A.A. Lubrecht

Film Thickness in Starved EHL Point Contacts

This paper presents a numerical study of the effects of inlet supply starvation on film thickness in EHL point contacts. Generally this problem is treated using the position of the inlet meniscus as the governing parameter; however, it is difficult to measure this in real applications. Thus, in this paper an alternative approach is adopted whereby the amount of oil present on the surfaces is used to define the degree of starvation. It is this property which determines both meniscus position and film thickness reduction. The effect of subsequent overrollings on film thickness decay can also be evaluated. In the simplest case a constant lubricant inlet film thickness in the Y direction is assumed and the film thickness distribution is computed as a function of the oil available. This yields an equation predicting the film thickness reduction, with respect to the fully flooded value, from the amount of lubricant initially available on the surface, as a function of the number of overrollings n. However, the constant inlet film thickness does not give a realistic description of starvation for all conditions. Some experimental studies show that the combination of side flow and replenishment action can generate large differences in local oil supply and that the side reservoirs play an important role in this replenishment mechanism. Thus the contact centre can be fully starved whilst the contact sides remain well lubricated. In these cases, a complete analysis with a realistic inlet distribution has been carried out and the numerical results agree well with experimental findings.

Numerical Simulation of a Transverse Ridge in a Circular EHL Contact Under Rolling/Sliding

This paper investigates the influence of a transverse ridge on the film thickness in a circular EHL contact under rolling/sliding conditions. It is a numerical simulation of the optical EHL work of Kaneta et al. (1992). One of the purposes of this investigation is to check the validity of the algorithm and the Newtonian, isothermal lubricant assumption for film thickness predictions under these conditions (ph = 0.54 GPa). It will be shown that, both quantitatively, the film thickness on the central axis Y = 0, and qualitatively, the film thickness profile through “pseudo interference graphs”, the agreement between experiment and Newtonian isothermal theory is good. This supports the argument that the rheological and the thermal behavior of the fluid only slightly influence the film thickness and pressure distribution of the lightly loaded non-smooth contact case.

Transient Analysis of Surface Features in an EHL Line Contact in the Case of Sliding

This paper investigates in detail the influence of two different surface topographies on the pressure distribution and film thickness profile of a highly loaded (maximum Hertzian pressure 2 GPa) line contact as a function of the slide to roll ratio. To accomplish this the transient Reynolds equation is solved both in space and time. The first feature under investigation is localized, a so-called indentation, the second one is global: waviness. The observed lack of synchronism in the extremes of pressure and film thickness is explained theoretically by analyzing the Reynolds equation

Numerical analysis of the influence of waviness on the film thickness of a circular EHL contact

Surface roughness and/or surface imperfections are well known to significantly affect the performance of concentrated contacts. Any deviation from the smooth surface will act as a stress raiser for itself (bump) or of its neighborhood (dent), and will therefore reduce the fatigue life of the component it is part of. These imperfections can also act as initiation sites of other types of contact failure such as scuffing, when contact conditions such as load, speed and film thickness become more and more severe. With the help of increasing computer speeds and more efficient numerical techniques, a theoretical analysis of the failure of concentrated contacts becomes possible. The full answer will involve many aspects of the contact, including the generation of heat, thermal response of the lubricant and solids, non-Newtonian as well as surface chemistry effects. This paper concentrates on the way the lubricant film thickness is affected by waviness and tries to identify the locations and the conditions where the film thickness is minimal. The lubrication ofnonsmooth surfaces is a transient two-dimensional problem, which will be treated without any geometrical simplification. More precisely, this paper focuses on the influence of rolling speed and the slide-to-roll ratio on the film thickness separating a smooth surface and one with transverse waviness.

Starved Lubrication of Elliptical EHD Contacts

This paper focuses on the lubrication behavior of starved elliptical Elasto-HydroDynamic (EHD) contacts. Starvation is governed by the amount of lubricant available in the inlet region and can result in much thinner films than occurring under fully flooded conditions. Therefore, it would be desirable to be able to predict the onset and severity of starvation and to be able to relate film reduction directly to the operating conditions and lubricant properties. The aim of this work is to explore the influence of these parameters on starvation. A combined modeling and experimental approach has been employed. The numerical model has been developed from an earlier circular contact study [1]. In this model, the amount and distribution of the lubricant in the inlet region determines the onset of starvation and predicts the film decay in the contact. Numerical simulations for a uniform layer on the surface show that a single parameter, characteristic of the inlet length of the contact in the fully flooded regime, determines the starved behavior. Film thickness measurements under starved conditions were performed to validate this theory. For a circular contact excellent agreement was found. In theory the same mechanism applies to elliptic contacts, however, the behavior is more complicated.

Elastohydrodynamic lubrication of rough surfaces

Abstract The detailed understanding of elastohydrodynamic lubrication (EHL) with rough surfaces has become an important problem as the ratio of film thickness to surface roughness is decreasing. Recently it has been recognized that the roughness inside an EHL contact might be different from the roughness outside the contact owing to elastic deformation. As will be explained in this paper, a first step in understanding the deformation of a real rough surface is the detailed knowledge of the amplitude reduction of harmonic features, which forms the topic of this paper. For the line contact problem it is shown that the deformed amplitude of a harmonic feature (waviness) depends on the original amplitude of the feature, its wavelength and the contact operating conditions, including the slide-roll ratio. The amplitude reduction can be completely described by a single dimensionless parameter. For the point contact problem it is shown that the deformed amplitude of isotropic waviness depends on the original amplitude of the feature, its wavelength and the contact operating conditions. Once again, the amplitude reduction can be completely described by a single dimensionless parameter. The presented relations for line and circular contact can be used as a basis for a modified Λ parameter predicting the relation between the real ratio of film thickness to amplitude inside the EHL contact. A numerical example of the calculation of the deformation is given.

Amplitude Reduction of Waviness in Transient EHL Line Contacts

The problem of surface waviness in ElastoHydrodynamic Lubrication is commonly considered as a first step towards understanding the lubrication of rough surfaces. Both problems are generally transient. The current paper investigates the deformation of sinusoidal waviness in the contact, more precisely it studies the amplitude reduction of one-sided waviness in a transient EHL line contact. The film thickness amplitude at X = 0 is called A d (deformed amplitude). It is shown that for waviness amplitudes smaller than the film thickness A i H c , the ratio A d / A i is independent of the undeformed amplitude A i . In other words: for small amplitudes the deformed amplitude depends linearly on the initial amplitude A i . Rather surprisingly, the same behaviour is found for A i > H c . The results show that qualitatively waviness with short wavelengths λ/ b A d ≃ A i . Long wavelengths on the contrary, disappear nearly completely: A d ≪ A i thus A d / A i ≃ 0. However, quantitatively the amplitude reduction was found to depend also on the contact operating conditions. With a generalized coordinate ∇, instead of λ/ b , the relative amplitude A d / A i can be described by a single function of ∇ for all operating conditions: A d / A i = F (∇),∀( M, L ). A possible way of expressing ∇ is:∇ = λ/ bM 3/4 / L 1/2 .

Amplitude reduction of non-isotropic harmonic patterns in circular EHL contacts, under pure rolling

Surface roughness plays an important role in ElastoHydrodynamically Lubricated contacts, a role which is currently only partially understood. Recent work on waviness in EHL line contacts has shown and quantified the elastic deformation of the waviness inside the contact as a function of a single dimensionless parameter. In the present paper this work is extended to the circular contact problem. First it is shown that the amplitude reduction of an isotropic harmonic pattern can also be described as a function of a single dimensionless parameter. Subsequently, the effects of anisotropy are investigated varying from purely transverse to purely longitudinal. It is shown that one can create a single curve for the case varying from isotropic to longitudinal, and another for the case varying from isotropic to transverse. Both curves can be combined in a single formula.

Multigrid techniques: a fast and efficient method for the numerical simulation of elastohydrodynamically lubricated point contact problems

Abstract The introduction and further development of algorithms based on multigrid (multilevel) techniques has resulted in fast and efficient solvers for elastohydrodynamically lubricated (EHL) point contact problems. As a result the capability to simulate steady state and transient point contact problems numerically has greatly increased in the past decade. This has led to an increased understanding of the mechanisms controlling film formation and pressure in the contact in relation to the operating conditions. In this article an overview is given of the essential ingredients of an efficient multigrid algorithm for an EHL point contact problem. Results are presented for some characteristic problems that illustrate todays numerical simulation capability. It is concluded that, with respect to EHL, one of the main questions of the last part of the century has been answered, i.e. how to solve efficiently the modelling equations such that realistic and highly loaded situations can be simulated. The challenge that researchers and engineers now face is how to translate the new insights into simple rules for design and engineering, and to establish clearly the limits of validity of the models that are used in simulations both on the scale of the contact as a whole as well as on a subcontact scale.

Pressure profiles measured within lubricated contacts in presence of dented surfaces. Comparison with numerical models

In this paper, dented contacts have been studied in an EHL ball on disk device under pure sliding conditions. Dents with diameter of half the Hertzian contact radius were positioned in the center of the contact. The measured pressure profiles, obtained from Raman microspectrometry, are very different from those expected. A huge pressure peak is observed at the place where the lubricant leaves the dent, leading to very high pressure gradients. The effect of the dent shoulders is also visible. These results are discussed and compared to numerical ones. Finally, some consequences on life prediction of dented surfaces are presented.