Abstract: This article focuses on the reverse meshing spur gear fertilizer distributor to explore the impact of the deflection angle on its fertilizer discharge performance. By determining the theoretical fertilizer discharge amount through the “mass attribute” function in SolidWorks and simulating the fertilizer discharge process using the discrete element simulation software EDEM, a single-factor test was conducted with the deflection angle of the fertilizer distributor as the test factor and the coefficient of variation of fertilizer uniformity as the evaluation index. The results show that within the range of 0 – 90° of the fertilizer distributor deflection angle, the coefficient of variation of fertilizer uniformity decreases as the angle increases, and when the angle is 90°, the fertilizer performance is the best.
1. Introduction
Fertilizer plays a crucial role in promoting high agricultural yields and is essential for the rapid development of agriculture in China. Fertilizing machinery is an important tool in agricultural production, and the uniform distribution of fertilizer in the field by the fertilizing machinery is crucial for increasing agricultural production and income. The fertilizer distributor, as a key component of the fertilizing machinery, directly affects the fertilizing status of the entire machine. Currently, the most widely used fertilizer distributor on the market is the external groove wheel fertilizer distributor, which has the advantages of simple structure, reliable operation, and low price. However, its structural design defects can lead to low fertilizer uniformity, resulting in reduced fertilizer utilization, resource waste, environmental pollution, and decreased yields. Therefore, improving the fertilizer uniformity of the fertilizer distributor and the rational application of fertilizer have become important issues in the research process of the fertilizer distributor. In the study of reverse gear fertilizer distributors, it was found that changing the traditional installation method of the fertilizer distributor, that is, changing the angle between it and the traveling direction of the fertilizing machine, can have a certain impact on the fertilizer discharge performance of the fertilizer distributor. Therefore, this article takes the reverse meshing spur gear fertilizer distributor as the research object to explore the impact of the deflection angle on the fertilizer discharge performance.
2. Working Principle and Parameter Design of the Reverse Meshing Spur Gear Fertilizer Distributor
The reverse meshing spur gear fertilizer distributor consists of a left fertilizer discharge gear, a right fertilizer discharge gear, a fertilizer box, and a fertilizer outlet. The two gears of this fertilizer distributor are meshed with each other. During operation, the fertilizing machine transmits power to the left fertilizer discharge gear through a hexagonal shaft, causing the left fertilizer discharge gear to rotate counterclockwise. Therefore, the left and right gears discharge fertilizer through the tooth grooves in a counterclockwise and clockwise rotation state respectively. Based on the maximum operating speed of the machine of 3m/s, the crop row spacing of 65 cm, the fertilizer bulk density of 1.2 g/cm³, and the fertilizer filling coefficient and limit fertilization amount of 750 kg/hm², the tooth width of this fertilizer distributor is set to 30 mm, the number of teeth is 8, and the module is 6 mm for theoretical calculation.
The fertilizer discharge gear is a spur gear, and its tooth grooves carry fertilizer for discharge. Therefore, the theoretical fertilizer discharge amount of the fertilizer distributor is related to the volume of the tooth grooves. The volume of a single tooth groove of the fertilizer discharge gear is calculated by the “mass attribute” function in the three-dimensional software SolidWorks. The specific operation is as follows: draw the addendum circle on the gear end face as a sketch, convert the corresponding lines of the tooth profile and the bottom of the tooth groove into entities by “converting entity references”, remove the redundant lines of the addendum circle by “trimming entities”, and then stretch out the tooth groove filling block with the remaining part as a sketch. The stretching length is 30 mm, and the “merge results” option is not checked. Then, open the “mass attribute” in the “evaluation” and select the tooth groove filling block. The volume of 4196.27 mm³ can be displayed in the “mass attribute” pop-up interface. During the fertilizer discharge process of the reverse meshing spur gear fertilizer distributor, fertilizer is filled into the tooth grooves and then discharged. Therefore, the volume of the tooth groove filling block is used to replace the volume of the fertilizer filled into the tooth grooves.
The total mass M of the fertilizer discharged by the fertilizer distributor is calculated by the formula:
where M is the total mass of the fertilizer discharged by the fertilizer distributor, g; n is the rotation speed of the fertilizer discharge wheel, r/min; t is the working time of the fertilizer distributor, s; v is the volume of a single tooth groove of the fertilizer discharge gear, mm³; p is the fertilizer bulk density, g/cm³; γ is the fertilizer filling coefficient. Through formula (1), it can be calculated that when the rotation speed of the fertilizer distributor reaches 160 r/min, the process requirements of the limit fertilization amount can be met.
3. Discrete Element Simulation Test
3.1 Simulation Parameter Settings
The contact model between fertilizer and fertilizer and between fertilizer and the fertilizer distributor is selected as the Hertz – Mindlin(no slip) contact model, which is the default contact model of the EDEM software. Referring to existing research, the average radius of the Stanley compound fertilizer used in the simulation is 1.64 mm, and the discrete element simulation parameters are set as shown in Table 1.
| Project | Particle Properties | Numerical Value |
|---|---|---|
| Fertilizer | Poisson’s Ratio | 0.25 |
| Shear Modulus/Pa | 1.0×10⁹ | |
| Density/kg·m⁻³ | 1861 | |
| Fertilizer Discharge Wheel, Shell | Poisson’s Ratio | 0.394 |
| Shear Modulus/Pa | 3.18×10³ | |
| Density/kg·m⁻³ | 1240 | |
| Fertilizer – Fertilizer | Recovery Coefficient | 0.11 |
| Static Friction Coefficient | 0.30 | |
| Rolling Friction Coefficient | 0.10 | |
| Fertilizer – Fertilizer Discharge Wheel, Shell | Recovery Coefficient | 0.41 |
| Static Friction Coefficient | 0.32 | |
| Rolling Friction Coefficient | 0.18 |
3.2 Fertilizer Distributor Discrete Element Model and Performance Evaluation
The reverse meshing spur gear fertilizer distributor is modeled in the three-dimensional software SolidWorks, saved as an stl file, and imported into the discrete element simulation software EDEM. The parameters are set according to Table 1. The total number of particles generated by the particle factory is set to 10,000, and the generation speed is 10,000 particles/s. At the same time, the rotation speed of the fertilizer discharge wheel is set to 60 r/min. A fertilizer collection plate is set below the fertilizer distributor, and its moving speed is set to 0.5 m/s. The simulation time step is 1.53×10⁻⁵ s, the data recording time interval is 0.01 s, and the total simulation time is 3.8 s. After the simulation is completed, the grid method is used to statistically analyze the fertilizer discharge amount data. The length of the fertilizer monitoring area a is set to 250 mm and divided into 10 parts, and the fertilizer mass in each grid is statistically analyzed respectively. The coefficient of variation of fertilizer uniformity is used as the evaluation index of the fertilizer discharge performance of the reverse meshing spur gear fertilizer distributor. The average value, standard deviation, and coefficient of variation of the fertilizer in the grid are calculated by formulas (2) – (4). At the same time, a fertilizer monitoring area b with a thickness of 30 mm is set at the fertilizer outlet to observe the change in the fertilizer mass during the fertilizer discharge process for analyzing the fertilizer discharge process.
where is the average mass of the fertilizer particles in each grid in the monitoring area a, g; is the total mass of the fertilizer in the -th grid, g; is the number of grids, ; is the standard deviation of the fertilizer mass in each grid in the monitoring area, g; is the coefficient of variation of the fertilizer uniformity in the monitoring area a.
The fertilizer mass changes fluctuately with time. This is because the two fertilizer discharge gears of the reverse meshing spur gear fertilizer distributor are meshed with each other, and the tooth grooves of the fertilizer discharge gears alternately move above the fertilizer outlet, so the fertilizer is alternately discharged by the fertilizer discharge gears, and the mass change shows fluctuations.
4. Single-Factor Test and Results
The deflection angle of the fertilizer distributor is the angle between the fertilizer distributor and the moving direction of the fertilizer collection plate, as shown in the top view of the fertilizer model. Let represent the deflection angle of the fertilizer distributor, and at the same time, let represent the angle between the fertilizer distributor and the traveling direction of the machine during the actual fertilizer discharge process, where . The fertilizer discharged from the reverse meshing spur gear fertilizer distributor by the left and right fertilizer discharge wheels has an initial velocity, and the angle between the initial velocity direction and the moving direction of the collection plate can affect the sparseness of the fertilizer distribution on the collection plate. Therefore, changing the size of can affect the distribution of the fertilizer on the collection plate.
Therefore, this article selects the deflection angle θ of the fertilizer distributor as the test factor. The range of θ is between 0 and 360°. Due to the symmetry of the fertilizer distributor in the front, back, left, and right directions, when θ is in the ranges of 0 – 90°, 90° – 180°, 180° – 270°, and 270° – 360°, the changes in the fertilizer discharge performance of the fertilizer distributor with the change of the deflection angle θ are the same. For the convenience of the test, the range of the deflection angle θ of the fertilizer distributor is selected as 0 – 90°, and 7 groups of tests are divided into 0°, 15°, 30°, 45°, 60°, 75°, and 90°. The change in the coefficient of variation of fertilizer uniformity.
Within the range of 0 – 90° of the fertilizer distributor deflection angle, the larger the deflection angle, the smaller the coefficient of variation of fertilizer uniformity, and when the deflection angle is 90°, the coefficient of variation of fertilizer uniformity is the smallest, and the fertilizer performance of the fertilizer distributor is the best, and the fertilizer distribution is the most uniform. This is mainly because the fertilizer discharged from the left and right fertilizer discharge gears has an initial velocity, and the direction of the velocity is alternately positive and negative. The angle between the velocity direction and the moving direction of the collection plate affects the distribution of the fertilizer on the collection plate. When the angle between the velocity direction and the moving direction of the collection plate is 0 – 90°, the distribution of the fertilizer on the collection plate is relatively concentrated. When the angle between the velocity direction and the moving direction of the collection plate is 90° – 180°, the distribution of the fertilizer on the collection plate is relatively sparse. Therefore, there is a certain difference in the distribution of the fertilizer discharged from the left and right fertilizer discharge gears on the collection plate. When the deflection angle of the fertilizer distributor is 90°, the angle between the initial velocity direction of the fertilizer discharged from the left and right fertilizer discharge gears and the moving direction of the collection plate is 90°, and the distribution of the fertilizer discharged from the left and right fertilizer discharge gears on the collection plate is the same. Therefore, when the deflection angle of the fertilizer distributor is 90°, that is, when the angle between the fertilizer distributor and the traveling direction of the machine is 90°, the fertilizer performance of the fertilizer distributor is the best.
5. Conclusions
Taking the reverse meshing spur gear fertilizer distributor as the research object to explore the impact of the deflection angle on the fertilizer discharge performance, the theoretical fertilizer discharge amount is determined through the “mass attribute” function in SolidWorks, and the fertilizer discharge process is simulated by the discrete element simulation software EDEM. A single-factor test is conducted with the deflection angle of the fertilizer distributor as the test factor and the coefficient of variation of fertilizer uniformity as the evaluation index. The results show that within the range of 0 – 90° of the fertilizer distributor deflection angle, the coefficient of variation of fertilizer uniformity decreases as the angle increases, and when the angle is 90°, that is, when the angle between the fertilizer distributor and the traveling direction of the machine is 90°, the coefficient of variation of fertilizer uniformity is the smallest, and the fertilizer performance of the fertilizer distributor is the best.
6. Future Research Directions
Although the research in this article has obtained certain results on the impact of the deflection angle of the reverse meshing spur gear fertilizer distributor on the fertilizer discharge performance, there are still some aspects that can be further explored. For example, the influence of different fertilizer types and particle sizes on the fertilizer discharge performance under different deflection angles can be studied. In addition, the optimization of the structure of the reverse meshing spur gear fertilizer distributor based on the research results can also be considered to further improve its fertilizer discharge performance. Moreover, the combination of the reverse meshing spur gear fertilizer distributor with other components of the fertilizing machinery to study the overall performance of the fertilizing machinery is also an important research direction in the future.
In conclusion, the research on the reverse meshing spur gear fertilizer distributor has important theoretical and practical significance for improving the fertilizer application efficiency in agricultural production and promoting the sustainable development of agriculture.