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.     

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.     

Theoretical study on the lubrication failure for the lubricants with a limiting shear stress

It is observed that the non-slip boundary conditions in the classical lubrication theory are not valid for lubricant with a limiting shear stress. By determining the position of the maximum shear stress and changing velocity boundary condition to stress condition, slip lubrication equations are deduced. With numerical solution of the equations, the location and scale of the boundary slip are analyzed. Finally, after the influences of the slip on the lubrication properties are discussed, results show that a significant decrease of the load carrying capacity causes slip lubrication failure.     

Hydrodynamic lubrication analysis of journal bearing considering misalignment caused by shaft deformation

Hydrodynamic lubrication characteristics of a journal bearing, taking in to consideration the misalignment caused by shaft deformation, are analyzed. Film thickness expression of the misaligned journal bearing is inferred. Film pressure, load-carrying capacity, attitude angle, end leakage flow-rate, frictional coefficient, and misalignment moment of a journal bearing are calculated for different values of misalignment degree and eccentricity ratio. The results show that there are obvious changes in film pressure distribution, the highest film pressure, film thickness distribution, the least film thickness, and the misalignment moment when misalignment takes place. Therefore, it is necessary to consider misalignment caused by shaft deformation when analyzing the lubrication of journal bearing.     

CFD analysis of journal bearing hydrodynamic lubrication by Bingham lubricant

Design of smart journal-bearing systems is an important issue that opens up the possibility for semi-active dynamic control of bearing behavior. Recent studies show that there is an increasing interest in designing hydrodynamically lubricated bearings using electro-rheological fluids (ERFs) or magneto-rheological fluids (MRFs). Both smart fluids behave like Bingham fluids, and thus the Bingham plastic model is used to describe the grease and the electro-rheological (ER) and magneto-rheological (MR) fluids behavior of the non-Newtonian fluid flow. The performance characteristics of a hydrodynamic journal bearing lubricated with a Bingham fluid are derived by means of three-dimensional computational fluid dynamics (3-D CFD) analysis. The FLUENT software package is used to calculate the hydrodynamic balance of the journal using the so-called “dynamic mesh” technique. The results obtained from the developed 3-D CFD model are found to be in very good agreement with experimental and analytical data from previous investigations on Bingham fluids.Journal-bearing performance characteristics, such as relative eccentricity, attitude angle, pressure distribution, friction coefficient, lubricant flow rate, and the angle of maximum pressure, are derived and presented for several length over diameter (L/D) bearing ratios and dimensionless shear numbers T₀ of the Bingham fluid. The above diagrams are presented in the form of Raimondi and Boyd charts, and can easily be used in the design and analysis of journal bearings lubricated with Bingham fluids. The core profile formed in the bearing is also calculated and presented for various bearing eccentricities, L/D ratios, and shear numbers T₀, and found to be in very good agreement with previous experimental and theoretical investigations. The analysis presented here leads to charts that could be used by the designer engineer to design smart journal bearings.     

Estimation of the performance of a narrow porous journal bearing with hydrodynamic turbulent lubrication considering slip velocity and arbitrary wall thickness

A closed-form mathematical analysis is presented for the hydrodynamic lubrication of a 360° short porous metal journal bearing with arbitrary wall thickness which is press fitted in a solid housing and works with a turbulent film of newtonian lubricant. A new pressure equation is used. The bearing is assumed to be narrow, and therefore circumferential flow of the lubricant in the clearance region is negligible in comparison with that in the axial direction which makes the governing differential equation simpler to solve. However, this simplification is not applicable to darcian flow in the porous matrix so that a three-dimensional Laplace equation is required to describe the continuity of flow in the pores. The film curvature is included by retaining terms containing $\text{C}\text{R}{}_1$ in the expression for film thickness. The curvature of the permeable bearing matrix, which allows it to have an arbitrary wall thickness, is taken into account by a direct approach. Infinite Fourier series and their orthogonal properties are utilized for the determination of the turbulent hydrodynamic pressure distribution from which the load-carrying capacity and attitude angle are calculated. All the results of interest are simple and fully analytical in nature permitting easy and economical calculation of numerical data over a very wide range of parameters.     

Numerical analysis of plain journal bearing under hydrodynamic lubrication by water

The article aims to provide references for designing water-lubricated plain journal bearings. Considering the differences between the physical properties of the water and of the oil, the effects of eccentricity ratio on pressure distribution of water film are analyzed by computational fluid dynamics (CFD). Then numerical analysis of journal bearings with different dimensions is undertaken under different rotational speeds. Based on the analysis, a reference is produced for selecting the initial diameter dimension which is used to design an efficient water-lubricated plain bearing under the given load and rotational speed. At last, the reference is verified by an experimental case.     

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。     

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.     

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.     

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.     

Hydrodynamic lubrication of a porous slider bearing with slip velocity

An inclined porous slider bearing is analysed with slip velocity at the porous boundary considered. The expressions for dimensionless loadcarrying capacity, friction and the centre of pressure are obtained in the form of integrals. Minimization of the slip parameter is essential to increase the load capacity.     

A study of thermohydrodynamic lubrication in a circular journal bearing

An analytical method to determine the film temperature of circular journal bearings was developed, which considers the cavitation of the oil film and also recirculation and mixing of the lubricant. The results were verified experimentally. The theory is in good agreement with experiment over a wide range of operating conditions. The effects of journal speed, clearance ratio, lubricant viscosity and specific load on the bearing temperature were examined, and the following conclusions derived. (1) T_b,max, the maximum temperature on the bearing metal surface, increases considerably with the increase of speed and lubricant viscosity and with the decrease of clearance ratio. (2) With the increase of speed, the angular position of T_b,max varies considerably towards the direction of journal rotation from the upper stream side of the location of minimum film thickness, h_min, to the lower stream side of it. The change of angular position of T_b,max is greater than that of h_min. The contrary happens with decrease of the clearance ratio. (3) These characteristics of T_b,max correspond to those of the maximum temperature, T_f,max, in the oil film.     

A stability analysis for a hydrodynamic three-wave journal bearing

The influence of the wave amplitude and oil supply pressure on the dynamic behavior of a hydrodynamic three-wave journal bearing is presented. Both, a transient and a small perturbation technique, were used to predict the threshold to fractional frequency whirl (FFW). In addition, the behavior of the rotor after FFW appeared was determined from the transient analysis. The turbulent effects were also included in the computations.Bearings having a diameter of 30 mm, a length of 27.5 mm, and a clearance of 35 μm were analyzed. Numerical results were compared to experimental results obtained at the NASA GRC. Numerical and experimental results showed that the above-mentioned wave bearing with a wave amplitude ratio of 0.305 operates stably at rotational speeds up to 60,000 rpm, regardless of the oil supply pressure. For smaller wave amplitude ratios, a threshold of stability was found. It was observed that the threshold of stability for lower wave amplitude strongly depends on the oil supply pressure and on the wave amplitude.When the FFW occurs, the journal center maintains its trajectory inside the bearing clearance and therefore the rotor can be run safely without damaging the bearing surfaces.     

界面滑移条件下弹流油膜的试验观察

在极低速纯滑动条件下完成高粘度聚丁烯弹流油膜的光干涉测量试验,观察到明显的油膜入口凹陷现象。试验结果表明,入口凹陷的深度随载荷的增加而增加,随卷吸速度的增加存在一个极大值。试验中润滑剂的粘度越高,入口凹陷越容易出现。纯滑动条件下,油膜厚度对速度和载荷的依赖关系明显偏离了经典的弹流理论。试验中观察到的入口凹陷证明了已有入口凹陷弹流数值分析的正确性。     

Fretting wear behavior of TiB2-based materials against bearing steel under water and oil lubrication

Lubricated fretting tests in water and paraffin oil were performed with a monolithic TiB₂, a TiB₂-based cermet with 16 vol.% Ni₃(Al, Ti) binder, a sialon–TiB₂ (60/40) composite and a ZrO₂–TiB₂ (70/30) composite against ball bearing grade steel. Based on the measured friction and wear data, the ranking of the investigated fretting couples was evaluated. Furthermore, the morphological investigations of the worn surfaces and transfer layers are carried out and the wear mechanisms for the investigated friction couples are elucidated. While fretting in water, experiments revealed that tribochemical reactions, coupled with mild abrasion, played a major role in the wear behavior of the studied material combinations. ZrO₂–TiB₂ (70/30)/steel wear couple has been found to have the highest fretting wear resistance among the different tribocouples under water lubrication. Under oil lubrication, extensive cracking of the paraffin oil at the fretting contacts, caused by tribodegradation, leads to the deposition of a carbon-rich lubricating layer, which significantly reduced friction and wear of all the investigated tribosystems.     

液体动压径向滑动轴承润滑状态的可靠性分析

文章分析了影响轴承液体润滑状态,可靠性因素,提出了用预测相对间隙变异系数的方法确定轴承直径间隙和制造公差,从而保证轴承润滑状态达到预期的可靠度要求。     

Linear stability analysis of hydrodynamic journal bearings under micropolar lubrication

The dynamic characteristics of hydrodynamic journal bearings lubricated with micropolar fluids are presented. The modified Reynolds equation is obtained using the micropolar lubrication theory. Applying the first order perturbation of the film thickness and steady state film pressure, the dynamic characteristics in terms of the components of stiffness and damping coefficients, critical mass parameter and whirl ratio are obtained with respect to the micropolar property for varying eccentricity ratios and slenderness ratios. The results show that micropolar fluid exhibits better stability in comparison with Newtonian fluid.     

A pre-verifiable calibration model of wall shear stress thermal sensor driven by constant current

This paper presents a pre-verifiable calibration model, which can accurately characterize the measurement behavior of the flexible wall shear stress thermal sensor in constant current drive mode. In this calibration model, the fitting parameter $a$ can be pre-verified with $I{R}_a$, which provides a method to verify the accuracy of calibration instruments and data. In repetitive experiments, the average related normalized standard deviation ${\epsilon }_{\tau }$ is 1.26%, which indicates that our calibrations are reliable. And the relative deviations $\eta$ between $a$ and $I{R}_a$ are below 1.15% in all experiments, which indicates that the calibration model can pre-verify the reliability of calibration instruments and data among different sensors and different drive currents.