Coriolis vibrating gyroscope modelling for parametric identification and optimal design

Coriolis vibrating gyroscopes can be modeled by a planar resonator, using masses, springs and damping. In this paper, the corresponding equations are studied in order to characterize real vibrating cells. It is shown how to present the problem to allow efficient numerical simulations and analytic developments. In particular, the use of the method of Averaging is fundamental, simplifying most of the calculations. All aspects of the oscillations are described and synthesized into a set of either geometrical parameters or canonical quantities, such as the energy of the trajectory. Thus, the properties of vibrating cells can be evaluated, and different operating modes as open-loop or closed-loop are exploited. Computer tools are developed to identify the flaws of real cells. Among them, a MODELICA simulator computes the time series of the gyroscope outputs for any stimulus, including transients, and a MAXIMA Taylor expansion code generates the analytical expressions of steady state and transients for start/stop. Both methods agree within 0.5%.