Measured and Predicted Transfer Functions Between Rotor Motion and Pad Motion for a Rocker-Back Tilting-Pad Bearing in LOP Configuration

2011 ◽  
Author(s):  
Jason C. Wilkes
Keyword(s):  
Transfer Functions ◽  
Analytical Models ◽  
Single Frequency ◽  
Frequency Dependent ◽  
Damping Coefficients ◽  
Operating Region ◽  
Direct Measurements ◽  
Trailing Edges ◽  
Tilting Pad ◽  
Stiffness And Damping

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. Continuing to test TBJBs in the same fashion is not likely to produce an explanation for the discrepancies between measured and predicted damping. Most analytical models for TPJBs are based on the assumption that explicit dependence on pad motion can be eliminated by assuming a solution for rotor motion such that the amplitude and phase of pad motions are predicted by rotor-pad transfer functions. Direct measurements of pad motion during test excitation are needed to produce measured transfer functions between rotor and pad motion, and a comparison between these measurements and predictions is needed to identify model discrepancies. A test setup was designed to fulfill these objectives. Motion probes were added to the loaded pad to obtain accurate measurement of pad radial and tangential motion, as well as tilt, yaw and pitch. For the remainder of this work, the loaded pad refers to the pad whose pivot sits on the static load line. Testing was performed primarily at low speeds and high loads, since this is the operating region for which predictions are most erroneous. Single frequency excitations were performed ranging from 10–350 Hz, producing rotor and pad motion, acceleration, and force vectors. This motion was used to determine frequency-dependent bearing impedances and rotor-pad transfer functions. A new pad perturbation model is proposed including the effects of pad angular, radial, and circumferential pad motion. This model was implemented in a Reynolds-based TPJB code to predict the frequency-dependent bearing impedances and rotor-pad transfer functions. These predictions are compared with measurements and discussed. Good agreement was found between the amplitude of the measured and predicted transfer functions concerning tilt and radial motions for low to moderate loads, but deviated in accuracy at the highest loaded case. Circumferential (sliding) pad motion was predicted and observed; however, the effect of this degree of freedom on dynamic bearing coefficients has not been quantitatively assessed. For the bearing investigated, radial motion accounted for more than 67% of total motion of the fluid-film height at the leading and trailing edges of the pad when operating at 4400 rpm under heavily loaded conditions. The measurements show that predicting TPJB stiffness and damping coefficients without accounting for pad pivot deformation will not produce satisfactory outcomes.

Improving Tilting-Pad Journal Bearing Predictions: Part II—Comparison of Measured and Predicted Rotor-Pad Transfer Functions for a Rocker-Pivot Tilting-Pad Journal Bearing

2012 ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Static Load ◽  
Journal Bearing ◽  
Transfer Functions ◽  
Analytical Models ◽  
Strain Gages ◽  
Dynamic Changes ◽  
Direct Measurements ◽  
Tilting Pad ◽  
Load Vector ◽  
Tilting Pad Journal Bearing

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).

Improving Tilting-Pad Journal Bearing Predictions—Part II: Comparison of Measured and Predicted Rotor-Pad Transfer Functions for a Rocker-Pivot Tilting-Pad Journal Bearing

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Static Load ◽  
Journal Bearing ◽  
Transfer Functions ◽  
Model Development ◽  
Analytical Models ◽  
Dynamic Changes ◽  
Direct Measurements ◽  
Tilting Pad ◽  
Load Vector ◽  
Tilting Pad Journal Bearing

As described in Part I (Wilkes et al., 2012, “Improving Tilting-Pad Journal Bearing Predictions—Part I: Model Development and Impact of Rotor Excited Versus Bearing Excited Impedance Coefficients,” ASME J. Eng. Gas Turb. Power, 135(1), p. 012503), most analytical models for tilting-pad journal bearing (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. 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 gauges 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).

Tilting Pad Journal Bearings: A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot Flexibility

2012 ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Operating Temperature ◽  
Excitation Frequency ◽  
Full Model ◽  
Stability Calculation ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

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 frequency was only measured at the most heavily loaded conditions.

An Analytical Complete Model of Tilting-Pad Journal Bearing Considering Pivot Stiffness and Damping

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Zhiyong Yan ◽  
Yi Lu ◽  
Tiesheng Zheng
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Local Coordinate System ◽  
Dynamical Behavior ◽  
Complete Model ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Generalized Force ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model, as well as mathematical method, which contains 2n+2 degrees of freedom, is presented for calculating the dynamical characteristics of tilting-pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement, and the generalized force vector are chosen. The concise transformation of generalized displacement, generalized force, and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using the Newton–Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration. Numerical results show that the reduced damping coefficients and the threshold speed can be effectively enhanced by giving suitable pad pivot stiffness and damping simultaneously, and this analytical method can be applied to analyze dynamical behavior of the tilting-pad journal bearing rotor system.

Three-Dimensional Thermo-Elasto-Hydrodynamic Computational Fluid Dynamics Model of a Tilting Pad Journal Bearing—Part II: Dynamic Response

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Jongin Yang ◽  
Alan Palazzolo
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Dynamic Response ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Static Response ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Part II presents a novel approach for predicting dynamic coefficients for a tilting pad journal bearing (TPJB) using computational fluid dynamics (CFD) and finite element method (FEM), including fully coupled elastic deflection, heat transfer, and fluid dynamics. Part I presented a similarly novel, high fidelity approach for TPJB static response prediction which is a prerequisite for the dynamic characteristic determination. The static response establishes the equilibrium operating point values for eccentricity, attitude angle, deflections, temperatures, pressures, etc. The stiffness and damping coefficients are obtained by perturbing the pad and journal motions about this operating point to determine changes in forces and moments. The stiffness and damping coefficients are presented in “synchronously reduced form” as required by American Petroleum Institute (API) vibration standards. Similar to Part I, an advanced three-dimensional thermal—Reynolds equation code validates the CFD code for the special case when flow Between Pad (BP) regions is ignored, and the CFD and Reynolds pad boundary conditions are made identical. The results show excellent agreement for this validation case. Similar to the static response case, the dynamic characteristics from the Reynolds model show large discrepancies compared with the CFD results, depending on the Reynolds mixing coefficient (MC). The discrepancies are a concern given the key role that stiffness and damping coefficients serve instability and response predictions in rotordynamics software. The uncertainty of the MC and its significant influence on static and dynamic response predictions emphasizes a need to utilize the CFD approach for TPJB simulation in critical machines.

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

2010 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul E. Allaire ◽  
John C. Nicholas
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Calculations ◽  
Leading Edge ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Subject ◽  
Stiffness And Damping

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.

Stability of Rotor-Bearing Systems With Generalized Support Flexibility and Damping and Aerodynamic Cross-Coupling

1975 ◽  
Vol 97 (3) ◽  
pp. 461-469 ◽  
Author(s):  
R. E. Warner ◽  
A. I. Soler
Keyword(s):  
Cross Coupling ◽  
Frequency Dependent ◽  
Oil Film ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Single Mass ◽  
Tilting Pad Bearings

This paper examines stability of the flexible single mass rotor, acted on by motion induced forces due to aero-dynamic cross-coupling and supported most generally by oil film tilting pad bearings which are in turn mounted on flexible, damped supports. Plotted results include the frequency dependent spring and damping coefficients for the 4-pad tilting pad bearing, damping coefficients for the 360-deg squeeze bearing and stability plots of rotor-bearing systems including aerodynamic cross-coupling, the 4-pad tilting pad bearing and the 150-deg partial arc bearing with various support arrangements.

Rotordynamic Force Coefficients of a Hybrid Brush Seal: Measurements and Predictions

2009 ◽  
Author(s):  
Luis San Andre´s ◽  
Adolfo Delgado ◽  
Jose´ Baker
Keyword(s):  
Test System ◽  
Operating Conditions ◽  
Single Frequency ◽  
Viscous Damping ◽  
Domain Identification ◽  
Damping Coefficients ◽  
Brush Seal ◽  
Brush Seals ◽  
Lift Off ◽  
Stiffness And Damping

Brush seals effectively control leakage in air breathing engines, albeit only applied for relatively low-pressure differentials. Hybrid brush seals (HBS) are an alternative to resolve poor reliability resulting from bristle tip wear while also allowing for reverse shaft rotation operation. A HBS incorporates pads contacting the shaft on assembly; and which under rotor spinning, lift off due to the generation of a hydrodynamic pressure. The ensuing gas film prevents intermittent contact, reducing wear and thermal distortions. The paper presents rotordynamic measurements conducted on a test rig for evaluation of HBS technology. Single frequency shaker loads are exerted on a test rotor holding a hybrid brush seal and measurements of rotor displacements follow for operating conditions with increasing gas supply pressures and two rotor speeds. A frequency domain identification method delivers the test system stiffness and damping coefficients. The HBS stiffness coefficients are not affected by rotor speed though the seal viscous damping shows a strong frequency dependency. The identified HBS direct stiffness decreases ∼15% as the supply/discharge pressure increases Pr = 1.7 to 2.4. The HBS cross-coupled stiffnesses are insignificant, at least one order of magnitude smaller than the direct stiffnesses. A structural loss factor (γ) and dry friction coefficient (μ) represent the energy dissipated in a HBS by the bristle-to-bristle and bristle-to-pads interactions. Predictions of HBS stiffness and damping coefficients correlate well with the test derived parameters. Both model predictions and test results show the dramatic reduction of the seal equivalent viscous damping coefficients as the excitation whirl frequency increases.

scholarly journals Numerical Simulation of Nonlinear Oil Film Forces of Tilting-Pad Guide Bearing in Large Hydro-unit

2000 ◽  
Vol 6 (5) ◽  
pp. 345-353 ◽  
Author(s):  
Li-Feng Ma ◽  
Xin-Zhi Zhang
Keyword(s):  
Reynolds Equation ◽  
Nonlinear Simulation ◽  
Motion Patterns ◽  
Damping Coefficients ◽  
Nonlinear Motion ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Angular Velocities ◽  
Stiffness And Damping ◽  
Bearing System

A new numerical method is proposed for predicting the nonlinearity of tilting-pad guide bearing oilfilm force in the rotor-bearing system in a large hydro-unit. Nonlinear displacement and velocity of the journal center, as well as nonlinear tilting angles and angular velocities of the pads in non-stationary Reynolds equation are taken into account. This method is also suited for other small rotor-bearing system. As an example, the response due to a momentarily created unbalance is Calculated. The nonlinear motion patterns of the pad and journal whirling orbit are obtained. Finally, the nonlinear orbit is compared to the linear one that could be calculated from linear stiffness and damping coefficients. It is shown that there are important differences between those two orbits and that the nonlinear simulation is more accurate.

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