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ASME GT2012-68212

2012 ASME Turbo Expo Conference, June 11-15 ,2012, Copenhagen, DK. 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. Luis San Andrés Mast-Childs Professor, Fellow ASME Texas A&M University. ASME GT2012-68212.

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ASME GT2012-68212

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  1. 2012 ASME Turbo Expo Conference, June 11-15 ,2012, Copenhagen, DK DAMPINGAND INERTIA COEFFICIENTSFOR TWO OPEN ENDSSFDs WITH A CENTRAL GROOVE: MEASUREMENTS AND PREDICTIONS Luis San Andrés Mast-Childs Professor, Fellow ASME Texas A&M University ASME GT2012-68212 accepted for journal publication Supported by Pratt & Whitney Engines (UTC)

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

  3. SFD with a central groove oil inlet Feed groove 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. Conventional knowledge regards a groove is indifferent to the kinematics of journal motion, thus effectively isolating the adjacent film lands.

  4. P&W SFD Test Rig Static loader Isometric view Shaker assembly (Y direction) Shaker assembly (X direction) Top view Static loader Shaker in Y direction Shaker in X direction SFD test bearing

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

  6. SFD bearing design Piston ring seal (location) Test Journal Bearing Cartridge Supply orifices (3) Circumferential groove Flexural Rod (4, 8, 12) Main support rod (4) Journal Base Pedestal in

  7. Flow through squeeze film lands Oil inlet in ISO VG 2 oil Oil inlet temperature, Ts =25 oC Density, ρ=785 kg/m3 Viscosity μ at Ts=2.96 cPoise Flow rate, Qin=4.92 LPM

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

  9. SFD configurations tested 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. Parameter Identification Y X Journal also moves during excitation of the bearing • *SFDs do not have stiffnesses = reaction forces due to changes in static displacement.

  11. Parameter Identification Single frequency orbits Y Applied Loads • CW X • Two linearly independent load vectors F1 and F2 Y • CCW X displacements & accelerations • Loads F, displacement xand accelerations a recorded at each frequency

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

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

  14. Typ. impedances- lubricated SFD HXX Im(HYX)[MN/m] Re(HXX)[MN/m] Physical modelRe(HXX)= K-w2Mand Im(HXX)=Cwagree with test data. DampingC is constant over the frequency range Frequency (Hz) Frequency (Hz) CXX Im(H)/w f f start end 40 CXX [MNs/m] C XX 20 0 Frequency (Hz) 0 100 200 300 Short SFDeS=0; r =0.05cB

  15. SFD force coefficients - theory Centered journal (es=0), no lubricant cavitation Two film lands separated by a plenum: central groove has no effect on squeeze film forces. Damping Inertia Stiffness KXX = KYY = KXY = KYX = 0 Y X

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

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

  18. SFD direct damping coefficients 6 = 0.44 e c s B 5 4 = 0.29 e c s B 3 = 0 e s 2 1 Damping coefficients C XX SFD 0 0.0 0.2 0.4 0.6 1.0 0.8 0.44 e = c s B = 0.29 e c s B = 0 e s vs orbit amplitude Y Damping coefficients 45o CXX es X c CXX , CYY first decrease and then increase with orbit amplitude. Coefficients are isotropic CXX ~ CYY 6 Damping coefficients 5 CYY 4 3 2 1 Damping coefficients C YY SFD 0 0.0 0.2 0.4 0.6 0.8 1.0 Orbit amplitude (r /cB) Short SFD (12.7 mm lands, c=0.138 mm)

  19. SFD added mass coefficients 35 = 0.44 e c s Mass coefficients B 30 25 20 =0.29 e c s B 15 = 0 e s 10 5 Mass Coefficients M XX SFD 0 0.0 0.2 0.4 0.6 0.8 1.0 35 Mass coefficients 30 0.44 e = c s B 25 20 15 = 0.29 e c s B = 0 e s 10 5 Mass Coefficients M YY SFD 0 0.0 0.2 0.4 0.6 0.8 1.0 Orbit amplitude (r /cB) vs orbit amplitude Y 45o MXX es X c MXX , MYY decrease with amplitude of motion, as prior tests* and theory show** MYY • *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)

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

  21. SFD direct damping coefficients 6 Damping coefficients 4 2 C XX SFD 0 0.0 0.2 0.4 0.6 6 Damping coefficients 4 2 Amplitudes of motion: C YY SFD 0 0.0 0.2 0.4 Static eccentricity ratio ( ) e /c S A vs static eccentricity All orbits (circular & elliptic) Y 45o es X c CXX CXX ~ CYY with amplitude of motion & orbit shape. SFD forcedresponse isindependentof BC kinematics. CYY Long SFD (25.4 mm lands, c=0.141 mm)

  22. SFD added mass coefficients 12 Mass coefficients 10 8 6 4 2 M XX SFD 0 0.0 0.2 0.4 0.6 12 Added Mass Coefficients Mass coefficients 10 8 6 4 Amplitudes of motion: 2 M YY SFD 0 0.0 0.2 0.4 0.6 Static eccentricity ratio ( ) e /c Added Mass Coefficients S A vs static eccentricity All orbits (circular & elliptic) Y 45o es X c MXX MXX ~ MYYnot strong function of amplitude of motion or orbital shape & increasing with static eccentricity MYY Long SFD (25.4 mm lands, c=0.141 mm)

  23. Recorded dynamic pressures in groove and film lands

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

  25. groove 0.28 bar psi 0 -0.28 bar Number of periods Dynamic pressures: films & groove Whirl frequency 130 Hz film lands psi 0.69 bar Top and bottomfilm lands showsimilarpressures. 0 -0.69 bar Number of periods Dynamic pressure in thegrooveis not zero! Long SFD. es=0, r=0.1cA. PG = 0.72 bar

  26. Dynamic pressures: films & groove film lands psi 0.69 bar 0 -0.69 bar Number of time periods groove Number of time periods 0.69 bar psi 0 -1.40 bar Number of time periods Whirl frequency 200 Hz Film and groove dynamic pressuresincrease with excitation frequency. Pressure wavesshow spikes(high frequency content), typical ofair ingestion& entrapment Long SFD. es=0, r=0.1cA. PG = 0.72 bar

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

  28. Ratio of groove/film land pressures 3/8”~70 c 1 “ 0.5” 1” Groove generates large hydrodynamic pressures! groove lands (top) P-P pressure ratios 1.0 0 100 200 c=5.5 mil (0.141 mm) Frequency (Hz)

  29. Comparisons to predictions from a modern model

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

  31. Damping coefficients 10 Short SFD, dη = 2.8cB C ( prediction ) XX C ( test data ) 8 XX C ( prediction ) 6 YY C ( test data ) YY Damping Coefficients (Short SFD) 4 2 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Static eccentricity ratio (es / cB) Short SFD Predicted coefficients agree well with test data. Damping coefficients increase moderately with static eccentricity Test coefficients are ~ isotropic, but predicted are unequal, CXX > CYY Test coefficients are ~ 4-6 larger than simplified formulas circular orbits r/c = 0.1

  32. Inertia coefficients 40 M (prediction) M (test data) XX YY 30 M (prediction) M (test data) YY XX 20 Inertia Coefficients (Short SFD) 10 Short SFD, dη = 2.8cB 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Static eccentricity ratio (es / cB) Short SFD Predictions match well the test data. Inertia coefficients increase moderately with static eccentricity. Predicted MXX > MYY Test coefficients are ~ 20-30 larger than simplified formulas circular orbits r/c = 0.1

  33. Damping coefficients 10 Long SFD, dη = 1.6cA 8 6 Damping Coefficients (Long SFD) 4 2 C ( prediction ) XX C ( test data ) XX 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 C ( prediction ) YY C ( test data ) Static eccentricity ratio (es / cA) YY Long SFD Predicted coefficients agree well with test data. Damping coefficients increasemore rapidly for the long damper. The test and predicted coefficients are not very sensitive to static eccentricity (es). Test coefficients are ~ 3-4 larger than simplified formulas circular orbits r/c = 0.1

  34. Inertia coefficients 12 10 8 6 Inertia Coefficients (Long SFD) 4 M (test data) YY M (test data) XX 2 Long SFD, dη = 1.6cA M (prediction) 0 M (prediction) YY XX 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Static eccentricity ratio (es / cA) Long SFD Inertia coefficients are underpredicted Coefficients grow moer rapidly with static eccentricity than in short damper. Tests and predicted force coefficients are not sensitive to static eccentricity (es) Test coefficients are ~ 8-10 larger than simplified formulas circular orbits r/c = 0.1

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

  36. Conclusions & update • Central grove is NOT a zone of constant pressure: dynamic pressures as large as in film lands. • Classical theorypredicts too low damping & inertias: 1/7 of test values • 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.

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

  38. Relevant Past Work • 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.

  39. TAMU references SFDs

  40. 10 5 8 4 6 3 Damping coefficients Damping coefficients 4 2 2 1 0 0 c 1 c c c 10 100 1 c c 10 100 Groove depth (dη) Groove depth (dη) Select effective groove depth Predictions overlaid with test data to estimate effective groove depth Short SFD Long SFD test data test data Predictions Predictions dη = 2.8cB dη = 1.6cA dη = 2.8 cB dη = 1.6 cA

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