MEMS穿孔板微执行器动态Pull-in特性分析

本文基于穿孔板静电微执行器的基本模型,在忽略和考虑压膜阻尼效应的两种情况下,采用能量法推导了静电微执行器的动态Pull-in参数公式,并结合ANSYS软件得到动态Pull-in参数的仿真值。通过对比两种情况下的Pull-in电压和Pull-in位移,得出了阻尼比变化对动态Pull-in参数的影响。结果表明,压膜阻尼效应会增大Pull-in电压、减小Pull-in位移;当阻尼比大于0.4,动态Pull-in电压值将与静态Pull-in电压值一致;当阻尼比大于0.5,动态Pull-in位移值将与静态Pull-in位移值一致。     

Dynamic response of a torsional micromirror to electrostatic force and mechanical shock

In this paper dynamic characteristics of a capacitive torsional micromirror under electrostatic forces and mechanical shocks have been investigated. A 2DOF model considering the torsion and bending stiffness of the micromirror structure has been presented. A set of nonlinear equations have been derived and solved by Runge–Kutta method. The Static pull-in voltage has been calculated by frequency analyzing method, and the dynamic pull-in voltage of the micromirror imposed to a step DC voltage has been derived for different damping ratios. It has been shown that by increasing the damping ratio the dynamic pull-in voltage converges to static one. The effects of linear and torsional shock forces on the mechanical behavior of the electrostatically deflected and undeflected micromirror have been studied. The results have shown that the combined effect of a shock load and an electrostatic actuation makes the instability threshold much lower than the threshold predicted, considering the effect of shock force or electrostatic actuation alone. It has been shown that the torsional shock force has negligible influence on dynamic response of the micromirror in comparison with the linear one. The results have been calculated for linear shocks with different durations, amplitudes, and input times.     

微机械轮式角振动陀螺气体阻尼特性研究

轮式角振动陀螺气体阻尼效应是影响其动态特性的主要因素。在充分研究轮式角振动陀螺结构特征的基础上,创建了角振动陀螺驱动模态滑膜阻尼数学解析模型,并给出了改进解析模型。利用有限差分算法求解极坐标系下雷诺方程,建立了敏感模态压膜阻尼简化分析模型。在5 Pa到105 Pa压强范围内,进行了简化分析模型计算,同时对计算结果进行了与ANSYS 仿真结果的比对。理论模型计算与仿真结果表明,敏感模态压膜阻尼是轮式角振动陀螺气体阻尼的主要产生机制。进而,从结构设计和控制电路的角度,给出了减小气体阻尼效应的有效方法。     

Speed-energy optimization of electrostatic actuators based onpull-in

The speed and total energy required to accomplish pull-in switching of a generic electrostatic actuator is examined. It is found that the value of the source resistance of the voltage drive used for switching has a profound effect on both switching speed and energy requirements. The source resistance governs the charging time for the actuating capacitor. As long as this time is slower than the time required to accelerate the moving mass to maximum speed in the presence of damping, the total energy required for switching can be dramatically reduced without a significant increase in switching time. Indeed, there exists a clear optimum source-resistance value that minimizes the product of switching time and switching energy. These findings are demonstrated theoretically and then applied to specific examples from the literature. In addition, the limiting case of very large source resistance, essentially a current drive, is evaluated and compared to the voltage-driven case. It is found that for equivalent switching times, the current drive requires less total energy for a switching event     

Dynamic pull-in of parallel-plate and torsional electrostatic MEMS actuators

An analysis of the dynamic characteristics of pull-in for parallel-plate and torsional electrostatic actuators is presented. Traditionally, the analysis for pull-in has been done using quasi-static assumptions. However, it was recently shown experimentally that a step input can cause a decrease in the voltage required for pull-in to occur. We propose an energy-based solution for the step voltage required for pull-in that predicts the experimentally observed decrease in the pull-in voltage. We then use similar energy techniques to explore pull-in due to an actuation signal that is modulated depending on the sign of the velocity of the plate (i.e., modulated at the instantaneous mechanical resonant frequency). For this type of actuation signal, significant reductions in the pull-in voltage can theoretically be achieved without changing the stiffness of the structure. This analysis is significant to both parallel-plate and torsional electrostatic microelectromechanical systems (MEMS) switching structures where a reduced operating voltage without sacrificing stiffness is desired, as well as electrostatic MEMS oscillators where pull-in due to dynamic effects needs to be avoided.     

带有凸条平板的MEMS结构压膜阻尼效应分析

针对带有凸条平板的MEMS结构压膜阻尼效应,利用基本Reynolds方程和特定的第一类边界条件,给出一种压膜阻尼系数的解析分析方法。在带有凸条平板的MEMS微开关设计与制作的基础上,利用引入该压膜阻尼系数的Simulink模型仿真分析了微开关的动态响应特性,得到的阈值加速度与其落锤测试结果是一致的,从而验证了所提出的带有凸条平板压膜阻尼效应理论分析的正确性。     

Using dynamic voltage drive in a parallel-plate electrostatic actuator for full-gap travel range and positioning

The nonlinear dynamics of the parallel-plate electrostatically driven microstructure have been investigated with the objective of finding a dynamic voltage drive suitable for full-gap operation. Nonlinear dynamic modeling with phase-portrait presentation of both position and velocity of a realistic microstructure demonstrate that instability is avoided by a timely and sufficient reduction of the drive voltage. The simulation results are confirmed by experiments on devices fabricated in an epi-poly process. A 5.5-V peak harmonic drive voltage with frequency higher than 300 Hz allows repetitive microstructure motion up to 70% of gap without position feedback. The results of the analysis have been applied to the design of a new concept for positioning beyond the static pull-in limitation that does include position feedback. The measured instantaneous actuator displacement is compared with the desired displacement setting and, unlike traditional feedback, the voltage applied to the actuator is changed according to the comparison result between two values. The "low" level is below the static pull-in voltage and opposes the motion, thus bringing the structure back into a stable regime, while the "high" level is larger than the static pull-in voltage and will push the structure beyond the static pull-in displacement. Operation is limited only by the position jitter due to the time delay introduced by the readout circuits. Measurements confirm flexible operation up to a mechanical stopper positioned at 2 /spl mu/m of the 2.25 /spl mu/m wide gap with a 30 nm ripple.     

Analysis of a novel RF MEMS switch using different meander techniques

In this paper, two types of RF MEMS switches namely step structure and Normal beam structure are designed and analyzed using different meander techniques. Three techniques namely plus, zigzag and three-square meander were used to lower the pull-in voltage. The actuating beam is designed with the rectangular perforations affects the performance of a switch by lowering the pull-in voltage, switching speed and results in better isolation. In this paper a comparative analysis is done for all three meander techniques with and without perforations on the beam. Total six structures have been designed with the combination three meanders and two different beam structures. The proposed stepdown structure exhibits high performance characteristics with a very low pull-in voltage of 1.2 V having an airgap of 0.8 µm between the actuation electrodes. The gold is used as beam material and HfO₂ as the dielectric material such that the upstate and downstate capacitance is seen as 1.02 fF and 49 fF. The FEM analysis is done to calculate the spring constant and thereby the pull-in voltage and behavior of the switch is studied with various parameters. The switch with a step structure and three-square meander configuration has shown best performance of all by requiring a pull-in voltage of 1.2 V and lower switching time of 0.2 µs. The proposed switch also exhibits good RF performance characteristics with an insertion loss below − 0.07 dB and return loss below − 60 dB over the frequency range of 1–40 GHz. At 28 GHz a high isolation of − 68 dB is exhibited.

     

Dynamical characteristics of fluid-conveying microbeams actuated by electrostatic force

In this paper, the dynamic characteristics and pull-in instability of electrostatically actuated microbeams which convey internal fluids are investigated. A theoretical model is developed by considering the elastic structure, laminar flow and electrostatic field to characterize the dynamic behavior. In addition, the energy dissipation induced by the fluid viscosity is studied through analyzing the fluid–structure interactions between the laminar fluid flow and oscillating microbeam by comprehensively considering the effects of velocity profile and fluid viscosity. The results indicate that the system is subjected to both the pull-in instability and the fluid-induced instability. It is demonstrated that as the flow velocity increases, both the static pull-in voltage and the dynamic one decrease for clamped–clamped microbeams while increase for clamped-free microbeams. It is also shown that the applied voltage and the steady flow can adjust the resonant frequency. The perturbation viscous flow caused by the vibration of microbeam is manifested to result in energy dissipation. The quality factor decreases with the increment of both the mode order and flow velocity. However, when the oscillating flow dominates, the flow velocity has no obvious effect.     

Voltage and pull-in time in current drive of electrostaticactuators

The absolute maximum value of the voltage developed across an electrostatic actuator when driven by a current source has been calculated as well as an absolute minimum for the pull-in time. These two results are calculated for a drive using a δ-pulse of current and numerical assessment is given to show that for a nonzero parasitic capacitance, a realistic shape of the current pulse, or a finite value of the damping coefficient do not increase the maximum value of the voltage developed beyond that limit and that the pull-in time is always larger than the analytical minimum. A scaled-up macromodel of an electrostatic actuator has been used to register voltage transients to validate the theoretical predictions     

大型挤压油膜阻尼器非线性动力学分析与优化研究进展

挤压油膜阻尼器（Squeeze Film Dampers,SFDs）是旋转机械中常用的一类支承阻尼结构装置,能够改善转子系统的动力特性.当前工程实际中已经大量使用的两类不同结构形式的挤压油膜阻尼器,仍然存在着减振效果不稳定甚至会导致转子失稳,以及阻尼器动力学机制不清楚、建模和分析精度差、设计方法欠缺等理论技术难题.本文首先介绍两类典型SFD的结构形式和主要失效模式,然后详细叙述SFD动力学分析与优化设计方法在发展过程中的代表性研究成果,涉及SFD动力学特性、转子 SFD系统动力学特性研究、SFD动力学设计与优化等几个方面的研究,并对SFD的试验测试技术方面的成果进行评述.在此基础上,探讨目前先进航空发动机用大型挤压油膜阻尼器亟须开展的基础研究任务,特别强调了数据驱动与动力学解析模型融合的SFD动力学建模、分析与设计优化的发展方向.     

Dynamic characteristics of voltage induced reciprocated bending in double cantilever configuration of asymmetric comb drive MEMS

The dynamic characteristics of an electrostatically actuated double cantilever beam, often found in asymmetric comb drive microstructures, have been investigated in the present paper. A coupled electromechanical problem is formulated and solved to obtain different performance parameters like pull-in voltage, frequency response etc. Effects of various critical factors on the dynamic pull-in characteristics have been discussed elaborately. It has been further observed through extensive studies that, the dynamic pull-in characteristics differ considerably from the static characteristics for the double beam configuration. Finally, these observations have been supported by experimental results with a fabricated (in SOIMUMPS process) double cantilever based microstructure, using a simple in-house developed low cost test set up. A typical case of design of a closed loop MEMS (microelectromechanical systems) capacitive accelerometer has also been discussed where the present study finds ready applications to predict the dynamic pull-in characteristics more accurately than the conventional lumped model.     

Design, fabrication and characterization of a high fill-factor micromirror array for wavelength selective switch applications

This paper presents the design, fabrication and characterization of a high fill-factor micromirror array in application of wavelength selective switch (WSS). The micromirror array consists of 52 independent micromirrors. Each micromirror is composed of a cantilever-type micromirror plate (800 μm × 120 μm) with a bumper and an eight-terraced bottom electrode with a limiting plane. A cantilever beam is designed to obtain the rotation angle of micromirror plate and achieve a high fill-factor for the micromirror array. Meanwhile, the bumper and limiting plane are used to prevent the damage possibly caused by the pull-in effect or some vibration instance. An eight-terraced electrode is utilized for reducing the driving voltage. The micromirror array with a high fill-factor in excess of 97% has been successfully achieved using the bulk micromachining technologies. The measured static and dynamic characteristics show that the micromirror can achieve a maximal rotation angle of 0.87° with a Direct Current (DC) driving voltage of 156 V. The turn-on responding time is 0.57 ms, and the turn-off responding time is 4.36 ms. Furthermore micromirror plate can be easily released from the pull-in state without damaged due to the novel bumper design. The switching function between the two output ports of a WSS optical system has also been demonstrated.     

On the dynamic pull-in of electrostatic actuators with multiple degrees of freedom and multiple voltage sources

This study considers the dynamic response of electrostatic actuators with multiple degrees of freedom that are driven by multiple voltage sources. The critical values of the applied voltages beyond which the dynamic response becomes unstable are investigated. A methodology for extracting a lower bound for this dynamic pull-in voltage is proposed. This lower bound is based on the stable and unstable static response of the system, and can be rapidly extracted because it does not require time integration of momentum equations. As example problems, the dynamic pull-in of two prevalent electrostatic actuators is analyzed.     

Tilt-angle stabilization of electrostatically actuated micromechanical mirrors beyond the pull-in point

Recently proposed optical subsystems utilizing microelectromechanical system (MEMS) components are being developed for use in optical crossconnects, add-drop multiplexers, and spectral equalizers. Common elements to these subsystems are electrostatically actuated micromechanical mirrors that steer optical beams to implement the subsystem functions. In the past, feedback control methods were used to obtain precise mirror orientations to minimize loss through optical switch fabrics or to stabilize attenuation through spectral equalizers. However, the mirror tilt angle range is limited because of inherent instability beyond a critical tilt angle (pull-in angle), and the usual feedback schemes do not counteract this effect. This work presents a feedback control method to enable operation of electrostatic micromirrors beyond the pull-in angle, yielding advantages including greater scalability of switch arrays and increased dynamic range of optical attenuators. Both static and dynamic tilting behaviors of electrostatic micromirrors under the feedback control are studied. In addition, a practical implementation of the feedback control system by using linear voltage control law is developed. A voltage slightly larger than the pull-in voltage is first applied when the mirror is at small angle positions, and the voltage is then linearly reduced as the mirror approaches the desired position. Experimental measurements, showing that tilt angles beyond the pull-in point can be achieved, are in good agreement with theoretical analysis.     

Squeeze film effects on dynamic performance of MEMS μ-mirrors-consideration of gas rarefaction and surface roughness

The squeeze film behavior of MEMS torsion mirrors is modeled, analyzed and discussed. Effects of gas rarefaction (first-order slip-flow model with non-symmetric accommodation coefficients, ACs) and surface roughness are considered simultaneously by using the average Reynolds type equation (ARTE). Based on the operating conditions with small variations in film thickness and pressure, the ARTE is linearized. A coordinate transformation, by stretching or contracting the axes by referring to the roughness flow factors, is proposed to transform the linearized ARTE into a diffusion type modal equation. The dynamic coefficients (stiffness and damping coefficients) are then derived and expressed in analytical form. The results show that the tilting frequency (or Γ₀ squeeze number), roughness parameters (γ Peklenik numbers, σ standard deviation of composite roughness) and gas rarefaction parameters (D inverse Knudsen number, ACs) are all important parameters on analyzing the dynamic performance of MEMS torsion mirrors.     

弹性环挤压油膜阻尼器支撑下的柔性转子系统动力学分析

弹性环挤压油膜阻尼器(Elastic ring squeeze film damper, ERSFD)具有良好的支撑作用和减振效果,但由于其结构和流场耦合行为极为复杂,使得已有的物理模型难以完整表现出ERSFD的力学特性.为了进一步探究ERSFD的力学机理,本文借助有限元仿真平台,采用双向流固耦合的计算方法,剖析弹性环与油膜之间的相互作用,获取ERSFD中油膜压力的分布规律.在此基础上,利用最小二乘法进一步拟合出ERSFD等效刚度、等效阻尼与转子轴颈扰动位移的映射关系,并将其分别引入柔性转子系统动力学模型中.通过数值计算研究了ERSFD支撑下柔性转子系统的振动响应,分别给出了不同转速下转子系统的响应分岔图、轴心轨迹等.同时,通过对比分析,进一步揭示了ERSFD所诱发出的转子系统丰富的非线性动力学行为,有助于对ERSFD轴承支撑特性的理解.     

静电悬浮转子微陀螺高努森数下的空气阻尼力矩

针对工作于高真空密封腔中的静电悬浮MEMS陀螺微转子,为建立其旋转动力学模型,实现高精度恒速旋转控制,需要得到高努森数条件下的空气阻尼力矩特性。结合复杂结构的轮状扁平微转子,根据分子动理论和Christian模型,推导出压膜阻尼力矩特性;根据稀薄气体动力学,在考虑腔室内壁和转子表面具有不同切向动量适应系数的条件下,推导出滑膜阻尼力矩解析公式。以根据腔内空气流动特征进行的分区直接蒙特卡罗模拟(DSMC)结果为参考,总阻尼力矩系数的解析误差约为16%,表明解析模型具有较好的精度,对于高努森数条件下类似微器件的建模和系统设计具有较高的实用价值。     

Reduction of squeeze-film damping in a wafer-level encapsulated RF MEMS DC shunt switch

This paper presents the design, fabrication and characterization aspects of a wafer-level encapsulated RF MEMS shunt switch with a perforated base substrate and a corrugated diaphragm. A three-wafer stacking concept was proposed to achieve a RF MEMS shunt switch based on metal-metal contact. The introduction of damping holes in the base substrate wafer is proven to be an effective way to reduce squeeze-film damping and thus increase the switching speed of the switch. It is also demonstrated by analytical calculation that some factors play important roles on the damping characteristics, such as the physical location of damping holes in the base substrate, hole size, and number of holes per radius ring. By means of the implementation of damping holes, the pull-in and release time of the fabricated MEMS switch are significantly reduced by about 13 times, from 5.4 ms to 0.435 ms and 40.6 ms to 3.2 ms, respectively.     

Equivalent area nonlinear static and dynamic analysis of electrostatically actuated microstructures

Nonlinear dynamic investigation of electrostatically actuated micro-electro-mechanical-system (MEMS) microcantilever structures is presented. The nonlinear analysis aims to better quantify, than the linear model, the instability threshold associated with electrostatically actuated MEMS structures, where the pull-in voltage of the microcantilever is determined using a phase portrait analysis of the microsystem. The microcantilever is modeled as a lumped mass-spring system. The nonlinear electrostatic force is incorporated into the lumped microsystem through an equivalent area of the microcantilever for a given electrostatic potential. Electro-mechanical force balance plots are obtained for various electrostatic potentials from which the static equilibrium positions of the microcantilever are obtained and the respective conservative energy values are determined. Subsequently, phase portrait plots are obtained for the corresponding energy values from which the pull-in voltage is estimated for the microsystem. This pull-in voltage value is in good agreement with the previously published results for the same geometric and material parameters. The results obtained for linear electrostatic models are also presented for comparison.