Influence Of Electrostatic Force Nonlinearity On Dynamic Characteristics Of Multi-dof Micro Gyroscope

Micromechanical gyroscope is a kind of MEMS inertial device driven by electrostatic force,which is used to measure angular velocity and angular displacement.It is widely used in the military and civil fields with the characteristics of reliable performance,small size,fast response,low energy consumption,cheapness and intelligence,and has a good market and development prospects.Compared with the traditional single degree of freedom(SDOF)micro gyroscope,the multi degree of freedom(MDOF)micro gyroscope has the characteristics of high sensitivity,wide bandwidth and high robustness by adding the DOF of the drive and sensor,which greatly makes up for the design defect of SDOF micro gyroscope’s narrow bandwidth.However,due to the increase of DOF,its structure becomes more complex,which increases the difficulty of machining,and the nonlinear factors in the system will also increase.These nonlinear factors will lead to the unstable working of micro gyroscope,and even cause the failure of linear design.Therefore,research on the nonlinear dynamic of MDOF micro gyroscope has important theoretical significance and engineering application value for controlling and eliminating the effects of nonlinearity.To reveal the effect of nonlinear factors on the static and dynamic performance of MDOF micro gyroscope,this paper takes a kind of double drive and double sensor 4-DOF micro mechanical gyroscope as the research object.And the effect of electrostatic force nonlinearity and comb inclination angle on performance of 4-DOF micro gyroscope is studied by the methods of theoretical analysis and numerical simulation respectively.To analyze the effect of nonlinear factors on the dynamic characteristics of micro gyroscope,the linear dynamic equation of micro gyroscope is solved by complex index method.Then the nonlinear dynamic equation is analyzed by Hamilton principle and multi-scale method respectively.The effect of comb spacing and DC bias voltage on the static and dynamic performance of micro gyroscope is explored.The study found that: the pull-in voltage decreases with the decrease of comb spacing in the case of electrostatic nonlinearity.In addition,the occurrence of pull-in will be promote when decreasing comb spacing or increasing DC bias voltage.The conditions for the secondary pull-in of the system are found under the combined action of electrostatic force nonlinearity and stiffness nonlinearity.There are critical values for comb spacing and DC bias voltage,which is the boundary point of whether the electrostatic force nonlinearity has an effect.The critical values can be determined by nonlinear dynamic analysis.The research results can provide theoretical basis for the parameter design of micro gyroscope and solve the problem of linear design failure.As the DC bias voltage is constant,the electrostatic force nonlinearity increases with the decrease of comb spacing when its comb spacing is less than the critical value,and the system remains linear when it more than its critical value.The system can avoid the effect of the electrostatic force nonlinearity when the DC bias voltage is less than its critical value,the system has soft characteristics and the electrostatic force nonlinearity increases with the increase of the DC bias voltage when it more than its critical value.The effect of electrostatic force nonlinearity on the bandwidth can be ignored duo to the great robustness of MDOF micro gyroscope.But the shift of resonance frequency and the electrostatic force nonlinearity will reduce the sensitivity and stability of micro gyroscope.Etching error is an inevitable defect in micromachining.To make the dynamic model of MDOF micro gyroscope more refined,the effect of comb inclination angle caused by machining error on its dynamic performance is analyzed under linear and nonlinear conditions.The study found that: The comb inclination angle will lead to the shift of resonance frequency under linear condition,at the same time,the sensitivity will be greatly reduced,but the bandwidth will not be affected.The comb inclination angle has the stiffness hardening effect on the response output under electrostatic force nonlinearity,and the hardening effect is the strongest when the comb inclination angle is equal to 0.15 degree.The hardening effect decreases with the increase of the angle when the inclination angle more than 0.15 degree.The stiffness hardening caused by comb inclination can partially offset the stiffness softening effect caused by electrostatic nonlinearity,and can improve the sensitivity and dynamic stability of micro gyroscope.