Rayleigh Step Research Articles

The Effect of Two-Phase Lubricant on Bearing Performances

The effect of small, spherical, rigid particles, droplets or bubbles (henceforth referred to as particles) on the performance of a hydrodynamic bearing is theoretically investigated. A low Reynolds number solution for a single particle is utilized to obtain the integrated effect of a dilute suspension. Two examples are addressed: a long Rayleigh step slider and a long journal bearing. It is found that load-carrying capacity is negligibly affected by the presence of the particles, whereas the friction is increased appreciably. Presented at the 41st Annual Meeting in Toronto, Ontario, Canada May 12–15, 1986

Elastohydrodynamic lubrication study of different slider bearings in laminar and turbulent regimes

The piezoviscous property of lubricants enhances bearing deformation; this is more marked at high speeds when the lubricant flow is turbulent. In this paper, in which the mutual dependence of lubricant viscosity, hydrodynamic pressure in the fluid film and elasticity of the bearing is considered, the steady state solutions of the corresponding governing equations of the flow field and of the bearing deformations are determined in laminar and turbulent flow conditions using a nested iteration scheme. The bearing deformation is thus accounted for in computing the performance characteristics of taper-land and Rayleigh step slider bearings. The effects of various geometrical parameters (the slope of the fluid film and the taper-land ratio), the pressure-viscosity coefficient α ( α = 0, 0.25 and 0.50) and the linearized turbulence coefficients (which take values of 0, 2500 and 5000) that are based on the theory of Ng and Pan on the performance characteristics of the slider bearings are studied with reference to the non-dimensional deformation coefficient.

An Analytical Solution for Thermal Behavior of the Step Thrust Bearing

An analytical solution to the energy equation is presented for the one-dimensional step thrust bearing. Constant lubricant properties are assumed which decouples the momentum and energy equations resulting in a known velocity distribution according to the usual lubrication theory. The energy equation is then linear and yields to a separation of variables solution which results in Sturm-Liouville problems for both domains of the step, which are married at the discontinuity. Conduction, convection and dissipation are all considered and convenient non-dimensional parameters are developed for their relative magnitudes. Expressions for temperature distribution, (along and across the film) heat transfer, and dissipation rates are developed. Results are presented for the Rayleigh step geometry although any other step configuration is easily handled. A wide range of thermal behavior is obtained (rising or falling temperatures, higher temperatures before or after the step, etc.) depending on the dimensionless parameters. The solution presented cannot substitute for the more detailed numerical studies but does offer advantages. The effects of various thermal modes of operation are easily studied and the method is relatively simple to use requiring only a small computer program to evaluate the eigenvalues and eigenfunctions. In addition, general conclusions drawn here can probably be applied with caution to more complex bearing geometries.

On the optimization of fluid film bearings

In a classical paper slightly after the turn of the century, Lord Rayleigh obtained the optimum one dimensional slider bearing profile, the Rayleigh step. His criteria for optimality was that the load capacity per unit length of the bearing be maximum among all profiles having a given minimum film thickness. Since Rayleigh, an open question has been the determina­tion of the optimum two dimensional bearing profile based on the same criteria as above. In this paper we propose a method for answering that question using algorithms which we have recently developed for this class of problems.

Analysis of the Shrouded Rayleigh Step Pad for an Incompressible Fluid Film with the Centrifugal Inertia Effect Included

A computer program was developed to calculate the load capacity of the hydrodynamic forces generated within an incompressible fluid film by a shrouded Rayleigh step pad for application in a radial seal design. The program makes use of the central-difference operator, defined for cylindrical coordinates, to approximate the pressure gradient over the pad. Solution of the lubrication equation with the centrifugal inertia effect included is achieved by employing a noniterative numerical routine. Pressure maps and flow fields based on the geometry for a Rayleigh pad were obtained. Results indicate that the selection of a pad geometry such that the design load intersects the dimensionless load capacity curve at a separation ratio between two and four will yield the most favorable operating characteristics, i.e., the best trade-off between high load capacity, high film stiffness, high tangential flow, and a minimum temperature rise.

Finite element solution of the three-dimensional flow problem and of reynold's equation for incompressible and compressible fluids

The theoretical basis for application of finite element techniques to a general three-dimensional flow problem is presented. The finite element solution of Reynold's equation for incompressible and compressible fluids has been programmed and applied to the particular case of gas lubricated Rayleigh step journal bearing. The calculated pressure distribution and the load and attitude angle are given for different compressibility numbers and journal lengths. The results are compared with those obtained with simplifying assumptions.

The optimum one-dimensional hydrodynamic gas rayleigh step bearing

The optimum one-dimensional hydrodynamic gas rayleigh step bearing

Performance characteristics of spiral-grooved and shrouded Rayleigh step profiles for high-speed noncontacting gas seals: Cheng H. S., Castelli, V., Chow, C. Y. Transactions of the American Society of Mechanical Engineers, Journal of Lubrication Technology, Vol 91, Series F, No 1 (January 1969) pp 60–68

Performance characteristics of spiral-grooved and shrouded Rayleigh step profiles for high-speed noncontacting gas seals: Cheng H. S., Castelli, V., Chow, C. Y. Transactions of the American Society of Mechanical Engineers, Journal of Lubrication Technology, Vol 91, Series F, No 1 (January 1969) pp 60–68

Rayleigh Step Journal Bearing, Part II—Incompressible Fluid

A theoretical analysis of the pressure distribution, load, capacity, and attitude angle for a single-step concentric as well as a multistep infinite length eccentric Rayleigh step journal bearing is performed. The results from the single-step concentric analysis indicated that the maximum load capacity is obtained when the film thickness ratio is 1.7 and the ratio of the angle subtended by the ridge to the angle subtended by the pad is 0.35. The results from the infinite length eccentric analysis indicated that one step placed around the journal was optimal. For eccentricity ratios greater than or equal to 0.2 the maximum load occurred for a bearing without a step or a Sommerfeld bearing. For eccentricity ratios less than 0.2 the optimal film thickness ratio is 1.7 while there are three optimal ratios of angle subtended by the ridge to the angle subtended by the pad of 0.4, 0.45, and 0.5 depending on whether load capacity or stability or both load capacity and stability is more important in the application being considered.

Performance characteristics of spiral-groove and shrouded rayleigh step profiles for high-speed non-contacting gas seals : H. S. Cheng, V. Castelli and C. Y. Chow, JOLT, trans. ASME, ser. F, 91 (1969) 60–68; 21 figs., 7 refs.

Performance characteristics of spiral-groove and shrouded rayleigh step profiles for high-speed non-contacting gas seals : H. S. Cheng, V. Castelli and C. Y. Chow, JOLT, trans. ASME, ser. F, 91 (1969) 60–68; 21 figs., 7 refs.

Performance Characteristics of Spiral-Groove and Shrouded Rayleigh Step Profiles for High-Speed Noncontacting Gas Seals

Current methods in gas lubrication have been used in this paper to analyze the gas-film characteristics in a high-speed, face-type gas seal. Detailed analyses are presented for two different surface geometries, the spiral-groove-orifice seal and the shrouded Rayleigh step seal. Results are presented in three parts. The first part shows the performance of a spiral-groove seal without the orifices, and also the difference in performance when the grooves are located at the high pressure, low pressure, or both sides. The second part gives typical performance of a nonparallel film profile for the spiral-groove-orifice seal as well as for the shrouded Rayleigh step seal. In the last part, a comparison is made between the two seal geometries on their tolerance to coning or dishing under a constant seal load.

The Rayleigh step bearing applied to a gas-lubricated journal of finite length. (65-WA/ Lub-2) : F. R. Archibald and B. J. Hamrock, pp. 38–46; 12 figs., 7 refs.

Concrete is the most commonly used alley flooring in confined dairy herds because of its qualities of construction and ease of cleaning. Nevertheless, the hardness, abrasiveness, and slipperiness of concrete floors have adverse effects on animal well-being and health, and yielding rubber flooring is becoming popular as a way of improving the flooring conditions on walkways. The aim of this study was to investigate preferences of dairy cows for rubber compared with concrete flooring under the conditions of a commercial dairy farm. The study was conducted in an organic dairy herd with free-stall housing. Floor preference was tested on groups of standing cows in a 120-m2 holding pen before milking, and 1 yr later on a 12- × 3-m walkway. The holding pen and the walkway were divided lengthwise into 2 identical sections. Two types of solid rubber mats (soft and extra soft) were tested against solid concrete in the holding pen. Slatted and solid rubber mats were tested against slatted concrete in the walkway. Each floor type was tested over 4 d on the left side and 4 d on the right side of the holding pen and the walkway, respectively. Concrete flooring on both sides of the sections was tested as a control before the testing of different section materials. All observations of the distribution of cows in the sections were made from video recordings captured in association with the afternoon milking. The number of cows on each section was recorded approximately every 7 min in the holding pen, and continuously on the walkway. A significantly higher proportion of cows stood on the side with the soft and extra soft rubber mats (65.1 ± 2.7 and 69.3 ± 2.6%, respectively, mean ± SEM) compared with the control distribution when only the solid concrete was available (50.9 ± 3.9%). A significantly higher proportion of nonlame cows walked exclusively on the side with the slatted (64.5 ± 5.4%, d 4) or solid rubber mats (68.2 ± 5.1%, d 4) compared with controls (28.9 ± 4.3%). Lame cows within a group of walking cows did not show a higher preference for soft flooring as distinct as nonlame cows (52.7 ± 6.9 and 59.4 ± 6.2% for the solid and slatted rubber mats, respectively, at d 4 vs. 40.3 ± 6.2% for control), presumably because of competition with other, higher ranked cows. It was concluded that the majority of cows preferred to walk and stand on soft rubber rather than on concrete flooring.

Behavior of Hydrostatic and Hydrodynamic Noncontacting Face Seals

In this paper, the pressure generation and static stability of face-type seals are discussed and an expression is developed to estimate the effectiveness of hydrodynamic action in these seals. Some design data are presented for the hydrostatic step seal, hydrostatic-orifice compensated seal, hybrid spiral-groove seal, and the shrouded Rayleigh step seal. These data are applicable to large-diameter seals for compressible fluids. The seal ring distortions due to initial imperfection, pressure, and thermal expansion are discussed. Approaches to estimate and to minimize the effects of these distortions are outlined. Finally, the ability of a face seal to track the vibrations of the runner is also discussed and methods required to determine the dynamic tracking for rigid or flexible seals are described.

Design of Floated Shoe Close Clearance Seals for Supersonic Jet Engine Compressors

The increase in engine efficiency to be gained by substituting a floated close running air seal at the high pressure end of large jet engine compressors, in place of the labyrinth seal, has prompted an intensive effort to design such seals for experimental evaluation. This paper describes the design of both a radial and an axial version in which multiple segmental shoes are floated 0.001 in. from the high speed runner surface. In the radial version, the shoes are free to float radially in order to follow runner runout. In the axial version, the shoes track the runner runout by floating axially in a carrier which moves to accommodate 0.4 inch of differential expansion. Floating is achieved through hydrostatic action sustained by the pressure difference across the seal. A shrouded Rayleigh step profile on the primary (high speed rubbing) seal surface provides additional protection. An order of magnitude reduction in leakage rate is predicted.

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.

On the load capacity of the hydromagnetically lubricated slider bearing

The load capacity of liquid metal lubricated slider bearings subject to an applied magnetic field transverse to the film is investigated. The optimum profile is determined and found to be the Rayleigh step form with the riser location and step height ratio dependent on the strength of the magnetic field. Load capacity is favored by large magnetic fields, small film thicknesses and electrically insulating bearing surfaces. Only modest load increases can be obtained from conventional magnets of reasonable size. Substantial load increases could be accomplished by the recently developed superconducting electromagnets.