Asymptotic analysis of lubricated heavily loaded point contacts with skewed direction of entrained lubricant

The paper is devoted to the application of the early developed asymptotic approach to solution of the steady isothermal problem of elastohydrodynamic lubrication (EHL) for heavily loaded point contacts with skewed direction of entrained lubricant. It is shown that the whole contact region can be subdivided into three subregions: the central one, which is far away from the other two regions occupied by the ends of the horseshoe‐shaped pressure/gap distribution. The central region, in turn, can be subdivided into the Hertzian region and two adjacent boundary layers — the inlet and exit zones. Moreover, in the central region in the inlet and exit zones, the EHL problem can be reduced to asymptotically valid equations identical to the ones obtained in the inlet and exit zones of heavily loaded line EHL contacts. These equations can be analytically analysed and numerically solved on the basis of the stable methods using a specific regularization approach, which were developed for lubricated line contacts. Cases of pre‐critical and over‐critical lubrication regimes are considered. The by‐product of this asymptotic analysis is an easy analytical derivation of formulas for the lubrication film thickness for pre‐critical and over‐critical starved and fully flooded lubrication regimes. The latter allows for simple analysis of the film thickness as a function of the contact eccentricity and the direction of the entrained lubricant at the inlet in the contact. Copyright © 2013 John Wiley & Sons, Ltd.     

Asymptotic analysis of a lubricated heavily loaded spinning and rolling ball in a parabolic raceway

In the paper, the previously developed asymptotic approach to solution of the steady isothermal problem of elastohydrodynamic lubrication (EHL) for heavily loaded point contacts is applied to a lubricated point contact with rolling and spinning. It is shown that the whole contact region can be subdivided into three subregions. The central region can be subdivided into the Hertzian region and two adjacent boundary layers — the inlet and exit zones. The main results of the paper are threefold: (i) it is shown that in the central parts of the inlet and exit zones, the mechanisms and the equations controlling the behaviour of the lubrication contact parameters in heavily loaded point and line EHL contacts are identical, (ii) asymptotically precise formulas for the central and exit lubrication film thickness for pre‐critical and over‐critical starved and fully flooded lubrication regimes are analytically derived, and (iii) the inlet and exit zone asymptotically valid equations are uniform across all steady heavily loaded line and point EHL contacts for lubricants with the same rheology. These asymptotically valid equations were analysed and numerically solved in previously published work based on the stable methods utilising the specific regularisation approach developed for lubricated line contacts. Cases of pre‐critical and over‐critical lubrication regimes are considered. The formulas for the lubrication film thickness for pre‐critical and over‐critical starved and fully flooded lubrication regimes allow for simple analysis of the film thickness as a function of spinning angular speed, angle of the entrained lubricant and other pertinent contact characteristics. Copyright © 2013 John Wiley & Sons, Ltd.     

Laser-induced fluorescence for film thickness mapping in pure sliding lubricated, compliant, contacts

A laser-induced fluorescence (LIF) technique has been used to measure fluid film thickness in a compliant, sliding contact under low-load/low-pressure conditions. The soft contact between an elastomer hemisphere and a glass disc is lubricated by a liquid containing fluorescent dye. The contact is then illuminated with 532 nm laser light through the glass disc, and viewed with a fluorescence microscope. From the intensity of emitted radiation, film thickness maps of the contact are determined. Previous calibration procedures have used a separate calibration piece and test specimen with possible errors due to differences in reflectivity between the calibration and test specimens. In the work reported in this paper a new calibration process is employed using the actual test sample, thereby avoiding such errors.Results are reported for a sliding contact between PDMS and glass, lubricated with glycerol and water solutions under fully flooded and starved conditions. It was found that, for glycerol, the measured film thickness is somewhat lower than numerical predictions for both lubrication conditions. It is suggested that a combination of thermal effects and the hygroscopic nature of glycerol may cause the lubricant viscosity to drop resulting in thinner films than those predicted for fully flooded contacts. Starvation occurs above a critical entrainment speed and results in considerably thinner films than predicted by fully flooded I-EHL theory. A numerical study has been carried out to determine the effect of the observed starvation on film thickness. Predicted, starved film thickness values agree well with those obtained experimentally.     

流体动压润滑油膜厚度及油池的荧光测量

基于面接触润滑油膜厚度荧光测量系统,研究润滑油中荧光剂强度与剪应变率的关系,筛选得到适合油膜厚度测量的润滑油和荧光剂的组合,并研究荧光强度和油膜厚度之间的关系。结果表明:R6G荧光剂和PEG400润滑油组合与Coumarin6荧光剂和PAO8润滑油组合的荧光强度不受剪应变率影响,可用于油膜厚度的荧光测量;荧光强度和油膜厚度存在单值线性关系,通过测量荧光强度可以求解油膜厚度。建立接触区周围油膜厚度及油池分布的测量方法,研究载荷和速度对油膜厚度以及接触区周围润滑剂的迁移特性的影响。结果表明:油膜厚度随速度增加而增加,随载荷增加而减小;随着速度增加,滑块入口处油池产生润滑剂堆积,出口处油池出现双侧脊分离,两侧面油池无明显变化;油池的变化是表面力、机械分离力和离心力综合作用的结果。     

Theoretical and Experimental Investigations on EHL Point Contacts with Different Entrainment Velocity Directions

Film thickness prediction plays an important role in evaluating the performance and durability of machine elements under elastohydrodynamic lubrication (EHL). However, current formulae may not be appropriate for general conditions occurring in real contacts. This study investigates the effect of different lubricant entrainment velocity angles on film thickness distribution. For this purpose, a steady-state isothermal EHL model is used under a wide range of parameter sets including varying sum velocity, contact pressure, and sum velocity angle. Considerable differences in the trend of the central film thickness with respect to the lubricant entrainment velocity angle for low and high loaded contacts are shown. The results are compared with experimental measurements by means of an optical ball-on-disc tribometer and a twin-disc machine using capacitance method. Good agreement between numerical results and experimental measurements was found.     

An Investigation of Lubricant Film Thickness in Sliding Compliant Contacts

An optical interferometric technique has been used to investigate fluid film thickness in sliding, isoviscous elastohydrodynamic contacts (I-EHL). Monochromatic two-beam interferometry has been employed to map lubricant film thickness across a range of applied loads and entrainment speeds. The contact was formed between an elastomer sphere and plain glass disc, illuminated under red light, λ= 630 nm. Experimental work has employed sunflower oil and glycerol/water solutions as the test lubricants, due to their similar refractive indices and varying viscosity. A black-and-white-image-intensified camera has been employed to capture interference images and a computer processing technique used to analyse these images, pixel by pixel, and create film thickness maps based on their gray-scale intensity representations. Comparison of film thickness results to theoretical models shows reasonable qualitative agreement. Experimental results show both a reduced horseshoe, which is limited to the rear of the contact, and wedge-shaped film thickness profile within the Hertzian contact region. This is unlike conventional hard EHL contacts where the horseshoe-shaped pressure constriction extends around the contact toward the inlet. Experimental results suggest that film thickness profiles take on a convergent wedge shape similar to that used in many hydrodynamic bearings. It is likely that this wedge is largely responsible for generating fluid pressure and therefore the load-carrying capacity of the contact.     

Film thickness in point contacts under generalized Newtonian EHL conditions: Numerical and experimental analysis

The current paper contributes to the understanding of the behaviour of a smooth point EHL contact with a generalized Newtonian lubricant under pure rolling. The film thickness distribution was computed using a numerical simulation with measured rheological lubricant properties. The numerical predictions, obtained solving the generalized Reynolds equation were compared with film thicknesses measured in an optical ball-on-disc device. The numerical results correctly predict the absolute film thickness and the film thickness increase with rolling speed.     

Effect of Interfacial Properties on EHL Under Pure Sliding Conditions

This paper presents an experimental study of the effect of boundary slip on the lubricating film shape and friction of an elastohydrodynamic lubrication (EHL) contact under isothermal conditions. Ball and disc pure sliding experiments were carried out with a high viscosity polybutene oil using a conventional optical EHL test rig. The film shape and friction were measured simultaneously. The results obtained from two discs with different coatings were compared. One disc was coated only with Cr, the partially reflective layer, and the other had an extra layer of SiO₂ coating on top. When running under mild conditions of low load and speed, there was no evidence of any boundary slip effect. However, when the load increased, the Cr-coated disc produced lower film thickness and friction than the SiO₂-coated disc. The Cr-coated surface had a larger contact angle, i.e., smaller surface energy, than the SiO₂ surface, which reflects the weak bonding between the molecules of the surface and the lubricant. The study concludes that surfaces with low surface energy promote boundary slip at the EHL contact, leading to a reduction in friction and film thickness.     

Monochromatic image analysis of elastohydrodynamic lubrication film thickness by fringe intensity computation

Point contact film thickness in elastohydrodynamic lubrication (EHL) is analyzed by image processing method for the images from an optical interferometer with monochromatic incident light. Interference between the reflected lights both on half mirrorCr coating of glass disk and on super finished ball makes circular fringes depending on the contact conditions such as sliding velocity, applied load, viscosity-pressure characteristics and viscosity of lubricant under ambient pressure. In this situation the film thickness is regarded as the difference of optical paths between those reflected lights, which make dark and bright fringes with monochromatic incident light. The film thickness is computed by numbering the dark and bright fringe orders and the intensity (gray scale image) in each fringe regime is mapped to the corresponding film thickness. In this work, we developed a measuring technique for EHL film thickness by dividing the image patterns into two typical types under the condition of monochromatic incident light. During the image processing, the captured image is converted into digitally formatted data over the contact area without any loss of the image information of interferogram and it is also interpreted with consistency regardless of the observer’ s experimental experience. It is expected that the developed image processing method will provide a valuable basis to develop the image processing technique for color fringes, which is generally used for the measurement of relatively thin films in higher resolution.     

Basics of EHL for practical application

Elastohydrodynamic lubrication (EHL) is present in all lubricated components whose elements roll together, including gears, rolling bearing, cams and constant velocity joints. These are characterised by having very localised and thus very high pressure contact, of order 1 to 3 GPa, between the elements. Two important practical properties of EHL contacts are the lubricant film thickness and the friction, and lubricant and machine designers and users need to be able to predict both of these. In principle, they can be determined from full numerical solution of the elastohydrodynamic problem. However, this is quite difficult and time‐consuming and requires detailed knowledge of the rheology of the lubricant film at high pressure and shear rate. This paper is aimed at practising engineers and describes alternative approaches, i.e. how EHL can be applied to predict film thickness and friction in practical applications. Copyright © 2014 John Wiley & Sons, Ltd.     

Obtaining the pressure spike and maximum shear stress from optical interferometry data

In order to predict and optimise highly loaded contact performance, accurate lubricant data is crucial. The lubricant's high-pressure rheological behaviour is by far the least known parameter. However, this is the key factor to realistic modeling of non-Newtonian Elasto-Hydrodynamic lubrication. In this paper a new approach is described to extract such data from optical interferometric film thickness measurements of EHL contacts. The approach is relatively straightforward and cheap compared to “out of contact” rheological experiments using specialized equipment.A measured high-resolution film thickness distribution was positioned using a computed film thickness distribution as a reference. The reference is computed using the same operating conditions as the measurement. Subsequently, from the computed film thickness difference, a pressure difference file is obtained by deconvolution. Adding this pressure difference to the computed pressure file associated with the computed reference film thickness, provides a corrected pressure distribution, as it has appeared in the experimental contact. In this paper results are presented for the pressure spike region of the contact, in which significant shear stresses occur. The basic approach and its difficulties are described as well as some “tricks”, such as the reduction of (local) noise resulting from the ill-posedness of the deconvolution. It is shown that simple averaging over a circle segment in the pressure spike zone, results in significant noise reduction and a very good ‘measured’ pressure spike.     

Study of Boundary Slippage Using Movement of a Post-Impact EHL Dimple Under Conditions of Pure Sliding and Zero Entrainment Velocity

A well-recognized phenomenon of typical traction tests of elastohydrodynamic lubrication (EHL) contacts is finite maximum traction at increasing speeds, which led to the postulation that the limiting shear stress of liquid lubricants, a high-pressure rheological property, existed. If slippage occurs at the oil–solid boundary, the limiting traction measured is not necessarily an intrinsic property of the lubricant but rather a function of interfacial properties between the bounding solid surface and the lubricant. A recent report presented experimental evidence of boundary slippage at EHL contacts using a simple methodology based on differences in the speed of oil entrapment and the apparent entrainment. The reported experiments were carried out under pure sliding conditions. The phenomenon may also be explained by internal slippage in the bulk fluid film because of the limiting shear stress of the lubricant. To clarify this, similar experiments were repeated under zero entrainment velocity (ZEV) conditions. Evidence of the highly pressurized lubricant at the center of the oil entrapment sliding against the solid bounding surface was obtained. The purpose of this article is to discuss whether the slippage is attributed to the limiting shear stress of the oil or the critical shear stress of the oil/solid interfaces, and how to differentiate the magnitudes of the critical shear stress of the two bounding surfaces in a conventional optical EHL test rig.     

EHL Performance of the Lubricant With Shear Strength: Part I — Boundary Slippage and Film Failure

This paper analytically investigates the isothermal line contact elastohydrodynamic lubrication of three lubricants with much different shear strengths under the nondimensional operating parameters of w = 2.15e-4 and U = 2.53e-10 applying the lubricant ideal viscoplastic rheological model. The boundary slippage of the low-shear-strength lubricant occurring in the EHL inlet zone was found and results in a much thinner film compared to the classical EHL theory prediction. The film boundary slippage and its growth with the slide/roll ratio variation of tile low-shear\- strength lubricant exhibit special phenomena, which are much different from those of the high-shear-strength lubricant. The easy occurrence of film failure in concentrated contact in the case of high sliding speed, heavy load, large slide/roll ratio, and low-shear-strength lubricant was concluded due to the severe friction heating on the surface conjunction and the lubricant thermal desorption on tile lubricant/surface boundary. The EHL film failure mechanism was further recognized.     

A Limiting Solution for the Dependence of Film Thickness on Velocity in EHL Contacts with Very Thin Films

In recent years there have been substantial improvements in the capabilities of numerical modeling of elastohydrodynamic lubricant (EHL) films and it is now possible to analyze a very wide range of conditions rather than needing to rely on extrapolation using classical film thickness regression equations such as those of Dowson and Higginson. However, a new controversy has arisen concerning the film thickness-velocity dependence in EHL contacts at very low speeds and high loads, with some predictions showing a film thickness much less than that predicted by the classical equations. The present article applies the well-established limiting analysis, first presented by Grubin-Ertel, to the inlet of the EHL contact. It is shown that when the load is high and the speed is low (and the pressure gradient is very high in the inlet) an accurate resolution of the inlet pressure rise is critical for the determination of the film thickness. Discretization errors of this type might be responsible for discrepancies between the classical equations and some recently published numerical predictions.     

Thermal point contact EHL analysis of rolling/sliding contacts with experimental comparison showing anomalous film shapes

The paper presents an experimental and numerical investigation of non-conformal lubricated contacts in which anomalous film shapes occur. The experiments were concerned with the contact between a steel ball and the plane surface of a glass disc at various slide-roll ratios. A paraffin base mineral oil was used as a lubricant and friction coefficients and film thicknesses were measured. It was found that for slide-roll ratios with the disk moving faster anomalous elastohydrodynamic lubrication (EHL) films were obtained characterized by a “dimple” in the central region of the contact. Numerical thermal-elastohydrodynamic analyses were carried out to simulate both film thickness and friction corresponding to the experimental conditions using Newtonian and Ree-Eyring rheological models. Initial results from this study suggest that neither of these lubricant models predict the correct detailed film shape and the experimental friction at the same time. An alternative lubricant model including both thermal and limiting shear stress effects (wall slippage) is currently under development.     

Evidence of lubricant slip on steel surface in EHL contact

The limiting traction provided by typical elastohydrodynamically lubricated (EHL) contacts leads to the postulation that liquid lubricants are subject to limiting shear stress, which is generally accepted as an intrinsic property of the lubricants. The results of recent optical EHL research show that lubricant at EHL contacts may slip on the Cr-coated glass surface under certain circumstances. This paper presents further evidence that high pressure EHL film can slip on a steel surface. Because the steel/steel contacts are common in typical traction drives and the interfaces are therefore oil/steel, the deduction of the limiting shear stress of lubricants from the measured limiting traction may simply reflect a property of the system should boundary slippage occur.     

流变模型对剪切稀化流体弹流油膜厚度影响的研究

基于Carreau流变模型和Ree—Eyring流变模型,对剪切稀化流体线接触弹流润滑进行了完全数值分析,得到了同一种润滑油在不同流变模型下的弹流油膜厚度。将理论分析得到的油膜厚度、经典弹流膜厚公式计算的油膜厚度以及实测的油膜厚度进行了对比,结果表明：基于Carreau流变模型的理论分析结果更能反映剪切稀化流体的实际弹流油膜厚度;在相同工况下,基于Ree—Eyring流变模型的理论分析结果低估了剪切稀化流体的油膜厚度,经典弹流膜厚公式过高地估计了剪切稀化流体的油膜厚度。研究结果表明：幂函数形式的流变模型更能反映剪切稀化流体的流变特性。     

Effect of Starvation on Traction and Film Thickness in Thermo-EHL Line Contacts with Shear-Thinning Lubricants

The effect of starvation on traction and film thickness behavior in thermo-EHL rolling/sliding line contacts has been studied using full EHL simulations. The simulations employed the free volume equation for viscosity–pressure–temperature relationship and Carreau viscosity model to describe the shear-thinning behavior of the EHL lubricant. The simulation results were used to develop equations for estimating the factors by which the traction coefficient increases and film thickness decreases as a function of the degree of starvation. For the situations involving inadequate lubricant supply at the inlet, these factors can be used to correct the traction coefficient and central film thickness predicted with the assumption of fully flooded condition.     

Elastohydrodynamic Lubrication of Rough Surfaces under Oscillatory Line Contact with Non-Newtonian Lubricant

This paper presents the results of a transient analysis of elastohydrodynamic lubrication (EHL) of two parallel cylinders in line contact with a non-Newtonian lubricant under oscillatory motion. Effects of the transverse harmonic surface roughness are also investigated in the numerical simulation. The time-dependent Reynolds equation uses a power law model for viscosity. The simultaneous system of modified Reynolds equation and elasticity equation with initial conditions was solved using the multigrid, multilevel method with full approximation technique. The film thickness and the pressure profiles were determined for smooth and rough surfaces in the oscillatory EHL conjunctions, and the film thickness predictions were verified experimentally.

For an increase in the applied load on the cylinders or a decrease in the lubricant viscosity, there is a reduction in the minimum film thickness, as expected. The predicted film thickness for smooth surfaces is slightly higher than the film thickness obtained experimentally, owing primarily to cavitation that occurred in the experiments. The lubricant film under oscillatory motion becomes very thin near the ends of the contact when the velocity goes to zero as the motion direction changes, but a squeeze film effect keeps the fluid film thickness from decreasing to zero. This is especially true for surfaces of low elastic modulus. Harmonic surface roughness and the viscosity and power law index of the non-Newtonian lubricant all have significant effects on the film thickness and pressure profile between the cylinders under oscillatory motion.     

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.