Post on 24-Dec-2015
transcript
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
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:
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