Classical Elastohydrodynamic Lubrication Research Articles

A Traction (Friction) Curve Is Not a Flow Curve

With the uncertainty regarding the global energy future, the ability to lubricate concentrated contacts with sufficiently thick liquid films while minimizing friction is of extreme importance. The assumptions of classical elastohydrodynamic lubrication have remained unchanged since the early days. It has not been possible to test many of these assumptions without the measurement of the viscosity at elastohydrodynamic lubrication (EHL) pressures, and viscometer measurements have been ignored. One of these assumptions has been the equivalence of a traction curve to a rheological flow curve for the lubricant. This notion should have been discarded forty years ago, simply because it required the pressure–viscosity behavior to be unlike the behavior observed in viscometers. At the heart of the problem is the fact that the pressure within the EHL contact is not homogeneous and the liquid properties are highly dependent on pressure, making the contact a very poor rheology laboratory. These past failures must be avoided in the future.

Squeeze lubrication between soft solids: A numerical study

Squeezing a lubricating film between viscoelastic solids is a process with many applications, ranging from biomechanics to industrial engineering. The problem is addressed by means of an innovative numerical strategy coupling a finite difference solver for the lubricant fluid dynamics and a Boundary Element approach, which provides the deformation field in the solid. Results show marked differences compared to classical elasto-hydrodynamic lubrication (EHL): Pressure and film thickness depend, in fact, on the material viscoelastic relaxation, peaking at the two edges of the lubricated contact area. This implies, also for the minimum and central thickness values, time-dependent trends that significantly deviate from EHL solution and, thus, point out the necessity of accounting for the actual viscoelastic rheology of the lubricated solids.

The Pressure and Temperature Dependency of Relative Volume, Low Shear Viscosity, and Non-Newtonian High Shear Viscosity in SAE AS5780 HPC, MIL-PRF-23699 HTS, and DOD-PRF-85734 Lubricants

This work quantifies the high-pressure rheological performance of two jet engine turbine oils and three helicopter transmission oils. The jet engine oils are qualified for both the MIL-PRF-23699 high thermal stability and AS5780 high performance classifications, and the helicopter oils are classified against DOD-PRF-85734. Rheological properties include relative volume, low shear, and high shear viscosity. Relative volume measurements are presented for temperatures ranging from 20 to 100 °C and up to 300 MPa. Low shear viscosity measurements range from 20 to 100 °C and up to 1 GPa. Apparent shear or high shear viscosity measurements varied pressure up to 550 MPa and shear stresses up to 5 MPa. The non-Newtonian limit for each lubricant was observed. Rheological models obtained from the measurements include the Tait and Murnaghan relative volume models, the Williams-Landel-Ferry (WLF) modified Yasutomi low shear viscosity model, and both the modified Carreau-Yasuda and double modified Carreau-Yasuda shear viscosity models. The regressed models highlight shortcomings of classical elastohydrodynamic lubrication (EHL) expressions in describing the measured lubricants’ rheological response. These property models support the development of modern EHL calculations as they relate to high-performance aerospace applications.

Fluid–Solid Interaction Modeling of Elastohydrodynamic Lubrication Point Contacts

Abstract Elastohydrodynamically lubricated point contact was investigated using a two-way partitioned fluid–solid interaction (FSI) model. ansys Mechanical finite element modeling software was used to compute elastic (and plastic) deformation of the solid bodies, while ansys fluent computational fluid dynamics software was used to model the fluid with the Navier–Stokes equations. The current model is not limited by Reynolds equation assumptions, allowing for the investigation of pressure, viscosity, and temperature variation across point contact elastohydrodynamic lubrication (EHL) films. Solid body material stress distribution and fluid behavior such as cavitation were also investigated. The details of model development are described. Validation of the model is presented across a range of loads and speeds for cases when the Reynolds equation is applicable. The results are in excellent agreement. Various slide-to-roll ratios were investigated considering a non-Newtonian fluid with thermal effects to characterize lubricant properties within the EHL film. Results demonstrate notable lubricant viscosity and temperature variations within the EHL film thickness both along and perpendicular to the rolling direction for cases with high slide-to-roll ratio. Cavitation was also considered, and cavitation bubble lengths were found to agree well with results found in open literature. Finally, the effects of material plasticity on solid body response were investigated. The FSI model developed in this research provides new insights on a classical EHL problem.

The unresolved definition of the pressure-viscosity coefficient

In the classical approach to elastohydrodynamic lubrication (EHL) a single parameter, the pressure-viscosity coefficient, quantifies the isothermal pressure dependence of the viscosity for use in prediction of film thickness. Many definitions are in current use. Progress toward a successful definition of this property has been hampered by the refusal of those working in classical EHL to acknowledge the existence of accurate measurements of the piezoviscous effect that have existed for nearly a century. The Hamrock and Dowson pressure-viscosity coefficient at high temperature requires knowledge of the piezoviscous response at pressures which exceed the inlet pressure and may exceed the Hertz pressure. The definition of pressure-viscosity coefficient and the assumed equation of state must limit the use of the classical formulas, including Hamrock and Dowson, to liquids with high Newtonian limit and to low temperature. Given that this problem has existed for at least fifty years without resolution, it is reasonable to conclude that there is no definition of pressure-viscosity coefficient that will quantify the piezoviscous response for an analytical calculation of EHL film thickness at temperatures above ambient.

Tribological properties of a helical gear pair considering interfacial slip between lubricant and tooth surface

AbstractIn this study, an interfacial slip model including the limiting shear stress is proposed and applied to the thermal elastohydrodynamic lubrication (EHL) analysis of a helical gear pair. The main difference between the proposed model and the classical EHL model is that, the term of entrainment velocity in Reynolds equation is modified. The influences of interfacial slip, thermal effect, initial limiting shear stress and operating conditions on the tribological properties are evaluated. Due to the interfacial slip, the pressure distribution moves towards the inlet region, and the fluctuation distributions of entrainment velocity and film thickness are similar to the trigonometric function. The influence of thermal effect on interfacial slip cannot be ignored, especially in the case of high speed and heavy load. As the input torque and input rotational speed increase, the interfacial slip gradually extends to the whole meshing process.

Elastohydrodynamic Lubrication Modeling by a Cosserat Continuum Theory for Small Polymer Journal Bearings

Abstract Recent experiments have shown that the elastic deformation behaviors of a polymeric material are consistent with the Cosserat elasticity under nonuniform deformation at a millimeter scale. Thus, an elastohydrodynamic lubrication model in the framework of the Cosserat continuum theory is proposed to explore the lubrication performance that deviates from the classical elastohydrodynamic lubrication theory for the small polymer journal bearings with millimeter size. The elastic deformation of the bearing sleeve made of polymeric material and the pressure distribution in a lubricating film are obtained through an iterative solution of the equation of the Cosserat elasticity and the modified Reynolds’ equations with considering the boundary slippage. The effect of bearing size and Cosserat characteristic lengths for torsion and bending on the lubrication performance of the small polymer journal bearings is studied using the proposed Cosserat elastohydrodynamic lubrication model. It was found that the small changes in film thickness due to the Cosserat effect can result in large changes in film pressure. The Cosserat characteristic length of bending possesses a significant effect on the lubrication behaviors of the journal bearings, because the size effect is mainly caused by the increased apparent modulus due to the bending elastic deformation of the bearing sleeve. The boundary slip behaviors dependent on the Cosserat characteristic length are also studied using the Cosserat elastohydrodynamic model, and the numerical results show that the Cosserat characteristic length changes the optimal geometric parameters of the slip zone in terms of load carrying capacity for the small polymer journal bearings.

The rheological assumptions of classical EHL: What went wrong?

Abstract The field of elastohydrodynamic lubrication (EHL) now has two very different approaches to the problem. For the first approach, two assumptions regarding the pressure, temperature and shear dependence of viscosity have been essential to the way that classical EHL developed over the last forty years. 1. The liquid in the inlet zone responds in Newtonian fashion. 2. The shear stress versus shear rate relationship of the liquid has the same form as the average shear stress versus average shear rate obtained from a traction curve. The new, quantitative, approach employs viscosities measured in instruments which do not rely upon these assumptions. There has been a rapid succession of advances in understanding of film forming and friction under the new approach.

Soft Matter Lubrication: Does Solid Viscoelasticity Matter?

Classical lubrication theory is unable to explain a variety of phenomena and experimental observations involving soft viscoelastic materials, which are ubiquitous and increasingly used in e.g. engineering and biomedical applications. These include unexpected ruptures of the lubricating film and a friction-speed dependence, which cannot be elucidated by means of conventional models, based on time-independent stress-strain constitutive laws for the lubricated solids. A new modeling framework, corroborated through experimental measurements enabled via an interferometric technique, is proposed to address these issues: Solid/fluid interactions are captured thanks to a coupling strategy that makes it possible to study the effect that solid viscoelasticity has on fluid film lubrication. It is shown that a newly defined visco-elasto-hydrodynamic lubrication (VEHL) regime can be experienced depending on the degree of coupling between the fluid flow and the solid hysteretic response. Pressure distributions show a marked asymmetry with a peak at the flow inlet, and correspondingly, the film thickness reveals a pronounced shrinkage at the flow outlet; friction is heavily influenced by the viscoelastic hysteresis which is experienced in addition to the viscous losses. These features show significant differences with respect to the classical elasto-hydrodynamic lubrication (EHL) regime response that would be predicted when solid viscoelasticity is neglected. A simple yet powerful criterion to assess the importance of viscoelastic solid contributions to soft matter lubrication is finally proposed.

Design and Experiment Study on a New Type of Lubrication Simulation System for Thrust-Ball Bearing in Confined Space

Many machine components work within an elastohydrodynamic lubrication (EHL) regime. Unconfined space is widely used in EHL formulas for to evaluate film thickness, which is related to operating conditions and material properties. In classical theoretical EHL studies, film pressure matches the loading balance and the location of the lubricated components can be adjusted. In the present study, the lubrication performance is analyzed based on a confined space. A thrust ball bearing lubrication simulation system is designed and used to examine the relationship between velocity and film thickness. It was found that the central film thickness and minimum film thickness increased as entrainment velocity increased. Fluctuations in the film thickness curve were observed, which may have arisen from slight gap variations in the ball-plate contact area.

Classical EHL Versus Quantitative EHL: A Perspective Part II—Super-Arrhenius Piezoviscosity, an Essential Component of Elastohydrodynamic Friction Missing from Classical EHL

Ninety years of high-pressure measurements with many different types of viscometers have shown that faster-than-exponential (super-Arrhenius) pressure dependence of viscosity is universal for glass-forming liquids and, therefore, all typical liquid lubricants. Dielectric spectroscopy at elevated pressure also yields super-Arrhenius response in the dependence on pressure of the primary relaxation time. In contrast, classical elastohydrodynamic lubrication (EHL) has gone to great lengths to ignore this phenomenon, including fictional accounts of the results of viscometry. As a result of this, classical EHL is unable to quantitatively account for one of the most important properties affecting friction at low sliding velocity, the low-shear viscosity. Differences in friction between similar liquids at low sliding velocity can be explained by their different inflection pressures. Some observed liquid response to shear stress at high pressure can be explained with the measured super-Arrhenius pressure dependence. It should be clear that, had classical EHL employed realistic pressure dependence of viscosity from its beginning, the field would have been in a better position today to solve engineering problems which involve the differences among molecular structures.

Pressure–viscosity response in the inlet zone for quantitative elastohydrodynamics

The descriptions employed in classical elastohydrodynamic lubrication (EHL) of the piezoviscous effect at low pressures characteristic of the inlet zone are simply inaccurate for low viscosity liquids. This article offers the 1952 McEwen equation for accurately describing the pressure–viscosity effect at low inlet pressures for those liquids with sufficiently high inflection pressure that the faster-than-exponential response does not significantly affect the viscosity in the inlet. The parameters of this model have significance for the classical EHL film thickness formulas and these parameters are listed for several low viscosity liquids including a refrigerant.

Classical EHL Versus Quantitative EHL: A Perspective Part I—Real Viscosity-Pressure Dependence and the Viscosity-Pressure Coefficient for Predicting Film Thickness

That classical elastohydrodynamic lubrication (EHL) is not a quantitative field can be illustrated by its failure to provide a consistent and rigorous definition of the viscosity-pressure coefficient. Indeed, if the pressure dependence of viscosity cannot be accurately described, then the viscosity-pressure coefficient cannot be defined. Classical EHL has employed fictional narratives to justify the pressure dependences that have been utilized. In this context, the purpose of this perspective article is to review specific and real needs from EHL and to show that data and models describing the viscosity-pressure dependence are already available and how they can properly be used. The final aim is to encourage researchers to change their philosophy of classical EHL to a quantitative approach, in which every hypothesis and every result, whether experimental or numerical, would be justified on the basis of acceptable physics.

Pure Squeeze Motion in a Magneto-Elastohydrodynamic Lubricated Spherical Conjunction

The pure squeeze magneto-elastohydrodynamic lubrication (MEHL) motion of circular contacts with an electrically conducting fluid in the presence of a transverse magnetic field is explored under constant load condition. The differences between classical elastohydrodynamic lubrication and MEHL are discussed. The results reveal that the effect of an externally applied magnetic field is equivalent to enhancing effective lubricant viscosity. Therefore, as the Hartmann number increases, the enhancing effect becomes more obvious. Furthermore, the transient pressure profiles, film shapes, normal squeeze velocities, and effective viscosity during the pure squeeze process under various operating conditions are discussed.

Influence of spinning on the rolling EHL films

Spinning cannot be ignored in some elastohydrodynamically lubricated contacts. In this paper, spinning is incorporated into an elastohydrodynamic lubrication (EHL) contact of pure rolling and its influences on EHL films are studied. Results show that with increase in spinning, the symmetry of the film shape gets lost, and the minimum film thicknesses, located respectively at the two side-lobes, decrease and show more dependence on loads. The speed indices of the film thickness at the side lobes are higher than those of the classical EHL theory predicted. Numerical work has also been carried out to clarify the experiment measurements.

Contact–fluid interfacial slippage in hydrodynamic lubricated contacts

Contact–fluid interfacial slippage in hydrodynamic lubricated contacts

Rheological Characteristics for Thin Film Elastohydrodynamic Lubrication

ABSTRACTThis paper uses three lubrication models to explore the differential phenomenon in the status of thin film lubrication (TFL). According to the viscous adsorption theory, the modified Reynolds equation for thin film elastohydrodynamic lubrication (TFEHL) is derived. In this theory, the film thickness between lubricated surfaces is simplified as three fixed layers across the film, and the viscosity and density of the lubricant vary with pressure in each layer. Under certain conditions, such as a rough or concentrated contact of a nominally flat surface, films may be of nanometer scale. The thin film elastohydrodynamic lubrication (EHL) analysis is performed on a surface forces (SF) model which includes van der waals and solvation forces. The results show that the proposed TFEHL model can reasonably calculate the film thickness and the average relative viscosity under thin film EHL. The adsorption layer thickness and the viscosity influence significantly the lubrication characteristics of the contact conjunction. The differences in pressure distribution and film shape between surface forces model and classical EHL model were obvious, especially in the Hertzian contact area. The solvation force has the greatest influence on pressure distribution.

Analysis of grease lubrication of a ball bearing using acoustic emission measurement

The behaviour of grease lubrication in a rolling bearing is less known than that of oil in the same type of tribological system. In recent years the research of grease lubrication has shown several features of the grease lubrication that differ from the classical elastohydrodynamic lubrication theory of oil lubrication, notably that starvation is more prominent under grease-lubricated conditions. The goal of the present investigation was to clarify, by using a real bearing installation and realistic running conditions, how the fundamental properties of the lubricating grease influence the lubrication in a rolling bearing. The fundamental properties of the greases considered in the study were thickener concentration, base oil viscosity, base oil bleeding rate and consistency. Results obtained with grease lubrication were verified with pure oil lubrication. The analysis of grease lubrication in the present investigation is based on the relative differences in the pulse count rate of the acoustic emission (AE) generated by the running of the bearing. In order to make the correct decisions about the lubrication situation of a bearing, the fundamentals of the behaviour of grease lubrication in rolling bearings and its influence on the AE signal have to be known. Moreover, AE has proven to be a good tool to study grease lubrication in situ in a bearing. The results show that starvation of the lubrication situation increases with increasing thickener content and decreases with lowered base oil viscosity. This is in agreement with film thickness measurements made in ball-and-disc type equipment.

A Lubrication Deviation From the Classical EHL Theory by the Lubricant Viscoplasticity: Part I — Film Thickness Dependence

This paper studies film thickness in isothermal pure rolling elastohydrodynamic lubrication (EHL) considering lubricant viscoplasticity. The central film thickness formula based on lubricant viscoplasticity regressed out by this study shows a deviation of elastohydrodynamic lubrication from the conventional theory under high rolling speeds and heavy loads. This deviation actually describes the elastohydrodynamic film thickness when the lubricant shear strength and the maximum endurable shear stress on the lubricant-surface interface in EHL inlet zones degrades due to high temperature.

Rheology of Perfluoropolyalkylether Fluids in Elastohydrodynamic Lubrication

The rheological characteristics of two branched and two linear, commercial perfluoropolyalkylether (PFPAE) fluids were studied under high pressures and temperatures. The effects of branching and carbon-to-oxygen (C :O) ratio on the pressure-viscosity-temperature behavior and on the non-Newtonian behavior of these fluids were studied experimentally under high pressures and temperatures. The branching and the higher C :O ratio seemed to increase the pressure-viscosity coefficients of these fluids. The effects of the viscosity and the pressure-viscosity coefficient on the capabilities of these fluids to generate elastohydrodynamic lubrication (EHL) film thickness were studied and compared with experimental measurements. All of the fluids studied seemed to follow the Roelands viscosity model and classical EHL theory (1). The C :O ratio also influenced the temperature dependence of the limiting-shear-strength proportionality constant. The results show that for similar-viscosity fluids, the linear PFPAE with higher C :O ratio is most desirable for wide temperature use.