Influence Of Stiffness Nonlinearity On Dynamic Characteristics Of Double Sense Micro-gyroscope

Micro-gyroscope is a kind of micro-sensor that measures the angular velocity of a carrier.The micro-gyroscope has many advantages such as small size,low cost,high performance and high reliability compared to traditional gyroscope.It has very important application value and great contribution in military and civilian fields.In recent years,experts at home and abroad have made in-depth exploration on higher performance MEMS gyroscopes.At present,the research on the theory of single-degree-of-freedom and multi-degree-of-freedom gyroscope linear systems was relatively mature.Most of the models were based on ideal linear dynamic analysis,while ignoring the seriousness of the problem that the ubiquitous nonlinear factors in the micro-gyroscope would make the linear dynamic design failed.Therefore,in the study of single-drive double-sense micro-gyroscope with three degrees of freedom,electrostatic force nonlinearity under the edge effect and stiffness nonlinearity are considered,theoretical analysis and a numerical calculation are used to study the influence of nonlinear factors on the micro-gyro.The results provide a theoretical basis for further analysis of double sense gyroscopes complex nonlinear dynamic.To compare the influence of linear stiffness and nonlinear stiffness on the output signal of double sense micro-gyroscope,firstly,the effect of Coriolis force on the test output is considered,the linear steady response of double sense equation is solved by complex exponential method.Secondly,the multi-scale method is used to perturbation analyze of driving nonlinear dynamic equation to investigate the effect of driving stiffness nonlinearity on double sense micro-gyroscope system main resonance’s amplitude frequency curve,resonance frequency,sensitivity and bandwidth are discussed.It is found that single-drive micro-gyroscope driving bandwidth will affect the stability of the detection bandwidth and the sensitivity of the micro-gyroscope regardless of whether or not to consider nonlinearity;Driving stiffness nonlinearity leads to the shift of the driving resonance frequency,and the offset is positively correlated with the nonlinear stiffness coefficient,but main resonance peak has nothing to do with the nonlinearity stiffness.The first and second amplitude curves show typical nonlinear hardening characteristics at the driving modal frequency,and the weaker stiffness nonlinearity also leads to driving direction,detection one and two amplitudes decrease significantly at the driving frequency;Driving stiffness nonlinearly induces amplitude-frequency curve jumps,resonance frequency offset,multiple solutions and solutions instability phenomenon that have a significant impact on the output signal,also reduce the stability of the micro-gyro detection signal and produces large deviations compared to sensitivity results based on the linear system.The research results have guiding value for improving the micro-gyro sensitivity stability.The effects of electrostatic force nonlinearity and the stiffness cubic nonlinearity on the dynamic characteristics of the double sense gyroscope are analyzed.The conclusions: the nonlinear instantaneous natural frequency is related to the driving peak and positively correlated with the stiffness cube nonlinearity,and the growth rate increases with the increase of peak.The smaller the non-overlap length of the comb teeth,the larger the DC bias voltage,the larger the frequency offset,the softening property of the electrostatic force is also stronger;By adjusting the hardening property caused by driving stiffness nonlinearity can balance the softening property brought by electrostatic force,which not only makes the amplitude-frequency curve shows an ideal linear state,but also avoids the occurrence of frequency instability and amplitude jump caused by hardening and softening properties,and also obtains higher sensitivity and eliminates the effect of nonlinearity on the gyroscope bandwidth.The results provide a theoretical basis for eliminating or reducing the electrostatic force nonlinear of the micro-gyroscope.The sense stiffness nonlinearity directly affects the sense output of micro-gyro,and the multi-scale method is used to solve the nonlinear stiffness dynamic equation of the micro-gyro sense direction.A method of effectively dealing with the coupling terms of high-dimensional nonlinear equations is proposed.The impacts of the sense stiffness nonlinearity on the amplitude frequency curves and resonance frequency of the double sense gyroscopes are investigated.It is found that the sense stiffness nonlinearity results in a serious amplitude jump of sense one and two amplitude frequency curves at the sense mode frequency,and sensitivity instability between the frequency range of sense one and the driving mode,that is,the stability of micro-gyro performance is damaged.The stability of the gyro sensitivity and bandwidth instable range are very sensitive to the cubic nonlinear stiffness of the elastic beam.When the stiffness nonlinearity reaches a certain value,its slight increase seriously affects the micro-gyro sensitivity stability and a obvious increase to bandwidth instable range,which can lead to the failure of linear system design.The results provide the guiding value for improving the performance of multidimensional gyroscopes and other complex nonlinear dynamics.