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

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

3 Test rig description

4 Flow path & main features in Test rig main features Journal diameter: 5.0 Film clearance: (A) 5.55mil (B) 5.43mil Film length: (A) 2x1, (B) 2 x 0.5 Centering stiffness: variable ISO VG 2 oil

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

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

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

8 Pressure sensors

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

10 Long and short SFDs (circular orbits) compare SFD damping C XX ~ C YY Short (L=0.5 inch) C XX ~ C YY Long (L=1 inch) Ratio of coefficients ~ (L/c 3 ) 3

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

12 Film and groove dynamic pressures Long open ends SFD. Centered bearing e s =0, circular orbit r=0.1c A. Groove pressure P G = 0.72 bar Frequency=250 Hz Lands Groove L/D=0.2 x 2

13 Film and groove peak-peak pressures Long open ends SFD. Centered bearing e s =0, circular orbit r=0.1c A. Groove pressure P G = 0.72 bar Frequency Hz Bottom land Top land groove Land length=1 in Groove width=0.5 in depth = 3/8 in (75 c)

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

15 Open and sealed ends long SFD (circular orbits) compare SFD damping C XX ~ C YY Open ends C XX ~ C YY Sealed ends

16 Test data for open and sealed ends (circular orbits) compare SFD inertia M XX, M YY Open ends M XX, M YY Sealed ends

17 Conclusions: Learning from tests and predictions

18 Summary of learning Open ends long damper shows ~ 7 times more damping than short length damper. Inertia coefficients are two times larger. SFD force coefficients are more a function of static eccentricity (max. 40%c) than amplitude of whirl (max 40%c) changing little with ellipticity of orbit (aspect ratios 1:1, 2:1 & 5:1) Piston ring faces orientation affects leakage and force coefficients. Long Sealed SFD shows ~2.6 times more damping than open ends SFD Code benchmarked for long and short SFDs (open and sealed ends).

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

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

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

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

23 SFD example Journal Diameter5.0 in Total Length1.0 in Land Clearance5.0 mil NO Central Groove Feed holes3 (120deg) Axial Length0.5 in Ambient Pressure0.0 psig Supply Pressure10 psig Cavitation Pressure psig Supply Temperature77 o F Viscosity at Tsupply 0.43 Reyns Density49 lb/ft 3

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

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

26 SFD reaction forces The SFD instantaneous reaction force superimposes a dynamic force to a static force, i.e., F=F static +F dyn. The dynamic components of the SFD reaction forces are modeled in a linearized form as where z 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=2 /. 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. z and 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: H XX, H XY,H YX, H YY

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

30 SFD Real Impedances vs. frequency H YY fits well model K-M 2 H XX will give M<0 Frequency range Hz

31 SFD Ima Impedances vs. frequency H YY fits OK model C H XX gives average C Frequency range Hz

32 SFD NL-Linear force coefficients Linear force model M xx M yy M xy M yx lbm C xx C yy C xy C yx lbf-s/in K xx K yy K xy K yx lbf/in 2.12E E E E+01 F Y vs F X Frequency range Hz SFD NL force response DISSIPATED ENERGY IN A PERIOD or MOTION lbf-in Non-linear (from time transient response) Linear from ALL force coefficients

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

34 Budget ( ) Support for graduate student (20 h/week) x $ 1,800 x 12 months$ 21,600 Fringe benefits (0.6%) and medical insurance ($191/month)$ 2,419 Travel to (US) technical conference$ 1,200 Tuition three semesters ($3,802 x 3)$ 10,138 Supplies for test rig $ 1,500 Total Cost: $ 37,108

35 Questions (?)