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.     

Combined effects of surface roughness and viscosity variation due to additives on long journal bearing

Abstract

The combined effects of surface roughness and viscosity variation due to additives on long journal bearing are analytically studied. The variation in viscosity along the film thickness is considered. The presence of solid particles in the lubricant is an increased effective viscosity, which increases the load carrying capacity and decreases the frictional coefficient, whereas the viscosity variation tends to decrease both the load carrying capacity and coefficient of friction for non-micropolar fluid case. The modified Reynolds type equation for surface roughness has been derived on the basis of Eringen’s micropolar fluid theory. The generalised stochastic random variable with non-zero mean, variance and skewness is assumed to mathematically model the surface roughness on the bearing surface. Numerical results were obtained for the fluid film pressure, load carrying capacity and the coefficient of friction. It is observed that the combined effect is to increase the load carrying capacity and to decrease the coefficient of friction, which improves the performance of the bearing.     

Static and dynamic characteristics of finite exponential film shaped slider bearings lubricated with micropolar fluid

Abstract

In this paper, the general dynamic Reynolds equation of sliding–squeezing surfaces of exponential shaped slider bearings with micropolar fluid is solved numerically for the assessment of dynamic characteristics. The two Reynolds type equations governing the steady performance and the perturbed characteristics are obtained using the perturbation technique and are solved numerically using the finite difference method. The results are compared with that of the inclined plane slider bearing. It is found that the exponential shaped slider bearing lubricated with micropolar fluids results in higher steady state film pressure, load carrying capacity and better dynamic stiffness and damping characteristics.     

The effect of additives in the lubricant of a composite bearing with an inclined stepped surface

A micropolar fluid, which is characterized by the presence of suspended rigid particles with microstructure, can be used as a model for lubricants containing suspended additive particles. The theory is applied to the study of the lubrication of an inclined stepped composite bearing with an additive-containing lubricant. The theory yields results showing an increase in the load-carrying capacity and a reduction in the coefficient of friction which are in agreement with experimental observations.     

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.     

Effects of lubricant additives on the performance of hydrodynamically lubricated journal bearings

A non-Newtonian rheological model to investigate theoretically the effects of lubricant additives on the steady state performance of hydrodynamically lubricated finite journal bearings is introduced. In this model, the non-Newtonian behavior resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman-extended Darcy equations are utilized to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry, and non-Newtonian behavior of the lubricant on the steady-state performance characteristics such as pressure distribution, load carrying capacity, side leakage flow, and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load carrying capacity and reduce both the coefficient of friction and the side leakage as compared to the Newtonian lubricants.     

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.     

Lubricant additives effects on the hydrodynamic lubrication of misaligned conical–cylindrical bearings

Conical–cylindrical bearings are used in electrohydraulic servo systems to improve the control accuracy, eliminate the static friction and increase the normal load‐carrying capacity. A non‐Newtonian rheological model to investigate theoretically the effects of lubricant additives on the performance of misaligned conical–cylindrical bearings is proposed in this study. In this model, the non‐Newtonian behaviour resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman‐extended Darcy equations are utilised to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. The misalignment of the cylinder rod is also considered. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry and non‐Newtonian behaviour of the lubricant on the steady‐state performance characteristics such as pressure distribution, load‐carrying capacity and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load‐carrying capacity and reduce the coefficient of friction as compared to the Newtonian lubricants. Furthermore, the misalignment of the piston rod has significant effects on the performance of conical–cylindrical bearings. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical analysis of journal bearings lubricated with micropolar fluids including thermal and cavitating effects

A numerical study of the non-Newtonian behavior for a finite journal bearing lubricated with micropolar fluids is undertaken considering both thermal and cavitating effects. The modified Reynolds equation and energy equation are derived based on Eringen's micropolar fluid theory. The solution to the modified Reynolds equation is determined using the Elord's cavitation algorithm. The effects of the size of material characteristic length and the coupling number on the thermohydrodynamic performance of a journal bearing are investigated. It is shown, compared with Newtonian fluids, that micropolar fluids exhibit the increase in load capacity and temperature, but the decrease in coefficient of friction and side leakage flow. It is also indicated that, in the full film region, micropolar fluids increase the values of non-dimensional density, while in the cavitated region, both micropolar fluids and Newtonian fluids yield the same values of the fractional film content.     

Analysis of squeeze film performance between rough porous infinitely long parallel plates with porous matrix of non-uniform thickness under presence of magnetic fluid lubricant

Abstract

The performance of a magnetic fluid based squeeze film between infinitely long porous rough parallel plates with porous matrix of non-uniform thickness has been investigated. The bearing surfaces are considered to be transversely rough. The stochastic film thickness characterising the random roughness is assumed to be asymmetric with non-zero mean and variance. A magnetic fluid is used as a lubricant and the external magnetic field is oblique to the lower plate. With usual assumptions of hydrodynamic lubrication the associated Reynolds' equation is solved with suitable boundary conditions. Then expressions for pressure distribution, load carrying capacity and response time are obtained. It is observed that the load carrying capacity increases nominally due to magnetic fluid lubricant resulting in improved performance. But it is also seen that the composite roughness of the bearing surfaces introduces an adverse effect which gets more compounded due to the thickness ratio. However, the negative effect can be compensated to certain extent by the magnetic fluid lubricant in the case of negatively skewed roughness. This compensation further enhances when negative variance is involved. This study tends to suggest that the thickness ratio may play a crucial role for a better performance of the magnetic fluid based bearing system besides providing an additional degree of freedom.     

Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model

A numerical solution for the hydrodynamic lubrication of finite porous journal bearings considering the flexibility of the liner is introduced. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region and fluid film region, respectively. A stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included into the lubrication analysis. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearing, is implemented in the solution scheme. The present analysis predictions for pressure distributions, load carrying capacity, and friction factor are in good agreement with three different sets of experimental results available in the literature. Furthermore, the effects of dimensionless permeability parameter, and stress jump parameter on performance parameters such as load carrying capacity, side leakage, friction factor, and attitude angle, are presented and discussed.     

The squeeze film in an inclined porous slider bearing

The behaviour of a squeeze film in an inclined porous slider bearing is analysed. Expressions for pressure, load capacity, friction, coefficient of friction and the position of the centre of pressure are obtained. Pressure, load capacity and friction are increased as a result of squeeze. The coefficient of friction is decreased and the centre of pressure is unaffected. An expression for the time-height relation is given.     

The squeeze film in a porous composite slider bearing

The squeeze film behaviour in a porous composite slider bearing is analysed. Expressions for the pressure, the load capacity, the friction and the position of the centre of pressure are obtained. The pressure, load capacity and friction are increased owing to the squeeze and the position of the centre of pressure moves slightly towards the inlet face. An expression for the time-height relation is also obtained. The response time for a composite slider bearing is greater than that for an inclined slider bearing.     

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.     

复合材料水润滑艉轴承结构设计研究

基于ANSYS CFX流固耦合数值计算方法,对水润滑复合材料艉轴承的润滑性能及结构设计开展研究,阐述了不同水槽结构、间隙比、长径比、直径等对轴承承载力以及水膜压力、轴承变形量、最小水膜厚度、轴承摩擦因数的影响规律。并利用水润滑轴承试验台研究了不同水槽结构对轴承启动摩擦转矩、转变速度以及摩擦因数的影响。研究表明,轴承摩擦因数、水膜最大压强、轴承最大变形随水槽数增多而增大;轴承承载力、最小水膜厚度随间隙比增大而减小,随长径比增大而增大。总结了直径为100~500 mm、长径比为2~3、间隙比为0.1%~0.2%的水润滑艉轴承承载力的变化规律,为水润滑艉轴承设计提供一定的理论依据。     

Effect of deformation in magnetic fluid based transversely rough short bearing

Abstract

This investigation aims to analyse the performance of a magnetic fluid based rough short bearing incorporating a deformation effect. The associated stochastically averaged Reynolds equation is solved with suitable boundary conditions to obtain the expression for pressure distribution, which results in the calculation of the load carrying capacity. The expression for the friction is obtained for both plates. It is seen that the load carrying capacity increases nominally as a result of the magnetic fluid lubricant. Furthermore, the film thickness ratio increases the load carrying capacity. It is found that the load carrying capacity increases as the ratio of the length/outlet film thickness increases, while this trend is reversed in the case of magnetisation. Moreover, it is noticed that friction remains unaltered because of the magnetic fluid lubricant. Furthermore, it is interesting to note that the deformation also unalters the friction. This article suggests that the negative effect of the standard deviation can be neutralised up to a certain extent by the combined positive effect of the magnetisation parameter, the film thickness ratio and the ratio of the length/outlet film thickness, especially when the deformation is relatively less. Therefore, this study offers some scopes for extending the bearing’s life. Finally, the bearing can support a load even in the absence of flow, unlike in the case of conventional lubricant.     

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.     

Micropolar fluid squeeze film lubrication of finite porous journal bearing

In this paper, the effect of micropolar fluid on the static and dynamic characteristics of squeeze film lubrication in finite porous journal bearings is studied. The finite modified Reynolds equation is solved numerically using the finite difference technique and the squeeze film characteristics are obtained. According to the results obtained, the micropolar fluid effect significantly increases the squeeze film pressure and the load-carrying capacity as compared to the corresponding Newtonian case. Under cyclic load, the effect of micropolar fluid is to reduce the velocity of the journal centre. Effect of porous matrix is to reduce the film pressure, load-carrying capacity and to increase the journal centre velocity.     

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.     

A study of optimum load capacity of slider bearings lubricated with power law fluids

A general theoretical study of an infinitely wide lubricated slider bearing is presented, considering the lubricant to be an incompressible, isothermal, power law fluid. A set of algebraic equations is developed to obtain the pressure gradient for any value of the power law index. To illustrate the mathematical development, the set of equations is used to calculate the pressure gradient for two special forms of slider bearings, viz., inclined and parabolic slider bearings. In these two cases, the variation of pressure, load capacity, coefficient of friction, etc. for a range of fluid- and bearing-parameters is presented. In order to obtain optimum load capacity for an inclined and a parabolic slider bearing, the variations of load capacity, coefficient of friction, etc., with respect to the simultaneous changes of the inlet–oulet film height ratio and of the power law index of lubricants are also analysed. The results are presented both numerically and graphically. The results reveal that in the cases of an inclined and a parabolic slider bearings the inlet–outlet film height ratio for the optimum load capacity depends on the power law index of lubricants. Further, for each value of power law index, there exists a value of inlet–outlet film height ratio for which the frictional coefficient is minimum.