Multilevel solution for thermal elastohydrodynamic lubrication of rolling/sliding circular contacts

A fast multigrid approach is presented for the analysis of thermal elastohydrodynamic lubrication (EHL) under rolling/sliding circular contacts at high loads and high slip ratios with low computing time on a personal computer. This fast solver combines directiteration, multigrid, Newton-Raphson, Gauss-Seidel iteration, and multilevel multi-integration methods into one working environment that can reduce the computational complexity from O(n³ to O(nlnn) for the thermal EHL problem under rolling/sliding circular contacts. Since the couped Reynolds and energy equations are simultaneously solved by the Newton-Raphson scheme, the iteration for the convergence solution is less than those of the classical approach. Results show that thermal effects on the pressure profile and film thickness are significant for a wide range of loads, speeds and slip ratios. The maximum midfilm and surface temperature rise in the Hertzian contact region increases with increasing slip ratio, dimensionless speed, and load. The minimum film thickness decreases with increasing load and slip ratio, and decreasing dimensionless speed.     

Thermal effects in elastohydrodynamic lubrication of line contacts using a non-Newtonian lubricant

A Reynolds' equation, using Winer's viscoplastic model to express the non-Newtonian fluid property, is derived for line-contact EHL problems. The numerical solutions are obtained to the incorporated Reynolds', elasticity, and energy equations for pressure, film thickness, and temperature distribution between two surfaces simultaneously having rolling and sliding motions. The results are presented for thermal non-Newtonian lubrication, to observe the difference between Winer's equation and Trachman's expression on temperature distribution, pressure, and film thickness. The variation in friction coefficient with slip shear rate is in agreement with other experimental data.     

A deterministic model for line-contact partial elastohydrodynamic lubrication

A deterministic model for partial elastohydrodynamic lubrication (EHL) is presented in this paper. The modelling methodology adopts some of the concepts used in the stochastic modelling of partial EHL and some of the procedures for deterministic calculation of asperity pressures. The model is shown to be capable of simulating the basic process of asperity interaction and solid-to-solid contact within an EHL conjunction of rough surfaces. Deterministic results of transient partial EHL in line contacts are obtained when one pair or multiple pairs of asperities collide. The model may help to gain a fundamental understanding of the transient behaviour of asperity interactions in lubricated concentrated contacts of rough surfaces. Asperity pressures may be calculated more accurately than the conventional analyses under dry and static contact conditions. The work represents a first attempt in deterministic modelling of tribo-contacts operating in the mixed regime of micro-EHL and boundary lubrication. Future work will aim at developing more realistic models incorporating factors such as three-dimensional asperity contacts, asperity plastic deformation, thermal effects and the effect of tribo-chemistry.     

A theoretical simulation of thermal elastohydrodynamic lubrication for a Newtonian fluid in impact motion

In this work, the thermal elastohydrodynamic lubrication (TEHL) in an impact motion is explored using multigrid (MG) method and column by column scanning techniques. A steel ball impacts onto an infinite steel plane lubricated with a thin layer of oil. The study starts from a smooth contact problem and the results are compared with the corresponding isothermal ones. Then surface waviness is imposed on the steel ball surface to check the fluctuation in the oil film.     

On the shear stress of elastohydrodynamic lubrication in elliptical contacts

Results of mathematical modelling of elastohydrodynamic lubrication of rolling contacts are presented. Effects of dimensionless parameters such as speed, normal load, elliptical parameters and coefficient of limiting shear stress on shear stress distributions have been studied. Moreover, profiles on hydrodynamic pressure and film thickness in EHD contacts have been studied. It has been found that shear stress profiles on two contact surfaces in entraining direction are similar with each other in some way. Shear stresses of fluid film on contact surfaces vary with many factors, which reveals the mechanism of traction in elastohydrodynamically lubricated contacts.     

Effects of surface coating on elastohydrodynamic lubrication of line contacts

A numerical solution to the elastohydrodynamic lubrication (EHL) problem of two coated elastic bodies in line contact is introduced. The non‐Newtonian behavior of the lubricant is incorporated into EHL analysis using Eyring's nonlinear viscous model. The surface elastic deformations are computed from full elasticity analysis of layered elastic half‐space. The iterative Newton–Raphson technique is used in the numerical solution. Subsurface stresses are calculated using two different techniques, the numerical integral scheme based on Fourier transformation and the finite element method. The effects of surface coating (material and thickness) on the pressure profile and subsurface stresses are presented and discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

A study on the effect of starvation in mixed elastohydrodynamic lubrication

The effect of starvation in mixed elastohydrodynamic lubrication (EHL) regime is studied. Numerical simulations are conducted for both line and point (elliptical) contacts with the consideration of the surface roughness. The degree of starvation is linked directly to the reduction in the lubricant mass flow rate. Results are presented to gain insight on the influence of starvation on the film thickness as well as the interaction between the surface asperities. Extensive sets of simulation results are used to quantify the effect of starvation in the EHL of rough surfaces. Expressions are developed to predict the percentage of the load carried by the surface asperities (asperity load ratio) as well as the reduction of the central and minimum film thickness in the starved mixed EHL.     

An analysis of the mechanisms of grease lubrication in rolling element bearings

There are over eighteen billion bearings in use in the world, and most are grease lubricated. Grease is chosen for a variety of reasons: it gives low friction, is easily confined, and has a long lubricating life at low cost. In many applications, the grease is expected to lubricate effectively over a wide range of conditions and for extended periods. For such applications, lubricant failure leads to instantaneous and rapidly increasing damage of the components and eventually breakdown. Thus, an improved understanding of the fundamental aspects of grease lubrication has far-ranging technical and economic implications. Despite the overwhelming importance of this subject, very little is known about the mechanisms of grease lubrication and the relationship between composition, lubrication performance, and life. This paper attempts to summarise current understanding of grease lubrication mechanisms in rolling element bearings and to consolidate the different aspects of this complex topic.     

Investigation into the traction coefficient in elastohydrodynamic lubrication

The elastohydrodynamic traction coefficients of two Chinese aviation lubricating oils were investigated for various loads, rolling velocities, and lubricant inlet temperatures using a self‐made test rig. Traction coefficient versus slide‐to‐roll ratio curves were generated. The concept of critical load varying with the lubricant temperature is proposed. This paper presents a new empirical formula for the dynamic performance design of high‐speed rolling bearings, that relates traction coefficient with normal load, rolling velocity, and lubricant inlet temperature. The coefficients of the formula may be computed by regression analysis of the experimental data. Two example calculations are presented. The predicted results from the formula agree well with experimental observations.     

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 ² _N), 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.     

Molecular dynamics simulations of elastohydrodynamic lubrication oil film

This paper reviews recent research in molecular dynamics studies of the traction properties of hydrocarbon fluids under elastohydrodynamic lubrication, focusing on the technical problems that arise on making predictions of the traction properties of an oil film with a submicron thickness at the actual sliding contacts of the machine elements by at a nanoscale molecular simulation. The effect of the oil film thickness and shear rate are examined including the result of a submicron thickness simulation of the oil film using a tera‐flops computer. The mechanism of the phase transition of the fluids under high pressure, the boundary slip, and the momentum transfer related to the molecular structure of the fluids are also presented. Copyright © 2010 John Wiley & Sons, Ltd.     

线接触脂润滑热弹性流体动力润滑数值分析

基于Ostwald模型建立的脂润滑控制方程与能量方程联合求解,通过压力-温度的循环来计算线接触脂润滑热弹性流体动力润滑数值解。分析了一般工况参数对润滑膜压力分布和润滑膜形状的影响,探讨了不同工况下热效应对脂润滑弹流数值解的影响。     

Grease lubrication of rolling element bearings — role of the grease thickener

The contribution of grease thickener to lubricant film formation was examined in this paper. Lubricant film thickness and friction were measured for different grease thickener types in a bearing simulation device. The results showed that the greases formed thick (20–80nm), low friction surface layers at low speeds, which were much greater than the corresponding base oil film. These films appeared to be formed by the physical deposition of thickener in the track during overrolling of the grease. This was confirmed by infrared reflection analysis, which showed the deposited films to have increased thickener content. The ability of grease to form renewable physically deposited solid films has significant implications for optimising lubricant formulation for certain applications, e.g. bearings operating at high temperatures and low speeds where a conventional elastohydrodynamic lubricating film would be inadequate. Copyright © 2007 John Wiley & Sons, Ltd.     

Theoretical investigation of transient elastohydrodynamic lubrication with newtonian solid–liquid lubricants

This paper reports a theoretical investigation of transient elastohydrodynamic lubrication of a line contact. A time‐dependent Reynolds equation and elasticity equations for compressible solid–liquid lubricants were solved using finite volume and multigrid techniques. The lubricants used were mineral oils mixed with very small solid particles, MoS2 and PTFE which can be treated as Newtonian fluids. The two surfaces were initially at rest and in contact. The transient oil film pressure and oil film thickness were calculated numerically. This simulation showed the significant effects of solid particles on the lubrication characteristics. Copyright © 2006 John Wiley & Sons, Ltd.     

Influence of surface roughness on normal-sliding lubrication

Contact between machine components can involve normal, sliding and rolling motion, either singly or in combination. Combined normal and sliding motion, which occur for example in the meshing of gear teeth and in heavily-loaded rolling elements, can present problems for lubrication. The purpose of the present experimental study was to investigate how surface roughness affects the lubricant film characteristics under conditions of combined normal and sliding motion. The experimental arrar gement consisted of a rotating roller which impacted a stationary ball in the presence of a lubricant. Under the same conditions of normal surface approach, increasing the surface roughness significantly decreased the level of roller sliding that could occur without breakdown of the lubricating film. This behaviour was similar to a step function. Of the several surface roughness parameters investigated, only those which involved the maximum peak-to-valley height correlated well with experimental results. In general, surface roughness had a greater effect on oil film breakdown than did either viscosity or load.     

Micromechanics and electrical conductivity of point contacts in boundary lubrication

Research methods based on recording parameters of electrical conductivity are considered for future application in nanotribology. Design relationships of conductivity are presented for idealized models of interface under conditions of boundary lubrication; contributions of various conductivity types in the total contact conductivity are estimated. An application methodology is described for the methods to study the properties of boundary lubricating layers. Some of the results obtained from the study of strength and frictional properties of boundary lubricating nanometre layers under normal load and sliding conditions are discussed.     

Transient thermo‐elastohydrodynamic lubrication of gear teeth

During a gear mesh cycle, load, rolling and sliding velocities, curvature, and temperature change rapidly. In this paper, a transient, thermo‐elastohydrodynamic lubrication model is presented that has been used to study the lubrication parameters at 250 contact points along the path of a contact. The working flanks were assumed to be smooth. The line load was calculated at every contact point, using the finite‐element method. Dynamic loading was not considered. The steady‐state temperature field of the working flanks was used to obtain the surface temperature at the inlet of each contact point, determined by an experimental‐analytical method presented previously. In this model, the lubricant is considered to follow the Ree‐Eyring constitutive equation. The influences of both pressure and temperature on density, thermal conductivity, and specific heat of the lubricant are also taken into account. Results are presented for an FZG type A gear pair lubricated with an FVA No. 4 reference oil; these include film shape, pressure and temperature distributions, as well as friction coefficient.     

Analysis of micro-elastohydrodynamic lubrication for engineering contacts

The paper describes methods which have been developed for theoretical analysis of elastohydrodynamic lubrication (EHL) in situations where the nominal oil film thickness is of the same order as the height of roughness asperities on the surfaces in contact. In such contacts the roughness significantly affects the distribution of pressure, and pressures much higher than predicted on the basis of smooth surface theory are obtained even under conditions where a full fluid film is present. This has consequences for surface fatigue processes such as pitting, and the presence of roughness is also considered to be a crucial factor in the occurrence of scuffing in which hydrodynamic film failure leads to adhesion and severe distress of the surfaces. The major aim of the work is to develop a better undertanding of the physics of scuffing based upon models of film failure in the presence of roughness.     

Theoretical investigation of transient elastohydrodynamic lubrication with newtonian solid‐liquid lubricants

This paper reports a theoretical investigation of transient elastohydrodynamic lubrication of a line contact. A time‐dependent Reynolds equation and elasticity equations for compressible solid‐liquid lubricants were solved using finite volume and multigrid techniques. The lubricants used were mineral oils mixed with very small solid particles, MoS₂ and PTFE, which can be treated as Newtonian fluids. The two surfaces were initially at rest and in contact. The transient oil film pressure and oil film thickness were calculated numerically. This simulation showed the significant effects of solid particles on the lubrication characteristics.     

脂润滑轮毂轴承弹流润滑数值分析

基于Ostwald模型建立脂润滑控制方程,运用多重网格法求得等温线接触脂润滑弹性流体动力润滑数值解,得到钢球-沟道的压力分布、油膜形状及最小油膜厚度。针对轿车轮毂轴承的典型应用工况条件,分析工况参数对油膜压力分布和油膜形状的影响。结果表明:脂润滑弹流膜具有与油润滑膜相同的二次压力峰和出口颈缩现象。在轿车轮毂轴承可能的承载条件下,随着载荷的减小,二次压力峰的高度降低,其位置向入口区移动;一定承载条件下,速度增加时,膜厚相应增加,油膜的平行部分缩短,二次压力峰的高度增加,其位置也向入口区移动;一定承载和卷吸速度下,润滑脂流变参数增大时,二次压力峰的高度升高,其位置向入口区移动,膜厚相应增加。