Bimodal parametric excitation of a micro‐ring gyroscope

Abstract

AbstractParametric excitation in vibratory systems is known well over hundred years. Recently it is also being exploited in Micro‐electromechanical Systems (MEMS). One example of these are micro‐ring gyroscopes, which are used in the automotive, the navigation and in the space industries. The sensitivity of such gyroscopes can be impaired by signal noise induced through parasitic capacitance between drive and sense electrodes. Applying parametric excitation and exploiting parametric amplification recently was shown to open new promising paths. On the theoretical side of parametric vibrations, recently it was found that the simultaneous parametric excitations in two coordinates or more with phase difference can lead to very interesting phenomena. The micro‐ring gyroscope is a good example of making use of parametric excitation and amplification to solve some of the problems in the modern MEMS. This work aims at modelling a micro‐ring gyroscope with two simultaneous phase lagged parametric excitations. The equations of motion can be derived using Hamilton's principle, both for an inextensible as well as for the extensible ring, and in the fully symmetric cases the eigenvalue problem can be solved analytically. The completely symmetric problem, leads to two eigenfunctions for any given eigenfrequency, except for the fundamental ones. The axial symmetry is in general destroyed by the way in which the vibrating ring is elastically supported by discrete elastic supports. Instead of truly double eigenfrequencies, the problem then has pairs of two closely spaced eigenfrequencies. In the simplest case, the ring can then be described by two generalized coordinates. Making use of direct excitation of each of the modes, as well as parametric excitation, makes it possible to exploit parametric resonance and parametric amplification. This has been applied before for the micro‐ring gyroscope, however not for the case of parametric excitation in two coordinates and with phase lag between the two parametric excitations. Taking into account this phase lag as an additional parameter, opens several new ways of sensing the angular velocity of the moving base of the micro‐ring gyroscope.