Study on the Influence of Grooved-Wheel Working Parameters on Fertilizer Emission Performance and Parameter Optimization

Abstract

The grooved-wheel fertilizer machine is one of the most widely used pieces of fertilization equipment. However, detailed information on the fertilizer filling status and the mechanism of particle interactions during the operation of the grooved wheel remains limited. To delve into the underlying mechanisms through which working parameters affect fertilization performance, this study, building upon prior research, conducted a qualitative analysis and numerical investigation of fertilizer particles using the Discrete Element Method. The analysis examined the impact of three working parameters, namely the grooved-wheel speed, working length, and forward speed of the fertilization equipment, on the morphology, forces, and kinetic properties of the fertilizer particles. Combining this analysis with orthogonal experimental research, we optimized the aforementioned working parameters. Both simulation and benchtop experimental results indicate that the grooved-wheel speed and working length influence the fertilizer filling status, while the forward speed of the equipment has no effect on the filling status. The connection between fertilizer force and kinetic changes is influenced by particle-free space. The lowest coefficient of variation (CV) for fertilization uniformity was observed at the grooved-wheel speed of 53.64 r/min, the wheel working length of 33.45 mm, and the forward speed of 0.7–1 m/s. The research findings contribute to a better understanding of the influencing mechanism of particle movement and fertilization outcomes in the operation of grooved-wheel fertilizer spreaders. This understanding enables precise control of the fertilizer application process, facilitating accurate and efficient fertilization. As a result, it enhances fertilizer utilization rates and reduces agricultural costs.

1. Introduction

In modern society, to meet the relentless demand for food due to population growth, many agricultural producers continually strive for high crop yields and extensively use chemical fertilizers in agricultural production. However, the growth rate of crop yields does not proportionally match the rate of fertilizer use. Excessive fertilizer application is a significant issue, leading to increased agricultural production costs, resource wastage, soil compaction, soil acidification, and a decline in land productivity. This, in turn, intensifies the dependence of crop yields on fertilizer application, creating a vicious cycle. Deep fertilization technology is used to divide the fertilizer one or two times during the growth period of the crop and apply the fertilizer to the side depth position of 3–5 cm from the side of the root system of the crop seedling and the soil depth of 5–8 cm. The fertilizer was concentrated at a certain lateral depth from the root system of crop seedlings, which could improve the utilization rate of fertilizer. Therefore, it is considered to be one of the most important methods to promote crop growth and improve productivity [1,2]. In modern mechanized farming systems, deep fertilization is primarily accomplished by deep placement devices during field operations. However, the effectiveness of fertilizer application (fertilizer uniformity) is primarily determined by the fertilizer discharge devices within the deep placement device [3,4]. Therefore, studying the influence of fertilizer discharge devices on fertilizer uniformity is of significant practical value for enhancing fertilizer utilization efficiency and reducing environmental pollution.

The fertilizer distribution mechanism in fertilizer spreaders primarily utilizes the grooved-wheel design, intended for precision fertilizer application. This mechanism employs a wheeled structure, typically featuring multiple grooved or raised surfaces. During the operation of the fertilizer distribution mechanism, these grooves or raised features facilitate the even dispensing of fertilizer into the soil [5]. It offers advantages such as a simple structure, precise flow control, and convenience. However, it suffers from issues of pronounced pulsation and poor stability during the fertilization process [6]. To enhance the working effectiveness of the grooved-wheel fertilizer discharge, researchers have extensively studied its structural parameters [7]. Zhu et al. focused on the straight-toothed wheel structure, analyzing the effects of key structural parameters, including the wheel radius, number of teeth, working length, and groove profile, on fertilization performance. The results revealed that the number of concave grooves significantly influenced the fertilizing performance, while the wheel radius had a notable impact. The optimal combination of structural parameters was found to be a wheel radius of 30 mm, seven concave grooves, an effective working length of 20 mm, and a groove cross-sectional shape with a rounded arc. Under this configuration, the coefficient of variation for fertilizer discharge uniformity was 1.75% [8]. In the preceding research phases of this study, the Discrete Element Method (DEM) was employed to qualitatively analyze and numerically investigate the effects of primary wheel the structural parameters encompassing groove depth, tooth ridge thickness, and helix angle on fertilizer filling status, forces, and kinetic properties. Additionally, through orthogonal experimental analysis, structural parameter optimization was carried out. The results demonstrated that the best fertilization uniformity performance was achieved when the groove depth was 9 mm, the tooth ridge thickness was 2 mm, and the helix angle was set at 45° [9].

However, during field operations, fertilizer application machinery does not operate in isolation within a steady-state environment; it is influenced by various working parameters, including the forward speed of the equipment. For instance, Wang et al. investigated the impacts of three working factors, specifically the wheel’s working length, the rotational speed of the fertilizer discharge shaft, and the opening angle of the fertilizer discharge tongue, on the fertilizer discharge quantity. They quantified the degree to which these parameters affected the fertilizer discharge quantity [10]. The aforementioned studies primarily employed a combination of discrete element simulation and orthogonal experiments or utilized bench-scale experiments with the integration of 3D rapid prototyping technology. These studies yielded insights into the influence of working parameters on fertilization performance. However, most of the existing research has focused on the observation and analysis of post-fertilization states, with a limited understanding of the physical parameter variations and particle interaction mechanisms during the movement of fertilizer particles. A more profound understanding of the relationships among the forces, displacements, and kinetic energies of fertilizer particles under different working parameters and their impact on fertilization uniformity is needed.

With the advancement of computer technology, the DEM and its numerical simulation software, EDEM (2018), have found widespread application in the field of agricultural engineering, enabling the detailed tracking of particle motion [11,12,13]. By establishing a simulation model based on the DEM and EDEM software (2018), performance analysis and numerical simulations of the fertilizer discharge process of an out-wheel variable-rate fertilizer applicator have become feasible. Building on this research, investigations into various working parameters of the applicator and fertilizer application control strategies have been conducted to explore the factors affecting fertilizer discharge stability [14,15]. However, the study of fertilizer particle dynamics and transport behavior of the grooved-wheel fertilizer discharge under different working parameters has not been thoroughly addressed, and it has yet to benefit from the utilization of advanced DEM techniques.

This study aims to investigate the impact of wheel configuration parameters on fertilization effectiveness. Three factors, namely the grooved-wheel speed, wheel working length, and forward speed of the equipment, were selected for examination. Through the application of the DEM, we replicated the motion of fertilizer particles inside a grooved-wheel fertilizer discharge mechanism during field operations. Our goal is to analyze the correlation and differential mechanisms between the changes in particle forces and kinetic energies and the patterns of fertilizer particle transport. This exploration seeks to uncover the intrinsic relationship between the transport behavior of fertilizer particles and the discharge performance under varying working parameters, providing a more comprehensive understanding of particle states. This knowledge contributes to a better comprehension of the discharge behavior of the grooved-wheel fertilizer discharge during field operations. To validate the feasibility of the DEM simulation, practical experiments were conducted using 3D printing technology. Additionally, an orthogonal experimental approach was employed to determine the optimal working parameters of the wheel. This research aims to serve as a reference for the optimization design of grooved-wheel fertilizer discharge systems.

2. Materials and Methods

2.1. Structure Composition of Grooved-Wheel Type Fertilizer Discharger

Building upon prior work, we employed a well-performing out-wheel structure, as illustrated in Figure 1a. This structure features a groove depth of 9 mm, a 2 mm tooth ridge thickness, and a 45° helix angle. In order to maintain uniformity with actual fertilizer discharge processes, we simplified the discharge model by removing components that did not come into contact with the fertilizer, as depicted in the schematic in Figure 1b. The simplified discharge model primarily consists of the wheel, fertilizer box, and brushes. As the focus of optimization in this study, we utilized a 3D printer to produce wheels with varying working lengths, as represented in Figure 1c.

2.2. Grooved-Wheel Working Parameter Analysis

Factors influencing the working effectiveness of the grooved-wheel fertilizer discharge include the wheel working length, the grooved-wheel speed, and the forward speed of the equipment. During the operation of the discharge, fertilizer enters the grooved wheel primarily due to its own gravitational force. The driving mechanism rotates the out-wheel, which, protected by the casing and brushes, conveys the fertilizer to the discharge area. The fertilizer is then guided into the discharge pipe under the influence of gravity, centrifugal force, and thrust, completing the entire discharge process [16].

In accordance with the principles of fertilizer discharge, the formula for calculating the quantity of fertilizer distributed in one rotation of the out-wheel component is as follows:

$$q_1=\frac{\rho \tau zsL}{1000}$$

(1)

$$q_2=\frac{2\rho \pi RL\lambda }{1000}$$

(2)

$$q=q_1+q_2$$

(3)

where, in Equation (1), $q_1$ represents the mass of fertilizer forcibly expelled from the grooves of the wheel, in g/r; $\rho$ represents the density of fertilizer particles, $g/c{m}^3$; $\tau$ represents the filling coefficient of the grooves; z represents the number of grooves; s represents the cross-sectional area of a single groove, in mm²; L represents the effective length of the wheel, in mm. In Equation (2), $q_2$ represents the mass of fertilizer expelled by the driving layer, in g/r; R represents the radius of the wheel, in mm; $\lambda$ represents the driving layer coefficient of fertilizer particles, in mm. In Equation (3), $q$ represents the mass of fertilizer expelled in a rotation of the wheel, in g/r. It can be observed from Equations (1)–(3) that the choice of the working length L of the wheel impacts the filling effectiveness within the grooves, consequently leading to variations in particle forces and kinetic energy. This, in turn, affects the uniformity and stability of fertilization [17].

Based on Figure 2, the force analysis of fertilizer particles during the operation of the wheel yields the following equation for the particle forces:

$$F_S=m{(2\pi n)}^{2}r$$

(4)

$$F_K=4m{v}_r\pi n$$

(5)

$$v_r=\frac{d{s}_r}{dt},a_y=\frac{d^2{s}_r}{d{t}^2}$$

(6)

$$Ek=\frac{1}{2}m(v^2-v{\prime }^2)$$

(7)

In Equation (4), m represents the mass of an individual particle, in grams; F_S represents the centrifugal force acting on the particle, in Newtons. In Equation (5), Fk denotes the Coriolis force generated by the sliding motion of the particle relative to the wheel’s teeth. In Equation (6), $v_r$ represents the tangential speed of the particle relative to the outer wall of the wheel, in meters per second; $a_y$ is the tangential acceleration of the particle along the outer wall of the wheel, in radians per second; s_r represents the tangential sliding distance of the particle along the outer wall of the wheel, in millimeters. Equation (7) defines Ek as kinetic energy, in joules. It can be observed from Equations (4)–(7) that the magnitude of the grooved-wheel speed directly determines the forces acting on fertilizer particles, and the resulting variations in speed affect kinetic energy. Consequently, this has an impact on the uniformity and stability of fertilization.

From Figure 3, it can be observed that during the fertilization process, fertilizer particles are in a state of projection after being ejected from the wheel. The magnitude of the speed of fertilizer particles can be represented as follows:

$$v_x=v_m-4{\pi }^{2}n\cos \sigma$$

(8)

$$S=v_{x}t$$

(9)

In Equation (8), $v_x$ represents the horizontal speed of the fertilizer as it leaves the fertilizer outlet, and $v_m$ is the forward speed of the fertilization equipment. Equation (9) defines S as the displacement from the point where the fertilizer detaches from the outlet to where it lands in the furrow. In Equation (8), it can be noted that both the grooved-wheel speed and the forward speed of the fertilization equipment jointly affect the fertilizer ejection speed. Additionally, the forward speed of the equipment also impacts the motion state of the fertilizer within the wheel. In conclusion, this study primarily centers on the primary working parameters associated with the grooved wheel, namely, the wheel’s working length, the grooved-wheel speed, and the forward speed of the equipment.

2.3. Determination and Selection of Simulation Parameters of Fertilizer Particles

2.3.1. Development of Discrete Element Simulation Platform

In this study, we selected rice-specific compound fertilizer produced by the China National Chemical Corporation (Chem China, Beijing, China) (Sinochem Group Co., Ltd., Beijing, China) as our research subject. This fertilizer is composed of a mixture containing 92% Quick-Acting Fertilizer (QAF) and 8% Slow-Release Fertilizer (SRF). In the blended fertilizer, the QAF has a density of 1.57 g/cm³, and the SRF has a density of 1.32 g/cm³. In this study, we randomly selected 100 intact granules, which included both QAF and SRF types. We performed three-dimensional measurements of their dimensions, specifically length, width, and height, using a vernier caliper manufactured by (Nanjing Sutech Measuring Instruments Co., Ltd., Nanjing, China). The equivalent diameter of the QAF granules was determined to be 3.16 mm, with a sphericity of 0.91. In contrast, the SRF granules exhibited an equivalent diameter of 3.40 mm, with a sphericity of 0.95. When the sphericity of granules exceeds 90%, they can be approximated as spherical units [18]. Therefore, in this paper, individual spherical entities were used to represent QAF and SRF. Following mathematical and statistical procedures, we constructed histograms to depict the frequency of granule sample discharges. Additionally, we overlaid probability density curves to represent the theoretical discharge, as shown in Supplementary Figure S1. It is evident that the frequency discharge patterns of the equivalent diameters for both QAF and SRF closely resemble a normal discharge probability density curve, exhibiting characteristics of a normal discharge function. Consequently, in discrete element simulations, granule models for QAF and SRF were generated based on the equivalent diameter, following a normal distribution pattern.

2.3.2. Discrete Element Contact Model

As a result of the significant interactions and impacts between the fertilizer granules inside the grooved-wheel fertilizer spreader and between the granules and the spreader’s components, contact and collision processes play a crucial role in the transmission of forces and torques within the granule assembly. Accurate calculation of intergranular forces and torques is, therefore, essential. Considering that under normal operating conditions, the moisture content of the fertilizer is low, surface capillary forces between fertilizer granules and electrostatic forces between granules are negligible. Therefore, the granules are treated as non-cohesive bodies. Additionally, as this study primarily focuses on the movement of granules within the spreader and does not consider granule breakage, the Hertz-Mindlin (no-slip) model has demonstrated both precision and computational efficiency in this context [19]. Therefore, this paper employs the Hertz-Mindlin contact model to update the positions of fertilizer particles at any given moment during their transport. Subsequently, it utilizes the force-displacement relationship to update the forces and moments acting on the fertilizer particles by iteratively repeating this process to trace the granule motion at various time points.

It is worth noting that material property values significantly impact simulation accuracy. In the case of the spreader, the fertilizer box and the grooved wheel in contact with the fertilizer granules are fabricated from Polylactic Acid (PLA) material, while the brush is composed of nylon [20]. Preliminary research has summarized the material properties and other relevant contact parameters used in the DEM, as shown in Supplementary Table S1.

2.3.3. Experimental Simulation Method

The model depicted in Figure 1b was incorporated into the DEM simulation software (2018), with a 1:1 scale. The particle manufacturing facility was positioned directly above the fertilizer box. Particles naturally accumulated within the fertilizer box as a result of gravitational forces, using a method involving rainfall. Initial particle velocities were set at 100 mm/s, with a total of 60,000 particles, comprising 55,200 QAF particles and 4800 SRF particles. The particle generation rate was set at 60,000 particles/s, and a 0.5 s pause was imposed to allow the particles to come to a complete stop before initiating the simulation. Consequently, the grooved wheel was set in motion after 1.5 s. To maintain consistency with the bench-scale experiments, reduce simulation intricacy, and minimize simulation time, the fertilizer collection bag was instructed to travel in the positive x-axis direction at the specified speed 1.8 s later. This indirectly simulated the forward motion of the spreading device. The simulation used a time step of 20%, resulting in a total simulation duration of 10 s, with simulation data recorded at 0.01s intervals. On a computer system equipped with two Xeon 5218 central processing units (CPUs) with 128 gigabytes of RAM, a single set of simulations required approximately 74 h to complete. The simulation process is illustrated in Figure 4 [21].

2.3.4. Evaluation Method of Fertilizer Performance

In order to accurately assess the fertilization efficiency of the grooved wheel with different structural parameters during EDEM simulation experiments, the uniformity of spreading was selected as the evaluation metric [22,23]. To ensure precise measurement of the fertilizer mass in each region during stable operation of the spreading device, an area directly beneath the spreader was designated as zone 1. For an accurate assessment of the spreading efficiency, the sampling area for the evaluation of the spreading efficiency consisted of sections 6 to 75 within the fertilizer collection bag (a total of 70 sections). Each of these sections was associated with a Grid Bin Group, as illustrated in Figure 5.

Fertilizer uniformity is a critical performance metric for fertilizer applicators. It refers to the evenness of fertilizer distribution within the target area during field application. Typically, the coefficient of variation (CV) of fertilizer distribution, as shown in Equation (10), is commonly used as the evaluation criterion for the fertilization effect.

$$CV=\frac{S}{\overline{x}}\times 100\%$$

(10)

Here, S represents the standard deviation of the mass of fertilizer particles; and $\overline{x}$ represents the average mass of fertilizer particles within each grid unit, measured in grams. A smaller CV indicates a more favorable uniformity effect [24].

Due to the opaqueness of most fertilizer applicators, it is challenging to visually observe the filling and movement of fertilizer particles within the applicator through experimental observations. Moreover, the movement of particles within the applicator is a complex process. Hence, while assessing the fertilization performance using the CV, it is crucial to perform an extensive analysis of the attributes of fertilizer particles within the fertilizer applicator using the DEM. According to theoretical analysis, variations in the working parameters of the grooved wheel are bound to result in changes in the filling mass or the forces experienced by fertilizer particles. Additionally, as noted by Sun et al., variations in the kinetic energy of the fertilizer particles are associated with the grooved wheel’s structure [25]. To comprehend the connections between various stages in the fertilizer particle loading and unloading process, we conducted a statistical analysis of the average forces experienced by these particles. These forces were measured both as they rotated with the grooved wheel after filling and just prior to their exit from the brushes. Simultaneously, we monitored the total kinetic energy of the fertilizer particles as they dislodged from the brushes but had not yet come into contact with the outer shell of the fertilizer applicator.

2.4. Bench Test Platform

To validate the accuracy of the EDEM numerical simulation, a self-assembled fertilization experimental setup was used to conduct fertilization performance experiments on the grooved-wheel fertilizer applicator. The self-assembled fertilizer experimental setup is shown in Figure 6. During the experiments, the side-deep fertilization device was securely mounted on the experimental frame. The groove-wheel speed was controlled using a motor speed controller, while the conveyor belt speed was adjusted by varying the frequency of the conveyor motor in order to simulate the field conditions. Due to space constraints at the site, an 8000 mm long fertilizer collection bag was situated onto the conveyor belt to gather the fertilizers. The remaining parameters of the fertilizer collection bag matched those used in the simulation to ensure the accuracy of the experimental data.

2.5. Single-Factor Experiment Design

Based on the analysis of critical working factors associated with the grooved wheel, experiments were conducted to investigate the patterns related to the three primary working parameters of the fertilization device: The grooved-wheel speed, grooved-wheel working length, and forward speed. These parameter values were determined in accordance with findings from market analysis and the agronomic needs specific to rice field fertilization, resulting in the following ranges: The grooved-wheel speed from 25 to 65 r/min, the grooved-wheel working length from 8 to 40 mm, and the forward speed from 0.2 to 1.8 m/s. Each of these parameters was individually subjected to single-factor experiments with five levels, which included the grooved-wheel speeds (25, 35, 45, 55, and 65 r/min), grooved-wheel working lengths (8, 16, 24, 32, and 40 mm), and forward speeds (0.2, 0.6, 1, 1.4, and 1.8 m/s). During the single-factor experiments for the grooved-wheel rotation speed, the grooved-wheel working length and forward speed were fixed at 32 mm and 1 m/s, respectively. Similarly, for the single-factor experiments on the grooved-wheel working length, the grooved-wheel speed and forward speed were fixed at 45 r/min and 1 m/s, and for the single-factor experiments on forward speed, the grooved-wheel speed and the working length of the grooved wheel were consistently maintained at 45 revolutions per minute (r/min) and 32 mm (mm), individually.

3. Results and Discussion

3.1. The Influence of the Grooved-Wheel Speed

The grooved-wheel speed is considered a significant influencing factor affecting fertilization effectiveness [26]. In this study, the grooved-wheel speed was set within the range of 25–65 r/min. Experimental results demonstrated that lower rotation speeds resulted in poorer fertilization uniformity, as reduced speeds led to fewer collisions between fertilizer particles and insufficient filling of the grooved-wheel space. Conversely, higher rotation speeds increased the collision frequency among fertilizer particles, resulting in more complete space filling. Furthermore, this study will expound on its underlying mechanisms concerning fertilizer particle motion, force interactions, kinetic energy variations, fertilization uniformity, and the application rate.

3.1.1. Analysis of Movement State of Fertilizer Particles

The initial interaction between fertilizer particles and the grooved wheel occurs within the fertilizer-filling region. Effective filling of the fertilizer is fundamental to the fertilization process; therefore, it is essential to observe and analyze the filling status in this area. In order to visually depict the discharge of fertilizer within the grooves, a cross-sectional view is applied at the symmetric positions of the grooved wheel, as shown in Figure 7a. The kinetic energy monitoring zone is illustrated in Figure 7b, and cross-sectional diagrams of the fertilizer-filling status at various horizontal positions in the filling area are presented in Figure 8.

Figure 8 provides a clear depiction of the radial distribution of fertilizer particles within the grooves of the grooved wheel in the filling region. When the grooved wheel rotates at 25 r/min and 35 r/min, the particle discharge is similar, resulting in limited free space between the particles. This reduced free space prevents smaller particles from fully filling the gaps. However, at a grooved-wheel rotation speed of 45 r/min, the filling status undergoes a significant change. The increased free space between particles allows some smaller particles to fill the gaps between the fertilizer particles. When the grooved-wheel speed reaches 55 r/min and 65 r/min, the free space further expands, enabling more particles of different sizes to fill in. In comparison to the discharge of fertilizer at 45 r/min, the filling of fertilizer in the grooves becomes more complete at these higher speeds.

Figure 9 depicts the trends in speed and mass variations of fertilizer particles within the grooves. It clearly illustrates the pulsation phenomena of fertilizer particles on speed and mass profiles under different grooved-wheel speeds. From Figure 9a, it can be observed that as the rotation speed increases from 25 r/min to 65 r/min, the average speed of fertilizer particles within the grooved wheel’s grooves gradually rises. With the increase in speed, particle speed changes from periodic pulsation to non-periodic pulsation. As shown in Figure 9b, the mass of particles discharged from the grooves of the grooved wheel per unit of time is positively correlated with particle speed. In other words, higher grooved-wheel speeds result in faster particle velocities and greater mass discharged per unit time [27]. However, the pulsation period of fertilizer mass within the grooves does not directly correspond to the speed pulsation period. This discrepancy may be attributed to the restraining effect of the brushes, which hinders the outward movement of particles and, consequently, affects the filling status of fertilizer within the grooves.

3.1.2. Analysis of Force and Kinetic Energy of Fertilizer Particles

Figure 10a showcases the fluctuations in average forces encountered by fertilizer particles as they are discharged with the rotation of the grooved wheel. It is evident that peak fluctuations occur at different speeds, but the frequency of peak occurrence gradually decreases with increasing speed. When the grooved-wheel speed reaches 65 r/min, the peaks are at their maximum, signifying the highest force experienced by the fertilizer particles. This phenomenon is attributed to the increase in kinetic energy carried by the fertilizer as the grooved-wheel speed increases after filling. On one hand, the wall of the grooved wheel exerts a significant force on the fertilizer. On the other hand, the collision that occurs during the high-speed movement of the fertilizer as it makes contact with the brush also influences the force experienced by the fertilizer.

Figure 10b illustrates the variation in the kinetic energy of the fertilizer particles within the grooved wheel. It is evident that the kinetic energy of the fertilizer particles increases with an escalation in the grooved-wheel speed. At lower speeds, the kinetic I have checked and revised all energy exhibits periodic variations. However, as the speed increases, the kinetic energy surges, but the frequency of the kinetic energy peak occurrence diminishes. This is attributed to the compression of free space between the particle groups due to the influence of speed when the speed is high. Consequently, the fertilizer particles experience a greater acceleration, leading to a more stable kinetic energy pattern. Conversely, a reduction in grooved-wheel speed leads to an increase in the relative free space between particle groups, resulting in higher collision frequencies among fertilizer particles. Consequently, this leads to more frequent fluctuations in kinetic energy.

3.1.3. Effect of Grooved-Wheel Speed on Fertilization Uniformity and Fertilization Amount

To examine the influence of the grooved wheel’s rotational speed on the practical outcome of fertilization, we conducted simulation experiments and statistically analyzed the CV of fertilization mass and the corresponding mass of discharged fertilizer over time. The results are presented in Figure 8. It is evident that the CV of fertilization mass decreases gradually with an increase in rotation speed, indicating that higher rotation speed contributes to an improved fertilization effect (smaller CV implies better performance). However, with the increase in rotation speed, the mass of discharged fertilizer also increases linearly [28,29]. Upon closer examination (Figure 11a), at lower rotation speeds, the fluctuations in discharged fertilizer mass over time become more pronounced, with both the number of peaks and their amplitudes decreasing as the rotation speed increases. The findings across different aspects, including forces, kinetic energy, and motion states, indicate that the grooved-wheel speed causes shifts in the forces acting on fertilizer particles. These shifts result in fluctuations in their kinetic energy and subsequently influence their motion state within the grooves. As rotation speed increases, the reduced free space within the particle assembly results in denser filling, with fewer particle displacements and collisions. Consequently, the motion state of the fertilizer within the grooves, in turn, influences the peak values and amplitudes of forces, kinetic energy, and fertilization mass. In summary, a higher rotation speed leads to greater particle forces, more kinetic energy, a higher mass of discharged fertilizer per unit collection bag, and a smaller CV. Furthermore, the fluctuation in forces, kinetic energy, and the mass of discharged fertilizer per unit collection bag decreases, approaching a more stable state.

3.2. The Influence of the Working Length of the Grooved Wheel

3.2.1. Analysis of Movement State of Fertilizer Particles

Figure 12 illustrates the motion of fertilizer particles under different grooved-wheel working lengths. When the grooved wheel has a working length of 8 mm, the limited radial space results in the lowest fertilizer-filling mass. As the grooved wheel’s working length increases, more fertilizer particles can be accommodated within a single groove. Given that the cross-sectional design of the grooves remains consistent for different working lengths, the circumferential discharge of fertilizer particles is similar. However, it is worth noting that an increase in the grooved wheel’s working length extends the length of the inclined grooves. This, in turn, subjects the fertilizer particles at the lower end of the inclined grooves to forces such as gravity, wall-induced forces, and compressive forces. Consequently, the free space between fertilizer particle clusters at the lower end of the inclined grooves decreases, leading to a denser filling.

Based on Figure 13a, it can be observed that the average speed of fertilizer particles in the grooves increases with an increase in working length. However, the speed of fertilizer particles exhibits an initial sharp variation followed by a gradual stabilization. This behavior is attributed to the fact that when the grooved wheel’s working length is relatively short, fertilizer particles experience displacement due to the forces exerted by the groove’s inclined surface and gravity. Nevertheless, the limited free space within the groove results in a smaller displacement of the fertilizer particles during their discharge [30]. As the working length increases, the increased free space allows for greater displacement of the fertilizer particles during discharge, ultimately leading to higher average velocities with longer working lengths. To quantify the discharge of fertilizer within the inclined grooves, the mass of fertilizer within the grooves was calculated. As depicted in Figure 13b, the mass of fertilizer filling increases with an increase in the working length of the grooved wheel. However, for shorter working lengths, there is more pronounced fluctuation and larger amplitude in the filling mass. This is because, as a result of shorter working lengths, the confined space within the grooves results in rapid filling and discharge of fertilizer particles over a short period. As the working length of the grooved wheel increases, the increased space within the grooves necessitates a certain period of displacement for the fertilizer particles to exit, leading to a smoother change in particle mass per unit of time.

3.2.2. Analysis of Force and Kinetic Energy of Fertilizer Particles

As shown in Figure 14a, the values of the forces exerted on fertilizer particles indicate that different working lengths of the grooved wheel have an insignificant impact on the variations in particle forces. This observation suggests that the consistent cross-sectional profile of the grooved wheel is maintained as the working length increases. Therefore, the squeezing forces exerted on the fertilizer particles by the groove walls remain consistent. However, different working lengths of the grooved wheel can influence the filling status and descent displacement of fertilizer particles, which, in turn, affect the changes in particle forces. Additionally, the contact transfer interactions between the fertilizer particles weaken as the groove length increases. Consequently, compared to the phenomenon observed with shorter grooved-wheel lengths, which exhibit multiple peaks and larger force peaks, the force profile becomes smoother with longer groove lengths. The pattern of kinetic energy variation of fertilizer particles within the grooved wheel is illustrated in Figure 14b. It is evident that, with an increase in the working length of the grooved wheel, the kinetic energy experienced by the fertilizer particles also increases. Furthermore, it is noteworthy that the peaks in force and kinetic energy do not correspond one-to-one. This disparity may be attributed to the combined influence of the brushing and the interaction with the inner wall of the fertilizer discharge device as the particles move, as well as the inherent rheological properties of the particle assembly.

3.2.3. Effect of the Working Length of the Grooved Wheel on Fertilization Uniformity and Fertilization Amount

To provide a more precise analysis of the impact of grooved-wheel working length on the operational efficiency of fertilizer discharge, we conducted quantitative assessments of fertilizer discharge uniformity (CV) and the associated discharge quantity [31]. These measurements were carried out through a combination of simulation and experimental testing across various working lengths of the grooved wheel, specifically 8 mm, 16 mm, 24 mm, 32 mm, and 40 mm. These tests were conducted at a fixed rotation speed of 45 r/min and a forward speed of 1 m/s. As the working length of the grooved wheel extends, there is a corresponding rise in the discharged mass of fertilizer [32]. When the grooved wheel length reaches 40 mm, the CV reaches its minimum value. This observation is reflected in Figure 15b, which shows that at this point, there are fewer peaks in fertilizer kinetic energy. Therefore, it can be inferred that, to a certain extent, increasing the residence time of fertilizer particles in the grooves improves fertilizer uniformity. Thus, increasing the grooved wheel working length will increase the discharge quantity to some extent and reduce the CV value. Overall, the influence of the grooved-wheel working length on the grooved wheel’s performance is significant.

3.3. The Influence of Forward Speed

3.3.1. Analysis of Movement State of Fertilizer Particles

As shown in Figure 16, fertilizer discharge changes in the grooved wheel with different forward speeds can be found when fertilizer filling conditions are roughly the same under different forward speeds, and the filling state cannot reflect the influence of forward speeds on the movement state of fertilizer particles.

As shown in Figure 17, it is evident that with the increase in forward machinery speed, particle speed increases [33]. This increase in particle speed is primarily attributed to the inertia force carried by the particles during their ejection by the high-speed-moving machinery. Hence, higher forward machinery velocities result in greater particle velocities. However, there is no discernible pattern in the variation of fertilizer mass per unit of time with increasing forward speed (Figure 17b). This phenomenon occurs because, under constant grooved-wheel speed and working length, the grooved wheel’s capacity to carry fertilizer remains constant.

3.3.2. Analysis of Force and Kinetic Energy of Fertilizer Particles

As shown in Figure 18a, the impact of forward speed on the force experienced by fertilizer particles follows a pattern similar to that of the influence of the grooved-wheel speed on fertilizer particle forces. In both cases, as the speed increases, the force on the fertilizer particles gradually intensifies.

Observing Figure 18b, we can note that the kinetic energy of fertilizer particles increases as the forward speed increases speed. However, it is noteworthy that under different forward velocities, the periodicity of kinetic energy fluctuation of fertilizer particles remains similar, with minimal amplitude variations. This consistency can be attributed to the diminishing available space for the fertilizer particles as they travel at elevated forward velocities, increasing the number of contacts between the particles, brushes, grooved wheels, and other particles. The resulting collision energy consequently rises. However, it should be emphasized that various forward velocities merely correspond to the application of force in the direction of work to the fertilizer particles, resulting in similar patterns of kinetic energy fluctuation under different forward velocities.

3.3.3. Effect of the Forward Speed of the Grooved Wheel on Fertilization Uniformity and Fertilization Amount

Through a combination of simulation modeling and experimental data obtained from an actual test setup, we conducted a statistical analysis of the fertilization uniformity (CV) and the discharged fertilizer mass under various forward velocities. The results are presented in Figure 19. Notably, we observed a decrease in the mass of discharged fertilizer with an increase in the forward speed. This stands in contrast to the fertilization performance with respect to the grooved-wheel speed and grooved-wheel working length, where an increase in speed led to greater fertilization. The cause of this phenomenon can be attributed to the decrease in fertilizer particle mass within the groove as the forward speed of the implement increases. The reduced duration spent beneath the machine for a specific working length subsequently leads to a diminished overall fertilizer application. Correspondingly, we discovered that the CV increases with higher forward velocities, reaching its minimum value at a forward speed of 0.2 m/s. In summary, these findings collectively demonstrate the significant influence of forward speed on the performance of the grooved wheel.

3.4. Design and Analysis of Orthogonal Experiment

We have uncovered a significant correlation between three parameters: The grooved-wheel speed (A), grooved-wheel working length (B), and forward speed of equipment (C), and the uniformity of fertilization through simulation analysis. Based on the principles observed through single-factor analysis, we have established the following parameter ranges: A within 30–60 r/min, B spanning 10–40 mm, and C ranging from 0.5 to 1.5 m/s. Subsequently, we employed the CV as our evaluative metric and devised a quadratic orthogonal rotation combination experiment that integrates three factors with five levels each. This approach facilitates the further optimization of the grooved wheel’s working parameters and the identification of the most favorable combination of parameters. Detailed descriptions of the experimental factors and levels are available in

Table 1. Factors and levels of orthogonal experiment.

Levels	Grooved-Wheel Speed (r/min)	Working Length of Grooved-Wheel (mm)	Forward Speed (m/s)
1.682	60	40	1.5
1	53.92	33.92	1.3
0	45	25	1
−1	36.08	16.08	0.7
−1.682	30	10	0.5

.

In the design of orthogonal experiments, it is imperative to account for the interplay between various factors. The interaction between two factors is termed a first-level interaction, whereas the interaction involving three or more factors is referred to as a high-level interaction. It is worth noting that, in many practical scenarios, high-level interactions are typically disregarded [13]. We adopted a three-factor five-level quadrature rotation combination design scheme. A total of 23 groups of tests were designed, and the test scheme and results are shown in

Table 2. Orthogonal experiment result.

No.	Factor						Performanceindex
	A (r/min)	B (mm)	C (m/s)	A × B	A × C	B × C	y%
1	−1	−1	−1	−1	−1	−1	20.69
2	1	−1	−1	−1	−1	1	9.39
3	−1	1	−1	−1	1	−1	11.97
4	1	1	−1	1	−1	−1	6.28
5	−1	−1	1	1	−1	1	21.50
6	1	−1	1	−1	1	−1	19.94
7	−1	1	1	−1	−1	1	17.17
8	1	1	1	1	1	1	12.15
9	−1.682	0	0	0	0	0	20.70
10	1.682	0	0	0	0	0	9.73
11	0	−1.682	0	0	0	0	21.55
12	0	1.682	0	0	0	0	8.69
13	0	0	−1.682	0	0	0	7.60
14	0	0	1.682	0	0	0	20.51
15	0	0	0	0	0	0	17.32
16	0	0	0	0	0	0	18.94
17	0	0	0	0	0	0	17.77
18	0	0	0	0	0	0	19.29
19	0	0	0	0	0	0	18.23
20	0	0	0	0	0	0	16.67
21	0	0	0	0	0	0	19.57
22	0	0	0	0	0	0	17.43
23	0	0	0	0	0	0	16.90

.

3.4.1. Variance Analysis

According to the results of the quadratic orthogonal rotation combination test in the table, quadratic regression analysis was carried out, and the quadratic regression equation of the variation coefficient y of fertilizer discharge uniformity was obtained as follows:

$$\begin{array}{l}y=10.98+0.01x_1+0.40x_2+16.57x_3+3.38\times {10}^{-3}{x}_1{x}_2+\\ 0.49x_1{x}_3-0.01x_2{x}_3-0.01x_1{}^2-0.02x_2{}^2-13.67x_3{}^2\end{array}$$

(11)

The significance test of the regression equation and its coefficients was carried out. The variance analysis of each factor on the variation coefficient of fertilizer discharge uniformity is shown in

Table 3. Significance test sheet.

Sources of Variance	Sum of Squares	Freedom	Mean Squares	F	p-Value Prob > F	Significance
A	129.28	1	129.28	66.76	<0.0001	$\ast \ast$
B	120.30	1	120.30	62.12	<0.0001	$\ast \ast$
C	142.68	1	142.68	73.67	<0.0001	$\ast \ast$
A × B	0.58	1	0.58	0.30	0.5942
A × C	13.55	1	13.55	6.99	0.0202	$\ast$
B × C	0.011	1	0.011	5.428 × 10−3	0.9424
A2	10.69	1	10.69	5.52	0.0352	$\ast$
B2	30.45	1	30.45	15.72	0.0016	$\ast \ast$
C2	24.06	1	24.06	12.42	0.0037	$\ast \ast$
e	8.88	8	1.11

Note: ** shows this item is very significant (< 0.01); * shows this item is significant (> 0.01 and < 0.05); e shows residual error.

.

To accurately assess the hierarchical importance of the three working parameters of the grooved wheel and their influence on fertilization performance, especially when considering the interdependencies between these variables, a variance analysis is indispensable. This analysis is conducted on the outcomes of the simulation experiment to ascertain their statistical significance. Table 3 provides the outcomes of the variance analysis, where F(A) < 0.0001, F(B) < 0.0001, and F(C) < 0.0001. Hence, it is evident that factors A, B, and C exert a highly significant influence on the experimental outcomes. The interaction term A × C significantly affects the results, whereas it is evident that the interaction terms A × B and B × C have a relatively minor influence on the results. In summary, the order of importance for the dominant and ancillary factors influencing fertilization uniformity is as follows: C, A, B, A × C, A × B, and B × C.

3.4.2. Response Surface Analysis of Interaction between Factors

The response surface for the coefficient of variation with regard to the uniformity of fertilization concerning various factors was obtained using Design-Expert 8.0.6 software, as shown in Figure 15. From Figure 20a, it can be observed that at a zero level of machine forward speed, the coefficient of variation for fertilization uniformity decreases as the grooved wheel’s rotational speed and working length increase, a trend similar to the impact observed under single-factor conditions. This indicates that under the interaction of working parameters, grooved-wheel speed and working length remain the primary factors affecting fertilization uniformity, with parameter interactions having a relatively minor impact. As seen in Figure 20b, at a zero level of working length, the coefficient of variation for fertilization uniformity decreases with increasing grooved-wheel speed and increases with increasing machine forward speed. The response surface reveals that compared to grooved-wheel speed, machine forward speed has a more significant impact on the coefficient of variation for fertilization uniformity. This is because machine forward speed more significantly affects the amount of fertilization over a unit of working length. Figure 20c shows that when the grooved-wheel speed is at zero, the coefficient of variation for fertilization uniformity increases with increasing machine forward speed and decreases with increasing working length. The response surface indicates that grooved-wheel speed has a more substantial impact on the coefficient of variation for fertilization uniformity compared to the working length. Consequently, combining the above analysis, the order of influence of the various working parameters on the coefficient of variation for fertilization uniformity is as follows: forward speed > grooved-wheel speed > working length. When considering factor interactions, it was found that only the interaction between grooved-wheel speed and machine forward speed has an impact on fertilization uniformity. This underscores that the single-factor variations in working parameters have a greater influence on particle motion than the interactions between factors on particle motion.

3.5. Performance Comparison of Optimized Working Parameters

The range of solved parameters is used to minimize the objective function under constraint conditions, where the optimization objective function and constraints are denoted as $\min y(x_1,x_2,x_3)$, $36.08 \mathrm{r}/\min \le x_1\le 53.92 \mathrm{r}/\min$, $16.08 \mathrm{mm}\le x_2\le 33.92 \mathrm{mm}$, and $0.7 \mathrm{m}/\mathrm{s}\le x_3\le 1.3 \mathrm{m}/\mathrm{s}$. Based on the results of orthogonal rotation experiments, the grooved-wheel speed, working length, and forward speed are set to 53.64 r/min, 33.45 mm, and 0.71 m/s, respectively. Under this combination, the coefficient of variation for fertilization uniformity is 4.95%. To validate the determined working parameter combination, verification experiments were conducted in May 2023 on the seed/fertilizer performance test bench. The average coefficient of variation for fertilization uniformity in the verification results was 5.44%, which slightly deviated from the optimization results. In the environment of the test bench, experimental factors are more complex. Fertilizers undergo changes in their relevant physical parameters due to their hygroscopic nature, which can introduce deviations from the parameters set in simulation experiments. Additionally, there are variations in particle geometry. Significantly, during the bench experiments, equipment vibration and air resistance affect the movement of fertilizer particles, causing them to diffuse more during the fertilization process [34]. This diffusion affects the uniformity of fertilization, albeit within acceptable margins of error [35]. In contrast, simulation conditions are more simplified and do not account for these complex factors. Therefore, differences between simulated and actual values might exist. Despite these variances, overall, the differences between simulated and actual values are relatively small. Consequently, the simulation can effectively reflect the patterns of grooved-wheel parameters in real-world environments within a certain margin of error. This suggests that within a reasonable margin of error, simulation can serve as a valuable tool for predicting changes in grooved-wheel working parameters in real-world conditions and can provide insights into the optimization of precise intelligent agricultural equipment.

This study is compared with the most advanced research results, as shown in

Table 4. Comparison of results.

	Structure Parameters		Working Parameters		CV (%)
Optimize the rear grooved wheel	Depth of groove (mm)	9	Grooved-wheel speed (r/min)	53.64	4.95
	Ridge thickness (mm)	2	Working length (mm)	33.45
	Lead angle (°)	45	Forward speed (m/s)	0.71
Wang et al. [9]	Depth of groove (mm)	9	Grooved-wheel speed (r/min)	45	9.08
	Ridge thickness (mm)	2	Working length (mm)	40
	Lead angle (°)	45	Forward speed (m/s)	1
Zhu et al. [8]	Depth of groove (mm)	*	Grooved-wheel speed (r/min)	20	5.48
	Ridge thickness (mm)	*	Working length (mm)	20
	Lead angle (°)	*	Forward speed (m/s)	0.5
Villette et al. [26]	Depth of groove (mm)	15	Grooved-wheel speed (r/min)	30	31.48
	Ridge thickness (mm)	2	Working length (mm)	30
	Lead angle (°)	60	Forward speed (m/s)	0.6
He et al. [36]	Depth of groove (mm)	8.5	Grooved-wheel speed (r/min)	40	14.62
	Ridge thickness (mm)	*	Working length (mm)	21
	Lead angle (°)	*	Forward speed (m/s)	*

Note: * original manuscript not explained.

. It can be seen that most studies have focused on the influence of structural parameters on fertilizer uniformity and have achieved good results. Our research focuses on the working parameters of the grooved-wheel fertilizer discharger to explore the fertilizer movement characteristics and fertilization effect. It can be found that good structural parameters plus optimal working parameters can achieve the best working results (CV = 4.95%) compared to the most advanced research results.

4. Conclusions

This study employed the DEM to conduct an in-depth investigation into the influence patterns of three primary operating parameters of grooved wheels, namely the grooved-wheel speed, working length, and forward speed, on the coefficient of variation for fertilization uniformity (CV) and the discharged mass. The study also provided particle-scale information, which is beneficial for a better understanding of the particle movement status within the grooved wheel’s fertilizer discharge under different operating parameters. The research results revealed that microscale information about the particle movement process could be well represented through factors like the particle filling state, speed, force, and kinetic energy. From an individual factor standpoint, grooved-wheel speed and working length of the grooved wheel both impact particle forces, resulting in variations in particle speed and kinetic energy. These alterations subsequently influence particle-free space, which, in turn, has implications for both the coefficient of variation (CV) and the discharged mass. In contrast, forward speed primarily influences the unit length of machine stay time and, consequently, impacts CV. Grooved-wheel speed and working length are positively correlated with fertilization uniformity, while forward speed is inversely related. Building upon single-factor analysis, a three-factor, five-level quadratic orthogonal rotation combination experiment was conducted. Significance analysis revealed that the order of primary factors affecting fertilization uniformity is forward speed > grooved-wheel speed > grooved-wheel working length. The lowest CV for fertilization uniformity was achieved when grooved-wheel speed, working length, and forward speed were set to 53.64 r/min, 33.45 mm, and 0.71 m/s, respectively (simulated CV of 4.95%, bench test result of 5.44%). In summary, the utilization of simulation technology contributes to the acquisition of microscale hidden flow characteristics of particle movement, facilitating a profound understanding of the dynamic response mechanism of particle groups due to variations in machine operating parameters. This has significant implications for accelerating equipment development and promoting the advancement of precision agriculture.