Hydrodynamic Lubrication Of Rough Surfaces Research Articles

Theoretical analysis of effect of MHD, couple stress and slip velocity on squeeze film lubrication characteristics of Long Cylinder and Infinite Rough Plate

The current research examines how a long cylinder, and an infinitely flat surface are affected by surface roughness, MHD, couple stress, and slip velocity using the stochastic theory of hydrodynamic lubrication of rough surfaces as developed by Christensen. Squeeze film time, load carrying capacity, and pressure are calculated using a derived mathematical form of Reynolds' modified equation that accounts for surface roughness and coupling stress. The amount of time needed to squeeze a film under a specific pressure and load can be determined using an analytical method called Reynolds' equation. The lubrication characteristics are graphically represented for various parameters. When a magnetic field occurs and the slip velocity increases, the pressure of the squeeze film, its capacity to carry loads, and the time it takes are all significantly increased. The lubricating properties caused a decrease or increase in the values of the longitudinal (transverse) roughness parameter.

Multiscale Modeling Applied to the Hydrodynamic Lubrication of Rough Surfaces for Computation Time Reduction

This paper presents a multiscale finite element method applied to the simulation of a lubricating film flowing between rough surfaces. The objective of this approach is to study flows between large rough surfaces needing very fine meshes while maintaining a reasonable computation time. For this purpose, the domain is split into a number of subdomains (bottom-scale meshes) connected by a coarse mesh (top-scale). The pressure distribution at the top-scale is used as boundary conditions for the bottom-scale problems. This pressure is adjusted to ensure global mass flow balance between the contiguous subdomains. This multiscale method allows for a significant reduction of the number of operations as well as a satisfactory accuracy of the results if the top-scale mesh is properly fitted to the roughness lateral scale. Furthermore the present method is well-suited to parallel computation, leading to much more significant computation time reduction.

Homogenization in Hydrodynamic Lubrication: Microscopic Regimes and Re-Entrant Textures

The form of the Reynolds-type equation which governs the macroscopic mechanics of hydrodynamic lubrication interfaces with a microscopic texture is well-accepted. The central role of the ratio of the mean film thickness to the texture period in determining the flow factor tensors that appear in this equation had been highlighted in a pioneering theoretical study through a rigorous two-scale derivation (Bayada and Chambat, 1988, “New Models in the Theory of the Hydrodynamic Lubrication of Rough Surfaces,” ASME J. Tribol., 110, pp. 402–407). However, the resulting homogenization theory still remains to be numerically investigated. For this purpose, after a comprehensive review of the literature, three microscopic regimes of lubrication will be outlined, and the transition between these three regimes for different texture types will be extensively demonstrated. In addition to conventional textures, representative re-entrant textures will also be addressed.

On the ferrofluid lubricated squeeze film characteristics between a rotating sphere and a radially rough plate

Ferrofluid lubricated squeeze film bearing design system formed by a rotating upper spherical surface and a radially rough lower flat plate considering variable magnetic field, which is oblique to the lower plate, have been analyzed. The variable magnetic field is important because of its advantage of generating maximum field at the required active contact zone. The problem is motivated because squeeze film behaviour is widely observed in many industrial applications like in machine tools, gears, rolling elements, hydraulic systems, engines, clutch plates, force pendulum apparatus, etc. Moreover, the squeeze film behaviour is also observed in skeletal joints of human body. On the basis of ferrohydrodynamic theory and Christensen’s stochastic theory for hydrodynamic lubrication of rough surfaces, the modified Reynolds equation is derived and expressions for squeeze film characteristics are obtained which are calculated numerically and interpreted. While deriving Reynolds equation effects of various parameters like rotation, width of the nominal minimum film thickness and squeeze velocity are also considered.

Effects of pressure-dependent viscosity variation on the squeeze film lubrication between a sphere and a rough flat plate with couple stress fluids

In this paper, a theoretical study of the combined effects of surface roughness and the variation of viscosity with pressure on the squeeze film lubrication between sphere and a flat plate is presented. Based on the Christensen’s stochastic theory for the hydrodynamic lubrication of rough surfaces, two types of one-dimensional surface roughness (radial and azimutal) patterns are considered. The generalized averaged Reynold’s equation for Stokes couple stress fluids accounting for the pressure dependent viscosity is mathematically derived for the problem under consideration. The standard perturbation technique is used to solve the averaged nonlinear Reynold’s equation and an approximate analytical solution for the fluid film mean pressure is obtained for the two types of one-dimensional roughness patterns. It is found that, the effects of couple stresses and pressure dependent viscosity variation are to improve the squeeze film characteristics.

Effect of surface roughness on magneto-hydrodynamic squeeze-film characteristics between a sphere and a porous plane surface

Purpose– The purpose of this article is to analyse the effects of surface roughness on the magneto-hydrodynamic (MHD) squeeze-film characteristics between a sphere and a porous plane surface, which have not been studied so far.Design/methodology/approach– The analytical model takes into account the effect of porosity by assuming that the flow in the porous matrix obeys modified Darcy's law. The stochastic MHD Reynold's type equation is derived by using the Christensen's stochastic method developed for hydrodynamic lubrication of rough surfaces. Two types of one-dimensional surface roughness (radial and azimuthal) patterns are considered.Findings– The expressions for the mean MHD squeeze-film pressure and mean load-carrying capacity are obtained numerically. The results are shown graphically for selected representative parametric values. It is found that the response time increases significantly for the MHD case as compared to the corresponding non-conducting lubricants. The effect of roughness parameter is to increase/decrease the load-carrying capacity and the response time for azimuthal/radial roughness patterns as compared to the smooth case. Also, the effect of porous parameter is to decrease the load-carrying capacity and response time as compared to the solid case.Originality/value– In this paper, an attempt has been made to analyse the combined effects of surface roughness and permeability on the MHD squeeze-film characteristics between a sphere and a plane surface.

Effect of Surface Roughness on MHD Couple Stress Squeeze-Film Characteristics between a Sphere and a Porous Plane Surface

The combined effects of couple stress and surface roughness on the MHD squeeze-film lubrication between a sphere and a porous plane surface are analyzed, based upon the thin-film magnetohydrodynamic (MHD) theory. Using Stoke’s theory to account for the couple stresses due to the microstructure additives and the Christensen’s stochastic method developed for hydrodynamic lubrication of rough surfaces derives the stochastic MHD Reynolds-type equation. The expressions for the mean MHD squeeze-film pressure, mean load-carrying capacity, and mean squeeze-film time are obtained. The results indicate that the couple stress fluid in the film region enhances the mean MHD squeeze-film pressure, load-carrying capacity, and squeeze-film time. The effect of roughness parameter is to increase (decrease) the load-carrying capacity and lengthen the response time for azimuthal (radial) roughness patterns as compared to the smooth case. Also, the effect of porous parameter is to decrease the load-carrying capacity and increase the squeeze-film time as compared to the solid case.

Squeeze film characteristics between a sphere and a rough porous flat plate with micropolar fluids

The effects of surface roughness on the squeeze film characteristics between a sphere and flat plate covered with a thin porous layer are investigated in this paper. The sphere and the plate are separated with a non-Newtonian lubricant of a micropolar fluid. The well-established Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to incorporate the effects of surface roughness into the Reynolds equation. The film pressure distribution is solved and other squeeze film characteristics, such as the load-carrying capacity,and time–height relationship, are obtained. The results indicate that lubrication by a micropolar fluid will increase the load-carrying capacity and lengthen the squeeze film time, regardless to the surface rough and porosity of the flat plate. It is also found that excessive permeability of the porous layer causes a significant drop in the squeeze film characteristics and minimises the effect of surface roughness. For the case of limited or no permeability, the azimuthal roughness is found to increase the load-carrying capacity and squeeze time, whereas the reverse results are obtained for the case of radial roughness.

Effect of surface roughness on couple stress squeeze film lubrication of long porous partial journal bearings

PurposeThe aim of this paper is to investigate the effect of surface roughness on the squeeze film characteristics of long porous partial journal bearings with couple stress fluids as lubricant.Design/methodology/approachThe Stokes couple stress fluid model is included to account for the additives effects of lubricant. The Christensen's stochastic method developed for the hydrodynamic lubrication of rough surfaces is used to derive the stochastic Reynolds type equation accounting for the surface roughness and couple stresses. In the context of Christensen's stochastic theory for the hydrodynamic lubrication of rough surfaces, two types of one‐dimensional surface roughness (longitudinal and transverse) patterns are considered. The non‐linear first order differential equation governing the journal center movement is solved numerically by using the fourth order R‐K method.FindingsFrom the numerical computations of the results, it is found that, the effect of couple stresses is to increase the load carrying capacity and also the response time. The effect of surface roughness is to increase (decrease) the load carrying capacity and the response time for transverse (longitudinal) roughness pattern. However, the effect of permeability parameter is to decrease the load carrying capacity and also to decrease the response time as compared to the solid case.Originality/valueThe original findings on the combined effects of surface roughness and couple stresses on the squeeze film characteristics of long porous partial journal bearing are of use to the bearing designers.

Surface roughness effect on finite journal bearings with flexible porous liners

The effects of surface roughness on the static characteristics of finite porous journal bearings under hydrodynamic lubrication conditions are investigated in this paper. The well-established Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to incorporate the effects of surface roughness into the Reynolds equation. The analysis takes into account the flexibility of the porous liner by using a thin liner model. The effects of velocity slip at the surface of the porous medium are considered in the analysis by using the Beavers-Joseph criterion. The mathematical model is then solved numerically by finite-difference methods for mean hydrodynamic pressure, which in turn gives the hydrodynamic load. The effects of the surface roughness parameter, surface pattern, eccentricity ratio, length-to-diameter ratio, permeability parameter, and flexibility parameter on the hydrodynamic load-carrying capacity, attitude angle, and friction factor are discussed.

Effect of surface roughness on the couple-stress squeeze film between a sphere and a flat plate

In this paper, a theoretical study of the effect of surface roughness on the hydrodynamic lubrication of couple-stress squeeze film between a sphere and a flat plate is presented on the basis of Christensen's stochastic theory for hydrodynamic lubrication of rough surfaces. The modified Reynolds equation accounting for the couple stresses and the surface roughness is mathematically derived. The modified Reynolds equation is solved for the fluid film pressure and the bearing characteristics, such as the load carrying capacity and the time–height relationship, are obtained. It is found that the surface roughness considerably influences the squeeze film characteristics. The load carrying capacity and squeeze film time are found to increase for an azimuthal roughness pattern as compared to the corresponding smooth case, whereas the reverse trend is observed for a radial roughness pattern.

Surface roughness effects on squeeze films in curved circular plates

The stochastic theory of hydrodynamic lubrication of rough surfaces is used to study the effect of surface roughness on the performance of the squeeze film between circular curved plate and a flat plate. In the context of stochastic theory, two types of one‐dimensional roughness patterns (circumferential and radial roughness) are considered. The stochastic Reynolds equation for the two types of roughness patterns is derived. The closed form expressions for the mean squeeze film pressure, mean load carrying capacity and the squeeze film time are obtained. It is found that, the circumferential one‐dimensional surface roughness pattern increases the mean squeeze film pressure and the load carrying capacity whereas the radial one‐dimensional roughness pattern affects the squeeze film characteristics.

Effect of surface roughness on characteristics of couplestress squeeze film between anisotropic porous rectangular plates

The effect of surface roughness on the couplestress squeeze film behavior between two rectangular plates, when one plate has a porous facing with anisotropic permeability, is analyzed by taking into account the slip velocity at the fluid and porous material interface. The stochastic Reynolds equation accounting for the couple stresses and randomized surface roughness structure is mathematically derived. Modified equations for the mean pressure, mean load-carrying capacity and squeeze film time are obtained by using the Christensen stochastic theory for hydrodynamic lubrication of rough surfaces. The effects of surface roughness, couplestresses and anisotropic permeability on the squeeze film characteristics are discussed. It is found that the surface roughness effects are more pronounced for couplestress fluids as compared to the Newtonian fluids.

Surface roughness effects in a short porous journal bearing with a couple stress fluid

In this paper, a theoretical study of the effect of surface roughness in hydrodynamic lubrication of a porous journal bearing with couplestress fluid as lubricant is made. The modified Reynolds equations accounting for the couple stresses and randomized surface roughness structure are mathematically derived. The Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to study the effects of surface roughness on the static characteristics of a short porous journal bearing with couplestress fluid as lubricant. Further, it is assumed that, the roughness asperity heights are small compared to the film thickness. It is observed that, the effects of surface roughness on the bearing characteristics are more pronounced for couplestress fluids as compared to the Newtonian fluids.

Surface Roughness Effects in Infinitely Long Porous Journal Bearings

Christensen’s stochastic theory of hydrodynamic lubrication of rough surfaces is used to study the effect of surface roughness in an infinitely long porous journal bearing operating under steady conditions. It is shown that the surface roughness considerably influences the bearing performance; the direction of the influence depends on the roughness type.

Effect of Velocity Slip in an Infinitely Long Rough Porous Journal Bearing

The paper considers the effect of velocity slip in rough porous journal bearings operating in the hydrodynamic regime. On the basis of stochastic theory of hydrodynamic lubrication of rough surfaces developed by Christensen and incorporating Beavers and Joseph slip condition at the porous bearing interface, different forms of Reynolds—type equations, as applicable to porous bearings are derived for various types of surface roughness pattern. As an application of the theory, the case of an infinitely long porous journal bearing operating under steady conditions is analyzed. It is shown that roughness—slip interaction considerably affects the bearing performance.

Effects of Surface Texture on Hydrodynamic Lubrication of Dynamically Loaded Journal Bearings

The effects of two-sided purely longitudinal, transverse and isotropic surface roughness on the hydrodynamic lubrication of dynamically loaded finite journal bearings are analyzed using Christensen's stochastic model of hydrodynamic lubrication of rough surfaces and considering running-in effect on roughness height distributions. A detailed study of the above system in terms of the nominal minimum film thickness and the maximum film pressure demonstrates that the effects of roughness are closely tied to the roughness texture and structure, features of nominal geometry, and operating factors.

New Models in the Theory of the Hydrodynamic Lubrication of Rough Surfaces

Recent advances in mathematical analysis of problems described by several small parameters equations are used to revisit the general roughness problem. In this paper, we put forward a new qualitative study of a thin film flow with a rapidly varying gap. Using an asymptotic analysis of the three-dimensional Stokes system we obtain a family of new generalized Reynolds equations. We are led to distinguish three different cases in which the periodic roughness wavelength is on the order of, greater or shorter than the mean thickness of the gap.

Effect of surface roughness on the squeeze film between rotating porous annular discs with arbitrary porous wall thickness

The stochastic theory of hydrodynamic lubrication of rough surfaces is used to study the effect of surface roughness on the response of a squeeze film between two rotating annular discs when one disc has a porous facing. An exact solution, valid for arbitrary wall thickness is given for the film pressure and pressure in the bearing material. The results are compared with the approximate solution and the range of influencing parameters for which the approximate solution is satisfactory from a practical view point, is determined.

The Hydrodynamic Lubrication of Rough Surfaces Based on a New Perturbation Approach

A new method for treating roughness problems in hydrodynamic lubrication is presented. The approach consists of an expansion of the pressure by means of the perturbation parameter ε which is the ratio of the characteristic wavelengths across and along the direction of motion, respectively. This parameter may also be interpreted as the inverse of the Peklenik number of the surface texture. It is found that the zeroth components are those of To̸nder’s approximate theory. The terms are modified so as to remain finite at infinite ε. It is demonstrated that the corrections thus obtained are very accurate for configurations which are not disconnected pockets, even for very large roughness amplitudes. Such pockets are well treated, however, for moderate roughnesses. The method is applicable to statistically symmetric cases and may be easily extended to two-sided roughness. The application of the approach is quite straightforward numerically and does not require the boundary conditions of sample roughnesses to be known.