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

1999 ◽  
Vol 121 (1) ◽  
pp. 148-156 ◽  
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.

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

2019 ◽  
Vol 234 (5) ◽  
pp. 778-792
Author(s):  
Ujjal Baidya ◽  
Sanjoy Das ◽  
Santanu Das
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Vertical Direction ◽  
Journal Bearings ◽  
Load Parameter ◽  
Steady State Condition ◽  
Relaxation Scheme ◽  
Analytical Work ◽  
Successive Over Relaxation ◽  
Micropolar Lubrication

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.

The Effect of Lubricant Inertia in Journal-Bearing Lubrication

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.

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

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.

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

2017 ◽  
Vol 232 (8) ◽  
pp. 927-939 ◽  
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.

Static and Dynamic Characteristics of Self-Acting, Partial-Arc, Gas Journal Bearings

1964 ◽  
Vol 86 (2) ◽  
pp. 405-413 ◽  
Author(s):  
R. J. Wernick ◽  
C. H. T. Pan
Keyword(s):  
Power Series ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Standard Form ◽  
Journal Bearings ◽  
Static And Dynamic Characteristics ◽  
Stability Derivatives ◽  
Bearing Loads ◽  
Gas Journal Bearing

The Reynolds equation applicable to a self-acting partial-arc gas journal bearing is perturbed in terms of the compressibility number Λ. The resulting set of equations is then put into a standard form and Galerkin’s method is used to obtain bearing loads and stability derivatives. These results are expressed in a power series in Λ.

Static and Dynamic Characteristics of Externally Pressurized Porous Gas Journal Bearing With Four Degrees-of-Freedom

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Shuyun Jiang ◽  
Shengye Lin ◽  
Chundong Xu
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Static Load ◽  
Journal Bearing ◽  
Load Capacity ◽  
Linear Perturbation ◽  
Static And Dynamic Characteristics ◽  
Bearing Number ◽  
Gas Journal Bearing

This paper studies the static and dynamic coefficients of an externally pressurized porous gas journal bearing. The finite difference method is used to solve the Reynolds equation of the bearing to obtain the static load capacity. The linear perturbation method is adopted to derive the perturbation equations considering four degrees-of-freedom (4DOF), namely, the translational movements in x and y directions and the rotational movements around x and y directions. The effects of various parameters on the dynamic behaviors of the journal bearing are studied. These parameters include the bearing number, the supply pressure, the feeding parameter, the length-to-diameter ratio, the porosity parameter, the eccentricity ratio, and tilting angles. Simulated results prove that the proposed method is valid in estimating the static and dynamic characteristics of a porous gas journal bearing with 4DOF.

Zero-Load Stability of Rotating Externally Pressurized Gas-Lubricated Journal Bearings

1970 ◽  
Vol 92 (2) ◽  
pp. 325-334 ◽  
Author(s):  
David P. Fleming ◽  
R. E. Cunningham ◽  
W. J. Anderson
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Digital Computer ◽  
Pressure Ratio ◽  
Journal Bearings ◽  
Small Eccentricity ◽  
Attitude Angle ◽  
Stability Data ◽  
Bearing Number ◽  
Load Stability

A small eccentricity analysis was performed for a bearing having two feeding planes, each of which is assumed to be a line source. Numerical results were obtained for a range of bearing number, pressure ratio, feeding parameter, and orifice recess volume by means of a digital computer. Steady-state load and attitude angle were obtained, as well as stability data. Stability decreased markedly with increasing recess volume; moreover, for large recess volume and low bearing number, an increase in pressure ratio decreased stability. There was no correlation between stability and steady-state attitude angle for any of the cases studied. Fair agreement was obtained with available experimental data.

Rarefaction Effect on the Characteristics of Micro Gas Journal Bearings

2009 ◽  
Author(s):  
Haijun Zhang ◽  
Qin Yang
Keyword(s):  
Knudsen Number ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Clearance Ratio ◽  
Attitude Angle ◽  
Modified Reynolds Equation ◽  
Bearing Number

Journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in MEMS deriving from the extremely shallow structures. Thus, the micro gas journal bearings are characterized by a very small length-diameter ratio, defined as the ratio of the bearing length to its diameter and a paradoxically large bearing clearance ratio, defined as the ratio of the average radial clearance to the bearing radius. Given the definition of the reference Knudsen number for micro gas journal bearings, the range of the reference Knudsen number is illustrated according to the viscosity values of air under different temperatures. With the reference Knudsen number being included, the modified Reynolds equation for micro gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The finite difference method (FDM) is employed to solve the modified Reynolds equation to obtain the pressure distribution, load capacities and attitude angles for micro gas journal bearings under different reference Knudsen numbers, bearing numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with gas rarefaction strengthened, and the attitude angle changes conversely. Moreover, when the bearing number is smaller, the effect of gas rarefaction on the non-dimensional load capacity and attitude angle is less.

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

1995 ◽  
Vol 117 (4) ◽  
pp. 717-723 ◽  
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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