Modified Reynolds Equation for Squeeze-Film Air Damping of Slotted Plates in MEMS Devices

A differential equation for calculating squeeze-film air damping in slotted plates is developed by modifying the Reynolds equation. A term is added to account for the effect of airflow through the slots on the air damping of the plate. The end effect of the airflow in the slots is also treated by substituting an effective channel length for the geometric channel length （i. e. the thickness of the plate）..The damping pressure distribution, damping force, and damping force coefficient of the slotted plates can be found by solving the equation under appropriate boundary conditions. With restrictions on the thickness and the lateral dimensions of the slotted plate removed,the equation provides a useful tool for analysing the squeeze-film air damping effect of slotted plates with finite thickness and finite lateral dimensions. For a typical slotted plate structure, the damping force coefficient obtained by this equation agrees well with that generated by ANSYS.

A Generalized Reynolds' Equation For Squeeze-Film Air Damping in MEMS

A differential equation that is generally effective for squeeze film air damping of perforated plate and non perforated plate as well as in MEMS devices is developed.For perforated plate,the thickness and the dimensions of the plate are not limited.With boundary conditions,pressure distribution and the damping force on the plate can be found by solving the differential equation.Analytical expressions for damping pressure and damping force of a long strip holeplate are presented with a finite thickness and a finite width.To the extreme conditions of very thin plate and very thin hole,the results are reduced to the corresponding results of the conventional Reynolds' equation.Thus, the effectiveness of the generalized differential equation is justified.Therefore,the generalized Reynolds' equation will be a useful tool of design for damping structures in MEMS.

Effects of Squeeze-film Air Damping on Properties of MEMS Inertial Switch in Fuse

The squeeze-film air damping exists in a lot of micro-electronic-mechanical system (MEMS) devices unavoidably. The effects of air damping in traditional inertial switch with spring-mass system can be ignored for its large volume and mass. But, many properties of MEMS switch, such as sensitivity, resolution and contact time, are affected by the air damping caused from the squeezed air film between two parallel plates moving relatively. Based on the conservation laws for mass and flux and the nonlinear Reynolds equation, the coefficient of squeeze-film damping was derived. The dynamic responses of the inertial switch with and without squeeze-film damping were simulated by using software ANSYS. The simulated results show that the sensitivity and contact time of the switch descend by about 5% and 15%, respectively, when the effects of squeeze-film damping are considered.

Effects of air damping on quality factors of different probes in tapping mode atomic force microscopy

The AFM probe in tapping mode is a continuous process of energy dissipation,from moving away from to intermittent contact with the sample surfaces.At present,studies regarding the energy dissipation mechanism of this continuous process have only been reported sporadically,and there are no systematic explanations or experimental verifications of the energy dissipation mechanism in each stage of the continuous process.The quality factors can be used to characterize the energy dissipation in TM-AFM systems.In this study,the vibration model of the microcantilever beam was established,coupling the vibration and damping effects of the microcantilever beam.The quality factor of the vibrating microcantilever beam under damping was derived,and the air viscous damping when the probe is away from the sample and the air squeeze film damping when the probe is close to the sample were calculated.In addition,the mechanism of the damping effects of different shapes of probes at different tip–sample distances was analyzed.The accuracy of the theoretical simplified model was verified using both experimental and simulation methods.A clearer understanding of the kinetic characteristics and damping mechanism of the TM-AFM was achieved by examining the air damping dissipation mechanism of AFM probes in the tapping mode,which was very important for improving both the quality factor and the imaging quality of the TM-AFM system.This study’s research findings also provided theoretical references and experimental methods for the future study of the energy dissipation mechanism of micro-nano-electromechanical systems.

Efficient molecular model for squeeze-film damping in rarefied air

Based on the energy transfer model(ETM) proposed by Bao et al.and the Monte Carlo(MC) model proposed by Hutcherson and Ye, this paper proposes an efficient molecular model(MC-S) for squeeze-film damping(SQFD) in rarefied air by releasing the assumption of constant molecular velocity in the gap.Compared with the experiment data, the MC-S model is more efficient than the MC model and more accurate than ETM.Besides, by using the MC-S model, the feasibility of the empirical model proposed by Sumali for SQFD of different plate sizes is discussed.It is proved that, for various plate sizes, the accuracy of the empirical model is relatively high.At last, the SQFD of various vibration frequencies is discussed, and it shows that, for low vibration frequency, the MC-S model is reduced to ETM.

High-Performance Single-Side Fabricated (111)-Silicon Dual-Cantilever Accelerometer with Squeeze-Film Air Damping Modulation

This study proposes a novel design and micromachining process for a dual-cantilever accelerometer.Comb and curved-surface structures are integrated into the sensing structure to modulate the squeeze-film damping,thus effectively optimizing the response frequency bandwidth.Owing to the high stress concentration on the dual-cantilever integrated with a fully sensitive piezoresistive Wheatstone bridge,a high sensitivity to acceleration is achieved.In addition,the dual-cantilever accelerometer is fabricated using a specifically developed low-cost and high-yield(111)-silicon single-side bulk-micromachining process.The test results show that the proposed dualcantilever accelerometer exhibits a sensitivity of 0.086—0.088 mV/g/3.3 V and a nonlinearity of±(0.09%—0.23%)FS(full-scale).Based on dynamic characterization,an adequate frequency bandwidth of 2.64 kHz is verified.Furthermore,a resonant frequency of 4.388 kHz is measured,and a low quality factor(Q)of 7.62 is obtained,which agrees well with the design for air-damping modulation.The achieved high performance renders the proposed dual-cantilever accelerometer promising in applications such as automotive and consumer electronics.

NONLINEAR DYNAMICS OF LATERAL MICRO-RESONATOR INCLUDING VISCOUS AIR DAMPING

The nonlinear dynamics of the lateral micro-resonator including the air damping effect is researched. The air damping force is varied periodically during the resonator oscillating, and the air damp coefficient can not be fixed as a constant. Therefore the linear dynamic analysis which used the constant air damping coefficient can not describe the actual dynamic characteristics of the mi-cro-resonator. The nonlinear dynamic model including the air damping force is established. On the base of Navier-Stokes equation and nonlinear dynamical equation, a coupled fluid-solid numerical simulation method is developed and demonstrates that damping force is a vital factor in micro-comb structures. Compared with existing experimental result, the nonlinear numerical value has quite good agreement with it. The differences of the amplitudes （peak） between the experimental data and the results by the linear model and the nonlinear model are 74.5% and 6% respectively. Nonlinear nu-merical value is more exact than linear value and the method can be applied in other mi-cro-electro-mechanical systeme （MEMS） structures to simulate the dynamic performance.

MFM Study:the Air Damping Effect on Magnetic Imaging of CoNbZr Thin Film

This paper studies the CoNbZr soft magnetic thin film by magnetic force microscopy （MFM）. By measuring in atmosphere circumstance, the magnetic force images display some clear dark dots which are corresponding to the clusters in the topography images welL Then the dark dots disappear in magnetic force images, scanning in high vacuum. This indicates that the dark dots are caused by air damping between the vibrating tip and the sample. An interpretation for the above observation is given.

Design, Development and Testing of an Air Damper to Control the Resonant Response of a SDOF Quarter-Car Suspension System

An air damper possesses the advantages that there are no long term changes in the damping properties, there is no dependence on working temperature and additionally, it has less manufacturing and maintenance costs. As such, an air damper has been designed and developed based on the Maxwell type model concept in the approach of Nishihara and Asami [1]. The cylinder-piston and air-tank type damper characteristics such as air damping ratio and air spring rate have been studied by changing the length and diameter of the capillary pipe between the air cylinder and the air tank, operating air pressure and the air tank volume. A SDOF quarter-car vehicle suspension system using the developed air enclosed cylinder-piston and air-tank type damper has been analyzed for its motion transmissibility characteristics. Optimal values of the air damping ratio at various values of air spring rate have been determined for minimum motion transmissibility of the sprung mass. An experimental setup has been developed for SDOF quarter-car suspension system model using the developed air enclosed cylinder-piston and air-tank type damper to determine the motion transmissibility characteristics of the sprung mass. An attendant air pressure control system has been designed to vary air damping in the developed air damper. The results of the theoretical analysis have been compared with the experimental analysis.

Damping of a Simple Pendulum Due to Drag on Its String

A basic classical example of simple harmonic motion is the simple pendulum, consisting of a small bob and a massless string. In a vacuum with zero air resistance, such a pendulum will continue to oscillate indefinitely with a constant amplitude. However, the amplitude of a simple pendulum oscillating in air continuously decreases as its mechanical energy is gradually lost due to air resistance. To this end, it is generally perceived that the main role in the dissipation of mechanical energy is played by the bob of the pendulum, and that the string’s contribution is negligible. The purpose of this research is to experimentally investigate the merit of this assumption. Thus, we experimentally investigate the damping of a simple pendulum as a function of its string diameter and compare that to the contribution from its bob. We find out that although in some cases the effect of the string might be small or even negligible, in general the string can play a significant role, and in some cases even a greater role on the damping of the pendulum than its bob.

The Effect of Mass Ratio and Air Damper Characteristics on the Resonant Response of an Air Damped Dynamic Vibration Absorber

In this paper, it is shown that, a road vehicle 2DOF air damped quartercar suspension system can conveniently be transformed into a 2DOF air damped vibrating system representing an air damped dynamic vibration absorber (DVA) with an appropriate change in the ratio μ of the main mass and the absorber mass i.e. when mass ratio μ >> 1. Also the effect of variation of the mass ratio, air damping ratio and air spring rate ratio, on the motion transmissibility at the resonant frequency of the main mass of the DVA has been dis- cussed. It is shown that, as the air damping ratio in the absorber system increases, there is a substantial decrease in the motion transmissibility of the main mass system where the air damper has been modeled as a Maxwell type. Optimal value of the air damping ratio for the minimum motion transmissibility of the main mass of the system has been determined. An experimental setup has been designed and developed with a control system to vary air pressure in the damper in the absorber system. The motion transmissibility characteristics of the main mass system have been obtained, and the optimal value of the air damping ratio has been determined for minimum motion transmissibility of the main mass of the

Sensitivity Analysis of Air Gap Motion with Respect to Wind Load and Mooring System for Semi-Submersible Platform Design

A design of semi-submersible platform is mainly based on the extreme response analysis due to the forces experienced by the components during lifetime. The external loads can induce the extreme air gap response and potential deck impact to the semi-submersible platform. It is important to predict air gap response of platforms accurately in order to check the strength of local structures which withstand the wave slamming due to negative air gap. The wind load cannot be simulated easily by model test in towing tank whereas it can be simulated accurately in wind tunnel test. Furthermore, full scale simulation of the mooring system in model test is still a tuffwork especially the stiffness of the mooring system. Owing to the above mentioned problem, the model test results are not accurate enough for air gap evaluation. The aim of this paper is to present sensitivity analysis results of air gap motion with respect to the mooring system and wind load for the design of semi-submersible platform. Though the model test results are not suitable for the direct evaluation of air gap, they can be used as a good basis for tuning the radiation damping and viscous drag in numerical simulation. In the presented design example, a numerical model is tuned and validated by ANSYS AQWA based on the model test results with a simple 4 line symmetrical horizontal soft mooring system. According to the tuned numerical model, sensitivity analysis studies of air gap motion with respect to the mooring system and wind load are performed in time domain. Three mooring systems and five simulation cases about the presented platform are simulated based on the results of wind tunnel tests and sea-keeping tests. The sensitivity analysis results are valuable for the floating platform design.

基于分数阶的空气弹簧建模及电动汽车主动悬架控制研究

电控空气悬架系统(electrically controlled air suspension, ECAS)具有调节悬架刚度和车身高度的功能,可有效改善车辆乘坐舒适性和操纵稳定性。以某乘用车ECAS为对象,利用分数阶理论描述橡胶气囊的黏弹性阻尼特性,考虑等效阻尼及滞回特性对其热力学模型进行了优化,结果与实验数据吻合良好,验证了优化后的空气弹簧模型的精确性。在此基础上,考虑车辆纵横向动力学特性与Dugoff轮胎模型,建立14自由度整车ECAS动力学模型,提出模型预测(model predictive control, MPC)主动悬架控制方法,以可测变量为控制器输入,实现直线及转向行驶工况下的主动控制。仿真与整车台架实验研究表明,分数阶修正模型可以很好地反映ECAS变刚度特性,基于MPC的主动悬架控制策略能实时调整空气弹簧刚度,控制车身姿态,有效改善电动汽车行驶时的平顺性与稳定性。论文的研究方法为车辆悬架系统建模及主动控制提供了一种新思路。

环境风下高铁双弓-网系统动态受流特性研究

为了研究环境风对高速铁路双弓-网系统动态受流性能的影响,首先,以位于我国西部大风区的兰新高铁为研究对象,基于模态分析法建立双弓-网耦合系统模型;其次,运用空气动力学理论推导作用于接触网线索上的环境风载荷;然后,考虑横风向空气阻尼的影响,探究空气阻尼作用下双弓受流特性;最后,采用4阶自回归(autoregression,简称AR)模型建立接触网沿线脉动风场,着重分析风速和风攻角对双弓受流的影响。结果表明:横风向空气阻尼对双弓受流产生的影响较小;脉动风下风速越大则风向越趋于垂向,双弓受流性能更易恶化;后弓受流性能相较前弓对风速和风攻角的变化更加敏感。双弓-网系统风振响应分析可为优化风环境下弓网受流质量和接触网防风参数设计提供参考。

高过载软回收系统内弹道双向耦合特性分析

为探究高过载软回收系统中弹前压力对内弹道的影响,在20000 g过载指标要求下,建立了弹前具有高压缓冲气体作用下的双向耦合内弹道仿真模型,采用FLUENT软件计算弹前压力,并利用UDF将弹前压力与经典内弹道进行双向耦合仿真分析。在5.51 kg装药情况下,对质量为90 kg的弹仓进行高过载仿真,结果表明:2 MPa的弹前预充气体压力会造成膛内最大压力增大2.32%;预充气体为5、8、10 MPa的情况下,弹仓的最大速度分别降低7.32%、12.36%和15.61%;弹仓质量为70 kg和80 kg时,弹仓最大速度分别增大9.63%和4.56%;气体介质种类不同对弹前压力造成影响较小,选择空气作为缓冲介质最优。以弹前压力与内弹道之间的双向耦合模型为基础,分析预充气压、弹仓质量、预充气体介质对内弹道特性的影响,为空气阻尼软回收试验的内弹道研究提供了理论参考。

空气阻尼网孔式弹性垫板对车辆-轨道动力学性能的影响分析

空气阻尼网孔式垫板可以通过调整其关键结构参数达到灵活调整其静刚度和阻尼系数的目的。有限元计算表明,空气阻尼网孔式垫板的静刚度会随节流孔尺寸或气室体积比的增大而增大,而阻尼系数则会随之减小。与传统垫板相比,空气阻尼网孔式垫板具有更小的刚度和更大的阻尼。建立车辆-轨道系统动力学模型并通过现场试验验证其准确性。动力学计算表明,随着节流孔尺寸或气室体积比的减小,相应的钢轨、道床和车体垂向振动加速度、轮轨垂向力和脱轨系数均会减小,而钢轨垂向位移会增大。同时,空气阻尼网孔式垫板与传统垫板相比具有更好的减振性能,该垫板可以有效降低列车通过引起的垂向振动加速度、轮轨垂向力和脱轨系数,有利于确保列车安全平稳运行并对轨下结构起一定的保护作用。

基于实时数据采集的摆动力学综合实验

在单摆实验基础上,利用转动传感器设计了摆运动的综合实验。准确测量摆动过程中摆角、摆动角速度随时间变化状态,研究了小角度摆动情况下摆球的实时运动状态,验证了单摆小角度摆动的简谐运动,并通过数据拟合准确测定本地重力加速度为9.77 m/s^(2),百分误差仅为0.22%;同时,研究了大角度摆动时摆球的欠阻尼运动,并测定了摆动过程的空气阻尼系数为0.00224 s^(-1)。该方案通过瞬时量的测量实现了多个动力学知识点的探究,能够有效促进学生对相关知识的理解,激发学生探究运动过程中物理量变化规律的热情。

OWC air chamber performance prediction under impulse turbine damping effects

Oscillating water columns(OWCs)are most widely used in coastal wave energy conversion.The air duct opens into the atmosphere through the air turbine,which is the power take-off device,and this results in a pressure drop across the air chamber.However,because of the complex configure of the impulse turbine and its high rotation speed,it is difficult to install it in the experimental simulator and numerical model.Therefore,the turbine damping effects on the operation of the OWC air chamber are induced to predict its performance more accurately.Orifice plates are used as a substitute for the impulse turbine as it generates a similar pressure drop and power output;the experimental and numerical pressure drops and output powers are compared.A 3D numerical wave tank based on the two-phase VOF model is established using the commercial CFD code Fluent,which can predict air flow and pressure variations in the chamber and duct.Water surface elevations,air flow velocity and pressure variation inside the chamber with the orifice plate are studied numerically,and validated by the corresponding experimental data.The air chamber of the Yongsoo OWC pilot plant is used as the engineering project case.The operating performance of the air chamber installed with a 0.428D orifice plate as the substitute for the designed impulse turbine is computed and analyzed.It is found that the turbine damping effects will cause around 30%reduction in the peak values of the pneumatic energy output of the OWC air chamber in the resonant wave domain.

空气弹簧组件对列车磁悬浮系统的影响

[目的]为研究作为组件之一的空气弹簧对列车磁悬浮系统的影响,解决磁浮列车磁悬浮系统因空气弹簧的影响而导致的悬浮性能变差的问题,开展了空气弹簧对磁悬浮系统性能影响的机理研究和仿真分析。[方法]首先建立不含空气弹簧的磁悬浮模型,并在此基础上设计控制算法,根据磁悬浮系统的性能指标,设计其最优控制参数;在控制算法和最优控制参数确定之后,再将空气弹簧的影响考虑到磁悬浮系统模型中,以研究空气弹簧的刚度对磁悬浮性能的影响。采用MATLAB软件对磁悬浮系统的性能进行了仿真,仿真过程中,在不改变控制参数时改变空气弹簧的刚度,以观测磁悬浮性能的变化情况;当磁悬浮性能变差时,通过优化控制参数,使得磁悬浮性能保持最优。[结果及结论]仿真结果表明:当空气弹簧的刚度在某一范围内时,刚度越大越不利于磁悬浮系统的稳定;在空气弹簧的刚度增大时,适当增加控制系统的刚度和阻尼会有利于磁悬浮系统的稳定。

惯性张量测量研究综述

惯性张量是描述刚体做定点转动时转动惯性的量度,是控制系统设计的关键参数。近年来,飞行器技术的发展使得精确测量大尺寸异形体的惯性张量的需求变得十分迫切。首先,回顾了惯性张量测量的研究历程及当前存在的问题,分别讨论了扭摆法、复摆法、能量法和参数法等方法的测量原理。然后,探讨了这些测量方法在测量大尺寸异形体的惯性张量时需要面对的诸如测量误差的来源和误差补偿等问题。最后,总结了惯性张量测量的发展历程,并指出了目前研究存在的问题和后续的研究方向。