Squeeze Film Lubrication Research Articles

Numerical solution of finite modified Reynolds equation for couple stress squeeze film lubrication of porous journal bearings

In this paper, the rheological effect of couple stress fluids on the static and dynamic characteristics of squeeze film lubrication in finite porous journal bearings is studied. The finite modified Reynolds equation is derived from the Stokes constitutive equations for couple stress fluids and is solved numerically by using the finite difference technique. The applied load is considered as a sinusoidal function of time to simulate the bearings operating under cyclic loads. Under a cyclic load, the effect of couple stress is to reduce the velocity of the journal centre and to increase the minimum permissible height of the squeeze film.

Squeeze film lubrication between circular stepped plates of couple stress fluids

In this paper, a theoretical analysis of the effects of couple stresses on the squeeze film lubrication between circular stepped plates is presented. Modified Reynolds type equation is derived for the couplestress fluids. Closed form solution is obtained. According to the results obtained, the influence of couple stresses enhances the squeeze film pressure, load carrying capacity, and decreases the response time as compared to classical Newtonian-lubricant case. The load carrying capacity decreases as step height increases.

Roughness Effect on Squeeze Film Characteristics of Porous Circular Plates Lubricated with Couple Stress Fluid

This paper describes the combined effect of surface roughness and couple stress fluid on the performance characteristics of squeeze film lubrication between two circular plates. Using microcontinuum theory for the couple stress fluid and the Christensen stochastic model for the surface roughness, the modified Reynolds equation is derived by assuming the roughness asperity heights to be small compared to the film thickness. An eigenvalue problem involving Bessel functions enables analysis of the Reynolds equation. The expressions for mean pressure, load-carrying capacity, and squeeze film time are obtained for various probability distribution functions (pseudo normal, rectangular, and inverse square root distributions) that characterize the roughness of the lubricating surfaces. The influence of roughness and couple stress on bearing characteristics is presented in terms of the relative percentage in load for all these roughness patterns. © 2009 Begell House, Inc.

Squeeze Film Lubrication in Silicone Oil: Experimental Test of the No-Slip Boundary Condition at Solid−Liquid Interfaces

The hydrodynamic force between a spherical glass particle (radius ∼ 10 μm) and a smooth, flat glass plate in Newtonian silicone oil (viscosity, η ∼ 95 mPa s) was measured using the atomic force microscopy (AFM) colloidal probe technique and was compared to Reynolds lubrication theory. When the particle and plate were coated with a hydrophobic silane, the measured forces were consistent with Reynolds lubrication theory without the need to introduce the concept of a slip length. When the particle was hydrophilic, the results were more variable, sometimes being consistent with the no-slip boundary condition and sometimes being better fitted by invoking a constant slip length (up to 33 nm). The hydrophilic system was not well characterized because the hydrophilic solid may have entrained or attracted a layer of water (η = 0.001 Pa s) of unknown thickness, which would lubricate the flow and explain the apparent slip length. In addition, all AFM force measurements suffer from the problem that the solids occasio...

Surface roughness effects on the static and dynamic behaviour of squeeze film lubrication of short journal bearings with micropolar fluids

The theoretical study of the effect of surface roughness on the squeeze film lubrication of short journal bearings with no journal rotation under fluctuating loads with micropolar fluids is made. A more general form of surface roughness is mathematically modelled by a stochastic random variable with non-zero mean, variance, and skewness. The generalized average Reynolds type equation is derived for the squeeze film lubrication of rough journal bearings with micropolar fluids as lubricant. The closed form expressions for the bearing characteristics are obtained. The cases of a constant applied load and an alternating applied load are analysed. Under a cyclic load the micropolar fluids provide a reduction in the journal centre velocity. Further, it is observed that, the presence of microstructure additives and the negatively skewed surface roughness on the bearing surface increases the load carrying capacity and decreases the journal centre velocity.

Combined effects of surface roughness and couple stresses on static and dynamic behaviour of squeeze film lubrication of porous journal bearings

The combined effects of surface roughness and the couple stresses on the static and dynamic characteristics of squeeze film lubrication in porous journal bearings with no journal rotation are theoretically studied. The Stokes couple stress fluid model is considered to model the lubricants with additives. The surface roughness on the porous journal bearing is mathematically modelled by a random variable with non-zero mean, variance and skewness. The generalised stochastic Reynolds type equation is derived for the problem under consideration. The applied load is considered as a sinusoidal function of time to simulate the bearings operating under cyclic loads. The closed form expressions for the bearing characteristics are obtained for the short porous journal bearings. It is observed that the negatively skewed surface roughness and couple stresses improve the performance of the porous journal bearings as compared to the smooth journal bearings with Newtonian lubricants. However, the presence of positively skewed surface roughness on the bearing surface affects its performance.

Effect of surface roughness on the squeeze film lubrication between curved annular plates

PurposeThis paper aims to study the effects of surface roughness on the characteristics of squeeze film lubrication between curved annular plates.Design/methodology/approachThe modified Reynolds type equation governing the fluid film pressure is derived. The stochastic method for rough surfaces developed by Christensen is to derive stochastic type equation and has been solved for two types of one‐dimensional roughness patterns. Closed form expressions of mean squeeze film pressure and mean load carrying capacity are obtained.FindingsThe bearing characteristics are computed for various values of roughness parameter. It is found that the effect of radial (circumferential) roughness pattern is to shift the point of maximum pressure towards the inlet (outlet) edge and also observe that the mean load‐carrying capacity increases (decreases) for the circumferential (radial) roughness pattern compared with the corresponding smooth case, for both concave and convex pad geometries.Research limitations/implicationsThe analysis is useful in obtaining suitable mathematical model of physical problems. The one which we have considered here is the idealized form of functioning of bearings in general. Analysis of finer models requires pure numerical schemes, for which the present model is a base.Practical applicationsFindings of the present paper have applications in machine elements like clutch plates and collar bearings.Originality/valueInclusions of surface roughness effect on the characteristics of bearings are original contributions in tribology.

Combined effects of surface roughness and couple stresses on squeeze film lubrication between porous circular stepped plates

In this paper, combined effects of surface roughness and couple stresses on squeeze film lubrication between porous circular stepped plates is analysed. In the context of Christensen stochastic theory for the study of surface roughness two types of one-dimensional surface roughness pattern, viz., azimuthal roughness pattern and radial roughness pattern are considered. The stochastic modified Reynolds equation for these two types of roughness patterns is derived for the couple-stress fluid. The Beavers-Joseph slip boundary condition on the fluid-porous interface is utilized. Closed form expressions for the mean load carrying capacity and squeeze film time are obtained. It is found that the squeeze film characteristics are improved for the azimuthal surface roughness pattern. However, the performance of the squeeze film bearing suffers due to the presence of radial roughness pattern.

Combined effects of non-Newtonian rheology and fluid inertia forces on the non-linear transient behaviour in circular squeeze films

On the basis of the momentum integral method and the microcontinuum theory, the combined effects of total fluid inertia forces and non-Newtonian couple stresses on the non-linear squeeze film characteristics between parallel circular discs are presented. The squeeze-film lubrication equation is derived from the Stokes couple-stress motion equation retaining total fluid inertia terms to take into account the effects of non-Newtonian couple stresses resulting from the base oil blended with various types of additives, and the effects of local fluid inertia and convective fluid inertia. The non-linear motion equation for the squeezing disc is then numerically solved by using fourth-order Runge-Kutta method. Comparing with the Newtonian-lubricant inertialess case, the combined effects of fluid inertia forces and non-Newtonian couple stresses provide a significant increment in the response time of the squeeze film. The operating life of squeeze film discs are therefore lengthened, especially for larger couple stress parameters, Reynolds numbers and body inertia parameters. A design example is provided to facilitate the engineers assessing the extent to design the non-linear squeezing film discs considering the combined effects of total fluid inertia forces and non-Newtonian couple stresses.

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.

Frictionless compression testing using load-applying platens made from porous graphite aerostatic bearings

In compression testing of soft materials at high strains, friction between a sample and the load-applying platens induces a differential lateral expansion that is visually evident as barreling. Barreling reduces the accuracy of the tests as a means of establishing accurate material properties. Current techniques for reducing friction, which involve liquid squeeze film lubrication, may not achieve true frictionless interfaces, are messy, and may adversely affect some samples. This article examines the use of porous graphite aerostatic bearings as a frictionless testing interface. The physics of a soft material under compressive loading by porous air bearings is investigated with simple finite element analysis and air flow models. An aerostatic bearing assembly is also constructed and compared to other friction reduction techniques. The results of these experiments indicate that there are benefits to using air bearings as they are clean, chemically inert, extremely stiff, reduce friction to levels comparable to existing methods, have negligible squeeze film effect, are repeatable, and allow for cyclic compression testing.

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.

On the squeeze film lubrication of long porous journal bearings with couple stress fluids

PurposeThis paper aims to advance the squeeze film characteristics of long partial journal bearings with couple stress fluid studied by Lin to include the effect of permeability on the squeeze film lubrication of long partial porous journal bearings with couple stress fluids.Design/methodology/approachA semi‐analytical and semi‐numerical solution for the squeeze film lubrication of long porous partial journal bearings lubricated with couple stress fluid is presented in the paper. The modified Reynolds equation governing the fluid film pressure is derived. The modified Reynolds equation is solved analytically and closed form expressions for the squeeze film pressure and load carrying capacity are presented. The first‐order non‐linear equation for the time‐height relation is solved numerically with the given initial condition. The effect of couple stresses and permeability on the squeeze film characteristics are discussed.FindingsIt is found that the effect of couple stresses is to increase the load carrying capacity and to lengthen the squeeze film time as compared to the corresponding Newtonian case. The effect of permeability is to reduce the load carrying capacity and to decrease the squeeze film time as compared to the corresponding solid case.Originality/valueIn the design of porous partial journal bearings, the reduction in the load carrying capacity and the response time can be compensated by the use of lubricants with proper microstructures by which the bearing life can be increased.

Squeeze-Film Lubrication of the Human Ankle Joint Subjected to the Cyclic Loading Encountered in Walking

Squeeze-film lubrication of the human ankle joint during walking is numerically analyzed, the effect of surface sliding being neglected at this stage. Biphasic mixture models are considered for synovial fluid (an ideal and viscous fluid phases) and for articular cartilage (an ideal interstitial fluid and an elastic porous matrix). In the model, the ideal fluid phase passes through the articular surface and matrix pores. The cartilage matrix is considered both normal and pathological (with primary osteoarthrosis). Calculations show that water and small solutes of synovial fluid imbibe into the articular cartilage during the stance period, while the interstitial fluid of the cartilage exudes and enriches the lubricant during the swing period in a central part of the contact at each step. Soon after the onset of walking, repeatedly near the load culmination of each step, the synovial fluid should be turned into a synovial gel and, shortly after, changed back again into a fluid there. In the pathological case, the protective synovial gel layer is quickly depleted after several steps and the surfaces may come briefly into contact in each cycle. With normal cartilage, however, the protective intermittent gel film (formed briefly at each step) maintains its thickness for a longer time. Normal cartilage also behaves more favorably, when a long walk is broken and then resumed shortly afterwards. With normal articular cartilage, maintenance of a lubricating fluid film is much aided by the cyclic nature of the loading encountered in walking, compared with the steady loading in standing where the fluid film is quickly filtered out into a protective permanent gel film.

On the squeeze effect of lubricants with additives between rough porous rectangular plates

AbstractThis paper describes a theoretical analysis of the combined effects of unidirectional surface roughness and the lubricant additives on the performance characteristics of a porous squeeze film lubrication between two rectangular plates of finite dimensions. The lubricant with microstructure additives is modeled as a Stokes couplestress fluid. The stochastic Reynolds type equation is derived to account for the effects due to surface roughness and lubricant additives. The problem is solved analytically using the stochastic method developed by Christensen. It is found that, there exists a critical value of the aspect ratio above which the roughness effects are pronounced due to the size effects of the lubricant additives. Further, this critical value is dependent on the microstructure size of additives. The coarser the microstructure, higher is the critical value of the aspect ratio.

Appropriate radial clearance of ceramic-on-ceramic total hip prostheses to realize squeeze-film lubrication

Objective. Estimation of appropriate radial clearance of ceramic-on-ceramic total hip prostheses to realize squeeze-film lubrication. Background. Some clinical results show that severe wear occurs at ceramic-on-ceramic interfaces of total hip prostheses if the design parameters are improper. Appropriate design is required to realize the optimum lubrication of joint prostheses. Design. Squeeze-film thickness of total hip prostheses with different radial clearances was numerically estimated under the physiological conditions of normal walking. Methods. The changes in the fluid film thickness between ceramic balls and a ceramic cups with radial clearances of various values from 10 to 80 μm were numerically estimated under the assumption of normal walking conditions by means of elastohydrodynamic squeeze-film lubrication theory including the three-dimensional theory of elasticity. Results. The minimum film thickness remained over 0.02 μm during a few walking steps with a radial clearance under 20 μm and a head diameter of 28 mm. On the other hand, the fluid film was squeezed out during a few steps when the radial clearance was greater than 30 μm. Conclusions. Squeeze-film lubrication can be realized in a ceramic-on-ceramic total hip prosthesis if the radial clearance is smaller than 20 μm on a head of 28 mm diameter. Relevance Fluid film lubrication is necessary to prevent the severe wear of ceramic joint prostheses. The present investigation shows which radial clearance of ceramic-on-ceramic hip prostheses is appropriate for squeeze-film lubrication under physiological conditions in daily action.

Squeeze-film of unconformal, compliant and layered contacts

Compliant and permeable layered surfaces are used in natural synovial joints and have been proposed for the bearing surface in artificial joint replacements. The squeeze-film lubrication mechanism plays an important role in long-term performance of both natural and artificial joints. The full lubrication solution of the present problem including compliance and permeability is not available yet in the literature. The present study analyses the squeeze effect for a layered contact in two distinct cases: • Impermeable and compliant layer for a spherical contact, based on Winkler assumption. For a spherical hip joint, yields to an optimal clearance, which gives the most persistent film. • Porous and deformable layer with variable permeability, imbibed with lubricant, for spherical and plane contact, based on a novel mechanism, named Ex-Poro-Hydrodynamic (XPHD). The results obtained put in evidence an optimum initial compacticity for the porous matrix. The comparison with the well known model of McCutchen [Wear 1962;5:1-17] shows good agreement.

Lubricant additives effects on the squeeze film lubrication between anisotropic porous rectangular plates

In the present paper, the squeeze film lubrication between anisotropic porous rectangular plates with lubricants containing polar additives has been studied. The lubricants containing additives has been modelled as a Stokes couple stress fluid. The more realistic Beavers‐Joseph slip boundary conditions are used to derive the most general form of Reynolds equation, which account for the effects due to the lubricant additives and the anisotropic nature of porous material. The eigen type of expressions are obtained for the fluid film pressure, load carrying capacity and squeeze film time. It is observed that the effect of the lubricant additives is to increase the load carrying capacity and the squeeze film time as compared to the Newtonian lubricants. Further for anisotropic porous surface, the maximum load carrying capacity is attained for the rectangular (non‐square) plates.

Couple-stress squeeze films between porous rectangular plates

In this paper, the squeeze-film lubrication theory between two isotropic porous rectangular plates has been advanced to analyse the effects of couple stresses arising due to the presence of microstructure additives in the lubricant, using the Stokes theory of couple-stress fluids. The most general form of the modified Reynolds equation is derived for the squeeze-film lubrication of the porous rectangular plates by taking into account of the velocity slip at the porous interface. An eigentype of expression is obtained for the squeeze-film pressure. The effects of the isotropic permeability, the couple stresses and the velocity slip parameters on the characteristics of the squeeze-film lubrication are discussed. A significant increase in the load-carrying capacity and the delayed squeeze-film time are observed for the couple-stress fluids in comparison with Newtonian fluids.

The influence of the acetabular labrum seal, intact articular superficial zone and synovial fluid thixotropy on squeeze-film lubrication of a spherical synovial joint

A model of synovial fluid (SF) filtration by articular cartilage (AC) in a step-loaded spherical synovial joint at rest is presented. The effects of joint pathology (such as a depleted acetabular labrum, a depleted cartilage superficial zone consistent with early osteoarthritis and an inflammatory SF) on the squeezed synovial film are also investigated. Biphasic mixture models for AC (ideal fluid and elastic porous transversely isotropic two-layer matrix) and for SF (ideal and thixotropic fluids) are applied and the following results are obtained. If the acetabular labrum is able to seal the pressurised SF between the articular surfaces (as in the normal hip joint), the fluid in the synovial film and in the cartilage within the labral ring is homogeneously pressurised. The articular surfaces remain separated by a fluid film for minutes. If the labrum is destroyed or absent and the SF can escape across the contact edge, the fluid pressure is non-homogeneous and with a small jump at the articular surface at the very moment of load application. The ensuing synovial film filtration by porous cartilage is lower for the normal cartilage (with the intact superficial zone) than if this zone is already depleted or rubbed off as in the early stage of primary osteoarthritis. Compared with the inflammatory (Newtonian) SF, the normal (thixotropic) fluid applies favourably in the squeezed film near the contact centre only, yielding a thicker SF film there, but not affecting the minimum thickness in the fluid film profile at a fixed time. For all that, in the unsealed case for both the normal and pathological joint, the macromolecular concentration of the hyaluronic acid–protein complex in the synovial film quickly increases due to the filtration in the greater part of the contact. A stable synovial gel film, thick on the order of 10 −7 m, protecting the articular surfaces from the intimate contact, is formed within a couple of seconds. Boundary lubrication by the synovial gel is established if sliding motion follows until a fresh SF is entrained into the contact. This theoretical prediction is open for experimental verifications.