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Article(id=1241446430527771541, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241446328396476740, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.07.018, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1704038400000, receivedDateStr=2024-01-01, revisedDate=1708099200000, revisedDateStr=2024-02-17, acceptedDate=null, acceptedDateStr=null, onlineDate=1773913493996, onlineDateStr=2026-03-19, pubDate=1752508800000, pubDateStr=2025-07-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773913493996, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773913493996, creator=13701087609, updateTime=1773913493996, updator=13701087609, issue=Issue{id=1241446328396476740, tenantId=1146029695717560320, journalId=1227999626482147330, year='2025', volume='47', issue='7', pageStart='1', pageEnd='158', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773913469647, creator=13701087609, updateTime=1773916972123, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241461018921062969, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241446328396476740, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241461018921062970, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241446328396476740, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=144, endPage=151, ext={EN=ArticleExt(id=1241446430817178520, articleId=1241446430527771541, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Study on two-scale unified constitutive model and damping mechanism of rubber conveyor belt with steel wire rope core, columnId=1241446430376776595, journalTitle=Journal of Mechanical Strength, columnName=·Design·Calculation·, runingTitle=null, highlight=null, articleAbstract=

Constitutive analysis of steel wire rope conveyor belt is a key problem for conveyor belt design optimization and energy conservation. Maxwell model and Burgers model based on viscoelastic theory and transient dynamics were constructed. Considering the fretting friction damping between steel wires and the mutual damping between steel wire rope and conveyor belt, a mixed constitutive model was constructed. Under the condition of 0-30 ℃, the relationship between the parameters of the constitutive model was established, the simulation curve was fitted and solved by Matlab, and the accuracy of the mixed constitutive model was verified by taking 40 ℃ as the control group. The verification results show that the maximum error between the conveyor belt represented by this constitutive model and the experiment is 5. 88%, demonstrating that this constitutive model can better characterize the rubber conveyor belt with steel wire rope core. The universality of this model is verified by the method of simulation and prediction. It provides a theoretical basis for the structural optimization and energy-saving analysis of conveyor belt.

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FENG Jinping, E-mail：
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钢丝绳输送带的本构分析是优化输送带设计和节能的关键问题，采用黏弹性理论及瞬态动力学的知识构建了基于表征钢丝绳的Maxwell模型和表征橡胶基体的Burgers模型，考虑了钢丝绳间的微动摩擦阻尼和钢丝绳与输送带之间的相互阻尼，构建了其混合本构模型，运用外加激励载荷的方法，在0~40 ℃条件下，建立本构模型间各参数之间的关系，运用Matlab对仿真曲线进行拟合、求解，在环境温度为40 ℃的条件下，对混合本构模型的准确性进行了验证。结果表明，模型预测数据与实测数据具有良好的一致性，其中最大误差为5.88%。证明此本构模型能够比较好地表征钢丝绳芯橡胶输送带，运用仿真加预测的方法，验证此模型的普适性。此研究为输送带结构优化和节能分析提供理论基础。

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冯金平，男，1997年生，浙江台州人，硕士；主要研究方向为机械工程；E-mail：。
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李建刚，男，1976年生，辽宁阜新人，博士，讲师；主要研究方向为机电系统设计与仿真；E-mail：。

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李建刚，男，1976年生，辽宁阜新人，博士，讲师；主要研究方向为机电系统设计与仿真；E-mail：。

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李建刚，男，1976年生，辽宁阜新人，博士，讲师；主要研究方向为机电系统设计与仿真；E-mail：。

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orderNo=3, keyword=钢丝绳输送带), Keyword(id=1241446449414721877, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, language=CN, orderNo=4, keyword=温度效应)], refs=[Reference(id=1241446454699545027, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, doi=null, pmid=null, pmcid=null, year=2023, volume=35, issue=6, pageStart=85, pageEnd=87, url=null, language=null, rfNumber=［1］, rfOrder=0, authorNames=马涛, journalName=西部探矿工程, refType=null, unstructuredReference=马涛. 煤矿井下带式输送机运行的相关问题研究[J]. 西部探矿工程，2023，35（6）：85-87., articleTitle=煤矿井下带式输送机运行的相关问题研究, refAbstract=null), Reference(id=1241446454779236805, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, doi=null, pmid=null, pmcid=null, year=2023, volume=35, issue=6, pageStart=85, pageEnd=87, url=null, language=null, rfNumber=［1］, rfOrder=1, authorNames=MA Tao, journalName=West-China Exploration Engineering, refType=null, 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Constitutive parameters of rubber matrix

, figureFileSmall=null, figureFileBig=null, tableContent=
温度
Temperature θ/℃		EK1/MPaEK2/MPaηK1/MPaηK2/MPa
038.451.589.77 210.3
1041.350.191.97 191.0
2043.549.393.47 171.7
3046.547.494.77 151.2
), ArticleFig(id=1241446453453836710, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, language=CN, label=表1, caption=

橡胶基体本构参数

, figureFileSmall=null, figureFileBig=null, tableContent=
温度
Temperature θ/℃		EK1/MPaEK2/MPaηK1/MPaηK2/MPa
038.451.589.77 210.3
1041.350.191.97 191.0
2043.549.393.47 171.7
3046.547.494.77 151.2
), ArticleFig(id=1241446453629997480, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, language=EN, label=Tab. 2, caption=

Constitutive parameters of wire rope

, figureFileSmall=null, figureFileBig=null, tableContent=
温度
Temperature θ/℃		EG1/MPaηG1/MPa
012 473.42 540.4
1011 317.22 421.8
2010 213.72 303.6
309 180.72 185.9
), ArticleFig(id=1241446453718077866, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, language=CN, label=表2, caption=

钢丝绳本构模型参数

, figureFileSmall=null, figureFileBig=null, tableContent=
温度
Temperature θ/℃		EG1/MPaηG1/MPa
012 473.42 540.4
1011 317.22 421.8
2010 213.72 303.6
309 180.72 185.9
), ArticleFig(id=1241446453835518380, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, language=EN, label=Tab. 3, caption=

Constitutive parameters of mixed model at 40 ℃

, figureFileSmall=null, figureFileBig=null, tableContent=
E'K1E'K2η'K1η'K2E'G1η'G1
49.446.596.97 132.68 310.92 082.0
), ArticleFig(id=1241446453994901935, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, language=CN, label=表3, caption=

40 ℃下混合模型本构模型参数

, figureFileSmall=null, figureFileBig=null, tableContent=
E'K1E'K2η'K1η'K2E'G1η'G1
49.446.596.97 132.68 310.92 082.0
), ArticleFig(id=1241446454074593713, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, language=EN, label=Tab. 4, caption=

Basic parameters of rubber matrix

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 Parameter值 Value
型号ModelST1600
强度Intensity/（N/mm2）1 600
钢丝绳间距Wire rope spacing/mm12
上覆盖胶厚度Thickness of upper covering glue/mm6
下覆盖胶厚度Thickness of lower covering glue/mm6
带厚度Strip thickness/mm17
), ArticleFig(id=1241446454162674101, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, language=CN, label=表4, caption=

橡胶基体基本参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数 Parameter值 Value
型号ModelST1600
强度Intensity/（N/mm2）1 600
钢丝绳间距Wire rope spacing/mm12
上覆盖胶厚度Thickness of upper covering glue/mm6
下覆盖胶厚度Thickness of lower covering glue/mm6
带厚度Strip thickness/mm17
), ArticleFig(id=1241446454259143094, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, language=EN, label=Tab. 5, caption=

Basic parameters of wire rope

, figureFileSmall=null, figureFileBig=null, tableContent=
参数Parameter值Value
型号Model7×9IWS
钢丝绳股直径Wire rope strand diameter/mm1.6
侧股捻角Side strand twist angle/(°)20
中心股捻距Central unit lay length/mm17
其余股捻距Other strand twist lengths/mm51.5
芯丝直径Core wire diameter/mm0.6
侧丝直径Lateral wire diameter/mm0.4
), ArticleFig(id=1241446454393360826, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430527771541, language=CN, label=表5, caption=

钢丝绳基本参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数Parameter值Value
型号Model7×9IWS
钢丝绳股直径Wire rope strand diameter/mm1.6
侧股捻角Side strand twist angle/(°)20
中心股捻距Central unit lay length/mm17
其余股捻距Other strand twist lengths/mm51.5
芯丝直径Core wire diameter/mm0.6
侧丝直径Lateral wire diameter/mm0.4
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钢丝绳芯橡胶输送带两尺度统一本构模型与阻尼机制研究
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李建刚 , 冯金平 , 王鑫 , 刘思远 , 高仲杰 , 吴建军
机械强度 | ·设计·计算· 2025,47(7): 144-151
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机械强度 | ·设计·计算· 2025, 47(7): 144-151
钢丝绳芯橡胶输送带两尺度统一本构模型与阻尼机制研究
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李建刚 , 冯金平 , 王鑫, 刘思远, 高仲杰, 吴建军
作者信息
  • 辽宁工程技术大学 机械工程学院，阜新　123000

    • 李建刚，男，1976年生，辽宁阜新人，博士，讲师；主要研究方向为机电系统设计与仿真；E-mail：。

通讯作者:

冯金平，男，1997年生，浙江台州人，硕士；主要研究方向为机械工程；E-mail：。
Study on two-scale unified constitutive model and damping mechanism of rubber conveyor belt with steel wire rope core
Jiangang LI , Jinping FENG , Xin WANG, Siyuan LIU, Zhongjie GAO, Jianjun WU
Affiliations
  • School of Mechanical Engineering, Liaoning Project Technology University, Fuxin 123000, China
出版时间: 2025-07-15 doi: 10.16579/j.issn.1001.9669.2025.07.018
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摘要
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钢丝绳输送带的本构分析是优化输送带设计和节能的关键问题，采用黏弹性理论及瞬态动力学的知识构建了基于表征钢丝绳的Maxwell模型和表征橡胶基体的Burgers模型，考虑了钢丝绳间的微动摩擦阻尼和钢丝绳与输送带之间的相互阻尼，构建了其混合本构模型，运用外加激励载荷的方法，在0~40 ℃条件下，建立本构模型间各参数之间的关系，运用Matlab对仿真曲线进行拟合、求解，在环境温度为40 ℃的条件下，对混合本构模型的准确性进行了验证。结果表明，模型预测数据与实测数据具有良好的一致性，其中最大误差为5.88%。证明此本构模型能够比较好地表征钢丝绳芯橡胶输送带，运用仿真加预测的方法，验证此模型的普适性。此研究为输送带结构优化和节能分析提供理论基础。

混合本构模型  /  相互阻尼  /  钢丝绳输送带  /  温度效应

Constitutive analysis of steel wire rope conveyor belt is a key problem for conveyor belt design optimization and energy conservation. Maxwell model and Burgers model based on viscoelastic theory and transient dynamics were constructed. Considering the fretting friction damping between steel wires and the mutual damping between steel wire rope and conveyor belt, a mixed constitutive model was constructed. Under the condition of 0-30 ℃, the relationship between the parameters of the constitutive model was established, the simulation curve was fitted and solved by Matlab, and the accuracy of the mixed constitutive model was verified by taking 40 ℃ as the control group. The verification results show that the maximum error between the conveyor belt represented by this constitutive model and the experiment is 5. 88%, demonstrating that this constitutive model can better characterize the rubber conveyor belt with steel wire rope core. The universality of this model is verified by the method of simulation and prediction. It provides a theoretical basis for the structural optimization and energy-saving analysis of conveyor belt.

Mixed constitutive model  /  Mutual damping  /  Wire rope conveyor belt  /  Temperature effect
李建刚, 冯金平, 王鑫, 刘思远, 高仲杰, 吴建军. 钢丝绳芯橡胶输送带两尺度统一本构模型与阻尼机制研究. 机械强度, 2025 , 47 (7) : 144 -151 . DOI: 10.16579/j.issn.1001.9669.2025.07.018
Jiangang LI, Jinping FENG, Xin WANG, Siyuan LIU, Zhongjie GAO, Jianjun WU. Study on two-scale unified constitutive model and damping mechanism of rubber conveyor belt with steel wire rope core[J]. Journal of Mechanical Strength, 2025 , 47 (7) : 144 -151 . DOI: 10.16579/j.issn.1001.9669.2025.07.018
正文
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0　引言
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钢丝绳输送带广泛应用于煤炭的运输，其结构由钢丝绳和覆盖胶组成，远距离、大运量、高速度的优点使其逐渐成为运输领域发展的主流。但由于打滑、撕裂、跑偏等问题频发，大幅降低了钢丝绳输送带的工作效率，严重时还会造成生命财产的损失[1-3]。而研究输送带本构模型就是为了探索解决此类问题[4-5]。因此，对输送带进行本构模型的研究是十分必要的。随着输送带在运输领域的广泛运用，国内外学者对其本构模型进行了深入研究。倪亚军等[6-11]运用仿真和试验论证的方法对输送带的黏弹性和损坏程度等进行研究，认为Maxwell模型可以较好地表征钢丝绳，固体模型能够较好地表征橡胶输送带，但Burgers模型比线性固体模型能更准确地反映其黏弹特性。LUO等[12-16]对超弹性材料进行动态特性分析，对Ogden、Yeoh和Arruda-Boyce模型参数进行识别并进行本构模型的求解。闫昱全等[17-19]分别运用Mooney-Rivlin模型和Bilinear-Isotropic模型对输送带材料力学特性、静态特性和模型误差等进行分析，得出在不同载荷下各钢丝绳的变形趋势，为绿色带式输送机提供了理论参考。
综上所述，现有的研究普遍采用线性固体模型描述橡胶的黏弹性，运用Maxwell模型描述钢丝绳，以及基于两者并联组合而成的本构模型。但Burgers模型表征的橡胶输送带的黏弹性比线性固体模型精度更高，如今很少有学者研究基于Burgers与Maxwell混合的本构模型。因此，本文结合热黏弹性理论，通过施加激励载荷，在0~30 ℃内进行试验，运用Matlab软件对试验数据进行耦合、分析，建立本构模型中各参数之间的关系，并在40 ℃环境下对模型进行验证，建立了钢丝绳微动摩擦阻尼和钢丝绳与输送带相互阻尼条件下输送带混合本构模型，为输送带结构优化和节能分析提供参考。
1　Burgers-Maxwell模型机制研究
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ST1600输送带的结构如图1所示，其主要由覆盖胶、芯胶和钢丝绳组成。其中，钢丝绳和橡胶本构模型的准确性是影响带式输送机结构优化和节能分析的关键因素。其混合本构模型是否合理直接影响输送带设计时的准确性。
通过查找相关文献确定黏弹性模型及本构模型的连接方式。程相文等[20]154-157[21]1085-1089[22]111-114分别对Kelvin-固体模型、Maxwell-标准线性固体模型、ZWT模型、Burgers模型进行试验与仿真分析，得出Burgers模型表征的橡胶基体的黏弹性比线性固体模型的精度高，Maxwell模型表征的钢丝绳的黏弹性精度更高。此外，Maxwell模型存在一定的黏弹性，且弹性部分符合胡克定律[23]1-11。基于此，本文在以上研究的基础上，提出了采用Burgers模型表征覆盖胶的黏弹性、Maxwell模型表征钢丝绳的黏弹性，并对其进行并联处理，得到钢丝绳输送带的本构模型（图2），希望以此为输送带的本构研究提供新的参考方向。
如图2所示，EK1、EK2分别为覆盖胶的弹性模量；ηK1、ηK2分别为覆盖胶对应的阻尼系数；EG1为钢丝绳的弹性模量；ηG1为钢丝绳对应的黏性系数。
基于上述混合本构模型，建立其在动载荷下的平衡方程。由于Burges本构模型涉及4个未知量，为了建立合适的激励函数，因此使用含有2个正弦函数的复合结构。令参与试验的输送带长为L；拉伸频率为ω；时间为t；拉伸幅值分别为M1、M2。则位移激励为
建立输送带微元之间的几何关系，即
式中，ε为动应变；A1、A2均为应变幅值。
联立式（1）、式（2），混合本构模型动应变为
1.1　建立覆盖胶Burgers模型
输送带覆盖胶在运行过程中会产生瞬态弹性变形、随时间变化的蠕变变形以及塑性流动引起的永久性变形，并且输送带在拉伸的过程中会存在一定的滞后性，所以Burgers模型能很好地模拟输送带橡胶覆盖胶的黏弹性性质。其本构模型[24]为
式中，σK为覆盖胶的应力，则
联立式（1）、式（2）和式（4）求解可得
式中，C1、C2为常数。
一般情况p2的值很小，当时间趋于无穷时，e-[ p1/(2p2)] t趋近于0。
令覆盖胶的端面横截面积为Sd，则其等效外载荷为
即
1.2　建立钢丝绳Maxwell模型
钢丝绳股和股之间存在间隙，因此钢丝绳表现出一定的黏弹特性，并且其响应几乎由弹簧确定，因此Maxwell模型可以很好地模拟钢丝绳的黏弹性性质。其本构模型[25]为
式中，σG为钢丝绳应力；pG、qG的计算式分别为
将式（1）~式（3）代入式（9）化简，可得
式中，C为常数。
一般情况下pG的值很小，当时间趋于无穷时，e-t/pG趋近于0。
令其截面积为SG，则钢丝绳的激励载荷方程可以等效为
1.3　建立钢丝绳芯输送带混合本构模型
由建立的混合本构模型及程相文等[20]154-157、陈洪月等[21]1085-1089[22]111-114、夏剑冬等[23]1-11提出的混合本构模型组合原理可知，此输送带的等效外载荷可以看成由等距分布的多根钢丝绳和橡胶等效外载荷叠加而成，即其等效外载荷为
式中，N为钢丝绳捆数。
1.4　本构模型参数辨识
覆盖胶相应的等效外载荷激励方程式（8）可表达为
其中，参数a、b、c、d的计算式分别为
若对仿真的力-时间曲线进行拟合，可以分别求得a、b、c、d的值。通过Matlab软件的Fsolve函数可以分别求解出p1、q1、p2、q2的值。最终通过式（16）可以求出Burgers模型的各项参数。
钢丝绳相应的外载荷激励方程式（12）可等效为
其中，参数e、f、g、h的计算式分别为
若对得到的力-时间曲线进行拟合，可分别得到e、f、g、h的值。通过Matlab软件的Fsolve函数可以分别求解出pG和qG的值，则
根据前文所列的方程，若要求得本构模型的各参数，需要建立模型，进行有限元仿真，运用Matlab软件求解出结果。因此，建立符合实际要求的模型并对其进行参数识别非常必要。
2　混合本构模型参数辨识
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2.1　模型准备
通过查找国家标准GB/T 9770—2013中的ST1600型钢丝绳芯输送带，将输送带切成长为1 100 mm，宽为75 mm的橡胶基体及等长钢丝绳，橡胶基体截面尺寸如图3所示。采用万能拉伸试验机和数显温控箱进行试验，如图4所示。
2.2　本构模型参数求解
分别在0、10、20、30 ℃的温度下对模型进行试验，加载频率为0.1 Hz、幅值为1.25 mm，试验获得的力与加载位移之间的关系如图5、图6所示。
由图5、图6可知，随着温度的增加，试验曲线下移，迟滞环的面积逐渐减小，说明输送带的拉伸能耗随着温度的增加而逐渐降低。在Matlab软件里对得到的时间与力的曲线进行拟合，联立式（15）~式（19）可以得到基于Burgers模型表征的橡胶基体的本构参数，如表1所示，Maxwell模型所表征的钢丝绳参数，如表2所示。
温度对黏弹材料的影响为指数函数关系[26]。因此，，。其中，i=K、G；j=1，2；钢丝绳的TC=200 ℃；橡胶的TC=60 ℃；e为自然常数。通过表1、表2拟合可以得到本构模型参数的近似曲线。对和两边同时取对数可得
式中，T为环境温度。
通过Matlab软件进行拟合可得到橡胶基体的本构模型参数如式（21）所示，钢丝绳的本构模型参数如式（22）所示。
2.3　模型预测与验证
为了验证拟合公式是否合理，以及本构模型是否可行，在40 ℃的环境下，取长为1 100 mm、截面为75 mm × 17 mm的输送带进行拉伸试验，得到拉伸数据。把40 ℃分别代入式（21）、式（22）得到数据如表3所示。
由图3的截面图可知，此输送带包含6根钢丝绳，故将N = 6代入式（13），可通过式（10）~式（18）求得在40 ℃下混合本构模型预测得到的力-位移曲线，将其与试验曲线进行对比（图7），预测曲线与试验曲线的误差曲线如图8所示，其最大相对误差为5.88%，说明此模型表征的钢丝绳芯橡胶输送带精度较好。
3　混合本构模型普适性分析
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3.1　钢丝绳芯输送带材料模型
ST1600输送带主要由覆盖胶和钢丝绳芯组成，其中覆盖胶为橡胶材料，而钢丝绳芯为碳素钢材料。橡胶是超弹性材料，目前Mooney-Rivlin模型、Ogden模型、G-H模型、Yeoh模型为4种常用的超弹性本构模型，钢丝绳采用Bilinear-Isotropic模型，并在工程中得到广泛的应用。
3.2　覆盖胶模型
Yeoh模型是一种基于高形变率动态松弛试验数据的非线性材料模型，其应变能密度函数为
式中，JB为第1应变能张量；v为体积模量；I为相对体积变化，由于橡胶几乎不可压缩，所以I = 1；Ci0为材料常数。
此模型在拉伸时的应力为
式中，γ为变形张量。
Mooney-Rivlin模型相比于Yeoh模型还考虑了第2应变不变量I2的贡献，其应变能函数[27]为
式中，C10、C01均为材料常数，并且G = E/[ 2(1 + v) ] = 2(C10 + C01 )[28]。
此模型在拉伸时的应力为
Mooney-Rivlin模型是G-H模型的一种特殊形式，G-H模型的应变能密度函数[29]可以表示为
式中，Cij为材料常数，通常由试验数据拟合而成；n为展开次数。当n = 1时，可转化为Mooney-Rivlin模型。G-H模型在拉伸时的应力为
Ogden模型适合描述非定常剪切模量和轻微压缩的材料行为。处理大应变时，3阶Ogden模型可达最高精度，其应变能函数可以表示为
式中，αj 、 βj均为材料常数；n为展开次数。
此模型在拉伸时的应力为
3.3　钢丝绳芯橡胶输送带模型建立
通过查找国家标准GB/T 9770—2013普通用途钢丝绳芯输送带标准，选取ST1600型输送带为研究对象，橡胶基体参数参照表4，选取钢丝绳，其股直径、捻距等参数参照表5，在SolidWorks软件进行建模，所建模型如图9所示。
以2 mm大小对其进行网格划分，如图10所示。其中，橡胶基体的网格质量全部在0.9以上，钢丝绳在0.8以上，与钢丝绳连接的橡胶基体由于非连接处非分析重点，其网格质量只有0.75，但连接处网格质量较高，达到0.9以上。
在Workbench软件中分别设置材料为第3.2节中的覆盖胶模型、Burgers模型和Maxwells模型。通过施加外激励载荷，进行拉伸仿真得到的应力-应变曲线如图11所示。由图11可知，Yeoh模型精度最差，G-H模型、Mooney-Rivlin模型、Ogden模型和Burgers模型精度差别不大。
3.4　仿真验证
将N = 1、L = 10 cm代入式（13），通过式（10）~式（18）可预测得到基于Burgers-Maxwell本构模型所表征输送带下的力-位移曲线，把图9所建立的输送带整体赋予橡胶基体Burgers模型，赋予钢丝绳Maxwell模型，赋予钢丝绳与输送带界面间为区域接触，钢丝绳与钢丝绳间为区域接触，把钢丝绳与输送带的一端面固定，得到其力-位移曲线，将其与仿真曲线进行对比，如图12所示。由图12可知，Burges-Maxwell模型能够较好地表征钢丝绳芯橡胶输送带。
4　结论
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在考虑了钢丝绳间微动摩擦阻尼和钢丝绳与输送带之间相互阻尼的条件下，运用黏弹性理论及瞬态动力学的相关理论，构建了基于表征钢丝绳的Maxwell模型和表征橡胶基体的Burgers模型的混合本构模型，通过试验与仿真相结合的方法对模型的准确性及适用性进行了分析。主要结论如下：
1）考虑钢丝与钢丝间以及钢丝与橡胶界面之间存在微动摩擦阻尼，建立了基于Burgers-Maxwell模型所表征的钢丝绳橡胶输送带混合本构模型。
2）通过试验与理论验证可知，在加载频率为0.1 Hz，幅值为1.25 mm，环境条件为0~40 ℃进行拉伸试验时，随着温度的增加，EK1、ηK1逐渐增大，EK2、ηK2、EG1、ηG1逐渐减小。
3）在环境温度为40 ℃的条件下，对混合本构模型的准确性进行了验证，钢丝绳橡胶输送带的试验曲线与预测曲线之间的最大相对误差为5.88%，验证了混合本构模型的准确性。
4）对本文所建立的本构模型与目前工程上广泛应用的模型进行了仿真对比，证明了本文所建立的本构模型具有较好的精度。
5）对钢丝绳输送带的力-位移曲线进行了预测，并与仿真曲线进行了对比。结果表明，所提本构模型可以应用于钢丝绳芯橡胶输送带，验证了所提模型的普适性。
基金
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  • 国家自然科学基金项目(52174115)
文献
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2025年第47卷第7期
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doi: 10.16579/j.issn.1001.9669.2025.07.018
  • 接收时间：2024-01-01
  • 首发时间：2026-03-19
  • 出版时间：2025-07-15
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  • 收稿日期：2024-01-01
  • 修回日期：2024-02-17
基金
National Natural Science Foundation of China(52174115)
国家自然科学基金项目(52174115)
作者信息
    辽宁工程技术大学 机械工程学院，阜新　123000

通讯作者:

冯金平，男，1997年生，浙江台州人，硕士；主要研究方向为机械工程；E-mail：。
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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