Author Contributions
Conceptualization, Z.G. and S.M.; methodology, Z.G.; software, T.J.; validation, H.L.; formal analysis, Z.G.; investigation, Z.G.; resources, Z.G.; data curation, Z.G.; writing—original draft preparation, Z.G.; writing—review and editing, S.M.; visualization, C.W.; supervision, M.Z. and C.W. project administration, S.M.; funding acquisition, Z.G. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Rape stem contact parameters test bench. (1) Material box, (2) Baffle plate, (3) Test plate angle adjustment device, (4) Test plate, (5) Frame, (6) Base plate angle adjustment device, and (7) base plate.
Figure 1.
Rape stem contact parameters test bench. (1) Material box, (2) Baffle plate, (3) Test plate angle adjustment device, (4) Test plate, (5) Frame, (6) Base plate angle adjustment device, and (7) base plate.
Figure 2.
Test of the rape stems’ coefficient of restitution. h1 is the vertical distance between the baffle plate and the center of the test plate, m; α is the angle between the test plate and the horizon, (°); h2 is the vertical distance between the test plate and the base plate m; v1 is the normal fractional velocity of rape stem before the collision, m/s; v2 is the normal fractional velocity of rape stem after the collision, m/s; S is the horizontal distance between rape stem–bottom plate contact point and the center of the test plate, m.
Figure 2.
Test of the rape stems’ coefficient of restitution. h1 is the vertical distance between the baffle plate and the center of the test plate, m; α is the angle between the test plate and the horizon, (°); h2 is the vertical distance between the test plate and the base plate m; v1 is the normal fractional velocity of rape stem before the collision, m/s; v2 is the normal fractional velocity of rape stem after the collision, m/s; S is the horizontal distance between rape stem–bottom plate contact point and the center of the test plate, m.
Figure 3.
Coefficient of static friction test method. θs is the friction angle, (°).
Figure 3.
Coefficient of static friction test method. θs is the friction angle, (°).
Figure 4.
Coefficient of rolling friction test method. θr is the angle between base plate and frame, (°); Gs is rape stem gravity, N; Ff is rolling resistance, N; M1 is rolling torque, N·m; M2 is rolling resistance torque, N·m.
Figure 4.
Coefficient of rolling friction test method. θr is the angle between base plate and frame, (°); Gs is rape stem gravity, N; Ff is rolling resistance, N; M1 is rolling torque, N·m; M2 is rolling resistance torque, N·m.
Figure 5.
Rape stem repose angle test. (a) Physical test; (b) Simulation test.
Figure 5.
Rape stem repose angle test. (a) Physical test; (b) Simulation test.
Figure 6.
Rape stem repose angle test. (a) Diameter = 6.0 mm; (b) Diameter = 7.0 mm; (c) Diameter = 4.0 mm.
Figure 6.
Rape stem repose angle test. (a) Diameter = 6.0 mm; (b) Diameter = 7.0 mm; (c) Diameter = 4.0 mm.
Figure 7.
Rape stem flexible discrete element model. (a) Rigid discrete unit; (b) Rigid discrete element model; (c) Flexible discrete element model.
Figure 7.
Rape stem flexible discrete element model. (a) Rigid discrete unit; (b) Rigid discrete element model; (c) Flexible discrete element model.
Figure 8.
Rape stem three-point bending test: (a) Physics test; (b) Simulation test.
Figure 8.
Rape stem three-point bending test: (a) Physics test; (b) Simulation test.
Figure 9.
Rape stem repose angle test. (a) Image of rape stem pile; (b) Binarized image; (c) Boundary Fitting; (d) Test result.
Figure 9.
Rape stem repose angle test. (a) Image of rape stem pile; (b) Binarized image; (c) Boundary Fitting; (d) Test result.
Figure 10.
Pareto charts.
Figure 10.
Pareto charts.
Figure 11.
The effect of interaction factors on repose angle: (a) y1 = f (A 0.4605, E, 0.0315); (b) y1 = f (0.4665, D, E, 0.507); (c) y1 = f (0.4665, D, 0.0315, F).
Figure 11.
The effect of interaction factors on repose angle: (a) y1 = f (A 0.4605, E, 0.0315); (b) y1 = f (0.4665, D, E, 0.507); (c) y1 = f (0.4665, D, 0.0315, F).
Figure 12.
The effect of interaction factors on maximum damage force. y2 = f (G, 5.50 × 108, I).
Figure 12.
The effect of interaction factors on maximum damage force. y2 = f (G, 5.50 × 108, I).
Figure 13.
Displacement–force variation curve of rape stems under three-point bending.
Figure 13.
Displacement–force variation curve of rape stems under three-point bending.
Table 1.
Simulation parameter.
Table 1.
Simulation parameter.
Parameter | Value |
---|
Intrinsic parameter | Rape stem | Poisson’s ratio | 0.4 a |
Density/kg·m−3 | 486 b |
Shear modulus/Pa | 1.1 × 107 a |
Steel | Poisson’s ratio | 0.3 a |
Density/kg·m−3 | 7850 a |
Shear modulus/Pa | 7.9 × 1010 a |
Contact parameter | Rape stem–rape stem | Coefficient of restitution (A) | 0.322~0.611 c |
Coefficient of static friction (B) | 0.381~0.752 c |
Coefficient of rolling friction (C) | 0.013~0.032 c |
Rape stem–steel | Coefficient of restitution (D) | 0.298~0.623 c |
Coefficient of static friction (E) | 0.284~0.730 c |
Coefficient of rolling friction (F) | 0.021~0.042 c |
Table 2.
Bonding parameter.
Table 2.
Bonding parameter.
Factor | Level |
---|
−1 | 0 | 1 |
---|
Stiffness per unit area (G)/N·m−3 | 1.0 × 109 | 5.5 × 109 | 1.0 × 1010 |
Shear Stiffness per unit area (H)/N·m−3 | 1.0 × 108 | 5.5 × 108 | 1.0 × 109 |
Bonded radius (I)/mm | 1.0 | 1.5 | 2.0 |
Table 3.
Results of Plackett–Burman simulation test of rape stems’ contact paramaters.
Table 3.
Results of Plackett–Burman simulation test of rape stems’ contact paramaters.
Test No. | A | B | C | D | E | F | y1 |
---|
1 | 0.611 | 0.752 | 0.032 | 0.298 | 0.284 | 0.021 | 21.29 |
2 | 0.611 | 0.381 | 0.013 | 0.298 | 0.73 | 0.021 | 25.58 |
3 | 0.4665 | 0.5665 | 0.0225 | 0.4605 | 0.507 | 0.0315 | 27.18 |
4 | 0.611 | 0.752 | 0.013 | 0.298 | 0.284 | 0.042 | 24.89 |
5 | 0.611 | 0.381 | 0.032 | 0.623 | 0.73 | 0.021 | 30.33 |
6 | 0.611 | 0.752 | 0.013 | 0.623 | 0.73 | 0.042 | 33.60 |
7 | 0.4665 | 0.5665 | 0.0225 | 0.4605 | 0.507 | 0.0315 | 26.95 |
8 | 0.322 | 0.381 | 0.013 | 0.623 | 0.284 | 0.042 | 24.45 |
9 | 0.322 | 0.752 | 0.032 | 0.623 | 0.284 | 0.021 | 20.78 |
10 | 0.322 | 0.752 | 0.032 | 0.298 | 0.73 | 0.042 | 25.17 |
11 | 0.322 | 0.381 | 0.032 | 0.298 | 0.73 | 0.042 | 34.36 |
12 | 0.322 | 0.752 | 0.013 | 0.623 | 0.73 | 0.021 | 26.11 |
13 | 0.611 | 0.381 | 0.032 | 0.623 | 0.284 | 0.042 | 25.26 |
14 | 0.322 | 0.381 | 0.013 | 0.298 | 0.284 | 0.021 | 17.69 |
Table 4.
ANOVA of Plackett–Burman test.
Table 4.
ANOVA of Plackett–Burman test.
Factor | Standardized Effects | Sum of Squares | Contribution/% | Significance Ranking |
---|
A | 2.065 | 12.793 | 4.305 | 3 |
B | −0.972 | 2.832 | 0.953 | 5 |
C | 0.813 | 1.985 | 0.668 | 6 |
D | 1.925 | 11.117 | 3.741 | 4 |
E | 6.800 | 138.720 | 46.687 | 1 |
F | 4.328 | 56.203 | 18.916 | 2 |
Table 5.
Results of rape stems’ contact-parameter-response surface simulation test.
Table 5.
Results of rape stems’ contact-parameter-response surface simulation test.
Test No. | A | D | E | F | y1 |
---|
1 | 0.322 | 0.298 | 0.507 | 0.0315 | 22.88 |
2 | 0.611 | 0.298 | 0.507 | 0.0315 | 23.88 |
3 | 0.322 | 0.623 | 0.507 | 0.0315 | 22.77 |
4 | 0.611 | 0.623 | 0.507 | 0.0315 | 25.91 |
5 | 0.4665 | 0.4605 | 0.284 | 0.021 | 17.98 |
6 | 0.4665 | 0.4605 | 0.73 | 0.021 | 24.72 |
7 | 0.4665 | 0.4605 | 0.284 | 0.042 | 23.88 |
8 | 0.4665 | 0.4605 | 0.73 | 0.042 | 31.40 |
9 | 0.322 | 0.4605 | 0.507 | 0.021 | 22.35 |
10 | 0.611 | 0.4605 | 0.507 | 0.021 | 26.12 |
11 | 0.322 | 0.4605 | 0.507 | 0.042 | 27.40 |
12 | 0.611 | 0.4605 | 0.507 | 0.042 | 27.35 |
13 | 0.4665 | 0.298 | 0.284 | 0.0315 | 18.58 |
14 | 0.4665 | 0.623 | 0.284 | 0.0315 | 17.98 |
15 | 0.4665 | 0.298 | 0.73 | 0.0315 | 23.79 |
16 | 0.4665 | 0.623 | 0.73 | 0.0315 | 31.40 |
17 | 0.322 | 0.4605 | 0.284 | 0.0315 | 20.41 |
18 | 0.611 | 0.4605 | 0.284 | 0.0315 | 19.08 |
19 | 0.322 | 0.4605 | 0.73 | 0.0315 | 23.87 |
20 | 0.611 | 0.4605 | 0.73 | 0.0315 | 29.72 |
21 | 0.4665 | 0.298 | 0.507 | 0.021 | 27.25 |
22 | 0.4665 | 0.623 | 0.507 | 0.021 | 21.82 |
23 | 0.4665 | 0.298 | 0.507 | 0.042 | 26.19 |
24 | 0.4665 | 0.623 | 0.507 | 0.042 | 29.29 |
25 | 0.4665 | 0.4605 | 0.507 | 0.0315 | 27.18 |
26 | 0.4665 | 0.4605 | 0.507 | 0.0315 | 24.72 |
27 | 0.4665 | 0.4605 | 0.507 | 0.0315 | 27.01 |
Table 6.
ANOVA for contact-parameter-response surface test’s results.
Table 6.
ANOVA for contact-parameter-response surface test’s results.
Source | Coefficient Estimate (Coded Factors) | Sum of Squares | df | Mean Square | F-Value | p-Value |
---|
Model | \ | 349.62 | 14 | 24.97 | 11.66 | <0.0001 ** |
A | 1.03 | 12.8 | 1 | 12.8 | 5.97 | 0.0309 * |
D | 0.5515 | 3.65 | 1 | 3.65 | 1.70 | 0.2163 |
E | 3.92 | 183.94 | 1 | 183.94 | 85.85 | <0.0001 ** |
F | 2.11 | 53.2 | 1 | 53.20 | 24.83 | 0.0003 ** |
AD | 0.5345 | 1.14 | 1 | 1.14 | 0.53 | 0.4792 |
AE | 1.80 | 12.89 | 1 | 12.89 | 6.02 | 0.0304 * |
AF | −0.9551 | 3.65 | 1 | 3.65 | 1.70 | 0.2164 |
DE | 2.05 | 16.84 | 1 | 16.84 | 7.86 | 0.0159 * |
DF | 2.13 | 18.19 | 1 | 18.19 | 8.49 | 0.013 * |
EF | 0.1959 | 0.1535 | 1 | 0.154 | 0.072 | 0.7935 |
A² | −1.10 | 6.47 | 1 | 6.47 | 3.02 | 0.1077 |
D² | −1.10 | 6.47 | 1 | 6.47 | 3.02 | 0.1078 |
E² | −2.22 | 26.23 | 1 | 26.23 | 12.24 | 0.0044 ** |
F² | 0.6495 | 2.25 | 1 | 2.25 | 1.05 | 0.3257 |
Intercept | 26.30 | \ | \ | \ | \ | \ |
Residual | \ | 25.71 | 12 | 2.14 | \ | \ |
Lack of Fit | \ | 21.94 | 10 | 2.19 | 1.16 | 0.5479 |
Pure Error | \ | 3.77 | 2 | 1.89 | \ | \ |
Cor Total | \ | 375.33 | 26 | | \ | \ |
Table 7.
Bonding parameter Box–Behnken simulation result.
Table 7.
Bonding parameter Box–Behnken simulation result.
Test No. | G/N·m−3 | H/N·m−3 | I/mm | y2/N |
---|
1 | 5.50 × 109 | 1.00 × 109 | 2.0 | 54.80 |
2 | 5.50 × 109 | 1.00 × 109 | 1.0 | 16.16 |
3 | 1.00 × 1010 | 1.00 × 108 | 1.5 | 35.90 |
4 | 1.00 × 109 | 1.00 × 108 | 1.5 | 8.72 |
5 | 5.50 × 109 | 5.50 × 108 | 1.5 | 27.60 |
6 | 1.00 × 109 | 5.50 × 108 | 1.0 | 4.91 |
7 | 5.50 × 109 | 5.50 × 108 | 1.5 | 27.90 |
8 | 1.00 × 1010 | 5.50 × 108 | 2.0 | 86.50 |
9 | 5.50 × 109 | 1.00 × 108 | 2.0 | 47.80 |
10 | 1.00 × 1010 | 5.50 × 108 | 1.0 | 19.26 |
11 | 5.50 × 109 | 5.50 × 108 | 1.5 | 25.30 |
12 | 1.00 × 1010 | 1.00 × 109 | 1.5 | 41.80 |
13 | 5.50 × 109 | 1.00 × 108 | 1.0 | 14.51 |
14 | 1.00 × 109 | 5.50 × 108 | 2.0 | 31.20 |
15 | 1.00 × 109 | 1.00 × 109 | 1.5 | 12.43 |
Table 8.
ANOVA for bonding parameter Box–Behnken simulation result.
Table 8.
ANOVA for bonding parameter Box–Behnken simulation result.
Source | Coefficient Estimate (Coded Factors) | Sum of Squares | df | Mean Square | F-Value | p-Value |
---|
Model | \ | 6184.30 | 9 | 687.14 | 40.93 | 0.0004 ** |
G | 15.77 | 1990.80 | 1 | 1990.80 | 118.59 | 0.0001 ** |
H | 2.28 | 41.68 | 1 | 41.68 | 2.48 | 0.1759 |
I | 20.68 | 3422.13 | 1 | 3422.13 | 203.86 | <0.0001 ** |
GH | 0.5475 | 1.20 | 1 | 1.20 | 0.0714 | 0.7999 |
GI | 10.24 | 419.23 | 1 | 419.23 | 24.97 | 0.0041 ** |
HI | 1.34 | 7.16 | 1 | 7.16 | 0.4263 | 0.5426 |
G² | −0.0354 | 0.0046 | 1 | 0.0046 | 0.0003 | 0.9874 |
H² | −2.19 | 17.63 | 1 | 17.63 | 1.05 | 0.3524 |
I² | 8.57 | 271.15 | 1 | 271.15 | 16.15 | 0.0101 * |
Intercept | 26.93 | \ | \ | \ | \ | \ |
Residual | \ | 83.93 | 5 | 16.79 | | |
Lack of Fit | \ | 79.89 | 3 | 26.63 | 13.16 | 0.0714 |
Pure Error | \ | 4.05 | 2 | 2.02 | \ | \ |
Cor Total | \ | 6268.24 | 14 | \ | \ | \ |