Effect of velocity slip on porous-walled squeeze films

The analysis of the squeeze films between porous discs of various shapes is extended to include the effect of velocity slip at the fluid and porous material interface. Modified equations for calculating the pressure, load carrying capacity and the film thickness and time relation are presented. A simple mathematical analogue for determination of the squeeze film behaviour for porous discs with slip consideration from the already available solution (without slip) is given.     

Effect of velocity-slip on the squeeze film between porous reactangular plates

The analysis of the squeeze film between porous rectangular plates⁴ is extended to include the effect of velocity slip at the fluid and porous material interface. Modified equations for calculating the pressure, the load-carrying capacity, and the film thickness and time relation are presented. The results indicate that the existence of slip velocity will further reduce the load-carrying capacity and the response time of the squeeze film.     

Effects of velocity slip,anisotropy and tilt on the steady state performance of aerostatic porous annular thrust bearings

The analysis predicts the steady state performance characteristics of externally pressurized annular porous gas thrust bearings of finite pad thickness. The modified Reynolds equation, governing the flow in the bearing clearance, is derived from the Navier-Stokes equations using the Beavers-Joseph slip velocity condition at the porous interface. The anisotropy of the porous matrix and the tilt of the bearing are also taken into account. The dimensionless load capacity, the mass rate of flow and the static stiffness are computed numerically and presented in the form of charts for various operating parameters and bearing dimensions. The effect of slip is to reduce the load capacity and to increase the mass rate of flow for all values of the feeding parameter.     

Analysis of an anisotropic porous slider bearing considering slip velocity

A porous slider bearing with anisotropic permeability and slip velocity is considered. Expressions for the load-carrying capacity, friction, coefficient of friction and the position of the centre of pressure are obtained in integral form. Anisotropic permeability and slip affect these bearing characteristics.     

Effect of slip flow in aerostatic porous rectangular thrust bearings

A theoretical analysis of the static characteristics of aerostatic porous rectangular thrust bearings with uniform film thickness is presented. A modified form of the Beavers-Joseph slip velocity boundary condition is applied at the interface of the porous pad and the lubricating film. When the thickness of the pad is small compared with the other two dimensions, the pressure distribution in the porous media is obtained in closed form and the modified Reynolds equation can be solved numerically by the finite difference method. The load capacity, mass flow rate of the gas and static stiffness are expressed in dimensionless form and calculated numerically for different operating parameters. Velocity slip reduces the load capacity and the mass flow rate of the gas and depends on the feed parameter for its effect on stiffness.     

Micropolar squeeze films in porous hemispherical bearings

Micropolar fluid theory is used to analyse the behaviour of squeeze films in porous hemispherical bearings using velocity slip conditions. It is shown that porosity and slip decrease the load capacity and squeeze time. The effect of micropolarity is to increase them, especially when the bearing clearance is small.     

A simplified method for the correction of velocity slip and inertia effects in porous aerostatic thrust bearings

Inertia effects in porous material, as well as velocity slip at the porous bearing surface, have hindered the use of simple mathematical models for the analyses of porous aerostatic bearings. Experimental evidence indicated that velocity slip at the porous surface did not obey the Beavers model, but could be approximated by an added equivalent clearance. This experimentally determined clearance value did not bear any direct relationship with the surface roughness of the test specimen. Good agreement between theoretical and experimental results of static load capacity of a porous ceramic test bearing, however, demonstrated the use of this equivalent clearance method, in conjunction with a proposed approximation to correct for inertia effects, as an effective modification to the simple one-dimensional model by Sheinberg.     

The hydromagnetic squeeze film between porous circular disks with velocity slip

The effect of velocity slip on the behaviour of a squeeze film between two circular disks when a uniform magnetic field is applied between them was studied. The upper disk which has a porous facing backed by a solid housing approaches the lower disk with a uniform velocity. Results are presented for the pressure distribution, the load-carrying capacity and the film thickness as a function of time. The load-carrying capacity decreases as the permeability parameter increases and decreases further as the slip parameter increases.     

Steady state solution of finite hydrostatic porous oil journal bearings with tangential velocity slip

A theoretical investigation has been made into the static characteristics of hydrostatic porous oil bearings with tangential velocity slip at the porous interface. A numerical method has been employed to solve the governing differential equations with a wide range of bearing parameters. Slip has been conventionally treated by choosing permeability factors and slip coefficients as independent parameters, and also more realistically by choosing practical values of shaft radius/radial clearance and slip coefficients as independent parameters. The effect of slip, eccentricity ratio, slenderness ratio, speed parameter and anisotropy of permeability on the load carrying capacity, friction coefficient, attitude angle and the oil flow rate has also been investigated. The results are presented in the form of graphs which may be useful for design of such bearings.     

流体静压多孔质球面轴承静态性能分析

对流体静压多孔质球面轴承进行理论分析,给出了其有限元计算方法,同时利用实验验证理论计算的正确性。结果表明,气体静压实验数值和有限元计算结果吻合良好,实验数值和有限元计算结果之间的误差小于10%,产生误差的原因是有限元数值计算没有考虑到流体的惯性效应、速度滑移、多孔质球窝的变形以及轴承表面粗糙度的影响;气体静压球面轴承的承载能力和静态刚度明显小于液体静压球面轴承,气体静压球面轴承刚度低的主要原因是所用的多孔材料孔隙度较大,即多孔材料的渗透率较大。     

Theoretical analysis and experimental investigation of a porous metal bearing

To improve the tribological behaviour of porous bearings a new type of self-lubricated porous metal bearing is introduced with special non-uniform distribution of permeability. It has been manufactured using a practical production process, its local permeability varying regularly along its circumference. Theoretical analysis and experimental investigation show that: the new bearing has lower friction and higher load capacity than that of ordinary porous bearings, and there is no initial temperature rise and friction increase with the new bearing. The limiting pV(tested) value of the new bearing is about 200% that of an ordinary porous bearing. Considering non-uniform permeability and the effects of curvature, cavitation and velocity slip, a modified Reynolds equation for the oil film and lubrication equation for the porous matrix are derived. A numerical solution for the equations is obtained. Some aspects of the lubrication mechanism in porous bearings and ways of improving load capacity are also discussed.     

Ferrofluid lubrication in porous inclined slider bearing with velocity slip

The effects of slip velocity and the material constant in a porous inclined slider bearing lubricated with a ferrofluid were theoretically studied by using Jenkins model. Expressions were obtained for pressure, load capacity, friction on the slider, coefficient of friction and position of the centre of pressure. The increase in slip parameter caused decrease in load capacity as well as friction and increase in the coefficient of friction without altering the centre of pressure much. As the material constant increased, the load capacity decreased, friction and coefficient of friction increased and the position of the centre of pressure shifted slightly towards the inlet of the bearing.     

局部多孔质气浮止推轴承的设计研究

建立了局部多孔质气浮轴承的理论模型,该模型考虑了轴承气膜交界面处的切向速度滑移。利用有限元方法对所建立的模型进行了理论仿真,轴承静态特性的仿真与试验结果取得了较好的一致性,说明经过修改后的雷诺方程可以用来作为局部多孔质气浮轴承研究的理论模型。利用该模型成功计算出不同渗透系数、不同厚度及不同直径的局部多孔质气浮轴承的流量、承载及刚度特性,并给出了相应的变化曲线。根据仿真结论,提出了局部多孔质气浮止推轴承的设计准则。另外,从理论上将该类轴承与全多孔质类型气浮轴的承特性进行了对比,表明局部多孔质气浮轴承有着优良的特性,有很好的应用前景。     

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.     

The effects of velocity slip on externally pressurized gas porous thrust bearings

A numerical analysis is presented for the velocity slip on an externally pressurized gas porous bearing consisting of a circular pad with a central partially gas-supplied area and sealed circumferential area. Non-axial flow is assumed in the porous matrix. The modified Beavers-Joseph boundary condition of velocity slip is applied at the interface of the porous matrix and lubricating film. The result shows that the solution with the consideration of velocity slip on porous surface tends to agree with the experimental data for increasingly higher values of bearing number.     

Effect of axial pinch on the porous walled squeeze film with velocity slip

The problem of studying the effect of axial current induced pinch on squeeze film behaviour with velocity slip between two annular disks, the upper disk having a porous facing, is analysed. Analytical results are obtained for pressure distribution, load capacity and time-height relations. The pinch effect considerably modifies the action of the squeeze film.     

Squeeze film lubrication of a short porous journal bearing with couple stress fluids

This paper presents the theoretical investigations of the rheological effects of the couple stress fluids on the static and dynamic behaviour of the pure squeeze films in the porous journal bearings. The present study predicts the effects of percolation of the polar additives (microstructures) into the porous matrix on the performance of squeeze films in the porous journal bearings. The most general modified Reynolds-type equation is derived for a porous journal bearing with no journal rotation. The analysis takes into account of the tangential velocity slip at the porous interface by using the BJ-slip condition. The cases of a short porous journal bearing under a constant applied load and that under an alternating load are analyzed. As compared to the Newtonian lubricants, the lubricants which sustain the couple stresses yield an increase in the load carrying capacity. Under a cyclic load the couple stress fluids provide a reduction in the journal velocity and an increase in the minimum permissible height of squeeze films.     

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.     

Effects of velocity slip on the elastohydrodynamic lubrication of short, porous journal bearings

The studies of Beavers and Joseph indicated that velocity slip takes place at the permeable boundary of porous bearings. The purpose of this article is to make an analytical study of a short, porous journal bearing taking into account both the effects of velocity slip at the film-bearing interface and the flexibility of the bearing. An analytical solution for the performance of such bearings is obtained in terms of several parameters involving porosity, slip coefficient, bearing dimensions and speed.     

Analysis of aerostatic porous journal bearings using the slip velocity boundary conditions

A theoretical analysis of the static characteristics of aerostatic porous journal bearings is presented using the slip velocity boundary condition at the interface of the lubricating film and porous surface of the bearing. With thin wall bearings, the pressure in the porous bushing is obtained in closed form and the modified Reynolds equation is solved numerically using the finite difference method. The load capacity and the mass rate of flow are expressed non-dimensionally and are calculated numerically for different operating conditions. Variation in $\text{W}\text{?}$ and $\text{G}\text{?}$ with the feeding parameter and other parameters is shown graphically. The effect of velocity slip on $\text{W}\text{?}$ and $\text{G}\text{?}$ for different operating conditions was studied. The theoretical results are compared with a similar available solution using a three-dimensional flow model in the bushing. There is near-perfect agreement.