The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings
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Recent comprehensive experimental data showcasing the force coefficients of commercial size tilting pad journal bearings has brought to rest the long standing issue on the adequacy of the [K,C,M] physical model to represent frequency independent bearing force coefficients, in particular viscous damping. Most experimental works test tilting pad journal bearings (TPJBs) with large preloads, operating over a large wide range of rotor speeds, and with null to beyond normal specific loads. Predictions from apparently simple fluid film bearing models stand poor against the test data which invariably signals to theory missing pivot and pad flexibility effects, and most importantly, ignoring significant differences in bearing and pad clearances due to actual operation, poor installation and test procedures, or simply errors in manufacturing and assembly. Presently, a conventional thermo hydrodynamic bulk flow model for prediction of the pressure and temperature fields in TPJBs is detailed. The model accounts for various pivot stiffness types, all load dependent and best when known empirically, and allows for dissimilar pad and bearing clearances. The algorithm, reliable even for very soft pad-pivots, predicts frequency reduced bearing impedance coefficients and over a certain frequency range delivers the bearing stiffness, damping and virtual mass force coefficients. Good correlation of predictions against a number of experimental results available in the literature bridges the gap between a theoretical model and the applications. Predicted pad reaction loads reveal large pivot deflections, in particular for a bearing with large preloaded pads, with significant differences in pivot stiffness as a function of specific load and operating speed. The question on how pivot stiffness acts to increase (or decrease) the bearing force coefficients, in particular the dynamic stiffness versus frequency, remains since the various experimental data show contradictory results. A predictive study with one of the test bearings varies its pivot stiffness from 10% of the fluid film stiffness to an almost rigid one, 100 times larger. With certainty, bearings with nearly rigid pivot stiffness show frequency independent force coefficients. However, for a range of pad pivot stiffness, 1/10 to ten times the fluid film stiffness, TPJB impedances vary dramatically with frequency, in particular as the excitation frequency grows above synchronous speed. The bearing virtual mass coefficients become negative, thus stiffening the bearing for most excitation frequencies.
