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Article(id=1241446433648341783, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241446328396476740, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.07.019, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1701014400000, receivedDateStr=2023-11-27, revisedDate=1704297600000, revisedDateStr=2024-01-04, acceptedDate=null, acceptedDateStr=null, onlineDate=1773913494741, onlineDateStr=2026-03-19, pubDate=1752508800000, pubDateStr=2025-07-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773913494741, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773913494741, creator=13701087609, updateTime=1773913494741, 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=152, endPage=158, ext={EN=ArticleExt(id=1241446433908388632, articleId=1241446433648341783, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Study on the static model of composite metal rubber, columnId=1241446430376776595, journalTitle=Journal of Mechanical Strength, columnName=·Design·Calculation·, runingTitle=null, highlight=null, articleAbstract=

A theoretical model of composite metal rubber (C-MR) was established on the basis of static mechanical test. A novel preparation process was used to prepare C-MR, which was subjected to static mechanical tests. The mechanical model of C-MR was established by combining the static mechanical models of wove-metal rubber (W-MR) and tangled-metal rubber (T-MR), and the effects of different knitting and winding ratios on the mechanical properties of C-MR were investigated. The comparison between the test data and the theoretical model shows that the theoretical model can predict the mechanical properties of C-MR effectively. The results show that the knitting and winding ratio has a significant effect on the mechanical properties of C-MR, and the larger the knitting and winding ratio is, the larger the stiffness and damping properties of C-MR are. The conclusion can provide a theoretical support for the preparation and application of C-MR.

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NI Weiyu, E-mail：
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在静态力学试验的基础上，建立一种复合型金属橡胶（Composite-Metal Rubber, C-MR）的理论模型。采用一种新型制备工艺制备C-MR，对其进行静态力学试验。结合编织型金属橡胶（Wove-Metal Rubber, W-MR）和缠绕型金属橡胶（Tangled-Metal Rubber, T-MR）的静力学模型，建立了C-MR的力学模型，并研究了不同编缠比对C-MR力学特性的影响。试验数据和理论模型对比结果表明，该理论模型能够有效预测C-MR的力学特性。并且发现，编缠比对C-MR的力学特性有显著影响，编缠比越大，C-MR的刚度和阻尼特性越大。研究结论可为C-MR的制备和应用提供理论支持。

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倪维宇，男，1986年生，江苏兴化人，硕士，高级实验师；主要研究方向为机械结构动力学优化设计与测试技术；E-mail：。
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余慧杰，男，1978年生，福建南靖人，博士，教授，硕士研究生导师；主要研究方向为电子设备可靠性设计、隔振系统设计；E-mail：。

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余慧杰，男，1978年生，福建南靖人，博士，教授，硕士研究生导师；主要研究方向为电子设备可靠性设计、隔振系统设计；E-mail：。

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余慧杰，男，1978年生，福建南靖人，博士，教授，硕士研究生导师；主要研究方向为电子设备可靠性设计、隔振系统设计；E-mail：。

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Journal of Mechanical Strength，2023，45（2）：331-340.（In Chinese）, articleTitle=Experimental investigation on the tri-directional quasi-static of pot-shaped metal rubber, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1241446440921265051, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, xref=null, ext=[AuthorCompanyExt(id=1241446440929653660, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, companyId=1241446440921265051, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China), AuthorCompanyExt(id=1241446440933847965, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, companyId=1241446440921265051, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, 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Parameters of C-MR specimen with different knitting and winding ratios

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编缠比
Knitting and winding ratio CMR		丝径
Wire diameter/ mm		外径
Outer diameter
D/mm		相对密度
Relative density
0（W-MR）dw = 0.08—0.15
0.4、0.5、0.6dT = 0.08
dw = 0.08		0.80.15
1（T-MR）dT = 0.080.80.15
), ArticleFig(id=1241446447460184106, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, language=CN, label=表1, caption=

不同编缠比C-MR试件参数

, figureFileSmall=null, figureFileBig=null, tableContent=
编缠比
Knitting and winding ratio CMR		丝径
Wire diameter/ mm		外径
Outer diameter
D/mm		相对密度
Relative density
0（W-MR）dw = 0.08—0.15
0.4、0.5、0.6dT = 0.08
dw = 0.08		0.80.15
1（T-MR）dT = 0.080.80.15
), ArticleFig(id=1241446447535681581, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, language=EN, label=Tab. 2, caption=

Process parameters of C-MR specimen for parameter identification

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试件编号
Specimen number		编缠比
Knitting and winding ratio CMR		丝径
Wire diameter/ mm		外径
Outer diameter
D/mm		相对密度
Relative density
10（W-MR）dw=0.08—0.15
2、3、40.4、0.5、0.6dT=0.08
dw=0.08		0.80.15
51（T-MR）dT=0.080.80.15
), ArticleFig(id=1241446447627956274, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, language=CN, label=表2, caption=

用于参数识别的C-MR试件工艺参数

, figureFileSmall=null, figureFileBig=null, tableContent=
试件编号
Specimen number		编缠比
Knitting and winding ratio CMR		丝径
Wire diameter/ mm		外径
Outer diameter
D/mm		相对密度
Relative density
10（W-MR）dw=0.08—0.15
2、3、40.4、0.5、0.6dT=0.08
dw=0.08		0.80.15
51（T-MR）dT=0.080.80.15
), ArticleFig(id=1241446447703453750, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, language=EN, label=Tab. 3, caption=

Fitting results of C-MR specimen

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试件编号
Specimen number		CMRc1c2c3R2
100.566 0-0.503 00.159 20.996 8
20.42.006 2-1.945 50.626 40.994 1
30.53.797 5-3.533 61.158 10.998 0
40.65.606 5-5.769 11.952 20.997 1
5112.502 2-10.071 53.251 70.998 7
), ArticleFig(id=1241446447808311356, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, language=CN, label=表3, caption=

C-MR试件拟合结果

, figureFileSmall=null, figureFileBig=null, tableContent=
试件编号
Specimen number		CMRc1c2c3R2
100.566 0-0.503 00.159 20.996 8
20.42.006 2-1.945 50.626 40.994 1
30.53.797 5-3.533 61.158 10.998 0
40.65.606 5-5.769 11.952 20.997 1
5112.502 2-10.071 53.251 70.998 7
), ArticleFig(id=1241446447892197441, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, language=EN, label=Tab. 4, caption=

Process parameters of C-MR specimen for validation

, figureFileSmall=null, figureFileBig=null, tableContent=
试件编号
Specimen number		编缠比
Knitting and winding ratio CMR		丝径
Wire diameter/mm		外径
Outer diameter
D/mm		相对密度
Relative density
60.2dT = 0.1
dw = 0.1		0.80.15
70.9dT = 0.1
dw = 0.1		2.00.15
), ArticleFig(id=1241446447984472132, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, language=CN, label=表4, caption=

用于验证的C-MR试件工艺参数

, figureFileSmall=null, figureFileBig=null, tableContent=
试件编号
Specimen number		编缠比
Knitting and winding ratio CMR		丝径
Wire diameter/mm		外径
Outer diameter
D/mm		相对密度
Relative density
60.2dT = 0.1
dw = 0.1		0.80.15
70.9dT = 0.1
dw = 0.1		2.00.15
), ArticleFig(id=1241446448097718345, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, language=EN, label=Tab. 5, caption=

Results of the residual analysis

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试件编号
Specimen number		CMRRRMSER2
60.22.943 40.991 1
70.94.776 90.997 3
), ArticleFig(id=1241446448169021519, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446433648341783, language=CN, label=表5, caption=

残差分析结果

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试件编号
Specimen number		CMRRRMSER2
60.22.943 40.991 1
70.94.776 90.997 3
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复合型金属橡胶的静力学模型研究
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余慧杰 , 侯伟平 , 陈成 , 倪维宇
机械强度 | ·设计·计算· 2025,47(7): 152-158
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机械强度 | ·设计·计算· 2025, 47(7): 152-158
复合型金属橡胶的静力学模型研究
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余慧杰 , 侯伟平, 陈成, 倪维宇
作者信息
  • 上海理工大学 机械工程学院，上海　200093

    • 余慧杰，男，1978年生，福建南靖人，博士，教授，硕士研究生导师；主要研究方向为电子设备可靠性设计、隔振系统设计；E-mail：。

通讯作者:

倪维宇，男，1986年生，江苏兴化人，硕士，高级实验师；主要研究方向为机械结构动力学优化设计与测试技术；E-mail：。
Study on the static model of composite metal rubber
Huijie YU , Weiping HOU, Cheng CHEN, Weiyu NI
Affiliations
  • School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
出版时间: 2025-07-15 doi: 10.16579/j.issn.1001.9669.2025.07.019
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摘要
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在静态力学试验的基础上，建立一种复合型金属橡胶（Composite-Metal Rubber, C-MR）的理论模型。采用一种新型制备工艺制备C-MR，对其进行静态力学试验。结合编织型金属橡胶（Wove-Metal Rubber, W-MR）和缠绕型金属橡胶（Tangled-Metal Rubber, T-MR）的静力学模型，建立了C-MR的力学模型，并研究了不同编缠比对C-MR力学特性的影响。试验数据和理论模型对比结果表明，该理论模型能够有效预测C-MR的力学特性。并且发现，编缠比对C-MR的力学特性有显著影响，编缠比越大，C-MR的刚度和阻尼特性越大。研究结论可为C-MR的制备和应用提供理论支持。

复合型金属橡胶  /  静态力学试验  /  力学特性  /  力学模型

A theoretical model of composite metal rubber (C-MR) was established on the basis of static mechanical test. A novel preparation process was used to prepare C-MR, which was subjected to static mechanical tests. The mechanical model of C-MR was established by combining the static mechanical models of wove-metal rubber (W-MR) and tangled-metal rubber (T-MR), and the effects of different knitting and winding ratios on the mechanical properties of C-MR were investigated. The comparison between the test data and the theoretical model shows that the theoretical model can predict the mechanical properties of C-MR effectively. The results show that the knitting and winding ratio has a significant effect on the mechanical properties of C-MR, and the larger the knitting and winding ratio is, the larger the stiffness and damping properties of C-MR are. The conclusion can provide a theoretical support for the preparation and application of C-MR.

Composite metal rubber  /  Static mechanical test  /  Mechanical property  /  Mechanical model
余慧杰, 侯伟平, 陈成, 倪维宇. 复合型金属橡胶的静力学模型研究. 机械强度, 2025 , 47 (7) : 152 -158 . DOI: 10.16579/j.issn.1001.9669.2025.07.019
Huijie YU, Weiping HOU, Cheng CHEN, Weiyu NI. Study on the static model of composite metal rubber[J]. Journal of Mechanical Strength, 2025 , 47 (7) : 152 -158 . DOI: 10.16579/j.issn.1001.9669.2025.07.019
正文
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0　引言
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金属橡胶是一种兼具刚度与阻尼且具有特殊力学性能的材料[1]，其力学性能受到金属丝种类和金属丝内部微观结构的影响，其内部微观结构主要由制备工艺决定。以往的研究将这类材料归为同一种结构，但是根据制备工艺的不同，金属橡胶又可以分为缠绕型金属橡胶（Tangled-Metal Rubber, T-MR）与编织型金属橡胶（Wove-Metal Rubber, W-MR）。
过去很多学者对金属橡胶的耗能机制[2]、力学模型[3]、力学性能以及影响参数[4]进行了广泛的研究。彭威等[5]从微弹簧的径向与轴向变形机制出发，建立的本构模型具有合理的微观基础。卢成壮等[6]基于金属橡胶内部微元螺旋卷结构建立力学模型，通过静态加载试验发现螺旋卷之间的接触状态和数量是影响金属橡胶刚度和阻尼的主要因素。李拓等[7]通过对编织-嵌槽型金属橡胶的相关结构进行简化并建立力学模型，试验表明该模型可以很好地表征编织-嵌槽型金属橡胶的力学行为；李拓等[8]通过静态压缩试验对比编织-嵌槽型金属橡胶与普通金属橡胶的力学性能，发现编织-嵌槽型金属橡胶的力学性能更好。对T-MR和W-MR的2种制备工艺的分析表明，不同的制备工艺其内部的微观结构存在显著差异，因此，其力学性能也可能不同。以往的研究只对其中一种制备工艺制备而成的金属橡胶成品进行静力学研究，并没有综合考虑结合T-MR和W-MR的力学特性研究复合型金属橡胶（Composite-Metal Rubber, C-MR）的力学特性。基于此，以微元弹簧模型和单元网格模型为基础，结合空心圆柱形金属橡胶静态压缩过程特点，建立C-MR的准静态压缩力学模型，通过静态测试试验分析并验证本构模型。
1　C-MR准静态压缩力学模型
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金属橡胶的微观结构与制备工艺有关。T-MR由连续不断的螺旋卷互相勾连叠加组成，且螺旋卷的节距固定，内部空隙均匀分布，从微观结构看可视为多段微元弹簧的串联与并联［图1（a）］，可将单个微元弹簧［图1（b）］视为金属橡胶的基本组成单元[9]。螺旋卷的丝径和外径即是微元弹簧的丝径和中径，相对密度则反映了金属橡胶中微元弹簧的数量。在静态加载中，通过微元弹簧彼此的滑移接触产生的干摩擦，消耗大量外部能量从而达到阻尼耗能的作用。
W-MR通过筒布卷叠成毛坯后压制成型，其成型面一般由筒布的侧边形成，故W-MR的内部结构一般为垂直于成型面横向排布的网格单元［图2（a）］[10-11]。而在受到载荷时，W-MR内部由金属丝组成的网格可以分为2种情况：一种是由金属丝之间勾连而形成的横向梁单元，该单元在W-MR受到垂直于成型面的载荷时并不会产生变形，上、下层梁单元之间的距离因变形而减小；另一种是由单金属丝弯曲形成的横向U形单元，该单元在W-MR受到垂直于成型面的载荷时其U形底部不变形，而两个U形接头处由于内部的轴向力很小，发生了弯曲变形进而带动上、下层的横向梁单元彼此靠近。可将W-MR的内部结构进行简化，变为单纯由横向梁单元与横向V形单元组成的单元网格结构［图2（b）］。
余慧杰等[12]在现有金属橡胶力学模型的基础上，根据弹簧理论推导出金属橡胶载荷-位移关系式。经过大量试验和理论分析，采用三次多项式对金属橡胶材料的力与位移关系式进行表达可以得到非常精确的结果，因此最后建立的金属橡胶微元弹簧模型[13]为
式中，KT为T-MR微元弹簧的刚度；G为弹簧的剪切模量；d为微元弹簧丝径；D为微元弹簧中径（螺旋卷外径）；ρˉ为金属橡胶的相对密度；S、H分别为金属橡胶的成型面面积、成型面高度；FT为T-MR微元弹簧的载荷；c1、c2、c3均为待定系数，可通过试验数据识别得到；x为金属橡胶的整体位移。
W-MR的内部结构一般为垂直于成型面横向排布的网格单元[14]。YANG等[15]根据W-MR内部每层单元网格都是并联的关系，建立的W-MR静力学模型为
式中，kx为W-MR每一层的刚度；L为金属丝筒布长度；z为单元网格的横向宽度；E为金属丝材料的弹性模量；l为单个V形单元的一半边长度；θ为V形单元的V形角度。实际制备过程中，考虑到金属丝筒布的宽度为HW，单元网格的高度为h = 2lsin( θ 2 )，纵向的每一层之间彼此串联，故W-MR的总刚度KW为
式（3）中的刚度为定值，没有体现出W-MR整体受载时大变形的非线性刚度变化，加入高次项与待定系数进行高次函数修正，修正后的载荷FW与位移表达式为
金属丝筒布在编织时因为编织的物理特性，筒布的径密度不变即单元网格的横向宽度z不变，L × HW和z的比值固定，且与金属橡胶的相对密度成正比，A为两者之间的比例系数。
复合型金属橡胶的宏观结构可以看成是由等效单元多行、多列分别阵列而成的，并且等效单元之间通过行内并联的方式结合在一起，因此C-MR总体结构可以视为T-MR与W-MR互相并联[16]。其工艺参数除了金属丝丝径、螺旋卷外径与相对密度之外，复合型金属橡胶内部螺旋卷质量和整个复合型金属橡胶质量的比值，即编缠比CMR对其力学特性也会有影响，即
式中，mT、mW分别为复合型金属橡胶内部螺旋卷和外部编织网的质量；mC为复合型金属橡胶的质量。
引入编缠比系数后，T-MR的刚度为
式中，dT为T-MR的丝径。则W-MR的刚度为
式中，dW为W-MR的丝径。
如图3所示，C-MR可以视为由2个不同外形尺寸的T-MR和W-MR互相并联嵌套构成，则整体刚度为两者刚度的叠加，把式（6）、式（7）相加，得到C-MR的刚度系数KC为
通过加入编缠比对式（8）进行修正，且由于C-MR同样具有鲜明的非线性刚度特性，将其通过高次多项式进行表示。故C-MR的静态本构模型[17]为
当式（9）中的CMR为0时，则得到
此时，CMR转化为W-MR的编缠比。当CMR = 1时得到
此时，CMR转化为T-MR的编缠比。
2　金属橡胶材料试件制备与试验
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为研究不同的制备工艺对金属橡胶的压缩力学性能的影响，采用304H不锈钢（07Cr19Ni10）作为金属橡胶的材料，与普通304不锈钢相比，其含碳量更高，机械性能更优越。总体的制备工艺流程如图4所示。
C-MR的制备工艺流程可以分为以下几个步骤：①将一定量的金属丝分别加工成长度合适且连续均匀的螺旋卷和筒状网布；②如制备T-MR，将螺旋卷绕制成毛坯，作为C-MR的基底；③在绕制的C-MR基底上，用金属丝筒网布进行覆盖和卷叠，使其包裹住内部的基底成为一个整体的毛坯；④将整体毛坯放入模具中进行冲压成型。
2.1　试验方法
本文采用CMT5105型微机控制电子万能试验机对制备的金属橡胶进行静态压缩试验，所制备的金属橡胶外形尺寸为ϕ10 mm×ϕ5 mm×8.5 mm。试验机通过上、下夹手分别夹紧夹具的上、下夹柱，上夹手固定，下夹手可沿上、下方向缓速移动，通过夹具对金属橡胶施加静态载荷并读取反馈数据至控制程序。控制方法采用等速位移力控制，在足够缓慢的加载位移（0.05 mm/min）下，载荷可视为没有冲击的静态加载。金属橡胶的静态力学试验如图5所示。
2.2　复合型金属橡胶的力学特性对比
表1所列为本次制备的所有C-MR试件的参数。对制备的C-MR试件进行静态加载试验，得到图6（a）所示的加载-卸载曲线。由图6（a）可以看出，随着编缠比增大，曲线整体斜率增大，逐渐向非线性刚度大的方向偏移，并且加载过程中的硬特性阶段也随着编缠比的增大越来越明显。把CMR=0、CMR=1与其他封闭曲线做对比，结果表明，不同制造工艺的金属橡胶具有的耗能特性也不同。
由图6（b）可以看出，在相同加载位移下编缠比越大的C-MR试件刚度越大。当加载位移小于2 mm时，刚度曲线均较为平缓，此阶段金属橡胶内部金属丝间隙逐渐减小，通过金属丝之间的滑移做功消耗振动能量，此阶段为软特性阶段；而在加载位移超过2 mm时，刚度明显增大，曲线的斜率开始快速增加，此阶段金属橡胶内部从滑移状态变为挤压状态，金属丝之间的间隙已经非常小，宏观表现为金属橡胶变“硬”，此阶段为硬特性阶段，且编缠比越大的C-MR试件呈现的硬特性现象越明显。图6（c）表明，在相同相对密度下，随着编缠比增大，能量耗散系数也随之增大。
图6体现了编缠比对金属橡胶静力学特性的影响。由图6可以看出，随着编缠比逐渐增大，缠绕型金属橡胶结构的占比增多，金属橡胶的静刚度和能量耗散系数都逐渐增大。除此之外，同样体现了在工艺参数相同的情况下，3种不同方法制备的金属橡胶之间静力学特性的差异[18]。从编缠比CMR=0的W-MR，到编缠比逐渐增加，直至CMR=1的T-MR，金属橡胶的刚度与能量耗散系数都逐渐增大。
从金属橡胶耗能原理[19]分析可知，在T-MR内部微元弹簧串联并联，在软特性阶段，微元弹簧之间产生挤压、摩擦与变形来消耗受到的载荷能量，为线接触；W-MR内部为单元网格的层叠和嵌合，在软特性阶段，网格之间先正交滑动，后随着加载位移的增大，网格之间角度减小转为挤压与摩擦来消耗受到的载荷能量，多为网格线圈之间的点接触。与W-MR相比，T-MR之间的线接触有更大的接触面积，能更快进入硬特性阶段，从而可以消耗更多的能量。
3　参数识别与验证
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3.1　参数识别
使用表2中5种不同编缠比的C-MR试件静态加载数据用于参数识别，得到结果如图7所示。
通过这5组试验数据的参数识别，得到拟合的待定系数c1、c2、c3，其值与编缠比CMR之间的对应关系如表3所示。由图7与表3中的均方根误差值可以看出，该模型对单个C-MR试件的拟合结果较为准确。通过表3可拟合求得由编缠比表示c1、c2、c3的多项式级数。
将式（12）代入式（9）中即可得到C-MR力学模型为
3.2　对比验证
为验证本文提出的C-MR静力学模型具有泛用性，分别制备了编缠比CMR为0.2、0.9的试件，其工艺参数如表4所示，分别进行静态加载试验并将相关工艺参数代入式（9），得到C-MR模型理论值与试验值对比，其结果如图8所示。
对理论预测值与试验值进行残差分析，结果如表5所示。由表5可知，两者的均方根误差（Root Mean Square Error，RMSE）都较小，且模型对于2个试件的决定系数R2都接近1，表明由该C-MR力学模型得到的理论值与试验得到的实际值较为吻合。这说明本文提出的力学模型能够较准确地描述C-MR的力学特性，其中包含了C-MR的各参数，如编缠比、丝径、外径、相对密度、金属橡胶的材料属性和外形尺寸等，参数较为全面，且能直观地反映出各参数与C-MR静刚度特性之间的定量关系。因此，本文提出的力学模型可以很好地反映C-MR的静态力学性能。
4　结论
收起
本文结合T-MR和W-MR的制备工艺，开发了一种新的制备工艺制备复合型金属橡胶C-MR。研究了在相同相对密度下、不同编缠比的C-MR的力学性能。根据静态测试结果，对C-MR的静力学模型进行了参数识别与试验验证。得到主要结论如下：
1）其他工艺参数相同的情况下，复合型金属橡胶C-MR的编缠比与整体的刚度和能量耗散系数成正相关。对于本文开发的复合型金属橡胶C-MR，可通过调节编缠比，得到适合各种工况的刚度、阻尼。在相对密度不变，即制备金属橡胶的材料用量不变的情况下，扩大了金属橡胶的设计范围，对提高金属橡胶材料与构件设计具有指导作用，使金属橡胶能够更好地应用于实际工程。
2）基于微元弹簧模型和单元网格模型，建立了C-MR的准静态压缩力学模型。对比试验数据与拟合值发现，两者拟合度较好，这说明该模型可以较准确地描述受静态载荷时C-MR的准静态压缩力学特性。
文献
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2025年第47卷第7期
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doi: 10.16579/j.issn.1001.9669.2025.07.019
  • 接收时间：2023-11-27
  • 首发时间：2026-03-19
  • 出版时间：2025-07-15
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  • 收稿日期：2023-11-27
  • 修回日期：2024-01-04
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    上海理工大学 机械工程学院，上海　200093

通讯作者:

倪维宇，男，1986年生，江苏兴化人，硕士，高级实验师；主要研究方向为机械结构动力学优化设计与测试技术；E-mail：。
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2种不同金属材料的力学参数
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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
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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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