Analytical model of electrostatic actuators for micro gas pumps

We analytically predict the performance of electrostatic actuators for diaphragm micro gas pumps by combining energy minimization and the analytical solution for membrane deformation under uniform pressure. The tangential strain of the membrane is considered in the calculation of membrane deflection. Models for both single- and double-cavity pumps are established to define the restriction of the upper cavity on the membrane during actuation. The shape lines of the membrane in a double-cavity structure are demonstrated under different voltages. The influence of dielectric thickness and cavity geometry on pumping consequence is also discussed. In accordance with other simulation results on diaphragm displacement and chamber pressure rise, an electrostatic diaphragm micro gas pump with a relatively thin dielectric layer and a cavity of comparatively small depth and radius suitably generates high pressure rise. Furthermore, a double-cavity structure enhances pressure rise for the restriction of the upper cavity on the membrane during deformation.     

Simulation model for micromechanical angular rate sensor

A simulation model for an angular rate sensor, a gyroscope, is presented. The device is based on a micromechanical dual torsional mass system which is actuated electrostatically and sensed capacitively. Model equations describing a dynamic, non-linear system are first presented and then realized as an electrical equivalent circuit. The vibrational modes of the system are modelled with coupled resonator circuits. The electrostatic and Coriolis forces as well as variable capacitances in the small air gaps are modelled with non-linear controlled current sources. External forces, torques and electrical actuation can act as inputs to the device. The model presented allows numerical sensor simulations concurrently with the interfacing electronics in the time and frequency domains. The model is verified by comparing its simulation results to measured frequency responses and capacitance-voltage characteristics.     

Analytical model of electrostatic actuators for micro gas pumps

We analytically predict the performance of electrostatic actuators for diaphragm micro gas pumps by combining energy minimization and the analytical solution for membrane deformation under uniform pressure. The tangential strain of the membrane is considered in the calculation of membrane deflection. Models for both single- and double-cavity pumps are established to define the restriction of the upper cavity on the membrane during actuation. The shape lines of the membrane in a double-cavity structure are demonstrated under different voltages. The influence of dielectric thickness and cavity geometry on pumping consequence is also discussed. In accordance with other simulation results on diaphragm displacement and chamber pressure rise, an electrostatic diaphragm micro gas pump with a relatively thin dielectric layer and a cavity of comparatively small depth and radius suitably generates high pressure rise. Furthermore, a double-cavity structure enhances pressure rise for the restriction of the upper cavity on the membrane during deformation.

     

Lift-off of a conducting sessile drop in an electric field

A conducting drop in partial wetting regime, placed on the lower electrode of a parallel-plate capacitor and surrounded by a dielectric fluid, is considered. The drop, initially flattened by gravity, is elongated by the electrostatic force and possibly lifts-off when a uniform DC electric field is applied. The electrostatic force and the lift-off condition were calculated in two previous articles, respectively, for undeformable and for slightly deformable drops in the absence of gravity (zero Eötvos number). In this paper, numerical models are put to work to study accurately the complex lift-off process resulting from the competition between gravitational, electrical and capillary forces. Large deformations of the drop surface at any value of the Eötvos number may be addressed by such a numerical procedure. Computational results allow assessing the accuracy and limits of previous analytical and asymptotic relations.     

Exact piezothermoelastic axisymmetric solution of a finite transversely isotropic cylindrical shell

This work presents an exact piezothermoelastic solution of a finite transversely isotropic piezoelectric cylindrical shell under axisymmetric thermal, pressure and electrostatic excitation. The general solution of the governing equations is obtained in terms of potential functions which satisfy the boundary conditions at the ends. The axisymmetric loadings are expanded as a Fourier series in the axial coordinate. The coefficients in the infinite set of potential functions are obtained by solving sets of six algebraic equations resulting from the satisfaction of boundary conditions at the inner and outer surfaces of the shell for each Fourier component. The inverse problem of inferring the applied temperature and pressure fields from the given measured distribution of electrical potential difference between the inner and outer surfaces of the shell has also been solved. Numerical results are presented for typical pressure, thermal and electrostatic loadings.     

A Lagrangian approach for electrostatic analysis of deformableconductors

Deformable conductors are frequently encountered in microelectromechanical systems (MEMS). For example, in electrostatic MEMS, microstructures undergo deformations because of electrostatic forces caused by applied potentials. Computational analysis of electrostatic MEMS requires an electrostatic analysis to compute the electrostatic forces acting on micromechanical structures and a mechanical analysis to compute the deformation of micromechanical structures. Typically, the mechanical analysis is performed by a Lagrangian approach using the undeformed position of the structures. However, the electrostatic analysis is performed by using the deformed position of the conductors. In this paper, we introduce a Lagrangian approach for electrostatic analysis. In this approach, when the conductors undergo deformation or shape changes, the surface charge densities on the deformed conductors can be computed without updating the geometry of the conductors. The Lagrangian approach is a simple, but critical, idea that radically simplifies the analysis of electrostatic MEMS     

An investigation into the electrostatic force representation for electrically actuated microelectromechanical systems

The ever-increasing demand for microelectromechanical systems (MEMS) in modern electronics has reinforced the need for extremely accurate analytical and reduced-order models to aid in the design of MEMS devices. Many MEMS designs consist of cantilever beams with a tip mass attached at the free end to act as a courter electrode for electrical actuation. One critical modeling aspect of electrically actuated MEMS is the electrostatic force that drives these systems. The two most used representations in the literature approximate the electrostatic force between two electrodes as a point force. In this work, the effects of the representation of the electrostatic force for electrically actuated microelectromechanical systems are investigated. The system under investigation is composed of a beam with an electrode attached to its end. The distributed force, rigid body, and point mass electrostatic force representations are modeled, studied, and their output results are compared qualitatively. Static and frequency analyses are carried out to investigate the influences of the electrostatic force representation on the static pull-in, fundamental natural frequency, and mode shape of the system. A nonlinear distributed-parameter model is then developed in order to determine and characterize the response of electrically actuated systems when considering various representation of the electrostatic forces. The results show that the size of the electrode may strongly affect the natural frequencies and static pull-in when the point mass, rigid body, and plate representations are considered. From nonlinear analysis, it is also proven that the representation may affect the hardening behavior of the system and its dynamic pull-in. This modeling and analysis give guidelines about the usefulness of the electrostatic force representations and possible erroneous assumptions that can be made which may result in inaccurate design and optimal performance detection for electrostatically actuated systems.

     

A study of hand grip pressure distribution and EMG of finger flexor muscles under dynamic loads

A matrix of miniature and flexible pressure sensors is proposed to measure the grip pressure distribution (GPD) at the hand-handle interface of a vibrating handle. The GPD was acquired under static and dynamic loads for various levels of grip forces and magnitudes of vibration at different discrete frequencies in the 20–1000 Hz range. The EMG of finger flexor muscles was acquired using the silver-silver chloride surface electrodes under different static and dynamic loads. The measured data was analysed to study the influence of grip force, and magnitude and frequency characteristics of handle vibration on: (i) the local concentration of forces at the hand-handle interface; and (ii) the electrical activity of the finger flexor muscles. The results of the study revealed high interface pressure near the tips of index and middle fingers, and base of the thumb under static grip conditions. This concentration of high pressure shifted towards the middle of the fingers under dynamic loads, irrespective of the grip force, excitation frequency, and acceleration levels. The electrical activity of the finger flexor muscles increased considerably with the grip force under static as well as dynamic loads. The electrical activity under dynamic loads was observed to be 1·5–6·0 times higher than that under the static loads.     

Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation

A rigorous formulation of the solvation forces (first derivatives) associated with the electrostatic free energy calculated from numerical solutions of the linearized Poisson-Boltzmann equation on a discrete grid is described. The solvation forces are obtained from the formal solution of the linearized Poisson-Boltzmann equation written in terms of the Green function. An intermediate region for the solute-solvent dielectric boundary is introduced to yield a continuous solvation free energy and accurate solvation forces. A series of numerical tests show that the calculated forces agree extremely well with finite-difference derivatives of the solvation free energy. To gain a maximum efficiency, the nonpolar contribution to the free energy is expressed in terms of the discretized grid used for the electrostatic problem. The current treatment of solvation forces can be used to introduce the influence of a continuum solvation model in molecular mechanics calculations of large biological systems.     

Computational dynamics method for evaluating the mobility of charged biomolecules passing through the electrical potential field within the ion selective channel on an excitable membrane

A mathematical method is introduced to characterize the electrokinetic behavior (electrophoresis) of a biomolecular particle which passes through a specific channel pore on an excitable biological membrane. The basic approach was first proposed by Booth (1950). The system was described by an equation of continuity and an equation of motion in which the driving force involves the diffusion effect, the hydrostatic pressure, and the electrostatic potential. By assuming linear relations between the velocity and the applied electrical field, solutions for the potential, pressure, and velocity were given by a series expansion of the charges on the particle. To examine the influence of ions surrounding the particle and forming an ionic cloud, the Debye–Huckel parameter was introduced. As the thickness of the double layer around the particle increased, the potential, velocity, pressure, and viscosity were changed significantly. The maximum influence was obtained when the radius of the particle became equal to the thickness of the double layer. Although this theory is valid for a charged, spherical, nonconducting particle only, the method is available for evaluating the kinetic behavior of a biomolecule that passes through a channel pore on a cellular membrane.This work was presented, in part, at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24–26, 2003     

Coupled electrostatic and mechanical FEA of a micromotor

The electrostatic forces occurring in a novel double stator axial-drive variable capacitance micromotor (VCM) are studied as a function of rotor-stator overlap, applied voltage, rotor support morphology, and rotor thickness. Analytical equations are developed using parallel plate assumptions, and results are compared with those obtained with 3D Finite Element Analysis (FEA) for tangential, axial, and radial electrostatic forces. The influence of the axial forces on the rotor deflections are studied using iterative indirect coupled field analysis, where the axial forces obtained from the electrostatic 3D FE model are iteratively applied to a structural FE model until stable rotor deflections are obtained. It was found that the axial forces, taking the rotor deflection into account, are twice as high as those obtained by analytical evaluation neglecting rotor deflections and about 70 times higher than the radial forces at a typical operating voltage of 100 V. Inclusion of bushing supports results in lower axial forces and decreases the influence of rotor tilt. Tangential forces likely to be exerted on the rotor at start-up are also examined and compared with analytical predictions. The study demonstrates that FEA provides more accurate results than analytical equations due to the geometry and field simplifications assumed in the latter     

Influences of perforation ratio in characteristics of capacitive micromachined ultrasonic transducers in air

Capacitive micromachined ultrasonic transducers (CMUTs) with a perforated membrane have been fabricated and characterized in air. Two types of CMUT device have been fabricated having perforation ratio (area ratio of holes = AR) of 10% and 20%, and analyzed about electrical and mechanical characteristics. The perforation ratio (AR) of membrane substantially influences on the electrostatic force and mechanical restoring force of the device since it leads to the area variation of electrode and membrane, it subsequently influences on the sensitivity and frequency response of the CMUT device. The electrostatic force and mechanical restoring force were improved by decreasing the AR and increasing the DC bias voltage. The open-circuit sensitivity of a CMUT having AR 10% membrane, 8.45 μV/Pa, is larger than that of AR 20%, 4.07 μV/Pa at DC 15 V. Furthermore, the resonance behaviors were observed in the range of 60-80 kHz, and the resonance frequency could be changed by varying the applied DC voltage and AR.     

SOLIDIS: a tool for microactuator simulation in 3-D

SOLIDIS is an engineering software tool tailored for the coupled three-dimensional (3-D) analysis of microactuators. Surface electrostatic forces, thermomechanics, and piezoelectric effects are correctly treated. The solution algorithms implemented enable efficient and accurate static analysis and optimization of MEMS actuators. Adaptive mesh refinement results in near-optimal meshes in the sense of achieving maximum accuracy for a given number of mesh nodes. A zone partitioning scheme permits efficient simulation of complex actuator structures. Additional key issues are mesh updating using a Monte Carlo algorithm to account for the actuator's movement and the application of smoothing algorithms for the extraction of accurate electrostatic forces     

Capacitive micromachined ultrasonic transducer: transmission performance evaluation under different driving parameters and membrane stress for underwater imaging applications

Transmission performance of a CMUT element in terms of output pressure and displacements was evaluated. A SIMULINK model of single CMUT element based on mechanical model of MEMS capacitor was used and the analyses were performed under different ac and dc conditions. 2.6 µm thick Si, Poly-Si and Si₃Ni₄ membranes with a radius 60 µm were used to obtain results for underwater imaging application. Relation between membrane stress and outputs of CMUT was also investigated using SIMULINK model for commonly used CMUT membrane made of Si₃Ni₄ and polysilicon membrane under different electrical driving parameters. It was observed that different ac signal inputs (sine, square and sawtooth) showed different effects on CMUTs pressure and displacement characteristics. Our results indicated that the maximum output pressure and displacement were obtained in a square waveform. In addition, although stress on membrane increases the displacement and pressure of CMUT membrane made of Poly-Si, quality factor inversely proportional to stress on membrane. Membrane stress has adverse effect on Si₃Ni₄ membrane transmission outputs. The used model in this study might enable to determine optimum driving electrical inputs and stress on membrane to control CMUT outputs in terms of output pressure, displacement, quality factor and bandwitdh.

     

Silicon vibration sensor arrays with electrically tunable band selectivity

 Frequency selective vibration sensors for wear state recognition have been fabricated using surface near silicon bulk micromechaning (SCREAM). Capacitive detection combs convert the mechanical vibration into an electrical signal. Operating in a frequency selective resonant mode allows direct extraction of spectral information without Fourier transformation. To enlarge the measurement range they provide a frequency tuning capability by stress-stiffening which is achieved by electrostatic forces. Using force enhancing lever mechanism frequency variation of up to 100% of the base frequency has been measured with tuning voltages of 50 V. By arranging multiple cells with stepped base frequencies and overlapping tuning ranges the covered frequency range is widely extended. A fabricated array of ten cells is capable to continuously scan the range from 1 to 10 kHz. Received: 30 April 2001/Accepted: 11 June 2001     

Shape optimizations and static/dynamic characterizations of deformable microplate structures with multiple electrostatic actuators

Micromirrors used in many optoelectronic devices can be considered as microplates. The functions and accuracy of the micromirrors depend on the static and dynamic deflection shapes of microplates. The objective of this study is to develop an efficient method for predicting the shapes of the microplates subjected to unsymmetrical electrostatic forces produced by electrostatic actuators such that micromirrors can be effectively optimized and controlled in their real time operation. The non-classical boundary conditions which result from the microfabrication process were modeled with artificial springs at the edges. A classical energy method using boundary characteristic orthogonal polynomials was applied to formulate the equations of motion of the microsystem. Based on this method, influence functions were built and least squares method was used to optimize the desired deflection under electrostatic forces from the electrostatic actuators. Softening effect of the electrostatic stiffness was also evaluated and considered in the simulation. Static deflections and dynamic responses were compared with those from finite element analysis (FEA) using Reduced Order Modeling (ROM) method. This study found that the static and dynamic responses of microplates predicted from the proposed method were highly consistent with those calculated from FEA. However, the proposed method is simpler and more efficient than FEA and can be conveniently used for any non-classical boundary condition situations. These features make the proposed method useful to effectively control and optimize the shape of a microplate with multiple electrostatic actuators.     

A Bidirectional Electrostatic Microvalve With Microsecond Switching Performance

This paper describes a new bidirectional high-pressure gas electrostatic microvalve that opens and closes in 50 or less. The microvalve consists of a valve-closing electrode, a flexible movable membrane, and a valve-opening electrode that is directly opposed to the valve-closing electrode. The membrane contains an embedded electrode, so the valve can zip closed when a potential is applied between the membrane and the valve-closing electrode. The valve-opening electrode allows the valve to open again in a rapid discontinuous motion, without requiring a large applied potential. A pressure-balance port is used to enhance the microvalve switching speed and to allow the valve to close against applied pressures greater than 8.3 atm (840 kPa). The gas conductance through the valve is 2.8 nl/Pa ldr s (17 sccm/atm), and the fluid leakage measured zero over the entire pressure range up to a burst pressure of 10.8 atm (1.1 MPa). Measurements show that the valve can open or close in 50 or less for applied pressures up to 126 kPa. In an extended lifetime test, a sample microvalve has been opened and closed 47 million times before failure.     

Analytical investigation and numerical verification of Casimir effect on electrostatic nano-cantilevers

In this paper, the two-point boundary value problem (BVP) of the nano-cantilever deflection subjected to Casimir and electrostatic forces is investigated using analytical and numerical methods to obtain the instability point of the nano-beam. In the analytical treatment of the BVP, the nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. Then, closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the beam are computed under the combined effects of electrostatic and Casimir forces. Electrostatic microactuators and freestanding nanoactuators are considered as special cases of our study. The detachment length and the minimum initial gap of freestanding nanocantilevers, which are the basic design parameters for NEMS switches, are determined. The results of the analytical study are verified by numerical solution of the BVP. The centerline of the beam under the effect of electrostatic and Casimir forces at small deflections and at the point of instability is obtained numerically to test the validity of the shape function assumed for the beam deflection in the analytical investigation. Finally, the large deformation theory is applied in numerical simulations to study the effect of the finite kinematics on the pull-in parameters of nano-canilevers.     

A design methodology for a bulk-micromachined two-dimensional electrostatic torsion micromirror

This paper presents a design methodology for a two-dimensional (2-D) electrostatic torsion micromirror fabricated with bulk-micromachining technology. The theoretical models in mechanical and electrostatic fields presented here provide insights into the influences of different design parameters on micromirror performance. Parametric numerical models built in ANSYS are used to more accurately predict its performance and further refine the design parameter values derived from the theoretical models. By use of the electrical analogy method, an equivalent electrical circuit is built in PSPICE to predict the static and dynamic performance of this micromirror, with the numerical simulation results as the input parameters. The equivalent electrical circuit has been demonstrated to be a simple and powerful approach to characterize the performance of this 2-D torsion micromirror. The test results for this micromirror reveal very good agreement between experimental and numerical results, taking into account fabrication tolerances and experimental accuracies. Incorporating the fabrication tolerances of bulk-micromachining technology, this design methodology can be readily applied to performance characterization and design optimization.     

基于电路-概率理论的对神经电刺激不稳定性的定性分析

神经电刺激通过影响中枢或外周神经系统,进而治疗某疾病。在实际应用中,神经电刺激响应强度的不稳定性较为棘手,一般认为是由于电刺激扰动了神经轴突的膜电位,造成了神经电刺激强度的不稳定性。然而,由于神经电刺激缺乏宏观可计算模型,其膜电位扰动在电刺激中具体产生何种影响,长期以来未得到有效结论。该研究基于电路-概率理论,对神经电刺激不稳定性进行定性分析,有效地分析了膜电位的扰动对电刺激的影响。实验结果表明,在体实验数据和定性仿真的电流幅值-不稳定性曲线具有高度一致性,说明电路-概率理论可能对电刺激产生的膜电位扰动有较为准确的解释。该研究对神经电刺激的实际应用具有指导性意义。