analytical solutions for squeeze film effect model
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Analytical Solutions for Squeeze Film y qEffect Model
Presented byPresented by
Eshan DharEshan DharSr No:10258
Department of Mechanical EngineeringIndian Institute of Science BangaloreIndian Institute of Science Bangalore,
Bangalore‐560012
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IntroductionIntroduction
Squeeze film effect naturally occurs in dynamicMEMS structures because most of theseMEMS structures because most of thesesystems have parallel plates or beams thattrap a thin film of gas between the plate andtrap a thin film of gas between the plate andthe fixed substrate.
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IntroductionIntroduction
Figure taken from [1]
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Squeeze Film Damping MechanismSqueeze Film Damping Mechanism
Figure taken from [1]
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Squeeze Film ModelingSqueeze Film Modeling
Continuity Equation:
(1)
Navier – Strokes equation:
(2)
(3)
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Squeeze Film ModelingSqueeze Film Modeling
Since the gap is much smallerthan the surface dimensionsand due to small v & uand due to small v & uconvective inertia terms areignored.
(4)
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Squeeze Film ModelingSqueeze Film Modeling
After neglecting the unsteady inertia term
(5)
Using (9) and the no slip B.C we get
(6)(6)
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Squeeze Film ModelingSqueeze Film Modeling
We now integrate (1) across –h/2 to h/2 using (6)We now integrate (1) across –h/2 to h/2 using (6)
(7)
and assuming isothermal flow conditionsand assuming isothermal flow conditions
(8)
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Squeeze Film ModelingSqueeze Film Modeling
Using perturbation parametersUsing perturbation parameters
We get the linearized compressible Reynolds equation
( ) d l d
(9)
Eq (9) is now non‐dimensionalized using
(10) where
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Solution by separation of variablesSolution by separation of variables
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Solution by separation of variablesSolution by separation of variables
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Solution by separation of variablesSolution by separation of variables
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Solution by separation of variablesSolution by separation of variables
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Solution by separation of variablesSolution by separation of variables
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Solution by separation of variablesSolution by separation of variables
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Solution by separation of variablesSolution by separation of variables
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Solution by separation of variablesSolution by separation of variables
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Solution by separation of variablesSolution by separation of variables
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Solution by separation of variablesSolution by separation of variables
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ResultsResults
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ResultsResults
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ReferencesReferences[1] Rud.ra Pratap, Suhas Mohite and Ashok Kumar Pandey “Squeeze film effect in MEMS devices”[2] H. C. Nathanson, W. E. Newell, R. A. Wickstrom, and J. R. Davis, \The resonant gate transistor,"
IEEE Transaction on Electron Devices ED‐14, No. 3, pp. 117{133, 1967.[3] [online], \Available:http://www.analogdevices.com," Analog devices Inc .[4] T. Juneau and A. P. Pisano, \Micromachined dual axis input axis angular rate sensor," Tech. Dig.[4] T. Juneau and A. P. Pisano, \Micromachined dual axis input axis angular rate sensor, Tech. Dig.
Proc. Solid‐State Sensor Actuator Workshop , pp. 299{302, 1996.