Thin Film Lubrication for MEMS Devices John B. Merrill November, 2004 Sandia National Laboratory.

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

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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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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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A modern tilt-pad thrust bearing from Kingsbury Corp.

http://www.kingsbury.com/

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U

x

y

Pressure Profile:

P0

Pmax

P0m

mgdxdzPxPlift Net 0

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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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• 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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• 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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• 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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• 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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• 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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Thin Film Lubrication for MEMS Devices John B. Merrill November, 2004 Sandia National Laboratory.

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