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Research Papers: Gas Turbines: Structures and Dynamics

# Tilting Pad Journal Bearings: On Bridging the Hot Gap Between Experimental Results and Model Predictions

[+] Author and Article Information
Luis San Andrés

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

Yujiao Tao

Analytical Engineering Group,
Samsung Techwin,
Houston, TX 77079
e-mail: y.tao@samsung.com

Yingkun Li

Mechanical Engineering Department,
Texas A&M University,
College Station, TX 77843-3123
e-mail: ayouyi-1988@tamu.edu

The bearing stiffness (K) quoted is an average from those determined at loads 345 kPa to 3101 kPa and at a rotor speed of 7 krpm. No other effort is pursued to characterize the pivot stiffness, as varying with either the applied load or the shaft speed.

The test bearing has end seals (oil does not evacuate to ambient) and the flow rate at each speed remains constant for all load conditions. No effort in Ref. [2] is placed to determine whether the test bearing is over flooded with lubricant.

The selected frequency range (0–320 Hz) for parameter identification is similar to the frequency range in the experiments [3].

The model assumes an adiabatic thermal condition and the characteristic parameters (k, c, m) are calculated with the cold clearance Cp.

There are comprehensive computational models for tilting pad bearings including thermomechanical effects. However, the archival literature does not provide simple bearing design charts as in Refs. [18] and [19].

The effect of turbulent flow is not accounted for in the predictive model.

1Work conducted as a Graduate Research Assistant at Texas A&M University.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 15, 2014; final manuscript received July 21, 2014; published online September 16, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(2), 022505 (Sep 16, 2014) (11 pages) Paper No: GTP-14-1398; doi: 10.1115/1.4028386 History: Received July 15, 2014; Revised July 21, 2014

## Abstract

The accurate prediction of the forced performance of tilting pad journal bearings (TPJBs) relies on coupling a fluid film model that includes thermal energy transport, and on occasion fluid inertia, to the structural stiffness of the pads' pivots and the thermomechanical deformation of the pads' surfaces. Often enough, the flexibility of both pads and pivots is ignored prior to the bearing actual operation; practice dictating that force coefficients, damping in particular, decrease dramatically due to pivot flexibility. Even in carefully conducted experiments, components' flexibilities are invoked to explain dramatic differences between measurements and predictions. A multiple-year test program at TAMU has demonstrated the dynamic forced response of TPJBs can be modeled accurately with matrices of constant stiffness K, damping C, and added mass M coefficients. The K-C-M model, representing frequency independent force coefficients, is satisfactory for excitation frequencies less or equal to the shaft synchronous speed. However, as shown by San Andrés and Tao (2013, “The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings,” ASME J. Eng. Gas Turbines Power, 135, p. 112505), pivot flexibility reduces the applicability of the simple constant parameter model to much lower excitation frequencies. Presently, a fluid film flow model predicts the journal eccentricity and force coefficients of a five-pad rocker-back TPJB tested at TAMU under a load-between-pad (LBP) configuration. The predictions agree well with the test results provided the model uses actual hot bearing clearances and an empirical characterization of the pivot stiffness. A study follows to determine the effects of pad preload, $r¯P$ = 0.0, 0.27 (test article), and 0.50, as well as the load orientation, LBP, and load-on-pad (LOP), on bearing performance with an emphasis on ascertaining the configuration with most damping and stiffness, largest film thickness, and the least drag friction. In the study, a rigid pivot and two flexible pivots are considered throughout. Further examples present the effective contribution of the pads' mass and mass moment of inertia and film fluid inertia on the bearing force coefficients. To advance results of general character, predictions are shown versus Sommerfeld number (S), a design parameter proportional to shaft speed and decreasing with applied load. Both LBP and LOP configurations show similar performance characteristics; the journal eccentricity increasing with pivot flexibility. For LBP and LOP bearings with 0.27 preload, pivot flexibility decreases dramatically the bearing damping coefficients, in particular, at the low end of S, i.e., large loads. The model and predictions aid to better design TPJBs supporting large specific loads.

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## Figures

Fig. 1

Schematic view of a tilting pad and journal, coordinate system, and nomenclature

Fig. 2

Load configuration and pad arrangements of test bearing in Refs. [2,3]. Cold bearing clearance CB = 81 μm and preload r¯p = 0.27.

Fig. 3

TPJB journal center displacements (e) versus specific load (W/LD). Rotor speed Ω = 7 krpm. Current predictions and test data from Ref. [3].

Fig. 4

TPJB predicted oil film temperatures and measured pad subsurface temperatures [3]. Specific load W/(LD) = 3101 kPa and journal speed Ω = 7 krpm and 16 krpm. Pad inlet thermal mixing coefficient λ = 0.65 and 0.75. Inlet oil temperature 43 °C.

Fig. 5

Real part of TPJB impedance coefficients, Re(ZXX) and Re(ZYY), versus excitation frequency. Specific load W/(LD) = 1723 kPa and journal speed Ω = 7 krpm and 16 krpm. Predictions and tests [3].

Fig. 6

Imaginary part of TPJB impedance coefficients, Im(ZXX) and Im(ZYY), versus excitation frequency. Specific load W/(LD) = 1723 kPa and journal speed Ω = 7 krpm and 16 krpm. Predictions and tests [3].

Fig. 7

TPJB static stiffness coefficients (K) versus specific load W/(LD). Rotor speed Ω = 7000 rpm and 16,000 rpm. Current predictions and tests [3].

Fig. 8

TPJB damping coefficients (C) versus specific load W/(LD). Rotor speed Ω = 7000 rpm and 16,000 rpm. Current predictions and tests [3].

Fig. 9

TPJB virtual mass coefficients (M) versus specific load W/(LD). Rotor speed Ω = 7000 rpm and 16,000 rpm. Current predictions and tests [3].

Fig. 10

Journal eccentricity for a TPJB (L/D=0.6). Pad preload r¯p = 0, 0.27, and 0.5. LBP and LOP confs. Pivot stiffness kpiv = 2.36, 5.89, and ∞.

Fig. 11

Friction coefficient for a TPJB (L/D=0.6). Pad preload r¯p = 0, 0.27, and 0.5. LBP and LOP confs. Pivot stiffness kpiv = 2.36, 5.89, and ∞.

Fig. 12

Stiffness coefficients (k) for TPJBs. Pad preload r¯p = 0, 0.27, and 0.5. LBP and LOP configurations. Pivot stiffness kpiv = 2.36, 5.89, and ∞.

Fig. 13

Damping coefficients (c) for TPJBs. Pad preload r¯p = 0, 0.27, and 0.5. LBP and LOP configurations. Pivot stiffness kpiv = 2.36, 5.89, and ∞.

Fig. 14

Virtual mass coefficients (m) for TPJBs. Pad preload r¯p = 0, 0.27, and 0.5. LBP and LOP configurations. Pivot stiffness kpiv = 2.36, 5.89, and ∞.

Fig. 15

Effect of pad and fluid inertia on the real part of TPJB impedances, Re(ZXX) and Re(ZYY), versus excitation frequency. Specific load W/(LD) = 3103 kPa, journal speed Ω = 7 krpm and 16 krpm. Test data from Ref. [3].

Fig. 16

Effect of pad and fluid inertia on the imaginary part of TPJB impedances, Ima(ZXX) and Ima(ZYY), versus excitation frequency. Specific load W/(LD) = 3103 kPa, journal speed Ω = 7 krpm and 16 krpm. Test data from Ref. [3].

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