A fatigue life prediction method of rolling bearing under elliptical contact elastohydrodynamic lubrication

In order to more accurately predict the contact fatigue life of rolling bearing, a prediction method of fatigue life of rolling bearing is proposed based on elastohydrodynamic lubrication （EHL）, the 3-paameter Weibull distribution ad fatigue strength. First,the contact stress considering elliptical EHL is obtained by mapping film pressure onto the Hertz zone. Then,the basic strength model of rolling bearing based on the 3-parameter Weibull distribution is deduced by the series connection reliability theory. Considering the effect of the type of stress, variation of shape and fuctuation of load, the mathematical models of the 尸 -tS-TV curve of the minimum life and the characteristic life for rolling bearing are established, respectively, and thus the prediction model of fatigue life of rolling bearing based on the 3-paameter Weibull distribution and fatigue strength is further deduced. Finally, the contact fatigue life obtained by the proposed method ad the latest international standard （IS0281： 2007） about the fatigue life prediction of rolling bearing are compared with those obtained by the statistical method. Results show that the proposed prediction method is effective and its relative error is smaier than that of the latest international standard （IS0281： 2007） with reliability R 〉 0. 93.

ELASTOHYDRODYNAMIC LUBRICATION OF LOGARITHMIC PROFILE ROLLER CONTACTS

An account of numerical solutions to the isothermal and flooded elastohydrodynamic lubrication(EHL)of a logarithmic profile roller,which is rolling over a flat plane,is given The analysis takes account of sideways flow of lubricant in the inlet region of the contact When the results are presented in suitable non dimensional groups,it is shown that more uniformly pressure and shape of the film distributing in axial direction is taken place under light loading As the increase of the load,the end closure is displayed and the oil pressure rises sharply at the ends The seal action formed by the end closure makes the film thickness a little And the minimum film thickness is transferred from the central to the ends and the value is reduced rapidly As the increase of the speed,the end closure becomes much serious The optimum crowning value obtained in EHL state is larger than the design value obtained in elastostatic contact state for the same working conditions In order to verify the correctness of theory,optical interferometry is applied to measure the oil film thickness between a logarithmic profiled roller and a glass plate under pure rolling conditions It is found the agreement between numerical solutions and experiments is very good.

Elastohydrodynamic Lubrication Studies on Effects of Crowning Value in Roller Bearings

The purpose of this paper is to present a comparison of numerical calculations and experiment results of optical interferometry in finite line contact for the elastohydrodynamic lubrication(EHL) problem of Lundberg's profiled cylindrical roller under the conditions of flooded state, moderate load and material parameter. It shows clearly the effects of crowning value on the variations of oil film shape and thickness. The agreement between numerical analysis and experiment results is very good. The results indicate there must be an optimum crowning value that will induce the thickest and most even oil film in EHL state for a given working condition, and this value is larger than the design value in dry contact state for the same working conditions.

Jacobian-free Newton-Krylov subspace method with wavelet-based preconditioner for analysis of transient elastohydrodynamic lubrication problems with surface asperities

This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free Newtongeneralized minimal residual(GMRES) from the Krylov subspace method(KSM). The acceleration of the GMRES iteration is accomplished by a wavelet-based preconditioner.The profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of bearings.The analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest.

The size-dependent elastohydrodynamic lubrication contact of a coated half-plane with non-Newtonian fluid

Based on the couple-stress theory,the elastohydrodynamic lubrication(EHL)contact is analyzed with a consideration of the size effect.The lubricant between the contact surface of a homogeneous coated half-plane and a rigid punch is supposed to be the non-Newtonian fluid.The density and viscosity of the lubricant are dependent on fluid pressure.Distributions of film thickness,in-plane stress,and fluid pressure are calculated by solving the nonlinear fluid-solid coupled equations with an iterative method.The effects of the punch radius,size parameter,coating thickness,slide/roll ratio,entraining velocity,resultant normal load,and stiffness ratio on lubricant film thickness,in-plane stress,and fluid pressure are investigated.The results demonstrate that fluid pressure and film thickness are obviously dependent on the size parameter,stiffness ratio,and coating thickness.

非稳态点接触EHL问题高效直接算法研究

发展了一种研究非稳态点接触弹流润滑(Elastohydrodynamic Lubrication,简称EHL)的快速直接算法。在弹流求解过程中,通过分析计算域网格离散的特点,对离散后的Reynolds方程采取按列分块、逐列求解的求解策略,使每个时间步长上求解的方程维数显著减小,从而极大地提高了计算效率。运用新算法获得了点接触EHL纯挤压工况下油膜和压力演变过程中的典型特征,证明了新算法的正确性;数值实验和比较证明,新算法具有复合直接迭代法无可比拟的高效率,与逐行迭代法相比,新算法也具有显著的、更高的计算效率,并且随着网格数量的增加,新算法的高效性愈加凸显。

Influence of water evaporation on elastohydrodynamic lubrication with water-containing polyalkylene glycols

The reduction of frictional power losses in power transmitting gears takes a crucial role in the design of energy-and resource-efficient drivetrains.Water-containing lubricants like glycerol and polyalkylene glycols have shown great potential in achieving friction within the superlubricity regime with coefficients of friction lower than 0.01 under elastohydrodynamic lubrication.Additionally,a bio-based production of the base stocks can lead to the development of green lubricants.However,one challenge associated with the application of water-containing lubricants to gearboxes is the evaporation of water and its impact on the lubricant properties.In this study,the influence of water evaporation on elastohydrodynamic friction and film thickness was investigated for three water-containing polyalkylene glycols.Two nominal water contents of 20 wt%and 40 wt%and two viscosities were considered.The results show that the friction increases continuously with higher evaporated water content,while the overall friction level remains low in nearly water-free states.A similar trend is observed for film thickness,where the strong increase in viscosity results in a notable increase in film thickness.Nevertheless,the sensitivity of friction and film thickness to water evaporation is low for small amounts of evaporated water.This allows generous thresholds for permissible variations in water content.

STUDY ON THE LUBRICATION FACTOR OF INVOLUTE SPUR GEARS

Based on a lot of numerical solutions to the problems of the thermalnon-Newtonian elastohydrodynamic lubrication and some fatigue tests with rollers, the lubricationfactor of involute spur gears (called gear for short) is investigated. The results suggest that gearlubrication effects bear close relations to a dimensionless parameter D which is syntheticallydetermined by gearing rotational speed, load, material, dimension and lubricant viscosity. When D<=8, the gear fatigue life increases as the lubricant viscosity is increased; When D>8, however, thelife decreases with the viscosity addition, which is in marked contrast to the lubrication factorZ_L recommended by the International Standard for Computing Cylindrical Gear Strength. At the end, aset of formulae for calculating gear lubrication factors suitable for different working conditionsare advanced.

Influence of Lubrication Performance on the Service Life of Rolling Mill Bearings

In order to confirm the early failure cause of a four-row cylindrical roller bearing at the backup roll position of a six-high cold sheet mill, its lubrication behavior under harsh operating conditions is investigated. Through establishing and solving the Elastohydrodynamic Lubrication （EHL） model of the roller-inner raceway contact region, the minimum oil film thickness and the real lubrication performance are achieved. The results show the bearing failures come from the poor oil film thickness in the case of high temperature and low rotational speed, which leads to contact wear. So various approaches to improve bearing life via improving lubrication are compared. It has been proved decreasing surface roughness of both contact bodies is an effective way.

A GENERALIZED REYNOLDS EQUATION BASED ON NON-NEWTONIAN FLOW IN LUBRICATION MECHANICS

A generalized Reynolds equation based on non-Newtonian flow is derived in this paper.This equation is suitable for a number of non-Newtonian flow models and can be solved numerically to obtain pressure fields in thermalhydrodynamically or elastohydrodynamically lubricated fluid films.A mathematical ap- proach is given for solving simultaneously the shearing stress,shearing rate,velocity and equivalent viscosity.To show the application of this equation,two rheological models which have been widely used in lubrication mechnaics are incorporated into this equation to obtain numerical solutions to the line contact thermal elastohydrodynamic lubrication problem.

A new general rheological model for rheological lubrication

Limitation and deficiency of main thcoogical models at present are descrital and analyzed, and seteralgeneral rheological models are discussed and compared with each other, and basic demands for a general model aresummarized. The constitutive eqUation is proposetl for a new general theobocal model. The general medel feaaressimple structure and wide coverage, and can take the Place of many edsting thcofogical ed. The whel has suc-cessfully been used for Elastohydrodynamic lubrication calculation.

分形粗糙面的主轴承弹流脂润滑分析

为探究弹性流体动压润滑(弹流润滑)状态下RV减速器主轴承接触表面之间的润滑特性,基于润滑脂的非牛顿特性以及粗糙表面分形理论,提出一种主轴承的点接触弹流脂润滑数值模型。首先,对该模型进行数值求解,得到脂膜压力、脂膜厚度的分布规律;然后,将其分别与其他点接触弹流润滑模型的数值结果和实验结果进行对比,验证了所建模型的正确性;最后,分析了主轴承表面光滑和粗糙状态下流变指数、分形维数、卷吸速度、载荷和润滑脂黏度对润滑性能的影响。结果表明:润滑脂的非牛顿性越明显,脂膜厚度越小且颈缩现象愈加不明显,接触区附近脂膜压力越符合赫兹压力分布,二次压力峰逐渐消失;考虑主轴承分形粗糙表面的弹流润滑特征更切合实际,增大分形维数,接触区真实接触面积增大,有利于降低脂膜压力,增加脂膜厚度;卷吸速度、载荷和润滑脂黏度对脂膜厚度分布的影响显著,对脂膜压力分布的影响较小;脂膜厚度以及最小膜厚越大,主轴承接触区脂膜不易破坏且越容易形成动压润滑。

NUMERICAL ANALYSIS OF ELAS－TOHYDRODYNAMIC LUBRICATION WITH TRANSIENT VISCOSITY

The transient vistosity response of a lubricant following the pressure charge in a EHDcontact is consideied in the line-contact isothermal elastohydrodynamic lubrication analyses. Soobtained pressure distribution and the oil film thickness are different from those obtained with equi-librium viscosity.

齿轮表面摩擦学设计与表面织构化研究进展

我国国防事业的飞速发展对航空高速齿轮提出了更高要求,而有关齿轮副表面摩擦学设计仍是薄弱环节。表面织构技术已成为摩擦学领域的研究热点,在减摩抗磨、减振、抗粘附和抗蠕爬等多个领域展示出良好的应用潜力。有关齿面织构化设计研究尚处于起步阶段,还远未能形成规范成熟的设计理念和方法。对当前在齿轮表面摩擦学设计及表面织构化方面的研究工作进行全面综述。首先从齿轮表面摩擦学设计基本要求展开介绍,指出表面粗糙度和表面纹理是齿轮副表面摩擦学设计的关键,而大量研究已经证实,不管是滚动还是滑动摩擦,并非表面越光滑摩擦学性能越优异,在齿轮副表面织构化设计方面的研究工作已经展开。随后对现有齿轮副表面织构化的研究工作进行梳理,总结齿面织构化处理后带来的性能增益,主要包括减摩抗磨效应、表面强化效应、减振和降温效应。接着,介绍齿轮弹流润滑数值计算方面的研究进展,总结在表面纹理、表面织构对齿轮副的弹流润滑特性影响机制方面的研究。随后,对齿轮副表面织构加工技术进行对比分析,主要包括织构激光刻蚀、织构掩膜电解和织构微磨料射流等特种加工技术的优劣。对现有研究不足和潜在研究方向进行展望,从织构设计和加工等方面对齿轮表面织构化设计提供指导,研究结果可为未来航空高速齿轮副表面织构化设计提供科学指导和数据支撑,填补该领域研究空白并扩大表面织构应用领域。

线接触弹流润滑摩擦副刚度阻尼拟合公式

弹流润滑油膜具有显著的弹簧阻尼作用,对齿轮、滚动轴承、凸轮等高副接触零件的动力学性能具有重要影响,然而目前关于弹流摩擦副刚度阻尼的认识还不统一。运用数值方法求解线接触弹流润滑摩擦副的摩擦学-动力学耦合模型,获得线接触弹流润滑摩擦副在简谐激励下的阻尼环,通过阻尼环识别出线接触弹流润滑摩擦副的刚度和阻尼;用变量控制的方法研究载荷、卷吸速度、材料参数等对线接触弹流润滑摩擦副刚度和阻尼的影响,并分析载荷、卷吸速度影响线接触弹流润滑摩擦副刚度阻尼的机制。结果表明,线接触弹流润滑摩擦副刚度阻尼随载荷增加而变大,随速度增加而减小。在数值解的基础上,拟合出线接触弹流润滑摩擦副刚度和阻尼公式,结果显示,载荷对弹流润滑摩擦副的刚度和阻尼影响最显著,而且弹流润滑摩擦副的刚度随载荷、速度和材料参数的变化幅度比阻尼的大。对拟合公式精度的检验表明,在很宽的参数范围内,拟合公式计算结果与数值解的相对误差小于10%,所提出的刚度和阻尼拟合公式具有很高的精确性。

表面局部缺陷角接触球轴承弹流润滑性能研究

根据高速角接触球轴承自旋的运动特征,同时考虑轴承高速摩擦生热的影响,建立了表面具有局部缺陷的角接触球轴承弹流润滑模型。采用多重网格法获得弹流润滑各参数数值解,同时计算出轴承油膜刚度。研究了自旋、热效应和表面局部缺陷对球轴承弹流润滑性能的影响规律,计算结果表明:考虑自旋条件时,轴承的油膜厚度减小、压力增大,油膜刚度增大;随着轴承温度升高,轴承油膜厚度减小,油膜压力和油膜刚度增大;当润滑油流经轴承表面局部缺陷时,缺陷区域轴承润滑油油膜厚度增大,油膜压力减小,而非缺陷区域轴承最小油膜厚度减小,最大油膜压力增大,油膜刚度增大。

深沟球轴承织构化滚道表面润滑性能的数值分析

织构化深沟球轴承摩擦副表面的接触形式、织构形态对轴承润滑性能的影响机制尚不明确。为探究微织构对深沟球轴承椭圆接触摩擦副表面弹流润滑性能的影响,基于弹流润滑理论,考虑滚道织构对于摩擦表面间油膜厚度的影响作用,建立一种适用于深沟球轴承的织构化表面接触弹流润滑分析模型。然后,采用多重网格法进行数值计算,根据结果分析不同载荷及卷吸速度下织构深度和半径对接触表面油膜压力和厚度分布的影响规律。结果表明,摩擦副表面的润滑性能随着载荷的增大而变差,随着卷吸速度的增大而变好;织构化表面的流体动压效应则随着织构深度的增加而逐渐增大,随着织构半径的增大而逐渐减小,当典型深沟球轴承的滚道织构深度在1.5~2.7μm,半径在3~7μm范围时,织构化摩擦副表面的润滑性能表现最佳,证明适当的织构型式可有效改善深沟球轴承摩擦副表面的润滑性能。研究织构对深沟球轴承摩擦副表面的润滑特性规律,可以为椭圆接触类型摩擦副的织构化优化设计提供理论参考。

燃油介质作动器往复密封摩擦热效应及磨损特性分析

发动机矢量推力作动器采用燃油作为传动介质,燃油的低黏度将使作动器密封接触面处于不良润滑条件,密封件摩擦磨损问题突出。针对燃油介质作动器不同压力、作动速度及油液温度的工作环境,建立往复密封热弹流混合润滑数值仿真模型,分析往复密封接触面摩擦热效应对油膜行为的影响,确定热分析边界条件,计算密封系统的瞬态温度分布。根据热分析结果,对油液黏度及密封区域内的油膜厚度进行修正,考虑密封件润滑条件探究摩擦热效应对密封性能与磨损特性的作用机理,分析不同工况条件对油膜厚度、摩擦力和磨损深度分布的影响,为设计高性能航空密封件奠定理论基础。

State of the art of friction modelling at interfaces subjected to elastohydrodynamic lubrication(EHL)

Elastohydrodynamic lubrication(EHL)is a type of fluid-film lubrication where hydrodynamic behaviors at contact surfaces are affected by both elastic deformation of surfaces and lubricant viscosity.Modelling of contact interfaces under EHL is challenging due to high nonlinearity,complexity,and the multi-disciplinary nature.This paper aims to understand the state of the art of computational modelling of EHL by(1)examining the literature on modeling of contact surfaces under boundary and mixed lubricated conditions,(2)emphasizing the methods on the friction prediction occurring to contact surfaces,and(3)exploring the feasibility of using commercially available software tools(especially,Simulia/Abaqus)to predict the friction and wear at contact surfaces of objects with relative reciprocating motions.

脂润滑弧齿锥齿轮热弹流润滑与效率研究

基于油动重载四旋翼无人机的特殊应用条件,研究了无人机齿轮箱内脂润滑弧齿锥齿轮的润滑状态及啮合效率.推导了适用于弧齿锥齿轮的脂润滑雷诺方程,采用计算油膜剪切力和微凸体接触摩擦力组成的复合摩擦系数代替摩擦系数经验公式的方法,研究了在无人机各种工况下的齿面润滑情况和啮合效率.结果表明,本研究中提出的考虑粗糙度的脂润滑雷诺方程能够很好预测文献中的试验结果;弧齿锥齿轮的齿面较为复杂,不能用油润滑的中心油膜厚度算法近似估计脂润滑弧齿锥齿轮整个齿面上的润滑状态;1个啮合周期内的齿面摩擦系数在节点处最大;低转速情况下,齿面将进入混合润滑状态;1个啮合周期内啮合效率的变化与啮合位置密切相关,在啮入点处效率最低;在转速不变的前提下,润滑脂黏度越高,效率损失越大.