The Eigenvalue Dependence of Reduced Tilting Pad Bearing Stiffness and Damping Coefficients

1988 ◽  
Vol 31 (4) ◽  
pp. 411-419 ◽  
Author(s):  
L. E. Barrett ◽  
P. E. Allaire ◽  
B. W. Wilson
Keyword(s):  
Damping Coefficients ◽  
Tilting Pad ◽  
Bearing Stiffness ◽  
Stiffness And Damping

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.

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.

Behavior of Tilting–Pad Journal Bearings With Large Machining Error on Pads

2016 ◽  
Author(s):  
Phuoc Vinh Dang ◽  
Steven Chatterton ◽  
Paolo Pennacchi ◽  
Andrea Vania ◽  
Filippo Cangioli
Keyword(s):  
Static Load ◽  
Dynamic Stiffness ◽  
Maximum Pressure ◽  
Load Direction ◽  
Machining Error ◽  
Damping Coefficients ◽  
Machining Errors ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

The use of tilting pad journal bearings (TPJBs) has increased in recent years due to their stabilizing effects on the rotor bearing system. Most of the studies addressing steady state and dynamic behaviors of TPJBs have been evaluated by means of thermo-hydrodynamic (THD) models, assuming nominal dimensions for the bearing, (i.e., the physical dimensions of all pads are identical and loads applied along the vertical direction). However machining errors could lead to actual bearing geometry and dimensions different from the nominal ones. In particular, for TPJB the asymmetry of the bearing geometry has not been well-investigated and can lead to an unexpected behavior of the bearing. The asymmetry of the bearing geometry can arise from large machining errors on only one or more pads, as a consequence of a pivot failure or after bad-mounting of the pads during assembly. These conditions can sometimes be detected by high values of the pad temperature, as measured by the temperature probes installed on the bearing pads, or by the abnormal vibration caused by pad-flutter phenomena. In this paper the authors investigate large machining errors on the pad thickness for a five-pad TPJB and analyze their effects on the bearing operating characteristics. Pad thickness errors correspond to a different preload factor or clearance for each pad. A sensitivity analysis was performed for several combinations of pad thickness using a THD model and the behavior of the bearing was analyzed, including dynamic stiffness and damping coefficients, clearance profile, shaft locus, minimum oil-film thickness, power loss, flow rate, and maximum pressure. The experimental case of a five pads TPJB with an intentional large machining error on the thickness of the pads is also described in the paper. The bearing has a nominal diameter of 100 mm, a diameter to length ratio (L/D) equal to 0.7 and can run at up to 3000 rpm. The experimental measurements are compared with the results obtained from the analytical model. The results show that the effects of asymmetry of the bearing geometry are more evident if the direction of the static load applied on the rotor bearing system, which is different from the vertical load, is also considered. For instance, the shape of shaft locus obtained by experimental tests changing the static load direction at a constant speed is an irregular pentagon if it is compared to the case of the nominal bearing. Based on our findings, we concludes that the machining error on the pads has a large influence on the shaft locus, minimum oil-film thickness and maximum pressure on pads, especially at high rotational speed, but has little effect on the flow rate and power loss. In addition, this error significantly affects the dynamic stiffness and damping coefficients, both in terms of rotational speed and load direction.

Measurement of Static and Dynamic Properties of a Tilting Pad Bearing and Comparison With Theory

1993 ◽  
Author(s):  
Thomas Bonner ◽  
John H. Vohr
Keyword(s):  
Dynamic Properties ◽  
Lubrication Theory ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Phase Angles ◽  
Good Agreement

Abstract Measurements were made of the static and dynamic properties of a seven inch diameter, four-pad, tilting pad bearing with both centrally pivoted and 60% offset pads. Data was recorded at 1500, 1800 and 3000 RPM and covered a range of Sommerfeld numbers from .055 to .625. Dynamic properties were measured by applying unbalance weights of various magnitudes to the rotor and measuring the synchronous response amplitudes and phase angles. Good agreement was obtained between measured properties and those predicted using linearized stiffness and damping coefficients obtained from isoviscous lubrication theory.

On the Dynamic Behavior of Hybrid Journal Bearings

1976 ◽  
Vol 98 (1) ◽  
pp. 90-94 ◽  
Author(s):  
S. M. Rohde ◽  
H. A. Ezzat
Keyword(s):  
Dynamic Behavior ◽  
High Frequency ◽  
Journal Bearings ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Bearing Stiffness ◽  
Coupling Stiffness ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Stiffness And Damping

An analysis of the dynamic behavior of hybrid journal bearings is presented. The analysis accounts for the compressibility of the lubricant in the bearing recesses and supply line. Results show that when the journal is subjected to high frequency excitation the bearing stiffness and damping can change drastically. The behavior is characterized by a “break frequency” beyond which the bearing stiffness increases sharply. This is accompanied by a rapid decrease in bearing damping. It is also shown that the cross-coupling stiffness coefficients are reduced at high excitation frequencies. The asymptotic behavior of the stiffness and damping coefficients is examined at both ends of the frequency spectrum.

Experimental Identification of Linearized Oil Film Coefficients of Cylindrical and Tilting Pad Bearings

1995 ◽  
Vol 117 (3) ◽  
pp. 593-599 ◽  
Author(s):  
P. Arumugam ◽  
S. Swarnamani ◽  
B. S. Prabhu
Keyword(s):  
Journal Bearings ◽  
Response Functions ◽  
Flexible Rotor ◽  
The Finite Element Method ◽  
Theoretical Simulation ◽  
Oil Film ◽  
Damping Coefficients ◽  
Experimental Identification ◽  
Tilting Pad ◽  
Stiffness And Damping

The dynamic behavior of the rotating machinery supported by the hydrodynamic journal bearings is significantly influenced by the dynamic characteristics of the oil film. In the present work an efficient identification method is used to identify the stiffness and damping coefficients of the tilting pad and cylindrical journal bearings of a flexible rotor-bearing system. The method uses FRFs (Frequency Response Functions) obtained by the measurements and the finite element method. The accuracy and feasibility of the method were tested and demonstrated by theoretical simulation. The possible effects of oil-film inertia is also verified by the theoretical simulation. The method can be further extended to identify twelve linearized oil-film coefficients.

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