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Research Papers: Hydrodynamic Lubrication

Three-Dimensional Dynamic Model of TEHD Tilting-Pad Journal Bearing—Part II: Parametric Studies

[+] Author and Article Information
Junho Suh

Mem. ASME
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: junhosuh77@gmail.com

Alan Palazzolo

Mem. ASME
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: a-palazzolo@tamu.edu

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received May 9, 2014; final manuscript received February 10, 2015; published online May 11, 2015. Assoc. Editor: Mihai Arghir.

J. Tribol 137(4), 041704 (Oct 01, 2015) (15 pages) Paper No: TRIB-14-1108; doi: 10.1115/1.4030021 History: Received May 09, 2014; Revised February 10, 2015; Online May 11, 2015

This paper presents a new analysis method for a thermo-elasto-hydro-dynamic (TEHD) tilting pad journal bearing (TPJB) system to reach a static equilibrium condition adopting nonlinear transient dynamic solver, whereas earlier studies have used iteration schemes such as Newton–Raphson method. The theoretical TPJB model discussed in Part I of this research is combined into a newly developed algorithm to perform a bearing dynamic analysis and present dynamic coefficients. In the nonlinear transient dynamic solver, physical and modal coordinates coexist for computational efficiency, and transformation between modal and physical coordinate is performed at each numerical integration time step. Variable time step Runge–Kutta numerical integration scheme is adopted for a reliable and fast calculation. Nonlinear time transient dynamic analysis and steady thermal analysis are combined to find the static equilibrium condition of the TPJB system, where the singular matrix issue of flexible pad finite element (FE) model is resolved. The flexible pad TPJB model was verified by comparison with other numerical results. Simulation results corresponding with the theoretical model explained in Part I are presented and discussed. It explains how the TPJB dynamic behavior is influenced by a number of eigenvector of flexible pad FE model and pad thickness. Preload change under fluid and thermal load is examined.

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References

Figures

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Fig. 4

Temperature distribution on shaft, fluid film, and bearing pads (1035 kPa, 7000 rpm)

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Fig. 2

Algorithm for thermodynamic rotor–bearing transient analysis

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Fig. 1

Algorithm for static equilibrium analysis of shaft–bearing system

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Fig. 3

Comparison of direct dynamic coefficients for three approaches: (a) Kxx, (b) Kyy, (c) Cxx, and (d) Cyy

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Fig. 5

Comparison of dynamic coefficients between Kulhanek and Childs [8] and current research. (a) Stiffness coefficient at 0 kPa, (b) damping coefficient at 0 kPa, (c) stiffness coefficient at 1035 kPa, (d) damping coefficient at 1035 kPa, (e) stiffness coefficient at 2400 kPa, and (f) damping coefficient at 2400 kPa.

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Fig. 6

Cross coupled dynamic coefficients: (a) Stiffness coefficient at 1035 kPa, (b) damping coefficient at 1035 kPa, (c) stiffness coefficient at 2400 kPa, and (d) damping coefficient at 2400 kPa

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Fig. 15

Average temperature

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Fig. 7

Nonlinear pivot stiffness with varying rotor spin speeds at 2400 kPa

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Fig. 8

Bearing pad FE model

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Fig. 9

Mode shapes of flexible pad with rocker-pivot: (a) First mode (0 Hz, rigid body mode), (b) fourth mode (15,450 Hz), (c) tenth model (33,639 Hz), and (d) 20th mode (55,475 Hz)

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Fig. 10

Stiffness coefficients with varying number of modes

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Fig. 11

Damping coefficients with varying number of modes

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Fig. 12

Static equilibrium conditions with varying number of modes

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Fig. 13

Average film thickness with varying number of modes

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Fig. 14

Average thermal expansion of journal and pads (TEHD model)

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Fig. 19

Average and peak temperature in shaft, lubricant, and pad

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Fig. 16

Peak temperature in shaft, lubricant, and pads

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Fig. 17

Three different pad thickness: (a) Initial pad thickness (model No. 1), (b) 70% thickness (model No. 2), and (c) 40% thickness (model No. 3)

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Fig. 18

Pad thickness effects on stiffness coefficient: (a) Stiffness coefficient, (b) damping coefficient, and (c) static equilibrium condition

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Fig. 20

Pivot stiffness with different pad thicknesses

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Fig. 21

Minimum film thickness with different pad thicknesses

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Fig. 22

Measurement of preload change: (a) Nonoffset model and (b) offset model

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Fig. 23

Thermal deformation of pad No. 1 at 16 Krpm: (a) 100% pad thickness, (b) 70% pad thickness, and (c) 40% pad thickness

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Fig. 24

Elastic deformation of pad No. 1 at 16 Krpm: (a) 100% pad thickness, (b) 70% pad thickness, and (c) 40% pad thickness

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Fig. 25

Preload change due to the thermal and fluid load: (a) 100% pad thickness, (b) 70% pad thickness, and (c) 40% pad thickness

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