GT2012-68212 1 ASME GT2012-68212 Luis San Andrés Mast-Childs Professor, Fellow ASME Texas A&M...

GT2012-68212

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ASME GT2012-68212

Luis San Andrés Mast-Childs Professor, Fellow ASME

Texas A&M University

Supported by Pratt & Whitney Engines (UTC)

2012 ASME Turbo Expo Conference, June 11-15 ,2012, Copenhagen, DK

accepted for journal publication

DAMPING AND INERTIA COEFFICIENTSFOR TWO OPEN ENDS

SFDs WITH A CENTRAL GROOVE: MEASUREMENTS AND PREDICTIONS

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In aircraft gas turbines and compressors, squeeze film

dampers aid to attenuate rotor vibrations and to provide

mechanical isolation.

SFD operation & design

SFD with dowel pin

X

Y

X

Y

Too little damping may not be enough to reduce vibrations.

Too much damping may lock damper & degrades system rotordynamic

performance

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SFD with a central groove

Conventional knowledge regards a groove is indifferent to the kinematics of journal motion, thus effectively isolating the adjacent film lands.

housing

journal

lubricant film

shaft

anti-rotation pin

ball bearing

Feed

groove

oil inlet Pressurized lubricant flows through a

central groove to fill the squeeze

film lands.

Dynamic pressures generate fluid film

reaction forces aiding to damp

excessive amplitudes of

rotor whirl motion.

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P&W SFD Test Rig

Static loader

Shaker assembly (Y direction)

Shaker assembly (X direction)

Static loader

Shaker in X direction

Shaker in Y direction

Top view

Isometric view

SFD test bearing

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Test rig description

shaker Xshaker Y

Static loader

SFD

base

support rods

X

Y

Shaker X Shaker Y

Static loader

SFD

Base

Static loader

X

Y

Support rods

X Y

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SFD bearing design

in

Geometry of open ends SFD

Journal diameter: 127 mm (5.0 inch)

Film clearance: 0.138mm (5 mil)

Land length: 2 x 25.4 mm (2 x 1 inch)

Support stiffness: 4.38 – 26.3 MN/m

(25 – 150 klbf/in)

Bearing Cartridge

Test Journal

Main support rod (4)

Journal BasePedestal

Piston ring seal (location)

Flexural Rod (4, 8, 12)

Circumferential groove

Supply orifices (3)

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Oil inlet temperature, Ts = 25 oCDensity, ρ = 785 kg/m3

Viscosity μ at Ts= 2.96 cPoiseFlow rate, Qin= 4.92 LPM

Oil inlet

in

ISO VG 2 oil

Flow through squeeze film lands

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Objective & tasks

Evaluate dynamic load performance of SFD with a central groove.

X

Ystatic load

e

c

45o

X

Y

r

eS

centered and off-centered circular orbits

Dynamic load measurements: circular & elliptical orbits (centered and off centered) and identification of test system and SFD force coefficients

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Oil out, Qb

BaseSupportrod

Bearing Cartridge

Journal (D) Oil out, Qt

Oil in, Qin

Central groove

L

½ L

L

End groove

End groove

Oil outOil collector

c

Oil out, Qb

BaseSupportrod

Bearing Cartridge


Oil in, Qin

Central groove

L

½ L

L

End groove

End groove


BaseSupportrod

Bearing Cartridge


Oil in, Qin

Central groove

L

½ L

L

End groove

End groove


c

SFD configurations tested

Short SFD (B) Long SFD (A)

Journal diameter, D 127 mm

Land length, L 12.7 mm 25.4 mm

Radial clearance, c CB = 0.138 mm CA = 0.141 mm

Groove axial length, LG 12.7 mm

Depth, dG 9.5 mm

Oil wetted length, 2L + LG 38.1 mm 63.5 mm

Groove static pressure, PG 0.52 bar 0.72 bar

Oil inlet temperature, Ts 25 oC

Lubricant ISO VG 2

Density, ρ 785 kg/m3

Viscosity μ at Ts 2.96 cPoise

Flow rate, Qin 4.92 LPM

Geometry and oil properties for open ends SFD

Support stiffness range Ks = 4.4 – 26.3 MN/m (variable)Max. static load (8 kN),Max. amplitude dynamic load (2.24 kN)

Range of excitation frequencies: 35 – 250 Hz

Re s c

2

= 1.1-8.3 in film lands

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Parameter Identification

X

Y

Journal also moves during excitation of the bearing

2

2

X

Y

ax x

ay y

*SFDs do not have stiffnesses = reaction forces due to changes in static displacement.

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Applied Loads

CCW

displacements & accelerations

Two linearly independent load vectors F1 and F2

CW

Y

X

X

Y

1 11

1 1

cos( )Re

sin( )i tX X

Y Y

F t Fe

F t iF

F

2 22

2 2

cos( )Re

sin( )i tX X

Y Y

F t Fe

F t iF

F

1 11

1 1

( )

( )i tx t X

z ey t Y

2 22

2 2

( )

( )i tx t X

z ey t Y

1a 2a

Single frequency orbits

Loads F, displacement x and accelerations a recorded at each frequency

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EOMs (2 DoF)time domain

EOM (Frequency Domain)

Impedance function H(ω)

BCM s SFD s SFD s SFDa + M M z K K z + C +C z F

2M BCi M s SFD s SFD SFD sK K C +C M M z F F a

11 2 1 2 XX XYM M

YX YY

H H

H H

H F F z z

1 2 1 2 M M H z z F F

2Re( ) ; Im( )XX XX XX XX XXH K M H C Physicalmodel

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IVFM solution

SFD force coefficients

(K, C, M)SFD = (K, C, M) – (K, C, M)S

SFD coefficients Test system Support structure

Flexibility function G(ω)

1G H

Iteration on weighted least squares to minimize the estimation error in:

= transfer functions (displacement/force)

* Instrumental Variable Filter Method (IVFM) (Fritzen, 1986, J.Vib, 108) Measurement errors affect little identified parameters

IVF Method*

GH=I+e

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Physical model Re(HXX)= K-2M and Im(HXX)=C

agree with test data.

Damping C is constant over the frequency

range

Typ. impedances- lubricated SFD

HXX

CXX

Short SFD eS=0; r =0.05cB

0 100 200 30060

40

20

0

20Real (Hxx)

fstart fend

0 100 200 3000

10

20

30Im (Hxx)

fstart fend

rxxIm 0.976

rxxre 0.997

0 100 200 3000

10

20

30Im (Hyy)

fstart fend

0 100 200 30060

40

20

0

20

40Real (Hyy)

fstart fend

ryyIm 0.954ryyre 0.995

0 100 200 30060

40

20

0

20Real (Hxx)

fstart fend

0 100 200 3000

10

20

30Im (Hxx)

fstart fend

rxxIm 0.976

rxxre 0.997

0 100 200 3000

10

20

30Im (Hyy)

fstart fend

0 100 200 30060

40

20

0

20

40Real (Hyy)

fstart fend

ryyIm 0.954ryyre 0.995

Re

2 0.997XXR

Im

2 0.976XXR

Im(H

YX)[

MN

/m]

Frequency (Hz) Frequency (Hz)

Re(

HX

X)[

MN

/m]

0 100 200 3000

20

40

Im(H)/wf start f end

CXX

CX

X [M

Ns/

m]

Frequency (Hz)

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SFD force coefficients - theory

3* * *

tanh2 12 π 1XX YY

LR DC C C L

LcD

3* * *

tanhπ2 1XX YY

LLR DM M M

LcD

Centered journal (es=0), no lubricant cavitationTwo film lands separated by a plenum: central groove has no effect on squeeze film forces.

Damping

Inertia

Stiffness KXX = KYY = KXY = KYX = 0X

Y

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Normalization of experimental coefficients

SHOW ratio with respect to predictions from classical theory:

Identification procedure gives NO cross-coupled coefficients for test SFDs.

*CC

C *

MMM

Long damperLand length 1”, 5.55 mil

C*A = 6.79 kN.s/m, M*A = 2.98 kg

Short damperLand length 0.5” , 5.43 mil

C*A = 0.92 kN.s/m, M*A = 0.39 kgRatio~(L/c)3~7.5

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Experimental SFD force coefficients open ends short length damper

1/2 inch lands, c=5.43 mil = 0.138 mm

Top Land

Bottom Land

0.5 inch

0.5 inch

Central groove

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SFD direct damping coefficients

Orbit amplitude (r /cB)

CXX , CYY

first decrease and then increase with

orbit amplitude. Coefficients are

isotropicCXX ~ CYY

CXX

CYY

0

1

2

3

4

5

6

0.0 0.2 0.4 0.6 0.8 1.0

C XX SFD

0

1

2

3

4

5

6

0.0 0.2 0.4 0.6 0.8 1.0

C YY SFD

es = 0

es = 0.44 cB

es = 0.29 cB

es = 0

es = 0.44 cB

es = 0.29 cB

Dam

pin

g

coef

fici

ents

Dam

pin

g

coef

fici

ents

vs orbit amplitude

Short SFD (12.7 mm lands, c=0.138 mm)

X

Y

esc

45o

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SFD added mass coefficients vs orbit amplitude

Orbit amplitude (r /cB)

0

5

10

15

20

25

30

35

0.0 0.2 0.4 0.6 0.8 1.0

M XX SFD

0

5

10

15

20

25

30

35

0.0 0.2 0.4 0.6 0.8 1.0

M YY SFD

Mas

s co

effi

cien

tsM

ass

coef

fici

ents

MXX

MYY

es= 0

es=0.29 cB

es= 0.44 cB

es= 0es = 0.29 cB

es =0.44 cB

MXX , MYY

decrease with amplitude of motion,

as prior tests* and theory show**

*Design and Application of SFDs in Rotating Machinery (Zeidan, San Andrés, Vance, 1996,

Turbomachinery Symposium)

** SFDs: Operation, Models and Technical Issues (San Andrés, 2010)

Short SFD (12.7 mm lands, c=0.138 mm)

X

Y

esc

45o

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Experimental SFD force coefficients open ends long damper

1 inch lands, c=5.55 mil=0.141 mm

Central groove

Top Land

1.0 inch

1.0 inch

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SFD direct damping coefficients vs static eccentricity

Amplitudes of motion:

CXX ~ CYY with amplitude of motion

& orbit shape.SFD forced response is

independent of BC kinematics.

All orbits (circular & elliptic)

CXX

CYY

0

2

4

6

0.0 0.2 0.4 0.6

CXXSFD

0

2

4

6

0.0 0.2 0.4

Static eccentricity ratio ( eS/cA)

CYYSFD

Dam

pin

g

coef

fici

ents

Dam

pin

g

coef

fici

ents

Long SFD (25.4 mm lands, c=0.141 mm)

X

Y

esc

45o

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SFD added mass coefficients vs static eccentricity

MXX

MYY

Amplitudes of motion:

12

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6

Static eccentricity ratio ( eS/cA)

MYYSFD

0

2

4

6

8

10

0.0 0.2 0.4 0.6

MXXSFD

Mas

s co

effi

cien

tsM

ass

coef

fici

ents

MXX ~ MYY not strong function of amplitude of

motion or orbital shape &increasing with static

eccentricity

All orbits (circular & elliptic)

Long SFD (25.4 mm lands, c=0.141 mm)

X

Y

esc

45o

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Recorded dynamic pressures in groove and film lands

1.0 “1.0 “

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Dynamic pressuresPiezoelectric pressure sensor (PCB) locations

Bearing Cartridge

PCB groove

PCB bottom land

PCB top land

Piezoelectric sensors: 2 in the top land,

2 in the bottom land 2 in the groove

Side view: Sensors located at middle plane of film lands

Mid-plane

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Dynamic pressures: films & groove

0 1 2 3 410

5

0

5

10

top land (120 deg)bottom land (120 deg)

Pressures at film lands

time (-)

pres

sure

(psi

)

Whirl frequency 130 Hz

Number of periods

psi 0.69 barfilm lands

0

-0.69 bar

Top and bottom film lands show similar

pressures.

Dynamic pressure in the groove is

not zero!0

0 1 2 3 44

2

0

2

4

groove (165 deg)groove (285 deg)

Pressures at central groove

time (-)

pres

sure

(psi

)psigroove

0.28 bar

-0.28 bar

Number of periods

Long SFD. es=0, r=0.1cA. PG = 0.72 bar

1.0 “1.0 “

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Film and groove dynamic pressures

increase with excitation frequency.

Pressure waves show spikes (high

frequency content), typical of air ingestion & entrapment

0 1 2 3 420

10

0

10

groove (165 deg)groove (285 deg)

Pressures at central groove

time (-)

pres

sure

(ps

i)

Number of time periods


psi

0.69 barfilm lands

0.69 bar

0

-0.69 bar

0

-1.40 bar

0 1 2 3 410

5

0

5

10

top land (120 deg)bottom land (120 deg)

Pressures at film lands

time (-)

pre

ssu

re (

psi

)

groove


psi

Long SFD. es=0, r=0.1cA. PG = 0.72 bar

Dynamic pressures: films & groove

Whirl frequency 200 Hz

1.0 “1.0 “

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Peak-peak dynamic pressures

Frequency [Hz]

Piezoelectric pressure sensor (PCB) location

Bearing Cartridge

bottom land

top land

groove

P-P

dy

na

mic

pre

ssu

re (

psi

)

0 100 2000

10

20

30

40

Top land (120)Bottom land (120)Groove (165)

peak-peak pressures

Frequency (Hz)

P-P

pres

sure

(psi

)

2.8 bar

2.1 bar

1.4 bar

0.7 bar

0.0 bar

Frequency (Hz)

Top land (120o)

Groove (165o)

Bottom land (120o)

Mid-plane

Groove pressures are as large as in the film lands.At the highest whirl frequency, groove pressure > 50% film land pressures

40

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0 100 2000

1

2

3

4Top land (120)Top land (240)

peak-peak pressures

frequency (Hz)

P-P

pre

ssu

re (

psi

)Ratio of groove/film land pressures

Frequency (Hz)

P-P

pre

ssu

re r

atio

s

100 2000

c=5.5 mil(0.141 mm)

groovelands (top)

1.0

Groove generates

large hydrodynamic

pressures!

3/8”~70 c

1 “ 0.5” 1”

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Comparisons to predictions from a modern model

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z

LLG

do

Bearing

Journal

End seal

c : clearance

Lubricant in

Lubricant out

orifice

groove

film land

dG

D, diameter

Lubricant in

recirculationzone

Effective groove depth

streamline

Lubricant out

separation line

d

Lubricant in

recirculationzone

Effective groove depth

streamline

Lubricant out

separation line

d

Model SFD with a central groove

2

3 3 2

212

P P h hh h h

R R z z t t

SFD geometry and nomenclature

Solve modified Reynolds equation (with fluid inertia)

Use effective depth d= Xc

* San Andrés, Delgado, 2011, GT2011-45274.

GT2012-68212

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Predicted coefficients agree well with test data.

CXX (test data)

CXX (prediction)

CYY (test data)CYY (prediction)

Static eccentricity ratio (es / cB)

Dam

pin

g C

oef

fici

ents

(S

ho

rt S

FD

)

10Short SFD, dη = 2.8cB

0

2

4

6

8

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Damping coefficients Short SFD

Damping coefficients increase moderately with

static eccentricity

Test coefficients are ~ isotropic, but predicted are

unequal, CXX > CYY

Test coefficients are ~ 4-6 larger than simplified

formulas

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MYY (test data)

MYY (prediction)

MXX (test data)

MXX (prediction) Predictions match well the

test data.

Static eccentricity ratio (es / cB)

Iner

tia

Co

effi

cien

ts (

Sh

ort

SF

D)

40

Short SFD, dη = 2.8cB

0

10

20

30

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Inertia coefficients increase moderately with static

eccentricity.

Predicted MXX > MYY

circular orbits r/c = 0.1

Inertia coefficients Short SFD


formulas

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CYY (test data)

CYY (prediction)

CXX (test data)

CXX (prediction)

Static eccentricity ratio (es / cA)

Dam

pin

g C

oef

fici

ents

(L

on

g S

FD

) 10Long SFD, dη = 1.6cA

0

2

4

6

8

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Damping coefficients increase more rapidly for the

long damper.

The test and predicted coefficients are not very

sensitive to static eccentricity (es).

Predicted coefficients agree well with test data.


Damping coefficients Long SFD


formulas

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MYY (test data)

MXX (prediction)

MXX (test data)

MYY (prediction)

Inertia coefficients are underpredicted

Static eccentricity ratio (es / cA)

Iner

tia

Co

effi

cien

ts (

Lo

ng

SF

D)

12

Long SFD, dη = 1.6cA

0

4

6

8

10

0.0 0.1 0.2 0.3 0.4 0.5 0.6

2

Coefficients grow moer rapidly with static

eccentricity than in short damper.

Tests and predicted force coefficients are not

sensitive to static eccentricity (es)


Inertia coefficients Long SFD


formulas

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ConclusionsFor both dampers and most test conditions: cross-

coupled damping and inertia force coefficients are small.

Long damper has ~ 7 times more damping than short length damper. Inertia coefficients are two times larger.

SFD force coefficients are more a function of static eccentricity than amplitude of whirl. Coefficients change little with ellipticity of orbit.

•Predictions from modern predictive tool agree well with the test force coefficients.

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Conclusions

More work conducted with both dampers (short and long) with

• SEALED ends (piston rings)

• with larger clearances (2c)

• 0-1-2 orifices plugged (3-2-1 holes active)

will be reported at a later date.

Current damper installation has NO central groove.

• Central grove is NOT a zone of constant pressure: dynamic pressures as large as in film lands.

• Classical theory predicts too low damping & inertias: 1/7 of test values

& update

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Thanks to • Pratt & Whitney Engines

• students Sanjeev Seshaghiri, Paola Mahecha, Shraddha Sangelkar, Adolfo Delgado,

Sung-Hwa Jeung, Sara Froneberger, Logan Havel, James Law.

Acknowledgments

Learn more at http://rotorlab.tamu.edu

Questions (?)

GT2012-68212

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• Della Pietra and Adilleta, 2002, The Squeeze Film Damper over Four Decades of Investigations. Part I: Characteristics and Operating Features, Shock Vib. Dig, (2002), 34(1), pp. 3-26, Part II: Rotordynamic Analyses with Rigid and Flexible Rotors, Shock Vib. Dig., (2002), 34(2), pp. 97-126.

• Zeidan, F., L. San Andrés, and J. Vance, 1996, "Design and Application of Squeeze Film Dampers in Rotating Machinery," Proceedings of the 25th Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, September, pp. 169-188.

• Zeidan, F., 1995, "Application of Squeeze Film Dampers", Turbomachinery International, Vol. 11, September/October, pp. 50-53.

• Vance, J., 1988, "Rotordynamics of Turbomachinery," John Wiley and Sons, New York

Parameter identification: • Tiwari, R., Lees, A.W., Friswell, M.I. 2004. “Identification of Dynamic Bearing Parameters: A

Review,” The Shock and Vibration Digest, 36, pp. 99-124.

Relevant Past Work

GT2012-68212

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TAMU references2011 San Andrés, L., and Delgado, A., “A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals

Operating Eccentrically,” ASME Paper GT2011-45274

2010 Delgado, A., and San Andrés, L., 2010, “A Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Grooved Oil Seal Rings”, ASME Journal of Tribology Vol. 132

Delgado, D., and San Andrés, L., 2010, “Identification of Squeeze Film Damper Force Coefficients from Multiple-Frequency, Non-Circular Journal Motions,” ASME J. Eng. Gas Turbines Power, Vol. 132 (April), p. 042501 (ASME Paper No. GT2009-59175)

2009 Delgado, A., and San Andrés, L., 2009, “Nonlinear Identification of Mechanical Parameters on a Squeeze Film Damper with Integral Mechanical Seal,” ASME Journal of Engineering for Gas Turbines and Power, Vol. 131 (4), pp. 042504 (ASME Paper GT2008-50528)

2003 San Andrés, L., and S. Diaz, 2003, “Flow Visualization and Forces from a Squeeze Film Damper with Natural Air Entrainment,” ASME Journal of Tribology, Vol. 125, 2, pp. 325-333

2001 Diaz, S., and L. San Andrés, 2001, "Air Entrainment Versus Lubricant Vaporization in Squeeze Film Dampers: An Experimental Assessment of their Fundamental Differences,” ASME Journal of Gas Turbines and Power, Vol. 123 (4), pp. 871-877

2000 Tao, L., S. Diaz, L. San Andrés, and K.R. Rajagopal, 2000, "Analysis of Squeeze Film Dampers Operating with Bubbly Lubricants" ASME Journal of Tribology, Vol. 122, 1, pp. 205-210

1997 Arauz, G., and L. San Andrés, 1997 "Experimental Force Response of a Grooved Squeeze Film Damper," Tribology International, Vol. 30, 1, pp. 77-86

1996 San Andrés, L., 1996, "Theoretical and Experimental Comparisons for Damping Coefficients of a Short Length Open-End Squeeze Film Damper," ASME Journal of Engineering for Gas Turbines and Power, Vol. 118, 4, pp. 810-815

SFDs

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Select effective groove depth

Predictions overlaid with test data to estimate effective groove depth

dη = 2.8cB

0

2

4

6

8

10

1 10 100

Groove depth (dη)

Dam

pin

g c

oef

fici

ents

c c c

Short SFD

0

1

2

3

4

5

1 10 100

Groove depth (dη)D

amp

ing

co

effi

cien

tsc c c

Long SFD

PredictionsPredictions

test data

test data

dη = 1.6cA

dη = 2.8 cB dη = 1.6 cA

GT2012-68212 1 ASME GT2012-68212 Luis San Andrés Mast-Childs Professor, Fellow ASME Texas A&M...

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Transcript of GT2012-68212 1 ASME GT2012-68212 Luis San Andrés Mast-Childs Professor, Fellow ASME Texas A&M...