Hybrid Flexure Pivot-Tilting Pad Gas Bearings: Analysis and Experimental Validation

2006 ◽  
Vol 128 (3) ◽  
pp. 551-558 ◽  
Author(s):  
Luis San Andrés
Keyword(s):  
High Speed ◽  
Experimental Validation ◽  
Operating Speed ◽  
Dynamic Force ◽  
Low Friction ◽  
Gas Bearings ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
System Time

Gas film bearings offer unique advantages enabling successful deployment of high-speed microturbomachinery. Current applications encompass micro power generators, air cycle machines, and turbo expanders. Mechanically complex gas foil bearings are in use; however, their excessive cost and lack of calibrated predictive tools deter their application to mass-produced oil-free turbochargers, for example. The present investigation advances the analysis and experimental validation of hybrid gas bearings with static and dynamic force characteristics desirable in high-speed turbomachinery. These characteristics are adequate load support, good stiffness and damping coefficients, low friction and wear during rotor startup and shutdown, and most importantly, enhanced rotordynamic stability at the operating speed. Hybrid (hydrostatic/hydrodynamic) flexure pivot-tilting pad bearings demonstrate superior static and dynamic forced performance than other geometries as evidenced in a high-speed rotor-bearing test rig. A computational model including the effects of external pressurization predicts the rotordynamic coefficients of the test bearings and shows good correlation with measured force coefficients, thus lending credence to the predictive model. In general, direct stiffnesses increase with operating speed and external pressurization, whereas damping coefficients show an opposite behavior. Predicted mass flow rates validate the inherent restrictor-type orifice flow model for external pressurization. Measured coast-down rotor speeds demonstrate very low-friction operation with large system time constants. Estimated drag torques from the gas bearings indirectly validate the recorded system time constant.

On the dynamic stability of high-speed gas bearings: stability study and experimental validation

2011 ◽  
Vol 2 (2) ◽  
pp. 342-351
Author(s):  
T. Waumans ◽  
J. Peirs ◽  
J. Reynaerts ◽  
F. Al-Bender
Keyword(s):  
Dynamic Stability ◽  
Stability Problem ◽  
High Speed ◽  
Experimental Validation ◽  
Stability Study ◽  
Gas Bearings ◽  
Aerostatic Bearings ◽  
Bearing Dynamics ◽  
Wide Operating ◽  
Operating Temperature Range

For high-speed applications, gas lubricated bearings offer very specific advantages over other,more conventional bearing technologies: a clean and oil-free solution, virtually wear-free operation, lowfrictional losses, wide operating temperature range, etc. However, the principal drawback involved in theapplication of high-speed gas bearings concerns the dynamic stability problem. Successful applicationtherefore requires control of the rotor-bearing dynamics so as to avoid instabilities.After a detailed study of the dynamic stability problem and the formulation of a convenient stability criterium,a brief overview is given of the currently existing bearing types and configurations for improving the stability.In addition, three strategies are introduced: (i) optimal design of plain aerostatic bearings; (ii) modification ofthe bearing geometry to counteract the destabilising effects in the gas film; and (iii) introduction of dampingexternal to the gas film as to compensate for the destabilising effects.These strategies are worked out into detail leading to the formulation of a series of design rules. Theireffectiveness is validated experimentally at a miniature scale. In recent experiments a rotational speed of1.2 million rpm has been achieved with a 6 mm rotor on aerodynamic journal bearings, leading to a recordDN-number of 7.2 million.

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.

Material Considerations for High Temperature Tilting Pad Gas Bearings

1968 ◽  
Vol 90 (4) ◽  
pp. 818-828 ◽  
Author(s):  
S. F. Murray ◽  
M. B. Peterson
Keyword(s):  
High Temperature ◽  
Contact Area ◽  
High Speed ◽  
Contact Problems ◽  
Sliding Contact ◽  
Gas Bearings ◽  
Hydrodynamic Bearing ◽  
Tilting Pad ◽  
Short Time

This paper is concerned with the sliding contact problems encountered in tilting pad gas bearings operating at temperatures up to 1400 deg F. Both the pivots and the bearing surfaces are considered. Short time experimental evaluations of pivot damage are summarized. The results of start-stop and high-speed rub tests on a single tilting pad hydrodynamic bearing are also described. Based on the results obtained to date, damage-resistant coatings are available for use on the bearing surfaces at high temperature. There are also suitable pivot materials, but the pivot must be properly designed to minimize slip in the contact area.

Analysis on Dynamic Performance of Hydrodynamic Tilting-Pad Gas Bearings Using Partial Derivative Method

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Yang Lihua ◽  
Qi Shemiao ◽  
Yu Lie
Keyword(s):  
Analytical Method ◽  
Gas Turbines ◽  
High Speed ◽  
Dynamic Performance ◽  
Gas Bearings ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Dynamic Performances ◽  
Perturbation Frequency ◽  
San Andres

Tilting-pad gas bearings are widely used in high-speed rotating machines due to their inherent stability characteristics. This paper advances the analytical method for prediction of the dynamic performances of tilting-pad gas bearings. The main advantage of the analytical method is that the complete set of dynamic coefficients of tilting-pad gas bearings can be obtained. The predictions show that the perturbation frequency has the strong effects on the dynamic coefficients of gas bearings. In general, at lower perturbation frequency, the equivalent direct stiffness coefficients increase with frequency, whereas equivalent direct damping coefficients dramatically reduce. For higher perturbation frequency, the dynamic coefficients are nearly independent of the frequency. Moreover, the equivalent dynamic coefficients of four-pad tilting-pad gas bearing obtained by the method in this paper are in good agreement with those obtained by Zhu and San Andres [(2007), “Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery,” ASME J. Eng. Gas Turbines Power, 129(4), pp. 1020–1027] in the published paper. The results validate the feasibility of the method presented in this paper in calculating the dynamic coefficients of gas-lubricated tilting-pad bearings.

Experimental Response of Simple Gas Hybrid Bearings for Oil-Free Turbomachinery

2006 ◽  
Vol 128 (3) ◽  
pp. 626-633 ◽  
Author(s):  
Deborah A. Osborne ◽  
Luis San Andre´s
Keyword(s):  
High Speed ◽  
Damping Ratio ◽  
Dynamic Force ◽  
Test Results ◽  
Low Friction ◽  
Foil Bearings ◽  
Feed Pressure ◽  
Micropower Generators ◽  
Lift Off ◽  
Stiffness And Damping

Gas film bearings offer unique advantages enabling successful deployment of high-speed microturbomachinery (<0.4 MW). Current applications encompass micropower generators, air cycle machines and turbo expanders. Mechanically complex gas foil bearings are in use; however, their excessive cost and lack of calibrated predictive tools deters their application to mass-produced systems. The present investigation provides experimental results for the rotordynamic performance of a small rotor supported on simple and inexpensive hybrid gas bearings with static and dynamic force characteristics desirable in high-speed turbomachinery. These characteristics are adequate load support, stiffness and damping coefficients, low friction and wear during rotor startup and shutdown, and most importantly, enhanced rotordynamic stability. The test results evidence the paramount effect of feed pressure on early rotor lift-off and substantially higher threshold speeds of rotordynamic instability. Higher supply pressures also determine larger bearing direct stiffnesses, and thus bring an increase in the rotor-bearing system critical speed albeit with a reduction in damping ratio.

Rotordynamic Characteristics of a Five Pad, Rocker-Pivot, Tilting Pad Bearing in a Load-on-Pad Configuration; Comparisons to Predictions and Load-Between-Pad Results

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Dara W. Childs ◽  
Clint R. Carter
Keyword(s):  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Bulk Flow ◽  
Quadratic Functions ◽  
Dynamic Force ◽  
Unit Load ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Computational Fluid Dynamics Analysis ◽  
Tilting Pad

Rotordynamic data are presented for a rocker-pivot tilting pad bearing in load-on-pad (LOP) configuration for (345–3101 kPa) unit loads and speeds from 4000 rpm to 13,000 rpm. The bearing was directly lubricated through a leading edge groove with five pads, 0.282 preload, 60% offset, 57.87 deg pad arc angle, 101.587 mm (3.9995 in.) rotor diameter, 0.1575 mm (0.0062 in.) diametral clearance, and 60.325 mm (2.375 in.) pad length. Measured results were reported for this bearing by Carter and Childs (2008, “Measurements Versus Predictions for the Rotordynamic Characteristics of a 5-Pad, Rocker-Pivot, Tilting-Pad Bearing in Load Between Pad Configuration,” ASME Paper No. GT2008-50069) in the load-between-pad (LBP) configuration. Results for the LOP are compared with predictions from a bulk-flow Navier–Stokes model (as utilized by San Andres (1991, “Effect of Eccentricity on the Force Response of a Hybrid Bearing,” STLE Tribol. Trans., 34, pp. 537–544)) and to the prior LBP results. Frequency effects on the dynamic-stiffness coefficients were investigated by applying dynamic-force excitation over a range of excitation frequencies. Generally, the direct real parts of the dynamic-stiffness coefficients could be modeled as quadratic functions of the excitation frequency, and accounted for by adding a mass matrix to the conventional [K][C] model to produce a frequency-independent [K][C][M] model. Measured added-mass terms in the loaded direction approached 60 kg. The static load direction in the tests was y. The direct stiffness coefficients Kyy and Kxx depend strongly on the applied unit load, more so than speed. They generally increased linearly with load, shifting to a quadratic dependence at higher unit loads. At lower unit loads, Kyy and Kxx increase monotonically with running speed. The experimental results were compared with predictions from a bulk-flow computational fluid dynamics analysis. Stiffness orthotropy was apparent in test results, significantly more than predicted, and it became more pronounced at the heavier unit loads. Measured Kyy values were consistently higher than predicted, and measured Kxx values were lower. Comparing the LOP results to prior measured LBP results for the same bearing, at higher loads, Kyy is significantly larger for the LOP configuration than LBP. Measured values for Kxx are about the same for LOP and LBP. At low unit loads, stiffness orthotropy defined as Kyy/Kxx is the same for LOP and LBP, progressively increasing with increasing unit loads. At the highest unit load, Kyy/Kxx=2.1 for LOP and 1.7 for LBP. Measured direct damping coefficients Cxx and Cyy were insensitive to changes in either load or speed, in contrast to predictions of marked Cyy sensitivity for changes in the load. Only at the highest test speed of 13,000 rpm were the direct damping coefficients adequately predicted. No frequency dependency was observed for the direct damping coefficients.

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.

Experimental Studies on Flexure Pivot Tilting Pad Gas Bearings With Pad Radial Compliance

2007 ◽  
Author(s):  
Kyuho Sim ◽  
Aaron Rimpel ◽  
Daejong Kim
Keyword(s):  
High Speed ◽  
Experimental Studies ◽  
Experimental Results ◽  
Frequency Dependent ◽  
Gas Bearings ◽  
Force Coefficients ◽  
Tilting Pad ◽  
Operation Frequency ◽  
Large Rotor ◽  
Good Agreement

This paper presents experimental studies on imbalance responses of a rotor supported by two flexure pivot tilting pad gas bearings with radial compliance. The radial compliance was aimed to accommodate large rotor centrifugal growth inherent with high speed operation. Frequency-dependent rotordynamic force coefficients calculated from developed software were used to predict critical speeds and onset speed of instability and compared with experimental results. Two results show very good agreement.

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.

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