GT2009-59175 SFD Force Coefficients- Multiple Frequency I DENTIFICATION of SQUEEZE FILM DAMPER FORCE C OEFFICIENTS from MULTIPLE-FREQUENCY NON-CIRCULAR

GT2009-59175 SFD Force Coefficients- Multiple Frequency

IDENTIFICATION of SQUEEZE FILM DAMPER FORCE

COEFFICIENTS from MULTIPLE-FREQUENCY

NON-CIRCULAR JOURNAL MOTIONS

ASME GT2009-59175

Luis San Andrés Mast-Childs Professor

Texas A&M University

Adolfo Delgado

Mechanical Engineer

GE Global Research Center

Supported by TAMU Turbomachinery Research Consortium

2009 ASME Turbo Expo Conference, June 2009

accepted for journal publication


housing

journal

lubricant film

shaft

ball bearing

anti-rotation pin

Typical squeeze film damper (SFD) configuration

In aircraft gas turbines and compressors, squeeze film dampers aid to attenuate rotor vibrations and to provide mechanical isolation.

Too little damping may not be enough to reduce vibrations.

Too much damping may lock damper & degrades system rotordynamic performance

SFD Operation & Design Issues

In a SFD, the journal whirls but does not spin. The lubricant film is squeezed due to rotor motions, and fluid film (damping) forces are generated as a function of the journal velocity.


housing

journal

lubricant film

shaft

ball bearing

anti-rotation pin

Typical squeeze film damper (SFD) configuration

SFD Operation & Design IssuesDamper performance depends

ona) Geometry (L, D, c)b) Lubricant (density, viscosity)c) Supply pressure and

through flowd) Sealing devicese) Operating speed (frequency)

• Flow regimes: (laminar, superlaminar, turbulent)• Type of lubricant cavitation:

gaseous or vaporair ingestion & entrapment


Intershaft dampers are subject to whirl motions resulting from the combined

imbalance response of both the LP and the HP shafts.

In multi-spool engines, intershaft dampers are located in the interface

between rotating shafts

Intershaft Dampers

Schematic view of intershaft [*]

Objective: to investigate the forced performance of SFD

for non-circular motions with multi-frequencies

[*] Gupta K., and Chatterjee S., 2007, “Dynamics of an Improved Inter Shaft Squeeze Film Damper: Theory and Experiment,” ASME paper No. GT2007-27534.

LP shaft

HP shaft

Multiple frequency excitation.


Intershaft SFDs• Della Pietra and Adilleta (2002): Comprehensive review of research conducted on SFDs

over last 40 years. • (1975) Hibner • (1991) Al-Shafei • (2008) Defaye et al.

Parameter identification in SFDs: • Tiwari et al. (2004): Comprehensive review of parameter identification in fluid film

bearings.• (1986) Roberts et al, • (1990) Ellis et al. , • (1999) Diaz and San Andrés • (2006-2008) San Andrés and Delgado (SFD & MECHANICAL SEAL)

Relevant Past Work

GT 2006-91238, GT 2007-24736, GT 2008-50528


Bearing Assembly

Shaft

Plexiglas Bearing

Journal

Top Support Plate

Steel Rods

127mm (5 in)

Bottom Support Plate

Accelerometer

Discharge Orifice

Vertical Plate

Ring Carrier

Shaker Load Cell

Eddy Current Sensor

Oil Inlet Hose

TRC SFD Vertical Test Rig

Schematic view of test rig


SFD bearing design

Oil inlet

O-rings

Ring carrier

Discharge groove

Plexiglas Bearing

Journal

HousingTop plate

Bottom plate

Eddy current sensor

O-rings

Vertical plate

Discharge orifice

Pipe insert

Shaft

L=25.4 mm, D=127 mm, c=0.127 mm

(5 mil)

Open end configuration


Open End Configuration

Clearance c= 0.127 mm (5 mil)Diameter D = 127 mm (5 inch)Length L = 25.4 mm (1 inch)

ISO VG 2 oil

Flow through squeeze film land

Feed plenum

Inlet groove

Squeeze film land

Discharge groove


Multiple frequency excitations

Multiple frequency excitation force:

X Displacement [m]

Y Displacement [m]

ISO VG 2Feed pressure= 31 kPa

Temperature (avg.)= 24 0C

Max. clearance: 127 mm

130

130

-130

65-65

-65

65

Low speed shaft: fixed frequency (25 Hz)+

High speed shaft: sine sweep (30 Hz to 120 Hz)

Three excitation vectors:

Case 1 Low and high speed shafts in phase

Case 2 Low and high speed shafts 90 deg out of phase

Case 3 Excitation vector amplitude increases (constant amplitude response)

-130


( ) ( )

( ) ( )xx yx xx xy

xy yy yx yy

SFD SFD SFD SFDx

y SFD SFD SFD SFDSFD

C e C e M MF x x

F C e C e y M M y

Parameter IdentificationEquations of motion

SFD coefficients(function of

instantaneous journal

eccentricity e)

0

0s f sx sx x x

s f sy sy y y SFD

M M C x K x F Fx

M M C y K y F Fy

Non-circular whirl motions

3 (2 1)1 2

3 (2 1)1 2

( , , ) ...

( , , ) ...

k k k

k k k

k k k

k k k

t t n tDx x k x k nx k

t t n tD y y k y k ny k

F e x x e x e x e

F e y y e y e y e

Dissipative non-linear force function of journal position e and velocity v

Added mass coefficient constant for test journal

amplitudes (< 60% c) For parameter identification only 1x component is considered (dissipates mechanical energy)


Parameter Identification

x

x xx xy

y yy yx

F H x H y

F H y H

1 2

1 2

1

1 2

1 2

x xxx xy

yx yy y y

F FH H x x

H H y yF F

2

2

Re( )

Re( )

iii s s ii

ij ij SFDij

H K M

H K M

Im( ); , .

Im( ) , , .

iisi SFDii

ijSFDij

HC C i x y

HC i j x y

For each excitation force frequency component (sine sweep)

From two independent vectors with Hii1 = Hii2 ; i=x,y

Dynamic stiffnesses Damping coefficients


Excitation Force & Displacement

X Displacement [m]

Y Displacement [m]

130

130

-130

65-65

-65

65

Clearance: 127 mm

1

( )

( )s

s

F t

F t

F

0 1( ) sin(2 ) sin(2 );sF t A f t B f t t

Case 1

Time trace (Force)

2

( )

( )s

s

F t

F t

F

Fixed frequency Linear sweep

Case 1: LS & HS in phase

Highly elliptical motions


[1] Delgado, A., 2008, “A Linear Fluid Inertia Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Grooved Oil Seal Rings,” Ph.D. Dissertation, December, Texas A&M University, C/S, TX.


Re(Hxx)= Kxx-Mxx2

Identification Range

Dynamic stiffness

Frequency spectra

Displacement

Force

x

y

25 Hz

Identification Range

xF

yF

Sine sweepSingle Frequency +

Case 1

Classical theory predicts = 2.1 kg (3 times smaller)

FREQUENCY DOMAIN

Parameter xx yy Identified Mass, (M) 16.3 kg 16.1kg

Squeeze film inertia (MSFD) 6.1 kg 5.9 kg

r2 (goodness of curve fit) 0.97 0.98 Added mass coefficient from 6.6 kg

[1]


0 0.2 0.4 0.6 0.8 10

5

10

15

Amplitude/clearance

Dam

ping

Coe

ffic

ient

[kN

.s/m

]


Cross-coupled coefficients negligible (No lubricant cavitation)

Im(Hxx/)

Predictions (circular centered orbits)

Predictions (small radial motions about an off-centered position)

Damping coefficients bracketed by predictions from

full film short length SFD model (open ends)

Case 1

e

Dam

pin

g c

oef

fici

ent

[kN

.s/m

]

Amplitude/clearance

Damping coefficient


Excitation Force & Displacementclearance: 127 mm ( )

( )s

c

F t

F t

F

Case 2

X Displacement [m]

Y Displacement [m]

130

130

-130

65-65

-65

65

0 1

0 1

( ) sin(2 ) sin(2 );

( ) cos(2 ) cos(2 );

s

c

F t A f t B f t t

F t A f t B f t t

Fixed frequency Linear sweep

Case 2: LS & HS out of phase

Non circular whirl motions

Time trace (Force)


Parameter Identification Case 2

Frequency spectra

x

y

xF

yF

Parameter xx yy System Mass, (Ms) 16.3 kg 16.7kg

Squeeze film inertia (MSFD) 5.9 kg 6.5 kg

r2 (goodness of curve fit) 0.97 0.97 Fluid Mass, (Mf) [kg] 0.62

Re(Hxx)= Kxx-Mxx2

Force

Displacement

Similar added mass coefficients as in Case 1

FREQUENCY DOMAIN

Dynamic stiffness


0 0.2 0.4 0.6 0.8 10

5

10

15

Amplitude/clearance

Dam

ping

Coe

ffic

ient

[kN

.s/m

]

Parameter Identification Case 2

e

Dam

pin

g c

oef

fici

ent

[kN

.s/m

]

Amplitude/clearance

For excitation loads (Fx, Fy) out of phase by 90 degree, identified damping coefficients are closer to predictions for circular (centered) motions

Im(Hxx/)

FREQUENCY DOMAIN

Damping coefficient



Excitation Force & Displacement ( )

( )s

c

F t

F t

FSimilar to case 2 but with increasing

amplitude of excitation load

Case 3

3 constant motion amplitudes~20 um, ~40 um, ~ 60 um



0 0.2 0.4 0.6 0.8 10

5

10

15

Amplitude/clearanceD

ampi

ng C

oeff

icie

nt [

N.s

/m]

Dam

pin

g c

oef

fici

ent

[kN

.s/m

]Amplitude/clearance

Linear (single) damping coefficient

e

Im(Hxx)

Im(Hxx)

Im(Hxx)

~20 um

~40 um

~ 60 umDamping coefficient



• SFD force coefficients could be identified for multiple-frequencies when expressed as generic functions of journal position and velocity. The motion with amplitude at main excitation frequency is one that leads to dissipation of mechanical energy.

• Classical SFD (open ends) model predictions: centered circular orbits and small amplitude motions about off-centered position ENCLOSE the identified damping coeffs.

• Novel model added mass coefficient correlates well with test data. Classical theory predicts mass coefficients 3 times smaller than test values. Large mass due to effects of inlet and discharge grooves.

Conclusions:


Thanks to TAMU Turbomachinery Research Consortium

Acknowledgments

Questions ?

Learn more at http://phn.tamu.edu/TRIBGroup

Documents

GT2009-59175 SFD Force Coefficients- Multiple Frequency I DENTIFICATION of SQUEEZE FILM DAMPER FORCE C OEFFICIENTS from MULTIPLE-FREQUENCY NON-CIRCULAR