Reynolds equation, apparent slip, and viscous friction in a three-layered fluid film

2008 ◽  
Vol 222 (3) ◽  
pp. 369-380 ◽  
Author(s):  
M-H Meurisse ◽  
G Morales Espejel
Keyword(s):  
Reynolds Equation ◽  
Viscous Friction ◽  
Fluid Film ◽  
Apparent Slip ◽  
Layered Fluid

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

Two Dimensional Modified Reynolds Equation Including Pressure Dependent Viscosity Effect

2012 ◽  
Author(s):  
Jung Gu Lee ◽  
Alan Palazzolo
Keyword(s):  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Fluid Film ◽  
Maximum Pressure ◽  
Elastic Solids ◽  
Pressure Distributions ◽  
Pressure Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity ◽  
Modified Equation

The Reynolds equation plays an important role for predicting pressure distributions for fluid film bearing analysis, One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. However, in elastohydrodynamic lubrication (EHL) where the lubricant is subjected to extremely high pressure, this assumption should be reconsidered. The 2D modified Reynolds equation is derived in this study including pressure-dependent viscosity, The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the ball bearing case (elastic solids). The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations.

Hydrodynamic Model for Cold Strip Rolling

1967 ◽  
Vol 182 (1) ◽  
pp. 153-162 ◽  
Author(s):  
D. S. Bedi ◽  
M. J. Hillier
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Entropy Production ◽  
Coefficient Of Friction ◽  
Hydrodynamic Model ◽  
Reynolds Equation ◽  
Viscous Friction ◽  
Strip Rolling ◽  
Roll Pressure ◽  
Cold Strip Rolling

The theory of rolling is modified to allow calculation of a hydrodynamic film thickness and viscous friction coefficient using Reynolds equation for the lubricant. Calculations are made for the case where the fluid film covers the arc of contact. The film thickness is assumed uniform and is determined by the principle of minimum rate of entropy production. It is shown that the apparent coefficient of friction varies significantly over the arc of contact. At small reductions the roll load tends to decrease with speed of rolling, while at high reductions the load tends to increase. The point of maximum roll pressure does not coincide with the neutral plane; and under certain rolling conditions there may be no maximum in the pressure over the arc of contact.

Magneto-rheological fluid slot-entry journal bearing considering thermal effects

2019 ◽  
Vol 30 (18-19) ◽  
pp. 2831-2852 ◽  
Author(s):  
Krishnkant Sahu ◽  
Satish C Sharma
Keyword(s):  
Thermal Effects ◽  
Journal Bearing ◽  
Fluid Model ◽  
Viscous Friction ◽  
Fluid Film ◽  
Applied Current ◽  
Bingham Model ◽  
Geometric Imperfection ◽  
Fluid Film Bearings ◽  
Magneto Rheological

In recent times, controlling the performance of fluid film bearings smartly has become an important area for the fluid film bearing designers. This study deals with the numerical simulation of a magneto-rheological fluid–lubricated two-lobe hybrid slot-entry journal bearing. To make the operating condition more exact and realistic, the influence of geometric imperfection of the journal arising from manufacturing inaccuracies and thermal effect has been considered. Dave magneto-rheological fluid model, a constitutive relation of the Bingham model, and finite element method have been used in this article to simulate the behavior of the magneto-rheological fluid in a slot-entry bearing. The results indicate that the heat generated because of viscous friction rises the temperature of the magneto-rheological fluid, which changes the bearing performance significantly. Considering barrel-shaped journal and magneto-rheological fluid (applied current, Ic = 4 A), the performance of two-lobe slot-entry bearing is superior in terms of the value of [Formula: see text] approximately by a magnitude of 2%, 41%, 181%, 168%, 75%, and 41%, respectively, as compared to that of the base bearing (smooth [Formula: see text], two-lobe bearing, operating with a Newtonian fluid, Ic = 0 A).

A Study of Thermohydrodynamic Squeeze Films

1974 ◽  
Vol 96 (2) ◽  
pp. 198-205 ◽  
Author(s):  
S. M. Rohde ◽  
H. A. Ezzat
Keyword(s):  
Heat Conduction Equation ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Time Dependent ◽  
Fluid Film ◽  
Squeeze Film ◽  
3 Dimensional ◽  
Temperature Distributions ◽  
Film Parameter ◽  
The Mathematical Model

This paper presents an analysis of the thermohydrodynamic performance of squeeze films. The mathematical model consists of a 3-dimensional Reynolds equation, a 3-dimensional time dependent energy equation, and a 3-dimensional time dependent heat conduction equation. The system of equations is solved numerically. Fluid film pressure and temperature distributions and the temperature distribution in the solids are presented. Fluid film velocity profiles as a function of time are also shown. The load-time characteristics for different operative conditions are studied. It is shown that a thermohydrodynamic squeeze-film parameter can give rise to a phenomenon which radically changes the fluid film performance.

Nonlinear Effects in a Plain Journal Bearing: Part 1—Analytical Study

1991 ◽  
Vol 113 (3) ◽  
pp. 555-561 ◽  
Author(s):  
F. K. Choy ◽  
M. J. Braun ◽  
Y. Hu
Keyword(s):  
Equilibrium Position ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Fluid Film ◽  
Liquid Oxygen ◽  
Solution Technique ◽  
Space Applications ◽  
Linear Solution ◽  
Film Pressure ◽  
Linear And Nonlinear

Hydrodynamic/hydrostatic journal bearings have been widely used in various types of high speed rotating machinery. For space applications, the issue of using cryogenic fluids as working lubricants has steadily gained in significance. The primary goal of this paper is to model the nonlinearities that occur in a hydrodynamic journal bearing with both cryogenic and oil lubricants. Results will be examined through bearing fluid film pressure distribution and bearing linear and nonlinear stiffness characteristics. The numerical model that couples a variable property Reynolds equation with the dynamics of the rotor is solved by means of a finite difference solution technique. The procedure for the fluid film pressure solution involves an iterative scheme that solves the Reynolds equation coupled with the equations of state for liquid oxygen (LO2). The pressure curve is then integrated to calculate bearing supporting forces. A two-dimensional Newton-Raphson iteration method is used to locate the journal equilibrium position from which both linear and nonlinear bearing stiffness are evaluated by means of the small perturbation technique. The effects of load on the linear/nonlinear plain journal bearing characteristics are analyzed and presented in a parametric form. The relationship between the accuracy of the linear solution and the various orders (3rd, 5th, and 7th power for ΔX) of the nonlinear approximation are also discussed. The validity of both linear and nonlinear solutions at various distances from the journal equilibrium position is also examined. A complete parametric study on the effects of load, temperature, operating speed, and shaft misalignment will be given in Part 2 of this paper.

Turborotor Instability: Effect of Initial Transients on Plane Motion

1969 ◽  
Vol 91 (4) ◽  
pp. 625-630 ◽  
Author(s):  
R. H. Badgley ◽  
J. F. Booker
Keyword(s):  
Reynolds Equation ◽  
Approximate Solutions ◽  
Initial Position ◽  
Plane Motion ◽  
Journal Bearings ◽  
Rigid Body Dynamics ◽  
Fluid Film ◽  
Body Dynamics ◽  
Instability Effect ◽  
Static Eccentricity

The rigid-body dynamics of rotors supported in plain, cylindrical, cavitated, fluid-film journal bearings are investigated numerically by Runge-Kutta extrapolation techniques. Expressions for journal force due to the fluid-film are developed for the short-bearing (Ocvirk), long-bearing (Sommerfeld), and finite-length-bearing (Warner) approximate solutions to the Reynolds equation. Stability of plane motion is investigated for each solution under the assumption of light initial impact. The long-bearing solution appears to be most conservative (that is, it predicts the onset of instability at lower angular velocity ratios than the other solutions) for static eccentricity ratios between 0 and 0.5, while the finite-bearing solution, with bearing length-to-diameter ratio L/D equal to 1, appears most conservative at higher static eccentricity ratios. Variations in L/D between 0.5 and 2.0 appear not to affect journal path shapes appreciably. Variations in initial journal center velocity are found to be important, at least with the short-bearing solution: large initial velocities are observed to produce instability for certain parameter combinations which are stable under small initial position or velocity disturbances. In all cases investigated, instability is not observed above static eccentricity ratios of 0.83.

scholarly journals About the Accuracy and the Grid Convergence of the Numerical Solution of the Energy Equation in Fluid Film Lubrication

2018 ◽  
Author(s):  
Silun Zhang ◽  
Mohamed-Amine Hassini ◽  
Mihai Arghir
Keyword(s):  
Numerical Solution ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Computation Time ◽  
Fluid Film ◽  
Hydrodynamic Analysis ◽  
One Dimensional ◽  
Grid Convergence ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The present work is focused on the numerical solution of the complete energy equation used in fluid film lubrication. The work was motivated by the fact the complete energy equation has no analytic solution that could be used for validations. Its accuracy and computation time are related to the employed numerical method and to the grid resolution. The natural discretization method (NDM) applied on different grids is systematically compared with the spectral method (the Lobatto Point Colocation Method or LPCM) with different polynomial degrees. A one dimensional inclined slider is used for the numerical tests and the energy equation is artificially decoupled from Reynolds. This approach enables to focus all the attention on the numerical solution of the energy equation. The results show that the LPCM is one or two orders of magnitudes more efficient than the NDM in terms of computation time. The energy equation is then coupled with Reynolds equation in a thermo-hydrodynamic analysis of the same 1D slider; the numerical results confirm again the efficiency of the LPCM. A thermo-hydrodynamic analysis of a two-lobe journal bearing is then presented as a practical application.

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