Step Bearing Research Articles

Research on the Lubrication Performance of Hydrostatic Thrust Bearings Considering Dynamic Pressure Effect and Oil Film Pressure Loss

A lubrication performance mathematical model considering the dynamic pressure effect and pressure loss is proposed for stepped hydrostatic thrust bearings. The influence mechanism of rotational speed and load on the static pressure, dynamic pressure, pressure loss, total pressure, and total temperature of the clearance oil film is systematically discussed through a combination of theory, simulation, and experiment. The investigation found that the total temperature of the oil film decreases with increasing load and increases with increasing rotational speed. The pressure loss also becomes increasingly significant with higher rotational speeds. The dynamic pressure is not limited by the load but increases with the increase in rotation speed. The oil film pressure loss is jointly borne by static pressure and dynamic pressure within the range of 0 to 160 rpm and mainly borne by static pressure within the range of 160 to 200 rpm. Additionally, the trends of static pressure, dynamic pressure, total pressure, and temperature in the experiment are nearly consistent with those predicted by numerical simulations, thereby validating the effectiveness of the research methodology employed in this article.

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.

Performance of Multiscale Hydrodynamic Step Bearing with Inhomogeneous Surfaces

Performance of Multiscale Hydrodynamic Step Bearing with Inhomogeneous Surfaces

Investigation on the Dynamic Pressure Effect of Clearance Oil Film at a Stepped Hydrostatic Thrust Bearing Working in Heavy Loading Duty

The dynamic pressure effect of the clearance oil film of stepped hydrostatic thrust bearing is studied by taking the double rectangular cavity oil cushion as an example. According to the hydrodynamics theory, the dynamic pressure of lubricating oil film in different clearance height regions is theoretically deduced and calculated. The dynamic pressure effect of the clearance oil film in the stepped hydrostatic thrust bearing is studied through the combination of theoretical calculation, simulation, and experimental verification. It is found that the experimental value of the dynamic pressure is between the theoretical value and the simulated value, which is basically not affected by the load. In the speed range of 0 r/min–200 r/min, compared with the viscosity of lubricating oil, the speed is the main factor affecting the dynamic pressure of the oil film of the stepped hydrostatic thrust bearing. The dynamic pressure value of the clearance oil film increases in a stepped fashion along the radial direction of the double rectangular cavity oil cushion. The dynamic pressure value has an obvious upward trend at the junction of the circumferential right oil cavity and the sealing edge and then decreases to 0 after reaching the peak value.

Investigating lubrication performance in HSCP with sliding-frictional pairs of stepped bearings

Investigating lubrication performance in HSCP with sliding-frictional pairs of stepped bearings

Investigating lubrication performance in HSCP with sliding-frictional pairs of stepped bearing

Investigating lubrication performance in HSCP with sliding-frictional pairs of stepped bearing

MULTISCALE SIMULATION OF HYDRODYNAMIC STEP BEARING WITH ULTRA-LOW CLEARANCE INVOLVING SURFACE ROUGHNESS

The numerical calculation was carried out for the multiscale hydrodynamic step bearing with ultra-low clearance and nanoscale surface roughness based on the newly developed multiscale approach. The moving surface was assumed as perfectly smooth and the stationary surface was imposed with the sinusoidal surface roughness. Due to the surface roughness, locally the physically adsorbed boundary layer may be only present, while in other areas, the sandwich films consisting of both the adsorbed boundary layers and the intermediate continuum fluid film may be present. In this bearing, the fluid film may be locally severely squeezed so that the local film pressure is very high. In this circumstance, the influences of the film pressure on both the film viscosity and density were considered. The results show that with the increase of the surface roughness, the hydrodynamic pressure and carried load of the bearing are very significantly increased especially for a stronger fluid-bearing surface interaction; the fluid piezo-viscous effect becomes stronger with the increases of both the surface roughness and the fluid-bearing surface interaction strength.

Energy-Conserved Hydrodynamic Lubricated Components with Wall Slippage

The hydrodynamic thrust slider and journal bearings as well as hydrodynamic lubricated gears with the merit of energy conservation by the wall slippage are reviewed. The principle for designing these hydrodynamic contacts is to artificially set the wall slippage on the stationary surface in the hydrodynamic inlet zone. To design the wall slippage on the moving surface in the hydrodynamic outlet zone can also give additional benefits. The technical merits of these mechanical components are the improved load-carrying capacity and the lowed friction coefficient, i.e., the energy conservation due to the wall slippage. Owing to the designed wall slippage, the carried load of the hydrodynamic step bearing can be increased by 200%~400% while its friction coefficient can be reduced by 50%~85%, and the load-carrying capacity of the hydrodynamic journal bearing can be increased by nearly 100% while at the same time, its friction coefficient can be reduced by more than 60%. For hydrodynamic lubricated gear contacts, by covering ultrahydrophobic or oilphobic coatings on the slower moving surface, the friction coefficient can be approaching to vanishing and the contact load-carrying capacity can be increased very significantly for large slide-roll ratios under medium or heavy loads.

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.

Performance of a hydromagnetic squeeze film on a rough circular step bearing: a comparision of different porous structures

This investigation deals with a comparative analysis of the impact of spongy structure based on the model of Kozeny-Carman and Irmay on a hydromagnetic squeeze film in a rough circular step bearing. Christensen and Tonder’s stochastic averaging process has been utilized to determine the role of an arbitrary transverse surface irregularity. The distribution of the pressure in the bearing is obtained by solving the concerned generalised stochastically averaged equation of Reynolds’ with appropriate boundary conditions. The outcomes show that increasing values of magnetization results in an augmented load. The impact of the surface irregularity (transverse) has been found to be adverse. In addition, the negative effect of the surface irregularity and porosity can be minimised by the positive impact of magnetization, at least in the case of the globular sphere model of Kozeny-Carman. Furthermore, the lower strength of the magnetic field results in an approximately similar performance for both these models. This study offers the possibility that the Kozeny-Carman model could be deployed in comparison with Irmay’s model.

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

Multiscale Analysis of Hydrodynamic Step Bearing with Ultra Low Surface Separations

The paper presents the multiscale analysis for the hydrodynamic step bearing with ultra low surface clearances where only the physical adsorbed layer is present in the outlet zone and the continuum fluid flow mainly occurs in the inlet zone. This bearing can occur under heavy loads. The flow in the outlet zone is described by the nanoscale flow equation, while the flow in the inlet zone is described by the multiscale flow equation incorporating both the adsorbed layer flow and the intermediate continuum fluid flow. The pressure and carried load of the bearing were derived. Exemplary calculations show that the fluid-bearing surface interaction has the strongest influence on the pressure and carried load of this bearing when the bearing surface clearance is as small as possible, the bearing step size is close to the surface clearance in the outlet zone and the value of the geometrical parameter is the optimum one, which depends on the fluid-bearing surface interaction. For the strong fluid-bearing surface interaction, the carried load of the bearing can be 10 times higher than that calculated from the classical hydrodynamic lubrication theory.

DESIGN OF POROUS STEP BEARING BY CONSIDERING DIFFERENT FERRO FLUID LUBRICATION FLOW MODELS

The aim of this article is to carry out analysis to enhance the performance of the ferro fluid lubricated porous step bearing. The porous coating is assorted to the lower flat impermeable surface. A step is there in upper surface which approaching to lower surface. This study considered that magnetic field is flexible and oblique to the lower surface. By considering Jenkins Model, expressions for pressure and load capacity are obtained. The non-dimensional load capacity is also calculated for various parameters. Based on results, it is observed that load capacity increases if suitable step size is considered. Also, comparison between R. E. Rosensweig Model and Jenkins Model is carried out. Finally, it is advised to design a porous step bearing, one should consider Jenkins Model over R. E. Rosensweig Model.

Theoretical Disquisition on the Static and Dynamic Characteristics of an Adaptive Stepped Hydrostatic Thrust Bearing with a Displacement Compensator

Stepped hydrostatic thrust bearings used in metal-cutting machines are characterized by high load capacity and damping, which ensure the stable operation of structures. However, in comparison with throttle thrust bearings, they have a high compliance. It is preferable that, in addition to the main bearing function, a modern hydrostatic bearing has the ability to provide low (including negative) compliance for the implementation of an adaptive function in order to actively compensate for the deformation of the machine resilient system, thereby increasing the accuracy of metalworking. This paper considers the design of a stepped hydrostatic thrust bearing, which, in order to reduce the compliance to negative values, features a technical improvement consisting of the use of an active displacement compensator on an elastic suspension. In this paper, the results of mathematical modeling and theoretical research of stationary and non-stationary modes of operation of the adaptive thrust bearing are presented. The possibility of a significant reduction in the static compliance of the structure, including the negative compliance values, is shown. It was found that negative compliance is provided in a wide range of loads, which can be up to 80% of the range of permissible bearing loads. The study of the dynamic characteristics showed that with a targeted selection of parameters that ensure optimal performance, the adaptive thrust bearing is able to operate stably in the entire range of permissible loads. It has been established that an adaptive stepped hydrostatic thrust bearing with a displacement compensator has a high stability margin, sufficient to ensure its operability when implementing the adaptive function.

Effects of Surface Roughness and Supply Inertia on Steady Performance of Hydrostatic Thrust Bearings Lubricated with Non-Newtonian Fluids

Abstract The objective of present theoretical analysis is to study the combined effects of surface roughness and fluid inertia (including the inertia of the fluid in the supply region) on the steady performance of stepped circular hydrostatic thrust bearings lubricated with non-Newtonian pseudoplastic fluids using Rabinowitsch stress-strain model. To account for the effects of surface roughness, the classical Christensen theory of rough surface has been taken. Analytic expressions for film pressure in bearing regions have been established for radial and circumferential patterns of roughness. Numerical results for film pressure, load carrying capacity and lubricant flow rate has been plotted and analysed. Due to surface roughness and fluid inertia in overall regions, significant improvement in performance properties have been observed.

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.

Study on Multiscale Hydrodynamic Step Bearing

In a step bearing, when the surface separation is so low that it is comparable with the thickness of the physical adsorbed layer on the bearing surface, the physical adsorbed layer should have an influence on the bearing performance. The present paper presents a multiscale analysis for this multiscale hydrodynamic bearing by considering the effect of the adsorbed layer but neglecting the interfacial slippage on any interface. The adsorbed layer flow is described by the nanoscale flow equation, and the intermediate continuum fluid flow is simulated based on the Newtonian fluid model. The pressure distribution and carried load of the bearing were derived. Exemplary calculations show that when the surface separation in the bearing outlet zone is below 100nm but no less than 10nm, for a weak fluid-bearing surface interaction both the pressure and carried load of the bearing are just slightly higher than those calculated from the conventional hydrodynamic lubrication theory, for a medium fluid-bearing surface interaction the differences are further enlarged, and for a strong fluid-bearing surface interaction the differences are mostly enlarged. The results show the very significant multiscale effect in this bearing resulting in the pronounced improvement of the load-carrying capacity of the bearing by the medium and strong fluid-bearing surface interactions when the surface separation in the bearing outlet zone is below 100nm.

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.

Effect of the Interfacial Slippage on the Moving Surface in a Hydrodynamic Step Bearing

The effect of the interfacial slippage on the moving surface in a hydrodynamic step bearing is analytically investigated based on the interfacial limiting shear strength model. The calculation results show that when the interfacial slippage occurs on the whole moving surface but is absent on the whole stationary surface, the load-carrying capacity of the bearing is independent on the sliding speed but is intimately dependent on the contact-fluid interfacial shear strength on the moving surface, and the carried load of the bearing is normally heavily reduced as compared to that calculated from conventional hydrodynamic lubrication theory especially for high sliding speeds; The friction coefficient of this mode of bearing is significantly higher than that of the conventional hydrodynamic step bearing for a high sliding speed, but the case is opposite for a low sliding speed. The results show the potential application value of this mode of bearing for reducing the friction at a low sliding speed or the necessity of preventing the occurrence of the interfacial slippage on the moving surface in a hydrodynamic step bearing at a high sliding speed.