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.

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.

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.

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.

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.

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.

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

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Dara Childs ◽  
Joel Harris
Keyword(s):  
Power Loss ◽  
Journal Bearing ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Test Conditions ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Static Performance ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Static performance characteristics and rotordynamic coefficients were experimentally determined for a four-pad, ball-in-socket, 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 function of the excitation frequency. Aside from the cross-coupled damping coefficients, a frequency-independent [M]-[C]-[K] model did a good job of fitting the measurements. The added-mass coefficient was frequently dropped, leaving only a frequency-independent stiffness and damping coefficient. Test conditions included speeds from 4000 rpm to 12,000 rpm and unit loads from 0 kPa to 1896 kPa (0–275 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 radial clearance of 95.3 μm (3.75 mils). However, measurements indicated significant bearing crush with a radial bearing clearance of 99.6 μm (3.92 mils) in the axis 45 deg counterclockwise from the loaded axis and 54.6 μm (2.15 mils) in the axis 45 deg clockwise from the loaded axis (assuming counterclockwise rotation). The pad length is 101.60 mm (4.00 in.), giving L/D=1.00. The pad arc angle is 73 deg, and the pivot offset ratio is 65%. Testing was performed using a test rig described by Kaul (1999, “Design and Development of a Test Setup for the Experimental Determination of the Rotordynamic and Leakage Characteristics of Annular Bushing Oil Seals,” MS thesis, Texas A&M University, College Station, TX), and rotordynamic coefficients were extracted using a procedure adapted from the work of Childs and Hale (1994, “A Test Apparatus and Facility to Identify the Rotordynamic Coefficients of High-Speed Hydrostatic Bearings,” ASME J. Tribol., 116, pp. 337–344). A bulk-flow Navier–Stokes model was used for predictions, using adiabatic conditions for the fluid in the bearing. 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 higher than predicted. Attitude angles varied from 6 deg to 39 deg and decreased with load. Power loss was underpredicted at low speeds and very well predicted at high speeds, with a maximum value of 25 kW (34 hp). The maximum detected pad temperature was 71°C(160°F) while the temperature increase from inlet to maximum pad temperature location was overpredicted by 10–40%. Direct stiffness and damping coefficients were significantly overpredicted, but the addition of a stiffness-in-series correction vastly improved the agreement between theory and experiment. Direct added masses were zero or negative at low speeds and increased with speed up to a maximum of about 50 kg; they were normally greater in the x (unloaded) direction. Although significant cross-coupled stiffness terms were present, they always had the same sign, and the bearing had a whirl frequency ratio of zero netting unconditional stability over all test conditions.

Cooling Effect and Dynamic Characteristics of Oil Film of Partial Tilting Pad Bearing

2007 ◽  
Author(s):  
Kyung-Bo Bang ◽  
Jeong-Hun Kim ◽  
Cheol-Hong Kim
Keyword(s):  
Dynamic Characteristics ◽  
Journal Bearing ◽  
Hydrodynamic Pressure ◽  
Oil Film ◽  
Rotating Speed ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Oil Flow ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

In the present paper, we suggest a new type of tilting pad journal bearing to decrease oil film temperature and eliminate pad fluttering during operation. This bearing consists of tilting pad journal bearing at low casing and fixed arc type journal bearing at upper casing. Namely we changed a tilting pad bearing with a fixed arc type bearing at upper casing. To investigate the effects of changing the bearing shape, the static and dynamic characteristics were compared experimentally with conventional tilting pad journal bearing. For the static characteristics, oil film temperature, hydrodynamic pressure and oil film thickness were measured with the variation of rotating speed, bearing load and oil flow rate. The stiffness and damping coefficients of oil film were also obtained using the response subjected to harmonic external force to evaluating the dynamic characteristics. The results show that the suggested type of bearing has effect on reducing oil film temperature and increasing stiffness and damping coefficients of oil film.

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.

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