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.     

Hydrodynamic lubrication of short porous bearings

A theoretical analysis is presented for the hydrodynamic lubrication of short porous metal bearings that are press-fitted into a solid housing. It is customary with such bearings to neglect the circumferential flow of the lubricant compared to the axial flow and consequently the modified Reynolds equation has a simpler form. However, this device is not resorted to while considering the flow of the lubricant within the bearing material, and consequently the three dimensional Laplace equation describing such flow is solved. The pressure continuity at the bearing-film interface is maintained and the modified Reynolds equation is solved by the Galerkin method. Numerical results obtained on a digital computer indicate a progressive reduction in the load capacity and increment in the friction parameter and attitude angle as the permeability parameter is increased. These results significantly aid the rational design of short porous bearings.     

Characteristics of partial porous journal bearings of finite length considering curvature and slip velocity

A self acting, finite length, partial porous journal bearing with arbitrary load angle has been analysed to obtain the characteristics assuming the active film of a homogeneous single phase liquid lubricant extends over the whole bearing arc span. The adhesion condition used in earlier porous bearing analysis is no longer valid, due to the presence of the thin layer of fluid moving streamwise just beneath the surface of the porous bearing material, a new modified lubrication equation is used for the present analysis. Film curvature has been considered. The curvature effect of the thick porous bearing matrix is taken into account by a direct but new approach which makes possible the use of the separation of variables for the first time in such a problem. Collocation technique is utilised to determine the hydrodynamic pressure from which characteristics are evaluated as usual. The results are fully analytical in nature, simple, yet exact and accurate, permitting easy and economical calculation of numerical data over a very wide range of parameters.     

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.     

Investigation of slip effects in plane porous journal bearings

Slip effects in plane porous journal bearings are considered realistically: only the slip coefficient is treated as an independent parameter and the porosity and the ratio of clearance to journal radius are the other factors which determine the effects of slip. The effects of velocity slip on the static performance as well as on the dynamic performance of the bearings are determined.     

Study of conical whirl instability of hydrodynamic porous oil journal bearings with tangential velocity slip

A theoretical analysis is presented for the stability characteristics of the conical whirling of an unloaded rigid rotor supported in hydrodynamic porous oil journal bearings with tangential velocity slip on the bearing film interface. The rotor has a two degree of freedom motion in self-excited conical whirling. In the stability analysis, the effect of various parameters on stability has also been investigated.     

An elastohydrodynamic study on two-axial-groove journal bearings

An elastohydrodynamic study of two-axial-groove journal bearings operating in laminar and superlaminar flow regimes is presented. The effect of transition is included in turbulence analysis. Static and dynamic performance characteristics are presented for several values of deformation coefficient and Reynolds number. Illustrative examples are cited to demonstrate the significance of the present investigation.     

Numerical study of the thermo-hydrodynamic lubrication phenomena in porous journal bearings

In this work, a numerical simulation is presented for the thermo-hydrodynamic self-lubrication aspect analysis of porous circular journal bearing of finite length with sealed ends. It consists in analyzing the thermal effects on the behavior of circular porous journal bearings. The Reynolds equation of thin viscous films is used taking into account the oil leakage into the porous matrix, by applying Darcy’s law to determine the fluid flow in the porous media. The presented results are in good agreement with those cited in the literature. The effects of dimensionless permeability parameter and eccentricity ratio on performance parameters are presented and discussed. The results showed that the temperature influence on the journal bearings performance is important in some operating cases, and that a progressive reduction in the pressure distribution, in the load capacity and attitude angle is a consequence of the increasing permeability.     

Effect of velocity slip on squeeze films in porous bearings

The performance of squeeze films in porous journal bearings was analysed using the Beavers-Joseph criterion of velocity slip at a porous boundary. Closed-form expressions were obtained for the pressure distribution in an infinitely long bearing and also in an infinitely narrow bearing. Numerical results evaluated from these expressions are presented in graphical form to illustrate the influence of velocity slip.     

Effect of velocity slip in axially undefined porous bearings

A theoretical analysis of the performance characteristics of axially undefined journal bearings was carried out. The analysis takes into account the velocity slip at the surface of the porous medium by using the Beavers-Joseph criterion. Results are presented for various bearing characteristics and compared with earlier results obtained by using the no-slip condition.     

Hydrodynamic lubrication of a porous slider bearing with slip velocity

An inclined porous slider bearing is analysed with slip velocity at the porous boundary considered. The expressions for dimensionless loadcarrying capacity, friction and the centre of pressure are obtained in the form of integrals. Minimization of the slip parameter is essential to increase the load capacity.     

基于弹流知识的球轴承设计

基于点接触弹流知识与赤兹接触理论,对球轴承设计参数沟道半径系数和滚动体直径与节圆直径的比进行了分析,结果表明,沟道半径系数对微型轴承其取值范围较大;对小的沟道半径系数,滚动体直径与节圆直径的比的大小对形成油膜的能力影响较小,并且最大接触压力随沟道半径系数的变化大,而随滚动体直径与节圆直径的比的变化不大。     

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.     

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.     

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.     

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.     

Hydromagnetic lubrication equation for an anisotropic porous slider with slip velocity

A general differential equation is derived for the lubrication of an anisotropic porous slider in the presence of a transverse magnetic field. The effect of slip velocity is considered.     

Micropolar fluid lubrication of one-dimensional journal bearings

A study of the characteristics of one-dimensional journal bearings shows that the load capacity increases and the coefficient of friction decreases as the parameter $\text{μ}{}_1$, which characterizes the microstructure of the base oil due to the presence of additives, increases. The time of approach increases as the parameter $\text{μ}{}_1$ increases.     

Estimation of the performance of a narrow porous journal bearing with hydrodynamic turbulent lubrication considering slip velocity and arbitrary wall thickness

A closed-form mathematical analysis is presented for the hydrodynamic lubrication of a 360° short porous metal journal bearing with arbitrary wall thickness which is press fitted in a solid housing and works with a turbulent film of newtonian lubricant. A new pressure equation is used. The bearing is assumed to be narrow, and therefore circumferential flow of the lubricant in the clearance region is negligible in comparison with that in the axial direction which makes the governing differential equation simpler to solve. However, this simplification is not applicable to darcian flow in the porous matrix so that a three-dimensional Laplace equation is required to describe the continuity of flow in the pores. The film curvature is included by retaining terms containing $\text{C}\text{R}{}_1$ in the expression for film thickness. The curvature of the permeable bearing matrix, which allows it to have an arbitrary wall thickness, is taken into account by a direct approach. Infinite Fourier series and their orthogonal properties are utilized for the determination of the turbulent hydrodynamic pressure distribution from which the load-carrying capacity and attitude angle are calculated. All the results of interest are simple and fully analytical in nature permitting easy and economical calculation of numerical data over a very wide range of parameters.     

Pure rolling elastohydrodynamic lubrication of short stroke reciprocating motion

The behavior of point contact elastohydrodynamic lubrication (EHL) films under pure rolling short stroke reciprocating motion is investigated using both optical interferometry technique and theoretical analysis. The EHL films are recorded with a high-speed color camera and simulated with multigrid techniques. General variation of oil film under point contact reciprocating motion is explained by a comparison between a fully flooded simulation and an experiment with a frequency of 7.78 Hz. Influence of starvation is considered by another simulation under a higher working frequency of 14.4 Hz and the simulated results are compared with experimental results. Both simulations show good agreements quantitatively with experiments. In addition, general tribo-characteristics of EHL under fully flooded and starved conditions are discussed.