Abstract
The influence of stochastic fluctuations in the input angular rate of a class of single axis mass-spring microelectromechanical (MEM) gyroscopes on the system stability is investigated. A white noise fluctuation is introduced in the coupled 2-DOF model that represents the system dynamics for the purposes of stability prediction. Numerical simulations are performed employing the resulting set of stochastic differential equations (SDEs) that govern the system dynamics. The SDEs are discretized using the higher-order Milstein scheme for numerical computations. Simulations via the Euler scheme, as well as the measure of the largest Lyapunov exponent are employed for validation purposes due to a lack of similar analytical solutions or experimental data. Responses have been predicted under different noise fluctuation magnitudes and different input angular rates for stability investigations. A parametric study is performed to estimate the noise intensity stability threshold for a range of quality factor values at different input angular rates. The predicted results show a nonlinear dependence of the threshold on the quality factors for different input rates. Under typical gyroscope operating conditions, a realistic frequency mismatch appears to have insignificant influence on system stability. It is envisaged that the present quantitative predictions will aid improvements in performance, reliability, and the design process for this class of devices.
Highlights
Numerous emerging applications use a micro-machined angular rate sensor or gyroscope as a stand-alone unit or as part of an inertial measurement unit (IMU)
Microelectromechanical systems (MEMS) devices can be exposed to shock during fabrication, deployment and operation [3], as well as vibratory excitation resulting from the environment
The current study focuses on the stability of the single axis mass-spring gyroscope subjected to stochastic angular speed fluctuation
Summary
Numerous emerging applications use a micro-machined angular rate sensor or gyroscope as a stand-alone unit or as part of an inertial measurement unit (IMU). The effect of stochastic fluctuations in the input angular rate on the stability of a single-axis mass-spring vibratory gyroscope has been investigated by Asokanthan and Wang [10]. The effect of wide-band random fluctuation in the input angular rate on the dynamic stability of the single axis mass-spring structure gyroscope is the main interest of the present study. The higher-order Milstein scheme is employed to simulate the time response so that the stochastic response of2,ax FOR single axis mass-spring rate gyroscopes can be quantified for certain parameters of Vibration 2018, PEER. Thresholds.InThe quality factors andMilstein the magnitude of the angular speed the effects present of study, the higher-order scheme is employed to simulate thefluctuation, time responseassowell as the that the stochastic response of a single axisbeen mass-spring rate gyroscopes can be quantified for certain frequency mismatch on system stability have quantified.
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