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.

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.

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.

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.

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).

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.

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 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.

Stochastic uncertain lubrication in gear transmission subjected to tribodynamic loading

A stochastic uncertain tribodynamic model is established for a spur gear pair for the first time.The stochastic uncertainty of pinion rotation speed propagated to lubrication performance is investigated.The probability density function of the minimum lubricant film thickness hmin evolves over time periodically at interval of an engagement process.Correspondence between abrupt increase in meshing force and amplification of hmin uncertainty is found.Robust and reliable lubrication performance can be achieved by suppressing the hmin uncertainty and decreasing the lubrication failure probability.This can be done by increasing lubricant viscosity,and decreasing input torque and uncertainty level of input rotation speed.This work lays a solid foundation for robust and reliability based optimization for tribodynamic gear system.

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.

A combined experimental and analytical method to determine the EHL friction force distribution between rollers and outer raceway in a cylindrical roller bearing

Friction force is a crucial factor causing power loss and fatigue spalling of rolling element bearings.A combined experimental and analytical method is proposed to quantitatively determine the elastohydrodynamic lubrication(EHL)friction force distribution between rollers and outer raceway in a cylindrical roller bearing(CRB).An experimental system with the instrumented bearing and housing was developed for measuring radial load distribution and friction torque of bearings.A simplified model of friction force expressed by dimensionless speed,load,and material parameters was given.An inequality constrained optimization problem was established and solved by using an experimental data-driven learning algorithm for determining the uncertain parameters in the model.The effect of speed,load,and lubricant property on friction force and friction coefficient was discussed.

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.

Liquid superlubricity of lubricants containing hydroxyl groups and their aqueous solution under rolling/sliding conditions

Macroscale rolling/sliding conditions are in the superlubricity,a little-studied topic so far.The purpose of this paper is to examine the formation of elastohydrodynamic lubrication(EHL)films by water-based lubricants(glycerol and polyethylene glycol(PEG)),providing superlubricous friction.Experiments were carried out on an optical ball-on-disc tribometer under rolling/sliding conditions.The film thickness was measured by the thin film colorimetric interferometry,and the viscosity of liquids was measured by rotational and high-pressure falling body viscometers.The results show that tribochemical reactions are not the mandatory reason for friction to reach the superlubricity level when using the water-based lubricants.The studied liquids themselves are almost Newtonian.With the addition of water,the signs of shear thinning behavior disappear even more.Suitable conditions for this type of lubricant can be predicted using the known Hamrock–Dowson equations.An anomaly in the thickness of the lubricants was observed as an abrupt change at certain conditions.The more PEG there is in the lubricant,the higher the thickness at the beginning of the jump.

On the relevance of analytical film thickness EHD equations for isothermal point contacts: Qualitative or quantitative predictions?

Thin film and elastohydrodynamic lubrication regimes are rather young domains of tribology and they are still facing unresolved issues.As they rely upon a full separation of the moving surfaces by a thin (or very thin) fluid film,the knowledge of its thickness is of paramount importance,as for instance to developing lubricated mechanisms with long lasting and efficient designs.As a consequence,a large collection of formulae for point contacts have been proposed in the last 40 years.However,their accuracy and validity have rarely been investigated.The purpose of this paper is to offer an evaluation of the most widespread analytical formulae and to define whether they can be used as qualitative or quantitative predictions.The methodology is based on comparisons with a numerical model for two configurations,circular and elliptical,considering both central and minimum film thicknesses.