甘蔗茎秆离散元仿真粘结模型参数标定

doi:10.13304/j.nykjdb.2024.0348

摘要/Abstract

摘要：

为提高离散元法对甘蔗收获机械设计与优化的准确性和可靠性，以全熟期甘蔗茎秆为研究对象，结合甘蔗茎秆物理试验和离散元仿真方法，选用EDEM中的Hertz-Mindlin with Bonding模型建立甘蔗茎秆粘结模型，并对仿真模型中的相关参数进行标定。物理试验中甘蔗茎秆最大剪切力均值为574.5 N。以最大剪切力为评价指标设计Plackett-Burman试验、Steepest Ascent试验和Box-Behnken试验确定甘蔗茎秆粘结模型参数，并通过试验来验证仿真模型的可靠性。结果表明，甘蔗茎秆粘结模型法向接触刚度为7.60×10⁸ N·m^-1、切向接触刚度为4.35×10⁸ N·m^-1、粘结半径为1.883 9 mm。以此参数组合进行验证仿真试验，得到茎秆最大剪切力均值为562.64 N，与物理试验值相对误差为2.06%。以上表明，建立的甘蔗茎秆剪切模型与标定参数结果可用于离散元仿真研究。研究结果对甘蔗收获机设计具有指导意义。

关键词: 甘蔗茎秆, 离散元法, 最大剪切力, 粘结参数标定

Abstract:

To improve the accuracy and reliability of the discrete element method for the design and optimization of sugarcane harvesting machinery， the full-matured sugarcane stalk was taken as the research object， and the Hertz-Mindlin with Bonding model in EDEM was chosen to establish the bonding model of sugarcane stalk by combining the physical test of the stalk and the discrete element simulation method， and the relevant parameters in the simulation model were calibrated. The average value of the maximum shear force of sugarcane stalks in the physical test was 574.5 N. The Plackett-Burman test， Steepest Ascent test and Box-Behnken test were designed to determine the parameters of the sugarcane stalk bonding model using the maximum shear force as the evaluation index， and the reliability of the simulation model was verified by the test. The results showed that the normal stiffness of the sugarcane stalk bonding model was 7.60×10⁸ N·m^-1， the shear stiffness was 4.35×10⁸ N·m^-1， and bonded disk radius was 1.883 9 mm. According to this parameter combination， the average maximum stem shear force obtained by simulation was 562.64 N， and the relative error with the test value was only 2.06%. Above results showed that the sugarcane stalk shear model and calibration parameter results established in this paper could be used for discrete element simulation research， which had guiding significance for the design of sugarcane harvester.

Key words: sugarcane stalk, discrete element method, maximum shear force, bond parameter calibration

中图分类号:

S225

张宏友, 张程, 钟铭深, 黄磊, 张永华, 徐连江. 甘蔗茎秆离散元仿真粘结模型参数标定[J]. 中国农业科技导报, 2025, 27(10): 105-117.

Hongyou ZHANG, Cheng ZHANG, Mingshen ZHONG, Lei HUANG, Yonghua ZHANG, Lianjiang XU. Parameter Calibration of Sugarcane Stalk Bonding Model Based on Discrete Element Method[J]. Journal of Agricultural Science and Technology, 2025, 27(10): 105-117.

图/表 17

图1 滚动摩擦测量

Fig. 1 Rolling friction measurement

图2 碰撞恢复系数测量

Fig. 2 Schematic diagram of collision recovery coefficient measurement

图3 Bonding模型示意图

Fig. 3 Diagram of the bonding model

表1 甘蔗茎秆仿真模型参数

Table 1 Parameters of sugarcane stalk simulation model

参数 Parameter		数值 Value	文献 Reference
基本参数 Basic parameter	甘蔗茎秆泊松比 Sugarcane stalk Poisson’s ratio	0.35	［24-26］
	甘蔗茎秆密度 Sugarcane stalk density/（kg·m^-3）	1 040^※
	甘蔗茎秆剪切模量 Sugarcane stalk shear modulus/Pa	1.08×10⁷	［25‑26］
	45钢泊松比 45 steel Poisson’s ratio	0.30	［27］
	45钢密度 45 steel density/（kg·m^-3）	7 850	［27］
	45钢剪切模量 45 steel shear modulus/Pa	7.94×10¹⁰	［27］
	甘蔗茎秆与45钢之间的碰撞恢复系数e₁ Collision recovery coefficient between sugarcane stalks and 45 steel e₁	0.452^※
	甘蔗茎秆与45钢之间的静摩擦因数μ₁ Static friction factor between sugarcane stalk and 45 steel μ₁	0.350^※
	甘蔗茎秆与45钢之间的滚动摩擦因数f₁ Rolling friction factor between sugarcane stalk and 45 steel f₁	0.054^※
	甘蔗茎秆之间的碰撞恢复系数e₂ Collision recovery coefficient between sugarcane stalks e₂	0.423^※
	甘蔗茎秆之间的静摩擦因数μ₂ Static friction factor between sugarcane stalks μ₂	0.541^※
	甘蔗茎秆之间的滚动摩擦因数f₂ Rolling friction factor between sugarcane stalks f₂	0.045^※
粘结参数 Bonding parameter	法向接触刚度 Normal stiffness per unit area/（N·m^-1）	5×10⁸~9×10⁸	［28‑29］
	切向接触刚度 Shear stiffness per unit area/（N·m^-1）	3×10⁸~6×10⁸	［28‑29］
	临界法向应力 Critical normal stress/Pa	3×10⁷～5×10⁷	［28‑29］
	临界切向应力 Critical shear stress/Pa	2×10⁷～6×10⁷	［28‑29］
	粘结半径 Bonded disk radius/mm	1.80～1.95	［28‑29］

图4 甘蔗茎秆剪切模型

Fig. 4 Sugarcane stalk shear model

表2 Plackett-Burman试验取值范围

Table 2 Value range for Plackett-Burman test

因素 Factor	编码 Encoding
因素 Factor	-1	1
x₁：法向接触刚度Normal stiffness per unit area/（N·m^-1）	5×10⁸	9×10⁸
x₂：切向接触刚度Shear stiffness per unit area/（N·m^-1）	3×10⁸	6×10⁸
x₃：临界法向应力Critical normal stress/Pa	3×10⁷	5×10⁷
x₄：临界切向应力Critical shear stress/Pa	2×10⁷	6×10⁷
x₅：粘结半径Bonded disk radius/mm	1.80	1.95

图5 剪切力变化曲线

Fig. 5 Shear force change curve

表3 Plackett-Burman试验方案与结果

Table 3 Plackett-Burman test protocol and results

序号 Number	因素 Factor					F₀：最大剪切力 Maximum shear/N
序号 Number	x₁：法向接触刚度Normal stiffness per unit area/（N·m^-1）	x₂：切向接触刚度Shear stiffness per unit area/（N·m^-1）	x₃：临界法向应力Critical normal stress/Pa	x₄：临界切向应力Critical shear stress/Pa	x₅：粘结半径Bonded disk radius/mm	F₀：最大剪切力 Maximum shear/N
1	9×10⁸	6×10⁸	3×10⁷	6×10⁷	1.95	747.7
2	5×10⁸	6×10⁸	5×10⁷	2×10⁷	1.95	578.8
3	5×10⁸	3×10⁸	5×10⁷	2×10⁷	1.95	640.3
4	9×10⁸	6×10⁸	5×10⁷	2×10⁷	1.80	459.9
5	9×10⁸	6×10⁸	3×10⁷	2×10⁷	1.80	577.8
6	9×10⁸	3×10⁸	3×10⁷	2×10⁷	1.95	1 100.1
7	5×10⁸	3×10⁸	3×10⁷	2×10⁷	1.80	360.5
8	9×10⁸	3×10⁸	5×10⁷	6×10⁷	1.80	556.3
9	9×10⁸	3×10⁸	5×10⁷	6×10⁷	1.95	999.4
10	5×10⁸	6×10⁸	3×10⁷	6×10⁷	1.95	614.5
11	5×10⁸	3×10⁸	3×10⁷	6×10⁷	1.80	330.4
12	5×10⁸	6×10⁸	5×10⁷	6×10⁷	1.80	230.9

表4 Plackett-Burman试验方差分析

Table 4 Analysis of variance of Plackett-Burman test

方差来源 Source of variance	平方和 Sum of squares	自由度 Degree of freedom	均方 Mean square	F值 F value	P值 P value
模型Model	6.884×10⁵	5	1.377×10⁵	24.56	0.000 6^**
x₁：法向接触刚度Normal stiffness per unit area	2.368×10⁵	1	2.368×10⁵	42.24	0.000 6^**
x₂：切向接触刚度Shear stiffness per unit area	5.036×10⁴	1	5.036×10⁴	8.98	0.024 1^*
x₃：临界法向应力Critical normal stress	0.587×10⁴	1	0.587×10⁴	1.05	0.345 7
x₄：临界切向应力Critical shear stress	0.473×10⁴	1	0.473×10⁴	0.84	0.393 9
x₅：粘结半径Bonded disk radius	3.906×10⁵	1	3.906×10⁵	69.67	0.000 2^**
残差 Residual error	3.364×10⁴	6	0.561×10⁴
总和 Total	7.220×10⁵	11

表5 Steepest Ascent试验结果

Table 5 Steepest ascent test results

序号 Number	因素 Factor			F₀：最大剪切力 Maximum shear/N	σ：相对误差 Relative error/%
序号 Number	x₁：法向接触刚度Normal stiffness per unit area/（N·m^-1）	x₂：切向接触刚度Shear stiffness per unit area/（N·m^-1）	x₅：粘结半径Bonded disk radius/mm	F₀：最大剪切力 Maximum shear/N	σ：相对误差 Relative error/%
1	5×10⁸	3.00×10⁸	1.800 0	371.0	35.42
2	6×10⁸	3.75×10⁸	1.837 5	520.7	9.36
3	7×10⁸	4.50×10⁸	1.875 0	568.6	1.03
4	8×10⁸	5.25×10⁸	1.912 5	648.5	12.88
5	9×10⁸	6.00×10⁸	1.950 0	718.1	25.00

表6 粘结参数Box-Behnken试验因素编码

Table 6 Bonding parameters Box-Behnken test factor code

编码 Encoding	因素 Factor
编码 Encoding	x₁：法向接触刚度Normal stiffness per unit area/（N·m^-1）	x₂：切向接触刚度Shear stiffness per unit area/（N·m^-1）	x₅：粘结半径Bonded disk radius/mm
-1	6×10⁸	3.75×10⁸	1.837 5
0	7×10⁸	4.50×10⁸	1.875 0
1	8×10⁸	5.25×10⁸	1.912 5

表7 粘结参数Box-Behnken试验方案与结果

Table 7 Bonding parameters Box-Behnken test scheme and results

序号 Number	因素 Factor			F₀：最大剪切力 Maximum shear/N	σ：相对误差 Relative error/%
序号 Number	x₁：法向接触刚度Normal stiffness per unit area/（N·m^-1）	x₂：切向接触刚度Shear stiffness per unit area/（N·m^-1）	x₅：粘结半径Bonded disk radius/mm	F₀：最大剪切力 Maximum shear/N	σ：相对误差 Relative error/%
1	7×10⁸	4.50×10⁸	1.875	546.9	4.80
2	7×10⁸	4.50×10⁸	1.875	560.8	2.38
3	6×10⁸	3.75×10⁸	1.875	638.6	11.16
4	7×10⁸	4.50×10⁸	1.875	549.5	4.35
5	8×10⁸	4.50×10⁸	1.838	503.8	12.31
6	8×10⁸	3.75×10⁸	1.875	586.7	2.12
7	7×10⁸	4.50×10⁸	1.875	549.3	4.39
8	7×10⁸	5.25×10⁸	1.838	528.4	8.02
9	6×10⁸	5.25×10⁸	1.875	534.0	7.05
10	7×10⁸	3.75×10⁸	1.838	550.3	4.21
11	7×10⁸	5.25×10⁸	1.913	605.7	5.43
12	7×10⁸	4.50×10⁸	1.875	564.5	1.74
13	8×10⁸	4.50×10⁸	1.913	621.3	8.15
14	6×10⁸	4.50×10⁸	1.838	534.9	6.89
15	8×10⁸	5.25×10⁸	1.875	625.8	8.93
16	6×10⁸	4.50×10⁸	1.913	575.0	0.09
17	7×10⁸	3.75×10⁸	1.913	653.9	13.82

表8 粘结参数Box-Behnken方差分析

Table 8 Box-Behnken analysis of variance for bonding parameters

方差来源 Source of variance	平方和 Sum of squares	自由度 Degree of freedom	均方 Mean square	F值 F value	P值 P value
模型 Model	29 108.10	9	3 234.23	57.20	< 0.000 1^**
x₁	379.50	1	379.50	6.71	0.035 9^*
x₂	2 298.42	1	2 298.42	40.65	0.000 4^**
x₅	14 322.78	1	14 322.78	253.30	< 0.000 1^**
x₁x₂	5 162.42	1	5 162.42	91.30	< 0.000 1^**
x₁x₅	1 497.69	1	1 497.69	26.49	0.001 3^**
x₂x₅	172.92	1	172.92	3.06	0.123 8
x $12$	277.96	1	277.96	4.92	0.062 1
x $22$	4 853.06	1	4 853.06	85.83	< 0.000 1^**
x $52$	53.81	1	53.81	0.95	0.361 8
残差 Residual error	395.81	7	56.54
失拟项 Lack of fit	146.77	3	48.92	0.79	0.561 1
纯误差 Pure error	249.04	4	62.26
总和 Total	29 503.90	16

表8 粘结参数Box-Behnken方差分析

Table 8 Box-Behnken analysis of variance for bonding parameters

方差来源 Source of variance	平方和 Sum of squares	自由度 Degree of freedom	均方 Mean square	F值 F value	P值 P value
模型 Model	29 108.10	9	3 234.23	57.20	< 0.000 1^**
x₁	379.50	1	379.50	6.71	0.035 9^*
x₂	2 298.42	1	2 298.42	40.65	0.000 4^**
x₅	14 322.78	1	14 322.78	253.30	< 0.000 1^**
x₁x₂	5 162.42	1	5 162.42	91.30	< 0.000 1^**
x₁x₅	1 497.69	1	1 497.69	26.49	0.001 3^**
x₂x₅	172.92	1	172.92	3.06	0.123 8
x $12$	277.96	1	277.96	4.92	0.062 1
x $22$	4 853.06	1	4 853.06	85.83	< 0.000 1^**
x $52$	53.81	1	53.81	0.95	0.361 8
残差 Residual error	395.81	7	56.54
失拟项 Lack of fit	146.77	3	48.92	0.79	0.561 1
纯误差 Pure error	249.04	4	62.26
总和 Total	29 503.90	16

图6 交互因素对最大剪切力和相对误差的响应曲面

Fig. 6 Response surfaces of interaction factors to maximum shear force and relative error

表9 标定粘结参数

Table 9 Calibration bonding parameters

参数

Parameter

数值

Numerical value

法向接触刚度

Normal stiffness per unit area/（N·m^-1）

7.60×10⁸

切向接触刚度

Shear stiffness per unit area/（N·m^-1）

4.35×10⁸

临界法向应力

Critical normal stress/Pa

4×10⁷

临界切向应力

Critical shear stress/Pa

4×10⁷

粘结半径

Bonded disk radius/mm

1.883 9

图7 甘蔗茎秆仿真剪切

Fig. 7 Sugarcane stalk simulation shear

图8 物理试验与仿真试验曲线

Fig. 8 Curves of physical test and simulation test

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