The Influence of Pad Flexibility on the Dynamic Coefficients of a Tilting Pad Journal Bearing

1987 ◽  
Vol 109 (1) ◽  
pp. 65-70 ◽  
Author(s):  
Jorgen W. Lund ◽  
Lars Bo Pedersen
Keyword(s):  
Approximate Method ◽  
Small Amplitude ◽  
Journal Bearing ◽  
Damping Properties ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Hydrodynamic Solution ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing ◽  
Good Agreement

An approximate method is developed to include the flexibility of the pad in the calculation of the stiffness and damping properties of a tilting pad journal bearing. It is a small-amplitude perturbation solution in which the pad deformation is accounted for solely by the change in clearance. A comparison of results with those obtained from a more complete elasto-hydrodynamic solution shows good agreement.

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.

Improvement and Analysis for a Gaseous Cavitation Model Applied in a Tilting-Pad Journal Bearing

2019 ◽  
Author(s):  
Aoshuang Ding ◽  
Xuesong Li ◽  
Yuhong Li
Keyword(s):  
Journal Bearing ◽  
Three Dimensional ◽  
Cavitation Model ◽  
Local Pressure ◽  
Cavitation Process ◽  
Air Volume ◽  
Tilting Pad ◽  
Sst Model ◽  
Tilting Pad Journal Bearing ◽  
Good Agreement

Abstract Considering the gaseous cavitation rate is influenced by local pressure, a transient gaseous cavitation model is developed from an equilibrium gaseous cavitation model in consideration of transient gaseous cavitation theories and the Bunsen solubility. With the shear stress transport (SST) model with low-Re correction and air backflow from the bearing outlets, the transient gaseous cavitation model is applied to the three-dimensional simulations of an entire tilting-pad journal bearing at 3000 rpm speed and under 180 kN load. The simulated bearing pressure and load are in good agreement with the experimental data, indicating that the transient gaseous cavitation model performs well in the bearing simulations. Based on the comparisons of the simulated air and dissolved air distributions between the transient and equilibrium gaseous cavitation models, the simulated cavitation process of the transient gaseous cavitation is proved to be not in equilibrium and mass transfer occur between the backflow air and oil. The purpose of building the transient gaseous cavitation model is thus met. Analyses of the air distributions indicate that high cavitation rates and low dissolution rates makes air volume a major part of the total air volume and close to the physical gaseous cavitation process.

Identification of Dynamic Coefficients of a Five-Pad Tilting Pad Journal Bearing up to Highest Surface Speeds

2020 ◽  
Author(s):  
Philipp Zemella ◽  
Thomas Hagemann ◽  
Bastian Pfau ◽  
Hubert Schwarze
Keyword(s):  
Flow Rate ◽  
Time Domain ◽  
Static Load ◽  
Journal Bearing ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Oil Flow ◽  
Tilting Pad Journal Bearing ◽  
The Impact

Abstract Tilting-pad journal bearings are widely used in turbomachinery industry due to their positive dynamic properties at high rotor speeds. However, the exact description of this dynamic behavior is still part of current research. This paper presents measurement results for a five-pad tilting-pad journal bearing in load between pivot configuration. The bearing is characterized by a nominal diameter of 100 mm, a length of 90 mm, and a pivot offset of 0.6. Investigations include results for surface speeds between 25 and 120 m/s and specific bearing loads ranging from 0.0 to 3.0 MPa. Results of theoretical predictions are commonly derived from perturbation of stationary operation under static load. Therefore, experimental results for stationary operation including pad deflection under static load are presented first to characterize the investigated bearing. Measured results indicate considerable non-laminar flow in the upper region of the investigated range of rotor speeds. Second, dynamic excitation test are performed with excitation frequencies up to 400 Hz to evaluate dynamic coefficients of a stiffness (K) and damping (C) KC-model, and additionally, a KCM-model using additional virtual mass (M) coefficients. KCM-coefficients are obtained by fitting frequency dependent KC-characteristics to the KCM-model structure using least square approach. The wide range of rotating and excitation frequencies leads to subsynchronous as well as supersynchronous vibrations. Excitation forces are applied with multi-sinus and single-sinus characteristics. The latter one allows evaluation of KC-coefficients at the particular frequency ratio in the time domain. Here, frequency and time domain evaluation algorithms for dynamic coefficients are used in order to assess their special properties and quality. The impact of surface speed, bearing load, and oil flow rate on measured and predicted KCM-coefficients is investigated. Measured and predicted results can be well fitted to a KCM-model and show a significant influence of the ratio between fluid film and pivot support stiffness on the speed dependent characteristic of bearing stiffness coefficients. However, the impact of this ratio on damping coefficients is considerably lower. Further investigations on the impact of oil flow rates indicate that a significant decrease of direct damping coefficients exists below a certain level of starvation. Above this limit, direct damping coefficients are nearly independent of oil flow rate. Results are analyzed in detail and demands on improvements for predictions are derived.

Static Performance Characteristics and Rotordynamic Coefficients for a Four-Pad Ball-in-Socket Tilting Pad Journal Bearing

2008 ◽  
Author(s):  
Joel Harris ◽  
Dara Childs
Keyword(s):  
Power Loss ◽  
Journal Bearing ◽  
Excitation Frequency ◽  
Performance Characteristics ◽  
Rotordynamic Coefficients ◽  
Test Conditions ◽  
Tilting Pad ◽  
Static Performance ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Static performance characteristics and rotordynamic coefficients were experimentally determined for a four-pad, spherical-seat, tilting-pad journal bearing in load-between-pad configuration. Measured static characteristics include journal static equilibrium position, estimated power loss, and trailing-edge pad temperatures. Rotordynamic coefficients were determined from curve fits of measured complex dynamic-stiffness coefficients as a functions of the excitation frequency. A frequency-independent [M]-[C]-[K] model did a good job of fitting the measurements. Test conditions included speeds from 4 to 12 krpm and unit loads from 0 to 1896 kPa (0 to 275 psi). The bearing uses cool inlet oil to decrease the pad operating temperatures and increase the bearing’s load and speed capacity. The bearing has a nominal diameter of 101.78 mm (4.0070 in). Measurements indicated significant bearing crush with a radial bearing clearance of 99.63 μm (3.92 mils) in the axis 45° counterclockwise from the loaded axis and 54.60 μm (2.15 mils) in the axis 45° clockwise from the loaded axis. The pad length is 101.60 mm (4.00 in), giving L/D = 1.00. The pad arc angle is 73°, and the pivot offset ratio is 65%. Testing was performed using a test rig described by Kaul [1], and rotordynamic coefficients were extracted using a procedure adapted from Childs and Hale [2]. A bulk-flow Navier-Stokes model was used for predictions, using adiabatic conditions for the fluid in the bearings. However, the model assumes constant nominal clearances at all pads, and an average clearance was used based on measured clearances. Measured static eccentricities and attitude angles were significantly lower than predicted. Attitude angles varied from 6° to 39° and decreased with load. Power loss was well-predicted, with a maximum value of 25 kW (34 hp). The maximum detected pad temperature was 71°C (160°C) while the temperature rise from inlet to exit was over-predicted by 8°C (14°F). Direct stiffness and damping coefficients were significantly over-predicted, but the addition of a simple pivot-stiffness in series with the measured stiffness and damping values vastly improved the agreement between theory and experiment. Direct added masses were negative to a higher degree for Myy (y load direction) at low speeds and increased with speed. With the exception of Myy at zero load, they became positive before reaching 8,000 rpm. Although significant cross-coupled stiffness terms were present, they always had the same sign, producing a whirl frequency ratio of zero and netting unconditional stability over all test conditions.

Research on the Complete Dynamic Model of Tilting-Pad Journal Bearings Including Fluid Film Temperature Effect

2012 ◽  
Vol 157-158 ◽  
pp. 589-594
Author(s):  
Zhen Shan Zhang ◽  
Xu Dong Dai
Keyword(s):  
Journal Bearing ◽  
Dynamic Properties ◽  
Fluid Film ◽  
Effect Of Temperature ◽  
Rotor Systems ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Precise Prediction ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings

Considering the coupling moving of shaft and pads, a theoretical model for calculating the complete dynamic coefficients (CDCs) of tilting-pad journal bearing (TPJB) is described in this paper. The model includes the influence of fluid film temperature. Based on this model, the effect of fluid film temperature on journal equilibrium position, pads inclinations, and complete dynamic coefficients is investigated for given load cases. The numerical results indicate that the effect of temperature is not neglected for the dynamic properties of TPJB. The solution will provide useful tool for precise prediction of dynamic behavior of the rotor systems supported by TPJB.

Calculation of Stiffness and Damping Properties of Gas Bearings

1968 ◽  
Vol 90 (4) ◽  
pp. 793-803 ◽  
Author(s):  
J. W. Lund
Keyword(s):  
Static Load ◽  
Journal Bearing ◽  
Computational Method ◽  
Gas Bearings ◽  
Rotating Speed ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing ◽  
Gas Bearing

The dynamic characteristics of a gas bearing can be represented by a set of spring and damping coefficients (impedances) which are functions of the static load on the bearing, the rotating speed and the whirl frequency of the journal. For a rotor supported in gas bearings, these coefficients can be used directly in a critical speed calculation or an unbalance response calculation. In addition, the coefficients can be employed in a stability investigation. The paper gives the computational method for obtaining the spring and damping coefficients and, also, describes how they are used in rotor calculations and stability studies. Numerical results are given in graphical and tabular form for a tilting pad journal bearing and a three-lobe journal bearing.

Excitation Frequency Effects on the Stiffness and Damping Coefficients of a Five-Pad Tilting Pad Journal Bearing

1999 ◽  
Vol 121 (3) ◽  
pp. 517-522 ◽  
Author(s):  
Hyun Cheon Ha ◽  
Seong Heon Yang
Keyword(s):  
Frequency Ratio ◽  
Journal Bearing ◽  
Excitation Frequency ◽  
Shaft Speed ◽  
Frequency Effects ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Bearing Load ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

An experimental study is performed to investigate the frequency effects of the excitation force on the linear stiffness and damping coefficients of a LOP (load on pad) type five-pad tilting pad journal bearing with the diameter of 300.91 mm and the length of 149.80 mm. The main parameter of interest in the present work is excitation frequency to shake the test hearing. The excitation frequency is controlled independently, using orthogonally mounted hydraulic exciters, as follows: 1) excitation frequency ratio in the x-axis direction νx = 0.5, 2) excitation frequency ratio in the y-axis direction νy = 0.6, 0.7, 0.8, 0.9. The magnitude of the excitation force is controlled to make sure that the test hearing has a linear behavior during the test. The relative movement between the bearing and shaft, and the acceleration of the bearing casing are measured as a function of excitation frequency using the different values of bearing load and shaft speed. Measurements show that the variation of excitation, frequency has quite a little effect on both stiffness and damping coefficients. The stiffness coefficients of the five-pad tilting pad journal bearing slightly decrease as the excitation frequency ratio increases, while the damping coefficients slightly increase with excitation frequency ratio, especially in the case of lower speed and higher load. Both direct stiffness and damping coefficients in the direction of bearing load decrease with an increase of shaft speed, but increase with the bearing load.

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