2009 ASME/STLE International Joint Tribology Conference

Texas A&M UniversityMechanical Engineering Department

Paper IJTC2009-15188

Material is based upon work supported by NASA NNH06ZEA001N-SSRW2, Fundamental Aeronautics: Subsonic Rotary Wing Project and the Texas A&M Turbomachinery Research Consortium

Luis San Andrés Mast-Childs Professor

Fellow ASME, Fellow STLE

Keun Ryu Research Assistant

October 2009

Experimental Structural Stiffness and Damping of a 2nd Generation Foil Bearing

for Increasing Shaft Temperatures

Series of corrugated foil structures (bumps) assembled within a bearing sleeve.

Integrate a hydrodynamic gas film in series with one or more structural support layers.

Use coatings to reduce friction at start-up & shutdown

Applications: APUs, ACMs, micro gas turbines, turbo expanders

Tolerant to misalignment & contamination

High temperature capability Damping from dry-friction and

operation with stable limit cycles

Gas Foil Bearings – Bump Type

Gas Foil Bearings (+/-)

Proven reliability with load capacity Reduce system weight & volume. High temperature (jet engine hot)

No scheduled maintenance Tolerate high vibration and absorb shock loads

Less load capacity than rolling & oil lubricated bearings Wear during start up & shut down (coating survival) Still little test data for rotordynamic force coefficients

at TAMU, predictive models benchmarked to test data, including thermal management schemes

Motivation

• GFB load capacity, stiffness and damping

depends mainly on its underspring structure.

Tests & analysis verified.

• High temperature affects GFB force response.

Changes in clearance & material properties,

coating endurance.

• Operation temperature range (low to high to

low) modifies structural properties.

Objectives

- Identify FB structural stiffness and structural loss factor from dynamic load tests

Measure dynamic force performanceOf 2nd generation foil bearing – no shaft spinning & at increasing temperatures

- Quantify the effect of bearing temperature and dynamic load (amplitude & frequency) on FB force coefficients.

- Support with reliable test data concurrent development of GFB predictive computational tool.

Overview – GFB dynamic load

Salehi et al. (2003): Identify FB dynamic stiffness and equivalent viscous damping. Damping increases with static load but decreases with amplitude of motion and frequency.

ROOM TEMPERATURE

Heshmat and Ku (1994): Dynamic load tests: FB dynamic forced performance depends on frequency.

Rubio and San Andrés (2005): From dynamic load tests, obtain FB energy dissipation parameters: equivalent viscous damping OR structural loss factor OR dry-friction coefficient: FB stiffness decreases with dynamic load amplitude. Viscous damping decreases with frequency. LOSS FACTOR represents best FB mechanical energy dissipation

Structure only – no shaft spinning

Lee et al. (2006): develop FE model accounting for thermal effects. Operating temperature to 500°C reduces FB stiffness and damping. Predictions agree with test data.

Howard et al. (2001): Determine experimentally GFB forced performance for increasing shaft speed, static load, and temperature. From impact load tests: viscous damping is dominant for lightly loaded GFB at high temperature. Dry-friction type damping is + significant for heavily loaded GFB.

HIGH TEMPERATURE

Kim, Breedlove and San Andrés (2009): Identify FB structural stiffness and loss factor for operation at elevated shaft temperature (200 C). Tests with dynamic loads varying in amplitude and frequency.

Overview – GFB dynamic load

Top foil

Cartridge sheet

Bumps

FB nominal dimensions

Parameter [Dimension] Symbol Value

Cartridge inner diameter [mm] D 37.92

Cartridge outer diameter [mm] DO 44.58

Axial bearing length [mm] L 25.40

Number of bumps NB 24× 3

Bump pitch [mm] s 4.64

Bump length [mm] 2lo 3.95

Bump foil thickness [mm] t 0.102

Bump height [mm] h 0.51

Top foil thickness [mm] tT 0.127

Bump arc radius [mm] rB 4.08

Bearing Top foil inner diameter [mm]

DT 36.545

Generation II FBThree (axial) bump strip layers, each

with 24 bumps. Patented solid lubricant coating (up to 800°F) on top foil surface.

Test foil bearing

Other data proprietary

Shaft OD 36.556 mm: Highly preloaded FB

Test setup for static load

Apply load and measure FB displacement to determine FB static structural stiffness

Room temperature tests

Lathe chuck

Live center

Test bearing

Rotor

Load cell

Eddy current sensor

90° bearing orientation

FB loose fit into 3.08 mm thick bearing shell

Uncoated rigid shaft supports floating FB.

Load cell

Direction of static load

gDisplacement

sensor

FB deflection vs static load

F ≠ K X

Nonlinear F(X): Stiffness hardening

Large hysteresis loop = mechanical energy dissipationdue to dry-friction between top foil contacting bumps and bump strip layers contacting bearing cartridge sheet

Room temperature tests

Shaft OD 36.556 mm: Highly preloaded FB

FB static structural stiffness

Cubic polynomial curve fit over span of applied loads

F=F0+K1X+K2X2+K3X3

K=K1+2K2X+3K3X2

Distinctive hardening effect as FB deflection increases

Room temperature tests

Test setup for dynamic loads

Bearing housing

Eddy current sensor

Load cell

Test shaft

Cartridge heater

Thermocouples

Shaker

Single frequency dynamic load in

horizontal direction

Test bearing

Bearing housing

Index fixture

90° bearing orientation

Uncoated rigid, non-rotating, hollow shaft supports floating FB.

FB Displacement controlled [µm] 7.4, 11.1, 14.8, and 18.5

Frequency Range, Hz 50-200 (increment: 25 Hz)

Shaft Temperature, °C 23, 103, 183, and 263

Bearing Mass M, kg 0.785 (load cell + attachment hardware)

FB press fitted onto 15.5 mm thick bearing

housing!

134 mm

Ø 25 mm

Indexing fixture

Ø 25.4 mm

Shaft heating using electric heater

Ø 36.56 mm

T1T3 Th

Significant temperature

gradient along shaft axis.

Cartridge heater warms unevenly

shaft and bearing

T4

Steady state temperature (heater 1 hr operation)

Test BearingBearing housing

T276 mm

Control shaker load to keep FB motion

amplitude at 7.3 µm

Waterfalls of dynamic load and FB displacement

0 200 400 600 800 1000 12000

50

100

150

200

Frequency [Hz]

Dyn

amic

loa

d [N

]

1X

1X

Th = 23°C

25 Hz

400 Hz

25 Hz

400 HzAmplitude of load

decreases with frequency.

Single frequency FB motion (a

measure of linearity)

Frequency (Hz)

Mo

tio

n a

mp

litu

de

(m

)D

ynam

ic l

oad

(N

)

Room temperature tests

Dynamic load vs excitation frequency

FB motion amplitude increases

Th = 23°C

FB motion amplitude increases

Th = 263°C

At high frequency, less force needed to maintain same motion amplitude

Amplitude of dynamic load decreases with frequency and increases with FB motion amplitudes

Parameter Identification (no shaft rotation)

( )eq tM x K x C x F

Meq

Keq

Ceq

Fext

x Lf =244 mm Lf =221 mm L= 248 mm

Equivalent Test System: 1DOF

K stiffness, Ceq viscous damping OR loss factor

Harmonic force & displacements

Impedance Function

( ) i tx t X e ( ) i tOF t F e

2( )Oeq

FZ K M i C

X

Energy dissipated

by either viscous damping or material structural losses

2

dis eqE C X2

disE K X

Real part of (F/X) decreases with FB motion amplitude and increases with shaft temperature

Real part of (F/X) vs frequency

Motion amplitude increases

Th = 23°C

Motion amplitude increases

Th = 263°C

2Re OFK M

X

System natural frequency decreases as FB motion amplitude increases (typical of nonlinear system with softening stiffness)

Th = 23°C

Highly preloaded FB: K decreases as FB motion amplitude increases due to decrease in # of active bumps

2Re OFK M

X

2Re 50OFK M at Hz

X

Dynamic structural K compared to static structural K

Motion amplitude increases

Dynamic load

Static load

At larger FB deflections, static K is larger than dynamic K

FB stiffness: effect of freq. & amplitude

Room temperature tests

Th = 23°C

Equivalent viscous damping decreases with excitation frequency and FB motion amplitude.

FB viscous damping: effect of freq. & amplitude

Im O

eq

FXC

Motion amplitude increases

Room temperature tests

KFB motion

amplitude: 14.8 µm

TEST FB cartridge OD is constrained within thick bearing housing.FB radial clearance decreases as shaft temperature raises!

FB stiffness and viscous damping increase with shaft temperature and decrease with frequency.

Heater temperature increases

eqCHeater temperature increases

K & Ceq: effect of shaft temperature

Loss factor vs frequency

FB motion amplitude:

14.8 µmHeater temperature increases

Structural (material) loss factor represents best energy dissipation in a FB

FB loss factor increases with excitation frequency and decreases slightly with shaft temperature. Large damping expected in rotordynamic measurements

eqC

K

Effect of temperature on loss factor

Post-test condition of test FB

Before operation

Distinguishing “wear” marks on bump foils and

cartridge ID

After extensive dynamic load tests

Marks evidence dry-friction of bumps against top foil and cartridge ID

Conclusions FB structural stiffness and equivalent viscous damping decrease with frequency.

As FB motion amplitude increases, less underlying bumps become active, thus reducing FB stiffness and damping

As shaft temperature increases (max 263 C), FB structural stiffness and equivalent viscous damping increase. As temperature increases, shaft OD grows while FB ID contracts; thus

reducing the FB bearing radial clearance.

FB structural loss factor decreases slightly with temperature;

yet it increases with frequency, a desirable feature for high rotor speed operation.

2nd gen FB with assembly preload

Test results WILL further anchor available GFB predictive tool (XL_GFB_THD©)

2009 hot rotor-GFB test rig

Gas flow meter (Max. 500 LPM). Drive motor (max. 65 krpm) )

Instrumentation for high temperature. Insulation casing

Insulated safety cover

Infrared thermometer

Flexible coupling

Drive motor

Cartridge heater

Test GFBs

Test hollow shaft (1.1 kg, 38.1mm OD,

210 mm length)

Tachometer

Eddy current sensors

Hot heater inside rotor spinning 30

krpm

Max. 360 °C

Video: Operation of hot rotor-GFB test rig

Acknowledgments/ Thanks to

• NASA GRCDr. S. Howard & Dr. C. DellaCorte

• Dr. Tae Ho Kim at KIST (Korea)• TAMU Turbomachinery Research Consortium

• NSF REUP• MiTi©

http://phn.tamu.edu/TRIBGroup Learn more at:

Questions?

BACKUP

SLIDE

System motion of equation

Parameter identification procedureParameter identification procedure

sgn( ) cos( )DRY OM x K x F x F t

( ) ( ) sin( )OW F t x t dt F X

2V eq eqE C x dx C X sgn( ) 4F DRY DRYE F x dx F X

2

sinOeq

FWC

X X

sin

4 4O

DRY

FWF

X

sin

4DRY

fO

F

F

2( ) eq

FK M iC

x

Work (W) by the shaker on the test FB

Energy dissipated by equiv. viscous damping Energy dissipated by FB dry friction

Equating external work input to energy dissipation (W ~ Ev or W~EF)

FB dynamic structural stiffness and equivalent viscous damping (frequency domain):

<= Dry-friction coefficient