Identification of SFD force coefficients Large Clearance Open Ends SFD

Transcription

1 32 nd Turbomachinery Research Consortium Meeting Identification of SFD force coefficients Large Clearance Open Ends SFD TRC-SFD Luis San Andrés Mast-Childs Professor May 212 TRC Project 32513/1519FB Linear Nonlinear Force Coefficients for SFDs 1

2 SFD with a central groove anti-rotation pin journal lubricant film shaft ball bearing oil inlet Feed groove Pressurized lubricant flows through a central groove to fill the squeeze film lands. 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. Dynamic pressures in the film lands generate reaction forces aiding to damp excessive amplitudes of rotor whirl motion. 2

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

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

5 SFD Test Rig cut section Test Journal Bearing Cartridge Circumferential groove Piston ring seal (location) Supply orifices (3) Test rig main features Journal diameter: 5. inch Film clearance: 9.9 mil Film length: 2 x 1 inch Support stiffness: 1 klbf/in Flexural Rod (4, 8, 12) Main support rod (4) Pedestal Journal Base in 5

6 Lubricant flow path Oil inlet in ISO VG 2 oil 6

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 e static load 45 o X X e S r c centered and offcentered circular orbits 7

8 Structure static stiffness Pull test using static loader to determine static structure stiffness static radial load (lbf) F X K S ~ 1 klb f /in static radial load (N) e S static radial eccentricity, (mil) (11.6 μm) 8

9 Structural parameters Dry test system Circular Centered Orbits Frequency 5-21 Hz US XX SI Direct US SI Stiffness K s 17 klbf/in 19 MN/m 12 klbf/in 21 MN/m Damping C s 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 M BC 48 lb 22 kg 48 lb 22 kg Natural frequency f ns 148Hz 156Hz Damping ratio ξ s 4% 4% 9

10 SFD dimensions & operating conds. Maximum static load 324 lbf Centered and off-centered, e S = 1, 2, and 3 mil Frequency range: 5-21 Hz, Orbit amplitude r =.5 mil ISO VG 2 Oil Oil in, Qin Viscosity at 73 o F [cpoise] 3.1 Journal (D) Oil out, Qt Density [kg/m 3 ] 785 End groove Inlet pressure [psig] Outlet pressure [psig] 1.6 Central groove c L ½L L Bearing Cartridge End groove Radial Clearance [mil] Journal Diameter [inch] Central groove length [inch] & depth Land length, L [inch] x 2 Oil out Base Oil out, Qb Oil collector Support rod Total Length [inch] 2.5 1

11 SFD force coefficients IVFM parameter identification method SFD Difference between lubricated system and dry system (baseline) coefficients C SFD =C lubricated -C s M SFD =M lubricated -M BC c DR system parameters K s = 1 klbf/in M BC = 48 lb C s = 8-9 lbf-s/in Nat freq = Hz Damping ratio = 4% es 45 o X K SFD =K lubricated -K s 11

12 SFD force coefficients - theory Centered journal (e s =), no lubricant cavitation Two film lands separated by a plenum: central groove has no effect on squeeze film forces. Damping 3 tanh L * * * R C CXX C 2 12π L 1 D c L D Inertia 3 * * * π LR M MXX M 2 1 c tanh L D L D Stiffness K XX = K = K X =K X = X 12

13 SFD force coefficients - theory Damping 3 tanh L * * * R C CXX C 2 12π L 1 D c L D c=5.5 mil c=9.9 mil C * = 7,121 N.s/m (4.7 lb f.s/in) C * = 1,255 N.s/m (7.16 lb f.s/in) Inertia 3 * * * π LR M MXX M 2 1 c tanh L D L D X c=5.5 mil c=9.9 mil M * = 2.98 kg (6.58 lb m ) M * = 1.67 kg (3.69 lb m ) 13

14 Experimental SFD damping coeffs. Open ends SFD Circular orbits (r =.5 mil) SFD (1 inch land lengths) c es 45 o X Damping coefficients (lbf-s/in) kns/m C SFD C c=5.5 mil C XX c=5.5 mil classical theory (4.6 lbf.s/in) classical theory (7.1 lbf.s/in) C c=9.9 mil C XX c=9.9 mil static eccentricity, e S (mil) (89 μm) 14

15 Experimental SFD inertia coeffis. Open ends SFDs Circular orbits (r =.5 mil) SFD (1 inch land lengths) c es 45 o X Added mass coefficients (lb) M SFD M XX c= 5.5 mil M c= 5.5mil M c= 9.9 mil M XX c= 9.9 mil classical theory ( lb) static eccentricity, e S (mil) 89 μm 36 kg 15

16 Pressure sensors in bearing Top view: Sensors around bearing circumference Pressure sensor locations and Pressure sensor 25.4 mm 12.7 mm Top Land Central groove Pressure sensor Bottom Land 25.4 mm, and 63.5 mm Central groove Pressure sensor Side view: Sensors located at middle plane of film lands BC 16

17 Dynamic pressures: films & groove Whirl frequency 13 Hz pressure (psi) psi film lands bar -.69 bar ASME GT Top and bottom film lands show similar pressures. psi pressure (psi) top land (12 deg) bottom land (12 deg) Number time (-) of periods 4.28 bar bar 4 groove (165 deg) groove (285 deg) groove Number time (-) of periods Dynamic pressure in the groove is not zero! e s =, circular orbit r=.5 mil. Groove pressure P G =.72 bar 17

18 Peak-peak lubricant pressures P-P dynamic pressure (psi) 27 (kpa) Top land (12) Top land (24) Bottom land (12) Bottom land (24) Groove (165) Groove (285) 1 2 c=5.5 mil Lands (top & bottom) 1 2 Frequency (Hz) groove Piezoelectric pressure sensors (PCB) location groove Bearing Cartridge top land bottom land 18 Midplane

19 Peak-peak lubricant pressures P-P dynamic pressure (psi) Top land (12) Top land (24) Bottom land (12) Bottom land (24) Groove (165) Groove (285) 1 2 c=9.9 mil groove 1 2 Frequency (Hz) lands (top & bottom) Piezoelectric pressure sensors (PCB) location groove Bearing Cartridge top land bottom land 19 Midplane

20 Ratio of groove/film land pressures P-P pressure ratios Top land (12) Top land (24) groove lands (top) 1. Groove generates large hydrodyna mic pressures! 1 2 c=5.5 mil 1 2 Frequency (Hz) 3/8 ~7 c

21 Ratio of groove/film land pressures P-P pressure ratios Top land (12) Top land (24) groove lands (top) 1. Groove generates larger hydrodyna mic pressures!! Larger than in the film! 1 2 c=9.9 mil 1 2 Frequency (Hz) 3/8 ~35 c

22 Model SFD with a central groove SFD geometry and nomenclature Lubricant in orifice Bearing do Use effective depth d =1.6c Lubricant in dg groove LG L c : clearance film land z End seal Lubricant out Journal D, diameter recirculation zone d Effective groove depth separation line streamline Lubricant out Solve modified Reynolds equation (with fluid inertia) h h 12 h R R z z t t P P h 2 h

23 Example predicted pressure field Feed hole (3 x 12 deg) groove Inner Film Pressure Pressure (bar) land Static pressure at groove shows circumferenti al variation due to feed holes spacing axial coordi nate S1 z S circ coordinate (node #) 3/8 ~35 c

24 Damping coefficients: test & predictions Model predicts Damping coefficients (lb f-s/in) C SFD C c=5.5 mil classical theory (4.6 lbf.s/in) C XX c=5.5 mil classical theory (7.1 lbf.s/in) C c=9.9 mil lines : predictions symbols: test data C XX c=9.9 mil small c SFD: larger damping coefficient than test values large c SFD: less damping than test values static eccentricity, es (mil) 24

25 Inertia coefficients: test & predictions Model predicts Added mass coefficients (lb) M SFD M XX c=5.5 mil M c=9.9 mil classical theory ( lb) M c=5.5mil M XX c=9.9 mil lines : predictions symbols: test data small c SFD: less inertia than test values Large c SFD: larger inertia than test values Classical theory predicts ~ 1/7 of test values static eccentricity, es (mil) 25

26 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

27 P&W funded project (212) Modify test rig and construct SFD w/o a central groove, conduct measurements of film pressures and identify force coefficients. 27

28 Proposed tasks TRC (212-13) 1. Test damper w/o groove with dynamic loads (2-3 Hz) inducing offcentered elliptical orbital motions to reach.8c. 2. Identify SFD force coefficients from test impedances, and correlate coefficients with linear force coefficients and experimental coefficients for smallest whirl amplitude (.5c). 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. centered journal off-centered journal X circular orbits X elliptical orbits X 28

29 TRC Budget (212-13) eight months Support for graduate student (2 h/week) x $ 2,2 x 8 months Fringe benefits (.6%) and medical insurance ($197/month) Travel to (US) technical conference Tuition three semesters ($227 credit hour x 15 ch x 1.7 fees multiplicative factor) Supplies for test rig Total Cost: ear II $ 17,6 $ 1,682 $ 1,2 $ 5,789 $ 2,2 $ 28,47 ear I started on Jan 212 centered journal X off-centered journal X X circular orbits elliptical orbits 29

30 Acknowledgments Thanks to Pratt & Whitney Engines Turbomachinery Research Consortium Sung-Hwa Jeng, RA for making the presentation Learn more Questions (?) 3