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.     

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.     

An inverse solution for finite journal bearings lubricated with couple stress fluids

This paper presents an inverse solution for finite journal bearings lubricated with couple stress fluids to estimate the eccentricity ratio and the couple stress parameter for a given experimentally measured pressure distribution. The least-squares optimization technique is used to solve the inverse problem. An efficient numerical scheme is developed to solve the direct lubrication problem, which consists of the modified Reynolds equation, the film thickness equation, and the boundary conditions for the pressure field. The flexibility of the bearing liner is considered in the film thickness equation by a simple elastic model. The proposed inverse algorithm was tested using numerically simulated pressure distribution. The results showed that as the percentage of random error added to the numerically calculated pressure data points increases, the number of iterations required for convergence increases slightly, and the accuracy of the predictions decreases especially in the case of elastic liner.     

The finite volume solution of the Reynolds equation of lubrication with film discontinuities

The present work deals with the numerical solution of the Reynolds equation of lubrication in the specific case where the film thickness is discontinuous. The present approach is obtained within the framework of a finite volume discretization and enables concentrated inertia effects to be taken into account, as described by a generalized Bernoulli equation. The classic finite volume formulation is included as a special case when discontinuities are absent. Some numerical examples show that the conservative properties of the finite volume discretization are maintained even when the pressure field is discontinuous. A typical application shows that the film discontinuities should always be taken into account in a consistent physical manner in order to eliminate the awkward question of their impact on global results of technological interest.     

Elasto-hydrodynamic lubrication analysis of partial arc journal bearings

Centrally loaded partial arc bearings having deformable bearing surfaces have been analysed. The coupled Reynolds equation satisfying the pressure field in the fluid and the three-dimensional elasticity equations governing the deformations in the bearing lining are solved simultaneously using the finite element method. The steady state solution for the coupled problem is obtained by using a doubly nested iteration scheme which determines the positive pressure field in the fluid film and the orientation of the load line. The influence of bearing deformation on the load capacity, attitude angle, friction coefficient parameter and oil flow are reported for 60° and 120° partial arc bearings. The analysis is extended for lubricants having pressure-dependent viscosity     

Performance of finite journal bearings in non-laminar lubrication regime

Fluid dynamic lubrication of journal bearings in a superlaminar regime, ie a transition or turbulent regime, is the subject-matter of this study.Results obtained by solving an appropriately modified Reynolds bidimensional equation have been put in the form of operating diagrams which allow the correct design of journal bearings in real conditions of flow     

Free boundary of lubricant film in ferrofluid journal bearings

The growing interest in ferrofluid bearings is caused by their excellent self-sealing ability. The understanding of behaviour of ferrofluid film boundary adjacent to ambient air is crucial for the proper design of the sealing unit of ferrofluid bearings. This paper is the first attempt to predict the shape of a ferrofluid free boundary in the presence of a static load and magnetic field. Analysis involves simultaneous integration of the Reynolds equation and the free boundary equation using perturbation technique with respect to shaft eccentricity. Magnetic field is shown to flatten ferrofluid free boundaries as well as to reduce cavitation region; both effects diminishing lubricant leakage.     

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.     

Roughness effects in a narrow porous journal bearing with arbitrary porous wall thickness

The paper uses Christensen's stochastic theory to study the effects of surface roughness in a narrow porous journal bearing. An exact solution, valid for arbitrary wall thickness, is given for the film pressure and pressure in the bearing material. The results are compared with the approximate solutions, and the range of various influencing parameters, for which the approximate analysis is satisfactory from a practical point of view is determined.     

Effects of couple stresses in the cyclic squeeze films of finite partial journal bearings

Based upon the microcontinuum theory, the present paper is to theoretically study the pure squeeze-film behavior of a finite partial journal bearing with non-Newtonian couple-stress lubricants operating under a time-dependent cyclic load. To take into account the couple stress effects resulting from the lubricant blended with various additives, the modified Reynolds equation governing the film pressure is obtained from Stokes equations of motion. The film pressure is numerically solved by using the Conjugate Gradient Method. Bearing characteristics are then calculated from the nonlinear motion equation of the journal. According to the results obtained, the effects of couple stresses result in a decrease in the value of eccentricity of the journal center. The finite partial bearing with a couple stress fluid as the lubricant yields an increase in the minimum permissible clearance and provides a longer time to prevent the journal-bearing contact.     

Squeeze film characteristics of finite journal bearings: couple stress fluid model

A theoretical study of squeeze film behaviour for a finite journal bearing lubricated with couple stress fluids is presented. On the basis of the microcontinuum theory, the modified Reynolds equation is obtained by using the Stokes equations of motion to account for the couple stress effects due to the lubricant blended with various additives. With the Conjugate Gradient Method of iteration the built-up pressure is calculated, and then applied to predict the squeeze film characteristics of the system. According to the results evaluated, the rheological influence of couple stress fluids is physically apparent. Compared with the case of a Newtonian lubricant, the couple stress effects increase the load-carrying capacity significantly and lengthen the response time of the squeeze film behaviour. On the whole, the presence of couple stresses improves the characteristics of finite journal bearings operating under pure squeeze film motion. The rheological effects of couple stress fluids agree with previous works.     

Experimental investigations of porous bearings under vertical sinusoidally fluctuating loads

There are many papers on the experimental investigations of porous bearings under static loads but there is no paper on the experimental investigations under dynamic loads. In the present paper, the results of experimental investigation of porous bearings under vertical sinusoidally fluctuating loads are presented. The friction force was measured under various conditions of fluctuating load/steady load ratio, journal frequency and load frequency. The investigations were carried out in the hydrodynamic lubrication regime in a specially designed and fabricated test rig. It was found that at any given rpm, as the fluctuating specific load/steady specific load ratio, P_f/P_s, increases, the mean coefficient of friction μ_m increases. It was also found that the mean coefficient of friction is not affected by the load frequency even when the load frequency is half of the journal frequency.     

A study of friction in worn misaligned journal bearings under severe hydrodynamic lubrication

Friction occurs in all mechanical systems such as transmissions, valves, piston rings, bearings, machines, etc. It is well known that in journal bearings, friction occurs in all lubrication regimes. However, shaft misalignment in rotating systems is one of the most common causes of wear. In this work, the bearing is assumed to operate in the hydrodynamic region, at high eccentricities, wear depths, and angular misalignment. As a result, the minimum film thickness is 5–10 times the surface finish, i.e., near the lower limit of the hydrodynamic lubrication when taking into account that in the latest technology CNC machines the bearing surface finish could be less than 1–2 μm.An analytical model is developed in order to find the relationship among the friction force, the misalignment angles, and wear depth. The Reynolds equation is solved numerically; the friction force is calculated in the equilibrium position. The friction coefficient is presented versus the misalignment angles and wear depths for different Sommerfeld numbers, thus creating friction functions dependent on misalignment and wear of the bearing. The variation in power loss of the rotor bearing system is also investigated and presented as a function of wear depth and misalignment angles.     

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.     

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.     

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.     

Self-organizing maps for surveying lubrication within squeeze film dampers

Self-organizing maps (SOMs) represent a well-known neural network technique particularly suited to classification tasks. Here, it is adopted to monitor the lubricating conditions within squeeze film dampers for rotor support and was aimed, in particular, at identifying the aspect of the pressure waves within the oil film. Pressure distribution is indeed significantly influenced by a number of factors, which affect damper operation. Results from past research in the field make it possible to infer that the pattern of pressure signals taken in the oil film represents a valuable source of information as regards the lubricating conditions within the damper. Surveillance procedures in the operation of turbomachinery could benefit from prompt detection of possible, unwanted changes in the characteristics of lubrication, for example, when modeling bearing operations within model-based schemes. In this paper, SOM capabilities are first evaluated, dealing separately with theoretically simulated data. The subsequent tests adopted theoretical data as a reference for identifying experimental conditions. Further tests were carried out to map experimental data. Despite constraints consisting in the damper motion being imposed during the theoretical and experimental tests, the results confirmed the potential of the method and encourage further tests in conditions which are closer to real operation.     

The solution of Reynolds equation under natural boundary conditions for hydrodynamic journal bearings

The solution of Reynolds equation for hydrodynamic pressures of the load-carrying lubricating layer in journal bearings is discussed.The accepted boundary conditions are shown to be helpful in explaining more accurately the physical meaning of the lubricant flow process and in assuming the boundary curvature for the load-carrying lubricant film in the convergent-divergent zone of the bearing clearance.New algorithms for determining the above curve boundary in the process of the numerical solution of a basic differential equation are suggested. The technique used for the theoretical study of the bearings made it possible to provide results of greater accuracy for their principal operating characteristics such as load-carrying capacity, frictional losses and lubricant consumption.     

Conical whirl instability of turbulent flow hybrid porous journal bearings

An analysis of conical whirl instability of an unloaded rigid rotor supported in a turbulent flow hybrid porous journal bearing has been presented, following Constantinescu's turbulent lubrication theory. The effect of bearing feeding parameter (β), Reynolds number (Re), ratio of wall thickness to journal radius (H/R) and anisotropy of porous material on the stability of rotor-bearing system has been investigated. It is observed that higher values of β gives better stability and higher stability is predicted if the porous bush is considered to be isotropic.