静电驱动下指数型变截面梁式陀螺仪的非线性特性与分析  

Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven

作　　者：张昆鹏 畅兆敏 郝淑英 张琪昌 冯晶晶 Kunpeng Zhang;Zhaomin Chang;Shuying Hao;Qichang Zhang;Feng(Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control,Schoolof MechanicalEngineering,Tianjin University of Technology,Tianjin 300384,China;National Demonstration Center for Experimental Mechanical and Electrical Engineering Education,Tianjin University of Technology Tianjin 300384,China;Tianjn Key Laorary of Noninearynamics and Conto,Soolof Mhancal Engineering,Tinjin UnverTianjn 30002,China)

机构地区：[1]Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control,Schoolof MechanicalEngineering,Tianjin University of Technology,Tianjin 300384,China [2]National Demonstration Center for Experimental Mechanical and Electrical Engineering Education,Tianjin University of Technology Tianjin 300384,China [3]Tianjn Key Laorary of Noninearynamics and Conto,Soolof MhancalEngineering,Tinjin UnverTianjn 30002,China

出　　处：《Acta Mechanica Sinica》2023年第3期168-184,共17页力学学报（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.12072234).

摘　　要：本文设计一类新型的指数型变截面梁式微陀螺,变截面指数梁的宽度与长度的关系为指数函数变化的形式,且指数梁的截面变化因子小于等于零,梁的厚度随梁长仍保持不变.考虑了曲率非线性和惯性非线性对系统的影响,利用扩展哈密顿原理、单模近似法和拉格朗日微分方程,建立了指数型变截面梁式非线性陀螺仪的振动控制方程、边界条件和非线性离散化模型,且考虑了陀螺仪驱动和检测两个方向上直流电压和交流电压对系统响应的影响,采用ADM法求解陀螺仪系统在不同截面变化因子下的静态响应,利用多尺度法对系统的非线性离散化模型进行摄动求解,分析各个参数对陀螺仪动态响应的影响规律.结果表明,随着截面变化因子的增大,指数梁陀螺仪的吸合电压和一阶固有频率逐渐增加,并呈现近似线性的变化规律.通过调节指数梁截面变化因子,可以控制科氏力响应峰值频率和检测峰值频率的差值.利用指数梁陀螺仪系统的硬化非线性特征,当交流电压施加在指数梁厚度方向时,选择合适的指数截面变化因子、阻尼比和交流电压,可以使指数梁式陀螺仪系统获得更好的带宽性能及线性可测范围;当交流电压施加在指数梁宽度方向,选取合适的截面变化因子,不仅可以获得较高的系统灵敏度性能,同时增加陀螺仪对外部输入角速度的线性可测范围.In this paper,a novel vibrating beam gyroscope with exponential variable cross-section is designed.Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change.The exponential shape factor(ESF)of beam is less than or equal to zero,and the thickness of the beam remains constant with the beam length.The effects of curvature nonlinearity and inertia nonlinearity on the system are considered.The vibration control equations,boundary conditions,and nonlinear discretization model of the exponential beam micro-gyroscope(EBMG)are developed by using the extended Hamiltonian principle,the single-mode approximation method,and the Lagrange differential equations.The effects of direct current(DC)and alternating current(AC)voltages on the system response in both the drive and sense directions of the gyroscope are analyzed.The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method(ADM).The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope.The results show that with the increase of the ESF,the pull-in voltage and the first-order natural frequency of the EBMG increase gradually,and have a linear change pattern approximately.By adjusting the ESF,the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled.Utilizing the nonlinear harden characteristics of the EBMG system,when the AC voltage is applied in the thickness direction of exponential beam,the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF,damping ratio,and AC voltage;when the AC voltage is applied in the width direction of the exponential beam,the EBMG can not only obtain the higher sensitivity performance,but also increase the linear detectable range by choosing an appropriate ESF.

关 键 词：Exponential beam MICRO-GYROSCOPE Nonlinear characteristics BANDWIDTH Sensitivity 

分 类 号：O3[理学—力学]