Dynamic Behaviour of a MEMS-Gyroscope Subjected to Stochastic Angular Rate Perturbations

2008 ◽  
Author(s):  
Tianfu Wang ◽  
Samuel F. Asokanthan
Keyword(s):  
Spectral Density ◽  
Dynamic Behaviour ◽  
Angular Rate ◽  
Damping Ratio ◽  
Stochastic Averaging ◽  
Correlated Noise ◽  
Mems Gyroscope ◽  
Mean Square Stability ◽  
Stochastic Fluctuations ◽  
Mass Type

Instabilities in a vibratory MEMS gyroscope that is subject to stochastic fluctuations in input angular rates are investigated. The vibratory-type gyroscope considered in the present study is of the spring-mass type. For the purpose of acquiring stability conditions, when the angular rate input is subject to small intensity stochastic fluctuations, dynamic behaviour of stochastically perturbed linear gyroscopic systems is studied in detail. An asymptotic approach based on the method of stochastic averaging has been employed for this purpose, and closed-form conditions for mean square stability of dynamic response are obtained for the case of exponentially correlated noise. Results are shown to depend only on those values of the excitation spectral density near twice the natural frequencies and the combination frequencies of the system. The presented results remain valid if the stochastic parametric excitation has a small correlation time compared with the system relaxation time. Stability predictions have been illustrated via stability diagrams in the power-spectral–density-damping-ratio space. Further, to illustrate the applicability of the results in practice, conditions for varying input angular rates are mapped. Although, the above conditions are predicted for the spring-mass type gyroscope, the predictions can be easily translated to other vibratory gyroscope designs.

The Dynamic Behaviour of Passively Compensated, Hydrostatic Journal Bearings with Various Numbers of Recesses

1976 ◽  
Vol 18 (6) ◽  
pp. 292-302 ◽  
Author(s):  
P. B. Davies
Keyword(s):  
Dynamic Behaviour ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Steady State Solution ◽  
Flow Equation ◽  
External Excitation ◽  
Signal Flow Graphs ◽  
Flow Compensation ◽  
Circular Functions ◽  
Flow Graphs

A previously established small-perturbation analysis is developed to express the unsteady-state continuity-of-flow equation for an isolated recess in a passively compensated, multirecess, hydrostatic journal bearing in terms of generalized co-ordinates. The concise form of this equation enables motion of the shaft about the concentric position to be described by equations which are derived in closed form for bearings with orifice, capillary or constant flow compensation and any number of recesses. These equations of motion, and hence the expressions for the receptances which describe the response of a bearing to external excitation, are shown to be of exactly the same form for all bearings of the type considered. Furthermore, the damping ratio and natural frequency in any particular case are determined by a single dynamic constant which is shown to be equal to a linear combination of circular functions and a limited number of coefficients which may be found explicitly by routine use of signal flow graphs. The results of the analysis, which is exact within the stated assumptions, are compared with those of other workers and the steady-state solution of the equations of motion is shown to give an expression for static stiffness which is useful for design purposes. Numerical values of the dynamic constant for bearings with between 3 and 20 recesses are given graphically.

scholarly journals Towards a biomimetic gyroscope inspired by the fly's haltere using microelectromechanical systems technology

2014 ◽  
Vol 11 (99) ◽  
pp. 20140573 ◽  
Author(s):  
H. Droogendijk ◽  
R. A. Brookhuis ◽  
M. J. de Boer ◽  
R. G. P. Sanders ◽  
G. J. M. Krijnen
Keyword(s):  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Fast Response ◽  
Gyroscopic System ◽  
Drive Mode ◽  
Mems Gyroscope ◽  
Coriolis Forces ◽  
Mems Technology ◽  
Large Measurement ◽  
Theoretical Performance

Flies use so-called halteres to sense body rotation based on Coriolis forces for supporting equilibrium reflexes. Inspired by these halteres, a biomimetic gimbal-suspended gyroscope has been developed using microelectromechanical systems (MEMS) technology. Design rules for this type of gyroscope are derived, in which the haltere-inspired MEMS gyroscope is geared towards a large measurement bandwidth and a fast response, rather than towards a high responsivity. Measurements for the biomimetic gyroscope indicate a (drive mode) resonance frequency of about 550 Hz and a damping ratio of 0.9. Further, the theoretical performance of the fly's gyroscopic system and the developed MEMS haltere-based gyroscope is assessed and the potential of this MEMS gyroscope is discussed.

The Effects of Correlated Noise on Bifurcation in Birhythmicity Driven by Delay

2018 ◽  
Vol 28 (10) ◽  
pp. 1850127 ◽  
Author(s):  
Lijuan Ning ◽  
Zhidan Ma
Keyword(s):  
Averaging Method ◽  
Harmonic Approximation ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Self Control ◽  
Correlated Noise ◽  
State Variables ◽  
Stationary Probability Density Function ◽  
Fpk Equation ◽  
Control Feedback

We consider bifurcation regulations under the effects of correlated noise and delay self-control feedback excitation in a birhythmic model. Firstly, the term of delay self-control feedback is transferred into state variables without delay by harmonic approximation. Secondly, FPK equation and stationary probability density function (SPDF) for amplitude can be theoretically mapped with stochastic averaging method. Thirdly, the intriguing effects on bifurcation regulations in a birhythmic model induced by delay and correlated noise are observed, which suggest the violent dependence of bifurcation in this model on delay and correlated noise. Particularly, the inner limit cycle (LC) is always standing due to noise. Lastly, the validity of analytical results was confirmed by Monte Carlo simulation for the dynamics.

Experimental Response of a Preloaded Vibro-Impacting Hertzian Contact

2001 ◽  
Author(s):  
Emmanuel Rigaud ◽  
Joël Perret-Liaudet
Keyword(s):  
Dynamic Behaviour ◽  
Damping Ratio ◽  
Primary Resonance ◽  
External Input ◽  
Hertzian Contact ◽  
Normal Forces ◽  
Linear Dynamic ◽  
Input Amplitude ◽  
Linear Resonance ◽  
Amplitude System

Abstract This paper concerns the non-linear dynamic response of a vibro-impacting Hertzian contact. Sinusoidal and random external normal forces are considered. We focus on the primary resonance and include vibro-impact responses in order to analyze the main characteristics of the system associated to both Hertzian and contact loss non-linearities. Under very small input amplitude, contact exhibits an almost linear resonance. Linearized resonance frequency and damping ratio are identified. Increasing the external input amplitude, the softening behaviour induced by Hertzian nonlinear stiffness is clearly demonstrated for both sinusoidal and random inputs. For higher input amplitude, system exhibits vibro-impacts. The contact loss non-linearity strongly governs the dynamic behaviour of the system.

scholarly journals Optimum Resolution Bandwidth for Spectral Analysis of Stationary Random Vibration Data

1993 ◽  
Vol 1 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Allan G. Piersol
Keyword(s):  
Spectral Analysis ◽  
Spectral Density ◽  
Power Spectral Density ◽  
Random Vibration ◽  
Damping Ratio ◽  
Frequency Resolution ◽  
Power Spectral ◽  
Averaging Time ◽  
Resolution Bandwidth

This article presents a methodology for selecting the frequency resolution bandwidth for the spectral analysis of stationary random vibration signals in an optimum manner. Specifically, the resolution bandwidth that will produce power spectral density estimates with a minimum mean square error is determined for any given measurement duration (averaging time), and methods of approximating the optimum bandwidth using practical spectral analysis procedures are detailed. The determination of the optimum resolution bandwidth requires an estimate for the damping ratio of the vibrating structure that produced the measured vibration signal and the analysis averaging time. It is shown that the optimum resolution bandwidth varies approximately with the 0.8 power of the damping ratio and the bandwidth center frequency, and the −0.2 power of the averaging time. Also, any resolution bandwidth within ±50% of the optimum bandwidth will produce power spectral density (PSD) estimates with an error that is no more than 25% above the minimum achievable error. If a damping ratio of about 5% for structural resonances is assumed, a constant percentage resolution bandwidth of 1/12 octave, but no less than 2.5 Hz, will provide a near optimum PSD analysis for an averaging time of 2 seconds over the frequency range from 20 to 2000 Hz. A simple scaling formula allows the determination of appropriate bandwidths for other damping ratios and averaging times.

scholarly journals Analysis of Correlation in MEMS Gyroscope Array and its Influence on Accuracy Improvement for the Combined Angular Rate Signal

Micromachines ◽  
2018 ◽  
Vol 9 (1) ◽  
pp. 22 ◽  
Author(s):  
Liang Xue ◽  
Xinguo Wang ◽  
Bo Yang ◽  
Weizheng Yuan ◽  
Guangmin Yuan
Keyword(s):  
Angular Rate ◽  
Accuracy Improvement ◽  
Mems Gyroscope

scholarly journals System Identification of a MEMS Gyroscope

1999 ◽  
Vol 123 (2) ◽  
pp. 201-210 ◽  
Author(s):  
Robert T. M’Closkey ◽  
Steve Gibson ◽  
Jason Hui
Keyword(s):  
System Identification ◽  
Angular Rate ◽  
Experimental System ◽  
Primary Objective ◽  
Input Output ◽  
Output Data ◽  
Mems Gyroscope ◽  
Principal Axes ◽  
Frequency Split ◽  
Insight Into

This paper reports the experimental system identification of the Jet Propulsion Laboratory MEMS vibratory rate gyroscope. A primary objective is to estimate the orientation of the stiffness matrix principal axes for important sensor dynamic modes with respect to the electrode pick-offs in the sensor. An adaptive lattice filter is initially used to identify a high-order two-input/two-output transfer function describing the input/output dynamics of the sensor. A three-mode model is then developed from the identified input/output model to determine the axes’ orientation. The identified model, which is extracted from only two seconds of input/output data, also yields the frequency split between the sensor’s modes that are exploited in detecting the rotation rate. The principal axes’ orientation and frequency split give direct insight into the source of quadrature measurement error that corrupts detection of the sensor’s angular rate.

scholarly journals Dynamic calibration of digital angular rate sensors

ACTA IMEKO ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 394
Author(s):  
B. Seeger ◽  
L. Klaus ◽  
D. Nordmann
Keyword(s):  
Dynamic Behaviour ◽  
Angular Rate ◽  
Calibration Procedure ◽  
Dynamic Calibration ◽  
European Research ◽  
Digital Output ◽  
Research Project ◽  
Mems Gyroscopes ◽  
Output Only ◽  
Insight Into

MEMS gyroscopes/angular rate sensors are often equipped with a digital output only. As part of a European research project, the dynamic calibration of sensors with digital output is being investigated. In the following, the operation principle of digital gyroscopes is described, a possible way to derive correct timestamped data from those sensors using a digital acquisition unit is explained and a calibration procedure is presented. The calibration of the analogue input of the digital acquisition unit, which is a prerequisite to derive correct phase responses, is described. Measurements with digital sensors proved the working principles and gave insight into the dynamic behaviour of those gyroscopes.

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