GT2012-68212
2012 ASME Turbo Expo Conference, June 11-15 ,2012, Copenhagen,
DK
DAMPING AND INERTIA COEFFICIENTS
FOR TWO OPEN ENDS
SFDs WITH A CENTRAL GROOVE:
MEASUREMENTS AND PREDICTIONS
Luis San Andrés
Mast-Childs Professor, Fellow ASME
Texas A&M University
ASME GT2012-68212
accepted for journal publication
1
Supported by Pratt & Whitney Engines (UTC)
SFD operation & design
GT2012-68212
In aircraft gas turbines and
compressors, squeeze film
dampers aid to attenuate rotor
vibrations and to provide
mechanical isolation.
w
SFD with dowel pin
Y
X
Too little damping may not be
enough to reduce vibrations.
Too much damping may lock damper
& degrades system rotordynamic
performance
2
SFD with a central groove
lubricant
film
anti-rotation
pin
shaft
journal
w
oil inlet
Feed
groove
ball
bearing
housing
Conventional knowledge regards a groove
is indifferent to the kinematics of journal
motion, thus effectively isolating the
adjacent film lands.
GT2012-68212
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.
3
P&W SFD Test Rig
Isometric view
GT2012-68212
Static loader
Shaker assembly
(Y direction)
Shaker assembly
(X direction)
Top view
Shaker in
Y direction
Static loader
Shaker in
X direction
SFD test
bearing
4
Test rig description
shaker Y
GT2012-68212
Static loader
Static loader
shaker X
Shaker Y
Shaker X
Y
X
SFD
SFD
Static loader
Y
Y
support rods
Support
rods
base
Base
X
X
5
SFD bearing design
GT2012-68212
Geometry of open ends SFD
Piston ring seal
(location)
Test Journal
Bearing Cartridge
Supply orifices (3)
Circumferential
groove
Flexural Rod
(4, 8, 12)
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)
Main support
rod (4)
Journal Base
Pedestal
in
6
Flow through squeeze film lands
Oil
inlet
GT2012-68212
in
ISO VG 2 oil
Oil inlet temperature, Ts = 25 oC
Density, ρ = 785 kg/m3
Viscosity μ at Ts= 2.96 cPoise
Flow rate, Qin= 4.92 LPM
7
Objective & tasks
GT2012-68212
Evaluate dynamic load performance of SFD
Y
with a central groove.
static load
e
X
Dynamic load
measurements: circular &
elliptical orbits (centered and
off centered) and identification
of test system and SFD force
coefficients
45o
c
Y
eS
X
r
centered and offcentered circular
orbits
8
SFD configurations tested
Geometry and oil properties for open ends SFD
Oil in, Qin
Journal (D)
GT2012-68212
Oil out, Qt
End groove
c
L
Central
groove
½L
L
Bearing
Cartridge
Short SFD (B)
Journal diameter, D
Oil out, Qb
Land length, L
Oil collector
Radial clearance, c
Oil out
Base
Support
rod
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  
  w c

Long SFD (A)
End groove
= 1.1-8.3 in film lands
12.7 mm
25.4 mm
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
Lubricant
Density, ρ
Viscosity μ at Ts
Flow rate, Qin
2
127 mm
25 oC
ISO VG 2
785 kg/m3
2.96 cPoise
4.92 LPM
9
Parameter Identification
GT2012-68212
Y
X
 x   w 2 x   a X 
 y   2    a 
   w y   Y 
Journal also moves during
excitation of the bearing
10
*SFDs do not have stiffnesses = reaction forces due to changes in static displacement.
Parameter Identification
GT2012-68212
Single frequency orbits
Applied Loads
Two linearly
independent
load vectors
F1 and F2
Y
1
1




 iwt 
F
cos(
w
t
)
F
1
X
X
F 
  Re   1  e 
1
  FY sin(wt ) 
 iFY 

  FX  iwt 
 FX cos(wt ) 
F 
e 
  Re  
2
2

  FY sin(wt ) 
  iFY 

2
CW
X
Y
2
2
CCW
X
 x1 (t )   X 1  iwt 2  x 2 (t )   X 2  iwt
z   1    1 e z   2    2 e
 y (t )   Y 
 y (t )   Y 
1
displacements
& accelerations
a1
a2
Loads F, displacement x and accelerations a recorded at each frequency
11
Parameter Identification
EOMs (2 DoF)
time domain
EOM
(Frequency
Domain)
GT2012-68212
M BC a+  Ms  MSFD  z   Ks  KSFD  z + Cs +CSFD  z  F
 K s  K SFD   i w  Cs + CSFD   w 2  M SFD  M s   z  FM  F  M BC a
H  z 1 z 2   FM 1 FM 2 
Impedance
function H(ω)
Physical
model
 H XX
H
 HYX
H XY 
1
2
1
2 1
 FM FM   z z 

HYY 
Re( H XX )  K XX  w M XX ; Im( H XX )  w CXX
2
12
Parameter Identification
GT2012-68212
IVF Method*
Flexibility
function G(ω)
IVFM solution
GH
1
= transfer functions (displacement/force)
Iteration on weighted least squares to
minimize the estimation error in:
GH=I+e
SFD force
coefficients
(K, C, M)SFD = (K, C, M) – (K, C, M)S
SFD coefficients
Test system
* Instrumental Variable Filter Method (IVFM) (Fritzen, 1986, J.Vib, 108)
Measurement errors affect little identified parameters
Support structure
13
Typ. impedances- lubricated SFD
fstart
Re(HXX)[MN/m]
fstart
0
HXX20

 40
fend
fend
0
 20
 40
 60
0
rxxre 
0100
2 0.997
Rrxx
 0.997
XXre
0.997
Re
100200
200300
300
Im (Hxx) Im (Hxx)
30
30
Im(HYX)[MN/m]
20
 60
Real (Hxx)
Real (Hxx)
20
fstart
fstart
rxxIm 
2
 0.976
 0.976
rxx
RXX
ImIm
20
20
10
10
0
0
0
Frequency (Hz)
GT2012-68212
0100
f
end
0.976
100200
fend
200300
Frequency (Hz)
Im(H)/w
CXX [MNs/m]
f start
CXX40
0
40
40
fstart
CXX
0
 60
0
200
300
Im (Hyy) Im (Hyy)
fstart
fstart
20
20
10
10
0100
100200
200300
300
0
0
Short SFD eS=0; r =0.05cB
0
0100
fend
fend
ryyIm 
ryyre  0.995
ryyre  0.995
Frequency
(Hz)
 40
 40
100
30
30
fend
fend
20
20
0
 20
0
 20
 60
Real (Hyy)Real (Hyy)
fstart
20
f end
100200
300
Physical
model
Re(HXX)= K-w2M
and Im(HXX)=Cw
agree with test
data.
Damping C is
constant over
0.954 the frequency
range
ryyIm 
0.954
200300
300
14
SFD force coefficients - theory
GT2012-68212
Centered journal (es=0), no lubricant cavitation
Two film lands separated by a plenum: central groove has no
effect on squeeze film forces.
 tanh  L  
R 
 D 
*
 CYY  2 12 π  L   1 
L

c 
D 

3
Damping
*
C *  C XX

L  
π  LR3  tanh  D  
 2
1
L

c 
D 

Inertia
*
*
M *  M XX
 M YY
Stiffness
KXX = KYY = KXY = KYX = 0
Y
X
15
GT2012-68212
Normalization of experimental coefficients
SHOW ratio with respect to predictions from classical theory:
C C
Long damper
Land length 1”, 5.55 mil
C*
C*A = 6.79 kN.s/m,
M M
M
*
M*A = 2.98 kg
Ratio~(L/c)3~7.5
Short damper
Land length 0.5” , 5.43 mil
C*A = 0.92 kN.s/m,
M*A = 0.39 kg
Identification procedure gives NO cross-coupled
coefficients for test SFDs.
16
GT2012-68212
Experimental SFD force coefficients
open ends short length damper
1/2 inch lands, c=5.43 mil = 0.138 mm
0.5 inch
Top Land
Central groove
0.5 inch
Bottom Land
17
CXX
Damping coefficients
SFD direct damping coefficients
6
45o
5
es = 0.29 cB
4
c
es
X
3
es = 0
2
1
XX SFD
0.0
Damping coefficients
Y
es = 0.44 cB
C
Damping coefficients
0
CYY
GT2012-68212
vs orbit
amplitude
0.2
6
0.4
0.6
0.8
1.0
es = 0.44 cB
5
4
es = 0.29 cB
3
es = 0
2
1
C
Damping coefficients
0
YY SFD
0.0
0.2
0.4
0.6
0.8
1.0
CXX , CYY
first decrease and
then increase with
orbit amplitude.
Coefficients are
isotropic
CXX ~ CYY
Orbit amplitude (r /cB)
18
Short SFD (12.7 mm lands, c=0.138 mm)
SFD added mass coefficients
MXX
Mass coefficients
35
Y
e s = 0.44 c B
30
45o
25
c
e s =0.29 c B
20
15
X
e s= 0
5
XX SFD
0.0
0.2
0.4
0.6
0.8
1.0
35
Mass coefficients
es
10
M Coefficients
Mass
0
MYY
GT2012-68212
vs orbit amplitude
30
e s =0.44 c B
25
20
15
e s = 0.29 c B
MXX , MYY
decrease with
amplitude of motion,
as prior tests* and
theory show**
es= 0
10
5
M
Mass
Coefficients
0
YY SFD
0.0
0.2
0.4
0.6
0.8
1.0
Orbit amplitude (r /cB)
*Design and Application of SFDs in Rotating
Machinery (Zeidan, San Andrés, Vance, 1996,
Turbomachinery Symposium)
** SFDs: Operation, Models and Technical
Issues (San Andrés, 2010)
19
Short SFD (12.7 mm lands, c=0.138 mm)
GT2012-68212
Experimental SFD force coefficients open
ends long damper
1 inch lands, c=5.55 mil=0.141 mm
Top Land
1.0 inch
Central groove
1.0 inch
20
SFD direct damping coefficients
GT2012-68212
vs static
eccentricity
Y
All orbits (circular & elliptic)
CXX
Damping coefficients
45o
6
c
Amplitudes of motion:
2
6
Damping coefficients
X
4
0
CYY
es
CXXSFD
0.0
0.2
0.4
0.6
4
2
CYYSFD
0
0.0
0.2
0.4
CXX ~ CYY
with amplitude of motion
& orbit shape.
SFD forced response is
independent of BC
kinematics.
Static eccentricity ratio ( eS/cA)
21
Long SFD (25.4 mm lands, c=0.141 mm)
SFD added mass coefficients
vs staticGT2012-68212
eccentricity
Y
All orbits (circular & elliptic)
45o
MXX
Mass coefficients
12
c
10
es
X
8
6
Amplitudes of motion:
4
2
M XX SFD
0
0.0
0.2
0.4
0.6
MYY
Mass coefficients
12
Added
Mass Coefficients
10
MXX ~ MYY not strong
function of amplitude of
motion or orbital shape &
increasing with static
eccentricity
8
6
4
2
M YY SFD
0
0.0
0.2
0.4
0.6
Static eccentricity ratio ( e S /c A )
Added
Mass Coefficients
22
Long SFD (25.4 mm lands, c=0.141 mm)
GT2012-68212
Recorded dynamic pressures in groove
and film lands
1.0 “
23
Dynamic pressures
Piezoelectric pressure sensor (PCB) locations
GT2012-68212
Side view:
Sensors located at middle plane of film lands
Bearing Cartridge
PCB
groove
Mid-plane
PCB top land
PCB bottom land
Piezoelectric sensors:
2 in the top land,
2 in the bottom land 24
2 in the groove
Dynamic pressures: films & groove
GT2012-68212
Whirl frequency 130 Hz
Pressures
film lands
film atlands
pressure (psi)
psi 10
0.69 bar
5
0
0
5
 10
-0.69 bar
0
1
2
3
Top and bottom film
lands show similar
pressures.
4
time (-) of periods
Number
top land (120 deg)
bottom land (120 deg)
Pressuresgroove
at central groove
pressure (psi)
psi
4
0.28 bar
2
0
0
2
4
0
1
2
3
4
Dynamic pressure in
the groove is
not zero!
-0.28 bar
Number
of periods
time (-)
groove (165 deg)
groove (285 deg)
1.0 “
Long SFD. es=0, r=0.1cA. PG = 0.72 bar
25
Dynamic pressures: films & groove
GT2012-68212
Whirl frequency 200 Hz
filmat film
lands
Pressures
lands
pressure (psi)
psi 10
0.69 bar
5
0
0
5
 10
-0.69 bar
0
1
2
3
4
Number time
of time
(-) periods
top land (120 deg)
bottom land (120 deg)
Number of time periods
groove
Pressures at central groove
pressure (psi)
psi
0.69 bar
10
0
0
 10
 20
Film and groove
dynamic pressures
increase with
excitation frequency.
-1.40 bar
0
1
2
3
Pressure waves show
spikes (high
frequency content),
typical of air
ingestion &
entrapment
4
(-) periods
Numbertime
of time
groove (165 deg)
groove (285 deg)
1.0 “
Long SFD. es=0, r=0.1cA. PG = 0.72 bar
26
P-Ppressure
pressure (psi) (psi)
P-P dynamic
peak-peak pressures
Peak-peak dynamic
pressures
Top land (120)
Bottom land (120)
Groove (165)
40
40
2.8 bar
Top land
30
(120o)
GT2012-68212
Piezoelectric pressure sensor
(PCB) location
Bearing Cartridge
2.1 bar
groove
20
top land
bottom land
Bottom land (120o)
10
0
1.4 bar
Groove (165o)
0.7 bar
0.0 bar
0
100
200
Frequency
[Hz] (Hz)
Frequency (Hz)
Frequency
Mid-plane
Groove pressures are as large as in the film lands.
At the highest whirl frequency, groove pressure > 50% film
land pressures
27
Ratio of groove/film land pressures
GT2012-68212
peak-peak pressures
Top land (120)
Top land (240)
Groove
generates
large
hydrodynamic
pressures!
groove
lands (top)
3
P-P pressure (psi)
P-P pressure ratios
4
2
1
0
0
1.0
0
100
100
200
200
frequency (Hz)
c=5.5 mil
(0.141 mm)
3/8”~70 c
Frequency (Hz)
1“
0.5”
1”
28
GT2012-68212
Comparisons to predictions from a
modern model
29
Model SFD with a central groove
SFD geometry and nomenclature
Use effective depth
d= Xc
Lubricant in
Bearing
orifice
Lubricant in
do
dG
groove
GT2012-68212
L
c : clearance
LG
film land
recirculation
zone
End seal
Lubricant out
separation line
streamline
d
Journal
z
D, diameter
Effective groove depth
Lubricant out
Solve modified Reynolds equation (with fluid inertia)
  3 P
h
R    R 
2
   3 P
h

h
2
h

h
  12 
2

z

z

t

t



30
* San Andrés, Delgado, 2011, GT2011-45274.
Damping Coefficients (Short SFD)
Damping coefficients
10
Short SFD
Short SFD, dη = 2.8cB
Predicted coefficients
agree well with test data.
CXX (prediction)
8
GT2012-68212
CXX (test data)
6
Damping coefficients
increase moderately with
static eccentricity
4
2
0
0.0
CYY (prediction)
CYY (test data)
0.1
0.2
Test coefficients are ~
isotropic, but predicted are
unequal, CXX > CYY
0.3
0.4
Static eccentricity ratio (es / cB)
circular orbits r/c = 0.1
0.5
0.6
Test coefficients are ~ 4-6
larger than simplified
formulas
31
Inertia coefficients
Inertia Coefficients (Short SFD)
40
M
YY
Short SFD
M
(test data)
XX
GT2012-68212
Predictions match well the
test data.
(prediction)
30
20
M
YY
(prediction)
Inertia coefficients increase
moderately with static
eccentricity.
MXX (test data)
10
Predicted MXX > MYY
Short SFD, dη = 2.8cB
0
0.0
0.1
0.2
0.3
0.4
Static eccentricity ratio (es / cB)
circular orbits r/c = 0.1
0.5
0.6
Test coefficients are ~ 20-30
larger than simplified
formulas
32
Damping Coefficients (Long SFD)
Damping coefficients
10
Long SFD
GT2012-68212
Predicted coefficients agree
well with test data.
Long SFD, dη = 1.6cA
CXX(prediction)
8
6
Damping coefficients
increase more rapidly for the
long damper.
C (test data)
XX
4
2
CYY(prediction)
CYY(test data)
0
0.0
0.1
The test and predicted
coefficients are not very
sensitive to static
eccentricity (es).
0.2
0.3
0.4
Static eccentricity ratio (es / cA)
circular orbits r/c = 0.1
0.5
0.6
Test coefficients are ~ 3-4
larger than simplified
formulas
33
Inertia coefficients
Long SFD
Inertia coefficients are
underpredicted
Inertia Coefficients (Long SFD)
12
MYY (test data)
10
MXX (test data)
Coefficients grow moer
rapidly with static
eccentricity than in short
damper.
8
6
MYY (prediction)
MXX (prediction)
Tests and predicted force
coefficients are not
sensitive to static
eccentricity (es)
4
2
GT2012-68212
Long SFD, dη = 1.6cA
0
0.0
0.1
0.2
0.3
0.4
Static eccentricity ratio (es / cA)
circular orbits r/c = 0.1
0.5
0.6
Test coefficients are ~ 8-10
larger than simplified
formulas
34
Conclusions
GT2012-68212
For both dampers and most test conditions: crosscoupled damping and inertia force coefficients are small.
SFD force coefficients are more a function of static
eccentricity than amplitude of whirl. Coefficients change
little with ellipticity of orbit.
Long damper has ~ 7 times more damping than short
length damper. Inertia coefficients are two times larger.
•Predictions from modern predictive tool agree well with
the test force coefficients.
35
Conclusions & update
GT2012-68212
• 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
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.
36
Acknowledgments
Thanks to
GT2012-68212
• Pratt & Whitney Engines
• students Sanjeev Seshaghiri, Paola Mahecha,
Shraddha Sangelkar, Adolfo Delgado,
Sung-Hwa Jeung,
Sara Froneberger, Logan Havel, James Law.
Questions (?)
Learn more at http://rotorlab.tamu.edu
37
Relevant Past Work
GT2012-68212
•
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.
38
TAMU references
SFDs
GT2012-68212
2011
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, NonCircular 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 GT200850528)
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
39
Film Damper," ASME Journal of Engineering for Gas Turbines and Power, Vol. 118, 4, pp. 810-815
Select effective groove depth
GT2012-68212
Predictions overlaid with test data to estimate effective groove depth
Short SFD
Long SFD
5
8
6
4
test data
2
Predictions
0
1c
dη = 2.8cB
10 c
Groove depth (dη)
dη = 2.8 cB
100 c
Damping coefficients
Damping coefficients
10
4
3
test data
2
Predictions
1
0
1 c dη = 1.6cA
10 c
100 c
Groove depth (dη)
dη = 1.6 cA
40