Static and Dynamic Properties of Partial Journal Bearings

1963 ◽  
Vol 85 (2) ◽  
pp. 247-255 ◽  
Author(s):  
Paul C. Warner
Keyword(s):  
Differential Equation ◽  
Journal Bearing ◽  
Dynamic Properties ◽  
Journal Bearings ◽  
Wide Range ◽  
Governing Differential Equation

The liquid lubricated partial journal bearing is analyzed in an approximate yet accurate manner in order to obtain its static and dynamic properties. The solution of the governing differential equation is analytical rather than numerical, permitting inexpensive computation of results over a very wide range of the parameters involved.

Characteristics of Herringbone-Grooved, Gas-Lubricated Journal Bearings

1965 ◽  
Vol 87 (3) ◽  
pp. 568-576 ◽  
Author(s):  
J. H. Vohr ◽  
C. Y. Chow
Keyword(s):  
Differential Equation ◽  
Journal Bearing ◽  
Groove Depth ◽  
Radial Force ◽  
Journal Bearings ◽  
Speed Ratio ◽  
Plain Bearing ◽  
Relative Speed ◽  
Whirl Speed ◽  
Limiting Case

A differential equation is obtained for the smoothed “overall” pressure distribution around a herringbone-grooved, gas-lubricated journal bearing operating with a variable film thickness. The equation is based on the limiting case of an idealized bearing for which the number of grooves approaches an infinite number. A numerical solution to the differential equation is obtained valid for small eccentricities. This solution includes the case where the journal is undergoing steady circular whirl. In addition to the usual plain bearing parameters L/D, Λ, and whirl speed ratio ω3/(ω1 + ω2), the behavior of a grooved bearing also depends on four additional parameters: The groove angle β, the relative groove width α, the relative groove depth H0, and a compressibility number, Λs, which is based on the relative speed between the grooved and smooth members of the bearing. Results are presented showing bearing radial force and attitude angle as functions of β, α, H0, Λs, Λ, and whirl speed ratio.

The Influence of Fluid Inertia on the Dynamic Properties of Journal Bearings

1975 ◽  
Vol 97 (2) ◽  
pp. 159-165 ◽  
Author(s):  
E. Reinhardt ◽  
J. W. Lund
Keyword(s):  
Journal Bearing ◽  
Dynamic Properties ◽  
Journal Bearings ◽  
Graphical Form ◽  
Inertial Forces ◽  
Virtual Mass ◽  
Fluid Inertia ◽  
Eccentricity Ratio ◽  
First Order ◽  
First Order Perturbation

Based on a first-order perturbation solution in a modified Reynolds number an analysis is presented to determine the effect of the fluid film inertial forces on the dynamic properties of a journal bearing. The corrections to the regular amplitude and velocity coefficients are found to be small, but the accompanying acceleration coefficients which may correspond to a virtual mass of several times the mass of the journal itself, could become significant for short rotors. Numerical results are given in graphical form with dimensionless coefficients as functions of the operating eccentricity ratio.

Dimensional Analysis in Design

1988 ◽  
Vol 110 (3) ◽  
pp. 401-407 ◽  
Author(s):  
J. R. Schnittger
Keyword(s):  
Differential Equation ◽  
Dimensional Analysis ◽  
Journal Bearing ◽  
Mechanical Design ◽  
Turbine Blades ◽  
Helical Spring ◽  
Disk Brake ◽  
Governing Differential Equation ◽  
Bearing Vibration ◽  
New Guidelines

New guidelines for dimensional analysis remove traditional road-blocks to its widespread use in mechanical design. Cases, with or without prior formula given, are exposed as well as those with a governing differential equation. The examples include bevel gear, helical spring, centrifugal pump, journal bearing, vibration of turbine blades, and a disk brake. A matrix method to determine nondimensional groups is reviewed.

Steady-State and Dynamic Analyses of Gas-Lubricated Hybrid Journal Bearings

1969 ◽  
Vol 91 (1) ◽  
pp. 171-180 ◽  
Author(s):  
W. Shapiro
Keyword(s):  
Steady State ◽  
Journal Bearing ◽  
Load Capacity ◽  
External Pressure ◽  
Journal Bearings ◽  
Preliminary Design ◽  
Wide Range ◽  
Dynamic Analyses ◽  
Flow Charts ◽  
Hybrid Bearing

The inherent limitations of load capacity and stability of hydrodynamic gas-lubricated bearings can be reduced by introducing external pressure and creating a hybrid bearing. Numerical computerized analyses of a hybrid journal bearing are discussed; separate developments are presented for steady-state and dynamic characteristics. The steady-state analysis provides performance over a wide range of operating parameters; the more complicated and lengthy dynamic analysis determines stability of the bearing-rotor system using geometry based upon steady-state results. Simplified flow charts of the computer programs are included. The analyses are applied to the preliminary design of a hybrid journal bearing.

Flow of Damp Powder in a Rotating Impervious Cone

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Arnaud F. M. Bizard ◽  
Digby D. Symons ◽  
Norman A. Fleck ◽  
David Durban
Keyword(s):  
Differential Equation ◽  
Axisymmetric Flow ◽  
Central Zone ◽  
Operating Conditions ◽  
Order Ordinary Differential Equation ◽  
Spherical Coordinate ◽  
Explicit Analytical Solution ◽  
Wide Range ◽  
Governing Differential Equation ◽  
The Mean

A one dimensional analytical model is developed for the steady state, axisymmetric flow of damp powder within a rotating impervious cone. The powder spins with the cone but migrates up the wall of the cone (along a generator) under centrifugal force. The powder is treated as incompressible and Newtonian viscous, while the shear traction at the interface is taken to be both velocity and pressure dependent. A nonlinear second order ordinary differential equation is established for the mean through-thickness velocity as a function of radius in a spherical coordinate system, and the dominant nondimensional groups are identified. For a wide range of geometries, material parameters, and operating conditions, a midzone exists wherein the flow is insensitive to the choice of inlet and outlet boundary conditions. Within this central zone, the governing differential equation reduces to an algebraic equation with an explicit analytical solution. Furthermore, the bulk viscosity of the damp powder does not enter this solution. Consequently, it is suggested that the rotating impervious cone is a useful geometry to measure the interfacial friction law for the flow of a damp powder past an impervious wall.

Analysis of Gas-Lubricated Foil Journal Bearings

1983 ◽  
Vol 105 (4) ◽  
pp. 647-655 ◽  
Author(s):  
H. Heshmat ◽  
J. A. Walowit ◽  
O. Pinkus
Keyword(s):  
Differential Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Bearing Surface ◽  
Operational Parameters ◽  
Operational Variables ◽  
Bearing Behavior ◽  
Load Angle ◽  
Gas Journal Bearing ◽  
Selection Of

This work is concerned with an evaluation of the performance of a gas journal bearing using a spring supported compliant foil as the bearing surface. The analysis, conducted for both single and multipad configurations, is concerned with the effects that the various structural, geometric, and operational variables have on bearing behavior. Following the solution of the relevant differential equation, tabular or graphical solutions are provided for a range of relevant geometric and operational parameters. The solutions include values of the colinear and cross-coupled spring coefficients due to both structural and hydrodynamic stiffness. Desirable design features with regard to start of bearing arc, selection of load angle, number of pads and degree of compliance are discussed.

Analysis of Multirecess Hydrostatic Journal Bearing Operating With Micropolar Lubricant

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Suresh Verma ◽  
Vijay Kumar ◽  
K. D. Gupta
Keyword(s):  
Reynolds Equation ◽  
Theoretical Study ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Performance Characteristics ◽  
Constant Flow ◽  
The Finite Element Method ◽  
Lubricant Flow ◽  
Wide Range ◽  
Flow Valve

This paper presents a theoretical study of the performance characteristics of a constant flow valve compensated multirecess hydrostatic journal bearings operating with micropolar lubricant. The finite element method and iterative procedure have been used to solve the modified Reynolds equation governing the micropolar lubricant flow in the bearing. The performance characteristics are presented for a wide range of nondimensional load, lubricant flow, and micropolar parameters. It has been observed that the micropolar parameters significantly influence the performance characteristics of the bearing.

The Effect of Elastic Distortions on Journal Bearing Performance

1967 ◽  
Vol 89 (4) ◽  
pp. 409-415 ◽  
Author(s):  
J. O’Donoghue ◽  
D. K. Brighton ◽  
C. J. K. Hooke
Keyword(s):  
Exact Solution ◽  
Pressure Distribution ◽  
Elastic Deformation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Wide Range ◽  
Constant Viscosity ◽  
Outside Diameter

This paper presents a solution to the problem of hydrodynamic lubrication of journal bearings taking into account the elastic distortions of the shaft and the bearing. The exact solution for determining the elastic deformation for a given pressure distribution around a bearing is given, together with the reiterative procedure adopted to find the pressure distribution which satisfies both the hydrodynamic and elastic requirements of the system. Results are given which have been derived for a material with a Poisson’s ratio of 0.28, but other values such as 0.33 do not incur substantial errors. The results can be applied to a wide range of operating conditions using the nondimensional group of terms suggested in the paper. The bearing is assumed to be infinite in length, and infinite in thickness. The latter assumption is shown to be valid for a particular case where the outside diameter of the bearing shell is 3.5 times the shaft diameter. A further assumption in the calculation is a condition of constant viscosity of the lubricant existing around the bearing.

A Sommerfeld Solution for Finite Bearings With Circumferential Grooves

1960 ◽  
Vol 82 (2) ◽  
pp. 321-326 ◽  
Author(s):  
J. V. Fedor
Keyword(s):  
Differential Equation ◽  
Excellent Agreement ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Algebraic Complexity ◽  
Eccentricity Ratio ◽  
Finite Form ◽  
Oil Film ◽  
Method Of Solution ◽  
Friction Curve

A method of solution is developed that circumvents the algebraic complexity in the solution of Reynolds differential equation applied to full journal bearings. The method leads to equations for journal-bearing characteristics that are in finite form. Salient features of the complete-oil-film solution are: As the eccentricity ratio b approaches 1, the load capacities of all finite bearings approach that of the infinite bearing; also, the friction curve intercept, (r/c)f, is 1 for all finite bearings when b equals 1. Results are compared with calculated values published by Muskat and Morgan for 0 < b < 0.6. Excellent agreement is found throughout the compared range.

scholarly journals The Prediction of Liquid Film Journal Bearing Performance with a Consideration of Lubricant Film Reformation: Part 1: Theoretical Results

1985 ◽  
Vol 199 (2) ◽  
pp. 95-102 ◽  
Author(s):  
D Dowson ◽  
C M Taylor ◽  
A A S Miranda
Keyword(s):  
Liquid Film ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Lubricant Film ◽  
Supply Rate ◽  
Film Rupture ◽  
Supply Pressure ◽  
Wide Range ◽  
The Reformation ◽  
Theoretical Results

Analyses of liquid film journal bearings rarely consider the reformation of the lubricant film. This reformation normally takes place in the vicinity of a supply groove and is influenced by, amongst other parameters, the lubricant supply pressure. In a previous paper the authors have described in detail the implementation of an algorithm to locate automatically and efficiently the locus of film rupture and reformation boundaries using a digital computer. In the present paper results are presented for a wide range of important variables. In particular, the prediction of lubricant supply rate is studied carefully and compared with data presented in a widely used design aid which does not account in detail for the influence of film reformation.

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