Squeeze Film Air Research Articles

Damping Ratio Analysis of a Silicon Capacitive Micromechanical Accelerometer

In most MEMS devices, the moving micro-structures are surrounded by air which significantly affects their dynamics behaviors. The correct prediction of the squeeze-film air damping ratio is essential in MEMS (Micro-Electro-Mechanical System) devices design. In the paper, a static test is proposed to measure the squeeze-film air damping ratios of capacitive MEMS accelerometer under different pressures. The unsealed chip of capacitive accelerometer is placed in vacuum extraction equipment and an open loop circuit is developed to apply step signal in the test. By charging the pressure and measuring the overshoot Mp and the settling time ts from the time response of the system, the damping ratio ξ under different pressures can be calculated. Finite element method (FEM) based on the modified Reynolds equation is utilized to simulate the transient response of the micro-structure. Good correlation between experiment and FEM analysis is obtained. The proposed static test in this paper provides a new method to more easily measure the dynamic performances of micro-structures under various pressures.

Dynamic pull-in stability of torsional nano/micromirrors with size-dependency, squeeze film damping and van der Waals effect

Recently, electrostatic torsional nanomirrors are applied widely in various industries. In previous lectures, coefficient of squeeze film air damping in the gap between main plate and substrate has been constant, while this coefficient is the function of viscosity and air pressure and has nonlinear equation. In this paper, the effect of nonzero initial conditions also, and the effect of nonlinear coefficient of squeeze film air damping on the stability of torsional nanomirrors using higher order continuum theories are investigated. First considering two-degree-of-freedom coupled bending/torsion system, the governing equations of system are derived, then using the fourth order Runge-Kutta method and nonzero initial conditions, the equations of motion are solved. Dynamic pull-in instability voltage is obtained and by plotting of response curves and phase portraits, the size effect is investigated. Study of phase portraits shows that size effect causes increasing in the range of stability of nanomirror and increasing of length scale parameter increases the mentioned surface area. As well as assuming constant squeeze film air damping causes the error in investigating of its behavior. Therefore in equation of motion, for getting more accurate response, this coefficient must be considered nonlinear.

Influence of the Disturbance Frequency on the Dynamic Characteristics of an Ultrasonic Gas Squeeze Film

ABSTRACTDynamic characteristics of an air ultrasonic squeeze film are affected by disturbance of the levitating object. A completely analytical model for the dynamic characteristics of the air squeeze film taking into consideration the effects of the disturbance acting on the levitating object was established by using compressible gas hydrodynamic lubricating theory. The models were solved by nonlinear numerical methods. Dynamic characteristics of the air squeeze film at specific cases were obtained and the effects of the disturbance amplitude and frequency on dynamic characteristics were discussed. It is found that these influences are significant. Experiments on stiffness and damping coefficients of the squeeze film measurement were carried out. The results showed some discrepancy with the theoretical values.

Size modulated transition in the fluid–structure interaction losses in nano mechanical beam resonators

An understanding of the dominant dissipative mechanisms is crucial for the design of a high-Q doubly clamped nanobeam resonator to be operated in air. We focus on quantifying analytically the viscous losses—the squeeze film damping and drag force damping—that limit the net quality factor of a beam resonator, vibrating in its flexural fundamental mode with the surrounding fluid as air at atmospheric pressure. Specifically, drag force damping dominates at smaller beam widths and squeeze film losses dominate at larger beam widths, with no significant contribution from structural losses and acoustic radiation losses. The combined viscous losses agree well with the experimentally measured Q of the resonator over a large range of beam widths, within the limits of thin beam theory. We propose an empirical relation between the maximum quality factor and the ratio of maximum beam width to the squeeze film air gap thickness.

Analytical modeling of squeeze air film damping of biomimetic MEMS directional microphone

Squeeze air film damping is introduced in microelectromechanical systems due to the motion of the fluid between two closely spaced oscillating micro-structures. The literature is abundant with different analytical models to address the squeeze air film damping effects, however, there is a lack of work in modeling the practical sensors like directional microphones. Here, we derive an analytical model of squeeze air film damping of first two fundamental vibration modes, namely, rocking and bending modes, of a directional microphone inspired from the fly Ormia ochracea׳s ear anatomy. A modified Reynolds equation that includes compressibility and rarefaction effects is used in the analysis. Pressure distribution under the vibrating diaphragm is derived by using Green׳s function. From mathematical modeling of the fly׳s inspired mechanical model, we infer that bringing the damping ratios of both modes in the critical damping range enhance the directional sensitivity cues. The microphone parameters are varied in derived damping formulas to bring the damping ratios in the vicinity of critical damping, and to show the usefulness of the analytical model in tuning the damping ratios of both modes. The accuracy of analytical damping results are also verified by finite element method (FEM) using ANSYS. The FEM results are in full compliance with the analytical results.

Power Optimization by Mass Tuning for MEMS Piezoelectric Cantilever Vibration Energy Harvesting

A cantilever with an end mass is one of the most popular designs for piezoelectric MEMS vibration energy harvesting. The inclusion of a proof mass near the free end of a micro-cantilever can significantly enhances the power responsiveness of a vibration energy harvester per unit acceleration. However, the accommodation of the proof mass comes at the expense of the active piezoelectric area. This paper numerically and experimentally investigates this compromise, and explores the optimal proof-mass-to-cantilever-length ratio for power maximization. It was found that an end mass occupying about 60%–70% of the total cantilever length is optimal within linear response, and they notably outperform comparable cantilevers with 40% and 50% of end mass. In addition, nonlinear squeeze film air damping within the chip package was found to adversely affect the cantilevers with larger mass more significantly. A harvester prototype with 70% of the length covered by end mass (5 mm3) was able to generate 1.78 $\mu \text{W}$ at 0.6 ms $^{-2}$ and up to 20.5 $\mu \text{W}$ at 2.7 ms $^{-2}$ and 210 Hz when not limited by nonlinear damping. This result outperforms the previously reported counterparts in the literature by nearly an order of a magnitude in terms of power density normalized against acceleration squared. [2015-0116]

Air damping models for micro- and nano-mechanical beam resonators in molecular-flow regime

Researches on energy dissipation of micro- and nano-mechanical beam resonators into the surrounding air are classified into two models, air drag force damping of the resonant beam vibrating in free space and squeeze film air damping of the resonant beam vibrating nearby walls. Appropriate application of these two models are crucial to the design of high-Q micro- and nano-mechanical beam resonators. In this paper, we will present a detail analysis on appropriate application range of these two models for evaluating air damping in micro- and nano-mechanical beam resonators. The two models are applied for investigating damping in the cantilevered and bridged beam resonators. The obtained analysis results show the significance difference between the two models for estimating the quality factor of the micro- and nano-mechanical beam resonators. The criterion for the distinction between the two models is derived by using the ratio factor of damping coefficients of micro- and nano-mechanical beam resonators.

Effect of Squeeze Film Damping and AC Actuation Voltage on Pull-in Phenomenon of Electrostatically Actuated Microswitch

The effect of squeeze air-film and AC actuation voltage on dynamic stability of microswitch actuated electrostatically has been investigated in squeeze film domain. The dynamics of the device has been developed considering the load arising from the squeezed air film between the microcantilever attached plate and the grounded substrate. Using trajectories in phase plane and time history, characteristics of the pull-in phenomena have been studied in the presence of DC voltage combined with AC component. Pull-in voltage is observed to be less as compared to the conventional micro-cantilever devices which are actuated only due to DC loading. Furthermore, the dynamic pull-in voltage tends to approach static pull-in voltage, when the squeeze film damping is considered. The study indicates that although electrostatic forces cause softening characteristics, geometric nonlinearity produces a stiffening effect on the microstructure and the nonlinearities play a significant role when pull-in occurs. The ability to resist the bending deformation has become higher as the overall damping has been enhanced due to the effect squeeze film damping. The consideration of higher order nonlinearities while modeling electrostatic forces, predicts more accurate response. This research gives a desirable insight of dynamic behavior of MEMS device under the influence of squeeze film effect.

Power analysis for the design of a large area ultrasonic tactile touch panel

Tactile interfaces are intuitive but lack of haptic feedback. One method to provide tactile feedback is to change the friction coefficient of the touch surface. Several small-size tactile devices have been developed to provide programmable friction coefficient based on the squeeze air film effect. This effect is produced by ultrasonic vibration of the tactile plate thanks to piezoceramics. In order to design larger embedded tactile feedback areas, a key issue is the power consumption. In this paper, we present the power analysis of a tactile device which is based on the squeeze film effect. We first investigate the source of power consumption by a series of measurements. Then, an analytical model is developed to estimate the power, which gives the conclusion that, when the vibration amplitude is constant, the power consumption is not related to the number of piezoelectric actuators. According to this result, we design a large area (198mm × 138mm) tactile plate with only eight piezoelectric actuators. Experimental results show that the power consumption of the large tactile plate is less than 2 Watts. Moreover, we also find that the power consumption of the large tactile plate was predictable with the measurement results from small plates with an average error of less than 10%.

Dynamics of quartz tuning fork force sensors used in standoff photoacoustic detection

In this paper, a two-degrees-of-freedom model with two coupled oscillators is established to study the dynamics of quartz tuning fork force sensors. Air squeeze-film damping is considered in this model. When the laser power is 40 mW and the distance between the tuning fork and detected objects is approximately 0.5 m, the resonance amplitude of the tuning fork under the electromagnetic radiation pressure of the laser can reach 0.22 pm. Electromagnetic radiation pressure and resonance amplitude have the tendency to exponentially decay along with the distance between the tuning fork and detected objects. The influence of laser power and distance between the tuning fork and detected objects on electromagnetic radiation pressure is also considered. Lastly, an experimental device is set up to verify the calculation result of the model. Analysis shows that the experimental data are in good agreement with the theoretical calculation results.

The squeeze-film air damping of circular and elliptical micro-torsion mirrors

This paper proposes an analytical solution to calculate the squeeze-film air damping of circular and elliptical micro-torsion mirrors. To derive the expressions of squeeze-film air-damping torque, the nonlinear Reynolds equation, which governs the air behavior of torsion mirror, is solved by the method of eigenfunction expansions in polar coordinate and elliptical coordinate, respectively. The series solutions are integrated and summed up to deduce the damping torque of circular and elliptical torsion mirrors. The formulas of circular mirror and elliptical mirror are deduced independently, and their results match when the eccentricity of the elliptical mirror approaches zero. Besides, the results of the formulas are consistent with numerical simulation. Both of them verifies the damping torque formulas in this paper.

Entropy generation analysis of squeeze film air damping in torsional micromirrors

In the present study, the entropy generation analysis of a torsional micromirror is investigated. Using dynamic mesh method, the governing equations are solved numerically. For three different cases, the geometrical and dynamical properties of micromirror and squeeze film air damping are varied. Their effects on entropy generation and the distribution of the hydrodynamic parameters of micromirror are reported. As shown in the results, the frequency and aspect ratio of the micro plate have a direct relation with the volumetric entropy generation rate. In addition, the tilting angle's amplitude has just a small effect on the borders of the mirror. In conditions with higher frequency or smaller aspect ratios, the asymmetry of hydrodynamic parameter distributions are observed.

Design and finite element modeling of series-shunt configuration based RF MEMS switch for high isolation operation in K–Ka band

High isolation and low insertion loss is highly regarded for the devices designed for high frequency applications. A compact radio-frequency microelectromechanical systems switch on quartz substrate is presented in this paper. The high isolation is achieved by incorporating two membranes in series and shunt configuration on a single substrate while maintaining the compactness of the switch dimensions. The ohmic and capacitive switch membranes are designed in a cavity over co-planar waveguides on substrate. Spring constant, pull-in voltage, pressure distribution, squeeze film air damping, Q-factor, R, L and C for switch are calculated and analyzed by finite element modeler. Eigenfrequency analysis is also carried out using FEM to analyse the mode shape for first 6 eigenfrequencies. Biasing pads are provided on both ends of the switch for electrostatic actuation. Membranes with low spring constant are designed and optimized to work on same voltage level. Stress on membranes is analyzed and taken care of by the including meanders. This proposed switch is showing excellent isolation of $$75$$75 dB and low insertion loss of $$0.13$$0.13 dB at $$28$$28 GHz with need of actuation voltage of $$22.5$$22.5 V for both membranes in complete switch area of $$0.4$$0.4 mm$$^2$$2. The switch has wide bandwidth of $$30$$30 GHz from K and Ka band with above $$62$$62 dB of isolation.

Air Damping Analysis in Comb Microaccelerometer

Air damping significantly influences the dynamical characteristics of MEMS accelerometers. Its effects at micro-scale level sharply depend on the structure layouts and size of MEMS devices. The damping phenomenon of comb microaccelerometers is investigated. The air between fixed plate electrodes and movable plate electrodes cannot flow freely and is compressed. The air damping, therefore, exhibits both viscous effects and stiffness effects. The former generates a drag force like that in macromechanical systems, and the damping force is proportional to the velocity of movable electrodes. The latter stiffens the rigidity of structure, and the stiffening level is related to the gap value of capacitors, internal pressure, and temperature. This paper focuses on the dependence of the squeeze film air damping on capacitor gaps. The simulation and experiments indicate that the squeeze film effect is sharply affected by the gap value when the structural dimensions decrease. And the influence of fabrication errors is considered in damping design in comb microaccelerometers.

Numerical Studies of the Squeeze-Film Damping of MEMS Devices with Perforations in the Non-Continuum Regime

Predicting squeeze-film air damping of resonators in rare air is crucial in the design of high-Q devices for various applications. In the past, there have been two approaches to treat the squeeze-film air damping in non-continuum regime: using effective viscosity coefficient and using the molecular dynamics method. And most of the previous work focused on devices in which the rarefaction effects of air are not significant. For such cases, continuum theory is often adequate. However, we have investigated the air damping on oscillating structures in the free molecular regime in which classical continuum theory is no longer valid. Based on this premise, Hutcherson (2004 J. Micromesh. Microeng. 14 1726-1733) has developed a molecular dynamics simulation code and used in predicting quality factors of an oscillating micro-plate at low pressures. However, his work is valid only for non-perforated micro-plate. This paper, a brief description of the molecular dynamics method is presented first. Then a molecular dynamics simulation code has been developed and used in predicting quality factors of a perforated oscillating micro-plate in free molecular regime. And we have found that the molecular dynamics simulation results have shown an excellent agreement with the experimental data of Kwok et al. Finally, the limitations of the present molecular dynamics simulation code have been reported.

The Squeeze Film Damping Effect on Dynamic Responses of Micro-Electromechanical Resonators

The air squeeze film damping effect on the dynamic responses of clamped micro- electromechanical resonators is investigated in this study. A dynamic model for a clamped micro- electromechanical resonator with the damping consideration is derived using Lagrange’s equation. The corresponding resonator eigen solutions are formulated and solved by employing the assumed-mode method. The effect of different parameters; i.e. the resonator size, ambient temperature and pressure on the squeeze film damping characteristics were simulated and investigated. The results indicate that the squeeze film damping effect may significantly affect the dynamic responses of micro-scale electromechanical resonator.

Study of a Novel MEMS Accelerometer with Low Noise Reduced by Actuators

A novel MEMS (Micro Electronic Mechanical System) capacitive accelerometer is presented, which is mainly composed of supporting beam, seismic mass, grid strip capacitances, comb capacitances and electrostatic driver. The damping of grid strip capacitances with variable overlapping area is mainly affected by the slide film air damping, which is small and neglectful, and the damping between comb capacitor is squeeze film air damping. The comb sensing gap can be reduced by electrostatic actuators by which the aspect ratio can reach to 75:1 which greatly depress the limitation of DRIE (Deep reactive ion etching) process on high aspect ratio, and the initial sensing capacitance increases from 2.97 pf to 14.87 pf. The squeeze film damping is reduced from 0.046 Nm/s to 0.0015 Nm/s by designing the comb-shaped grooves on the fixed comb electrodes. The comb initial sensing gap is optimized according to formation factors of system noise, and the noise is reduced from 1.395 μg/√HZ to 0.591 μg/√HZ. The simulation results show that the accelerometer sensitivity achieves 8.40 pf/g, which is two times of the conventional devices.

Comparative performance of squeeze film air journal bearings made of aluminium and copper

Two tubular squeeze film journal bearings, made from Al 2024 T3 and Cu C101, were excited by driving the single-layer piezoelectric actuators at a 75-V AC with a 75-V DC offset. The input excitation frequencies were coincident with the 13th modal frequency, at 16.32 and 12.18 kHz for the respective Al and Cu bearings, in order to produce a ‘triangular’ modal shape. The paper also provided a CFX model, used to solve the Reynolds equation and the equation of motion, to explain the squeeze film effect of an oscillating plate with pressure end leakage. The dynamic characteristics of both bearings were studied in ANSYS and then validated by experiments with respect to their squeeze film thickness and load-carrying capacity. It was observed that whilst both bearings did levitate a load when excited at mode 13, the Al bearing showed a better floating performance than Cu bearing. This is due to the fact that the Al bearing had a higher modal frequency and a greater amplitude response than the Cu bearing.

Levitation characteristics of a squeeze-film air journal bearing at its normal modes

A tubular squeeze-film journal bearing was designed such that it flexed its shell at its normal modes producing a triangular modal shape. The shell motion was created by a single-layer piezoelectric actuator powered at 75 V AC with a 75 V DC offset and the driving frequency coincided with the modal frequency of the bearing. The paper provided a theory that shows the existence of a positive pressure in a squeeze film responsible for the levitation phenomenon. The various modes of vibration of the tubular bearing, made from AL2024-T3, were obtained from a finite element model implemented in ANSYS. Two normal modes, the 13th and 23rd, at the respective theoretical frequencies of 16.37 and 25.64 kHz, were identified for further investigation by experiments with respect to the squeeze-film thickness and its load-carrying capacity. While the bearing at both modes could cause levitation, the 13th mode has a greater load-carrying capacity because its modal shape produced a much lower end leakage.

Design of Proof Mass and System-Level Simulation of a Micromachined Electrostatically Suspended Accelerometer

A six-axis Micromachined Electrostatically Suspended Accelerometer (MESA) which is based on LIGA-type microfabrication was designed. MESA employs a levitated perforated plate as its proof mass. Three main purposes are considered for the design of the perforated proof mass: (1) reducing squeeze-film effect; (2) improving the dynamic response of MESA; (3) facilitating the etching of sacrificial layer under the plate. This paper utilized a finite element model for evaluating air squeeze film damping effect of perforated proof mass. Among several designs of perforated proof mass, the best choice was found. Besides, a system-level model created in CoventorWare is used to evaluate the effect of squeeze film damping and the dynamic response of the MESA.