For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in.) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency-dependent stiffness and damping. Measured hot-bearing clearances are approximately 30% smaller than measured cold-bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation fi-equency was only measured at the most heavily loaded conditions.
The nature of dry-friction whip and whirl is investigated through experimental and numerical methods. A test rig was designed and constructed to demonstrate and record the character of multimode dry-friction whip and whirl. These tests examined steady-state whip and whirl characteristics for a variety of rub materials and clearances. A simulation model was constructed using tapered Timoshenko beam finite elements to form multiple-degree-of-freedom rotor and stator models. These models were reduced by component mode synthesis to discard high-frequency modes while retaining physical coordinates at the rub location to model rotor-stator interaction using a nonlinear contact model with Coulomb friction. Simulations were performed for specific test cases, and compared against experimental data; these comparisons are favorable. Experimental data analysis showed multiple whirl and whip regions, despite claims of previous investigators that these regions are predicted analytically but not produced in simulations or experiments. Spectral analysis illustrates the presence of harmonic sidebands that accompany the fundamental whirl solution. These sidebands are more evident in whip, and can excite higher-frequency whirl solutions.
As described in Part I [1], 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 (TFs). In short, these transfer functions specify the amplitude and phase of pad motion (angular, radial, translational, etc.) in response to an input rotor motion. 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).
The floating-bearing-test-rig concept was initially developed by Glienicke in 1966 and has since been used to test many tilting-pad journal bearings (TPJBs). The impedances measured during these tests have been compared to rotor/journal-perturbed impedance predictions. Since the inertial acceleration of a pad is different for bearing-perturbed and rotor-perturbed motions, the bearing's reaction force components for bearing-perturbed and journal-perturbed motions will also differ. An understanding of how bearing-perturbed and rotor-perturbed impedances differ is needed to assess the validity of past, present, and future comparisons between TPJB test data and predictions. A new TPJB perturbation model is developed including the effects of angular, radial, and transverse 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 rotor, while both the bearing and rotor motions are perturbed in the present analysis. The applicability of comparing rotor-perturbed bearing impedance predictions to impedances measured on a bearing-perturbed test rig is assessed by comparing rotor-perturbed and bearing-perturbed impedance predictions for an example bearing.
Though many approaches have been proposed in the literature to model the reaction forces in a catcher bearing (CB), there are still phenomena observed in experimental tests that cannot be explained by existing models. The following paper presents a novel approach to model a CB system. Some of the elements in the model have been previously introduced in the literature; however, there are other elements in the proposed model that are new, providing an explanation for the forward whirling phenomena that has been observed repeatedly in the literature. The proposed CB model is implemented in a finite element rotordynamic package, and nonlinear time-transient simulations are performed to predict published experimental results of a high speed vertical sub-scale compressor; with no other forces present in the model, the agreement between simulations and experimental data is favorable. The results presented herein show that friction between the journal and axial face of the catcher bearing results in a forward cross-coupled force that pushes the rotor in the direction of rotation. This force is proportional to the coefficient of friction between the axial face of the rotor and catcher bearing and the axial thrust on the rotor. This force results in synchronous whirl when the running speed is below a combined natural frequency of the rotor-stator system, and constant frequency whip when the speed is above a whip frequency.
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