thin film lubrication for mems devices john b. merrill november, 2004 sandia national laboratory
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Thin Film Lubrication Thin Film Lubrication for MEMS Devicesfor MEMS Devices
John B. MerrillJohn B. Merrill
November, 2004November, 2004
Sandia National Laboratory
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THIN FILM LUBRICATION FOR MEMS DEVICES
ME 595 FALL 2004
What we will cover:
•The classic Reynolds equation
•Modern modifications to the Reynolds equation for micro- and nano-scale behavior
•Modern applications of thin film lubrication in MEMS devices
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THIN FILM LUBRICATION FOR MEMS DEVICES
ME 595 FALL 2004
The Classic Reynolds Equation…
Osbourne Reynolds
1842 - 1912
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U
h
x
y
x
hU
y
P
μ
h
yx
P
μ
h
x
21212
33
The classic Reynolds equation governs the development of hydrodynamic load support between two non-parallel planes in constant relative motion. The relation between the film thickness and pressure profile can be determined if enough boundary and initial conditions are known.
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ME 595 FALL 2004
A modern tilt-pad thrust bearing from Kingsbury Corp.
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U
x
y
Pressure Profile:
P0
Pmax
P0m
mgdxdzPxPlift Net 0
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ME 595 FALL 2004
Modifications to the Classic Reynolds Equation for Micro-Flows
• First Order, Slip Flow
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PHx
Λdy
dPPHKn
σ
σ
ydx
dPPHKn
σ
σ
x v
v
v
v
33 2
612
61
•Includes slip-flow boundary conditions using TMAC
•Knudsen layer modeled with kinetic gas theory
•Valid for Kn << 1
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ME 595 FALL 2004
Modifications to the Classic Reynolds Equation for Micro-Flows
• Second Order
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x
hUρ
t
hρhλhλ
hρ
y
p
μyhλhλ
hρ
x
p
μx
022
322
3
2
1
62
1
62
1
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Modifications to the Classic Reynolds Equation for Micro-Flows
• F-K Model
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0300
PHΛPH
dX
dTPPHDQ
dX
dPPHDQ
dX
d wTP
•Basis of derivation is linearized Boltzmann equation
•Includes thermal creep flow
•Uses a polynomial curve-fit to establish the nondimensional flowrate for Poiseuille flow (QP)
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Modifications to the Classic Reynolds Equation for Micro-Flows
• Nanoscale Effect
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0~1~ 3
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Y
PPHQ
YbPHΛ
X
PPHQ
X pp
•QP is a function of NP (the “nanoscale effect”), which is a function of Kn.
•Where film thickness is same order as mean-free-path, mean-free-path must be adjusted to account for collissions with the boundaries.
•Nanoscale effect can be applied to any other model’s boundary conditions.
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Nanoscale Effect versus Knudsen number
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Modifications to the Classic Reynolds Equation for Micro-Flows
• Molecular Models
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PHdX
dΛ
dY
dP
P
HKξHKξPH
dY
d
dX
dP
P
HKξHKξPH
dX
dnnnn
22232223 6666
•Previous models simplified collisions by modeling both molecules as Hard Spheres.
•Advanced molecular analysis utilizes Variable Hard Sphere (VHS) and Variable Soft Sphere (VSS) to calculate a modified mean-free-path.
•Uses empirical constants
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Modifications to the Classic Reynolds Equation for Micro-Flows
• DSMC (Direct Simulation Monte Carlo)
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DSMC Method:
•A stochastic model
•The control volume is divided into a number of cells, each filled with gas molecules that behave like hard spheres.
•The cell volume must be no larger than the cubic mean free path.
•Boundary conditions and initial conditions are subjected to a random collision function until the results are stable.
•Computation time and capacity can be extreme.
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Summary of Modified Reynolds Equations:
Model Range Min. h (air at STP) Comments
Classic
First-Order
Second Order
FK
NanoscaleEffect
MolecularModel
D S M C
Kn ≤ .01
.01 < Kn < 0.1
Kn ≤ 1
Kn > 1
Kn > 10
all
6500 nm
650 nm
65 nm
> 0
> 0
0
Limited to macro devices
Overestimates support load
Underestimates support load
Tabular gas data required
Difficult algorithms
Tabular gas data required
Massive computational requirements
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Example 1: The MIT MicroturbineExample 1: The MIT Microturbine
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Let’s look at an example…the MIT MicroTurbine:
•Developed beginning in 1997
•Designed to produce 10-20 W of electric power
•0.05 N [0.011 lbf] of thrust
•Fuel consumption under 10 g/hr (H2 vapor fuel)
•Thrust-to-weight ratio of 12:1
•Flow is weird – it is supersonic (M 1.4), yet laminar (Re = 20,000)!
•Shaft speed = 1,200,000 rpm (rotor tip speeds > 500 m/s)
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3.7 mm
21 mm
Compressor Rotor
Diffuser Vane Combustor
Nozzle Guide VaneTurbine Rotor
ExhaustJournal Bearing
Inlet
Thrust Bearing
Starting Air In
4.2 mm
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Turbine Rotor Spiral-Groove Thrust Bearing
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300 µm 11 mg
400 µm
Ø 10µm holes
Spiral Grooves
1.5 µm
1.0 µm
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Example 2: Micro Disk DrivesExample 2: Micro Disk Drives
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TYPICAL MAGNETIC STATIONARY HEAD
ROTATING DISK
10-50 nm
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0.85 inch
1.00 inch
1.00 inch
1.00 inch
4.0 GB
5.0 GB
4.0 GB
4.4 GB
7 GB/in2
6 GB/in2
5 GB/in2
5.5 GB/in2
10 g
19 g
16 g
16 g
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Where are we going…?
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Turbine Thrust-to-Weight Ratios
0
2
4
6
8
10
12
14
1930 1940 1950 1960 1970 1980 1990 2000 2010
Jumo 004B turbojet (Messerschmitt Me 262)
Pratt & Whitney J-57 (F-100, B-52)
GE YJ79-GE-3 Turbojet (F-4C)
GE TF34 turbofan (S-3, A-10)
Rolls-Royce EJ200 (Eurofighter Typhoon)
GE F110-GE-129 (F-16)
GE/Rolls-Royce (F-136 JSF)
MIT MicroTurbine
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•McHugh, J., (2003), “Albert Kingsbury – His Life and Times,” Sound and Vibration, publication of Kingsbury Corp., October.•Karniadakis, G.E. and Beskok, A., (2002), Micro Flows, Fundamentals and Simulation, Springer-Verlag, New York, pp. 167-168, and Panton, R.L., 1996, Incompressible Flow, (2ed) John Wiley & Sons, Inc., New York, pp. 669-672.
•Burgdorfer, A., (1959), “The Influence of the Molecular Mean Free Path on the Performance of Hydrodynamic Gas Lubricated Bearings,” ASME J. of Basic Engineering Trans., 81, pp. 94-909, as cited in Alexander p. 3855 and Karniadakis p. 169.
•Hsia, Y.T. and Domoto, G.A., (1983), “An Experimental Investigation of Molecular Rarefaction Effects in Gas Lubricated Bearings at Ultra-Low Clearances,” ASME J. Tribol., 105, pp. 120-130.
•Fukui, S. and Kaneko, R., (1988), “Analysis of Ultra Thin Gas Film Lubrication Based on Linearized Boltzmann Equation: First report – Derivation of a Generalized Lubrication Equation Including Thermal Creep Flow, ASME J. Tribology, 110, pp. 253-262, as cited in Alexander p. 3855 and Karniadakis p. 171.
•Peng, Y., Lu, X. and Luo, J., (2004), “Nanoscale Effect on Ultrathin Gas Film Lubrication in Hard Disk Drive, “ ASME J. Trib., 126, pp. 347-352.
•Sun, Y., Chan, W.K. and Liu, N., (2002), “A Slip Model with Molecular Dynamics,” J. of Micromechanics and Microengineering, 12, pp. 316-322.
•Huang, W., Bogy, D.B. and Garcia, A.L. (1997), “Three-Dimensional Direct Simulation Monte Carlo Method for Slider Air Bearings,” Phys Fluids 9 (6), pp.1764-1769, with permission.
•Epstein, A.H.et al, (1997), “Micro-Heat Engines, Gas Turbines, and Rocket Engines – The MIT Microengine Project,” Amer. Inst. Of Aeronautics and Astronautics, Inc., Presented at the 28th AIAA Fluid Dynamics Conference, June 1997, Snowmass Village, CO. Paper 97-1773.
•Ausubel, J.H., (2004), “Big Green Energy Machines,” The Industrial Physicist, 10(5), pp. 20-24.•Wong, C.W., Zhang, X, Jacobsen, S.A. and Epstein, A.H., (2004), “A Self-Acting Gas Thrust Bearing for High-Speed Microrotors,” J. of Microelectromechanical System, 13(2), pp. 158-164.
•Sedy, J., (1980), “Improved Performance of Film Riding Gas Seals Through Enhancement of Hydrodynamic Effects,” ASLE Transactions, 23(1), pp. 35-44.
•Epstein, A.H., (2003), “Millimeter-Scale, MEMS Gas Turbine Engines,” Proceedings of ASME Turbo Expo 2003 Power for Land, Sea, and Air, ©ASME Press. Epstein et al, ref. 9.
•Breuer, K., (2001), “Lubrication in MEMS,” CRC Handbook on MEMS, CRC Press.•Hitachi’s UltraStar 36ZX, a 36.7 GB disk drive.•Grochowski, E., IBM Almaden Research Center, Silicon Valley, CA.•Menon, A.K. and Gupta, B.K., (2004), “Nanotechnology: A Data Storage Perspective,” DataTech, publication of the Read-Rite Corporation, Freemont, CA.
•Carnes, K., (2004), “Hard-Driving Lubrication,” Tribology and Lubrication Technology, 60(11), STLE, pp. 30-38. Note the quote from Dr. Bogy on p. 32, who helped this author interpret the DSMC analysis in ref. 8.
References
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