Identification of SFD force coefficients Large Clearance Open Ends - - PowerPoint PPT Presentation

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Luis San Andrés

Mast-Childs Professor

Identification of SFD force coefficients

Large Clearance Open Ends SFD

TRC-SFD-01-2012 Linear Nonlinear Force Coefficients for SFDs

32nd Turbomachinery Research Consortium Meeting

TRC Project 32513/1519FB

May 2012

2 Typical squeeze film damper (SFD) with a central groove

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

• il inlet

Pressurized lubricant flows through a central groove to fill the squeeze film lands. Dynamic pressures in the film lands generate 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 X shaker 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

5

SFD Test Rig – cut section

in

Test rig main features Journal diameter: 5.0 inch Film clearance: 9.9 mil Film length: 2 x 1 inch Support stiffness: 100 klbf/in Bearing Cartridge Test Journal Main support rod (4) Journal Base Pedestal Piston ring seal (location) Flexural Rod (4, 8, 12) Circumferential groove Supply orifices (3)

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Lubricant flow path

Oil inlet

in

ISO VG 2 oil

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Objective & tasks

Evaluate dynamic load performance of SFD with a central groove.

Dynamic load measurements: circular orbits

(centered and off centered) and identification of test system and SFD force coefficients

X Y static load e c 45o

X Y

r eS

centered and off- centered circular

• rbits

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Structure static stiffness

100 200 300 400 0.5 1 1.5 2 2.5 3 3.5 4

static radial eccentricity, (mil)

static radial load (lbf)

e S

K S ~ 100 klbf/in

X Y F

• Pull test using static loader to determine static structure stiffness

1780 1335 890 445

static radial load (N)

(101.6 μm)

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Structural parameters

• Dry test system
• Circular Centered

Orbits

• Frequency 50-210 Hz

4% 4%

ξs

Damping ratio

Hz 156 Hz 148

fns

Natural frequency

22 kg 48 lb 22 kg 48 lb

MBC

System Mass

• 1 kg
• 3 lb
• 2 kg
• 4 lb

M

Mass

1.6kN-s/m 9 lbf-s/in 1.4 kN-s/m 8 lbf-s/in

Cs

Damping

21 MN/m 120 klbf/in 19 MN/m 107 klbf/in

Ks

Stiffness

SI US SI US YY XX Direct

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SFD dimensions & operating conds.

• Maximum static load 324 lbf
• Centered and off-centered, eS= 1, 2, and 3 mil
• Frequency range: 50-210 Hz, Orbit amplitude r = 0.5 mil

2.5 Total Length [inch] 1.0 x 2 Land length, L [inch] 0.500 0.375 Central groove length [inch] & depth 5.0 Journal Diameter [inch] 9.9 Radial Clearance [mil] Outlet pressure [psig] 1.6 Inlet pressure [psig] 785 Density [kg/m3] 3.10 Viscosity at 73 oF [cPoise]

ISO VG 2 Oil

Oil out, Qb

Base Support rod Bearing Cartridge Journal (D)

Oil out, Qt Oil in, Qin

Central groove

L ½ L L

End groove End groove

Oil out Oil collector

c

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SFD

Ks = 100 klbf/in MBC = 48 lb Cs= 8-9 lbf-s/in Nat freq = 148-156 Hz Damping ratio = 4%

DRY system parameters

CSFD=Clubricated - Cs MSFD=Mlubricated - MBC KSFD=Klubricated - Ks

Difference between lubricated system and dry system (baseline) coefficients

SFD force coefficients

IVFM parameter identification method X Y es c

45o

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SFD force coefficients - theory

3 * * *

tanh 2 12π 1

XX YY

L R D C C C L L c D                        

3 * * *

tanh π 2 1

XX YY

L LR D M M M L c D                   Centered journal (es=0), no lubricant cavitation Two film lands separated by a plenum: central groove has no effect on squeeze film forces.

Damping Inertia Stiffness

KXX = KYY = KXY=KYX=0

X Y

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SFD force coefficients - theory

3 * * *

tanh 2 12π 1

XX YY

L R D C C C L L c D                        

3 * * *

tanh π 2 1

XX YY

L LR D M M M L c D                  

Damping Inertia

C* = 1,255 N.s/m (7.16 lbf.s/in) c=9.9 mil C* = 7,121 N.s/m (40.7 lbf.s/in) c=5.5 mil M* = 1.67 kg (3.69 lbm) c=9.9 mil M* = 2.98 kg (6.58 lbm) c=5.5 mil

X Y

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Experimental SFD damping coeffs.

• Open ends SFD
• Circular orbits (r = 0.5 mil)

SFD (1 inch land lengths)

20 40 60 80 100 120 140 160 180 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

static eccentricity, e S (mil) Damping coefficients (lbf-s/in)

C SFD

C XX c=9.9 mil C YY c=9.9 mil C YY c=5.5 mil C XX c=5.5 mil

classical theory (7.1 lbf.s/in) classical theory (40.6 lbf.s/in)

31.5 kNs/m (89 μm)

X Y es c

45o

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Experimental SFD inertia coeffis.

• Open ends SFDs
• Circular orbits (r = 0.5 mil)

SFD (1 inch land lengths)

10 20 30 40 50 60 70 80 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

static eccentricity, e S (mil) Added mass coefficients (lb)

M SFD

M XX c= 9.9 mil M YY c= 9.9 mil M YY c= 5.5mil M XX c= 5.5 mil

classical theory (3.7 - 6.6 lb)

89 μm

36 kg

X Y es c

45o

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Pressure sensors in bearing

Pressure sensor Bottom Land

Pressure sensor locations

and

Central groove

and

,

Central groove

Top Land

BC 25.4 mm 25.4 mm

Side view: Sensors located at

middle plane of film lands

Top view: Sensors around bearing circumference

63.5 mm 12.7 mm

Pressure sensor Pressure sensor Pressure sensor Bottom Land

Pressure sensor locations

and

Central groove

and

,

Central groove

Top Land

BC 25.4 mm 25.4 mm

Side view: Sensors located at

middle plane of film lands

Top view: Sensors around bearing circumference

63.5 mm 12.7 mm

Pressure sensor Pressure sensor

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Dynamic pressures: films & groove

1 2 3 4 10  5  5 10 top land (120 deg) bottom land (120 deg) time (-) pressure (psi)

Whirl frequency 130 Hz

Number of periods

psi

0.69 bar

film lands

es=0, circular orbit r=0.5 mil. Groove pressure PG = 0.72 bar

• 0.69 bar

Top and bottom film lands show similar pressures. Dynamic pressure in the groove is not zero!

1 2 3 4 4  2  2 4 groove (165 deg) groove (285 deg) time (-) pressure (psi)

psi groove

0.28 bar

• 0.28 bar

Number of periods

ASME GT2012-68212

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Peak-peak lubricant pressures

100 200 10 20 30 Top land (120) Top land (240) Bottom land (120) Bottom land (240) Groove (165) Groove (285)

Frequency (Hz) P-P dynamic pressure (psi)

100 200 30 20 10

c=5.5 mil groove Lands

(top & bottom)

207 (kPa)

Piezoelectric pressure sensors (PCB) location Bearing Cartridge bottom land top land groove

Mid- plane

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100 200 5 10 15 Top land (120) Top land (240) Bottom land (120) Bottom land (240) Groove (165) Groove (285)

Peak-peak lubricant pressures

Frequency (Hz)

100 200 15 10 5

c=9.9 mil groove lands

(top & bottom)

Piezoelectric pressure sensors (PCB) location Bearing Cartridge bottom land top land groove

Mid- plane

P-P dynamic pressure (psi)

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100 200 1 2 3 4 Top land (120) Top land (240)

Ratio of groove/film land pressures

Frequency (Hz) P-P pressure ratios

100 200

c=5.5 mil groove lands (top)

1.0

Groove generates large hydrodyna mic pressures!

3/8”~70 c 1 “ 0.5” 1”

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100 200 1 2 3 4 Top land (120) Top land (240)

Ratio of groove/film land pressures

Frequency (Hz) P-P pressure ratios

100 200 1.0

c=9.9 mil groove lands (top)

Groove generates larger hydrodyna mic pressures!! Larger than in the film!

1 “ 0.5” 1” 3/8”~35 c

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z L LG do Bearing Journal

End seal

c : clearance Lubricant in Lubricant out

• rifice

groove film land

dG D, diameter

Lubricant in recirculation zone

Effective groove depth

streamline

Lubricant out

separation line

d

Lubricant in recirculation zone

Effective groove depth

streamline

Lubricant out

separation line

d

Model SFD with a central groove

2 3 3 2 2

12 P P h h h h h R R z z t t                             

SFD geometry and nomenclature Solve modified Reynolds equation (with fluid inertia)

Use effective depth d=1.6c

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1 9 17 25 33 41 49 57 65 73 81 89 S1 S8 0.00 0.10 0.20 0.30 0.40 0.50 0.60 circ coordinate (node #)

axial coordi nate

0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0.0-0.1

Inner Film Pressure



Feed hole (3 x 120 deg) groove land z Pressure (bar)

1 9 17 25 33 41 49 57 65 73 81 89 S1 S8 0.00 0.10 0.20 0.30 0.40 0.50 0.60 circ coordinate (node #)

axial coordi nate

0.5-0.6 0.4-0.5 0.3-0.4 0.2-0.3 0.1-0.2 0.0-0.1

Inner Film Pressure



Feed hole (3 x 120 deg) groove land z Pressure (bar)

Example predicted pressure field

Static pressure at groove shows circumferenti al variation due to feed holes spacing

groove 3/8”~35 c 1 “ 0.5” 1”

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20 40 60 80 100 120 140 160 180 200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

static eccentricity, eS (mil) Damping coefficients (lb f-s/in)

CSFD

CXX c=9.9 mil CYY c=9.9 mil CYY c=5.5 mil CXX c=5.5 mil

lines : predictions

symbols: test data

classical theory (7.1 lbf.s/in) classical theory (40.6 lbf.s/in)

Damping coefficients: test & predictions

Model predicts

small c SFD:

larger damping

coefficient than test values large c SFD:

less damping

than test values

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Inertia coefficients: test & predictions

10 20 30 40 50 60 70 80 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Added mass coefficients (lb)

MSFD

MXX c=9.9 mil MYY c=9.9 mil MYY c=5.5mil MXX c=5.5 mil

classical theory (3.7 - 6.6 lb)

static eccentricity, eS (mil)

lines : predictions

symbols: test data

Classical theory predicts ~ 1/7

• f test values

Model predicts

small c SFD:

less inertia than

test values Large c SFD:

larger inertia than

test values

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Conclusions

• Central grove is NOT a zone of constant pressure:

dynamic pressures as large as in film lands.

• Classical theory predicts too low SFD added masses:

1/7 of test values

• Using an effective shallow groove depth, new model

predictions agree well with test results. Conducted measurements of dynamic load response in large clearance (c=9.9 mil) open ends SFD with circular

• rbits, centered and off-centered.

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P&W funded project (2012)

Modify test rig and construct SFD w/o a central groove, conduct measurements of film pressures and identify force coefficients.

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Proposed tasks TRC (2012-13)

X Y X Y X Y elliptical orbits circular orbits centered journal

• ff-centered journal
• 1. Test damper w/o groove with dynamic loads (20-300 Hz) inducing off-

centered elliptical orbital motions to reach 0.8c.

• 2. Identify SFD force coefficients from test impedances, and correlate

coefficients with linear force coefficients and experimental coefficients for smallest whirl amplitude (0.05c).

• 3. Perform numerical experiments, similar to the physical tests, to

extract linearized SFD force coefficients from the nonlinear forces. Quantify goodness of linear-nonlinear representation from an equivalence in mechanical energy dissipation.

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TRC Budget (2012-13)

X Y X Y X Y elliptical orbits circular orbits centered journal

• ff-centered journal

$ 28,470

Total Cost:

$ 2,200 Supplies for test rig $ 5,789 Tuition three semesters ($227 credit hour x 15 ch x 1.7 fees multiplicative factor) $ 1,200 Travel to (US) technical conference $ 1,682 Fringe benefits (0.6%) and medical insurance ($197/month) $ 17,600 Support for graduate student (20 h/week) x $ 2,200 x 8 months

Year II eight months

Year I started

• n Jan 2012

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Acknowledgments

Thanks to

• Pratt & Whitney Engines
• Turbomachinery Research Consortium
• Sung-Hwa Jeng, RA for making the presentation

Learn more http:/rotorlab.tamu.edu

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