Transcript Document

32nd Turbomachinery Research Consortium Meeting
Identification of SFD force
coefficients
Large Clearance Open Ends SFD
TRC-SFD-01-2012
Luis San Andrés
Mast-Childs Professor
May 2012
TRC Project 32513/1519FB
Linear Nonlinear Force Coefficients for SFDs
1
SFD with a central groove
lubricant
film
anti-rotation
pin
shaft
journal

oil inlet
Feed
groove
ball
bearing
housing
Typical squeeze film damper (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.
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.
2
P&W SFD test rig
Isometric view
Static loader
Shaker assembly (Y
direction)
Shaker assembly
(X direction)
Top view
Static loader
Shaker in Y
direction
Shaker in X
direction
SFD test
bearing
3
Test rig description
shaker Y
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
4
SFD Test Rig – cut section
Test rig main features
Piston ring seal
(location)
Test Journal
Bearing Cartridge
Supply orifices (3)
Journal diameter: 5.0 inch
Film clearance: 9.9 mil
Film length: 2 x 1 inch
Support stiffness: 100 klbf/in
Circumferential groove
Flexural Rod
(4, 8, 12)
Main support
rod (4)
Journal Base
Pedestal
in
5
Lubricant flow path
Oil
inlet
in
ISO VG 2 oil
6
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
Y
Y
static load
e
eS
45o
X
X
r
c
centered and offcentered circular
orbits
7
Structure static stiffness
•Pull test using static loader to determine static structure stiffness
static radial load (lbf)
F
Y
1335
300
X
200
890
100
445
K S ~ 100 klbf/in
0
0
0.5
1
1.5
2
2.5
static radial eccentricity,
3
e S(mil)
3.5
4
(101.6 μm)
8
static radial load (N)
1780
400
Structural parameters
• Dry test system
• Circular Centered
Orbits
• Frequency 50-210 Hz
Direct
XX
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%
9
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 Oil
Oil in, Qin
Viscosity 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
0.500
0.375
Land length, L [inch]
1.0 x 2
Total Length [inch]
2.5
Journal (D)
Oil out, Qt
End groove
Central
groove
c
L
½L
L
Bearing
Cartridge
End groove
Oil out, Qb
Oil collector
Oil out
Base
Support
rod
10
SFD force coefficients
Y
IVFM parameter identification method
45o
c
SFD
Difference between lubricated
system and dry system
(baseline) coefficients
CSFD=Clubricated - Cs
MSFD=Mlubricated - MBC
es
X
DRY system parameters
Ks = 100 klbf/in
MBC = 48 lb
Cs= 8-9 lbf-s/in
Nat freq = 148-156 Hz
Damping ratio = 4%
KSFD=Klubricated - Ks
11
SFD force coefficients - theory
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
Inertia
*
C *  C XX
*
*
M *  M XX
 M YY

L  
π  LR3  tanh  D  
 2
1
L

c 
D 

Y
Stiffness
KXX = KYY = KXY=KYX=0
X
12
SFD force coefficients - theory
Damping
C C
*
*
XX
3
L  
 R   tanh  D  
 C  2 12 π  L   1 
L

c 
D


*
YY
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)
Inertia
Y
X
*
*
M *  M XX
 M YY

L  
π  LR3  tanh  D  
 2
1
L

c 
D


c=5.5 mil
M* = 2.98 kg (6.58 lbm)
c=9.9 mil
M* = 1.67 kg (3.69 lbm)
13
Experimental SFD damping coeffs.
• Open ends SFD
• Circular orbits (r = 0.5 mil)
Y
45o
c
es
X
Damping coefficients (lb f-s/in)
SFD (1 inch land lengths)
31.5 kNs/m
180
160
C SFD
C YY c=5.5 mil
140
120
C XX c=5.5 mil
100
80
60
classical theory (40.6 lbf.s/in)
C YY c=9.9 mil
40
20
classical theory (7.1 lbf.s/in)
0
0.0
0.5
1.0
1.5
C XX c=9.9 mil
2.0
2.5
3.0
3.5
(89 μm)
static eccentricity, e S (mil)
14
Experimental SFD inertia coeffis.
Y
• Open ends SFDs
• Circular orbits (r = 0.5 mil)
45o
c
Added mass coefficients (lb)
SFD (1 inch land lengths)
es
80
X
36 kg
M SFD
70
M XX c= 5.5 mil
60
M YY c= 5.5mil
50
40
M YY c= 9.9 mil
30
20
M XX c= 9.9 mil
10
classical theory (3.7 - 6.6 lb)
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
89 μm
static eccentricity, e S (mil)
15
Pressure sensors in bearing
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
BC
16
Dynamic pressures: films & groove
Whirl frequency 130 Hz
Pressures
film lands
filmatlands
psi10
pressure (psi)
ASME GT2012-68212
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
time (-)of periods
groove (165 deg)
groove (285 deg)
17
es=0, circular orbit r=0.5 mil. Groove pressure PG = 0.72 bar
P-P pressure (psi)
P-P dynamic pressure (psi)
Peak-peak lubricant pressures
Piezoelectric pressure sensors
(PCB) location
peak-peak pressures
207 (kPa)
30
30
2020
Top land (120)
Top land (240)
Bottom land (120)
Bottom land (240)
Groove (165)
Groove (285)
Bearing
Cartridge
Lands
(top & bottom)
groove
top land
bottom
land
1010
groove
000
100
100
frequency (Hz)
c=5.5 mil
Frequency (Hz)
200
200
Midplane
18
pressure (psi)
P-P dynamic
P-P pressure (psi)
Peak-peak lubricant pressures
Piezoelectric pressure sensors
(PCB) location
peak-peak pressures
1515
Top land (120)
Top land (240)
Bottom land (120)
Bottom land (240)
Groove (165)
Groove (285)
1010
Bearing
Cartridge
groove
groove
top land
bottom
land
55
lands
00
(top & bottom)
0
100
100
frequency (Hz)
c=9.9 mil
Frequency (Hz)
200
200
Midplane
19
Ratio of groove/film land pressures
peak-peak pressures
Top land (120)
Top land (240)
Groove
generates
large
hydrodyna
mic
pressures!
groove
lands (top)
3
P-P pressure (psi)
P-P pressure ratios
4
2
1
0 00
1.0
100
100
200
200
frequency (Hz)
c=5.5 mil
3/8”~70 c
Frequency (Hz)
1“
0.5”
1”
20
Ratio of groove/film land pressures
peak-peak pressures
Top land (120)
Top land (240)
groove
lands (top)
3
P-P pressure (psi)
P-P pressure ratios
4
2
1
0
1.0
0
100
100
Groove
generates
larger
hydrodyna
mic
pressures!!
Larger than
in the film!
200
200
frequency (Hz)
c=9.9 mil
Frequency (Hz)
3/8”~35 c
1“
0.5”
1”
21
Model SFD with a central groove
SFD geometry and nomenclature
Lubricant in
Use effective depth
d=1.6c
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 fluid inertia)
  3 P
h
R    R 
2
   3 P
h

h
2
h
 h
  12 
2

z

z

t

t



22
Example predicted pressure field
Feed hole (3 x 120 deg)
groove
groove
0.60
0.5-0.6
0.4-0.5
0.50
0.3-0.4
0.2-0.3
0.1-0.2
0.40
0.0-0.1
0.30
land
z
81
89
axial
coordi
nate
S8

49
57
65
0.00
73
17
25
33
0.10
41
9
1
0.20
S1
Inner Film
Pressure
Pressure
(bar)
Static
pressure at
groove shows
circumferenti
al variation
due to feed
holes spacing
circ coordinate (node #)
1“
3/8”~35 c
0.5”
1”
23
Damping coefficients: test & predictions
Damping coefficients (lb f-s/in)
Model predicts
200
180
CSFD
lines :
predictions
CYY c=5.5 mil
160
symbols:
test data
140
large c SFD:
less damping
than test values
CXX c=5.5 mil
120
100
small c SFD:
larger damping
coefficient than
test values
CXX c=9.9 mil
80
60
CYY c=9.9 mil
classical theory (40.6 lbf.s/in)
40
20
classical theory (7.1 lbf.s/in)
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
static eccentricity, e S (mil)
24
Inertia coefficients: test & predictions
Added mass coefficients (lb)
Model predicts
80
70
MSFD
small c SFD:
less inertia than
test values
lines :
predictions
MXX c=5.5 mil
MYY c=5.5mil
60
symbols:
test data
Large c SFD:
larger inertia than
test values
50
40
MYY c=9.9 mil
30
20
Classical
theory
predicts ~ 1/7
of test values
MXX c=9.9 mil
10
classical theory (3.7 - 6.6 lb)
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
static eccentricity, e S (mil)
25
Conclusions
Conducted measurements of dynamic load response in
large clearance (c=9.9 mil) open ends SFD with circular
orbits, centered and off-centered.
• 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.
26
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.
27
Proposed tasks TRC (2012-13)
1. Test damper w/o groove 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
X
elliptical orbits
28
TRC Budget (2012-13)
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
$
Total Cost:
Year I started
on Jan 2012
Y
centered journal
X
circular orbits
2,200
$ 28,470
Y
Y
off-centered journal
X
X
elliptical orbits
29
Acknowledgments
Thanks to
• Pratt & Whitney Engines
• Turbomachinery Research Consortium
• Sung-Hwa Jeng, RA for making the presentation
Learn more
http:/rotorlab.tamu.edu
Questions (?)
30