Transcript Slide 1

SFD EXPERIMENTAL TESTING & ANALYTICAL METHODS DEVELOPMENT
High Load SFD Test Rig
Identification of SFD
force coefficients
Luis San Andrés
Mast-Childs Professor
May 2011
1
PW-SFD test rig (2010)
Static loader
Shaker assembly
(Y direction)
Shaker assembly
(X direction)
Static loader
Shaker in
Y direction
Shaker in
X direction
SFD test
bearing
2
Test rig description
Static loader
shaker Y
shaker X
SFD
Y
Static loader
support rods
base
X
3
Flow path & main features
Oil in, Qin
Test rig main features
in
Journal (D)
Oil out, Qt
End groove
Central
groove
c
L, 2L
L
L, 2L
Bearing
Cartridge
Journal diameter: 5.0”
Film clearance: (A) 5.55mil (B) 5.43mil
Film length: (A) 2x1”, (B) 2 x 0.5“
Centering stiffness: variable
End groove
ISO VG 2 oil
Oil out, Qb
Oil collector
Oil out
Base
Support
rod
4
Test rig cross section – rods installation
All dimensions in inches
9
8
4 x Φ 7/8
5.6
BC OD Φ7.50
12 x Φ 7/8
Test rig materials
Φ4.75
4.755
Journals, journal base, pedestal,
bearing cartridge, Main support rods
: AISI 1020 steel
Flexural rods: Alloy Steel per ASME
Φ11.00
B18.3
5
Eddy current sensors and accelerometers
Top view
Sensor locations
Y Piezoelectric
accelerometer
θ= 180o and 270o
θ= 90o
Top Land
Eddy current
sensor
(Proximity
probe)
Central
groove
θ= 180o
X eddy current sensor
(X proximity probe)
θ= 0o
Journal B
X Piezoelectric
accelerometer
Bottom
Land
θ= 0o and 90o
Top Land
Y eddy current sensor
(Y proximity probe)
θ= 270o
Side view: Sensors located in central groove
Piezoelectric
Accelerometer
Bottom
Land
6
Pressure sensors
θland = 210o and 330o
Top view
Top Land
0.5 inch
PCB (pressure
sensors)
Central
groove
0.5 inch
Bottom
Land
Locations
Journal B
,
θland = 330o
and
θland = 210o
Top Land
PCB (Dynamic)
1.5 inch
Central
groove
PCB and Entran
Bottom
Land
Side view: Sensors located at
middle plane of film lands
BC
7
Pressure sensors
8
Test results for
(c) SFD force coefficients –
Comparison between short and
long open ends dampers
9
Direct damping coefficient [lbf-s/in]
compare SFD damping
250
200
CXX ~ CYY
Long (L=1 inch)
150
3
C XX1inch
100
C XX 0.5 inch
50



3
 LA 
1
 c 
5.55  7.49
A


3
3
0.5
 LB 
 c 
5.43
B


Cxx 1/2 inch
Cyy 1/2 inch
Cxx 1 inch
Cyy 1 inch
CXX ~ CYY
Short (L=0.5 inch)
0
0
0.5
1
1.5
2
2.5
3
Static eccentricity e s [mil]
3
Ratio of coefficients ~ (L/c3)
Long and short SFDs (circular orbits)
10
compare SFD inertia
Added Mass coefficients [lb]
50
45
MXX , MYY
40
35
Long (L=1 inch)
30
25
MXX , MYY
20
15
10
M XX1inch
5
M XX 0.5inch
0
0




 LA 
1
 c 
5.55  1.96
A


0.5
 LB 
 c 
5.43
B

0.5
1
1.5
Mxx 1/2 inch
Myy 1/2 inch
Mxx 1 inch
Myy 1 inch
2
2.5
Short (L=0.5 inch)
3
Static eccentricity e s [mil]
Ratio of coefficients ~ (L/c)
Long and short SFDs (circular orbits)
11
Film and groove dynamic pressures
pressure (psi)
Pressures at film lands
10
Lands
5
0
5
 10
0
1
2
3
4
Frequency=250 Hz
time (-)
top land (120 deg)
bottom land (120 deg)
pressure (psi)
Pressures at central groove
10
Groove
0
Top Land
1 inch
 10
 20
PCB (pressure
sensors)
0
1
2
time (-)
groove (165 deg)
groove (285 deg)
3
Central
groove
4
1 inch
L/D=0.2 x 2
Bottom
Land
Long open ends SFD. Centered bearing es=0, circular orbit r=0.1cA.
Groove pressure PG = 0.72 bar
12
Film and groove
peak-peak
pressures
peak-peak pressures
Top land (120)
Bottom land (120)
Groove (165)
P-P pressure (psi)
40
Frequency20-250 Hz
Land length=1 in
Groove width=0.5 in
depth = 3/8 in (75 c)
30
20
PCB (pressure
sensors)
10
Top Land
groove
0
0
100
Frequency (Hz)
1 inch
Central
groove
200
1 inch
Bottom
Land
Long open ends SFD. Centered bearing es=0, circular orbit r=0.1cA.
Groove pressure PG = 0.72 bar
13
Test results for
(d) SFD force coefficients –
Comparison between open ends
and sealed ends long dampers
B
journal
I
Top land
A
groove
A
Bottom land
II
B
BC
14
compare SFD damping
B
Damping coefficients (lb f-s/in)
SFD (1 inch land lengths)
circular orbits
journal
I
Top land
A
groove
A
450
Sealed ends CYY (B-B)
Bottom land
II
Sealed ends CXX(B-B)
CSFD
400
B
CXX ~ CYY
350
BC
B-B sealed SFD
Sealed ends
300
250
open ends CYY
200
CXX ~ CYY
open ends CXX
150
Open ends
100
0.0
0.5
1.0
1.5
2.0
2.5
Eccentricity es (mil)
Open and sealed ends long SFD (circular orbits)
15
compare SFD inertia
Added mass coefficients (lb)
SFD (1 inch land lengths)
circular orbits
100
90
MXX , MYY
Sealed ends MYY(B-B)
Sealed ends
80
70
Sealed ends MXX(B-B)
60
Open ends MYY
50
40
MXX , MYY
open ends MXX
30
Open ends
20
MSFD
10
0
0.0
0.5
1.0
1.5
2.0
2.5
Eccentricity es (mil)
Test data for open and sealed ends (circular orbits)16
Conclusions:
Learning from tests and
predictions
17
Summary of learning
Open 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).
18
Proposed work (TRC)
Linear-Nonlinear Force
Coefficients for Squeeze
Film Dampers
Whirl Orbit Analysis for Identification of SFD
force coefficients
19
Types of journal motion
x= R
x= R
e: amplitude of motion
rX, rY : amplitudes of motion
whirl frequency
h
Film
thickness

Y
eYo
R
whirl frequency

eXo
Y
2rY
e
eo
whirling
journal
X
(a) small amplitude journal motions
2rX
X
(b) large amplitude journal motions
Applications:
K,C, M (force coefficients) FX, FY (reaction forces)
RBS stability analysis
RBS imbalance response
& transient load effects
20
SFD predictive code
Orbit
1.0
0.8
2r Y

0.6
2 rX
0.4
0.2
Y/c
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
-1.0
-0.8
-0.6
-0.4
0.0
-0.2 0.0
-0.2
0.2
0.4
0.6
0.8
-0.4
-0.6
-0.8
-1.0
X/c
21
1.0
Purpose of whirl orbit analysis
Orbit
1.0
0.8
0.6
0.4
0.2
Y/c
for specified whirl orbit and
over specifiedfrequency
range:
• predict SFD reaction forces
vs. time,
• conduct Fourier analysis, &
• identify SFD linearized
force coefficients
-1.0
0.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-0.2
-0.4
-0.6
-0.8
-1.0
X/c
22
SFD example
Journal Diameter
5.0 in
Total Length
1.0 in
Land Clearance
5.0 mil

Bearing
D
Y
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 mReyns
Density
49 lb/ft3
Journal
Feed hole
X
Pa, ambient
pressure
Ps, supply
L
pressure
Section A-A
A
Open Ends SFD with feed holes
23
whirl orbit induces forces
h - with holes - no central groove
SFD open ends L=1.0 inch - with holes - no central groove
1.0
Reaction forces
0.8
locus
-0.8
-0.6
-0.4
0.0
-0.2 0.0
60.0
approx using
Fourier series
0.2
0.4
0.6
0.8
1.0
-0.2
-0.4
40.0
FY
eY/c
0.4
0.2
-1.0
80.0
0.6
20.0
-0.6
-0.8
-1.0
eX/c
lbf
0.0
-250.0
-200.0
-150.0
-100.0
-50.0
0.0
50.0
100.0
-20.0
-40.0
Eccentric (Off-center)
Elliptical orbit
-60.0
-80.0
es/c=0.5c
r/c=0.25c
-100.0
FX
Fundamental 1X Force
SFD reaction force
24
SFD Forces: predicted and 1X
FD open ends L=1.0 inch - with holes - no central groove
Frequency 180 Hz
100
lbf
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
-50
SFD 1X forces do
not reproduce
NL forces
-100
-150
-200
-250
SFD reaction force
1.0
locus
0.8
FX
FY
SFD open ends L=1.0 inch - with holes - no central groove
Journal eccentricity locus
Fraction of Period
0.6
eY/c
Bearing reaction force
es/c=0.5c
r/c=0.25c
Fundamental 1X Force
50
0.4
0.2
FX_1Fourier
-1.0
-0.8
-0.6
-0.4
0.0
-0.2 0.0
0.2
0.4
0.6
0.8
1.0
-0.2
FY_1Fourier
-0.4
-0.6
-0.8
-1.0
eX/c
25
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
Fdyn  KSFD z  CSFD z + MSFD z
where z is a vector of dynamic displacements and
(K, C, M)SFD are matrices of stiffness, viscous damping and
inertia force coefficients
26
Analysis (I)
The dynamic or time varying part of the SFD reaction force is
periodic with fundamental period T=2p/.
Using Fourier series decomposition,
it  
Fdyn  F1e
i  2t  
 FII e
i  3t  
 FIII e
 ....
To first order effects (fundamental frequency)
Fdyn  F1e
i t  
where
F1   K SFD   2 M SFD  i  CSFD  z1  H z1
H   K SFD   M SFD  i  CSFD 
2
is the matrix of damper impedances
27
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:
F1
F2   H z1 z2 
leads to the determination of the impedances:
HXX, HXY,HYX, HYY
28
Analysis (III)
The analysis stacks impedances for a set of frequencies
(k=1,2,….N) from which, by linear curve fits, one
determines :
2
SFD
SFD
K
 M

 Re(H )
CSFD 
 Im(H )
29
SFD Real Impedances vs. frequency
SFD open ends L=1.0 inch - with holes - no central groove
2.50E+04
Impedances (real part)
lbf/in
HXX will give M<0
Re(H)
2.00E+04
1.50E+04
1.00E+04
5.00E+03
0.00E+00
50
100
-5.00E+03
Hyy
200
250
SFD open ends L=1.0 inch - with holes - no central groove
H
YY fits well model K-M2
-1.00E+04
Hxx
150
Journal eccentricity locus
1.0
locus
Whirl frequency (Hz)
0.8
0.6
eY/c
0
0.4
0.2
-1.0
-0.8
-0.6
-0.4
0.0
-0.2 0.0
Hxy
-0.4
Hyx
-0.8
Frequency range 20-200 Hz
0.2
0.4
0.6
0.8
1.0
-0.2
-0.6
-1.0
eX/c
30
Impedances (imag part)
SFD
Ima Impedances vs. frequency
SFD open ends L=1.0 inch - with holes - no central groove
lbf/in
1.00E+05
HXX gives
average C
Ima(H)
8.00E+04
6.00E+04
4.00E+04
2.00E+04
HYY fits OK model C
0.00E+00
0
50
100
150
SFD open ends L=1.0 inch - with holes - no central groove
200
250
Journal eccentricity locus
1.0
locus
-2.00E+04
Hyy
Hxy
Hyx
Frequency range 20-200 Hz
0.6
eY/c
Hxx
0.8
Whirl frequency (Hz)
0.4
0.2
-1.0
-0.8
-0.6
-0.4
0.0
-0.2 0.0
0.2
0.4
0.6
0.8
1.0
-0.2
-0.4
-0.6
-0.8
-1.0
eX/c
31
SFD NL-Linear force coefficients
Frequency range 20-200 Hz
Kxx
Kyy
Kxy
Kyx
lbf/in
lbf/in
lbf/in
lbf/in
2.12E+03
-2.11E+02
-6.35E+01
-6.13E+01
Fourier
analysis
Linearized
forces
Nonlinear
forces
100
50
0
-100
-80
-60
-40
-20
0
Cxx
Cyy
Cxy
Cyx
lbf-s/in
lbf-s/in
lbf-s/in
lbf-s/in
68.5
37.7
-0.6
-0.6
Mxx
Myy
Mxy
Myx
-200
lbm
lbm
lbm
lbm
SFD NL force response-250
-5.0
2.0
0.2
0.2
40
60
80
-50
-100
-150
FY vs FX
1.0 inch - with holes - no central groove
locus
20
1.0
Linear force model
0.8
eY/c
0.6
DISSIPATED ENERGY IN
A PERIOD or MOTION
0.4
0.2
-1.0
-0.8
-0.6
-0.4
0.0
-0.2 0.0
0.2
0.4
0.6
0.8
1.0
-0.2
-0.637
Non-linear (from time
transient response)
-0.590
Linear from ALL force
coefficients
-0.4
-0.6
-0.8
-1.0
eX/c
lbf-in
32
Proposed tasks (2011-12)
1. Test ACTUAL short length open ends damper with dynamic loads (20300 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.
Y
centered journal
X
circular orbits
Y
Y
off-centered journal
X
X
elliptical orbits
33
Budget (2011-12)
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
$
Total Cost:
Y
centered journal
X
circular orbits
Y
1,500
$ 37,108
Y
off-centered journal
X
X
elliptical orbits
34
Questions (?)
35