Experimental Response of a Rotor Supported on Rayleigh Step Gas Bearings

2005 ◽  
Author(s):  
Xuehua Zhu ◽  
Luis San Andre´s
Keyword(s):  
High Speed ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Radial Clearance ◽  
Large Magnitude ◽  
Gas Bearings ◽  
Rotor Surface ◽  
Stiffness And Damping ◽  
Rapid Deployment ◽  
Damping Capability

Reliable gas bearings will enable the rapid deployment of high speed oil-free micro-turbomachinery. This paper presents analysis and experiments of the dynamic performance of a small rotor supported on Rayleigh step gas bearings. Comprehensive tests demonstrate that Rayleigh step hybrid gas bearings exhibit adequate stiffness and damping capability in a narrow range of shaft speeds, up to ∼ 20 krpm. Rotor coast down responses were performed with two test bearing sets with nominal radial clearance of 25 μm and 38 μm. A near-frictionless carbon (NFC) coating was applied on the rotor to reduce friction at liftoff and touchdown. However, the rotor could not lift easily and severe rubbing occurred at shaft speeds below ∼ 4,000 rpm. The tests show that the supply pressure raises the rotor critical speed and decreases the system damping ratio, while only affecting slightly the rotor-bearing system onset speed of instability. Whirl frequencies are nearly fixed at the system natural frequency (∼ 120 Hz) with subsynchronous amplitude motions of very large magnitude that prevented rotor operation above ∼ 20 krpm. The geometry of the Rayleigh steps distributed on the rotor surface generates a time varying pressure field, resulting in a sizable 4X super synchronous component of bearing transmitted load. Predictions show the synchronous stiffness and damping coefficients decrease with shaft speed. Predicted threshold speeds of instability are much lower than measured values due to the analytical model limitations assuming a grooved stator. The predicted synchronous responses to imbalance correlate well with the measurements. The Rayleigh step gas bearings are the most unreliable rigid bearing configuration tested to date.

Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery

2007 ◽  
Vol 129 (4) ◽  
pp. 1020-1027 ◽  
Author(s):  
Xuehua Zhu ◽  
Luis San Andrés
Keyword(s):  
High Speed ◽  
Low Cost ◽  
Damping Ratio ◽  
Extreme Temperature ◽  
Gas Bearings ◽  
Speed Increase ◽  
Feed Pressure ◽  
Motor Test ◽  
Direct Stiffness ◽  
Commercial Applications

Micro-turbomachinery demands gas bearings to ensure compactness, light weight, and extreme temperature operation. Gas bearings with large stiffness and damping, and preferably of low cost, will enable successful commercial applications. Presently, tests conducted on a small rotor supported on flexure pivot hydrostatic pad gas bearings (FPTPBs) demonstrate stable rotordynamic responses up to 100,000rpm (limit of the drive motor). Test rotor responses show the feed pressure raises the system critical speed (increase in bearing direct stiffness) while the viscous damping ratio decreases. Predictions correlate favorably with experimentally identified (synchronous) direct stiffness bearing force coefficients. Identified experimental gas bearing synchronous damping coefficients are 50% or less of the predicted magnitudes, though remaining relatively constant as the rotor speed increases. Tests without feed pressure show the rotor becomes unstable at ∼81krpm with a whirl frequency ratio of 20%. FPTPBs are mechanically complex and more expensive than cylindrical plain bearings. However, their enhanced stability characteristics and predictable rotordynamic performance makes them desirable for the envisioned oil-free applications in high speed micro-turbomachinery.

Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions

2006 ◽  
Vol 129 (3) ◽  
pp. 850-857 ◽  
Author(s):  
Luis San Andrés ◽  
Dario Rubio ◽  
Tae Ho Kim
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Load Capacity ◽  
Test System ◽  
Foil Bearings ◽  
Rotor Imbalance ◽  
Synchronous Motion ◽  
Damping Characteristics ◽  
Rotor Surface ◽  
Stiffness And Damping

Gas foil bearings (GFBs) satisfy the requirements for oil-free turbomachinery, i.e., simple construction and ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal damping, as well as frequency and amplitude dependent stiffness and damping characteristics. This paper provides experimental results of the rotordynamic performance of a small rotor supported on two bump-type GFBs of length and diameter equal to 38.10mm. Coast down rotor responses from 25krpm to rest are recorded for various imbalance conditions and increasing air feed pressures. The peak amplitudes of rotor synchronous motion at the system critical speed are not proportional to the imbalance introduced. Furthermore, for the largest imbalance, the test system shows subsynchronous motions from 20.5krpm to 15krpm with a whirl frequency at ∼50% of shaft speed. Rotor imbalance exacerbates the severity of subsynchronous motions, thus denoting a forced nonlinearity in the GFBs. The rotor dynamic analysis with calculated GFB force coefficients predicts a critical speed at 8.5krpm, as in the experiments; and importantly enough, unstable operation in the same speed range as the test results for the largest imbalance. Predicted imbalance responses do not agree with the rotor measurements while crossing the critical speed, except for the lowest imbalance case. Gas pressurization through the bearings’ side ameliorates rotor subsynchronous motions and reduces the peak amplitudes at the critical speed. Posttest inspection reveal wear spots on the top foils and rotor surface.

Dynamic Characterization of an Integral Squeeze Film Bearing Support Damper for a Supercritical CO2 Expander

2017 ◽  
Author(s):  
Bugra Ertas ◽  
Adolfo Delgado ◽  
Jeffrey Moore
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Mechanical Impedance ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Damping Behavior ◽  
Impedance Testing ◽  
Stiffness And Damping ◽  
Onset Of Cavitation

The present work advances experimental results and analytical predictions on the dynamic performance of an integral squeeze film damper (ISFD) for application in a high-speed super-critical CO2 (sCO2) expander. The test campaign focused on conducting controlled orbital motion mechanical impedance testing aimed at extracting stiffness and damping coefficients for varying end seal clearances, excitation frequencies, and vibration amplitudes. In addition to the measurement of stiffness and damping; the testing revealed the onset of cavitation for the ISFD. Results show damping behavior that is constant with vibratory velocity for each end seal clearance case until the onset of cavitation/air ingestion, while the direct stiffness measurement was shown to be linear. Measurable added inertia coefficients were also identified. The predictive model uses an isothermal finite element method to solve for dynamic pressures for an incompressible fluid using a modified Reynolds equation accounting for fluid inertia effects. The predictions revealed good correlation for experimentally measured direct damping, but resulted in grossly overpredicted inertia coefficients when compared to experiments.

Dynamic Performance Analysis on High-Speed Railway Continuous Girder Bridge

2011 ◽  
Vol 280 ◽  
pp. 186-190
Author(s):  
Shou Tan Song ◽  
Ji Wen Zhang ◽  
Xin Yuan
Keyword(s):  
High Speed ◽  
Moving Load ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Wheel Load ◽  
Dynamic Coefficients ◽  
Bridge Structures ◽  
Continuous Girder Bridge ◽  
Girder Bridge ◽  
Dynamic Performance Analysis

The dynamic performance of continuous girder under the train in a series of speed is studied through examples, and the main conclusions are given in the following. The resonance mechanism of continuous girder is similar to simply supported beam. The vehicle wheel load forms regular moving load series, which induces periodical action and resonance of the bridge. The damping ratio of bridge itself has less effect on the amplitude at the loading stage, but significant effects appear when the load departs from the bridge. The count of continuous spans also has less impact on the dynamic coefficients, so three continuous spans can be adopted for calculation and analysis. Span and fundamental frequency have significant influence on dynamic coefficients of bridge structures. To extend the span of the bridge structure can reduce the dynamic coefficient while keeping its frequency invariant. The fundamental frequencies of different bridges are corresponding to certain resonant speeds, which calls for the attention in the design.

Comparison of Rotordynamic Analysis Predictions With the Test Response of Simple Gas Hybrid Bearings for Oil Free Turbomachinery

2003 ◽  
Author(s):  
Deborah A. Wilde ◽  
Luis San Andre´s
Keyword(s):  
High Speed ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Rotor Speed ◽  
Gas Bearings ◽  
Model Predictions ◽  
Rotor Bearing ◽  
Frequency Ratios ◽  
Bearing System ◽  
Good Agreement

Current applications of gas film bearings in high-speed oil-free micro-turbomachinery (<0.4 MW) require calibrated predictive tools to successfully deploy their application to mass-produced systems, for example oil-free turbochargers. The present investigation details the linear rotordynamic analysis of a test rotor supported on externally pressurized gas bearings. Model predictions are compared with the test rotordynamic response determined through comprehensive experiments conducted on a small rotor supported on three lobed hybrid (hydrostatic/hydrodynamic) rigid gas bearings. Predictions for the rotor-bearing system synchronous response to imbalance show good agreement with measurements during rotor coast downs, and manifest a decrease in damping ratio as the level of external pressurization increases. The rotor-bearing eigenvalue analysis forwards natural frequencies in accordance with the measurements, and null damping ratios evidence the threshold speeds of rotordynamic instability. Estimated whirl frequency ratios are typically 50% of rotor speed, thus predicting sub synchronous instabilities at lower rotor speeds than found experimentally when increasing the magnitude of feed pressurization. Rationale asserting the nature of the discrepancies calls for further analysis.

Hydrostatic Gas Journal Bearings for Micro-Turbomachinery

2004 ◽  
Vol 127 (2) ◽  
pp. 157-164 ◽  
Author(s):  
L. X. Liu ◽  
C. J. Teo ◽  
A. H. Epstein ◽  
Z. S. Spakovszky
Keyword(s):  
Natural Frequency ◽  
Analytical Model ◽  
High Speed ◽  
Experimental Testing ◽  
Fluid Dynamic ◽  
Damping Ratio ◽  
Journal Bearings ◽  
Fiber Optic Sensor ◽  
Gas Bearings ◽  
Aspect Ratios

Several years ago an effort was undertaken at MIT to develop high-speed rotating MEMS (Micro Electro-Mechanical Systems) using computer chip fabrication technology. To enable high-power density the micro-turbomachinery must be run at tip speeds of order 500m∕s, comparable to conventional scale turbomachinery. The high rotating speeds (of order 2 million rpm), the relatively low bearing aspect ratios (L∕D<0.1) due to fabrication constraints, and the laminar flow regime in the bearing gap place the micro-bearing designs to an exotic spot in the design space for hydrostatic gas bearings. This paper presents a new analytical model for axially fed gas journal bearings and reports the experimental testing of micro gas bearings to characterize and to investigate their rotordynamic behavior. The analytical model is capable of dealing with all the elements of, (1) micro-devices, (2) dynamic response characteristics of hydrostatic gas bearings, (3) evaluation of stiffness, natural frequency and damping, (4) evaluation of instability boundaries, and (5) evaluation of effects of imbalance and bearing anisotropy. First, a newly developed analytical model for hydrostatic gas journal bearings is introduced. The model consists of two parts, a fluid dynamic model for axially fed gas journal bearings and a rotordynamic model for micro-devices. Next, the model is used to predict the natural frequency, damping ratio and the instability boundary for the test devices. Experiments are conducted using a high-resolution fiber optic sensor to measure rotor speed, and a data reduction scheme is implemented to obtain imbalance-driven whirl response curves. The model predictions are validated against experimental data and show good agreement with the measured natural frequencies and damping ratios. Last, the new model is successfully used to establish bearing operating protocols and guidelines for high-speed operation.

scholarly journals Measurement Research of Motorized Spindle Dynamic Stiffness under High Speed Rotating

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaopeng Wang ◽  
Yuzhu Guo ◽  
Tianning Chen
Keyword(s):  
High Speed ◽  
Production Efficiency ◽  
Dynamic Stiffness ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Machining Accuracy ◽  
Motorized Spindle ◽  
Response Curves ◽  
Tool Technology ◽  
High Speed Machine

High speed motorized spindle has become a key functional unit of high speed machine tools and effectively promotes the development of machine tool technology. The development of higher speed and more power puts forward the stricter requirement for the performance of motorized spindle, especially the dynamic performance which affects the machining accuracy, reliability, and production efficiency. To overcome the problems of ineffective loading and dynamic performance measurement of motorized spindle, a noncontact electromagnetic loading device is developed. The cutting load can be simulated by using electromagnetic force. A new method of measuring force by force sensors is presented, and the steady and transient loading force could be measured exactly. After the high speed machine spindle is tested, the frequency response curves of the spindle relative to machine table are collected at 0~12000 rpm; then the relationships between stiffness and speeds as well as between damping ratio and speeds are obtained. The result shows that not only the static and dynamic stiffness but also the damping ratio declined with the increase of speed.

Dynamic Analysis of High-Speed Hybrid Thrust Bearings

2013 ◽  
Vol 365-366 ◽  
pp. 304-308
Author(s):  
Lei Wang
Keyword(s):  
Dynamic Analysis ◽  
High Speed ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Dynamic Performance ◽  
Orifice Diameter ◽  
Thrust Bearings ◽  
Supply Pressure ◽  
Bearing Stiffness ◽  
Stiffness And Damping

An analysis is conducted and solutions are provided for the dynamic performance of high speed hybrid thrust bearing. By adopting bulk flow theory, the turbulent Reynolds equation is solved numerically with the different orifice diameter and supply pressure. The results show that increasing supply pressure can significantly improve the bearing stiffness and damping, while the orifice diameters make a different effect on the bearing stiffness and damping.

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.

scholarly journals Influence of Floating Ring Seal Working Condition Parameters on the Dynamic Characteristics of Transient Gas Film

2021 ◽  
Vol 2108 (1) ◽  
pp. 012087
Author(s):  
Lishan Xu ◽  
Weizheng Zhang ◽  
Junjie Lu ◽  
Zhu Liu
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Spiral Groove ◽  
Low Leakage ◽  
Ring Seal ◽  
Stiffness And Damping Coefficient ◽  
Small Perturbation Method ◽  
Stiffness And Damping

Abstract The high requirements for sealing performance in high-speed rotating machinery has led to the design of floating seal with annular spiral groove that offer the advantages of low leakage and extended stability. However, efforts to model the dynamic performance of these floating seal have suffered from the great complexity of the flow field. The present work addresses this issue by establishing a transient Reynolds formulation of a floating seal with annular spiral groove in a rotating coordinate system based on the small perturbation method. In addition, the influence of radial eccentricity and film thickness on the solution divergence and calculation accuracy is calculated. The dynamic stiffness and dynamic damping matrixes are built. Then the variation rules of the dynamic stiffness and damping coefficient of the gas film with structure and working conditions are investigated in detail. The results show that the floating ring seal is more suitable for the service conditions of small film thickness, low pressure, high speed and large eccentricity. Accordingly, the results obtained lay a theoretical foundation for evaluating real-world applications of floating ring seal.

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