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Effect of nonlinear electrostatic forces on the dynamic behaviour of a capacitive ring-based Coriolis Vibrating Gyroscope under severe shock

Chouvion, Benjamin; McWilliam, Stewart; Popov, Atanas A.

Authors

Benjamin Chouvion

ATANAS POPOV atanas.popov@nottingham.ac.uk
Professor of Engineering Dynamics



Abstract

This paper investigates the dynamic behaviour of capacitive ring-based Coriolis Vibrating Gyroscopes (CVGs) under severe shock conditions. A general analytical model is developed for a multi-supported ring resonator by describing the in-plane ring response as a finite sum of modes of a perfect ring and the electrostatic force as a Taylor series expansion. It is shown that the supports can induce mode coupling and that mode coupling occurs when the shock is severe and the electrostatic forces are nonlinear. The influence of electrostatic nonlinearity is investigated by numerically simulating the governing equations of motion. For the severe shock cases investigated, when the electrode gap reduces by ∼60%∼60%, it is found that three ring modes of vibration (1θ,2θ1θ,2θ and 3θ3θ) and a 9th order force expansion are needed to obtain converged results for the global shock behaviour. Numerical results when the 2θ2θ mode is driven at resonance indicate that electrostatic nonlinearity introduces mode coupling which has potential to reduce sensor performance under operating conditions. Under some circumstances it is also found that severe shocks can cause the vibrating response to jump to another stable state with much lower vibration amplitude. This behaviour is mainly a function of shock amplitude and rigid-body motion damping.

Citation

Chouvion, B., McWilliam, S., & Popov, A. A. (2018). Effect of nonlinear electrostatic forces on the dynamic behaviour of a capacitive ring-based Coriolis Vibrating Gyroscope under severe shock. Mechanical Systems and Signal Processing, 106, https://doi.org/10.1016/j.ymssp.2017.12.043

Journal Article Type Article
Acceptance Date Dec 29, 2017
Online Publication Date Feb 12, 2018
Publication Date Jun 30, 2018
Deposit Date Feb 20, 2018
Publicly Available Date Feb 13, 2019
Journal Mechanical Systems and Signal Processing
Print ISSN 0888-3270
Electronic ISSN 0888-3270
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 106
DOI https://doi.org/10.1016/j.ymssp.2017.12.043
Keywords Vibrating ring gyroscope; Electrostatic forcing; Shock response; Nonlinear dynamics
Public URL http://eprints.nottingham.ac.uk/id/eprint/49884
Publisher URL https://www.sciencedirect.com/science/article/pii/S0888327017306805
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0

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