Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness and Different Pad Preloads

Abstract

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to non-synchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are considered using a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced non-synchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.