An Improved Analytical Solution for Self-Acting, Gas-Lubricated Journal Bearings of Finite Length

1961 ◽  
Vol 83 (2) ◽  
pp. 188-192 ◽  
Author(s):  
J. S. Ausman
Keyword(s):  
Analytical Solution ◽  
Finite Length ◽  
Load Capacity ◽  
Journal Bearings ◽  
Perturbation Solution ◽  
Order Perturbation ◽  
Small Eccentricity ◽  
First Order ◽  
Bearing Load ◽  
First Order Perturbation

An improved analytical solution designated the “linearized ph” solution is obtained for gas-lubricated journal bearings of finite length. Whereas the older first-order perturbation solution is useful for small eccentricity ratios (ε < 1/2), the linearized ph solution may be used for high eccentricity ratios. As such it permits estimation of ultimate bearing load capacity. The linearized ph solution is expressed in the form of simple corrections to the first-order perturbation solution, and as such can be computed quickly and easily.

Externally Pressurized Gas Journal Bearings With Porous Inserts

1980 ◽  
Vol 102 (1) ◽  
pp. 113-116 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Journal Bearings ◽  
Order Perturbation ◽  
Eccentricity Ratio ◽  
First Order ◽  
First Order Perturbation

An analytical solution of externally pressurized gas journal bearings with porous inserts as restrictors is presented. The solution is based on a first-order perturbation method with respect to eccentricity ratio.

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.

The Hybrid Isothermal Air Lubricated Journal Bearing

1979 ◽  
Vol 101 (4) ◽  
pp. 444-450 ◽  
Author(s):  
V. Kamala
Keyword(s):  
Comparative Study ◽  
Carrying Capacity ◽  
Journal Bearing ◽  
Order Perturbation ◽  
Load Carrying Capacity ◽  
Eccentricity Ratio ◽  
Small Eccentricity ◽  
First Order ◽  
Load Carrying ◽  
First Order Perturbation

This paper analyzes the load-carrying capacity of the hybrid air lubricated journal bearing. Assuming a small eccentricity ratio, a first order perturbation solution is obtained. The air is fed to the bearing through inherent restrictor with feeding holes distributed around the circumference in one, two, and three feeding planes (Fig. 1). The number of feeding holes in each plane is sufficiently large to permit the feeding planes being treated as the line sources. The results are given for the load-carrying capacity and the attitude angle. A comparative study is made of the three types of gas feeding arrangements.

Gas-Lubricated Cylindrical Journal Bearings of the Finite Length: Static Loading

1961 ◽  
Vol 28 (4) ◽  
pp. 535-543 ◽  
Author(s):  
B. Sternlicht
Keyword(s):  
Finite Length ◽  
Static Loading ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
First Order ◽  
Advantages And Disadvantages ◽  
Iterative Solutions ◽  
Constant Magnitude ◽  
First Order Perturbation

This paper presents numerical solutions of the Reynolds equation for finite length, gas-lubricated cylindrical journal bearings under static loading (this corresponds to a load of constant magnitude and direction with respect to the bearing). It is shown that the incompressible results are but only limiting cases to the more general compressible solutions. The results of the two solutions are dovetailed together through the use of two dimensionless parameters: the inverse of the Sommerfeld number and the compressibility number. Comparisons of the iterative solutions and the first-order perturbation and the “linearized ph” methods are made. The advantages and disadvantages of these methods of analysis are discussed.

Theoretical Analysis of Pneumatic Instability of Externally Pressurized Porous Gas Journal Bearings Considering Velocity Slip

1988 ◽  
Vol 110 (4) ◽  
pp. 730-733 ◽  
Author(s):  
M. C. Majumder ◽  
B. C. Majumdar
Keyword(s):  
Perturbation Theory ◽  
Theoretical Analysis ◽  
Mass Parameter ◽  
Velocity Slip ◽  
Journal Bearings ◽  
Order Perturbation ◽  
Rigid Rotor ◽  
First Order ◽  
First Order Perturbation

An analysis based on first-order perturbation theory is presented for the determination of pneumatic instability of a rigid rotor supported on externally pressurized porous gas journal bearings considering velocity slip. The variation of threshold mass parameter with feeding parameter for various supply pressures and L/D ratios under slip and no slip conditions is shown. It has been observed that there is a little decrease in stability when slip is taken in the analysis.

On Journal Bearings of Finite Length With Variable Viscosity

1959 ◽  
Vol 26 (2) ◽  
pp. 179-183
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Finite Length ◽  
Reynolds Equation ◽  
Variable Viscosity ◽  
Load Capacity ◽  
Journal Bearings ◽  
Heun Functions ◽  
Load Vector ◽  
Constant Viscosity

Abstract An exact solution of the Reynolds equation for journal bearings of finite length with viscosity as a function of pressure is found. The analytical solution is expressed in terms of Heun functions. The load capacity and the attitude angle are derived. It is found that the load vector, in general, is not perpendicular to the line of journal and bearing centers as shown in the constant-viscosity case.

scholarly journals Perturbation Solution for Four-Stream Infrared Radiative Transfer

2020 ◽  
Vol 77 (4) ◽  
pp. 1497-1507
Author(s):  
Jiangnan Li ◽  
Howard W. Barker
Keyword(s):  
Radiative Transfer ◽  
Perturbation Method ◽  
Zero Order ◽  
Perturbation Solution ◽  
Order Perturbation ◽  
Dual Wavelength ◽  
Perturbation Equation ◽  
First Order ◽  
Using Data ◽  
First Order Perturbation

Abstract A four-stream solution of the longwave radiative transfer is proposed. It is based on the exact perturbation method utilizing the absorption approximation equation as the zero-order solution. Scattering is handled by the first-order perturbation equation. The two- and four-stream approximations are compared both offline and using data from CALIPSO’s dual-wavelength lidar.

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