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Article(id=1241446432046117650, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241446328396476740, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.07.014, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1702310400000, receivedDateStr=2023-12-12, revisedDate=1705507200000, revisedDateStr=2024-01-18, acceptedDate=null, acceptedDateStr=null, onlineDate=1773913494359, onlineDateStr=2026-03-19, pubDate=1752508800000, pubDateStr=2025-07-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773913494359, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773913494359, creator=13701087609, updateTime=1773913494359, 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=108, endPage=116, ext={EN=ArticleExt(id=1241446433606398742, articleId=1241446432046117650, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Construction and research of radial contact pressure distribution model for heavy-duty engineering wheels, columnId=1241446430376776595, journalTitle=Journal of Mechanical Strength, columnName=·Design·Calculation·, runingTitle=null, highlight=null, articleAbstract=

Aiming at the inaccuracy of the finite element analysis (FEA) of heavy-duty engineering wheels under the radial loading condition, a new simulation analysis model based on the results of wheel-tire contact pressure test was established. Firstly, a stress data corresponding to the wheel under inflation pressure condition alone undergo testing, and a loading model for inflation pressure was formulated using a Gaussian function of 4th order. Secondly, a stress data collected while the wheel experiences combined inflation pressure and radial load were analyzed. The influence of inflation pressure was isolated, allowing for the development of a circumferential loading model and an axial loading model for the radial load,using a Fourier function of 4th order and a sinusoidal function of 4th order, respectively. Finally, the validation of the loading model was conducted through Ansys simulation. The outcomes demonstrate the calculation error of mere-approximately 1. 943% in relation to the measured data for the key calibration points. Additionally, the observed stress distribution manifests a remarkable degree of consistency. This substantiates the accuracy and reliability inherent in the proposed radial contact pressure distribution model.

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WU Chaohua, E-mail：
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针对重型工程车轮在径向载荷工况下有限元分析（Finite Element Analysis, FEA）的不准确问题，基于车轮-轮胎接触压力测试结果，构建了一种新的仿真分析模型。首先，测试车轮仅在充气压力工况下的应力数据，并以4阶高斯函数拟合充气压力加载模型；然后，测试车轮在充气压力和径向载荷共同作用下的应力数据，消去充气压力的影响，并以4阶傅里叶函数和4阶正弦和函数分别拟合径向载荷周向加载模型和轴向加载模型；最后，通过Ansys软件仿真验证加载模型。结果显示，与实测数据相比，关键校核点的计算误差仅为1.943%。此外，应力分布也显示出高度的一致性，证明了径向接触压力分布模型的准确性和可靠性较高。

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吴超华，男，1980年生，湖北孝感人，博士，副教授，硕士研究生导师；主要研究方向为智能装备系统设计与优化、先进材料界面设计与性能调控；E-mail：。
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叶昊哲，男，1999年生，安徽安庆人，硕士研究生；主要研究方向为工程车轮结构设计与优化；E-mail：。

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叶昊哲，男，1999年生，安徽安庆人，硕士研究生；主要研究方向为工程车轮结构设计与优化；E-mail：。

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叶昊哲，男，1999年生，安徽安庆人，硕士研究生；主要研究方向为工程车轮结构设计与优化；E-mail：。

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journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图4, caption=车轮3D网格模型, figureFileSmall=bz/Fs0LBNfDeFtXhMxPd4A==, figureFileBig=IXC/5Nv+Ja1NI4i/IuLd1w==, tableContent=null), ArticleFig(id=1241446452078112936, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 5, caption=Diagram of inflation pressure loading, figureFileSmall=kiPXVppK0pHoIwZu/vB8OA==, figureFileBig=ZcknCPDFMVH1/D5mKMNoBQ==, tableContent=null), ArticleFig(id=1241446452237496491, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图5, caption=充气压力加载示意图, figureFileSmall=kiPXVppK0pHoIwZu/vB8OA==, figureFileBig=ZcknCPDFMVH1/D5mKMNoBQ==, tableContent=null), ArticleFig(id=1241446452426240175, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 6, caption=Diagram of wheel-tire contact pressure loading, figureFileSmall=fZ7eXBQcwlYOidqRrn01YA==, figureFileBig=6AEzPUoFAapjxHN9MCUerA==, tableContent=null), ArticleFig(id=1241446452585623729, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图6, caption=车轮-轮胎接触压力加载示意图, figureFileSmall=fZ7eXBQcwlYOidqRrn01YA==, figureFileBig=6AEzPUoFAapjxHN9MCUerA==, tableContent=null), ArticleFig(id=1241446452682092724, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 7, caption=Simulation result of STEARNS loading model（θ0=45°）, figureFileSmall=sgjz1T3sbdxVrMnq6oyqbQ==, figureFileBig=UDnIWyX5gy1PAsLWcMrGCA==, tableContent=null), ArticleFig(id=1241446452774367415, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图7, caption=STEARNS模型加载仿真结果（θ0=45°）, figureFileSmall=sgjz1T3sbdxVrMnq6oyqbQ==, figureFileBig=UDnIWyX5gy1PAsLWcMrGCA==, tableContent=null), ArticleFig(id=1241446452866642106, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 8, caption=Strain gauge, figureFileSmall=wzq0BWYoQmixp9dEu//5qg==, figureFileBig=uUq7wlF51juxzfizAo6sWg==, tableContent=null), ArticleFig(id=1241446452967305404, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图8, caption=应变仪, figureFileSmall=wzq0BWYoQmixp9dEu//5qg==, figureFileBig=uUq7wlF51juxzfizAo6sWg==, tableContent=null), ArticleFig(id=1241446453059580094, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 9, caption=Testing bench of radial load, figureFileSmall=j6ucQmE9e9mh0CJpXpRv5Q==, figureFileBig=nQ4jNixydUx7NpaUWCQVTg==, tableContent=null), ArticleFig(id=1241446453135077568, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图9, caption=径向载荷试验台, figureFileSmall=j6ucQmE9e9mh0CJpXpRv5Q==, figureFileBig=nQ4jNixydUx7NpaUWCQVTg==, tableContent=null), ArticleFig(id=1241446453218963650, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 10, caption=Strain testing, figureFileSmall=ijvprmIA8M9aLBbN8PO3wA==, figureFileBig=nhnXkkwgaSfju0ctmuK4JQ==, tableContent=null), ArticleFig(id=1241446453328015556, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图10, caption=应变测量, figureFileSmall=ijvprmIA8M9aLBbN8PO3wA==, figureFileBig=nhnXkkwgaSfju0ctmuK4JQ==, tableContent=null), ArticleFig(id=1241446453416095942, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 11, caption=Location of circumferential testing points, figureFileSmall=TfTsxOx5u4lmBBHDjbxqPg==, figureFileBig=MAdqUrc0WIzExnlFBfEZUw==, tableContent=null), ArticleFig(id=1241446453504176329, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图11, caption=周向测点位置, figureFileSmall=TfTsxOx5u4lmBBHDjbxqPg==, figureFileBig=MAdqUrc0WIzExnlFBfEZUw==, tableContent=null), ArticleFig(id=1241446453650976971, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 12, caption=Loaction of axial testing points, figureFileSmall=8HFvZgs8ZEc6yGTnzIBM4A==, figureFileBig=qyDqlVqDRWsmNNWbsstxkA==, tableContent=null), ArticleFig(id=1241446453739057355, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图12, caption=轴向测点位置, figureFileSmall=8HFvZgs8ZEc6yGTnzIBM4A==, figureFileBig=qyDqlVqDRWsmNNWbsstxkA==, tableContent=null), ArticleFig(id=1241446453839720653, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 13, caption=Comparison between circumferential results of STEARNS distribution model simulation and testing results, figureFileSmall=tbBs1BMDKO6neyhmdQE0eQ==, figureFileBig=DzvIKHoR3vFBvvkzZgomRQ==, tableContent=null), ArticleFig(id=1241446453919412431, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图13, caption=STEARNS分布模型仿真周向结果与实测结果对比, figureFileSmall=tbBs1BMDKO6neyhmdQE0eQ==, figureFileBig=DzvIKHoR3vFBvvkzZgomRQ==, tableContent=null), ArticleFig(id=1241446454003298513, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 14, caption=Comparison between axial results of STEARNS distribution model simulation and testing results, figureFileSmall=eAudg4iwzQy3q+UWQ2v7uA==, figureFileBig=RVrsKPcmrU/3W7DMBLTZEw==, tableContent=null), ArticleFig(id=1241446454078795987, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图14, caption=STEARNS分布模型仿真轴向结果与实测结果对比, figureFileSmall=eAudg4iwzQy3q+UWQ2v7uA==, figureFileBig=RVrsKPcmrU/3W7DMBLTZEw==, tableContent=null), ArticleFig(id=1241446454171070675, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 15, caption=Static inflation stress on the wheel rim stopper and the wheel rim surface, figureFileSmall=f4bR2c4AXEpxFubHh+d68Q==, figureFileBig=hD0ireVAC464J0/zrQY/iQ==, tableContent=null), ArticleFig(id=1241446454259151060, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图15, caption=轮缘挡圈和轮辋表面的充气静应力, figureFileSmall=f4bR2c4AXEpxFubHh+d68Q==, figureFileBig=hD0ireVAC464J0/zrQY/iQ==, tableContent=null), ArticleFig(id=1241446454355620053, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 16, caption=Dynamic contact stress at the upper end of the rim stopper, figureFileSmall=V9lglY2+BZemPDP4yIoVdw==, figureFileBig=CHsQWbmI7yfEneDXNeKiDg==, tableContent=null), ArticleFig(id=1241446454426923223, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图16, caption=轮缘挡圈上端动态接触应力, figureFileSmall=V9lglY2+BZemPDP4yIoVdw==, figureFileBig=CHsQWbmI7yfEneDXNeKiDg==, tableContent=null), ArticleFig(id=1241446454506615001, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 17, caption=Dynamic contact stress at the lower end of the rim stopper, figureFileSmall=z3MSsSL3Ee1l9WgaxPYxQA==, figureFileBig=XBL0Sr8bdFE+OblQzFnf9Q==, tableContent=null), ArticleFig(id=1241446454586306779, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图17, caption=轮缘挡圈下端动态接触应力, figureFileSmall=z3MSsSL3Ee1l9WgaxPYxQA==, figureFileBig=XBL0Sr8bdFE+OblQzFnf9Q==, tableContent=null), ArticleFig(id=1241446454661804253, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 18, caption=Dynamic contact stress on the bead seat of the outside wheel, figureFileSmall=AuO35iJsQHTPmELWu1aflQ==, figureFileBig=396yLon9D/5hLdXrbXnTWg==, tableContent=null), ArticleFig(id=1241446454749884639, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图18, caption=车轮外侧胎圈座动态接触应力, figureFileSmall=AuO35iJsQHTPmELWu1aflQ==, figureFileBig=396yLon9D/5hLdXrbXnTWg==, tableContent=null), ArticleFig(id=1241446454837965025, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 19, caption=Dynamic contact stress on the bead seat of the inside wheel, figureFileSmall=RRc0gGq7KHby+5o9v8G01A==, figureFileBig=GYY1ifGUpz8Cfgf7X/xH0Q==, tableContent=null), ArticleFig(id=1241446454955405539, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图19, caption=车轮内侧胎圈座动态接触应力, figureFileSmall=RRc0gGq7KHby+5o9v8G01A==, figureFileBig=GYY1ifGUpz8Cfgf7X/xH0Q==, tableContent=null), ArticleFig(id=1241446455131566310, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 20, caption=Fitting curve of axial distribution of inflation pressure, figureFileSmall=7aqMiAPWZHllizVZimzZDg==, figureFileBig=zeaww9C4JrCpfhnQquURkg==, tableContent=null), ArticleFig(id=1241446455278366952, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图20, caption=充气压力轴向分布拟合曲线, figureFileSmall=7aqMiAPWZHllizVZimzZDg==, figureFileBig=zeaww9C4JrCpfhnQquURkg==, tableContent=null), ArticleFig(id=1241446455345475818, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 21, caption=Fitting curve of radial load circumferential distribution for Point 1, figureFileSmall=P+E0d9JC0uaobeU3gQA14g==, figureFileBig=3q5HR/vqBw5BSAh3E3fB2g==, tableContent=null), ArticleFig(id=1241446455429361899, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图21, caption=测点1径向载荷周向分布拟合曲线, figureFileSmall=P+E0d9JC0uaobeU3gQA14g==, figureFileBig=3q5HR/vqBw5BSAh3E3fB2g==, tableContent=null), ArticleFig(id=1241446455517442285, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 22, caption=Fitting curve of radial load circumferential distribution for Point 2, figureFileSmall=CvMp+Kk0pFopYkHV/briAw==, figureFileBig=hpOkvksl4rXeLnINQIq6QA==, tableContent=null), ArticleFig(id=1241446455639077101, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图22, caption=测点2径向载荷周向分布拟合曲线, figureFileSmall=CvMp+Kk0pFopYkHV/briAw==, figureFileBig=hpOkvksl4rXeLnINQIq6QA==, tableContent=null), ArticleFig(id=1241446455773294830, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 23, caption=Fitting curve of radial load circumferential distribution for Point 3, figureFileSmall=D6+ZOhWb4FNRg60zrBPbRw==, figureFileBig=BEYVXAiy409TD5g+xZ8ldw==, tableContent=null), ArticleFig(id=1241446455907512559, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图23, caption=测点3径向载荷周向分布拟合曲线, figureFileSmall=D6+ZOhWb4FNRg60zrBPbRw==, figureFileBig=BEYVXAiy409TD5g+xZ8ldw==, tableContent=null), ArticleFig(id=1241446456041730289, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 24, caption=Fitting curve of radial load circumferential distribution for Point 4, figureFileSmall=KFAKK2cwfpEzevbxH4YwDQ==, figureFileBig=ct2UoxWE4G117Panqxu43w==, tableContent=null), ArticleFig(id=1241446456146587890, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图24, caption=测点4径向载荷周向分布拟合曲线, figureFileSmall=KFAKK2cwfpEzevbxH4YwDQ==, figureFileBig=ct2UoxWE4G117Panqxu43w==, tableContent=null), ArticleFig(id=1241446456255639796, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 25, caption=Fitting curve of radial load circumferential distribution for Point 5, figureFileSmall=/4xrCUj18jlEozn4m+aSIg==, figureFileBig=v+tekKvCX5r6Tb14Kqhk7g==, tableContent=null), ArticleFig(id=1241446456343720181, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图25, caption=测点5径向载荷周向分布拟合曲线, figureFileSmall=/4xrCUj18jlEozn4m+aSIg==, figureFileBig=v+tekKvCX5r6Tb14Kqhk7g==, tableContent=null), ArticleFig(id=1241446456427606263, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 26, caption=Fitting curve of radial load circumferential distribution for Point 6, figureFileSmall=ByLsn094A2ISMxkJc2WKtg==, figureFileBig=MPigxLB3PDtQAxpXp/q80w==, tableContent=null), ArticleFig(id=1241446456528269561, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图26, caption=测点6径向载荷周向分布拟合曲线, figureFileSmall=ByLsn094A2ISMxkJc2WKtg==, figureFileBig=MPigxLB3PDtQAxpXp/q80w==, tableContent=null), ArticleFig(id=1241446456607961338, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 27, caption=Fitting curve of radial load circumferential distribution for Point 7, figureFileSmall=T3MmW/g1+mjxuvys7mA2zg==, figureFileBig=SUK8Qru9DJhsT0tWwUMg8g==, tableContent=null), ArticleFig(id=1241446456721207548, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图27, caption=测点7径向载荷周向分布拟合曲线, figureFileSmall=T3MmW/g1+mjxuvys7mA2zg==, figureFileBig=SUK8Qru9DJhsT0tWwUMg8g==, tableContent=null), ArticleFig(id=1241446456817676542, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 28, caption=Fitting curve of radial load circumferential distribution for Point 8, figureFileSmall=L63mXizT2keiOLaHXEn8RQ==, figureFileBig=SlHtIUioLZA4HBgzZ+owfw==, tableContent=null), ArticleFig(id=1241446456897368320, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=图28, caption=测点8径向载荷周向分布拟合曲线, figureFileSmall=L63mXizT2keiOLaHXEn8RQ==, figureFileBig=SlHtIUioLZA4HBgzZ+owfw==, tableContent=null), ArticleFig(id=1241446456998031616, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Fig. 29, caption=Fitting curve of radial load axial 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label=Tab. 1, caption=

Stress data of circumferential testing points

, figureFileSmall=null, figureFileBig=null, tableContent=
测点位置
Testing point location/（°）		von Mises应力
von Mises stress R/MPa
-6040.337
-5098.781
-40179.798
-30261.871
-20287.987
-10307.322
0321.907
10314.815
20303.103
30281.779
40182.981
50101.231
6043.980
), ArticleFig(id=1241446457958527251, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=表1, caption=

周向测点应力数据

, figureFileSmall=null, figureFileBig=null, tableContent=
测点位置
Testing point location/（°）		von Mises应力
von Mises stress R/MPa
-6040.337
-5098.781
-40179.798
-30261.871
-20287.987
-10307.322
0321.907
10314.815
20303.103
30281.779
40182.981
50101.231
6043.980
), ArticleFig(id=1241446458034024725, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=EN, label=Tab. 2, caption=

Stress data of axial testing points

, figureFileSmall=null, figureFileBig=null, tableContent=
测点序号
Number of testing points		von Mises应力
von Mises stress R/MPa
139.654
2178.354
3119.332
489.625
5321.019
6101.335
7198.236
870.221
955.895
10172.559
1198.682
12307.235
1377.892
14123.325
15177.956
1633.095
), ArticleFig(id=1241446458138882326, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446432046117650, language=CN, label=表2, caption=

轴向测点应力数据

, figureFileSmall=null, figureFileBig=null, tableContent=
测点序号
Number of testing points		von Mises应力
von Mises stress R/MPa
139.654
2178.354
3119.332
489.625
5321.019
6101.335
7198.236
870.221
955.895
10172.559
1198.682
12307.235
1377.892
14123.325
15177.956
1633.095
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重型工程车轮径向接触压力分布模型的构建与研究
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叶昊哲 1 , 吴超华 1 , 全勇智 2 , 史晓亮 1 , 罗威 1
机械强度 | ·设计·计算· 2025,47(7): 108-116
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机械强度 | ·设计·计算· 2025, 47(7): 108-116
重型工程车轮径向接触压力分布模型的构建与研究
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叶昊哲1 , 吴超华1 , 全勇智2, 史晓亮1, 罗威1
作者信息
  • 1.武汉理工大学 机电工程学院，武汉　430070
  • 2.柳州瑞东机械制造有限公司，柳州　545027

    • 叶昊哲，男，1999年生，安徽安庆人，硕士研究生；主要研究方向为工程车轮结构设计与优化；E-mail：。

通讯作者:

吴超华，男，1980年生，湖北孝感人，博士，副教授，硕士研究生导师；主要研究方向为智能装备系统设计与优化、先进材料界面设计与性能调控；E-mail：。
Construction and research of radial contact pressure distribution model for heavy-duty engineering wheels
Haozhe YE1 , Chaohua WU1 , Yongzhi QUAN2, Xiaoliang SHI1, Wei LUO1
Affiliations
  • 1.School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China
  • 2.Liuzhou Ruidong Machinery Manufacturing Co., Ltd., Liuzhou 545027, China
出版时间: 2025-07-15 doi: 10.16579/j.issn.1001.9669.2025.07.014
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针对重型工程车轮在径向载荷工况下有限元分析（Finite Element Analysis, FEA）的不准确问题，基于车轮-轮胎接触压力测试结果，构建了一种新的仿真分析模型。首先，测试车轮仅在充气压力工况下的应力数据，并以4阶高斯函数拟合充气压力加载模型；然后，测试车轮在充气压力和径向载荷共同作用下的应力数据，消去充气压力的影响，并以4阶傅里叶函数和4阶正弦和函数分别拟合径向载荷周向加载模型和轴向加载模型；最后，通过Ansys软件仿真验证加载模型。结果显示，与实测数据相比，关键校核点的计算误差仅为1.943%。此外，应力分布也显示出高度的一致性，证明了径向接触压力分布模型的准确性和可靠性较高。

钢制车轮  /  径向载荷  /  接触压力分布  /  有限元分析  /  仿真计算模型

Aiming at the inaccuracy of the finite element analysis (FEA) of heavy-duty engineering wheels under the radial loading condition, a new simulation analysis model based on the results of wheel-tire contact pressure test was established. Firstly, a stress data corresponding to the wheel under inflation pressure condition alone undergo testing, and a loading model for inflation pressure was formulated using a Gaussian function of 4th order. Secondly, a stress data collected while the wheel experiences combined inflation pressure and radial load were analyzed. The influence of inflation pressure was isolated, allowing for the development of a circumferential loading model and an axial loading model for the radial load,using a Fourier function of 4th order and a sinusoidal function of 4th order, respectively. Finally, the validation of the loading model was conducted through Ansys simulation. The outcomes demonstrate the calculation error of mere-approximately 1. 943% in relation to the measured data for the key calibration points. Additionally, the observed stress distribution manifests a remarkable degree of consistency. This substantiates the accuracy and reliability inherent in the proposed radial contact pressure distribution model.

Steel wheel  /  Radial load  /  Contact pressure distribution  /  Finite element analysis  /  Simulation calculation model
叶昊哲, 吴超华, 全勇智, 史晓亮, 罗威. 重型工程车轮径向接触压力分布模型的构建与研究. 机械强度, 2025 , 47 (7) : 108 -116 . DOI: 10.16579/j.issn.1001.9669.2025.07.014
Haozhe YE, Chaohua WU, Yongzhi QUAN, Xiaoliang SHI, Wei LUO. Construction and research of radial contact pressure distribution model for heavy-duty engineering wheels[J]. Journal of Mechanical Strength, 2025 , 47 (7) : 108 -116 . DOI: 10.16579/j.issn.1001.9669.2025.07.014
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0　引言
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随着现代交通工具不断发展，车轮性能对交通运输的安全、效率和经济效益产生了直接而深远的影响。根据国家标准GB/T 5909—2021[1]，车轮需满足该标准要求的弯曲疲劳和径向疲劳台架试验要求。有限元仿真技术为企业提供了一种低成本、高效率的方法，用于评估和改进车轮的弯曲和径向疲劳性能。这有助于提高产品质量、降低研发成本、缩短产品开发周期、增强企业竞争力。
STEARNS等[2]262-268通过试验和有限元分析（Finite Element Analysis，FEA）比较，得出了轮胎对车轮作用力分布近似余弦函数；DAS[3]对铝合金车轮轮毂进行了在径向疲劳试验工况下的静力学分析及结构优化；MEGHASHYAM等[4]对辐条式车轮的辐条进行了静力学分析和模态分析，提出了结构优化建议；韦东来等[5]将动态接触转化成节点可相对移动的缓冲过渡层，提出了径向疲劳模型中轮胎与轮辋接触问题的解决方法；杨云端等[6]通过Ansys nCode DesignLife软件校核了某款车轮的动态径向疲劳寿命；单颖春等[7]482-487通过试验构建了一种新的车轮-轮胎接触压力分布模型；王新伟等[8]对货车车轮进行了弯曲和径向试验工况下的结构强度分析；覃海艺等[9]626-630基于动力显式有限元法对径向试验工况下的车轮进行了仿真模拟；刘俊辉等[10]16-20对车轮轮胎总成进行了径向载荷仿真分析；王朝华等[11]基于疲劳损伤累计理论对铝合金车轮轮毂寿命进行了预测。
目前，国内外研究人员[12-18]对车轮径向载荷仿真计算大多按照STEARNS等[2]262-268提出的在轮辋胎圈座上以一定角度范围内按余弦函数分布压力加载。但是，在为企业进行重型工程车轮径向载荷仿真分析的过程中发现，按照STEARNS[2]262-268提出的方法加载后，所得结论与实测数据相比，应力数值有较大偏差，应力分布也是如此。单颖春等[7]482-487对STEARNS等[2]262-268提出的模型的分析误差进行了深入研究，提出了基于试验数据的径向载荷仿真分析模型。然而，按照单颖春等[7]482-487提出的模型加载计算，其仿真结果与实测数据相比，周向方向的应力数值仅有略微偏差、应力分布相近；轴向方向应力数值偏差较大，应力分布也不尽相同。此外，覃海艺等[9]626-630[10]16-20选择研究车轮轮胎总成。不过，考虑到轮胎材料的复合性和大变形问题，再加上车轮-轮胎接触耦合问题，将会导致车轮轮胎总成力学模型过于复杂。
综上所述，STEARNS等[2]262-268提出的模型和单颖春等[7]482-487提出的模型都存在固有的局限性，在车轮径向载荷计算中会产生不可避免和不可接受的误差；由于车轮轮胎总成力学模型的高度复杂性，相关研究往往将简单问题复杂化。因此，本文倾向于寻求构建更接近于实际工况的车轮径向接触压力分布模型。
1　径向疲劳试验与STEARNS模型
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1.1　径向疲劳试验
根据国家标准GB/T 5909—2021，辐板式车轮的径向疲劳试验方法如图1所示。试验设备由转鼓、车轮轮胎总成、车轮固定座组成，转鼓最小直径为1 700 mm，转鼓宽度应大于轮胎宽度。径向力Fr在转鼓与车轮的中心连线上，在Fr的作用下，车轮与转鼓外表面贴合，车轮在转鼓驱动下旋转。
1.2　STEARNS载荷模型
STEARNS径向载荷分布模型如图2所示。其中，W0为车轮最大径向分布力；Wr为车轮径向分布力；b为胎圈座受力宽度；θ0为径向载荷作用最大偏转角。
根据STEARNS模型，车轮径向分布力与最大径向分布力关系为
式中，θ为Wr和W0的作用点与胎圈座几何中心所构成的圆心角。
径向载荷计算式为
式中，Fr为径向载荷；Fv为额定负载，由车轮或者汽车制造厂规定；K为强化系数，由车轮材料、轮辋规格、最低循环系数综合确定。
对式（1）积分，可得
式中，rb为胎圈座半径。
2　STEARNS分布模型仿真分析与测试
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2.1　STEARNS分布模型仿真分析
在径向仿真试验中，车轮主要承受来自轮胎的充气压力和外部径向载荷。根据国家标准GB/T 5909 — 2021要求，轮胎充气压力为1 MPa；根据STEARNS分布模型，径向载荷作用下，车轮-轮胎接触压力分布为。其中，广西某车轮制造企业提供如下参数：额定负载Fv为182.5 kN；强化系数K为2；胎圈座受力宽度b为50 mm；胎圈座半径rb为317. 5 mm；螺栓型号为M22；θ0分别取36°、45°、60°。某车轮模型的中心截面如图3所示。
网格质量对有限元分析有较大的影响，但Ansys软件的网格划分功能并不能满足工程中复杂特征装配体的要求。因此，采用HyperMesh软件划分网格后，再将网格模型导入Ansys软件。车轮3D网格模型如图4所示，网格尺寸为4 mm。
在轮胎的充气压力和径向载荷作用下，车轮-轮胎接触压力加载区域如图5、图6所示。仿真分析结果如图7所示。
2.2　车轮径向载荷测试
对径向载荷作用下车轮-轮胎接触压力进行实地测试前，应确保轮辋表面干燥无杂质；将车轮安装在固定座后，应将应变仪归零。接着将轮胎充气至额定胎压并观察应变仪数据变化。在测试过程中，应保持车轮静止不动。应变仪采用eDAQ型的应变仪、径向载荷试验台分别如图8、图9所示。
试验开始后，通过控制台向车轮施加径向载荷。在载荷不断增加的过程中，应连续采集应变数据并观察数值是否异常；当载荷增加至设定值后，应观察应变数据是否趋向稳定。
根据以往设计校核经验，车轮径向受载时，其应力最大值一般出现在轮辋-轮缘挡圈过渡圆角处，故应力测点布置在轮辋-轮缘过渡圆角处。应变测量、周向测点位置分别如图10、图11所示。
图10中2组应变片周向间隔60°，每测量1组静态充气压力后，操作试验台使车轮转动10°，如此反复6次，即可获取图11中所有测点位置的应力数据。经处理后的测试数据如表1所示。
上述测点位置由以往设计经验确定，但是考虑到试验的严谨性，也应对轮辋轴向应力分布进行测试。轴向测点位置如图12所示。
选择测点位置的周向角度时，应在应力较大处设置，以免因其总体应力数值相对较小而导致无法印证轴向应力分布。依此思路，又根据表1中实测数据，可以选取0°作为轴向测试的选取方向。处理后的试验数据如表2所示。
2.3　仿真结论与实测数据对比分析
在Ansys软件的计算结果分析模块中，按照图11和图12中的测点分布的具体位置，分别查询最大载荷偏转角θ0=36°、45°、60°的仿真计算所得的等效应力值。将所得仿真等效应力值与实测等效应力值绘制于同一图中，以便对两者进行对比分析。STEARNS分布模型仿真分析结果与实测结果对比如图13、图14所示。
由图13可知，与实测数据相比，在高应力区（周向测点0°）应力数值上，按θ0=36°、45°、60°加载的仿真结果分别小21.8%、27. 6%、28. 9%；在应力分布上，当θ0=45°时，与实测数据相似，然而当θ0=36°、60°时，其次级区域（周向测点-10°和10°）与实测数据相差较大。由图14可知，与实测数据相比，按θ0=36°、45°、60°加载的仿真结果，不但在高应力区（轴向测点5）应力数值分别小29. 6%、30.1%、35. 6%，而且在轮缘挡圈和胎圈座处的应力分布有较大差异。
根据上述分析，按照STEARNS分布模型进行径向载荷仿真分析，在模型重要校核区域，其仿真结果的误差接近30%且应力分布也有较大差异，这样的分析结果是难以接受的。因此，为了提高仿真计算的准确度、达到企业设计校核标准的要求，亟须对径向载荷压力分布模型进行优化。
3　车轮径向载荷分布模型构建及验证
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在径向疲劳试验中，轮胎充气压力直接作用于轮辋中部、间接作用于车轮-轮胎接触部分；径向载荷直接作用于轮胎，间接作用于车轮-轮胎接触部分。然而，间接作用于车轮-轮胎接触部分的充气压力、车轮-轮胎接触中轮缘挡圈部分的接触压力，以及车轮-轮胎接触压力的轴向分布差异，在仿真分析中往往被忽视，导致车轮径向载荷仿真分析产生相对误差。
3.1　车轮-轮胎接触压力测试
为了得到可靠的车轮径向载荷分布模型，应进行如下试验测试。首先，以图12中的测点位置设置应变片，并将车轮轮胎总成装配固定并充气至额定胎压1 MPa。在仅施加充气压力的情况下，测取轮缘和轮辋表面的静应变数据。然后，将应变仪数据清零，施加径向载荷并以20 km/h的速度转动车轮，分别测取轮缘和轮辋表面由径向载荷间接引起的动态接触应变数据。依照上述方法，即可测取轮胎充气压力和外部的径向载荷对车轮应力的各自独立的影响。轮缘挡圈和轮辋表面的充气静应力曲线如图15所示，轮缘挡圈和轮辋表面由径向载荷间接引起的、车轮转动一周内的动态接触应力曲线如图16~图19所示。
由图15可知，轮缘挡圈和轮辋表面由充气压力间接引起的接触应力主要特点如下：主要分布于胎圈座，对轮缘挡圈上端几乎没有影响。由图16~图19可知，轮缘挡圈和轮辋表面由径向载荷间接引起的动态接触应力主要特点如下：从周向分布的角度看，各个测点位置都主要分布在径向载荷集中点两侧周向50°范围内，周向两侧50°~180°内应力数值趋于稳定；从轴向分布的角度看，主要分布在轮缘挡圈过渡圆角、轮辋-轮缘挡圈过渡圆角、胎圈座中部；从测点应力对称性的角度看，测点1~测点8与其各自关于轮辋中心对称的测点9~测点16在应力数值和应力分布上高度一致。
根据上述分析可知，忽略充气压力作用、将充气压力和径向载荷视为同一分布是不合理的，忽略车轮-轮胎接触应力的轴向分布差异也是不合理的，应根据不同的应力分布特点分别拟合对应加载函数，并结合对应加载区域分步骤加载。
3.2　车轮径向载荷分布模型构建
根据车轮-轮胎接触应力测试结果及其分析，确定如下车轮径向载荷压力分布模型构建方法。对于充气压力，在直接接触区域，施加1 MPa均布压力载荷；在间接接触区域，根据轮辋表面充气静应力拟合其轴向分布数学模型，再依此模型施加周向均布压力。对于径向载荷，根据轮缘挡圈和轮辋表面由径向载荷间接引起的动态接触应力，拟合周向-轴向分布数学模型，再依此模型施加压力。
在拟合数据前，应将数据做归一化处理；在拟合数据时，应使用多种经典拟合函数，并结合函数拟合优度指标不断优化。
根据图15及其相关分析，可以忽略充气压力对轮缘挡圈上端的影响，故数据拟合对象为测点3~测点14。再结合一般拟合经验，经过多次拟合试验，以4阶高斯函数拟合充气压力轴向分布为最佳。其曲线函数为
式中，i为函数项数；a、b、c为各项常系数；e为自然对数底数。各项归一化拟合参数如下：
上述参数的拟合优度指标判定系数和均方根误差分别为0.986 6，0.031 4。充气压力轴向分布试验数据与其拟合曲线对比如图20所示。
根据图16~图19及其相关分析，因为车轮应力分布关于其中心具有对称性，所以只需构建测点1~测点8的周向-轴向分布数学模型。再结合一般拟合经验，经过多次拟合试验，以4阶傅里叶函数拟合径向载荷压力周向分布为最佳，其曲线函数如式（7）所示；以4阶正弦和函数拟合径向载荷压力轴向分布为最佳，其曲线函数如式（8）所示。
式中，i为函数项数；a、b、w为各项常系数；c为常数。各项归一化拟合参数如下：
上述参数平均拟合优度指标判定系数和均方根误差分别为0.910 6，0.091 4。径向载荷压力周向分布试验数据与其拟合曲线对比如图21~图28所示。
式中，i为函数项数；a、b、c为各项常系数。各项归一化拟合参数如下所示：
上述参数拟合优度指标判定系数和均方根误差分别为0.936 6、0.071 4。径向载荷压力轴向分布试验数据与其拟合曲线对比如图29所示。
3.3　车轮径向载荷分布模型验证与比较
单颖春等[7]482-487在STEARNS模型的基础上，将车轮-轮胎的接触区域由径向载荷集中点两侧各θ0范围内扩展至360°完整圆周范围内，并以4阶正弦和函数拟合车轮-轮胎接触模型，得到单颖春模型，拟合其函数如式（8）所示，拟合函数参数如下：
式中，α为拟合常数，该值为所需仿真模型径向载荷与单颖春模型径向载荷之比。本文模型载荷为182.5 kN，单颖春模型载荷为71 kN，故α = 2. 57。
将单颖春等[7]482-487构建的车轮-轮胎径向载荷分布模型加载至车轮，然后将仿真模型导入Ansys WorkBench软件进行计算，分析结果如图30所示。将本文构建的车轮-轮胎径向载荷压力分布模型分步加载至车轮，然后将仿真模型导入Ansys WorkBench软件进行计算，分析结果如图31所示。
将本文所构建的车轮-轮胎径向接触压力分布模型分析结果与STEARNS模型分析结果、单颖春模型分析结果、实测数据绘制于一图。径向载荷周向仿真分析结果对比如图32所示，径向载荷轴向仿真分析结果对比如图33所示。
由图32和图33可知，对于STEARNS模型仿真计算结果而言，在周向高应力区的应力数值较小，在应力危险点（周向测点0°）的误差达29.947%；轴向应力分布也有较大差异，应力曲线在次级区域（轴向测点4）的极值点误差高达54. 43%且下降梯度过大。对于单颖春模型仿真计算结果而言，在周向高应力区的应力数值偏小，在应力危险点（周向测点0°）的误差达15. 658%；轴向应力分布吻合度较低，应力曲线在次级区域（轴向测点4）的极值点误差高达24. 74%且下降梯度较大。对于本文构建的加载模型仿真计算结果而言，在高应力区的吻合度较高，在应力危险点的误差仅为1. 943%；无论是周向还是轴向应力分布，其吻合度都相对较高。
STEARNS模型整体计算结果较小，不利于车轮设计和质量校核，可能导致安全问题；应力分布差异过大，不利于车轮结构优化，难以保障车轮设计生产的经济性。单颖春模型整体计算结果偏小，不利于应力危险点校核、应力次级区域结构优化。
本文认为导致STEARNS模型和单颖春模型仿真误差的原因如下：上述模型针对的研究对象是汽车车轮，与重型工程车轮在结构、尺寸等方面存在显著差异。此外，STEARNS模型和单颖春模型都忽视了车轮-轮胎接触压力的轴向分布差异、车轮-轮胎接触中轮缘挡圈部分的接触压力，且STEARNS模型仅在高应力区进行模拟仿真计算而忽视了其他次级区域，因而相较于单颖春模型，其分析结果误差更大。
4　结论
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针对重型工程车轮在径向加载下有限元分析不准确问题，构建了一种新的仿真分析模型。通过试验和仿真计算，得出如下主要结论：
1）基于车轮-轮胎接触压力测试结果，针对重型工程车轮在径向载荷工况下有限元仿真计算结果的准确性问题，本文构建了一种新的仿真计算加载模型。该模型相较于STEARNS模型和单颖春模型，具有更高的应力数值准确度和更接近于实际的应力分布。
2）本文模型可用于结构、尺寸相似的重型工程车轮在径向载荷工况下的仿真计算。然而，随着车轮结构的改进，加载函数及加载区域可能发生变化，但本文开展的相关研究可为构建车轮径向载荷仿真分析加载模型提供理论和实践参考。
基金
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  • 国家自然科学基金项目(52375201)
  • 武汉理工大学产学研科技合作项目(20231h0544)
文献
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参考文献 引证文献
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2025年第47卷第7期
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doi: 10.16579/j.issn.1001.9669.2025.07.014
  • 接收时间：2023-12-12
  • 首发时间：2026-03-19
  • 出版时间：2025-07-15
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  • 收稿日期：2023-12-12
  • 修回日期：2024-01-18
基金
National Natural Science Foundation of China(52375201)
国家自然科学基金项目(52375201)
Wuhan University of Technology Industry-University-Research Science and Technology Cooperation Project(20231h0544)
武汉理工大学产学研科技合作项目(20231h0544)
作者信息
    1.武汉理工大学 机电工程学院，武汉　430070
    2.柳州瑞东机械制造有限公司，柳州　545027

通讯作者:

吴超华，男，1980年生，湖北孝感人，博士，副教授，硕士研究生导师；主要研究方向为智能装备系统设计与优化、先进材料界面设计与性能调控；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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