Optimal Design and Experiment of Electronically Controlled Inclined Spiral Precision Fertilizer Discharger

Abstract

In order to solve the traditional single-spiral fertilizer discharger issue of the fluctuation of fertilizer-discharge flow and the problem of precise fertilizer discharge, the innovative design of a cantilevered oblique placement of a fertilizer-discharging spiral structure in the form of an inclined spiral fertilizer discharger was realized, in which, through the fertilizer spiral’s full end-filled extrusion, uniform delivery of the discharge was achieved. Discrete element simulation was used to compare the fertilizer-discharge characteristics of inclined and traditional single-spiral fertilizer dischargers, and the results proved that the inclined spiral fertilizer discharger effectively reduced the fluctuation of the fertilizer-discharge flow rate. Through a theoretical analysis preformed to determine the theoretical fertilizer discharge and the main parameters affecting the uniformity of fertilizer discharge, we identified the tilting angle of the fertilizer discharger (θ) and the distance from the termination spiral blade to the fertilizer outlet (l). A two-factor, five-level quadratic generalized rotary combination experiment was conducted with two parameters (θ and l) as the experiment factors and the variation coefficient of fertilizer-discharge uniformity (σ) as the experiment indicator. The experimental results showed that for σ, θ was a highly significant effect, l was a significant effect, and σ was less than 8.5%; when θ was 35.02° and l was 16.87 mm, the fertilizer-discharge performance was better. A bench experiment was used to compare the traditional and inclined spiral fertilizer dischargers, and the results showed that the relative error of the variation coefficient between the bench and the simulation experiment under this combination was 2.28%. And compared with the traditional spiral fertilizer discharger’s σ average increase of 80.79%, the effect of fertilizer discharge was better than the traditional spiral fertilizer discharger. A fertilizer application controller was developed, and the bench performance was tested based on the measured fertilizer-discharge flow rate fitting equation of this combined inclined spiral fertilizer discharger. The results show that the electronically controlled inclined spiral fertilizer discharger has an average deviation of 3.12% from the preset value, which can be used to regulate the flow of fertilizer discharged through the fertilizer controller to realize precise fertilizer application, and this study can provide a reference for the optimal design of the spiral fertilizer discharger.

1. Introduction

China will continue to build a diversified food supply system in the future, and its agricultural competitiveness will increase significantly. Under the strategic conditions based on the strategy of storing food on land and technology, the foundation of China’s food security will continue to be strengthened [1,2]. The application of chemical fertilizer is the material basis for guaranteeing food production, wherein achieving a reduction in the total amount of agricultural chemical fertilizer applied, increasing the amount of organic fertilizer resources returned to the field, and improving the utilization rate of chemical fertilizer are crucial [3,4,5]. Mechanized and rational application of fertilizer can reduce human labor and greatly improve the effective utilization of fertilizer [6,7]. Nowadays, China’s rural areas have achieved comprehensive poverty alleviation, comprehensively entering the era of rural revitalization. This cannot be separated from precision agriculture technology, and precision fertilizer application is one of the core links in precision agriculture technology [8,9,10], as related scholars have conducted a lot of research on precision fertilizer application.

Debayan Mondal et al. [11] designed a spiral conveying device for conveying granular bulk materials with a better conveying effect, analyzed the material filling situation in the spiral cavity, and investigated the performance characteristics and trends of the spiral for conveying fertilizers at different rotational speeds. Dun et al. [12] designed a spiral extrusion-type discharger for fine amounts of fertilizer, through the fertilizer-filled cavity spiral extrusion conveying and discharging fertilizer. They conducted a simulation experiment and a bench experiment to verify the effect of each method on the installation of fertilizer port inclination in order to optimize the length of the fertilizer port and determine the parameters of the optimized discharger’s fertilizer-discharging uniformity and ability to discharge the amount of fertilizer with a small loss. Zha et al. [13] designed a retaining wheel auger fertilizer applicator with parameter optimization using EDEM 2020, which was confirmed to meet the requirements of the national standard uniformity through bench and field experiments, and solved the problem of the traditional auger fertilizer applicator that only relies on the rotational speed to regulate the amount of fertilizer applied as well as the problem of poor uniformity of fertilizer application at low speeds. Guo et al. [14] designed a bi-directional spiral fertilizer discharger for lateral deep fertilization of rice and simulated the fertilizer-discharging operation based on EDEM to determine the effect of different fertilizer-discharging rotational speeds on the fertilizer-discharging uniformity under the normal travel speed of the machine. The above study proved that the structural characteristics of the spiral fertilizer-discharging wheel itself led to the existence of fertilizer in the cavity, which was not filled, and the phenomenon of fertilizer-discharging pulsation cannot be calculated accurately by the fertilizer-discharging flow. Therefore, this paper designs a kind of inclined spiral fertilizer discharger, which is placed in an inclined way based on gravity to make the fertilizer pile up to fill the cavity, improve the stable filling coefficient, and make it possible to control the fertilizer-discharge flow by controlling the rotational speed accurately in order to realize a uniform and precise amount of controllable fertilizer discharge.

In this paper, by analyzing the problem of the uneven fluctuation of fertilizer-discharge flow with a traditional spiral fertilizer discharger, the structural form of a single-spiral fertilizer discharger was optimized and improved to design a kind of inclined spiral fertilizer discharger. We analyzed the variational influence of the structural parameters of the fertilizer discharger on the fertilizer-discharging performance and conducted an analysis of variance on the variation coefficient of the fertilizer-discharging uniformity of the fertilizer discharger under different parameters by using the interaction of the discrete element simulation technique and the response surface experiment. The 3D rapid prototyping technology was used to manufacture and assemble the inclined spiral fertilizer discharger and equipped with the designed electronically controlled fertilizer discharger controller for the bench experiment to realize the amount of fertilizer discharged at different rotational speeds and to provide a reference for the further optimization of the spiral fertilizer discharger.

2. Materials and Methods

2.1. Structural Composition of Electronically Controlled Inclined Spiral Precision Fertilizer Discharger

The structure of the electronically controlled inclined spiral precision fertilizer discharger mainly consists of the inclined spiral fertilizer discharger, fertilizer application controller, and motor, as shown in Figure 1. Fertilizer discharge requires the operation of the integrated fertilizer controller, which is commonly used to manage various fertilizer flow curves. This control enables the motor to drive the rotation of the fertilizer-discharge shaft, thereby activating the inclined spiral fertilizer discharger. The controller features an intelligent human–machine interface for inputting new fertilizer-discharge flow curves to update its functionality. The spiral fertilizer wheel is a crucial component for executing the fertilizer-discharge process. During operation, within the fertilizer sleeve shell and under the influence of the spiral blades on the fertilizer wheel, the fertilizer at the bottom rotates above the fertilizer-discharge port. The fertilizer particles are propelled by the inclined spiral blades and affected by both gravity and stacking pressure, resulting in a gradual and uniform overflow through the discharge outlet. This ensures consistent and precise fertilizer distribution.

The design of the inclined spiral fertilizer discharger addresses two main factors. Firstly, traditional spiral fertilizer dischargers experience cyclic opening and closing of the spiral discharging wheel and fertilizer outlet, leading to cyclically uneven discharge of fertilizer particles with significant fluctuations. Secondly, in traditional designs, the fertilizer filling rate in the sleeve shell typically does not exceed 80% [15]. This results in varying volumes of fertilizer discharged over time from the spiral blades at the outlet. To address the aforementioned issues, we designed the inclined spiral fertilizer discharger to stabilize and increase the cavity with fertilizers. By maintaining a distance between the termination of the spiral blades and the fertilizer outlet, we created a buffer to mitigate fluctuations and resolve issues such as cyclic discharge and inconsistent instantaneous volumes of fertilizer. The rotational speed of the spiral fertilizer discharging wheel is directly proportional to the fertilizer-discharge rate, establishing a linear relationship. This allows for precise calculation and control of the fertilizer-discharge rate, thereby enhancing the uniformity of fertilizer distribution and improving the controllable precision of fertilizer application.

2.2. Theoretical Analysis of Inclined Spiral Fertilizer Discharger

2.2.1. Theoretical Discharge Capacity of Inclined Spiral Fertilizer Discharger

The basic structural parameters established for the inclined spiral fertilizer discharger, focusing on its core component (double-head spiral fertilizer discharging wheel) in this study, are as follows: spiral blade outer diameter D₁ = 50 mm, spiral blade inner diameter D₂ = 26 mm, pitch S = 36 mm, and average blade thickness k = 2 mm. These parameters ensure compliance with the maximum fertilizer-discharge capacity of 375 kg/hm² as specified in GB/T35487-2017. To determine the maximum rotational speed of the fertilizer-discharge wheel, the fertilizer composite coefficient C was identified based on reference [16], and the maximum speed of the spiral fertilizer-discharge wheel was calculated using Equation (1).

$$\frac{C}{\sqrt{D_1}}\ge N_{max}$$

(1)

where C is the fertilizer composite factor, C = 50; D₁ is the spiral blade outer diameter, mm; N_max is the maximum speed of the spiral fertilizer wheel, r/min.

Both the inclined spiral fertilizer discharger and the traditional spiral fertilizer discharger operate based on the spiral conveyor mechanism [17]. However, the primary distinction between these two types of theoretical fertilizer dischargers lies in the fertilizer filling rate within the discharger shell cavity. This can be calculated using Formulas (4) and (5) to determine the theoretical fertilizer-discharge amount for the inclined spiral discharger, where the filling coefficient is assumed to be 1.

$$q=\left[\frac{\pi \left(D_1^2-D_2^2\right)S}{4}-jkh\frac{\sqrt{{\left[\pi \left(D_1+D_2\right)\right]}^2+4S^2}}{2}\right]\rho \phi$$

(2)

where q is the fertilizer-discharge per cycle, g; D₂ is the spiral blade inner diameter, mm; S is the pitch of the spiral, mm; j is the number of spiral blades; k is the average blade thickness, mm; ρ is the fertilizer density, g/mm³; φ is the filling factor of fertilizer-discharge spirals, %.

$$Q=qt\omega$$

(3)

where Q is the fertilizer discharged quantity, g; t is the rotation time, s; ω is the fertilizer wheel speed, rad/s.

2.2.2. Fertilizer-Discharge Performance Parameter Analysis

During the operation of the inclined spiral fertilizer discharger, fertilizer particles come into contact with the cavity wall. To determine the minimum inclination angle of the discharger and its impact on performance, a force analysis was conducted at the point of maximum friction on the fertilizer, assuming ideal ambient conditions with no air humidity. This analysis included an examination of the fertilizer’s motion state, as illustrated in Figure 2.

$$W_f=L\cdot F_f=\mu \left(mgcos\theta +m{\omega }^{2}R\right)L$$

(4)

where W_f is the energy loss due to friction between shell and fertilizer, J; F_f is the friction on fertilizer, N; μ is the coefficient of friction; θ is the tilting angle of the fertilizer-discharge unit, °; R is the overall fertilizer center of mass radius, m; L is the fertilizer overall actual distance traveled, m.

$$v_P=\frac{\omega S}{2\pi }co{s}^2\gamma$$

(5)

where v_p is the overall fertilizer moving speed along θ inclination angle, m/s; γ is helix inclination, °.

$$Wv=\frac{m\cdot {v_p}^2\cdot cos\theta }{2}$$

(6)

where W_v is the kinetic energy of fertilizer slanting along θ inclination angle, J; v_r is the overall fertilizer circumferential velocity, m/s.

The above discussion reveals that the tilt angle θ of the inclined spiral fertilizer discharger significantly affects its fertilizer-discharge performance. θ should exceed the angle of repose of the fertilizer, which, according to relevant literature [18,19,20], typically ranges from 20 to 30 degrees for commonly used fertilizers. For the inclined spiral discharge mechanism to ensure proper cavity filling, the fertilizer needs to undergo a backflow process along the inner wall of the cavity. Without this backflow condition, the fertilizer would simply be pushed outward along the cavity’s inner wall during discharge, preventing proper accumulation and full filling of the fertilizer discharger, thus deviating from its design concept. Therefore, considering the practical contact characteristics of the material, the inclined angle θ of the inclined spiral fertilizer discharger is set to not be less than 30° to ensure effective and consistent fertilizer discharge.

As depicted in Figure 3, the distance from the terminating spiral blade of the fertilizer-discharge wheel to the fertilizer outlet (referred to as l) impacts the fertilizer filling rate and delivery performance. This additional distance is crucially considered, with its primary influence on the filling space typically extending approximately three-quarters of the blade’s pitch.

$$W_l=mglsin\theta$$

(7)

where l is the fertilizer-discharge wheel termination spiral blade to fertilizer outlet distance, mm; W_l is the kinetic energy of fertilizer on l during the discharging of fertilizer, J.

Inclined spiral fertilizer discharger in the process of transporting fertilizer can be based on the principle of following the law of conservation of energy, expressed as the by the following formula:

$$W_T=W_v+W_l-W_f-W_o$$

(8)

where W_T is the inclined spiral fertilizer discharger total fertilizer delivery capacity, J; W_o is other energy loss, J.

Previous analysis found that the size of the inclined spiral fertilizer discharger l directly impacts the fertilizer filling rate. For this reason, the tilting angle of 35° is an example of the theoretical analysis of the filling process concerning the fertilizer discharger fertilizer simulation state, with the use of SolidWorks 2022 software (Dassault Systemes, Waltham, MA, USA) for the slanting spiral fertilizer discharger z-distance of the fertilizer filling condition in three-dimensional modeling [21], as shown in Figure 4.

The evaluation function of the software was used to measure the volumetric attributes and the three-dimensional model of the fertilizer capacity space, and the three-dimensional stacking state of the spiral discharge wheel was selected for volumetric identification, as shown in Figure 5.

To explore the relationship between different values of l and the filling rate, volumetric analysis was conducted to examine how variations in l affect the filling of the fertilizer exhauster cavity. Formula (9) was employed for parametric modeling and volumetric assessment, revealing trends in cavity z-distance filling rates. The findings are presented in Figure 6. From 0 to 20 mm, the cavity filling rate increased significantly; when the value for reaching the full filling state was greater than 20 mm, the filling rate remained unchanged, and it can be seen that l has a direct impact on the cavity filling condition. When l is longer, the filling condition is without fluctuations and exhibits a smooth phenomenon; l was comprehensively determined up to 40 mm.

$$e=\frac{V_m}{V}\times 100\%$$

(9)

where e is the fertilizer filling rate of cavity z-distance, %; V_m is the volume of space occupied by fertilizer of cavity z-distance, mm³; V is the overall spatial volume of cavity z-distance, mm³.

A higher fertilizer filling rate enhances the uniformity of fertilizer discharge. Based on the analysis above, it is evident that adjusting the tilting angle θ and size l of the fertilizer discharger influences the speed of fertilizer transport by the inclined spiral mechanism. Therefore, optimizing both θ and l of the fertilizer discharger is essential to achieve optimal performance.

2.3. Discrete Element Simulation

2.3.1. Simulation Parameter Setting

The discrete element method (DEM) is a numerical computational approach used to analyze the dynamics and mechanical properties of complex discrete systems [22,23,24]. In order to evaluate the comparative advantages and disadvantages of the inclined spiral fertilizer discharger over traditional spiral designs, simulations of the discharge processes for both types were conducted using EDEM 2022 discrete element simulation software (DEM Solutions company, MI, USA). To determine the parameters of fertilizer particles, 100 grains of compound fertilizers from Hebei Sanhe Fertilizer Co. Ltd. (Xingtai, China) were randomly selected, and their physical force parameters were measured using electronic digital vernier calipers. The equivalent diameter D and sphericity δ of the fertilizer particles were calculated according to Equations (10) and (11) with the values of D = 3.281 mm and δ = 93.4%, respectively. Given the high sphericity (>90%), the simulation model adopted pure spherical shapes for the fertilizer particles.

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

(10)

where D is the equivalent diameter of compound fertilizers, mm; H is the length of compound fertilizers, mm; W is the width of compound fertilizers, mm; T is the height of compound fertilizers, mm.

$$\delta =\frac{D}{L}$$

(11)

where δ is the sphericity of compound fertilizers, %.

The fertilizer discharging device is constructed from PLA plastic material. It is assumed that the discharging process occurs in a dry, humidity-free environment, maintaining the fertilizer in a static state of non-caking bulk particles without bonding effects. The Hertz–Mindlin (no-slip) contact model was employed to simulate interactions between fertilizer particles and between particles and the discharge device. Contact mechanics parameters for the simulation model were determined based on relevant literature and reference experimental methods [25,26], as presented in

Table 1. Discrete element simulation parameterization.

Project	Attributes	Value
Fertilizer particles	Poisson’s Ratio	0.25
	Shear modulus/Pa	2.8 × 107
	Density/kg·m−3	1320
PLA plastic	Poisson’s Ratio	0.43
	Shear modulus/Pa	1.3 × 109
	Density/kg·m−3	1240
Interaction between fertilizer particles	Coefficient of restitution	0.11
	Static friction coefficient	0.3
	Rolling friction coefficient	0.1
Fertilizer particles—PLA plastic	Coefficient of restitution	0.41
	Static friction coefficient	0.32
	Rolling friction coefficient	0.18

.

2.3.2. Simulation Model Building

SolidWorks 2022 3D software (Dassault Systemes, MA, USA) was utilized to create a 1:1 scale model of the inclined spiral fertilizer discharger. The resulting STL format file was then imported into EDEM 2022 software (DEM Solutions company, MI, USA) for conducting discrete element simulation experiments [27,28,29]. In the upper part of the fertilizer tank, a particle factory is established. The fertilizer particles are uniformly sized with equal diameters, free-falling under gravity in a dynamically generated process. The particle generation rate is set to 20,000 particles per second with a generation duration of 3 seconds. After all fertilizer particles are generated and settled, the fertilizer-discharge wheel begins rotation. To collect the discharged fertilizer and minimize the impact and bouncing between the fertilizer particles and the collection plate, a 10 mm long and 4 mm deep square groove is positioned alongside the fertilizer outlet of the discharger. This groove spans the entire length of the 2000 mm wide fertilizer collection plate, which is 300 mm in width. To facilitate data extraction in the monitoring area and comparative analysis with the traditional single-spiral fertilizer discharger, the rotational speed of the fertilizer discharger discharge wheel was set at 60 r/min, and the moving speed of the fertilizer collection plate was set at 0.2 m/s. To reduce the complexity of the movement of the fertilizer discharger, according to the principle of relative kinematics, the fertilizer collecting plate was set to move in the direction of the −x axis at a speed of −0.2 m/s, which was used to simulate the working state of the fertilizer discharger moving forward. The total simulation time was 15 s, and the data recording interval was 0.01 s. The simulation model of the inclined spiral fertilizer discharger in EDEM 2022 (DEM Solutions company, MI, USA) is depicted in Figure 7.

2.3.3. Fertilizer-Discharge Performance Evaluation Method

To accurately evaluate the effect of different fertilizer discharger structural parameters on uniformity in the discrete element simulation experiment, the variation coefficient of fertilizer-discharge uniformity was used as an experiment index of the fertilizer-discharge performance of the inclined spiral discharger to study the change in fertilizer discharge in a single rotation cycle of this discharger.

According to the forward speed of the fertilizer discharger, the distance traveled by the spiral rotating one turn of the fertilizer discharger on the fertilizer collection plate is 0.2 m. Along the x-axis of the fertilizer collection plate, the uniformity monitoring area was set up with a uniformly divided grid of 10 cells with a length of 290 mm and a width of 20 mm, marked with the number from 1 to 10 in the x-axis in the positive direction of the sequential arrangement of the marking, to determine the statistics of the quality of fertilizer in each cell; the statistical grid setup is shown in Figure 8. The mean mass of fertilizer discharged, standard deviation, and variation coefficient of uniformity of discharged fertilizer were calculated for each cell grid of the fertilizer-discharge performance experiment using Equations (12) and (13). The larger the value of the variation coefficient of fertilizer-discharge uniformity, the worse the fertilizer-discharge uniformity of the fertilizer discharger for that parameter

$$m_a=\frac{{\displaystyle \sum _{i=1}^{10}{m}_i}}{x}\left(i=1, 2,\cdots ,10\right)$$

(12)

where m_a is the average mass of fertilizer particles in grid cells, g; m_i is the mass of fertilizer particles in the i-th cell grid, g; x is the number of equalized cell grids for one turn of the fertilizer-discharge wheel, x = 10.

$${\sigma }_e=\frac{1}{m_a}\sqrt{\frac{{\displaystyle \sum _{i=1}^{10}{\left(m_i-m_a\right)}^2}}{x-1}}\times 100\%\left(i=1, 2,\cdots ,10\right)$$

(13)

where σ_e is the variation coefficient of the uniformity of fertilizer discharge per cyclic cycle, %.

2.3.4. Comparative Analysis of Inclined and Traditional Spiral Fertilizer Dischargers Characteristics

Based on the double-ended spiral blade, we set the same working length, the same blade inner and outer diameter of the spiral fertilizer-discharge wheel, and the same shell sleeve inner diameter to perform a comparative analysis of the simulation experiment. The inclined spiral fertilizer discharger with an inclination angle of 30° and a distance of 10 mm from the terminating spiral blade to the fertilizer outlet is taken an example, and the simulation comparison is shown in Figure 9.

Figure 9 shows a sharp contrast between the filling of the two types of fertilizer discharger cavities, with (a) the cavity in the figure being poorly filled with fertilizer and (b) the inclined spiral discharger effectively approximating the filling rate to one. Changes in the filling rate of the cavity directly affect the size of the filling coefficient. The spiral fertilizer discharger filling coefficient is the same distance from the spatial section of the fertilizer particles in the volume of the cavity volume ratio; the filling coefficient of the numerical value of the fluctuation of the single-spiral fertilizer discharger discharge stability and volatility has a direct impact on the flow of fluctuations, ensuring the effect of fertilizer and the equalization of the effect of fertilizer. To observe the effect of the change in filling coefficient on the performance of fertilizer discharge, the fertilizer collection plate was set to move to catch the fertilizer at 0.2 m/s under the fertilizer outlet, and the two kinds of fertilizer-discharge effects are shown in Figure 10.

Figure 10 shows that the uniformity of fertilizer discharge of the inclined spiral fertilizer discharger is significantly improved. To verify its accuracy, based on the discrete element simulation, a model of the fertilizer outlet was established in the exact size of the fertilizer quantity monitoring area for the collection of fertilizer particle data and a preliminary comparative analysis of the two types of fertilizer discharger at different times under the fluctuation coefficient trend; the results are shown in Figure 11. The fertilizer particle number fluctuation of the traditional spiral fertilizer discharger is much more significant than that of the inclined spiral fertilizer discharger. Its fluctuation is very poor, and the fertilizer number of the overall amplitude of the change is more significant. The overall volatility of the inclined spiral fertilizer discharger is balanced and stable, and the comparison shows that the uniformity of this fertilizer discharger is better. Therefore, studying the effect of inclined spiral fertilizer dischargers on uniformity is informative.

2.4. Single-Factor Experiment Analysis

To determine the effect of the inclination angle and l of the fertilizer discharger on the uniformity of fertilizer discharge, a one-factor experimental study was carried out at different inclination angles and l values using discrete element simulation.

2.4.1. Fertilizer Drainer Tilt Angle

Based on the experiment performed to determine the l of 20 mm, a factor experiment was carried out using the tilting angle settings of 30°, 35°, 40°, 45°, and 50°, respectively, to study the effect of the fertilizer discharger on the variation coefficient of the uniformity of fertilizer discharging at different tilting angles and to determine the relationship between the variation coefficient of the uniformity of the discharging and the tilting angle of the fertilizer discharger, as shown in Figure 12a.

The experiment results show that with the increase in the tilting angle of the fertilizer discharger, the variation coefficient of fertilizer-discharge uniformity decreases and then increases, the tilting angle reaches the minimum value in the range of 37.5°~42.5°, and there are maximum values near 30° and 50°. The difference with the intermediate data is significant. The data state is “concave”, so to take the uniformity of fertilizer discharge, it is necessary to determine the range of the tilting angle between 35° and 45° under the condition of the minimum variation coefficient of fertilizer discharge. Therefore, to take the uniformity of fertilizer discharge under the condition of a minimum variation coefficient, it is determined that the tilting angle of the fertilizer discharger takes a value in the range of 35°~45°.

2.4.2. Fertilizer-Discharge Wheel Termination Spiral to Fertilizer Outlet Distance

Changes in fertilizer filling rate affect the uniformity of fertilizer discharge. The previous section indicates no effect on the filling condition of the fertilizer drainer when l is too long. Therefore, based on the experiment performed to determine that the slanting inclination angle of the fertilizer discharger is 40°, different l values of 0 mm, 10 mm, 20 mm, 30 mm, and 40 mm were used to carry out a single-factor experiment to study the effect of different l values on the variation coefficient of fertilizer discharging uniformity, and the relationship between the variation coefficient of fertilizer discharging uniformity and l was obtained, as shown in Figure 12b.

The experiment results show that as l increases, the variation coefficient of fertilizer uniformity first decreases, then increases while remaining slightly flat, and then increases. A minimum endpoint exists at 10 mm between 0 and 20 mm. Uniformity is best at this point. Another decrease in the variation coefficient of homogeneity was observed again at 30 mm. This situation is because the pitch of the double-ended helical blade reaches a multiplicative relationship with a value somewhere in the vicinity of 10 mm and 30 mm. The rotational motion of the two spiral blades is superimposed in unit lead cycles when the double-ended spiral fertilizer-discharge wheel nudging process is realized. This results in a more even flow of discharged fertilizer. Therefore, the vicinity of 10 mm and 30 mm is presented as “concave” with a very small value, but the minimum value of the variation coefficient of 10 mm proves that the value of the vicinity of the uniformity is better compared to the value of the l value range between 0 and 20 mm.

3. Response Surface Experiment

Combined with the results of the one-factor experiment, in this study, the fertilizer discharger tilting angle range of 35° to 45° and l range of 0 mm to 20 mm were selected for a two-factor, five-level, secondary generalized rotating combination design experiment, and the factor level codes are shown in

Table 2. Experiment factor level.

Level	Fertilizer Discharger Tilt Angle/°	Fertilizer-Discharge Wheel Termination Blade to Fertilizer Outlet Distance/mm
+1.414	45	20
1	43.54	17.07
0	40	10
−1	36.46	2.93
−1.414	35	0

.

3.1. Experiment Results and Analysis

The experiment results are shown in

Table 3. Experiment results.

Serial Number	Experiment Factors		Experiment Indicator
	θ/°	l/mm	σ/%
1	36.46	2.93	9.412
2	43.54	2.93	10.107
3	36.46	17.07	9.466
4	43.54	17.07	16.716
5	35.00	10.00	10.38
6	45.00	10.00	15.403
7	40.00	0.00	10.023
8	40.00	20.00	13.969
9	40.00	10.00	12.119
10	40.00	10.00	12.029
11	40.00	10.00	10.526
12	40.00	10.00	9.369
13	40.00	10.00	8.874

, where θ and l indicate the factor coding values and σ is the variation coefficient of fertilizer-discharge uniformity.

Multiple regression was fitted to the experimental data to obtain a regression equation for the variation coefficient of fertilizer-discharge uniformity. The analysis of variance of the model is shown in

Table 4. Analysis of variance.

Evaluation Indicators	Source of Variance	Sum of Square	DF	Mean Square	F Value	p Value
Variation coefficient of fertilizer-discharge uniformity	Model	64.21	5	12.84	8.06	0.0081
	θ	28.31	1	28.31	17.76	0.0040
	l	18.74	1	18.74	11.76	0.0110
	θl	10.74	1	10.74	6.74	0.0356
	θ2	5.63	1	5.63	3.53	0.1023
	l2	1.42	1	1.42	0.89	0.3768
	Residual	11.16	7	1.59
	Lack of fit	2.31	3	0.77	0.35	0.7938
	Pure error	8.85	4	2.21
	Total variation	75.36	12

Note: p < 0.01 (highly significant), 0.01 < p < 0.05 (significant), p > 0.05 (not significant).

. The experiment of the significance of the regression model for the variation coefficient of fertilizer-discharge uniformity was highly significant (p < 0.01), and the experiment of the misfit term for the variation coefficient of fertilizer-discharge uniformity was non-significant (p > 0.05), indicating that the regression model was well fitted to the experimental range. For the variation coefficient model of fertilizer-discharge uniformity, the effect of θ on the equation was highly significant (p < 0.01), the effect of l and θl on the equation was significant (p < 0.05), and the rest of the terms did not have any effect on the equation (p > 0.05). The regression equation of the factors with the variation coefficient of uniformity of fertilizer discharge is obtained by removing the insignificant effect of the coefficients in the regression equation:

$$\sigma =129.39-5.88\theta -2.59l+0.07\theta l$$

(14)

where σ is the variation coefficient of fertilizer-discharge uniformity, %.

3.2. Response Surface Analysis

The effects of the factors on the experiment indices are shown in Figure 13. The variation coefficient of fertilizer-discharge uniformity decreases gradually as the tilting angle of the fertilizer discharger increases, and the variation coefficient of fertilizer-discharge uniformity decreases gradually as l increases. The fertilizer discharger tilting angle is too high, l is too long, and the fertilizer extrusion conveying difficulty easily falls as a heap, thus resulting in the uneven discharge of fertilizer. The fertilizer discharger tilting angle is small, l is too tiny, the fertilizer is not filled with solid and failed to fill the cavity, there is no accumulation of extrusion area, and there cannot be a fine extrusion of fertilizer, so there is a phenomenon of non-uniformity of fertilizer discharging.

3.3. Location Analysis of Fertilizer-Discharge Uniformity

A flow monitoring area is established at the fertilizer-discharge port, and data monitoring of fertilizer discharge for different regional parameters in the contour map generates flow curves and calculates the corresponding flow fluctuation coefficients, as shown in Figure 14. l is 17.07 mm when reaching the smooth fertilizer-discharge stage, time is slower, and the amount of fertilizer discharge is more significant; here, the red line fluctuation is the largest and the green line has fluctuations, but the relative time fluctuation amplitude is relatively smooth. On the other hand, for the blue and black lines, although the overall fluctuation is more uniform, the fluctuation pole difference per unit of time is more significant, so the fluctuation coefficient is also slightly higher. In addition to this, the four parameters of the fertilizer discharger also vary in the amount of fertilizer discharged; the green line parameter of the fertilizer discharger discharged the most significant amount of fertilizer, which can be proved in the same structural design; with a slight angle, a significant l parameter of the fertilizer discharger is most likely to achieve the fertilizer volume requirements.

The spatial position distribution of fertilizer particles in the monitoring area between 7 and 8 s was extracted, and the spatial state of fertilizer particles in the monitoring area is shown in Figure 15. Figure 15a,b show fertilizer particles’ position distribution when the tilting angle is 43.54°. Both parameters of the fertilizer discharger have interruptions in the process of discharging fertilizer, and the uniformity of discharging fertilizer is poor. Here, l is 17.07 mm when the intermediate partition is more serious; the fertilizer discharge at the fertilizer pile falls, which is due to the tilting angle and l being more significant in the case of a spiral conveyor, and the large fertilizer amount of the filling cavity pile is too high and full, resulting in the fertilizer pile falling; the exit is fluctuating, gushing out. In Figure 15a, in the high angle, short distance parameters, the fertilizer pile drop phase is less obvious, but there is still an intermittent phase in the middle, and the uniformity of fertilizer discharge is general.

Figure 15c,d show the distribution of fertilizer particles when the tilting angle is 36.46°, and the fertilizer particles are uniformly distributed in the fertilizer discharging process under the two parameters without any intermittent phenomenon. The stacking interface of Figure 15d is smooth without bulging, while the stacking interface of Figure 15c has up and down bulging. Because the tilting angle is certain, l is shorter; the spiral conveying process will be due to the cycle of fertilizer wheel rotation, resulting in the accumulation of fertilizer, which will also be a cycle of gradual overflow to the fertilizer outlet, so there will be the phenomenon of fluctuations in the interface of the accumulation of the phenomenon. In Figure 15a,b, in an overall comparison with Figure 15c,d, fertilizer-discharge uniformity is better. The flow fluctuation excellence for the four different cases can also be derived through equation (14). When both θ and l are high parameters, σ becomes consequently higher. The uniformity is poor at this point. Moreover, when either θ or l is a low parameter, the σ value decreases with some better uniformity. Therefore, before optimization, it can be concluded that the parameters are within a specific range of poorer uniformity of fertilizer discharge for combinations with large inclination angles and long distances. This conclusion is consistent with the results of the simulation analysis.

3.4. Parameter Optimization

A smaller variation coefficient of fertilizer-discharge uniformity indicates a more uniform fertilizer discharge. Regarding relevant literature [30,31], Fang et al. from Jilin University studied the offset spiral tooth fertilizer-discharge device. The final optimization in the variation coefficient of fertilizer-discharge uniformity does not exceed 10.42%. Song et al. from Gansu Agricultural University studied the optimal parameters of a spiral fluted wheel fertilizer discharger. The variation coefficient for optimum uniformity of fertilizer discharge was optimized to be 8.56%. For this reason, this study sets evaluation metrics for further optimization concerning the above-optimized value. So, the variation coefficient of fertilizer-discharge uniformity was set to be ≤8.5% to obtain the parameter combinations for the best combination of fertilizer discharger with the lowest coefficient of variation. The optimization equations are shown in Equation (15) and were developed using the multi-objective optimization method with Design-Expert 8.0.6 (State-East Company, Minneapolis, MN, USA).

$$\left\{\begin{array}{l}35\le \theta \le 45\\ 0\le l\le 20\\ \sigma =\left(\theta ,l\right)\\ \sigma \le 8.5\%\end{array}\right.$$

(15)

Based on the above optimization Equation (15), the optimization of the coefficient of variation for fertilizer-discharge uniformity from the fertilizer discharger is illustrated in Figure 16. The yellow-shaded region in Figure 16 is the region of the best combination of θ and l. And the optimization intervals are as follows: fertilizer discharger tilting angle of 35°~36° and l of 12.5~20 mm.

To achieve the optimal fertilizer-discharge effect of the fertilizer discharger, the inclined spiral fertilizer discharger with a tilting angle of 35.02° and l of 16.87 mm was randomly selected from the best optimized yellow region to establish a simulation model. To check the optimum values optimized for the parameters, a simulation experiment was designed to verify the experiment. The uniformity of fertilizer discharge of the fertilizer discharger with this parameter was verified by simulation experiments using the discrete element method. The variation coefficient of the fertilizer-discharge uniformity was found to be 8.129% by simulation verification, which aligns with the theoretically optimized optimum range value.

4. Bench Experiment and Results

4.1. Fertilizer-Discharge Uniformity Bench Experiment

To verify the accuracy of the optimal structural parameters of the inclined spiral fertilizer discharger, an experiment fertilizer was selected from the compound fertilizers of Hebei Sanhe Fertilizer Co. Ltd. (Xingtai, China), and a bench experiment was carried out to verify the fertilizer discharger concerning the optimized optimal structural parameters.

The experiment was carried out in August 2023 at the Intelligent Agricultural Machinery and Equipment Engineering Laboratory of Harbin Cambridge College, based on the PLA plastic material using a 3D printer for the inclined spiral fertilizer discharger. The experiment setup is shown in Figure 17, which mainly includes a fertilizer box, inclined spiral fertilizer discharger, motor controller, drive motor, fertilizer application controller, fertilizer collection box, and conveyor belt. For efficient collection of fertilizer particles discharged during the stabilization phase of the fertilizer discharger, the fertilizer collection box was positioned 100 mm away from the fertilizer outlet. The experiment involved the following steps: experiment start, start the motor, set the fertilization controller, set the conveyor belt speed at 0.2 m/s and start, discharge after the fertilizer is stable, fertilizer falls into the fertilizer collection plate to start collecting, a single measurement of two fertilizer discharging cycles (through the conveyor belt movement of the fertilizer discharged by the fertilizer-discharge collection, 10 fertilizer collection box collections of fertilizer for a cycle). At the end of the experiment, the fertilizer in each fertilizer collection box was weighed using Japanese GX-8K electronic scales produced by Shenzhen Kyoto Tamasaki Electronics Co., Ltd. (Shenzhen, China), and the single experiment was repeated three times to take the average value.

The grid method was used to count the data on the uniformity of fertilizer discharge (the number of fertilizer collection boxes at 60 r/min was used as an example), and the variation coefficient of uniformity was obtained through Equations (12) and (13); the fertilizer collection box in the bench experiment was 20 mm × 60 mm, and the grid division of the bench experiment is shown in Figure 18.

To verify the effect of the fertilizer discharger to improve the uniformity and the accuracy of the simulation optimization results, based on the same fertilizer discharging wheel parameters and rotational speed of 60 r/min, the best parameters of the inclined spiral fertilizer discharger and the single-spiral fertilizer discharger were selected to carry out a comparative experiment of fertilizer discharging uniformity. This can be seen in the wave profile of Figure 11 from the previous study. The particle emission rate of conventional fertilizer discharge varies from 0 to 120 particles per unit time. The particle number in obliquely discharged fertilizer ranges from 45 to 75. The range of fluctuations in the values for the slant discharge method is much smaller than that for the conventional discharge method. The comparison of the fertilizer-discharge effect in Figure 10 can also visualize the superiority of the fertilizer-discharge effect of the two. Therefore, in the comparative results of the validation test, the inclined rows of fertilizer should exhibit better uniformity than the conventional rows. Each experimental trial was conducted three times per group to calculate the mean values, with the experimental outcomes presented in

Table 5. Comparative experiment results.

Fertilizer Discharger Type	Experiment Method	Uniformity Coefficient of Variation/%
Inclined spiral fertilizer discharger	Simulation experiment	8.129
	Bench experiment	8.314
Single-spiral fertilizer discharger	Bench experiment	43.271

. The relative error of the variation coefficient between the bench experiment and the simulation experiment of the inclined spiral fertilizer discharger was 2.28%, and the validation experiment was basically in agreement with the simulation experiment. The variation coefficient was reduced by 80.79% compared with that of the single-spiral fertilizer discharger. The results of the comparison were consistent with the previous study, and this study can provide a reference for the optimal design of the spiral fertilizer discharger.

4.2. Fertilizer Controller Performance Bench Experiment

To derive the relationship between fertilizer-discharge flow rate and rotational speed, the quality of fertilizer discharge was selected as the evaluation index, and the experiment rotational speeds were set at 30, 60, 90, 120, 150, and 180 r/min. The experiment fertilizer was selected as urea from CNSG Anhui Hong Sifang Co., Ltd. (Hefei, China), with an average diameter of 2.57 mm and 94.66% sphericity. Fertilizer discharged at different rotational speeds in the same time unit was weighed using Japanese GX-8K electronic scales produced by Shenzhen Kyoto Tamasaki Electronics Co., Ltd. (Shenzhen, China). Three experiments were repeated, and the average value was taken as the experiment result. Origin64 (OriginLab Corporation, Northampton, MA, USA) was applied to linearly fit the relationship between the fertilizer-discharge flow rate and the rotational speed of the fertilizer-discharge wheel; the fitted functional equation is y = 0.243x + 2.937, and the coefficient of determination is R² = 0.998. The results demonstrate a direct linear correlation, suggesting that the rotational speed of the fertilizer-discharge wheel can linearly adjust the fertilizer-discharge flow rate.

To achieve precise control of fertilizer-discharge flow rate, a fertilizer controller was developed based on the equation y = 0.243x + 2.937 to form an electronically controlled inclined spiral precision fertilizer discharger to control the rotational speed to achieve precision fertilizer application as shown in Figure 19. To test the working performance of the fertilizer controller and ensure precise control of the rotational speed of the fertilizer-discharge wheel, four rotational speeds were randomly selected within the range of 60~180 r/min, and the fertilizer-discharge flow rate experiment was carried out through the electronically controlled inclined spiral precision fertilizer discharger. Experiment control involved toggling a touchscreen interface to initiate and halt fertilizer discharge into the collection box. The fertilizer discharged from the same working time unit was collected, and the fertilizer from the collection box was tared and weighed. And the experiment was repeated three times. The average value was taken as the experimental result and compared with the preset value obtained from the equation. The experiment results are shown in

Table 6. Comparison results of fertilizer-discharge flow rate.

Rotational Speed/r·min−1	Preset Value/g·s−1	Measured Value/g·s−1	Errors/%
71	20.19	20.831	3.17
114	30.639	29.649	3.34
155	40.602	41.793	2.93
173	44.976	46.349	3.05

. The results show that the average deviation of the fertilizer flow rate of the fertilizer controller controlling the fertilizer discharger from the preset value is 3.12%, and this result indicates that the electronically controlled fertilizer discharger controller can accurately control the rotational speed of the fertilizer discharger according to the linear equations to realize the precise regulation of the fertilizer discharge.

In conclusion, research work on electronically controlled inclined screw precision fertilizer dischargers under the existing optimization conditions is inevitably deficient. Referring to the related literature [32,33], the experimental team could add the consideration of the effect of different shapes of fertilizers and coated fertilizers on the uniformity of the discharger to future research on the inclined spiral fertilizer discharger. Moreover, the present study is based on idealized conditions for analyzing the movement of particles between groups of particles. In contrast, factors such as air conditions and moisture content should be explored more accurately and added to more in-depth studies. Additionally, enhancing evaluation metrics during bench experiments will offer robust data to support optimal design and future research directions for fertilizer dischargers.

5. Conclusions

• This study addresses the issue of uneven fertilizer discharge caused by the cyclic opening and closing of the spiral blade and fertilizer-discharge port of the spiral fertilizer discharger, as well as insufficient fertilizer filling. An inclined spiral fertilizer discharger was designed by adopting the principle of tilted extrusion conveying of the spiral wheel full of fertilizer in an oblique tilting angle way, and the influence of the tilting angle of the discharger θ and the distance from the termination blade of the fertilizer-discharge wheel to the fertilizer outlet l on the performance of the discharging of fertilizers was theoretically analyzed. Additionally, a discrete meta-simulation model of the fertilizer discharge was developed using EDEM 2022 to explore its performance under various structural parameters.
• Based on single-factor experiments, a two-factor, five-level quadratic universal rotating combination design simulation experiment was conducted. The experiment factors included the tilting angle θ of the fertilizer discharger and the distance l from the termination blade of the fertilizer-discharge wheel to the outlet, while the variation coefficient of fertilizer-discharge uniformity served as the experimental index. A regression model was established to analyze the impact of these factors on the experimental outcomes. The results indicated that the tilting angle and the distance from the termination blade significantly influenced the variation coefficient of fertilizer-discharge uniformity (p < 0.01 and p < 0.05, respectively). With a requirement of σ < 8.5% and minimizing manufacturing costs, the optimal parameters of the fertilizer discharger were determined: a tilting angle of 35.02° and a distance from the termination blade to the outlet of 16.87 mm.
• Bench validation experiments were conducted to verify the accuracy of the optimization analysis results. The experiment results show that the relative error of the variation coefficient of fertilizer-discharge uniformity between the bench experiment and simulation experiment is 2.28%, which is 80.79% lower than the average variation coefficient of fertilizer-discharge uniformity of single-spiral fertilizer discharger, and the optimized fertilizer discharger has good uniformity of fertilizer discharge. A fertilizer application controller was designed using the optimal parametric equation for fertilizer-discharge flow. Bench experiment results showed an average deviation of 3.12%, which proved that the controller could precisely regulate the fertilizer-discharge flow by adjusting the rotational speed.