A direct comparison between experimental and numerical results for the passage of an array of 3D flat-top, square shaped surface features through an EHL point contact is presented. Results for pure rolling conditions show that the features' deformation in the high-pressure region is governed by their ability to entrap lubricant both underneath and in the grooves during their passage through the inlet zone. Film perturbations associated with each defect occur as locally enhanced regions of lubricant and film thickness microconstrictions. Under sliding conditions the features sustain further deformations as they traverse the high-pressure conjunction and meet the highly viscous lubricant entrapped in the grooves, which moves at a different velocity. Lubricant is also seen to accumulate just in front or behind the features depending on the slide-to-roll ratio. Overall, the results highlight the importance of understanding the effects of the defects structure and the lubricant rheology on the film thickness to unravel the effects of real roughness patterns.

Recent experimental observations by Félix-Quiñonez, Ehret and Summers ( Trans. ASME, J. Tribology, 2003, 125, 252–259) for a single, flat-top transverse ridge passing through an elastohydrodynamic lubrication (EHL) point contact under various slide-roll ratios have revealed some unexpected features. In particular, under sliding conditions the ridge was observed to sustain additional deformations in the high-pressure region of the contact and an entrapped amount of lubricant was seen to accompany the ridge during its passage through the conjunction and, contrary to current knowledge, appeared not to move at the entraining velocity. This paper analyses the experimental observations by means of a direct comparison with numerical simulations. The numerical results show that the main contributing factor towards the experimentally observed accumulation of lubricant is a reduced lubricant viscosity via shear thinning effects. For the operating conditions considered in this study, internal heating of the lubricant is found to be negligible. In addition, it is shown that the amount of lubricant accumulation is dependent on the geometry of the ridge. Compared to a defect with a Gaussian shape, it is further shown that a greater accumulation of lubricant occurs with the flat-top ridge due to the generation of larger pressure gradients.

An image analysis technique is employed to measure lubricant film thickness fluctuations introduced by a single flat-top transverse ridge passing under pure rolling conditions through an elastohydrodynamically lubricated contact. The experimental observations are compared with the film thickness profiles predicted by the discrete Fourier transform method for real surface roughness given by Morales-Espejel et al. in 2000. The results show that the theoretical approach adequately predicts the overall film thickness, thus giving credence to its potential practical application. On a local scale, however, important differences are seen regarding the deformed shape of the feature.

The micro-elastohydrodynamic lubrication of a single transverse ridge is revisited using an experimental technique, which combines an optical interferometry technique and a high-speed color video camera. The purpose of this study is to augment prior experimental analyses, by providing a complete and detailed history of the ridge associated with changes in film thickness as it passes through a high-pressure conjunction. An enhanced experimental procedure has been developed to enable an automatic analysis of the interferograms. In particular the methodology allows abrupt changes in film thickness and rapid variations of interference orders to be taken into account. The observations presented in this paper exhibit interesting and fascinating features that have not been previously reported. In particular it is observed that under rolling/sliding conditions the ridge undergoes further deformations as it proceeds to the exit to the contact. In addition, there appears to be an important contribution of pressure flow to the transport of lubricant and, contrary to current understanding, entrapped lubricant is seen to accompany the ridge as it passes through the contact, therefore appearing not to move at the entraining velocity.

For a comprehensive set of lubricants the friction coefficients were determined under very high pressures and shear rates by means of a ball impact experiment. Measurements of the limiting shear stresses were obtained for a large range of pressures, from about 2 to 4GPa, as typically encountered in elastohydrodynamic contacts. It was shown that under these conditions the limiting shear stresses increased less than proportionally with the pressure; i.e. the coefficients of friction were decreasing functions of the pressures. The results were compared with previously reported values from the literature and in general good agreement was obtained.

The numerical developments described in Part 1 are extended to incorporate the consideration of non-Newtonian effects, and fully coupled solutions of the thermal non-Newtonian elastohydrodynamic lubrication point contact problem are presented. The numerical findings are compared with a series of experimental results performed by Cann and Spikes with a steel-sapphire point contact in pure sliding conditions. Fair agreement with the experimental results is obtained in terms of surface temperature. Comparison of the results under identical conditions but with a steel-steel contact is also undertaken and shows that a steel-sapphire contact represents a good simulator of a steel-steel contact in terms of temperature and film thickness. The influence of the viscosity relationship is also considered and reveals that the Yasutomi et al. equation leads to only a marginal difference compared with the Roelands equation for the cases considered.

The assumptions of a quadratic temperature profile and mean viscosity across the film, which are frequently used in the analysis of thermal elastohydrodynamic lubrication (EHL), are examined and discussed. Two different approaches for solving the thermal EHL problem are compared for line contact conditions, namely (a) a one-dimensional model based upon both the assumption of a quadratic temperature profile and the adoption of the mean physical properties across the film and (b) a two-dimensional model which includes changes in temperature and physical properties of a lubricant across the film and which takes into account the conditions of reverse flow and heat convection across the film occurring at the inlet region. A multi-grid algorithm is implemented to solve these two conditions. The temperature profile and the general solutions in the conjunction obtained in both approaches are compared. For the one-dimensional model, results reveal that temperature peaks just prior to the inlet of the conjunction. This feature is not apparent in the two-dimensional model and results in lower values in film thickness and larger frictional coefficients than in the two-dimensional model. In the high-pressure region, both equations yield almost the same mean temperature.

The development of a new ball impact apparatus for the measurement of the traction behaviour of solidified lubricants is described. The normal and tangential forces between an oily plate and an obliquely impacting ball were measured directly on two different forms of apparatus by means of piezoelectric transducers. From the measured forces the coefficient of friction during impact could be calculated. For one particular oil, Santotrac 50, a full set of results is given and these are shown to be in good agreement with values reported previously by others using different forms of experimental equipment.

A range of industrial processes involve the spreading of thin layers of liquid or molten polymeric materials that subsequently solidify. Their function may be: to form a protective barrier; to give added value to a particular product (magnetic/optical storage media, etc.); the production of laminates, tapes, sheets ([5], [7], [8], [12]). Their quality depends ultimately on the homogeneity of the resultant polymer film or surface covering.

The formation of Kaneta's dimples are investigated under different sliding conditions using a high-speed video camera. Of interest is the observation of an unstable regime in which trains of dimples are formed and propagate throughout the high-pressure conjunction at regular intervals while the running conditions are steady. This study shows that such a situation can be associated with a type of stick-slip phenomenon in which adherence at the wall is periodically lost. A simple time-dependent model is developed to validate this concept. The model extends the consideration of interfacial slip previously proposed and accounts for a periodic variation in slip with time. The results reveal that such a condition effectively allows trains of single dimples to move throughout the conjunction. A refined modelling of the conditions at the wall/lubricant interface is, however, required in the future if a better understanding of the conditions which trigger such instabilities is to be obtained.

Solutions of the thermal elastohydrodynamically lubricated point contact problems are presented for both low and high Peclet number conditions. The surface temperatures are calculated using the full expression of the moving heat source equation given by Carslaw and Jaeger. Of interest is the potential of the method to predict solutions for pure sliding conditions in which one surface velocity is zero. The energy equation is treated as a two-dimensional problem by approximating the variation in temperature across the film with a quadratic profile. To solve the strongly non-linear set of equations which govern the problem a relaxation scheme is proposed which takes advantage of the weak coupling between the Reynolds equation and energy equation in the high-pressure region of the contact. The iterative process corresponds to a two-stage process in which pressure and temperature are relaxed independently. The numerical scheme provides a stable and fast convergence and has the added advantage of allowing the isothermal relaxation schemes for pressure previously developed to be reused.

Simulations are carried out of an experimental procedure in which a ball impacts a thin layer of lubricant on a disk to form a dimple of entrapped lubricant. Thereafter pure sliding conditions are imposed to release the entrapped lubricant from the contact. Conditions of slip between the core of the lubricant and the wall are investigated to explain the slower release of the lubricant observed in pure sliding conditions when the ball alone is in motion. A slip value up to 63 per-cent at 1 GPa enables numerical simulations to match the time of release of the entrapped lubricant measured experimentally.

A multigrid scheme is presented for solving the set of equations which governs the thermal EHL problem. The formulation of the problem is based upon the consideration of the lubricant as a Newtonian fluid, and the assumption of a parabolic profile of temperature of the lubricant across,the film. The numerical procedure proposed extends a thermal formulation developed by Lee et al [1] to analyse elliptical contacts with spin effects. An alternative numerical scheme is developed which builds upon the recent advances made to solve the isothermal problem, providing a high level of discretisation and a robust convergence for a large range of loads, and entraiment velocities. Results confirm that increase in pressure, entraiment velocity, piezo-viscosity index, slide/roll ratio and spin leads to a substantial increase in temperature in the high pressure region. The present Newtonian approach predicts remarkable high temperatures across the film. A more accurate estimate of the energy loss within the contact requires, however, the development of a non-Newtonian formulation and the present work represents a step towards this ultimate objective.

The development of understanding of the phenomenon of elastohydrodynamic lubrication (EHL) throughout the twentieth century is reviewed. The development of solutions for both line and point contacts is considered for both fully flooded and starved conditions. Particular attention is given to the introduction of non-Newtonian rheological models and numerical methods. Progress in the analysis of impact and general non-steady-state conditions is reviewed, together with the consideration of rough surface and micro-EHL. Attention is drawn to the need to consider realistic models of real surfaces and real fluids in future studies.

New numerical results, based upon the concept of solidification, are produced which match the intriguing dimple observed by Kaneta in elastohydrodynamic lubrication of point contacts under pure sliding conditions. It is shown that Kaneta's dimple is consistent with transport conditions of a solidified lubricant in the high-pressure region of the conjunction. The difference of velocity between the average velocity of the solidified core and the mean entraining velocity is referred to as 'slip'. The value of slip is shown to be related to the stress at the wall, which is deduced from the limiting shear stress.

The effects of various surface textures, described either by an orientated waviness or an uniform distribution of asperities, are compared under pure rolling conditions for elastohydrodynamic lubricated point contacts. Time-dependent solutions, obtained with a Multigrid Multi-Integration method, reveal that the orientation of the waviness, in these conditions, has only a moderate effect on the values of minimum film thickness and maximum pressure. These results are in contrast to those obtained under pure sliding conditions, where the orientation of the surface texture leads to important differences in terms of minimum film thickness. In pure sliding, it is shown that the best lubrication condition is produced for the transverse waviness.

A multigrid multi-integration method has been used to solve the elastohydrodynamic lubrication (EHL) point contact problem over a large range of loads. Solutions obtained with the multigrid method are compared with those computed with an effective influence Newton method. Good agreement has been obtained, which validates the results obtained by both of these independent methods. Smooth surface problems have been used to test the multigrid method, but an example that takes into account a wavy surface has demonstrated the robustness and the large potential of the multigrid method to analyse EHL problems with three-dimensional surface roughness.

In recent years, EHL point contact analysis has greatly benefited from the development of new numerical techniques. Amongst these, the multigrid multi-integration method has opened real perspectives not only in simulations of smooth surface contacts, but also in the consideration of rough surfaces and transient effects. Brandt [1], Lubrecht [2] and Vernier [3] have demonstrated the quality of such a solver, which allows high levels of discretisation, and enhances stability and robustness. Using this technique, an investigation on the effect of waviness orientation in EHL point contacts under high load situations has been carried out. Pure sliding is considered and the waviness is placed on the stationary surface. Under severe loading conditions the maxima of waviness are largely flattened and large pressure ripples are produced. The orientation of the waviness strongly influences the behaviour of the flow at the entrance of the contact, which in turn considerably effects the deformation of the surfaces inside the contact area. Leakage flows and accumulation of lubricant at the inlet introduce surface constrictions and grooves, which propagate all along the contact in the direction of the flow. Results show that the transverse waviness presents the best lubrication capability. The lowest minimum film thickness is obtained when the waviness is orientated at about 60° compared to the direction of the surface velocity.

This paper deals with the modelling of viscoelastic flows in transient regimes using the Modified Phan Tien and Tanner (MPTT) model. This model is the most recent one which can predict stress overshoot in unsteady shear flow and is based on the description of the liquid microstructure rather than empirical and mathematical developments. Here, the analysis of the squeeze between parallel plates ir Presented it is an alternative in quantifying and understanding the two main factors which may enhance the carrying capacity (inertia effect and viscoelastic behavior) situation which can occur, for instance, in the case of overloading in journal bearings. A boundary element methods is used here to model such complex flow. The main factors have been extracted and the restrictions due to a rough estimate of the lubricants flow are shown.

The study of bearings subjected to impulsive loads have previously showed that inertia effects and surface accelerations play an important role in the bearing response. Although the lubricant was considered Newtonian, this assumption is no longer valid with modern lubricant. In industrial applications, mineral lubricants are added to several long soluble chains of polymer in order to conserve optimum properties under different operating conditions. The addition of these polymers results in the drop of viscosity under high shear-rate, in the range of 10−6–10−8s−1. This study presents a continuation of previous works. It examines the influence of both effects, the decrease in viscosity and the fluid inertia, in a journal bearing under impulsive loads. Using the power-law model, the results show important differences in shaft responses compared to the Newtonian cases. Furthermore, in high shear-thinning effects, a reduction of lubricant capacity to absorb sudden dynamic loads is observed.