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Francesco Bottiglione - Research Interests
Dr. Bottiglione's research interestes are in the fields of:

Contact Mechanics and Seals

Theories of contact between rough surfaces in elastic regime

Theory of contact mechanics between randomly rough elastic surfaces is an unsolved problem yet, that is still the object of a large scientific debate. A correct knowledge of the topological and mechanical properties of the contact between real surfaces, and the possibility to forecast such properties are, indeed, of fundamental importance for applications (electrical and heat conduction, contact seals, friction, …).

Figure 1: Schematic of multi-asperity contact as in the original idea of Greenwood and Williamson, 1966.

A comparison between some of the most relevant theories has been carried on: the multi-asperity contact theories, based on the original idea of Greenwood and Williamson of 1966 (GW) and the Persson’s theory of contact mechanics. A property of the contact between elastically deformable randomly rough surfaces, which has been verified with both experimental and numerical approaches, is the proportionality between the actual area of contact and the external applied load for small loads. Both asperity contact models and Persson’s theory predict a linear relation between the area of true contact and the applied external load, but the two theories differ for the constant of proportionality.

Figure 2: The non dimensional contact area as a function of the non dimensional applied squeezing load. Persson’s theory of contact mechanics (red curve) and its asymptotic law at small loads (dashed red line) approache very well up to 30% the nominal contact area and the result does not depend on the parameter α. The behaviour of asperity models is qualitatively in agreement with the GW-C model here shown (black line) with its asymptote (black dashed). The asymptotic law approaches the full calculation only at vanishingly small loads and the results are deeply affected by α.

 

However, this is not the only difference between the two approaches. Indeed, the fully calculated predictions of asperity contact models very rapidly deviates from the predicted linear relation already for very small and in many cases unrealistic vanishing applied loads and contact areas. Moreover, this deviation becomes more and more important as the PSD breadth parameter  α (as defined by Nayak) increases. Therefore, the asymptotic linear relation of multiasperity contact theories turns out to be only an academic result. On the contrary, Persson’s theory is not affected by  α and shows a linear behaviour between contact area and load up to 10–15% of the nominal contact area, i.e. for physical reasonable loads and in agreement with recent experimental and numerical findings. It has been also proven that, at high separation, all multiasperity contact models, which take into account the influence of summit curvature  variation as a function of summit height, necessarily converge to a (slightly) improved version of the GWmodel, and a unifying mathematical formulation of all multi-asperity models has been finally explained.

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Leakage mechanisms of seals

Several mechanical devices need some components which prevent fluid flow under a pressure gradient. These components are typically mechanical seals. A typical flat seal is usually made of a relatively soft elastic block that is squeezed against a stiffer body so that the nominally flat contact interface behaves as a wall the liquid cannot pass through. However, two nominally flat surfaces in contact always permit some fluid to leak because the surface roughness makes the contact between the sealing surfaces imperfect: the actual contact area is not the apparent one at all.

Figure 3: Schematic of the contact interface between two real rough surfaces. Non contact areas (white) can coalesce (percolation) to form a connected channel (cyan) which can carry the fluid flow from one side to the opposite side of the seal. The channel is not regular and the pressure falls through restrictions (red circles).

 

As a consequence, the fluid can find a path to percolate and leak between the two chambers at different pressures. Although seals are often one of most critical components in practical engineering applications (e.g. in ball valves, common rail systems, transmission boxes, …) their design has been based always on a trial and error methodology. A research activity has been carried on in this field at different levels.  First of all, an existing theory of leak rate of seals named “single junction” has been applied to understand the effect that some parameters (as the main sizes of the seal, the rms roughness of the substrate, the squeezing load, …) have on the insulating quality of the contact seal.

Figure 4: The hydraulic conductivity of the seal interface is shown as a function of the squeezing pressure of contact. The influence of the surface rms roughness is shown. Calculations have been performed following the single junction model (dashed lines) and the CPA approach (continuous lines).

 

Then a novel theoretical approach to estimate the fluid leakage in flat seals was developed. Such approach is based on the analogy between the seal-substrate interface and a porous medium. It has been assumed that the interface is constituted of a random distribution of non-contact patches (the pores) and small but numerous contact spots (islands). Leakage may occur only through the pores, of which the lateral size and height are distributed according to a probability density function that we calculate on the basis of a recent theory of contact mechanics. A percolation scheme, which had never been proposed before, has been thought to explain the topology of the contact and non contact spots. Within this percolation scheme, the Critical Path Analysis (CPA) has been applied to calculate the hydraulic conductivity of the medium and the results have been compared with other very recent calculations  (single junction theory). At present, numerical procedures of analysis of  the percolation properties and the fluid conductivity of the contact interface are being developed.

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Francesco Bottiglione

bottiglione

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Email: f.bottiglione@poliba.it

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