scholarly journals Hybrid Gas Bearings With Controlled Supply Pressure to Eliminate Rotor Vibrations While Crossing System Critical Speeds

2008 ◽  
Author(s):  
Luis San Andre´s ◽  
Keun Ryu
Keyword(s):  
Critical Speed ◽  
Pressure Control ◽  
Sudden Increase ◽  
Critical Speeds ◽  
Gas Bearings ◽  
Supply Pressure ◽  
Simple Strategy ◽  
Tilting Pad ◽  
Bearing Stiffness ◽  
Bearing Force

Micro-turbomachinery (MTM) implements gas bearings in compact units of enhanced mechanical reliability. Gas bearings, however, have little damping and wear quickly during transient rub events. Flexure pivot tilting pad bearings offer little or no cross-coupled stiffnesses with enhanced rotordynamic stability; and when modified for hydrostatic pressurization, demonstrate superior rotordynamic performance over other bearing types. External pressurization stiffens gas bearings thus increasing system critical speeds, albeit reducing system damping. Most importantly, measurements demonstrate that external pressurization is not needed for rotor super critical speed operation. In practice, the supply pressure could be shut off at high rotor speeds with substantial gains in efficiency. The paper introduces a simple strategy, employing an inexpensive air pressure regulator to control the supply pressure into the hybrid bearings, to reduce or even eliminate high amplitudes of rotor motion while crossing the system critical speeds. Rotor speed coast-down tests with the pressure controller demonstrate the effectiveness of the proposed approach. A simple on-off supply pressure control, i.e. a sudden increase in pressure while approaching a critical speed, is the best since it changes abruptly the bearing stiffness coefficients and moves the system critical speed to a higher speed. A rotordynamic analysis integrating predicted bearing force coefficients forwards critical speeds in agreement with the test results. Predicted rotor responses for the controlled supply conditions show an excellent correlation with measured data. The experiments validate the predictive tools and demonstrate the controllable rotordynamic characteristics of flexure pivot hybrid gas bearings.

scholarly journals Hybrid Gas Bearings With Controlled Supply Pressure to Eliminate Rotor Vibrations While Crossing System Critical Speeds

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Luis San Andrés ◽  
Keun Ryu
Keyword(s):  
Critical Speed ◽  
Pressure Control ◽  
Sudden Increase ◽  
Critical Speeds ◽  
Gas Bearings ◽  
Supply Pressure ◽  
Simple Strategy ◽  
Tilting Pad ◽  
Bearing Stiffness ◽  
Bearing Force

Microturbomachinery implements gas bearings in compact units of enhanced mechanical reliability. Gas bearings, however, have little damping and wear quickly during transient rub events. Flexure pivot tilting pad bearings offer little or no cross-coupled stiffnesses with enhanced rotordynamic stability; and when modified for hydrostatic pressurization, demonstrate superior rotordynamic performance over other bearing types. External pressurization stiffens gas bearings thus increasing system critical speeds, albeit reducing system damping. Most importantly, measurements demonstrate that external pressurization is not needed for rotor supercritical speed operation. In practice, the supply pressure could be shut off at high rotor speeds with substantial gains in efficiency. This paper introduces a simple strategy, employing an inexpensive air pressure regulator to control the supply pressure into the hybrid bearings, to reduce or even eliminate high amplitudes of rotor motion while crossing the system critical speeds. Rotor speed coast-down tests with the pressure controller demonstrate the effectiveness of the proposed approach. A simple on-off supply pressure control, i.e., a sudden increase in pressure while approaching a critical speed, is the best since it changes abruptly the bearing stiffness coefficients and moves the system critical speed to a higher speed. A rotordynamic analysis integrating predicted bearing force coefficients forwards critical speeds in agreement with the test results. Predicted rotor responses for the controlled supply conditions show an excellent correlation with measured data. The experiments validate the predictive tools and demonstrate the controllable rotordynamic characteristics of flexure pivot hybrid gas bearings.

Estimating Critical Speeds of Stepped Shafts with Flexible Bearings

1971 ◽  
Vol 8 (03) ◽  
pp. 327-333
Author(s):  
R. H. Salzman
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Design Stage ◽  
Normal Range ◽  
Critical Speeds ◽  
Stepped Shaft ◽  
Bearing Stiffness ◽  
Variable Support ◽  
Method Show ◽  
Good Agreement

This paper presents a semi-graphical approach for finding the first critical speed of a stepped shaft with finite bearing stiffness. The method is particularly applicable to high-speed turbine rotors with journal bearings. Using Rayleigh's Method and the exact solution for whirling of a uniform shaft with variable support stiffness, estimates of the lowest critical speed are easily obtained which are useful in the design stage. First critical speeds determined by this method show good agreement with values computed by the Prohl Method for the normal range of bearing stiffness. A criterion is also established for determining if the criticals are "bearing critical speeds" or "bending critical speeds," which is of importance in design. Discusser E. G. Baker

Measurements of the Rotordynamic Response of a Rotor Supported on Porous Type Gas Bearing

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Wanhui Liu ◽  
Kai Feng ◽  
Yanwei Huo ◽  
Zhiyang Guo
Keyword(s):  
Critical Speed ◽  
Vibration Mode ◽  
Damping Ratio ◽  
Nonlinear Behavior ◽  
Impulse Turbine ◽  
Gas Bearings ◽  
Supply Pressure ◽  
Gas Bearing ◽  
Rotor Dynamic ◽  
Deceleration Time

A test rig is built in this study to measure the rotordynamic response of a rotor supported on porous-type gas bearings. A rotor with a double impulse turbine at one end is driven by compressed air and supported on two porous type journal gas bearings and a pair of bump-type thrust gas bearings. The rotor is accelerated to ∼25 krpm and coasted down in the test. The rotor dynamic response is measured for different bearing supply pressures (i.e., 0.40 MPa, 0.45 MPa, and 0.50 MPa) and imbalance masses (i.e., 85 mg, 150 mg, and 215 mg). Synchronous and subsynchronous amplitudes are extracted from the rotor responses. The critical speed increases as the bearing supply pressure increases, but the damping ratio decreases. The onset speed of subsynchronous motion increases, and the subsynchronous amplitude decreases as the bearing supply pressure increases. The deceleration time is more than 5 min for a bearing supply pressure of 0.5 MPa, which reveals the very low drag friction of the porous gas bearings. The synchronous amplitude increases as the imbalance increases for all the tested bearing supply pressures. The critical speeds for different imbalances are almost the same, except for the out-of-phase imbalance condition under a bearing supply pressure of 0.50 MPa, in which the critical speed increases as the imbalance increases. The normalized synchronous amplitude shows the rotor-bearing system behaves almost in a linear fashion for all in-phase imbalance conditions. Nonlinear behavior is shown around the critical speed for the 215 mg out-of-phase imbalance condition under a bearing supply pressure of 0.50 MPa. The onset speed of the subsynchronous motion decreases as the imbalance increases under the in-phase imbalance condition. The predominant mode of vibration changes from cylindrical to conical and then back to cylindrical as the rotor speed decreases during the coast down test for the in-phase imbalance conditions. However, the rotor vibration mode is predominantly conical during the whole coast down test for the out-of-phase imbalance conditions.

Imbalance Response of a Rotor Supported by Hybrid Air Foil Bearings

2011 ◽  
Author(s):  
Daejong Kim ◽  
Prajwal Shetty ◽  
Donghyun Lee
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Hydrodynamic Instability ◽  
High Reliability ◽  
Load Capacity ◽  
Damping Ratio ◽  
Foil Bearings ◽  
Supply Pressure ◽  
Bearing Stiffness ◽  
Frequency Ratios

Air foil bearings (AFB’s) are widely used in small to midsized turbomachinery. They are simple in construction, offer very low drag friction, and have very high reliability at high speed operations. This paper presents experimental imbalance response of a 4.84 kg rigid rotor (operating below bending critical speed) supported by two hybrid air foil bearings with 50 mm in diameter. The concept of “hybrid” in this paper utilizes the hydrostatic augmentation of the load capacity during the start up and shut down. The hybrid air foil bearings were designed with three top foils for enhanced stability. Imbalance responses in cylindrical mode are presented up to 44,000rpm with different supply pressures. As the supply pressure is increased from 2.67 to 4 bar, the bearing stiffness increases slightly, resulting in slightly larger vibration (and reduced damping ratio) during the trans-critical speed operation. Hydrodynamic instability was observed with whirl frequency ratios of about 0.17∼0.2 depending on the supply pressures. Tests were also conducted to investigate the effect of supply pressure on the rotordynamic stability. The test results show that the hybrid operation is very effective to suppress the subsynchronous vibrations at high speeds.

Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part II: Effect of Tilt-Pad Bearings and Foundation Dynamics

1987 ◽  
Vol 109 (1) ◽  
pp. 8-14 ◽  
Author(s):  
J. M. Vance ◽  
B. T. Murphy ◽  
H. A. Tripp
Keyword(s):  
Critical Speed ◽  
Natural Frequencies ◽  
State Of The Art ◽  
Dynamic Properties ◽  
Experimental Measurements ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Speed Prediction ◽  
Bearing Stiffness ◽  
Stiffness And Damping

This is the second of two papers describing results of a research project directed at verifying computer programs used to calculate critical speeds of turbomachinery. This part describes measurements made to determine the characteristics of tilt-pad bearings and foundation dynamics. Critical speeds of a 166 kg laboratory rotor on tilt-pad bearings are then compared with predictions from a state-of-the-art damped eigenvalue computer program. Measured natural frequencies of a steam turbine are also compared with computer predictions. Accuracy of critical speed prediction is shown to depend on accuracy of 1) the “free-free” rotor models, 2) the bearing stiffness and damping coefficients, and 3) the dynamic properties of the foundation, which can be represented by an impedance that must be determined by experimental measurements.

Design and Hydrodynamic Performance of Hybrid Flexural Pivot Gas Bearings for High Speed Oil-Free Micro Turbomachinery

2005 ◽  
Author(s):  
Kyuho Sim ◽  
Daejong Kim
Keyword(s):  
High Speed ◽  
Hydrodynamic Performance ◽  
Bending Vibrations ◽  
Hydrodynamic Mode ◽  
Critical Speeds ◽  
Gas Bearings ◽  
Radial Stiffness ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Final Design

This paper introduces new flexural pivot tilting pad gas bearings for high speed oil-free micro turbomachinery. The new flexural pivot tilting pad gas bearings have a special web geometry that provides a radial stiffness to accommodate rotor growths and high vibrations at critical speed, a pitching stiffness to accommodate rotor-bearing misalignments or rotor bending vibrations, and a very small tilting stiffness for rotor stability. Comprehensive numerical simulations involving orbit simulations and coast-down simulations were performed to investigate the effects of preloads and pivot offsets on the critical speeds and onset speeds of instability. Higher preload and pivot offset increased both critical speeds of the rotor-bearing system and onset speeds of instability due to the increased wedge effect. Design procedures of radial stiffness were presented considering both rotor centrifugal and thermal growths. From simple adiabatic solution of temperature distribution of gas film under pure hydrodynamic mode, enough bearing clearance at pivot was found to be a very important design aspect for high speed hydrodynamic gas bearings. Asymmetric radial stiffness was chosen as a final design to meet the target design speed of 180 krpm for bearing diameter of 28.52mm. Suggested tilting pad gas bearing with asymmetric radial stiffness was predicted to be very stable even under high external destabilizing forces.

Turbomachinery Dual Rotor-Bearing System Analysis

2002 ◽  
Author(s):  
Hsiao-Wei D. Chiang ◽  
Chih-Neng Hsu ◽  
Wes Jeng ◽  
Shun-Hsu Tu ◽  
Wei-Chen Li
Keyword(s):  
Finite Element ◽  
Transfer Matrix ◽  
Critical Speed ◽  
System Analysis ◽  
Design Parameters ◽  
Critical Speeds ◽  
Rotor Design ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Bearing System

It is very common for aircraft engines to have dual rotor or even triple rotor designs. Due to the complexity of having multiple rotor design, the transfer matrix methods have used in the past to deal with multiple rotor-bearing systems. However, due to transfer matrix method’s assumptions, sometimes resulted in numerical stability problems or root-missing problems. The purpose of this paper is to develop a systematic theoretical analysis of the dynamic characteristics of turbomachinery dual rotor-bearing systems. This dual rotor-bearing system analysis will start with a finite element (FEM) rotor-bearing system dynamic model, then using different methods to verify the analysis results including critical speed map and bearing stiffness. In an inertia coordinate system, a general model of continuous dual rotor-bearing systems is established based on a lagrangian formulation. Gyroscopic moment, rotary inertia, bending and shear deformations have been included in the model. From a point of view of the systematic approach, a solution of the finite element method is used to calculate the critical speeds by several different methods, which in turn can help to verify this dual rotor-bearing system approach. The effects of the speed ratio of dual rotors on the critical speed will be studied, which in turn can be used as one of the dual rotor design parameters. Also, both critical speeds are in effect functions of dual rotor speeds. Finally, the bearing stiffness between high speed and low speed shafts not only affect the critical speeds of the dual rotor system, but also affect the mode shapes of the system. Therefore, the bearing stiffness in between is of even greater importance in turbomachinery dual rotor or multiple rotor design.

Flexure Pivot Tilting Pad Hybrid Gas Bearings: Operation With Worn Clearances and Two Load-Pad Configurations

2007 ◽  
Author(s):  
Luis San Andre´s ◽  
Keun Ryu
Keyword(s):  
High Speed ◽  
High Performance ◽  
Test System ◽  
Viscous Drag ◽  
Widespread Application ◽  
Critical Speeds ◽  
Gas Bearings ◽  
Foil Bearings ◽  
Modal Damping ◽  
Tilting Pad

Gas film bearings enable the successful deployment of high-speed micro-turbomachinery. Foil bearings are in use; however, cost and lack of calibrated predictive tools prevent their widespread application. Other types of bearing configurations, simpler to manufacture and fully engineered, are favored by commercial turbomachinery manufacturers. Externally pressurized tilting pad bearings offer a sound solution for stable rotor support. This paper reports measurements of the rotordynamic response of a rigid rotor, 0.825 kg and 28.6 mm in diameter, supported on flexure pivot tilting pad hybrid gas bearings. The tests are performed for various imbalances, increasing supply pressures, and under load-on-pad (LOP) and load-between-pad (LBP) configurations. Presently, the initial condition of the test bearings shows sustained wear and dissimilar pad clearances after extensive testing reported earlier, see Ref. [1]. In the current measurements, there are no noticeable differences in rotor responses for both LOP and LBP configurations due to the light-weight rotor, i.e. small static load acting on each bearing. External pressurization into the bearings increases their direct stiffnesses and reduces their damping, while raising the system critical speeds with a notable reduction in modal damping ratios. The rotor supported on the worn bearings shows a ∼10% drop in first critical speeds and roughly similar modal damping than when tested with pristine bearings. Pressurization into the bearings leads to large times for rotor deceleration, thus demonstrating the little viscous drag typical of gas bearings. Rotor deceleration tests with manually controlled supply pressures eliminate the passage through critical speeds, thus paving a path for rotordynamic performance without large amplitude motions over extended regions of shaft speed. The rotordynamic analysis shows critical speeds and peak amplitudes of motion agreeing very well with the measurements. The synchronous rotor responses for increasing imbalances demonstrate the test system linearity. Superior stability and predictable performance of pressurized flexure pivot gas bearings can further their implementation in high performance oil-free microturbomachinery. More importantly, the measurements show the reliable performance of the worn bearings even when operating with enlarged and uneven clearances.

scholarly journals Study on Dynamic Response of Assembly Type Gear-Rotor System

2011 ◽  
Vol 2-3 ◽  
pp. 912-917
Author(s):  
Ji Shuang Dai ◽  
Peng Zhang ◽  
Chao Feng Li ◽  
Bo Wang ◽  
Bang Chun Wen
Keyword(s):  
Dynamic Response ◽  
Working Conditions ◽  
High Speed ◽  
Critical Speed ◽  
Rotor System ◽  
Coupled Systems ◽  
Tilting Pad ◽  
Bearing Stiffness ◽  
Unbalance Force ◽  
Stiffness Characteristics

The dynamic model of a rotor system of assembled compressor is established. Based on the single axis analysis, and considering the tilting-pad bearing stiffness characteristics with speed variations, the paper analyses whole system’s nature characteristic with gearing mesh factors. It mainly expands with the form of amplitude-frequency drawing and spectrum charts, and examines the dynamic response with each key position of coupled systems under the two working conditions. The results show that, because of the existence of gear meshing effect, Low speed axis and high-speed axis in the corresponding speed shaft appeared a few larger vibration amplitudes, at high speed axis add unbalance force, can arouse resonance of this axis in the first two order critical speed, but in the other axis don’t have obvious display.

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

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