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TRC 2008

TRC 2008. The Effect of (Nonlinear) Pivot Stiffness on Tilting Pad Bearing Dynamic Force Coefficients – Analysis. Jared Goldsmith Research Assistant Dr. Luis San Andres Mast-Childs Professor. TRC Project 32513/1519 T3. XLTRC 2.

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TRC 2008

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  1. TRC 2008 The Effect of (Nonlinear) Pivot Stiffness on Tilting Pad Bearing Dynamic Force Coefficients – Analysis Jared Goldsmith Research Assistant Dr. Luis San Andres Mast-Childs Professor TRC Project 32513/1519 T3

  2. XLTRC2 Enhance tilting pad bearing model by including nonlinear pivot flexibility for rocker, spherical, and flexure type pivots Project Goals

  3. Tilting Pad Journal Bearing Pivot Types Y Y PAD ROTATION PAD ROTATION X X Y PAD ROTATION X FLEXURE WEB Tilting Pad Bearings

  4. Film Thickness journal speed rotational stiffness radial stiffness film thickness Pad clearance ( ) and preload ( ) and journal eccentricity ( ) Pad angular rotation ( ), radial ( ) and transverse displacement ( ) for Film thickness: Tilting pad journal bearing & coordinates

  5. Perturbation Analysis Consider small amplitude journal and pad motions about static equilibrium position (SEP) Applying an external static load with components ( ) to the journal determines its static equilibrium position ( ) with fluid static pressure field , film thickness , and corresponding equilibrium pad rotation and deflections ( ) Consider small amplitude journal center motions ( ) of frequency about the static equilibrium point. Hence and for Small amplitude journal motions about an equilibrium position

  6. Load and Pad EOMs Bearing Journal Rotation Y Fluid film X The sum of the pad fluid film forces balance the external load applied on the journal, i.e., Force and Moment EOMs for pad: Matrix representing pad inertia and mass Bearing forces and Pad Equations of Motion

  7. Nonlinear Pad Pivot Radial Force Radial Deflection Consider a typical nonlinear force ( ) versus pivot radial deflection ( ) in a bearing pivot The assumption of small amplitude motions about an equilibrium position allows the pivot reaction radial force to be expressed as where is the static load on the pivot and is the force due to radial displacement Typical Nonlinear Pivot

  8. Pad Forces and Moment Pad Fluid Film Forces = integration of hydrodynamic pressure fields on pad Moment on Pad: Substitution of zeroth and first order pressure fields gives Fluid film impedances: Forces and moments acting on a pad

  9. Reduced Force Coefficients Assuming the pads move with the same excitation frequency ωas the journal whirl frequency, the frequency reduced coefficients are where and Matrices representing pivot stiffness and damping coefficients Frequency reduced force coefficients for tilting pad bearing

  10. Progress Pivot Pivot housing Modified tilting pad bearing model now accounts for spherical and rocker nonlinear pivot stiffness • Assumptions: • Spherical pivot – point contact • Rocker pivot – line contact Spherical pivot stiffness versus load Tilting pad bearing pivot

  11. Test Bearing Bearing Parameters Values Rotor diameter 101.59 mm Y Pad axial length 60.33 mm Pad number (arc length) 5 (57.87) Pivot offset 60% Radial pad clearance .1105 mm PAD ROTATION Radial bearing clearance .0792 mm Preload 0.282 X Pad inertia 2.49E-4 kg- Mobile DTE ISO 32 Viscosity @ 40° C 31 cSt Viscosity @ 100° C 5.5 cSt Density @ 15°C 850 kg/m3 Specific heat 1951 J/(kg-K) Carter and Childs* five pad, rocker pivot, tilting pad bearing (LBP) and (LOP) Fluid Properties * ASME Paper No. GT2008-5069 Test bearing description

  12. (LBP) Rotordynamic Force Coefficients Carter and Childs measured and predicted nonsynchronous direct stiffness Rotor speed = 4000 RPM Bearing loaded in –Y direction (LBP) The TPB model (rigid pivot) generally over predicts stiffness and damping coefficients Experimental and predicted direct stiffness and damping coefficients

  13. Static Results Original XLTRC2 (rigid pivot) and modified XLTRC2 (flexible pivot) predicted direct static stiffnesses versus static load Rigid pivot Flexible pivot Rotor speed = 4000 RPM Bearing loaded in –Y direction (LBP) Direct static stiffnesses versus load

  14. Static Results Original XLTRC2 (rigid pivot) and modified XLTRC2 (flexible pivot)predicted journal eccentricity versus static load Rigid pivot Flexible pivot Rotor speed = 4000 RPM Bearing loaded in –Y direction (LBP) Journal eccentricity versus load

  15. Future work • Perform extensive comparisons between predictions and Childs et al. experimental TPB stiffness and damping coefficients • Include pivot friction for spherical pivots Future work

  16. Statement of work • Account for pad clearance variations due to thermal and mechanical deformation effects • 2. Improve I/O operations for Excel interface • 3. Implement informed eccentricity “guess” for starting calculations Future work

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