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.

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.

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.

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.

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.

Elastohydrodynamic lubrication properties and friction behaviors of several ester base stocks

This paper reports a series of studies on the lubricant properties,elastohydrodynamic film thickness,and coefficients of friction of several commercially available ester base stocks,i.e.,diisooctyl phthalate(DIOP),diisodecyl phthalate(DIDP),diisotridecyl phthalate(DITDP),diisooctyl sebacate(DOS),diisotridecyl sebacate(DTDS),trihydroxymethylpropyl trioleate(TMPTO),and pentaerythritol tetraoleate(PETO).The results include densities and viscosities from 303 to 398 K,and elastohydrodynamic lubricant film thicknesses and friction in the boundary,mixed and full-film lubrication regimes measured at several temperatures,loads,and speeds.These ester base stocks have different lubrication abilities owing to their chain lengths,geometric configurations,and molecular rigidity.This study provides quantitative insight into the use of ester-based lubricants for low friction through the entire lubrication regime(boundary to full film)by utilization of suitable type and size of the ester base stocks.

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.

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.

A fast compound direct iterative algorithm for solving transient line contact elastohydrodynamic lubrication problems

A fast compound direct iterative algorithm for solving transient line contact elastohydrodynamic lubrication （EHL） problems is presented. First, by introducing a special matrix splitting iteration method into the traditional compound direct iterative method, the full matrices for the linear systems of equations are transformed into sparse banded ones with any half-bandwidth; then, an extended Thomas method which can solve banded linear systems with any half-bandwidth is derived to accelerate the computing speed. Through the above two steps, the computational complexity of each iteration is reduced approximately from O（N^3/3） to O（β^2N）, where N is the total number of nodes, and β is the half-bandwidth. Two kinds of numerical results of transient EHL line contact problems under sinusoidal excitation or pure normal approach process are obtained. The results demonstrate that the new algorithm increases computing speed several times more than the traditional compound direct iterative method with the same numerical precision. Also the results show that the new algorithm can get the best computing speed and robustness when the ratio, half-bandwidth to total number of nodes, is about 7.5% 10.0% in moderate load cases.

THE ANALYSIS OF THE TREE－DIMENSIONAL ELASTOHYDRODYNAMIC LUBRICATIONFOR HEAVILY－LOADED FINITE JOURNAL BEARINGS IN NON－NEWTONIAN LUBRICANTS

A generalized Reynolds' equation governing power-law non-Newtonian fluids and three dimensional elasticity equations corresponding to realistic three dimensional bearing geometries are numerically solved in this paper. An iterative scheme, which is called the weighted average method here, is used to deal with the iterative convergence of the three dimensional elastohydrodynamic lubrication equations. The scheme is successfully employed in overcoming the difficulty of the convergence at high eccentricity ratios. Inthis work, the influence of flow indices and bearing materials on the performance parameters of elastohydrodynamic lubrication for heavily-loaded finite journal bearings in non-Newtonian fluid are investigated.

Contact Behavior of Worn Bearings with Elastoplastic Functionally Graded Coating Based on Mixed Elastohydrodynamic Lubrication

The dynamic contact behavior of worn bearings with elastoplastic functionally graded coating is studied,and the interacting effect between worn band and functionally graded surface is analyzed.The surface deformation and roughness are included in the film thickness.The mixed elastohydrodynamic lubrication combined with point contact model is introduced to analyze the oil pressure in the contact zone.By using the Fourier transform method and Papkovich-Neuber potential function,the displacements and stress fields in the elastoplastic functionally graded coating are obtained.The second-order central difference method is used to solve the Reynolds equation.It is found that the repeated surface interaction can result in the sharp increase in pressure in bearings,and the oil pressure increases with increasing graded index.The entrainment of oil in the inlet and outlet zones becomes more evident if a large graded index is selected.

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。

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。