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.     

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.     

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 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.     

Inertia effects in a conical porous bearing with a viscoelastic lubricant

The effects of the inertia and porosity of the bearing material were investigated for conical and squeeze film bearings with a viscoelastic lubricant by the method of averaged inertia. The inertia forces reduce the loadbearing capacity. The porosity of the material decreases the pressure and the load capacity. The effect of the elasticity of the lubricant is to increase the pressure and the load-bearing capacity at any point. The effects of the characteristics of the bearing on the pressure and the load-bearing capacity are presented graphically.     

气体静压径向轴承气膜流场及承载特性分析

研究偏心率及不同供气压强条件下,气体静压径向轴承节流孔附近的气膜流场特性及承载力变化情况,并通过优化节流孔张角,提高轴承承载力。建立气体静压径向轴承三维模型,划分网格并确立模型的边界条件,采用Fluent软件对轴承内部气膜流场进行仿真计算。计算结果表明,气体静压径向轴承偏心率的增加,会导致区域气膜的压力差增大,从而提高轴承的承载力。轴承承载力同样会随着供气压强的增大而增大,但增幅会随着供气压强的增大而逐渐变小。但当供气压强增加到临界值时,由于节流孔附近激波的出现,将导致承载力随着供气压强的进一步增大而降低。通过改变轴承节流孔张角,可消除轴承气膜内的涡流现象,并改善气膜流场特性,降低能量损失,提高轴承承载力。经过分析对比,发现最优节流孔张角介于50°到60°之间。     

近场超声悬浮承载能力及影响因素的理论及实验研究

应用流体动力润滑理论分别建立固定悬浮体以及自由悬浮体的超声气体挤压膜气膜压力模型,并对模型进行数值求解,获得超声频振荡气体挤压膜的压力分布及承载能力,在此基础上利用Christensen平均模型讨论了表面粗糙度对承载能力的影响。结果表明：气体挤压膜具有较大的承载能力,且承载能力大小主要取决于挤压运动的振幅和频率,其中,振幅对气体挤压膜承载力影响最为显著,而频率影响次之。低频范围内,频率对承载力的影响较大,而随着频率的升高其影响逐渐趋于平稳。构造适当的表面纹理可以在一定程度上提高气体挤压膜的承载力。研究结果可以为超声悬浮器件或涉及挤压膜问题的微纳器件设计提供参考。     

The load capacity of a squeeze film between curved porous rotating circular plates

The squeeze film between rotating circular plates is analysed. The curved upper plate approaches the flat non-porous plate normally. The Reynolds equations are uncoupled by using the Morgan—Cameron approximation and closed-form solutions are obtained. Expressions for the pressure and load capacity of the bearing are given. The effect of rotating fluid inertia is to reduce the load capacity of the bearing.     

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.     

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.     

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.     

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.     

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.     

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.     

Squeeze fluid film of spherical hydrophobic surfaces with wall slip

Isothermal squeeze film flow of Newtonian fluid between spherical hydrophobic surfaces with wall slip is investigated using a limiting shear stress model and complementary algorithm. Wall slip velocity is controlled by the liquid–solid interface limiting shear stress. It is found that the wall slip dramatically decreases the hydrodynamic support force of the squeeze fluid film. In the case of large wall slip the hydrodynamic support force increases only slightly with the decrease in the film thickness. We find that wall slip decreases with increasing film thickness and limiting shear stress, but increases with increasing fluid viscosity and approaching velocity. An empirical equation is given for prediction of the fluid load support capacity. The possible effect of pressure on wall slip is also discussed. It is found that fluid pressure suppresses wall slip after the proportionality coefficient of limiting shear stress reaches a critical threshold. However, almost no effect is found when it is below this critical threshold. Good agreements exist between the present theoretical predictions and some existing experimental observations.     

Integrated Numerical Analysis on the Performance of a Hybrid Gas-Lubricated Bearing Utilizing Near-Field Acoustic Levitation

Aerodynamic bearings utilizing near-field acoustic levitation, as a novel hybrid gas-lubricated bearing, can operate with high precision and high rotational speed with low power loss and wear. This article systematically studied the acting mechanisms of aerodynamic and squeeze effects on the static and dynamic characteristics of a hybrid gas-lubricated bearing. The resonance frequencies and mode shapes of the bearing were obtained from a finite element analysis and validated by published experimental measurements. The effects of static elastic deformation, dynamic elastic deformation, and bearing clearance on the load capacity were analyzed. A nonlinear numerical model coupling the air film and the structural vibration was also developed to investigate the stability of the hybrid gas-lubricated bearing. The predicted bearing load capacity shows reasonable agreement with the experimental data. Results show that the bearing using only the aerodynamic effect has a large load capacity but poor stability. By utilizing the squeeze film effect, especially at a proper resonance frequency, the load capacity of the hybrid gas-lubricated bearing can be improved and its stability can also be remarkably promoted.     

Squeeze film characteristics of long partial journal bearings lubricated with couple stress fluids

On the basis of microcontinuum theory, a theoretical analysis of hydrodynamic squeeze film behaviour for long partial journal bearings lubricated by fluids with couple stresses is presented. To take into account the couple stress effects due to the lubricant containing additives or suspended particles, the modified Reynolds equation governing the film pressure is derived by using the Stokes constitutive equations. Various bearing characteristics are then calculated. According to the results obtained, the influence of couple stress effects on the performance of the system is physically apparent and not negligible. Compared with the Newtonian lubricant case, the couple stress effects provide an enhancement in the load-carrying capacity and lengthen the response time of the squeeze film action. On the whole, the presence of couple stresses signifies an improvement in the squeeze film characteristics of the system.     

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.     

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.     

Load-carrying capacity generation in squeeze film action

The mechanism of squeeze action is explored using results of numerical analyses and physical explanations. The relationship between the mean film force and the load the squeeze film could support is established. It is concluded that the high viscous resistance around the contact boundary is the source of squeeze air film build-up. Repeated compression and expansion of air contribute to the formation of unsymmetric pressure field and load-carrying capacity.