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Article(id=1244336193853305228, tenantId=1146029695717560320, journalId=1244323073571209252, issueId=1244336186114819067, articleNumber=null, orderNo=null, doi=10.13695/j.cnki.12-1222/o3.2025.10.010, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1716998400000, receivedDateStr=2024-05-30, revisedDate=null, revisedDateStr=null, acceptedDate=1751558400000, acceptedDateStr=2025-07-04, onlineDate=1774602467262, onlineDateStr=2026-03-27, pubDate=1761753600000, pubDateStr=2025-10-30, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774602467262, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774602467262, creator=13701087609, updateTime=1774602467262, updator=13701087609, issue=Issue{id=1244336186114819067, tenantId=1146029695717560320, journalId=1244323073571209252, year='2025', volume='33', issue='10', pageStart='955', pageEnd='1060', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774602465418, creator=13701087609, updateTime=1774604459075, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244344548185452773, tenantId=1146029695717560320, journalId=1244323073571209252, issueId=1244336186114819067, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244344548185452774, tenantId=1146029695717560320, journalId=1244323073571209252, issueId=1244336186114819067, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1034, endPage=1042, ext={EN=ArticleExt(id=1244336194134323600, articleId=1244336193853305228, tenantId=1146029695717560320, journalId=1244323073571209252, language=EN, title=Response modeling and failure analysis of MEMS ring gyroscopes under high overload, columnId=1244336189055025158, journalTitle=Journal of Chinese Inertial Technology, columnName=Inertial Instrument Research and Design, runingTitle=null, highlight=null, articleAbstract=

Regarding the shock failure of a micro-electro-mechanical system (MEMS) vibrating ring gyroscope (VRG) under high overload, structural dynamic response modeling and failure mechanism analysis are conducted. Based on vibration and elastic wave theories, a dynamic response model of gyroscopic structures to high-g shocks is established. Based on the established dynamic impact response model of the MEMS ring gyroscope, the adhesion and fracture failure mechanisms of the MEMS ring gyroscope are analyzed. The equilibrium displacement for adhesion failure and the sensitive location for fracture failure are derived, and the impact expression at the point of failure is obtained. Through high overload experiments, the impact amplitude and pulse width at the critical failure of the MEMS ring gyroscope a re determined. Raman spectroscopy is used to test the surface stress of the MEMS ring gyroscope after high overload application, and the stress-sensitive locations are found to be consistent with theoretical derivations.

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针对一种MEMS环形陀螺在高过载下出现冲击失效现象，对其进行了结构动力学响应建模与失效机理分析。基于准静态、振动和弹性波理论建立了陀螺结构对环境冲击的动力学响应模型。在所建立的MEMS环形陀螺动力学冲击响应模型基础上，分析了MEMS环形陀螺的吸合和断裂失效机理，推导得到发生吸合失效发生时的平衡位移和断裂失效发生时的敏感位置，并获得了失效发生时的冲击表达式。通过高过载实验获得了MEMS环形陀螺临界失效时所加载的冲击幅值和脉宽。利用拉曼光谱仪对高过载作用后的MEMS环形陀螺的表面应力进行测试，应力敏感位置与理论推导一致。

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曹慧亮（1986—），男，教授，博士生导师，从事MEMS惯性器件研究。
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魏雯强（1997—），男，博士研究生，主要研究方向为MEMS陀螺。

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魏雯强（1997—），男，博士研究生，主要研究方向为MEMS陀螺。

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魏雯强（1997—），男，博士研究生，主要研究方向为MEMS陀螺。

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journalId=1244323073571209252, articleId=1244336193853305228, language=CN, orderNo=3, keyword=动力学响应), Keyword(id=1244336218108965855, tenantId=1146029695717560320, journalId=1244323073571209252, articleId=1244336193853305228, language=CN, orderNo=4, keyword=失效机理), Keyword(id=1244336219614720995, tenantId=1146029695717560320, journalId=1244323073571209252, articleId=1244336193853305228, language=CN, orderNo=5, keyword=冲击实验)], refs=[Reference(id=1244336224475918446, tenantId=1146029695717560320, journalId=1244323073571209252, articleId=1244336193853305228, doi=null, pmid=null, pmcid=null, year=2023, volume=31, issue=9, pageStart=932, pageEnd=939, 954, url=null, language=null, rfNumber=[1], rfOrder=0, authorNames=魏雯强, 鲁征浩, 陈方, journalName=中国惯性技术学报, refType=null, unstructuredReference=魏雯强, 鲁征浩, 陈方, 等. 芯片级多轴集成微陀螺方案对比与发展趋势分析[J]. 中国惯性技术学报, 2023, 31(9): 932-939, 954., articleTitle=芯片级多轴集成微陀螺方案对比与发展趋势分析, refAbstract=null), Reference(id=1244336224576581745, tenantId=1146029695717560320, 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Size parameters value of MEMS VRG

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参数特征数值/μm参数特征数值/μm
R谐振环半径3000br谐振环宽度50
bs支撑梁宽度30h结构厚度150
r曲梁半径100l1直梁长度300
l2直梁长度400l3直梁长度1500
), ArticleFig(id=1244336222378766419, tenantId=1146029695717560320, journalId=1244323073571209252, articleId=1244336193853305228, language=CN, label=表1, caption=

MEMS环形陀螺结构尺寸参数数值

, figureFileSmall=null, figureFileBig=null, tableContent=
参数特征数值/μm参数特征数值/μm
R谐振环半径3000br谐振环宽度50
bs支撑梁宽度30h结构厚度150
r曲梁半径100l1直梁长度300
l2直梁长度400l3直梁长度1500
), ArticleFig(id=1244336222504595544, tenantId=1146029695717560320, journalId=1244323073571209252, articleId=1244336193853305228, language=EN, label=Tab.2, caption=

Distance vector D (l) of the selected support beam

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D（l）（r和θ为单位向量）
（l1+10r+l3-l）r
（l1+10r+rsinψ1）r+rsinψ1θ，ψ1=（l-l3）/2πr
（l1+9r）r+（r+l-l3-πr/2）θ
（l1+8r+rcosψ2）r+（r+l2+rsinψ2）θ，ψ1=（l-l2-l3-πr/2）/2πr
（l1+7r）r+（l-l2-l3-3πr/2）θ
), ArticleFig(id=1244336222605258844, tenantId=1146029695717560320, journalId=1244323073571209252, articleId=1244336193853305228, language=CN, label=表2, caption=

支撑梁上的距离矢量D（l）

, figureFileSmall=null, figureFileBig=null, tableContent=
D（l）（r和θ为单位向量）
（l1+10r+l3-l）r
（l1+10r+rsinψ1）r+rsinψ1θ，ψ1=（l-l3）/2πr
（l1+9r）r+（r+l-l3-πr/2）θ
（l1+8r+rcosψ2）r+（r+l2+rsinψ2）θ，ψ1=（l-l2-l3-πr/2）/2πr
（l1+7r）r+（l-l2-l3-3πr/2）θ
), ArticleFig(id=1244336224081653856, tenantId=1146029695717560320, journalId=1244323073571209252, articleId=1244336193853305228, language=EN, label=Tab.3, caption=

Amplitude and pulse width of shock that lead to failure of MEMS VRG

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失效冲击类型幅值/g脉宽/μs
吸合平面内惯性冲击44,176.8150.6
断裂平面内惯性冲击115,799.5749.8
平面外惯性冲击92,368.6150.3
应力波冲击172,084,6923.4
), ArticleFig(id=1244336224161345635, tenantId=1146029695717560320, journalId=1244323073571209252, articleId=1244336193853305228, language=CN, label=表3, caption=

MEMS环形陀螺发生失效时冲击的幅值和脉宽

, figureFileSmall=null, figureFileBig=null, tableContent=
失效冲击类型幅值/g脉宽/μs
吸合平面内惯性冲击44,176.8150.6
断裂平面内惯性冲击115,799.5749.8
平面外惯性冲击92,368.6150.3
应力波冲击172,084,6923.4
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高过载下MEMS环形陀螺的响应建模与失效分析
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魏雯强 1 , 王瑾 1 , 蔡麒 1 , 田慧敏 1 , 黄泓侨 1 , 曹慧亮 2
中国惯性技术学报 | 惯性仪表研究与设计 2025,33(10): 1034-1042
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中国惯性技术学报 | 惯性仪表研究与设计 2025, 33(10): 1034-1042
高过载下MEMS环形陀螺的响应建模与失效分析
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魏雯强1, 王瑾1, 蔡麒1, 田慧敏1, 黄泓侨1, 曹慧亮2
作者信息
  • 1.中北大学　仪器与电子学院，太原　030051
  • 2.北京理工大学　集成电路与电子学院，北京　100081

    • 魏雯强（1997—），男，博士研究生，主要研究方向为MEMS陀螺。

通讯作者:

曹慧亮（1986—），男，教授，博士生导师，从事MEMS惯性器件研究。
Response modeling and failure analysis of MEMS ring gyroscopes under high overload
Wenqiang WEI1, Jin WANG1, Qi CAI1, Huimin TIAN1, Hongqiao HUANG1, Huiliang CAO2
Affiliations
  • 1.School of Instrument and Electronics, North University of China, Taiyuan 030051, China
  • 2.School of Integrated Circuits and Electronics, Beijing Institute of Technology, Beijing 100081, China
出版时间: 2025-10-30 doi: 10.13695/j.cnki.12-1222/o3.2025.10.010
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摘要
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针对一种MEMS环形陀螺在高过载下出现冲击失效现象，对其进行了结构动力学响应建模与失效机理分析。基于准静态、振动和弹性波理论建立了陀螺结构对环境冲击的动力学响应模型。在所建立的MEMS环形陀螺动力学冲击响应模型基础上，分析了MEMS环形陀螺的吸合和断裂失效机理，推导得到发生吸合失效发生时的平衡位移和断裂失效发生时的敏感位置，并获得了失效发生时的冲击表达式。通过高过载实验获得了MEMS环形陀螺临界失效时所加载的冲击幅值和脉宽。利用拉曼光谱仪对高过载作用后的MEMS环形陀螺的表面应力进行测试，应力敏感位置与理论推导一致。

MEMS环形陀螺  /  高过载  /  动力学响应  /  失效机理  /  冲击实验

Regarding the shock failure of a micro-electro-mechanical system (MEMS) vibrating ring gyroscope (VRG) under high overload, structural dynamic response modeling and failure mechanism analysis are conducted. Based on vibration and elastic wave theories, a dynamic response model of gyroscopic structures to high-g shocks is established. Based on the established dynamic impact response model of the MEMS ring gyroscope, the adhesion and fracture failure mechanisms of the MEMS ring gyroscope are analyzed. The equilibrium displacement for adhesion failure and the sensitive location for fracture failure are derived, and the impact expression at the point of failure is obtained. Through high overload experiments, the impact amplitude and pulse width at the critical failure of the MEMS ring gyroscope a re determined. Raman spectroscopy is used to test the surface stress of the MEMS ring gyroscope after high overload application, and the stress-sensitive locations are found to be consistent with theoretical derivations.

MEMS VRG  /  high overload  /  dynamic response  /  failure mechanism  /  shock experiment
魏雯强, 王瑾, 蔡麒, 田慧敏, 黄泓侨, 曹慧亮. 高过载下MEMS环形陀螺的响应建模与失效分析. 中国惯性技术学报, 2025 , 33 (10) : 1034 -1042 . DOI: 10.13695/j.cnki.12-1222/o3.2025.10.010
Wenqiang WEI, Jin WANG, Qi CAI, Huimin TIAN, Hongqiao HUANG, Huiliang CAO. Response modeling and failure analysis of MEMS ring gyroscopes under high overload[J]. Journal of Chinese Inertial Technology, 2025 , 33 (10) : 1034 -1042 . DOI: 10.13695/j.cnki.12-1222/o3.2025.10.010
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MEMS陀螺仪作为角速率传感器，以其低成本和高可靠性等优点，被广泛应用于智能炮弹、无人机系统、汽车工程和地质勘探等军用、民用领域[1-5]，且不可避免地在高过载环境下使用[6-8]。MEMS环形陀螺（Vibratory Rate Gyroscope，VRG）被公认为是高性能的MEMS陀螺，具有对称结构和与工作模态分离的惯性模态，能够很好地抵抗环境冲击和不良振动[9-11]。
MEMS环形陀螺基于哥氏原理，结构中的谐振环提供检测角速率的哥氏质量。在高过载下，谐振环产生位移响应，支撑梁作为谐振环与锚点的连接结构存在应力分布。由于谐振环在平面内的位移会改变接口电容的输出信号，之前的研究研究工作将关注重点放置在平面内振动造成的影响。Sieberer S等人研究了高过载下MEMS环形陀螺的冲击响应受非线性静电力的影响[12]，MEMS环形陀螺的振动模态在冲击和静电力的耦合作用下发生模态耦合。Chouvion B等人研究了MEMS环形陀螺振动参数在高过载下发生变化的动态特性[13]。在高过载冲击作用下，MEMS环形陀螺将出现吸合和断裂失效。在高冲击作用下，活动机构产生较大摆幅，在静电力作用下致使电容机构贴合[14]，最终使陀螺失效。断裂失效通常出现在应力较为集中的地方[15]，如锚点和支撑梁附近，此状态无法逆转。本文的关注重点是空间维度下MEMS环形陀螺对高过载的冲击响应，并基于振动和弹性波理论建立了MEMS环形陀螺在对应类型冲击作用下的动力学响应模型。基于已建立的MEMS环形陀螺冲击动力学响应模型，计算得到了MEMS环形陀螺发生吸合时的惯性位移；获得了结构中冲击应力敏感位置，以及敏感位置处应力对冲击载荷的映射表达式。此外，本文通过冲击实验，验证了结构的应力敏感位置，获得了MEMS环形陀螺发生临界失效时的冲击幅值和脉宽。
1　高过载下MEMS环形陀螺的冲击响应建模
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1.1　MEMS环形陀螺结构与冲击作用原理
本文的研究对象为MEMS环形陀螺[16]，其结构如图1所示，主要由谐振环、谐振环内外两侧对称设置的8组独立电极、八根S形支撑梁和锚点。尺寸参数特征见表1。
高过载环境对传感器的冲击形式主要有两种：惯性力的作用和应力波的传播。根据Srikar和Senturia提出的理论，MEMS机械结构对冲击的响应由特定参数及其相互关系决定[17]，即微机械结构的固有振动周期τv、冲击脉冲持续时间τ和应力波传递时间τw（应力波到达传播边界的时间）：
式（1）中λinertia和ωinertia分别为MEMS环形陀螺惯性模态的频率和圆频率，（l1+2l2+l3+3l+5πr）为应力波的传播距离。
高过载环境对传感器的冲击a（t）可用半正弦脉冲表示[18]：
如图2所示，对冲击载荷的类型作如下定义和划分[19]：当τ<2/λw时，为应力波冲击，记为aw（t）；当2/λw≤τ<5/λv时，为振动冲击，记为av（t）；当τ≥5/λv时，为准静态冲击，记为aq.s（t）。由于准静态冲击和振动冲击的作用效果为谐振环产生惯性位移，故统称为惯性冲击。
1.2　MEMS环形陀螺的惯性冲击响应
惯性冲击作用下，谐振环上某一点的位移可分解为径向、周向和平面外三个方向的分量。记冲击在平面内的分量为ain（t），与驱动轴夹角为φ；记冲击在平面外的分量为aout（t）。平面内惯性位移可由极坐标系描述，坐标系起始轴与驱动轴重合。在角位置为θ处的惯性位移可分解为径向位移u（θ）、切向位移v（θ）和面外位移w（θ）[15]：
式（3）中q（t）和p（t）为MEMS陀螺平面内、外惯性模态的广义位移。在惯性模态中，谐振环不发生弯曲，故不提供应变能而只提供动能：
单根S形支撑梁的刚度可分解为沿环径向kr、周向kθ和平面外方向kout，根据能量法[16]可获得其关于尺寸的表达式：
式（5）中E为结构材料的弹性模量。
S形支撑梁与锚点连接端可认为是固定端，与谐振环连接端可认为是自由端，与谐振环在该处的位移相同。支撑梁的质量远小于谐振环，故不提供动能，其在惯性模态中提供的应变能为[16]：
谐振环与内、外电极构成电容，由于电极之间的间隙很小，可以认为是一个连续的环形电极[20]。直流电势vdc施加在所有的内、外电极上，相反的交流电势vac，施加在驱动轴两端的内、外电极上，电势能为：
式（7）中的第一项提供驱动力，第二项提供静电势。
将式（4）~式（7）代入拉格朗日方程，可得惯性模态的动力学响应方程：
式（8）中mr=2πρRbrh为环的质量，ρ为结构材料密度，cq和cp为面内惯性模态和面外惯性模态的阻尼。由上式可得平面内、外惯性模态频率ωq和ωp：
如前文所述，当冲击脉宽τ满足τ≥5/λv时为准静态冲击。基于准静态理论，冲击可视为恒定加速度作用，惯性位移的响应为：
当冲击脉宽τ满足2/λw≤τ<5/λv为振动冲击，根据杜哈美积分可得陀螺敏感结构对冲击的惯性位移响应[16]：
式（11）中ζq=cq/（mrωq）和ζp=cp/（mrωp）为模态的阻尼比。
1.3　MEMS环形陀螺的应力波冲击响应
MEMS环形陀螺对应力波冲击的响应分析对象为结构中的S型支撑梁。支撑梁由直梁和曲梁连接而成。应力波在两者中的传播特性不同。由于平面内曲梁的存在，应力波在平面内传播时存在拉伸、剪切和弯曲波相互耦合，故优先分析应力波在支撑梁平面内的传播特性。
如图3（a）所示，us、ws和φs分别为直梁中心线上质点（距离梁起始位置线长度为x处）的轴向拉伸位移、在平面内的横向剪切位移和截面转动角度，并构成位移矩阵Ds=[us，ws，φs]；Ns、Qs和Ms分别为质点所在截面的轴力、剪切力和弯矩，并构成内力矩阵Fs=[Ns，Qs，Ms]。基于Timoshenko理论[21]有：
式（12）中Hs为直梁中位移到内力的传递矩阵，K为Timoshenko修正系数，A=bsh和I=（bs）3h分别为截面的面积和惯性矩。
整个截面处的动力学方程为：
设式（13）有谐波解Ds=[Ws，Φs，Us]exp[i（ωt+kx）]，Ws，Φs和Us为各谐波的幅值，ω为频率，k为波数，i为虚数单位。
将谐波解代入式（12）、式（13）可得直梁中拉伸波波数ks1和剪切波波数ks2、ks3的表达式：
位移矩阵Ds可表示为如下形式：
式（15）中Ps（t）=exp（iωt）[Ps1，Ps2，Ps3]为直梁中基波幅值矩阵；+/-表示应力波的传播方向；Ψs（x）为位移转化矩阵，且有。
由式（12）~式（15）可解得为：
式（16）中αsj=[（ksj）2-2ρω2（1+v）]/（iksjKE）且j=2，3。
直梁上平面内一点的位移和内力为：
对于直梁在平面外的位移和内力，将式（17）中的I=（bs）3h替代为Iout=（bs）3h。
如图3（b）所示，uc、wc和φc分别为曲梁中心线上质点（距离梁起始位置角度为θc处）的切向拉伸位移、径向剪切位移和截面转动角度，并构成位移矩阵Dc=[uc，wc，φc]；Ns、Qs和Ms分别为质点所在截面的轴力、剪切力和弯矩，并构成内力矩阵Fs=[Ns，Qs，Ms]。基于Timoshenko理论，曲梁中位移到内力的传递矩阵：
式（18）中kr=（Iin/A）1/2为曲梁截面的回转半径。
整个截面处的动力学方程为：
设式（19）有谐波解Dc=[Wc，Φc，Uc]exp[i（ωt+kθc）]，Wc，Φc和Uc为各谐波的幅值。
将谐波解代入式（19）可得曲梁中拉伸波波数kc1、剪切波波数kc2、弯曲波波数kc3的表达式：
式（20）中ξmax，ξmin，ξmid为ξi实数最大、最小和中间值，具体表达式为：
位移矩阵Dc可表示为式（24）：
式（24）中Pc（t）=exp（iωt）[Pc1，Pc2，Pc3]T为曲梁中基波幅值矩阵；+/-表示应力波的传播方向；Ψc（θc）为位移转化矩阵，且有。
由式（18）~式（20）可解得为：
βj和γj（j=1，2，3）的具体表达式为：
曲梁上平面内一点的内力为：
如图4所示，在应力波传导路径中存在截面突变，发生在支撑梁和锚点、谐振环连接处。锚点处可视为不等截面直杆的复合杆，谐振环处可视为曲梁。
当应力波由大端向小端传播时出现产生应力波放大现象[22,23]，并定义放大系数M，其值与杆的厚度和截面形状无关而仅与截面积相关：
对于支撑梁和谐振环连接处，该界面的位移与内力连续条件为：
记波矢量、、和有以下关系：
由式（17）和式（27）的推论可得：
若定义应力波加速度沿支撑梁径向、切向和平面外方向分解为aw，r（t）、aw，θ（t）和aw，out（t），由式（2）和式（16）从锚点进入梁结构的各初始谐波分量、和为：
式（32）中ka1、ka2和ka3由式（14）中的bs替代为ba=（3l4-bs）得到，αaj=[（kaj）2-2ρω2（1+v）]/（ikajKE）。
由式（17）、式（27）、式（28）和式（31）可得应力波到达谐振环时产生的平面内位移Dfinal与内力Ffinal：
将式（33）中的I=（bs）3h替代为Iout=（bs）3h即可得到应力波到达谐振环时的平面外位移与内力。
2　高过载下MEMS环形陀螺的失效分析
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2.1　MEMS环形陀螺的吸合失效
高过载冲击环境冲击作用下，陀螺中可活动的谐振环由于受冲击作用产生较大位移。电极电容间静电力随极板间距呈非线性增长，当静电力大于支撑梁提供的弹性回复力时，谐振环将持续位移并最终与电极板发生吸合失效。极板与谐振环间的总静电力Fe可由式（7）得到：
由式（6）可得机械结构提供的回复力Fk为：
令总静电力Fe与机械回复力Fk相等，即可得到平衡位移qe为：
当MEMS环形陀螺对冲击作用的惯性位移响应q大于平衡位移qe时，总静电力Fe将大于机械回复力Fk，发生吸合失效。
2.2　MEMS环形陀螺的断裂失效
MEMS环形陀螺的机械结构由单晶硅制成，具有高硬度但脆性的材料属性，当受冲击产生的结构应力超过许用应力时将出现裂纹直至断裂，将影响MEMS环形陀螺的性能。一般认为单晶硅的断裂应力为790 MPa[24]。
由式（5）和式（10）可知，在惯性冲击下各支撑梁自由端在：
由于支撑梁靠近锚点段受到自由端等效作用力的弯矩更大，故选取如图5所示的支撑梁段进行应力分析。定义外力在截面l（距离锚点的路径）处的距离矢量D（l），其在各段中的表达式如表2所示。
可计算得到各等效作用力在l截面上产生的最大应力为：
平面内冲击造成的应力峰值出现在梁j=2，7上的支撑梁和锚点间的连接处，平面外冲击造成的应力峰值出现在各支撑梁与锚点的连接处，对于惯性冲击，最大应力的表达式为：
对于应力波冲击造成的结构应力，面外方向无敏感位置，面内应力敏感位置在支撑梁和锚点、谐振环的连接界面处。由上一节的推导可知在这两个位置的内力矩阵Fw为：
应力与内力满足以下关系：
式（41）中σw，1和τw，1分别为的正应力和剪应力。
3　高过载冲击实验
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由式（1）得弹性波传递时间τw≈24.31 μs。通过扫描MEMS环形陀螺的频率，确定平面内惯性模态频率为6284 Hz，所对应的时间尺度为159.13 μs。通过有限元仿真，平面外的惯性模态频率为7278 Hz，所对应的时间尺度为137.40 μs。
如图6所示，使用霍普金森杆对MEMS环形陀螺进行冲击实验。陀螺仪固定在透射杆尾端。通过衍射光栅干涉仪和应变检测仪采集冲击的幅值和脉宽。霍普金森杆能产生加速度幅值在10，000~300，000 g（g为重力加速度）之间，脉冲宽度在20~50 μs之间的冲击。当冲击的脉宽小于24 μs或在24 μs左右时为应力波冲击，脉宽大于24 μs时为振动冲击。
发生失效时的加载冲击幅值和脉宽见表3。表3中对惯性冲击与应力波击的区分，仅针对该MEMS环形陀螺的机械结构，且依据第1.1节提出的概念进行。通过在MEMS环形陀螺上加载具有相似幅度和脉宽的冲击，验证失效临界条件的重复性。
对上电后的MEMS环形陀螺上加载加速度幅值为44，176.81 g、脉宽为50.6 μs的平面内振动冲击时，出现吸合失效。如图7所示，MEMS环形陀螺的谐振环对振动冲击产生惯性位移响应，贴合在外电极上，支承梁在谐振环的带动下产生恒定静态位移。
对未上电的MEMS环形陀螺上加载加速度幅值为115，799.57 g、脉宽为49.8 μs的平面内振动冲击时，支撑梁和锚点连接处发生断裂，如图8所示。当加载加速度幅值为92，368.61 g、脉宽为50.3 μs的平面外振动冲击时，支撑梁锚点连接处发生断裂，如图9所示。由于冲击脉冲宽度接近于MEMS环形陀螺的面外模态频率所对应的时间尺度，因此造成失效的幅值要比面内振动引起失效的幅值小。对未上电的MEMS环形陀螺上加载加速度幅值为172，084.69 μs、脉宽为23.4 μs的应力波冲击时，支撑梁和锚点、谐振环连接处发生断裂，如图10所示。在不同条件冲击下，MEMS环形陀螺发生断裂的位置和理论推导的应力敏感位置相一致。
拉曼光谱可用于MEMS环形陀螺机械结构的应力分析[25]。如图11所示，在MEMS环形陀螺结构的支承梁上选取六个测量点。在MEMS环形陀螺上加载平面内和平面外冲击，加速度幅值约为40，000 g，脉冲宽度约为30 μs。拉曼光谱应力测试结果如图12所示，应力敏感位置为测试点3和4，与理论分析一致。
4　结论
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本文以具有S形支撑梁的MEMS环形陀螺为研究对象，基于准静态、振动和弹性波理论，建立了MEMS环形陀螺敏感结构在高过载冲击下的动力学响应模型。在此基础上，针对MEMS器件在高过载环境中的典型失效模式，分析了MEMS环形陀螺的失效机理。计算了发生吸合失效时的惯性位移表达式。推导了惯性响应和应力波响应时MEMS环形陀螺支撑梁结构中的应力敏感位置。对冲击下分层失效的物理过程进行建模，给出了层间截面中应力表达式。通过冲击实验获得了MEMS环形陀螺失效的临界冲击幅值和脉宽。本文为优化和提高MEMS环形陀螺抗冲击能力提供了动力学建模和失效分析基础。
基金
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  • 国家自然科学基金(U2230206)
  • 国家重点研发计划(2022YFB3205000)
文献
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2025年第33卷第10期
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doi: 10.13695/j.cnki.12-1222/o3.2025.10.010
  • 接收时间：2024-05-30
  • 首发时间：2026-03-27
  • 出版时间：2025-10-30
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  • 收稿日期：2024-05-30
  • 录用日期：2025-07-04
基金
国家自然科学基金(U2230206)
国家重点研发计划(2022YFB3205000)
作者信息
    1.中北大学　仪器与电子学院，太原　030051
    2.北京理工大学　集成电路与电子学院，北京　100081

通讯作者:

曹慧亮（1986—），男，教授，博士生导师，从事MEMS惯性器件研究。
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