Acta Agriculturae Zhejiangensis ›› 2024, Vol. 36 ›› Issue (4): 932-942.DOI: 10.3969/j.issn.1004-1524.20230649
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													KONG De1,2(
), YE Ziran2, TAN Xiangfeng2, DAI Mengdi2, ZHAO Xianliang1,*(
), KONG Dedong2,*
												  
						
						
						
					
				
Received:2023-05-18
															
							
															
							
															
							
																	Online:2024-04-25
															
							
																	Published:2024-04-29
															
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								KONG De,ZHAO Xianliang,KONG Dedong   
													CLC Number:
KONG De, YE Ziran, TAN Xiangfeng, DAI Mengdi, ZHAO Xianliang, KONG Dedong. Measurement of physical contact parameters and discrete element simulation calibration of lettuce seeds[J]. Acta Agriculturae Zhejiangensis, 2024, 36(4): 932-942.
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URL: http://www.zjnyxb.cn/EN/10.3969/j.issn.1004-1524.20230649
| 参数Parameters | 平均值Mean value | 
|---|---|
| 三轴尺寸(长×宽×厚)Three axis dimensions (length×width×thickness)/mm×mm×mm | 3.747×1.059×0.547 | 
| 千粒重1 000 grain weight/g | 1.144 | 
| 密度Density/(kg·m-3) | 1 650 | 
Table 1 Basic physical parameters of lettuce seeds
| 参数Parameters | 平均值Mean value | 
|---|---|
| 三轴尺寸(长×宽×厚)Three axis dimensions (length×width×thickness)/mm×mm×mm | 3.747×1.059×0.547 | 
| 千粒重1 000 grain weight/g | 1.144 | 
| 密度Density/(kg·m-3) | 1 650 | 
| 指标Index | 1 | 2 | 3 | 4 | 5 | 6 | 
|---|---|---|---|---|---|---|
| 厚度形变量ΔN | 0.2 | 0.16 | 0.2 | 0.16 | 0.21 | 0.19 | 
| Thickness deformation ΔN/mm | ||||||
| 宽度形变量ΔM | 0.18 | 0.07 | 0.16 | 0.09 | 0.16 | 0.05 | 
| Width deformation ΔM/mm | 
Table 2 Deformation index of lettuce seeds
| 指标Index | 1 | 2 | 3 | 4 | 5 | 6 | 
|---|---|---|---|---|---|---|
| 厚度形变量ΔN | 0.2 | 0.16 | 0.2 | 0.16 | 0.21 | 0.19 | 
| Thickness deformation ΔN/mm | ||||||
| 宽度形变量ΔM | 0.18 | 0.07 | 0.16 | 0.09 | 0.16 | 0.05 | 
| Width deformation ΔM/mm | 
| 仿真参数 Simulation parameters  |  低水平 Low level(-1)  |  高水平 Hight level(+1)  | 
|---|---|---|
| 生菜种子泊松比Poisson’s ratio of lettuce seed (A) | 0.1 | 0.4 | 
| 生菜种子剪切模量Shear modulus of lettuce seed (B)/MPa | 3.9 | 6.5 | 
| 生菜种子-生菜种子恢复系数Lettuce seed-lettuce seed restitution coefficient (C) | 0.10 | 0.24 | 
| 生菜种子-生菜种子静摩擦系数Lettuce seed-lettuce seed static friction coefficient (D) | 0.37 | 0.58 | 
| 生菜种子-生菜种子滚动摩擦系数Lettuce seed-lettuce seed rolling friction coefficient (E) | 0.10 | 0.32 | 
| 生菜种子-Q345碰撞恢复系数Lettuce seed-Q345 restitution coefficient (F) | 0.30 | 0.41 | 
| 生菜种子-Q345静摩擦系数Lettuce seed-Q345 static friction coefficient (G) | 0.35 | 0.46 | 
| 生菜种子-Q345滚动摩擦系数Lettuce seed-Q345 rolling friction coefficient (H) | 0.01 | 0.28 | 
| 虚拟参数Virtual parameter (J~L) | -1 | +1 | 
Table 3 Plackett-Burman simulation parameter range table
| 仿真参数 Simulation parameters  |  低水平 Low level(-1)  |  高水平 Hight level(+1)  | 
|---|---|---|
| 生菜种子泊松比Poisson’s ratio of lettuce seed (A) | 0.1 | 0.4 | 
| 生菜种子剪切模量Shear modulus of lettuce seed (B)/MPa | 3.9 | 6.5 | 
| 生菜种子-生菜种子恢复系数Lettuce seed-lettuce seed restitution coefficient (C) | 0.10 | 0.24 | 
| 生菜种子-生菜种子静摩擦系数Lettuce seed-lettuce seed static friction coefficient (D) | 0.37 | 0.58 | 
| 生菜种子-生菜种子滚动摩擦系数Lettuce seed-lettuce seed rolling friction coefficient (E) | 0.10 | 0.32 | 
| 生菜种子-Q345碰撞恢复系数Lettuce seed-Q345 restitution coefficient (F) | 0.30 | 0.41 | 
| 生菜种子-Q345静摩擦系数Lettuce seed-Q345 static friction coefficient (G) | 0.35 | 0.46 | 
| 生菜种子-Q345滚动摩擦系数Lettuce seed-Q345 rolling friction coefficient (H) | 0.01 | 0.28 | 
| 虚拟参数Virtual parameter (J~L) | -1 | +1 | 
| 序号 No.  |  仿真参数 | 休止角 Repose angle (θ)/(°)  | |||||||
|---|---|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | G | H | ||
| 1 | +1 | +1 | -1 | +1 | +1 | +1 | -1 | -1 | 45.817 | 
| 2 | -1 | +1 | +1 | -1 | +1 | +1 | +1 | -1 | 42.151 | 
| 3 | +1 | -1 | +1 | +1 | -1 | +1 | +1 | +1 | 44.119 | 
| 4 | -1 | +1 | -1 | +1 | +1 | -1 | +1 | +1 | 48.106 | 
| 5 | -1 | -1 | +1 | -1 | +1 | +1 | -1 | +1 | 37.111 | 
| 6 | -1 | -1 | -1 | +1 | -1 | +1 | +1 | -1 | 43.129 | 
| 7 | +1 | -1 | -1 | -1 | +1 | -1 | +1 | +1 | 36.871 | 
| 8 | +1 | +1 | -1 | -1 | -1 | +1 | -1 | +1 | 32.005 | 
| 9 | +1 | +1 | +1 | -1 | -1 | -1 | +1 | -1 | 37.151 | 
| 10 | -1 | +1 | +1 | +1 | -1 | -1 | -1 | +1 | 39.028 | 
| 11 | +1 | -1 | +1 | +1 | +1 | -1 | -1 | -1 | 54.726 | 
| 12 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 29.396 | 
Table 4 Plackett-Burman test protocol and results
| 序号 No.  |  仿真参数 | 休止角 Repose angle (θ)/(°)  | |||||||
|---|---|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | G | H | ||
| 1 | +1 | +1 | -1 | +1 | +1 | +1 | -1 | -1 | 45.817 | 
| 2 | -1 | +1 | +1 | -1 | +1 | +1 | +1 | -1 | 42.151 | 
| 3 | +1 | -1 | +1 | +1 | -1 | +1 | +1 | +1 | 44.119 | 
| 4 | -1 | +1 | -1 | +1 | +1 | -1 | +1 | +1 | 48.106 | 
| 5 | -1 | -1 | +1 | -1 | +1 | +1 | -1 | +1 | 37.111 | 
| 6 | -1 | -1 | -1 | +1 | -1 | +1 | +1 | -1 | 43.129 | 
| 7 | +1 | -1 | -1 | -1 | +1 | -1 | +1 | +1 | 36.871 | 
| 8 | +1 | +1 | -1 | -1 | -1 | +1 | -1 | +1 | 32.005 | 
| 9 | +1 | +1 | +1 | -1 | -1 | -1 | +1 | -1 | 37.151 | 
| 10 | -1 | +1 | +1 | +1 | -1 | -1 | -1 | +1 | 39.028 | 
| 11 | +1 | -1 | +1 | +1 | +1 | -1 | -1 | -1 | 54.726 | 
| 12 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 29.396 | 
| 参数 Parameters  |  自由度 Degree of freedom  |  平方和 Sum of squares  |  F值 F-value  |  P值 P-value  | 
|---|---|---|---|---|
| A | 1 | 11.54 | 7.33 | 0.113 7 | 
| B | 1 | 8.87 | 5.63 | 0.141 0 | 
| C | 1 | 55.43 | 35.20 | 0.027 3* | 
| D | 1 | 152.66 | 96.95 | 0.010 2* | 
| E | 1 | 53.06 | 33.69 | 0.028 4* | 
| F | 1 | 8.65 | 5.49 | 0.143 8 | 
| G | 1 | 15.06 | 9.56 | 0.090 6 | 
| H | 1 | 1.16 | 0.738 2 | 0.480 8 | 
Table 5 Significance analysis of Plackett-Burman test parameters
| 参数 Parameters  |  自由度 Degree of freedom  |  平方和 Sum of squares  |  F值 F-value  |  P值 P-value  | 
|---|---|---|---|---|
| A | 1 | 11.54 | 7.33 | 0.113 7 | 
| B | 1 | 8.87 | 5.63 | 0.141 0 | 
| C | 1 | 55.43 | 35.20 | 0.027 3* | 
| D | 1 | 152.66 | 96.95 | 0.010 2* | 
| E | 1 | 53.06 | 33.69 | 0.028 4* | 
| F | 1 | 8.65 | 5.49 | 0.143 8 | 
| G | 1 | 15.06 | 9.56 | 0.090 6 | 
| H | 1 | 1.16 | 0.738 2 | 0.480 8 | 
| 序号 No.  |  生菜种子-生菜种子恢复系数 Lettuce seed-lettuce seed restitution coefficient (C)  |  生菜种子-生菜种子静摩擦系数 Lettuce seed-lettuce seed static friction coefficient (D)  |  生菜种子-生菜种子滚动摩擦系数 Lettuce seed-lettuce seed rolling friction coefficient (E)  |  休止角 Repose angle (θ)/(°)  |  相对误差 Relative error/%  | 
|---|---|---|---|---|---|
| 1 | 0.100 | 0.370 | 0.100 | 31.192 | 12.36 | 
| 2 | 0.128 | 0.412 | 0.144 | 33.755 | 5.16 | 
| 3 | 0.156 | 0.454 | 0.188 | 36.801 | 3.40 | 
| 4 | 0.184 | 0.496 | 0.232 | 38.307 | 7.63 | 
| 5 | 0.212 | 0.538 | 0.276 | 44.334 | 24.82 | 
| 6 | 0.240 | 0.580 | 0.320 | 46.705 | 31.23 | 
Table 6 The steepest climbing test of lettuce seed significant parameters
| 序号 No.  |  生菜种子-生菜种子恢复系数 Lettuce seed-lettuce seed restitution coefficient (C)  |  生菜种子-生菜种子静摩擦系数 Lettuce seed-lettuce seed static friction coefficient (D)  |  生菜种子-生菜种子滚动摩擦系数 Lettuce seed-lettuce seed rolling friction coefficient (E)  |  休止角 Repose angle (θ)/(°)  |  相对误差 Relative error/%  | 
|---|---|---|---|---|---|
| 1 | 0.100 | 0.370 | 0.100 | 31.192 | 12.36 | 
| 2 | 0.128 | 0.412 | 0.144 | 33.755 | 5.16 | 
| 3 | 0.156 | 0.454 | 0.188 | 36.801 | 3.40 | 
| 4 | 0.184 | 0.496 | 0.232 | 38.307 | 7.63 | 
| 5 | 0.212 | 0.538 | 0.276 | 44.334 | 24.82 | 
| 6 | 0.240 | 0.580 | 0.320 | 46.705 | 31.23 | 
| 序号 No.  |  生菜种子-生菜种子Lettuce seed-lettuce seed | 休止角 Repose angle (θ)/(°)  | ||
|---|---|---|---|---|
| 恢复系数 restitution coefficient (C)  |  静摩擦系数 static friction coefficient (D)  |  滚动摩擦系数 rolling friction coefficient (E)  | ||
| 1 | 0.128 | 0.412 | 0.188 | 32.954 | 
| 2 | 0.184 | 0.412 | 0.188 | 34.251 | 
| 3 | 0.128 | 0.496 | 0.188 | 37.154 | 
| 4 | 0.184 | 0.496 | 0.188 | 38.053 | 
| 5 | 0.128 | 0.454 | 0.144 | 33.426 | 
| 6 | 0.184 | 0.454 | 0.144 | 34.239 | 
| 7 | 0.128 | 0.454 | 0.232 | 35.099 | 
| 8 | 0.184 | 0.454 | 0.232 | 36.604 | 
| 9 | 0.156 | 0.412 | 0.144 | 31.114 | 
| 10 | 0.156 | 0.496 | 0.144 | 36.375 | 
| 11 | 0.156 | 0.412 | 0.232 | 34.787 | 
| 12 | 0.156 | 0.496 | 0.232 | 37.057 | 
| 13 | 0.156 | 0.454 | 0.188 | 35.723 | 
| 14 | 0.156 | 0.454 | 0.188 | 35.564 | 
| 15 | 0.156 | 0.454 | 0.188 | 35.792 | 
| 16 | 0.156 | 0.454 | 0.188 | 35.664 | 
| 17 | 0.156 | 0.454 | 0.188 | 35.591 | 
Table 7 Box-Behnken experimental design and results
| 序号 No.  |  生菜种子-生菜种子Lettuce seed-lettuce seed | 休止角 Repose angle (θ)/(°)  | ||
|---|---|---|---|---|
| 恢复系数 restitution coefficient (C)  |  静摩擦系数 static friction coefficient (D)  |  滚动摩擦系数 rolling friction coefficient (E)  | ||
| 1 | 0.128 | 0.412 | 0.188 | 32.954 | 
| 2 | 0.184 | 0.412 | 0.188 | 34.251 | 
| 3 | 0.128 | 0.496 | 0.188 | 37.154 | 
| 4 | 0.184 | 0.496 | 0.188 | 38.053 | 
| 5 | 0.128 | 0.454 | 0.144 | 33.426 | 
| 6 | 0.184 | 0.454 | 0.144 | 34.239 | 
| 7 | 0.128 | 0.454 | 0.232 | 35.099 | 
| 8 | 0.184 | 0.454 | 0.232 | 36.604 | 
| 9 | 0.156 | 0.412 | 0.144 | 31.114 | 
| 10 | 0.156 | 0.496 | 0.144 | 36.375 | 
| 11 | 0.156 | 0.412 | 0.232 | 34.787 | 
| 12 | 0.156 | 0.496 | 0.232 | 37.057 | 
| 13 | 0.156 | 0.454 | 0.188 | 35.723 | 
| 14 | 0.156 | 0.454 | 0.188 | 35.564 | 
| 15 | 0.156 | 0.454 | 0.188 | 35.792 | 
| 16 | 0.156 | 0.454 | 0.188 | 35.664 | 
| 17 | 0.156 | 0.454 | 0.188 | 35.591 | 
| 方差源 Source of variance  |  平方和 Sum of squares  |  自由度 Degree of freedom  |  均方 Mean square  |  P值 P-value  | 
|---|---|---|---|---|
| 模型Model | 46.630 0 | 9 | 5.180 0 | 0.000 1** | 
| C | 2.550 0 | 1 | 2.550 0 | 0.000 1** | 
| D | 30.160 0 | 1 | 30.160 0 | 0.000 1** | 
| E | 8.810 0 | 1 | 8.810 0 | 0.000 1** | 
| CD | 0.039 6 | 1 | 0.039 6 | 0.100 1 | 
| CE | 0.119 7 | 1 | 0.119 7 | 0.013 3* | 
| DE | 2.240 0 | 1 | 2.240 0 | 0.000 1** | 
| C2 | 0.003 2 | 1 | 0.003 2 | 0.607 6 | 
| D2 | 0.005 5 | 1 | 0.005 5 | 0.501 7 | 
| E2 | 2.680 0 | 1 | 2.680 0 | 0.000 1** | 
| 残差Residual | 0.077 3 | 7 | 0.011 0 | |
| 失拟项Lack of fit | 0.042 2 | 3 | 0.014 1 | 0.322 7 | 
| 纯误差Pure error | 0.035 2 | 4 | 0.008 8 | |
| 总和Sum | 46.710 0 | 16 | 
Table 8 Box-Behnken test regression model analysis of variance
| 方差源 Source of variance  |  平方和 Sum of squares  |  自由度 Degree of freedom  |  均方 Mean square  |  P值 P-value  | 
|---|---|---|---|---|
| 模型Model | 46.630 0 | 9 | 5.180 0 | 0.000 1** | 
| C | 2.550 0 | 1 | 2.550 0 | 0.000 1** | 
| D | 30.160 0 | 1 | 30.160 0 | 0.000 1** | 
| E | 8.810 0 | 1 | 8.810 0 | 0.000 1** | 
| CD | 0.039 6 | 1 | 0.039 6 | 0.100 1 | 
| CE | 0.119 7 | 1 | 0.119 7 | 0.013 3* | 
| DE | 2.240 0 | 1 | 2.240 0 | 0.000 1** | 
| C2 | 0.003 2 | 1 | 0.003 2 | 0.607 6 | 
| D2 | 0.005 5 | 1 | 0.005 5 | 0.501 7 | 
| E2 | 2.680 0 | 1 | 2.680 0 | 0.000 1** | 
| 残差Residual | 0.077 3 | 7 | 0.011 0 | |
| 失拟项Lack of fit | 0.042 2 | 3 | 0.014 1 | 0.322 7 | 
| 纯误差Pure error | 0.035 2 | 4 | 0.008 8 | |
| 总和Sum | 46.710 0 | 16 | 
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