Thermal effects in elastohydrodynamic lubrication of line contacts using a non-Newtonian lubricant

A Reynolds' equation, using Winer's viscoplastic model to express the non-Newtonian fluid property, is derived for line-contact EHL problems. The numerical solutions are obtained to the incorporated Reynolds', elasticity, and energy equations for pressure, film thickness, and temperature distribution between two surfaces simultaneously having rolling and sliding motions. The results are presented for thermal non-Newtonian lubrication, to observe the difference between Winer's equation and Trachman's expression on temperature distribution, pressure, and film thickness. The variation in friction coefficient with slip shear rate is in agreement with other experimental data.     

Grease lubrication in isothermo-elastohydrodynamic line contact

Elastohydrodynamic analysis is conducted and a numerical solution is presented for the film thickness in grease lubrication in isothermal, fully-flooded rolling line contact with or without slip. By making use of a perturbational method, a modified Reynolds equation is established, which can be used with various constitutive equations if the equivalent viscosity can be expressed as a function of the shear rate. Verification of this analysis is carried out by experimentally determining the minimum film thickness with an X-ray transmission technique, with satisfactory agreement. The effect of temperature on the apparent viscosity of grease is also discussed.     

Analytical model for the thermo-hydrodynamic behaviour of a thin lubricant film

The thermo-hydrodynamic behaviour of lubricant films strongly depends on the operating conditions (pressure, speed), on the physical properties of the lubricant, on the temperature level and, furthermore, it is often nonlinear. The thermo-hydrodynamic study of a thin fluid film confined between two parallel planes on relative motion is presented in this paper. The case considered is that of not fully developed thermal conditions and physical properties of the lubricant independent of temperature. A 2D analytical solution is proposed to determine the temperature distribution. The physical parameters affecting the characteristic length, beyond which the flow becomes thermally developed, are determined.     

Analytical model for predicting friction in line contacts

This paper presents the development of an analytical model for the prediction of the friction coefficient in line contacts under thermal elastohydrodynamic lubrication (TEHL). A new theoretical equation is deduced for determining the friction coefficient, taking into account the rheology of common lubricants under TEHL. This approach also considers the heat generated and its penetration into the bulk of the contacting solids. Therefore, the increase in temperature and ensuing variations in the operating conditions are determined. In order to illustrate the use of the new model and verify its accuracy, an experimental stage is performed in a tribological test rig. The predictions of the proposed model are compared with the results obtained in the test rig and other data reported in the literature for diverse lubricants, showing a good agreement in every case. © 2015 The Authors Lubrication Science published by John Wiley & Sons Ltd.     

Calculation of Stribeck curves for line contacts

A mixed lubrication model is presented by which Stribeck curves can be calculated. By means of the Stribeck curve the transitions from boundary lubrication to mixed lubrication and the transitions from mixed lubrication to elasto-hydrodynamic lubrication can be predicted and subsequently the lubrication regime in which a particular contact operates can be predicted. Calculations are restricted to line contacts, because of the wide range of applications of line contacts or of very wide elliptical contacts.     

Thermal effect in hydrodynamic lubrication of line contacts-Piezoviscous effect neglected

Thermal effect in high-speed rolling element bearings has been investigated numerically following a computationally efficient method developed by Elrod and Brewe [11. Viscous shear heating effects on both film thickness and rolling friction are investigated for a line-contact geometry assuming fully flooded lubrication. Thermal load-carrying capacity and rolling friction of the line contact have been numerically calculated for varying rolling speeds from 5 to 40 m/s and dimensionless film thickness between 10⁻⁴ and 10⁻³. Results indicate marked influence of viscous shear heating on the load-carrying capacity, film thickness and rolling traction at high rolling speeds. Neglecting thermal effect at high rolling speeds would lead to gross overestimation of load capacity, film thickness and traction. Results are presented for pressure and temperature distribution within the contact for various rolling speeds and film thicknesses.     

Reduced order finite element model for elastohydrodynamic lubrication: Circular contacts

This paper presents an extension of the reduced order finite element model to the case of circular elastohydrodynamic lubricated (EHL) contacts under isothermal Newtonian considerations. The line contact model was developed and validated in a previous work (Advances in Engineering Software, 2013; 56:51−62). The model is based on a finite element discretization of the EHL equations: Reynolds, linear elasticity and load balance with a reduced order model for the linear elasticity part. All equations are solved simultaneously in a fully-coupled framework using a damped-Newton procedure allowing fast convergence rates for the global solution. This model combines fast convergence rates, reduced memory requirements and negligible model reduction errors compared to the full model which makes it an attractive tool for EHL contact performance prediction.     

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.     

Compliant-poroelastic lubrication in cartilage-on-cartilage line contacts

ABSTRACT

The mechanisms of friction in natural joints are still relatively unknown and attempts at modelling cartilage-cartilage interfaces are rare despite the huge promise they offer in understanding bio-friction. This article derives a model combining finite strain, porous and thin-film flow theories to describe the lubrication of cartilage-on-cartilage line contacts. The material is modelled as compliant and poroelastic in which the micro-scale fibrous structure is interstitially filled with synovial fluid. This fluid flows over the interface between the bodies and is coupled to pressure generated by relative motion in the thin-film region formed under load. A Stribeck analysis demonstrated that this type of contact is determinable to conventional elastic lubrication but that the friction performance is improved by this interfacial flow. Moreover, the inclusion of periodic flow conditions when contact is onset is a specific novelty which elucidates new observations in the lubrication mechanisms pertaining to natural joints.     

Multilevel solution for thermal elastohydrodynamic lubrication of rolling/sliding circular contacts

A fast multigrid approach is presented for the analysis of thermal elastohydrodynamic lubrication (EHL) under rolling/sliding circular contacts at high loads and high slip ratios with low computing time on a personal computer. This fast solver combines directiteration, multigrid, Newton-Raphson, Gauss-Seidel iteration, and multilevel multi-integration methods into one working environment that can reduce the computational complexity from O(n³ to O(nlnn) for the thermal EHL problem under rolling/sliding circular contacts. Since the couped Reynolds and energy equations are simultaneously solved by the Newton-Raphson scheme, the iteration for the convergence solution is less than those of the classical approach. Results show that thermal effects on the pressure profile and film thickness are significant for a wide range of loads, speeds and slip ratios. The maximum midfilm and surface temperature rise in the Hertzian contact region increases with increasing slip ratio, dimensionless speed, and load. The minimum film thickness decreases with increasing load and slip ratio, and decreasing dimensionless speed.     

Inverse approach for calculating pressure and viscosity in elastohydrodynamic lubrication of line contacts

This paper proposes an inverse approach which generates a smoothed pressure distribution based upon a small number of measuring points of the film thickness and overcomes the problems of pressure fluctuations. The Reynolds equation of line contacts is then employed to determine the value of the pressure–viscosity index. To investigate the sensitivity of the results to measurement errors, different errors are deliberately implemented in the numerical calculations. Results show that the traditional direct inverse method requires many measuring points of film thickness to establish the amplitude and location of the pressure spike, but the inverse approach can obtain accurate results using just 29 measuring points. When errors in the film thickness measurements, it is found that the inverse approach still yields a reasonably smooth curve for the pressure profile. When film thickness measurement errors are excluded, the proposed approach is very close to the exact value of the pressure–viscosity index. Even when errors in the film thickness are deliberately introduced, the inverse approach still provides a satisfactory value of the pressure–viscosity index. The resulting apparent viscosity errors are much smaller than those generated when using the direct method. The implemented errors in load and effective elastic modulus have a significant effect on the accuracy of the results, but that the influence of errors in average velocity and in the viscosity at ambient pressure is insignificant. In these implemented errors, the resolution of the film thickness measurement plays the most important role in determining the accuracy of the apparent viscosity.     

Numerical multilevel investigation for the evaluation of pressure distribution in ehl circular contacts from film thickness measurements

An analysis of circular contacts under elastohydrodynamic lubrication using a hybrid technique is presented. In particular, attention has been focused on the pressure distribution calculation. A versatile code has been developed to evaluate the pressure distribution starting from three‐dimensional film thickness maps obtained from the analysis of interferometric images. The code has been developed in C++ and is based on the multigrid technique. This hybrid technique has a basic advantage over the full numerical approach in that the pressure is obtained without making any assumptions about the lubricant itself. The main drawback of the method is that high‐resolution interferometric images are required.     

Effectiveness of lubricant additives for copper‐alloy‐steel sliding contacts

A selection of additives and their performance and compatibility with a variety of copper alloys have been evaluated in an SRV test set‐up. The tests show a remarkable variation of tribological behaviour with a clear relation to both the type of lubricant / additive and the type of alloy. One ester‐based additive showed outstanding friction and wear reduction for some groups of copper alloys. In order to better understand the fundamental mechanisms, we applied a variety of surface analyses, such as 3D confocal white light microscopy, scanning electron microscopy and X‐ray photoelectron microscopy. Copyright © 2010 John Wiley & Sons, Ltd.     

Friction properties of perfluorinated polyethers for hot‐dipped tin low‐level separable electrical contacts

Tin coatings are used as a final protection for cuprous substrates involved in low‐level electrical contacts. High friction forces and fretting phenomena remain a cause of electrical failure of connector terminals, and so should be minimised. A lubricant layer can improve the life and reliability of connector terminals but such a layer must ensure low and stable resistance values even under severe temperature conditions. Work has been undertaken to investigate the lubricant layer most suitable for the protection of tinned electrical contacts. Perfluorinated polyethers (PFPEs) were chosen for their inertness. The aim was to correlate various physico‐chemical properties of branched or linear PFPEs, with their frictional and electrical properties. The long‐term electrical properties of a contact are shown to be linked to the initial wear mode in the contact.     

Amplitude reduction in EHL line contacts under rolling sliding conditions

Surface roughness plays an important role in the performance of highly loaded elastohydrodynamically lubricated contacts. As the pressures are very high, each of the surface roughness components deforms differently, and as a result the roughness inside the highly loaded contact is different from the measured roughness. Under pure rolling conditions the amplitude reduction theory describes the waviness deformation as a function of wavelength and operating conditions. The current work suggests that similar predictions are possible under rolling sliding conditions, provided that the wavy surface velocity u₂ exceeds the smooth surface velocity u₁. For u₂<u₁ the maximum value of A_d/A_i depends on the slide to roll ratio and may be significantly less than 1.0.     

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.     

Influence of polymeric fluid additives in EHL rolling/sliding line contacts

The effect of polymeric fluid additives on EHL behavior of rolling/sliding line contacts is investigated numerically at low as well as high loads. The polymer-modified oil is represented by a homogeneous mixture of Newtonian base oil and power law fluid with varying concentration, viscosity ratio and power law index. The Reynolds equation incorporating the mixed rheological fluid model is derived using perturbation method. The EHL characteristics computed for polymer-modified oils are found to depend upon the effective viscosity of the lubricant mixture which is governed by the superposition of shear thinning behavior and piezo-thickening effect of the polymeric fluid additive. Since the reference viscosity of polymeric fluid additives is much higher than that of base oil, therefore, polymer-modified oils are shown to yield thicker fluid films in most of the cases. The results show a significant variation in maximum fluid pressure and minimum fluid film thickness with the volume fraction, reference viscosity ratio and power law index of the polymeric fluid additive.     

Computational fluid dynamics and full elasticity model for sliding line thermal elastohydrodynamic contacts

Classically, the EHD problem is solved using the Reynolds assumptions to model the fluid behaviour, and the Boussinesq elastic deformation equation to model the solid response, both being coupled with the load balance equation. The development of an alternative approach is presented here in order to solve at once the Navier-Stokes equations (mass conservation and momentum equilibrium), the full elasticity and energy equations for the line EHD problem in a fluid-structure interaction approach.The Finite Element Method is used to solve the mathematical formulation in a fully coupled way, inspired from Habchi et al. (2008) [1]. After linearisation with the Newton procedure, all the physical quantities (pressure, velocity field, deformations and temperature) are solved together in a unique system. An important benefit of this approach is the possibility to implement in a simple manner the non-Newtonian and thermal effects; in fact all the quantities can vary through the film thickness. The extension to non-Newtonian rheology and the pressure and temperature dependencies for the viscosity and density are taken into account in a direct way to allow an acceptable prediction of the friction coefficient. Gradients across the film thickness and temperature fields in both the fluid and the two solids are naturally computed and analysed. As a case study, we focus first on the pure sliding cylinder-on-plane contact. It is shown that thermal effects due to friction in the central zone of the contact play a role in heating the lubricant at the inlet zone, via heat conduction in the solids. By increasing the Slide-to-Roll Ratio (SRR), the occurrence of dimples and the subsequent effects in different parts of the contact under zero entrainment velocity conditions are then studied.     

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.