On the modified Reynolds equation model for the prediction of squeeze-film gas damping in a low vacuum

Leung, Roger; Thurber, Travis; Ye, Wenjing

doi:10.1007/s10404-011-0840-3

Cited by 13 publications

(5 citation statements)

References 28 publications

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“…In addition to the problem of quantitative discrepancy, the ETM shows abnormal behavior as the aspect ratio goes high. According to equation (6) we have:…”

Section: Etm and Its Difficultiesmentioning

confidence: 99%

“…For the prediction of quality factor of squeeze film air damping of micro plates in the free molecular regime, there exist two main categories of models: the continuum based models and the free molecule based models. The first category of models is based on Reynolds equation coupled with the 'effective coefficient of viscosity' [4][5][6] and the second category of models is based on the kinetic theory of gas molecules.…”

Section: Introductionmentioning

confidence: 99%

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A generalized energy transfer model for squeeze-film air damping in the free molecular regime

Bao

et al. 2018

J. Micromech. Microeng.

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A generalized energy transfer model (ETM) for squeeze-film air damping of micro plates in the free molecular regime is developed. The development of the model is based on: (1) the modification of the ETM proposed by Bao et al by using the weighted average of square traveling distance (l is the molecular traveling distance in the gap) to replace the plain average of , (2) the incorporation of the Monte Carlo (MC) model by Hutcherson and Ye so that some assumptions in Bao’s model causing the overestimation of quality factor are released, and (3) the use of Sumali’s empirical formula to relate the ETM to MC model quantitatively. The generalized ETM developed in this paper features: (1) a closed form equation for predicting quality factor according to the parameters of the system, (2) without suffering from the abnormal behavior when the aspect ratio of the plate goes high, and (3) good agreement with experimental results. As a result, the ETM can find practical applications in MEMS.

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“…In addition to the problem of quantitative discrepancy, the ETM shows abnormal behavior as the aspect ratio goes high. According to equation (6) we have:…”

Section: Etm and Its Difficultiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A generalized energy transfer model for squeeze-film air damping in the free molecular regime

Bao

et al. 2018

J. Micromech. Microeng.

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“…The viscosity of fluid is constant in whole fluid region Based on above assumptions, general form of Reynolds equation can be obtained from simplification of Navier-Stokes equation, and also from the combination of balance equation and continuous equation of fluid flow in the wedge clearance. [18][19][20] Following is the Reynolds equation…”

Section: Reynolds Equationmentioning

confidence: 99%

Analytical solution of Reynolds equation under dynamic conditions

Gong

Wang

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part J:

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The flow in the clearance heavily influences the lubrication performance of journal bearing. Therefore, it is important to study the flow mechanism in journal bearing. As known, the pressure distribution in bearing clearance can be described with Reynolds equation. In this paper, unsteady form of Reynolds equation was simplified and nondimensionalized at first, based on certain assumptions. Then, the equation was solved with regular perturbation method, obtaining the analytical solution. At the end, the results of our work were compared with the results of “infinitely short journal bearing” model, Vignolo et al. (Approximate analytical solution to Reynolds equation for finite length journal bearings. Tribol Int 2011; 44: 1089–1099), and numerical simulations. The comparison implies that our results show more coincidence with the numerical results in a wider range.

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“…Since its simplicity, the effective viscosity approach could be very powerful. However, none of the above expressions have been proved to work well in all conditions [7]. The second approach for modeling fluid rarefaction is based on the molecular dynamics (MD).…”

Section: Modeling Of Fluid Rarefactionmentioning

confidence: 99%

A numerical study of squeeze-film damping in MEMS-based structures including rarefaction effects

Pantano

Pagnotta

Nigro

2012

Frattura Ed Integrità Strutturale

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In a variety of MEMS applications, the thin film of fluid responsible of squeeze-film damping results to be rarefied and, thus, not suitable to be modeled though the classical Navier-Stokes equation. The simplest way to consider fluid rarefaction is the introduction of a slight modification into its ordinary formulation, by substituting the standard fluid viscosity with an effective viscosity term. In the present paper, some squeeze-film damping problems of both parallel and torsion plates at decreasing pressure are studied by numerical solving a full 3D Navier-Stokes equation, where the effective viscosity is computed according to proper expressions already included in the literature. Furthermore, the same expressions for the effective viscosity are implemented within known analytical models, still derived from the Navier-Stokes equation. In all the considered cases, the numerical results are shown to be very promising, providing comparable or even better agreement with the experimental data than the corresponding analytical results, even at low air pressure.Thus, unlike what is usually agreed in the literature, the effective viscosity approach can be efficiently applied at low pressure regimes, especially when this is combined with a finite element analysis (FEA). SOMMARIO.In molte applicazioni MEMS, il sottile strato di fluido responsabile del fenomeno dello squeezefilm damping risulta essere rarefatto e, quindi, non modellabile mediante l'equazione classica di Navier-Stokes. Il modo più semplice per tener conto della rarefattezza del fluido consiste nell'introduzione di una piccola modifica all'interno della sua formulazione ordinaria, ovvero nella sostituzione della viscosità del fluido con una viscosità effettiva. Nel presente lavoro, vengono presi in considerazione alcuni problemi di squeeze-film damping, riguardanti casi in cui le piastre coinvolte sono dotate di moto normale traslatorio e casi in cui esse sono dotate, invece, di moto torsionale. Tali problemi vengono risolti mediante una modellazione numerica 3D dell'equazione di Navier-Stokes, in cui la viscosità effettiva viene calcolata mediante apposite espressioni già note in letterature. Inoltre, queste stesse espressioni sono utilizzate all'interno di modelli analitici già conosciuti, derivati anch'essi dall'equazione di Navier-Stokes. In tutti i casi qui considerati, i risultati numerici sono molto promettenti, in quanto essi sono caratterizzati da uno scostamento dai dati sperimentali uguale o inferiore a quello fornito dai corrispettivi risultati analitici, anche a basse pressioni. Quindi, nonostante quanto sia usualmente asserito in letteratura, il metodo della viscosità effettiva può essere efficientemente adottato anche a bassi regimi di pressione, specie se in combinazione con analisi numeriche agli elementi finiti (FEA).

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On the modified Reynolds equation model for the prediction of squeeze-film gas damping in a low vacuum

Cited by 13 publications

References 28 publications

A generalized energy transfer model for squeeze-film air damping in the free molecular regime

A generalized energy transfer model for squeeze-film air damping in the free molecular regime

Analytical solution of Reynolds equation under dynamic conditions

A numerical study of squeeze-film damping in MEMS-based structures including rarefaction effects

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