Surface roughness effects on curved pivoted slider bearings with couple stress fluid

In this paper the effect of surface roughness on the performance of curved pivoted slider bearings is studied. A more general type of surface roughness is mathematically modelled by a stochastic random variable with nonzero mean, variance and skewness. The averaged modified Reynolds type equation is derived on the basis of Stokes microcontinuum theory for couple stress fluids. The closed‐form expressions for the mean pressure, load‐carrying capacity, frictional force and the centre of pressure are obtained. Numerical computations show that the performance of the slider bearing is improved by the use of lubricants with additives (couple stress fluid) as compared to Newtonian lubricants. Further, it is observed that the negatively skewed surface roughness increases the load‐carrying capacity and frictional force and reduces the coefficient of friction, whereas the positively skewed surface roughness on the bearing surface adversely affects the performance of the pivoted slider bearings. Copyright © 2006 John Wiley & Sons, Ltd.     

Hydrodynamic analysis of rough curved pivoted porous slider bearings with couple stress fluid

Abstract

The purpose of this paper is to study the effect of surface roughness on the performance of curved pivoted porous slider bearings lubricated with couple stress fluid. The modified B–J slip boundary condition is utilised at the porous/fluid film interface to derive the Reynolds type equation for the problem under consideration. To mathematically model the surface roughness due to non-uniform rubbing of bearing surfaces, a stochastic random variable with non-zero mean, variance and skewness is considered. The closed form solution is obtained for the averaged Reynolds equation, and the compact expressions for the mean fluid film pressure mean load carrying capacity, frictional force and the centre of pressure are obtained. The numerical computations of the results show the improved performance due to the couplestresses and the presence of negatively skewed surface roughness. However, the presence of porous facing and positively skewed surface roughness affects the performance of the pivoted porous slider bearing.     

Effect of Surface Roughness on Hydrodynamic Lubrication of Slider Bearings

The effect of surface roughness on the performance of hydrodynamic slider bearings is studied. A generalized form of surface roughness characterized by a stochastic random variable with non-zero mean, variance and skewness is assumed to define the bearing surface topography. Various film shapes such as: plane slider, exponential, secant and hyperbolic are considered. The results are obtained for the general lubricant film shape in integral form which are numerically computed for the shapes under consideration. The results are presented both graphically as well as in tabular form. The performance of a rough bearing can be considered in terms of an identical smooth bearing with an equivalent film thickness. It is observed, for the lubricant film shapes under consideration, that the increasing positive values of α, σ and ε decrease the load carrying capacity, frictional force and temperature rise while it increases the coefficient of friction. Increasing positive values of α and ε shift the center of pressure towards the outlet edge. For negative values of α, the increasing value reverses the trend of the effect on performance characteristics which is in conformity with the physical aspects of the problem. A similar trend is observed in case of the effect of negative values of ε. Thus, a negatively skewed surface roughness modifies the performance of the slider bearings whereas the performance of a bearing suffers on account of positively skewed surface roughness. Moreover, it is noticed that in the case of exponential and hyperbolic slider bearings the effect of increasing values of σ is more pronounced whereas in case of plane slider and secant shaped slider this effect is marginal.     

Effect of surface roughness on the hydrodynamic lubrication of porous step-slider bearings with couple stress fluids

This paper presents the theoretical study of the effect of surface roughness on the hydrodynamic lubrication of porous step-slider bearings. A more general form of surface roughness is mathematically modeled by a stochastic random variable with non-zero mean, variance and skewness. The generalized average Reynolds-type equation is derived for the rough porous step-slider bearing lubricated with Stokes couple stress fluid. The closed-form expressions for the mean load carrying capacity, frictional force and the coefficient of friction are obtained. The performance of the rough porous step-slider bearing is compared with a corresponding smooth porous step-slider bearing. The numerical computations of the results show that the negatively skewed surface roughness pattern increases the load carrying capacity and decreases the coefficient of friction whereas the adverse effects were found for the positively skewed surface roughness pattern.     

Surface roughness effects in porous inclined stepped composite bearings lubricated with micropolar fluid

In this paper, the effect of surface roughness on the performance characteristic of porous inclined stepped composite bearings is studied. A generalised form of surface roughness is mathematically modelled by a stochastic random variable with non‐zero mean, variance and skewness. The generalised average Reynolds‐type equation is derived for the rough porous inclined stepped composite bearings with micropolar fluid. The closed‐form expressions are obtained for the fluid film pressure, load‐carrying capacity and frictional force. The results are presented for three different types of bearing system. The numerical computations of the results show that the negatively skewed surface roughness pattern increases fluid film pressure and load‐carrying capacity and decreases the coefficient of friction, whereas adverse effects were found for the positively skewed surface roughness pattern. Further, the rough porous inclined stepped composite bearing provides the largest load‐carrying capacity and the least coefficient of friction as compared with the porous plane slider and porous composite tapered concave bearings. Copyright © 2012 John Wiley & Sons, Ltd.     

Inertia Effects on Inclined Slider Bearings Lubricated by a Couple Stress Fluid

This article deals with a numerical investigation of fluid inertia effects on inclined slider bearings lubricated by couple stress fluids. Convective inertial forces are considered in the film fluid. A reduced version of the Navier-Stokes equations is thus derived. The non-Newtonian couple stress behavior of the lubricant is described based on the microcontinuum Stokes theory. The governing partial differential equations are discretized by finite differences based on boundary layer–type equations. The resulting algebraic equations are solved using a Gauss-Seidel method. Compared to the case of the non-inertia Newtonian lubricant, the couple effects of fluid inertia forces and non-Newtonian couple stresses provide a significant improvement in slider bearing load capacity.     

A numerical method for the calculation of lubricant pressures in bearings with mixed lubrication

A model for mixed lubrication, assuming that the total normal load applied to the plane of the lubricated surfaces is carried partly by the hydrodynamic action of the lubrication film and partly by asperity contacts and that the total friction force between the lubricated surfaces is partly due to viscous friction and partly to asperity contacts, was used to develop a numerical solution for pressure distribution in a bearing experiencing mixed lubrication. The geometry treated and the pressure distribution obtained were for a simple slider bearing, but the method could easily be extended to other shapes. The model is based on measured roughness of a real surface. Real load carrying capacity and drag can therefore be determined since they are related directly to bearing pressure distribution     

Squeeze film characteristics of conical bearings with combined effects of piezo-viscous dependency and non-Newtonian couple stresses

In this paper, the analysis of squeeze film characteristics of conical bearings with combined effects of piezo-viscous dependency and couple stress fluid is presented. On the basis of the Stokes microcontinuum theory of couple stress fluid model and Barus experimental research, a modified Reynolds equation is derived, the standard perturbation technique is used to solve the highly non-linear Reynolds equation and approximate analytical solution is obtained for the squeeze film pressure, load carrying capacity and squeeze film time. According to the results obtained, the effect of viscosity pressure dependency on the squeeze film lubrication of conical bearings with couple stress fluids is to improve the load carrying capacity significantly and lengthen the squeeze film time as compared to iso-viscous Newtonian case.     

Coupled effects of surface roughness and flow rheology on elastohydrodynamic lubrication

The coupled effects of surface roughness and flow rheology on elastohydrodynamic lubrication (EHL) circular contact problems are analyzed and discussed. The averaged type Reynolds equation utilizing the average flow model on the interactions between couple stress fluids and surface roughness, the elastic deformation equation, the viscosity–pressure and density–pressure relations equations, and the force balance equation are solved numerically by the multilevel multi-integration (MLMI) algorithm to calculate the pressure distributions and film thickness shapes. The results show that the transverse type roughness and standard deviation of composite roughness enhance the pressure and film thickness in the central contact region. Moreover, the longer the characteristic length of the couple stress fluids is, the smaller the pressure distribution is in the central contact region and the greater the film thickness is in all regions.     

Lubrication of a narrow porous journal bearing with a couple stress fluid

This paper describes a theoretical investigation of the rheological effects of couple stress fluids on the performance of narrow porous journal bearings. A most general modified Reynolds equation is derived for narrow porous journal bearings using the Stokes constitutive equations for couple stress fluids. The fluid in the film region and in the porous region has been modelled as a couple stress fluid. The analysis takes into account velocity slip at the porous interface using the Beavers‐Joseph criterion. A closed‐form expression for field pressure is obtained for narrow journal bearings. Eigen‐type expressions for field variations are obtained. The dimensionless load‐carrying capacity, attitude angle, and coefficient of friction are presented for different operating parameters. It is observed that narrow porous journal bearings with couple stress fluids as lubricant show a significant increase in load‐carrying capacity with reduced coefficient of friction as compared to the Newtonian case. The present study predicts the effects of the percolation of polar additives (microstructures) into the porous matrix on the bearing performance.     

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

Abstract

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 magneto‐hydrodynamic couple‐stress squeeze film lubrication between circular stepped plates

In this paper, a theoretical analysis of the problem of magneto‐hydrodynamic couple‐stress squeeze film lubrication between rough circular stepped plates is presented. The modified averaged Reynolds equation is derived for the two types of one‐dimensional roughness structures, namely the radial roughness pattern and the azimuthal roughness pattern. The closed‐form expressions are obtained for the mean squeeze film pressure, load‐carrying capacity and squeeze film time. The results are presented for different operating parameters. It is observed that the effect of azimuthal (radial) roughness pattern on the bearing surface is to increase (decrease) the mean load‐carrying capacity and squeeze film time. The applied magnetic field increases the load‐carrying capacity and lengthens the squeezing time. Copyright © 2012 John Wiley & Sons, Ltd.     

On the hydrodynamic liquid lubrication analysis of slider/disk interface

A numerical solution for ultrathin hydrodynamic liquid lubrication of slider/disk interface is introduced. Both surface roughness effects and non-Newtonian behavior of the liquid lubricant are incorporated into the hydrodynamic lubrication analysis. A non-Newtonian liquid is used as the lubricant, and its behavior is described by a power-law rheological model. The contact pressure is calculated for a Gaussian surface roughness. The hydrodynamic load capacity is calculated by using an averaged form for the Reynolds equation. The finite difference scheme, with Gauss–Seidel iterative-relaxation method, is applied to solve the average Reynolds equation. The effects of surface roughness parameter, surface pattern parameter, and the power-law exponent on hydrodynamic pressure distribution, hydrodynamic load capacity are studied and discussed.     

Coupled couple stress and surface roughness effects on elasto‐hydrodynamic contact

This paper deals with the combined effects of couple stress and surface roughness to inspect the elasto‐hydrodynamic performance of slider bearing systems. On the basis of the couple stress Stokes theory and homogenisation method, the homogenised generalised Reynolds equation including the slider bearing stationary surface deformation is derived. The total deformation include the deformation of smooth surface, taken into account by the elastic thin layer model, and the deformation of roughness corresponding to a sinusoidal normal displacement on an elastic half space of identical wavelength. The governing equations are discretised by the finite difference method, and the obtained algebraic equations are solved using the iterative overrelaxation Gauss–Seidel technique. The load‐carrying capacity and friction coefficient are presented for transverse, longitudinal and anisotropic roughness patterns for different values of the couple stress parameter in both rigid and deformable cases. The simulation results indicate that the interaction between couple stress, surface roughness and elastic deformation effects is significant. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

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.     

Micropolar fluid squeeze film lubrication between rough anisotropic poroelastic rectangular plates: special reference to synovial joint lubrication

Abstract

The effect of anisotropic permeability on micropolar squeeze film lubrication between poroelastic rectangular plates is studied. The non-Newtonian synovial fluid is modelled by Eringen’s micropolar fluid, and the poroelastic nature of cartilage is taken in to account. The stochastic modified Reynolds equation, which incorporates the elastic as well as randomised surface roughness structure of cartilage with micropolar fluid as lubricant, is derived. Modified equations for the mean fluid film pressure, mean load carrying capacity and squeeze film time are obtained using the Christensen’s stochastic theory for the study of roughness effects. The effects of surface roughness, micropolar fluid and anisotropic permeability on the squeeze film characteristics of synovial joint are discussed. It is found that the surface roughness effects are more pronounced for micropolar fluids as compared to the Newtonian fluids, and the anisotropic nature of permeability of cartilage off-squares the plate size for optimum performance.     

Porous inclined stepped composite bearings with micropolar fluid

Abstract

This paper describes the theoretical analysis of the effect of micropolar fluid on the lubrication characteristics of porous inclined stepped composite bearing. The lubricant with additives in the film region and also in the porous region is modelled as Eringen's micropolar fluid, which is characterised by the presence of suspended rigid particles with microstructures. The generalised Reynolds type equation is derived for the most general porous bearing configuration (porous composite bearings) lubricated with micropolar fluid. The closed form expressions are obtained for the fluid film pressure, load carrying capacity, frictional force and coefficient of friction. These expressions can be utilised to obtain the performance characteristics of four different bearing systems, namely, porous plane inclined slider, porous composite tapered land bearing, porous stepped bearing and composite porous tapered concave bearing. It is observed that the micropolar fluid lubricants provide an increased load carrying capacity and decreased coefficient of friction as compared to the corresponding Newtonian case.     

热效应对粗糙表面倾斜轴颈轴承润滑性能的影响

联立基于平均流量模型的广义Reynolds方程、三维能量方程和固体热传导方程等,计算了计及热效应时,不同表面形貌和轴颈倾斜角下的轴承油膜压力、油膜温度、油膜反力、端泄流量、摩擦系数和保持轴承稳定工作的力矩.考虑和不考虑热效应的轴承润滑特性计算结果表明,计入热效应时,表面形貌和润滑油粘压效应对偏心率较大的轴颈倾斜轴承润滑性能影响较大.     

Inertial MHD Couple Stress Effects on Infinitely Wide Slider Bearings

This article presents a numerical study of magnetohydrodynamic (MHD) infinitely wide plane inclined slider bearings including both fluid inertia and non-Newtonian couple stress effects. Fluid inertia forces are considered in the film fluid using a simplified form of the Navier-Stokes equations. The non-Newtonian couple stress behavior of the lubricant is described based on the microcontinuum Stokes theory. The governing equations are discretized by finite differences using a boundary layer–type equations resolution. The resulting algebraic equations are solved using the Gauss-Seidel method. It is found that the couple effects of fluid inertia forces, MHD, and non-Newtonian couple stresses provide a significant improvement in the slider bearing load capacity compared to the case of the noninertia Newtonian nonconducting lubricant. The use of conducting lubricant diminishes the negative effect of inertia forces on the friction coefficient.