基于Carreau流变模型的圆柱滚子轴承热混合润滑分析*

为了研究圆柱滚子轴承接触区的混合润滑性能,建立基于Carreau非牛顿流体的热混合润滑模型,求解非牛顿流体线接触热混合润滑数值解。研究滑滚比、卷吸速度及载荷对线接触混合润滑特性的影响,并与相同工况下牛顿流体热混合润滑的结果进行对比。结果表明：随着滑滚比、卷吸速度及载荷的增大,油膜温度都会升高,Carreau非牛顿流体的温度要低于牛顿流体的温度;油膜厚度随着滑滚比、载荷的增大而减小,随着卷吸速度的增大而增大,Carreau非牛顿流体与牛顿流体膜厚相差不大;随着滑滚比的增大,2种流体的平均摩擦因数均增大,随着卷吸速度和载荷的增大,2种流体的载荷比均减小。     

Elastohydrodynamic Lubrication of Rough Surfaces under Oscillatory Line Contact with Non-Newtonian Lubricant

This paper presents the results of a transient analysis of elastohydrodynamic lubrication (EHL) of two parallel cylinders in line contact with a non-Newtonian lubricant under oscillatory motion. Effects of the transverse harmonic surface roughness are also investigated in the numerical simulation. The time-dependent Reynolds equation uses a power law model for viscosity. The simultaneous system of modified Reynolds equation and elasticity equation with initial conditions was solved using the multigrid, multilevel method with full approximation technique. The film thickness and the pressure profiles were determined for smooth and rough surfaces in the oscillatory EHL conjunctions, and the film thickness predictions were verified experimentally.

For an increase in the applied load on the cylinders or a decrease in the lubricant viscosity, there is a reduction in the minimum film thickness, as expected. The predicted film thickness for smooth surfaces is slightly higher than the film thickness obtained experimentally, owing primarily to cavitation that occurred in the experiments. The lubricant film under oscillatory motion becomes very thin near the ends of the contact when the velocity goes to zero as the motion direction changes, but a squeeze film effect keeps the fluid film thickness from decreasing to zero. This is especially true for surfaces of low elastic modulus. Harmonic surface roughness and the viscosity and power law index of the non-Newtonian lubricant all have significant effects on the film thickness and pressure profile between the cylinders under oscillatory motion.     

基于弹流润滑的滚子轴承参数研究

基于弹流润滑理论研究滚子轴承结构参数对其润滑特性的影响。结合弹性接触变形方程以及流体动力学润滑方程,建立适合于滚子轴承的弹流润滑模型,研究在不同椭圆率、载荷、卷吸速度以及黏度等因素作用下滚子轴承的摩擦学性能变化规律。结果表明：椭圆率、载荷、卷吸速度以及黏度会不同程度地影响压力峰值及二次压力峰等参数;随着椭圆率的增大,油膜厚度以及压力显著增大;随着载荷的增大,总体压力、压力峰值、二次压力峰及其尖锐度明显增大,但最小油膜厚度略有下降;黏度与最小油膜厚度以及压力存在着明显正相关关系;卷吸速度与油膜厚度存在着微弱正相关关系,与油膜压力存在着微弱负相关关系。因此,一定程度上增大椭圆率并减小载荷,有利于提高润滑性能。     

渐开线直齿圆柱齿轮非牛顿瞬态弹流润滑分析

齿轮的润滑设计都是应用理想牛顿流体的结果,但实际上,在中、轻载荷下Ree Eyring流体更符合实际。因 此研究齿轮在非牛顿润滑下的瞬态弹流机理,对于指导齿轮润滑问题的设计更具有工程实际价值。本文应用数值 稳定性好、收敛速度快和计算精度高的多重网格算法,得到了用Ree Eyring流体润滑的齿轮瞬态弹流问题的完全数 值解。     

Elastohydrodynamic Films Under Periodic Load Variation: An Experimental and Theoretical Approach

The elastohydrodynamic lubrication regime occurs in systems where large elastic deformations, the hydrodynamic action of a converging wedge and eventually large variation of viscosity of the fluid combine to determine the formation of a continuous fluid film that separates the solid surfaces. Experimental and theoretical works, over the past few decades, have elucidated the role of various working and material parameters on the lubricant film thickness which plays a crucial role in protecting the solid surfaces from direct contact and ultimately from failure. These mechanisms are well understood for steady-state conditions; however, elastohydrodynamic contacts most often experience transient conditions, including variation of geometry, velocity of surfaces or load. In this case, the mechanisms of film formation are more complex involving film squeeze in addition to the mechanisms mentioned above. Experimental and theoretical modelling of transient phenomena in elastohydrodynamic lubrication include sudden variation of entrainment speed or load and changing geometry. No systematic experimental study on the effect of harmonic load vibration upon the elastohydrodynamic films has been published before. In order to cover this gap, this paper presents the results of an experimental study and of a simple theoretical approach on the behaviour of the elastohydrodynamic film thickness under harmonic variation of load.     

涂层材料热特性参数对点接触弹流润滑的影响

为探究涂层材料热特性参数对点接触弹流润滑的影响,选择3种不同方法制备的类金刚石（DLC）涂层和氧化锆陶瓷涂层,构建考虑涂层热特性的点接触弹流润滑模型,分析涂层材料、涂层厚度和润滑剂的流变性对接触区润滑性能的影响。结果表明：在弹流润滑状态下具有不同热特性的4种表面涂层导致了膜厚的差异,固体表面温度及润滑区温度场会随涂层热惯性变化;热惯性最小的DLC涂层加在快速运动表面能获得更高的膜厚;随着涂层厚度的增加,会引起固体表面的温度升高,使摩擦因数降低;非牛顿流体对压力、膜厚的影响很小,但与牛顿流体相比,能获得相对较低的温度。在弹流润滑状态下,涂层覆在快表面对于减小摩擦、提高膜厚是有益的。     

A general elastohydrodynamic lubrication analysis of artificial hip joints employing a compliant layered socket under steady state rotation

A general numerical methodology was developed in the present study to analyse the elastohydrodynamic lubrication problem of a compliant layered socket against a rigid ball under steady state rotation representing flexion and extension during walking, with particular reference to artificial hip joint replacements. The general numerical methodology consisted of using the Newton-Raphson method to solve the Reynolds equation, simultaneously with the full elasticity equation using the finite element method in combination with the fast Fourier transform technique. Two specific types of acetabular cup were considered, one with ultra-high molecular weight polyethylene used in current total hip joint replacements, and one with polyurethane proposed for compliant layered 'cushion form bearings' for future developments. The film thickness and the pressure distribution for both cups were obtained under a wide range of operating conditions. The predicted central or average film thicknesses within the contact conjunction were compared with those estimated from various simplified theories available in the literature. A simple analytical methodology was consequently established to estimate the lubricating film thickness in a compliant layered socket, based on the corresponding ball-on-plane model and the consideration of the curvature effect.     

Tribology of human and artificial joints.

Studies of human joint lubrication mechanisms have led to the conclusion that under normal healthy conditions they are fluid film lubricated. The main features responsible for allowing this mechanism to operate are the dynamic nature of the loading and the compliance of the bearing surfaces (articular cartilage). In contrast, artificial joints, being made of much more rigid materials, have been demonstrated to be lubricated by a mixed regime, where some load is carried by the fluid film and some by solid to solid contact. Since some surface contact takes place then wear remains a problem and friction is much higher than in human joints. The use of compliant surface bearings for artificial joints has been explored and shown to be of great advantage, reproducing the effects of natural joints. However, elastomeric materials are known to degrade in aqueous solutions so this aspect has been examined to ensure a reasonable life in the human body. Joints of the lower limb--hip, knee, and ankle--have similar load and motion patterns and behave in a similar way in terms of lubrication. Joints of the hand are not in any way similar in their behaviour and so a typical upper limb joint, the finger, has been studied to see if improvements can be made to the design of replacement artificial joints. Novel suggestions like plastic on plastic joints have been shown to be an alternative which is worthy of further consideration.     

Elastohydrodynamic lubrication analysis of a functionally graded layered bearing surface,with particular reference to 'cushion form bearings' for artificial knee joints

Elastohydrodynamic lubrication of a functionally graded layered (FGL) bearing surface, whose elastic modulus increases with depth from the bearing surface, was investigated in this study. The finite difference method was employed to solve the Reynolds equation, simultaneously with the elasticity equation of the bearing surface, under circular point contacts. The finite element method was adopted to solve the elasticity equation for the FGL bearing surface. The displacement coefficients thus obtained were used to calculate the elastic deformation of the bearing surface, required for the elastohydrodynamic lubrication analysis. Good agreement of the predicted film thickness and pressure distribution was obtained, between the present method and a previous study for a single layered bearing surface with a uniform elastic modulus. The general numerical methodology was then applied to an FGL bearing surface with both linear and exponential variations in elastic modulus, with particular reference to the 'cushion form bearing' for artificial knee joints. The predicted film thickness and pressure distribution were shown to be quite close to those obtained for a single layer under typical operating conditions representative of artificial knee joints, provided that the elastic modulus of the single layer was chosen to be the average elastic modulus of the graded layer.     

Calculation of sliding power loss in spur gear contacts

An engineering-level calculation model for sliding power loss in spur gear contacts is presented. Teeth contact through the line of action is modelled as a constantly changing roller contact whose radius, speed, and load can be calculated from the gear geometry under the given operating conditions. The gear mesh cycle is approximated by a large number of elastohydrodynamic contacts. A constant film thickness and a Hertzian pressure distribution are assumed in each contact. The model includes non-Newtonian lubricant behaviour together with temperature and mixed lubrication effects in contact. The numerical solver is reasonably fast in evaluating effectively the sliding power loss dependence on the essential gear and lubricant parameters. The features and behaviour trends of the calculated sliding power losses have a close similarity with published results obtained from measurements and experiment-based power loss models with mineral oil. The limiting shear stress of the lubricant is observed to have an essential role in the power loss behaviour especially at high loads.     

Elastic deformation in thin film hydrodynamic lubrication

An elastohydrodynamic numerical simulation is conducted for one-dimensional fixed slider plane bearings. The numerical model takes into account the piezoviscous effect of the lubricant and elastic deformation of the bounding surfaces to solve the one-dimensional Reynolds equation. It is found that a small elastic deformation of less than 100 nm plays an important role in load capacity in thin film hydrodynamic lubrication. As the film thickness decreases, a flat film shape appears from the leading side of the contact area. The expansion of the flat film thickness over the contact area leads to considerably lower load capacity.     

脂润滑轮毂轴承弹流润滑数值分析

基于Ostwald模型建立脂润滑控制方程,运用多重网格法求得等温线接触脂润滑弹性流体动力润滑数值解,得到钢球-沟道的压力分布、油膜形状及最小油膜厚度。针对轿车轮毂轴承的典型应用工况条件,分析工况参数对油膜压力分布和油膜形状的影响。结果表明:脂润滑弹流膜具有与油润滑膜相同的二次压力峰和出口颈缩现象。在轿车轮毂轴承可能的承载条件下,随着载荷的减小,二次压力峰的高度降低,其位置向入口区移动;一定承载条件下,速度增加时,膜厚相应增加,油膜的平行部分缩短,二次压力峰的高度增加,其位置也向入口区移动;一定承载和卷吸速度下,润滑脂流变参数增大时,二次压力峰的高度升高,其位置向入口区移动,膜厚相应增加。     

航空发动机主轴圆柱滚子轴承弹流动态性能仿真

基于现代弹流理论和弹性力学理论建立了圆柱滚子轴承等温稳态、非等温时变及其接触面粗糙的热弹流分析模型和应力分析模型,用数值分析方法对模型进行了求解,并对圆柱滚子轴承弹流动态性能和滚动体接触应力进行了仿真。仿真结果表明,轴承速度、载荷、粗糙度是影响轴承弹流性能的主要因素;在不考虑其它因素情况下,接触区内中部的接触应力最高。     

直齿轮传动非牛顿流体瞬态弹流润滑研究

综合考虑润滑流体的非牛顿特性以及齿轮传动的瞬态效应，采用Bair-Winer粘塑模型推导了非牛顿流体雷诺方程，建立了非牛顿流体瞬态弹流润滑模型；进行直齿轮传动非牛顿流体弹流润滑数值分析，获得了齿轮传动沿啮合线的油膜压力、油膜形状以及摩擦因数的分布。结果表明：在非牛顿流体工况下，油膜厚度、油膜压力以及轮齿表面摩擦因数均有所降低,因此在齿轮弹流润滑研究中应考虑流体的非牛顿特性的影响。     

Thin film elastohydrodynamic lubrication—a power-law fluid model

A 1-D modified Reynolds equation for power-law fluid is derived from the viscous adsorption theory for thin film elastohydrodynamic lubrication (TFEHL). The lubricating film between solid surfaces is modeled as three fixed layers, which are two adsorption layers on each surface and a middle layer between them. The comparisons between classical non-Newtonian EHL and non-Newtonian TFEHL are discussed. Results show that the TFEHL model can reasonably calculate the pressure distribution, the film thickness, the velocity distribution and the average viscosity. The thickness and viscosity of the adsorption layer and the flow index influence the lubrication characteristics of the contact conjunction significantly. The film thickness increases with the increase of flow index. As the flow index becomes greater, the dimple in the film shape moves towards the center of the contacts. The effect of flow index produces an obvious difference in the pressure distribution. The greater the flow index, the greater the pressure spike, and the pressure spike tends to move toward the center. The larger the flow index, the more the velocity varies in both the middle layer and adsorption layers along the Z-axis. The greater the thickness and viscosity of the adsorption layer and the flow index, the greater the deviation in central film thickness versus speed between EHL model and TFEHL model produced in the very thin film regime.     

点接触润滑状态转化的实验观察

利用球-盘接触润滑油膜厚度的光干涉测量法，通过卷吸速度或载荷的改变实验研究了弹性流体动力润滑与流体动力润滑转化过程中油膜厚度的变化规律。实验结果显示这2种润滑状态之间存在明显的过渡区。与已有的理论一致，在弹性流体动力润滑区和流体动力润滑区，油膜厚度与卷吸速度或载荷在对数坐标中呈直线关系。在两者的过渡区，固体表面的弹性变形量随卷吸速度或载荷的变化发生明显的变化，油膜厚度与速度或载荷的关系不再为对数坐标中简单的线性关系。使用已有的润滑状态区理论不能得到实验观测到的润滑状态的转化过渡区。     

Quantitative analysis of joint lubrication

A comprehensive theoretical analysis of the extent of elastohydrodynamic lubrication in human joints is presented. The analytical model is developed from existing experimental data on the geometry, loading, kinetics and elastic properties of the hip joint and the viscous properties of synovial fluid. Results of a computer-generated numerical solution of the lubrication equations are given which demonstrate that elastohydrodynamic lubrication does not persist within human joints. An alternative lubrication mechanism based on the information obtained from the analysis is discussed.     

Numerical analysis of TEHL line contact problem under reciprocating motion

This paper presents a full numerical analysis to simulate the thermal elastohydrodynamic lubrication (TEHL) of steel–steel line contact problem under reciprocating motion. The equation system is solved using multigrid techniques. General tribological behaviors of TEHL under reciprocating motion are explained. Comparison between thermal and isothermal results reveals the importance of thermal effect in prediction of the traction coefficient and film thickness. The influences of frequency, stroke length, and applied load on the variations of film thickness, pressure and traction coefficient during one working cycle are discussed. Furthermore, the influence of slide–roll ratio on tribo-characteristics of oil film under same entraining velocity is revealed.     

Generalized non-Newtonian elastohydrodynamic lubrication

Realistic prediction of the behaviour of a lubricant in elastohydrodynamic contact requires consideration of proper rheological model(s) that take the non-Newtonian characteristics of the fluid into account. A general formulation and solution methodology is presented that can treat an elastohydrodynamic lubrication problem with any simple, non-Newtonian constitutive equation.