The Nonlinear Dynamics Research Of A Vibrating Ring-type MEMS Gyroscope

With the continuous development and progress of science and technology,the micro-electromechanical system(MEMS)technology has become more and more mature,which has gradually promoted the development of inertial sensors.The MEMS gyroscope is an inertial sensor for measuring the angular velocity of a rotating object.Different from the traditional gyroscope,the former is mainly based on the Coriolis effect principle,using vibration mass components instead of the traditional momentum wheel to measure angular velocity,while the latter is mainly based on the principle of conservation of angular momentum.Compared with traditional gyroscopes,this kind of gyroscope has many advantages,such as small size,light weight,low power consumption,strong anti-overload ability and low price.It has been widely used in aerospace and national defense and military fields.However,because the MEMS gyroscope is composed of many components,and these components have some non-linear characteristics,or there are some non-linear phenomena between them,it is of great theoretical significance to study the non-linear vibration response characteristics of the MEMS gyroscope system in the future industrial application.In this paper,the vibration ring-type MEMS gyroscope is taken as the research object.The working mechanism and response characteristics of the gyroscope and the influence of important parameters on the system response are analyzed.The harmonic oscillator of this gyroscope is mainly a symmetrical ring structure.The focus is on the pair of degenerate elliptical modes,one of which is taken as the drive mode and the other as the sense mode for the sensor.In addition,these two modes are coupled by Coriolis effect and geometric nonlinearity effect.Nonlinearity is mainly caused by the stiffness of the ring and the potential energy between the ring and the electrode,which will inevitably affect the response.Finally,in order to change the structural stiffness of the system,piezoelectric thin film is added to the gyroscope.At the same time,parametric excitation is introduced to discuss its instability characteristics.The main research contents of this paper are divided into the following parts.(1)Introduce the working principle of micro-gyroscope and establish the dynamic model of ring structure gyroscope system.Based on the assumption of thin shell theory,the non-linear dynamic equation of gyroscope system with rotating ring structure is established by Lagrange method.(2)Neglecting the non-linear term in the dynamic equation,the linear system of gyroscope is studied theoretically.By solving the linear equation,the dynamics of the gyroscope system is studied,and the effects of different damping,driving voltage and angular velocity on the system response are discussed.In addition,the mechanism of the response amplitude of the sensitive direction changing with the angular velocity is extended.(3)The nonlinearity in gyroscope system is studied theoretically.The response of the nonlinear dynamic equation is analyzed by numerical method and multi-scale method.The influence of different parameters on the non-linear amplitude-frequency response is discussed,and the corresponding amplitude-frequency characteristics are explained.(4)The stiffness of the ring is changed by pasting piezoelectric film on the ring in the gyroscope,and then the frequency of the system is changed.Similarly,the dynamic equation of the system is established by Lagrange method,ignoring the non-linear term in the equation.The influence of different bias voltage and piezoelectric voltage on the following factors is studied: natural frequency of the ring at rest,quality factor Q,amplitude-frequency response,modal frequency of the two directions when the ring rotates,and the change of amplitude with angular velocity.Finally,parametric excitation is introduced and the instability characteristics of parametric excitation system are analyzed by multi-scale method.