Nonlinear Internal Resonance And Parametric Performance Study Of Hybrid Driven T-beam Gyroscope

Micro-gyroscopes are MEMS sensors that measure the angular velocity of a carrier.Most of the existing linear micromechanical gyros follow the design concept of modematching,which results in large response amplitudes.The gyroscope system usually operates in an environment with high quality factor,which makes the gyroscope’s response sensitivity drop dramatically once the matching requirement is difficult to be met.To solve this problem,this paper is based on a T-beam electrostatic drive resonator,which is improved to a T-beam gyroscope by adding a piezoelectric film.Since the driving and detection modes of the gyroscope are designed with a 2:1 frequency relationship,the low-order detection modes are excited by nonlinear coupling selfparameters,and the unique structure of the T-beam has a square nonlinearity,which enhances the response bandwidth,and the sensitivity performance of the gyroscope is enhanced by a hybrid piezoelectric-electrostatic and reference-excitation-electrostatic drive.The details of the study are as follows.Firstly,the dynamics models of the gyroscope with hybrid piezo-electrostatic drive and hybrid parametric-electrostatic drive are established,and the first two orders of inplane modes of the T-beam are obtained by Hamilton’s principle and dimensioned to obtain an accurately tuned 2:1 internal resonance structure.The Lagrangian principle is used to establish the dynamical model and the Galliakin discretization is used to obtain the reduced-order model with two degrees of freedom,which retains the quadratic inertial nonlinear terms of the coupled two-order modes while retaining the higherorder terms of the electrostatic force to study the static absorption phenomenon.The parametric stability characteristics of the parametrically stabilized system are solved by using the Flokay principle combined with the multiscale regression method,and the influence law of different parameters on the parametric stability characteristics.The response of the hybrid piezo-electrostatic driven gyroscope is analyzed for three different detection bandwidths in vacuum and non-vacuum environments with two quality factors.The results show that the quadratic nonlinearity of the gyroscope is more obvious in the vacuum environment and therefore the gain is higher,but the detection bandwidth is slightly narrower;the quadratic nonlinearity of the gyroscope is slightly weaker in the non-vacuum environment,so there is a significant detection plateau in the detection response and a better bandwidth can be obtained,but the sensitivity is reduced.With the hybrid drive,the input energy of the gyroscope is significantly higher,which makes the gyroscope’s performance improved in both operating environments,especially in the lower quality factor operating environment,the advantage of the hybrid drive is more obvious.The nonlinear mode coupling of the gyroscope makes the gyroscope response with significant quadratic nonlinearity,which improves the response bandwidth,and the energy saturation characteristic of 2:1internal resonance makes the gyroscope gain increase significantly.For the parametric-electrostatic driven gyroscope,the response characteristics of three different detection bandwidths are analyzed in this paper,and the amplification effect of the parametric excitation is obvious when comparing the detection mode response under another hybrid drive.In the non-vacuum operating environment,also due to the amplification of the parametric excitation,the square nonlinear characteristics of the system are more obvious.At this time,if you want to maintain the detection frequency response of the detection platform,the response bandwidth is less than that of the piezoelectric-static drive.In summary,the vacuum environment is more suitable for parametric-static driven gyroscope,while the non-vacuum environment,if you want to obtain a larger bandwidth response can be used piezo-electrostatic driven gyroscope.