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Article(id=1228805176614646006, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228805175335383281, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2025.04.004, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1691510400000, receivedDateStr=2023-08-09, revisedDate=1695225600000, revisedDateStr=2023-09-21, acceptedDate=null, acceptedDateStr=null, onlineDate=1770899584201, onlineDateStr=2026-02-12, pubDate=1744214400000, pubDateStr=2025-04-10, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770899584201, onlineIssueDateStr=2026-02-12, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770899584201, creator=13701087609, updateTime=1770899584201, updator=13701087609, issue=Issue{id=1228805175335383281, tenantId=1146029695717560320, journalId=1225147924628267009, year='2025', volume='38', issue='4', pageStart='663', pageEnd='888', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770899583895, creator=13701087609, updateTime=1770901458539, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228813038325789525, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228805175335383281, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228813038329983830, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228805175335383281, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=697, endPage=705, ext={EN=ArticleExt(id=1228805176832749816, articleId=1228805176614646006, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Dynamic modeling of rolling linear guideway joint based on bushing element, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The bushing element is established for dynamic modeling of rolling linear guideway joints based on the movement characteristics of guideway. The effectiveness of the bushing element is verified by the numerical and experimental examples. Base on the fact that the guideway joint has significant influence on the dynamic performance of the whole structure，the model updating technique combined with the substructure method is proposed for parameter identification of bushing element. A simulation example of dumbbell structure is used to verify the effectiveness of the proposed parameter identification method. Based on the simulation example，a dumbbell structure with single slider rolling guideway is used for bushing element parameter identification and model verification. The effectiveness and universality of the bushing model is verified by a rolling linear guideway structure which contains four sliders. The engineering application of the bushing element is verified by the structure of rolling linear guideway moving platform of special ring welding machine. The results show that the bushing model is simple for application，the dynamic modeling error for single slider rolling linear guideway is within 5% and the error for four sliders rolling guideway system is within 12%，and the error of engineering structure of moving platform with four sliders is about 11%.

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根据滚动直线导轨副的结构特性，提出基于bushing单元的滚动直线导轨结合部动力学建模方法，并通过算例仿真计算和实物实验，验证了利用bushing单元对滚动直线导轨动力学特性建模的有效性。基于零件的结合部能显著影响整体结构的动力学特性的特点，采用子结构法与模型修正技术结合的方式，识别滚动直线导轨的bushing单元参数。通过构建哑铃状结构的仿真算例，对bushing单元参数进行仿真识别，以验证识别算法的准确性。以仿真算例的三维机械结构为基础，以含有单个滑块的哑铃状滚动直线导轨结构为实验对象，通过实物实验识别导轨的参数并验证模型的有效性。在以上仿真与实物实验的基础上，设计制造了含有4个滑块的滚动直线导轨机械结构，通过理论分析和模态实验对比，验证bushing单元建模的有效性和通用性。以专用轮毂环焊机的床身-滚动导轨移动平台结构为实验对象，进行工程应用验证。结果表明：采用bushing单元模拟滚动直线导轨滚动结合部的建模过程简单；相同模态振型的有限元分析与实验测试获得的前5阶模态频率对比表明，基于bushing单元的单滑块滚动直线导轨结构的固有频率误差不高于5%；基于bushing单元的四滑块滚动直线导轨结构固有频率误差不高于12%；基于bushing单元的环焊机床身滚动导轨移动平台结构的固有频率误差最高为11%。

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雷声（1988—），男，博士，副教授。E-mail：
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何秀权（1984—），男，硕士，工程师。E-mail：

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何秀权（1984—），男，硕士，工程师。E-mail：

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Parameter of bushing element

, figureFileSmall=null, figureFileBig=null, tableContent=
参数值Ky/(N·m-1)Kz/(N·m-1)Tx/(N·m·rad-1)Ty/(N·m·rad-1)Tz/（N·m·rad-1)
准确值5×1071×1075×1043×1052×105
初值3×1073×1071×1051×1051×105
), ArticleFig(id=1229121425341207393, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=CN, label=表1, caption=

bushing单元参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数值Ky/(N·m-1)Kz/(N·m-1)Tx/(N·m·rad-1)Ty/(N·m·rad-1)Tz/（N·m·rad-1)
准确值5×1071×1075×1043×1052×105
初值3×1073×1071×1051×1051×105
), ArticleFig(id=1229121425450259301, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=EN, label=Tab. 2, caption=

Identified bushing parameters of rolling linear guideway joint

, figureFileSmall=null, figureFileBig=null, tableContent=
Ky/(N·m-1)Kz/(N·m-1)Tx/(N·m·rad-1)Ty/(N·m·rad-1)Tz/(N·m·rad-1)
4.69×1083.23×108231.33.46×1056.97×105
), ArticleFig(id=1229121425567699820, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=CN, label=表2, caption=

识别的滚动直线导轨结合部bushing参数

, figureFileSmall=null, figureFileBig=null, tableContent=
Ky/(N·m-1)Kz/(N·m-1)Tx/(N·m·rad-1)Ty/(N·m·rad-1)Tz/(N·m·rad-1)
4.69×1083.23×108231.33.46×1056.97×105
), ArticleFig(id=1229121425659974516, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=EN, label=Tab. 3, caption=

Mode shapes of rolling linear guideway structure

, figureFileSmall=null, figureFileBig=null, tableContent=
运动方向理论振型文献[24]实验振型
绕x轴转动
绕z轴转动
绕y轴转动
沿z轴移动
沿y轴移动
), ArticleFig(id=1229121425752249208, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=CN, label=表3, caption=

滚动直线导轨结构模态振型

, figureFileSmall=null, figureFileBig=null, tableContent=
运动方向理论振型文献[24]实验振型
绕x轴转动
绕z轴转动
绕y轴转动
沿z轴移动
沿y轴移动
), ArticleFig(id=1229121425836135289, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=EN, label=Tab. 4, caption=

Modal frequencies and errors of rolling linear guideway structure under different models

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数文献[24]模型实验值/Hz本文模型/Hz本文模型误差/%文献[24]模型理论值/Hz文献[24]模型误差/%
1阶266.7279.6-4.85276.5-3.82
2阶356.5356.50317.53.65
3阶4174170462.2-10.95
4阶943.2938.80.46907.110.83
5阶1 195.91 196.40——
), ArticleFig(id=1229121425957770116, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=CN, label=表4, caption=

不同模型的滚动直线导轨连接结构的模态频率及误差

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数文献[24]模型实验值/Hz本文模型/Hz本文模型误差/%文献[24]模型理论值/Hz文献[24]模型误差/%
1阶266.7279.6-4.85276.5-3.82
2阶356.5356.50317.53.65
3阶4174170462.2-10.95
4阶943.2938.80.46907.110.83
5阶1 195.91 196.40——
), ArticleFig(id=1229121426058433416, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=EN, label=Tab. 5, caption=

Mode shapes of guideway structure with four sliders

, figureFileSmall=null, figureFileBig=null, tableContent=
运动方向理论振型实验振型
绕z轴转动
绕y轴转动
绕x轴转动
沿y轴移动
), ArticleFig(id=1229121426150708105, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=CN, label=表5, caption=

四滑块导轨结构模态振型

, figureFileSmall=null, figureFileBig=null, tableContent=
运动方向理论振型实验振型
绕z轴转动
绕y轴转动
绕x轴转动
沿y轴移动
), ArticleFig(id=1229121426251371408, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=EN, label=Tab. 6, caption=

Modal frequencies and errors of guideway structure with four sliders

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数实验值/Hz本文模型/Hz误差/%
1阶745.2718.83.54
2阶1 022.3952.56.83
3阶1 154.21 046.69.32
4阶1 403.91 240.711.62
), ArticleFig(id=1229121426343646101, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=CN, label=表6, caption=

四滑块导轨结构模态频率及误差

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数实验值/Hz本文模型/Hz误差/%
1阶745.2718.83.54
2阶1 022.3952.56.83
3阶1 154.21 046.69.32
4阶1 403.91 240.711.62
), ArticleFig(id=1229121426427532186, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=EN, label=Tab. 7, caption=

Modal frequencies and errors of ring welder

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数实验值/Hz理论值/Hz误差/%
1阶213.8226.6-5.97
2阶230.8242.7-5.16
3阶300.5333.8-11.08
4阶306.6329.2-7.37
5阶341.2361.2-3.10
), ArticleFig(id=1229121426536584099, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228805176614646006, language=CN, label=表7, caption=

环焊机模态频率及误差

, figureFileSmall=null, figureFileBig=null, tableContent=
阶数实验值/Hz理论值/Hz误差/%
1阶213.8226.6-5.97
2阶230.8242.7-5.16
3阶300.5333.8-11.08
4阶306.6329.2-7.37
5阶341.2361.2-3.10
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基于bushing单元的滚动直线导轨结合部动力学建模
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何秀权 1 , 雷声 1 , 毛宽民 2
振动工程学报 | 2025,38(4): 697-705
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振动工程学报 | 2025, 38(4): 697-705
基于bushing单元的滚动直线导轨结合部动力学建模
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何秀权1 , 雷声1 , 毛宽民2
作者信息
  • 1.中南民族大学计算机科学学院，湖北　武汉　430074
  • 2.华中科技大学机械科学与工程学院，湖北　武汉　430074

    • 何秀权（1984—），男，硕士，工程师。E-mail：

通讯作者:

雷声（1988—），男，博士，副教授。E-mail：
Dynamic modeling of rolling linear guideway joint based on bushing element
Xiuquan HE1 , Sheng LEI1 , Kuanmin MAO2
Affiliations
  • 1.School of Computer Science，South-Central Minzu University，Wuhan 430074，China
  • 2.School of Mechanical Science and Engineering，Huazhong University of Science and Technology，Wuhan 430074，China
出版时间: 2025-04-10 doi: 10.16385/j.cnki.issn.1004-4523.2025.04.004
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摘要
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根据滚动直线导轨副的结构特性，提出基于bushing单元的滚动直线导轨结合部动力学建模方法，并通过算例仿真计算和实物实验，验证了利用bushing单元对滚动直线导轨动力学特性建模的有效性。基于零件的结合部能显著影响整体结构的动力学特性的特点，采用子结构法与模型修正技术结合的方式，识别滚动直线导轨的bushing单元参数。通过构建哑铃状结构的仿真算例，对bushing单元参数进行仿真识别，以验证识别算法的准确性。以仿真算例的三维机械结构为基础，以含有单个滑块的哑铃状滚动直线导轨结构为实验对象，通过实物实验识别导轨的参数并验证模型的有效性。在以上仿真与实物实验的基础上，设计制造了含有4个滑块的滚动直线导轨机械结构，通过理论分析和模态实验对比，验证bushing单元建模的有效性和通用性。以专用轮毂环焊机的床身-滚动导轨移动平台结构为实验对象，进行工程应用验证。结果表明：采用bushing单元模拟滚动直线导轨滚动结合部的建模过程简单；相同模态振型的有限元分析与实验测试获得的前5阶模态频率对比表明，基于bushing单元的单滑块滚动直线导轨结构的固有频率误差不高于5%；基于bushing单元的四滑块滚动直线导轨结构固有频率误差不高于12%；基于bushing单元的环焊机床身滚动导轨移动平台结构的固有频率误差最高为11%。

动力学建模  /  参数识别  /  滚动直线导轨  /  导轨结合部  /  bushing单元

The bushing element is established for dynamic modeling of rolling linear guideway joints based on the movement characteristics of guideway. The effectiveness of the bushing element is verified by the numerical and experimental examples. Base on the fact that the guideway joint has significant influence on the dynamic performance of the whole structure，the model updating technique combined with the substructure method is proposed for parameter identification of bushing element. A simulation example of dumbbell structure is used to verify the effectiveness of the proposed parameter identification method. Based on the simulation example，a dumbbell structure with single slider rolling guideway is used for bushing element parameter identification and model verification. The effectiveness and universality of the bushing model is verified by a rolling linear guideway structure which contains four sliders. The engineering application of the bushing element is verified by the structure of rolling linear guideway moving platform of special ring welding machine. The results show that the bushing model is simple for application，the dynamic modeling error for single slider rolling linear guideway is within 5% and the error for four sliders rolling guideway system is within 12%，and the error of engineering structure of moving platform with four sliders is about 11%.

dynamic modelling  /  parameter identification  /  rolling linear guideway  /  guideway joint  /  bushing element
何秀权, 雷声, 毛宽民. 基于bushing单元的滚动直线导轨结合部动力学建模. 振动工程学报, 2025 , 38 (4) : 697 -705 . DOI: 10.16385/j.cnki.issn.1004-4523.2025.04.004
Xiuquan HE, Sheng LEI, Kuanmin MAO. Dynamic modeling of rolling linear guideway joint based on bushing element[J]. Journal of Vibration Engineering, 2025 , 38 (4) : 697 -705 . DOI: 10.16385/j.cnki.issn.1004-4523.2025.04.004
正文
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滚动直线导轨副作为常用的传动机构，广泛应用于机械系统中，是机械系统传动的核心功能部件。机床上出现的振动问题60%源于结合部，滚动直线导轨作为机床核心结合部，其动力学特性对整体机械系统的动态特性有着重要影响[1-2]，构建通用的滚动导轨直线结合部的动力学模型并获取准确的模型参数，是机床整机动态特性分析和结构优化设计的关键技术之一。常见的滚动直线导轨结合部模型有弹簧模型[3-7]、八节点六面体模型[8-9]和虚拟介质层模型[10-11]。基于弹簧模型的参数识别方法大多根据滚动直线导轨结合部的接触特性，采用Hertz接触理论进行导轨的动力学模型构建及参数识别。孙伟等[12]采用Hertz接触原理建立直线导轨的接触动力学模型，并以NSK公司LH45导轨为实验验证对象进行刚度的求解。田红亮等[13]基于赫兹点接触的椭圆接触区域计算原理，构建了导轨结合部的法向力学模型，并研究重载下的导轨结合部的接触特性及其变化规律[4]。这种基于接触理论的建模方法从导轨结合部的动力学特性形成的原理出发，建模精度较高，但由于导轨中滚动体的数目多，建模时常需对每个滚动体相对滚道间建立独立的弹簧单元，工作量大，不利于工程应用。为此，部分学者为降低建模工作量，采用基于等效弹簧的建模思路，用数个弹簧来模拟直线导轨结合部，以方便工程应用。蒋书运等[3]基于Hertz接触理论与弹性理论Boussinesq求解，推导出导轨结合部接触力及接触力矩之间的关系，建立了交叉滚柱直线导轨结合部五自由度静刚度模型，并采用数值迭代法求解出直线导轨的综合静刚度。王禹林等[14]设计了导轨副综合静刚度测试实验平台，通过偏心载荷的加载及变形量的测试换算，计算出了导轨5个方向的静刚度。
由于结合部对整体结构动力学特性有较大的影响，有学者采用基于动态特性测试的方法对导轨刚度参数进行识别，此类参数识别主要有基于模态参数的识别法和基于频响函数的识别法两大类。由于模态参数能反映结构的动态特性，因此基于模态参数的结合部参数识别的应用较为广泛，李磊等[15-16]采用半功率法识别出了导轨不同方向的刚度。然而，基于模态参数的识别方法其识别精度受结构影响较大，当整体结构模态未能反映结合部动态特性时，结合部参数对整体结构动态特性影响较小，参数识别结果可能出现不收敛的情况，采用此类方法尤其需注意整体结构的设计[17]。孙伟等[18]根据动刚度矩阵与频响函数互逆这一原理，提出了基于频响函数测试的导轨结合部参数识别方法，并以THK导轨为例，识别出了滑块与导轨之间的法向刚度。基于频响函数的参数识别方法通常需要求解高维超静定方程[19]，由于共振峰值附近的测试误差会显著放大[20]，而远离共振峰值处的频响函数值较小，频响函数的信噪比相对较低，因此，基于频响函数的参数识别容易受到测试噪声的影响[21]。在建模方面，等效弹簧的建模思路便于工程应用，但仅仅采用几个弹簧模型来模拟整个导轨结合部，忽略了结合部的耦合特性，建模精度会受到较大影响。毛宽民等[8]提出无质量的八节点六面体单元模型，该模型充分考虑了导轨接触面内的刚度耦合情况，并将导轨滑块移动方向的刚度设置为零，以模拟滑块运动方向的自由度；然后基于导轨结合部对整体结构的动力学性能有较大影响的特性，利用实测频响函数，采用最小二乘法识别导轨结合部八节点六面体模型的参数。杨勇等[22]在此模型理论的基础上进一步分析多导轨结合部与被连接件之间的耦合联系，建立了结合部组的等效动力学模型，并通过频响函数识别出了等效模型的参数。这种建模方法精度高，但模型参数过多，使用不方便。杨尧等[10]采用虚拟介质层模拟导轨结合部，这种模型使用方便，但忽略了滚动直线导轨的滑块沿着导轨方向可以自由滑动这一特性，这类模型的建模精度也不高。ANSYS单元库中的bushing单元[23]可以通过两个面定义接触，通过耦合方程将bushing单元的刚度分配到接触面内所有节点上，建立针对两个面间接触特性的力学模型，其工程应用十分方便。然而，鲜有研究将bushing单元应用于滚动导轨结合部动力学建模中。
本文从工程应用的角度出发，探索将bushing单元用于滚动直线导轨结合部动力学建模。首先根据滚动直线导轨结合部的连接特性，提出利用bushing单元建立滚动直线导轨结合部的动力学模型；以bushing单元的5个刚度参数模拟直线导轨的接触刚度；通过bushing单元的耦合特性，将刚度参数分配到接触面内的所有节点上。然后基于结合部能显著影响整体结构动力学性能这一特性，提出子结构法与模型修正相结合的参数识别方法，通过数值算例仿真验证参数识别方法的有效性。根据仿真算例的三维模型结构，设计加工出实验试件，并通过实物实验识别出滚动直线导轨结合部的参数，对比仿真识别的参数和实物实验识别出的参数，从而验证采用bushing单元对直线导轨动力学特性建模方法的合理性和准确性。本文研究为滚动直线导轨结合部动力学建模及模型的工程应用提供了一种途径。
1　动力学建模
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直线导轨结构主要由滚珠、导轨和滑块组成，其中导轨和滑块的配合面中均有一段沟槽，滚珠安装在沟槽之中。导轨滑块通过滚珠将滑块所受到的压力传到导轨上，滚动直线导轨的性能与沟槽形状密切相关。三维空间中的零部件具备x、y、z三个方向的平动及绕着这三个方向的转动。对于直线导轨而言，在预压力的作用下，滑块除了可以沿导轨轴向移动外，其余的5个运动均受到约束，整体结构具有5个刚度，其受力情况如图1（a）所示。图中，Fy和Fz分别为导轨受到的y和z方向的力，Mx、My和Mz分别为导轨受到的x、y和z方向的力矩。
ANSYS单元库中bushing单元的刚度特性如图1（b）所示。该单元与弹簧单元的最大不同在于弹簧单元只建立了弹簧两个节点之间的连接关系，单根弹簧无法表征实际接触面内各节点之间的接触情况。而bushing单元可以通过平衡约束方程，建立bushing单元刚度与单元作用区域内的所有节点之间的耦合关系，并通过这种耦合关系将bushing单元的刚度分配到接触面内的所有节点上，从而建立导轨与滑块两个相互作用面之间的接触耦合关系。
根据滚动直线导轨结合部整体结构的运动形态及受力特性，采用ANSYS中的bushing单元模拟结合面的接触特性：单元参数Kx、Ky、Kz分别为bushing单元沿着三个坐标轴的线性刚度；Tx、Ty、Tz分别为bushing单元绕着3个坐标轴的扭转刚度。为建模及应用方便，忽略导轨和滑块的沟槽及两者间的滚珠，将导轨与滑块的两个侧面简化为平面；同时考虑到导轨的实际受力面为滑块与导轨的接触面，因此将bushing单元的作用面大小设定为与滑块侧面相同。建模时，在导轨的两个外侧面与滑块的两个对应内侧面间分别建立bushing单元，整个滑块导轨结合部由两个bushing单元组成。基于bushing单元的滚动直线导轨结合部动力学模型及有限元建模情况如图2所示。
单个滑块导轨结合部由2个bushing单元组成，每个bushing单元包含3个沿轴方向的线性刚度及3个绕轴线的扭转刚度。由于导轨沿着x轴方向不受约束，沿着x轴方向的线性刚度定义为0。考虑到导轨的刚度与预载荷大小、承载情况、导轨分布均有关，定义bushing单元的参数为：
式中，F为导轨的预压力，以表征不同预压时的刚度；P为整体结构的外载荷，以表征外载荷对滚动直线导轨刚度的影响；N为导轨的类型，以表征单圆弧、双圆弧、类双圆弧及不同滚珠列数的影响。
采用bushing单元模拟直线导轨中滑块与导轨结合部的受力情况，建立基于bushing单元滚动直线导轨结合部动力学模型，包含Ky、Kz、Tx、Ty及Tz共5个未知参数。所建立的bushing单元模型可以直接从workbench的单元库中调用，其建模过程十分简单。在进行动力学分析时，系统根据导轨两个侧面相连实体部分的网格划分情况建立约束方程，将bushing单元的刚度分配到作用区域内的所有节点处，以进行相应的刚度分配及节点耦合，适应不同网格尺寸及分析精度要求。
2　参数识别方法
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根据所建立的直线导轨中滑块与导轨结合部的bushing单元模型，识别出5个刚度相关的参数是bushing单元模型参数识别的核心。本节提出bushing单元模型参数识别的方法思路：由于导轨结合部对系统的动力学参数有较大影响，为此可以设计出只包含导轨结合部特性未知、其他结构的特性均已知的直线导轨连接实验结构；将实验结构中的导轨结合部等效为一个参数待识别的子结构，测试整体实验结构的动力学特性参数；利用子结构法和模型修正技术，进行滚动直线导轨结合部bushing单元参数识别。
为了使整体结构的前5阶模态尽可能反映出导轨结合部的模态振型，需要弱化导轨结合部，以便更好地激发导轨结合部的模态。因此，构建的理论模型需要给滑块加一定的配重，同时导轨也需要安装在有一定重量的底座上。采用bushing单元连接导轨的两个侧面，整体理论模型的结构如图3所示。
在模型修正中，通常用相同振型下的固有频率衡量测试结构及修正结构的动态特性的相似性。因此，采用相同振型下的固有频率作为模型修正的最终目标，设置的参数识别控制条件为：
式中，和分别为系统的i阶理论固有频率和实验固有频率；m为参与修正的模态数目；ɛ为相同振型下固有频率误差允许范围；Xp为bushing单元识别参数，其中p为需要识别的参数数目。
针对含bushing单元的滚动直线导轨结合部模型，以相同振型下的模态频率为修正目标，构造bushing单元参数识别方程：
其中：
式中，A为bushing单元参数识别方程，其各项元素表示参与识别的各阶理论固有频率对bushing单元相关参数的灵敏度；b为相同振型下实验模态频率与理论频率的差值。
为验证基于子结构法和模型修正技术相结合的方法识别bushing单元参数的有效性，以表1中第一行给定值作为bushing单元参数的准确值，以此构建含导轨结合部的整体系统，通过理论分析获得此系统的模态参数，作为后续bushing单元模型参数识别的实验固有频率和实验振型。
根据基于子结构法的bushing单元参数识别思路，采用MATLAB与ANSYS相结合的方式，编写相应的参数识别程序，以表1中第二行初值作为参数识别的初始值，采用前5阶固有频率作为修正的目标，进行bushing单元的刚度识别，迭代过程如图4和5所示。
从图4和5反映的结果中可以看出：对于含bushing单元的理论模型，采用模型修正法，经数次迭代计算后即可识别出bushing单元的参数。以上数值仿真算例证明了采用模型修正法进行bushing单元的参数识别的有效性，也验证了所采用的机械结构可用于滚动直线导轨结合部bushing单元的参数识别，为第3节基于实验测试结果的bushing单元参数识别准确性提供了理论算例依据。
3　建模有效性验证
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为验证bushing单元模型的有效性，本文采用文献[24]中的实验结构及测试结果，用第2节提出的模型修正法，识别滚动直线导轨结合部bushing单元的参数。将bushing单元的建模结果与文献[24]中八节点模型的建模结果进行比较，通过在相同实验条件下模型精度的对比，验证bushing单元建模的有效性。以文献[24]中凯特精机LG45EA型的滚动直线导轨为例，实验试件的结构及尺寸如图6所示。
以文献[24]中结构的前5阶模态振型及模态频率为目标值，按照第2节提出的bushing单元参数方法进行参数识别。线性刚度Ky、Kz及扭转刚度Tx、Ty、Tz的修正过程及结果分别如图7和8所示。
通过图7和8可以看出，经过9次迭代之后，bushing单元参数识别结果趋于稳定，bushing单元刚度参数修正迭代稳定后结果如表2所示。
图9为采用双坐标轴表示的迭代过程中前3阶理论模态频率及误差的变化情况。图9中左侧坐标轴表示理论模态频率随迭代过程的变化情况，右侧坐标表示理论模态频率的误差随迭代过程的变化情况。根据图9所示的结果，经过数次迭代后，整体模态频率及误差趋于稳定。
为验证bushing单元模型的有效性，将表2中识别获得的bushing单元参数代入理论模型中，计算含滚动直线导轨结合部整体结构的理论模态，并将本文理论模型的结果与文献[24]中的结果进行对比。理论振型与实验振型对比如表3所示，相同振型下的模态频率的对比如表4所示。
由表4可知，本文提出的模型能反映结合部前5阶的模态振型，而文献[24]中的模型只给出了前4阶模态振型。在相同的模态振型下，本文提出的bushing单元模型理论模态固有频率与实验频率之间的误差均小于5%，且第2、3、5阶的理论模态频率与实验频率基本一致，该结果明显高于文献[24]中的八节点六面体模型的精度。这是由于bushing单元通过耦合，将刚度参数分配到实际作用面内的所有节点上，因此建模精度比较高；采用的实验试件充分激发了导轨结合部的前5阶模态，因此，噪声对识别过程及参数识别的精度影响也很小。以上结果证明了采用bushing单元进行滚动直线导轨结合部建模的有效性。
4　模型通用性验证
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滚动直线导轨广泛应用于机械传动结构中。为了验证所识别参数的通用性，设计一个含有4个滑块的滚动直线导轨实验平台，选用的导轨型号与第3节参数识别时所用的型号一致，均为凯特精机生产的LG45EA型滚动直线导轨。利用LMS系统测试移动平台的模态频率及振型。为模拟自由状态，需将整体结构悬挂。实验系统如图10所示。
用8个bushing单元模拟具有4个滑块的导轨滑块结合部，bushing单元的参数即为表2中所识别的参数。用workbench建立结构的有限元模型，并进行模态分析，比较理论分析及实验测试的结果。各阶模态振型和频率对比分别如表5和6所示。
从表6中可以看出，在振型相同的情况下，前4阶实验测试与理论分析的固有频率误差不超过12%。由于实验中采用的导轨型号和参数与第3节实验装置使用的完全一致，采用4个滑块连接结构的整体误差在可以接受的范围之内，说明建立的bushing单元模型具有通用性。
5　工程应用
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以专用轮毂环焊机的床身移动平台结构为研究对象，进一步验证bushing单元在实际工程结构上的应用。实验前，拆除包括电机、丝杠在内的可能对导轨结构产生影响的其他部件，仅保留含有4个滑块和2根导轨的LG45型滚动直线导轨副、床身及移动平台结构。为减少边界条件对结构的影响，本实验中利用绳带将整体结构悬挂用以模拟自由边界。用LMS锤击法进行模态测试。整体结构上布置168个测点，实验测试系统和测点布置分别如图11和12所示。
通过锤击法测得所有测点的频响函数后，进行模态分析获得整体结构的模态频率及振型。采用bushing单元模拟导轨滑块结合部，用workbench建立有限元模型进行模态分析。获得前5阶理论模态振型，为分析实验振型及模态振型之间的对应关系，将实验模态振型导出，根据实验测点布置情况，从workbench理论分析结果中导出相应测点的理论模态振型，并计算前5阶实验测试模态振型和理论分析模态振型的MAC值，结果如图13所示。
通过MAC值分析对比发现，前5阶模态的MAC值的峰值基本都接近0.7，说明模态振型基本匹配。其中，第3、4阶的实验模态振型与理论模态振型次序不同，其原因在于第3、4阶模态频率比较接近，由于模态频率有一定误差，造成振型次序变化。以实验测试模态振型结果为基准，在相同的模态振型下，各阶模态频率理论值与实测值的对比及误差如表7所示。
实验结果表明，采用bushing单元建立滚动导轨结合部动力学模型，轮毂环焊机床身移动平台的整体结构除第3阶模态频率误差接近11%之外，其余4阶模态频率误差均在8%以内。相同模态振型下各阶模态频率的误差较小，说明建立的导轨结合部bushing单元模型可用于工程分析。
6　结论
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（1）提出了基于bushing单元的滚动直线导轨结合部动力学建模方法，以bushing单元5个刚度参数表征滚动直线导轨结合部的接触刚度，并通过bushing单元节点及导轨接触面间的耦合特性，表征导轨结合部内的刚度参数分配。
（2）提出了基于子结构法和模型修正技术相结合的bushing单元刚度参数辨识方法，并通过仿真算例，验证了所提参数识别方法用于导轨结合部bushing单元参数识别的准确性。
（3）根据含滚动直线导轨结合部的实验试件识别bushing单元参数，结果表明采用bushing单元模拟滚动直线导轨结合部时，前5阶模态频响的最大误差小于5%，验证了滚动直线导轨结合部bushing单元建模的有效性。
（4）制造了含4个滑块的滚动直线导轨传动机构，以识别bushing单元参数模拟滚动直线导轨结合部，实验测试结果表明，相同模态振型下的频率误差小于12%，验证了滚动直线导轨结合部bushing单元建模的通用性。
（5）以含4个滑块的轮毂环焊机的床身移动平台结构为实验对象，相同振型下前5阶模态频率误差最大在11%左右，验证了建立的滚动直线导轨结合部bushing单元模型在工程结构中的应用。
基金
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  • 国家自然科学基金资助项目(52105135)
  • 湖北省自然科学基金资助项目(2020CFB174)
文献
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2025年第38卷第4期
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doi: 10.16385/j.cnki.issn.1004-4523.2025.04.004
  • 接收时间：2023-08-09
  • 首发时间：2026-02-12
  • 出版时间：2025-04-10
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  • 收稿日期：2023-08-09
  • 修回日期：2023-09-21
基金
国家自然科学基金资助项目(52105135)
湖北省自然科学基金资助项目(2020CFB174)
作者信息
    1.中南民族大学计算机科学学院，湖北　武汉　430074
    2.华中科技大学机械科学与工程学院，湖北　武汉　430074

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雷声（1988—），男，博士，副教授。E-mail：
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https://castjournals.cast.org.cn/joweb/zdgcxb/CN/10.16385/j.cnki.issn.1004-4523.2025.04.004
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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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