The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Luis San Andrés ◽  
Yujiao Tao
Keyword(s):  
Experimental Data ◽  
Journal Bearings ◽  
Fluid Film ◽  
Virtual Mass ◽  
Force Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Bearing Force ◽  
Film Stiffness ◽  
Tilting Pad Journal Bearings

Recent comprehensive experimental data showcasing the force coefficients of commercial size tilting pad journal bearings has brought to rest the long standing issue on the adequacy of the [K,C,M] physical model to represent frequency independent bearing force coefficients, in particular viscous damping. Most experimental works test tilting pad journal bearings (TPJBs) with large preloads, operating over a large wide range of rotor speeds, and with null to beyond normal specific loads. Predictions from apparently simple fluid film bearing models stand poor against the test data which invariably signals to theory missing pivot and pad flexibility effects, and most importantly, ignoring significant differences in bearing and pad clearances due to actual operation, poor installation and test procedures, or simply errors in manufacturing and assembly. Presently, a conventional thermo hydrodynamic bulk flow model for prediction of the pressure and temperature fields in TPJBs is detailed. The model accounts for various pivot stiffness types, all load dependent and best when known empirically, and allows for dissimilar pad and bearing clearances. The algorithm, reliable even for very soft pad-pivots, predicts frequency reduced bearing impedance coefficients and over a certain frequency range delivers the bearing stiffness, damping and virtual mass force coefficients. Good correlation of predictions against a number of experimental results available in the literature bridges the gap between a theoretical model and the applications. Predicted pad reaction loads reveal large pivot deflections, in particular for a bearing with large preloaded pads, with significant differences in pivot stiffness as a function of specific load and operating speed. The question on how pivot stiffness acts to increase (or decrease) the bearing force coefficients, in particular the dynamic stiffness versus frequency, remains since the various experimental data show contradictory results. A predictive study with one of the test bearings varies its pivot stiffness from 10% of the fluid film stiffness to an almost rigid one, 100 times larger. With certainty, bearings with nearly rigid pivot stiffness show frequency independent force coefficients. However, for a range of pad pivot stiffness, 1/10 to ten times the fluid film stiffness, TPJB impedances vary dramatically with frequency, in particular as the excitation frequency grows above synchronous speed. The bearing virtual mass coefficients become negative, thus stiffening the bearing for most excitation frequencies.

The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings

2013 ◽  
Author(s):  
Luis San Andrés ◽  
Yujiao Tao
Keyword(s):  
Experimental Data ◽  
Journal Bearings ◽  
Fluid Film ◽  
Virtual Mass ◽  
Force Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Bearing Force ◽  
Film Stiffness ◽  
Tilting Pad Journal Bearings

Recent comprehensive experimental data showcasing the force coefficients of commercial size tilting pad journal bearings has brought to rest the long standing issue on the adequacy of the [K,C,M] physical model to represent frequency independent bearing force coefficients, in particular viscous damping. Most experimental works test TPJBs with large preloads, operating over a large wide range of rotor speeds, and with null to beyond normal specific loads. Predictions from apparently simple fluid film bearing models stand poor against the test data which invariably signals to theory missing pivot and pad flexibility effects, and most importantly, ignoring significant differences in bearing and pad clearances due to actual operation, poor installation and test procedures, or simply errors in manufacturing and assembly. Presently, a conventional thermo hydrodynamic bulk flow model for prediction of the pressure and temperature fields in TPJBs is detailed. The model accounts for various pivot stiffness types, all load dependent and best when known empirically, and allows for dissimilar pad and bearing clearances. The algorithm, reliable even for very soft pad-pivots, predicts frequency reduced bearing impedance coefficients and, over a certain frequency range, delivers the bearing stiffness, damping and virtual mass force coefficients. Good correlation of predictions against a number of experimental results available in the literature bridges the gap between a theoretical model and the applications. Predicted pad reaction loads reveal large pivot deflections, in particular for a bearing with large preloaded pads, with significant differences in pivot stiffness as a function of specific load and operating speed. The question on how pivot stiffness acts to increase (or decrease) the bearing force coefficients, in particular the dynamic stiffness vs. frequency, remains since the various experimental data show contradictory results. A predictive study with one of the test bearings varies its pivot stiffness from 10% of the fluid film stiffness to an almost rigid one, 100 times larger. With certainty, bearings with nearly rigid pivot stiffness show frequency independent force coefficients. However, for a range of pad pivot stiffness, 1/10 to ten times the fluid film stiffness, TPJB impedances vary dramatically with frequency, in particular as the excitation frequency grows above synchronous speed. The bearing virtual mass coefficients become negative, thus stiffening the bearing for most excitation frequencies.

Tilting Pad Journal Bearings: On Bridging the Hot Gap Between Experimental Results and Model Predictions

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Luis San Andrés ◽  
Yujiao Tao ◽  
Yingkun Li
Keyword(s):  
Gas Turbines ◽  
Journal Bearings ◽  
Forced Response ◽  
Fluid Film ◽  
General Character ◽  
Fluid Inertia ◽  
Force Coefficients ◽  
Tilting Pad ◽  
Excitation Frequencies ◽  
Tilting Pad Journal Bearings

The accurate prediction of the forced performance of tilting pad journal bearings (TPJBs) relies on coupling a fluid film model that includes thermal energy transport, and on occasion fluid inertia, to the structural stiffness of the pads' pivots and the thermomechanical deformation of the pads' surfaces. Often enough, the flexibility of both pads and pivots is ignored prior to the bearing actual operation; practice dictating that force coefficients, damping in particular, decrease dramatically due to pivot flexibility. Even in carefully conducted experiments, components' flexibilities are invoked to explain dramatic differences between measurements and predictions. A multiple-year test program at TAMU has demonstrated the dynamic forced response of TPJBs can be modeled accurately with matrices of constant stiffness K, damping C, and added mass M coefficients. The K-C-M model, representing frequency independent force coefficients, is satisfactory for excitation frequencies less or equal to the shaft synchronous speed. However, as shown by San Andrés and Tao (2013, “The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings,” ASME J. Eng. Gas Turbines Power, 135, p. 112505), pivot flexibility reduces the applicability of the simple constant parameter model to much lower excitation frequencies. Presently, a fluid film flow model predicts the journal eccentricity and force coefficients of a five-pad rocker-back TPJB tested at TAMU under a load-between-pad (LBP) configuration. The predictions agree well with the test results provided the model uses actual hot bearing clearances and an empirical characterization of the pivot stiffness. A study follows to determine the effects of pad preload, r¯P = 0.0, 0.27 (test article), and 0.50, as well as the load orientation, LBP, and load-on-pad (LOP), on bearing performance with an emphasis on ascertaining the configuration with most damping and stiffness, largest film thickness, and the least drag friction. In the study, a rigid pivot and two flexible pivots are considered throughout. Further examples present the effective contribution of the pads' mass and mass moment of inertia and film fluid inertia on the bearing force coefficients. To advance results of general character, predictions are shown versus Sommerfeld number (S), a design parameter proportional to shaft speed and decreasing with applied load. Both LBP and LOP configurations show similar performance characteristics; the journal eccentricity increasing with pivot flexibility. For LBP and LOP bearings with 0.27 preload, pivot flexibility decreases dramatically the bearing damping coefficients, in particular, at the low end of S, i.e., large loads. The model and predictions aid to better design TPJBs supporting large specific loads.

Tilting Pad Journal Bearings: On Bridging the Hot Gap Between Experimental Results and Model Predictions

2014 ◽  
Author(s):  
Luis San Andrés ◽  
Yujiao Tao ◽  
Yingkun Li
Keyword(s):  
Journal Bearings ◽  
Forced Response ◽  
Fluid Film ◽  
General Character ◽  
Fluid Inertia ◽  
Force Coefficients ◽  
Mass Moment ◽  
Tilting Pad ◽  
Excitation Frequencies ◽  
Tilting Pad Journal Bearings

The accurate prediction of the forced performance of tilting pad journal bearings (TPJB) relies on coupling a fluid film model that includes thermal energy transport, and on occasion fluid inertia, to the structural stiffness of the pads’ pivots and the thermomechanical deformation of the pads’ surfaces. Often enough, the flexibility of both pads and pivots is ignored prior to the bearing actual operation; practice dictating that force coefficients, damping in particular, decrease dramatically due to pivot flexibility. Even in carefully conducted experiments, components’ flexibilities are invoked to explain dramatic differences between measurements and predictions. A multiple-year test program at TAMU has demonstrated the dynamic forced response of TPJBs can be modeled accurately with matrices of constant stiffness K, damping C, and added mass M coefficients. The K-C-M model, representing frequency independent force coefficients, is satisfactory for excitation frequencies less or equal to the shaft synchronous speed. However, as shown by the authors in Ref. [1], pivot flexibility reduces the applicability of the simple constant parameter model to much lower excitation frequencies. Presently, a fluid film flow model predicts the journal eccentricity and force coefficients of a five-pad rocker-back TPJB tested at TAMU under a load-between-pad (LBP) configuration. The predictions agree well with the test results provided the model uses actual hot bearing clearances and an empirical characterization of the pivot stiffness. A study follows to determine the effects of pad preload, r¯p = 0.0, 0.27 (test article) and 0.50, as well as the load orientation, LBP and load-on-pad (LOP), on bearing performance with an emphasis on ascertaining the configuration with most damping and stiffness, largest film thickness, and the least drag friction. In the study, a rigid pivot and two flexible pivots are considered throughout. Further examples present the effective contribution of the pads’ mass and mass moment of inertia and film fluid inertia on the bearing force coefficients. To advance results of general character, predictions are shown versus Sommerfeld number (S), a design parameter proportional to shaft speed and decreasing with applied load. Both LBP and LOP configurations show similar performance characteristics; the journal eccentricity increasing with pivot flexibility. For LBP and LOP bearings with 0.27 preload, pivot flexibility decreases dramatically the bearing damping coefficients, in particular at the low end of S, i.e., large loads. The model and predictions aid to better design TPJBs supporting large specific loads.

Effect of Pad Flexibility on the Performance of Tilting Pad Journal Bearings—Benchmarking a Predictive Model

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Luis San Andrés ◽  
Yingkun Li
Keyword(s):  
Test Data ◽  
Flow Model ◽  
Film Flow ◽  
High Surface ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Force Coefficients ◽  
Tilting Pad ◽  
The Impact ◽  
Tilting Pad Journal Bearings

Tilting pad journal bearings (TPJBs) supporting high-performance turbomachinery rotors have undergone steady design improvements to satisfy ever stringent operating conditions that include large specific loads, due to smaller footprints, and high surface speeds that promote flow turbulence and hence larger drag power losses. Simultaneously, predictive models continuously evolve to include minute details on bearing geometry, pads and pivots' configurations, oil delivery systems, etc. In general, predicted TPJB rotordynamic force coefficients correlate well with experimental data for operation with small to moderately large unit loads (1.7 MPa). Experiments also demonstrate bearing dynamic stiffnesses are frequency dependent, best fitted with a stiffness-mass like model whereas damping coefficients are adequately represented as of viscous type. However, for operation with large specific loads (>1.7 MPa), poor correlation of predictions to measured force coefficients is common. Recently, an experimental effort (Gaines, J., 2014, “Examining the Impact of Pad Flexibility on the Rotordynamic Coefficients of Rocker-Pivot-Pad Tiling-Pad Journal Bearings,” M.S. thesis, Mechanical Engineering, Texas A&M University, College Station, TX) produced test data for three TPJB sets, each having three pads of unequal thickness, to quantify the effect of pad flexibility on the bearings' force coefficients, in particular damping, over a range of load and rotational speed conditions. This paper introduces a fluid film flow model accounting for both pivot and pad flexibility to predict the bearing journal eccentricity, drag power loss, lubricant temperature rise, and force coefficients of typical TPJBs. A finite element (FE) pad structural model including the Babbitt layer is coupled to the thin film flow model to determine the mechanical deformation of the pad surface. Predictions correlate favorably with test data, also demonstrating that pad flexibility produces a reduction of up to 34% in damping for the bearing with the thinnest pads relative to that with the thickest pads. A parametric study follows to quantify the influence of pad thickness on the rotordynamic force coefficients of a sample TPJB with three pads of increasing preload, r¯p  = 0, 0.25 (baseline) and 0.5. The bearing pads are either rigid or flexible by varying their thickness. For design considerations, dimensionless static and dynamic characteristics of the bearings are presented versus the Sommerfeld number (S). Pad flexibility shows a more pronounced effect on the journal eccentricity and the force coefficients of a TPJB with null pad preload than for the bearings with larger pad preloads (0.25 and 0.5), in particular for operation with a small load or at a high surface speed (S > 0.8).

A Flow Starvation Model for Tilting Pad Journal Bearings and Evaluation of Frequency Response Functions: A Contribution Toward Understanding the Onset of Low Frequency Shaft Motions

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Luis San Andrés ◽  
Bonjin Koo ◽  
Makoto Hemmi
Keyword(s):  
Frequency Response ◽  
Low Frequency ◽  
Journal Bearings ◽  
Response Functions ◽  
Frequency Range ◽  
Flow Conditions ◽  
Force Coefficients ◽  
Lubricant Flow ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearings

Direct lubrication tilting pad journal bearings (TPJBs) require less oil flow, reduce power consumption, and offer cooler pad temperatures for operation at high surface speeds. Although apparently free of hydrodynamic instability, the literature shows that direct lubrication TPJBs exhibit unexpected shaft vibrations with a broadband low frequency range, albeit small in amplitude. Published industrial practice demonstrates the inlet lubrication type, a reduced supply flow rate causing film starvation, and the bearing discharge conditions (evacuated or end sealed) affect the onset, gravity, and persistency of the subsynchronous vibration (SSV) hash motions. The paper presents a physical model to predict the performance of TPJBs with flow conditions ranging from over flooded to extreme starvation. Lubricant starvation occurs first on an unloaded pad, thus producing a (beneficial) reduction in drag power. As the supplied flowrate decreases further, fluid starvation moves toward the loaded pads and affects the film temperature and power loss, increases the journal eccentricity, and modifies the dynamic force coefficients of each tilting pad and thus the whole bearing. For a point mass rotor supported on a TPJB, the analysis produces eigenvalues and frequency response functions (FRFs) from three physical models for lateral rotor displacements: one with frequency reduced (4 × 4) bearing stiffness (K) and damping (C) coefficients and another with constant K–C–M (inertia) coefficients over a frequency range. The third model keeps the degrees of freedom (DOF) (tilting) of each pad and incorporates the full matrices of force coefficients including fluid inertia. Predictions of rotordynamic performance follow for two TPJBs: one bearing with load between pads (LBP) configuration, and the other with a load on a pad (LOP) configuration. For both examples, under increasingly poor lubricant flow conditions, the damping ratio for the rotor-bearing low frequency (SSV) modes decreases, thus producing an increase in the amplitude of the FRFs. For the LOP bearing, a large static load produces a significant asymmetry in the force coefficients; the rotor bearing has a small stiffness and damping for shaft displacements in the direction orthogonal to the load. A reduction in lubricant flow only exacerbates the phenomenon; starvation reaches the loaded pad to eventually cause the onset of low frequency (SSV) instability. The bearing analyzed showed similar behavior in a test bench. The predictions thus show a direct correlation between lubricant flow starvation and the onset of SSV.

Effect of Pad Flexibility on the Performance of Tilting Pad Journal Bearings: Benchmarking a Predictive Model

2015 ◽  
Author(s):  
Luis San Andrés ◽  
Yingkun Li
Keyword(s):  
Test Data ◽  
Flow Model ◽  
Film Flow ◽  
High Surface ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Poor Correlation ◽  
Force Coefficients ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearings

Tilting pad journal bearings (TPJBs) supporting high performance turbomachinery rotors have undergone steady design improvements to satisfy ever stringent operating conditions that include large specific loads due to smaller footprints, and high surface speeds that promote flow turbulence and thus larger drag power losses. Simultaneously, predictive models continuously evolve to include minute details on bearing geometry, pads and pivots’ configurations, oil delivery systems, etc. In general, predicted TPJB rotordynamic force coefficients correlate well with experimental data for operation with small to moderately large unit loads (1.7 MPa). Experiments also demonstrate bearing dynamic stiffnesses are frequency dependent, best fitted with a stiffness-mass like model whereas damping coefficients are adequately represented as of viscous type. However, for operation with large specific loads (> 1.7 MPa), poor correlation of predictions to measured force coefficients is common. Recently, an experimental effort [1] produced test data for three TPJB sets, each having three pads of unequal thickness, to quantify the effect of pad flexibility on the bearings’ force coefficients, in particular damping, over a range of load and rotational speed conditions. This paper introduces a fluid film flow model accounting for both pivot and pad flexibility to predict the bearing journal eccentricity, drag power loss, lubricant temperature rise and force coefficients of typical TPJBs. A finite element pad structural model including the Babbitt layer is coupled to the thin film flow model to determine the mechanical deformation of the pad surface. Predictions correlate favorably with test data, also demonstrating that pad flexibility produces a reduction of up to 34% in damping for the bearing with the thinnest pads relative to that with the thickest pads. A parametric study follows to quantify the influence of pad thickness on the rotordynamic force coefficients of a sample TPJB with three pads of increasing preload, rp = 0, 0.25 (baseline) and 0.5. The bearing pads are either rigid or flexible by varying their thickness. For design considerations, dimensionless static and dynamic characteristics of the bearings are presented versus the Sommerfeld number (S). Pad flexibility shows a more pronounced effect on the journal eccentricity and the force coefficients of a TPJB with null pad preload than for the bearings with larger pad preloads (0.25 and 0.5), in particular for operation with a small load or at a high surface speed (S>0.8).

A Flow Starvation Model for Tilting Pad Journal Bearings and Evaluation of Frequency Response Functions: A Contribution Towards Understanding the Onset of Low Frequency Shaft Motions

2017 ◽  
Author(s):  
Luis San Andrés ◽  
Bonjin Koo ◽  
Makoto Hemmi
Keyword(s):  
Frequency Response ◽  
Low Frequency ◽  
Journal Bearings ◽  
Response Functions ◽  
Frequency Range ◽  
Flow Conditions ◽  
Force Coefficients ◽  
Lubricant Flow ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearings

Direct lubrication tilting pad journal bearings (TPJBs) require of less oil flow, reduce power consumption and offer cooler pad temperatures for operation at high surface speeds. Although apparently free of a hydrodynamic instability, the literature shows that direct lubrication TPJBs exhibit unexpected shaft vibrations with a broadband low frequency range, albeit small in amplitude. Published industrial practice demonstrates the inlet lubrication type, a reduced supply flow rate causing film starvation, and the bearing discharge conditions (evacuated or end sealed) affect the onset, gravity and persistency of the sub synchronous (SSV) hash motions. The paper presents a physical model to predict the performance of TPJBs with flow conditions ranging from over flooded to extreme starvation. Lubricant starvation occurs first on an unloaded pad, thus producing a (beneficial) reduction in drag power. As the supplied flowrate decreases further, fluid starvation moves towards the loaded pads and affects the film temperature and power loss, increases the journal eccentricity, and modifies the dynamic force coefficients of each tilting pad and thus the whole bearing. For a point mass rotor supported on a TPJB, the analysis produces eigenvalues and frequency response functions (FRFs) from three physical models for lateral rotor displacements: one with frequency reduced (4×4) bearing stiffness (K) and damping (C) coefficients and another with constant K-C-M (inertia) coefficients over a frequency range. The third model keeps the degrees of freedom (tilting) of each pad and incorporates the full matrices of force coefficients including fluid inertia. Predictions of rotordynamic performance follow for two TPJBs: one bearing with load between pads (LBP) configuration, and the other with a load on a pad (LOP) configuration. For both examples, under increasingly poor lubricant flow conditions, the damping ratio for the rotor-bearing low frequency (SSV) modes decreases, thus producing an increase in the amplitude of the FRFs. For the LOP bearing, a large static load produces a significant asymmetry in the force coefficients; the rotor-bearing has a small stiffness and damping for shaft displacements in the direction orthogonal to the load. A reduction in lubricant flow only exacerbates the phenomenon; starvation reaches the loaded pad to eventually cause the onset of low frequency (SSV) instability. The bearing analyzed showed similar behavior in a test bench. The predictions thus show a direct correlation between lubricant flow starvation and the onset of SSV.

Characterization of Five-Pad Tilting-Pad Journal Bearings Using an Original Test-Rig

2011 ◽  
Author(s):  
S. Chatterton ◽  
P. Pennacchi ◽  
A. Vania ◽  
E. Tanzi ◽  
R. Ricci
Keyword(s):  
Film Thickness ◽  
Gas Turbines ◽  
Journal Bearings ◽  
Fluid Film ◽  
Test Rig ◽  
Theoretical Evaluation ◽  
Oil Film ◽  
Tilting Pad ◽  
Fluid Film Thickness ◽  
Tilting Pad Journal Bearings

Tilting-pad journal bearings are installed with increased frequency owing to their dynamic stability characteristics in several rotating machine applications, typically in high rotating speed cases. This usually happens for new installations in highspeed compressors or during revamping operations of steam and gas turbines for power generation. The selection from a catalogue, or the design of a new bearing, requires the knowledge of the bearing characteristics such as babbitt metal temperatures, fluid-film thickness, load capacity, stiffness and damping coefficients. Temperature and fluid-film thickness are essential for the safety of the bearing. Babbitt metal is subject to creep at high temperatures, as it happens at high speed operations. On the contrary, at low speed or with high loads, oil-film thickness could be too low, resulting in metal to metal contact. Oil-film dynamic coefficients are largely responsible of the dynamic behaviour and of the stability of the rotor-tilting-pad-bearing system. Therefore, the theoretical evaluation and/or the experimental estimation of these coefficients are mandatory in the design phase. The theoretical evaluation of these coefficients for tilting pad journal bearings is difficult due to their complex geometry, boundary and thermal conditions and turbulent flow, whereas an experimental characterization requires a suitable test rig. The paper describes the test rig designed to this purpose and its unusual configuration with respect to other test rigs available in literature. Some preliminary tests performed for the bearing characterization are also shown.

Sign in / Sign up

Export Citation Format

Share Document