Parameter Calibration of Sugarcane Stalk Bonding Model Based on Discrete Element Method

doi:10.13304/j.nykjdb.2024.0348

Abstract

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

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

CLC Number:

S225

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.

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.

Figures/Tables 17

Fig. 1 Rolling friction measurement

Fig. 2 Schematic diagram of collision recovery coefficient measurement

Fig. 3 Diagram of the bonding model

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］

Fig. 4 Sugarcane stalk shear model

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

Fig. 5 Shear force change curve

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

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

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

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

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

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

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

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

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

Fig. 7 Sugarcane stalk simulation shear

Fig. 8 Curves of physical test and simulation test

References 38

[1]	贾笛迩,高欣欣,刘高源,等.云南省丘陵山地甘蔗全程机械化发展的研究进展[J].热带农业科学,2022,42(2):115-120.
	JIA D E, GAO X X, LIU G Y, et al.. Research progress in the development of sugarcane mechanization in the hilly and mountainous regions of Yunnan province [J]. Chin. J. Trop. Agric., 2022, 42(2): 115-120.
[2]	吴传云,王建合,杨瑶,等.我国经济作物产业发展现状与机械化趋势分析[J].中国农机化学报,2024,45(1):1-13.
	WU C Y, WANG J H, YANG Y,et al..Analysis of the development status and mechanization trends of economic crop industry in China [J]. J. Chin. Agric. Mech., 2024, 45(1): 1-13.
[3]	赵莹.我国甘蔗收获机械化推广应用现状与发展建议[J].中国农机化学报,2016,37(9):236-244, 269.
	ZHAO Y. Extending situation and development proposal on sugarcane harvesting mechanization in China [J]. J. Chin. Agric. Mech., 2016, 37(9): 236-244, 269.
[4]	谢伟,欧阳琛,蒋蘋,等.面向夹持采收的油菜薹夹段茎秆离散元参数标定与优化[J].农业工程学报,2024,40(7):104-116.
	XIE W, OUYANG C, JIANG P, et al.. Calibrating and optimizing the discrete element parameters for clamping section stems during rape shoot harvesting [J]. Trans. Chin. Soc. Agric. Eng., 2024, 40(7): 104-116.
[5]	盛越,田海清,王迪,等.玉米根系离散元模型建立及仿真参数标定研究[J].农机化研究,2023,45(2):164-170.
	SHENG Y, TIAN H Q, WANG D, et al.. Study on establishment of discrete element model of maize root system and calibration of simulation parameters [J]. J. Agric. Mech. Res., 2023, 45(2): 164-170.
[6]	陈涛,衣淑娟,李衣菲,等.苜蓿现蕾期茎秆离散元模型建立与参数标定[J].农业机械学报,2023,54(5):91-100.
	CHEN T, YI S J, LI Y F, et al..Establishment of discrete element model and parameter calibration of alfalfa stem in budding stage [J]. Trans. Chin. Soc. Agric. Mach., 2023, 54(5): 91-100.
[7]	廖宜涛,廖庆喜,周宇,等.饲料油菜薹期收获茎秆破碎离散元仿真参数标定[J].农业机械学报,2020,51(6):73-82.
	LIAO Y T, LIAO Q X, ZHOU Y, et al.. Parameters calibration of discrete element model of fodder rape crop harvest in bolting stage [J]. Trans. Chin. Soc. Agric. Mach., 2020, 51(6): 73-82.
[8]	张兆国,徐红伟,薛浩田,等.三七茎秆离散元参数标定与试验[J].农业机械学报,2023,54(11):61-70, 91.
	ZHANG Z G, XU H W, XUE H T,et al..Calibration and experiment of discrete element parameters of Panax notoginseng stem [J]. Trans. Chin. Soc. Agric. Mach., 2023, 54(11): 61-70, 91.
[9]	马紫涛,赵智豪,全伟,等.基于EDEM的水稻残茬秸秆离散元仿真参数标定[J].中国农业科技导报,2023,25(11):103-113.
	MA Z T, ZHAO Z H, QUAN W,et al..Calibration of discrete element parameter of rice stubble straw based on EDEM [J]. J. Agric. Sci. Technol., 2023, 25(11): 103-113.
[10]	LIU W H, SU Q, FANG M, et al.. Parameters calibration of discrete element model for corn straw cutting based on Hertz-Mindlin with bonding [J/OL]. Appl. Sci., 2023,13(2):1156 [2024-03-28]. .
[11]	SHI Y Y, JIANG Y, WANG X C, et al.. A mechanical model of single wheat straw with failure characteristics based on discrete element method [J].Biosyst. Eng., 2023, 230: 1-15.
[12]	郝文录,刘恒新,朱良,等. 农业机械试验条件测定方法的一般规定: [S].北京:中国标准出版社,2008.
[13]	顿国强,王雷,纪欣鑫,等. 金乡紫皮蒜种离散元参数标定与试验验证[J].中国农业科技导报, 2024, 26(8): 131-139.
	DUN G Q, WANG L, JI X X, et al.. Calibration and verification of discrete element parameters of Jinxiang purple garlic seeds [J]. J. Agric. Sci. Technol., 2024, 26(8): 131-139.
[14]	张荣芳, 周纪磊, 刘虎, 等. 玉米颗粒粘结模型离散元仿真参数标定方法研究[J].农业机械学报,2022,53():69-77.
	ZHANG R F, ZHOU J L, LIU H, et al.. Research on parameter calibration method for discrete element simulation of corn particle bonding model [J]. Trans. Chin. Soc. Agric. Mach., 2022, 53(S1): 69-77.
[15]	陈林,余南辉,王立宗,等.米糠和碎米的接触参数测量与离散元仿真标定[J].中国农业科技导报,2024,26(2):127-136.
	CHEN L, YU N H, WANG L Z,et al..Measurement of contact parameters and discrete element simulation calibration of rice bran and broken rice [J]. J. Agric. Sci. Technol., 2024, 26(2): 127-136.
[16]	GUAN Z H, MU S L, LI H T, et al.. Flexible DEM model development and parameter calibration for rape stem [J/OL]. Appl. Sci., 2022,12(17):8394 [2024-03-28]. .
[17]	涂鸣,曹涛,万志华,等.菱角离散元粘结参数标定与剪切试验[J].华中农业大学学报,2023,42(4):270-278.
	TU M, CAO T, WAN Z H,et al..Calibration and shear experiments of discrete element bonding parameters for water caltrop [J]. J. Huazhong Agric. Univ., 2023, 42(4): 270-278.
[18]	刘俊安.基于离散元方法的深松铲参数优化及松土综合效应研究[D].北京:中国农业大学,2018.
	LIU J A. Parameter optimization and comprehensive effect of subsoiling shovel based on discrete element method [D]. Beijing: China Agricultural University, 2018.
[19]	HAN D D, ZHOU Y, NIE J S, et al.. DEM model acquisition of the corn ear with bonded particle model and its simulated parameters calibration [J/OL].Granul. Matter,2024,26(2):54 [2024-03-28]. .
[20]	张锋伟,宋学锋,张雪坤,等.玉米秸秆揉丝破碎过程力学特性仿真与试验[J].农业工程学报,2019,35(9):58-65.
	ZHANG F W, SONG X F, ZHANG X K, et al.. Simulation and experiment on mechanical characteristics of kneading and crushing process of corn straw [J]. Trans. Chin. Soc. Agric. Eng., 2019, 35(9): 58-65.
[21]	胡国明.颗粒系统的离散元素法分析仿真:离散元素法的工业应用与EDEM软件简介[M].武汉:武汉理工大学出版社,2010: 95-102.
[22]	江涛,吴崇友,汤庆,等.基于ANSYS和EDEM的小麦茎秆切割仿真研究[J].江苏农业科学,2018,46(17):231-234.
[23]	SCHRAMM M, TEKESTE M Z.Wheat straw direct shear simulation using discrete element method of fibrous bonded model [J]. Biosyst. Eng., 2022, 213: 1-12.
[24]	刘庆庭,区颖刚,卿上乐,等.甘蔗茎秆在扭转、压缩、拉伸荷载下的破坏试验[J].农业工程学报,2006,22(6):201-204.
	LIU Q T, OU Y G, QING S L,et al..Failure tests of sugarcane stalks under torsion,compression and tension load [J]. Trans. Chin. Soc. Agric. Eng., 2006, 22(6): 201-204.
[25]	朱容芳,杨望,罗郑楷,等.收获期宿根蔗的基本参数试验研究[J].农机化研究,2023,45(9):116-121.
	ZHU R F, YANG W, LUO Z K, et al.. Experimental study on basic parameters of perennial sugarcane in harvest period [J]. J. Agric. Mech. Res., 2023, 45(9): 116-121.
[26]	任甲辉,武涛,刘庆庭,等.蔗段离散元仿真建模方法与参数标定[J].华南农业大学学报,2022,43(3):124-132.
	REN J H, WU T, LIU Q T, et al.. Discrete element simulation modeling method and parameter calibration of sugarcane segment [J]. J. South China Agric. Univ., 2022, 43(3): 124-132.
[27]	张喜瑞,胡旭航,刘俊孝,等.香蕉秸秆离散元仿真粘结模型参数标定与试验[J].农业机械学报,2023,54(5):121-130.
	ZHANG X R, HU X H, LIU J X,et al..Calibration and verification of bonding parameters of banana straw simulation model based on discrete element method [J]. Trans. Chin. Soc. Agric. Mach., 2023, 54(5): 121-130.
[28]	史瑞杰,戴飞,赵武云,等.胡麻茎秆离散元柔性模型建立与接触参数试验验证[J].农业机械学报,2022,53(10):146-155.
	SHI R J, DAI F, ZHAO W Y, et al.. Establishment of discrete element flexible model and verification of contact parameters of flax stem [J].Trans.Chin.Soc.Agric.Mach.,2022,53(10):146-155.
[29]	周宇.饲料油菜切碎过程离散元仿真模型参数确定及验证[D].武汉:华中农业大学,2019.
	ZHOU Y. Parameter determination and verification of discrete element simulation model for fodder rapeseed chopping process [D]. Wuhan: Huazhong Agricultural University, 2019.
[30]	张国忠,陈立明,刘浩蓬,等.荸荠离散元仿真参数标定与试验[J].农业工程学报,2022,38(11):41-50.
	ZHANG G Z, CHEN L M, LIU H P,et al..Calibration and experiments of the discrete element simulation parameters for water chestnut [J].Trans.Chin.Soc.Agric.Eng.,2022,38(11):41-50.
[31]	童世合,邵明玺,曹猛,等.基于DEM的玉米秸秆离散元模型参数标定[J].中国农机化学报,2023,44(2):69-75.
	TONG S H, SHAO M X, CAO M, et al.. Parameter calibration of corn straw discrete element model based on DEM [J]. J. Chin. Agric. Mech., 2023, 44(2): 69-75.
[32]	ZHANG T, ZHAO M Q, LIU F, et al.. A discrete element method model of corn stalk and its mechanical characteristic parameters [J]. BioResources, 2020, 15(4): 9337-9350.
[33]	廖宜涛,王在腾,廖庆喜,等.果荚初期饲料油菜茎秆离散元接触模型参数标定[J].农业机械学报,2020,51():236-243.
	LIAO Y T, WANG Z T, LIAO Q X, et al.. Calibration of discrete element model parameters of forage rape stalk at early pod stage [J]. Trans. Chin. Soc. Agric. Mach., 2020,51(S1):236-243.
[34]	侯杰,谢方平,王修善,等.水稻茎秆接触物理参数测定与离散元仿真标定[J].江西农业大学学报,2022,44(3):747-758.
	HOU J, XIE F P, WANG X S,et al..Measurement of contact physical parameters of flexible rice straw and discrete element simulation calibration [J]. Acta Agric. Univ. Jiangxiensis, 2022, 44(3): 747-758.
[35]	温翔,杨望,郭无极,等.切段式甘蔗收割机排杂离散元仿真参数标定及验证[J].中国农机化学报,2020,41(1):12-18.
	WEN X, YANG W, GUO W J,et al..Parameter determination and validation of discrete element model of segmented sugarcane harvester for impurity removal [J].J.Chin.Agric.Mech., 2020, 41(1):12-18.
[36]	SHI Z, LIU X P, ZHANG Y L, et al.. Bond parameter calibration and crushing process analysis of brown rice kernels [J/OL]. Processes, 2023,11(10):2992 [2024-03-28]. .
[37]	李晖,王宝钢,史子昂,等.基于EDEM的膨化饲料离散元参数标定及其破碎机制研究[J].中国饲料,2024(7):126-132.
	LI H, WANG B G, SHI Z A, et al..Calibration of discrete element parameters of extruded feed based on EDEM and study on its crushing mechanism [J]. China Feed., 2024(7): 126-132.
[38]	SCHRAMM M, TEKESTE M Z, PLOUFFE C,et al..Estimating bond damping and bond Young's modulus for a flexible wheat straw discrete element method model [J].Biosyst.Eng.,2019,186:349-355.