LA EDAD BIOLÓGICA EN ANTROPOLOGÍA FORENSE

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occur within the nominal Hertzian contact zone. This situation is referred to as the mixed lubrication. The concept of mixed lubrication first appeared at the proceedings of the eleventh Leeds-Lyon Symposium on Tribology, with the topic “Mixed lubrication and lubricated wear”. Mixed lubrication occurs between boundary and hydrodynamic lubrication, as the name would suggest. The fluid film thickness is slightly greater than the surface roughness, so there is very little asperity (high point) contact, but the surfaces are still close enough together to affect each other. In a mixed lubrication system, the surface asperities themselves can form miniature non-conformal contacts.

Rough surface EHL and mixed lubrication have been studied in the last decades mainly with two types of approaches. The first is the statistical approach. In the early days of rough surface EHL studies, owing to the limitation of computing abilities and lack of advanced algorithms, some statistical parameters of the surface topography were used to describe the roughness effect on contact performances. This is why this type is called the statistical approaches. Greenwood and Williamson [11] proposed a basic elastic model considering rough surfaces. They based this on the assumption that all asperities can be represented by paraboloids, and calculated the separation of the surfaces, as well as the nominal pressure between two surfaces. This nominal pressure is not the real pressure, but should be interpreted as the average statistical pressure. In their calculations, they gave the asperities a Gaussian height distribution. The model works well when the load is such that the asperity tips of the rough materials are compressed within the elastic limit. Using the G-W model it is important to know its restrictions. One of the most important features of the model is that it is a statistical analysis, and therefore a very large number of asperity contacts are expected within the nominal contact area. Accordingly, the model deals with the part of the roughness spectrum where the wavelengths are small compared with the

contact area. Another assumption made in the GW model is that the asperities deform independently from each other, so the asperities may therefore not merge. The GW model is also extended by others. Greenwood and Tripp [13] extended this model to the contact of two nominally flat rough surfaces, and the Chang-Etsion-Bogy model [57] can separate the plastic and the elastic supported loads, to name a few. Asperity interactions can also be treated with the statistical approach. Johnson et al. [58] used the Fourier series to study a bi-sinusoidal isotropic surface in contact with a flat plate case, while Vergne et al. [59] used an integral formulation of the elasticity theory to study the elastic contact between two and three asperities and a flat plate. Zhao and Chang [60] modelled the asperity interaction in elastic-plastic contact of rough surfaces using the Saint Venant’s Principle and Love’s formula [61]. The average flow model, first proposed by Patir and Cheng [62], is also used extensively. Zhu et al. [63] developed a mixed line contact EHL model, and Zhu and Cheng [64] subsequently studied mixed point contact EHL. In the two studies the metal-to-metal asperity pressure was computed using the GT model. Epstein et al. [65] used an improved flow factor method in a micro-macro approach to study the effect of roughness on the fatigue life in a mixed EHL contact. Reference [66] contains a detailed review on progresses in the area of probabilistic EHL modelling, as well as a review on the most recent EHL studies that utilized probabilistic modelling.

The second approach is the deterministic approach. Owing to the rapid development of computer ability and advanced numerical algorithms, the deterministic approach has been widely used recently. This approach can capture details of asperity deformation and interaction because the roughness information is

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three-dimensional roughness profile. In the case of a heavily loaded line contact, the Hertzian contact width can be wider than 1 mm, while the length of the line contact is several centimeters. A typical measurement performed on an optical profilometer at 1 m lateral resolution gives about 5 MB of double precision data for less than half a square millimetre of rough surface [66]. Despite this, the deterministic approach can provide detailed information inside the nominal contact area, which is a must for a further surface failure analysis.

Key issues encountered when developing mixed EHL models are discussed by Zhu [67]:

i. How to handle surface roughness. Two main approaches are used when dealing with surface roughness: stochastic and deterministic. Stochastic approaches use a small number of statistic parameters to describe the rough surface characteristics and their influences on contact and lubrication. They cannot predict localized details and peak values within nominal contact regions. This information may be directly correlated to surface failures such as micropitting. The other methods are the deterministic approaches, which have drawn more attention in the last twenty years owing to advancements in computer technologies.

ii. How to model surface contact and hydrodynamic lubrication simultaneously. Currently there are two types of models. One simulates contact and lubrication separately with different approaches. For instance, a dry contact model can be used for asperity contact areas and the Reynolds equation applies to the areas where the lubricant exists. In this approach, it may be difficult to determine borders and handle boundary conditions between contact and lubrication areas, especially when random or irregular surface roughness is involved. The other approach is the unified way proposed by Hu and Zhu [4]. This approach based upon the fact that dry contact is a special case of lubricated contact at ultra-low viscosity or ultra-low speed. Therefore,

dry contact can be simulated with lubrication models as long as the numerical solver is sufficiently robust to handle ultra-low viscosity and ultra-low speed.

The progress of mixed lubrication studies mainly relies on the development of knowledge in two fields: an integrative knowledge of fluid film and boundary lubrication, and a sufficient recognition of rough surface interaction.