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Drilling is one of the most common machining operations in the aeronautic and aerospace industries. For assembling parts, a large number of holes are usually drilled into the parts so that they can be joined later by rivets. As these holes are subjected to fatigue cycles, they have to be checked regularly for maintenance or repair, since small cracks or damage in its contour can quickly cause breakage of the part, which can have dangerous consequences. This paper focuses on finding the best combinations of cutting parameters to perform repair and maintenance operations of holes in stacked hybrid magnesium–titanium–magnesium components in an efficient, timely, and sustainable (without lubricants or coolants) manner, under dry drilling conditions. For the machining trials, experiments were designed and completed. A product of a full factorial 23 and a block of two factors (3 × 2) was used with surface roughness as the response variable measured as the mean roughness average. Analysis of variance (ANOVA) was used to examine the results. A set of optimized tool and cutting conditions is presented for performing dry drilling repair operations.

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Abstract:One of the lightest metallic materials used in the aeronautics, aerospace, and automotive industries, among others, is magnesium, due to its excellent weight/strength ratio. Most parts used in these industries need to be made of materials that are rigid, strong, and lightweight, but sometimes the materials do not simultaneously satisfy all of the properties required. An alternative is to combine two or more materials, giving rise to a hybrid component that can satisfy a wider range of properties. The pieces machined in these industrial fields must satisfy stringent surface roughness requirements that conform to the design specifications. This work shows an experimental study to analyse the surface roughness reached in hybrid components made up of a base of magnesium alloy (UNS M11917) and two inserts of aluminium alloy (UNS A92024) obtained by turning. Its purpose is to determine the influence of the factors and their possible interactions on the response variable, the surface roughness Ra. The study is carried out using a design of experiments (DOE). A product of a full factorial 2 3 and a block of two factors 3 × 2 was selected. The factors identified as possible sources of variation of the surface roughness are: depth of cut, feed rate, spindle speed, type of tool, location with respect to the specimen (LRS), and location with respect to the insert (LRI). Data were analysed by means of the analysis of variance (ANOVA) method. The main conclusion is the possibility to carry out the repair and maintenance of parts of magnesium-aluminum hybrid components by dry turning; that is, without cutting fluids and, therefore, in the most sustainable way that the process can be carried out. In addition, different combinations of cutting parameters have been identified that allow these operations to be carried out in an efficient manner, reducing mechanization times and, therefore, also the direct and indirect costs associated with them.

Magnesium is one of the lightest metallic materials and is well known and widely used in the aeronautic and aerospace industries. The pieces machined in these industrial fields must satisfy stringent surface roughness requirements to achieve a product quality that conforms to the design specifications. The aim of this investigation is to optimise efficiently the dry turning of magnesium pieces to achieve a surface roughness within technical requirements. A cost-effective and flexible statistical optimisation procedure, which is based on the technical specifications of surface roughness as well as on a robust experimental design, identified different optimal cutting conditions that provide a surface finish which meets the roughness specifications in magnesium parts. Furthermore, as a consequence of such optimisation procedure, the machining time was reduced, and the aerospace companies could select among the optimal operating conditions by also considering productivity, safety and environment criteria to control production of the surfaces finish.

If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e. δ(X) := inf{δ ≥ 0 : X is δ-hyperbolic } .

If X is a geodesic metric space and x 1 , x 2 , x 3 ∈ X, a geodesic triangleThe space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by δ(X) the sharp hyperbolicity constant of X, i.e. δ(X) = inf{δ ≥ 0: X is δ-hyperbolic}. In this paper we characterize the product graphs G 1 × G 2 which are hyperbolic, in terms of G 1 and G 2 : the product graph G 1 × G 2 is hyperbolic if and only if G 1 is hyperbolic and G 2 is bounded or G 2 is hyperbolic and G 1 is bounded. We also prove some sharp relations between the hyperbolicity constant of G 1 × G 2 , δ(G 1 ), δ(G 2 ) and the diameters of G 1 and G 2 (and we find families of graphs for which the inequalities are attained). Furthermore, we obtain the precise value of the hyperbolicity constant for many product graphs.

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