Lund’s Tilting Pad Journal Bearing Pad Assembly Method

2003 ◽  
Vol 125 (4) ◽  
pp. 448-454 ◽  
Author(s):  
John C. Nicholas
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Design Tools ◽  
Analysis And Design ◽  
Simple Addition ◽  
Assembly Method ◽  
Elasticity Equations ◽  
Tilting Pad ◽  
Tilting Pad Bearings ◽  
Tilting Pad Journal Bearing

This paper summarizes the development during the last 50 years of tilting pad journal bearing analysis and design. The major impetus of this development was a landmark paper published by Jørgen Lund in 1964, “Spring and Damping Coefficients for the Tilting-Pad Journal Bearing.” His paper contained the first widely published dynamic coefficients for tilting pad bearings along with his pad assembly method equations. In the 38 years since Lund’s publication, many other authors have written tilting pad journal bearing codes, the first of which were based on Lund’s assembly method. These assembly method codes were utilized for many years to analyze and design tilting pad bearings for improved rotordynamic performance. During this time, some key design tools were developed utilizing Lund’s method. Other authors have written newer codes which solve the energy and elasticity equations iteratively with the pressure equation, including pad degrees of freedom. With the simple addition of a turbulence correction and heat balance, many designers continue to utilize Lund’s method, shunning the more modern codes.

Lund’s Pad Assembly Method for Tilting Pad Journal Bearings

2001 ◽  
Author(s):  
John C. Nicholas
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Analysis And Design ◽  
Simple Addition ◽  
Assembly Method ◽  
Elasticity Equations ◽  
Tilting Pad ◽  
Tilting Pad Bearings ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings

Abstract This paper summarizes the development during the last 50 years of tilting pad journal bearing analysis and design. The major impetus of this development was a landmark paper published by Jorgen Lund in 1964, “Spring and Damping Coefficients for the Tilting-Pad Journal Bearing.” His paper contained the first widely published dynamic coefficients for tilting pad bearings along with his pad assembly method equations. In the 37 years since Lund’s publication, many other authors have written tilting pad journal bearing codes, the first of which were based on Lund’s assembly method. These assembly method codes were utilized for many years to analyze and design tilting pad bearings for improved rotordynamic performance. During this time, some key design tools were developed utilizing Lund’s method. Other authors have written newer codes which solve the energy and elasticity equations iteratively with the pressure equation, including pad degrees of freedom. With the simple addition of a turbulence correction and heat balance, many designers continue to utilize Lund’s method, shunning the more modern codes.

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.

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.

Linear Stability Analysis of a Tilting-Pad Journal Bearing System

2006 ◽  
Vol 129 (2) ◽  
pp. 348-353 ◽  
Author(s):  
Guang Qiao ◽  
Liping Wang ◽  
Tiesheng Zheng
Keyword(s):  
Linear Stability ◽  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Critical Mass ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Assembly Technique ◽  
The Stability ◽  
Tilting Pad Journal Bearing ◽  
Bearing System

This paper describes a mathematical model to study the linear stability of a tilting-pad journal bearing system. By employing the Newton-Raphson method and the pad assembly technique, the full dynamic coefficients involving the shaft degrees of freedom as well as the pad degrees of freedom are determined. Based on these dynamic coefficients, the perturbation equations including self-excited motion of the rotor and rotational motion of the pads are derived. The complex eigenvalues of the equations are computed and the pad critical mass identified by eigenvalues can be used to determine the stability zone of the system. The results show that some factors, such as the preload coefficient, the pivot position, and the rotor speed, significantly affect the stability of tilting-pad journal bearing system. Correctly adjusting those parameter values can enhance the stability of the system. Furthermore, various stability charts for the system can be plotted.

Including Pivot Friction in Pad Motion for a Tilting Pad Journal Bearing With Ball-Socket Pivots

2017 ◽  
Author(s):  
Feng He
Keyword(s):  
Journal Bearing ◽  
Hydrodynamic Pressure ◽  
Contact Friction ◽  
Hertz Contact ◽  
Friction Coefficients ◽  
Synchronous Motion ◽  
Tilting Pad ◽  
Tilting Pad Bearings ◽  
Bearing Loads ◽  
Tilting Pad Journal Bearing

Tilting pad journal bearing has its wide application in turbomachinery. For years, frictionless contact has been assumed for all the contact types in bearing coefficients prediction of tilting pad bearings. Existing experimental data demonstrates contact friction does present in pivots and can prevent pads from effective tilting, which is especially true for the surface contact pivot, e.g. ball-socket pivot. However, no open literature is available to discuss individual pad motion with consideration of pivot contact friction and document the effects on the dynamic behaviors of tilting pad bearings. This paper tries to improve the understanding in this area by discussing the pad motion of a tilting pad bearing with ball-socket pivots subject to pivot friction. A model, which couples the journal motion, hydrodynamic pressure from oil film and contact pressure within the pivots, is established. Instead of Hertz contact, a conformal contact model is applied for the ball-socket contact. Through the coupled transient analyses, the effects of contact friction coefficients, bearing dynamic and static loading, and pivot size on pads motion of a 5-pads load-on-pad bearing are considered and compared. The results show that the presence of friction within ball-socket pivots does not guarantee “locked up” pads motion, but only limits pads from effective tilting for a given range of friction coefficients. Larger dynamic load increases pad tilting amplitude; this does not mean that enlarged tilting magnitudes reduce pivot friction moments for the pads. With varying bearing loads, the pivot friction could result in non-synchronous motion of pads tilting and pivots deformation and bring these non-synchronous components into the journal vibration. Size-reduced pivots are found to diminish the effects of pivot friction and offer preferred pads dynamics and journal vibration.

scholarly journals Improvement of Tilting-Pad Journal Bearing Operating Characteristics by Application of Eddy Grooves

Lubricants ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 18
Author(s):  
Eckhard Schüler ◽  
Olaf Berner
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Load Capacity ◽  
Fluid Film ◽  
Operating Characteristics ◽  
Fluid Film Bearings ◽  
Tilting Pad ◽  
Bearing Load ◽  
Bearing Loads ◽  
Tilting Pad Journal Bearing

In high speed, high load fluid-film bearings, the laminar-turbulent flow transition can lead to a considerable reduction of the maximum bearing temperatures, due to a homogenization of the fluid-film temperature in radial direction. Since this phenomenon only occurs significantly in large bearings or at very high sliding speeds, means to achieve the effect at lower speeds have been investigated in the past. This paper shows an experimental investigation of this effect and how it can be used for smaller bearings by optimized eddy grooves, machined into the bearing surface. The investigations were carried out on a Miba journal bearing test rig with Ø120 mm shaft diameter at speeds between 50 m/s–110 m/s and at specific bearing loads up to 4.0 MPa. To investigate the potential of this technology, additional temperature probes were installed at the crucial position directly in the sliding surface of an up-to-date tilting pad journal bearing. The results show that the achieved surface temperature reduction with the optimized eddy grooves is significant and represents a considerable enhancement of bearing load capacity. This increase in performance opens new options for the design of bearings and related turbomachinery applications.

Dynamic Analysis of Tilting-Pad Journal Bearing—Influence of Pad Deformations

1994 ◽  
Vol 116 (3) ◽  
pp. 621-627 ◽  
Author(s):  
H. Desbordes ◽  
M. Fillon ◽  
C. Chan Hew Wai ◽  
J. Frene
Keyword(s):  
Film Thickness ◽  
Pressure Field ◽  
Journal Bearing ◽  
Maximum Pressure ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Dimensional Finite Element ◽  
The One ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings

A theoretical nonlinear analysis of tilting-pad journal bearings is presented for small and large unbalance loads under isothermal conditions. The radial displacements of internal pad surface due to pressure field are determined by a two-dimensional finite element method in order to define the actual film thickness. The influence of pad deformations on the journal orbit, on the minimum film thickness and on the maximum pressure is studied. The effects of pad displacements are to decrease the minimum film thickness and to increase the maximum pressure. The orbit amplitude is also increased by 20 percent for the large unbalance load compared to the one obtained for rigid pad.

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