scholarly journals On the modified Reynolds equation for journal bearings in a case of non-Newtonian Rabinowitsch fluid model

2018 ◽  
Vol 145 ◽  
pp. 03007
Author(s):  
Juliana Javorova ◽  
Jordanka Angelova
Keyword(s):  
Numerical Modeling ◽  
Constitutive Equation ◽  
Theoretical Analysis ◽  
Continuity Equation ◽  
Reynolds Equation ◽  
Fluid Model ◽  
Type Equation ◽  
Hydrodynamic Pressure ◽  
Journal Bearings ◽  
Dimensionless Equation

In this paper, a theoretical analysis of hydrodynamic plain journal bearings with finite length at taking into account the effect of non-Newtonian lubricants is presented. Based upon the Rabinowitsch fluid model (cubic stress constitutive equation) and by integrating the continuity equation across the film, the nonlinear modified 2D Reynolds type equation is derived in details so that to study the dilatant and pseudoplastic nature of the lubricant in comparison with Newtonian fluid. A dimensionless equation of hydrodynamic pressure distribution in a form appropriate for numerical modeling is also presented. Some particular cases of 1D applications can be recovered from the present derivation.

Dynamic Stiffness and Damping Coefficients of Aerostatic, Porous, Journal Bearings

1978 ◽  
Vol 20 (5) ◽  
pp. 291-296 ◽  
Author(s):  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Continuity Equation ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Dynamic Pressure ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Damping Coefficients ◽  
Design Charts ◽  
Stiffness And Damping

A periodic (displacement) disturbance is imposed on an aerostatic, porous, journal bearing of finite length under steady-state conditions. The dynamic pressure distribution is obtained by a pressure perturbation analysis of Reynolds equation and a modified flow continuity equation in a porous medium. Dynamic stiffness and damping coefficients for different operating conditions are calculated numerically, using a digital computer, and presented in the form of design charts.

Relationship between elliptical form error and rotation accuracy of hydrostatic journal bearing

2017 ◽  
Vol 69 (6) ◽  
pp. 905-911 ◽  
Author(s):  
Jun Zha ◽  
Yaolong Chen ◽  
Penghai Zhang
Keyword(s):  
Kinetic Equation ◽  
Continuity Equation ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Form Error ◽  
Machining Error ◽  
Content Type ◽  
Precision Design ◽  
Error Averaging

Purpose The form error of shaft and hole parts is inevitable because of the machining error caused by rotation error of tool axis in machine tools where the elliptical form error is the most common in shaft and bearing bush. The purpose of this paper is to present the relationship between the elliptical form error and rotation accuracy for hydrostatic journal bearing in precision spindle and rotation table. Design/methodology/approach An error averaging effect model of hydrostatic journal bearing is established by using Reynolds equation, pressure boundary conditions, flux continuity equation of the land and kinetic equation of shaft in hydrostatic journal bearing. The effects of shaft and bearing bush on rotation accuracy were analyzed quantitatively. Findings The results reveal that the effect of shaft elliptical form error on rotation accuracy was six times larger than bearing bush. Therefore, to improve the rotation accuracy of hydrostatic journal bearing in spindle or rotation table, the machining error of shaft should be controlled carefully. Originality/value An error averaging model is proposed to evaluate the effect of an elliptical form error on rotation accuracy of hydrostatic journal bearings, which solves the Reynolds equation, the flux continuity equation and the kinetic equation. The determination of form error parameters of shaft and bearing bush can be yielded from finding results of this study for precision design of hydrostatic journal bearings.

Analysis of Steady-State Penetration in Viscoplastic Porous Materials

2004 ◽  
Author(s):  
Oana Cazacu ◽  
N. D. Cristescu
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Constitutive Equation ◽  
Continuity Equation ◽  
Type Equation ◽  
Combined Effects ◽  
Interface Conditions ◽  
Yield Limit ◽  
Shear Yield ◽  
Resistance To Penetration

A study of the steady-state motion of a porous medium over a rigid wedge-shaped penetrator was conducted. In order to describe the combined effects of strain rate and compaction on yielding, a rigid viscoplastic constitutive equation was used. The deviatoric response was modeled with a non-homogeneous Bingam type equation with shear yield limit dependent on the current density. The system of partial differential equations consisting of the constitutive equation, the continuity equation, and the balance of momentum was solved for different interface conditions. The resistance to penetration as a function of the striking velocity, target properties (density dependent yield, locking pressure, locking density), friction coefficient as well as wedge semi-angle was obtained. The wedge semi- angle corresponding to a minimum in resistance to penetration in mortar for various impact conditions also resulted from this investigation.

Linear Stability Analysis of Journal Bearings Lubricated With a Non-Newtonian Rabinowitsch Fluid

2017 ◽  
Vol 35 (1) ◽  
pp. 107-112 ◽  
Author(s):  
J. R. Lin ◽  
T. C. Hung ◽  
C. H. Lin
Keyword(s):  
Linear Stability ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Fluid Model ◽  
Journal Bearings ◽  
Stable Region ◽  
Stability Boundaries ◽  
Linear Dynamic ◽  
Newtonian Dynamic ◽  
Plastic Lubricants

AbstractThe linear stability boundaries of journal bearings lubricated with a non-Newtonian fluid have been investigated in this paper. Based on the Rabinowitsch fluid model, a non-Newtonian dynamic Reynolds equation for journal bearings is derived and then applied to analyze the linear dynamic characteristics of short journal bearings. Comparing with the Newtonian-lubricant case, the non-Newtonian rheology of dilatant lubricants provides a larger area of linearly stable region. However, the non-Newtonian properties of pseudo-plastic lubricants results in a reverse trend for the short journal bearing.

Dynamic Characteristic of Multirecess Externally Pressurized Oil Journal Bearing

1978 ◽  
Vol 100 (4) ◽  
pp. 467-471 ◽  
Author(s):  
M. K. Ghosh
Keyword(s):  
Perturbation Theory ◽  
Theoretical Analysis ◽  
Dynamic Characteristic ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Harmonic Vibrations ◽  
Damping Characteristics ◽  
Stiffness And Damping ◽  
Generalized Reynolds Equation

This paper describes a theoretical analysis of the dynamic behavior of multirecess externally pressurized oil journal bearings for a nonrotating journal subjected to plane harmonic vibrations. The generalized Reynolds’ equation for a finite bearing has been solved using perturbation theory. Stiffness and damping characteristics of a capillary compensated bearing are given.

ANALYSIS OF HYDRODYNAMIC LUBRICATION OF JOURNAL BEARINGS WITH OIL OF NON-NEWTONIAN PROPERTIES

Tribologia ◽  
2018 ◽  
Vol 272 (2) ◽  
pp. 127-138
Author(s):  
Andrzej MISZCZAK ◽  
Grzegorz SIKORA
Keyword(s):  
Shear Rate ◽  
Carrying Capacity ◽  
Apparent Viscosity ◽  
Hydrodynamic Lubrication ◽  
Type Equation ◽  
Hydrodynamic Pressure ◽  
Journal Bearings ◽  
Third Order ◽  
The Third ◽  
Order Of Magnitude

In this paper, the presented issue concerns hydrodynamic lubrication of the journal bearings with the oil of non-Newtonian properties. For the analysis of the hydrodynamic lubrication, a constitutive model of the third order was assumed. The assumed model consist of a Newtonian part –pI+ηA1 and non-Newtonian part β3·tr(A1 2)A1. The main part of this paper concerns transformation, nondimensionalization, and an estimation of the order of magnitude of the equation, which describes the apparent viscosity. Apparent viscosity describes changes in the dynamic viscosity with shear rate. In this way, the prepared model of apparent viscosity is used in momentum equations. These equations are integrated in order to designate components of the velocity vector. By substitution of the proper boundary conditions, a modified Reynolds type equation is obtained. A further stage of the research will be proceeding of the numerical calculations of the hydrodynamic pressure distribution followed by the designation of the carrying capacity, friction force, and friction coefficient while taking changes of the viscosity from shear rate into account (apparent viscosity).

Adiabatic analysis of microtextured porous journal bearings functioned with power law fluid model

2019 ◽  
Vol 233 (10) ◽  
pp. 1541-1553 ◽  
Author(s):  
N Sharma ◽  
S Kango ◽  
RK Sharma
Keyword(s):  
Power Law ◽  
Reynolds Equation ◽  
Fluid Model ◽  
Journal Bearings ◽  
Power Law Fluid ◽  
Average Temperature ◽  
Capacity Coefficient ◽  
Load Carrying ◽  
Temperature Parameter ◽  
Micro Dimples

The present work contributes to a pragmatic approach for improving the performance of porous journal bearings by incorporating different textures. The textures in the form of micro dimples (spherical (Sph) and ellipsoidal (Eps)) were incorporated on the bearing surface, whereas power law fluid was employed as working lubricant of non-Newtonian nature. The permeability effect has been considered through Darcy’s equation to derive a modified Reynolds equation. To account for the temperature parameter, the modified energy equation has also been derived for adiabatic conditions and solved numerically. The presence of textures and lubricant rheology influences the load-carrying capacity, coefficient of friction, attitude angle, axial fluid flow, and average temperature of porous journal bearings.

Numerical Simulation of Magnetic Fluid Lubrication

2010 ◽  
Vol 154-155 ◽  
pp. 1498-1501
Author(s):  
Li Jun Wang ◽  
Xiao Kang Yan ◽  
Fei Hu Li ◽  
Zi Xin Dong
Keyword(s):  
Magnetic Field ◽  
Bearing Capacity ◽  
Magnetic Fluid ◽  
Reynolds Equation ◽  
Fluid Model ◽  
Journal Bearings ◽  
Static Characteristics ◽  
Hydrodynamic Analysis ◽  
Lubrication Performance ◽  
The Magnetic Field

This paper was concerned with theoretical analysis and the static characteristics of the journal bearing lubricated with magnetic fluid. A general Reynolds equation based on magnetic fluid model is obtained, which can be easily extended to other non-Newtonian fluids and this equation can provide theoretical basis for hydrodynamic analysis of magnetic fluid journal bearings. For the case of static loaded magnetic journal bearings, the influence of magnetic fluid effects on the lubrication performance is studied under various eccentricity ratios, magnetic intensity and concentration. The numerical results show that: with the increasing of concentration, the bearing capacity is obviously increased; the increase magnitude is larger when the eccentricity ratio is large. Under the effect of magnetic field, the bearing capacity increasing with the increasing of magnetic field intensity. When the eccentricity is small, the side leakage is highly decreased. It can be completely eliminate by appropriately designing the bearing geometry and the magnetic field which can’t be existed in normal journal bearings.

Bifurcation Analysis of Self-Acting Gas Journal Bearings

2001 ◽  
Vol 123 (4) ◽  
pp. 755-767 ◽  
Author(s):  
Cheng-Chi Wang ◽  
Cha’o-Ku`ang Chen
Keyword(s):  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Rotational Velocity ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Finite Differences Method ◽  
Subharmonic Response ◽  
Rotor Center ◽  
Rotor Mass

This paper studies the bifurcation of a rigid rotor supported by a gas film bearing. A time-dependent mathematical model for gas journal bearings is presented. The finite differences method and the Successive Over Relation (S.O.R) method are employed to solve the Reynolds’ equation. The system state trajectory, Poincare´ maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions. The analysis shows how the existence of a complex dynamic behavior comprising periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.

The Effect of Journal Bearing Misalignment on Load and Cavitation for Non-Newtonian Lubricants

1986 ◽  
Vol 108 (4) ◽  
pp. 645-654 ◽  
Author(s):  
R. H. Buckholz ◽  
J. F. Lin
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Surface Boundary ◽  
Film Rupture ◽  
Aspect Ratios ◽  
Free Surface Boundary Condition ◽  
Load Carrying ◽  
Boundary Location ◽  
Surface Boundary Condition

An analysis for hydrodynamic, non-Newtonian lubrication of misaligned journal bearings is given. The hydrodynamic load-carrying capacity for partial arc journal bearings lubricated by power-law, non-Newtonian fluids is calculated for small valves of the bearing aspect ratios. These results are compared with: numerical solutions to the non-Newtonian modified Reynolds equation, with Ocvirk’s experimental results for misaligned bearings, and with other numerical simulations. The cavitation (i.e., film rupture) boundary location is calculated using the Reynolds’ free-surface, boundary condition.

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