Figure 1.
Size distribution. The vertical direction is the Z-axis, the hilum direction is the Y-axis, and the horizontal direction is the X-axis. O is the center of sorghum seed; L, B, and T are the length, breadth, and thickness of the sorghum seed (mm), respectively.
Figure 1.
Size distribution. The vertical direction is the Z-axis, the hilum direction is the Y-axis, and the horizontal direction is the X-axis. O is the center of sorghum seed; L, B, and T are the length, breadth, and thickness of the sorghum seed (mm), respectively.
Figure 2.
Triaxial size normal distribution fitting curve.
Figure 2.
Triaxial size normal distribution fitting curve.
Figure 3.
Compression experiment diagram.
Figure 3.
Compression experiment diagram.
Figure 4.
Schematic of the test principle of the free-fall experiment. Φ is the inclination angle of the inclined plane (36° in the free-fall experiment of sorghum seeds–sorghum seeds, 0° in the free-fall experiment of sorghum seeds–photosensitive resin material). In free-fall experiment of sorghum seeds–sorghum seeds, the inoculation template is seeds plate; in the free-fall experiment of sorghum seeds–photosensitive resin material, the inoculation template is photosensitive resin plate.
Figure 4.
Schematic of the test principle of the free-fall experiment. Φ is the inclination angle of the inclined plane (36° in the free-fall experiment of sorghum seeds–sorghum seeds, 0° in the free-fall experiment of sorghum seeds–photosensitive resin material). In free-fall experiment of sorghum seeds–sorghum seeds, the inoculation template is seeds plate; in the free-fall experiment of sorghum seeds–photosensitive resin material, the inoculation template is photosensitive resin plate.
Figure 5.
Analysis of collision motion between sorghum seeds. A and B are any two points on the seed trajectory; VX and VY are the horizontal and vertical sub-velocities (mm/s), respectively, after seeds collision; H is the is the drop height of seed (150 mm); h1 and h2 are the vertical displacements (mm); and l1 and l2 are the horizontal displacements (mm).
Figure 5.
Analysis of collision motion between sorghum seeds. A and B are any two points on the seed trajectory; VX and VY are the horizontal and vertical sub-velocities (mm/s), respectively, after seeds collision; H is the is the drop height of seed (150 mm); h1 and h2 are the vertical displacements (mm); and l1 and l2 are the horizontal displacements (mm).
Figure 6.
Analysis of collision motion of seeds–photosensitive resin plate. H is the drop height of seed (150 mm); h is the rebound height of the seed.
Figure 6.
Analysis of collision motion of seeds–photosensitive resin plate. H is the drop height of seed (150 mm); h is the rebound height of the seed.
Figure 7.
Schematic diagram of the test principle of the slope slip experiment. In static friction coefficient of sorghum seeds–sorghum seeds, the inoculation template is seeds plate; in the static friction coefficient of sorghum seeds–photosensitive resin material, the inoculation template is photosensitive resin plate.
Figure 7.
Schematic diagram of the test principle of the slope slip experiment. In static friction coefficient of sorghum seeds–sorghum seeds, the inoculation template is seeds plate; in the static friction coefficient of sorghum seeds–photosensitive resin material, the inoculation template is photosensitive resin plate.
Figure 8.
Analysis diagram of rolling experiment. H1 is the seeds drop height (30 mm), l is the displacement of the seed after rolling (mm), FN is the support force of the photosensitive resin plate on the seed (N), FG is the gravity of the seeds itself, and Ff is the rolling friction force (N).
Figure 8.
Analysis diagram of rolling experiment. H1 is the seeds drop height (30 mm), l is the displacement of the seed after rolling (mm), FN is the support force of the photosensitive resin plate on the seed (N), FG is the gravity of the seeds itself, and Ff is the rolling friction force (N).
Figure 9.
Angle of repose of sorghum seeds. (a) Image of both sides of stacked seeds; (b) angle of repose least squares fitting diagram.
Figure 9.
Angle of repose of sorghum seeds. (a) Image of both sides of stacked seeds; (b) angle of repose least squares fitting diagram.
Figure 11.
3D scanning of sorghum seeds. (a) Point cloud data map. (b) 3D model diagram.
Figure 11.
3D scanning of sorghum seeds. (a) Point cloud data map. (b) 3D model diagram.
Figure 12.
Sorghum seed model of EDEM.
Figure 12.
Sorghum seed model of EDEM.
Figure 13.
Simulation diagram of collision restitution coefficient of seeds–photosensitive resin material. H is the seeds drop position (150 mm), and Y1 is the rebound height of the seeds in the simulation (mm).
Figure 13.
Simulation diagram of collision restitution coefficient of seeds–photosensitive resin material. H is the seeds drop position (150 mm), and Y1 is the rebound height of the seeds in the simulation (mm).
Figure 14.
Simulation experiment diagram of static friction coefficient of seeds–photosensitive resin material. Y2 is the inclination angle of the inclined plate (deg).
Figure 14.
Simulation experiment diagram of static friction coefficient of seeds–photosensitive resin material. Y2 is the inclination angle of the inclined plate (deg).
Figure 15.
Simulation measurement diagram of rolling friction coefficient of seeds–photosensitive resin material. Y3 is the horizontal scrolling distance of the seeds model (deg).
Figure 15.
Simulation measurement diagram of rolling friction coefficient of seeds–photosensitive resin material. Y3 is the horizontal scrolling distance of the seeds model (deg).
Figure 16.
EDEM simulation of angle of repose experiment. (a) Model establishment; (b) simulation of seeds drop; (c) simulation model of angle of repose.
Figure 16.
EDEM simulation of angle of repose experiment. (a) Model establishment; (b) simulation of seeds drop; (c) simulation model of angle of repose.
Figure 17.
Second-order polynomial fitting curve of the collision restitution coefficient of sorghum seeds–photosensitive resin material.
Figure 17.
Second-order polynomial fitting curve of the collision restitution coefficient of sorghum seeds–photosensitive resin material.
Figure 18.
Second-order polynomial fitting curve of the static friction coefficient of sorghum seeds–photosensitive resin material.
Figure 18.
Second-order polynomial fitting curve of the static friction coefficient of sorghum seeds–photosensitive resin material.
Figure 19.
Second-order polynomial fitting curve of the rolling friction coefficient of sorghum seeds–photosensitive resin material.
Figure 19.
Second-order polynomial fitting curve of the rolling friction coefficient of sorghum seeds–photosensitive resin material.
Figure 20.
Comparison of sorghum seeds angle of repose experiments. (a) Physical experiment; (b) simulation experiment.
Figure 20.
Comparison of sorghum seeds angle of repose experiments. (a) Physical experiment; (b) simulation experiment.
Table 1.
Design of the single-factor experiment for collision recovery coefficient. (X1 is the collision restitution coefficient of seeds–photosensitive resin material, and Y1 is the highest rebound height of the seed collision in each simulation group.)
Table 1.
Design of the single-factor experiment for collision recovery coefficient. (X1 is the collision restitution coefficient of seeds–photosensitive resin material, and Y1 is the highest rebound height of the seed collision in each simulation group.)
Group Number | X1 | Y1/mm |
---|
1 | 0.40 | 12.68 |
2 | 0.45 | 16.54 |
3 | 0.50 | 23.81 |
4 | 0.55 | 25.67 |
5 | 0.60 | 33.00 |
6 | 0.65 | 39.38 |
7 | 0.70 | 44.54 |
8 | 0.75 | 49.56 |
9 | 0.80 | 54.04 |
Table 2.
Design of the single-factor experiment for static friction coefficient. (X2 is the static friction coefficient, and Y2 is the simulation value of the inclined plate inclination angle (deg).)
Table 2.
Design of the single-factor experiment for static friction coefficient. (X2 is the static friction coefficient, and Y2 is the simulation value of the inclined plate inclination angle (deg).)
Group Number | X2 | Y2/deg |
---|
1 | 0.32 | 17.75 |
2 | 0.33 | 18.83 |
3 | 0.34 | 19.20 |
4 | 0.35 | 19.50 |
5 | 0.36 | 19.97 |
6 | 0.37 | 20.17 |
7 | 0.38 | 20.68 |
Table 3.
Design of the single-factor experiment for rolling friction coefficient. (X3 is the rolling friction coefficient of sorghum seeds–photosensitive resin material, and Y3 is the rolling distance (mm).)
Table 3.
Design of the single-factor experiment for rolling friction coefficient. (X3 is the rolling friction coefficient of sorghum seeds–photosensitive resin material, and Y3 is the rolling distance (mm).)
Number of Groups | X3 | Y3/mm |
---|
1 | 0.02 | 124.75 |
2 | 0.04 | 101.64 |
3 | 0.06 | 93.43 |
4 | 0.08 | 85.89 |
5 | 0.10 | 64.94 |
Table 4.
Test scheme and results of steepest ascent search experiment. (X4 is the collision restitution coefficient of sorghum seeds–sorghum seeds, X5 is the static friction coefficient of sorghum seeds–sorghum seeds, and X6 is the rolling friction coefficient of sorghum seeds–sorghum seeds.)
Table 4.
Test scheme and results of steepest ascent search experiment. (X4 is the collision restitution coefficient of sorghum seeds–sorghum seeds, X5 is the static friction coefficient of sorghum seeds–sorghum seeds, and X6 is the rolling friction coefficient of sorghum seeds–sorghum seeds.)
Number of Groups | X4 | X5 | X6 | Ɛ/% |
---|
1 | 0.400 | 0.350 | 0.040 | 4.640 |
2 | 0.450 | 0.400 | 0.052 | 1.030 |
3 | 0.500 | 0.450 | 0.064 | 4.040 |
4 | 0.550 | 0.500 | 0.076 | 4.650 |
5 | 0.600 | 0.550 | 0.088 | 10.370 |
6 | 0.650 | 0.600 | 0.100 | 13.690 |
Table 5.
Central composite design factor coding.
Table 5.
Central composite design factor coding.
Factor Level | X4 | X5 | X6 |
---|
−1.682 | 0.366 | 0.316 | 0.032 |
−1 | 0.400 | 0.350 | 0.040 |
0 | 0.450 | 0.400 | 0.052 |
1 | 0.500 | 0.450 | 0.064 |
1.682 | 0.534 | 0.484 | 0.072 |
Table 6.
Test results and scheme of central composite design experiment.
Table 6.
Test results and scheme of central composite design experiment.
Number of Groups | X4 | X5 | X6 | Ɛ/% |
---|
1 | 0.400 | 0.350 | 0.040 | 4.740 |
2 | 0.500 | 0.350 | 0.040 | 3.900 |
3 | 0.400 | 0.450 | 0.040 | 0.870 |
4 | 0.500 | 0.450 | 0.040 | 1.980 |
5 | 0.400 | 0.350 | 0.064 | 2.550 |
6 | 0.500 | 0.350 | 0.064 | 1.230 |
7 | 0.400 | 0.450 | 0.064 | 5.940 |
8 | 0.500 | 0.450 | 0.064 | 7.620 |
9 | 0.366 | 0.400 | 0.052 | 1.120 |
10 | 0.534 | 0.400 | 0.052 | 3.780 |
11 | 0.450 | 0.316 | 0.052 | 2.750 |
12 | 0.450 | 0.484 | 0.052 | 3.310 |
13 | 0.450 | 0.400 | 0.032 | 3.610 |
14 | 0.450 | 0.400 | 0.072 | 5.130 |
15 | 0.450 | 0.400 | 0.052 | 0.720 |
16 | 0.450 | 0.400 | 0.052 | 1.410 |
17 | 0.450 | 0.400 | 0.052 | 0.920 |
18 | 0.450 | 0.400 | 0.052 | 0.590 |
19 | 0.450 | 0.400 | 0.052 | 1.260 |
20 | 0.450 | 0.400 | 0.052 | 0.500 |
21 | 0.450 | 0.400 | 0.052 | 0.258 |
22 | 0.450 | 0.400 | 0.052 | 0.380 |
23 | 0.450 | 0.400 | 0.052 | 1.320 |
Table 7.
Analysis of variance for regression equation.
Table 7.
Analysis of variance for regression equation.
Source | Sum of Squares | df | Mean Square | F-Value | p-Value |
---|
Model | 84.93 | 9 | 9.44 | 30.58 | <0.0001 ** |
X4 | 1.91 | 1 | 1.91 | 6.20 | 0.0271 * |
X5 | 1.78 | 1 | 1.78 | 5.77 | 0.0319 * |
X6 | 5.20 | 1 | 5.20 | 16.84 | 0.0012 * |
X4X5 | 3.07 | 1 | 3.07 | 9.94 | 0.0076 * |
X4X6 | 0.0014 | 1 | 0.0014 | 0.0046 | 0.9467 |
X5X6 | 30.32 | 1 | 30.32 | 98.25 | <0.0001 ** |
X42 | 5.99 | 1 | 5.99 | 19.42 | 0.0007 * |
X52 | 10.63 | 1 | 10.63 | 34.45 | <0.0001 ** |
X62 | 26.53 | 1 | 26.53 | 85.95 | <0.0001 ** |
Residual | 4.01 | 13 | 0.3086 | | |
Lack of fit | 2.53 | 5 | 0.5059 | 2.73 | 0.0997 |
Pure error | 1.48 | 8 | 0.1853 | | |
Cor total | 88.94 | 22 | | | |
Table 8.
Overall discrete element simulation parameters.
Table 8.
Overall discrete element simulation parameters.
Parameter | Value | Source |
---|
Sorghum seeds density/g·cm−3 | 1.150 | This study |
Poisson’s ratio of sorghum seeds | 0.120 | This study |
Shear modulus of sorghum seeds/Pa | 1.03 × 107 | This study |
Density of photosensitive resin plate/g·cm−3 | 1.100 | Ref. [29] |
Poisson’s ratio of photosensitive resin plate | 0.410 | Ref. [29] |
Shear modulus of photosensitive resin plate/Pa | 9.57 × 108 | Ref. [29] |
Seeds–seeds collision restitution coefficient | 0.400 | This study |
Seeds–seeds static friction coefficient | 0.450 | This study |
Seeds–seeds rolling friction coefficient | 0.043 | This study |
Seeds–photosensitive resin material collision restitution coefficient | 0.690 | This study |
Seeds–photosensitive resin material static friction coefficient | 0.345 | This study |
Seeds–photosensitive resin material rolling friction coefficient | 0.040 | This study |