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Article(id=1245389864665989766, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245389858412282468, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0210, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1668960000000, receivedDateStr=2022-11-21, revisedDate=1678636800000, revisedDateStr=2023-03-13, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853681961, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853681961, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853681961, creator=13701087609, updateTime=1774853681961, updator=13701087609, issue=Issue{id=1245389858412282468, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='2', pageStart='1', pageEnd='232', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853680470, creator=13701087609, updateTime=1774854277127, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245392361031840387, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245389858412282468, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245392361031840388, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245389858412282468, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=89, endPage=97, ext={EN=ArticleExt(id=1245389865144140432, articleId=1245389864665989766, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Design and application of a novel type of pendulum isolation device using universal balls, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Aiming at the demand of seismic protection of free-standing objects, a pendulum isolation device based on universal balls was developed. The structural characteristics and operation principle were introduced, and the design of an isolation device for protecting a pagoda could serve as a case study. Then the finite element software was used to analyze the bearing capacity between the universal ball and the disc. The accuracy of the damping mechanism analysis model was verified by tests. The isolation effect of the device under the eight-degree extremely rare earthquakes was analyzed by time history method, and was compared with the traditional friction pendulum. The results show that the isolation device not only has simple structure and reliable performance, but also has the characteristics of low friction coefficient, small acceleration threshold for triggering slip and flexibly adjustable damping mechanism. The carrying capacity of the node-to-surface contact can meet the design requirement. By means of viscous damper at one end, the damping mechanism shows obvious velocity correlation, and damping force increases with the increase of velocity. The device can achieve the isolation target while satisfying the displacement limit. Compared with the traditional type, when the displacement and acceleration response are limited, the device can achieve better comprehensive isolation effect under various seismic conditions by reasonably adjusting parameters of the damping mechanism.

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针对浮放物体防震保护的迫切需求，研发了一款基于万向球的摆式隔震装置。首先介绍了它的构造特征与运行原理，并以某陈列佛塔为对象进行方案设计，利用有限元软件模拟万向球与圆盘间的接触关系，评估该装置的承载能力；然后通过试验验证了内部阻尼机构力学模型的准确性，采用时程分析法检验了该装置在8度极罕遇地震作用下的隔震效果，并与传统滑动摩擦摆的减震性能进行了对比。结果表明，该隔震装置不仅结构简单、性能可靠，而且具有摩擦系数低，起滑加速度阈值小，阻尼灵活可调的特点。装置中的点面接触具有一定的承载能力，能够满足设计需求。端部设置黏滞阻尼器的阻尼机构表现出明显的速度相关性，阻尼力会随速度的增大而增大。该装置隔震性能良好，在满足位移限值的情况下达到了设定的隔震目标，而且相比于传统型，在位移和加速度响应均需兼顾的情况下，通过合理调整阻尼机构的性能参数，该装置在各地震工况中能够取得更优的综合隔震效果。

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柏文（1990—），男，副研究员，博士，主要从事结构抗震研究。E-mail：
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赵守江（1984—），男，副研究馆员，硕士，主要从事文物减隔震研究。E-mail：

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赵守江（1984—），男，副研究馆员，硕士，主要从事文物减隔震研究。E-mail：

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Information of seismic waves

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地震名称地震台分量记录峰值/g
KobeNishi-AkashiNIS0900.503
Imperial ValleyDeltaH-DLT3520.351
NorthridgeCanyon Country-WLCLOS2700.482
), ArticleFig(id=1245389878637216008, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389864665989766, language=CN, label=表1, caption=

地震波信息

, figureFileSmall=null, figureFileBig=null, tableContent=
地震名称地震台分量记录峰值/g
KobeNishi-AkashiNIS0900.503
Imperial ValleyDeltaH-DLT3520.351
NorthridgeCanyon Country-WLCLOS2700.482
), ArticleFig(id=1245389878750462226, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389864665989766, language=EN, label=Table 2, caption=

Index of material properties

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材质E0/GPaσ0.01/MPaσ0.2/MPaσ1.0/MPaε0.2/%E0.2/GPa
S30408221197.72713350.31513.56
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材料性能指标

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材质E0/GPaσ0.01/MPaσ0.2/MPaσ1.0/MPaε0.2/%E0.2/GPa
S30408221197.72713350.31513.56
), ArticleFig(id=1245389878989537574, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389864665989766, language=EN, label=Table 3, caption=

Vibration response results of the isolation device under seismic waves

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地震波地面隔震装置
峰值加速度/（m/s2）峰值位移/cm峰值加速度/（m/s2）最大相对位移/cm残余位移/mm
Kobe5.8913.40.998.8-3.4
Imperial Valley5.8832.71.4618.1-1.4
Northridge5.8815.51.107.93.1
), ArticleFig(id=1245389879111172399, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389864665989766, language=CN, label=表3, caption=

地震波作用下隔震装置振动响应结果

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地震波地面隔震装置
峰值加速度/（m/s2）峰值位移/cm峰值加速度/（m/s2）最大相对位移/cm残余位移/mm
Kobe5.8913.40.998.8-3.4
Imperial Valley5.8832.71.4618.1-1.4
Northridge5.8815.51.107.93.1
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新型万向球摆式隔震装置的设计与应用
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赵守江 1 , 柏文 2, 3 , 戴君武 2, 3
地震工程与工程振动 | 2024,44(2): 89-97
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地震工程与工程振动 | 2024, 44(2): 89-97
新型万向球摆式隔震装置的设计与应用
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赵守江1 , 柏文2, 3 , 戴君武2, 3
作者信息
  • 1.故宫博物院，北京 100009
  • 2.中国地震局工程力学研究所 地震工程与工程振动重点实验室，黑龙江 哈尔滨 150080
  • 3.地震灾害防治应急管理部重点实验室，黑龙江 哈尔滨 150080

    • 赵守江（1984—），男，副研究馆员，硕士，主要从事文物减隔震研究。E-mail：

通讯作者:

柏文（1990—），男，副研究员，博士，主要从事结构抗震研究。E-mail：
Design and application of a novel type of pendulum isolation device using universal balls
Shoujiang ZHAO1 , Wen BAI2, 3 , Junwu DAI2, 3
Affiliations
  • 1.The Palace Museum, Beijing 100009, China
  • 2.Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
  • 3.Key Laboratory of Earthquake Disaster Mitigation, Ministry of Emergency Management, Harbin 150080, China
doi: 10.13197/j.eeed.2024.0210
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摘要
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针对浮放物体防震保护的迫切需求，研发了一款基于万向球的摆式隔震装置。首先介绍了它的构造特征与运行原理，并以某陈列佛塔为对象进行方案设计，利用有限元软件模拟万向球与圆盘间的接触关系，评估该装置的承载能力；然后通过试验验证了内部阻尼机构力学模型的准确性，采用时程分析法检验了该装置在8度极罕遇地震作用下的隔震效果，并与传统滑动摩擦摆的减震性能进行了对比。结果表明，该隔震装置不仅结构简单、性能可靠，而且具有摩擦系数低，起滑加速度阈值小，阻尼灵活可调的特点。装置中的点面接触具有一定的承载能力，能够满足设计需求。端部设置黏滞阻尼器的阻尼机构表现出明显的速度相关性，阻尼力会随速度的增大而增大。该装置隔震性能良好，在满足位移限值的情况下达到了设定的隔震目标，而且相比于传统型，在位移和加速度响应均需兼顾的情况下，通过合理调整阻尼机构的性能参数，该装置在各地震工况中能够取得更优的综合隔震效果。

摆式  /  隔震装置  /  万向球  /  阻尼机构  /  浮放物体  /  丝杠

Aiming at the demand of seismic protection of free-standing objects, a pendulum isolation device based on universal balls was developed. The structural characteristics and operation principle were introduced, and the design of an isolation device for protecting a pagoda could serve as a case study. Then the finite element software was used to analyze the bearing capacity between the universal ball and the disc. The accuracy of the damping mechanism analysis model was verified by tests. The isolation effect of the device under the eight-degree extremely rare earthquakes was analyzed by time history method, and was compared with the traditional friction pendulum. The results show that the isolation device not only has simple structure and reliable performance, but also has the characteristics of low friction coefficient, small acceleration threshold for triggering slip and flexibly adjustable damping mechanism. The carrying capacity of the node-to-surface contact can meet the design requirement. By means of viscous damper at one end, the damping mechanism shows obvious velocity correlation, and damping force increases with the increase of velocity. The device can achieve the isolation target while satisfying the displacement limit. Compared with the traditional type, when the displacement and acceleration response are limited, the device can achieve better comprehensive isolation effect under various seismic conditions by reasonably adjusting parameters of the damping mechanism.

pendulum  /  isolation device  /  universal ball  /  damping mechanism  /  free-standing objects  /  lead screw
赵守江, 柏文, 戴君武. 新型万向球摆式隔震装置的设计与应用. 地震工程与工程振动, 2024 , 44 (2) : 89 -97 . DOI: 10.13197/j.eeed.2024.0210
Shoujiang ZHAO, Wen BAI, Junwu DAI. Design and application of a novel type of pendulum isolation device using universal balls[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (2) : 89 -97 . DOI: 10.13197/j.eeed.2024.0210
正文
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0　引言
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近些年来，随着结构的抗震、隔震等研究趋于成熟，建筑结构的地震破坏得到了有效控制，而内部种类繁多的浮放物如贵重设备、精密仪器以及珍贵文物等却极易遭受破坏[1-3]，其抗震减震问题引起了越来越多的关注与研究[4-6]。虽然常规的栓、绑、支和固等方法可以起到一定的抗震保护作用[7]，但是一些自身抗震能力不足的高精尖仪器或脆弱文物，往往因无法承受环境振动作用而损坏。针对此类浮放物体，采用隔震装置更加适宜。
不同于巨大的建筑物，浮放物体一般体型小、质量轻，且装置用途灵活多样，因此如何能够较精确地调整其刚度、阻尼等性能参数是设计的关键。在诸多研发的隔震装置[8]中，摩擦摆支座是一种简单可靠、经济性较强的水平隔震装置。它除了具有对地震激励频率范围的低敏感性和高稳定性外，还具有较好的自限位、复位功能[9]，且其隔震周期不随上部结构质量的变化而变化。现阶段有关摩擦摆的研究多将摩擦界面做理想化设计，对工程应用的复杂性考虑较少。不同于摩擦摆在建筑工程中的应用，浮放物体隔震时，隔震装置上部荷载较轻，此时滑块与摩擦面之间稳定的低动摩擦系数不易满足，后期也难以调整，此外，隔震装置需要具有较低的起滑加速度阈值，而常用的高分子工程塑料对钢滑动的摩擦系数一般在0.1~0.4之间[10]，静摩擦系数比低速时的动摩擦系数要略大，效果不甚理想。
为此，对传统滑动摩擦摆支座进行了改进，提出了一种新型万向球摆式隔震装置，使之能够较好地适用于浮放物体的隔震保护中，与传统摩擦摆隔震装置相比，该装置变滑动摩擦为滚动摩擦，具有摩擦系数低，起滑加速度阈值小，阻尼灵活可调的优势。本文对该装置的构造和机理进行了探讨，以某陈列佛塔为对象进行方案设计，测其性能参数，利用有限元软件分析了构造的可靠性，并采用数值方法，分析了该装置的隔震性能。通过与传统摩擦摆隔震支座的对比，为隔震装置的方案筛选与参数优化提供了借鉴。
1　方案设计
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1.1　设计概况
该佛塔为故宫博物院所藏的一座9层雕花紫檀木塔，总高3.39 m，总重86.4 kg，如图1所示。塔身分为9层，加上基座和底部支架共11层。其中底部支架为正八边形，对边宽0.64 m。塔身各层为榫卯连接，辅以胶粘。由于佛塔为细高型，整体重心高，底部窄，所以稳定性较差，而繁复精巧的镂空雕刻又使得木塔格外脆弱。
北京市地处燕山地震带与华北地震带交汇处，又紧邻汾渭地震带和郯庐深大断裂地震带，历史上曾遭受过多次强烈地震的破坏和影响。由于不能将佛塔长期分拆装箱予以保护，而常规的支固措施又受到陈列环境和自身条件的制约，因此在其底部加装隔震装置是一种行之有效的方法。
在隔震装置设计时，依据佛塔所处地区的地脉动测试结果[11]，参考ATC-63报告推荐的地震动记录，选取与场地卓越频率相近的Kobe波和Northridge波作为输入地震动；考虑到装置的长周期特性，同时还选取了低频成分更丰富的Imperial Valley波。各地震波的频谱特性如图2所示。地震波的具体信息如表1所示。根据GB/T 51408—2021《建筑隔震设计标准》[12]，采用8度极罕遇地震（0.6 g）进行时程分析。以地震动峰值加速度（peak ground acceleration，PGA）作为调幅依据，分别调整上述3条地震波。
为了简化分析并提高安全度，适用于文物的隔震装置通常以物体不发生滑移以及其底部不发生脱离作为设计前提。结合佛塔的具体特征并适当增加安全储备，其目标性能设定为：在满足隔震装置自身位移限值的基础下，最大响应加速度控制在0.15 g以内。
1.2　装置研发
基于传统滑动摩擦摆的特点，新设计的万向球摆式隔震装置包括以下主要部件：底板、顶板、凹型圆盘、万向球和阻尼机构等[13]，如图3所示。凹型圆盘与万向球构成了单摆式隔震支座，使传统的滑动摩擦变成滚动摩擦，降低了摩擦系数。鉴于滚动摩擦系数变动幅度有限，隔震装置中间还增设了一套阻尼机构来调节耗能以便满足更多的应用需求。
万向球是由中心一颗大直径的主球和四周较小的滚球组成，其构造简单可靠且价格实惠，被广泛应用于物品传输系统中。本文研发的隔震装置优选主球朝上的万向球，此时凹型圆盘需要置于万向球上部。
装置中部的阻尼机构是由2套相同的单向水平阻尼组件对接而成，具体构造如图4所示。每套单向水平阻尼组件均由丝杠（含螺母）、旋转阻尼器、对接板、挡块、滑块及配套直线导轨等构成。其中螺母与对接板相连接，与丝杠配合后能够将直线运动转化为回转运动，进而带动端部的旋转阻尼器持续耗能；通过改变旋转阻尼器规格或丝杠的导程可以调整阻尼的性能。2套正交布置的单向阻尼组件即可解耦任意方向的水平运动。2块U型对接板间预留了竖向移动空间，能够适应凹型圆盘的高度变化，且翼缘及末端挡块可防止彼此扭转和脱离。综上可见，上述阻尼机构不仅可以方便和精确地调节阻尼性能，还能增强隔震装置的整体性。
根据佛塔的尺寸和隔震目标，参照上述地震波反应谱，初步设计隔震装置的长宽高分别为100 cm×100 cm×8.6 cm，总质量约为138.6 kg，其中万向球支撑的上半部质量为93.8 kg，极限位移±20 cm。顶板和底板均为铝材，厚度为12 mm；万向球选用KSM-38型，主球直径为38.1 mm，单体设计载重260 kg；凹型圆盘为不锈钢材质，曲率半径为2.5 m，单摆周期约3.14 s，中心厚度为8 mm；阻尼机构中的滚动直线导轨副选用EGH15CA型滑块及配套导轨，每根导轨上配2个滑块；不锈钢梯形丝杠的直径为12 mm，导程为36 mm，配套铜螺母；旋转阻尼器选用FRT-D3-501型黏滞阻尼器，即20 r/min时扭矩为（50±10）×10-3 N•m。
2　装置性能分析
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2.1　万向球接触分析
根据该隔震装置的构造特点，万向球与圆盘之间为点-面接触。它关系到装置的承载能力，是设计时需要重点考虑的要素之一。为此，采用有限元软件进行两者间的静态接触分析。
钢球和凹型圆盘材质相同，均为S30408不锈钢（06Cr19Ni10）。不锈钢属于典型的非线性和各向异性材料，根据文献[14-15]的研究，此处采用G-N本构关系模型进行数值模拟，具体参数如表2所示。为了能够真实反映材料可能存在的大应变塑性变形，试验所得的工程应力-应变关系曲线转化为真实应力-应变关系曲线。
在数值模拟时，鉴于接触斑尺寸远小于钢球和圆盘的尺寸，依据圣维南原理，取半径4 cm的圆盘和下半部分钢球作为分析对象，同时由于荷载和结构的对称性，选取1/4凹型圆盘和1/8钢球建立模型。模型选用SOLID95六面体单元进行离散，接触点附近的有限元网格最大尺寸小于0.5 mm。定义钢球为主面，凹型圆盘为从面，利用CONTA174单元和TARGE170单元建立接触关系，两者间的界面摩擦因数取0.1。
在钢球和圆盘的对称面施加对称约束，在凹型圆盘底部施加竖向约束，钢球顶面施加竖向荷载450 N，计算结果如图5和图6所示。
由图5可知，凹型圆盘的最大Von-Mises等效应力为305.8 MPa，最大应力发生在距离接触面一定深度约0.4 mm处，而钢球的最大Von-Mises等效应力为302.2 MPa，发生在距离接触面约0.2 mm处。由图6可知，凹型圆盘和钢球的弹塑性变形均很小，其中凹型圆盘的最大竖向变形量发生在接触中心位置，约为7.8 μm。相较于钢球的直径，该变形量极其微小，不会影响到滚动的顺畅性。因此，方案选用的材料和规格能够满足隔震装置承载力的需求，接触表面无需进行硬化处理。
2.2　阻尼特性分析
在运动过程中，隔震装置的阻尼力是由两部分组成：一部分是万向球与圆盘之间的滚动摩擦力，另一部分是图4中阻尼机构提供的复合阻尼力。该复合阻尼力除了由端部的旋转阻尼器提供外，还包括滑块与导轨之间以及丝杠与螺母之间产生的附加阻力。由于附加阻力受组件材质、规格、加工与装配精度等因素影响大，不确定性高，且作用等效于增大了万向球的滚动摩擦系数，因此通常会采取措施来降低其值。
试验时，先将一块表面光滑的不锈钢平板置于4个KSM-38型万向球上，测得平均摩擦系数约为0.012。然后取阻尼机构中的一套单向水平阻尼组件作为分析对象，其底部固定于振动台面上，对接板通过浮动接头与支架上的力传感器连接，如图7所示。丝杠的一端安装有旋转阻尼器，测得其复合阻尼力与速度的对应关系，如图8所示。然后去除旋转阻尼器，测得附加阻力约为1.9 N。进而拟合得到该单向水平阻尼组件的复合阻尼力表达式为
式中：Fd为复合阻尼力（N）；v为速度（m/s）。由式（1）所得拟合曲线如图8所示。
据式（1）可知，阻尼机构的力学模型是由非线性黏滞单元和摩擦单元组成。其中，摩擦单元提供的附加阻力可与万向球-圆盘间的滚动摩擦力合并一起进行动力学分析。由于该阻尼机构选用了滚动直线导轨副，既保障了在侧向力作用下运动的顺畅性，又使得附加阻力数值相对较小甚至能够忽略不计，因此，在简化分析时可直接对复合阻尼力的测试结果进行非线性拟合。
为了检验上述阻尼机构的分析模型是否能真实反映其特性，除正弦波激励外，还利用振动台面输入不规则波来测试该阻尼组件的复合阻尼力，并与理论分析结果进行对比[16]，如图9所示。选取的不规则波为Hector Mine地震Hector台站记录的HEC090加速度记录。
由图9可知，试验值和理论值整体上吻合良好。试验与分析所得曲线不仅在趋势上相符，而且各峰值吻合度较高，验证了分析模型的精度与适用性。同时，从曲线局部放大区域可看出，在阻尼力正负转换过程中，试验曲线出现了类似文献[17]中的荷载零值段，即在螺母折返后的小段位移范围内，荷载值为零。经查验，该现象的主要原因是为了保证顺畅，加工的梯形丝杠与螺母之间存有一定间隙。
2.3　地震响应数值模拟
基于已有的研究成果，传统摩擦摆系统的力学模型可为线弹性弹簧与摩擦阻尼器的结合[18]。由于该装置设置了图4中的阻尼机构，可提供额外的阻尼耗能，所以在水平地震动激励下，其动力微分方程为
式中：m为万向球所支撑的质量；u为相对位移；üg为地震动加速度；Fd为阻尼机构的复合阻尼力，具体见式（1）；Fh为万向球所提供的水平力，可表示成回复力和滚动摩擦力之和[19]。当摆动角度很小时，其简化式为
式中：R为凹型圆盘的半径；sgn（∙）为符号函数；μ为万向球的滚动摩擦系数；mg/R为装置的刚度。
为初步了解采用上述具体方案后隔震装置的特性，先进行自由衰减振动模拟，即对装置的顶板施加某一初始位移，待速度为零后自由释放，得到它的位移时程曲线。顶板无法回到初始零位置，且在中间平衡位置不会发生自由振荡。装置属于过（超）阻尼体系，如图10所示。
采用上述3条地震波分别进行数值模拟，获得了该隔震装置在各工况下的加速度和相对位移时程响应曲线，限于篇幅仅列出隔震装置在Kobe波激励下的振动响应时程曲线，如图11所示。由图可知，隔震装置的加速度响应明显小于输入地震动，幅度更加平稳。即便在地震作用后期，如时间20 s以后，输入加速度峰值仅为0.68 m/s2，隔震装置也会产生轻微的相对位移，起到隔震效果。同时，隔震装置的残余位移很小，能实现良好的复位。
从隔震装置的振动响应曲线中提取出所关注的最大相对位移、峰值加速度以及残余位移，汇总于表3。由表可知，3种工况下，隔震装置的最大相对位移均小于极限位移20 cm，未发生碰撞，且震后残余位移较小，加速度响应峰值也都在0.15 g以内，达到了预设目标。依据输入的加速度峰值和响应加速度峰值，可以得到装置的隔震效率分别为83%、75%、81%。经对比发现：在Imperial Valley波作用下，装置的地震响应最为剧烈。其原因与该条地震波0.2~2.4 Hz低频段占比高以及地面的峰值位移大有关。
2.4　与传统型对比分析
传统摩擦摆支座主要应用于土木工程领域[20]，上部荷载很大，因此多采用滑块设计以便能够利用面面接触提高承载力。通过改变接触面间的滑动摩擦系数来调整支座的阻尼参数，不过现实中若想取得预定的数值，对接触面的加工和装配精度要求很高。在新型隔震装置中，万向球与圆盘间的滚动摩擦系数低且调整范围窄，因此一般由增设的阻尼机构协助耗能，通过改变其设计参数来满足性能需求。在圆盘曲率半径和所支撑质量相同的前提下，若新型中的阻尼机构选用了摩擦型旋转阻尼器，通过合理选取参数，新型与传统型的动力方程可完全相同。若阻尼机构选用黏滞型，则2种隔震装置的性能差异本质上是黏滞阻尼和库伦阻尼的特性差异所造成的。
对于新型隔震装置，由于式（1）中黏滞单元的速度指数由端部阻尼器唯一确定，而阻尼系数可由丝杠的导程调整[17]，因此，设定其它参数与上述案例保持一致，仅阻尼系数c的值在5~300范围内连续变化，间隔为10。经地震响应分析后，得到各工况下阻尼系数与最大相对位移和峰值加速度的对应关系，如图12所示。其中红色曲线上的圆点分别对应一具体阻尼系数。
对于传统型摩擦摆，采用相同数量和规格的凹形圆盘且滑块所支撑的质量同为180.2 kg。分析时假定动、静摩擦系数一致，并且运动过程中保持不变。鉴于上部质量较轻，接触面间的压应力仅为几百千帕，因此，摩擦系数μ选取0.05~0.20段[21]，间隔为0.005。对采用不同摩擦系数的传统型摩擦摆进行地震响应分析，也得到了摩擦系数与最大相对位移和峰值加速度的对应关系，如图12所示。相应地，黑色曲线上的方点分别对应一具体摩擦系数。
图12相当于空间直角坐标系中的曲线在底部XY平面的垂直投影。该空间直角坐标系是以摩擦系数或阻尼系数为Z轴，最大相对位移为X轴以及峰值加速度为Y轴构成。图中曲线上的点从右到左分别对应摩擦系数或阻尼系数从小到大连续变化时隔震装置的振动响应。例如表3中隔震装置的响应结果对应于图中红色曲线从右起的第二十一个点，该点阻尼系数为205，与202.5相近。
总体上，随着摩擦系数的增大，各工况下传统型的峰值加速度均持续增大；相应地，最大相对位移除在Northridge波作用下的前段略有增大外，均随之持续减小。与之相比，各工况下新型的最大相对位移随着阻尼系数的增大而减小，而峰值加速度的变化趋势差异较大。具体地，在Kobe波作用下，新型的峰值加速度会随阻尼系数增大而增大；在Imperial Valley波作用下，峰值加速度先减小后增大，且前段减小幅度明显大于后段增涨幅度；在Northridge波作用下，峰值加速度先略有减小后持续增大，减小幅度要小于增涨幅度。
由图12可知，若位移不受限制，为了满足目标性能中峰值加速度的要求，传统型装置仅需寻求稳定的低摩擦系数即可，而新型装置则需对阻尼系数进行筛选。不过相比于传统型，各工况中通过采用合适的阻尼系数，新型装置能实现最低的峰值加速度，即它的隔震效率更高。需要注意的是，实际应用中，由于接触面压应力较低、且动摩擦系数通常跟速度相关，传统型摩擦摆想要实现很低的摩擦系数是很困难的。
若为了控制位移响应，则需提高阻尼耗能。由图12可知，当阻尼增大到一定程度，各工况中最大相对位移和峰值加速度均成负相关关系。过大的摩擦系数或阻尼系数虽然降低了最大相对位移，却也增大了峰值加速度。图12（a）、（b）、（c）中在峰值加速度较小且最大相对位移的同一区段，新型的曲线始终位于传统型的下方，表明即使两类装置均能满足设计目标，通过调整阻尼系数仍可以使新型装置的振动响应小于传统型。
对于上述案例的隔震目标，图12（b）中的Imperial Valley波起主要控制作用。图中峰值加速度0~1.5 m/s2，最大相对位移0~20 cm的重叠区域与传统型的曲线无交集，表明没有摩擦系数能够使装置在该工况下达到目标性能。此时，若采用传统型，只能加大装置的极限位移或降低目标性能。而新型装置若未安装图4中的阻尼机构，在Imperial Valley波作用下，最大相对位移将超过40 cm，远大于极限位移。
由此可见，在位移和加速度均受限的情况下，增设了黏滞型阻尼机构的万向球摆式隔震装置，其综合抑振效果更佳。相较于摩擦系数的难以精确控制，利用丝杠或端部的旋转阻尼器均可对阻尼参数进行调整，便于装置性能的优化。虽然上述仅为具体案例的对比研究，但分析方法尤其是绘图方式有利于2种隔震方案的筛选以及阻尼参数优化，便于工程实践。
3　结论
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针对浮放物体的地震防护需求，本文提出了一种万向球摆式隔震装置，阐述其构造特点与运行原理，结合案例进行设计，通过性能试验和数值分析，验证了方案的有效性，并与传统型的减震效果进行对比，可得到以下结论：
1）新型隔震装置是由万向球、凹型圆盘、阻尼机构以及顶底板构成。它结构简单，部件功能清晰，具备抗扭转和抗拔能力。
2）以某文物隔震装置为分析对象，采用数值方法检验其承载能力，同时对阻尼机构的特性进行试验。结果表明，万向球与圆盘间的点-面接触具有一定的承载能力，能够满足设计要求。端部设置黏滞阻尼器的阻尼机构表现出明显的速度相关性，阻尼力会随速度的增大而增大，阻尼机构的试验与理论结果相吻合，验证了它性能的可靠以及力学模型的准确性。
3）通过时程分析获得了该新型装置在8度极罕遇地震作用下的减震性能。其最大相对位移均未超出设计的极限位移，复位效果良好。加速度响应峰值也都在目标范围内，其隔震效率始终保持在75%及以上。
4）经过新型和传统型的对比发现，在选取的摩擦系数范围内，传统型的峰值加速度会随摩擦系数增大而增大，最大相对位移大体上随之减小，新型的最大相对位移随着阻尼系数的增大而减小，但峰值加速度的变化趋势差异较大。在位移和加速度响应均需兼顾的情况下，通过合理调整阻尼机构的阻尼参数，各工况中新型装置能够取得更优的综合隔震效果。
5）由于隔震装置的阻尼参数与振动响应结果（最大相对位移与峰值加速度）存在对应关系，可将三者绘制于以最大相对位移与峰值加速度为坐标的二维图中，图中每个点代表变量的一个具体值。该方法使得不同隔震装置的性能对比更简洁直观，有利于方案的筛选和参数优化。
基金
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  • 国家重点研发计划项目(2019YFC1521000)
  • 故宫博物院科研项目(KT2017-09)
文献
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2024年第44卷第2期
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doi: 10.13197/j.eeed.2024.0210
  • 接收时间：2022-11-21
  • 首发时间：2026-03-30
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  • 收稿日期：2022-11-21
  • 修回日期：2023-03-13
基金
国家重点研发计划项目(2019YFC1521000)
故宫博物院科研项目(KT2017-09)
作者信息
    1.故宫博物院，北京 100009
    2.中国地震局工程力学研究所 地震工程与工程振动重点实验室，黑龙江 哈尔滨 150080
    3.地震灾害防治应急管理部重点实验室，黑龙江 哈尔滨 150080

通讯作者:

柏文（1990—），男，副研究员，博士，主要从事结构抗震研究。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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