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.     

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.     

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.     

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.     

Squeeze films in full porous metal bearings

The behaviour of squeeze films in porous journal bearings under a steady load is analysed. A full journal bearing with a non-rotating journal is considered. The Reynolds equation governing the pressure in the film region is modified to take account of the mass exchange of the lubricant between the film and the bearing matrix. In the case of thin-walled bearing (H?R), the modified Reynolds equation takes a simpler form. However, since this equation cannot be solved directly as applied to a finite bearing, solutions in a closed form are found both for the long bearing and narrow bearing approximations. It is found that the permeability of the bearing matrix and the wall thickness of the bearing adversely affect the load capacity and greatly reduce the time needed for the journal to attain a given eccentricity. With a permeable bearing, there is the possibility of the journal coming into contact with the bearing (ε=l) in a finite time. Generally the performance of a long bearing is better than that of a narrow bearing.     

考虑颗粒分布影响的液-固二相流体润滑研究

对多颗粒分布的液-固二相流体润滑进行了研究。对有颗粒存在时的润滑区域进行划分,建立了多颗粒状态下的雷诺方程,引进颗粒的速度、大小、位置,颗粒间的距离等参数,在给定油膜承载力的情况下运用有限元法对有限长滑块进行了数值求解。结果表明:颗粒的存在使颗粒附近的压力分布有了明显的变化;油膜承载力越大,颗粒对压力分布、最小油膜厚度的影响越明显;颗粒处于运动状态或静止状态对压力分布和最小油膜厚度的影响趋势是一致的,但运动颗粒的影响程度较小些;颗粒间的距离、颗粒半径、颗粒数目对压力分布也有比较大的影响。     

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.     

Modified Reynolds Equation for Different Types of Finite Plates with the Combined Effect of MHD and Couple Stresses

We make an effort to analyze the behavior of squeeze film characteristics of different finite plates with couple stress fluid in the presence of a transverse magnetic field. On the basis of the Stokes couple stress fluid model and hydromagnetic flow model, a modified Reynold's equation is derived, which is solved by using appropriate boundary conditions to obtain squeeze film pressure, load-carrying capacity, and squeeze film time. The graphical representation of the results suggests that the different bearing systems register an enhanced performance with couple stresses compared to that of a bearing system working with a conventional lubricant in the presence of a transverse magnetic field. It is observed that the effect of applied magnetic field on the squeeze film lubrication between different finite plates with conducting couple stress fluids is to increase the load-carrying capacity significantly and to delay the time of approach compared to the corresponding nonconducting Newtonian case. It is seen that for all of the finite plates of different shapes, the circular shape gives the maximum load and time.     

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.     

Effect of roughness on hydromagnetic squeeze films between porous rectangular plates

The theoretical investigations made in this paper are to study the combined effects of unidirectional surface roughness and magnetic effect on the performance characteristics of a porous squeeze film lubrication between two rectangular plates. The stochastic Reynolds equation accounting for the magnetic effect and randomized surface roughness structure is mathematically derived. The expressions for dimensionless pressure, load carrying capacity and squeeze film time are obtained. Results are computed numerically and it is observed that a roughness effect enhances pressure, load carrying capacity and squeeze film time.     

Effect of pressure dependent viscosity on squeeze film characteristics of micropolar fluid in convex curved plates

In this paper, the effect of pressure dependent viscosity on the squeeze film characteristics between convex curved plates of a cosine form is presented. Micropolar fluid theory, which is a possible non-Newtonian model of a suspension of rigid particle additives, is applied to the study of the lubrication of cosine form convex curved plates. The modified Reynolds equation is solved for the fluid film pressure and then the cosine form by considering the exponential relationship in the viscosity variation. For iso-viscous lubricants, the effects of pressure dependent viscosities signify an increase in the values of the squeeze film pressure, the load capacity and the elapsed time. It provides useful information in designing the mechanisms of squeeze film plates for engineering application.     

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.     

Theoretical investigation of transient elastohydrodynamic lubrication with newtonian solid‐liquid lubricants

This paper reports a theoretical investigation of transient elastohydrodynamic lubrication of a line contact. A time‐dependent Reynolds equation and elasticity equations for compressible solid‐liquid lubricants were solved using finite volume and multigrid techniques. The lubricants used were mineral oils mixed with very small solid particles, MoS₂ and PTFE, which can be treated as Newtonian fluids. The two surfaces were initially at rest and in contact. The transient oil film pressure and oil film thickness were calculated numerically. This simulation showed the significant effects of solid particles on the lubrication characteristics.     

A new theory of lubrication for rough surfaces

A new theory of lubrication for rough surfaces is presented and a generalized form of the Reynolds equation is derived. A form of the Reynolds equation applicable to mixed lubrication conditions is obtained.In the case of a squeeze film it is shown that the load capacity increases as surface roughness increases.     

Squeeze films in porous circular disks

The squeeze film behaviour between two circular disks is analysed. The governing equations are derived when one disk has a porous facing. The fluid in the film region satisfies the modified Reynolds equation and the flow in the porous facing. satisfies the Laplace equation. These equations are solved in closed form and expressions are derived for pressure distribution, load capacity and time of approach for the plates. It is found that with a suitable value of permeability for the porous facing, the pressure distribution becomes more even leading to uniform wear of the entire facing; however, increasing permeability has an adverse effect on the load capacity and time of approach. Numerical data, useful in the design of clutch plates with a porous lining, is given in tabular form.     

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.     

Numerical investigation of pocketed slip slider bearing with non-Newtonian lubricant

Boundary slip as well as surface texturing is an effective method to improve the tribological performance of lubricated mechanical components. This article analyzes the combined effect of single texturing (pocketing) and wall slip on pressure that strongly related to the load-carrying capacity of slider bearing. The modified Reynolds equation for lubrication with non-Newtonian power-law fluid is proposed. The equation was solved numerically using a finite difference equation obtained by means of the micro-control volume approach. Further, numerical computations for slider bearing with several power-law indexes were compared with the presence of the pocket and slip. The numerical results showed that the characteristic of non-Newtonian is similar to Newtonian fluid with respect to hydrodynamic pressure distribution. The maximum load support is achieved when the pocket depth is equal to the film thickness.     

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.     

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.     

Squeeze film characteristics of parallel circular disks lubricated by ferrofluids with non-Newtonian couple stresses

The parallel circular squeeze film disks with a non-Newtonian ferrofluid in the presence of transverse magnetic fields are investigated in this paper. A modified Reynolds equation is derived by applying the Shliomis ferrohydrodynamic model incorporating the Stokes microcontinuum theory. Some special cases can be recovered from the present study. Comparing with the Newtonian non-ferrofluid case, the non-Newtonian ferrofluid lubricated squeeze films provide a higher load capacity and lengthen the approaching time. Some numerical results of the load capacity for various parameters are also included in a table for engineering applications.