An anisothermal,compressible, piezoviscous model for journal‐bearing lubrication

Compressibility plays a significant role in the load‐bearing capacity of a journal bearing. This paper offers more realistic modelling of the lubricant than presented in an earlier paper (Int. J. Numer. Meth. Fluids 2007; 55 (11):1091–1120) by including variable sound speed, piezoviscosity and both temperature and shear thinning. The load‐bearing capacity of the journal bearing is sensitive to all of these attributes of the model, but piezoviscosity is found to be the most significant. The equations of motion are adapted to a moving frame to explore the stability of the journal in a more dynamic setting and it is found that a free journal using this model will spiral outward exhibiting half speed whirl. The model is discretized in 2D, semi‐implicitly in time and using the spectral element method in space. Numerical results are presented that highlight the contributions of the different elements in the model to journal stability. Copyright © 2008 John Wiley & Sons, Ltd.     

Externally pressurized air journal bearing with multiple supply holes

A theoretical analysis is made to predict the load carrying capacity, flow requirement, and stiffness of an externally pressurized air lubricated journal bearing with several supply holes. The load, flow, and stiffness, expressed in dimensionless parameters, are presented for various bearing design parameters and eccentricity ratios. The design procedure of one such bearing either for maximum load capacity or for maximum stiffness is indicated.     

基于稀薄效应的微气体径向轴承稳态性能

针对微气体轴承给出参考努森数的定义,根据空气不同温度时的黏度,得到参考努森数的分布范围;考虑气体稀薄效应,给出基于Burgdorfer一阶滑移速度边界的微气体径向轴承润滑Reynolds方程的修正形式; 采用有限差分法求解修正的Reynolds方程,得到不同参考努森数$Kn_0$, 轴承数以及轴颈偏心率情况下轴承的压力分布、无量纲承载能力及偏位角. 数值分析表明:随气体稀薄程度的增强,气体径向轴承的压力明显降低,无量纲承载力降低,而轴承偏位角增大. 当偏心率小于0.6时,轴承偏位角变化平缓,受$Kn_0$数的影响不明显. 当轴承数较小时,气体稀薄程度对轴承的无量纲承载力、偏位角影响较小.      

Load enhancement effects due to polymer thickening in a short model journal bearing

A model bearing is described which is 20.0 mm in diameter and 2.5 mm in length; a short bearing of diameter to length ratio eight. The clearance is large (500 μm) and the rotor may be run true or eccentric on its own shaft; in each case the mean load and frictional (tangential) force is measured as the centreline eccentricity is varied.Comparison is made between the lubricating performance of Newtonian and highly elastic liquids; the latter give load enhancement ratios of up to 300 and reductions in coefficient of friction by factors of the order 30. These effects are greatly in excess of those obtained when dealing with bearing of diameter to length ratio close to unity; possible reasons for this are discussed.A Newtonian oil and a polymer-thickened oil are tested in the same way, the latter oil is found to give load enhancement ratios of 1.4 (true rotor) and 3.5 (eccentric rotor) with corresponding reductions of coefficients of friction by factors of 1.5 (true rotor) and 3.0 (eccentric rotor). Such effects had not previously been observed when using oils in the internal cylinder geometry (journal bearing type) although somewhat similar effects have been found in the external cylinder and squeeze film geometries.The rheological properties of the polymer-thickened solutions are measured and the relevance of the results to friction and load bearing discussed.     

二阶滑移边界对微型气浮轴承稳态性能的影响

考虑微型气浮轴承的尺寸特征,内部气流不再满足连续流的假设,根据Knudsen数可确定内 部气流为滑移流. 分别利用一阶速度滑移模型和二阶速度滑移模型对连续流的状态方程进行 修改,得到一阶滑移流和二阶滑移流机制下修正的雷诺方程. 利用有限差分法对连续流、一 阶滑移流和二阶滑移流的雷诺方程分别求解,得出相应的承载力和偏位角. 经过对比分析, 发现采用滑移流模型得到的轴承的稳态力学性能与连续流机制的结果存在较大差异,一阶滑 移流与二阶滑移流间的差异随偏心率增加而增加. 说明在MEMS环境下必须考虑滑移流效应 对微型气浮轴承稳态力学性能的影响. 在大偏心率工作状态下,二阶滑移流模型能够得到最 好的结果.     

复合表面径向滑动轴承的概念和性能预报

近年来的研究发现固液界面的滑移可以减小表面摩擦,但也会造成流体动力效应下降甚至消失.本文提出了复合表面滑动轴承的概念,轴套表面由具有不同吸附和滑移特性的复合表面组成,发现复合表面轴承比普通轴承有许多优点.通过改变轴套表面的滑移特性可以改变和优化轴承的各种性能,例如摩擦系数、承载力、润滑剂流量、承载角等.数值解表明,在轴承高压区改变轴套表面滑移特性,轴承的整体性能会有大幅度提高.例如,本文给出的初步优化设计方案使得摩擦系数降低50%以上,同时承载力可提高20%,并且承载角可以降低33%.本文提出的设计理念不但可用于设计出具有更优异特性的径向滑动轴承,而且可以设计出具有复合表面的轴向滑动轴承或滑块轴承.复合表面滑动轴承在降低轴承摩擦、提高承载能力方面有很大的空间可以探索.     

计及轴颈倾斜的径向滑动轴承湍流润滑分析

分析了轴颈倾斜状态下,径向滑动轴承的湍流润滑性能. 基于轴颈倾斜的统一Reynolds方程和能量方程,应用有限差分法求解了不同轴颈倾斜方位角、轴颈倾斜度、偏心率和平均雷诺数下的径向滑动轴承湍流润滑性能. 结果表明:轴颈倾斜方位角α=0°时,随着轴颈倾斜度的增大,轴承油膜的压力峰向轴承一端移动,轴承一端的轴向油膜温度梯度增大;α=90°时,随着轴颈倾斜度的增大,轴承油膜压力逐渐出现双峰分布,且向轴承两端移动,轴承两端的轴向温度梯度也不断增大. 在相同轴颈倾斜度增量下,轴承最大油膜压力、最高油膜温度、承载力和稳定工作力矩的增量随轴承中央截面偏心率的增大而增大. 相同轴颈倾斜度增量下,轴承最大油膜压力增量、最高油膜温度增量、承载力增量、摩擦系数减量和稳定工作力矩增量随平均雷诺数的增大而增大. 可见,径向滑动轴承湍流润滑分析中有必要考虑轴颈倾斜因素的影响.      

Performance of hydrodynamic journal bearing under the combined influence of textured surface and journal misalignment: A numerical survey

A wisely chosen geometry of micro textures with the favorable relative motion of lubricated surfaces in contacts can enhance tribological characteristics. In this paper, a computational investigation related to the combined influence of bearing surface texturing and journal misalignment on the performances of hydrodynamic journal bearings is reported. To this end, a numerical analysis is performed to test three texture shapes: square “SQ”, cylindrical “CY”, and triangular “TR”, and shaft misalignment variation in angle and degree. The Reynolds equation of a thin viscous film is solved using a finite differences scheme and a mass conservation algorithm (JFO boundary conditions), taking into account the presence of textures on both full film and cavitation regions. Preliminary results are compared with benchmark data and are consistent with a positive enhancement in misaligned bearing performances (load carrying capacity and friction). The results suggest that the micro-step bearing mechanism is a key parameter, where the micro-pressure recovery action present in dimples located at the second angular part of the bearing (from 180° to 360°) can compensate for the loss on performances caused by shaft misalignment, while the micro-pressure drop effect at the full film region causes poor performances. Considering the right arrangement of textures on the contact surface, their contours geometries can have a significant impact on the performance of misaligned journal bearings, particularly at high eccentricity ratios, high misalignment degrees and when the misalignment angle α approaches to $0\mathrm{°}$ or $180\mathrm{°}$.     

Evolution of the bearing capacity of dry loose sand with inclination of the load applied

Vehicle wheels apply on the soil loads of variable inclination. Increasing load inclination causes a decrease in the soil bearing capacity and produces more sinkage of wheels. In the present study the change of soil bearing capacity with load inclination is investigated. Plate-sinkage tests in which load inclination to the vertical is varied from zero to thirty degrees are elaborated. A modification of Bekker's bearing capacity equation to account for load inclination is proposed, and a comparison of experimental and predicted bearing capacity curves is shown.     

Lubrication theory for micropolar fluids and its application to a journal bearing with finite length

In this paper, the field equation of micropolar fluid with general lubrication theory assumptions is simplified into two systems of coupled ordinary differential equation. The analytical solutions of velocity and microrotation velocity are obtained. Micropolar fluid lubrication Reynolds equation is deduced. By means of numerical method, the characteristics of a finitely long journal bearing under various dynamic parameters, geometrical parameters and micropolar parameters are shown in curve form. These characteristics are pressure distribution, load capacity, coefficient of flow flux and coefficient of friction. Practical value of micropolar effects is shown, so micropolar fluid theory further closes to engineering application.     

Investigation of basic characteristics of the MHD bearing

The load-carrying capacity and the friction torque of a magnetohydrodynamic bearing are calculated. The calculation is made for specified boundaries of the lubricating layer (0, ) with a small magnitude of the radial gap. It is shown that the presence of an external magnetic field directed along the axis of the bearing and a radial electric field leads to a considerable increase of the load-carrying capacity of the electrically conductive lubricating layer. The condition for which the friction torque on the journal of an MHD bearing vanishes is found.     

可倾瓦径向滑动轴承完整动特性系数的分析模型

基于可倾瓦径向滑动轴承瓦块的扰动特性,提出了计算轴承完整动力系数的数学解析模型。在由单块瓦和轴颈构成的子系统上建立局部动坐标参考系,全局广义位移向量可以通过简练的步骤转换为局部动坐标系下轴颈的位移向量,利用求解固定瓦轴承动力特性的方法求得的局部动坐标系下的油膜力又可以精确地转换为全局坐标系下的表达形式,全局坐标系下的油膜力向量关于广义位移和广义速度的Jocabian矩阵形成轴承的完整动力特性系数;利用Newton-Raphson方法同时求解瓦块和轴颈在给定的静态载荷下的平衡位置,其中所需用到的系数矩阵恰好为轴承油膜力关于广义位移的Jocabian矩阵的负值,在得到平衡位置的同时可以获得轴承完整的刚度和阻尼矩阵。数值算例证明了此方法的有效性。     

Numerical investigation on the influence of surface texture on the performance of hydrodynamic journal bearing

Many researchers have adopted various techniques for improving the performance characteristics of journal bearing. Apart from other parameters, incorporation of different forms of surface texture (sinusoidal, dimple, spherical etc.) on bearing or shaft also helps to increase the load carrying capacity and reduce the friction coefficient etc. in the journal bearing. Present study investigates the influence of different forms of surface texture on finite journal bearing which has been considered in the form of negative texture (micro cavities) at different locations of bearing surface. The Governing equations are solved numerically through finite difference approach for analysis of texture effects on bearing characteristics. It has been observed that the presence of micro cavities at different locations of bearing surface help in enhancing the bearing performance. It has also been found that the negative half wave texture enhances the bearing performance more in comparison to full wave texture on bearing surface.     

Optimum clearance of a gas hydrostatic thrust bearing with maximum load capacity

The optimum design of a gas hydrostatic thrust bearing clearance is obtained using the methods of calculus of variations. The variational problem of determining the clearance shape giving the maximum load capacity is solved for a given external pressurization and various journal speeds. The structure of the optimum solution is found on the basis of the gas lubrication approximation with and without constraints on the height of the bearing pad (pocket). The calculation results embrace all possible values of the parameters. A comparison with optimum liquid bearings is carried out. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–78, July–August, 2000. The work was carried out with support from the Russian Foundation for Basic Research (projects Nos. 99-01-01211 and 96-15-96158).     

Fluid flow and thermal analysis of a circular journal bearing

In this paper, three dimensional momentum and continuity equations and three dimensional energy equations are solved simultaneously to obtain pressure, velocity and temperature field in the fluid of a hydrodynamic circular journal bearing. Solutions of these equations are obtained by using the powerful numerical technique, finite element method. For a range of values of eccentricity ratios, the static performance characteristics in terms of the load capacity, attitude angle, end leakage and the power loss are computed and the results are presented.

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Untersuchung des Strömungs- und Temperaturverhaltens eines Wellenlagers

Zusammenfassung In der Arbeit werden die dreidimensionalen Impuls-, Kontinuitäts- und Energiegleichungen gleichzeitig gelöst, um die Druck-, Geschwindigkeits- und Temperaturverteilung im Fluid eines hydrodynamischen Wellenlagers zu erhalten. Die Lösung wird mit Hilfe des wirksamen Werkzeugs der Finiten Elemente gewonnen. Für einen gewissen Bereich des Exzentrizitätsverhältnisses sind die statischen Betriebscharakteristiken als Funktion der Belastung, des Anstiegswinkels, der Leckage und des Reibungsdruckverlustes berechnet und dargestellt worden.

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Finite element calculation of viscoelastic flow in a journal bearing: II. Moderate eccentricity

Finite element calculations of two-dimensional flows of viscoelastic fluids in a journal bearing geometry reported in an earlier paper (J. Non-Newt. Fluid Mech. 16 (1984) 141-172) are extended to higher eccentricity (ρ = 0.4); at this higher eccentricity flow separation occurs in the wide part of the gap for a Newtonian fluid. Calculations for the second-order fluid (SOF), upper-convected Maxwell (UCM), and the Giesekus models are continued in increasing Deborah number for each model until either a limit point is reached or oscillations in the solution make the numerical accuracy too poor to warrant proceeding. No steady solutions to the UCM model were found beyond a limit point De_c, as was the case for results at low eccentricities. The value of De_c was moderately stabel to mesh refinement. A limit point also terminated the calculations with a SOF model, in contradiction to the theorems for uniqueness and existence for this model. The critical value of De increased drastically with increasing refinement of the mesh, as expected for solution pathology caused by approximation error. Calculations for the Giesekus fluid with the mobility parameter α ≠ O showed no limit points, but failed when irregular oscillations destroyed the quality of the solution. The behavior of the recirculation region of the flow and the load on the inner cylinder were very sensitive to the value of α used in the Giesekus model. The recirculation disappeared at low values of De except when the mobility parameter α was so small that the viscosity was almost constant over the range of shear rates in the calculations. The recirculation persisted over the entire range of accessible De for the UCM fluid, the limit of α = O of the Giesekus model. The behavior of the recirculation is coupled directly to the viscosity by calculations with an inelastic fluid with the same viscosity predicted by the Giesekus model.     

Optimum porous journal bearing ensuring maximum load capacity

The problem of an infinite journal bearing having an isothermal compressible lubricant and a porous bush and ensuring the optimum load capacity is solved. The optimum clearance profiles and bush dimensions and position are found for various properties of the bush and lubricant supply conditions.     

The influence of Oldroyd-B and PTT lubricants on moving journal bearing systems

The influence of viscoelasticity on the performance of statically and dynamically loaded journal bearings is considered. The lubricant in the system is modelled using either the Oldroyd-B or linear PTT models. Significant viscoelastic effects are presented for both moderate and narrow gap journal bearing configurations. The dynamical behaviour of the journal bearing system is shown to be dependent on the fluid model, the relaxation time and also the gap size.     

Inertia effects in externally pressurized bearing with viscoelastic lubricant

A theoretical investigation of inertia effects on the load capacity of an externally pressurized bearing with a visco-elastic lubricant is presented. The methods of iteration and averaged inertia have been employed to find an approximate solution of the resulting non linear differential equation. Graphical representation of results together with those for the case without inertia has been shown. It is found that the elasticity of the liquid increases the load bearing capacity and the pressure at a point in the lubricant film. There is a negative contribution to the load capacity by inertia forces.     

Rheodynamic lubrication of a journal bearing

Summary The problem of a journal bearing lubricated by a Bingham material has been solved. It has been found that the load capacity, and the moment of friction of the bearing are larger than in a journal bearing, lubricated with a Newtonian material.Nomenclature r radius of the journal - c radial clearance - r + c radius of the bearing - e eccentricity - w angular velocity of the journal - h thickness of the lubricant film at any point - thickness of the core - ø angular distance of a point, from the point, where film thickness is maximum - eccentricity ratio (e/c) - x distance along the bearing surface - y distance normal to the bearing surface - T shear stress in the lubricant - T ₀ yield value of a Bingham solid - viscosity of a Newtonian fluid - plastic viscosity of a Bingham solid - p fluid pressure in the lubricant film - Q volume flow of the lubricant - W ₀ load capacity of the bearing for ordinary lubricants - W load capacity of the bearing - M moment of friction - F coefficient of friction - ₁ maximum thickness of the inlet core - ₂ maximum thickness of the outlet core - ₁ circumferential extent of the inlet core in the journal bearing - ₂ circumferential extent of the outlet core in the journal bearing - h ₀ minimum hieght of core formation in the slider bearing - h _p maximum height of core formation in the slider bearing - u velocity of the fluid in the direction of x in the slider bearing - V velocity in the y direction - h ₁ height of the inlet core at the circumferential extent ₁ - h ₂ height of the outlet core at the circumferential extent ₂ - h ₃ height of the outlet core in the region ₂ - q Q/(cwr) - q ₀ value of q for Newtonian lubricants - p ₀ pressure at =0 - H h/c - H ₁ h ₁/c - H ₂ h ₂/c - B T ₀ C/wr = Bingham number