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

1984 ◽  
Vol 106 (3) ◽  
pp. 322-328 ◽  
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.

Effect of Slip Flow on the Steady-State Performance of Aerostatic Porous Journal Bearings

1984 ◽  
Vol 106 (1) ◽  
pp. 156-162 ◽  
Author(s):  
K. C. Singh ◽  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Load Capacity ◽  
Finite Thickness ◽  
Slip Flow ◽  
Velocity Slip ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Mass Rate ◽  
Steady State Performance

A theoretical solution is presented to predict the steady-state performance characteristics of aerostatic porous journal bearings of finite thickness considering three dimensional flow in the porous media. The analysis takes into account the velocity slip at the film bearing interface by using Beavers-Joseph criterion. Results are presented in dimensionless form for load capacity and mass rate of flow for different operating conditions and bearing dimensions. Solution is also obtained for modified slip velocity conditions and both the results are compared. It is observed that there is no agreement between two models except for few values of slip parameters. Hence, it is preferable to use the Beavers-Joseph model in order to account for all values of slip parameters. The effect of slip velocity on the static characteristics is discussed.

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.

Hydrodynamic Behaviors of the Gas-Lubricated Film in Wedge-Shaped Microchannel

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Xueqing Zhang ◽  
Qinghua Chen ◽  
Juanfang Liu
Keyword(s):  
Wall Temperature ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Stokes Equations ◽  
Load Capacity ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Hydrodynamic Properties ◽  
Obvious Effect ◽  
Navier Stokes Equations

As for the micro gas bearing operating at a high temperature and speed, one wedge-shaped microchannel is established, and the hydrodynamic properties of the wedge-shaped gas film are comprehensively investigated. The Reynolds equation, modified Reynolds equation, energy equation, and Navier–Stokes equations are employed to describe and analyze the hydrodynamics of the gas film. Furthermore, the comparisons among the hydrodynamic properties predicted by various models were performed for the different wedge factors and the different wall temperatures. The results show that coupling the simplified energy equation with the Reynolds or modified Reynolds equations has an obvious effect on the change of the friction force acting on the horizontal plate and the load capacity of the gas film at the higher wedge factor and the lower wall temperature. The velocity slip weakens the squeeze of the gas film and strengths the gas backflow. A larger wedge factor or a higher wall temperature leads to a higher gas film temperature and thus enhances the rarefaction effect. As the wall temperature is elevated, the load capacity obtained by the Reynolds equation increases, while the results by the Navier–Stokes equations coupled with the full energy equation rapidly decrease. Additionally, the vertical flow across the gas film in the Navier–Stokes equations weakens the squeeze between the gas film and the tilt plate and the gas backflow.

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.

Steady-State Characteristics of Aerostatic Porous Rectangular Thrust Bearings Incorporating the Effects of Velocity Slip, Anisotropy and Tilt

1983 ◽  
Vol 197 (3) ◽  
pp. 179-188 ◽  
Author(s):  
K C Singh ◽  
N S Rao ◽  
B C Majumdar
Keyword(s):  
Steady State ◽  
Load Capacity ◽  
Velocity Slip ◽  
Generalized Solution ◽  
Static Stiffness ◽  
Mass Rate ◽  
Thrust Bearings ◽  
Design Charts ◽  
Mass Flowrate ◽  
Steady State Performance

A generalized solution is presented in order to predict the steady-state performance characteristics of aerostatic porous rectangular thrust bearings of finite pad thickness. The analysis takes into account the Beavers-Joseph criterion for velocity slip at the bearing interface, the anisotropy of the porous material and the tilt of the bearing. Dimensionless load capacity, mass flowrate of the gas and static stiffness are computed numerically for different operating parameters and bearing dimensions and presented in the form of design charts. The effect of slip is to reduce the load capacity and increase the mass rate of flow.

Characteristics of Micro Gas Journal Bearings Based on Effective Viscosity

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Haijun Zhang ◽  
Changsheng Zhu ◽  
Qin Yang
Keyword(s):  
Knudsen Number ◽  
Effective Viscosity ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Eccentricity Ratio ◽  
Rarefied Flow ◽  
Attitude Angle ◽  
Modified Reynolds Equation ◽  
Bearing Number

According to the first order slip velocity boundary, a modified Reynolds equation for micro gas journal bearings is presented with consideration of effective viscosity under a rarefied flow condition. A modified Reynolds equation is attained and solved using the finite difference method. The nondimensional pressure, load capacity, and attitude angle for micro gas journal bearings under different reference Knudsen numbers (the ratio of ambient molecular mean free path to the average radial clearance), bearing numbers, and eccentricity ratios are obtained. The numerical analysis demonstrates that the slip model with effective viscosity is in a better agreement with the FK model derived by Fukui and Kaneko than that without effective viscosity. When the bearing number is constant, the pressure and load capacity decrease, and the attitude angle changes inversely with the increasing reference Knudsen number. The larger the eccentricity ratio, the larger change in attitude angle from effective viscosity. When eccentricity ratio is less than 0.6, the attitude angle changes softly, and the effect of effective viscosity is unobvious. When the eccentricity ratio is constant, the influence of effective viscosity on nondimensional load capacity and attitude angle becomes larger with the increasing bearing number, and the influence is more prominent with a larger reference Knudsen number.

scholarly journals Effects of velocity-slip and viscosity variation on journal bearings

2004 ◽  
Vol 46 (1) ◽  
pp. 143-155 ◽  
Author(s):  
R. Raghavendra Rao ◽  
K. R. Prasad
Keyword(s):  
Boundary Conditions ◽  
Coefficient Of Friction ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Velocity Slip ◽  
Journal Bearings ◽  
Viscous Layer ◽  
The Coefficient Of Friction ◽  
Viscosity Variation

AbstractA generalised form of the Reynolds equation for two symmetrical surfaces is derived by considering slip at the bearing surfaces. This equation is then used to study the effects of velocity-slip for the lubrication of journal bearings using half-Sommerfeld boundary conditions. Expressions for pressure and load capacity and the coefficient of friction are obtained and numerically analysed for various parameters. It is found that the load capacity decreases with slip. This is unfavourable for lubrication. The coefficient of friction decreases with a high viscous layer and increases with slip.

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.

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