Dynamics of MEMS-Based Angular Rate Sensors Excited via External Electrostatic Forces

2020 ◽  
Author(s):  
Ibrahim F. Gebrel ◽  
Ligang Wang ◽  
Samuel F. Asokanthan
Keyword(s):  
Dynamic Behavior ◽  
Electrostatic Force ◽  
Angular Rate ◽  
Equations Of Motion ◽  
Ring Structure ◽  
Dynamic Responses ◽  
Actuator Dynamics ◽  
Vibratory Gyroscopes ◽  
Thin Ring ◽  
The Mathematical Model

Abstract This paper investigates the dynamic behavior of rotating MEMS-based vibratory gyroscopes which employs a thin ring as the vibrating flexible element. The mathematical model for the MEMS ring structure as well as a model for the nonlinear electrostatic excitation forces are formulated. Galerkin’s procedure is employed to reduce the equations of motion to a set of ordinary differential equations. Understanding the effects of nonlinear actuator dynamics is considered important for characterizing the dynamic behavior of such devices. A suitable theoretical model to generate nonlinear electrostatic force that acts on the MEMS ring structure is formulated. Dynamic responses in the driving and the sensing directions are examined via time responses, phase diagram, and Poincare’ map plots when the input angular motion and the nonlinear electrostatic force are considered simultaneously. The analysis is envisaged to aid fabrication of this class of devices as well as for providing design improvements in MEMS Ring-based Gyroscopes.

scholarly journals Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes

Vibration ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 805-821
Author(s):  
Ibrahim F. Gebrel ◽  
Samuel F. Asokanthan
Keyword(s):  
Differential Equations ◽  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Electrostatic Force ◽  
Essential Element ◽  
Ring Structure ◽  
Dynamic Responses ◽  
Ongoing Research ◽  
Actuator Dynamics ◽  
External Forces

This study investigates the nonlinear dynamic response behavior of a rotating ring that forms an essential element of MEMS (Micro Electro Mechanical Systems) ring-based vibratory gyroscopes that utilize oscillatory nonlinear electrostatic forces. For this purpose, the dynamic behavior due to nonlinear system characteristics and nonlinear external forces was studied in detail. The partial differential equations that represent the ring dynamics are reduced to coupled nonlinear ordinary differential equations by suitable addition of nonlinear mode functions and application of Galerkin’s procedure. Understanding the effects of nonlinear actuator dynamics is essential for characterizing the dynamic behavior of such devices. For this purpose, a suitable theoretical model to generate a nonlinear electrostatic force acting on the MEMS ring structure is formulated. Nonlinear dynamic responses in the driving and sensing directions are examined via time response, phase diagram, and Poincare’s map when the input angular motion and nonlinear electrostatic force are considered simultaneously. The analysis is envisaged to aid ongoing research associated with the fabrication of this type of device and provide design improvements in MEMS ring-based gyroscopes.

Dynamic Behavior of the Band/Wheel Mechanical System of Industrial Band Saws

1995 ◽  
Author(s):  
Y. Y. Chung ◽  
C. K. Sung
Keyword(s):  
Mechanical System ◽  
Dynamic Behavior ◽  
Tilt Angle ◽  
Metal Cutting ◽  
Equations Of Motion ◽  
Continuity Condition ◽  
Dynamic Responses ◽  
Moving Beam ◽  
Band Saw ◽  
The Mathematical Model

Abstract This paper presents an analytical and experimental investigation on the dynamic behavior of the band/wheel mechanical system of an industrial metal-cutting band saws. In practice, as a result of the existence of the wheel tilt angle, a pair of roller bearings in which one of them is movable must be employed to twist the saw band perpendicular to the workpiece. Therefore, the saw band is modelled as a finite moving beam span that composes of three consecutive segments, in which the middle segment, that is, the cutting span, and the neighboring two segments may be assumed to be a straight and a twisted beams, respectively. The deformation of the band must satisfy the continuity condition at the connections between segments. The equations of motion governing the dynamic behavior of the beam span in axial, torsional and transverse directions are derived using mixed variational principle. The axial motion of the beam span couples linearly with its torsional motion. The dynamic responses and the natural frequencies of the beam are computed when parameters vary, such as the transport velocity of the saw band, band tension, wheel tilt angle, and the length of the cutting span. Finally, an experimental study is performed on an industrial band saw for the verification of the mathematical model and the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.

Dynamic Behavior of the Band/Wheel Mechanical System of Industrial Band Saws

1998 ◽  
Vol 120 (4) ◽  
pp. 842-847 ◽  
Author(s):  
Y. Y. Chung ◽  
C. K. Sung
Keyword(s):  
Mechanical System ◽  
Dynamic Behavior ◽  
Tilt Angle ◽  
Metal Cutting ◽  
Equations Of Motion ◽  
Continuity Condition ◽  
Dynamic Responses ◽  
Initial Tension ◽  
Saw Blade ◽  
Band Saw

This paper presents an analytical and experimental investigation on the dynamic behavior of the band/wheel mechanical system of an industrial metal-cutting band saws. In practice, this machine is equipped with two pairs of roller bearings to twist the saw blade perpendicularly to the surface of the workpiece. This results in the existence of the wheel tilt angle. The saw band is modeled as a finite moving beam span that composes three consecutive segments: the middle straight segment, that is, the cutting span, and the neighboring two segments that are considered as twisted beams. The deformation of the band must satisfy the continuity condition at the connections between segments. The equations of motion governing the dynamic behavior of the saw band in axial, torsional and transverse directions are derived using mixed variational principle. The axial motion of the span couples linearly with its torsional motion. The dynamic responses and the natural frequencies of the beam are computed when parameters vary, such as the transport velocity of the saw band, initial tension, wheel tilt angle, and the length of the cutting span. Finally, an experimental study is performed on an industrial band saw for the verification of the mathematical model and the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.

Dynamic Behavior of Finite Coupled Mindlin Plates With a Blocking Mass

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
XianZhong Wang
Keyword(s):  
Dynamic Behavior ◽  
Power Flow ◽  
Equations Of Motion ◽  
Flow Analysis ◽  
Input Power ◽  
Dynamic Responses ◽  
Structural Damping ◽  
Arbitrary Angle ◽  
Plate Equations ◽  
Coupled Plates

A power flow analysis of finite coupled Mindlin plates with a blocking mass at the junction of the coupled plates is investigated using the method of reverberation-ray matrix (MRRM). An exact solution is derived by the plate equations of motion to satisfy the boundary condition. The wave amplitude coefficients are obtained from the continuity conditions at driving force locations, and the line junction of two plates connected at an arbitrary angle. The blocking mass located at the junction of the two plates is modeled as a Timoshenko beam. The dynamic responses of the finite coupled Mindlin plates are verified by comparing with finite element method (FEM) results. The effects of the connected angles, blocking mass, and structural damping on the input power and transmitted power are calculated and analyzed. Numerical simulations of the finite coupled Mindlin plates with a blocking mass show that the present method can predict the dynamic behavior.

Dynamics of a Ring-Type Macro Gyroscope Under Electromagnetic External Actuation Forces

2018 ◽  
Author(s):  
Ibrahim F. Gebrel ◽  
Ligang Wang ◽  
Samuel F. Asokanthan
Keyword(s):  
Electromagnetic Force ◽  
Dynamic Behaviour ◽  
Essential Element ◽  
Ring Structure ◽  
Ring System ◽  
Response Behavior ◽  
External Excitation ◽  
Actuator Dynamics ◽  
Vibratory Gyroscopes ◽  
Galerkin's Procedure

This paper investigates the dynamic behaviour of a rotating ring that forms an essential element in ring-based vibratory gyroscopes that utilize oscillatory electromagnetic forces. Understanding the effects of nonlinear actuator dynamics is considered important for characterizing the dynamic behavior of such devices. A suitable theoretical model to generate nonlinear electromagnetic force that acts on the ring structure is formulated. In order to predict the dynamic behaviour of a ring system subjected to external excitation and body rotation, discretized equations obtained via Galerkin’s procedure is employed to investigate the time as well as frequency response behavior. Dynamic response in the driving and the sensing directions are examined via time responses, phase diagram, Poincare’ map and bifurcation plots when the input angular motion and the nonlinear electromagnetic force are considered simultaneously. The analysis is envisaged to aid ongoing experimental research as well as for providing design improvements in Ring-based Gyroscopes.

An Electrostatic Force Feedback Approach for Extending the Bandwidth of MEMS Vibratory Gyroscope

2011 ◽  
Vol 483 ◽  
pp. 43-47
Author(s):  
Jian Cui ◽  
Zhong Yang Guo ◽  
Qian Cheng Zhao ◽  
Zhen Chuan Yang ◽  
Yi Long Hao ◽  
...  
Keyword(s):  
Force Feedback ◽  
Control Method ◽  
Electrostatic Force ◽  
Angular Rate ◽  
Resonant Frequencies ◽  
Vibratory Gyroscope ◽  
Satisfactory Performance ◽  
Simulation Results ◽  
The Difference ◽  
The Mathematical Model

This paper proposed an effective approach for extending the bandwidth of MEMS vibratory gyroscope by employing the electrostatic force feedback control. The mathematical model for the bandwidth is established through the dynamic model of the gyroscope, which indicates that the bandwidth of the sensor depends on the difference between the resonant frequencies of the two working modes. The system bandwidth can be enlarged by utilizing electrostatic force rebalance control to null Coriolis force caused by external angular rate which can also improve the performance of the transient response. Simulation results forecast a satisfactory performance of the control system with suggested control method.

Dynamic analysis of a helical gear reduction by experimental and numerical methods

2020 ◽  
Vol 68 (1) ◽  
pp. 48-58
Author(s):  
Chao Liu ◽  
Zongde Fang ◽  
Fang Guo ◽  
Long Xiang ◽  
Yabin Guan ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Numerical Models ◽  
Helical Gear ◽  
Operating Conditions ◽  
Dynamic Responses ◽  
Lumped Mass ◽  
Gear Mesh

Presented in this study is investigation of dynamic behavior of a helical gear reduction by experimental and numerical methods. A closed-loop test rig is designed to measure vibrations of the example system, and the basic principle as well as relevant signal processing method is introduced. A hybrid user-defined element model is established to predict relative vibration acceleration at the gear mesh in a direction normal to contact surfaces. The other two numerical models are also constructed by lumped mass method and contact FEM to compare with the previous model in terms of dynamic responses of the system. First, the experiment data demonstrate that the loaded transmission error calculated by LTCA method is generally acceptable and that the assumption ignoring the tooth backlash is valid under the conditions of large loads. Second, under the common operating conditions, the system vibrations obtained by the experimental and numerical methods primarily occur at the first fourth-order meshing frequencies and that the maximum vibration amplitude, for each method, appears on the fourth-order meshing frequency. Moreover, root-mean-square (RMS) value of the acceleration increases with the increasing loads. Finally, according to the comparison of the simulation results, the variation tendencies of the RMS value along with input rotational speed agree well and that the frequencies where the resonances occur keep coincident generally. With summaries of merit and demerit, application of each numerical method is suggested for dynamic analysis of cylindrical gear system, which aids designers for desirable dynamic behavior of the system and better solutions to engineering problems.

Nonlinear Dynamics Behavior of Tethered Submerged Buoy under Wave Loadings

2020 ◽  
Vol 21 (1) ◽  
pp. 11-21
Author(s):  
Lin Zhao ◽  
Weihao Meng ◽  
Zhongqiang Zheng ◽  
Zongyu Chang
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Behavior ◽  
Coupling Factor ◽  
Dynamic Responses ◽  
Mooring Line ◽  
Second Law ◽  
Largest Lyapunov Exponent ◽  
Nonlinear Characteristic ◽  
Runge Kutta Method ◽  
Marine Engineering

AbstractTethered submerged buoy is used extensively in the field of marine engineering. In this paper considering the effect of wave, the nonlinear dynamics behavior of tethered submerged buoy is debated under wave loadings. According to Newton’s second law, the dynamic of the system is built. The coupling factor of the system is neglected, the natural frequency is calculated. The dynamic responses of the system are analyzed using Runge–Kutta method. Considering the variety of the steepness kA, the phenomenon of dynamic behavior can be periodic, double periodic and quasi-periodic and so on. The bifurcation diagram and the largest Lyapunov exponent are applied to judge the nonlinear characteristic. It is helpful to understand the dynamic behavior of tethered submerged buoy and design the mooring line of tethered submerge buoy.

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

2012 ◽  
Vol 28 (3) ◽  
pp. 513-522 ◽  
Author(s):  
H. M. Khanlo ◽  
M. Ghayour ◽  
S. Ziaei-Rad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Disk System ◽  
Partial Differential ◽  
Rayleigh Beam ◽  
Flexible Shaft

AbstractThis study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

scholarly journals FORCED RESPONSE VIBRATION OF SIMPLY SUPPORTED BEAMS WITH AN ELASTIC PASTERNAK FOUNDATION UNDER A DISTRIBUTED MOVING LOAD

2020 ◽  
Vol 4 (2) ◽  
pp. 1-7
Author(s):  
Fatai Hammed ◽  
M. A. Usman ◽  
S. A. Onitilo ◽  
F. A. Alade ◽  
K. A. Omoteso
Keyword(s):  
Shear Modulus ◽  
Moving Load ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Forced Response ◽  
Dynamic Responses ◽  
Moving Force ◽  
Pasternak Elastic Foundation

In this study, the response of two homogeneous parallel beams with two-parameter Pasternak elastic foundation subjected to a constant uniform partially distributed moving force is considered. On the basis of Euler-Bernoulli beam theory, the fourth order partial differential equations of motion describing the behavior of the beams when subjected to a moving force were formulated. In order to solve the resulting initial-boundary value problem, finite Fourier sine integral technique and differential transform scheme were employed to obtain the analytical solution. The dynamic responses of the two beams obtained was investigated under moving force conditions using MATLAB. The effects of speed of the moving force, layer parameters such as stiffness (K_0) and shear modulus (G_0 ) have been conducted for the moving force. Various values of speed of the moving load, stiffness parameters and shear modulus were considered. The results obtained indicates that response amplitudes of both the upper and lower beams increases with increase in the speed of the moving load. Increasing the stiffness parameter is observed to cause a decrease in the response amplitudes of the beams. The response amplitudes decreases with increase in the shear modulus of the linear elastic layer.

Sign in / Sign up

Export Citation Format

Share Document