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.     

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.     

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.     

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.     

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.     

Surface roughness effect on finite journal bearings with flexible porous liners

The effects of surface roughness on the static characteristics of finite porous journal bearings under hydrodynamic lubrication conditions are investigated in this paper. 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 analysis takes into account the flexibility of the porous liner by using a thin liner model. The effects of velocity slip at the surface of the porous medium are considered in the analysis by using the Beavers‐Joseph criterion. The mathematical model is then solved numerically by finite‐difference methods for mean hydrodynamic pressure, which in turn gives the hydrodynamic load. The effects of the surface roughness parameter, surface pattern, eccentricity ratio, length‐to‐diameter ratio, permeability parameter, and flexibility parameter on the hydrodynamic load‐carrying capacity, attitude angle, and friction factor are discussed.     

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.     

The squeeze film between rotating porous annular disks

The problem of a squeeze film between two rotating disks, one with a porous facing, is analyzed. The analytical model takes account of the porosity of one disk and the inertia due to centrifugal force on the fluid both in the film and in the porous region. The governing equations are derived according to lubrication theory. It is found that the fluid in the film region satisfies the modified Reynolds equation and the flow in the porous region satisfies Poisson's equation. The problem is solved analytically using Fourier expansions. Solutions for load capacity and pressure distribution are presented in series form. The film-thickness and time relation is given in integral form. Results are plotted for selected parameter values. The conditions under which inertia effects can be important are determined and as a result the criteria for neglecting the inertia effects are given.     

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 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.     

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.     

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.     

Hydrodynamic lubrication of rough slider bearings with couple stress fluids

The combined effects of couple stresses and surface roughness on the performance characteristics of hydrodynamic lubrication of slider bearings with various film shapes, such as plane slider, exponential, secant and hyperbolic, are studied. A stochastic random variable with non-zero mean, variance and skewness is used to mathematically model the surface roughness of the slider bearing’s. The Stokes couple stress fluid model is used to characterize the rheological behavior of the lubricant with polymer additives. The modified expressions for the bearing characteristics, namely pressure, load carrying capacity, center of pressure, frictional force are obtained for the general lubrication film shape on the basis of Stokes microcontinuum theory for couple stress fluids. Results are computed numerically for various film shapes under consideration. It is observed that, for all the lubricant film shapes under consideration, the negatively skewed surface roughness increases the load carrying capacity, frictional force and temperature rise, while it reduces the coefficient of friction. On the contrary, the reverse trend is observed for positively skewed surface roughness. Further, these effects are more pronounced for the couple stress fluids.     

Effect of Magnetic Field in Lubrication of Synovial Joints

A two region flow model has been developed in this paper in the presence of external magnetic field for the better understanding of synovial joint lubrication mechanism. The model consists of two parallel porous cartilageous surfaces separated by a thin film of non newtonian lubricant representing the synovial fluid which is assumed to behave like a paramagnetic fluid system. In this paper, we have represented the cartilage by a mixture of two interacting continua and synovial fluid by viscoelastic fluid. A transverse magnetic field is applied to the system. We have used the modified form of Darcy’s law given by Zahn and Rosenweig; to describe the penetration dynamics of magnetic fluids through porous media. Because of exact solution not being possible for the governing non-linear partial differential equations, the perturbation method has been used to obtain approximate solutions. The results have been obtained by computational techniques and compared by results available in the literature. In this paper, the possibility of increased efficiency of joint lubrication, particularly in diseased states by the application of applied magnetic fields has been explored. The applied magnetic field increases the load carrying capacity. Which helps in sustaining greater loads. Similarly, the viscoelastic parameter describes the increase in the concentration of the suspended hyaluronic acid molecules which, in turn, increases the overall viscosity of the lubricant, which also helps in sustaining greater loads.     

Analysis of normal stress effects in a squeeze film porous bearing

An analytical study of a porous bearing lubricated by a second-order fluid is considered. This investigation explains the working of general porous bearings and, in particular, describes the lubrication aspects of synovial joints. An approximate method for the solution of the governing fluid film equation and Darcy's equation for a porous region is used. Exact expressions for dimensionless pressure, load capacity and response time are obtained. The load capacity and response time for the diseased joint decrease compared with the healthy joint. The decrease in permeability of cartilage enhances the load capacity.     

化学反应膜对齿面润滑状态影响的研究

通过对齿面微观接触以及流体膜承载能力和边界膜承载能力相互关系的分析，从化学反应膜形成速度与磨损速度的平衡关系入手，建立了齿面化学反应膜对齿面润滑状态影响的数学模型，并通过试验验证了这一模型。结果表明：合适的化学反应膜，使表面形貌向着有利于润滑方向发展，使边界润滑向弹性流体润滑状态转变，从而提高齿面的承载能力。     

A Biphasic Model for Hip-Joint Replacement

The ball-and-socket geometry of the hip joint makes kinematic analysis of the joint motion relatively straightforward in comparison to other joints. The load-carrying surfaces of both ball and socket are covered with tough viscoelastic material known as cartilage. A number of lubrication theories have been proposed in the literature to account for the low coefficient of friction and low wear observed in healthy joints. The actual mechanism by which joints are capable of sustaining large repetitive loads with virtually no wear and with very little friction has not been fully understood. Therefore, analytical studies are presented for the understanding of the lubrication mechanism occurring in hip-joint replacements under restricted motion during standing or in the supporting phase during walking. The viscoelastic fluid has been considered to represent the synovial fluid in the fluid-film region. The problem described here has been analyzed in two regions (the porous matrix and the fluid-film region) separately along with suitable matching and boundary conditions at the interface. It has been concluded that the effect of the viscoelastic parameter for a particular gap is to increase the load capacity, indicating positive effects of the increase in concentration of suspended particles in the lubricant region. It has been observed that the coefficient of friction decreases with increasing values of the viscoelestic parameter. This is due to the fact that as the viscoelastic parameter increases, the concentration of hyaluronic acid molecules increases. It may also be noted from the results that the coefficient of friction decreases with increasing values of slip parameter. This shows that the slip velocity occurring at the porous boundary helps in maintaining normal functioning of human joints.     

A general model for porous medium flow in squeezing film situations

The present paper deals with a numerical investigation of the hydrodynamic lubrication of a porous squeeze film between two circular discs. To this purpose, the thin film (reduced) Navier Stokes equations and a generalised porous medium model are solved. The numerical results show that the effect of the porous disc is to reduce the lubricating properties of the fluid film. This effect is increased during the squeezing action. In addition, it is shown that the film pressure, the load‐carrying capacity and the velocity field based only on the Darcy model are predicted higher than those obtained from the generalised porous medium model. Copyright © 2009 John Wiley & Sons, Ltd.     

Steady-state thermo-hydrodynamic analysis of cylindrical fluid film journal bearing with an axial groove

A steady-state thermohydrodynamic analysis of an axial groove journal bearings in which oil is supplied at constant pressure is performed theoretically. Thermohydrodynamic analysis requires simultaneous solution of Reynolds equation, energy equation and heat conduction equations in the bush and the shaft. From parametric study it is found that the temperature of the fluid film raises due to frictional heat thereby viscosity, load capacity decreases. Increased shaft speed resulted in increased load carrying capacity, bush temperature, flow rate and friction variable. It is difficult to obtain the solution due to numerical instability when the bearing is operated at high eccentricity ratios.     

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。