1

Luis San Andrés Mast-Childs Professor

Identification of SFD force coefficients

Large Clearance Open Ends SFDTRC-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

oil 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.

3

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

4

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

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/inBearing Cartridge

Test Journal

Main support rod (4)

Journal BasePedestal

Piston ring seal (location)

Flexural Rod (4, 8, 12)

Circumferential groove

Supply orifices (3)

6

Lubricant flow path

Oil inlet

in

ISO VG 2 oil

7

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 orbits

8

Structure static stiffness

0

100

200

300

400

0 0.5 1 1.5 2 2.5 3 3.5 4

static radial eccentricity, (mil)

stat

ic r

adia

l lo

ad (

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

stat

ic r

adia

l lo

ad (

N)

(101.6 μm)

9

Structural parameters • Dry test system• Circular Centered Orbits • Frequency 50-210 Hz

DirectXX YY

US SI US SI

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

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

Mass M -4 lb -2 kg -3 lb -1 kg

System Mass MBC 48 lb 22 kg 48 lb 22 kg

Natural frequency fns 148Hz 156Hz

Damping ratio ξs 4% 4%

10

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

ISO VG 2 OilViscosity at 73 oF [cPoise] 3.10

Density [kg/m3] 785

Inlet pressure [psig] 1.6

Outlet pressure [psig] 0

Radial Clearance [mil] 9.9

Journal Diameter [inch] 5.0

Central groove length [inch]& depth

0.5000.375

Land length, L [inch] 1.0 x 2

Total Length [inch] 2.5

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

11

SFD

Ks = 100 klbf/inMBC = 48 lb

Cs= 8-9 lbf-s/inNat freq = 148-156 HzDamping 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

esc

45o

12

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=0 X

Y

13

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

Damping

Inertia

c=5.5 mil

C* = 7,121 N.s/m (40.7 lbf.s/in)

c=9.9 mil

C* = 1,255 N.s/m (7.16 lbf.s/in)

c=5.5 mil

M* = 2.98 kg (6.58 lbm)

c=9.9 mil

M* = 1.67 kg (3.69 lbm)X

Y

14

Experimental SFD damping coeffs.

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

SFD (1 inch land lengths)

0

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)

Dam

pin

g c

oef

fici

ents

(lb

f -s/in

)

C SFD

CXX c=9.9 mil

CYY c=9.9 mil

CYY c=5.5 mil

CXX 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

esc

45o

15

Experimental SFD inertia coeffis.

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

SFD (1 inch land lengths)

0

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)

Ad

ded

mas

s co

effi

cien

ts (

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

esc

45o

16

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

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

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

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

ASME GT2012-68212

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Peak-peak lubricant pressures

0 100 2000

10

20

30Top land (120)Top land (240)Bottom land (120)Bottom land (240)Groove (165)Groove (285)

peak-peak pressures

frequency (Hz)

P-P

pre

ssur

e (p

si)

Frequency (Hz)

P-P

dyn

amic

pre

ssu

re (

psi

)

100 200

30

20

10

0

c=5.5 mil

groove

Lands(top & bottom)

207 (kPa)

Piezoelectric pressure sensors (PCB) location

Bearing Cartridge

bottom land

top land

groove

Mid-plane

19

0 100 2000

5

10

15Top land (120)Top land (240)Bottom land (120)Bottom land (240)Groove (165)Groove (285)

peak-peak pressures

frequency (Hz)

P-P

pre

ssur

e (p

si)

Peak-peak lubricant pressures

Frequency (Hz)

100 200

15

10

5

0

c=9.9 mil

groove

lands (top & bottom)

Piezoelectric pressure sensors (PCB) location

Bearing Cartridge

bottom land

top land

groove

Mid-plane

P-P

dyn

amic

pre

ssu

re (

psi

)

20

0 100 2000

1

2

3

4Top land (120)Top land (240)

peak-peak pressures

frequency (Hz)

P-P

pre

ssur

e (p

si)

Ratio of groove/film land pressures

Frequency (Hz)

P-P

pre

ssu

re r

atio

s

100 2000

c=5.5 mil

groovelands (top)

1.0

Groove generates

large hydrodyna

mic pressures!

3/8”~70 c

1 “ 0.5” 1”

21

0 100 2000

1

2

3

4Top land (120)Top land (240)

peak-peak pressures

frequency (Hz)

P-P

pre

ssur

e (p

si)

Ratio of groove/film land pressures

Frequency (Hz)

P-P

pre

ssu

re r

atio

s

100 200

1.0

c=9.9 mil

groovelands (top)

Groove generates

larger hydrodyna

mic pressures!!Larger than in the film!

1 “ 0.5” 1”

3/8”~35 c

22

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=1.6c

23

19

1725

3341

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 coordinate

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)

19

1725

3341

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 coordinate

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”

24

0

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)

Da

mp

ing

co

eff

icie

nts

(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

0

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

Ad

de

d m

ass

co

eff

icie

nts

(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 of 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 orbits, centered and off-centered.

27

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.

28

Proposed tasks TRC (2012-13)

X

Y

X

Y

X

Y

elliptical orbitscircular orbits

centered journal off-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 orbitscircular orbits

centered journal off-centered journal

eight months Year II

Support for graduate student (20 h/week) x $ 2,200 x 8 months $ 17,600

Fringe benefits (0.6%) and medical insurance ($197/month) $ 1,682

Travel to (US) technical conference $ 1,200

Tuition three semesters ($227 credit hour x 15 ch x 1.7 fees multiplicative factor)

$ 5,789

Supplies for test rig $ 2,200

Total Cost: $ 28,470

Year I started on Jan 2012

30

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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