# Performance Analysis and Testing of Spiral Quantitative Fertiliser Distributors in Orchards
## 2 Materials and Methods
### Design of Critical Parts
#### 2.2.3 Fertilizing Apparatus
Finally, the amount of fertilizer applied must also be considered. The optimal speed is determined by considering the amount of fertilizer, the fertilizer's physical characteristics, and the design parameters of the conveying screw to determine the screw speed range. In the south of the orchard, consider the following fertilizer agronomic requirements as an example [22]: For a single fruit tree fertilizer application of 1 kg/m and a fertilizer machine forward speed of 2 km/h, and using Equation (6), the amount of fertilizer \(Q_{s}\) 1 t/h--that is, \(Q_{c}\) 1 t/h. Using the fertilizer characteristics and parameters, the filling coefficient \(\varphi\) is determined as 0.25, the comprehensive material characteristics of the coefficient A is 28 and the mass of fertilizer per unit of volume \(\lambda\) 1.25 t/m\({}^{3}\). The parameters of the pitch and diameter ratio of fertilizer and the ratio of the screw to the diameter are considered to select the optimal speed. The pitch and diameter coefficient of proportionality \(c\) is 0.9, and the transport coefficient \(\varepsilon\) of 0.9 is input into Formulas (4) and (5) to obtain an integrated coefficient \(K\) of 0.0565 and a spiral fertilizer discharger outer diameter of 94 mm. As the spiral blade should be designed as a standard series, it can be determined that the spiral fertilizer discharger outer diameter of \(D\) is 95 mm, the inner diameter of \(d\) is 34 mm, the spiral fertilizer discharger pitch \(S\) for the 80 mm and the average thickness of the screw threads b is 3 mm. By substituting these parameters into Equations (1)-(3), the single-turn fertilizer discharge \(q\) is 152.8 g. Combined with the single-ring fertilizer quantity in the theoretical analysis, it can provide stable and sufficient fertilizer flows to the conveyor screw when the outer diameter is 100 mm, the inner diameter is 40 mm, the pitch is 80 mm and the thickness of the screw thread is 7.5 mm. According to Equations (7) and (8), the rotation speed range was 30 RPM \(\leq n_{max}\leq\) 90 RPM. When the rotation speed was lower than 30 RPM, there were few sliding actions among fertilizers, and blocking phenomena occurred easily. When the rotation speed was higher than the critical rotation speed, the spiral blades primarily stirred fertilizers and generated minor effects on the axial advancement of fertilizer particles. With careful consideration, the rotation speed of the spiral blades was determined as the median (60 RPM). (1) Simulation verification test  
First, SolidWorks2021 was used to draw a 1:1 model of the fertilizer applicator to improve the efficiency of the simulation calculations. The structure of the fertilizer applicator was simplified, omitting the structures that do not affect fertilizer discharge--such as the furrowing device, mulching device and transmission [23]--saving the file in the IGS format. The IGS file was then imported into EDEM2021, considering the application of the AKON fertilizer to the southern border orchards. This study investigated the delivery of the Akin fertilizer in a steel fertilizer discharge device. The fertilizer particles were considered to be spherical, with no attachment between the fertilizer particles during the fertilizer discharge process and fertilizer application. The contact model was Hertz-Mindlin (no slip), and the required parameters were derived--as shown in Table 1--by referring to previous studies [24,25]. Secondly, a particle plant slightly smaller than the hopper size was set up at the top of the fertilizer applicator with a generation rate of 25 kg/s, falling freely under gravity to generate a total of 50 kg of fertilizer particles. A rectangular hopper with dimensions of 280 \(\times\) 200 \(\times\) 130 mm was established at the discharge port at the same time.