Post on 29-Mar-2015
transcript
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Luis San Andrés Mast-Childs Professor
SFD EXPERIMENTAL TESTING & ANALYTICAL METHODS DEVELOPMENT
High Load SFD Test RigIdentification of SFD
force coefficients
May 2011
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Static loader
Shaker assembly (Y direction)
Shaker assembly (X direction)
Static loader
Shaker in X direction
Shaker in Y direction
SFD test bearing
PW-SFD test rig (2010)
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Test rig description
shaker Xshaker Y
Static loader
SFD
basesupport rods
Static loader
X
Y
shaker Xshaker Y
Static loader
SFD
basesupport rods
Static loader
X
Y
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Flow path & main features
in
Oil out, Qb
BaseSupportrod
Bearing Cartridge
Journal (D) Oil out, Qt
Oil in, Qin
Central groove
L, 2L
L
L, 2L
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, 2L
L
L, 2L
End groove
End groove
Oil outOil collector
BaseSupportrod
Bearing Cartridge
Journal (D) Oil out, Qt
Oil in, Qin
Central groove
L, 2L
L
L, 2L
End groove
End groove
Oil outOil collector
c
Test rig main features
Journal diameter: 5.0”
Film clearance: (A) 5.55mil (B) 5.43mil
Film length: (A) 2x1”, (B) 2 x 0.5“
Centering stiffness: variable
ISO VG 2 oil
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Test rig cross section – rods installation
12 x Φ 7/8
8
9
5.6
4.755
All dimensions in inches
4 x Φ 7/8
Test rig materials
Journals, journal base, pedestal, bearing cartridge, Main support
rods : AISI 1020 steel
Flexural rods: Alloy Steel per ASME
B18.3
Φ4.75
BC OD Φ7.50
Φ11.00
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Sensor locations
Eddy current sensors and accelerometers
θ= 180o and 270o
Journal B
Top Land
Bottom Land
Central groove
Eddy current sensor (Proximity probe)
Side view: Sensors located in central groove
Top view
θ= 270o
θ= 180o
X Piezoelectric accelerometer
Y Piezoelectric accelerometer
θ= 90o
θ= 0oX eddy current sensor (X proximity probe)
Y eddy current sensor (Y proximity probe)
θ= 0o and 90o
Top Land
Bottom Land
Piezoelectric Accelerometer
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Pressure sensors
Side view: Sensors located at middle plane of film lands
Top view
θland = 210o
θland = 330o
θland = 210o and 330o
Journal B
Top Land
Bottom Land
Central groove
Bottom Land
and,Locations
Central groove
1.5 inch
0.5 inch
0.5 inch
Top Land
BC
PCB (pressure sensors)
PCB and Entran
PCB (Dynamic)
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Pressure sensors
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Test results for(c) SFD force coefficients – Comparison between short and long open ends dampers
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0
50
100
150
200
250
0 0.5 1 1.5 2 2.5 3
Static eccentricity e s [mil]
Dir
ec
t d
am
pin
g c
oe
ffic
ien
t [l
bf-
s/i
n]
Cxx 1/2 inchCyy 1/2 inchCxx 1 inchCyy 1 inch
Long and short SFDs (circular orbits)
compare SFD damping
CXX ~ CYY
Short (L=0.5 inch)
CXX ~ CYY
Long (L=1 inch)
Ratio of coefficients ~ (L/c3) 3
1
0.5
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3 3
15.55 7.49
0.55.43
inch
inch
A
XX A
XX B
B
LC c
C Lc
11
0
5
10
15
20
25
30
35
40
45
50
0 0.5 1 1.5 2 2.5 3
Static eccentricity e s [mil]
Ad
de
d M
as
s
co
eff
icie
nts
[lb
]
Mxx 1/2 inchMyy 1/2 inchMxx 1 inchMyy 1 inch
compare SFD inertia
MXX , MYY
Short (L=0.5 inch)
MXX , MYY
Long (L=1 inch)
Ratio of coefficients ~ (L/c)
1
0.5
15.55 1.96
0.55.43
inch
inch
A
XX A
BXX
B
LM c
LMc
Long and short SFDs (circular orbits)
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Film and groove dynamic pressures
Long open ends SFD. Centered bearing es=0, circular orbit r=0.1cA. Groove pressure PG = 0.72 bar
Frequency=250 Hz
0 1 2 3 410
5
0
5
10
top land (120 deg)bottom land (120 deg)
Pressures at film lands
time (-)
pres
sure
(ps
i) Lands
0 1 2 3 420
10
0
10
groove (165 deg)groove (285 deg)
Pressures at central groove
time (-)
pres
sure
(ps
i) GrooveTop Land
Bottom Land
Central groove
1 inch
PCB (pressure sensors)
1 inch
Top Land
Bottom Land
Central groove
1 inch
PCB (pressure sensors)
1 inch
L/D=0.2 x 2
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Film and groove peak-peak pressures
Long open ends SFD. Centered bearing es=0, circular orbit r=0.1cA. Groove pressure PG = 0.72 bar
Frequency20-250 Hz
Top Land
Bottom Land
Central groove
1 inch
PCB (pressure sensors)
1 inch
Top Land
Bottom Land
Central groove
1 inch
PCB (pressure sensors)
1 inch
0 100 2000
10
20
30
40
Top land (120)Bottom land (120)Groove (165)
peak-peak pressures
Frequency (Hz)
P-P
pre
ssu
re (
psi
)
Bottom land
Top land
groove
Land length=1 inGroove width=0.5 in depth = 3/8 in (75 c)
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Test results for(d) SFD force coefficients – Comparison between open ends and sealed ends long dampers
I
A
B
II
BC
groove
journal Top land
Bottom land
A
B
15Open and sealed ends long SFD (circular orbits)
compare SFD damping
CXX ~ CYY
Open ends
CXX ~ CYY
Sealed ends
100
150
200
250
300
350
400
450
0.0 0.5 1.0 1.5 2.0 2.5
Da
mp
ing
co
eff
icie
nts
(lbf-
s/in
)
Eccentricity es (mil)
SFD (1 inch land lengths)
CSFD
open ends CXX
circular orbits
open ends CYY
Sealed ends CYY (B-B)Sealed ends CXX(B-B)
I
A
A
B
B
II
BC
groove
journalTop land
Bottom land
B-B sealed SFD
I
A
A
B
B
II
BC
groove
journalTop land
Bottom land
B-B sealed SFD
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0
10
20
30
40
50
60
70
80
90
100
0.0 0.5 1.0 1.5 2.0 2.5
Ad
ded
mas
s co
effi
cien
ts (l
b)
Eccentricity es (mil)
SFD (1 inch land lengths)
MSFD
open ends MXX
Open ends MYY
circular orbits
Sealed ends MXX(B-B)
Sealed ends MYY(B-B)
Test data for open and sealed ends (circular orbits)
compare SFD inertia
MXX , MYY
Open ends
MXX , MYY
Sealed ends
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Conclusions: Learning from tests and predictions
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Summary of learningOpen ends long damper shows ~ 7 times more damping than
short length damper. Inertia coefficients are two times larger.
SFD force coefficients are more a function of static eccentricity (max. 40%c) than amplitude of whirl (max 40%c) changing little with ellipticity of orbit (aspect ratios 1:1, 2:1 & 5:1)
Piston ring faces orientation affects leakage and force coefficients. Long Sealed SFD shows ~2.6 times more damping than open ends SFD
Code benchmarked for long and short SFDs (open and sealed ends).
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Proposed work (TRC)
Whirl Orbit Analysis for Identification of SFD force coefficients
Linear-Nonlinear Force Coefficients for Squeeze
Film Dampers
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Types of journal motionx= R
Y
X
e
h
R
e: amplitude of motion
whirl frequency
eXo
eYo
whirlingjournal
Film thickness
x= R
Y
X
2rX
rX, rY : amplitudes of motion
whirl frequency
eo
2rY
(a) small amplitude journal motions (b) large amplitude journal motions
K,C, M (force coefficients)RBS stability analysis
Applications:
FX, FY (reaction forces)RBS imbalance response& transient load effects
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SFD predictive codeOrbit
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
X/c
Y/c
2rX
2rY
Code & GUI: virtual tool for prediction of SFD forced response
(a) Linear force coefficients (K,C,M)(b) Instantaneous reaction forces
along orbital path (c) Automated orbit analysis for NL
parameter identification
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Purpose of whirl orbit analysis
for specified whirl orbit and over specifiedfrequency range: • predict SFD reaction forces vs. time,• conduct Fourier analysis, &• identify SFD linearized force coefficients
Orbit
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
X/c
Y/c
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SFD example
Journal Diameter 5.0 in
Total Length 1.0 in
Land Clearance 5.0 mil
NO Central Groove
Feed holes 3 (120deg)
Axial Length 0.5 in
Ambient Pressure 0.0 psig
Supply Pressure 10 psig
Cavitation Pressure -14.70 psig
Supply Temperature 77 oF
Viscosity at Tsupply 0.43 Reyns
Density 49 lb/ft3
L
Journal
Bearing
X
Y
D
Feed hole
ASection A-A
Open Ends SFD with feed holes
Pa, ambient pressure
Ps, supply pressureL
Journal
Bearing
X
Y
D
Feed hole
ASection A-A
Open Ends SFD with feed holes
Pa, ambient pressure
Ps, supply pressure
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whirl orbit induces forces
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
eX/c
e Y/c
SFD open ends L=1.0 inch - with holes - no central groove
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
40.0
60.0
80.0
-250.0 -200.0 -150.0 -100.0 -50.0 0.0 50.0 100.0
FXF
Y
SFD open ends L=1.0 inch - with holes - no central groove
lbf
SFD reaction force
Fundamental 1X Force
es/c=0.5c r/c=0.25c
Eccentric (Off-center)Elliptical orbit
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SFD 1X forces do not reproduce NL forces
SFD Forces: predicted and 1X
-250
-200
-150
-100
-50
0
50
100
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Bea
rin
g r
eact
ion
fo
rce
FX
FY
FX_1Fourier
FY_1Fourier
Fraction of Period
SFD open ends L=1.0 inch - with holes - no central groove
lbfes/c=0.5c r/c=0.25c
SFD reaction force
Fundamental 1X Force
Frequency 180 Hz
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
eX/c
e Y/c
SFD open ends L=1.0 inch - with holes - no central groove
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SFD reaction forces
The SFD instantaneous reaction force superimposes a
dynamic force to a static force, i.e., F=Fstatic+Fdyn.
The dynamic components of the SFD reaction forces are modeled in a linearized form as
dyn SFD SFD SFDF K z C z + M z
where z is a vector of dynamic displacements and
(K, C, M)SFD are matrices of stiffness, viscous damping and inertia force coefficients
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Analysis (I)The dynamic or time varying part of the SFD reaction force is periodic with fundamental period T=2/.
Using Fourier series decomposition,
2 31 ....i t i t i te e e dyn II IIIF F F F
To first order effects (fundamental frequency)
1i te dynF F 2
1 i SFD SFD SFD 1 1F K M C z H z
2 i SFD SFD SFDH K M Cwhere
is the matrix of damper impedances
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Analysis (II)
The code predicts the SFD time varying reaction forces for the orbital path and delivers the fundamental Fourier components of motion and forces, i.e. z and F. Forward and backward whirl orbits ensure linear independence of the two SFD reaction forces.
Solution of the system of algebraic equations:
leads to the determination of the impedances:
HXX, HXY,HYX, HYY
1 2 1 2F F H z z
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Analysis (III)
The analysis stacks impedances for a set of frequencies (k=1,2,….N) from which, by linear curve fits, one determines :
)Re(2 HMK SFDSFD
)Im(HCSFD
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SFD Real Impedances vs. frequency
-1.00E+04
-5.00E+03
0.00E+00
5.00E+03
1.00E+04
1.50E+04
2.00E+04
2.50E+04
0 50 100 150 200 250Imp
edan
ces
(rea
l par
t)
Hxx
Hyy
Hxy
Hyx
SFD open ends L=1.0 inch - with holes - no central groove
lbf/in
Whirl frequency (Hz)
Re(H)
HYY fits well model K-M2
HXX will give M<0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
eX/c
e Y/c
SFD open ends L=1.0 inch - with holes - no central groove
Frequency range 20-200 Hz
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SFD Ima Impedances vs. frequency
-2.00E+04
0.00E+00
2.00E+04
4.00E+04
6.00E+04
8.00E+04
1.00E+05
0 50 100 150 200 250Imp
edan
ces
(imag
par
t)
Hxx
Hyy
Hxy
Hyx
SFD open ends L=1.0 inch - with holes - no central groove
lbf/in
Whirl frequency (Hz)
Ima(H)
HYY fits OK model C
HXX gives average C
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
eX/c
e Y/c
SFD open ends L=1.0 inch - with holes - no central groove
Frequency range 20-200 Hz
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SFD NL-Linear force coefficients
Linear force model
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
eX/c
e Y/c
SFD open ends L=1.0 inch - with holes - no central groove
Mxx Myy Mxy Myx
lbm lbm lbm lbm
-5.0 2.0 0.2 0.2
Cxx Cyy Cxy Cyx
lbf-s/in lbf-s/in lbf-s/in lbf-s/in
68.5 37.7 -0.6 -0.6
Kxx Kyy Kxy Kyx
lbf/in lbf/in lbf/in lbf/in
2.12E+03 -2.11E+02 -6.35E+01 -6.13E+01
-250
-200
-150
-100
-50
0
50
100
-100 -80 -60 -40 -20 0 20 40 60 80
FourieranalysisLinearizedforcesNonlinearforces
FY vs FX
Frequency range 20-200 Hz
SFD NL force response
DISSIPATED ENERGY IN A PERIOD or MOTION
lbf-in -0.637Non-linear (from time transient response)
-0.590Linear from ALL force coefficients
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Proposed tasks (2011-12)
X
Y
X
Y
X
Y
elliptical orbitscircular orbits
centered journal off-centered journal
1. Test ACTUAL short length open ends damper with dynamic loads (20-300 Hz) inducing off-centered elliptical orbital motions with amplitude ratios (5:1) 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.
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Budget (2011-12)
X
Y
X
Y
X
Y
elliptical orbitscircular orbits
centered journal off-centered journal
Support for graduate student (20 h/week) x $ 1,800 x 12 months $ 21,600
Fringe benefits (0.6%) and medical insurance ($191/month) $ 2,419
Travel to (US) technical conference $ 1,200
Tuition three semesters ($3,802 x 3) $ 10,138
Supplies for test rig $ 1,500
Total Cost: $ 37,108
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Questions (?)