Thermal Elastohydrodynamic Lubrication Research Articles

Non‐Newtonian transient thermoelastohydrodynamic lubrication analysis of an involute spur gear

AbstractThe lubrication design of gear is based on the assumption that the lubricant is an ideal Newtonian fluid. In fact, The Ree–Eyring fluid model is more in agreement with the lubricant rheological behaviour under medium or mild duty load. It is necessary for engineering lubrication design to study the non‐Newtonian transient thermal elastohydrodynamic lubrication (EHL) of gear. In the paper, a full numerical solution to the non‐Newtonian transient thermal EHL of gear is obtained by utilising the multi‐grid method, which has strong numerical stability, a quick convergence rate and a high degree of accuracy. Copyright © 2010 John Wiley & Sons, Ltd.

Some important aspects of thermal elastohydrodynamic lubrication

Thermal effect in elastohydrodynamic lubrication (EHL) has been the subject of study for the last four decades; however, some important aspects related to the physical behaviour of the lubricant in response to pressure, temperature, and shear rate remain largely neglected. This paper presents a brief review of the thermal EHL literature and sheds light on the importance of accurate characterization of the lubricant properties such as viscosity, density, rheology, and thermal conductivity. Full thermal EHL line contact simulations under steady-state and transient conditions show that using the ambient value of thermal expansivity, which has been the usual trend, may overestimate the central film thickness and introduce unrealistic features in transient EHL characteristics. Also, it is demonstrated that the most extensively used rheological equation – the sinh law – for characterizing the behaviour of shear-thinning lubricants underestimates the effect of viscous heating on EHL traction and film thickness.

Effects of the thermal conductivity of contact materials on elastohydrodynamic lubrication characteristics

Isothermal elastohydrodynamic lubrication (EHL) theory has brought the improvement in function, performance, and durability of machine elements with concentrated contacts. The main reason is that the theory can evaluate the lubrication characteristics, such as film thickness and pressure distributions, from the shape and size of contacting materials, lubricant viscosity at the entrance to the EHL conjunction, entrainment velocity, equivalent elastic modulus, and applied load. However, in order to estimate the film thickness and pressure distributions more accurately and to make clear the traction behaviour based on lubricant rheology, it is necessary to establish thermal EHL theory, which incorporates heat generation in the fluid film and heat transfer in the machine system on the foundation of isothermal EHL theory. The thermal conductivity of contact materials controls temperature in the fluid film and consequently the lubricant viscosity. Therefore, the EHL characteristics are affected remarkably by the thermal conductivity of contact materials. In this article, the effects of the thermal conductivity of contacting materials on the film thickness, pressure, and traction coefficient are described.

The Role of Heat Partition in Elastohydrodynamic Lubrication

The article is concerned with thermal elastohydrodynamic lubrication (TEHL) modeling of rolling/sliding contacts and in particular with relating the results of such models to experiments. Two kinds of lubricated rolling/sliding contact experiments are considered: (i) traction experiments where the overall frictional resistance to motion at the TEHL contact is measured and (ii) heat partition experiments where, in addition to the frictional resistance, the temperature distribution in the contacting components is measured and the heat flux into the individual components is determined. The article discusses the problem of choosing an accurate rheological model of the lubricant film that can reproduce the measurements of each of the experiments. It considers the difficulties in distinguishing between the commonly used non-Newtonian lubricant models of the shear thinning and the limiting shear stress types. It is suggested that the ability of the lubricant rheological model to replicate experimental heat partition behavior is a much more discriminating test of rheological behavior than the ability to reproduce experimental traction curves.

Stability analysis of rough journal bearings under TEHL with non-Newtonian lubricants

The combined effects of surface roughness and lubricants rheology on stability of a rigid rotor supported on finite journal bearing under thermal elastohydrodynamic lubrication have been investigated using the transient method. The newly derived time dependent modified Reynolds and the adiabatic energy equations were formulated using a non-Newtonian Carreau viscosity model. The simultaneous systems of modified Reynolds equation, elasticity equation, energy equation, and the rotor motion equation with initial conditions were solved numerically using multigrid multi-level method with full approximation technique. From the characteristic equation, the instability threshold is then obtained with various surface roughness parameters and the elastic modulus of the bearing liner materials. The results show that stability of the bearing system deteriorates with decreasing both the power law exponent and the elastic modulus of bearing liner material. The rough surface journal bearing with transverse pattern under TEHL regime exhibits better stability when compared with the rough surface journal bearing with longitudinal pattern.

Influence of pressure and temperature dependence of thermal properties of a lubricant on the behaviour of circular TEHD contacts

The aim of this paper is to study the effects of pressure and temperature dependence of a conventional lubricant's thermal properties on the behaviour of heavily loaded thermal elastohydrodynamic lubrication (TEHL) contacts. For this purpose, a typical mineral oil (Shell T9) is selected and the dependence of its transport properties on pressure and temperature is investigated. Appropriate models are then developed for these dependencies. The latter are included in a TEHL solver in order to investigate their effect on the behaviour of circular EHD contacts. The results reveal the necessity of a thermal analysis including the pressure and temperature dependence of thermal properties for a good estimation of film thicknesses and mostly traction coefficients in circular EHD contacts operating under severe conditions. Numerical results are compared with experiments, showing a very good agreement over the considered ranges. This thorough validation of a thermal EHL framework for the calculation of film thickness and friction offers a previously unavailable opportunity to investigate the effects of variations in material properties.

Effects of solid body temperature on the non-Newtonian thermal elastohydrodynamic lubrication behaviour in point contacts

In order to investigate the influence of body temperature of contact solids on the lubrication performance of machine components such as gears and roll-bearings, full numerical solution for the non-Newtonian thermal elastohydrodynamic lubrication (EHL) problem in point contacts has been achieved, assuming that the body temperature is different from the temperature of the supplied lubricating oil. The Ree—Eyring rheology model has been used to describe the non-Newtonian behaviour of the lubricant. The effects of the body temperature, the slide—roll ratio, and the velocity parameter have been discussed. The results for the body temperature being higher or lower than the temperature of the supplied oil have been compared with that of the conventional thermal EHL solution, where the temperature of the contact bodies and the temperature of the supplied oil are assumed to be the same. Results show that, if the entrainment velocity is not very high, the solid body temperature plays a dominant role in the EHL behaviour; however, the influence of body temperature decreases as the entrainment velocity increases. Comparisons between the non-Newtonian and Newtonian numerical results have been made under some operating conditions. It has been shown that, compared with the Newtonian solution, the non-Newtonian property of the lubricant can always lead to lower frictional coefficient and lower temperature, but has little effect on the film thickness, no matter the temperature of the contact bodies is lower than, equal to, or higher than that of the supplied oil.

Inverse approach for calculating temperature in EHL of line contacts

This paper proposes a thermal elastohydrodynamic lubrication (TEHL) inverse approach to estimate the pressure, temperature rise, and apparent viscosity distributions in an EHL line contact. Once the film shape is measured, the pressure and estimated film thickness distributions can be calculated from force balance and elastic deformation theories. By using these smoothing pressure and film thickness distributions, the Gauss–Seidel iteration is employed to calculate the temperature rise distribution from energy, surface temperature, and rheology equations. This approach overcomes the problems of pressure and temperature rise fluctuations, and generates accurate results of pressure and temperature rise distribution from a small number of measured points of film thickness, which also saves computing time. Results show that the direct inverse method requires a lot of measured points to establish the amplitude and location of the pressure and temperature rise spikes, whereas the inverse approach can obtain the accuracy results with only 31 measured points. With the error from the resolution in the film thickness measurements, this approach also presents a smooth curve of the pressure and temperature rise distributions with a small error. Furthermore, this approach still provides a good solution in apparent viscosity, whereas the direct method provides a much larger error in apparent viscosity.

Numerical analysis of non-Newtonian TEHL line contact problem based on real-coded genetic algorithm

This paper presents a new simple numerical method to solve the non-Newtonian thermal elastohydrodynamic lubrication (TEHL) line contact problem based on real-coded genetic algorithm (RGA). To solve the line contact TEHL problem by means of RGA, the initial population producing method is deeply investigated, an appropriate grid partition method is proposed and an appropriate evolutional computation technology is determined. Finally, the fitness evaluation function and the iterative stop qualifications are put forward. The algorithm is examined by some examples, and the results are compared with empirical solutions. The study shows that the application of RGA in the numerical analysis of the TEHL line contact problem is feasible, reliable and sufficiently accurate.

Thermal elastohydrodynamic lubrication of starved elliptical contacts

For the starved thermal elastohydrodynamic lubrication in elliptical contacts, a numerical solver based on the multi-grid technique was developed and numerical solutions were achieved. The influences of the thickness of oil-supply layer, elliptical ratio, entrainment velocity, slide-roll ratio, and the maximum Hertzian pressure on the lubrication behaviour were investigated. The thermal solutions were compared with isothermal solutions. The numerical results show that, for an oil-starved contact, the central and minimum film thicknesses predicted by both thermal and isothermal solutions change at the same trend as the thickness of the oil-supply layer increases. That is, as the thickness of the oil-supply layer increases, in the beginning both the central and minimum film thicknesses increase rapidly, however, their increasing rates become smaller gradually, at last, when the thickness of the oil-supply layer reaches a certain value, both the central and minimum film thicknesses almost stop increasing. Such situation was called a quasi-fully flooded state in this study. It has been found that the amount of the supplied oil for the quasi-fully flooded state differs with the elliptical ratio, and the maximum amount of the supplied oil is required by a circular contact.

Influence of Surface Roughness Wave on Thermal Elastohydrodynamic Lubrication of Involute Spur Gears

There is no perfect smooth surface in project.The elastohydrodynamic lubrication(EHL) oil film thickness between the two meshing gear teeth has the same order of magnitude with the cutting tooth surface roughness height in most cases.So the influence of surface roughness on the EHL of gears should not be ignored in engineering project.A series of sinusoidal waves are assumed on the tooth surface and the lubricant is assumed to be a Newtonian fluid.Based on the multi-grid(MG) method for solving the pressures, the multi-level multi-integration(MLMI) approach for evaluating the elastic deformations, a sequential column sweeping scheme for solving the energy equations, a numerical method for solving the pressures, film thicknesses, and temperatures in the lubricated regions is developed, and the full numerical solutions of involute spur gears are obtained.The influence of tooth surface roughness, thermal effects and transient effects on the EHL is taken into account.The influence of the roughness wave profile on the EHL is discussed.The results show that the tooth surface roughness has strong influence on the oil film pressure distribution and the temperature rise between the contact teeth.A series of roughness waves make oil film pressure and film thickness oscillating, and make the minimum film thickness thinner, the maximum pressure larger and the maximum oil temperature rise higher.So it is more likely to bring out the fatigue failure of the gear teeth.

Influence of Two-Sided Surface Waviness on the EHL Behavior of Rolling/Sliding Point Contacts Under Thermal and Non-Newtonian Conditions

The influence of the transversely and/or longitudinally oriented surface waviness on the lubricating behavior in the rolling/sliding elliptic contact composed of two steel bodies and lubricated with a non-Newtonian lubricant was investigated theoretically with full numerical solution of the thermal elastohydrodynamic lubrication. The entrainment velocity was assumed to be along the minor axis of the Hertzian contact ellipse. The waviness of each surface was given by a sinusoidal function. The non-Newtonian flow of the lubricant was described by the Eyring model with a constant Eyring shear stress at the ambient pressure and temperature. The velocity of the faster surface was assumed to be four times as that of the slower surface in order not only to highlight the thermal and non-Newtonian effects, but also to ensure a cyclic solution when both surfaces were with transversely oriented waviness. Starting from a quasisteady solution, the cyclic time-dependent solution was achieved numerically time step by time step. The results show that the thermal and non-Newtonian effects can be enlarged significantly by the surface waviness, and the worst configuration of the surface topography is that both surfaces are with longitudinal waviness.

Thermal Elastohydrodynamic Lubrication of Point Contacts Using a Newtonian/Generalized Newtonian Lubricant

The classical ElastoHydroDynamic (EHD) theory assumes a Newtonian lubricant and an isothermal operating regime. In reality, lubricating oils do not behave as perfect Newtonian fluids. Moreover, in most operating conditions of an engineering system, especially at high speeds, thermal effects are important and temperature can no longer be considered as constant throughout the system. This is one reason why there has always been a gap between numerical results and experimental data. This paper aims to show that this gap can be reduced by taking into consideration the heat generation that takes place in the contact and using appropriate rheological models. For this, a unique thermal ElastoHydrodynamic lubrication model is developed for both Newtonian and non-Newtonian lubricants. Pressure, film thickness and traction results are then compared to their equivalent isothermal results and experimental data. The agreement between thermal calculations and experiments reveals the necessity of considering thermal effects in EHD models.

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.

Thermal elastohydrodynamic lubrication of rolling/sliding line contacts using a mixture of Newtonian and power law fluids

Thermal elastohydrodynamic lubrication (EHL) behaviour of rolling/sliding line contacts is investigated numerically using a mixed rheological fluid model. The lubricant used is a homogeneous mixture of Newtonian base oil and power law fluid with varying volume fraction, viscosity ratio (VR), and power law index. The velocity distribution across the fluid film for the mixed rheological fluid model is obtained using perturbation method to derive Reynolds and mean temperature equations. The TEHL characteristics computed for the mixture are found to depend upon the effective viscosity of the lubricant which, besides thermal effect, is governed by the superposition of shear thinning and piezo-thickening effects of the non-Newtonian fluid additive. Thermal effect is found to be a function of additive volume fraction, VR, and power law index. The mixtures yield thicker fluid films along with an increase in coefficient of friction in most of the cases. Therefore, a judicious selection of additive fluid with an appropriate volume fraction is recommended in order to achieve fairly thick fluid films at tolerable levels of friction.

Influence of Solid Body Temperature on the Thermal EHL Behavior in Circular Contacts

In order to investigate the influence of the body temperature of contacting solids on the lubrication performance of machine components, such as gears and roller bearings, a full numerical solution for the thermal elastohydrodynamic lubrication (EHL) problem in circular contacts under steady state has been achieved. The analysis assumed that the body temperature is different from the temperature of the supplied lubricating oil. The effects of the body temperature, the slide-roll ratio, and the velocity parameter have been discussed. Results show that if the entrainment velocity is not very high, the solid body temperature plays a dominant role in the EHL behavior; however, the influence of the body temperature decreases as the entrainment velocity increases.

Analysis on the thermal elastohydrodynamic lubrication of tapered rollers in opposite orientation

Faced to the lubrication of the meshing teeth of helical gears, thermal elastohydrodynamic lubrication (TEHL) of two tapered rollers located in opposite orientation was studied numerically. It has been found from the full numerical solution that the lubricating performances of two tapered rollers differ significantly from that of a finite line contact. For tapered rollers, the distributions of pressure and film thickness depend strongly on the distribution of the effective radius in the direction of the roller length, and the distribution of temperature rise depends strongly on the local slide-roll ratio in the direction of the roller length. Side-leakage is inevitable in the elastohydrodynamic lubrication (EHL) of two tapered rollers, and thin films are produced in the ends by side-leakage, but the high pressures in the ends could be decreased by the end-shape modification, which is beneficial to the end lubrication. The temperature distribution is interesting, and the lowest temperature in the high-pressure area is close to the ambient temperature, which occurs in a place where the local slid-roll ratio is zero.

A study on starved micro-thermal elastohydrodynamic lubrication in simple sliding circular contacts

Numerical analyses based on Newtonian and Eyring fluid models are carried out to simulate the effects of inlet oil starvation in thermal elastohydrodynamic lubrication (TEHL) point contacts. It is assumed that the surface with transverse roughness is stationary and smooth surface is moving. Results of smooth TEHL contacts based on Newtonian fluid model are also presented as a reference. It is found that the temperature in the oil film increases suddenly at the inlet meniscus like the pressure build-up because of the discontinuous oil film at that boundary. The increasing degree of the inlet starvation raises the average temperature in the oil film for both smooth and rough contacts. The Newtonian maximum pressure and temperature for the rough contact occur at the macroscopic horseshoe-shaped constriction. Those of the Eyring fluid model still locate at the contact centre. As the degree of oil starvation increases, the differences in the pressure and film thickness distributions in rough elastohydrodynamic lubrication contacts between the Newtonian and Eyring fluid flow models decrease.

Elastohydrodynamic modelling of heat partition in rolling-sliding point contacts

This article presents the results of a series of thermal elastohydrodynamic lubrication (EHL) analyses of a set of disc experiments carried out by Patching et al. The authors have previously calculated the heat partition at each load stage fromthe experimental data, and the present work seeks to compare the heat partition developed in a thermal EHL analysis of the lubricant film with that calculated from the experiments. These EHL analyses show that the heat partition depends on the non-Newtonian formulation used. Only when the dissipation takes place by wall slip occurring at the faster moving surface do the heat partition results approach those determined from the experimental results. It is concluded that this combination of experimental heat partition results with associated EHL analysis can prove to be a much more discerning test of rheological behaviour in EHL contacts than is provided by measurement of traction.

Thermal elastohydrodynamic lubrication characteristics of couple stress fluids in rolling/sliding line contacts

A mathematical model is developed to analyse the effect of polymer additives on thermal elastohydrodynamic lubrication (EHL) behaviour under heavily-loaded rolling/sliding line contacts. The lubricant is assumed to be couple stress fluid and a non-dimensional couple stress parameter represents the molecular length of the additives. The Reynolds and mean temperature equations for the couple stress fluid (CSF) are derived using the rheological relationship presented by Stokes. The thermal EHL characteristics computed for polymer modified oils are found to have a strong dependence on the couple stress parameter. Polymer additives are shown to cause a significant increase in fluid-film thickness along with a noteworthy reduction in the coefficient of friction without any rise in fluid pressure. In addition, the polymer additives are found to cause a minimization of the thermal reduction in the fluid-film thickness as a well as decrease in fluid temperature, particularly under low speed-high load conditions, where fluid films are quite thin. These improvements are desirable in situations involving continuously varying slide to roll ratios, e.g. in gears.