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The Application of Parametric Excitation to a Micro-Ring Gyroscope

B.J. Gallacher, J.S. Burdess, A.J. Harris and J. Hedley
Insat University of Newcastle, UK

Keywords: parametric, excitation

Abstract:
This paper reports on a parametric excitation scheme that separates the drive and response frequencies of a micro-ring gyroscope in the ratio 10:1 approximately, with the aim of minimising electrical ''feedthrough''. Electrical feedthrough of the drive signal due to parasitic capacitance is a common problem in many MEMS devices actuated electrostatically, inductively and piezoelectrically and in the case of the gyroscope, limits its sensitivity to applied angular velocities. To date research into the application of parametric excitation to MEMS/NEMS has been restricted to subharmonic and superharmonic parametric resonances [1,2,3,4]. In this case the ratio of the drive and response frequencies has a maximum value of two, for first-order parametric resonance. For a multi-dimensional system, combination resonances are excited when the frequency of modulation of a system parameter is a multiple of either the sum or difference of two of the natural frequencies of the system. By ensuring the drive frequency is the sum of the natural frequency of a higher order mode and the natural frequency of the mode required to be excited, the ratio of the drive to response frequencies will be greater than two. In this paper, sum combination resonances between the 2nd and 5th order in-plane flexural modes are considered and are shown to be an alternative method of excitation suitable for the gyroscope. The equations of motion of the electrostatically actuated gyroscope shown in Figure (1) are in the form of a set of coupled Hill's equations with coupling via the electrostatic stiffness. A multiple time-scales perturbation method is used to analyse the response of the ring gyroscope to combination parametric excitation. As the flexural modes of the perfect ring are degenerate, the ring is analysed as a four degree of freedom system. The mode shapes used are illustrated in Figure (2). Slight mis-tuning between the otherwise degenerate modes is incorporated in the perturbation analysis. The results from the perturbation analysis are subsequently used to draw the stability map for the ring gyroscope when excited using a sum combination resonance between the modes of order n and m. Figure (3) illustrates the stability map for a gyroscope with a Q-factor of 20000 for mode orders n and m having values of 2 and 5, respectively.

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