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Article(id=1241786733579276304, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241786727631754095, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2025.0112, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1692547200000, receivedDateStr=2023-08-21, revisedDate=1698681600000, revisedDateStr=2023-10-31, acceptedDate=null, acceptedDateStr=null, onlineDate=1773994628566, onlineDateStr=2026-03-20, pubDate=1740672000000, pubDateStr=2025-02-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773994628566, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773994628566, creator=13701087609, updateTime=1773994628566, updator=13701087609, issue=Issue{id=1241786727631754095, tenantId=1146029695717560320, journalId=1241701559352995854, year='2025', volume='45', issue='1', pageStart='1', pageEnd='235', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773994627149, creator=13701087609, updateTime=1773996954801, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241796490583146988, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241786727631754095, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241796490583146989, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241786727631754095, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=113, endPage=120, ext={EN=ArticleExt(id=1241786733856100384, articleId=1241786733579276304, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Design and application of a new type of steel spring floating plate vibration isolation foundation platform, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Environmental vibration is an important factor that affects the normal operation of various precision instruments and equipment. To solve the problem that the environmental vibration exceeds the vibration limit for the normal operation of equipment, the design of steel spring vibration isolation base is investigated. Through experimental verification and calculation analysis, the relationship between the vertical and horizontal stiffness of steel spring is derived, and the fuzzy problem of horizontal stiffness of steel spring is solved. A novel steel spring floating slab vibration isolation base is designed based on the requirements. The finite element method is utilized to study the vibration reduction and isolation effects of the pedestal under different steel spring stiffnesses. The deformation of the pedestal above the equipment with uneven mass distribution, the deformation of the pedestal with moving parts, and the vibration level of the pedestal are analyzed respectively. The analysis results show that the new steel spring floating slab vibration isolation base exhibits excellent horizontal and vertical vibration isolation effects. When the natural frequency of the base is 4.2 Hz, the maximum vibration reduction efficiency for the environmental vibration above 12 Hz can exceed 90%. The equipment with small moving parts on the base also demonstrates good stability. When the 50 kg moving parts move from one end of the base to the other, the vertical deformation of the base is less than 800 μm. When the disturbance force generated by equipment vibration is less than 1.5 kN, the base can still maintain the vibration level of VC-C. The research results can provide valuable references for the vibration isolation design of equipment in similar industrial plants.

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环境振动是影响各类精密仪器设备正常运转的重要因素。针对环境振动超出设备正常运转振动限值问题，开展了钢弹簧隔振基台的设计研究。通过试验验证及计算分析推导出钢弹簧竖向刚度与水平刚度的关系式，解决了钢弹簧水平刚度取值模糊问题；根据需求设计了一种全新钢弹簧浮筑板隔振基台；利用有限元方法研究了该基台在不同钢弹簧刚度下的减隔振效果，分别分析了上方设备质量分布不均匀时基台的变形情况、存在运动部件时基台变形情况以及台面振动水平。结果表明：新型钢弹簧浮筑板隔振基台在水平向和竖向均具有良好的隔振效果，当基台固有频率为4.2 Hz时，对12 Hz以上环境振动的最大减振效率可达90%以上；对于基台上存在小件运动部件的设备也表现出良好的稳定性，50 kg运动部件从基台一端运行到另一端时，基台竖直变形均小于800 μm，且当设备自身振动产生的扰力<1.5 kN时，基台仍能保持VC-C的振动水平。研究结果可为类似工业厂房中设备的隔振设计提供参考。

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兰日清（1977—），男，正高级工程师，博士，主要从事工程振动控制技术研究。E-mail：
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梁新奇（1997—），男，硕士研究生，主要从事工程结构振动控制技术研究。E-mail：

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梁新奇（1997—），男，硕士研究生，主要从事工程结构振动控制技术研究。E-mail：

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Test results of horizontal stiffness of steel springs

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编号压缩0 mm压缩5 mm压缩10 mm压缩15 mm压缩20 mm压缩25 mm
0127.6328.7568.31129.25209.99212.15
0259.5561.83143.91277.63447.72447.74
03152.95151.05361.48658.411084.961086.01
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钢弹簧水平刚度测试结果

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编号压缩0 mm压缩5 mm压缩10 mm压缩15 mm压缩20 mm压缩25 mm
0127.6328.7568.31129.25209.99212.15
0259.5561.83143.91277.63447.72447.74
03152.95151.05361.48658.411084.961086.01
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List of frequency analysis working conditions

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工况理论频率/Hz竖向刚度/（N/mm）水平刚度/（N/mm）模拟频率/Hz误差/%工况理论频率/Hz竖向刚度/（N/mm）水平刚度/（N/mm）模拟频率/Hz误差/%
13.0261208.82.942.0065.5880206.85.41.67
23.5356284.83.461.1476.01047195.05.91.85
34.0465286.93.931.7586.51229185.76.381.86
44.5589243.44.421.7897.01426147.46.871.86
55.0727222.44.911.80107.51637163.77.361.87
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频率分析工况一览表

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工况理论频率/Hz竖向刚度/（N/mm）水平刚度/（N/mm）模拟频率/Hz误差/%工况理论频率/Hz竖向刚度/（N/mm）水平刚度/（N/mm）模拟频率/Hz误差/%
13.0261208.82.942.0065.5880206.85.41.67
23.5356284.83.461.1476.01047195.05.91.85
34.0465286.93.931.7586.51229185.76.381.86
44.5589243.44.421.7897.01426147.46.871.86
55.0727222.44.911.80107.51637163.77.361.87
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新型钢弹簧浮筑板隔振基台设计与应用
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梁新奇 1, 2 , 兰日清 1, 2 , 韩蓬勃 2 , 汪志昊 1 , 杨程 1, 2
地震工程与工程振动 | 研究论文 2025,45(1): 113-120
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地震工程与工程振动 | 研究论文 2025, 45(1): 113-120
新型钢弹簧浮筑板隔振基台设计与应用
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梁新奇1, 2 , 兰日清1, 2 , 韩蓬勃2, 汪志昊1, 杨程1, 2
作者信息
  • 1.华北水利水电大学 土木与交通学院，河南 郑州 450045
  • 2.国机集团科学技术研究院有限公司，国机集团工程振动控制技术研究中心，北京 100080

    • 梁新奇（1997—），男，硕士研究生，主要从事工程结构振动控制技术研究。E-mail：

通讯作者:

兰日清（1977—），男，正高级工程师，博士，主要从事工程振动控制技术研究。E-mail：
Design and application of a new type of steel spring floating plate vibration isolation foundation platform
Xinqi LIANG1, 2 , Riqing LAN1, 2 , Pengbo HAN2, Zhihao WANG1, Cheng YANG1, 2
Affiliations
  • 1.School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou 450045, China
  • 2.SINOMACH Engineering Vibration Control Technology Re-search Center, SINOMACH Academy of Science and Technology Co., Ltd., Beijing 100080, China
出版时间: 2025-02-28 doi: 10.13197/j.eeed.2025.0112
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摘要
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环境振动是影响各类精密仪器设备正常运转的重要因素。针对环境振动超出设备正常运转振动限值问题，开展了钢弹簧隔振基台的设计研究。通过试验验证及计算分析推导出钢弹簧竖向刚度与水平刚度的关系式，解决了钢弹簧水平刚度取值模糊问题；根据需求设计了一种全新钢弹簧浮筑板隔振基台；利用有限元方法研究了该基台在不同钢弹簧刚度下的减隔振效果，分别分析了上方设备质量分布不均匀时基台的变形情况、存在运动部件时基台变形情况以及台面振动水平。结果表明：新型钢弹簧浮筑板隔振基台在水平向和竖向均具有良好的隔振效果，当基台固有频率为4.2 Hz时，对12 Hz以上环境振动的最大减振效率可达90%以上；对于基台上存在小件运动部件的设备也表现出良好的稳定性，50 kg运动部件从基台一端运行到另一端时，基台竖直变形均小于800 μm，且当设备自身振动产生的扰力<1.5 kN时，基台仍能保持VC-C的振动水平。研究结果可为类似工业厂房中设备的隔振设计提供参考。

钢弹簧隔振器  /  水平刚度  /  环境振动  /  隔振基台  /  减隔振

Environmental vibration is an important factor that affects the normal operation of various precision instruments and equipment. To solve the problem that the environmental vibration exceeds the vibration limit for the normal operation of equipment, the design of steel spring vibration isolation base is investigated. Through experimental verification and calculation analysis, the relationship between the vertical and horizontal stiffness of steel spring is derived, and the fuzzy problem of horizontal stiffness of steel spring is solved. A novel steel spring floating slab vibration isolation base is designed based on the requirements. The finite element method is utilized to study the vibration reduction and isolation effects of the pedestal under different steel spring stiffnesses. The deformation of the pedestal above the equipment with uneven mass distribution, the deformation of the pedestal with moving parts, and the vibration level of the pedestal are analyzed respectively. The analysis results show that the new steel spring floating slab vibration isolation base exhibits excellent horizontal and vertical vibration isolation effects. When the natural frequency of the base is 4.2 Hz, the maximum vibration reduction efficiency for the environmental vibration above 12 Hz can exceed 90%. The equipment with small moving parts on the base also demonstrates good stability. When the 50 kg moving parts move from one end of the base to the other, the vertical deformation of the base is less than 800 μm. When the disturbance force generated by equipment vibration is less than 1.5 kN, the base can still maintain the vibration level of VC-C. The research results can provide valuable references for the vibration isolation design of equipment in similar industrial plants.

steel spring isolator  /  horizontal stiffness  /  environmental vibration  /  vibration isolation base  /  vibration reduction and isolation
梁新奇, 兰日清, 韩蓬勃, 汪志昊, 杨程. 新型钢弹簧浮筑板隔振基台设计与应用. 地震工程与工程振动, 2025 , 45 (1) : 113 -120 . DOI: 10.13197/j.eeed.2025.0112
Xinqi LIANG, Riqing LAN, Pengbo HAN, Zhihao WANG, Cheng YANG. Design and application of a new type of steel spring floating plate vibration isolation foundation platform[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (1) : 113 -120 . DOI: 10.13197/j.eeed.2025.0112
正文
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0　引言
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随着科学技术的快速发展，各类新型电子工业产品的加工精度越来越高，一些精密设备的加工精度甚至达到纳米级别[1]，而随着城市的发展，各类交通工具、动力设备和人类活动加重了环境振动，成为影响精密加工设备正常运行的重要因素[2-3]。因此，为精密加工设备设计防微振基台成为一项亟需解决的任务[4]。
众多学者已开展防微振基台的设计研究，如美国的激光干涉引力波天文台LIGO[5-6]的隔振系统是采用了低刚度弹簧加上摆隔振结构组成，试验验证表明系统在10 Hz处可减少环境中40 dB的振动；LUO等[7]提出了一种环层压阻尼隔振环系统，通过模型试验和仿真分析表明，该系统隔振效率可达95%以上；ZHAI等[8]设计了一种新型的永磁复合隔振系统并搭建了试验平台，结果表明该隔振系统在20~100 Hz时隔振效率大于80%，在100~500 Hz时隔振效率大于90%；许浩等[9]针对动力设备引起楼板振动问题采用了浮置平台隔振技术，大大的减少动力设备引起楼板振动问题，其中竖向振动响应减少35~45 dB，水平振动响应减少25~40 dB；闻荣伟[10]提出了一种基于洛伦兹力致动器主动负刚度的大型精密仪器系统隔微振控制方法，通过试验验证了该方法可有效减小振动对精密仪器的损坏程度；朱亮等[11]设计了一种由矩形弹簧和碟形弹簧相互并联的低频被动隔振系统，通过数值分析和实测证明验证了该系统的低频隔振性能。
根据现有研究，防微振基台主要包括高刚性基台[12]、钢弹簧隔振基台[13]、空气弹簧被动隔振基台和主动控制隔振基台等[14-15]。常规的基台设计一般为高刚性基台，其对高于基台固有频率的环境振动有一定的减振效果，但对低于固有频率的环境振动没有减振效果。空气弹簧隔振基台刚度小，系统整体较软，设备安装及运行过程中，容易造成平台变形较大。钢弹簧隔振基台的刚度可根据实际振动情况进行针对性设计，确保一定减隔振效果的同时也具有足够的稳定性。以往的研究一般采用大承载钢弹簧隔振，其要求钢弹簧底部的楼板或基础有足够承载力，但对于有些改造项目，楼板承载有限，为此设计了钢弹簧浮筑板基台。
钢弹簧浮筑板常用于地铁轨道减隔振及动力设备的减隔振中，将其应用到电子工业厂房内精密设备的减隔振方面的研究还较少。因此，本文开展钢弹簧浮筑板基台的减隔振研究，基于钢弹簧性能试验，推导了钢弹簧水平刚度与竖向刚度取值关系，并研究了基台的隔振效果和在偏心荷载、动荷载作用下基台的变形和台面振动水平，可为电子工业厂房环境振动影响精密仪器正常工作的减隔振设计提供参考。
1　钢弹簧性能试验
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实际工程的仿真分析中，建立弹簧单元时需输入弹簧竖向刚度和水平刚度，以往在模拟中，钢弹簧的水平刚度一般取为竖向刚度的0.70~0.85倍，但通过实际试验表明，钢弹簧的水平刚度与其承受荷载有关。
为了更加准确对钢弹簧隔振基台进行仿真分析，需确定水平刚度的取值办法，本文通过钢弹簧压剪试验[16]来研究其水平刚度的取值方法，试验时选取承载力分别为500、1000、2000 kg的钢弹簧进行测试，其对应弹簧系数为250、530、1290 N/mm。
1）竖向刚度
由压剪试验机分别对3种不同承载力的钢弹簧按照1 mm/s的速度施加竖向压力，测得3种型号弹簧力和位移关系曲线如图1（a）所示，实测竖向刚度值分别为253、533、1291 N/mm。
2）水平刚度
为更好地贴近钢弹簧在使用时的具体工况，在水平刚度试验中分别在预压0~25 mm情况下进行3种型号钢弹簧测试。
将不同压缩量水平刚度与竖向刚度对比可得两者变化关系图，如图1（b）所示，水平测试结果如表1所示。
对以上数据进行分析可得式（1）：
式中，x为弹簧竖向压缩量。
刚度计算公式为
将式（2）代入式（1）可得水平刚度在外界不同荷载时与竖向刚度的关系式，如式（3）所示：
式中：kH、kV、F分别为水平刚度、竖向刚度和单个弹簧所受竖向压力。
2　隔振基台设计
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2.1　工程背景
某从事半导体显示领域核心部件制造的精密厂房，其环境振动测试结果如图2所示，由于现场有动力设备运行，竖直向环境振动在12~18 Hz时已经超出VC-A[17]，故无法满足该厂房内精密设备要求的振动环境VC-C水平。
2.2　隔振原理
对设备与钢弹簧隔振基台构成的隔振系统进行隔振计算[18]。定义基台上部设备振幅与地面振动幅值之比η为传递比，则有：
式中：ζ为隔振系统阻尼比；γ为环境激励频率与基台的固有频率的比值；由式（4）可知，要使传递效率η小于1，则必须使γ值大于，基台才能起到隔振的效果，且当环境激励频率不变时，基台固有频率越低，传递率越低，隔振效果越好，但基台越软，变形也会随之增大。
3　基台有限元分析
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3.1　基台模型参数及工况
为同时满足隔振与承载需求。此次设计采用全新的设计方法，将钢弹簧隔振器内嵌于混凝土板层中，初步设计基台的长、宽、高尺寸分别为4200、3500、1000 mm。隔振基台底部为矩形钢管焊接而成的钢框架进行支撑，钢管内部浇筑混凝土，上部为混凝土平台板。
模型采用实体单元建模，混凝土材料为C35，钢弹簧隔振器个数总计24个，平台上部设备重量为13 000 kg，20个设备支撑站脚，模拟时采用集中荷载模拟上部设备，分析模型如图3所示。
从场地实测结果来看，环境振动超标部分集中于12 Hz以上，隔振基台固有频率前3阶为钢弹簧固有频率，继而是混凝土台面固有频率及底部钢结构支撑固有频率。分析可知，混凝土台面固有频率为50 Hz以上，底部支撑为200 Hz以上。而基台隔振系统固有频率至少需要低于8.5 Hz时，才能起到隔振效果，因此仅需考虑隔振基台中钢弹簧的频率即可[19]，为确定钢弹簧隔振器的选型，对此进行以下10种工况进行计算，刚度与频率公式参照式（5）[20]，具体参数如表2所示。
3.2　基台隔振效果分析
为验证模型的正确性，对仿真模型的1阶频率与理论频率进行对比，结果如表2所示。
将现场水平向、竖直向环境振动实测结果作为激励输入到有限元模型中，进行数值仿真分析，获得基台台面的时程反应数据，如图4所示。当环境激励不变时，随着基台自身固有频率的降低，其竖直向隔振效果提高。1/3倍频程分析结果如图5所示。由图可知，基台在自身固有频率处（3~7.5 Hz）会出现振动放大现象，当基台固有频率在6~7.5 Hz时，竖直方向整个频段可达VC-B水平，在3~5.5 Hz时，可达VC-C水平；水平向上振动等级均小于VC-C水平。为了达到较好的隔振效果，基台固有频率要尽量低，但设备又要求基台有足够的刚度，因此基台刚度与固有频率间需保持一定的平衡。
3.3　基台偏心作用下变形分析
当基台上部设备存在质量分布不均时，需对基台的竖直向的变形进行研究，确保基台竖直向变形在5 mm范围内。当频率在5.5 Hz以上时，基台振动超过VC-C水平，因此仅对基台固有频率在3~5 Hz时开展不均匀质量分布的竖向变形分析。模拟上部设备总计13 t，20个站脚，假设第1部分与第2部分（图6）质量总和差在0~2.1 t，对该情况进行基台变形分析。
由图7可知，基台台面的变形值会随上部设备质量偏差增大而增大，当固有频率在4.5 Hz以上时，设备两部分质量总和差不超2.1 t时可满足隔振层高低差在5 mm以内。
3.4　设备运行时基台变形分析
1）设备运动部件运动下基台变形分析
当上部设备存在运动部件且部件在运动时，需确保基台足够的稳定性才能保证生产正常进行，由该厂家提供的运动部件的重量为46 kg，模拟上部设备的运动部件重量为40~50 kg，长、宽、高分别为500、500、100 mm，其移动方向如图6所示。速度为100 mm/s，获得9个时间点基台的变形情况，如图8所示，分析可知，当上部设备存在不超过50 kg的运动部件时，基台的竖直向变形可控制在800 μm以下。
2）设备运行时基台振动水平分析
上部设备在运行时，自身也会产生一定的振动，由于钢弹簧基台整体偏软，需评估设备自身的振动是否会影响基台的防微振限值需求。根据厂家所提供设备参数，自身存在运转设备的转子质量为100~400 kg不等，模拟运转设备重量为50~500 kg，设备转速为1200 r/m，此时机器产生的扰力[21]为0.14~1.5 kN。1/3倍频程计算分析结果如图9所示，可知当设备运行产生的扰力小于1.5 kN时，基台振动水平仍能保持在VC-C水平以下。
3.5　工程实际应用
结合2.1节实际环境振动测试结果和设备的振动控制需求，设计竖向刚度为520 N/mm的钢弹簧隔振器基台，其固有频率为4.2 Hz。工厂设备安装后基台实际振动测试结果显示，基台表面竖向振动等级维持在VC-D水平，最大减振效果达90%以上，基台台面的实测与仿真分析结果如图10所示。
4　结论
收起
文中对钢弹簧浮筑板基台展开分析，首先对钢弹簧展开力学性能试验，然后通过有限元分析了钢弹簧浮筑板基台减振效率、基台在偏心荷载作用下的变形情况、基台存在运动部件时的变形情况以及台面振动水平，最后与实际工程应用进行对比，得到以下结论：
1）根据钢弹簧性能试验结果，钢弹簧水平刚度取值与弹簧竖向刚度和所承受竖向负载有关，通过推导及数据拟合，获得了弹簧水平刚度关系式，可为工程中弹簧参数模拟选取提供参考。
2）基台在竖向和水平向都具有较好的减振效果，外界振动频段在10 Hz以上时，可根据上方设备重量选取钢弹簧刚度使基台固有频率保持在4 Hz左右。此时，当基台上部设备存在50 kg运动部件时，可满足竖直向变形小于800 μm；当基台存在非运动设备运行产生的扰力小于1.5 kN时，基台的振动水平可保持在VC-C水平。
3）对比数值模拟和实际工程，基台对环境振动12 Hz以上振动抑制效果较好，此时钢弹簧隔振基台的固有频率可设计为4.2 Hz左右，减振效率可达90%以上。
基金
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  • 中国机械工业集团有限公司重大科技专项(SINOMAST-ZDZX-2020-03)
文献
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2025年第45卷第1期
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doi: 10.13197/j.eeed.2025.0112
  • 接收时间：2023-08-21
  • 首发时间：2026-03-20
  • 出版时间：2025-02-28
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  • 收稿日期：2023-08-21
  • 修回日期：2023-10-31
基金
中国机械工业集团有限公司重大科技专项(SINOMAST-ZDZX-2020-03)
作者信息
    1.华北水利水电大学 土木与交通学院，河南 郑州 450045
    2.国机集团科学技术研究院有限公司，国机集团工程振动控制技术研究中心，北京 100080

通讯作者:

兰日清（1977—），男，正高级工程师，博士，主要从事工程振动控制技术研究。E-mail：
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
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