The dynamics of a vibrating ring microgyroscope operating in the forced oscillation mode is investigated. The elastic and viscous anisotropy of the resonator and the nonlinearity of oscillations are taken into consideration. Additional nonlinear terms are suggested for the mathematical model of resonator dynamics. In addition to cubic nonlinearity, nonlinearity of the fifth degree is considered. By using the Krylov-Bogolyubov averaging method, equations containing parameters characterizing damping, elastic and viscous anisotropy, as well as coefficients of oscillation nonlinearity are deduced. The parameter identification problem is reduced to solving an overdetermined system of algebraic equations that are linear in the parameters to be identified. The proposed identification method allows testing at large oscillation amplitudes corresponding to a sufficiently high signal-to-noise ratio. It is shown that taking nonlinearities into account significantly increases the accuracy of parameter identification in the case of large oscillation amplitudes.
Accuracy improvement of MEMS gyros requires not only microelectronic development but also the investigations of the mathematical model of sensitive element dynamics. In the present paper, we study the errors of the vibrating microgyroscope which arise because of nonlinear dynamics of a sensitive element. A MEMS tuning fork gyroscope with elastic rods is considered. Nonlinear differential equations of bending vibrations of sensitive element on the moving basis are derived. Free nonlinear vibrations of gyroscopes as the flexible rod are studied. Nonlinear dynamics of gyroscope on the moving basis are investigated by asymptotic two scales method. Sensitive element frequencies split on two frequencies resulted from slowly changing angular velocity are taken into account in the equations of zero approximation. The differential equations for slowly changing amplitudes and phases of two normal waves of the oscillations measured by capacitor gauges and an electronic contour of the device are obtained from the equations of the first approximation.control of gyro oscillations, split of frequencies, identification, averaging method, two scales method, stability Citation:Martynenko Yu G, Merkuryev I V, Podalkov V V. Nonlinear dynamics of MEMS turning fork gyroscope.
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