On the effect of parallel and transverse stationary random surface roughness in hydrodynamics lubrication

1981 ◽  
Vol 374 (1759) ◽  
pp. 569-591 ◽  
Keyword(s):  
Surface Roughness ◽  
Reynolds Equation ◽  
Direct Evidence ◽  
Squeeze Film ◽  
Slider Bearing ◽  
Random Surface ◽  
Reynolds Equations ◽  
Random Functions ◽  
First Order ◽  
Parallel Surface

Modified versions of the Reynolds equation are derived with the aid of Stokes solutions for flows in channels with parallel and transverse surface roughness. The surface corrugations are of small amplitude and are represented by stationary random functions. Solutions to the modified and unmodified Reynolds equations for a wide slider bearing are pre­sented up to the first-order terms in the slope of the film thickness. The predictions of the modified Reynolds equations, while consistent with the Stokes solutions, are qualitatively opposite to that of the unmodified Reynolds equation. Direct evidence of the inadequacy of the unmodified Reynolds equation for a two-dimensional squeeze-film bearing with parallel surface roughness is also reported.

On the Effects of Homogeneous Reynolds Roughness in a Two-Dimensional Slider Bearing With Exponential Film Thickness

1982 ◽  
Vol 104 (2) ◽  
pp. 220-226 ◽  
Author(s):  
N. Phan-Thien ◽  
J. D. Atkinson
Keyword(s):  
Surface Roughness ◽  
Aspect Ratio ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Perturbation Approach ◽  
Mean Square ◽  
Two Dimensional ◽  
Slider Bearing ◽  
Characteristic Frequencies ◽  
Parallel Surface

The effects of rough surfaces on the performance of a two-dimensional slider bearing with a mean exponential film thickness is investigated using the Reynolds equation, whose application requires the aspect ratio of the bearing to be large and the amplitude and the characteristic frequencies of the roughness to be considerably smaller than a representative film thickness (all are dimensionless). This problem has been previously considered by Sun using a straightforward perturbation approach; here, a formulation due to Keller is adopted and we make explicit use of h0/l<<1, where l is the bearing length and h0 is a representative film thickness. It is shown that neglecting terms of 0(h0/l), the load enhancement is maximum and positive for a transverse surface roughness; and it is minimum and negative for a parallel surface roughness. In these two extreme cases, both load enhancements depend on the statistics of the surface only through its mean square and are exactly predicted by Christensen’s theory.

On the effects of the Reynolds and Stokes surface roughnesses in a two-dimensional slider bearing

1981 ◽  
Vol 377 (1770) ◽  
pp. 349-362 ◽  
Keyword(s):  
Surface Roughness ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Flow Direction ◽  
Two Dimensional ◽  
Slider Bearing ◽  
Homogeneous Surface ◽  
Parallel Surface ◽  
The Mean ◽  
The Stokes Equation

Perturbation solutions are presented to the Reynolds and the Stokes equations for a two-dimensional slider bearing with homogeneous surface roughness. In the Reynolds equation the surface roughness has a general two-dimensional form, and in the Stokes equation the surface roughness is parallel to the flow direction. For the parallel surface roughness, if the surface corrugations on two bearing plates are uncorrelated then an error of order 10% is made when using the Reynolds equation to correct for the surface roughness provided that λh ≼ 0.5. Here λ is a characteristic frequency of the corrugation and h is the mean film thickness. Furthermore, if λh ≽ 1.91 then the Stokes solution demands a positive load enhancement, whereas the Reynolds equation predicts a negative load enhancement that depends on λ through terms of order O ( h / L ), where 2 L is the bearing length.

On the Mean Reynolds Equation in the Presence of Surface Roughness: Squeeze-Film Bearing

1981 ◽  
Vol 48 (4) ◽  
pp. 717-720 ◽  
Author(s):  
N. Phan-Thien
Keyword(s):  
Surface Roughness ◽  
Flow Field ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Squeeze Film ◽  
Two Dimensional ◽  
Homogeneous Surface ◽  
Parallel Surface ◽  
Mean Pressure ◽  
The Mean

The mean Reynolds equation in the presence of surface roughness is derived using the techniques developed by Keller. This mean equation is nonlocal in the sense that the mean pressure at all points in the flow field has some effect on the mean pressure at any particular point. The performance of a two-dimensional squeeze film bearing with homogeneous surface roughness is considered next showing that the load is enhanced by a factor of 1 + ε2a2S/h2, where εa is the amplitude of the roughness, h is the film thickness, and S varies between −3 〈m2〉, for parallel surface roughness, to 6 〈m2〉 for transverse surface roughness. Here, the bearing surfaces are described by εam1 and h + εam2 and m = m2 − m1.

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.

Dynamics of Multilayer Microplates Considering Nonlinear Squeeze Film Damping

2006 ◽  
Author(s):  
M. T. Ahmadian ◽  
M. Moghimi Zand ◽  
H. Borhan
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Reynolds Equation ◽  
Finite Difference Methods ◽  
Shear Deformation Theory ◽  
Single Layer ◽  
Squeeze Film ◽  
First Order ◽  
Squeeze Film Damping ◽  
Good Agreement

This paper presents a model to analyze pull-in phenomenon and dynamics of multi layer microplates using coupled finite element and finite difference methods. First-order shear deformation theory is used to model dynamical system using finite element method, while Finite difference method is applied to solve the nonlinear Reynolds equation of squeeze film damping. Using this model, Pull-in analysis of single layer and multi layer microplates are studied. The results of pull-in analysis are in good agreement with literature. Validating our model by pull-in results, an algorithm is presented to study dynamics of microplates. These simulations have many applications in designing multi layer microplates.

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.

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.

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.

On the Mean Reynolds Equation in the Presence of Homogeneous Random Surface Roughness

1982 ◽  
Vol 49 (3) ◽  
pp. 476-480 ◽  
Author(s):  
N. Phan-Thien
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Spectral Density ◽  
Small Amplitude ◽  
Random Function ◽  
Reynolds Equation ◽  
Random Surface ◽  
Dimensionless Amplitude ◽  
The Mean

Assuming that the surface roughness is of small amplitude and can be modeled by a homogeneous random function in space, the classical Reynolds equation is averaged using a method due to J. B. Keller. The mean Reynolds equation is accurate up to terms of 0(ε2), where ε is the dimensionless amplitude of the surface roughness and has a nonlocal character. Furthermore, by exploiting the slowly varying property of the mean film thickness, this nonlocal character is eliminated. The resulting mean Reynolds equation depends on the surface roughness via its spectral density and, in the limits of either parallel or transverse surface roughness, it reduces to Christensen’s theory.

Sign in / Sign up

Export Citation Format

Share Document