Luis San Andrés Mast-Childs Professor

1. SFD EXPERIMENTAL TESTING & ANALYTICAL METHODS DEVELOPMENT High Load SFD Test Rig Identification of SFD force coefficients Luis San Andrés Mast-Childs Professor May 2011

2. PW-SFD test rig (2010) Static loader Shaker assembly (Y direction) Shaker assembly (X direction) Static loader Shaker in Y direction Shaker in X direction SFD test bearing

3. Test rig description

4. Flow path & main features in ISO VG 2 oil

5. Test rig cross section – rods installation All dimensions in inches 9 8 4 x Φ7/8 5.6 12 x Φ 7/8 BC OD Φ7.50 Test rig materials Journals, journal base, pedestal, bearing cartridge, Main support rods : AISI 1020 steel Flexural rods: Alloy Steel per ASME B18.3 4.755 Φ4.75 Φ11.00

6. Eddy current sensors and accelerometers Top view Sensor locations Y Piezoelectric accelerometer θ= 180oand 270o θ= 90o Top Land Central groove Eddy current sensor (Proximity probe) θ= 180o X eddy current sensor(X proximity probe) Bottom Land θ= 0o X Piezoelectric accelerometer Journal B θ= 0oand 90o Top Land Y eddy current sensor(Y proximity probe) θ= 270o Piezoelectric Accelerometer Bottom Land Side view: Sensors located in central groove

7. Pressure sensors θland = 210oand 330o Top view Top Land 0.5 inch PCB (pressure sensors) Central groove 0.5 inch Bottom Land Locations , Journal B θland = 330o and θland = 210o Top Land PCB (Dynamic) 1.5 inch Central groove PCB and Entran Bottom Land Side view: Sensors located at middle plane of film lands BC

8. Pressure sensors

9. Test results for • (c) SFD force coefficients – Comparison between short and long open ends dampers

10. compare SFD damping CXX ~ CYY Long (L=1 inch) CXX ~ CYY Short (L=0.5 inch) 3 Ratio of coefficients ~ (L/c3) Long and short SFDs (circular orbits)

11. compare SFD inertia MXX , MYY Long (L=1 inch) MXX , MYY Short (L=0.5 inch) Ratio of coefficients ~ (L/c) Long and short SFDs (circular orbits)

12. Film and groove dynamic pressures Lands Groove Frequency=250 Hz L/D=0.2 x 2 Long open ends SFD. Centered bearing es=0, circular orbit r=0.1cA. Groove pressure PG = 0.72 bar

13. Film and groove peak-peak pressures Frequency20-250 Hz Land length=1 in Groove width=0.5 in depth = 3/8 in (75 c) Top land Bottom land groove Long open ends SFD. Centered bearing es=0, circular orbit r=0.1cA. Groove pressure PG = 0.72 bar

14. Test results for • (d) SFD force coefficients – Comparison between open ends and sealed ends long dampers

15. compare SFD damping CXX ~ CYY Sealed ends CXX ~ CYY Open ends Open and sealed ends long SFD (circular orbits)

16. compare SFD inertia MXX , MYY Sealed ends MXX , MYY Open ends Test data for open and sealed ends(circular orbits)

17. Conclusions: Learning from tests and predictions

18. Summary of learning

19. Proposed work (TRC) Linear-Nonlinear Force Coefficients for Squeeze Film Dampers Whirl Orbit Analysis for Identification of SFD force coefficients

20. Types of journal motion Applications: K,C, M (force coefficients) RBS stability analysis FX, FY (reaction forces) RBS imbalance response & transient load effects

21. SFD predictive code • Code & GUI: virtual tool for prediction of SFD forced response • Linearforce coefficients (K,C,M) • Instantaneous reaction forces along orbital path • Automated orbit analysis for NL parameter identification

22. Purpose of whirl orbit analysis • for specified whirl orbit and over specified frequency range: • predict SFD reaction forces vs. time, • conduct Fourier analysis, & • identify SFD linearized force coefficients

23. SFD example

24. whirl orbit induces forces Eccentric (Off-center) Elliptical orbit es/c=0.5c r/c=0.25c Fundamental 1X Force SFD reaction force

25. SFD Forces: predicted and 1X Frequency 180 Hz es/c=0.5c r/c=0.25c Fundamental 1X Force SFD 1X forces do not reproduce NL forces SFD reaction force

26. SFD reaction forces The SFD instantaneous reaction forcesuperimposes a dynamic force to a static force, i.e., F=Fstatic+Fdyn. The dynamic components of the SFD reaction forces are modeled in a linearized form as wherez is a vector of dynamic displacements and (K, C, M)SFD are matrices of stiffness, viscous damping and inertia force coefficients

27. Analysis (I) The dynamic or time varying part of the SFD reaction force is periodic with fundamental period T=2p/w. Using Fourier series decomposition, To first order effects (fundamental frequency) where is the matrix of damper impedances

28. Analysis (II) The code predicts the SFD time varying reaction forces for the orbital path and delivers the fundamental Fourier components of motion and forces, i.e. zand F. Forward and backward whirl orbits ensure linear independence of the two SFD reaction forces. Solution of the system of algebraic equations: leads to the determination of the impedances: HXX, HXY,HYX, HYY

29. Analysis (III) The analysis stacks impedances for a set of frequencies (wk=1,2,….N) from which, by linear curve fits, one determines :

30. SFD Real Impedances vs. frequency HXX will give M<0 HYY fits well model K-Mw2 Frequency range 20-200 Hz

31. SFD Ima Impedances vs. frequency HXX gives average C HYY fits OK model Cw Frequency range 20-200 Hz

32. SFD NL-Linear force coefficients Frequency range 20-200 Hz SFD NL force response FY vs FX Linear force model

33. Proposed tasks (2011-12) • Test ACTUAL short length open ends damper with dynamic loads (20-300 Hz) inducing off-centered elliptical orbital motions with amplitude ratios (5:1) 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.

34. Budget (2011-12)

35. Questions (?)