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.

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.

Oil Film Stiffness of Double Involute Gears Based on Thermal EHL Theory

Lubrication failure is one of the main failure forms of gear failure.Time varying meshing stiffness is an important factor affecting the dynamic behavior of gears.However,the influence of oil film stiffness is usually ignored in the research process.In this paper,according to the meshing characteristics of double involute gears,based on the non-Newtonian thermal EHL theory,a new calculation method of normal and tangential oil film stiffness for double involute gears is established by the idea of subsection method.The oil film stiffness difference between double involute gears and common involute gears is analyzed,and the influence of tooth waist order parameters,working conditions,and thermal effect on the oil film stiffness are studied.The results reveal that there are some differences between normal and tangential oil film stiffness between double involute gears and common involute gears,but there is little difference.Compared with the torque,rotation speed and initial viscosity of the lubricating oil,the tooth waist order parameters have less influence on the oil film stiffness.Thermal effect has a certain influence on normal and tangential oil film stiffness,which indicates that the influence of thermal effect on the oil film can not be ignored.This research proposes a calculation method of normal and tangential oil film stiffness suitable for double involute gears,which provides a theoretical basis for improving the stability of the transmission.

点接触EHL二次压力峰和中心压力拟合公式

基于求解点接触弹流润滑(EHL)问题的高效直接算法,研究了点接触EHL状态下载荷、速度、材料参数对二次压力峰和中心压力的影响,在对大量数值解结果进行分析和回归的基础上,给出了二次压力峰和中心压力对载荷、速度、材料参数关系的拟合公式,并对拟合公式的精确性进行了检验,结果显示,在相当宽的参数范围内,所提出的拟合公式的计算结果与数值解的相对误差小于10%,为研究零件在点接触EHL状态下的最大应力及疲劳寿命预测提供了一个简单而实用的工具。

基于EHL理论的脂润滑轴承沟道表面缺陷研究

根据脂润滑轴承失效表现形式,分析了滚动轴承沟道表面缺陷产生的原因,建立了球-沟道表面缺陷条件下的脂润滑弹流数学模型和油膜厚度方程,采用数值计算方法分析了不同尺寸的表面缺陷及表面光滑条件下的脂润滑弹流润滑油膜压力和油膜厚度分布规律。结果表明:轴承工作过程中,球-沟道表面会形成位置、尺寸和形状随机分布的凸起和凹坑;相比于光滑表面,缺陷表面会引起油膜压力和油膜厚度显著变化,且对于同类型表面缺陷,随着缺陷尺寸的增大,引起油膜压力和油膜厚度分布变化的规律大致相同但效果增强;表面缺陷均会对轴承润滑脂的润滑效果造成不良影响。

滚子轴承特定结构耦合EHL控制转子非线性响应的数值研究

应用理论分析和数值计算,针对实际精密转子系统服役性能要求,研究弹流润滑(EHL)下滚子轴承特定结构对转子非线性动态行为的控制机制,讨论一些主要参数滚子振动状态的影响。结果表明:支承端峰峰(P-P)值随滚子个数、滚道曲率系数、润滑剂黏度变化显著,适当选取这些参数可跃过共振区并使运动幅值精度提高;振动谱以固有振动、通过振动及其谐波组合为主频,EHL起到阻尼器的作用,可以整体削减系统振幅。

渐开线直齿圆柱齿轮弹流(EHL)的非稳态特征(英文)

1 Putting forword the question and its calculating method The lubrication of involute spur gear transmission is the typical one of transient EHL line contact problem. It can't be described only with famous Dowson-Higginson equation, but it is a very complicated partial difference equation. So far, no any complete discussion has been seen at home and abroad, and it is a forward problem at this field in internation. So there is a number of deepgoing and much-needed work to do. It is correspondence with practical lubrication condition to explore the

弹塑性微峰接触的部分膜点EHL数值分析

在部分膜EHL润滑下 ,摩擦副表面微峰接触状况对零件表面应力及失效形式有直接的影响 .为此 ,在部分膜点接触EHL模型中引入更符合实际的表面微峰弹塑性接触模型来考察微峰接触载荷 ;并应用多重网格法针对多种表面微峰结构参数的影响进行了完全数值分析 .结果表明 ,粗糙度对油膜厚度的影响和表面纹理方向有关 ;相同粗糙度情况下 ,纵向纹理表面的接触载荷 >各向同性纹理表面的接触载荷 >横向纹理表面的接触载荷 .表面粗糙度较大时 ,峰顶参数对油膜压力和微峰接触压力有一定的影响 ,而对油膜形状影响甚微 ;表面越粗糙、表面凸峰越尖锐 ,微峰接触载荷则越大 .

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.

行星滚子牵引传动的弹性流体动力学（EHL）分析（二）

本文介绍新的最小油膜厚度公式和中心油膜厚度公式的推导，并应用上述结果对行星滚子牵引传动装置的弹流润滑机理作详细分析。

线接触EHL状态下中心压力和二次压力峰的拟合公式

研究了线接触EHL状态下载荷、速度、材料参数对中心压力和二次压力峰的影响,在对大量数值解结果进行分析和回归的基础上,给出了中心压力幅值和二次峰压力幅值的拟合公式,并对拟合公式的精确性进行了检验。结果表明,在相当宽的参数范围内,提出的拟合公式的精度令人满意,可以满足工程设计要求。

限制间隙条件下的点接触EHL特性分析

在经典的弹性流体动力润滑理论中,两接触体处于开放的空间中,其相对位置由施加的外载决定,即油膜压力的计算要满足载荷平衡条件。而当弹流润滑发生在限制空间中时,如滚动轴承中的润滑,接触体的相对位置受系统的约束,传统弹流理论并不能用于该工况下的润滑特性预测。本文对限制间隙条件下等温点接触弹流润滑问题进行了数值分析,研究了速度参数、材料参数和刚性间隙H00对油膜厚度和承载力影响。根据计算结果,回归出新的承载力以及膜厚计算公式。另外,对限制间隙条件下的润滑油膜特性进行了试验观察,将结果与数值分析进行了对比。

Grease film evolution in rolling elastohydrodynamic lubrication contacts

Although most rolling element bearings are grease lubricated,the underlying mechanisms of grease lubrication has not been fully explored.This study investigates grease film evolution with glass disc revolutions in rolling elastohydrodynamic lubrication(EHL)contacts.The evolution patterns of the grease films were highly related to the speed ranges and grease structures.The transference of thickener lumps,film thickness decay induced by starvation,and residual layer were recognized.The formation of an equilibrium film determined by the balance of lubricant loss and replenishment was analyzed.The primary mechanisms that dominate grease film formation in different lubricated contacts were clarified.

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.

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.

An intelligent method for contact fatigue reliability analysis of spur gear under EHL

To complete the contact fatigue reliability analysis of spur gear under elastohydrodynamic lubrication(EHL) efficiently and accurately, an intelligent method is proposed. Oil film pressure is approximated using quadratic polynomial with intercrossing term and then mapped into the Hertz contact zone. Considering the randomness of the EHL, material properties and fatigue strength correction factors, the probabilistic reliability analysis model is established using artificial neural network(ANN). Genetic algorithm(GA) is employed to search the minimum reliability index and the design point by introducing an adjusting factor in penalty function. Reliability sensitivity analysis is completed based on the advanced first order second moment(AFOSM). Numerical example shows that the established probabilistic reliability analysis model could correctly reflect the effect of EHL on contact fatigue of spur gear, and the proposed intelligent method has an excellent global search capability as well as a highly efficient computing performance compared with the traditional Monte Carlo method(MCM).

Influence of electric double layer on thin film lubrication and elastohydrodynamic lubrication

In the present paper, the influence of electric double layer (EDL) on thin film lubricationand elastohydrodynamic lubrication is studied. With modified Reynolds equation for electric doublelayer, the effect of zeta-potential on the film thickness and pressure is numerically calculated. Theresults show that the influence of electric double layer on the lubrication film thickness is significantonly for thin film. The minimum film thickness will increase greatly if the influence of EDL is con-sidered. As the initial film thickness increases, the effect will greatly decrease. The existence ofEDL will decrease the friction coefficient of the lubrication film. Furthermore, the above tendency isstill applicable even if the materials of the friction pair are different.

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。