ISROMAC-12 Luis San Andres Mast-Childs Professor February 2008 Issues on Stability, Forced Nonlinear Response and Control in Gas Bearing Supported Rotors

ISROMAC-12

Luis San AndresMast-Childs Professor

February 2008

Issues on Stability, Forced Nonlinear Response and Control in Gas

Bearing Supported Rotors for Oil-Free Microturbomachinery

Turbomachinery Laboratory, Mechanical Engineering Department

Texas A&M University (http://phn.tamu.edu/TRIBGroup)

The Twelfth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery

Microturbomachinery as per IGTI

ASME Paper No. GT2002-30404

Honeywell, Hydrogen and Fuel Cells Merit

Review

Automotive turbochargers, turbo expanders, compressors,

Distributed power (Hybrid Gas turbine & Fuel Cell), Hybrid vehicles

Drivers:deregulation in distributed power, environmental needs, increased reliability & efficiency

International Gas Turbine Institute

Max. Power ~ 250 kWatt

Micro Gas Turbines

MANUFACTURER OUTPUT POWER (kW)Bowman 25, 80

Capstone 30, 60, 200Elliott Energy

Systems35, 60, 80, 150

General Electric

175

Ingersoll Rand

70, 250

Turbec, ABB & Volvo

100

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

60kW MGT

www.microturbine.com

Hybrid System : MGT with Fuel Cell can reach efficiency > 60%

Ideal to replace reciprocating engines. Low footprint desirable

Largest power to weight ratio, Compact & low # of parts High energy density

Reliability and efficiency,Low maintenance

Extreme temperature and pressure

Environmentally safe (low emissions)

Lower lifecycle cost ($ kW)

High speed

Materials

Manufacturing

Processes & Cycles

Fuels

Rotordynamics & (Oil-free) Bearings & Sealing

Coatings: surface conditioning for low friction and wearCeramic rotors and components

Automated agile processesCost & number

Low-NOx combustors for liquid & gas fuelsTH scaling (low Reynolds #)

Best if free (bio-fuels)

MTM – Needs, Hurdles & Issues

Proven technologies with engineering analysis (anchored to test data) available for ready deployment

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.

Major issues: Little damping, Wear at start & stop, Instability (whirl & hammer) / Nonlinearity

Passenger vehicle turbocharger

Gas Bearings for Oil Free Turbomachinery

Gas Foil Bearings

Advantages: high load capacity (>20 psig), tolerance of misalignment and shocks, high temperature capability with advanced coatings

No. of finite elements between bumps

Axially distributed linear spring

Fixed end

Thin Shell

Shell Length Shell width

Finite element

Shell thickness

Simple elastic foundation modelHeavy 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

0

1

2

3

4

5

6

0 90 180 270 360Angular location [deg]

Dim

ensi

onle

ss p

ress

ure

, p/p

a[-

]

Y

Θ

Simple GFB

0

1

2

3

4

5

6

0 90 180 270 360Angular location [deg]

Dim

ensi

onle

ss p

ress

ure

, p/p

a[-

]

Y

Θ

Simple GFB

Note sagging of top foil between bumps

P/Pa

Ω

X

Y

Θ

WUniform elastic

foundationWith top foil

bending

Top Foil Model: 2D Finite Elements

Fast PC codes couple foil

structure to gas film

hydrodynamics

– GUI driven

Accuracy of Foil Bearing Model Predictions

Prediction

Shutdown

Test data

StartupStartup

Test data

Prediction

KIST test data (2003)

Benchmarked computational model!

Static load: 52 N

Rotor speed decreases

Driving motor Shutdowns

Prediction

10,000 cyclesTest

data:5,000 cycles

AIAA-2007-5094

Example 1: Subsynchronous motions

Subsynchronous amplitude recorded during rotor speed coastdown from 132 krpm (2,200 Hz)

Whirl amplitude remains ~ constant as subsynchronous frequency drops from 350 Hz to 180 Hz

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


Heshmat (2000) Flexible rotor- GFB system operation to 85 krpm (1.4 kHz): 1st bending critical speed:34 krpm (560 Hz)

Waterfall plot recorded during rotor speed coastdown test from 45 krpm (750 Hz)

Rotor orbit shape at 45k rpm

Large amplitude limit cycle motions above bending critical speed, whirl frequency = natural frequency (rigid body)

Lee et al. (2003, 04): Flexible rotor supported on GFBs with viscoelastic layer


Viscoelastic layer eliminates large motions at natural frequency & appearing above 1st bending critical speed.

50 kRPM (833 Hz)

Bump type GFBViscoelastic GFB

Synchronous vibration

1st bending mode

Rigid body mode

Bum

p ty

pe G

FB

Vis

coel

astic

GF

BSynchronous

vibration

Foil Bearing Test Rig

Driving motor (1HP, 50 krpm)

Flexible coupling

Optical Tachometer

Start motor(2HP, 25 krpm)

Foil bearing housing

Electromagnet loader

Test rotor

Centrifugal clutch (Engaged at ~50 krpm)

Cluth shoes

Spring

Wear ring

Ω

Shaft Diameter = 1.500” mass = 2.2 lb

Amplitudes of subsynchronous motions INCREASE as imbalance increases (forced nonlinearity)

Example 4: TAMU test rig

Speed (-)

Imbalance +

last two indices are multipliers for X & Y axis offset

0 100 200 300 400 500 600 700 8000

20

40

60

80

100

Frequency [Hz]

Am

plit

ud

e [

mic

ron

s]


0 100 200 300 400 500 600 700 8000

20

40

60

80

100

Frequency [Hz]

Am

plit

ud

e [

mic

ron

s]D

ispl

acem

ent

Am

plitu

de

(μm

) D

ispl

acem

ent

Am

plitu

de

(μm

)

Frequency (Hz)

u = 7.4 μm

1X 0.5X

2X

u = 7.4 μm


0 100 200 300 400 500 600 700 8000

20

40

60

80

100

Frequency [Hz]

Am

plit

ud

e [

mic

ron

s]


0 100 200 300 400 500 600 700 8000

20

40

60

80

100

Frequency [Hz]

Am

plit

ud

e [

mic

ron

s]D

ispl

acem

ent

Am

plitu

de

(μm

)

Frequency (Hz)

1X 0.5X

2X

25.7 krpm

2.6 krpm

12.5 krpm

20.5 krpm

u = 10.5 μm

Frequency (Hz)

u = 10.5 μm

26 krpm

Limit cycle: large subsync motions

aggravated by imbalance

Example 4: TAMU test rig

50 krpm 0 200 400 600 800 1000

0

20

40

60

80

100Drive end, vertical direction

Frequency [Hz]

Am

plitu

de [m

icro

ns]

2 krpm

1X

0 200 400 600 800 10000

20

40

60

80

100Free end, vertical direction

Frequency [Hz]

Am

plitu

de [m

icro

ns]

26 krpm Am

plit

ude

(μm

, 0-p

k)

Subsynchronous motions

Large amplitudes locked at natural frequency (50 krpm to 27 krpm) …… but stable limit cycle!

Rotor speed

decreases

Overview – GFB computational models

All GFB models predict (linearized) rotordynamic force coefficients.

No model readily available to predict nonlinear rotordynamic forced response

What causes the subsynchronous motions?

What causes the excitation of natural frequency?

Foil Bearing: stiffness & dissipation

FB structure is non linear (stiffness hardening), a typical source of sub harmonic motions for large (dynamic) loads. Hysteresis loop gives energy dissipation

Kim and San Andrés (2007):

Eight cyclic load - unload structural

tests Loading

Loading

Unloading

Unloading

F ≠ K X

Simple FB model allows quick nonlinear rotordynamic predictions

F = X (0.0675 -0.002 X + 0.0001 X2 )

Test data

Prediction

2 31 2 3sFBF K r K r K r

FB structural modelAIAA-2007-5094

Predicted nonlinear rotor motions

0 100 200 300 400 500 600 700 800

50

0

50

100

150Waterfall

Excitation frequency [Hz]

Am

plitu

de [u

m]

X1.2 krpm

36 krpm

Am

plitu

de [

μm]

1X Subsynchronous

rotor motions

Rotor speed: 30 →1.2 krpm (600 →20 Hz) Imbalance displacement, u = 12 μm (Vertical motion)

Subsynchronous (sub harmonic) whirl motions of large amplitude

AIAA-2007-5094

Major assumption – gas film of infinite stiffness

0 5 10 15 20 25 300

20

40

60

80

PredictionExperiment

Rotor speed [krpm]

Am

plitu

de

[um

]

0 5 10 15 20 25 300

20

40

60

80


Rotor speed [krpm]A

mpl

itud

e [u

m]

(a) Synchronous Motions (b) Subsynchronous Motions

Am

plit

ude

[μm

]

Comparison to test measurementsRotor drive end, vertical plane. Structural loss factor, γ =0.14.

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.

Synchronous motions

Test data

Predictions

Sync. and Subsync. Amplitudes

0 100 200 300 400 500 6000

20

40

60

80


Frequency [Hz]

Am

plitu

de [

um]

0 5 10 15 20 25 300

40

80

120

160

200


Rotor speed [krpm]

Fre

quen

cy [

Hz]

(a) Subsynchronous Amplitude vs frequency (b) Subsynchronous frequency vs speed

Am

plitu

de [

μm]

Amplitude vs. whirl frequency

Test data

Predictions

Frequency (Hz)

AIAA-2007-5094

WHIRL FREQUENCY RATIO

6 8 10 12 14 16 18 20 22 24 26 28 300

0.25

0.5

0.75

1

PredictionTest data [24] Test data [26]

Rotor speed [krpm]

Whi

rl f

requ

ency

rat

io (

WF

R)

WFR

Predictions and measurements show bifurcation of nonlinear response into distinctive whirl frequency ratios (1/2 & 1/3)

Test data(San Andres et al, 2006)

Predictions Test data(Kim and San Andres et al, 2007)

Rotor speed (krpm)

Comparison to test data AIAA-2007-5094

• 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).

Gas Foil Bearings

Closure 1

-FEED AIR PRESSURE: 40 kPa [6 psig] - 340 kPa [50 psig]

AIR SUPPLY

Rotordynamic tests with bearing side pressurization

Ps

Rotating journal

Pa

Bump spring

Top foil Bearing housing

Circumferential velocity

ΩRJ Axial

velocity Ω RJ

Outer gap

Inner gas film

X

Y

z x

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

Axial flow retards evolution of mean circumferential flow velocity within GFB, as in an annular seal

Onset of subsynchronous whirl motions

Rotor onset speed of subsyn-

chronous whirl

increases as side feed

pressure increases

(a) 0.35 bar

(b) 1.4 bar

(c) 2.8 bar

SynchronousSubsynchronous

NOS: 25 krpm

NOS: 30.5 krpm

NOS: 27 krpm

FFT of shaft motions at 30 krpm

(a) 0.35 bar

(b) 1.4 bar

(c) 2.8 bar

Whirl frequency locks at rigid body natural

frequency ( not affected by level of feed pressure

For Ps ≥ 2.8 bar rotor subsync. whirl motions

disappear;(stable rotor

response)ωsub= 132 Hz

ωsub= 147 Hz

ωsub= 127 Hz

Subsynchronous ωsyn= 508 Hz

Synchronous

(a) Gas foil bearing (b) Gas foil bearing with three shims

Journal Y

Θl

Ω Ω

Journal Y

X

Θp

ts

Θl

Θs Housing

Structural bump

Thin foil

Shim g

X

Original GFB Shimmed GFBShimmed GFB

Gas Foil Bearing with Metal Shims

Original GFB

Inserting metal shims underneath bump strips introduces a preload (centering stiffness) at low cost – typical industrial practice

400 200 0 200 400 600 800 10000

20

40

60

80

100Free end, vert ical direction

Frequency [Hz]

Am

plitu

de [u

m]

50 krpm

2 krpm

25 krpm

1X

Am

plitu

de [

μm]

(a) Waterfall

0 10 20 30 40 500

20

40

60

SUB SYNCSYNCHRONOUS

Rotor speed [krpm]

Am

plitu

de [

um, 0

-pk]

27 krpm

Am

plitu

de [

μm, 0

-pk]

Original GFBs

0.35 bar (5 psig)

Am

plit

ud

e (μ

m)

Rotor speed (krpm)

Am

plit

ud

e (μ

m, 0

-pk) Frequency (Hz)

400 200 0 200 400 600 800 10000

20

40

60

80

100

Frequency [Hz]A

mpl

itude

[mic

rons

]A

mpl

itude

[μm

]

50 krpm

2 krpm

25 krpm

1X

0 10 20 30 40 500

20

40

60

SUB SYNCSYNCHRONOUS

Rotor speed [krpm]

Am

plit

ude

[um

, 0-p

k]

40 krpm

Am

plit

ude

[μm

, 0-p

k]

Shimmed GFBs

0.35 bar (5 psig)

Rotor speed (krpm)

Am

plit

ud

e (μ

m, 0

-pk)

Am

plit

ud

e (μ

m)

Frequency (Hz)

Gas Foil Bearing with Metal Shims

Rotor-bearing modeling

Normalized 1X amplitudes: Predictions reproduce test measurements with great fidelity

0.35 bar (5 psig)

Shaft1141312111098765

432

Shaft11

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28

Axial Location [m]

Shaf

t Rad

ius

[m]

L: drive end , R: free end

Bearing supports Flexible coupling

Coupling added mass and inertia Measurement planes (shaft motion) Imbalance planes

XL2DFEFOILBEAR

predicts synchronous bearing force coefficients

Original GFBs

Shimmed GFBsImbalance increases by 1,2,3

Validation of predicted force coeffs.

Original GFBs

Effective stiffness vs. measurement location

Good agreement between predicted coefficients and GFB stiffness and damping estimated at natural frequency (10 krpm)

Effective damping vs. measurement location

Test data

Predictions

Test data

Predictions

Imbalance masses: 55mg,110mg, 165mg

0.35 bar (5 psig)Drive end

Free endYDE

XDE

XFEYFE

g

Drive end

Free endYDE

XDE

XFEYFE

g

DHDV

FVFH

Drive end

Free endYDE

XDE

XFEYFE

g

Drive end

Free endYDE

XDE

XFEYFE

g

DHDV

FVFH

PredictionsTest data

PredictionsTest data

Stiffness vs. Frequency Damping vs. Frequency

MTM GFB: 1X dynamic force coefficients2008 Gen III GFB prediction tool developed by TAMU for MTM OEM

Predictions agree with experimental dynamic force coefficients for Generation III Foil Bearing!

• 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.

Gas Foil Bearings

Closure 2

Gas Bearings for Oil Free Turbomachinery

Flexure Pivot Bearings

Advantages: Promote stability, eliminate pivot wear, engineered product with many commercial appls.

Positioning Bolt

X

Y

Load

LOP

Rotor/motor

Bearing

Sensors

Load cell

Air supply

Thrust pin

Gas Bearing Test Rig

As Pressure supply increases, critical speed raises and damping ratio decreases

Displacements at RB(H)

L R

V: verticalH: horizontal

LOP 0

5

10

15

20

0 5000 10000 15000 20000 25000 30000 35000 40000

Speed [rpm]

Am

pli

tud

e [

μm

, p

k-p

k]

5.08 bar

3.72 bar

2.36 bar

5.08 bar

3.72 bar

2.36bar

20 psig

40 psig

60 psig

Effect of feed pressure on rotor response

Question:If shaft speed

regulates feed

pressure, could large

rotor motions be

suppressed ?

Coast down rotor speed vs time

0

10

20

30

40

50

0 50 100 150 200

Coast down time [sec]

Ro

tor

spee

d [

krp

m]

15 krpm ~ 14 krpm

58.0 sec ~ 62.7 sec

~ 2 minute

Long time rotor coast down speed: exponential decay, typical of viscous drag

2.36 bar

210 rpm/s

Speed region for control of feed

pressure

Cheap Control of Bearing Stiffness

Automatic adjustment of supply pressure

Control of Feed Pressure into Gas Bearings

Step increase in supply pressure

Displacements at RB(H) L R

V: verticalH: horizontal

5.08 bar

2.36 barBlue line: Coast down

Red line: Set speed

2.36 bar5.08 bar

Rotor peak amplitude is completely eliminated by sudden increase in supply pressure

Test & predicted rotor responses

0

5

10

15

20

0 5000 10000 15000 20000 25000 30000 35000 40000

Speed [rpm]

Am

pli

tud

e [

μm

, p

k-p

k]

Test-O.C. #5, active Ps control, coast down

Prediction

5.08 bar 2.36 bar Supply pressure

2 bar

5 bar

speed

Ps

TestPrediction

TEST

PREDICT

Excellent correlation – Reliable Predictive model !

Flexure Pivot Hydrostatic Gas Bearings

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!

Dominant challenge for gas bearing technology

Current research focuses on coatings (materials), rotordynamics (stability) & high temperature (thermal management)

– 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

Need Low Cost & Long Life Solution!

AcknowledgmentsThanks 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

BACK UP SLIDES

Funded by 2003-2007: NSF, TRC, Honeywell2007-2009: NASA GRC, Capstone MT, TRC, Honeywell

Research in Gas Foil Bearings

Current work:

experimentally validated predictive model for high temperature gas foil bearings

Ideal gas bearings for MTM (< 0.25 MW )

Simple – low cost, small geometry, low part count, constructed from common materials, manufactured with elementary methods.

Load Tolerant – capable of handling both normal and extreme bearing loads without compromising the integrity of the rotor system.

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

• 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

Gas Foil Bearings – Bump type

Test Gas Foil Bearing Generation II. Diameter: 38.1 mm5 circ x 5 axial strip layers, each with 5 bumps (0.38 mm height)

Reference: DellaCorte (2000)Rule of Thumb

Test Bump-Type Foil Bearing

Oil-Free Bearings for Turbomachinery

JustificationCurrent 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 (< 60 kW) in microengines to midsize gas turbines (< 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

FB viscous damping OR dry friction

– Dynamic load (Fo) from 4 - 20 N,– Test temperatures from 25°C to ~115°C F = Fo cos(w.t)

x

0 100 200 300 400200

1100

2400

3700

5000

Room Temperature = 25 CTemperature 1 = 50 CTemperature 2 = 75 C

Frequency [Hz]

0 100 200 300 4000

1000

2000

3000

4000

Eq.

Vis

cous

Dam

ping

[N

.s/m

]

Frequency [Hz]

Fo increases

T = 25ºC

50 100 1500

0.05

0.1

0.15

0.2

0.25

Fric

tion

coe

ffic

ient

, m

Frequency [Hz]

Fo increases

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

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

No. of finite elements between bumps

Axially distributed linear spring

Fixed end

Thin Shell

Shell Length Shell width

Finite element

Shell thickness

Simple elastic foundation modelHeavy 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

Test data, Ruscitto, et al. 1978

(mid plane)

Prediction(edge, 2D)

Prediction(mid plane, 2D)

Test data,Ruscitto, et al. 1978

(edge)

Prediction (1D)

Prediction (simple model)

Top Foil Model: 2D Finite Elements

2

2

2 cos( )

2 sin( )

x

y

FB

FB

M x F M u t Mg

M y F M u t

EOMs: rigid rotor & in-phase imbalance condition

2 2( ) ( )

; ; with s s

x x

FB FBFB FB

F r F rF x x F y y r x y

r r

Assumption: minute gas film with infinite stiffness

,x y

x

y

Rotor motions

2 31 2 3sFBF K r K r K r

Li & Flowers, AIAA 96-1596

Equations of motion

Equations of Rotor Motion

Numerical integration of EOMs for increasing rotor speeds to 36 krpm (600 Hz), with imbalance (u) identical to that in experiments.

21 2 32 2 31

2

E E

n

K K x K xf

M

Natural frequency of rotor-GFB system for small amplitude motions about SEP:

Solutions obtained in a few seconds. Post-processing filters motions and finds synchronous and subsynchronous motions

= 132 Hz

0 5 10 15 20 25 300

20

40

60

80


Rotor speed [krpm]

Am

plitu

de

[um

]

0 5 10 15 20 25 300

20

40

60

80


Rotor speed [krpm]A

mpl

itud

e [u

m]


Am

plit

ude

[μm

]

Comparison to test measurementsRotor drive end, vertical plane. Structural loss factor, γ =0.14.

Good agreement between predictions to test data.Large amplitude subsynchronous motions cannot be predicted using linear rotordynamic analyses.

Synchronous motions

Test data

Predictions

0 5 10 15 20 25 300

20

40

60

80


Rotor speed [krpm]

Am

plitu

de

[um

]

0 5 10 15 20 25 300

20

40

60

80


Rotor speed [krpm]

Am

plitu

de

[um

]


Am

plit

ude

[μm

] Test data

Predictions

Subsynchronous motions

Sync. and Subsync. Amplitudes

Amplitude & Frequency of Subsync. Motions

0 100 200 300 400 500 6000

20

40

60

80


Frequency [Hz]

Am

plitu

de [

um]

0 5 10 15 20 25 300

40

80

120

160

200


Rotor speed [krpm]

Fre

quen

cy [

Hz]


Am

plitu

de [

μm]

Comparison to test dataRotor drive end, vertical plane. Structural loss factor, γ =0.14.

Subsynchronous whirl frequencies concentrate in a narrow band enclosing natural frequency (132 Hz) of test system

0 100 200 300 400 500 6000

20

40

60

80


Frequency [Hz]

Am

plitu

de [

um]

0 5 10 15 20 25 300

40

80

120

160

200


Rotor speed [krpm]F

requ

ency

[H

z]


Amplitude vs. frequency Frequency vs. rotor speed

Test data

Predictions

Test data

Predictions

Rotor speed (krpm)Frequency (Hz)

Model & Tests: Stability vs feed pressure

0

0.25

0.5

0.75

1

0 1 2 3Side feed pressure [bar]

Cri

tica

l mas

s [k

g]

Rotor half mass = 0.5 kg Stable

30 krpm operation

Stability analysis: threshold speed of instability in good

agreement with test data (onset speed of

subsynchronous motion )

Prediction

0

10

20

30

40

50

60

0 1 2 3Side feed pressure [bar]

Am

pli

tud

e [

μm

, 0 -

pk]

Series1

Series2

Series3

Subsynchronous

1X: Synchronous

Small subsynchronous rotor motions

Total motion

Test data

Side feed pressure: 60 psig (4.1 bar)

400 200 0 200 400 600 800 10000

20

40

60

80

100

Frequency [Hz]

Am

plitu

de [m

icro

ns]

Am

plitu

de [

μm]

50 krpm

2 krpm

25 krpm

1X

External pressurization reduces dramatically the amplitude of subsynchronous rotor motions.

1.4 bar

4.1 bar

2.8 bar

0.34 bar

Side pressure increases

Am

plit

ud

e (μ

m, 0

-pk)

Whi

rl fr

eque

ncy

(Hz)

Rotor speed (krpm)

Frequency (Hz)

Am

pli

tud

e (μ

m)

(b) Gas foil bearing with three shims

Y

Ω

Journal Y

X

Θp

ts

Θl

Θs

Structural bump

Shim

Shimmed GFB

Waterfall responses: Shimmed GFBs with side pressurization

MTM bearing: prediction vs. test data* Bearing prediction tool (Computer software & GUI) developed for MTM OEM

Structural static coefficients

Predictions agree with identified static load performance of Micro Gas Turbine Foil Bearings!

Displacement vs. load

Test data 3

Test data 1

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Test data 2

Unloading

Unloading

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Prediction

Documents

ISROMAC-12 Luis San Andres Mast-Childs Professor February 2008 Issues on Stability, Forced Nonlinear Response and Control in Gas Bearing Supported Rotors