Stability of Gas-Lubricated, Externally Pressurized Porous Journal Bearings

1975 ◽  
Vol 97 (3) ◽  
pp. 494-505 ◽  
Author(s):  
Dah-chen Sun
Keyword(s):  
Approximate Solution ◽  
Linear Theory ◽  
Frequency Ratio ◽  
Stability Problem ◽  
Journal Bearings ◽  
Eccentricity Ratio ◽  
Pneumatic Hammer ◽  
Stability Parameters ◽  
Supply Pressure ◽  
The Stability

A linear theory of hybrid instability, due to a combination of both whirl and pneumatic hammer, in gas-lubricated porous journal bearings is presented. An approximate solution to the stability problem is obtained by the use of a Galerkin expansion. Results are presented in terms of the variation of stability parameters, such as the threshold mass, the whirl frequency ratio, etc., with the compressibility number and eccentricity ratio. In addition, the effects of permeability, supply pressure, and bearing length are investigated.

Analysis of Pneumatic Instability of Externally Pressurized Porous Gas Journal Bearings

1979 ◽  
Vol 101 (1) ◽  
pp. 48-53 ◽  
Author(s):  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Theoretical Analysis ◽  
Mass Parameter ◽  
Journal Bearings ◽  
Order Perturbation ◽  
Rigid Rotor ◽  
Eccentricity Ratio ◽  
Dynamic Displacement ◽  
First Order ◽  
Supply Pressure ◽  
First Order Perturbation

A theoretical analysis is presented for the study of pneumatic instability for a rigid rotor supported in externally pressurized porous gas journal bearings. The analysis is based on a first-order perturbation with respect to the amplitude of dynamic displacement of rotor. The variation of threshold mass parameter with feeding parameter is shown. In addition, the effects of supply pressure, eccentricity ratio, L/D ratio, and porosity parameter are investigated and presented in the form of graphs.

On The Steady State and Dynamic Performance Characteristics of Floating Ring Bearings

1981 ◽  
Vol 103 (3) ◽  
pp. 389-397 ◽  
Author(s):  
Chin-Hsiu Li ◽  
S. M. Rohde
Keyword(s):  
Steady State ◽  
Linear Theory ◽  
High Speed ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Journal Bearings ◽  
Transient Problem ◽  
The Stability ◽  
Bearing System

An analysis of the steady state and dynamic characteristics of floating ring journal bearings has been performed. The stability characteristics of the bearing, based on linear theory, are given. The transient problem, in which the equations of motion for the bearing system are integrated in real time was studied. The effect of using finite bearing theory rather than the short bearing assumption was examined. Among the significant findings of this study is the existence of limit cycles in the regions of instability predicted by linear theory. Such results explain the superior stability characteristics of the floating ring bearing in high speed applications. An understanding of this nonlinear behavior, serves as the basis for new and rational criteria for the design of floating ring bearings.

A Theoretical Analysis of Whirl Instability and Pneumatic Hammer for a Rigid Rotor in Pressurized Gas Journal Bearings

1967 ◽  
Vol 89 (2) ◽  
pp. 154-165 ◽  
Author(s):  
J. W. Lund
Keyword(s):  
Theoretical Analysis ◽  
Time Constant ◽  
Pressure Ratio ◽  
Journal Bearings ◽  
Restricted Feeding ◽  
Rigid Rotor ◽  
Eccentricity Ratio ◽  
Pneumatic Hammer ◽  
Small Eccentricity ◽  
First Order

A theoretical analysis is presented for the threshold of instability for a rigid rotor supported in hydrostatic gas journal bearings. Both rotationally induced instability (hybrid instability) and pneumatic hammer are considered. The analysis is based on a first-order perturbation with respect to the eccentricity ratio (i.e., the results are limited to small eccentricity ratios) and makes use of the linearized Ph-method [2, 5, 8]. The pressurized gas is supplied to the bearing through restricted feeding holes in the center plane of the bearing and the analysis takes into account the discreteness of the feeding holes, the feeder hole time constant, and inherent compensation effects. Numerical results are given in form of 16 graphs, showing the threshold of instability as a function of supply pressure ratio, feeding parameter and eccentricity ratio. Also, the effect of the feeder hole time constant is investigated with respect to pneumatic hammer.

An Experimental Method for the Determination of Journal-Bearing Stability Parameters. Part 1: Theory

1979 ◽  
Vol 21 (3) ◽  
pp. 179-185 ◽  
Author(s):  
H. Marsh ◽  
J. E. L. Simmons
Keyword(s):  
Journal Bearing ◽  
Eccentricity Ratio ◽  
Stability Parameters ◽  
Operating Condition ◽  
Stable Operating ◽  
System Information ◽  
The Stability ◽  
Bearing System ◽  
Steady State Performance

In the design of a rotor-bearing system, information is usually available on the steady-state performance of the bearing. The designer can estimate the eccentricity ratio and attitude angle for any operating condition, but there is often little or no information which can be used to predict whether or not this is a stable operating condition. This paper describes the basic theory of bearing stability and shows how this can be used to help in the design of a novel apparatus for determining the stability parameters of any journal-bearing system.

Theoretical Contributions to the Study of Gas-Lubricated Journal Bearings

1962 ◽  
Vol 84 (1) ◽  
pp. 123-131
Author(s):  
Y. Katto ◽  
N. Soda
Keyword(s):  
Experimental Data ◽  
Approximate Solution ◽  
Theoretical Study ◽  
Journal Bearing ◽  
Isothermal Condition ◽  
Approximate Solutions ◽  
Journal Bearings ◽  
Eccentricity Ratio ◽  
Intermediate Condition ◽  
Comparison With Experimental Data

As a theoretical study of the hydrodynamic, gas-lubricated journal bearings, the paper presents approximate solutions with fair accuracy for high values of eccentricity ratio. In addition, an approximate solution available for clarifying the characteristics of journal bearing operating at low revolution speeds is reported. Comparison with experimental data reveals the fact that actual bearings operate under an intermediate condition between isothermal and adiabatic when running at high revolution speeds, while under the isothermal condition at low speeds.

scholarly journals Stability Analysis of an Externally Pressurized Gas-Lubricated Porous Thrust Bearing

1973 ◽  
Vol 95 (4) ◽  
pp. 457-468 ◽  
Author(s):  
Dah-Chen Sun
Keyword(s):  
Stability Analysis ◽  
Thrust Bearing ◽  
Film Flow ◽  
Light Weight ◽  
Symmetric Mode ◽  
Axially Symmetric ◽  
Thin Film Flow ◽  
Pneumatic Hammer ◽  
Supply Pressure ◽  
The Stability

A linear stability analysis is carried out for a porous thrust bearing considering only the axially symmetric mode of oscillation. It is found that the stability characteristics of the bearing are determined by three competing mechanisms, namely, the compressibility of the lubricant, the mass of the bearing, and the viscous resistance to the thin film flow. To avoid pneumatic hammer, the bearing should be designed to be light weight and to operate at the smallest possible film thickness and supply pressure.

On the Influence of the Supply Pressure on the Dynamic Stability of Hybrid Gas Journal Wave Bearings

2005 ◽  
Author(s):  
Florin Dimofte ◽  
Sorin Cioc ◽  
Robert F. Handschuh ◽  
David P. Fleming
Keyword(s):  
Hydrodynamic Instability ◽  
General Rule ◽  
Journal Bearings ◽  
Clearance Ratio ◽  
Stability Threshold ◽  
Supply Pressure ◽  
Bearing Clearance ◽  
Whirling Motion ◽  
Film Instability ◽  
The Stability

Gas journal bearings are very sensitive to the hydrodynamic instability known as subsynchronous whirl motion, especially when they are unloaded. The wave bearing concept can improve the bearing stability, meaning that the wave bearing can run stably up to higher speeds than the plain bearing. In addition, when whirling motion occurs due to the fluid film instability, the orbit of this motion can be contained within the bearing clearance. Another step ahead for improving bearing stability is to pressurize the bearing. Tests were conducted to verify the threshold of subsynchronous whirl motion of bearings with a 35 mm diameter and 30 mm length. Pressurized air is admitted to the bearings through inherent compensated holes located in two planes along the bearing length. Various numbers of holes and diameters were used. The tests were conducted at speeds up to 30,000 rpm and the supply pressure was varied from zero to 0.14 MPa. The pressure was measured within a 2% precision. Two values for the wave amplitude to bearing clearance ratio were used. Pressurizing the bearing with 0.14 MPa can make the bearing run stably up to a speed of 20,000 rpm, unlike an unpressurized bearing that can experience subsynchronous motion at speeds less than 1,000 rpm. It was found that the supply pressure has a strong stabilizing effect. As a general rule, a 10% change of the value of the supply pressure can modify the stability threshold speed with more than 1000 rpm.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

Some Structural Properties of Systolic Tree Automata

1989 ◽  
Vol 12 (4) ◽  
pp. 571-585
Author(s):  
E. Fachini ◽  
A. Maggiolo Schettini ◽  
G. Resta ◽  
D. Sangiorgi
Keyword(s):  
Structural Properties ◽  
Stability Problem ◽  
Sufficient Condition ◽  
Tree Automata ◽  
Necessary And Sufficient Condition ◽  
The Stability ◽  
Necessary And Sufficient

We prove that the classes of languages accepted by systolic automata over t-ary trees (t-STA) are always either equal or incomparable if one varies t. We introduce systolic tree automata with base (T(b)-STA), a subclass of STA with interesting properties of modularity, and we give a necessary and sufficient condition for the equivalence between a T(b)-STA and a t-STA, for a given base b. Finally, we show that the stability problem for T(b)-ST A is decidible.

Machine learning-based performance analysis of two-axial-groove hydrodynamic journal bearings

2021 ◽  
pp. 135065012199289
Author(s):  
Biswajit Roy ◽  
Sudip Dey
Keyword(s):  
Journal Bearing ◽  
Journal Bearings ◽  
Hydrodynamic Performance ◽  
Support Vector ◽  
Oil Viscosity ◽  
Hydrodynamic Analysis ◽  
Supply Pressure ◽  
Input Parameters ◽  
Precise Prediction ◽  
Output Behavior

The precise prediction of a rotor against instability is needed for avoiding the degradation or failure of the system’s performance due to the parametric variabilities of a bearing system. In general, the design of the journal bearing is framed based on the deterministic theoretical analysis. To map the precise prediction of hydrodynamic performance, it is needed to include the uncertain effect of input parameters on the output behavior of the journal bearing. This paper presents the uncertain hydrodynamic analysis of a two-axial-groove journal bearing including randomness in bearing oil viscosity and supply pressure. To simulate the uncertainty in the input parameters, the Monte Carlo simulation is carried out. A support vector machine is employed as a metamodel to increase the computational efficiency. Both individual and compound effects of uncertainties in the input parameters are studied to quantify their effect on the steady-state and dynamic characteristics of the bearing.

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