Hydrodynamic lubrication in fully plastic asperity contacts

A line contact inlet zone analysis is carried out for the hydrodynamic lubrication in a fully plastic asperity contact. A governing equation of the central film thickness i.e. the film thickness in the fully plastic contact area is derived. An equation predicting this film thickness is also derived. It is found that for the fully plastic contact, under relatively light loads the prediction accuracy for the central film thickness is good, while at the load heavy enough the prediction equation greatly overestimates the central film thickness and the central film thickness solved from the analytical governing equation is significantly low showing the asperity in boundary layer lubrication. For the fully plastic contact, the central film thickness is nearly half of that obtained based on the elastic contact assumption for relatively light loads or even lower for heavier loads. The hydrodynamic lubrication is found difficult to form in the fully plastic asperity contact for the carried load heavy enough or the significantly low sliding speed between the asperities. To achieve a high hydrodynamic lubrication film thickness in the fully plastic asperity contact it is recommended to employ a high sliding speed or a high fluid viscosity. However, in the fully plastic asperity contact, the potential hydrodynamic load-carrying capacity is limited and much smaller than that based on the elastic contact assumption or predicted by conventional line contact elasto-hydrodynamic lubrication theory.     

Boundary film shear elastic modulus effect in hydrodynamic contact. Part II: influence of operational parameters

The present paper is the subsequent research of the first part (Theor Comput Fluid Dyn, 2009). It investigates the boundary film shear elastic modulus effect in a hydrodynamic contact in different operating conditions. The hydrodynamic contact is one-dimensional, composed of two parallel plane surfaces, which are respectively rough rigid with rectangular micro projections in profile periodically distributed on the surface and ideally smooth rigid. The whole contact consists of cavitated area and hydrodynamic area. The hydrodynamic area consists of many micro Raleigh bearings which are discontinuously and periodically distributed in the contact. The hydrodynamic contact in a micro Raleigh bearing consists of boundary film area and fluid film area which, respectively, occur in the outlet and inlet zones. In boundary film area, the film slips at the upper contact surface due to the limited shear stress capacity of the film–contact interface, while the film does not slip at the lower contact surface due to the shear stress capacity of the film–contact interface large enough. In boundary film area, the viscosity, density, and shear elastic modulus of the film are varied across the film thickness due to the film–contact interactions, and their effective values are used in modeling which depends on the film thickness. In fluid film area, the film does not slip at either of the contact surfaces, and the shear elastic modulus of the film is neglected. It is found from the simulation results that the boundary film shear elastic modulus influences are normally negligible on the mass flow through the contact, the carried load of the contact and the overall film thickness of the contact, and the boundary film shear elastic modulus would normally influence the local film thickness in an elastic contact when the local film thickness is on the film molecule diameter scale. It is also found that the boundary film shear elastic modulus effect has the tendency of being increased with the reduction of the width of a micro contact. It is increased with the reduction of the boundary film–contact interfacial shear strength or with the increase of the critical boundary film thickness, while it is strongest at certain values of the contact surface roughness, the width ratio of fluid film area to boundary film area, and the lubricant film shear elastic modulus.

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Boundary film shear elastic modulus effect in hydrodynamic contact. Part I: theoretical analysis and typical solution

Boundary film shear elastic modulus effect is analyzed in a hydrodynamic contact. The contact is one-dimensional composed of two parallel plane surfaces, which are, respectively, rough rigid with rectangular micro projections in profile periodically distributed on the surface and ideally smooth rigid. The whole contact is consisted of cavitated area and hydrodynamic area. The hydrodynamic area consists of many micro Raleigh bearings which are discontinuously and periodically distributed in the contact. Analysis is thus carried out for a micro Raleigh bearing in this contact. The hydrodynamic contact in this micro Raleigh bearing consists of boundary film area and fluid film area which, respectively, occur in the outlet and inlet zones. In boundary film area, the film slips at the upper contact surface due to the limited shear stress capacity of the film–contact interface, while the film does not slip at the lower contact surface due to the shear stress capacity large enough at the film–contact interface. In boundary film area, the viscosity, density and shear elastic modulus of the film are varied across the film thickness due to the film–contact interactions, and their effective values are used in modeling, which depend on the film thickness. The analytical approach proposed by Zhang (J Mol Liq 128:60–64, 2006) and Zhang et al. (Int J Fluid Mech Res 30:542–557, 2003) is used for boundary film area. In fluid film area, the film does not slip at either of the contact surfaces, and the shear elastic modulus of the film is neglected. Conventional hydrodynamic analysis is used for fluid film area. The present paper presents the theoretical analysis and a typical solution. It is found that for the simulated case the boundary film shear elastic modulus effects on the mass flow through the contact, the overall film thickness of the contact and the carried load of the contact are negligible but the boundary film shear elastic modulus effect on the local film thickness of the contact may be significant when the boundary film thickness is on the 1 nm scale and the contact surfaces are elastic. In Part II will be presented detailed results showing boundary film shear elastic modulus effects in different operating conditions.

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介观双粗糙弹塑性流体动力润滑界面法向接触刚度模型

弹性流体动力润滑状态通常出现在机械高副零部件的点/线接触部位,如齿轮、轴承和蜗轮蜗杆等.宏观上点/线接触在介观层面表现为两粗糙表面的接触,在微观层面上则又表现为微凸体间的接触.由于在中/重载荷作用下,粗糙表面上的微凸体发生接触后会产生弹塑性/塑性变形,从而使得两粗糙表面的弹流润滑接触转变为弹塑性流体动力润滑接触.此外,界面的接触刚度决定了机械装备的整机刚度.为了精确获得弹性流体动力润滑状态下界面法向接触刚度及其主要影响因素,基于界面的法向接触刚度由固体接触刚度和润滑油膜刚度两部分构成的思想,根据固体弹塑性理论和流体动力学理论,分别对界面间微凸体侧接触及部分膜流体动力润滑进行分析,从微观入手揭示双粗糙表面弹塑性流体动力润滑接触机理,进而建立考虑微凸体侧接触弹塑性变形的流体动力润滑界面法向接触刚度模型.通过仿真分析,揭示了法向载荷、卷吸速度、表面粗糙度及润滑介质特性等因素对润滑界面法向接触刚度的影响规律.研究表明：在相同速度、粗糙度及润滑油黏度的工况下,固体接触刚度和油膜接触刚度均随着法向接触载荷的增加呈非线性增大;在相同载荷、速度及润滑油黏度的工况下,接触表面粗糙度越大,表面形貌对于润滑...     

Wrinkling of elastoplastic circular plates during stamping

Circular plates that are stamped into a shallow, biaxially curved die by a matching punch develop radial wrinkles near the periphery when the edge is not clamped. Thin ductile metal plates develop these wrinkles after some plastic deformation occurs at the center of the plate. In comparison with elastic wrinkling, the center deflection to thickness ratio for wrinkling is increased as a consequence of the plastic deformation. In elastoplastic plates, this critical deflection ratio is a decreasing function of the plate thickness parameter ξ_o     

表面凹槽对流体动压润滑油膜厚度的影响

利用自行研发的面接触光干涉油膜厚度测量系统,对表面凹槽滑块的流体动压润滑油膜厚度进行了试验测量,试验中以静止的微型凹槽滑块平面和旋转的光学透明圆盘平面构成润滑副,且两润滑平面始终保持平行;在固定的载荷(速度)条件下,对油膜厚度-速度(载荷)曲线进行测量.结果表明：凹槽的宽度,深度,方向和位置等因素对油膜厚度有着重要影响.同时采用经典Reynolds方程对油膜厚度进行了理论计算,结果表明理论值在某些条件下并不能解释试验结果.     

Elastoplastic Analysis with Limited Plastic Deformations and Displacements*

ABSTRACT

This paper presents solution methods for elastoplastic and shakedown analysis of linearly elastic, perfectly plastic bodies for which the conventional classical formulations of these problems are completed by constraints on overall plastic deformation and elastoplastic displacement. The methods are described in terms of nonlinear mathematical programming and provide solutions when the plastic reserves of the body are not fully exhausted, and the plastic performance and the plastic deformations are controlled. Application of the method is illustrated by an example.     

Deformation of a Convex Hydrogel Shell by Parallel Plate and Central Compression

To characterize the materials parameters and deformation of a convex shell of axial symmetry, a hydrogel contact lens is mechanically deformed by two loading configurations: (a) compression between two parallel plates and (b) central load applied by a shaft with a spherical tip. A universal testing machine with nano-Newton and submicron resolutions is used to measure the applied force, F, as a function of vertical displacement of the plate/shaft, w ₀, while a homemade laser aided topography system records the in-situ deformed shell profile and the contact radius or central dimple, a. A nonlinear shell theory and an iterative finite difference method are used to account for the large elastic deformation, the central buckling for the central load compression, and the interrelationship between the measureable quantities (F, w ₀, a).     

表面特性对纯滑弹流油膜形状和摩擦力的影响的试验研究

针对界面滑移效应可能产生较低的摩擦力,采用具有不同表面浸润性的玻璃盘,进行了纯滑弹流润滑试验.在采用SiO2镀膜玻璃盘的球-盘接触高聚物纯滑润滑试验中,从弹流到动压润滑的摩擦系数曲线呈现不同于传统Stribeck曲线的两个拐点.两个拐点分别与凹陷出现及弹性变形消失相关联.在较低载荷下,不同盘表面产生相近的干涉图像和摩擦系数曲线,高聚物的非牛顿效应产生的表观滑移可能是入口凹陷及非典型摩擦系数曲线的主因;在较高载荷下,盘滑试验中铬盘产生的摩擦系数和油膜厚度均较SiO2盘低,具有较低表面能的铬盘产生的界面滑移被认为是产生较低摩擦系数的主因.     

Investigation of surface texture influence on hydrodynamic performance of parallel slider bearing under transient condition

Although surface texture has been becoming an attractive technique for improving hydrodynamic performance in lubrication system, the study of surface texture mainly focus on the steady-state load conditions. This investigation evaluates the effect of surface texture on hydrodynamic performance under transient lubrication in parallel bearing. In the case, considering cavitation phenomena in liquid lubricating film, a mass conserving formulation based on Elrod–Adams model with JFO conditions is then employed. The implementation of numerical simulation is discretized in spatial and time domain for calculating the pressure distribution. The effect of different geometrical configurations of lubricated contact on hydrodynamic performance is evaluated. The results show that surface texture in parallel bearing yields a great improvement in terms of friction force and friction coefficient.     

考虑磨损的接触式端面密封模型及试验

针对油润滑窄端面接触式端面密封,建立了考虑端面稳定磨损的密封性能分析模型. 基于流体承载和固体接触承载共同平衡闭合力的传统思路,引入Archard磨损模型,创新性地提出沿窄端面径向方向磨损均匀假设,从而使用半解析方法得到近似固体接触力、流体承载力及介质膜厚分布. 在此基础上耦合密封环组件力和热变形,最终得到密封泄漏量、端面温度等性能参数. 相应台架试验结果也较好地验证了模型的正确性. 所建模型对于窄端面接触式端面密封的性能分析和密封优化设计具有指导意义.      

固液润湿性对流体动压润滑薄膜的影响

利用自行开发的微型面接触润滑油膜测量系统,研究了固液润湿性对流体动压润滑油膜厚度的影响.试验中以静止的微型滑块平面和旋转的光学透明圆盘平面形成润滑副.固液的润湿性通过接触角判定,不同材料的微滑块平面和润滑液体形成不同的界面.在保持载荷和面接触楔形角不变的条件下对油膜厚度-速度关系进行了测量.结果表明:对于固液润湿性强的界面,形成的油膜厚度与经典润滑理论有较好的一致性;当固液润湿性明显降低时,测量得到的油膜厚度减小.对于试验中观察到的界面效应,应用界面滑移理论进行了初步分析.     

Chaotic phenomena in the dynamic buckling of an elastic-plastic column under an impact

The present study is concerned with the dynamic anomalous response of an elastic-plastic column struck axially by a massm with an initial velocityv ₀. This simple example is considered in order to clarify the influence of the impact characteristics and the material plastic properties on the dynamic buckling phenomenon and particularly on the final vibration amplitudes of the column when it shakes down to a wholly elastic behaviour. The material is assumed to have a linear strain hardening with a plastic with a plastic reloading allowed. These material properties are the reason a number of elastic-plastic cycles to be realized prior to any wholly elastic stable behaviour, which causes different amounts of energy to be absorbed due to the plastic deformations.The column exhibits two types of behaviour over the range of the impact masses — a quasi-periodic and a chaotic response. The chaotic behaviour is caused by the multiple equilibrium states of the column when any small changes in the loading parameters cause small changes in the plastic strains which result in large changes in the response behaviour. The two types of behaviour are represented by displacement-time and phase-plane diagrams. The sensitivity to the load parameters is illustrated by the calculation of a Lyapunov-like exponent. Poincaré maps are shown for three particular cases.Notation c elastic wave propagation speed - m impact mass - m _c column mass - s step of the spatial discretization - t time - u(x,t) axial displacement - v ₀ initial velocity - w ₀(x) initial imperfections - w(x,t)+w ₀(x) total lateral displacements - x axial axis - z axis along the column thickness - A cross-section areahb - E Young's modulus - E _t hardening modulus (Figure 2) - M(x,t) bending moment - N(x,t) axial force - impact mass ratiom/m _c - (x,z) strain - Lyapunov-like exponent - material density - (x,z) stress     

A control volume-based discretization of the Reynolds equation for the numerical solution of elastohydrodynamic lubrication problems

This paper deals with the discretization of the one-dimensional Reynolds equation coupled with the film shape equation, that is used for the numerical solution of elastohydrodynamically lubricated contacts. The derivation of the developed discretization formula is based on the control volume approach. To reduce the discretization error caused by the upwind expression of the Couette (velocity) term, non-symmetric control volumes are used for discretization of the Reynolds equation, while for the elasticity equation the standard approach is used. A numerical method for the solution of the pressure and the film thickness profiles of elastohydrodynamically lubricated isothermal line contacts is presented. Results are presented for chosen typical parameters of a highly loaded contact. To show the formula efficiency, the convergence speed of both the presented discretization formula and a chosen comparative discretization formula (A.A. Lubrecht, Ph.D. Thesis, University of Twente, The Netherlands, 1987 and C.H. Venner, Ph.D. Thesis, University of Twente, The Netherlands, 1991) are checked. The results show that the presented formula gives better approximations of film thickness values for a given number of equidistant grid nodes. Moreover, the presented approach is probably suitable for more sophisticated cases, such as transient situations and elliptical contacts. © 1998 John Wiley & Sons, Ltd.     

An externally pressurised bearing with variable film thickness

Summary In this paper, a theoretical study of an externally pressurised bearing with variable film thickness has been presented. The load capacity and the frictional drag on the rotor have been determined. It has been shown that the frictional drag decreases as the angle, which the rotor surface makes with the stator, increases, but the load capacity and pressure do not depend upon it.Nomenclature angle between the rotor surface and the stator - angular velocity of the rotor - viscosity of the lubricant - h variable film thickness - L depth of the recess - p pressure - p _i inlet pressure - p _e exit pressure - Q rate of flow - r radial independent parameter - R ₀ radius of the recess - R outer radius of the stator - T frictional drag on the rotor - u radial velocity - v tangential velocity - w load capacity - z axial independent parameter     

流体润滑条件下BSA水溶液吸附膜的光干涉测量

利用面接触流体润滑光干涉测量装置,对BSA水溶液的润滑和吸附特性进行了试验研究.试验中润滑接触副由静止的钢块和旋转的玻璃盘组成,结果表明润滑膜厚度随速度的增加而增加,随载荷的增加而减小.BSA在钢滑块表面形成两种类型的吸附,一为连续的薄膜层,二为离散的蛋白质凝聚团簇.同时证实了钢块表面微观腐蚀的发生,并由入口区向出口区扩展,该腐蚀促进吸附膜的增长.吸附层的形成受润滑膜剪应变率和压力的影响,高的剪应变率和低的载荷有利于吸附膜的增长.     

多体系统碰撞动力学中接触力模型的研究进展

接触碰撞行为作为大自然与多体系统中的常见现象,其接触力模型对于多体系统的碰撞行为机理研究与性能预测至关重要.静态弹塑性接触模型与考虑能量耗散的连续接触力模型是研究接触碰撞行为的两类不同方法,在多体系统碰撞动力学中存在诸多共性与差异.本文分别从上述两类接触模型的发展历程入手,详细介绍了两类模型的区别与联系.首先,根据阻尼项分母中是否含有初始碰撞速度将连续接触力模型分为黏性接触力模型与迟滞接触力模型,讨论了能量指数与Hertz接触刚度之间的关系,阐述了现有连续接触力模型在计算弹塑性材料接触碰撞行为时存在的问题.其次,着重介绍了分段连续的准静态弹塑性接触力模型(可连续从完全弹性转换到完全塑性接触阶段),分析了利用此类弹塑性接触力模型计算碰撞行为的技术特点.同时,以恢复系数为桥梁和借助线性化的弹塑性接触刚度,避免了Hertz刚度对弹塑性接触刚度的计算误差,根据碰撞前后多体系统的能量与动能守恒推导了弹塑性接触模型等效的迟滞阻尼因子.探索了连续接触力模型与准静态弹塑性接触力模型之间的内在联系,数值计算结果定量说明了人为阻尼项代表的能量耗散与弹塑性接触力模型中加卸载路径代表的能量耗散具有等效性.另外...     

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     

Thickness reduction rate of plastically compressed metal plate by hardened rollers

The rate at which a solid deforms permanently depends on the load history, geometry and material properties. When a metal plate is compressed between two hardened rollers, its thickness reduces continuously if the material elements are deformed beyond their elastic limits. Those near the region of contact will experience more distortion as compared with those interior to the plate. This effect is analyzed incrementally in time by the theory of plasticity coupled with the strain energy density criterion. Failure is examined by assuming that the location of crack initiation coincides with the maximum of the minimum strain energy density function, (dW/dV)_min^max, when reaching its critical value. This is found to occur at the center of the plate depending on the rate of deformation. An increase in plate thickness reduction without failure can be achieved by taking smaller loading steps. Displayed graphically are numerical results for five different load histories that provide useful insights into the rate dependent process of metal forming.     

Particle convective heat transfer near the wall in a supercritical water fluidized bed by single particle model coupled with CFD-DEM

Supercritical water fluidized bed (SCWFB) is a promising reactor to gasify biomass or coal. Its optimization design is closely related to wall-to-bed heat transfer, where particle convective heat transfer plays an important role. This paper evaluates the particle convective heat transfer coefficient (h_pc) at the wall in SCWFB using the single particle model. The critical parameters in the single particle model which is difficult to get experimentally are obtained by the computational fluid dynamics-discrete element method (CFD-DEM). The contact statistics related to particle-to-wall heat transfer, such as contact number and contact distance, are also presented. The results show that particle residence time (τ), as the key parameter to evaluate h_pc, is found to decrease with rising velocity, while increase with larger thermal boundary layer thickness. τ follows a gamma function initially adopted in the gas–solid fluidized bed, making it possible to evaluate h_pc in SCWFB by a simplified single particle model. The theoretical predicted h_pc tends to increase with rising thermal gradient thickness at a lower velocity (1.5 U_mf), while first decreases and then increases at higher velocity (1.75 and 2 U_mf). h_pc occupies 30%–57% of the overall wall-to-bed heat transfer coefficient for a particle diameter of 0.25 mm. The results are helpful to predict the overall wall-to-bed heat transfer coefficient in SCWFB combined with a reasonable fluid convective heat transfer model from a theoretical perspective.