Rayleigh Step Bearing Research Articles

Stability Analysis of the Secondary Motion of a Textured Piston

Piston–cylinder pairs are very common in industrial mechanisms. While a piston is primarily designed for axial reciprocating motion, the occurrence of secondary motions—lateral and rotational—due to the small clearance between the piston and the cylinder may lead to frictional contact, energy loss, wear and an increase in unwanted leakage. This study focuses on mitigating the secondary motion of a ringless piston. The influence of a Rayleigh step bearing and partial surface texturing with numerous micro-dimples on the dynamic stability of the secondary motion is studied. A linear model was used to obtain the trajectory of the secondary motion and Floquet theory was applied to analyze the stability and draw stability maps. The influence of various texturing and step parameters, including the dimple area density and aspect ratio for partial texturing, as well as the length and depth of treatment for both partial texturing and step profiles, on the stability of the secondary motion was examined. The normalization method is presented, enabling the expansion of the results for various operating conditions and geometries. Conclusions and guidelines regarding the optimal parameters, in terms of a wider stability range and higher decay rate, are formulated.

Static and Dynamic Characteristics of Rough Porous Rayleigh Step Bearing Lubricated with Couple Stress Fluid

In tribology, the Rayleigh step bearing has the maximum load capacity of any feasible bearing geometry. Traditional tribology resources have demonstrated that the Rayleigh step has an ideal geometry which maximizes load capacity. Both in nature and technology, rough and textured surfaces are essential for lubrication. While surface roughness enhances the performance of the bearings as an efficiency measure, it still has a significant impact on the load-carrying capacity of the bearing. In the present study, we investigate the dynamic characteristics of the Rayleigh step bearing with the impact of surface roughness and a porous medium by considering a squeezing action. Couple stress fluid is considered a lubricant with additives in both the film as well as the porous region. Based on Stokes constitutive equations for couple stress fluids, Darcy’s law for porous medium, and stochastic theory for rough surfaces, the averaged Reynolds-type equation is derived. Expressions are obtained for the volume flow rate, steady-state characteristics, and dynamic characteristics. The influence of surface roughness and the porous medium on the Rayleigh step bearing is analyzed. We investigated the static and dynamic characteristics of the Rayleigh step bearing. As a result, the couple stress fluid increases (decreases) the steady load-carrying capacity, dynamic stiffness, and dynamic damping coefficients, and decreases (increases) the volume flow rate negatively (positively) skewed roughness in comparison with that of the Newtonian case. The results are compared with those of the smooth case.

Double-Layered Porous Rayleigh Step Slider Bearings Lubricated with Couplestress Fluids

Objective: To examine the performance of double-layered porous Rayleigh step slider bearings lubricated with couple stress fluid and to compare it with the performance of single layered porous Rayleigh step bearing. Methods: Based on the Stokes micro continuum theory of couple stress fluids, the modified Reynolds equation governing fluid film pressure is derived. Its analytical solution is and the closed form expressions for the fluid film pressure, frictional force and load carrying capacity are obtained. Findings: The numerical results for bearing characteristics such as pressure, load carrying capacity, frictional force are plotted graphically to study the effect of doublelayered porous facing. The effect of permeability of the porous layer is to decrease the load carrying capacity as it gives an easy path for the lubricant to pass through. This adverse effect can be compensated by introducing double layered porous facing with different permeabilities and the results presented here in this paper clearly shows the increase in load carrying capacity and decrease in co-efficient of friction for the double layered porous bearings as compared to that of single layered porous bearings. Novelty: Original research was conducted on double-layered porous Rayleigh step slider bearings with couple stress fluid by considering the effects of lubricant additives in the porous region and the results are compared with that of single layered porous bearings. Keywords: Rayleighstep slider bearing; permeability; Doublelayered porous; couple stress fluid Microcontinuum

Effect of directionally oriented random roughness on performance of a Rayleigh step bearing operating under Mixed-Elastohydrodynamic Lubrication

This article delineates the performance of a Rayleigh step bearing operating under Mixed-Elastohydrodynamic Lubrication (Mixed-EHL) with directionally oriented random roughness. Conformal contacts as experienced by Rayleigh Step Bearing has seldom being analyzed under such severe conditions. The pressure flow factor related to roughness orientation, density flow factor related to cavity formation and average film thickness have been taken into consideration to modify the generalized Reynolds equation. Progressive Mesh Densification (PMD) method has been used to solve the related equations iteratively. Larger pressure gets generated in the contact area of the bearing with transversely oriented roughness compared to bearing with other roughness orientation. The effect of cavitation number on mass flow rate and outlet temperature in transverse orientation is significant.

Application of topological optimisation methodology to finitely wide slider bearings operating under incompressible flow

The search for the optimal bearing geometry has been on for over a century. In a publication from 1918, Lord Rayleigh revealed the infinitely wide bearing geometry that maximises the load carrying capacity under incompressible flow, i.e. the Rayleigh step bearing. Four decades ago, Rohde, who continued on the same path, revealed the finitely wide bearing geometry that maximises the load carrying capacity, referred to as the Rayleigh-pocket bearing. Since then, the numerical results have been perfected with highly refined meshes, all converging to the same Rayleigh-pocket bearing. During recent years new methods for performing topology optimisations have been developed and one of those is the method of moving asymptotes, frequently used in the area of structural mechanics. In this work, the method of moving asymptotes is employed to find optimal bearing geometries under incompressible flow, for three different objectives. Among the results obtained are (i) show new bearing geometries that maximise the load carrying capacity, which performs better than the ones available, (ii) new bearing geometries minimising the coefficient of friction and (iii) new bearing geometries minimising the friction force for a given load carrying capacity are presented as well.

Two classes of sub-optimal shapes for one dimensional slider bearings with couple stress lubricants

Shape optimization of slider bearings operating with couple stress lubricants is performed here for the first time by using a novel direct optimal control approach, which defines the gradient of the film height as a control. The bearing load is maximized. One dimensional Reynolds and energy equations are used. Several constraints are taken into consideration. They avoid the occurrence of cavitation and ensure the validity of the Reynolds equation. The model is validated against a known analytical solution (the Rayleigh step bearing). Two simple design rules are inferred, which yield two different classes of sub-optimal shapes: the multi-stepped bearings and the multi-sloped bearings, respectively. Multi-stepped bearings consist of several steps and the couple stress parameter may affect the constant value of the film height between steps. Multi-sloped bearings consist of several inclined regions and the couple stress fluid parameter may affect the constant value of the film height between regions. The slider bearings operation under variable load is stable. A sensitivity analysis identified the design parameters which have the highest impact on bearing performance. The optimal slider bearing shapes obtained for Newtonian lubricants do not change when most common couple stress fluids are used. Isothermal models may be used successfully at lower values of the couple stress parameter.

Thermo-elastohydrodynamic lubrication simulation of the Rayleigh step bearing using the progressive mesh densification method

The paper deals with the numerical simulation of thermo-elastohydrodynamic lubrication (Thermo-EHL) condition in the Rayleigh step bearing. Thermo-EHL involves rheology of the lubricant and deformation of the structure simultaneously under the influence of pressure and temperature, which makes this regime of lubrication more complicated. It is difficult to obtain a converged and accurate solution with ease under this condition. The effect of computational mesh density plays a significant role in obtaining a converged solution rapidly. In this paper, the progressive mesh densification (PMD) method has been applied to solve the Thermo-EHL condition numerically. To find out the best possible scheme of PMD for obtaining a converged solution quickly, the results of PMD and fixed mesh density (FMD) have been compared. Based on the comparison, it has been observed that Scheme 3 of PMD takes around 30% fewer iterations compared with FMD under both elastohydrodynamic lubrication (EHL) and Thermo-EHL conditions. Adopting Scheme 3 of PMD, the effect of temperature on the load capacity, coefficient of friction, no-pressure zone, and pressure distribution in the Rayleigh step bearing has been studied. Reductions in pressure, no-pressure zone, frictional coefficient, and load capacity are observed under the Thermo-EHL condition compared to the EHL condition.

A numerical study on the negligibility of cross-film pressure variation in infinitely wide plane slider bearing, Rayleigh step bearing and micro-grooved parallel slider bearing

In lubrication theory, the cross-film pressure variation is assumed negligible. It is questionable whether this is generally true. To validate this assumption, a finite-element software was used to solve the Navier-Stokes equations for plane slider bearings, Rayleigh step bearings and micro-grooved parallel slider bearings. Results showed that the cross-film pressure variation is negligible for plane slider bearings and Rayleigh step bearings. A parametric investigation for micro-grooved parallel slider bearings showed that there is a limit on the Reynolds number below which the difference between the local and runner pressures exceeding 5% of bearing pressure occurs in a very small region. This study found the correlations for the determination of this limiting Reynolds number.

Effect of surface roughness and deformation on Rayleigh step bearing under thin film lubrication

PurposeThe aim of this paper is to study the effect of deterministic roughness and small elastic deformation of surface on flow rates, load capacity and coefficient of friction in Rayleigh step bearing under thin film lubrication.Design/methodology/approachReynolds equation, pressure-density relationship, pressure-viscosity relationship and film thickness equation are discretized using finite difference method. Progressive mesh densification (PMD) method is applied to solve the related equations iteratively.FindingsThe nature and shape of roughness play a significant role in pressure generation. It has been observed that square roughness dominates the pressure generation for all values of minimum film thickness. Deformation more than 100 nm in bounding surfaces influences the film formation and pressure distribution greatly. Divergent shapes of film thickness in step zone causes a delay of pressure growth and reduces the load capacity with decreasing film thickness. The optimum value of film thickness ratio and step ratios have been found out for the maximum load capacity and minimum coefficient of friction, which are notably influenced by elastic deformation of the surface.Practical implicationsIt is expected that these findings will help in analysing the performance parameters of a Rayleigh step bearing under thin film lubrication more accurately. It will also help the designers, researchers and manufacturers of bearings.Originality/valueMost of the previous studies have been limited to sinusoidal roughness and thick film lubrication in Rayleigh step bearing. Effect of small surface deformation due to generated pressure in thin film lubrication is significant, as it influences the performance parameters of the bearing. Different wave forms such as triangular, sawtooth, sinusoidal and square formed during finishing operations behaves differently in pressure generation. The analysis of combined effect of roughness and small surface deformation has been performed under thin film lubrication for Rayleigh step bearing using PMD as improved methods for direct iterative approach.

On the study of Rayleigh step slider bearings lubricated with non-Newtonian Rabinowitsch fluid

PurposeNowadays, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of non-Newtonian fluids has gained importance. This paper presents an analysis of the static characteristics of Rayleigh step slider bearing lubricated with non-Newtonian Rabinowitsch fluid, which has not been studied so far. The purpose of this paper is to derive the modified Reynolds equation for Rabinowitsch fluids for two regions and to obtain the optimum bearing parameters for the Rayleigh step slider bearings.Design/methodology/approachThe governing equations relevant to the problem under consideration are derived. The modified Reynolds equation is derived, and it is found to be highly non-linear and hence small perturbation method is adopted to find solution.FindingsFrom this study it is found that there is an increase in the load-carrying capacity, pressure and frictional coefficients for dilatant fluids as compared to the corresponding Newtonian case. Further, for dilatant lubricants the maximum load-carrying capacity is attained for the slightly larger values of entry region length of Rayleigh step bearing as compared to Newtonian and pseudoplastic lubricants.Originality/valueRabinowitsch fluid is used for the study of lubrication characteristics of Rayleigh step bearings. The author believes that the paper presents these results for the first time.

Load carrying capacity of a heterogeneous surface bearing

Abstract It has been shown before that liquids can slip at a solid boundary, which prompted the idea that parallel-surfaces bearings can be achieved just by alternating slip and non-slip regions in the direction of fluid flow. The amount of slip at the wall depends on the surface tension at the liquid–solid interface, which in turn depends on the chemical state of the surface and its roughness. In the present study a heterogeneous surface was obtained by coating half of a circular glass disc with a coating repellant to glycerol. A rotating glass disc was placed at a known/calibrated distance and the gap was filled with glycerol. With the mobile surface moving from the direction of slip to non-slip region it can be theoretically shown that a pressure build up can be achieved. The pressure gradient in the two regions is constant, similar to that in a Rayleigh step bearing, with the maximum pressure at the separation line. The heterogeneous disc was placed on a holder supported by a load cell thus the force generated by this pressure increase can be measured accurately. Tests were carried out at different sliding speeds and gaps and the load carried was measured and subsequently compared with theoretical calculations. This allowed the slip coefficient to be evaluated.

S1160206 摩耗による潤滑性能劣化を抑止するレイリーステップ軸受の設計コンセプト

This study presented a novel design concept of Rayleigh step bearing systems. First, a simplified model was developed to discuss the wear process in the sliding interface with a spatial distribution of normal pressure. From a simple calculation based on Archard's wear theory, it was found that the use of normal pressure distribution is effective to keep the initial step of the simulated Rayleigh step bearing. Thus, the design focusing on the pressure distribution on the sliding interface, which can be realized by the optimization of the choice of materials, shape, and the configuration of a supporting system, is effective to make a Rayleigh step bearing system with a high robustness. Subsequently, a simple friction test was performed, in which the change in the shape of sliding interface due to the development of friction wear was monitored. From the experiment, the validity of the above concept developed in this study was confirmed.

Study on the load-carrying mechanism of a parallel step bearing

In this paper, the load-carrying mechanism of a parallel step bearing was studied from two different viewpoints, i.e. step bearing and parallel bearing. It has a history of about 100 years that Rayleigh step bearing can give optimum load-carrying capacity for certain geometry. As to parallel bearing, several mechanisms have been proposed: the thermal wedge, the viscosity wedge, the thermal distortion, and the local hydrodynamic effect induced by surface irregularities. In this research, a custom-built fixed-incline slider-bearing test rig was used to measure the lubricant film thickness between a stationary parallel step slider and a rotating transparent disc. Film thickness was measured by interferometry at different sliding speeds. It is worth noting that both temperature and humidity were held constant in the experiments. Experimental results show that the measured curve of film thickness versus speed can be divided into two main distinct regions. One is the lower speed region, where the lubricant film is very thin and less dependent on the sliding speed. In addition, cavitation often occurs in lower speed region. The other is the higher speed region, where the lubricant film is thick and curves of film thickness versus sliding speed present linear relationship in the double logarithmic coordinate system. For different viscosities and loads, the experimental results are quite similar in spite of diverse transition speeds from lower speed region to higher speed region. Theoretical analyses indicate that the film-formation behavior in lower speed region can be attributed to the local hydrodynamic effect caused by the real surface irregularities on the smooth land of the step slider, while the load-carrying mechanism in higher speed region agrees well with the classical lubrication theory of Rayleigh step bearing.

CFD-Based Thermohydrodynamic Analysis of Rayleigh Step Bearings Considering an Inertia Effect

In this article, a numerical study investigating the thermohydrodynamic (THD) characteristics of Rayleigh step bearings running under steady, incompressible, and laminar conditions is presented. An attempt is also made to investigate the THD behaviours of step bearings when they are running under different speeds, geometrical factors, and Reynolds numbers. To reach this goal, the conservations of mass, momentum, and energy equations are solved simultaneously by the computational fluid dynamics (CFD) technique. Discretized forms of these equations are obtained by the finite volume method and solved using the SIMPLE algorithm. By this numerical method, the velocity, pressure, and temperature distributions in the lubricant flow are calculated. In this work, the set of governing equations are also solved with inertia terms and without these terms in order to investigate the effect of inertia. Also, an attempt is made to investigate the effects of runner surface velocity and bearing geometrical factors on the lubricant pressure and temperature distributions and also on two important bearing parameters, the load capacity and friction force. A comparison between the numerical results with theoretical findings in the open literature shows good consistency.

Numerical simulation and experimental research on passive hydrodynamic bearing in a blood pump

The current research of hydrodynamic bearing in blood pump mainly focuses on the bearing structure design. Compared with the typical plane slider bearing and Rayleigh step bearing, spiral groove bearing has excellent performance in load-carrying capacity. However, the load-carrying capacity would decrease significantly with increasing flow rate in conventional designs. In this paper, the special treatment is made to the upper spiral groove bearing to make sure that both the circulatory flowing and load-carrying capacity are high. Three-dimensional computational fluid dynamics(CFD) models in the space between rotor and shaft are developed by using FLUENT software. Effects of groove number, film height and groove depth on load-carrying capacity of the spiral groove bearings are investigated by orthogonal experiment design. The experimental results show that film height is the most remarkable factor to the load-carrying capacity. The variation tendency of load-carrying capacity reveals that the best combination of geometry is the one with groove number of 8, film height 0.03 mm and groove depth 0.08 mm. The velocity and pressure distributions in spiral groove bearings are also analyzed, and the analysis result shows that the distributions are in conformity with the design of the blood pump based on the principle of hydrodynamic bearing. The displacement of the rotor with the best combination parameters is tested by using laser displacement sensors, the testing result shows that the suspending performance is satisfactory both in axial and radial directions. This research proposes a bearing design method which has sufficient load-carrying capacity to support rotor as an effective passive hydrodynamic bearing.

Elastohydrodynamic simulation of Rayleigh step bearings in thin film hydrodynamic lubrication

An elastohydrodynamic numerical simulation is conducted for one-dimensional Rayleigh step bearings. The numerical model incorporates the piezoviscous effect of the lubricant and the elastic deformation of the bounding surfaces to solve the one-dimensional Reynolds equation. It is found that a small elastic deformation of less than 200nm is responsible for film formation in thin film hydrodynamic lubrication. As the film thickness decreases, the divergent shape in the step zone causes delay in pressure growth, resulting in considerable reduction of load capacity while the convergent shape in the land zone improves slightly load capacity in some cases. Rayleigh step bearings have higher load capacity than fixed plane bearings because of the remained step shape.

Study of inertia effect on thermohydrodynamic characteristics of Rayleigh step bearings by CFD method

This paper presents a numerical study about lubricant inertia effect on thermohydrodynamic (THD) characteristics of Rayleigh step bearings running under steady, incompressible and laminar condition. To reach this goal, the set of governing equations is solved numerically with and without considering the inertia terms. The discretized forms of the momentum and energy equations are obtained by the finite volume method and solved using the Computational Fluid Dynamic (CFD) technique. These equations are solved simultaneously because the dependency of lubricant viscosity with temperature. The hydrodynamic and thermal behaviors of the slider step bearings are demonstrated by presenting several figures including the lubricant pressure and temperature distributions with and without considering the fluid inertia effect. Numerical results show that inertia term has considerable effect on THD characteristics of step bearings, especially when they run with high velocity of runner surface.

Performance Analysis of the Rayleigh Step Bearing under the Coexistence State of Fluid with Laminar Flow and Turbulence

In the design of tribology pairs, the Rayleigh step bearing is known as a bearing with the highest load capacity amongst all other possible bearing geometries. This paper mainly discusses a new high-speed bearing with shallow and deep cavities on the inner surface of the bearing, and further the physical phenomena in laminar flow and turbulence regimes was revealed. In doing so, the pressure distribution was calculated first using the continuity equations and then performances in the whole flow domain such as pressure distribution, load-carrying capacity, friction force and friction coefficient were calculated. In addition, a set of optimum geometries are shown to provide the highest load capacity for the Rayleigh step bearing under varied Reynolds number. Finally, associated conclusions were drawn by comparison between results under the coexistence state and under the laminar state.

Analytical Solution to the Hydrodynamic Lubrication of Fan-Shaped Thrust Step Bearings

Step bearings are frequently used in industries for better load capacities. Analytical solutions to the Rayleigh step bearing and a rectangular slider with a finite width are available in literature, but none for a fan-shaped thrust step bearing. This study starts with a known solution to the Laplace equation in a cylindrical coordinate system, which is in the form of an infinite summation. A set of analytical solutions to pressure, load capacity, flow rate, and torque loss is derived in this paper for hydrodynamic lubrication problems encountered in the fan-shaped step bearing. These analytical solutions are compared with those for the rectangular slider and the Rayleigh step bearing to reveal relationships among them. When the inner radius becomes smaller, the load capacity increases, almost linearly in a certain region. The effects of inner radius, step height, and step location on pressure distribution and load capacity are studied in general and under a specific set of bearing geometry as an example. The presented solutions can be useful for designers to maximize bearing performance as well as for researchers to benchmark numerical lubrication models.

Impact of the cavitation model on the theoretical performance of heterogeneous slip/no-slip engineered contacts in hydrodynamic conditions

Today's industry faces intense pressure to reduce energy consumption and to extend components' lifetimes in order to reduce economic and environmental costs. During the last few years, it has been pointed out that fluid wall slip is likely to improve friction in low-loaded mechanisms; if the slip zone covers only a specific zone of the surface, improvement of both load and friction can be obtained. The physico-chemical heterogeneity of the surface acts as a geometrical discontinuity and induces pressure gradients analogous to those occurring in a Rayleigh step bearing. Such favourable behaviour can be inhibited if the location of the slip/no-slip areas causes cavitation. This article aims to show the importance of the choice of the cavitation model in the analysis of slip/no-slip hydrodynamic contacts. Current practice predicts the performance of cavitated devices by using the well-known Half-Sommerfeld or Swift—Stieber models. However, using a mass-flow conserving model such as the so-called Floberg—Elrod—Adams model can lead to qualitatively and quantitatively different conclusions. The simple case of a parallel slider bearing is of particular interest. If alternating slip/no-slip areas are introduced, then a non-zero load-carrying capacity can be obtained whose theoretical value dramatically depends on the cavitation model and even on the inlet flowrate of the lubricant.