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Article(id=1241446430838150041, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241446328396476740, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.07.012, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1702828800000, receivedDateStr=2023-12-18, revisedDate=1706544000000, revisedDateStr=2024-01-30, acceptedDate=null, acceptedDateStr=null, onlineDate=1773913494071, onlineDateStr=2026-03-19, pubDate=1752508800000, pubDateStr=2025-07-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773913494071, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773913494071, creator=13701087609, updateTime=1773913494071, 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=93, endPage=100, ext={EN=ArticleExt(id=1241446431039476634, articleId=1241446430838150041, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Modeling and influencing factor analysis of worn sprockets in mining scraper conveyor, columnId=1241446330749481285, journalTitle=Journal of Mechanical Strength, columnName=·Fatigue·Damage·Fracture·Failure Analysis·, runingTitle=null, highlight=null, articleAbstract=

Sprocket chain ring drive system is the core component of scraper conveyors. The wear of sprocket chain socket is one of the main fault of scraper conveyors. Started with the analysis of the meshing transmission characteristics of the sprocket chain socket, constructed the Archard linear wear model, calculated the wear depth of the chain socket’s linear under working conditions, measured the wear depth of the actual wear sprocket, and verified the accuracy of the Archard linear wear model. The deformation model of ring chain was constructed by finite element method, the shape change of chain socket busbar was predicted, and the shape of sprocket tooth surface after wear was reconstructed according to the change of direction and busbar. The influencing factors of chain socket wear were analyzed. The results show that increasing the hardness of sprocket material, reducing the chain speed, the load and the laying angle can reduce the chain wear. This study provides a basis for the study of the wear pattern of sprocket chain of scraper conveyors.

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WANG Peng, E-mail：
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链轮链环传动系统作为刮板输送机的核心部件，其链轮链窝发生磨损是刮板输送机的主要故障之一。从分析链轮链窝的啮合传动特性入手，构建Archard准线磨损模型，计算出工况下链窝准线的磨损深度，并对实际磨损链轮的磨损深度进行了测量，验证了磨损模型的准确性；使用有限元法构建圆环链形变模型，预测了链窝母线形状的变化情况，根据准线、母线的变化情况重构磨损后的链轮齿面形态；对链窝磨损的影响因素进行了分析。结果表明，增加链轮材料的硬度、降低链速、减少负载及降低铺设倾角等均会减少链窝磨损。该研究为刮板输送机链轮链窝磨损形态的研究提供了依据。

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王鹏，男，1988年生，黑龙江鸡西人，高级工程师；主要研究方向为矿井机电现场实践；E-mail：。

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王鹏，男，1988年生，黑龙江鸡西人，高级工程师；主要研究方向为矿井机电现场实践；E-mail：。

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王鹏，男，1988年生，黑龙江鸡西人，高级工程师；主要研究方向为矿井机电现场实践；E-mail：。

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Beijing：Higher Education Press，1992：485.（In Chinese）, articleTitle=null, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1241446448525529389, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, xref=null, ext=[AuthorCompanyExt(id=1241446448533917998, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, companyId=1241446448525529389, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=Shendong Coal Group Co, Ltd, CHN Energy Investment Group Co, Ltd, Yulin 719000, China), AuthorCompanyExt(id=1241446448542306608, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, companyId=1241446448525529389, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=国家能源投资集团有限责任公司 神东煤炭集团有限责任公司，榆林　719000)])], figs=[ArticleFig(id=1241446449838346594, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=EN, label=Fig. 1, caption=Meshing process of the ring chain and the chain sprocket, figureFileSmall=YSEmqNbplFWeVWa7hXpZWw==, figureFileBig=3BUZsaOmirBebwRNfyEFiA==, tableContent=null), ArticleFig(id=1241446449922232677, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=CN, label=图1, caption=链轮链环的啮合传动过程, figureFileSmall=YSEmqNbplFWeVWa7hXpZWw==, figureFileBig=3BUZsaOmirBebwRNfyEFiA==, tableContent=null), ArticleFig(id=1241446451134386540, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=EN, label=Fig. 2, caption=Meshing force between the ring chain and the chain sprocket, figureFileSmall=fQ1F76EIsIy3wW/ZRpAQPQ==, figureFileBig=Ur+vg3WgeBjN3t4WLnNOBQ==, tableContent=null), ArticleFig(id=1241446451285381487, tenantId=1146029695717560320, journalId=1227999626482147330, 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articleId=1241446430838150041, language=CN, label=图7, caption=链窝磨损前后齿面形态, figureFileSmall=5YIF6QVx/hlt4IkPH15k1g==, figureFileBig=JUnpJI2/2LsT8VZkyRWMhQ==, tableContent=null), ArticleFig(id=1241446452598198672, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=EN, label=Fig. 8, caption=Wear failure of the sprocket, figureFileSmall=RxiQa5SNZFg4q2NqadygiA==, figureFileBig=sW17o2ESpOMgSFz1/ptMcQ==, tableContent=null), ArticleFig(id=1241446452677890449, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=CN, label=图8, caption=磨损失效链轮, figureFileSmall=RxiQa5SNZFg4q2NqadygiA==, figureFileBig=sW17o2ESpOMgSFz1/ptMcQ==, tableContent=null), ArticleFig(id=1241446452770165140, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=EN, label=Fig. 9, caption=Laser scanning sprocket, figureFileSmall=gEIKgosv2r63ejdZ3crd+w==, figureFileBig=Du+CtKLpdHjjNwoGqM11vQ==, tableContent=null), ArticleFig(id=1241446452866634135, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=CN, label=图9, caption=激光扫描链轮, figureFileSmall=gEIKgosv2r63ejdZ3crd+w==, figureFileBig=Du+CtKLpdHjjNwoGqM11vQ==, tableContent=null), ArticleFig(id=1241446452937937306, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=EN, label=Fig. 10, caption=Influence of the material hardness on sprockets’ wear amount, figureFileSmall=VK+OrNMXX94gETpG4572gw==, figureFileBig=mxCmk5wzLV/u/Jov2jayxw==, tableContent=null), ArticleFig(id=1241446453038600603, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=CN, label=图10, caption=材料硬度对链窝磨损量的影响, figureFileSmall=VK+OrNMXX94gETpG4572gw==, figureFileBig=mxCmk5wzLV/u/Jov2jayxw==, tableContent=null), ArticleFig(id=1241446453139263902, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=EN, label=Fig. 11, caption=Influence of running speed of the ring chain on sprockets’ wear amount, figureFileSmall=tf1c8fRzL0CLDM+o7a7Scw==, figureFileBig=1BHIlZVDtJTLzjoseKUX9Q==, tableContent=null), ArticleFig(id=1241446453260898719, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=CN, label=图11, caption=圆环链运行速度对链窝磨损量的影响, figureFileSmall=tf1c8fRzL0CLDM+o7a7Scw==, figureFileBig=1BHIlZVDtJTLzjoseKUX9Q==, tableContent=null), ArticleFig(id=1241446453369950626, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=EN, label=Fig. 12, caption=Influence of the mass per unit length on sprockets’ wear amount, figureFileSmall=uFL7A3FaxGdKOgiPr2d+YQ==, figureFileBig=Cui1AjuzLRiuc7LZam2yQQ==, tableContent=null), ArticleFig(id=1241446453453836709, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=CN, label=图12, caption=物料的单位长度质量对链窝磨损量的影响, figureFileSmall=uFL7A3FaxGdKOgiPr2d+YQ==, figureFileBig=Cui1AjuzLRiuc7LZam2yQQ==, tableContent=null), ArticleFig(id=1241446453596443047, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=EN, label=Fig. 13, caption=Influence of the laying angle of scrapers on sprockets’ wear amount, figureFileSmall=Mlm+eVsgtuOORjJsj3GYNA==, figureFileBig=9q/DYne0M47LKRpiWn2wzA==, tableContent=null), ArticleFig(id=1241446453676134826, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=CN, label=图13, caption=铺设倾角对链窝磨损量的影响, figureFileSmall=Mlm+eVsgtuOORjJsj3GYNA==, figureFileBig=9q/DYne0M47LKRpiWn2wzA==, tableContent=null), ArticleFig(id=1241446453839712685, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=EN, label=Tab. 1, caption=

Actual working condition of the scraper conveyor

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基本参数Basic parameter值Value
链轮节圆直径Sprocket pitch circle diameter d/mm684
链轮齿数Number of sprocket teeth7
刮板输送机的输送能力
Scraper conveyor transmission capacity Q/(t/h)		3 700
圆环链的运行速度Chain speed v/(m/s)1.8
刮板链单位长度的质量
Mass per unit length of the scraper chain q0/(kg/m)		140
刮板机的铺设倾角
Laying angle of the scraper conveyor β/(°)		0
刮板链的长度Length of scraper chain L/m300
物料在溜槽中的阻力系数
Resistance coefficient of material in the chute f1		0.5
刮板链在溜槽里的阻力系数
Scraper chain drag coefficient in the chute f2		0.4
重力加速度Acceleration of gravity g/(m/s2 )9.8
), ArticleFig(id=1241446453994901936, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=CN, label=表1, caption=

刮板机的实际工况

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基本参数Basic parameter值Value
链轮节圆直径Sprocket pitch circle diameter d/mm684
链轮齿数Number of sprocket teeth7
刮板输送机的输送能力
Scraper conveyor transmission capacity Q/(t/h)		3 700
圆环链的运行速度Chain speed v/(m/s)1.8
刮板链单位长度的质量
Mass per unit length of the scraper chain q0/(kg/m)		140
刮板机的铺设倾角
Laying angle of the scraper conveyor β/(°)		0
刮板链的长度Length of scraper chain L/m300
物料在溜槽中的阻力系数
Resistance coefficient of material in the chute f1		0.5
刮板链在溜槽里的阻力系数
Scraper chain drag coefficient in the chute f2		0.4
重力加速度Acceleration of gravity g/(m/s2 )9.8
), ArticleFig(id=1241446454078788018, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446430838150041, language=EN, label=Tab. 2, caption=

Wear depth measurement of sprockets

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序号
Number		深度Depth b1/mm误差率Error rate ζ1/%深度Depth b2/mm误差率Error rate ζ2/%
126.5615.5327.2614.39
226.1913.9227.7916.62
326.0213.1827.6315.95
426.3314.5327.0113.34
527.0517.6627.8817.00
625.7812.1426.8512.67
726.4114.8827.2614.39
826.7216.2227.6716.11
926.2414.1426.8312.59
1025.9412.8327.2114.18
1126.3314.5326.8412.63
1227.1717.5927.2314.27
1326.5715.5727.8116.70
1425.8312.3526.7412.21
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链轮磨损深度测量值

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序号
Number		深度Depth b1/mm误差率Error rate ζ1/%深度Depth b2/mm误差率Error rate ζ2/%
126.5615.5327.2614.39
226.1913.9227.7916.62
326.0213.1827.6315.95
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矿用刮板输送机链轮磨损建模及影响因素分析
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王鹏
机械强度 | ·疲劳·损伤·断裂·失效分析· 2025,47(7): 93-100
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机械强度 | ·疲劳·损伤·断裂·失效分析· 2025, 47(7): 93-100
矿用刮板输送机链轮磨损建模及影响因素分析
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王鹏
作者信息
  • 国家能源投资集团有限责任公司 神东煤炭集团有限责任公司，榆林　719000

    • 王鹏，男，1988年生，黑龙江鸡西人，高级工程师；主要研究方向为矿井机电现场实践；E-mail：。

Modeling and influencing factor analysis of worn sprockets in mining scraper conveyor
Peng WANG
Affiliations
  • Shendong Coal Group Co, Ltd, CHN Energy Investment Group Co, Ltd, Yulin 719000, China
出版时间: 2025-07-15 doi: 10.16579/j.issn.1001.9669.2025.07.012
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摘要
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链轮链环传动系统作为刮板输送机的核心部件，其链轮链窝发生磨损是刮板输送机的主要故障之一。从分析链轮链窝的啮合传动特性入手，构建Archard准线磨损模型，计算出工况下链窝准线的磨损深度，并对实际磨损链轮的磨损深度进行了测量，验证了磨损模型的准确性；使用有限元法构建圆环链形变模型，预测了链窝母线形状的变化情况，根据准线、母线的变化情况重构磨损后的链轮齿面形态；对链窝磨损的影响因素进行了分析。结果表明，增加链轮材料的硬度、降低链速、减少负载及降低铺设倾角等均会减少链窝磨损。该研究为刮板输送机链轮链窝磨损形态的研究提供了依据。

链窝磨损  /  啮合传动特性  /  Archard准线磨损模型  /  圆环链形变模型

Sprocket chain ring drive system is the core component of scraper conveyors. The wear of sprocket chain socket is one of the main fault of scraper conveyors. Started with the analysis of the meshing transmission characteristics of the sprocket chain socket, constructed the Archard linear wear model, calculated the wear depth of the chain socket’s linear under working conditions, measured the wear depth of the actual wear sprocket, and verified the accuracy of the Archard linear wear model. The deformation model of ring chain was constructed by finite element method, the shape change of chain socket busbar was predicted, and the shape of sprocket tooth surface after wear was reconstructed according to the change of direction and busbar. The influencing factors of chain socket wear were analyzed. The results show that increasing the hardness of sprocket material, reducing the chain speed, the load and the laying angle can reduce the chain wear. This study provides a basis for the study of the wear pattern of sprocket chain of scraper conveyors.

Wear of chain sockets  /  Meshing transmission characteristic  /  Archard linear wear model  /  Deformation model of a circular ring chain
王鹏. 矿用刮板输送机链轮磨损建模及影响因素分析. 机械强度, 2025 , 47 (7) : 93 -100 . DOI: 10.16579/j.issn.1001.9669.2025.07.012
Peng WANG. Modeling and influencing factor analysis of worn sprockets in mining scraper conveyor[J]. Journal of Mechanical Strength, 2025 , 47 (7) : 93 -100 . DOI: 10.16579/j.issn.1001.9669.2025.07.012
正文
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0　引言
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煤炭是我国经济发展的重要战略资源，在众多能源中处于不可或缺的地位[1]。刮板输送机是综采设备的重要环节。在恶劣的工况下，驱动链轮的链窝磨损会导致传动系统动力传递效率下降、寿命缩短、噪声和振动增加，这是刮板输送机主要故障之一[2]。毛君等[3-4]采用理论与仿真相结合的方法，准确分析了链轮链环间的啮合接触力学特性。王淑平等[5-7]通过分析形变圆环链与链轮间的啮合传动特性，指出了准线和母线的磨损规律，提出了减少链窝磨损的方法。王振国[8]运用Ansys有限元模块对链轮链环的啮合传动状态进行仿真，提出了引起链轮链窝磨损的主要因素。王科文[9]借助Ansys Workbench仿真计算软件，对链轮链窝的结构进行改进，提出了有效降低链轮链窝磨损的结构。高红伟等[10-11]通过分析链轮的磨损机制，结合实际测量数据，总结了链轮链窝的磨损规律。
以上研究均是对驱动链轮磨损机制及磨损因素的总结与分析，未涉及对链轮链窝实际磨损量的计算与分析。针对目前链轮链窝研究中的不足，本文建立了链轮磨损后的链窝准线和母线的模型，重构链轮链窝的磨损形态，通过对链窝磨损影响因素的分析，得到了链轮的材料特性及不同的工况对于链轮链窝磨损量的影响。
1　链轮链环传动系统模型
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1.1　链轮链环传动系统的啮合过程
链轮链环之间的相对运动过程可以描述为圆环链在拉力F的作用下绕着静止链轮做运动，如图1所示。、、、分别为相邻两个平环链的两端圆环中心，如图1（a）所示，平环链1两端均啮入链轮链窝过渡圆弧面中心，与链轮达到稳定接触状态；当平环链1完成啮合后，如图1（b）所示，立环链2、平环链3以平环链1的右端圆环中心为圆心顺时针方向旋转，直至平环链3的左端圆环中心啮入链轮链窝过渡圆弧面中心，此时立环链2与链轮达到稳定啮合状态；随后平环链3以平环链3的左端圆环中心为圆心按顺时针方向旋转，如图1（c）所示，直至平环链3的右端圆环中心啮入链轮链窝过渡圆弧面中心，此时平环链3与链轮达到稳定啮合状态。按照此绕链过程，链轮链环不断接触完成啮合，进行动力传递。
1.2　啮合传动过程中的阻力分析
实际工况下，链轮圆环链传动系统所受的运行阻力主要由两部分组成，即刮板输送机有载侧的运行阻力W1与无载侧的运行阻力W2[12]，分别为
式中，q为刮板机所运物料的单位长度的质量，q=Q/（3.6v），v=ωR1（其中，Q为刮板输送机的输送能力；v为圆环链的运行速度；ω为链轮的运行角速度；R1为平环质心到链轮圆心的距离）；q0为刮板链单位长度的质量；f1为物料在溜槽中移动的阻力系数；f2为刮板链在溜槽里的阻力系数；g为重力加速度；L为刮板链的长度；β为刮板机的铺设倾角。
有载侧单个链环所受阻力W1*为刮板输送机有载侧的运行阻力W1折算到单个链环所受的阻力；无载侧单个链环所受阻力W2*为刮板输送机无载侧的运行阻力W2折算到单个链环所受的阻力。其表达式分别为
式中，m为链条数；n1、n2分别为有载侧和无载侧的链环数量。
1.3　啮合时链轮圆环链的接触力学分析
某一时刻圆环链平环啮入到链窝过渡圆弧面，与链轮达成稳定啮合的接触状态，如图2所示，对链轮链环进行受力分析，得
式中，N为接触点处链轮对平环的接触力（法向支持力）；F为圆环链立环对平环的拉力（圆环链所受阻力W1*）；α为支持力与水平方向的夹角；F1为链轮对平环的摩擦阻力；f为链轮链环再接触点的摩擦因数；γ为摩擦阻力F1与水平方向的夹角。
2　链轮链窝准线磨损计算模型
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2.1　Archard黏着磨损模型
Archard磨损模型指出了物体的磨损体积与其材料硬度、相对滑行距离和接触压力之间的关系[13]。其表达式为
式中，V为材料的体积磨损量；s为相对滑移距离；K为无量纲的磨损系数，与磨损面的润滑状态、磨损机制、接触温度等因素有关；W为接触面的法向接触载荷；H为磨损面较软材料的硬度值，HB。
在这里只研究链轮链环接触点处的磨损深度，故将式（4）变换为
将代入式（5）得
式中，A为接触面的面积；h为磨损深度；k为有量纲的磨损系数；p为接触面的接触压力。
由式（6）可知，对于磨损深度h的求解，涉及磨损系数k、接触面的接触压力p与相对滑移距离s的确定。
2.2　磨损系数
磨损系数k与摩擦材料的种类、接触面的表面粗糙度、润滑方式和实际工况等因素有关。JANAKIRAMAN等[14]通过对实际工况中不同的速度、载荷以及润滑条件和表面粗糙度等影响因素的综合分析，推导得出磨损系数k的求解回归公式，即
式中，E'为等效弹性模量；L'为无量纲的载荷；G为无量纲的润滑油压力-黏度系数；S为无量纲的复合表面粗糙度。其中，L'、G、S的计算式分别为
式中，W'为单位长度载荷；R'为等效半径；α'为压力-黏度系数；为复合粗糙度。
2.3　链轮链环间的Hertz接触模型
链轮链环传动系统在稳定啮合状态下，圆环链平环啮入到链窝过渡圆弧面，链环曲面与链轮链窝过渡圆弧曲面相互接触。根据Hertz接触理论[15]，在接触力的作用下，两曲面在接触处会发生局部弹性变形，接触面近似为圆形，且圆心处的接触应力最大。由图2可知，圆环链平环与链轮之间的接触力为N，则链轮链环间的最大接触应力δmax与接触圆的接触半径a分别为
式中，R1、R2分别为链环与链轮的接触半径；E为等效接触模量；E1、E2分别为链环与链轮的弹性模量；ν1、ν2分别为链环与链轮的泊松比。
链轮链环在接触点处的相对滑动距离s取Hertz接触圆的最大长度，即接触圆的接触直径2a，在接触点处的接触压力p取链轮链环间的最大接触应力δmax。
2.4　实际工况下准线磨损计算
针对SGZ 1000/3×1000双链刮板输送机在实际工况下进行研究，具体参数如表1所示。
代入前文建立的准线磨损模型，求解得到的过渡圆弧段准线中心的磨损量为h0，柱面准线磨损量为h1。
计算得，过渡圆弧段准线中心的磨损量h0为23.83 mm。
根据
计算得，柱面准线磨损量h1为22.99 mm。图3所示为链轮链窝在磨损前后其准线的变化。
3　链轮链窝母线磨损计算模型
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链轮链窝磨损后，链窝的母线的形状会发生改变，且与在负载作用下发生变形的链环外廓形变曲线一致。故通过研究圆环链受力变形的形变曲线来获得磨损后的母线形状。
3.1　圆环链有限元模型
根据圆环链在结构上对称的特点，为了简化计算模型，在这里将一个圆环链简化为1/4圆环链，如图4（a）所示。在圆环链的外圆圆心O处建立平面直角坐标系，在Y轴方向对圆环施加一轴向力F作为链轮链环传动系统中链环所受到的拉力。过外圆圆心O取任一与Y轴夹角为θ的平面，称为θ平面。对θ平面上圆环链截面的受力情况进行分析，作用在θ平面上的力为F/2，弯矩为M。故表达式为
式中，F1、F2分别为力F/2在圆环链截面上切向和法向的分力；d为圆环链的直径；d/2 + δ为图4（b）所示圆环链外圆圆心O到圆环链截面圆心Oθ的距离。
如图4（b）所示，圆环链截面的面积为A，抗弯截面系数W = πd3/32，对圆环链截面进行应力分析，由切向力F1对圆环链截面所引起的拉应力为σθ1，在距截面中心Oθ为t处由弯矩M引起的圆环链截面拉应力为σθ2，在距截面中心Oθ为t处的总的圆环链截面拉应力为σθt，且有
式中，以Oθ为原点，指向圆环链外圆圆心O为“+”，背离圆环链外圆圆心O为“-”。即在拉力F的作用下，圆环链内侧呈拉伸状态，外侧呈压缩状态。
由法向力F2对圆环链截面所引起的剪应力为τθ，其表达式为
如图5所示，对θ平面处的圆环链截面取一面积为dA的微元进行微元应力分析，在X、Y方向建立如下平衡方程：
式中，σX、σY分别为X、Y方向的线性拉应力；τXY、τYX分别为X、Y方向的切应力。
相互垂直的正应力之和为常数，即
根据切应力互等定理得
联立式（23）~式（26）得
根据式（23）~式（29）可以获得θ平面上的圆环链截面各点的应力状态。
3.2　圆环链形变量计算
为了求解圆环链的形变量，首先要求解各点的应变，计算式为
式中，εX、εY分别为拉应力σX、σY所引起的线性应变；γXY为切应力τXY引起的切应变。
对于实际工况下，链轮链窝磨损后母线的形状与圆环链外廓在X、Y方向所在平面的形变趋势一致，圆环链外廓在X、Y方向的位移分别为du、dv，计算式为
将圆环链参数代入式（33）得到圆环外廓曲线各点的位移。圆环链变形前后外廓形状如图6所示，在Y轴方向伸长1.6 mm，形变后的圆环外廓曲线即磨损后的母线形状。
链轮链窝曲面是由母线沿着准线移动而形成的曲面，图7（a）所示为该链轮链窝磨损前的齿面形态。根据计算得到的准线磨损量以及母线磨损后形状，重构磨损后的链轮链窝曲面，获得新的链轮齿面形态，如图7（b）所示。由图7（b）可以看出，磨损后的链窝准线向后移动，母线由圆弧状变为椭圆状。
4　理论模型验证
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4.1　测试链轮
为了验证上述磨损深度理论计算模型的正确性，本文选择了图8所示的SGZ 1000/3×1000矿用刮板输送机所用的ϕ48 mm×152 mm磨损失效链轮作为试验对象。
4.2　测量设备及方法
采用图9所示的RigelScan智能手持式激光3D扫描仪（测量精度为0.01 mm）进行扫描，扫描区域主要为链窝磨损部位，扫描得到磨损失效链轮的点云数据。扫描获得的点云数据由逆向工程软件Geomagic design X进行处理，形成数值点模型，导入三维建模软件中，与未磨损链轮模型进行布尔减运算，对比得到链轮链窝处磨损深度。
4.3　测量结果
本次试验共对14个磨损链轮链窝进行了测量计算，链窝准线处以及过渡圆弧处的磨损深度的测量结果b1、b2，准线误差率ζ1以及过渡圆弧处误差率ζ2如表2所示。其中，。
结果显示，理论计算值与实际测量值具有一定偏差。这是由于在实际工况下，刮板输送机所处环境恶劣，煤粉、碎石等介质进入传动系统中，导致链窝区域摩擦增大，磨损速度加快，但整体误差在18%以内。
5　链轮链窝磨损的影响因素分析
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本文应用Archard黏着磨损模型构建了链轮链窝的准线磨损模型。该模型表明，链轮链窝的磨损与多种因素有关。
5.1　链轮材料的硬度对链窝磨损的影响
根据表1，分析链轮在相同工况、不同的材料硬度下链窝磨损量的变化情况，如图10所示。结果表明，在相同的工况下，由于链轮材料的硬度不同，链窝会呈现不同的磨损情况，即随着链轮材料硬度的增加，链窝的磨损量呈现减少的趋势。故可以通过合理提高链轮材料的硬度来减少链轮的磨损，如选择合适的材料，对材料进行热处理等。
5.2　圆环链速度对链窝磨损的影响
根据表1，分析不同链速对刮板输送机链窝磨损的影响情况，如图11所示。结果表明，随着圆环链运行速度的不断增加，链窝过渡面以及柱面的磨损量均有明显的增加。这是由于速度增加，圆环链与链轮链窝间的滑动次数增加，导致链窝的磨损加剧。但另一方面，在不超出刮板输送机输送能力的情况下，速度越高，单位时间所运输的煤炭越多，可以提高刮板输送机的输送效率。
5.3　输送机工作负载对链窝磨损的影响
根据表1中刮板输送机的实际工况，分析不同负载，即物料的单位长度质量对刮板输送机链窝磨损的影响，如图12所示。结果表明，随着物料单位长度质量的不断增加，链窝过渡面以及柱面的磨损量均有明显的增加。这是由于随着物料单位长度质量的增加，刮板输送机的运行阻力增加，导致圆环链与链轮链窝间的接触力增加，进而加剧链窝的磨损。
5.4　输送机铺设倾角对链窝磨损的影响
根据表1，分析在不同的铺设倾角下刮板输送机链窝的磨损情况，如图13所示。结果表明，随着刮板输送机的铺设倾角的不断增加，链窝过渡面以及柱面的磨损量均有增加的趋势。因此在刮板输送机实际工作中，应在保证实际的生产效率以及安全的情况下，尽可能减小刮板输送机的铺设倾角，以减少链轮链窝的磨损。
6　结论
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通过以上的分析研究，得出如下结论：
1）根据链轮链窝的啮合传动特性，在Archard磨损理论计算通式基础上，提出一种适用于链轮链窝磨损深度的计算方法。经验证，计算值与测量值的整体误差在18%以内。
2）磨损后链窝曲面母线发生变化，由磨损前圆弧形状改变为磨损后的椭圆形状，且与圆环链受力形变后的形状一致。
3）通过对影响链轮链窝磨损的因素分析可知，增大链轮材料的硬度、降低铺设倾角可以有效减少链窝磨损。在保证输送任务的前提下，合理降低链速和物料的单位长度质量，可以有效减少链窝磨损。
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2025年第47卷第7期
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doi: 10.16579/j.issn.1001.9669.2025.07.012
  • 接收时间：2023-12-18
  • 首发时间：2026-03-19
  • 出版时间：2025-07-15
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  • 收稿日期：2023-12-18
  • 修回日期：2024-01-30
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    国家能源投资集团有限责任公司 神东煤炭集团有限责任公司，榆林　719000
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2种不同金属材料的力学参数
科
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Number of
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Percentage of
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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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