Comparison of Tilting-Pad Journal Bearing Dynamic Full Coefficient and Reduced Order Models Using Modal Analysis (GT2009-60269)

Abstract

There is a significant disagreement in the literature concerning the proper evaluation of the experimental identification and frequency response of tilting-pad journal bearings (TPJBs) due to shaft excitations. Two linear models for the frequency dependence of TPJBs have been proposed. The first model, the full coefficient or stiffness-damping (KC) model, considers Np tilting pads and two rotor radial motions for Np+2 degrees of freedom. The dynamic reduction of the KC model results in eight frequency-dependent stiffness and damping coefficients. The second model, based on bearing system identification experimental results, employs 12 frequency-independent stiffness, damping, and mass (KCM) coefficients; pad degrees of freedom are not considered explicitly. Experimental data have been presented to support both models. There are major differences in the two approaches. The present analysis takes a new approach of considering pad dynamics explicitly in a state-space modal analysis. TPJB shaft and bearing pad stiffness and damping coefficients are calculated using a well known laminar, isothermal analysis and a pad assembly method. The TPJB rotor and pad KC model eigenvalues and eigenvectors are then evaluated using state-space methods, with rotor and bearing pad inertias included explicitly in the model. The KC model results are also nonsynchronously reduced to the eight stiffness and damping coefficients and are expressed as shaft complex impedances. The system identification method is then applied to these complex impedances, and the state-space modal analysis is applied to the resulting KCM model. The damping ratios, natural frequencies, and mode shapes from the two bearing representations are compared. Two sample TPJB cases are examined in detail. The analysis indicated that four underdamped modes, two forward and two backward, dominate the rotor response over excitation frequencies from 0 to approximately running speed. The KC model predicts additional nearly critically damped modes primarily involving pad degrees of freedom, which do not exist in the identified KCM model. The KCM model results in natural frequencies that are 63–65% higher than the KC model. The difference in modal damping ratio estimates depends on the TPJB considered; the KCM estimate was 7–17% higher than the KC model. The results indicate that the KCM system identification method results in a reduced order model of TPBJ dynamic behavior, which may not capture physically justifiable results. Additionally, the differences in the calculated system natural frequency and modal damping have potential implications for rotordynamic analyses of flexible rotors.