Luis San Andres

1
February 2008
The Twelfth International Symposium on Transport
Phenomena and Dynamics of Rotating Machinery
Issues on Stability, Forced Nonlinear Response
and Control in Gas Bearing Supported Rotors for
Oil-Free Microturbomachinery
Luis San Andres Mast-Childs Professor
Turbomachinery Laboratory, Mechanical
Engineering Department Texas AM University
(http//phn.tamu.edu/TRIBGroup)
2
Microturbomachinery as per IGTI
Drivers deregulation in distributed power,
environmental needs, increased reliability
efficiency
Distributed power (Hybrid Gas turbine Fuel
Cell), Hybrid vehicles
Automotive turbochargers, turbo expanders,
compressors,
Honeywell, Hydrogen and Fuel Cells Merit Review
Max. Power 250 kWatt
International Gas Turbine Institute
3
Micro Gas Turbines
Microturbine Power Conversion Technology Review,
ORNL/TM-2003/74.
Cogeneration systems with high efficiency

• Multiple fuels (best if free)
• 99.99X Reliability
• Low emissions
• Reduced maintenance
• Lower lifecycle cost

Hybrid System MGT with Fuel Cell can reach
efficiency gt 60
Ideal to replace reciprocating engines. Low
footprint desirable
4
MTM Needs, Hurdles Issues
Largest power to weight ratio, Compact low
of parts High energy density Reliability and
efficiency, Low maintenance
Extreme temperature and pressure Environmen
tally safe (low emissions) Lower lifecycle cost
( kW)
High speed Materials Manufacturing Process
es Cycles Fuels
Rotordynamics (Oil-free) Bearings
Sealing Coatings surface conditioning for low
friction and wear Ceramic rotors and
components Automated agile processes Cost
number Low-NOx combustors for liquid gas
fuels TH scaling (low Reynolds ) Best if free
(bio-fuels)
Proven technologies with engineering analysis
(anchored to test data) available for ready
deployment
5
Gas Bearings for Oil-Free Turbomachinery
Thrust at TAMU Investigate bearings of low
cost, easy to manufacture (common materials),
easy to install align. Predictable Performance
a must! Combine hybrid (hydrostatic/hydrodynamic)
bearings with low cost coating for rub-free
operation at start up and shut down.

Passenger vehicle turbocharger
Major issues Little damping, Wear at start
stop, Instability (whirl hammer) / Nonlinearity
6
Gas Foil Bearings
Advantages high load capacity (gt20 psig),
tolerance of misalignment and shocks, high
temperature capability with advanced coatings
7

• Simple elastic foundation model
• Heavy load, ASME J. Eng. Gas Turbines Power,
  2008, 130 and high speed operation, ASME J.
  Tribol., 2006, 128.
• Finite element flat shell top foil models. 1D
  and 2D structural models, GT 2007-27249

With top foil bending
Uniform elastic foundation
Fast PC codes couple foil structure to gas film
hydrodynamics GUI driven
P/Pa
Note sagging of top foil between bumps
8
Accuracy of Foil Bearing Model Predictions
AIAA-2007-5094
KIST test data (2003)
Benchmarked computational model!
9
Example 1 Subsynchronous motions
Heshmat (1994) - Maximum speed 132 krpm, i.e.
4.61 106 DN. - Stable limit cycle operation but
with large amplitude subsynchronous motions.
Whirl frequency tracks rotor speed
Subsynchronous amplitude recorded during rotor
speed coastdown from 132 krpm (2,200 Hz)
10
Example 2 Subsynchronous motions
Heshmat (2000) Flexible rotor- GFB system
operation to 85 krpm (1.4 kHz) 1st bending
critical speed34 krpm (560 Hz)
Large amplitude limit cycle motions above bending
critical speed, whirl frequency natural
frequency (rigid body)
11
Example 3 Subsynchronous motions
Lee et al. (2003, 04) Flexible rotor supported
on GFBs with viscoelastic layer
50 kRPM (833 Hz)
Viscoelastic layer eliminates large motions at
natural frequency appearing above 1st bending
critical speed.
12
Foil Bearing Test Rig

• Shaft Diameter 1.500
• mass 2.2 lb

13
Limit cycle large subsync motions aggravated by
imbalance
Speed (-)
Amplitudes of subsynchronous motions INCREASE as
imbalance increases (forced nonlinearity)
26 krpm
14
Example 4 TAMU test rig
Large amplitudes locked at natural frequency (50
krpm to 27 krpm) but stable limit cycle!
15
Overview GFB computational models
What causes the subsynchronous motions? What
causes the excitation of natural frequency?
All GFB models predict (linearized) rotordynamic
force coefficients. No model readily available
to predict nonlinear rotordynamic forced response
16
Kim and San Andrés (2007) Eight cyclic load -
unload structural tests
F ? K X
FB structure is non linear (stiffness hardening),
a typical source of sub harmonic motions for
large (dynamic) loads. Hysteresis loop gives
energy dissipation
17
AIAA-2007-5094
Simple FB model allows quick nonlinear
rotordynamic predictions
18
Predicted nonlinear rotor motions
Rotor speed 30 ?1.2 krpm (600 ?20 Hz) Imbalance
displacement, u 12 µm (Vertical motion)
AIAA-2007-5094
Major assumption gas film of infinite stiffness
19
Sync. and Subsync. Amplitudes
Comparison to test measurements Rotor drive end,
vertical plane. Structural loss factor, ? 0.14.
AIAA-2007-5094
Amplitude vs. whirl frequency
Synchronous motions
Frequency (Hz)
Subsynchronous whirl frequencies concentrate in a
narrow band around natural frequency (132 Hz) of
test system. Large amplitude subsync motions
cannot be predicted using linear rotordynamic
analyses.
20
WHIRL FREQUENCY RATIO
Comparison to test data
AIAA-2007-5094
Rotor speed (krpm)
Predictions and measurements show bifurcation of
nonlinear response into distinctive whirl
frequency ratios (1/2 1/3)
21
Closure 1

• FB structure is highly non linear, i.e. stiffness
  hardening a common source of sub harmonic
  motions for large (dynamic) loads.
• Subsynchronous frequencies track shaft speed at
  ½ to 1/3 whirl ratios, locking at system natural
  frequency.
• Model predictions agree well with rotor response
  measurements (Duffing oscillator with multiple
  frequency response).

22
Rotordynamic tests with bearing side
pressurization
-FEED AIR PRESSURE 40 kPa 6 psig - 340 kPa 50
psig
IJTC2007-44047
Typically foil bearings DO not require
pressurization. Cooling flow needed for thermal
management to remove heat from drag or to reduce
thermal gradients in hot/cold engine sections
AIR SUPPLY
Axial flow retards evolution of mean
circumferential flow velocity within GFB, as in
an annular seal
23
Onset of subsynchronous whirl motions
(a) 0.35 bar
Rotor onset speed of subsyn-chronous whirl
increases as side feed pressure increases
(b) 1.4 bar
(c) 2.8 bar
24
FFT of shaft motions at 30 krpm
For Ps 2.8 bar rotor subsync. whirl motions
disappear (stable rotor response)
(a) 0.35 bar
(b) 1.4 bar
Whirl frequency locks at rigid body natural
frequency ( not affected by level of feed
pressure
(c) 2.8 bar
25
Gas Foil Bearing with Metal Shims
Shimmed GFB
Original GFB
Inserting metal shims underneath bump strips
introduces a preload (centering stiffness) at low
cost typical industrial practice
26
Gas Foil Bearing with Metal Shims
27
Rotor-bearing modeling
Original GFBs
XL2DFEFOILBEAR predicts synchronous bearing
force coefficients
0.35 bar (5 psig)
Shimmed GFBs
Imbalance increases by 1,2,3
Normalized 1X amplitudes Predictions reproduce
test measurements with great fidelity
28
Validation of predicted force coeffs.
Original GFBs
Imbalance masses 55mg,110mg, 165mg
0.35 bar (5 psig)
Effective damping vs. measurement location
Effective stiffness vs. measurement location
Good agreement between predicted coefficients and
GFB stiffness and damping estimated at natural
frequency (10 krpm)
29
MTM GFB 1X dynamic force coefficients
2008 Gen III GFB prediction tool developed by
TAMU for MTM OEM
Damping vs. Frequency
Stiffness vs. Frequency
Predictions agree with experimental dynamic force
coefficients for Generation III Foil Bearing!
30
Closure 2

• Predictive foil bearing FE model (structure
  gas film) benchmarked by test data.
• (Cooling) end side pressure reduces amplitude of
  whirl motions ( stable)
• Preloads (shims) increase bearing stiffness and
  raise onset speed of subsync. whirl.
• Predicted rotor 1X response and GFB force
  coefficients agree well with measurements.

31
Flexure Pivot Bearings
Advantages Promote stability, eliminate pivot
wear, engineered product with many commercial
appls.
32
Positioning Bolt
LOP
33
Displacements at RB(H)
Question If shaft speed regulates feed pressure,
could large rotor motions be suppressed ?
60 psig
40 psig
20 psig
LOP
As Pressure supply increases, critical speed
raises and damping ratio decreases
34
2.36 bar
210 rpm/s
2 minute
Long time rotor coast down speed exponential
decay, typical of viscous drag
35
Automatic adjustment of supply pressure
36
Displacements at RB(H)
5.08 bar
2.36 bar
5.08 bar
Blue line Coast down
2.36 bar
Red line Set speed
Rotor peak amplitude is completely eliminated by
sudden increase in supply pressure
Step increase in supply pressure
37
Excellent correlation Reliable Predictive model
!
38
Closure
Stable to 99 krpm!

• Supply pressure stiffens gas bearings and raises
  rotor critical speeds, though also reducing
  system modal damping.
• CHEAP Feed pressure control of bearing stiffness
  eliminates critical speeds (reduce amplitude
  motions)!
• Models predict well rotor response even for
  large amplitude motions and with controlled
  supply pressure!

39
Dominant challenge for gas bearing technology

• Bearing design manufacturing process better
  known. Load capacity needs minute clearances
  since gas viscosity is low.
• Damping rotor stability are crucial
• Inexpensive coatings to reduce drag and wear at
  low speeds and transient rubs at high speeds
• Engineered thermal management to extend operating
  envelope to high temperatures

Current research focuses on coatings (materials),
rotordynamics (stability) high temperature
(thermal management)
Need Low Cost Long Life Solution!
40
Acknowledgments
Thanks to Students Tae-Ho Kim. Dario Rubio,
Anthony Breedlove, Keun Ryu, Chad Jarrett NSF
(Grant 0322925) NASA GRC (Program
NNH06ZEA001N-SSRW2), Capstone Turbines, Inc.,
Honeywell Turbocharging Systems,
Foster-Miller, TAMU Turbomachinery Research
Consortium (TRC)
To learn more visit
http//phn.tamu.edu/TRIBGroup
41
BACK UP SLIDES
42
Research in Gas Foil Bearings
Funded by 2003-2007 NSF, TRC, Honeywell 2007-2009
NASA GRC, Capstone MT, TRC, Honeywell
Current work experimentally validated predictive
model for high temperature gas foil bearings
43
 Ideal gas bearings for MTM (lt 0.25 MW )
Load Tolerant capable of handling both normal
and extreme bearing loads without compromising
the integrity of the rotor system.
Simple low cost, small geometry, low part
count, constructed from common materials,
manufactured with elementary methods.  
High Rotor Speeds no specific speed limit (such
as DN) restricting shaft sizes. Small Power
losses.
Good Dynamic Properties predictable and
repeatable stiffness and damping over a wide
temperature range.
Reliable capable of operation without
significant wear or required maintenance, able to
tolerate extended storage and handling without
performance degradation.
Modeling/Analysis (anchored to test data)
readily available
44

• Series of corrugated foil structures (bumps)
  assembled within a bearing sleeve.
• Integrate a hydrodynamic gas film in series with
  one or more structural layers.

Applications ACMs, micro gas turbines, turbo
expanders

• Reliable with load capacity to 100 psi) high
  temperature
• Tolerant to misalignment and debris
• Need coatings to reduce friction at start-up
  shutdown
• Damping from dry-friction and operation with
  limit cycles

45
Reference DellaCorte (2000) Rule of Thumb
Test Gas Foil Bearing Generation II. Diameter
38.1 mm 5 circ x 5 axial strip layers, each with
5 bumps (0.38 mm height)
46
Oil-Free Bearings for Turbomachinery
Justification Current advancements in automotive
turbochargers and midsize gas turbines need of
proven gas bearing technology to procure compact
units with improved efficiency in an oil-free
environment. DOE, DARPA, NASA interests range
from applications as portable fuel cells (lt 60
kW) in microengines to midsize gas turbines (lt
250 kW) for distributed power and hybrid
vehicles.

• Gas Bearings allow
• weight reduction, energy and complexity savings
• higher cavity temperatures, without needs for
  cooling air
• improved overall engine efficiency

47
San Andres et al., 2007, ASME J. Eng. Gas
Turbines Power

• Dynamic load (Fo) from 4 - 20 N,
• Test temperatures from 25C to 115C

Viscous damping reduces with frequency. Natural
frequency easily excited at super critical speed
48

• Simple elastic foundation model
• Heavy load, ASME J. Eng. Gas Turbines Power,
  2008, 130 and high speed operation, ASME J.
  Tribol., 2006, 128.
• Finite element flat shell top foil models. 1D
  and 2D structural models, GT 2007-27249

49
EOMs rigid rotor in-phase imbalance condition
Li Flowers, AIAA 96-1596
Rotor motions

• Assumption minute gas film with infinite
  stiffness

50
Equations of Rotor Motion
Natural frequency of rotor-GFB system for small
amplitude motions about SEP
132 Hz
Numerical integration of EOMs for increasing
rotor speeds to 36 krpm (600 Hz), with imbalance
(u) identical to that in experiments.
Solutions obtained in a few seconds.
Post-processing filters motions and finds
synchronous and subsynchronous motions
51
Sync. and Subsync. Amplitudes
Comparison to test measurements Rotor drive end,
vertical plane. Structural loss factor, ? 0.14.
Subsynchronous motions
Synchronous motions
Good agreement between predictions to test
data. Large amplitude subsynchronous motions
cannot be predicted using linear rotordynamic
analyses.
52
Amplitude Frequency of Subsync. Motions
Comparison to test data Rotor drive end, vertical
plane. Structural loss factor, ? 0.14.
Amplitude vs. frequency
Frequency vs. rotor speed
Rotor speed (krpm)
Frequency (Hz)
Subsynchronous whirl frequencies concentrate in a
narrow band enclosing natural frequency (132 Hz)
of test system
53
Model Tests Stability vs feed pressure
30 krpm operation
Prediction
Stability analysis threshold speed of
instability in good agreement with test data
(onset speed of subsynchronous motion )
54
Waterfall responses Shimmed GFBs with side
pressurization
Side feed pressure 60 psig (4.1 bar)
0.34 bar
Amplitude (µm, 0-pk)
1.4 bar
2.8 bar
4.1 bar
Amplitude (µm)
Whirl frequency (Hz)
Frequency (Hz)
Rotor speed (krpm)
External pressurization reduces dramatically the
amplitude of subsynchronous rotor motions.
55
MTM bearing prediction vs. test data
Bearing prediction tool (Computer software
GUI) developed for MTM OEM
Structural static coefficients
Displacement vs. load
Predictions agree with identified static load
performance of Micro Gas Turbine Foil Bearings!