Rayleigh Step Bearing Research Articles

Analyse numérique du régime THD dans un patin échelon

A lack of thermohydrodynamic (THD) models adapted to discontinuous fluid film geometries can be noted in the lubrication-related literature. The finite differences method, largely used in THD analysis, cannot be easily applied to discontinuous flow domains. This article proposes two finite volumes based models, suitable for discontinuous domains. The first model, based on Reynolds generalized equation, lacks in accuracy near the discontinuity line, but gains in computing speed. The second model, based on Navier-Stokes equations, is more accurate but also significantly more demanding in terms of computing requirements. The two models are applied and compared on the simple geometry of a bi-dimensional Rayleigh step bearing. Different configurations are analyzed, allowing the validation of the Reynolds model for most of the cases encountered in fluid film lubrication.

The Influence of Injection Pockets on the Performance of Tilting-Pad Thrust Bearings—Part I: Theory

This is Part I of a two-part series of papers describing the effects of high-pressure injection pockets on the operating conditions of tilting-pad thrust bearings. In Part I a numerical model based on the Reynolds equation is developed extending the three-dimensional thermoelastohydrodynamic (TEHD) analysis of tilting-pad thrust bearings to include the effects of high-pressure injection and recesses in the bearing pads. The model is applied to the analysis of an existing bearing of large dimensions and the influence of the pocket is analyzed. In the analysis, the high-pressure oil injection used for hydrostatic jacking is turned off (i.e., only the effect of the pocket is studied). It is shown that a shallow pocket positively influences the performance of the bearing because it has characteristics similar to those of a Rayleigh-step bearing. In Part II of the paper (Heinrichson, N., Fuerst, A., and Santos, I. F., 2007, ASME J. Tribol., 129(4), pp. 904–912) measurements of pressure profiles and oil film thickness for a test-pad are compared to theoretical results. The analysis of Part II deals both with flow situations, where the high-pressure injection is turned off, as well as with situations where it is turned on for hydrostatic jacking.

A note on porous Rayleigh step bearings lubricated with couple-stress fluids

This paper presents the theoretical study of the effect of couple stresses on the optimum lubrication characteristics of porous Rayleigh step bearings. The lubricant with additives in the film region and also in the porous region is modelled as the Stokes couple-stress fluid. Modified Darcy type equations accounting for the polar effects in the porous region is considered and the generalized Reynolds type equation is derived for the lubrication of the porous Rayleigh step bearings. Exact solution of the generalized Reynolds type equation is obtained and the closed form expressions for the bearing characteristics are presented. Performance characteristics of the porous Rayleigh step bearing are presented for the various values of the non-dimensional parameters such as the couple-stress parameter and the permeability parameter. It is observed that the couple-stress fluid lubricants provide the increased load carrying capacity and the decreased coefficient of friction as compared to the corresponding Newtonian case. This theory suggests that, adverse effects of the presence of porous facing on the stator could be compensated with proper selection of lubricants with proper additives.

Reynolds' Model Suitability in Simulating Rayleigh Step Bearing Thermohydrodynamic Problems

A Reynolds-based numerical thermohydrodynamic analysis, performed on a discontinuous geometric domain, is unable to correctly predict the flow field in the close vicinity of the discontinuity. This limitation, due to the very hypotheses used to derive the Reynolds equation, explains the lack of studies treating such configurations. A Navier-Stokes–based model seems appropriate but its complexity and its requirements in terms of computing time are somewhat prohibitive. To compare the two models we have developed two independent, finite-volume-based numerical algorithms. They are applied to a simple two-dimensional geometric configuration (Rayleigh step bearing). This will allow us to prove that, for the configurations commonly encountered in hydrodynamic lubrication, the errors introduced by the Reynolds model are highly localized. The overall performance and running parameters are correctly determined with both models, rendering unnecessary the complex Navier-Stokes–based solution. Presented at the STLE Annual Meeting in Las Vegas, Nevada May 15-19, 2005 Review led by Gita Talmage

Thermohydrodynamic Lubrication Analysis Method of Slider Bearings with Steps on Bearing Surface

This paper shows a thermohydrodynamic lubrication (THL) analysis method to simulate slider bearings with steps on the bearing surface such as Rayleigh step bearing. To satisfy the flow continuity on the step region, virtual clearance and its derivatives are defined on the edges. This method allows the finite differential equations (Reynolds equation and energy equation) to be solved at both continuous and dicontinuous clearance region. The simulation result is in good agreement with the CFD calculation result. This paper also shows a simulation result of a finite width Rayleigh step bearing with side dams.

Numerical Modeling of a Newtonian and a Bingham Fluid in a Rayleigh Step Bearing

Numerical Modeling of a Newtonian and a Bingham Fluid in a Rayleigh Step Bearing

A simplified calculus method for a grease‐lubricated Rayleigh step bearing

AbstractThe paper presents a simplified method for the analytical calculus of a grease‐lubricated infinitely large Rayleigh step bearing.The principal problem of the grease flow through a Rayleigh step bearing is the shape of the stagnant core in the step region. This shape is determined using Navier‐Stokes equations resolved by the finite method element. The theoretical results are compared with those obtained experimentally by visualisation of the grease flow using the reflecting tracer method. The conclusion of the simplified method is that a Rayleigh step bearing lubricated with grease is equivalent to one lubricated with oil, but with a different configuration of the convergent interstice.

Non-Newtonian effects of second-order fluids on double-layered porous Rayleigh-step bearings

Theoretical study of double-layered porous Rayleigh-step bearings with second-order fluid as lubricant is presented. An approximate method for the solutions of the governing fluid film equations for a porous region is proposed. The expressions for the pressure distribution, load capacity and frictional coefficient are obtained in compact form. Calculations of the dimensionless load capacity, frictional force and frictional coefficients are presented for specific values of the material parameters. It is found that the double porous layer yields an increase in the load capacity and ensures decrease in frictional force at the porous lining as compared with the conventional porous Rayleigh-step bearings. The maximum dimensionless load-carrying capacity is found to occur at a slightly larger step ratio as compared with the conventional porous Rayleigh-step bearings.

An experimental investigation of the flow of an electro-rheological fluid in a Rayleigh step bearing

The transport properties of unexcited and excited electro-rheological (ER) fluid in combined Couette and Poiseuille flow are investigated. In particular the question of whether the fluid can be considered as a continuum with Bingham plastic constitutive properties, even though it is a two-phase solid-liquid mixture, is addressed. The hydrodynamic pressures generated using ER fluid in a Rayleigh step bearing at the limiting condition of zero net flow rate were measured. The properties exhibited by the fluid are compared with independently obtained data showing the continuum principle to be applicable to the flows examined.

Flow of a Power-Law Fluid in a Rayleigh Step

An exact solution of the lubrication equations of motion for flow in a Rayleigh step of infinite width is presented. The fluid is assumed to be incompressible, and the non-Newtonian behavior of the fluid is described by a power-law model. The dimensionless pressure gradient and load capacity are obtained by the solution of a system of six algebraic equations. Optimum dimensions and load capacity for Rayleigh step bearing are presented.

Porous slider bearing with couple stress fluid

Theoretical study of porous slider bearing with couple stress fluid as lubricant is made and the lubrication qualities of couple stress fluid are examined. The lower surface is covered by a thin porous material and the upper one, having arbitrary shape, moves in its own plane with constant velocity. Analytical expressions for load capacity, frictional force and the centre of pressure are derived. It yields increase in, load capacity and ensures the decrease in coefficient of friction. The problem is also discussed in the context of various geometries viz, (1) Rayleigh step bearings and (2) inclined slider bearings. Bounds on flow rate, frictional coefficient, centre of pressure and time-height relation are obtained and compared with classical case, Gross [1]. Suitable design parameters are predicted for the efficient lubrication of slider bearings.

Porous Rayleigh Step Bearing with Second‐Order Fluid

AbstractThe theoretical analysis of a porous Rayleigh Step bearing lubricated by a second‐order fluid is considered. An approximate method for the solution of the governing fluid film equations and Darcy's equations for a porous region is proposed. Compact expressions for the pressure distribution, load capacity and the frictional coefficient are obtained. Calculations of the dimensionless load capacity, frictional force and frictional coefficients are presented for specific values of the material parameters. It is found that the load carrying capacity decreases and the frictional force and frictional coefficients increase compared to that of the solid case. The maximum dimensionless load capacity is found to occur at a slightly smaller step ratio as compared to the solid case. It is of quite interest to note that the limiting forms of the expressions obtained approach the exact forms of the results of the Newtonian case quoted in detail in Hughes [15].

Rayleigh Step Bearing with Second-Order Fluid

An infinite Rayleigh step bearing with a second-order fluid as lubricant was studied and the lubrication qualities were examined. Compact expressions for the pressure distribution, load capacity, and frictional coefficient were obtained. Calculations of the dimensionless load capacity, frictional force and frictional coefficients are presented for specific values of the material parameters. A second-order fluid was found to yield an increase in the load capacity and to decrease the coefficient of friction compared to that of the Newtonian case. The maximum dimensionless load capacity was found to occur at a slightly smaller step ratio, as compared to the Newtonian case. Further, it was found that the frictional coefficient decreases with an increase in the bearing velocity, as expected for an ideal lubricant.

Experiments on the Stability of Various Water-Lubricated Fixed Geometry Hydrodynamic Journal Bearings at Zero Load

Stability tests were conducted with 3.8 centimeter-(1.5 in.-) diameter, 3.8 centimeter-(1.5 in.-) long, fixed geometry hydrodynamic journal bearings in water at 300 K (80 deg F) with zero load. Five fixed geometry bearings were rated in order of diminishing stability as follows: (1) three-tilted-lobe bearing (offset factor of 1.0), (2) herring-bone-groove bearing, (3) one-segment, three-pad, shrouded Rayleigh-step bearing, (4) three-tilted-lobe journal with axial grooves (offset factor of 1.0) mated with a plain bearing, and (5) three-centrally-lobed bearing with axial grooves (offset factor of 0.5). Maximum stability in lobed bearings and journals is achieved when the lobes are tilted so that the points of minimum film thickness occur near the trailing edges. The herringbone-groove journals had a maximum stability (maximum fractional frequency whirl onset speed) when the groove to ridge clearance ratio was closest to 2.1, as predicted by incompressible flow theory. The one-segment, three-pad shrouded Rayleigh-step bearing configuration was the most stable of the four step-bearing configurations tested. The tilted-lobe journals mated with plain bearings were unique in that, in some tests, the bearings could be run to a shaft speed twice the shaft speed at which initial fractional frequency whirl occurred before any sign of bearing distress was observed.

The optimum one-dimensional hydrodynamic gas rayleigh step bearing

The optimum one-dimensional hydrodynamic gas rayleigh step bearing

Closure to “Discussion of ‘The Rayleigh Step Bearing Applied to a Gas-Lubricated Journal of Finite Length’” (1968, ASME J. Lubr. Technol., 90, pp. 520–521)

Closure to “Discussion of ‘The Rayleigh Step Bearing Applied to a Gas-Lubricated Journal of Finite Length’” (1968, ASME J. Lubr. Technol., 90, pp. 520–521)

The Rayleigh Step Bearing Applied to a Gas-Lubricated Journal of Finite Length

A linearization method is employed on the Reynolds equation to obtain the load and friction torque of a Rayleigh step-film scheme applied to a journal bearing of finite length. The analysis is broken into two parts; i.e., the stepped and ridge regions. The film thickness is considered constant in each region thereby simplifying the linearized Reynolds equation. In addition to the usual plain-bearing parameters (the compressibility number, eccentricity ratio, and length-to-diameter ratio), the load and friction force of a stepped bearing depend on the ratio of the stepped clearance to ridge clearance, the ratio of the width of ridge to the width of the pad, and the number of pads. The solution for the load and friction force for a single pad is obtained in the form of a highly convergent series. A number of equal pads are disposed around a journal and the total bearing load is computed for various eccentricities. Computation from the infinite series is lengthy and a digital computer was used in order to carry out the calculational work. This enabled optima to be selected for each system composed of different numbers of pads. The friction torque and hence the bearing power loss were computed for every case.