Central Film Thickness Research Articles

Prediction of film thickness decay in starved elasto-hydrodynamically lubricated contacts using a thin layer flow model

The prediction of bearing life and performance requires detailed knowledge of the behaviour of elasto-hydrodynamically lubricated (EHL) contacts under varying conditions of load and lubricant supply during many load cycles. Considering starved lubrication, a model is developed that predicts the change of the supply layer to the EHL contact. As the film thickness inside a starved EHL contact is determined by the thickness and distribution of the supply layer, this model can be used to predict the film thickness decay. A formula for the central film thickness decay is obtained for the long-term operation of circular or elliptical contacts under starved conditions. The model is validated experimentally.

A Three-Dimensional Deterministic Model for Rough Surface Line-Contact EHL Problems

This paper reports the development of a novel three-dimensional (3D) deterministic model (3D L-EHL) for rough surface line-contact mixed-elastohydrodynamic lubrication (EHL) problems. This model is highly demanded because line contacts are found between many mechanical components, such as various gears, roller and needle bearings, cams and followers, and work rolls and backup rolls in metal-forming equipment. The macro aspects of a line-contact problem can be simplified into a two-dimensional (2D) model; however, the topography of contacting rough surfaces, microasperity contacts, and lubricant flows around asperities are often three-dimensional. The present model is based on Hu and Zhu’s unified 3D mixed-EHL model (Hu and Zhu, 2000, “Full Numerical Solution to the Mixed Lubrication in Point Contacts,” ASME J. Tribol., 122(1), pp. 1–9) originally developed for point contacts and the mixed fast Fourier transform (FFT)-based approach for deformation calculation formulated by Chen et al. (2008, “Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts With Normally Flat Surface,” ASME J. Appl. Mech., 75(1), 011022-1-11). It is numerically verified through comparisons with results from the line-contact Hertzian theory and the conventional 2D line-contact smooth-surface EHL formulas. Numerical examples involving 3D sinusoidal and digitized machined surfaces are also analyzed. Sample cases indicate that transverse roughness may yield greater film thickness than longitudinal roughness. This observation is qualitatively in agreement with the trend predicted by Patir and Cheng’s stochastic model (1978, “Effect of Surface Roughness on the Central Film Thickness in EHL Contacts,” Proceedings of the Fifth Leeds-Lyon Symposium on Tribology, London, pp. 15–21). However, the roughness orientation effect does not appear to be quantitatively as great as that shown in the work of Patir and Cheng for the same range of λ ratio.

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.

EHL Circular Contact Film Thickness Correction Factor for Shear-Thinning Fluids

An extensive set of full elastohydrodynamic lubrication point contact simulations has been used to develop correction factors to account for the effect of shear-thinning lubricant behavior on the central and minimum film thickness in circular contacts under pure rolling condition. The film thickness for a shear-thinning lubricant can be easily obtained by dividing the corresponding Newtonian film thickness by the appropriate correction factor. Comparisons of the film thickness values obtained using the correction factors have been matched with the published experimental results pertaining to shear-thinning lubricants with a variety of realistic flow and piezoviscous properties under a wide range of operating speed. The good agreement between them establishes the validity and versatility of the correction factors developed in this paper.

Scale Effects in Generalized Newtonian Elastohydrodynamic Films

Abstract The estimation or prediction of elastohydrodynamic lubrication (EHL) film thickness requires knowledge of the lubricant properties. Today, in many instances, the lubricant properties have been obtained from a measurement of the central film thickness and the assumption of a classical Newtonian film-thickness formula. This technique has the practical advantage of using an effective pressure-viscosity coefficient, which compensates for shear-thinning. We have shown by a perturbation analysis of limiting cases for fluid with Carreau rheology (represented by Newtonian and power fluid) and by a full EHL numerical solution for Carreau fluid that the practice of extrapolating from a laboratory scale measurement of film thickness to the film thickness of an operating contact may substantially overestimate the film thickness in the real machine if the machine scale is smaller and the lubricant is shear-thinning within the inlet zone. The intention here is to show that errors result from extrapolation of Newtonian formulas to different scale and not to provide advice regarding quantitative engineering calculations.

Central film thickness in time-varying normal approach of rolling elastohydrodynamically lubricated contacts

The effects of time-varying normal approach on the film formation of rolling elastohydrodynamically lubricated (EHL) contacts are studied by means of an inlet analysis. A modified Ertel—Grubin scheme is used to calculate the variation of central film thickness as a response of time-varying normal approach. The inlet shape approximation from Crook is used to derive simple analytical and semi-analytical solutions for the calculation of central film thickness and inlet pressures for situations of prescribed normal rigid-body displacement or prescribed load variation. The methodology is also adopted to model the pressure and clearance wave transport phenomenon shown earlier only with the use of full numerical solutions.

Correction Factor Formula to Predict the Central and Minimum Film Thickness for Shear-Thinning Fluids in EHL

Using a coarse-grained molecular dynamics simulation based on the bead-spring polymer model, we reproduced the film distribution of molecularly thin lubricant films with polar end groups coated on the disk surface and quantified the film-surface morphology using a molecular-probe scanning method. We found that the film-surface morphology changed periodically with increasing film thickness. The monolayer of a polar lubricant that entirely covers the solid surface provides a flat lubricant surface by exposing its nonpolar backbone outside of the monolayer. By increasing film thickness, the end beads aggregate to make clusters, and bulges form on the lubricant surface, accompanying an increase in surface roughness. The bulges continue to grow even though the averaged film thickness reaches or exceeds the bilayer thickness. With further increases in film thickness, the clusters start to be uniformly distributed in the lateral direction to clearly form a third layer. As for the formation of fourth and fifth layers, the process is basically the same as that for the second and third layers. Through our calculations of the intermolecular potential field and the intermolecular force field, these values are found to change periodically and are synchronized with the formation of molecule aggregations, which explains the mechanism of forming the layered structure that is inherent to a polar lubricant.

Thermal transient rough EHL line contact simulations by aid of computational fluid dynamics

Reynolds equation is the pre-dominantly used PDE for modelling the fluid flow or more accurately the fluid pressure in an elastohydrodynamic lubrication (EHL) contact. The equation is derived by combining the two conservation equations of momentum and continuity into a single equation for the fluid pressure. The numerical approach for theoretical investigations performed on EHL contacts in this work is somewhat different. The modelling of the fluid flow is based on a computational fluid dynamic (CFD) technique. The fluid flow is simulated by aid of the equations of momentum and continuity in a more complete form and when the thermodynamics is incorporated, the equation of energy. The aim of the investigation was to examine whether the CFD technique could be used to handle thermal transient rough EHL line contacts. It is shown that commercial CFD software can be modified to meet such requirements. The influence of thermal effects on the flow under sliding motion was investigated. The non-Newtonian model used in this work is the Ree–Eyring model. It is shown that the choice of the Eyring stress in the model influences flow in the contacts. If the thermal properties of the surrounding solids differ, it has been shown experimentally and theoretically that a dimple or increased central film thickness may appear in the EHL contacts. This work shows that the governing mechanisms that result in the dimple are also present in thermal transient rough EHL line contacts.

Simulation of dry and lubricated contacts in multi-body systems

The present paper investigates the modeling of counterformal elastohydrodynamic lubricated (EHL) contacts in multi-body system (MBS) environments. The aim is to obtain a representation of the dynamic behaviour of machine elements and characteristic values as the lubrication film thickness for lifetime calculations. Two contact models are presented for the study of cam-roller tappet and raceway-roller systems. The first model is a one-dimensional representation of the EHL contact behaviour. It is based on the calculation of the central lubrication film thickness by means of dimensionless values (functions of the operating conditions) and provides a simplified model of the mixed lubrication. The second one, still under development, investigates the modeling of 3D dry and lubricated contacts. The fluid-structure interaction is here fully considered and a discretised form of the contact problem is solved using an iterative algorithm. This paper proposes, in the latter case, some perspectives and a discussion of its implementation.

On some aspects of numerical solutions of thin-film and mixed elastohydrodynamic lubrication

Numerical solution of the thin-film and mixed elastohydrodynamic lubrication (EHL) is of great importance to the study of lubrication transition and breakdown, as well as surface failures caused by contact. However, in this region, converged and accurate numerical solutions become difficult, and effects of computational mesh density and differential schemes appear to be more significant. Also, there is currently a debate on how surface contact should be defined and analysed, and whether it is indeed possible to model contact through a grid-converged solution of the EHL equation system. This paper presents a set of analysed sample cases with different computational meshes, different cut-off values for handling contact, on different levels of central film thickness, from several hundred nanometres down to zero. Based on the results, some key issues are discussed (such as whether the contact can be modelled with the Reynolds equation system, how a contact should be defined and analysed, how computational meshes should be selected and managed, what the reasonable and satisfactory convergence accuracy should be, and so on). In addition, a progressive mesh densification (PMD) method is presented and compared with the multi-grid (MG) method. It is demonstrated that the PMD method may be able to significantly reduce computing time. On the other hand, the MG method may be good for thick-film cases with smooth surfaces or low frequency roughness, but is not desirable for the ultra-thin film and mixed EHL, especially when moderate and high frequency surface roughness is involved.

Viscosity Loss in PFPE Lubricant for Space Applications under EHL Conditions

An unbranched perfluoropolyether (PFPE) 815Z is the current ball bearing lubricant for space applications. Measurements of elastohydrodynamic lubrication (EHL) oil film thickness have been carried out to assess the lubricating performance of PFPE with average molecular weight of 9200 using an optical interferometric technique under mean Hertzian pressure 0.45 GPa. The film thickness of 815Z became less than predicted film thickness from Hamrock and Dowson formula for EHL central film thickness. There are two main explanations why PFPE is inferior to mineral oil in their ability to form EHL films, temporary viscosity loss and permanent viscosity loss. In order to elucidate the results, measurements of permanent viscosity loss under mean Hertzian pressure from 0.41 GPa to 2.67 GPa have been carried out using the thrust ball bearing. There results show that the degree of the permanent viscosity loss depends on Hertzian pressure, occurrence of permanent viscosity loss of 36 % with 2.67 GPa and 2 % with 0.41 GPa.

Relationships between Central Tear Film Thickness and Tear Menisci of the Upper and Lower Eyelids

To investigate the relationship between central tear film thickness (TFT) and tear menisci of the upper and lower eyelids using real-time optical coherence tomography (OCT). Both eyes of healthy subjects were imaged with a real-time OCT to obtain height, curvature, and area of upper and lower tear menisci simultaneously. Central TFT was indirectly measured by calculating the difference between baseline measurements of the central corneal thickness plus tear film and the true corneal thickness obtained after instillation of artificial tears. Results from two normal blinks were obtained from one eye at each visit and repeated the next day. The average central TFT was 3.4 +/- 2.6 microm. The upper tear meniscus curvature, height, and area were 239 +/- 112 microm, 268 +/- 68 microm, and 22,732 +/- 11,974 microm2 respectively. There were no significant differences in curvatures, heights, or areas between upper and lower tear menisci, nor were there any differences in measured variables between the two blinks at each visit or between the two repeated visits in the right and left eye groups (P > 0.05). The upper and lower tear menisci in each eye group on each day correlated strongly with curvature, height, and area (all P < or = 0.03). However, no tear meniscus variable was a significant predictor of TFT (all P > 0.44). OCT is a promising tool in the measurements of TFT and dimensional variables of tear menisci. Upper and lower tear menisci have nearly identical dimensions.

EHL simulation using the free-volume viscosity model

The free-volume viscosity model can accurately predict the temperature–pressure–viscosity relationship of lubricants. However, it is seldom used in elastohydrodynamic lubrication (EHL) simulation. This paper presents the application of the free-volume viscosity model in a Newtonian EHL simulation of a squalane-lubricated circular contact. Good agreement is observed between available experimental data and simulation results. The pressure–viscosity coefficients fit from viscometer data are also discussed. A recently developed definition of the coefficient is used to compare the coefficient value extracted from EHL film thickness interference measurements. Results indicate that the coefficient values from the curve fitting and EHL film thickness extraction agree well which has not been previously observed. Two factors help achieve this agreement: the new coefficient definition and smaller prediction error when using the Hamrock–Dowson formula in the cases studied. The effects of different pressure–viscosity relationships, including the exponential model, the Roelands model and the free-volume model, are investigated through an example with bright stock mineral oil. It is found that the real pressure–viscosity behavior predicted by the free-volume model yields a higher viscosity at the low-pressure area which results in a larger central film thickness. Therefore, due to use of the free-volume model, the present results are more consistent with experimental observations than previously reported numerical results.

Thin film elastohydrodynamic lubrication—a power-law fluid model

A 1-D modified Reynolds equation for power-law fluid is derived from the viscous adsorption theory for thin film elastohydrodynamic lubrication (TFEHL). The lubricating film between solid surfaces is modeled as three fixed layers, which are two adsorption layers on each surface and a middle layer between them. The comparisons between classical non-Newtonian EHL and non-Newtonian TFEHL are discussed. Results show that the TFEHL model can reasonably calculate the pressure distribution, the film thickness, the velocity distribution and the average viscosity. The thickness and viscosity of the adsorption layer and the flow index influence the lubrication characteristics of the contact conjunction significantly. The film thickness increases with the increase of flow index. As the flow index becomes greater, the dimple in the film shape moves towards the center of the contacts. The effect of flow index produces an obvious difference in the pressure distribution. The greater the flow index, the greater the pressure spike, and the pressure spike tends to move toward the center. The larger the flow index, the more the velocity varies in both the middle layer and adsorption layers along the Z-axis. The greater the thickness and viscosity of the adsorption layer and the flow index, the greater the deviation in central film thickness versus speed between EHL model and TFEHL model produced in the very thin film regime.

EHL inlet zone analysis with the contact‐lubricant interfacial limiting shear stress

PurposeTo develop a fairly different EHL inlet zone analysis for investigating the contact‐lubricant interfacial limiting shear stress effect on line contact EHL film thickness in isothermal conditions. This analysis is purposed to give fast and qualitatively correct results.Design/methodology/approachA Grubin‐like EHL inlet zone analysis is derived with closed form of the analytical results of the EHL film thickness, the EHL film pressure, the contact‐lubricant interfacial shear stress and the contact‐lubricant interfacial slipping velocity in the EHL inlet zone based on the assumption of the contact‐lubricant interfacial limiting shear stress in the EHL inlet zone. In this analysis, the lubricant is allowed to slip at the contact surface; The inlet contact surface shape is known from results referenced in this paper; The physical condition for the presence of the film slippage is incorporated; The lubricated area is divided into different kinds of film slippage zones where are, respectively, applied different governing equations. Three deterministic equations in this analysis are obtained and solving these coupled equations gives the solutions of the boundaries of the slip zone and the percentage reduction of the central film thickness by the contact‐lubricant interfacial limiting shear stress effect in this EHL.FindingsCompared with the earlier approaches to the present problem, the present analysis has the advantage of giving fast and qualitatively correct solutions. The results obtained from the present analysis show that the contact‐lubricant interfacial limiting shear stress effect on EHL film thickness is usually strong when the contact‐lubricant interfacial limiting shear stress in the EHL inlet zone is low; This effect can greatly reduce the global EHL film thickness especially in severe operating conditions.Practical implicationsA very useful material for the academic researcher and the engineer who are engaged in the study and measurement of the effect of the contact‐lubricant interfacial limiting shear stress on EHL film thickness and EHL film pressure.Originality/valueA fairly different EHL inlet zone analysis is originally developed based on the assumption of the contact‐lubricant interfacial limiting shear stress in the EHL inlet zone. The physical condition for the contact‐lubricant interfacial slippage is first incorporated in this analysis. Deterministic governing equations in this analysis are derived and solving these coupled equations gives the final solutions of the present problem. This analysis has the advantage of giving fast and qualitatively correct solutions. It convincible shows the contact‐lubricant interfacial limiting shear stress effect on EHL film thickness and EHL film pressure in the present EHL.

Effects of Differential Scheme and Mesh Density on EHL Film Thickness in Point Contacts

This paper investigates the effects of differential scheme and mesh density on elastohydrodynamic lubrication (EHL) film thickness based on a full numerical solution with a semi-system approach. The solution variation with different schemes and mesh sizes is revealed based on a set of numerical cases in a wide range of central film thickness from several hundred nanometers down to a few nanometers. It is observed that when the film is thick, the effects of differential schemes and mesh density are not significant. However, if the film becomes ultra-thin, e.g., below 10–20 nanometers, the influence of mesh density and differential schemes becomes more significant, and a proper dense mesh and differential scheme may be highly desirable. The present study also indicates that the solutions from the 1st-order backward scheme give the largest film thickness among all the solutions from different schemes at the same mesh size.

Influence of Harmonic Surface Roughness on the Fatigue Life of Elastohydrodynamic Lubricated Contacts

In recent years, owing to the increase in transmitted power, increase in temperature, and decrease in viscosity, elastohydrodynamic lubricated (EHL) contact conditions have become extremely severe. Consequently, roughness and surface features become increasingly important when compared with the lubricant film thickness, which can induce wear. Moreover, local pressure variations increasingly cause surface-induced fatigue. Therefore, the understanding of roughness behaviour in EHL contact performance has become important. Three decades ago, a widely used tool to predict contact performance was proposed by Dawson and Tallian. It is based on the central film thickness to composite roughness ( h3/σ) ratio. However, engineering fatigue life models require the stress level and the stressed volume to study the contact life reduction, and neither can be extracted directly from the h3/σ ratio. This article extends the amplitude reduction analysis. It proposes a new dimensionless parameter including central film thickness, roughness wavelength, and amplitude. It is shown that the pressure fluctuations depend solely on this parameter and that the fatigue life depends mainly on this parameter.

Effects of Couple Stresses on Pure Squeeze EHL Motion of Circular Contacts

AbstractA method for investigating the pure squeeze action in an isothermal elastohydrodynamically lubrication (EHL) problem, i.e., circular contacts lubricated with couple stress fluid, was developed. A constant load condition was used in the calculations. The initial conditions such as pressure profiles, normal squeeze velocities, and film shapes were obtained from the classical hydrodynamic lubrication theory at a specified large central film thickness. The coupled transient modified Reynolds, elasticity deformation, and load equilibrium equations are solved simultaneously. The simulation results reveal that the effect of the couple stress is equivalent to enhancing the lubricant viscosity, thus enlarging the film thickness. The effect of couple stress in thin film lubrication varies with film size. That is, the thinner the lubricating film is, the more obvious the effect of couple stress is. For larger characteristic length, materials parameter, and load, the central pressure, central film thickness, and rigid separation are larger than those of smaller characteristic length under the same load. The time needed to achieve maximum central pressure and the Hertzian pressure increases with increasing characteristic length.

Influence of temperature distributions in EHL film on its thickness under high slip ratio conditions

This paper describes the influence of temperature rise of oil film in Hertzian contact area on the film thickness or profile under high slip ratio conditions. Temperatures of both surfaces of a ball and a disk as well as average temperature across the oil film were measured by means of an improved infrared. Two kinds of optical band-pass filters were used to separate the radiations from the ball surface and the oil film through an infrared transparent disk made of sapphire glass. In case of temperature measurement of the disk surface, another sapphire glass disk was coated with 300 nm chromium layer on the contact surface to radiate the infrared from the disk surface and also to intercept the radiation from the ball surface and the oil film. Temperature profiles across the oil film were estimated by assuming a parabolic profile with the measured three kinds of temperatures. For case within 200% in slip ratio, both minimum and central film thickness decreased under constant entrainment velocity as slip ratio increased. Measured film shapes were not flat at central Hertzian contact region under high-slip condition and differed from the results by the conventional EHD theory assuming constant viscosity in the direction of film thickness. The profile of Couette flow varied due to the distribution of oil film temperature in thickness direction. The viscosity wedge action, that is the variation of the profile of Couette flow causes reduction of film thickness or deformation of film profile. For case over 200% in slip ratio, the relation between central film thickness and slip ratio under constant relative slide speed had a great difference from the results calculated from the formula presented by Chittenden et al.

Stribeck Friction Curve in Point EHL Contacts

The ultra thin film interferometry and conventional optical interferometry techniques are used to measure the central film thickness and friction force as a function of the dimensionless speed parameter. Experiments were conducted in point contacts with a mineral bright stock oil and a disk-like chemical compound by changing the temperature, entrainment velocity and surface roughness at a fixed slide-roll ratio. It has been found that the friction coefficient curve, i.e., the relationship between the friction coefficient and the dimensionless speed parameter, changes depending on lubrication regimes, even when the relationship between the central film thickness and the dimensionless speed parameter obeys EHL theory.