A Modified Average Reynolds Equation for Rough Bearings With Anisotropic Slip

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Hsiang-Chin Jao ◽  
Kuo-Ming Chang ◽  
Li-Ming Chu ◽  
Wang-Long Li
Keyword(s):  
Surface Roughness ◽  
Shear Stress ◽  
Shear Flow ◽  
Reynolds Equation ◽  
Slenderness Ratio ◽  
Atomic Scale ◽  
Stress Factors ◽  
Squeeze Film ◽  
Boundary Slip ◽  
Slip Conditions

A lubrication theory that includes the coupled effects of surface roughness and anisotropic slips is proposed. The anisotropic-slip phenomena originate from the microscale roughness at the atomic scale (microtexture) and surface properties of the lubricating surfaces. The lubricant flow between rough surfaces (texture) is defined as the flow in nominal film thickness multiplied by the flow factors. A modified average Reynolds equation (modified ARE) as well as the related factors (pressure and shear flow factors, and shear stress factors) is then derived. The present model can be applied to squeeze film problems for anisotropic-slip conditions and to sliding lubrication problems with restrictions to symmetric anisotropic-slip conditions (the two lubricating surfaces have the same principal slip lengths, i.e., b1x=b2x and b1y=b2y). The performance of journal bearings is discussed by solving the modified ARE numerically. Different slenderness ratios 5, 1, and 0.2 are considered to discuss the coupled effects of anisotropic slip and surface roughness. The results show that the existence of boundary slip can dilute the effects of surface roughness. The boundary slip tends to “smoothen” the bearings, i.e., the derived flow factors with slip effects deviate lesser from the values at smooth cases (pressure flow factors φxxp,φyyp=1; shear flow factors φxxs=0; and shear stress factors φf,φfp=1 and φfs=0) than no-slip one. The load ratio increases as the dimensionless slip length (B) decreases exception case is also discussed or the slenderness ratio (b/d) increases. By controlling the surface texture and properties, a bearing with desired performance can be designed.

Roughness Influence on Turbulent Flow Through Annular Seals

1994 ◽  
Vol 116 (2) ◽  
pp. 321-328 ◽  
Author(s):  
Victor Lucas ◽  
Sterian Danaila ◽  
Olivier Bonneau ◽  
Jean Freˆne
Keyword(s):  
Surface Roughness ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Flow ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Mixing Length ◽  
Local Shear ◽  
Wall Shear ◽  
Local Shear Stress

This paper deals with an analysis of turbulent flow in annular seals with rough surfaces. In this approach, our objectives are to develop a model of turbulence including surface roughness and to quantify the influence of surface roughness on turbulent flow. In this paper, in order to simplify the analysis, the inertial effects are neglected. These effects will be taken into account in a subsequent work. Consequently, this study is based on the solution of Reynolds equation. Turbulent flow is solved using Prandtl’s turbulent model with Van Driest’s mixing length expression. In Van Driest’s model, the mixing length depends on wall shear stress. However there are many numerical problems in evaluating this wall shear stress. Therefore, the goal of this work has been to use the local shear stress in the Van Driest’s model. This derived from the work of Elrod and Ng concerning Reichardt’s mixing length. The mixing length expression is then modified to introduce roughness effects. Then, the momentum equations are solved to evaluate the circumferential and axial velocity distributions as well as the turbulent viscosity μ1 (Boussinesq’s hypothesis) within the film. The coefficients of turbulence kx and kz, occurring in the generalized Reynolds’ equation, are then calculated as functions of the flow parameters. Reynolds’ equation is solved by using a finite centered difference method. Dynamic characteristics are calculated by exciting the system numerically, with displacement and velocity perturbations. The model of Van Driest using local shear stress and function of roughness has been compared (for smooth seals) to the Elrod and Ng theory. Some numerical results of the static and dynamic characteristics of a rough seal (with the same roughness on the rotor as on the stator) are presented. These results show the influence of roughness on the dynamic behavior of the shaft.

Pressure and Shear Flow in a Rough Hydrodynamic Bearing, Flow Factor Calculation

1997 ◽  
Vol 119 (3) ◽  
pp. 549-555 ◽  
Author(s):  
L. Lunde ◽  
K. To̸nder
Keyword(s):  
Finite Element Method ◽  
Surface Roughness ◽  
Finite Element ◽  
Shear Flow ◽  
Reynolds Equation ◽  
Flow Model ◽  
The Finite Element Method ◽  
Average Flow ◽  
Hydrodynamic Bearing ◽  
Average Flow Model

The lubrication of isotropic rough surfaces has been studied numerically, and the flow factors given in the so-called Average Flow Model have been calculated. Both pressure flow and shear flow are considered. The flow factors are calculated from a small hearing part, and it is shown that the flow in the interior of this subarea is nearly unaffected by the bearing part’s boundary conditions. The surface roughness is generated numerically, and the Reynolds equation is solved by the finite element method. The method used for calculating the flow factors can be used for different roughness patterns.

scholarly journals Hydrodynamic lubrication of rough surfaces

1982 ◽  
Vol 383 (1785) ◽  
pp. 439-446 ◽  
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Rough Surfaces ◽  
Homogenization Method ◽  
Squeeze Film ◽  
Spatial Average

Using the two-space homogenization method we derive an averaged Reynolds equation that is correct to O (< H 6 > — < H 3 > 2 ), where H is the total film thickness and the angle brackets denote a spatial average. Applications of this mean Reynolds equation to a squeeze-film bearing with a sinusoidal or an isotropic surface roughness are discussed.

Squeeze film behavior in porous transversely circular stepped plates with a couple stress fluid

2016 ◽  
Vol 33 (2) ◽  
Author(s):  
Santhana Krishnan Narayanan ◽  
A Chamkha ◽  
Sundarammal Kesavan
Keyword(s):  
Surface Roughness ◽  
Couple Stress ◽  
Design Methodology ◽  
Reynolds Equation ◽  
Closed Form Solution ◽  
Stochastic Theory ◽  
Classical Case ◽  
Form Solution ◽  
Couple Stress Fluid ◽  
Squeeze Film

Purpose The purpose of this work is to carry our a study of the effect of surface roughness on squeeze film behavior between two transversely circular stepped plates with couple stress lubricant when the upper circular stepped plate has porous facing which approaches the lower plate with uniform velocity. Design/methodology/approach The modified Stochastic Reynolds equation is derived for Christensen Stochastic theory for the rough surfaces. Closed form solution of the Stochastic Reynolds equation is obtained in terms of Fourier-Bessel series. Findings It is found that the effect of couple stress fluid and surface roughness is more pronounced compared to classical case. Originality/value The problem is original that it consider a couple stress fluid in this type of applications.

scholarly journals MULTIGRID METHOD FOR THE SOLUTION OF COMBINED EFFECT OF VISCOSITY VARIATION AND SURFACE ROUGHNESS ON THE SQUEEZE FILM LUBRICATION OF JOURNAL BEARINGS

2017 ◽  
Vol 46 (1) ◽  
pp. 1-8
Author(s):  
Vishwanath B. Awati ◽  
Ashwini Kengangutti ◽  
Mahesh Kumar N.
Keyword(s):  
Surface Roughness ◽  
Carrying Capacity ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Multigrid Method ◽  
Squeeze Film ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Viscosity Variation ◽  
Film Lubrication

The paper presents, the multigrid method for the solution of combined effect of surface roughness and viscosity variation on the squeeze film lubrication of a short journal bearing operating with micropolar fluid. The modified Reynolds equation which incorporates the variation of viscosity in micropolar fluid is analysed using Multigrid method. The governing modified Reynolds equation is solved numerically for the fluid film pressure and bearing characteristics viz. load carrying capacity and squeeze time. The analysis of the results predicts that, the viscosity variation factor decreases the load carrying capacity and squeeze film time, resulting into a longer bearing life. The results are compared with the corresponding analytical solutions.

Pressure and Shear Flow Factors Calculation for Orthotropic Rough Surfaces

2007 ◽  
Author(s):  
Ramona Dragomir ◽  
Dominique Bonneau ◽  
Patrick Ragot ◽  
Franc¸ois Robbe-Valloire
Keyword(s):  
Surface Roughness ◽  
Shear Flow ◽  
Reynolds Equation ◽  
Rough Surfaces ◽  
Cross Flow ◽  
Lubricated Contacts ◽  
General Average ◽  
The Cross

In general, average Reynolds equation is defined in terms of shear flow factors in order to determine the effects of surface roughness on partially lubricated contacts. This paper is essentially devoted to the application of flow factors model to real shaft and bearing surfaces, obtained by metrological measures. Additionally, the average Reynolds equation is completed by “cross” flow factors. The “cross” flow factors may have an important role if model is applied on either longitudinally or transversely oriented surfaces (surfaces with directional patterns oriented with an angle).

scholarly journals Effect of Surface Roughness and Viscosity-Pressure Dependency on the Couple Stress Squeeze Film Characteristics of Parallel Circular Plates

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Neminath Bhujappa Naduvinamani ◽  
Siddangouda Apparao ◽  
Ayyappa G. Hiremath
Keyword(s):  
Surface Roughness ◽  
Carrying Capacity ◽  
Couple Stress ◽  
Reynolds Equation ◽  
Squeeze Film ◽  
Load Carrying Capacity ◽  
Circular Plates ◽  
Pressure Dependency ◽  
Load Carrying ◽  
Film Characteristics

Combined effects of surface roughness and viscosity-pressure dependency on the couple stress squeeze film characteristics of parallel circular plates are presented. On the basis of Christensen’s stochastic theory, two types of one-dimensional roughness structures, namely, the radial roughness and azimuthal roughness patterns, are considered and the stochastic modified Reynolds equation for these two types of roughness patterns is derived for Stokes couple stress fluid by taking into account variation of viscosity with pressure. The standard perturbation technique is employed to solve the averaged Reynolds equation and closed form expressions for the mean fluid film pressure, load carrying capacity, and squeeze film time are obtained. It is found that the effects of couple stresses and viscosity-pressure dependency are to increase the load carrying capacity, and squeeze film time for both types of roughness patterns. The effect of azimuthal (radial) roughness pattern is to increase (decrease) these squeeze film characteristics as compared to the corresponding smooth case.

Thermal Elastohydrodynamic Lubrication of Non-Newtonian Fluids With Rough Surfaces

1997 ◽  
Vol 119 (4) ◽  
pp. 605-612 ◽  
Author(s):  
J. M. Wang ◽  
V. Aronov
Keyword(s):  
Surface Roughness ◽  
Shear Flow ◽  
Reynolds Equation ◽  
Rough Surfaces ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Newtonian Fluids ◽  
Perturbation Approach ◽  
Correction Factors ◽  
Power Law Fluids

The characteristics of thermal elastohydrodynamic lubrication by non-Newtonian fluids for rough surfaces is investigated theoretically. The general Reynolds equation for two-sided striated roughness lubricated by power law fluids is established using a perturbation approach. New correction factors for the pressure flow and the shear flow are derived; these factors integrate both lubricant rheology and surface roughness characteristics. A more effective numerical algorithm is adopted to obtain the solutions for wide ranges of operating conditions. Observations and discussion lead to further understanding of the various interactions among different factors in a elastohydrodynamic lubrication process.

Application of Average Flow Model to Lubrication Between Rough Sliding Surfaces

1979 ◽  
Vol 101 (2) ◽  
pp. 220-229 ◽  
Author(s):  
Nadir Patir ◽  
H. S. Cheng
Keyword(s):  
Shear Stress ◽  
Shear Flow ◽  
Flow Model ◽  
Stress Factors ◽  
Surface Pattern ◽  
Roughness Effects ◽  
Local Pressure ◽  
Average Flow ◽  
Flow Factor ◽  
Average Flow Model

The Average Flow Model introduced in an earlier paper is extended to include sliding contacts by deriving the shear flow factor for various roughness configurations. Similar to the pressure flow factors, the shear flow factor is obtained through numerical flow simulation on a model bearing having numerically generated roughness. The flow factors for isotropic and directional surfaces are expressed as empirical relationships in terms of h/σ, a surface pattern parameter γ defined as the ratio of x and y correlation lengths, and the variance ratio Vr1 which is the ratio of variance of surface 1 to that of the composite roughness. Expressions for the mean shear stress and horizontal force components due to local pressure in rough bearings are derived through the definition of shear stress factors, also obtained through simulation. The application of the average Reynolds equation to analyze roughness effects in bearings is demonstrated on a finite slider. The effects of the operating parameters as well as the roughness parameters on mean hydrodynamic load, mean viscous friction and mean bearing inflow are illustrated.

Sign in / Sign up

Export Citation Format

Share Document