Dynamic Characteristics of TEHD Tilt Pad Journal Bearing Simulation Including Multiple Mode Pad Flexibility Model

1995 ◽  
Vol 117 (1) ◽  
pp. 123-135 ◽  
Author(s):  
J. Kim ◽  
A. Palazzolo ◽  
R. Gadangi
Keyword(s):  
Heat Transfer ◽  
Elastic Deformation ◽  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Variable Viscosity ◽  
Global Analysis ◽  
Analysis Method ◽  
Stiffness And Damping ◽  
Modal Coordinates ◽  
Good Agreement

An approach for incorporating the heat transfer and elastic deformation effects into dynamic coefficient calculation is presented. A global analysis method is used, which finds the equilibrium pad tilt angles at each eccentricity position and includes cross-film variable viscosity, heat transfer effects in the lubricant, elastic deformation, heat conduction effects in the pads, and elastic deformation effect in the pivots. Deflection modes are used to approximate deformation of the top surface of the pads. The dynamic coefficients of a single pad are calculated at the equilibrium state of the bearing, based on numerical perturbation with respect to the bearing degrees of freedom. These include journal position, pad rotation, pivot deformation, and modal coordinates. The stiffness and damping coefficients are calculated and show very good agreement with experimental and numerical results from the existing literature.

Dynamic Characteristics of TEHD Tilt Pad Journal Bearing Simulation Including Multiple Mode Pad Flexibility Model

1993 ◽  
Author(s):  
Jinsang Kim ◽  
Alan Palazzolo
Keyword(s):  
Heat Transfer ◽  
Elastic Deformation ◽  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Variable Viscosity ◽  
Global Analysis ◽  
Analysis Method ◽  
Stiffness And Damping ◽  
Modal Coordinates ◽  
Good Agreement

Abstract An approach for incorporating the heat transfer and elastic deformation effects into dynamic coefficient calculation is presented. A global analysis method is used, which finds the equilibrium pad tilt angles at each eccentricity position and includes cross-film variable viscosity, heat transfer effects in the lubricant, elastic deformation, heat conduction effects in the pads, and elastic deformation effect in the pivots. Deflection modes are used to approximate deformation of the top surface of the pads. The dynamic coefficients of a single pad are calculated at the equilibrium state of the bearing, based on numerical perturbation with respect to the bearing degrees of freedom. These include journal position, pad rotation, pivot deformation, and modal coordinates. The stiffness and damping coefficients are calculated and show very good agreement with experimental and numerical results from the existing literature.

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.

A Variable Viscosity Approach for the Analysis of Steady State and Dynamic Characteristics of Two-Lobe Journal Bearing With TiO2 Based Nanolubricant

2017 ◽  
Author(s):  
Ashutosh Kumar ◽  
Sashindra Kumar Kakoty
Keyword(s):  
Steady State ◽  
Dynamic Characteristics ◽  
Journal Bearing ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Flow Coefficient ◽  
Viscosity Model ◽  
Nano Lubricant ◽  
The Stability ◽  
Stiffness And Damping

Steady-state and dynamic characteristics of two-lobe journal bearing, operating on TiO2 based Nano-lubricant has been obtained. The effective viscosity is obtained by using Krieger-Dougherty viscosity model for a given volume fraction of nanoparticle in the base fluid. Various bearing performance characteristics are then obtained by solving modified Reynolds equation for variable viscosity model and couple stress model. The stiffness and damping coefficients are also determined for various values of the volume fraction of the nanoparticle in the nanofluid. Results reveal that load carrying capacity and flow coefficient increase whereas friction variable decreases without affecting the stability condition of two-lobe journal bearing operating on TiO2 based nanolubricant. On the other hand attitude angle and dynamic coefficients remains constant for all the values of volume fraction of nanoparticle.

scholarly journals Response of a Warped Flexible Rotor with a Fluid Bearing

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Jim Meagher ◽  
Xi Wu ◽  
Chris Lencioni
Keyword(s):  
Experimental Data ◽  
Analytical Model ◽  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Equation Of Motion ◽  
Diagnostic Information ◽  
Flexible Rotor ◽  
Vibration Data ◽  
Rotor Model ◽  
Good Agreement

A two-complex-degrees-of-freedom model is developed and compared to experimental data for various amounts of rotor bow and its orientation to mass imbalance of the rotor. The equation of motion is developed by adding constant forces that rotate with the rotor to a Bently-Muszynska two-mode isotropic rotor model with a plane journal bearing. Diagnostic information discernable from probes at the bearing is explored and compared to midspan response, where previous research has concentrated. The model presented also extends earlier work by representing the effect of a nonrigid bearing. Good agreement between the analytical model and experiment demonstrates that the analysis presented can be useful to diagnose and balance residual shaft bow from probes located at the bearings, where vibration data are typically more available than midspan probes.

Flow and Heat Transfer of Nanofluids Over a Rotating Porous Disk with Velocity Slip and Temperature Jump

2015 ◽  
Vol 70 (5) ◽  
pp. 351-358 ◽  
Author(s):  
Chenguang Yin ◽  
Liancun Zheng ◽  
Chaoli Zhang ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Temperature Fields ◽  
Analysis Method ◽  
Governing Equations ◽  
Porous Disk ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Good Agreement

AbstractIn this article, we discuss the flow and heat transfer of nanofluids over a rotating porous disk with velocity slip and temperature jump. Three types of nanoparticles – Cu, Al2O3, and CuO – are considered with water as the base fluid. The nonlinear governing equations are reduced into ordinary differential equations by Von Karman transformations and solved using homotopy analysis method (HAM), which is verified in good agreement with numerical ones. The effects of involved parameters such as porous parameter, velocity slip, temperature jump, as well as the types of nanofluids on velocity and temperature fields are presented graphically and analysed.

Determination of Journal Bearing Stiffness and Damping at Hydropower Generators Using Strain Gauges

2005 ◽  
Author(s):  
Rolf K. Gustavsson ◽  
Mattias L. Lundstro¨m ◽  
Jan-Olov Aidanpa¨a¨
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Displacement Velocity ◽  
Condition Numbers ◽  
Strain Gauges ◽  
Pull Force ◽  
Bearing Load ◽  
Bearing Stiffness ◽  
Bearing Loads ◽  
Stiffness And Damping

In hydropower generators, the measurement of bearing load, vibration and shaft displacement are wildly used methods for indication of maintenance demand and troubleshooting. When measurement of bearing load and shaft displacement is performed the collected data make it possible to determine the bearing properties, such as stiffness and damping. In this paper a method to determine the bearing stiffness and damping properties for generator journal bearing in hydropower units is presented. The majority of hydropower generators are, however, not equipped with facilities for measurements of bearing loads. To provide the bearings with load sensors it is necessary to reconstruct the bearings, which is associated with heavy expenditures. In this paper an alternative method to obtain the bearing load is utilize, in which strain gauges installed on the generator bearing brackets is used. The collected data in the experiment were obtained from measurements on a 238 MW hydropower generator connected to a Francis type runner. The bracket that holds the generator bearing consists of 18 spokes and each of these spokes has been provided with strain gauges for load measurements. The displacement of the shaft has been measured relative to the generator-bearing casing. The generator-bearing model has been described as a system with two degrees of freedom containing both bearing stiffness and damping matrix as well as displacement and displacement velocity vector. When the calculation of the bearing properties are based on measured data, the irregularity in the calculated stiffness and damping has to be eliminated. To eliminate the unrealistic values of the calculated damping and stiffness, the samples that cause high condition numbers of the displacement–velocity matrix are neglected. The results of the calculation of bearing stiffness and damping are presented in polar plots. This method determines the bearing properties for the generator bearing in a certain point, the point where the generator shaft has its stationary position. The stationary position for the generator shaft depends on the static magnetic pull force acting on the generator rotor and the influence from the turbine. The influence on the bearing characteristics of nonstationary loads as acting on the bearing can be investigated. The non-stationary loads can for instance be rotor unbalance force, influence of thermal expansion and dynamical magnetic pull force. It is thereby possible to evaluate different loads effect on the generator bearing and in which way the bearing properties are affected.

Thermohydrodynamic Analysis of Process-Liquid Hydrostatic Journal Bearings in Turbulent Regime, Part II: Numerical Solution and Results

1995 ◽  
Vol 62 (3) ◽  
pp. 679-684 ◽  
Author(s):  
Zhou Yang ◽  
L. San Andres ◽  
D. W. Childs
Keyword(s):  
Journal Bearing ◽  
Nonlinear Differential Equations ◽  
Flow Characteristics ◽  
Turbulent Regime ◽  
Fluid Temperature ◽  
Numerical Predictions ◽  
Exit Temperature ◽  
Direct Stiffness ◽  
Stiffness And Damping ◽  
Good Agreement

A finite difference scheme is implemented to solve the nonlinear differential equations describing the turbulent bulk-flow on the film lands of a hydrostatic journal bearing (HJB). A Newton-Raphson scheme is used to update the recess pressures and to satisfy the mass continuity requirement at each bearing recess. Comparisons of numerical predictions from the thermohydrodynamic (THD) model with experimental measurements of mass flow rate, fluid temperature, and static stiffness coefficient from a LH2 test HJB article show very good agreement. In particular, the exit temperature of the bearing is lower than the supply temperature; i.e., the liquid temperature decreases along the bearing length. Similar values of direct stiffness and damping coefficients are predicted by the adiabatic THD model and other considering isothermal flow characteristics. However, the THD model predicts lower cross-coupled stiffness and whirl frequency ratio (WFR < 0.5). The results show that for the application presented, the LH2 hydrostatic bearing is more stable than previously thought.

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

2012 ◽  
Vol 134 (12) ◽  
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.

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