Transcript Document

33rd Turbomachinery Research Consortium Meeting
On the Forced Performance of a SFD Operating with
Large Amplitude Orbital Motions: Measurements and
Assessment of the Accuracy of the Linearized Force
Coefficients Model
TRC-SFD-01-2013
Luis San Andrés
Sung-Hwa Jeung
Mast-Childs Professor
Graduate Research Assistant
May 2013
TRC Project 32513/1519SF
Linear Nonlinear Force Coefficients for SFDs
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SFD with a central groove
lubricant
film
anti-rotation
pin
oil inlet
Feed
shaft
journal

groove
ball
bearing
housing
Typical squeeze film damper (SFD) with a central groove [1]
Conventional knowledge regards a
groove as indifferent to the kinematics
of journal motion, thus effectively
isolating the adjacent film lands.
Lubricant supplied
into a
circumferential
groove feeds
uniformly the
squeeze film
lands.
Whirl motion from
the journal
squeezes the
lubricant film
and generates
dynamic
pressures that
aid to damp the
rotor vibrations
2
SFD Test Rig – cut section
Test Journal
Bearing
Cartridge
Circumferential
groove
Piston ring seal
(location)
Supply orifices (3)
Main support
rod (4)
Flexural
Rod (4, 8,
12)
Journal Base
Pedestal
in
SFD Test Rig – cut section
Geometry (three feed holes 120o apart)
Journal Diameter, D
12.7 cm (5.0 in)
Land Length, LF
2.54 cm (1.0 in)
Radial Land Clearance, c
251 μm (9.9 mil)
Damper Axial Length
6.35 cm (2.5 in)
(two lands + groove), L
Feed orifice Diameter, ϕ
2.54 mm (0.1 inch)
Central Groove
Groove Axial length, LG
1.27 cm (0.5 inch)
Groove Depth, d
0.96 cm (0.38 inch)
Lubricant flow path
ISO VG 2 oil
Oil
inlet
in
Lubricant properties (ISO VG 2 )
Supply temperature, Tin
25 °C (77 °F)
Lubricant viscosity @ Tin , μ
2.96 cP
Lubricant density, ρ
785 kg/m3 (49 lb/ft3)
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Funded TRC (2012-13)
$ 28,470
1. Test damper with dynamic loads (20-300 Hz) inducing offcentered 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.
Y
centered journal
X
circular orbits
Y
Y
off-centered journal
X
elliptical orbits
X
Tests conducted
Excitation frequencies 10 – 100 Hz
Evaluate SFD dynamic force coefficients from
Y
Max. clearance (c) : 251 μm
es = 0.76 c
es = 0.51 c
es = 0.25 c
Static journal eccentricity
(e) to 76% of radial
clearance (c).
es = 0 c
X
Operating conditions
Orbit amplitude, r
Static eccentricity, es
Whirl frequency, 
Squeeze film Reynolds
No.
0.02 mm – 0.178 mm
0.0 – 0.190 mm
10 - 100 Hz
2
 max rmax
Res 

=5.26
X Displacement [μm]
7
Y Displacement [μm]
Circular orbit journal
motions with
orbit amplitudes (r) from
8% to 71% of radial
clearance (c).
Parameter identification procedure
Step 1 : Model system (2-DOF)
F
EOM: Time Domain
KL
CL
ML
EOM: Frequency Domain
[KL  iCL  2ML ]z  F  M BC a
Measured variables:
Unknown Parameters:
KL, CL, ML
(K, C, M)SFD = (K, C,M)L – (K, C, M)S
SFD coefficients
SFD
Test system
(lubricated)
Structure
Shaker force
Test SFD damping coefficients
Y
Damping coefficient
[kN.s/m]
CXX SFD
es = 0.51 c
es= 0.25
c
X
es= 0 c
eS=0.76c
12
10
eS=0.25c
eS=0.51c
8
es= 0.76 c
6
4
eS=0.0c
2
0.76
0.51
Static
0.25
eccentricity
0.00
0
0.1 0.2
0.3
0.4
0.5
Orbit amplitude (r/c)
0.6
0.7
(eS/c)
CXX ~CYY
Findings: SFD damping coefficients increase with increasing orbit amplitude
and static eccentricity. CXX increases dramatically above r/c > 50%
Test SFD added mass coefficients
Y
Added mass coefficient
[kg]
MXX SFD
es = 0.51 c
es= 0.25
c
X
es= 0 c
eS=0.76c
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16
14
12
10
8
6
4
2
0
es= 0.76 c
eS=0.51c
eS=0.25c
eS=0.0c
0.1 0.2
0.3
0.4
0.5
Orbit amplitude (r/c)
0.76
0.51 Static
0.25 eccentricity
0.00
0.6
0.7
(eS/c)
MXX ~MYY
Findings: SFD added mass coefficients increase with increasing static
eccentricity; but decrease with increasing orbit amplitude. MXX decreases
dramatically above r/c>50%
SFD effective force coefficients
For circular orbits (only), SFD forces reduce to
Fradial   K eff r
Ftangential  Ceff r
K X eff  K XX  CXY   M XX 2
C X  eff  
K XY

 C XX  M XY 
Y
r
r
-Fradial
X
-Ftangential
Test SFD effective stiffness
-Keff
structure
es/c=0.0
Findings: SFD effective stiffness decreases with increasing
excitation frequency and with orbit amplitude (a fluid inertia
effect).
Test SFD effective damping
Ceff
es/c=0.0
Findings: SFD effective damping increases with orbit
amplitude. Little dependency with frequency.
Pressure sensors in housing
Pressure sensor locations
Top view: Sensors around bearing circumference
and
Pressure
sensor
25.4 mm
12.7 mm
Top Land
Pressure
sensor
Central
groove
Bottom Land
25.4 mm
,
and
63.5 mm
Pressure
sensor
Central
groove
Side view: Sensors located at
middle plane of film lands
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14
BC
Film dynamic pressure profiles
es/c=0.0, 100 Hz
Central groove
Film lands
Magnitude of peak
pressure increases
with orbit amplitude.
Top and bottom film
lands show similar
pressures.
Dynamic pressure in
the groove is not nil.
Air ingestion region
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Film dynamic pressure profiles
A uniform pressure zone indicates air entrainment.
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Model SFD with a central groove
SFD geometry and nomenclature
Lubricant in
Use effective depth
Bearing
orifice
Lubricant in
do
dG
groove
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 temporal fluid inertia)
  3 P
h
R    R 
2
   3 P
h

h
2
h
 h
  12 
2

z

z

t

t



h : fluid film thickness
μ : lubricant viscosity
P : hydrodynamic pressure
R : journal radius
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Damping: predictions and test data
Y
c
es
45o
X
for small size orbits
(r/c=0.08).
predictions agree
with test
coefficients until
es=0.5 c.
At es/c=0.76
predictions are too
large (~28%)
classical theory (1.2 kN.s/m)
Test data much
larger than
simple theory
Model by San Andres (2011)
CXX
CYY
Test data
Test data
Prediction
Prediction
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Added mass: predictions & test data
Y
c
es
45o
X
Model predictions
agree well with
experimental
results.
Predicted added
masses increase
slightly with static
eccentricity
classical theory (1.67 kg)
Test data much
larger than
simple theory
Model by San Andres (2011)
MXX
MYY
Test data
Test data
Prediction
Prediction
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SFD mechanical energy dissipation
SFD reaction forces
Actual force
Linearized force
FSFD  L  MS z  CS z  KS z  M BCa
FSFDL  MSFDz  CSFDz  KSFDz
Mechanical work
Over a full period
of motion
E
 (F
X
x  FY y )dt
Work=Energy dissipation
100 Hz
EDIS<0 is negative work = energy dissipated by SFD
Findings: SFD work increases with increasing orbit amplitude.
Mechanical energy difference
100 Hz
Ediff 
0~5%
EDIS  EDISL
EDIS
~23%
Findings: Energy difference increases with increasing static eccentricity and
orbit amplitude. For r/c≤0.4 and es/c≤0.25, Ediff < ~5%
Conclusions
From circular orbit tests
(a) SFD damping coefficients increase with increasing orbit amplitude and
static eccentricity.
(b) SFD added mass coefficients increase with increasing static eccentricity
and decrease with increasing orbit amplitude.
Predictions correlate very well with test results for static eccentricity
es<0.5c and deviate with increasing orbit amplitude and static
eccentricity.
Goodness of linear force model
By means of comparing mechanical work in a period of motion; for
r/c≤0.4 and es/c≤0.25, linearized SFD forced parameters represent
well the actual SFD system
TRC-SFD-01-2013
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2013 proposal to TRC
Justification
Aircraft engines must endure sudden maneuver loads (blade
loss event, etc.)
Large size grinding machines require quick dissipation of
mechanical energy from sudden plunging motions (tool
contacts the working piece, etc.)
Ultra-short SFD (L/D < 0.2)
save space & weight; with lighter lubricants
to save fuel and reduce contamination; and
with tighter clearances because of better
materials & manufacturing.
2013 proposal to TRC
Objectives
•Conduct experiments to characterize the forced response of
a short length SFD (L/D=0.2) with sudden loads (400 lbf max).
•Build predictive tool to simulate SFD dynamic forced
performance.
Record SFD forced performance due to
sudden impulsive loads (amplitude and
time varying).
TRC Budget
2013-2014 Year III
Year III
Support for graduate student (20 h/week) x $ 2,200 x 12
months
$ 26,400
Fringe benefits (0.6%) and medical insurance ($197/month)
$
2,378
Travel to (US) technical conference
$
1,200
Tuition & fees three semesters ($227/credit hour)
$
8,688
Machine components and data storage
$
2,000
2013-2014 Year III $ 40,666
The TAMU SFD research program is the most renown in the
world. The proposed research is of interest of SFD
applications in gas turbines, hydrodynamic bearings in
compressors, cutting tool and grinding machines.
Thank you
Acknowledgments
Thanks to TAMU Turbomachinery Research
& Pratt & Whitney Engines
Questions (?)
Learn more at http://rotorlab.tamu.edu
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