On Electronically Restoring an Imperfect Vibratory Gyroscope to an Ideal State

Abstract

With regard to G.H. Bryan’s publication in 1890, we call the following Bryan’s law (or Bryan’s effect): “The vibration pattern of a revolving cylinder or bell revolves at a rate proportional to the inertial rotation rate of the cylinder or bell”. Bryan’s factor is the proportionality constant that can be theoretically calculated for an ideal vibratory gyroscope (VG). If a perfectly symmetric VG is not ideal, that is, if imperfections and damping are present, then the precession rate (pattern rotation rate) depends on a number of factors. Indeed it depends on the rotation rate of the vehicle it is attached to, mass-stiffness and symmetry imperfections as well as any anisotropic damping (linear or nonlinear) that may be present in the VG. Assuming perfect axissymmetry for the VG, we show how to negate the effects of manufacturing mass-stiffness imperfections as well as the effects of any type of tangentially anisotropic damping that might occur. We achieve this by showing exactly how to symmetrically arrange an electronic array about the symmetry axis. This array consists of curved capacitors under a mixture of a constant (fixed) charge and a small meander charge. We show exactly how the fixed voltage on the capacitor should be adjusted in order to eliminate the frequency split caused by the mass-stiffness imperfection. Furthermore, we show how the meander voltages of the capacitors should be adjusted in order to maintain principal vibration, eliminate quadrature vibration and restore spurious pattern drift in the VG so that it obeys Bryan’s law, restoring the precession rate to the ideal rate so that Bryan’s factor can be used for calibration purpose. Equations of motion are derived in the form of averaged ODEs that provide us insight into VG behaviour.

Dedicated to Charlotta E. Coetzee 1955 - 2012.