1. 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
Luis San Andrés
Mast-Childs Professor
Sung-Hwa Jeung
Graduate Research Assistant
May 2013
TRC Project 32513/1519SF
Linear Nonlinear Force Coefficients for SFDs

2. SFD with a central groove
Lubricant supplied into a circumferential groove feeds uniformly the squeeze film lands.
Feed
groove
oil inlet
Whirl motion from the journal squeezes the lubricant film and generates dynamic pressures that aid to damp the rotor vibrations
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.

3. SFD Test Rig – cut sectionin
Bearing Cartridge
Test Journal
Main support rod (4)
Journal Base
Pedestal
Piston ring seal (location)
Flexural Rod (4, 8, 12)
Circumferential groove
Supply orifices (3)

4. Geometry (three feed holes 120o apart)
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 (two lands + groove), L
6.35 cm (2.5 in)
Feed orifice Diameter, ϕ
2.54 mm (0.1 inch)
Central Groove
Groove Axial length, LG
1.27 cm (0.5 inch)
Groove Depth, dG
0.96 cm (0.38 inch)

5. Lubricant flow path ISO VG 2 oil Oil inlet
Lubricant properties (ISO VG 2 )
Supply temperature, Tin
25 °C (77 °F)
Lubricant Tin , μ
2.96 cP
Lubricant density, ρ
785 kg/m3 (49 lb/ft3)

6. Funded TRC ( )
$ 28,470
Test damper with dynamic loads ( Hz) inducing off-centered elliptical orbital motions to reach 0.8c.
Identify SFD force coefficients from test impedances, and correlate coefficients with linear force coefficients and experimental coefficients for smallest whirl amplitude (0.05c).
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.
Predictions: Effect of groove on SFD forced performance 6

7. Tests conducted Evaluate SFD dynamic force coefficients from
Excitation frequencies 10 – 100 Hz
Evaluate SFD dynamic force coefficients from
Circular orbit journal motions with
orbit amplitudes (r) from
8% to 71% of radial clearance (c).
Static journal eccentricity (e) to 76% of radial clearance (c).
Max. clearance (c) : 251 μm Y
es = 0.76 c
es = 0.51 c
es = 0.25 c
es= 0 c
Y Displacement [μm] X
X Displacement [μm]

8. Parameter identification procedure
Step 1 : Model system (2-DOF) F
Shaker force
EOM: Time Domain KL CL ML
EOM: Frequency Domain
Measured variables:
Unknown Parameters:
KL, CL, ML
SFD coefficients
(K, C, M)SFD = (K, C,M)L – (K, C, M)S
SFD
Test system
(lubricated)
Structure

9. Test SFD damping coefficientsY X
= 0 c
= 0.25 c
= 0.51 c
= 0.76 c
(eS/c)
eS=0.76c
eS=0.51c
eS=0.25c
eS=0.0c
CXX SFD
CXX ~CYY
Findings: SFD damping coefficients increase with increasing orbit amplitude and static eccentricity. CXX increases dramatically above r/c > 50%

10. Test SFD added mass coefficientsY X
= 0 c
= 0.25 c
= 0.51 c
= 0.76 c
MXX SFD
eS=0.76c
eS=0.51c
eS=0.25c
eS=0.0c
(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%

11. SFD effective force coefficients
For circular orbits (only), SFD forces reduce to Y
-Fradial rw X r
-Ftangential

12. -Keff Test SFD effective stiffness es/c=0.0
structure
es/c=0.0
Findings: SFD effective stiffness decreases with increasing excitation frequency and with orbit amplitude (a fluid inertia effect).

13. Ceff Test SFD effective damping es/c=0.0
Findings: SFD effective damping increases with orbit amplitude. Little dependency with frequency.

14. Pressure sensors in housing14

15. Film dynamic pressure profiles
Central groove
Film lands
es/c=0.0, 100 Hz
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

16. Film dynamic pressure profiles
A uniform pressure zone indicates air entrainment.

17. Model SFD with a central groove
SFD geometry and nomenclature
Use effective depth
Solve modified Reynolds equation (with temporal fluid inertia)
h : fluid film thickness P : hydrodynamic pressure
μ : lubricant viscosity R : journal radius

18. Damping: predictions and test dataY
45o c
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%) es X
classical theory (1.2 kN.s/m)
Test data much larger than simple theory
CXX
Prediction
Test data
CYY
Model by San Andres (2011)

19. Added mass: predictions & test dataY
45o
classical theory (1.67 kg) es c X
Model predictions agree well with experimental results.
Predicted added masses increase slightly with static eccentricity
Test data much larger than simple theory
MXX
Prediction
Test data
MYY
Model by San Andres (2011)

20. Over a full period of motion
SFD mechanical energy dissipation
SFD reaction forces
Actual force
Linearized force
Mechanical work
Over a full period of motion

21. Work=Energy dissipation
100 Hz
EDIS<0 is negative work = energy dissipated by SFD
Findings: SFD work increases with increasing orbit amplitude.

22. Mechanical energy difference
100 Hz
0~5%
~23%
Findings: Energy difference increases with increasing static eccentricity and orbit amplitude. For r/c≤0.4 and es/c≤0.25, Ediff < ~5%

23. Conclusions From circular orbit tests Goodness of linear force model
(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

24. 2013 proposal to TRC Justification Ultra-short SFD (L/D < 0.2)
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.

25. 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).
Sudden load

26. TRC Budget 2013-2014 Year III 2013-2014 Year III $ 40,666
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
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.

27. Thank you Questions (?) Acknowledgments Learn more at
Thanks to TAMU Turbomachinery Research
& Pratt & Whitney Engines
Questions (?)
Learn more at 27