Stability Criterion for Spiral Grooved Thrust Gas Bearings

1990 ◽  
Vol 112 (4) ◽  
pp. 734-737 ◽  
Author(s):  
V. N. Constantinescu ◽  
S. Galetuse
Keyword(s):  
Pressure Distribution ◽  
Dynamic Stability ◽  
Small Perturbation ◽  
Perturbation Analysis ◽  
Stability Criterion ◽  
Analytical Procedure ◽  
Previous Analysis ◽  
Unconditionally Stable ◽  
Thrust Bearings ◽  
Gas Bearing

A previous analysis of dynamic stability for a blocked center inward pumping spiral grooved thrust gas bearing is extended to two other types of similar bearings, namely annular thrust bearings with either inward or outward pumping. Both a numerical small perturbation analysis and an analytical procedure are used, the latter one being based on an approximate shape of the pressure distribution. The analysis provides a critical compressibility number up to which the bearings is unconditionally stable.

On the Dynamic Stability of the Spiral-Grooved Gas-Lubricated Thrust Bearing

1987 ◽  
Vol 109 (1) ◽  
pp. 183-188 ◽  
Author(s):  
V. N. Constantinescu ◽  
S. Galetuse
Keyword(s):  
Dynamic Stability ◽  
Small Perturbation ◽  
Thrust Bearing ◽  
Critical Mass ◽  
Practical Interest ◽  
Unconditionally Stable ◽  
Gas Bearings ◽  
Air Hammer

The dynamic stability of a blocked center inward pumping spiral grooved thrust bearing is investigated. For this purpose two methods are considered comparatively, namely a standard small perturbation one, and an extension of the method used previously to determine air-hammer phenomena in externally pressurized gas bearings. The first method gives a more detailed description of situations in which the film is stable or unstable, while the second one gives a limit for the speed (or compressibility parameter Λc) up to which the bearing is unconditionally stable. The second method is simpler and of practical interest since at higher speeds the critical mass furnished by the first method is of little practical interest (being too small).

Dynamic Stability of Mechanical Structures Containing Externally Pressurized Gas-Lubricated Thrust Bearings

1988 ◽  
Vol 110 (2) ◽  
pp. 271-278 ◽  
Author(s):  
P. Plessers ◽  
R. Snoeys
Keyword(s):  
Frequency Response ◽  
Stability Criterion ◽  
Feedback Loop ◽  
Response Functions ◽  
Thrust Bearings ◽  
Supporting Structure ◽  
Nyquist Criterion ◽  
The Stability ◽  
Stability Limits ◽  
Gas Bearing

A stability criterion is presented to evaluate instability phenomena in mechanical systems containing externally pressurized gas bearings. For this criterion, the gas bearing films and the supporting structure are characterized separately by means of frequency response functions. The overall system may be considered as a feedback-loop for which the Nyquist criterion will define stability limits. The analysis demonstrates the interaction between the dynamics of the supporting structure and the air gap. The stability criterion is generalized for systems containing more than one gas film. The stability criterion is verified experimentally.

A Simplified Stability Criterion for Nonconservative Systems

1979 ◽  
Vol 46 (2) ◽  
pp. 423-426 ◽  
Author(s):  
I. Fawzy
Keyword(s):  
Dynamic Stability ◽  
Stability Criterion ◽  
Degrees Of Freedom ◽  
Necessary Condition ◽  
Matrix Methods ◽  
Nonconservative System ◽  
Nonconservative Systems ◽  
The Stability ◽  
Lyapunov’S Theorem ◽  
Sufficient And Necessary Condition

Dynamic stability of a general nonconservative system of n degrees of freedom is investigated. A sufficient and necessary condition for the stability of such a system is developed. It represents a simplified criterion based on the famous Lyapunov’s theorem which is proved afresh using λ-matrix methods only. When this criterion is adopted, it reduces the number of equations in Lyapunov’s method to less than half. A systematic procedure is then suggested for the stability investigation and its use is illustrated through a numerical example at the end of the paper.

Dynamic stability of closed plasma configurations

1970 ◽  
Vol 4 (4) ◽  
pp. 645-665 ◽  
Author(s):  
Daniel R. Wells
Keyword(s):  
Global Stability ◽  
Dynamic Stability ◽  
Perturbation Analysis ◽  
Flow Fields ◽  
Experimental Results ◽  
Plasma Confinement ◽  
Gauge Symmetries ◽  
Mhd Stability ◽  
The Stability ◽  
Dynamical Principle

The global stability of closed plasma configurations is related to the dynamical principle of least constraint and the spacetime and gauge symmetries of the flow fields. This leads to an entirely new concept of MHD stability which is more basic than stability predictions which rely on a linearized perturbation analysis. The predictions of the theory are compared to recent experimental results obtained in studies of the stability of plasma confinement geometries. The theory predicts the violent ‘instabilities’ of these systems which are currently attributed to other mechanisms. Several pertinent details of the theory which are widely misinterpreted are discussed and clarified.

Modeling and Experimental Investigation of Micro-Hydrostatic Gas Thrust Bearings for Micro-Turbomachines

2005 ◽  
Author(s):  
C. J. Teo ◽  
Z. S. Spakovszky
Keyword(s):  
Dynamic Stability ◽  
High Speed ◽  
Thrust Bearing ◽  
Dynamic Instability ◽  
Axial Stiffness ◽  
Stable Operation ◽  
Essential Information ◽  
Flow Choking ◽  
Thrust Bearings

One of the major challenges 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 [1], Liu et al. [2] and Spakovszky and Liu [3] have mainly focused on the operation and stability of journal bearings. However, since thrust bearings play the vital role of providing axial support and stiffness, there is a need to gain a fuller understanding of their 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 microturbomachines. The analytical model, which combines a 1-D 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 for the required thrust bearing supply pressures and axial gaps required to prevent the leakage of water into the thrust bearings for various pump outlet pressures. Good agreement is observed between the model predictions and experimental results. In addition, a dynamic stability analysis is also performed, which indicates the occurrence of unstable axial oscillations due to flow choking effects in both forward and aft thrust bearings. These a-priori dynamic stability predictions were subsequently verified experimentally on a micro-turbocharger. The frequencies of unstable axial oscillations predicted using the model compare favorably to those determined experimentally, thus vindicating the validity of the model. A simple and useful dynamic stability criterion is established, where the occurrence of flow choking in both thrust bearings give rise to dynamic instability.

Dynamic Stability of FPSO-Shuttle Systems: An Analytical Procedure and Practical Results

2002 ◽  
Author(s):  
Ge´rson B. Matter ◽  
Joel S. Sales ◽  
Sergio H. Sphaier
Keyword(s):  
Dynamic Stability ◽  
Deep Water ◽  
Dynamic Systems ◽  
Time Domain ◽  
Equilibrium Position ◽  
Analytical Procedure ◽  
Time Domain Analysis ◽  
The Stability ◽  
The Time Domain ◽  
Floating Systems

The paper deals with the dynamics of floating systems (FPSO units) moored in deep water in the presence of currents. The offloading operation is carried out in a tandem arrangement from the FPSO to a Shuttle ship of lesser capacity. According to the classical theory of dynamic systems, a study of the behavior of floating units is performed by determining the equilibrium position and then analyzing the stability around this position. The time domain analysis is also used to compare the results. This procedure is extended to the case of systems in a spread mooring configuration and with turret.

Flat Central Pressure in Circular Elastic Contacts Between High Order Surfaces

2005 ◽  
Author(s):  
Emanuel Diaconescu ◽  
Marilena Glovnea
Keyword(s):  
Pressure Distribution ◽  
Electrical Contacts ◽  
High Order ◽  
Sixth Order ◽  
Central Pressure ◽  
Thrust Bearings ◽  
Revolution Surfaces ◽  
Bounding Surfaces

High order revolution surfaces are often used in electrical contacts/micro-contacts or in miniature thrust bearings. This paper advances general contact formulae for these bounding surfaces. In a particular case, these relations yield known Hertz pressure distribution and contact elements. Then, the contacts between fourth and sixth order surfaces are analyzed.

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