Frequency Dependency of Measured and Predicted Rotordynamic Coefficients for a Load-On-Pad Flexible-Pivot Tilting-Pad Bearing

Experimental dynamic-stiffness-coefficient results are presented for a high-speed, lightly loaded, load-on-pad, flexible-pivot tilting-pad (FPTP) bearing. Results show that the real parts of the direct dynamic-stiffness are quadratic functions of the excitation frequency. Frequency independent $[M]$⁠, $[K]$⁠, and $[C]$ matrices can be used in place of frequency dependent $[K]$ and $[C]$ matrices to model the FPTP bearing for the conditions tested. The model reduction that results in moving from twelve degrees of freedom (three degrees of freedom for each of four pads) to two degrees of freedom in the bearing reaction model seems to account for most of the observed and predicted frequency dependency. Predictions indicate that pad and fluid inertia have a secondary impact for excitation frequencies out to synchronous frequency. Experimental results are compared to numerical predictions from models based on: (i) The Reynolds equation, and (ii) a Navier-Stokes (NS) equations bulk-flow model that retains the temporal and convective fluid inertia terms. The NS bulk-flow model results correlate better with experimental dynamic stiffness results, including added-mass terms. Both models underestimate the measured added-mass coefficients for the full excitation range; however, they do an adequate job for excitation frequencies up to synchronous frequency. The advantage of using a frequency-independent $[M]-[K]-[C]$ model is that rotordynamic stability calculations become noniterative and much quicker than for a frequency dependent $[K]-[C]$ model. However, these results only apply to this bearing at the conditions tested. Conventional tilting pad and/or FPTP bearings with different geometry and operating conditions (or even this FPTP bearing at higher loads) may require a frequency-dependent $[K]-[C]$ model.