Scaling Laws for Ultra-Short Hydrostatic Gas Journal Bearings

2003 ◽  
Author(s):  
Z. S. Spakovszky ◽  
L. X. Liu
Keyword(s):  
High Speed ◽  
Large Scale ◽  
Scaling Laws ◽  
Damping Ratio ◽  
Journal Bearings ◽  
Gas Bearings ◽  
Outer Periphery ◽  
Order Of Magnitude ◽  
Design Speed ◽  
Annular Seals

The journal bearings of the MIT micro-devices are located at the outer periphery of the rotor and are designed to operate at rotational speeds of order 2 million rpm in order to enable high-power densities with turbomachinery tip speeds near 500 m/s. These journal bearings are very short compared to their relatively large bearing diameters such that the bearing L/D is typically less than 0.1, that is at least one order of magnitude smaller than in conventional gas bearings. Thus, the ultra-short micro gas journal bearings essentially act as short annular seals and operate at Reynolds numbers of order 300, two orders of magnitude lower than conventional annular seals. The concepts that hold for turbulent flow, large scale annular seals do not apply to micro bearings and the laminar flow regime sets new challenges in the design, implementation and operation of ultra-short, high-speed gas bearings. In order to reach the goal of operating the MIT micro devices at full design speed, the micro-bearing design must be improved and engineering solutions need to be found to overcome the challenges of high-speed bearing operation. This paper is the first to derive the scaling laws for the dynamics of ultrashort hydrostatic gas journal bearings. The theory is established from first principles and enables a physics based characterization of the dynamic behavior of ultra-short hydrostatic gas bearings. The derived scaling laws for natural frequency and damping ratio show good agreement with experimental data. A simple criterion for whirl instability is found that only depends on bearing geometry. The scaling laws together with this criterion are used to delineate engineering solutions critical for stable high-speed bearing operation. Design charts are developed which provide the link between fabrication tolerances, bearing performance, and the tolerable level of rotor unbalance for a minimum required whirl ratio.

Scaling Laws for Ultra-Short Hydrostatic Gas Journal Bearings

2005 ◽  
Vol 127 (3) ◽  
pp. 254-261 ◽  
Author(s):  
Z. S. Spakovszky ◽  
L. X. Liu
Keyword(s):  
High Speed ◽  
Large Scale ◽  
Scaling Laws ◽  
Damping Ratio ◽  
Journal Bearings ◽  
Gas Bearings ◽  
Outer Periphery ◽  
Order Of Magnitude ◽  
Design Speed ◽  
Annular Seals

The journal bearings of the MIT micro-devices are located at the outer periphery of the rotor and are designed to operate at rotational speeds of order two million rpm in order to enable high-power densities with turbomachinery tip speeds near 500m/s. These journal bearings are very short compared to their relatively large bearing diameters such that the bearing L/D is typically less than 0.1, that is at least one order of magnitude smaller than in conventional gas bearings. Thus, the ultra-short micro gas journal bearings essentially act as short annular seals and operate at Reynolds numbers of order 300, two orders of magnitude lower than conventional annular seals. The concepts that hold for turbulent flow, large scale annular seals do not apply to micro bearings and the laminar flow regime sets new challenges in the design, implementation and operation of ultra-short, high-speed gas bearings. In order to reach the goal of operating the MIT micro devices at full design speed, the micro-bearing design must be improved and engineering solutions need to be found to overcome the challenges of high-speed bearing operation. This paper is the first to derive the scaling laws for the dynamics of ultra-short hydrostatic gas journal bearings. The theory is established from first principles and enables a physics based characterization of the dynamic behavior of ultra-short hydrostatic gas bearings. The derived scaling laws for natural frequency and damping ratio show good agreement with experimental data. A simple criterion for whirl instability is found that only depends on bearing geometry. The scaling laws together with this criterion are used to delineate engineering solutions critical for stable high-speed bearing operation. Design charts are developed which provide the link between fabrication tolerances, bearing performance, and the tolerable level of rotor unbalance for a minimum required whirl ratio.

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.

Hydrostatic Gas Journal Bearings for Micro-Turbomachinery

2003 ◽  
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 500 m/s, comparable to conventional scale turbomachinery. The high rotating speeds (of order 2 million rpm), the relatively low bearing aspect ratios (L/D &lt; 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.

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.

Modeling and Experimental Investigation of Micro-hydrostatic Gas Thrust Bearings for Micro-turbomachines

2005 ◽  
Vol 128 (4) ◽  
pp. 597-605 ◽  
Author(s):  
C. J. Teo ◽  
Z. S. Spakovszky
Keyword(s):  
High Speed ◽  
Scaling Laws ◽  
Thrust Bearing ◽  
Journal Bearings ◽  
Axial Stiffness ◽  
Stable Operation ◽  
Successful Operation ◽  
Element Analysis ◽  
Essential Information ◽  
Thrust Bearings

One major challenge for the successful operation of high-power-density micro-devices lies in the stable operation of the bearings supporting the high-speed rotating turbomachinery. Previous modeling efforts by Piekos (2000, “Numerical Simulation of Gas-Lubricated Journal Bearings for Microfabricated Machines,” Ph.D. thesis, Department of Aeronautics and Astronautics, MIT), Liu et al. (2005, “Hydrostatic Gas Journal Bearings for Micro-Turbo Machinery,” ASME J. Vib. Acoust., 127, pp. 157–164), and Spakovszky and Liu (2005, “Scaling Laws for Ultra-Short Hydrostatic Gas Journal Bearings,” ASME J. Vib. Acoust. 127, pp. 254–261) have focused on the operation and stability of journal bearings. Thrust bearings play a vital role in providing axial support and stiffness, and there is a need to improve the understanding of their dynamic behavior. In this work, a rigorous theory is presented to analyze the effects of compressibility in micro-flows (characterized by low Reynolds numbers and high Mach numbers) through hydrostatic thrust bearings for application to micro-turbomachines. The analytical model, which combines a one-dimensional compressible flow model with finite-element analysis, serves as a useful tool for establishing operating protocols and assessing the stability characteristics of hydrostatic thrust bearings. The model is capable of predicting key steady-state performance indicators, such as bearing mass flow, axial stiffness, and natural frequency as a function of the hydrostatic supply pressure and thrust-bearing geometry. The model has been applied to investigate the static stability of hydrostatic thrust bearings in micro-turbine generators, where the electrostatic attraction between the stator and rotor gives rise to a negative axial stiffness contribution and may lead to device failure. Thrust-bearing operating protocols have been established for a micro-turbopump, where the bearings also serve as an annular seal preventing the leakage of pressurized liquid from the pump to the gaseous flow in the turbine. The dual role of the annular pad poses challenges in the operation of both the device and the thrust bearing. The operating protocols provide essential information on the required thrust-bearing supply pressures and axial gaps required to prevent the leakage of water into the thrust bearings. Good agreement is observed between the model predictions and experimental results. A dynamic stability analysis has been conducted, which indicates the occurrence of instabilities due to flow choking effects in both forward and aft thrust bearings. A simple criterion for the onset of axial rotor oscillations has been established and subsequently verified in a micro-turbocharger experiment. The predicted frequencies of the unstable axial oscillations compare well with the experimental measurements.

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 (&lt;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.

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

2004 ◽  
Author(s):  
Xuehua Zhu ◽  
Luis San Andre´s
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, lightweight 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 100,000 rpm (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 ∼ 81 krpm 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.

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

2006 ◽  
Vol 128 (3) ◽  
pp. 634-643 ◽  
Author(s):  
Deborah A. Osborne ◽  
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 microturbomachinery (<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 coastdowns, 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 subsynchronous 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.

scholarly journals Experimental Investigation of Load-Bearing Mechanism of Underwater Mined-Tunnel Lining

2021 ◽  
Vol 9 (6) ◽  
pp. 627
Author(s):  
Zhiqiang Zhang ◽  
Binke Chen ◽  
Qingnan Lan
Keyword(s):  
High Speed ◽  
Large Scale ◽  
Water Pressure ◽  
Tunnel Lining ◽  
Scale Model ◽  
Soil Pressure ◽  
Railway Tunnel ◽  
Load Bearing ◽  
Water Head ◽  
Design Speed

A series of model tests were performed to investigate the load-bearing mechanism of a mined railway tunnel lining under water pressure. To investigate the load-bearing characteristics of different types of linings, a fully closed water pressure exerting device for a noncircular section tunnel was invented. A large-scale model test (1:30) under combined water and soil pressures was conducted to investigate the mechanical characteristics, deformation, stress distribution, crack development process, and failure mode of the underwater mined-tunnel lining. The test results indicated that for the high-speed railway tunnel of Class IV surrounding rock with a design speed of 350 km/h, both the drainage lining and the waterproof lining were controlled by a small eccentric compression under the two test conditions. One had only water pressure, and the other had a variable water pressure and constant soil pressure. The key sections for controlling instability were the bottom of the wall and the inverted arch. The ultimate water head of the drainage lining was 49 m, and the ultimate water head of the waterproof lining was 78 m. In comparison with the drainage lining, the waterproof lining could significantly improve the water-pressure resistance. Thus, design loads of 30 and 60 m are recommended for the drainage and waterproof lining structures, respectively.

scholarly journals High-throughput Analysis of Arabidopsis Stem Vibrations to Identify Mutants with Altered Mechanical Properties

2018 ◽  
Author(s):  
Miyuki T. Nakata ◽  
Masahiro Takahara ◽  
Shingo Sakamoto ◽  
Kouki Yoshida ◽  
Nobutaka Mitsuda
Keyword(s):  
Mechanical Properties ◽  
High Throughput ◽  
High Speed ◽  
Large Scale ◽  
Growth Traits ◽  
Damping Ratio ◽  
Free Vibrations ◽  
Video Data ◽  
High Throughput Analysis ◽  
Throughput Analysis

AbstractMechanical properties are rarely used as quantitative indices for the large-scale mutant screening of plants, even in the model plant Arabidopsis thaliana. The mechanical properties of plant stems generally influence their vibrational characteristics. Here, we developed Python-based software, named AraVib, for the high-throughput analysis of free vibrations of plant stems, focusing specifically on Arabidopsis stem vibrations, and its extended version, named AraVibS, to identify mutants with altered mechanical properties. These programs can be used without knowledge of Python and require only an inexpensive handmade setting stand and an iPhone/iPad with a high-speed shooting function for data acquisition. Using our system, we identified an nst1 nst3 double-mutant lacking secondary cell walls in fiber cells and a wrky12 mutant displaying ectopic formation of secondary cell wall compared with wild type by employing only two growth traits (stem height and fresh weight) in addition to videos of stem vibrations. Furthermore, we calculated the logarithmic decrement, the damping ratio, the natural frequency and the stiffness based on the spring-mass-damper model from the video data using AraVib. The stiffness was estimated to be drastically decreased in nst1 nst3, which agreed with previous tensile test results. However, in wrky12, the stiffness was significantly increased. These results demonstrate the effectiveness of our new system. Because our method can be applied in a high-throughput manner, it can be used to screen for mutants with altered mechanical properties.

Sign in / Sign up

Export Citation Format

Share Document