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Research Papers: Hydrodynamic Lubrication

Investigation of the Squeeze Film Dynamics Underneath a Microstructure With Large Oscillation Amplitudes and Inertia Effects

[+] Author and Article Information
Nadim A. Diab

Assistant Professor
Department of Mechanical and
Mechatronics Engineering,
Rafik Hariri University,
Meshref 10-2010, Lebanon
e-mail: diabna@rhu.edu.lb

Issam A. Lakkis

Associate Professor
Department of Mechanical Engineering,
American University of Beirut,
Beirut 11-0236, Lebanon
e-mail: il01@aub.edu.lb

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received April 19, 2015; final manuscript received November 23, 2015; published online May 4, 2016. Assoc. Editor: Daniel Nélias.

J. Tribol 138(3), 031704 (May 04, 2016) (16 pages) Paper No: TRIB-15-1127; doi: 10.1115/1.4032951 History: Received April 19, 2015; Revised November 23, 2015

This paper presents direct simulation Monte Carlo (DSMC) numerical investigation of the dynamic behavior of a gas film in a microbeam. The microbeam undergoes large amplitude harmonic motion between its equilibrium position and the fixed substrate underneath. Unlike previous work in literature, the beam undergoes large displacements throughout the film gap thickness and the behavior of the gas film along with its impact on the moving microstructure (force exerted by gas on the beam's front and back faces) is discussed. Since the gas film thickness is of the order of few microns (i.e., 0.01 < Kn < 1), the rarefied gas exists in the noncontinuum regime and, as such, the DSMC method is used to simulate the fluid behavior. The impact of the squeeze film on the beam is investigated over a range of frequencies and velocity amplitudes, corresponding to ranges of dimensionless flow parameters such as the Reynolds, Strouhal, and Mach numbers on the gas film behavior. Moreover, the behavior of compressibility pressure waves as a function of these dimensionless groups is discussed for different simulation case studies.

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Figures

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Fig. 1

Three-dimensional schematic of the microbeam

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Fig. 2

Two-dimensional simulation domain

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Fig. 3

Flow velocity of gas film at first cell next to the beam within the gas film gap

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Fig. 4

Forces at beam's front and back faces

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Fig. 5

Flow velocity of gas film at first cell next to the beam within the gas film gap

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Fig. 6

Forces at beam's front and back faces

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Fig. 7

Density contours within the film gap thickness at τnorm=0.3

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Fig. 8

Density contours within the film gap thickness at τnorm=0.8

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Fig. 9

Normalized pressure and temperature distributions along plane of symmetry during a period of beam oscillation. Left: case (a) and right: case (b).

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Fig. 10

Evolution of normalized density distribution over a period of beam oscillation. Left: case (a) and right: case (b).

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Fig. 11

Pressure distribution along plane of symmetry as a function of velocity amplitude Va (set 1)

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Fig. 12

Pressure distribution along plane of symmetry as a function of frequency f (set 2)

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Fig. 13

Pressure waves peaks at the inside region as a function of Ma2 over a complete period of motion (set 3)

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Fig. 14

Dependence of the normalized wave speed in the squeeze film region on Mach number

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Fig. 15

Top view of the microbeam's 3D simulation domain

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Fig. 16

Side view of the microbeam's 3D simulation domain

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Fig. 17

Pressure peaks for the 2D and 3D microcantilever beams oscillating at 500 MHz and 1 GHz

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Fig. 18

Pressure contours in the cross-sectional plane of the 3D microcantilever beam oscillating at 1 GHz. Pressure variation at x = 5 from ground to beam tip is shown in the inset.

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Fig. 19

Velocity flow field for the cross-sectional plane of the 3D microcantilever beam oscillating at 1 GHz

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Fig. 20

Pressure contours in the cross-sectional plane of the 3D microcantilever beam oscillating at 500 MHz. Pressure variation at x = 5 from ground to beam tip is shown in the inset.

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Fig. 21

Velocity flow field for the cross-sectional plane of the 3D microcantilever beam oscillating at 500 MHz

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Fig. 22

Force distribution at the back beam face for the 2D and 3D microcantilever beams oscillating at 500 MHz and 1 GHz

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