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2012 ASME Turbo Expo Conference, June 11-15 ,2012, Copenhagen, DK. D AMPING AND I NERTIA C OEFFICIENTS F OR T WO O PEN E NDS SFDs WITH A C ENTRAL G ROOVE : M EASUREMENTS A ND P REDICTIONS. Luis San Andrés Mast-Childs Professor, Fellow ASME Texas A&M University. ASME GT2012-68212. - PowerPoint PPT Presentation
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GT2012-68212
1
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
GT2012-68212
2
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
GT2012-68212
3
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.
GT2012-68212
4
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
GT2012-68212
5
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
GT2012-68212
6
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)
GT2012-68212
7
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
GT2012-68212
8
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
GT2012-68212
9
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
Journal (D) Oil out, Qt
Oil in, Qin
Central groove
L
½ L
L
End groove
End groove
Oil outOil collector
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
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
GT2012-68212
10
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.
GT2012-68212
11
Parameter Identification
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
GT2012-68212
12
Parameter Identification
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
GT2012-68212
13
Parameter Identification
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
GT2012-68212
14
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)
GT2012-68212
15
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
GT2012-68212
16
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
GT2012-68212
17
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
GT2012-68212
18
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
GT2012-68212
19
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
GT2012-68212
20
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
GT2012-68212
21
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
GT2012-68212
22
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
GT2012-68212
23
Recorded dynamic pressures in groove and film lands
1.0 “1.0 “
GT2012-68212
24
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
GT2012-68212
25
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 “
GT2012-68212
26
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
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
Number of time periods
psi
Long SFD. es=0, r=0.1cA. PG = 0.72 bar
Dynamic pressures: films & groove
Whirl frequency 200 Hz
1.0 “1.0 “
GT2012-68212
27
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
GT2012-68212
28
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”
GT2012-68212
29
Comparisons to predictions from a modern model
GT2012-68212
30
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
31circular orbits r/c = 0.1
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
GT2012-68212
32
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
Test coefficients are ~ 20-30 larger than simplified
formulas
GT2012-68212
33
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.
circular orbits r/c = 0.1
Damping coefficients Long SFD
Test coefficients are ~ 3-4 larger than simplified
formulas
GT2012-68212
34
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)
circular orbits r/c = 0.1
Inertia coefficients Long SFD
Test coefficients are ~ 8-10 larger than simplified
formulas
GT2012-68212
35
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.
GT2012-68212
36
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
GT2012-68212
37
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
38
• 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
39
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
GT2012-68212
40
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