There is significant disagreement concerning the frequency response of tilting pad journal bearings (TPJBs) due to non-synchronous excitations. Two linear models for the frequency dependence of TPJBs have been proposed. The first model, the full-coefficient or KC model, considers Np tilting pads and rotor motions for Np + 2 degrees of freedom. Dynamic reduction of the KC model results in eight frequency-dependent stiffness and damping coefficients. The second model, based on results from bearing system identification experiments, yields twelve frequency-independent stiffness, damping, and mass (KCM) coefficients. Experimental data has been presented to support both models. There are major differences in the two approaches. The analysis in this paper takes a new approach of considering the 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 full system eigenvalues and eigenvectors are then evaluated using state-space methods, with rotor and bearing pad inertias included explicitly in the model. The full bearing coefficient results are also non-synchronously reduced to the 8 stiffness and damping coefficients are and 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 example TPJBs 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 running speed. The full coefficient, non-synchronously reduced model predicts additional critically damped or overdamped modes due to the additional degrees of freedom as compared to the identified KCM model. The KCM model results in natural frequencies that are 63–65 percent higher than the full coefficient model. The difference in modal damping ratio estimates depend on the TPJB considered, with KCM being 7–17 percent higher than the full coefficient model. The full coefficient model also indicates that the bearing pads contribute significantly to the underdamped modes. The results indicate that the system identification method results in a reduced order model of TPBJ dynamic behavior. Additionally, the differences in the modal calculated system natural frequency and modal damping have potential implications for rotordynamic analyses of flexible rotors, such as critical speed and stability analyses.
Comparison of Tilting-Pad Journal Bearing Dynamic Full Coefficient and Reduced Order Models Using Modal Analysis
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Dimond, TW, Younan, AA, & Allaire, PE. "Comparison of Tilting-Pad Journal Bearing Dynamic Full Coefficient and Reduced Order Models Using Modal Analysis." Proceedings of the ASME Turbo Expo 2009: Power for Land, Sea, and Air. Volume 6: Structures and Dynamics, Parts A and B. Orlando, Florida, USA. June 8–12, 2009. pp. 1043-1053. ASME. https://doi.org/10.1115/GT2009-60269
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