This study investigates the influence of deflection angle on fertilizer discharge uniformity in reverse meshing spur gear fertilizer distributors. Spur gears, characterized by their straight teeth and parallel shafts, form the core mechanism of this system. The distributor consists of counter-rotating spur gears enclosed in a fertilizer box, where the intermeshing teeth create dynamic cavities for precise fertilizer transport.
Working Principle and Theoretical Calculations
The discharge mechanism relies on the volumetric displacement created by spur gear rotation. Each gear tooth cavity volume (V) was calculated using SolidWorks mass properties analysis:
$$ V = 4196.27\ \text{mm}^3 $$
The theoretical fertilizer mass (M) discharged per unit time is expressed as:
$$ M = \frac{8n t V \rho \gamma}{3} \times 10^{-4} $$
Where:
– $n$ = Gear speed (rpm)
– $t$ = Operation time (s)
– $\rho$ = Bulk density (1.2 g/cm³)
– $\gamma$ = Filling coefficient (0.7)
| Parameter | Value |
|---|---|
| Gear module | 6 mm |
| Number of teeth | 8 |
| Face width | 30 mm |
| Maximum speed | 160 rpm |
Discrete Element Method (DEM) Simulation
EDEM simulations modeled the interaction between fertilizer particles and spur gear surfaces. The Hertz-Mindlin contact model governed particle dynamics with parameters:
| Property | Fertilizer | Spur Gear |
|---|---|---|
| Poisson’s Ratio | 0.25 | 0.394 |
| Shear Modulus (Pa) | 1×10⁷ | 3.18×10⁸ |
| Density (kg/m³) | 1861 | 1240 |
The discharge uniformity coefficient ($\sigma$) was calculated as:
$$ \sigma = \frac{s}{\bar{m}} \times 100\% $$
Where:
– $\bar{m}$ = Mean mass per grid
– $s$ = Standard deviation
Deflection Angle Optimization
The deflection angle ($\theta$) between spur gear axis and machine direction significantly affects particle distribution patterns. Experimental results demonstrate:
| θ (°) | σ (%) |
|---|---|
| 0 | 18.7 |
| 15 | 16.2 |
| 30 | 13.9 |
| 45 | 11.4 |
| 60 | 9.1 |
| 75 | 7.6 |
| 90 | 6.3 |
The optimal performance occurs at θ = 90°, where spur gear rotation creates symmetrical particle trajectories. This configuration minimizes directional bias in fertilizer distribution, achieving uniform coverage across the discharge path.
Dynamic Analysis
The velocity vector relationship between spur gear discharge direction ($v_g$) and machine motion ($v_m$) follows:
$$ \alpha = \arctan\left(\frac{v_g \sin\theta}{v_m + v_g \cos\theta}\right) $$
Where θ = 90° simplifies to:
$$ \alpha = \arctan\left(\frac{v_g}{v_m}\right) $$
This angular relationship ensures balanced lateral dispersion of fertilizer particles across the entire working width.
Conclusion
The reverse meshing spur gear fertilizer distributor demonstrates superior discharge uniformity at 90° deflection angle. This orthogonal configuration between spur gear axis and machine direction optimizes particle distribution through symmetrical flow patterns, reducing coefficient of variation to 6.3%. The findings provide critical design guidelines for precision fertilizer application systems using spur gear mechanisms.