown in Figure 4.

In the xoy plane, forces acting on the seed include friction from the slanting surface of the seed guide, thrust perpendicular to the surface, friction of the seed cluster on the seed in the tangential direction of the triage convex ridge, and gravity. The equation of equilibrium is as follows.

$$F_{c1}\cos {\alpha }_1+f_{m1}\sin {\alpha }_1=f_{m2}\cos {\alpha }_2$$

(1)

where F_c1 is the thrust perpendicular to the seed guide groove, N; f_m1 is the friction force along the incline, N; f_m2 is the population friction along the tangent to the triage convex ridge, N; α₁ is the angle between the slant of the seed guide groove and the x-axis, (°); and α₂ is the angle between the tangent to the triage convex ridge and the x-axis, (°).

In the yoz plane, forces acting on the seed include the crowding force on the seed cluster perpendicular to the incline, supporting force perpendicular to the incline, combined force along the y-axis, and gravity. Forces on the seed are in equilibrium in the z-axis direction. The equation of equilibrium is as follows.

$$F_{n2}\cos {\alpha }_1=F_s\cos {\alpha }_1+f_{m1}\sin {\alpha }_1$$

(2)

The f_m1 in Equation (2) is given in Equation (3) below.

$$f_{m1}=\mu F_{n1}$$

(3)

where F_n1 is the support force perpendicular to the incline, N; F_s is the crowding force from the seed cluster perpendicular to the inclined plane, N; and μ is the sliding friction factor between the seed and the seed discharge ring.

To facilitate the seamless downward progression of the seed within the designated guide groove, the resultant force acting upon the seed must be oriented consistently downward, conforming to the inclined plane of the triage convex ridge. The force equation is as follows.

$$G\cos {\alpha }_3+T_1\cos {\alpha }_3>f_{m1}$$

(4)

where G is the gravitational force acting on the seed, N; T₁ is the combined force along the y-axis, N; and α₃ is the inclination angle of the triage convex ridge, (°). The T₁ in Equation (4) is given in Equation (5) below.

$$T_1=F_{c1}\sin {\alpha }_1+f_{m2}\sin {\alpha }_2-f_{m1}\cos {\alpha }_1$$

(5)

A comprehensive analysis was conducted on both the internal architecture of the seed-metering device and the configuration of the seed discharge ring. It was found that when the inclination angle of the triage convex ridge α₃ was taken as 0°, the crowding pressure on the seeds on both sides of it by the seed population increased with time. Consequently, the seeds may be prone to breakage or erratic movements, ultimately compromising the quality of the seed-filling process. However, according to Equation (4), the larger the inclination angle of the triage convex ridge α₃, the smaller the Gcosα₃ and T₁cosα₃. Therefore, the lower the guiding force is on the seeds, and thus the less favorable the seed-filling. Further tests are necessary to definitively determine the optimal range of the inclination angle of the triage convex ridge α₃.

As soybean seeds rotate concurrently with the seed discharge ring, transitioning from the seed transport area to the seed-casting area, they relinquish the supportive force provided by the seed guard, enabling their steady ejection under the impetus of the seeding wheel. At this time, the seed is subjected to forces, including the thrust of the shaped hole F_c2, the thrust of the seeding wheel F_c3, centrifugal force J, and gravity G, which make up the combined force T₂. The combined force T₂ provides the seed with a plane velocity v of motion, which can be decomposed into a horizontal velocity v_x and a vertical velocity v_y. A schematic diagram of the seed-casting process is shown in Figure 5.

A Cartesian coordinate system xoy was established in the plane of the rotating seed discharge ring, with the center of gravity of the soybean seeds designated as the origin. The trajectory of the soybean seed is as follows.

$$\left\{\begin{array}{l}x=v_x{t}_1\\ y=v_y{t}_1+{\displaystyle \frac{g{t}_1^2}{2}}\end{array}\right.$$

(6)

where x is the displacement of the soybean seed in the horizontal direction, mm; y is the displacement of the soybean seed in the vertical direction, mm; v_x is the velocity of the soybean seed in the horizontal direction, m/s; v_y is the velocity of the soybean seed in the vertical direction, m/s; and t₁ is the seed-casting time, s. The v_x, and v_y in Equation (6) are given in Equations (7) and (8) below.

$$v_x=v\sin \beta$$

(7)

$$v_y=v\cos \beta$$

(8)

The v in Equations (7) and (8) is given in Equation (9) below.

$$v={\displaystyle \frac{n_p\pi r_1}{30}}$$

(9)

where β is the angle of the seed-casting, (°); n_p is the rotational speed of the seed discharge ring, r/min; and r₁ is the radius of the shaped hole, mm.

According to Equations (6)–(9), the equations for the trajectory of the soybean seed in the xoy plane were obtained as follows.

$$\left\{\begin{array}{l}x={\displaystyle \frac{n_p\pi r_1\sin \beta }{30}}{t}_1\\ y={\displaystyle \frac{n_p\pi r_1\cos \beta }{30}}{t}_1+{\displaystyle \frac{g{t}_1}{2}}\end{array}\right.$$

(10)

Under constant structural parameters of both the seed discharge ring and seeding wheel, the rotational velocity n_p of the ring governs the seed trajectory. Rigorous mechanical characterization is imperative for the rational design of the seed discharge ring, facilitating the precise analysis and calculation of its crucial parameters.

2.2.3. Design of the Seed Discharge Ring

The diameter of the seed discharge ring is instrumental in determining not only its overall size but also the magnitude of linear velocity and centrifugal force during its operation. Hence, its design necessitates meticulous consideration of specific operational conditions. It was found that the diameter of the seed discharge ring was directly proportional to the number of seed guide grooves and shaped holes [29]. Therefore, after determining the forward speed of the seeder and the seed spacing, the diameter of the seed discharge ring can be increased accordingly to reduce the rotation speed of the seed discharge ring.

The diameter range of the seed discharge ring is usually 140–260 mm [30]. For this study, the diameter of the seed discharge ring was taken as 240 mm and the width of the seed discharge ring was taken as 52 mm. The distance between the centers of the shaped holes on both sides of the seed discharge ring was designed to be 20 mm. 3D-printed technology was utilized for the fabrication of seed discharge rings using resin materials.

(1)

Design of the triage convex ridge

The structure of the triage convex ridge is shown in Figure 6. The triage convex ridge ensures that the seeds on either side are filled independently, without interference, during the seed-filling operations of the seed-metering device. An optimal angle of inclination for the triage convex ridge is beneficial for seed-filling operations. However, if the angle of inclination is excessively large, the height of the ridge becomes constrained, which impairs the ability of the seed cluster to separate into both sides simultaneously, thereby reducing its guiding capability. This reduces the ability of the seeds to fill the shaped holes.

The formula for the inclination angle of the triage convex ridge was obtained from Figure 6.

$${\alpha }_3=\arctan \left({\displaystyle \frac{l_2-\left(r_1-l_1\right)}{h_1}}\right)$$

(11)

where l₁ is the depth of the seed guide groove, mm; l₂ is the distance from o₂ to o₁, mm; h₁ is the height of the triage convex ridge, mm; o₁ is the midpoint of the distance between the centers of the shaped holes on both sides; and o₂ is the center of the shaped holes on one of the sides

The distance between points o₂ and o₁ is half the distance between the centers of the shaped holes on both sides, and therefore l₂ was taken as 10 mm. The triage convex ridge is limited by the positions of the brush wheel and the seeding wheel. Hence, the maximum height of the triage convex ridge was designed to be 25 mm, ensuring uninterrupted rotation of the brush and seeding wheels. The minimum height, exceeding the largest seed dimension, was set at 15 mm to facilitate seed separation on both sides and ensure guidance into the shaped holes via the seed guide groove. Therefore, the height of the triage convex ridge h₁ was taken in the range of 15–25 mm. The presence of diversion ridges effectively segmented the seed population into two distinct groups, each facilitated independently for seed-filling. As the rotary seed discharge ring rotates, the seed guide grooves adjacent to the diversion ridges meticulously direct the seeds toward their respective shaped holes. The inherent diversity among soybean varieties results in variations in their physical attributes, particularly in their dimensions. Consequently, larger seeds experience enhanced guiding forces during their trajectory, increasing their likelihood of successfully accessing the shaped holes. In contrast, smaller seeds encounter less pronounced guiding forces, which leads to a comparatively lower seed-filling efficiency. The determination of the range of height of the triage convex ridge provides the basis for the determination of the range of inclination angle of the triage convex ridge in a single-factor test.

(2)

Design of the shaped holes

• Structure and dimensions of the shaped hole

The structure of the shaped hole has a great influence on a seed-metering device’s seeding performance. A right-angled configuration at the shaped hole entrance may inflict damage on seeds during both the filling and cleaning processes. Therefore, the shaped holes were designed with chamfered corners with a radius of 1 mm, as shown in Figure 7.

The radius of a shaped hole being too large will lead to multiple smaller seeds entering, while the radius of a shaped hole being too small will result in larger seeds being unable to enter. The depth of the shaped hole was designed to hold one seed and only one seed to ensure a smooth seed-filling and seed-clearing process [31]. It was essential to adhere to the following constraints for the individual dimensions.

$$\left\{\begin{array}{l}0.75d_{\max }>r_1>0.5d_{\max }\\ {\overline{X}}_W>l_3>d_{\min }\end{array}\right.$$

(12)

where d_max is the maximum size of the seed, mm; ${\overline{X}}_W$ is the average of the width of the seed, mm; d_min is the minimum size of the seed, mm; and l₃ is the depth of the shaped hole, mm.

The widely cultivated Zhonghuang 37 soybean seed was employed in the test procedure. A sample of 100 seeds were randomly extracted from the seed cluster, and their dimensions (length L, width W, and thickness T) were meticulously measured. The measurements were recorded and subsequently processed. The outcomes of the processing are summarized in

Table 1. Statistical results of the soybean seeds’ geometric size.

Parameter	Length L/mm	Width W/mm	Thickness T/mm
Maximum value	10.18	8.18	7.38
Minimum value	7.06	6.4	5.22
Average value	8.19	7.49	6.55

.

Table 1 shows that the average values of the dimensions of the soybean seeds were 8.19 mm in length, 7.49 mm in width, and 6.55 mm in thickness. Upon substituting the dimensions into Equation (12), it was determined that the range of values for the radius of the shaped hole was 4.1–6.14 mm. Thus, when the seed size was excessively large (L > 6.14 mm), there was an elevated risk of missed seeding occurring. Conversely, if the seed size was overly small (L < 4.1 mm), there was an increased likelihood of replay phenomena taking place. The 1 mm gap between the seed discharge ring and the seed guard serves to prevent friction, with the seed that fills the shaped holes subsequently dropping down to the seed guard. Therefore, the depth of the shaped hole was reduced by 1 mm. The value of l₃ was taken to be within the range of 5.56–6.49 mm, and the depth of the shaped hole was rounded up to l₃ = 6 mm. The range of the shaped hole’s radius was subsequently determined through a rigorous single-factor test.

• Distribution of the shaped hole

The diameter of the seed discharge ring directly determines the number of shaped holes. When the operating speed and plant spacing are constant, the decrease in the rotation speed of the seed discharge ring can increase the number of shaped holes. Equation (13) shows the relationship between the rotation speed of the seed discharge ring, the number of shaped holes, and the forward speed of the seeder.

$$v={\displaystyle \frac{6zmn}{10000}}$$

(13)

where v is the forward speed of the seeder, km/h; z is the seed spacing, calculated by taking 10 cm; n is the rotation speed of the seed discharge shaft, r/min; and m is the number of shaped holes, piece.

Based on Equation (13), it was evident that the drive shaft’s rotational speed inversely correlated with the number of shaped holes, given constant seeder forward speed and plant spacing. Maintaining a constant diameter of the seed discharge ring, a reduced drive shaft speed translates to an increased number of shaped holes, enhancing seed-filling efficiency. However, an overly high number of holes may impede seed-filling. Therefore, determining the optimal maximum number of holes and the minimum spacing between them is crucial for ensuring smooth and efficient seed-filling. This simplifies the seed-filling process of a seed-metering device, as shown in Figure 8.

We assumed that the seed underwent horizontal projectile motion before entering the shaped hole from the seed guide groove. Then, the conditions for successful seed-filling would entail that the portion of the seed entering the shaped hole exceeded half of the seed itself, which corresponded to a drop height of more than 0.5d_max. The fall time required for successful seed-filling was ${\mathrm{t}}_2=\sqrt{{\displaystyle \frac{{\mathrm{d}}_{\max }}{\mathrm{g}}}}$, and the displacement in the horizontal direction S = v₀t₂. According to the reference literature [17], Equations (14)–(16) are necessary conditions for smooth seed-filling.

$$l_4\ge S+0.5d_{\max }$$

(14)

$$v_0={\displaystyle \frac{\omega D}{2}}$$

(15)

$$l_4\approx {\displaystyle \frac{\pi D}{m}}$$

(16)

where S is the distance the seed traveled in the horizontal direction, mm; l₄ is the distance between the shaped holes, mm; v₀ is the linear velocity of the seed discharge ring, rad/s; ω is the angular velocity of the seed discharge ring, rad/s; and D is the diameter of the seed discharge ring, mm.

The following relationship was obtained from Equations (14)–(16).

$$m\le {\displaystyle \frac{60\pi }{\pi n\sqrt{\frac{d_{\max }}{g}}+\frac{30d_{\max }}{D}}}$$

(17)

Equation (17) indicates that the number of shaped holes is directly proportional to the diameter of the seed discharge ring and inversely proportional to both the rotational speed of the drive shaft and the seed size. When the distance between the shaped holes is the smallest, the number of shaped holes is the largest and the following relationship was obtained.

$$l_4\approx {\displaystyle \frac{\sqrt{3}+1}{2}}{d}_{\max }$$

(18)

$$m{l}_4\approx m{\displaystyle \frac{\sqrt{3}+1}{2}}{d}_{\max }\approx \pi D$$

(19)

Collation yielded the following relationships.

$$m\approx {\displaystyle \frac{2\pi D}{\left(\sqrt{3}+1\right)}}{d}_{\max }$$

(20)

$$v_{0}t\le l_4$$

(21)

Substituting Equation (15) into Equation (21) yielded Equation (22).

$$n\le {\displaystyle \frac{\sqrt{g{d}_{\max }}\left(\sqrt{3}+1\right)\times 30}{\pi D}}$$

(22)

Given a seed discharge ring diameter of 240 mm and a maximum seed size of 8.19 mm, the calculated maximum rotational speed for the seed discharge ring, as determined by Equation (22), was 58.43 r/min. Calculation according to Equation (20) gave m ≈ 67.39 when the neighboring shaped holes were next to each other. To have enough space between the shaped holes during seed-filling, the number of shaped holes on one side of the triage convex ridge was taken as 50. At a seeder forward speed of 10 km/h, the seed discharge ring speed was 33.33 r/min, less than 58.43 r/min, and met the design requirements.

(3)

Design of the seed guide groove

The reasonable structure of the seed guide groove not only guides the seed into the shaped hole but also enhances the disturbance of the seed cluster. As the seed discharge ring rotates, the seed guide groove and seed cluster exert pressure on the seed in the seed guide groove. This force ensures that the seed outside the seed guide groove cannot influence the seed in the seed guide groove to enter the shaped hole. This ensures that the seed-filling is effective.

A Cartesian coordinate system XOY was established, with the origin positioned at the center O of the seed discharge ring, as depicted in Figure 9. To guarantee seamless seed entry into the shaped hole, the absolute trajectory of the seed must align precisely with the tangent of the circle defined by the top of the seed guide groove. At time t₄, point A₁ moves to point A₂, and the seed moves from point A₁ to point A₃.

After time t₄, point A₁ rotates to point A₃, at which point the velocity at this position is as follows.

$$v_1=v_2/\cos {\gamma }_2$$

(23)

$$\left\{\begin{array}{l}{v}_2=r_3\omega \\ {\gamma }_2=k\omega t_3\\ r_3=r_2/\cos {\gamma }_2\end{array}\right.$$

(24)

where v₁ is the velocity of the seed at point A₃, m/s; v₂ is the velocity component of the seed in the direction tangent to point A₃, m/s; γ₂ is the angle between line segment OA₁ and line segment OA₃, (°); r₂ is the radius of the base circle of the seed guide groove, mm; r₃ is the radius of the circle at point A₃, mm; k is the angular rate coefficient for soybeans, which was taken as 0.1 to 0.9; and t₃ is the time of movement of the soybean seed, s.

According to Equations (23) and (24), the following results were obtained.

$$v_1=r_2\omega /{\cos }^2\left(k\omega t_3\right)$$

(25)

After time t₄, the absolute motion trajectory of the soybean seed following the movement of the seed discharge ring is represented by the following equation.

$$l_{A_1{A}_3}={\displaystyle {\int }_0^{t_4}\frac{r_2\omega }{{\cos }^2\left(k\omega t_3\right)}d{t}_3=r_2\tan \left(k{\gamma }_1\right)/k}$$

(26)

where t₄ is the actual movement time of the soybean seed, s, and γ₁ is the angle between line segment OA₁ and line segment OA₂, (°).

The soybean seeds have a defined trajectory as the seed discharge ring rotates. To maximize the ability of the seed guide groove to guide the seed-filling, the curve equation of the seed guide groove was made to coincide with the relative motion trajectory of the seed. The expression of the curve equation is as follows.

$$\left\{\begin{array}{l}{x}_{A_3}=r_2\cos {\gamma }_3\\ y_{A_3}=r_2\sin {\gamma }_3\end{array}\right.$$

(27)

$${\gamma }_3={\gamma }_1-{\gamma }_2$$

(28)

$$r_2=r_3\cos {\gamma }_2$$

(29)

where γ₃ is the angle between line segment OA₂ and line segment OA₃, (°).

The following equation was obtained by combining Equations (27)–(29).

$$\left\{\begin{array}{l}{x}_{A_3}=r_2\left(\cos {\gamma }_1+\tan {\gamma }_2\sin {\gamma }_1\right)\\ y_{A_3}=r_2\left(\sin {\gamma }_1-\tan {\gamma }_2\cos {\gamma }_1\right)\end{array}\right.$$

(30)

$$\tan {\gamma }_2=l_{A_1{A}_3}/r_2$$

(31)

The result of the simplification of Equation (30) is as follows.

$$\left\{\begin{array}{l}{x}_{A_3}=r_2\left(\cos {\gamma }_2+{\displaystyle \frac{\tan \left(k{\gamma }_1\right)\sin {\gamma }_1}{k}}\right)\\ y_{A_3}=r_2\left(\sin {\gamma }_2+{\displaystyle \frac{\tan \left(k{\gamma }_1\right)\cos {\gamma }_1}{k}}\right)\end{array}\right.\hspace{1em}({\gamma }_1\in (0,\hspace{0.17em}\zeta \left)\right)$$

(32)

where $x_{A_3}$ is the coordinate of point A₃ on the x-axis in the absolute coordinate system, mm; $y_{A_3}$ is the coordinate of point A₃ on the y-axis in the absolute coordinate system, mm; and ζ is the upper bound of the range, (°).

The expression for r₃ is as follows.

$$r_3=r_2\sqrt{1+{\left(\tan \left(k{\gamma }_1\right)/k\right)}^2}$$

(33)

Equation (32) is the relative motion trajectory of the soybean seeds. The radius of the circumference in which the shaped hole is located must exceed r₃, so the value of γ₁ was in the range 37.17° < γ₁ < 42.02°. The optimal depth range for the seed guide groove was established to prioritize its role in guiding seed-filling over its tangential function in pushing the seed. This prevents the excessive depth of the seed guide groove from compromising the efficiency of seed-filling. The depth of the seed guide groove l₁ must be less than 0.5T_min, and according to Table 1, T_min = 5.22 mm, so the range of values for l₁: l₁ < 2.61 mm.

2.3. Test Conditions and Methods

2.3.1. Modeling and Parameter Setting

The operation of the seed-metering device was simulated using Altair EDEM 2021 discrete element simulation software. Soybean seeds were modeled using 5-ball collocation based on the known dimensional parameters of the soybean seeds [32]. The Hertz–Mindlin non-slip contact model was used for the seed-to-seed and seed-to-component contact models [33,34,35,36]. The parameters of the simulation model are presented in

Table 2. Simulation of model parameters.

Item	Parameters	Numerical Values
Soybean seed	Density/(kg·m−3)	0.4
	Shear modulus/MPa	11
	Poisson’s ratio	1053
	Moisture content/%	10.2
Resin	Density/(kg·m−3)	1454.80
	Shear modulus/MPa	120
	Poisson’s ratio	0.35
Soybean–soybean	Static friction coefficient	0.5
	Rolling friction coefficient	0.01
	Coefficient of restitution	0.6
Soybean–resin	Static friction coefficient	0.32
	Rolling friction coefficient	0.04
	Coefficient of restitution	0.35

.

In the parameter settings of EDEM, the 3D particle sizes were set to be generated according to a normal distribution based on the distribution of the three-axis sizes of the seeds. The coefficient of variation for the seed population was 0.157, with a total seed count of 1500. The total time of the simulation was 10 s, where the step size of the simulation was 0.0000314 s, and the data were saved at intervals of 0.01 s. The simulation’s boundary conditions were the following: (1) During the simulation, the operating speed was 8 km/h. The seed discharge ring, the drive disc, and the drive shaft rotated together counterclockwise in the same direction and their rotation speed was set to 160 deg/s. The brush wheel rotated clockwise at −525.71 deg/s. The seeding wheel rotated counterclockwise at a speed of 615.38 deg/s. And the remaining seed-metering device components were fixed. (2) The simulation material, including the front cover, as well as the front and rear seed chambers, were all constructed of resin. The seed discharge ring and seeding wheel were also composed of resin material. The bristles of the brush wheel were manufactured from nylon. The seed guard was constructed from high-strength steel. Lastly, the rear shell of the device was made of cast iron, selected for its strength and resistance to wear and tear. (3) The computational domains were the following: x-axis (maximum: 210 mm, minimum: 90 mm); y-axis (maximum: 265 mm, minimum: −20 mm); and Z-axis (maximum: 120 mm, minimum: −160 mm). The scope of the computational domain was combined with the seed-metering device structure to meet the needs of the simulation. The simulation process is shown in Figure 10.

2.3.2. Single-Factor Test

Following the structural design and theoretical analysis of the triage convex ridge, shaped hole, and seed guide groove, a targeted single-factor test was undertaken to refine the structural parameters. This endeavor sought to quantify the influence of diverse structural features on the performance index of the seed-metering device. In the single-factor test, the test factors were the inclination angle of the triage convex ridge α₃, the radius of the shaped hole r₁, and the depth of the seed guide groove l₁. The operational speed during the single-factor test was set at 8 km/h. When investigating the effect of the inclination angle of the triage convex ridge α₃ on seeding performance, each of the other factors took a fixed value: the radius of the shaped hole r₁ = 4.4 mm and the depth of the seed guide groove l₁ = 1.5 mm. When investigating the effect of the radius of the shaped hole r₁ on seeding performance, each of the other factors took a fixed value: the inclination angle of the triage convex ridge α₃ = 20.5° and the depth of the seed guide groove l₁ = 1.5 mm. When investigating the effect of the depth of the seed guide groove l₁ on seeding performance, each of the other factors took a fixed value: the inclination angle of the triage convex ridge α₃ = 20.5° and the radius of the shaped hole r₁ = 4.4 mm.

According to GB/T 6973-2005 [37] Testing methods of single seed drills (precision drills), the qualified rate, replay rate, and missed seeding rate were taken as test indices. The seeds discharged from the seed-casting point during the simulation were counted, and the qualified rate, replay rate, and missed seeding rate were calculated. When only one seed was found to have been discharged from the shaped hole, it was marked as passing. When two or more seeds were found to have been discharged from the shaped hole, they were marked as reseeding. When no seed was found to have been discharged from the shaped hole, it was marked as missed seeding.

The test methods for the qualified rate, replay rate, and missed seeding rate were the following: In the first step, the simulation was played back to record the total number of shaped holes that were traversed through the seed-casting point, starting from the first seed-filled shaped hole until the end of the simulation. This total is referred to as the total number of shaped holes turned through the seed-casting point. The number of shaped holes that dispensed only one seed while passing through the seed-casting point was designated as the qualified count. The number of shaped holes that dispensed two or more seeds was classified as the replay count, while the number of shaped holes that dispensed no seeds was termed the missed seeding count. In the second step, the recorded qualified count, replay count, and missed seeding count were divided by the total count to calculate the qualified rate, replay rate, and missed seeding rate, respectively. In the third step, the qualified rates, replay rates, and missed seeding rates from the three repeated simulation tests were averaged to yield the final test results.

2.3.3. Second-Order Orthogonal Rotation Combination Test

Based on the results of the single-factor test, the radius of the shaped hole and the depth of the seed guide groove were identified as pivotal test factors for further investigation. The range of values for the radius of the shaped hole was 4.16–4.5 mm and the range of values for the depth of the seed guide groove was 0.49–1.89 mm. A two-factor, five-level, second-order orthogonal rotation combination test was conducted with the qualified rate, replay rate, and missed seeding rate as test indicators. The measurement of test indicators was conducted in accordance with the methodology employed in the single-factor test, utilizing the two-factor level coding presented in

Table 3. Test factor coding.

Code	Radius of the Hole	Depth of Seed Guide Groove
	X1/mm	X2/mm
−1.414	4.09	0.2
−1	4.16	0.49
0	4.33	1.19
1	4.5	1.89
1.414	4.57	2.18

. These parameters provided the basis for the successful implementation of the orthogonal test and were processed using the data analysis software Design-Expert 13.0.

2.3.4. Bench Test

Bench tests are conducted to verify the reasonableness of the optimized results of parameters. The radius of the shaped hole was taken as 4.33 mm, and the depth of the seed guide groove was taken as 1.20 mm. The main working parts and the rear shell inside the 3D-printed seed-metering device formed the seed-metering device, which was mounted on a bench, as shown in Figure 11. According to GB/T 6973-2005 Testing methods of single seed drills (precision drills), the qualified rate, replay rate, and missed seeding rate were taken as test indicators. Bench test verification was carried out on the JSP-12 computer vision-measuring device performance test bench at 5 operating speeds of 6, 7, 8, 9, and 10 km/h. Each operating speed was tested three times and the results were recorded. Theoretical seed spacing was 10 cm. If the distance between two adjacent seeds in the row was greater than 5 cm and less than or equal to 15 cm, it was considered passing. Seed spacing less than or equal to 5 cm was considered to be reseeding. Seed spacing greater than 15 cm was considered to be a missed seeding.

2.3.5. Soil Trench Test

Using two-factor optimum parameter combination, a soil trench validation test was carried out at an operating speed of 8 km/h to investigate the seeding performance of the seed-metering device on the soil. The soil trench was 30 m long, 2.8 m wide, and 25 cm deep. The tests were carried out from 16 April to 26 April 2024 on the soil trench test bench in the laboratory of Shandong University of Technology. The physical properties of the soil were measured before the test. The soil moisture content was 12.6% at 0–10 cm and 14.3% at 10–20 cm. The soil compactness was 1.98 MPa at 0–10 cm and 2.5 MPa at 10–20 cm. The physical properties of the soil in the soil trench tests fell within the range of those encountered in field operations [38,39]. The bench frame with the seed-metering device was fixedly installed on the rear suspension beam of the soil trench trolley, as shown in Figure 12. The test indicators included the qualified rate, replay rate, and missed seeding rate, which were measured in the same way as in the bench test.

3. Results and Discussion

3.1. Single-Factor Test Results and Analyses

The results of the single-factor test are shown in

Table 4. Single-factor test results.

Factor	Level	Qualified Rate/%	Replay Rate/%	Missed Seeding Rate/%
Inclination angle of the triage convex ridge α3/°	12	91.32	8.48	0.2
	16.25	93.96	5.07	0.97
	20.5	95.13	3.99	0.88
	24.75	96.3	1.85	1.85
	29	96.49	1.07	2.44
Radius of the shaped hole r1/mm	4.1	93	1.22	5.78
	4.2	96.56	1.22	2.22
	4.3	95.67	2.55	1.78
	4.4	95.89	3.78	0.33
	4.5	95.11	4.67	0.22
	4.6	93.9	5.34	0.76
	4.7	93.34	6.11	0.55
Depth of the seed guide groove l1/mm	0.5	95.03	1.07	3.9
	1	96.98	1.36	1.66
	1.5	96.3	1.85	1.85
	2	94.64	4.78	0.59
	2.5	92.98	6.82	0.2

.

3.1.1. Effect of the Inclination Angle of the Triage Convex Ridge on the Test Index

It was known that l₂ = 10 mm, h₁ = 15–25 mm, r₁ = 4.4 mm, and l₁ = 1.5 mm. Substituting this into Equation (11), the range of values of the inclination angle of the triage convex ridge α₃ was calculated to be 11.97–29.57°. The inclination angles of the triage convex ridge were taken as 12°, 16.25°, 20.5°, 24.75°, and 29°. In order to more clearly show the change in the trend of the effect of the inclination angle of the triage convex ridge on the test index, the results of the test are shown in Figure 13.

Figure 13 shows that the qualified rate increased with the increased inclination angle of the triage convex ridge. When the inclination angle of the triage convex ridge increased to 24.75°, the changed trend of the qualified rate slowed down significantly.

The replay rate decreased with the increased inclination angle of the triage convex ridge and was lowest when the inclination angle of the triage convex ridge increased to 29°. The increase in the inclination angle of the triage convex ridge led to a reduction in the squeezing force on the seeds on both sides, which reduced the likelihood of multiple seeds entering the shaped hole.

The missed seeding rate gradually increased with the inclination angle of the triage convex ridge, peaking at 29°. At angles higher than this, the downward guiding force of the seed guide groove was diminished, thereby affecting the quality of seed filling. The optimal seeding performance was observed when the inclination angle was set at 29°, which was then chosen for conducting single-factor tests regarding the radius of the shaped hole and the depth of the seed guide groove.

Based on the observed trend in the qualified rate, as illustrated in Figure 13, it could be inferred that an increase in the inclination angle of the triage convex ridge resulted in improved seeding performance. Consequently, the maximum value of 29° was selected as the inclination angle of the triage convex ridge for subsequent testing.

3.1.2. Effect of the Radius of the Shaped Hole on the Test Index

Simulation pre-tests were performed for the radius range of the shaped hole due to the large radius range of the shaped hole. The pre-test results are shown in Figure 14a.

The analysis of the test results, presented in Figure 14a, indicated that the radius of the shaped hole r₁ had to range from 4.1 to 4.71 mm to achieve a qualified rate exceeding 93%. Conversely, at a radius of 4.9 mm, the qualified rate was observed to be 84.33%. When the radius of the shaped hole was larger than 4.9 mm, the qualified rate continued to decrease, and the requirement for the precision operation of the seeder could not be met. The range of values for the radius of the shaped hole r₁ was determined to be 4.1–4.7 mm, and 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, and 4.7 mm were selected for the single-factor test. The test outcomes are depicted in Figure 14b.

By analyzing the test results in Figure 14b, the following regression equation was obtained for the effect of the radius of the shaped hole on the seeding performance.

$$Y_1=99.167X_1^3-1337.8X_1^2+6004.4X_1-8871$$

(34)

$$Y_2=-37.5X_1^3+494.85X_1^2-2165.1X_1+3144.1$$

(35)

$$Y_3=-61.667X_1^3+842.44X_1^2-3834.8X_1+5816.8$$

(36)

where Y₁, Y₂, and Y₃ are the qualified rate, replay rate, and missed seeding rate, respectively, %, and X₁ is the radius of the shaped hole, mm.

The qualified rate exhibited a pronounced variation with the augmentation of the radius of the shaped hole, attaining a peak value of 96.56% at a radius of precisely 4.2 mm. Subsequently, a decline was observed as the radius surpassed 4.2 mm, reaching 4.3 mm, whereupon a marginal yet discernible increase occurred between 4.3 mm and 4.4 mm. This slight elevation was attributed to the mitigation of seed collisions at the entry point, thereby facilitating enhanced seed ingress. Notably, this transient increase did not undermine the overarching trend of the radius of the shaped hole’s influence on the qualified rate, which then resumed its continuous downward trajectory.

As the radius of the shaped hole increased, the replay rate augmented, with a deceleration in this trend observed when the radius surpassed 4.5 mm. As the radius of the shaped holes increased to a certain extent, the probability of multiple seeds entering the shaped holes continued to rise. However, the collisions among the seeds at the entrance of the shaped holes became more intense, resulting in a deceleration of this upward trend.

With the increase in the radius of the shaped holes, the missed seeding rate initially decreases. When the radius reaches 4.5 mm, the missed seeding rate begins to rise slightly. The reason for this is that the shaped hole size was excessive, exceeding 4.5 mm. This caused some seeds to collide at the mouth of the shaped hole and prevented them from entering the shaped hole.

According to regression Equations (34)–(36), when the radius of the shaped holes ranged from 4.1 to 4.5 mm, the qualified rate exceeded 95%, and the replay rate was below 5%. Furthermore, when the radius of the shaped holes ranged from 4.11 to 4.7 mm, the missed seeding rate was less than 5%. The highest qualified rate of 96.56% was achieved with a radius of the shaped hole of 4.2 mm.

3.1.3. Effect of the Depth of the Seed Guide Groove on the Test Index

In the single-factor test, the depth of the seed guide groove l₁ was taken as 0.5, 1, 1.5, 2, and 2.5 mm, where the seed guide grooves did not affect each other. To more clearly show the change in trend of the effect of the depth of the seed guide groove on the test index, the results of the test are depicted in Figure 15.

By analyzing the test results in Figure 15, the following regression equation was obtained for the effect of the depth of the seed guide groove on the seeding performance.

$$Y_1=1.7533X_2^3-10.233X_2^2+16.085X_2+89.336$$

(37)

$$Y_2=-0.7267X_2^3+4.9671X_2^2-6.3948X_2+3.196$$

(38)

$$Y_3=-1.04X_2^3+5.3229X_2^2-9.7586X_2+7.49$$

(39)

where Y₁, Y₂, and Y₃ are the qualified rate, replay rate, and missed seeding rate, respectively, %, and X₂ is the depth of the seed guide groove, mm.

The qualified rate increased with increasing depth of the seed guide groove, reaching a maximum value of 96.98% when the depth of the seed guide was increased to 1 mm, and then gradually decreased. As the depth of the seed guide groove increases, the capacity of the groove to direct seed movement toward the shaped hole is enhanced, thereby facilitating a more streamlined seed entry into the shaped hole. However, the depth of the seed guide groove was too large, causing multiple seeds to enter the same shaped hole, thereby reducing the qualified rate. The highest qualified rate of 97% was achieved with a depth of seed guide groove of 1.09 mm.

The replay rate increased slowly as the depth of the seed guide groove significantly increased when it increased to 1.5 mm. The lowest replay rate of 0.89% was achieved with a depth of the seed guide groove of 0.78 mm.

The missed seeding rate initially decreased with the depth of the seed guide groove; however, it augmented at 1–1.5 mm before resuming its downward trend beyond 1.5 mm. This increase in the missed seeding rate may be due to the increased ability of the seed guide groove to constrain the seed, resulting in some of the seeds colliding at the entrance of the shaped hole, thus failing to enter the shaped hole.

According to regression Equations (37)–(39), when the depth of the seed guide groove ranged from 0.49 to 1.89 mm, the qualified rate exceeded 95%. Additionally, when the depth of the seed guide groove was between 0.23 and 1.4 mm, the replay rate was below 2%. Finally, when the depth of the seed guide groove exceeded 1.01 mm, the missed seeding rate was below 2%.

3.2. Second-Order Orthogonal Rotation Combination Test Results and Analysis

Design-Expert 13.0 software was used to design a second-order orthogonal rotary combination test to investigate the effect of the radius of the shaped hole and the depth of the seed guide groove on the test indices. The test results are presented in

Table 5. Second-order orthogonal rotating combination test design and results.

No.	X1	X2	Qualified Rate	Replay Rate	Missed Seeding Rate
			Y1/%	Y2/%	Y3/%
1	−1	−1	91.23	0.29	8.48
2	1	−1	95.71	1.85	2.44
3	−1	1	96.39	2.92	0.69
4	1	1	95.03	4.39	0.58
5	−1.414	0	94.74	1.17	4.09
6	1.414	0	95.91	3.8	0.29
7	0	−1.414	92.69	0.58	5.27
8	0	1.414	95.32	4.39	0.29
9	0	0	96.2	1.46	2.34
10	0	0	96.49	2.15	1.36
11	0	0	96.3	1.27	2.43
12	0	0	96.49	1.75	1.76
13	0	0	96.79	1.66	1.55

Note: X₁ and X₂ are the factor-coded values for the radius of the shaped hole and the depth of the seed guide groove, respectively. The interaction between the radius of the shaped hole and the depth of the seed guide groove was significant. The effects of two factors on the test indices had a significant impact.

.

Regression analysis was conducted on the test results presented in Table 5, yielding the subsequent regression equations.

$$Y_1=-0.5832X_1^2-1.24X_2^2-1.46X_1{X}_2+0.5968X_1+1.02X_2+96.45$$

(40)

$$Y_2=0.3829X_1^2+0.3829X_2^2-0.0225X_1{X}_2+0.8437X_1+1.32X_2+1.66$$

(41)

$$Y_3=0.2916X_1^2+0.5866X_2^2+1.48X_1{X}_2-1.44X_1-2.09X_2+1.89$$

(42)

Analysis of variance was performed on the experimental data using Design-expert 13.0 software. The results are presented in

Table 6. Analysis of variance.

Source	Qualified Rate/%		Replay Rate/%		Missed Seeding Rate/%
	F Value	p-Value	F Value	p-Value	F Value	p-Value
Model	80.08	<0.0001	56.02	<0.0001	35.75	<0.0001
X1	35.90	0.0005	74.41	<0.0001	47.14	0.0002
X2	105.86	<0.0001	182.10	<0.0001	98.90	<0.0001
X1 X2	107.40	<0.0001	0.0265	0.8754	24.96	0.0016
X12	29.81	0.0009	13.33	0.0082	1.68	0.2360
X22	135.45	<0.0001	13.33	0.0082	6.80	0.0351
Lack of Fit	2.30	0.2187	0.2888	0.8323	2.29	0.2203

Note: 0.01 < p < 0.05 is generally significant, 0.001 < p < 0.01 is significant, and p < 0.001 is extremely significant.

.

The p-values of the models for qualified rate, replay rate, and missed seeding rate were all less than 0.001, and the differences were extremely significant. The respective F values for the lack of fit terms were 2.30, 0.2888, and 2.29, with corresponding p-values of 0.2187, 0.8323, and 0.2203, all exceeding the significance threshold of 0.05. The insignificant variations in the lack-of-fit terms indicate that the second-order regression equation, as fitted by the model, closely aligned with reality, offering a robust prediction of the test results. In the regression model for the qualified rate, replay rate, and missed seeding rate, the two factors and their interaction terms had extremely significant effects on the qualified rate, replay rate, and missed seeding rate.

Response surface plots were generated in Design-expert 13.0 software to analyze the relationship between the effects of the two factors on the test indices, as shown in Figure 16.

From Figure 16, it was evident that there was a significant interaction between the two factors. When the radius of the shaped hole was relatively small, both the qualified rate and replay rate increased with the depth of the seed guide groove, while the missed seeding rate decreased. This phenomenon can be attributed to the fact that an increased depth of the seed guide groove enhances the contact area with the seeds, thereby allowing for more effective guidance of the seeds into the shaped holes. Conversely, when the radius of the shaped hole was larger, seeds could more easily enter the shaped holes, resulting in an increase in both the qualified rate and replay rate, along with a decrease in the missed seeding rate. However, if the depth of the seed guide groove became excessively large, the guiding force exerted on the seeds may have become too strong, leading to a significant increase in the replay rate and, consequently, a decrease in the qualified rate.

When the depth of the seed guide groove was shallow, the qualified rate increased as the radius of the shaped hole expanded. This occurred because larger seeds encountered difficulties when attempting to enter smaller shaped holes, and a larger radius facilitated their entry, thereby enhancing seeding effectiveness. However, with a deeper seed guide groove, the qualified rate decreased as the radius increased. Although a larger radius allowed for easier entry, the deeper seed guide groove enhanced guidance, resulting in multiple seeds entering the same shaped hole more frequently. This phenomenon led to a higher replay rate and a subsequent decline in the qualified rate.

To explore the optimal parameter combination for each test factor and ensure that the conditions for optimization fell within a reasonable range of design parameters, an optimization solution was employed that aimed to maximize the qualified rate while minimizing the replay rate and missed seeding rate. Equation (43) presents the objective function along with the constraint range for the working parameters.

$$\left\{\begin{array}{l}\max Y_1\left(X_1,X_2\right)\\ \min Y_2\left(X_1,X_2\right)\\ s.t.\left\{\begin{array}{l}-1.414\le X_1\le 1.414\\ -1.414\le X_2\le 1.414\end{array}\right.\end{array}\right.$$

(43)

The optimization process was executed utilizing the “Optimization” module within Design-expert 13.0 software, yielding optimized parameters: the radius of the shaped hole was 4.33 mm and the depth of the seed guide groove was 1.20 mm. These conditions facilitated a qualified rate of 96.48%, a replay rate of 1.69%, and a missed seeding rate of 1.83%.

3.3. Bench Test Results and Analysis

A comparative analysis of the bench and simulation test results was conducted to validate the seeding quality achieved by the seed-metering device during actual operational conditions. The results of the test were averaged over three times, and the results are shown in

Table 7. Bench test results.

Factor	Level	Qualified Rate/%		Replay Rate/%		Missed Seeding Rate/%
		Test Value	Simulation Value	Test Value	Simulation Value	Test Value	Simulation Value
Operating speed /(km·h−1)	6	96.18	96.65	1.24	1.81	2.58	1.54
	7	95.34	96.02	1.02	1.93	3.64	2.05
	8	95.63	95.61	1.08	2.44	3.29	1.95
	9	95.44	95.45	0.81	2.11	3.75	2.44
	10	94.91	95.33	0.54	1.7	4.55	2.97

and Figure 17.

According to Table 7 and Figure 17, the test results from the bench and simulation were found to be closely aligned. The bench tests, conducted at five operating speeds—6, 7, 8, 9, and 10 km/h—yielded relatively favorable outcomes, with all tests achieving a qualified rate exceeding 94%, demonstrating stable seeding performance. At a forward speed of 8 km/h, the bench test recorded a qualified rate of 95.12%, a replay rate of 1.08%, and a missed seeding rate of 3.80%. This result closely corresponds to the data obtained from the regression model calculations, indicating the reliability of the optimized parametric combination.

According to Table 7 and Figure 17, it was observed that with an increase in the operating speed, both the qualified rate and the replay rate decreased, and the missed seeding rate increased. An increase in the forward speed of the seeder may have induced vibrations in the seed-metering device, potentially impeding the efficient entry of seeds into the shaped hole. Concomitantly, as the working speed intensified, the seed-metering device’s velocity escalated, curtailing the seed filling duration. This decrease in filling time resulted in a diminished seed-filling rate and a consequential rise in the missed seeding rate.

During the bench tests, the seed-metering device was mounted on a JSP-12 computer vision-measuring device performance test bench, with only the vibrations generated by the device’s own operation acting as a source of disturbance. In comparison to actual field operations, the system exhibited superior performance, facilitated more effective filling of the shaped holes, and achieved greater uniformity in seed spacing.

3.4. Soil Trench Test Results and Analysis

The soil trench test results are shown in

Table 8. Soil trench test results.

No.	Qualified Rate/%	Replay Rate/%	Missed Seeding Rate/%
1	93.50	2.28	4.22
2	93.11	1.71	5.18
3	93.33	2.12	4.55
Average value	93.31	2.04	4.65

.

According to Table 8, the seed-metering device operating at a speed of 8 km/h achieved a qualified rate of 93.31%, a replay rate of 2.04%, and a missed seeding rate of 4.65%. These findings suggest that the seed-metering device exhibits stable seeding performance, satisfying the criteria for precision sowing operations. The seeding quality of the seed-metering device in the soil trench test was reduced compared to the bench test. It may be that the vibration caused by the forward movement of the soil trench trolley during the soil trench test resulted in a more intense vibration of the seed-metering device, which reduced the quality of seed-filling and seed-casting. In addition, the bouncing roll of the seed as it hit the ground also reduced seeding quality. In the soil trench test, the soil trench trolley operated relatively smoothly and exhibited low vibration. In contrast, during field operations, the seeder may have experienced significant vibrations due to complex ground conditions, which could have adversely affected seeding outcomes. Therefore, the results of the soil trench test may have deviated from the empirical results obtained from the combined field tests.

4. Conclusions

(1)

A soybean double-row seed-metering device with a double-beveled seed guide groove was designed. Through the theoretical analysis of the working process of the seed-metering device, dynamic and kinematic models of the seeds were established. The main factors affecting the seeding performance were obtained as the following: the inclination angle of the triage convex ridge, the radius of the shaped hole, and the depth of the seed guide groove. The ranges of values for the inclination angle of the triage convex ridge, the radius of the shaped hole, and the depth of the seed guide groove were determined to be 11.97–29.57°, 4.1–4.7 mm, and 0–2.61 mm, respectively.

(2)

A discrete element simulation was employed to conduct a single-factor test, using the qualified rate, replay rate, and missed seeding rate as evaluation indicators. The test results were obtained as the following: the inclination angle of the triage convex ridge α₃ = 29°, the radius of the shaped hole r₁ = 4.16–4.5 mm, and the depth of the seed guide l₁ = 0.49–1.89 mm. The qualified rates of the tests were all greater than 95%, meeting the operational requirements of precision seeding.

(3)

A two-factor, five-level, second-order orthogonal rotation combination test was conducted with the radius of the shaped hole and the depth of the seed guide groove as test factors. A regression model between the evaluation indices of the radius of the shaped hole and the depth of the seed guide groove was developed. The test results showed that the radius of the shaped hole and the depth of the seed guide groove had a significant effect on each evaluation index. According to the regression model, the optimal parameter combination was 4.33 mm for the radius of the shaped hole and 1.20 mm for the depth of the seed guide groove. The qualified rate was 96.48%, the replay rate was 1.69%, and the missed seeding rate was 1.83%.

(4)

Bench tests were carried out, and the results showed that the test results from the bench and simulation were consistent. At the operating speed of 6–10 km/h, the qualified rate of seeding was above 94%. A soil trench test was conducted, and the results showed that the seed spacing qualified rate of the seed-metering device was 93.31% at an operating speed of 8 km/h. The replay rate was 2.04% and the missed seeding rate was 4.65%. This met the requirements of precision sowing operation. These research results can provide a reference for the innovative design of precision seed-metering devices.