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Research Papers: Gas Turbines: Structures and Dynamics

# Effect of Pad Flexibility on the Performance of Tilting Pad Journal Bearings—Benchmarking a Predictive Model

[+] Author and Article Information
Luis San Andrés

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

Yingkun Li

Texas A&M University,
College Station, TX 77843
e-mail: erica.li@sulzer.com

1Present address: Rotordynamics Engineer, Sulzer Pumps US Inc., Brookshire, TX 77423

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received June 22, 2015; final manuscript received August 7, 2015; published online September 16, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(12), 122503 (Sep 16, 2015) (15 pages) Paper No: GTP-15-1215; doi: 10.1115/1.4031344 History: Received June 22, 2015; Revised August 07, 2015

## Abstract

Tilting pad journal bearings (TPJBs) supporting high-performance turbomachinery rotors have undergone steady design improvements to satisfy ever stringent operating conditions that include large specific loads, due to smaller footprints, and high surface speeds that promote flow turbulence and hence larger drag power losses. Simultaneously, predictive models continuously evolve to include minute details on bearing geometry, pads and pivots' configurations, oil delivery systems, etc. In general, predicted TPJB rotordynamic force coefficients correlate well with experimental data for operation with small to moderately large unit loads (1.7 MPa). Experiments also demonstrate bearing dynamic stiffnesses are frequency dependent, best fitted with a stiffness-mass like model whereas damping coefficients are adequately represented as of viscous type. However, for operation with large specific loads (>1.7 MPa), poor correlation of predictions to measured force coefficients is common. Recently, an experimental effort (Gaines, J., 2014, “Examining the Impact of Pad Flexibility on the Rotordynamic Coefficients of Rocker-Pivot-Pad Tiling-Pad Journal Bearings,” M.S. thesis, Mechanical Engineering, Texas A&M University, College Station, TX) produced test data for three TPJB sets, each having three pads of unequal thickness, to quantify the effect of pad flexibility on the bearings' force coefficients, in particular damping, over a range of load and rotational speed conditions. This paper introduces a fluid film flow model accounting for both pivot and pad flexibility to predict the bearing journal eccentricity, drag power loss, lubricant temperature rise, and force coefficients of typical TPJBs. A finite element (FE) pad structural model including the Babbitt layer is coupled to the thin film flow model to determine the mechanical deformation of the pad surface. Predictions correlate favorably with test data, also demonstrating that pad flexibility produces a reduction of up to 34% in damping for the bearing with the thinnest pads relative to that with the thickest pads. A parametric study follows to quantify the influence of pad thickness on the rotordynamic force coefficients of a sample TPJB with three pads of increasing preload, $r¯p$  = 0, 0.25 (baseline) and 0.5. The bearing pads are either rigid or flexible by varying their thickness. For design considerations, dimensionless static and dynamic characteristics of the bearings are presented versus the Sommerfeld number (S). Pad flexibility shows a more pronounced effect on the journal eccentricity and the force coefficients of a TPJB with null pad preload than for the bearings with larger pad preloads (0.25 and 0.5), in particular for operation with a small load or at a high surface speed (S > 0.8).

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## References

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## Figures

Fig. 1

Schematic view of an idealized TPJB. Film thickness (h), pad surface deflection (up(θ,z)), pad rotation (δp), and pivot deflections (ξpiv, ηpiv) greatly exaggerated.

Fig. 2

(a) Typical FE model and mesh for a bearing pad and (b) boundary conditions on pad as modeled in Ref. [13]. ur, uθ, uz are the nodal displacements along the radial, angular, axial directions, and relative to pivot displacement.

Fig. 3

Fig. 4

Illustration of three pad bearing and set up for measurement of pivot stiffness

Fig. 5

Journal eccentricity (eY) along the load direction versus unit load W/(LD). Journal speed Ω = 6 krpm and 12 krpm. Predictions (without and with pad flexibility) and test data from Gaines [16]. Results shown for thin, medium, and thick pads.

Fig. 6

Maximum pad-surface temperature versus unit load W/(LD). Journal speed Ω = 6 krpm and 12 krpm. Predictions (without and with pad flexibility) and test data from Gaines [16]. Inlet oil temperature, Tin = 49 °C. Results shown for thin, medium, and thick pads.

Fig. 7

Real part of complex stiffnesses for TPJBs with pads ofthickness (a) t = 8.5 mm, (b) t = 10 mm, and (c) t = 11.5 mm. Shaft speed Ω = 6 krpm (100 Hz) and unit load W/(LD) = 1726 kPa. Test data from Gaines [16] and predictions (with and without pad flexibility).

Fig. 8

Real part of complex stiffnesses for TPJBs with pads of thickness (a) t = 8.5 mm, (b) t = 10 mm, and (c) t = 11.5 mm. Shaft speed Ω = 12 krpm (200 Hz) and unit load W/(LD) = 1726 kPa. Test data from Gaines [16] and predictions (with and without pad flexibility).

Fig. 9

Imaginary part of complex stiffnesses for TPJBs with pads of thickness (a) t = 8.5 mm, (b) t = 10 mm, and (c) t = 11.5 mm. Shaft speed Ω = 6 krpm (100 Hz) and unit load W/(LD) = 1726 kPa. Test data from Gaines [16] and predictions (with and without pad flexibility). Symbol □ on right vertical axis denotes product for prediction with pad flexibility.

Fig. 10

Imaginary part of complex stiffnesses for TPJBs with pads of thickness (a) t = 8.5 mm, (b) t = 10 mm, and (c) t = 11.5 mm. Shaft speed Ω = 12 krpm (200 Hz) and unit load W/(LD) = 1726 kPa. Test data from Gaines [16] and predictions (with and without pad flexibility). Symbol □ on right vertical axis denotes product for prediction with pad flexibility.

Fig. 11

Direct stiffnesses (kXX and kYY) versus unit load and two shaft speeds. Predictions (without and with pad flexibility) and test data from Gaines [16]. Results shown for thin, medium, and thick pads.

Fig. 12

Predicted film pressure and film thickness at bearing mid plane. Operation with unit load W/(LD) = 172 kPa and shaft speed Ω = 6 krpm. Location of the maximum film pressure for each pad: θ1 = 33 deg (pad 1), θ2 = 153 deg (pad 2), and θ3 = 273 deg (pad 3). Location of the minimum film thickness for each pad: θ1 = 53 deg (pad 1), θ2 = 173 deg (pad 2), and θ3 = 301 deg (pad 3).

Fig. 13

Direct damping coefficients (cXX and cYY) versus unit load and two shaft speeds. Predictions (without and with pad flexibility) and test data from Gaines [16]. Results shown for thin, medium, and thick pads.

Fig. 14

Direct virtual mass coefficients (mXX and mYY) versus unit load and shaft speed = 6 krpm. Predictions (without and with pad flexibility) and test data from Gaines [16]. Results shown for thin, medium, and thick pads.

Fig. 15

Three-pad TPJB journal eccentricity (e/Cp) versus Sommerfeld number (S). Pad stiffness kpad = 3.15, 7.33, ∞ (rigid) and kpiv = 16. Pad preload varies: LBP and LOP configurations. Specific load W/(LD) = 689 kPa, rotor speed Ω = 500–12,000 rpm.

Fig. 16

Three-pad TPJB drag friction coefficient (f) versus Sommerfeld number. Pad stiffness kpad = 3.15, 7.33, ∞ (rigid) and kpiv = 16. Pad preload varies: LBP and LOP configurations. Specific load W/(LD) = 689 kPa, rotor speed Ω = 500–12,000 rpm.

Fig. 17

Three-pad TPJB stiffness coefficients (kXX, kYY) versus Sommerfeld number (S). Pad stiffness kpad = 3.15, 7.33, ∞ (rigid) and kpiv = 16. Pad preload r¯p = 0, 0.5: LBP configuration. Specific load W/(LD) = 689 kPa, rotor speed Ω = 500–12,000 rpm.

Fig. 18

Three-pad TPJB stiffness coefficients (kXX, kYY) versus Sommerfeld number (S). Pad stiffness kpad = 3.15, 7.33, ∞ (rigid) and kpiv = 16. Pad preload r¯p = 0.25: LOP and LBP configurations. Specific load W/(LD) = 689 kPa, rotor speed Ω = 500–12,000 rpm.

Fig. 19

Three-pad TPJB damping coefficients (cXX, cYY) versus Sommerfeld number. Pad stiffness kpad = 3.15, 7.33, ∞ (rigid) and kpiv = 16. Pad preload r¯p = 0, 0.5: LBP configuration. Specific load W/(LD) = 689 kPa, rotor speed Ω = 500–12,000 rpm.

Fig. 20

Three-pad TPJB damping coefficients (cXX, cYY) versus Sommerfeld number (S). Pad stiffness kpad = 3.15, 7.33, ∞ (rigid) and kpiv = 16. Pad preload r¯p = 0.25: LOP and LBP confs. Specific load W/(LD) = 689 kPa, rotor speed Ω = 500–12,000 rpm.

Fig. 21

Three-pad TPJB virtual mass coefficients (mXX, mYY) versus Sommerfeld number (S). Pad stiffness kpad = 3.15, 7.33, ∞ (rigid) and kpiv = 16. Pad preload r¯p  = 0, 0.5: LBP conf. Specific load W/(LD) = 689 kPa, rotor speed Ω = 500–12,000 rpm.

Fig. 22

Three-pad TPJB virtual mass coefficients (mXX, mYY) versus Sommerfeld number (S). Pad stiffness kpad = 3.15, 7.33, ∞ (rigid) and kpiv = 16. Pad preload r¯p = 0.25: LOP and LBP confs. Specific load W/(LD) = 689 kPa, rotor speed Ω = 500–12,000 rpm.

## Errata

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