1. GT2012-68212 1 ASME GT2012-68212 Luis San Andrés Mast-Childs Professor, Fellow ASME Texas A&M University Supported by Pratt & Whitney Engines (UTC) 2012 ASME Turbo Expo Conference, June 11-15,2012, Copenhagen, DK accepted for journal publication D AMPING AND I NERTIA C OEFFICIENTS F OR T WO O PEN E NDS SFDs WITH A C ENTRAL G ROOVE : M EASUREMENTS A ND P REDICTIONS

2. GT2012-68212 2 In aircraft gas turbines and compressors, squeeze film dampers aid to attenuate rotor vibrations and to provide mechanical isolation. SFD operation & design  SFD with dowel pin Too little damping may not be enough to reduce vibrations. Too much damping may lock damper & degrades system rotordynamic performance

3. GT2012-68212 3 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 generate fluid film reaction forces aiding to damp excessive amplitudes of rotor whirl motion.

4. GT2012-68212 4 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

5. GT2012-68212 5 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

6. GT2012-68212 6 SFD bearing design in Geometry of open ends SFD Journal diameter: 127 mm (5.0 inch) Film clearance: 0.138mm (5 mil) Land length: 2 x 25.4 mm (2 x 1 inch) Support stiffness: 4.38 – 26.3 MN/m (25 – 150 klb f /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)

7. GT2012-68212 7 Oil inlet temperature, T s = 25 o C Density, ρ = 785 kg/m 3 Viscosity μ at T s = 2.96 cPoise Flow rate, Q in = 4.92 LPM Oil inlet in ISO VG 2 oil Flow through squeeze film lands

8. GT2012-68212 8 Objective & tasks Evaluate dynamic load performance of SFD with a central groove. X Y static load e c 45 o Dynamic load measurements: circular & elliptical orbits (centered and off centered) and identification of test system and SFD force coefficients

9. GT2012-68212 9 SFD configurations tested Short SFD (B)Long SFD (A) Journal diameter, D127 mm Land length, L12.7 mm25.4 mm Radial clearance, cC B = 0.138 mmC A = 0.141 mm Groove axial length, L G 12.7 mm Depth, d G 9.5 mm Oil wetted length, 2L + L G 38.1 mm63.5 mm Groove static pressure, P G 0.52 bar0.72 bar Oil inlet temperature, T s 25 o C LubricantISO VG 2 Density, ρ785 kg/m 3 Viscosity μ at T s 2.96 cPoise Flow rate, Q in 4.92 LPM Geometry and oil properties for open ends SFD Support stiffness range Ks = 4.4 – 26.3 MN/m (variable) Max. static load (8 kN), Max. amplitude dynamic load (2.24 kN) Range of excitation frequencies: 35 – 250 Hz = 1.1-8.3 in film lands

10. GT2012-68212 10 Parameter Identification X Y Journal also moves during excitation of the bearing *SFDs do not have stiffnesses = reaction forces due to changes in static displacement.

11. GT2012-68212 11 Parameter Identification Applied Loads CCW displacements & accelerations Two linearly independent load vectors F 1 and F 2 CW Y X X Y Single frequency orbits Loads F, displacement x and accelerations a recorded at each frequency

12. GT2012-68212 12 Parameter Identification EOMs (2 DoF) time domain EOM (Frequency Domain) Impedance function H (ω) Physical model

13. GT2012-68212 13 Parameter Identification IVFM solution SFD force coefficients (K, C, M) SFD = (K, C, M) – (K, C, M) S SFD coefficientsTest systemSupport structure Flexibility function G (ω) Iteration on weighted least squares to minimize the estimation error in: = transfer functions (displacement/force) * Instrumental Variable Filter Method (IVFM) (Fritzen, 1986, J.Vib, 108) Measurement errors affect little identified parameters IVF Method* GH=I+e

14. GT2012-68212 14 Physical model Re(H XX )= K-  2 M and Im(H XX )=C  agree with test data. Damping C is constant over the frequency range Typ. impedances- lubricated SFD H XX C XX Short SFD e S =0; r =0.05c B Im(H YX )[MN/m] Frequency (Hz) Re(H XX )[MN/m] 0100200300 0 20 40 Im(H)/w f start f end C XX C XX [MNs/m] Frequency (Hz)

15. GT2012-68212 15 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

16. GT2012-68212 16 Normalization of experimental coefficients SHOW ratio with respect to predictions from classical theory: Identification procedure gives NO cross-coupled coefficients for test SFDs. Long damper Land length 1”, 5.55 mil C* A = 6.79 kN.s/m, M* A = 2.98 kg Short damper Land length 0.5”, 5.43 mil C* A = 0.92 kN.s/m, M* A = 0.39 kg Ratio~(L/c) 3 ~7.5

17. GT2012-68212 17 Experimental SFD force coefficients open ends short length damper 1/2 inch lands, c=5.43 mil = 0.138 mm Top Land Bottom Land 0.5 inch Central groove

18. GT2012-68212 18 SFD direct damping coefficients Orbit amplitude (r /c B ) C XX, C YY first decrease and then increase with orbit amplitude. Coefficients are isotropic C XX ~ C YY C XX C YY 0 1 2 3 4 5 6 0.0 0.20.40.6 0.8 1.0 Damping coefficients C XX SFD 0 1 2 3 4 5 6 0.00.20.40.60.81.0 Damping coefficients C YY SFD e s = 0 e s = 0.44 c B e s = 0.29 c B e s = 0 e s = 0.44 c B e s = 0.29 c B Damping coefficients vs orbit amplitude Short SFD (12.7 mm lands, c=0.138 mm) X Y eses c 45 o

19. GT2012-68212 19 SFD added mass coefficients vs orbit amplitude Orbit amplitude (r /c B ) 0 5 10 15 20 25 30 35 0.00.20.40.60.81.0 Mass Coefficients M XX SFD 0 5 10 15 20 25 30 35 0.00.20.40.60.81.0 Mass Coefficients M YY SFD Mass coefficients M XX M YY e s = 0 e s =0.29 c B e s = 0.44 c B e s = 0 e s = 0.29 c B e s = 0.44 c B M XX, M YY decrease with amplitude of motion, as prior tests* and theory show** *Design and Application of SFDs in Rotating Machinery (Zeidan, San Andrés, Vance, 1996, Turbomachinery Symposium) ** SFDs: Operation, Models and Technical Issues (San Andrés, 2010) Short SFD (12.7 mm lands, c=0.138 mm) X Y eses c 45 o

20. GT2012-68212 20 Experimental SFD force coefficients open ends long damper 1 inch lands, c=5.55 mil=0.141 mm Central groove Top Land 1.0 inch

21. GT2012-68212 21 SFD direct damping coefficients vs static eccentricity Amplitudes of motion: C XX ~ C YY with amplitude of motion & orbit shape. SFD forced response is independent of BC kinematics. All orbits (circular & elliptic) C XX C YY 0 2 4 6 0.00.20.40.6 C XX SFD 0 2 4 6 0.00.20.4 Static eccentricity ratio ( e S /c A ) C YY SFD Damping coefficients Long SFD (25.4 mm lands, c=0.141 mm) X Y eses c 45 o

22. GT2012-68212 22 SFD added mass coefficients vs static eccentricity M XX M YY Amplitudes of motion: 12 0 2 4 6 8 10 12 0.00.20.40.6 Added Mass Coefficients Static eccentricity ratio ( e S /c A ) M YY SFD 0 2 4 6 8 10 0.00.20.40.6 Added Mass Coefficients M XX SFD Mass coefficients M XX ~ M YY not strong function of amplitude of motion or orbital shape & increasing with static eccentricity All orbits (circular & elliptic) Long SFD (25.4 mm lands, c=0.141 mm) X Y eses c 45 o

23. GT2012-68212 23 Recorded dynamic pressures in groove and film lands

24. GT2012-68212 24 Dynamic pressures Piezoelectric pressure sensor (PCB) locations Bearing Cartridge PCB groove PCB bottom land PCB top land Piezoelectric sensors: 2 in the top land, 2 in the bottom land 2 in the groove Side view: Sensors located at middle plane of film lands Mid-plane

25. GT2012-68212 25 Dynamic pressures: films & groove Whirl frequency 130 Hz Number of periods psi 0.69 bar film lands 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 Long SFD. e s =0, r=0.1c A. P G = 0.72 bar

26. GT2012-68212 26 Film and groove dynamic pressures increase with excitation frequency. Pressure waves show spikes (high frequency content), typical of air ingestion & entrapment Number of time periods psi 0.69 bar film lands 0.69 bar 0 -0.69 bar 0 -1.40 bar groove Number of time periods psi Long SFD. e s =0, r=0.1c A. P G = 0.72 bar Dynamic pressures: films & groove Whirl frequency 200 Hz

27. GT2012-68212 27 Peak-peak dynamic pressures Frequency [Hz] Piezoelectric pressure sensor (PCB) location Bearing Cartridge bottom land top land groove P-P dynamic pressure (psi) 2.8 bar 2.1 bar 1.4 bar 0.7 bar 0.0 bar Frequency (Hz) Top land (120 o ) Groove (165 o ) Bottom land (120 o ) Mid-plane Groove pressures are as large as in the film lands. At the highest whirl frequency, groove pressure > 50% film land pressures 40

28. GT2012-68212 28 Ratio of groove/film land pressures Frequency (Hz) P-P pressure ratios 100200 0 c=5.5 mil (0.141 mm) groove lands (top) 1.0 Groove generates large hydrodynamic pressures! 3/8”~70 c 1 “ 0.5” 1”

29. GT2012-68212 29 Comparisons to predictions from a modern model

30. GT2012-68212 30 Model SFD with a central groove SFD geometry and nomenclature Solve modified Reynolds equation (with fluid inertia) Use effective depth d  = Xc * San Andrés, Delgado, 2011, GT2011-45274.

31. GT2012-68212 31 circular orbits r/c = 0.1 Predicted coefficients agree well with test data. C XX (test data) C XX (prediction) C YY (test data) C YY (prediction) Static eccentricity ratio (e s / c B ) Damping Coefficients (Short SFD) 10 Short SFD, d η = 2.8c B 0 2 4 6 8 0.00.10.20.30.40.50.6 Damping coefficients Short SFD Damping coefficients increase moderately with static eccentricity Test coefficients are ~ isotropic, but predicted are unequal, C XX > C YY Test coefficients are ~ 4-6 larger than simplified formulas

32. GT2012-68212 32 M YY (test data) M YY (prediction) M XX (test data) M XX (prediction) Predictions match well the test data. Static eccentricity ratio (e s / c B ) Inertia Coefficients (Short SFD) 40 Short SFD, d η = 2.8c B 0 10 20 30 0.00.10.20.30.40.50.6 Inertia coefficients increase moderately with static eccentricity. Predicted M XX > M YY circular orbits r/c = 0.1 Inertia coefficients Short SFD Test coefficients are ~ 20-30 larger than simplified formulas

33. GT2012-68212 33 C YY (test data) C YY (prediction) C XX (test data) C XX (prediction) Static eccentricity ratio (e s / c A ) Damping Coefficients (Long SFD) 10 Long SFD, d η = 1.6c A 0 2 4 6 8 0.00.10.20.30.40.50.6 Damping coefficients increase more rapidly for the long damper. The test and predicted coefficients are not very sensitive to static eccentricity (e s ). Predicted coefficients agree well with test data. circular orbits r/c = 0.1 Damping coefficients Long SFD Test coefficients are ~ 3-4 larger than simplified formulas

34. GT2012-68212 34 M YY (test data) M XX (prediction) M XX (test data) M YY (prediction) Inertia coefficients are underpredicted Static eccentricity ratio (e s / c A ) Inertia Coefficients (Long SFD) 12 Long SFD, d η = 1.6c A 0 4 6 8 10 0.00.10.20.30.40.50.6 2 Coefficients grow moer rapidly with static eccentricity than in short damper. Tests and predicted force coefficients are not sensitive to static eccentricity (e s ) circular orbits r/c = 0.1 Inertia coefficients Long SFD Test coefficients are ~ 8-10 larger than simplified formulas

35. GT2012-68212 35 Conclusions For both dampers and most test conditions: cross- coupled damping and inertia force coefficients are small. Long damper has ~ 7 times more damping than short length damper. Inertia coefficients are two times larger. SFD force coefficients are more a function of static eccentricity than amplitude of whirl. Coefficients change little with ellipticity of orbit. Predictions from modern predictive tool agree well with the test force coefficients.

36. GT2012-68212 36 Conclusions More work conducted with both dampers (short and long) with SEALED ends (piston rings) with larger clearances (2c) 0-1-2 orifices plugged (3-2-1 holes active) will be reported at a later date. Current damper installation has NO central groove. Central grove is NOT a zone of constant pressure: dynamic pressures as large as in film lands. Classical theory predicts too low damping & inertias: 1/7 of test values & update

37. GT2012-68212 37 Thanks to Pratt & Whitney Engines students Sanjeev Seshaghiri, Paola Mahecha, Shraddha Sangelkar, Adolfo Delgado, Sung-Hwa Jeung, Sara Froneberger, Logan Havel, James Law. Acknowledgments Learn more at http://rotorlab.tamu.edu Questions (?)

38. GT2012-68212 38 Della Pietra and Adilleta, 2002, The Squeeze Film Damper over Four Decades of Investigations. Part I: Characteristics and Operating Features, Shock Vib. Dig, (2002), 34(1), pp. 3-26, Part II: Rotordynamic Analyses with Rigid and Flexible Rotors, Shock Vib. Dig., (2002), 34(2), pp. 97-126. Zeidan, F., L. San Andrés, and J. Vance, 1996, "Design and Application of Squeeze Film Dampers in Rotating Machinery," Proceedings of the 25th Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, September, pp. 169-188. Zeidan, F., 1995, "Application of Squeeze Film Dampers", Turbomachinery International, Vol. 11, September/October, pp. 50-53. Vance, J., 1988, "Rotordynamics of Turbomachinery," John Wiley and Sons, New York Parameter identification: Tiwari, R., Lees, A.W., Friswell, M.I. 2004. “Identification of Dynamic Bearing Parameters: A Review,” The Shock and Vibration Digest, 36, pp. 99-124. Relevant Past Work

39. GT2012-68212 39 TAMU references 2011San Andrés, L., and Delgado, A., “A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically,” ASME Paper GT2011-45274 2010Delgado, A., and San Andrés, L., 2010, “A Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Grooved Oil Seal Rings”, ASME Journal of Tribology Vol. 132 Delgado, D., and San Andrés, L., 2010, “Identification of Squeeze Film Damper Force Coefficients from Multiple-Frequency, Non- Circular Journal Motions,” ASME J. Eng. Gas Turbines Power, Vol. 132 (April), p. 042501 (ASME Paper No. GT2009-59175) 2009Delgado, A., and San Andrés, L., 2009, “Nonlinear Identification of Mechanical Parameters on a Squeeze Film Damper with Integral Mechanical Seal,” ASME Journal of Engineering for Gas Turbines and Power, Vol. 131 (4), pp. 042504 (ASME Paper GT2008- 50528) 2003San Andrés, L., and S. Diaz, 2003, “Flow Visualization and Forces from a Squeeze Film Damper with Natural Air Entrainment,” ASME Journal of Tribology, Vol. 125, 2, pp. 325-333 2001Diaz, S., and L. San Andrés, 2001, "Air Entrainment Versus Lubricant Vaporization in Squeeze Film Dampers: An Experimental Assessment of their Fundamental Differences,” ASME Journal of Gas Turbines and Power, Vol. 123 (4), pp. 871-877 2000Tao, L., S. Diaz, L. San Andrés, and K.R. Rajagopal, 2000, "Analysis of Squeeze Film Dampers Operating with Bubbly Lubricants" ASME Journal of Tribology, Vol. 122, 1, pp. 205-210 1997Arauz, G., and L. San Andrés, 1997 "Experimental Force Response of a Grooved Squeeze Film Damper," Tribology International, Vol. 30, 1, pp. 77-86 1996San Andrés, L., 1996, "Theoretical and Experimental Comparisons for Damping Coefficients of a Short Length Open-End Squeeze Film Damper," ASME Journal of Engineering for Gas Turbines and Power, Vol. 118, 4, pp. 810-815 SFDs

40. GT2012-68212 40 Select effective groove depth Predictions overlaid with test data to estimate effective groove depth d η = 2.8c B 0 2 4 6 8 10 1 100 Groove depth (d η ) Damping coefficients c c c Short SFD 0 1 2 3 4 5 1 10100 Groove depth (d η ) Damping coefficients c c c Long SFD Predictions test data d η = 1.6c A d η = 2.8 c B d η = 1.6 c A