On Squeeze Film Damping in Microsystems

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Victor Marrero ◽  
Diana-Andra Borca-Tasciuc ◽  
John Tichy
Keyword(s):  
Hydrodynamic Lubrication ◽  
Reynolds Numbers ◽  
Lubrication Theory ◽  
Squeeze Film ◽  
Solution Technique ◽  
Parallel Plates ◽  
Damping Force ◽  
Aspect Ratios ◽  
Squeeze Film Damping ◽  
High Reynolds

Classical hydrodynamic lubrication theory has been one of the most successful and widely used theories in all of engineering and applied science. This theory predicts that the force resisting the squeezing of a fluid between two parallel plates is inversely proportional to the cube of the fluid thickness. However, recent reports on liquid squeeze film damping in microsystems appear to indicate that experimentally measured damping force is proportional to the inverse of the fluid thickness to the first power—a large fundamental discrepancy from classical theory. This paper investigates potential limitations of lubrication theory in microsystems by theoretical and computational methods. The governing equations for a Newtonian incompressible fluid are solved subject to two-dimensional, parallel surface squeezing by an open-source computational fluid dynamics program called parallel hierarchic adaptive stabilized transient analysis (PHASTA), and by a classical similarity solution technique. At low convective Reynolds numbers, the damping force is determined as a function of the ratio of a reference film thickness H to a reference direction B along the film. Good agreement with classical lubrication theory is found for aspect ratios H/B as high as 1 despite the fact that lubrication theory requires that this ratio be “small.” A similarity analysis shows that when instantaneous convective Reynolds number is of order 10–100 (a range present in experiment), calculated damping deviates significantly from lubrication theory. This suggests that nonlinearity associated with high Reynolds numbers could explain the experimentally observed discrepancy in damping force. Dynamic analysis of beams undergoing small vibrations in the presence of a liquid medium further supports this finding.

Squeeze Film Flow in Arbitrarily Shaped Journal Bearings Subject to Oscillations

1978 ◽  
Vol 100 (3) ◽  
pp. 323-329 ◽  
Author(s):  
M. F. Modest ◽  
J. A. Tichy
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Film Flow ◽  
Linear Partial Differential Equation ◽  
Journal Bearings ◽  
Lubrication Theory ◽  
Squeeze Film ◽  
Solution Technique ◽  
Practical Applications ◽  
High Reynolds

Squeeze film flow in smooth but arbitrarily shaped infinite journal bearings is considered. The nonrotating shaft is subject to small sinusoidal oscillations. An analytic solution is presented which improves on the lubrication theory by including inertia terms in the equations of motion. The solution technique is to introduce a stream function by which the problem can be reduced to a linear partial differential equation, with time varying boundary conditions, which can be solved by conventional means. The solution to an illustrative problem is presented—the circular journal and bearing. The velocity field and pressure distribution differ qualitatively from those predicted by lubrication theory due to the existence of out-of-phase components. The results show that the lubrication solution for the amplitude of load and pressure can be significantly in error for high Reynolds number operation of a bearing at low eccentricity ratio. At high eccentricity ratios, however, the lubrication theory can be used with confidence, even at very extreme (high Reynolds number) conditions. Simple approximate closed form expressions for pressure and load are presented which are sufficiently accurate for engineering use (error <3 percent) in the range of practical applications.

scholarly journals Measurements of Squeeze Film Bearing Forces to Demonstrate the Effect of Fluid Inertia

1984 ◽  
Author(s):  
John A. Tichy
Keyword(s):  
Dynamic Systems ◽  
High Speed ◽  
Hydrodynamic Lubrication ◽  
Reynolds Numbers ◽  
Lubrication Theory ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Viscous Forces ◽  
Rotor Dynamic ◽  
Inertia Forces

Squeeze film dampers are commonly applied to high speed rotating machinery, such as aircraft engines, to reduce vibration problems. The theory of hydrodynamic lubrication has been used for the design and modeling of dampers in rotor dynamic systems despite typical modified Reynolds numbers in applications between ten and fifty. Lubrication theory is strictly valid for Reynolds numbers much less than one, which means that fluid viscous forces are much greater than inertia forces. Theoretical papers which account for fluid inertia in squeeze films have predicted large discrepancies from lubrication theory, but these results have not found wide acceptance by workers in the gas turbine industry. Recently, experimental results on the behavior of rotor dynamic systems have been reported which strongly support the existence of large fluid inertia forces. In the present paper direct measurements of damper forces are presented for the first time. Reynolds numbers up to ten are obtained at eccentricity ratios 0.2 and 0.5. Lubrication theory underpredicts the measured forces by up to a factor of two (100% error). Qualitative agreement is found with predictions of earlier improved theories which include fluid inertia forces.

Squeeze Film Damping Models Compared With Tests on Microsystems

2006 ◽  
Author(s):  
Hartono (Anton) Sumali ◽  
David S. Epp
Keyword(s):  
Experimental Data ◽  
Damping Ratio ◽  
Laser Doppler Vibrometer ◽  
Squeeze Film ◽  
Parallel Plates ◽  
Squeeze Film Damping ◽  
Wide Range ◽  
Oscillation Frequencies ◽  
Oscillating Plate ◽  
The Continuum

This paper compares three models for computing forces caused by gas film squeezed between parallel plates. The models are used to calculate damping forces on an oscillating plate at different oscillation frequencies. The damping forces are then used to calculate nondimensional damping ratios. The damping ratios are used in making comparisons among the models and with experimental data. The experiment used an oscillating MEMS plate suspended by folded springs. The substrate (base) was shaken with a piezoelectric transducer. The plate vibrated as a result, especially at the resonant frequency. The velocities of the suspended plate and of the substrate were measured with a laser Doppler vibrometer and a microscope. Experimental modal analysis gave the damping ratio. To achieve a wide range of squeeze numbers, the experiment was repeated under several different pressures. The measurement was also repeated on an array of plates. Experimental data indicate that, for atmospheric and higher pressures, squeeze-film damping forces can be modeled accurately with a very simple model. For lower pressures in the continuum regime, a more complete model by Veijola (2004) predicts the damping ratio very well.

scholarly journals Experimental Validation of a Squeeze-Film Damping Model Based on the Direct Simulation Monte Carlo Method

2007 ◽  
Author(s):  
Hartono Sumali ◽  
David S. Epp ◽  
John R. Torczynski ◽  
Michael A. Gallis
Keyword(s):  
Experimental Data ◽  
Monte Carlo ◽  
Experimental Validation ◽  
Tangential Velocity ◽  
Direct Simulation Monte Carlo ◽  
Squeeze Film ◽  
Direct Simulation ◽  
Parallel Plates ◽  
Squeeze Film Damping ◽  
Simulation Monte Carlo

A model for computing the force from a gas film squeezed between parallel plates was recently developed using Direct Simulation Monte Carlo simulations in conjunction with the classical Reynolds equation. This paper compares predictions from that model with experimental data. The experimental validation used an almost rectangular MEMS oscillating plate with piezoelectric base excitation. The velocities of the suspended plate and of the substrate were measured with a laser Doppler vibrometer and a microscope. Experimental modal analysis yielded the damping ratio of twelve test structures for several different gas pressures. Small perforation holes in the plates did not alter the squeeze-film damping substantially. These experimental data suggest that the model predicts squeeze-film damping forces accurately. From this comparison, it is seen that these structures have a tangential-velocity accommodation coefficient close to unity.

Flow Beneath a Ship at Small Underkeel Clearance

2006 ◽  
Vol 50 (03) ◽  
pp. 250-258
Author(s):  
Tim Gourlay
Keyword(s):  
Couette Flow ◽  
Reynolds Numbers ◽  
Parallel Plates ◽  
Bulk Carrier ◽  
Low Reynolds Numbers ◽  
Sea Floor ◽  
Flow Models ◽  
High Reynolds Numbers ◽  
Close Proximity ◽  
High Reynolds

This article looks at the case of a large, flat-bottomed ship, such as a bulk carrier, moving in close proximity to a flat sea floor. It is shown that the flow beneath the ship can be modeled as a shear flow between two parallel plates, one of which is moving. The resulting flow can be represented using laminar Couette flow at low Reynolds numbers (possible at model scale) or the very different turbulent Couette flow at high Reynolds numbers (full scale). Implications of these flow models on squat and viscous resistance are discussed.

Squeeze-Film Phenomena in Microresonators Dynamics: A Mathematical Modeling Point of View

2006 ◽  
Author(s):  
G. Nakhaie Jazar ◽  
M. Mahinfalah ◽  
A. Khazaei ◽  
M. H. Alimi ◽  
J. Christopherson
Keyword(s):  
Mathematical Modeling ◽  
Fluid Layer ◽  
Dynamic Properties ◽  
Contact Forces ◽  
Squeeze Film ◽  
Design Parameters ◽  
Damping Force ◽  
Engine Mounts ◽  
Squeeze Film Damping ◽  
Spring Force

Oscillating microplates attached to microbeams is the main part of many microresonators. There are several body and contact forces affecting a vibrating microbeam. Among them are some forces appearing to be significant in micro and nano size scales. Accepting an analytical approach, we present the mathematical modeling of a microresonator a nonlinear model for MEMS are presented, which accounts for the initial deflection due to polarization voltage, mid-plane stretching, and axial loads as well as the nonlinear displacement coupling of electric force. The equations are nondimensionalized and the design parameters are developed. However, the main purpose of this investigation is to present an applied model to simulate the squeeze-film phenomena. We separate the two characteristics of the squeeze-film phenomena and model the damping and stiffness effects individually. Motion of the microplate and flow of the gas underneath is similar to the function of a decoupler plate in hydraulic engine mounts (Golnaraghi and Nakhaie Jazar 2001, Nakhaie Jazar and Golnaraghi 2002). More specifically, the squeeze-film damping is qualitatively similar to the function of decoupler plate in hydraulic engine mounts, which is an amplitude dependent damping (Christopherson and Nakhaie Jazar 2005). It means squeeze-film damping effect is a positive phenomenon to isolate the vibration of microplate from the substrate. Following Golnaraghi and Nakhaie Jazar (2001), and utilizing the aforementioned similarity, we model the squeeze-film damping force, fsd, by a cubic function, where the coefficient Cs is assumed constant and must be evaluated experimentally. In the simplest case, we present the following fifth degree function to simulate the spring force, fss, of the squeeze film phenomenon, simply because at low amplitudes, w ≈ 0, the fluid layer is not strongly squeezed and there is no considerable resistance. On the other hand, at high amplitudes, w ≈ d, there is not much fluid to react as a spring. In addition, speed is proportionally related to the squeezeness of trapped fluid. The coefficient ks assumed constant and must be evaluated experimentally. The coefficients cs and ks are dependent on geometry as well as dynamic properties of the fluid, but assumed to be independent of kinematics of the microbeam such as displacement and velocity. Therefore, this investigation presents two mathematical functions to describe stiffness and damping characteristics of squeeze-film phenomena in a reduced-order model of microresonators.

On the motion of laminar wing wakes in a stratified fluid

1996 ◽  
Vol 327 ◽  
pp. 139-160 ◽  
Author(s):  
Philippe R. Spalart
Keyword(s):  
Numerical Solutions ◽  
Practical Importance ◽  
Reynolds Numbers ◽  
Boussinesq Approximation ◽  
Stratified Fluid ◽  
Small Scale ◽  
Aspect Ratios ◽  
Sufficient Energy ◽  
High Reynolds ◽  
Vortex Systems

We present numerical solutions for two-dimensional laminar symmetric vortex systems descending in a stably stratified fluid, within the Boussinesq approximation. Three types of flows are considered: (I) tight vortices; (II) those deriving from an elliptical wing lift distribution; and (III) those deriving from a ‘high-lift’ distribution, with a part-span flap on the wing. The non-dimensional stratification ranges from zero to moderate, as it does for airliners. For Types I and II, with high Reynolds numbers and weak stratification, the solutions confirm the theory of Scorer & Davenport (1970) (their article lacks a crucial link which we provide, equivalent to one of Crow (1974)). Contrary to common conceptions and observations in small-scale experiments, the descent velocity increases exponentially with time, as the distance between vortices decreases and the circulation of the vortices proper is conserved. With moderate stratification, wakes with sufficient energy also attain the accelerating régime, until the vortex cores make contact. However, they first experience a rebound, which is both of practical importance and out of reach of simple formulas. Type III wakes produce two durable vortex pairs which tumble, and mitigate the buoyancy effect by exchanging fluid with the surroundings. These phenomena are obscured by low wing aspect ratios, Reynolds numbers below about 105, or appreciable surrounding turbulence; this may explain why neither a clear rebound nor an acceleration can be reconciled with experiments to date. We argue that airliner wakes have very little inherent diffusion, and that a rapid end to the wake's descent must reveal effects other than simple buoyancy. In particular, stratification promotes the Crow instability.

scholarly journals Performance of Overset Mesh in Modeling the Wake of Sharp-Edge Bodies

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 66
Author(s):  
Suyash Verma ◽  
Arman Hemmati
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Sharp Edge ◽  
Solution Technique ◽  
Viscous Effects ◽  
Surface Pressure Distribution ◽  
Flow Features ◽  
Background Grid ◽  
High Reynolds ◽  
Flow Variables

The wake dynamics of sharp-edge rigid panels is examined using Overset Grid Assembly (OGA) utilized in OpenFOAM, an open-source platform. The OGA method is an efficient solution technique based on overlap of a single or multiple moving grids on a stationary background grid. Five test cases for a stationary panel at different angle of attack are compared with available computational data, which show a good agreement in predicting global flow variables, such as mean drag. The models also provided accurate results in predicting the main flow features and structures. The flow past a pitching square panel is also investigated at two Reynolds numbers. The study of surface pressure distribution and shear forces acting on the panel suggests that a higher streamwise pressure gradient exists for the high Reynolds number case, which leads to an increase in lift, whereas the highly viscous effects at low Reynolds number lead to an increased drag production. The wake visualizations for the stationary and pitching motion cases show that the vortex shedding and wake characteristics are captured accurately using the OGA method.

Simulation of the Squeeze Film Damping in a RF MEMS Switch

2013 ◽  
Vol 427-429 ◽  
pp. 116-119
Author(s):  
Xiang Guang Li ◽  
Qin Wen Huang ◽  
Yun Hui Wang
Keyword(s):  
Surface Pressure ◽  
Reynolds Equation ◽  
Dynamic Models ◽  
Mechanical Response ◽  
Rf Mems ◽  
Squeeze Film ◽  
Damping Force ◽  
Rf Mems Switch ◽  
Mems Switch ◽  
Squeeze Film Damping

Two different dynamic models have been presented to investigate the transient mechanical response of a RF MEMS switch under the effects of squeeze-film damping based on a modified Reynolds equation. Both the perforated and non-perforated structures are built for comparison. The models include realistic dimensions. The surface pressure, the damping force, and the tip displacement are simulated in three different ambient pressures, such as 500Pa, 5kPa, and 0.05MPa. The result shows that the increased damping leads to a substantial decrease in oscillation with increasing pressure for the non-perforated structure. Compared with the perforated pad, there is a much larger damping force acts on the non-perforated surface, and an obvious decrease in damping force with increasing pressure.

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