Theoretical Prediction of Journal Bearing Stability Characteristics Based on the Extent of the Slip Region on the Bearing Surface

Journal bearing performance depends on the boundary conditions at the interfaces between the fluid and the solid surfaces. In the derivation of the Reynolds equation used to predict the bearing performance, the no-slip boundary conditions of the fluid and the solid interfaces are used. Recent research has shown that a slip can occur on specially made surfaces, the conventional no-slip boundary conditions are not valid, and the Reynolds equation is no longer applicable. If the slip is allowed to occur in certain regions, the fluid flow in the bearing can be altered, and the bearing stability characteristics can be improved. In this article, the numerical stability analysis of a journal bearing based on the extent of the slip region on the bearing surface is analyzed. An extended Reynolds equation is derived based on the slip length model, using a no-slip boundary condition against the journal surface and the slip against the bearing surface. A linearized perturbation method is used to determine the stability limit of a rigid rotor supported on two symmetrical journal bearings. Using the linear stability analysis, the linearized stiffness and damping coefficients, the threshold speed, and the critical whirl ratio are evaluated. The effects of the slip parameter on the bearing stability performance are discussed. The results show that with a critical shear stress of zero, an increase in the stability threshold can be achieved with a higher value of the nondimensional slip length and a smaller extent of the slip region on the bearing surface.     

Effects of velocity slip on the elastohydrodynamic lubrication of short, porous journal bearings

The studies of Beavers and Joseph indicated that velocity slip takes place at the permeable boundary of porous bearings. The purpose of this article is to make an analytical study of a short, porous journal bearing taking into account both the effects of velocity slip at the film-bearing interface and the flexibility of the bearing. An analytical solution for the performance of such bearings is obtained in terms of several parameters involving porosity, slip coefficient, bearing dimensions and speed.     

Effect of velocity slip on squeeze films in porous bearings

The performance of squeeze films in porous journal bearings was analysed using the Beavers-Joseph criterion of velocity slip at a porous boundary. Closed-form expressions were obtained for the pressure distribution in an infinitely long bearing and also in an infinitely narrow bearing. Numerical results evaluated from these expressions are presented in graphical form to illustrate the influence of velocity slip.     

Influence of Wall Slip on the Dynamic Properties of a Rotor-Bearing System

Based on the limiting shear stress model, we used a multi-linearity finite element algorithm and quadratic programming technique to study the influence of wall slip (boundary slip) on the operation stability of a rigid rotor-bearing system. The shaft surface is designed as a no-slip surface. The bearing sleeve surface is designed as three types of surfaces: (a) no slip is allowed (traditional no-slip rotor-bearing system), (b) the entire sleeve surface has the same slip property (the homogeneous slip bearing), and (c) the sleeve surface is optimized to have an optimized slip zone (the optimized slip bearing). It is found that if the sleeve surface has a single slip property, the wall slip generally reduces the system operation stability, as well as the load-carrying capacity. However, if the sleeve surface is designed as the optimized slip surface, the wall slip enhances the system operation stability as well as the load-carrying capacity. Furthermore, the smaller the surface limiting shear stress, the better the dynamic stability and the higher the load-carrying capacity.     

Hydro-Roll: A Novel Bearing Design with Superior Thermal Characteristics

A novel journal bearing design, called hydro-roll, which combines a hydrodynamic journal bearing with a rolling-element bearing in series, is presented. The hydro-roll principally operates as a rolling-element bearing at low speeds and as a hydrodynamic bearing at high speed. When properly designed, the hydro-roll can offer superior performance over the conventional hydrodynamic bearing in terms of both wear and thermal characteristics. The hydro-roll prevents the severe wear which occurs during the start-up of hydrodynamic journal bearings since it operates as a rolling-element bearing whenever the sliding friction is too high. This characteristic has the important advantage of reducing the risk of catastrophic failure by bearing seizure.

At a steady high speed, the hydro-roll operates as a hydrodynamic journal bearing while the sleeve together with the inner race of the rolling-element bearing turn at a low speed. This study focuses on the thermal analysis of a journal bearing with a rotating sleeve in comparison to an identical stationary sleeve. The results indicate that the sleeve rotation reduces the risk of bearing failure due to local overheating of the sleeve. The minimum sleeve speed required for this effect is evaluated.     

Steadily loaded journal bearings: Quasi-3D mass-energy-conserving analysis

A finite-element approach to thermoelastohydrodynamic lubrication analysis is developed by extending a previous mass- and energy-conserving algorithm to include wall-convection boundary conditions, groove-mixing theory, and thermo-mechanical deformations. To this end, the cross-film-averaged energy equation is coupled with the heat conduction equations relevant to the bearing sleeve and the journal by fitting the temperature profile across the film thickness with a fourth-order polynomial. A finite-element condensation technique is used to reduce the unknowns in heat conduction equations in the bush and in the journal to the temperatures of the sleeve surface and journal axis, respectively. Applied to the analysis of steadily loaded journal bearings, the proposed method shows good agreement with published experimental results and incurs low computational cost.     

Numerical analysis of spiral oil wedge sleeve bearing including cavitation and wall slip effects

The modified Reynolds equation is established on the basis of critical shear stress model, in which the circumferential and axial wall slip of sleeve and journal surface is considered. Cavitation is treated using modified Elrod algorithm that simplifies the solution of modified Reynolds equation in the full‐film region. The modified Reynolds equations considering wall slip and cavitation effect for two‐dimensional sleeve bearing are established. The results show that wall slip decreases oil film pressure, carrying capacity, friction drag and temperature rise but increases end leakage and cavitation region. The obtained results using the mass‐conserving boundary condition are compared with the Reynolds boundary condition. Copyright © 2014 John Wiley & Sons, Ltd.     

界面滑移对圆柱形凹坑织构滑动轴承摩擦力的影响

为研究不同的滑移情况对圆柱形凹坑织构滑动轴承摩擦力的影响,建立含有圆柱形凹坑织构的滑动轴承在不同界面滑移状态下的摩擦力计算模型,探究影响织构化滑动轴承摩擦力的参数,并借助ANSYS分析不同滑移情况下界面滑移对圆柱形凹坑织构滑动轴承摩擦力的影响规律。结果表明:织构化滑动轴承的摩擦力主要是由轴颈线速度、油膜滑移比、轴承的进出油口压力、织构处油膜压力、织构深度、油膜厚度和承载力决定;不同滑移情况下织构模型的摩擦力均小于无织构模型;且在上下表面均滑移时,圆柱形凹坑织构在出口位置时表现出最优的承载和减摩效果;适当地增加圆柱形凹坑织构的深度可以改善模型的摩擦性能,但是过深的凹坑织构并不能发挥出其性能。     

Wall slip and hydrodynamics of two-dimensional journal bearing

In the present paper, based on the limiting shear stress model, a multi-linearity finite element algorithm and quadratic programming technique are used to study the influence of wall slip on the hydrodynamic lubrication performance of a two-dimensional journal bearing (finite length journal bearing). It is found that if the lubricated surfaces are designed as homogeneous slip surfaces, the hydrodynamic force will be decreased. If the shaft surface (rotation) is a slippery surface with very low limiting shear stress, almost no fluid load support can be generated. If the sleeve surface is designed as the homogeneous slip surface, a low fluid load support together with a small friction drag can be obtained. However, if the sleeve surface is designed as an optimized slip surface with a slip zone in the inlet region, a high load support and low friction coefficient can be obtained. Optimization of the shape and the size of the slip zone can give the journal bearing many advanced properties.     

Floating ring journal bearings: theory, design and optimization

The performance characteristics and design data for journal bearings with a precise floating ring inserted between the rotating journal and a rigid housing are investigated theoretically. Based on convenient boundary conditions, a theory has been developed to predict the floating ring behaviour. Performance charts are presented with curves provided with optimum design areas to help in practical design applications. Induced ring speed, hydrodynamic behaviour, oil film variation, load capacity and frictional drag could thus be analytically or graphically determined. Results indicate that the ring dimensions are a dominant factor in deciding the final bearing behaviour and that the oil film thickness between the ring and the housing is much thinner than that between the journal and the ring. The floating ring bearing showed less frictional power loss than a fixed sleeve bearing, but this may have been achieved at the expense of the load capacity.     

Numerical prediction of slip flow effect on gas-lubricated journal bearings for MEMS/MST-based micro-rotating machinery

The fluid dynamics of gas-lubricated journal bearings in micro-rotating machinery is different from those of larger size. One point to be considered is a slip flow effect. In this paper, the slip flow effect is considered in order to estimate load-carrying capacity and dynamic coefficients of micro gas-lubricated journal bearings. Based on a modified compressible Reynolds equation including slip flow effect, the first slip approximation was applied. To extract dynamic coefficients, the linearized dynamic equations were formulated by the perturbation method. Numerical predictions compared the static and dynamic characteristics considering slip flow at room-to-high temperature in a range of bearing numbers. The results including load-carrying capacity and dynamic coefficients demonstrate that the slip flow effect becomes significant with temperature increase as well as in the lower range of bearing numbers.     

Analysis of Micropolar and Power Law Fluid–Lubricated Slider and Journal Bearing with Partial Slip–Partial Slip Texture Configuration

An analysis of micropolar and power law fluid–lubricated partial slip–partial slip texture slider and journal bearings is presented. The nondimensional pressure and shear stress expressions for a partial slip texture configuration are analyzed using narrow groove theory. The parameters used in the analysis are nondimensional partial slip length, nondimensional partial slip–partial slip texture length, nondimensional depth of recess, ratio of land with slip to recess, nondimensional slip coefficient, coupling number; ratio of characteristic length to film gap, and power law index. A partial slip configuration with a higher slip coefficient yields an improvement in load capacity and reduction in coefficient of friction compared to a partial slip texture configuration for micropolar and power law shear thinning (pseudoplastic) fluid-lubricated slider and journal bearings.     

弹性金属塑料瓦径向滑动轴承启动过程热弹流分析

研究了采用弹性金属塑料轴瓦时径向滑动轴承的瞬态润滑特性。建立了该轴承的三维热弹流模型，通过数值求解对比了启动过程中采用弹性金属塑料轴瓦和金属材料轴瓦时油膜和轴瓦的瞬态温度场分布、轴瓦的热弹变形量，以及转子轴心轨迹。结果表明，在启动初期弹性金属塑料瓦径向滑动轴承的瓦体温度要高于金属瓦，转子偏心率也要大于采用金属瓦时的偏心率；因润滑油在弹性金属塑料瓦径向滑动轴承轴瓦表面存在一定的滑移速度，随着油膜边界滑移作用的出现，采用弹性金属塑料瓦径向滑动轴承时的油膜温度最终低于采用金属瓦时的温度，且转子的偏心率也最终小于采用余属瓦的偏心率。     

Dynamic Friction Model of Lubricated Surfaces for Precise Motion Control

A model is developed to describe dynamic friction effects in lubricated surfaces. The model covers the hydrodynamic, mixed and boundary lubrication regions. The dynamic friction model can predict the friction force for time-varying velocity, and is useful in precise motion control. The model presented is for a short journal bearing, but can be extended to other geometries of sliding surfaces, such as point and line contacts or rolling element bearings. The friction is related to a time variable fluid film thickness, resulting from journal vibrations relative to the sleeve. The proposed model agrees qualitatively with experimental results for lubricated line contact. Both show similar hysteresis-type friction curves under oscillating velocity.     

Bearing materials for small electric motors

Operation of small electrical machines with bearings under boundary lubrication conditions does not receive much attention in the literature. Yet there are some fifty million fhp (fractional horsepower) induction motors made every year. This article outlines the bearing types used in these motors and examines a new polymer lined bearing which seems attractive for many applications using sleeve or ball bearings     

The numerical analysis of the radial sleeve bearing with combined surface slip

In order to improve the carrying capacity and reduce the temperature rise in high speed and precise spindle systems, a combined surface radial sleeve bearing using the interfacial slip technique was discussed. An extended Reynolds equation was derived based on the modified slip length model considering the limiting shear stress. By means of the finite differential methods, the characteristic analysis and optimization of the slip region of the combined surface sleeve bearing were carried out, and it has been proved that there is still a considerable large load support in a parallel sliding gap. Comparing with the general journal bearing, the load capacity and end leakage rate of the combined surface sleeve bearing can be increased greatly and the load capacity can be increased by 1.75 times. The attitude angle, friction drag, temperature rise of the combined bearing can be decreased distinctly and the temperature rise can be decreased by 92.4%.     

Abrasive wear of bearing materials — a comparison of test methods

In a lubricated journal bearing, journal as well as bearing may suffer from wear if the lubricant contains hard abrasive particles. Wear may be particularly severe under conditions of boundary lubrication. Tests with 360° journal bearings show that, as far as friction and wear are concerned, the white metal SnSb8Cu4Cd and the bronze CuPb10Sn10 suffer equally from the addition of “air cleaner test dust” in the lubricant. In contrast, on addition of the abrasive, the composite process surface roughness of the bearing (which controls the ability of the bearing to re-establish thick film lubrication) remains virtually unaffected in the case of the white metal but increases considerably in the case of the bronze.The results of tests, performed with a block-on-ring method, do not agree well with those found with real journal bearings. Thus they are not suitable for qualifying materials for application in journal bearings lubricated with abrasive-containing lubricant.     

Numerical investigation of the combined effects of slip and texture on tribological performance of bearing

Slider bearings are used in many applications. An increase in the load support may allow for saving of energy. In this work, in order to enhance the load support and decrease the friction force, a combined textured surface bearing using boundary slip is discussed. A modified Reynolds equation with slip is adopted. With the main goal of evaluating the effects of slip and texture, a parametric analysis is performed. For the given operating conditions, texturing features as well as slip pattern are analysed in detail. The numerical analysis is undertaken under the condition of different gap ratio values and the slip-textured area. The results show that combined techniques of slip and texture have a significant effect on the improvement of the tribological performance of bearing, that is, a high load support but low friction force. The gap ratio of the bearing is shown to have a significant effect on the lubrication behaviour. It is found that even with a smallest gap ratio (parallel gap), a high load support can be produced. However, it is also shown that the gap ratio appears to contribute to the generated friction force and the volume flow rate more than the boundary slip. Further analysis indicates that the optimum slip-text zones for certain gap ratio are highlighted. These findings may provide references for designing hydrodynamic-textured slider bearing considering boundary slip.     

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.     

Analysis of stiffness and damping characteristics of externally pressurized gas-lubricated porous bearings under conical mode of vibration

This work gives a theoretical analysis of the dynamic behaviour of externally pressurized gas-lubricated porous bearings with journal rotation and with regard to the stiffness and damping in the conical mode of vibration. The theoretical analysis has been obtained by the simultaneous solution of the continuity equation of flow through a porous medium (derived from a modified version of Darcy's law) and the modified Reynolds equation (governing the pressure in the bearing clearance) by the finite difference method (successive over relaxation, central difference) satisfying the appropriate boundary conditions. The effects of journal speed, feeding parameter, supply pressure, porosity parameter and length-to-diameter ratio on the stiffness and damping coefficients have been investigated. A one-dimensional flow model without velocity slip is considered.