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.

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.

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.

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.

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.

HYDRODYNAMIC AND ELASTOHYDRODYNAMIC STUDIES OF A CYLINDRICAL JOURNAL BEARING

In this article,the effect of the bearing elastic deformation on the performance characteristics of a cylindrical journal bearing is analyzed.The variety of simulation models covers hydrodynamic（HD） and elastohydrodynamic（EHD） lubrication theories.The Reynolds equations governing the flow in the clearance space of the journal bearing are obtained by considering the effect of mass transfer across the fluid film.The finite element method with an iteration scheme was employed to solve both the Reynolds equation and the three-dimensional elasticity equation representing the displacement field in the bearing shell.The converged solutions for the lubricant flow and elastic deformation vector are obtained.Dynamic characteristics of the journal bearing are computed for HD and EHD theories.Numerical simulation results show that the flexibility of bearing liner has a significant influence on the performance of a cylindrical journal bearing.Indeed,the elastic deformations of the bearing liner extend the pressure area in the bearing and increase the minimum film thickness.Although,dynamic coefficient,load capacity and attitude angle decrease.

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.

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.

NUMERICAL SOLUTION OF THE THREE-DIMENSIONAL ELASTOHYDRODYNAMIC LUBRICATION FOR HEAVILY-LOADED FINITE JOURNAL BEARINGS

Elastohydrodynamic lubrication theory is combination of classical hydrodynamic lubrication and elastic theory. A coupling of finite element and boundary element method was applied to the analysis of 3-D elastohydro-dynamic lubrication for heavily-loaded finite journal bearings. In order to overcome difficulties of convergence at high eccentricity ratios, an iterative scheme was provided in this paper. The scheme called weighted average method was successfully carried out in the iterative procedures of a set of nonlinear equations that was constituted by a 2-D Reynolds' equation, a viscosity-pressure equation as well as 3-D elasticity equations. The analysis yields performances parameters and minimum film thickness of the finite journal bearings under heavy loading.

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.

Fluid-solid Interaction Model for Hydraulic Reciprocating O-ring Seals

Elastohydrodynamic lubrication characteristics of hydraulic reciprocating seals have significant effects on sealing and tribology performances of hydraulic actuators, especially in high parameter hydraulic systems. Only elastic deformations of hydraulic reciprocating seals were discussed, and hydrodynamic effects were neglected in many studies. The physical process of the fluid-solid interaction effect did not be clearly presented in the existing fluid-solid interaction models for hydraulic reciprocating O-ring seals, and few of these models had been simultaneously validated through experiments. By exploring the physical process of the fluid-solid interaction effect of the hydraulic reciprocating O-ring seal, a numerical fluid-solid interaction model consisting of fluid lubrication, contact mechanics, asperity contact and elastic deformation analyses is constructed with an iterative procedure. With the SRV friction and wear tester, the experiments are performed to investigate the elastohydrodynamic lubrication characteristics of the O-ring seal. The regularity of the friction coefficient varying with the speed of reciprocating motion is obtained in the mixed lubrication condition. The experimental result is used to validate the fluid-solid interaction model. Based on the model, The elastohydrodynamic lubrication characteristics of the hydraulic reciprocating O-ring seal are presented respectively in the dry friction, mixed lubrication and full film lubrication conditions, including of the contact pressure, film thickness, friction coefficient, liquid film pressure and viscous shear stress in the sealing zone. The proposed numerical fluid-solid interaction model can be effectively used to analyze the operation characteristics of the hydraulic reciprocating O-ring seal, and can also be widely used to study other hydraulic reciprocating seals.

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.

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.

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 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.

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.

EFFECT OF FRICTIONAL FORCE ON GEARING CONTACT FATIGUE STRENGTH

The model for computing frictional coefficient between two teeth faces at the state of mixed elastohydrodynamic lubrication is established. And then more than 80 sets of numerical calculations and six sets of disc fatigue tests are completed. The results show that when the film thickness ratio λ 〈1.6, frictional coefficient μ is drastically decreased as λ. rises; Thereafter it decreases smoothly until λ=4.5. When λ〉4.5, however, it goes up again with λ, which indicates that the excessive film thickness ratio will deteriorate gearing contact fatigue strength. At the end, the formulae for determining the frictional coefficients are formed.