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on specially made surfaces, the conventional no-slip boundary conditions are not valid, and the Reynolds equation is no longer applicable.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.     

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.     

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.     

微结构表面上流体流动的数值模拟

根据固液界面的复合接触模式,考察了液体在光栅表面上的流动。运用二阶中心差分方法对Navier-Stokes方程进行离散求解,采用了零滑移和零剪切交错边界条件,开发了一个用于计算二维流动参数的计算系统。运用该系统对二维管道进行了模拟,得到了管道内流体的速度分布和压强分布,并计算了管道的减阻情况。计算结果与以往类似结果对比说明了系统的理论基础和实施方案的正确性;计算结果表明,流体在光滑与光栅结构表面构成的管道中的压强分布存在一定差异,光栅结构表面具有一定的减阻性能。最后,通过对不同的表面结构参数进行数值实验,得出了用于减阻衡量的关系式。
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Full and partial boundary slippage effect on squeeze film bearings

Simple experiments were carried out to illustrate the effect of the boundary slippage on the load capacity of a squeeze film. The surface energy of the bearing surface was modified using laser excimer (UV laser). It was found that the load capacity can be reduced if the surfaces are modified to be hydrophobic. The boundary slippage effect on squeeze film was further studied theoretically to get more insight. The paper presents a mathematical model with a critical shear-stress criterion of slippage to describe the squeeze film effect. Three types of slippage, i.e. single zone partial slippage, single zone full slippage, and double zone partial slippage, are modeled. The analytical solution shows that the pressure distribution is a piecewise parabolic curve, where the pressure gradient can be discontinuous at the border of the slip and no-slip regions. Parametric studies illustrate the variations of the pressure and the boundary slippage under different conditions. It is demonstrated that with the increase of the length of the hydrophobic region, the maximum pressure does not increase continuously. Similar to the classical squeeze film bearing, the pressure decreases with the increase in the film thickness or the decrease in the approach velocity. The influences of the critical shear stress are also explored, and are found to significantly affect the squeeze behavior.     

Boundary slip surface design for high speed water lubricated journal bearings

This paper presents the development of a numerical model for high speed and water lubricated journal bearings with different boundary slip arrangements. The effect of boundary slip and its possible mechanism are analyzed and discussed. The results suggest that a suitable combination of slip/no-slip surfaces on the sleeve of a journal bearing enables improvement of the tribological performance through (i) suppressing the occurrence of cavitation, (ii) enhancing the load bearing capacity, and (iii) reducing the interfacial friction between bearing sleeve and shaft. Such improvement becomes more significant for the bearings with smaller eccentricity ratio, smaller width and larger diameter.     

An analytical approach on the tribological behaviour of pocketed slider bearings with boundary slip including cavitation

Slider bearing performance depends on the boundary conditions at the interface between the solid surfaces and the fluid. This paper presents the combined effect of pockets and boundary slip on the load support and friction of parallel sliding systems using analytical solutions for a simple pocketed bearing. The effect of cavitation was of particular interest with respect to the inlet suction mechanism. It was demonstrated that applying boundary slip in a pocketed slider bearing gives a reduction in load support compared with the textured bearing without wall slip. Adding slip over the whole surface could retard the presence of cavitation. The influence of boundary slip is explored, and was found to significantly affect the frictional behaviour. Copyright © 2016 John Wiley & Sons, Ltd.     

Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model

A numerical solution for the hydrodynamic lubrication of finite porous journal bearings considering the flexibility of the liner is introduced. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region and fluid film region, respectively. A stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included into the lubrication analysis. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearing, is implemented in the solution scheme. The present analysis predictions for pressure distributions, load carrying capacity, and friction factor are in good agreement with three different sets of experimental results available in the literature. Furthermore, the effects of dimensionless permeability parameter, and stress jump parameter on performance parameters such as load carrying capacity, side leakage, friction factor, and attitude angle, are presented and discussed.     

A Method for Measuring the Intensity of a Line Load Around a Shaft or Tube

The slip flow effect is considered to estimate the load capacity and the dynamic coefficients of an elastically-supported gas foil hearing when the local Knudsen number for the minimum film thickness is greater than 0.01. The compressible Reynolds equation with slip flow conditions is used to evaluate the load capacity. The linearized dynamic coefficient equations are obtained by the perturbation method. Numerical predictions compare the static and dynamic force performances considering slip flow at room-to-high temperate with the performance of elastically-supported foil bearing without slip flow for a range of bearing compliances and bearing numbers. It has been shown that the slip flow effect on the load capacity and the dynamic coefficients at high temperature is significant in the region of low bearing numbers.     

Abnormal behavior of a hydrodynamic lubrication journal bearing caused by wall slip

Reynolds lubrication theory assumes that there is no wall slip on the interfaces between the solids and lubricant. During recent years, however, it is found that wall slip often happens. The present paper analyzes the wall slip occurring in a hydrodynamic lubrication journal bearing. If the two surfaces have the same adhesion property wall slip always decreases the oil film load support capacity. If there is wall slip over all of the lubricated surfaces, the hydrodynamic effect of the journal bearing vanishes, and no load support exists. If the two lubricated surfaces have different adhesion properties, the wall slip effect is more complex and may cause the journal bearing to operate in an instable manner. In order to avoid the wall slip, the limiting shear stress at the bearing surface should be higher than that at the journal surface.     

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%.     

滑动轴承二维流场的滑移现象研究

目前对于二维流场及复杂流场的界面滑移分析很少,根据螺旋油楔滑动轴承能使润滑剂产生周向和轴向二维流动的独特的结构特点,考虑周向和轴向两方向的滑移建立基于极限切应力的数学模型,并通过试验和理论对比验证模型的正确性。试验方面运用"目标速度跟踪法"证实了周向和轴向都存在滑移,获知随着供油压力的提高滑移速度有所提高,并且提出轴瓦和轴表面的极限切应力;理论方面运用有限差分法和试验测得的轴瓦和轴表面极限切应力,求解四种状态的广义雷诺方程,发现滑移发生在极限切应力大、间隙小和油膜的封油面区域;考虑界面滑移时,螺旋油楔滑动轴承的承载力和摩擦阻力有所降低;偏心率、螺旋角和转速的变化,影响着承载力和摩擦阻力降低的幅度。     

边界滑移对柱塞偶件间油膜流动规律的影响

斜盘式轴向柱塞泵内柱塞偶件间油膜为相对运动的偶件提供润滑及密封作用。油膜流动将直接影响柱塞偶件的工作性能。深入分析偶件间油膜的流动规律对设计与优化柱塞偶件有重要意义。基于Navier-Stokes（N-S）方程,引入Navier边界滑移推导偶件间油膜流动方程,根据柱塞运动的周期性规律,分析单个周期内滑移长度和柱塞泵转速对油膜流动剪应力及流量的影响。研究发现：吸油阶段时近柱塞壁面处油膜剪应力随滑移长度增大而减小,流量随着滑移长度增大而增大,柱塞运动速度最大且滑移长度由1 μm增大到3 μm后,剪应力减小18%,流量增大13.59%;排油阶段柱塞运动速度越大,近柱塞壁面处剪应力和油膜流量与无滑移条件下的差距越小。在滑移长度为1 μm的条件下柱塞泵转速由1 500 r/min增大到4 000 r/min时,近柱塞壁面处的油膜剪应力与无滑移条件下相比降低明显,一个周期内油膜总流量与无滑移条件下相比差距减小。     

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.     

The effects of surface roughness on nanotribology of confined two-dimensional films

A molecular dynamics simulation is used to investigate the effect of surface roughness on the nano-rheology of ultra-thin films confined between two solid walls. The results show that friction is sensitive to the confining surface morphology and the fluid molecules near the two confining surfaces are in a layering solid-like structure. At a high shear rate, the interfacial layers of the film stick to the walls, resulting in partial slip inside the film and the development of shear stress in the viscous molecular fluid. The frictional resisting force is due to the shear in the viscous molecular fluid but not dependent on the critical yield stress of the solid-like structure as in the case of smooth boundaries.     

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.     

Study of Boundary Slippage Using Movement of a Post-Impact EHL Dimple Under Conditions of Pure Sliding and Zero Entrainment Velocity

A well-recognized phenomenon of typical traction tests of elastohydrodynamic lubrication (EHL) contacts is finite maximum traction at increasing speeds, which led to the postulation that the limiting shear stress of liquid lubricants, a high-pressure rheological property, existed. If slippage occurs at the oil–solid boundary, the limiting traction measured is not necessarily an intrinsic property of the lubricant but rather a function of interfacial properties between the bounding solid surface and the lubricant. A recent report presented experimental evidence of boundary slippage at EHL contacts using a simple methodology based on differences in the speed of oil entrapment and the apparent entrainment. The reported experiments were carried out under pure sliding conditions. The phenomenon may also be explained by internal slippage in the bulk fluid film because of the limiting shear stress of the lubricant. To clarify this, similar experiments were repeated under zero entrainment velocity (ZEV) conditions. Evidence of the highly pressurized lubricant at the center of the oil entrapment sliding against the solid bounding surface was obtained. The purpose of this article is to discuss whether the slippage is attributed to the limiting shear stress of the oil or the critical shear stress of the oil/solid interfaces, and how to differentiate the magnitudes of the critical shear stress of the two bounding surfaces in a conventional optical EHL test rig.     

The Influence of Surface Roughness on the Lubrication Properties of Adsorbing and Non-Adsorbing Biopolymers

The lubrication properties of a glycoprotein (pig gastric mucin or PGM) and a high-molecular-weight hydrosoluble polymer (guar gum) have been studied. Friction has been measured over a wide range of entrainment speeds and Stribeck curves have been obtained spanning the boundary, mixed and hydrodynamic lubrication regimes. The adsorption properties of the polymers have also been assessed using evanescent wave spectroscopy. The results show that the polymer that adsorbs on solid surfaces is able to reduce friction in the boundary lubrication regime (PGM). Guar, which does not adsorb on surfaces, shows high friction in boundary lubrication but still promotes the onset of mixed lubrication; thus friction starts to fall from its boundary values at low speeds. These results can be explained in classical terms of entrainment of polymer solution into the thin film conjunction and associated shear thinning in the contact inlet. With roughened surfaces, a shift of the Stribeck curves towards high speed is observed.     

Structures,solvation forces and shear of molecular films in a rough nano-confinement

Investigations of surface roughness effects on the structure, dynamics and rheology of a molecular fluid (hexadecane) confined between solid (gold) surfaces, through the use of large-scale molecular dynamics simulations, reveal a remarkable sensitivity to the confining surface morphology. A most significant reduction of the ordering propensity is found in films confined by stationary rough surfaces with a consequent strong suppression of solvation forces and the development of liquid-like dynamic and response characteristics. When the rough-surface boundaries are set in motion at a high shear rate, the interfacial layers of the film stick to the adjacent solid boundaries, resulting in partial slip inside the film with the development of shear stress in the viscous molecular fluid, unlike the case of atomically flat crystalline boundaries where slip of the confined film at the boundaries is accompanied by vanishingly small shear stress in the film. These results are discussed in the context of the effect of roughness on the boundary conditions used in modeling fluid flow past surfaces, and they suggest that morphological patterning of surfaces could provide ways for controlled modifications of frictional processes in thin-film lubricated nanotribological systems.     

Squeeze fluid film of spherical hydrophobic surfaces with wall slip

Isothermal squeeze film flow of Newtonian fluid between spherical hydrophobic surfaces with wall slip is investigated using a limiting shear stress model and complementary algorithm. Wall slip velocity is controlled by the liquid–solid interface limiting shear stress. It is found that the wall slip dramatically decreases the hydrodynamic support force of the squeeze fluid film. In the case of large wall slip the hydrodynamic support force increases only slightly with the decrease in the film thickness. We find that wall slip decreases with increasing film thickness and limiting shear stress, but increases with increasing fluid viscosity and approaching velocity. An empirical equation is given for prediction of the fluid load support capacity. The possible effect of pressure on wall slip is also discussed. It is found that fluid pressure suppresses wall slip after the proportionality coefficient of limiting shear stress reaches a critical threshold. However, almost no effect is found when it is below this critical threshold. Good agreements exist between the present theoretical predictions and some existing experimental observations.