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Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

[+] Author and Article Information
Samuel F. Asokanthan

Professor
Mem. ASME
Department of Mechanical and
Materials Engineering,
Western University,
London, ON N6A 5B9, Canada
e-mail: sasokant@uwo.ca

Soroush Arghavan

General Motors of Canada Ltd.,
101 McNabb Street,
Markham, ON L3R 4H8, Canada
e-mail: soroush.arghavan@gm.com

Mohamed Bognash

Department of Mechanical and
Materials Engineering,
Western University,
London, ON N6A 5B9, Canada
e-mail: mbognash@uwo.ca

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 1, 2016; final manuscript received March 24, 2017; published online May 30, 2017. Assoc. Editor: Mohammad Younis.

J. Vib. Acoust 139(4), 040904 (May 30, 2017) (7 pages) Paper No: VIB-16-1571; doi: 10.1115/1.4036452 History: Received December 01, 2016; Revised March 24, 2017

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

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Figures

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Fig. 1

Second flexural mode shapes of a ring: , node; , anti-node; , nodal line

Grahic Jump Location
Fig. 2

Example of stable time response

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Fig. 3

Example of marginally stable time response

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Fig. 4

Example of unstable time response

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Fig. 5

Under-prediction of results by Euler scheme

Grahic Jump Location
Fig. 6

Stability boundary in the  μ−ζ space (Ω0=2π rad/s)

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