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Research Papers: Gas Turbines: Structures and Dynamics

A Flow Starvation Model for Tilting Pad Journal Bearings and Evaluation of Frequency Response Functions: A Contribution Toward Understanding the Onset of Low Frequency Shaft Motions

[+] Author and Article Information
Luis San Andrés

Professor
Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843
e-mail: Lsanandres@tamu.edu

Bonjin Koo

Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843
e-mail: Bjkoo@tamu.edu

Makoto Hemmi

Center of Tech. Innov.-M.E.,
R&D Group. Hitachi, Ltd.,
Hitachinaka 312-0034, Japan
e-mail: Makoto.hemmi.js@hitachi.com

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 21, 2017; final manuscript received August 1, 2017; published online January 3, 2018. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(5), 052506 (Jan 03, 2018) (14 pages) Paper No: GTP-17-1382; doi: 10.1115/1.4038043 History: Received July 21, 2017; Revised August 01, 2017

Direct lubrication tilting pad journal bearings (TPJBs) require less oil flow, reduce power consumption, and offer cooler pad temperatures for operation at high surface speeds. Although apparently free of hydrodynamic instability, the literature shows that direct lubrication TPJBs exhibit unexpected shaft vibrations with a broadband low frequency range, albeit small in amplitude. Published industrial practice demonstrates the inlet lubrication type, a reduced supply flow rate causing film starvation, and the bearing discharge conditions (evacuated or end sealed) affect the onset, gravity, and persistency of the subsynchronous vibration (SSV) hash motions. The paper presents a physical model to predict the performance of TPJBs with flow conditions ranging from over flooded to extreme starvation. Lubricant starvation occurs first on an unloaded pad, thus producing a (beneficial) reduction in drag power. As the supplied flowrate decreases further, fluid starvation moves toward the loaded pads and affects the film temperature and power loss, increases the journal eccentricity, and modifies the dynamic force coefficients of each tilting pad and thus the whole bearing. For a point mass rotor supported on a TPJB, the analysis produces eigenvalues and frequency response functions (FRFs) from three physical models for lateral rotor displacements: one with frequency reduced (4 × 4) bearing stiffness (K) and damping (C) coefficients and another with constant K–C–M (inertia) coefficients over a frequency range. The third model keeps the degrees of freedom (DOF) (tilting) of each pad and incorporates the full matrices of force coefficients including fluid inertia. Predictions of rotordynamic performance follow for two TPJBs: one bearing with load between pads (LBP) configuration, and the other with a load on a pad (LOP) configuration. For both examples, under increasingly poor lubricant flow conditions, the damping ratio for the rotor-bearing low frequency (SSV) modes decreases, thus producing an increase in the amplitude of the FRFs. For the LOP bearing, a large static load produces a significant asymmetry in the force coefficients; the rotor bearing has a small stiffness and damping for shaft displacements in the direction orthogonal to the load. A reduction in lubricant flow only exacerbates the phenomenon; starvation reaches the loaded pad to eventually cause the onset of low frequency (SSV) instability. The bearing analyzed showed similar behavior in a test bench. The predictions thus show a direct correlation between lubricant flow starvation and the onset of SSV.

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References

Brockwell, K. , Dmochowski, W. , and DeCamillo, S. , 1994, “Analysis and Testing of the LEG Tilting Pad Journal Bearing-A New Design for Increasing Load Capacity, Reducing Operating Temperatures and Conserving Energy,” 23rd Turbomachinery Symposium, Dallas, TX, Sept. 13–15. http://oaktrust.library.tamu.edu/handle/1969.1/163501
He, M. , Allaire, P. , Barrett, L. , and Nicholas, J. , 2005, “Thermohydrodynamic Modeling of Leading-Edge Groove Bearings Under Starvation Condition,” Tribol. Trans., 48(3), pp. 362–369. [CrossRef]
DeCamillo, S. M. , He, M. , Cloud, C. H. , and Byrne, J. M. , 2008, “Journal Bearing Vibration and SSV Hash,” 37th Turbomachinery Symposium, Houston, TX, Sept. 7–11. https://www.kingsbury.com/pdf/journal-bearing-vibration-and-ssv-hash.pdf
Nicholas, J. C. , Elliott, G. , Shoup, T. P. , and Martin, E. , 2008, “Tilting Pad Journal Bearing Starvation Effects,” 37th Turbomachinery Symposium, Houston, TX, Sept. 7–11. https://pdfs.semanticscholar.org/bc64/74754c93304c2c67a09d23c902bf2d4ad276.pdf
Libraschi, M. , Catanzaro, M. , Crosato, O. , and Evangelisti, S. , 2013, “Review of Experimental Sub-Synchronous Vibrations on Large Size Tilting Pad Journal Bearings and Comparison With Analytical Predictions,” 42nd Turbomachinery Symposium, Houston, TX, Oct. 1–3. https://pdfs.semanticscholar.org/470d/ce82048d2f6e94a4f0f52db2869858e777b5.pdf
Dimond, T. W. , Younan, A. A. , and Allaire, P. , 2010, “Comparison of Tilting-Pad Journal Bearing Dynamic Full Coefficient and Reduced Order Models Using Modal Analysis,” ASME J. Vib. Acoust., 132(5), p. 051009. [CrossRef]
Whalen, J. K. , Cerny, V. , He, M. , and Polreich, V. , 2015, “The Effect of Starvation on the Dynamic Properties of Tilting Pad Journal Bearings,” 44th Turbomachinery Symposium, Houston, TX, Sept. 14–17.
San Andrés, L. , and Tao, Y. , 2013, “The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings,” ASME J. Eng. Gas Turbines Power, 135(11), p. 112505. [CrossRef]
San Andrés, L. , and Li, Y. , 2015, “Effect of Pad Flexibility on the Performance of Tilting Pad Journal Bearings-Benchmarking a Predictive Model,” ASME J. Eng. Gas Turbines Power, 137(12), p. 122503. [CrossRef]
San Andrés, L. , 1996, “Turbulent Flow, Flexure-Pivot Hybrid Bearings for Cryogenic Applications,” ASME J. Tribol., 118(1), pp. 190–200. [CrossRef]
San Andrés, L. , 2010, “Static and Dynamic Forced Performance of Tilting Pad Bearings: Analysis Including Pivot Stiffness,” Modern Lubrication Theory, Notes 16, Libraries Texas A&M University Repository, College Station, TX.
Zeidan, F. Y. , and Herbage, B. S. , 1991, “Fluid Film Bearing Fundamentals and Failure Analysis,” 20th Turbomachinery Symposium, Dallas, TX, Sept. 17–19. http://oaktrust.library.tamu.edu/handle/1969.1/163546
Smith, D. M. , 1933, “The Motion of a Rotor Carried by a Flexible Shaft in Flexible Bearings,” Proc. R. Soc. London, Ser. A, 142(846), pp. 92–118. [CrossRef]

Figures

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Fig. 1

Schematic view of a tilting pad and a journal, coordinate system, and nomenclature. Adapted from Ref. [8].

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Fig. 2

Schematic view of a pad with lubricant starvation. Qc and Qh denote the supply flow and upstream flow mixing at the pad inlet section.

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Fig. 3

Idealization of hydraulic network for a multiple pad bearing with lubricant delivered at a constant supply pressure (Ps)

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Fig. 7

Schematic view of a five-pad TPJB (load on pad # 2)

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Fig. 4

Predicted pressure profiles at bearing midplane for nominal flowrate and starved flow (71% and 41% of nominal flowrate). Shaft speed = 5000 rpm and specific load = 689 kPa.

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Fig. 5

Schematic view of a four pad TPJB with LBP configuration

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Fig. 10

Predicted horizontal (a) stiffness and (b) damping coefficients (K̃XX(1X),C̃XX(1X)) for LOP bearing versus shaft speed. Models with five-pads and three-pads (+ oil starvation at 88% of nominal flow). Static load = 1070 kPa.

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Fig. 6

FRF amplitude for rotor displacement |y/FY| versus frequency. (a) KCM model, (b) frequency reduced coefficients model, and (c) full force coefficients model. Operation with flow rate from fully flooded (100%) to starved (41%). Four-pad (LBP). Specific load 689 kPa. Journal speed 5 krpm.

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Fig. 8

Predicted fields at bearing midplane: (a) top film thickness, (b) middle pressure, and (c) bottom temperature rise for models with five-pads, three-pads, and three-pads with starved flow (88% of nominal flowrate). Shaft speed = 3600 rpm and static load = 1070 kPa.

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Fig. 11

Predicted (a) journal eccentricity (e/Cp), (b) stiffness, and (c) damping (K̃YY(1X),C̃YY(1X)) versus % of nominal flowrate for single pad bearing. Static load = 1070 kPa and shaft speed = 3600 rpm.

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Fig. 9

Predicted vertical (a) stiffness and (b) damping coefficients (K̃YY(1X),C̃YY(1X)) for LOP bearing versus shaft speed. Models with five-pads and three-pads (+ oil starvation at 88% of nominal flow). Static load = 1070 kPa.

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Fig. 14

Five-pads, three-pads, and single-pad bearing models: FRF amplitude for pads' tilt angle |δ/FX|. Shaft speed = 3600 rpm and static load = 117.4 kN.

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Fig. 15

Five-pads, three-pads, and single-pad bearing models: FRF amplitude for pads' tilt angle |δ/FY| from. Single pad model results are shown in (a) and (b). Shaft speed = 3600 rpm and static load = 117.4 kN.

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Fig. 12

Five-pads and three-pads bearing models: FRF amplitude for rotor lateral motions (a) |x/FX| and (b) |y/FX|. Shaft speed = 3600 rpm and static load = 117.4 kN.

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Fig. 13

Five-pads, three-pads, and single-pad bearing models: FRF amplitude for rotor lateral motions (a) |x/FY| and (b) |y/FY|. Shaft speed = 3600 rpm and static load = 117.4 kN.

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Fig. 16

Three-pads bearing model: FRF amplitude for rotor lateral motion (a) |x/FX| and (b) pad#2 tilt angle |δ2/FX|. Operation with flow rate from fully flooded (100%) to a starved flow condition (88%). Shaft speed = 3600 rpm, static load = 117.4 kN, and nominal flow = 209 LPM.

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Fig. 17

Single-pad bearing model: FRF amplitude for rotor lateral motion (a) |y/FY| and (b) pad#2 tilt angle |δ2/FY|. Operation with flow rate from fully flooded (100%) to a starved flow condition (52%). Shaft speed = 3600 rpm, static load = 117.4 kN, and nominal flow = 99 LPM.

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