Wilkes, Jason Christopher (2012-02). Measured and Predicted Rotor-Pad Transfer Functions for a Rocker-Pivot Tilting-Pad Journal Bearing. Doctoral Dissertation.
Thesis
Many researchers have compared predicted stiffness and damping coefficients for tilting-pad journal bearings (TPJBs) to measurements. Most have found that direct damping is consistently overpredicted. The thrust of this research is to explain the difference between measured and predicted stiffness and damping coefficients for TPJBs, and to provide some confidence to designers that TPJB dynamic coefficients can be accurately predicted. Most analytical models for TPJBs are based on the assumption that explicit dependence on pad motion can be eliminated by assuming harmonic rotor motion such that the amplitude and phase of pad motions resulting from radial and transverse rotor motions are predicted by rotor-pad transfer functions. In short, these transfer functions specify the amplitude and phase of pad motion (angular, radial, translational, etc.) in response to an input rotor motion. A new pad perturbation model is developed including the effects of angular, radial, and circumferential pad motion and changes in pad clearance due to pad bending compliance. Though all of these pad variables have previously been included in different analyses, there are no publications containing perturbations of all four variables. In addition, previous researchers have only perturbed the journal, while both the bearing and journal motions are perturbed in the present analysis, and the applicability of comparing rotor-perturbed bearing impedance predictions to impedances measured on a bearing-perturbed test rig is discussed. This perturbation model was implemented in a Reynolds-based TPJB code to predict the frequency-dependent bearing impedances and rotor-pad transfer functions. Direct measurements of pad motion during test excitation were recorded to produce measured transfer functions between rotor and pad motion, and a comparison between these measurements and predictions is given. Motion probes were added to the loaded pad (having the static load vector directed through its pivot) of a 5-pad TPJB to obtain accurate measurement of pad radial and tangential motion, as well as tilt, yaw, and pitch. Strain gages were attached to the side of the loaded pad to measure static and dynamic bending strains, which were then used to determine static and dynamic changes in pad curvature (pad clearance). Good agreement was found between the amplitude of the measured and predicted transfer functions concerning radial and transverse pad motions throughout the range of speeds and loads tested, while pad tilt was moderately underpredicted. For the bearing investigated, radial pad motions resulting from pivot compliance were as large as 60% of the radial component of shaft motion when operating at 4400 rpm under heavily loaded conditions. Hence, if a dynamic load applied to the shaft resulted in a shaft displacement of 25 microns (1 mil), the pad would displace radially 15 microns (0.6 mils), and the fluid film height would only decrease by 10 microns (0.4 mils). The consequence of this pad motion is that fluid film stiffness and damping forces produced by relative rotor-pad motions are significantly reduced, resulting in a bearing having significantly less direct stiffness and damping than predicted. A similar effect occurs when shaft motions produce significant changes in pad clearance due to pad compliance. For the pad tested here, the measurements show that predicting TPJB stiffness and damping coefficients without accounting for pad and pivot compliance will produce large errors, and is not advised. Transverse pad motion was predicted and observed. Based on phase measurements, this motion is lightly damped, and appears to be caused by pivot deflection instead of slipping. Despite observing a lightly damped phase change, an increase in magnitude at this natural frequency was not observed. Predicted direct stiffness and damping for unit loads from 0-3200 kPa (0-450 psi) fit through 1.5x running speed are within 18% of measure
