Deterministic solutions and thermal analysis for mixed lubrication in point contacts

A deterministic numerical model has been developed for simulation of mixed lubrication in point contacts. The nominal contact area between rough surfaces can be divided into two parts: the regions for hydrodynamic lubrication and asperity contacts (boundary lubrication). In the area where the film thickness approaches zero the Reynolds equation can be modified into a reduced form and the normal pressure in the region of asperity contacts can be thus determined. As a result, a deterministic numerical solution for the mixed lubrication can be obtained through a unite system of equations and the same numerical scheme. In thermal analysis, the solution for a moving point heat source has been integrated numerically to get surface temperature, provided that shear stresses in both regions of hydrodynamic lubrication and asperity contacts have been predetermined. A rheology model based on the limit shear stress of lubricant is proposed while calculating the shear stress, which gives a smooth transition of friction forces between the hydrodynamic and contact regions. The computations prove the model to be a powerful tool to provide deterministic solutions for mixed lubrication over a wide range of film thickness, from full-film to the lubrication with very low lambda ratio, even down to the region where the asperity contact dominates.     

弹流润滑在摩擦无级变速器疲劳分析中的应用

本文在摩擦传动弹流润滑理论分析与牵引机理试验研究的基础上，进行零件表面牵引力和表层内应力场的研究，而且利用这一方法来分析零件的抗疲劳强度。分析多种设计参数对零件疲劳寿命的影响，研究了壁面附近的滑动对摩擦传动的影响。     

A non-Newtonian model based on limiting shear stress and slip planes—parametric studies

Parametric studies and corresponding results are presented using a rheological model based on the limiting shear stress and possible occurrence of slip planes. The model is applied to elastohydrodynamically lubricated line contacts with smooth surfaces and isothermal conditions. A few investigations are carried out where different parameters are varied. The first study investigates the influence on the film thickness distribution due to a variation of the maximum Hertzian pressure when the slide-to-roll ratio is constant. The second study investigates how far the non-Newtonian region propagates at low slide-to-roll ratios for a few different values of the Hertzian pressure. The results show that it is a remarkably small slide-to-roll ratio necessary to cause slip planes in a large part of the Hertzian contact zone. A third study regards the influence of the entrainment velocity on the film thickness generation at different slide-to-roll ratios. Finally some rheological parameters are varied. First, only the limiting shear stress at atmospheric pressure (τ₀) is varied, and second, a few different lubricants are studied, each with their own set of rheological parameters.     

粗糙表面弹性微动接触数值研究

由于实际工程表面多为粗糙表面,这里研究了粗糙表面对微动接触中压力和切向应力的影响。研究接触过程中法向载荷保持不变,切向载荷为周期性的交变载荷。首先,建立接触算法和模型,其算法核心是利用共轭梯度法(CGM)计算微动接触中的表面压力及切向应力并使用快速傅里叶变换(FFT)加快计算速度。然后,在验证算法正确的基础上,分析正弦和非高斯粗糙表面接触的压力和切向应力的分布,通过对光滑与粗糙表面的研究对比,表明:(1)在正弦表面接触切向应力分布呈现尺寸效应;(2)在非高斯表面接触中,切向应力分布跟光滑表面形状类似;同时由于粗糙峰存在,粗糙表面下的切向应力比光滑表面下的要大,研究粗糙表面微动接触对实际工程具有重要意义。     

Stress Analysis on Layered Materials in Point Elastohydrodynamic-Lubricated Contacts

For multilayered or coated substrates in elastohydrodynamic-lubricated (EHL) contacts, the subsurface stress distributions under a normal load combined with shear traction have been analyzed in this article through computer simulations. The Papkovich-Neuber potentials and Fourier transform are adopted to deduce the pressure–displacement, pressure–stress, and shear traction–stress response functions in frequency domain for the coated substrates, and to calculate distributions of pressure and subsurface stress. The results from the analysis of EHL contacts on coated substrates are compared with those from dry contact model in which shear traction is assumed to obey Coulomb’s law. Effects of the Young’s modulus of coatings, the properties of lubricants, and the magnitude of traction are discussed. Similar to the results in dry contacts, hard coatings in lubricated cases tend to increase the von Mises stress, whereas soft coatings decrease the stress. Shear traction makes the max von Mises stress increasing and moving closer to surface. However, the changes in subsurface stress due to shear traction are less obvious in lubricated contacts. Comparison between EHL and dry contact models reveals that lubrication can reduce the von Mises stress in the coating layer due to smaller shear traction. The analyses show that pressure, film thickness, and subsurface stress distributions are influenced by surface coatings, sliding velocity, rheological models, and pressure–viscosity behaviors.     

Measurement of the Rheology of Lubricant Films Within Elastohydrodynamic Contacts

There is growing need for a reliable model of the rheological response of lubricants in elastohydrodynamic (EHD) contacts, not only to predict behaviour in full-film EHD conditions, but also for use in modelling mixed-film lubrication. One barrier to developing such a model is that measurements of friction actually represent averaged values over the whole, lubricated contact under study. However the fluid film conditions of temperature, pressure and strain rate generally vary over such contacts, which makes it difficult to determine constitutive shear-stress equations from friction measurements. This paper examines the various different techniques used to study the origins of EHD friction and the underlying film rheology. It then describes and applies a technique for obtaining the temperature rise maps of both solid surfaces in a rolling-sliding EHD contacts and thus shear-stress and friction maps. The work shows that the shear stress of the traction fluid studied increases approximately linearly with pressure and decreases approximately linearly with temperature in the high-pressure central region of EHD contacts.     

The Interfacial Shear Strength of Molybdenum Disulfide and Graphite Films

A number of interfacial shear properties of thin film of molybdenum disulfide (MoS₂) and oleophilic graphite are presented. The interfacial shear strength dependences on contact pressure and on temperature are compared with the data that have been accumulated for organic polymer film of comparable thickness. The interfacial shear strength results have been obtained using both plastically and elastically deforming contacts and the data are in good agreement.     

Rheological properties of greases in ehd contacts

A rheological model of four characteristic parameters is proposed to describe the effective viscosity of greases in ehd contacts. Experimental determinations of film thickness have been achieved in line and point contacts. The proposed model fits the viscometric results better than a Herschel-Bulkley model and allows calculation of the grease viscosity at the high shear rates found in a typical ehd contact. Rules are given to find the effective viscosity of greases in a practical situation     

Calculation of sliding power loss in spur gear contacts

An engineering-level calculation model for sliding power loss in spur gear contacts is presented. Teeth contact through the line of action is modelled as a constantly changing roller contact whose radius, speed, and load can be calculated from the gear geometry under the given operating conditions. The gear mesh cycle is approximated by a large number of elastohydrodynamic contacts. A constant film thickness and a Hertzian pressure distribution are assumed in each contact. The model includes non-Newtonian lubricant behaviour together with temperature and mixed lubrication effects in contact. The numerical solver is reasonably fast in evaluating effectively the sliding power loss dependence on the essential gear and lubricant parameters. The features and behaviour trends of the calculated sliding power losses have a close similarity with published results obtained from measurements and experiment-based power loss models with mineral oil. The limiting shear stress of the lubricant is observed to have an essential role in the power loss behaviour especially at high loads.     

The effect of surface texturing on thin EHD lubrication films

Surface texturing has been successfully used for conformal contacts in many tribological applications in an effort to diminish friction and wear. However, the use of such a surface modifications are still in nascent as far as highly loaded contacts between non-conformal surfaces are concerned. It is mainly caused by the fact that the presence of such micro-features within these contacts can significantly influence the pressure distribution within the contact. Nevertheless, it has been shown in recent studies that the surface texturing can also have beneficial tribological effects if the depth of micro-features is properly designed. This paper is devoted to the experimental study of the effect of the micro-dents of various depths on thin lubrication films to find an experimental evidence of the micro-feature depth threshold for surface texturing applications in highly loaded non-conformal surfaces. The behaviour of an array of micro-dents within thin EHD contacts has been studied by thin film colorimetric interferometry. The influence of surface texturing on lubricant film formation has been observed under sliding/rolling conditions. The significant effect of micro-dents depth on lubricant film thickness is observed for positive slide-to-roll ratio when the disc is moving faster than the micro-textured ball. The presence of deep micro-dents within lubricated contact results in film thickness reduction downstream. As the depth of micro-dents is reduced, this effect diminishes and beneficial effect of micro-dents on film thickness formation has been observed. No significant influence of micro-dents depth on lubricant film shape has been observed in case of negative slide-to-roll conditions when micro-dents do not cause film thickness reduction regardless of their depths.     

The contact and friction between flat belts and pulleys

Rubber coated nylon flat belts running over pulleys in practice display friction coefficients between 0·3 and 0·8. This paper studies the causes of the friction variations. Adhesive friction theory considers the friction force to be the product of the real areas of contact between the sliding surfaces and the shear stress at the contacts: these two quantities have been separately measured by running belts over transparent perspex pulleys and directly observing the contacts. It has been found that variations in contact from one belt to another due to their method of manufacture are as significant in explaining differences in their friction behaviour as are variations in shear stress caused by their different rubber formulations. Real areas of contact were less than one third of the apparent area and varied with load, elastic modulus and roughness of the belt surface in a way broadly understandable in terms of elastic contact mechanics. Shear stress were about 0·5 Nmm⁻², perhaps determined by hydrocarbon films. Some belts showed real areas of contact not directly proportional to load. This led to their friction coefficients being load dependent.     

Frictional forces between cohesive powder particles studied by AFM

A range of commercially important powders (hydrated alumina, limestone, titania and zeolite) and glass ballotini were attached to atomic force microscope cantilevers, and inter-particle friction forces studied in air using lateral force microscopy (LFM). The in situ calibration procedure for friction forces is described. LF images, line profiles, LF histograms, surface roughness, pull-off forces, and the load dependence of friction in the range 0-25 nN were studied for both particle-particle and particle-wall (steel) contacts. The single-particle friction results are discussed in terms of contact mechanics theory. Particle-particle contacts showed load-dependent friction, involving single asperity contacts (non-linear behaviour) or multi-asperity contacts (linear behaviour). Particle-wall contacts usually showed little load dependence and were more adhesive. The results are also related to shear stress-normal stress data (yield loci) for the same materials from bulk shear testers.     

成形板料表面的接触分形几何模型研究

提出一种新的方法用以描述板料与模具的接触问题。利用接触式轮廓仪对板料粗糙表面进行测量和分析，论证了成形板料表面的微观形貌可以用weierstrass—Mandelbrot分形函数来表征，所得到的参数是不依赖于测量尺度而变的“固有”参数。根据分形几何理论和接触力学理论，建立了板料与模具接触的接触面积与变形关系模型。     

Rolling contact fatigue of case-hardened chromium steel

The rolling contact fatigue of case-hardened steel surfaces in lubricated heavily loaded contact was studied. Three different case-hardening treatments were tested with a ratio of slide to roll of ?5%. Other ratios of slide to roll were used to determine the effect of tangential traction on the rolling contact fatigue endurance. When the actual contact width was measured after testing, the scatter of the fatigue results was reduced. The depth of the maximum plastic strain was determined by measuring the hardness before and after testing and was found to correspond to the occurrence of the lowest ratio of the critical shear stress to the amplitude of the load-induced orthogonal shear stress. The role of residual stresses in rolling contact fatigue is discussed. It was found that a more detailed knowledge of lubricant behaviour in heavily loaded contacts is needed to reveal the true distribution of tangential traction on the contact surface. This affects the angle of the plane and the value of the maximum amplitude of the shear stress beneath the contact zone.     

Effect of surface roughness parameters on mixed lubrication characteristics

In this paper, a computer program was developed to generate non-Gaussian surfaces with specified standard deviation, autocorrelation function, skewness and kurtosis, based on digital FIR technique. A thermal model of mixed lubrication in point contacts is proposed, and used to study the roughness effect. The area ratio, load ratio, maximum pressure, maximum surface temperature and average film thickness as a function of skewness and kurtosis are studied at different value of rms. Numerical examples show that skewness and kurtosis have a great effect on the contact parameters of mixed lubrication.     

On the thermal elastohydrodynamic lubrication in opposite sliding circular contacts

Cases of elastohydrodynamic lubrication (EHL) point contacts running under opposite sliding conditions have been studied with consideration of the thermal effect for various loads and entrainment velocities. A thermal EHL solver has been developed and proven to be able to deal even with extreme cases under an infinite slide–roll ratio. Results show that film profiles featuring a dimple can be formed in the contact zone when the slide–roll ratio exceeds a certain level. Moreover, the present study provides theoretical evidence for the lubricating film build up in the case where the two bounding surfaces run with equal but opposite velocities. An effective lubricating film under zero entrainment speeds was experimentally proven by Dyson and Wilson [1] (Proc Instn Mech Engrs, 1968–1969 183(3P) 81) in the 1960's, which, however, cannot be explained by the isothermal EHL theory.     

Mapping Shear Stress in Elastohydrodynamic Contacts

A new method has been, devised for investigating the theological properties of lubricant films in two-dimensional EHD contacts. A lubricated, sliding contact is produced between a sapphire flat and a steel ball. Thermal infrared emission microscopy is then employed to obtain 2-D maps of the variation of temperature rise due to friction across the contact. These maps are then used in conjunction with moving heal source theory to produce maps of energy dissipation and thus shear strength, of the lubricant film across the contact.

A series of mixtures of two lubricants, one giving high traction and one with low traction, have been studied using this technique to investigate the influence of lubricant, blending on shear stress and traction.     

Parametric Analysis of Rolling–Sliding Line Contacts Under Boundary and Near Boundary Lubrication Conditions

This article reports a parametric analysis of rolling–sliding line contacts in boundary and near-boundary lubrication with relevance to the contacts in rotorcraft drive systems in loss of lubrication. A recently developed mathematical model for boundary lubrication with friction, temperature, and tribochemistry is used in the analysis. The parameters studied include radius of the line contact, surface hardness, boundary film shear strength, fluid–solid load sharing, system bulk temperature, load, speed, and slide-to-roll ratio. The contact condition is measured by the temperature and friction power intensity along with the boundary film integrity and mode of deformation. The results of the analysis led to a number of suggestions and elaborations listed in the Conclusion regarding various design considerations of the contacts in rotorcraft drive systems against loss of lubrication.     

Contact mechanics of rough surfaces in tribology: multiple asperity contact

Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions. With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and height distributions. Implications of these models in friction and wear studies are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

An Analysis and Computational Procedure for EHL Film Thickness,Friction and Flash Temperature in Line and Point Contacts

General Elastohydrodynamic Lubrication Code (GEHLC) is a FORTRAN code for calculating the lubrication performance of line and point contacts used in machine elements such as gears, rolling bearings, cam and follower systems, and traction drives, etc. It adopts the most recent results published by Chittenden and Dowson et al. (1), to evaluate isothermal film thickness of point contacts, and uses the thermal reduction factor (2) to account for the inlet heating effects on the film thickness. By using Bair and Winer's analysis (3), a viscoelastic fluid model has been employed in this program to calculate shear stress in the film with bisection technique and In predict the coefficient of friction. Using this program one can also obtain flash temperature distribution on the two solid surfaces from a simplified heat conduction analysis based on work by Bolt (4), Jaeger (5), and Archard (6), et al. Typical results are presented for elliptical contacts used in rolling bearings.