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1 Luis San Andrés Mast-Childs Professor Identification of SFD force coefficients Large Clearance Open Ends SFD TRC-SFD-01-2012 Linear Nonlinear Force Coefficients for SFDs 32 nd Turbomachinery Research Consortium Meeting TRC Project 32513/1519FB May 2012

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2 Typical squeeze film damper (SFD) with a central groove 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. Feed groove oil inlet 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.

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3 P&W SFD test rig Static loader Shaker assembly (Y direction) Shaker assembly (X direction) Static loader Shaker in X direction Shaker in Y direction Top view Isometric view SFD test bearing

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4 Test rig description shaker X shaker Y Static loader SFD base support rods X Y Shaker X Shaker Y Static loader SFD Base Static loader X Y Support rods X Y

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5 SFD Test Rig – cut section in Test rig main features Journal diameter: 5.0 inch Film clearance: 9.9 mil Film length: 2 x 1 inch Support stiffness: 100 klbf/in 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)

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6 Lubricant flow path Oil inlet in ISO VG 2 oil

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7 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 X Y static load e c 45 o

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8 Structure static stiffness 0 100 200 300 400 00.511.522.533.54 static radial eccentricity, (mil) static radial load (lbf) e S K S ~100 klb f /in X Y F Pull test using static loader to determine static structure stiffness 1780 1335 890 445 static radial load (N) (101.6 μm)

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9 Structural parameters Dry test system Circular Centered Orbits Frequency 50-210 Hz Direct XXYY USSIUSSI Stiffness KsKs 107 klb f /in19 MN/m120 klbf/in21 MN/m Damping CsCs 8 lb f -s/in1.4 kN-s/m 9 lbf-s/in1.6 kN-s/m Mass M -4 lb-2 kg-3 lb-1 kg System Mass M BC 48 lb22 kg48 lb22 kg Natural frequency f ns 148Hz156Hz Damping ratio ξsξs 4%

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10 SFD dimensions & operating conds. Maximum static load 324 lb f Centered and off-centered, e S = 1, 2, and 3 mil Frequency range: 50-210 Hz, Orbit amplitude r = 0.5 mil ISO VG 2 Oil Viscosity at 73 o F [cPoise]3.10 Density [kg/m 3 ]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 Oil out, Q b Base Support rod Bearing Cartridge Journal (D) Oil out, Q t Oil in, Q in Central groove L ½ L L End groove Oil out Oil collector c

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11 SFD K s = 100 klbf/in M BC = 48 lb C s = 8-9 lbf-s/in Nat freq = 148-156 Hz Damping ratio = 4% DRY system parameters C SFD =C lubricated - C s M SFD =M lubricated - M BC K SFD =K lubricated - K s Difference between lubricated system and dry system (baseline) coefficients SFD force coefficients IVFM parameter identification method X Y eses c 45 o

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12 SFD force coefficients - theory Centered journal (e s =0), no lubricant cavitation Two film lands separated by a plenum: central groove has no effect on squeeze film forces. Damping Inertia Stiffness K XX = K YY = K XY =K YX =0 X Y

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13 SFD force coefficients - theory Damping Inertia c=5.5 milC * = 7,121 N.s/m (40.7 lb f.s/in) c=9.9 milC * = 1,255 N.s/m (7.16 lb f.s/in) c=5.5 milM * = 2.98 kg (6.58 lb m ) c=9.9 milM * = 1.67 kg (3.69 lb m ) X Y

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14 Experimental SFD damping coeffs. Open ends SFD Circular orbits (r = 0.5 mil) SFD (1 inch land lengths) 0 20 40 60 80 100 120 140 160 180 0.00.51.01.52.02.53.03.5 static eccentricity, e S (mil) Damping coefficients (lb f -s/in) C SFD C XX c=9.9 mil C YY c=9.9 mil C YY c=5.5 mil C XX c=5.5 mil classical theory (7.1 lbf.s/in) classical theory (40.6 lbf.s/in) 31.5 kNs/m (89 μm) Damping coefficients (kN/m) X Y eses c 45 o

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15 Experimental SFD inertia coeffis. Open ends SFDs Circular orbits (r = 0.5 mil) SFD (1 inch land lengths) 0 10 20 30 40 50 60 70 80 0.00.51.01.52.02.53.03.5 static eccentricity, e S (mil) Added mass coefficients (lb) M SFD M XX c=9.9 mil M YY c=9.9 mil M YY c=5.5mil M XX c=5.5 mil classical theory (3.7 - 6.6 lb) 89 μm 36 kg X Y eses c 45 o

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16 Pressure sensors in bearing

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17 Dynamic pressures: films & groove Whirl frequency 130 Hz Number of periods psi 0.69 bar film lands e s =0, circular orbit r=0.5 mil. Groove pressure P G = 0.72 bar 0 -0.69 bar Top and bottom film lands show similar pressures. Dynamic pressure in the groove is not zero! 0 psi groove 0.28 bar -0.28 bar Number of periods ASME GT2012-68212

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18 Peak-peak lubricant pressures Frequency (Hz) P-P dynamic pressure (psi) 100200 30 20 10 0 c=5.5 mil groove Lands (top & bottom) 207 (kPa) Piezoelectric pressure sensors (PCB) location Bearing Cartridge bottom land top land groove Mid- plane

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19 Peak-peak lubricant pressures Frequency (Hz) 100200 15 10 5 0 c=9.9 mil groove lands (top & bottom) Piezoelectric pressure sensors (PCB) location Bearing Cartridge bottom land top land groove Mid- plane P-P dynamic pressure (psi)

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20 Ratio of groove/film land pressures Frequency (Hz) P-P pressure ratios 100200 0 c=5.5 mil groove lands (top) 1.0 Groove generates large hydrodyna mic pressures! 3/8”~70 c 1 “ 0.5” 1”

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21 Ratio of groove/film land pressures Frequency (Hz) P-P pressure ratios 100200 1.0 c=9.9 mil groove lands (top) Groove generates larger hydrodyna mic pressures!! Larger than in the film! 1 “ 0.5” 1” 3/8”~35 c

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22 Model SFD with a central groove SFD geometry and nomenclature Solve modified Reynolds equation (with fluid inertia) Use effective depth d =1.6c

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23 Example predicted pressure field Static pressure at groove shows circumferenti al variation due to feed holes spacing groove 3/8”~35 c 1 “ 0.5” 1”

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24 0 20 40 60 80 100 120 140 160 180 200 0.00.51.01.52.02.53.03.54.0 static eccentricity, e S (mil) Damping coefficients (lb f -s/in) C SFD C XX c=9.9 mil C YY c=9.9 mil C YY c=5.5 mil C XX c=5.5 mil lines : predictions symbols: test data classical theory (7.1 lbf.s/in) classical theory (40.6 lbf.s/in) Damping coefficients: test & predictions Model predicts small c SFD: larger damping coefficient than test values large c SFD: less damping than test values

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25 Inertia coefficients: test & predictions 0 10 20 30 40 50 60 70 80 0.00.51.01.52.02.53.03.54.0 Added mass coefficients (lb) M SFD M XX c=9.9 mil M YY c=9.9 mil M YY c=5.5mil M XX c=5.5 mil classical theory (3.7 - 6.6 lb) static eccentricity, e S (mil) lines : predictions symbols: test data Classical theory predicts ~ 1/7 of test values Model predicts small c SFD: less inertia than test values Large c SFD: larger inertia than test values

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26 Conclusions 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. Conducted measurements of dynamic load response in large clearance (c=9.9 mil) open ends SFD with circular orbits, centered and off-centered.

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27 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.

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28 Proposed tasks TRC (2012-13) 1.Test damper w/o groove with dynamic loads (20-300 Hz) inducing off- centered 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.

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29 TRC Budget (2012-13) eight monthsYear 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 $ 2,200 Total Cost: $ 28,470 Year I started on Jan 2012

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30 Acknowledgments Thanks to Pratt & Whitney Engines Turbomachinery Research Consortium Sung-Hwa Jeng, RA for making the presentation Learn more http:/rotorlab.tamu.edu Questions (?)

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