Analysis of misaligned hydrodynamic porous journal bearings in the steady-state condition with micropolar lubricant

Impregnated porous bearings are used in different machines and other applications. In this work, an analytical work is investigated to evaluate the steady-state characteristics of such self-lubricated porous journal bearings in micropolar lubrication with misalignment. Bi-axial misalignments are considered, namely axial (along the vertical direction) and twisting (along the horizontal direction). Reynolds equation is modified to fit bearing misalignment, by incorporating the effects of micropolarity of the lubricant and porosity of the bush. Darcy’s equation that considers porosity and the misalignment Reynolds’s equation applicable for film region are numerically solved using finite difference method applying successive over-relaxation scheme employing appropriate boundary conditions to obtain the dimensionless fluid film pressure at steady state, which is used to get the steady-state characteristics e.g. load parameter, moment of misalignment, frictional force, and friction parameter.

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Numerical Analysis of Herringbone-Grooved Gas-Lubricated Journal Bearings Using a Multigrid Technique

Journal of Tribology ◽

10.1115/1.2833796 ◽

1999 ◽

Vol 121 (1) ◽

pp. 148-156 ◽

Cited By ~ 15

Author(s):

Takuji Kobayashi

Keyword(s):

Steady State ◽

Numerical Analysis ◽

Reasonable Agreement ◽

Reynolds Equation ◽

Journal Bearings ◽

Static And Dynamic Characteristics ◽

Slow Convergence ◽

Relaxation Scheme ◽

Bearing Number ◽

Successive Over Relaxation

In this paper, a multigrid technique is applied to the compressible Reynolds equation discretized by the divergence formulation in order to analyze both static and dynamic characteristics of herringbone-grooved gas-lubricated journal bearings. The developed code demonstrates quicker convergence than an optimized successive over-relaxation scheme, and the dominance in numerical efficiency is especially remarkable at higher values of bearing number where slow convergence is generally observed. Comparisons between the present nonlinear orbit solutions and previously published experimental results show reasonable agreement in both steady-state and dynamic stability performances.

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The Effect of Lubricant Inertia in Journal-Bearing Lubrication

Journal of Applied Mechanics ◽

10.1115/1.4011588 ◽

1957 ◽

Vol 24 (4) ◽

pp. 494-496

Author(s):

J. F. Osterle ◽

Y. T. Chou ◽

E. A. Saibel

Keyword(s):

Reynolds Number ◽

Steady State ◽

Reynolds Equation ◽

Journal Bearing ◽

Journal Bearings ◽

Hydrodynamic Theory ◽

Simple Relationship ◽

Inertia Effect ◽

Laminar Regime ◽

Steady State Operation

Abstract The Reynolds equation of hydrodynamic theory, modified to take lubricant inertia into approximate account, is applied to the steady-state operation of journal bearings to determine the effect of lubricant inertia on the pressure developed in the lubricant. A simple relationship results, relating this “inertial” pressure to the Reynolds number of the flow. It is found that the inertia effect can be significant in the laminar regime.

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Performance of Lightly Loaded Gas Journal Bearings in the Slip-Flow and Turbulent-Flow Regimes

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1968_010_055_02 ◽

1968 ◽

Vol 10 (4) ◽

pp. 363-366

Author(s):

M. D. Wood

Keyword(s):

Steady State ◽

Laminar Flow ◽

Turbulent Flow ◽

Reynolds Equation ◽

Dynamic Performance ◽

Slip Flow ◽

Flow Regimes ◽

Journal Bearings ◽

Performance Parameters ◽

Existing Data

The note compares recently published versions of the governing gas film equations for slip-flow and turbulent flow with Reynolds equation for laminar flow. The comparison shows how approximate values of steady-state and dynamic performance parameters may be deduced for the new conditions from existing data.

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Static characteristics of hydrostatic doubled-layered porous journal bearings with slip flow including additives percolation into pores under coupled stress lubrication

Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology ◽

10.1177/1350650117748096 ◽

2017 ◽

Vol 232 (8) ◽

pp. 927-939 ◽

Cited By ~ 4

Author(s):

Shitendu Some ◽

Sisir K Guha

Keyword(s):

Steady State ◽

Reynolds Equation ◽

Slip Flow ◽

Journal Bearings ◽

Static Characteristics ◽

Governing Equations ◽

Modified Reynolds Equation ◽

Film Interface ◽

Coupled Stress ◽

Steady State Performance

A theoretical analysis of the steady-state characteristics of finite hydrostatic double-layered porous journal bearings dealing with the effects of slip flow at the fine porous layer–film interface and percolation of additives into pores under the coupled stress fluid lubrication is presented. Based on the Beavers–Joseph’s criterion for slip flow, the modified Reynolds equation applicable to finite porous journal bearings lubricated with coupled stress fluids have been derived. The governing equations for flow in the coarse and fine layers of porous medium incorporating the percolation of polar additives of lubricant and the modified Reynolds equation are solved simultaneously using finite difference method satisfying appropriate boundary conditions to obtain the steady-state performance characteristics for various parameter namely percolation factor, slip coefficient, bearing feeding parameter, coupled stress parameter, and eccentricity ratio. The results are exhibited in the form of graphs, which may be useful for design of such bearing.

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G34 Steady-State Analysis of Oil Film in Very High Speed Journal Bearings with Centrifugal Force and Surface Tension Considered : Derivation of Modified Reynolds Equation and Its Application to Oil Film

The Proceedings of Conference of Kyushu Branch ◽

10.1299/jsmekyushu.2007.60.253 ◽

2007 ◽

Vol 2007.60 (0) ◽

pp. 253-254

Author(s):

Nobuhiko ISHIBASHI ◽

Kiyoshi HATAKENAKA

Keyword(s):

Surface Tension ◽

Steady State ◽

Centrifugal Force ◽

High Speed ◽

Reynolds Equation ◽

Journal Bearings ◽

Steady State Analysis ◽

Oil Film ◽

Modified Reynolds Equation ◽

Very High

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Misalignment Effect on the Static and Dynamic Characteristics of Hydrodynamic Journal Bearings

Journal of Tribology ◽

10.1115/1.2831542 ◽

1995 ◽

Vol 117 (4) ◽

pp. 717-723 ◽

Cited By ~ 15

Author(s):

Z. L Qiu ◽

A. K. Tieu

Keyword(s):

Dynamic Characteristics ◽

Reynolds Equation ◽

Static Load ◽

Load Capacity ◽

Vertical Direction ◽

Journal Bearings ◽

Static And Dynamic Characteristics ◽

Flow Friction ◽

The Stability ◽

Side Flow

This paper solves the Reynolds equation by the finite difference method in a fixed coordinate system with the static load acted in the vertical direction. All static and dynamic characteristics (including load capacity, attitude angle, side flow, friction force, misaligned moments, and eight linear force coefficients) of a horizontally grooved bearing under different eccentricity and misalignment conditions are presented and compared with available experimental data. The effects of misalignment on all these bearing characteristics and on the stability of the rotor-bearing system are analyzed.

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Nonlinear Dynamic Behaviors and Bifurcation of Symmetrical Rotor System Supported by Self-Acting Gas Jounal Bearings

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.97-101.2634 ◽

2010 ◽

Vol 97-101 ◽

pp. 2634-2638 ◽

Cited By ~ 1

Author(s):

Wei Min Wang ◽

Yan Jun Lu ◽

Zhi Jun Cao ◽

Yong Fang Zhang ◽

Lie Yu

Keyword(s):

Reynolds Equation ◽

Journal Bearing ◽

Period Doubling ◽

Journal Bearings ◽

Time Dependent ◽

Jeffcott Rotor ◽

Successive Over Relaxation ◽

Rotor Dynamic ◽

Gas Journal Bearing ◽

Bifurcation Behavior

The unbalanced response and corresponding bifurcation behavior of the rotor dynamic system supported by gas journal bearings are investigated. A time-dependent mathematical model is used to describe the pressure distribution of gas journal bearing with nonlinearity. The rigid Jeffcott rotor with self-acting gas journal bearing supports is modeled. The finite difference method and the Successive Over Relaxation (S.O.R.) method are employed to solve the time-dependent Reynolds equation of gas journal bearings. The bifurcation of unbalanced responses of the rotor is analyzed by a Poincaré map. The numerical results reveal periodic, period-doubling, quasi-periodic, and chaotic motion of rich and complex non-linear behaviors of the system.

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Numerical study of twin groove journal bearings performance under steady-state condition

Lubrication Science ◽

10.1002/ls.1257 ◽

2014 ◽

Vol 27 (2) ◽

pp. 83-102 ◽

Cited By ~ 4

Author(s):

Alireza Arab Solghar ◽

F. P. Brito ◽

Morteza Abdolzadeh ◽

Ali Farajpour

Keyword(s):

Steady State ◽

Numerical Study ◽

Journal Bearings ◽

State Condition ◽

Steady State Condition

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Stresses in Bearing Liner of Misaligned Hydrodynamically Lubricated Journal Bearings

ASME/STLE 2009 International Joint Tribology Conference ◽

10.1115/ijtc2009-15056 ◽

2009 ◽

Author(s):

Abdallah A. Elsharkawy ◽

Khaled J. Al-Fadhalah

Keyword(s):

Steady State ◽

Reynolds Equation ◽

Numerical Study ◽

Hydrodynamic Lubrication ◽

Large Degree ◽

Element Model ◽

Journal Bearings ◽

Stress Fields ◽

Combined Effects ◽

Journal Misalignment

A numerical study examined the combined effects of journal misalignment and hydrodynamic lubrication on the stress fields of bearing liner under steady state conditions. The oil pressure, obtained by solving Reynolds equation, is imposed on a finite element model of an elastic liner bearing to calculate its stress fields. It was found that large degree of misalignment increases remarkably the oil pressure, and consequently the stresses in the bearing liner become significantly higher.

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Hybrid Porous Gas Journal Bearings: Steady State Solution Incorporating the Effect of Velocity Slip

Journal of Tribology ◽

10.1115/1.3260923 ◽

1984 ◽

Vol 106 (3) ◽

pp. 322-328 ◽

Cited By ~ 14

Author(s):

K. C. Singh ◽

N. S. Rao ◽

B. C. Majumdar

Keyword(s):

Steady State ◽

Reynolds Equation ◽

Stokes Equations ◽

Load Capacity ◽

Velocity Slip ◽

Steady State Solution ◽

Static Characteristic ◽

Journal Bearings ◽

Mass Rate ◽

Modified Reynolds Equation

A theoretical analysis is presented to predict the steady state performance characteristics of externally pressurized rotating gas journal bearings incorporating the effect of velocity slip at the porous interface. The governing equation for flow in the porous media and the modified Reynolds equation derived from the Navier-Stokes equations satisfying the velocity slip boundary condition, are solved simultaneously for film pressure distribution. Due to the nonlinearity of modified Reynolds equation the solution is obtained by perturbation method using finite difference technique. The dimensionless load capacity, attitude angle and mass rate of flow are computed numerically for different operating parameters. The effect of slip on the static characteristic is discussed. Comparison of the results with similar available solution for the no-slip case shows good agreement.

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