María Villeta

On the hyperbolicity constant in graphs

If X is a geodesic metric space and x 1 , x 2 , x 3 ? X , a geodesic triangle T = { x 1 , x 2 , x 3 } is the union of the three geodesics x 1 x 2 ] , x 2 x 3 ] and x 3 x 1 ] in X . The space X is ? -hyperbolic (in the Gromov sense) if, for every geodesic triangle T in X , every side of T is contained in a ? -neighborhood of the union of the other two sides. We denote by ? ( X ) the sharpest hyperbolicity constant of X , i.e. ? ( X ) ? inf { ? ? 0 : X ?is? ? -hyperbolic } . In this paper, we obtain several tight bounds for the hyperbolicity constant of a graph and precise values of this constant for some important families of graphs. In particular, we investigate the relationship between the hyperbolicity constant of a graph and its number of edges, diameter and cycles. As a consequence of our results, we show that if G is any graph with m edges with lengths { l k } k = 1 m , then ? ( G ) ? ? k = 1 m l k / 4 , and ? ( G ) = ? k = 1 m l k / 4 if and only if G is isomorphic to C m . Moreover, we prove the inequality ? ( G ) ? 1 2 diam G for every graph, and we use this inequality in order to compute the precise value ? ( G ) for some common graphs.

Gromov hyperbolic cubic graphs

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}. We obtain information about the hyperbolicity constant of cubic graphs (graphs with all of their vertices of degree 3), and prove that for any graph G with bounded degree there exists a cubic graph G* such that G is hyperbolic if and only if G* is hyperbolic. Moreover, we prove that for any cubic graph G with n vertices, we have δ(G) ≤ min {3n/16 + 1; n/4}. We characterize the cubic graphs G with δ(G) ≤ 1. Besides, we prove some inequalities involving the hyperbolicity constant and other parameters for cubic graphs.

Surface Finish Optimization of Magnesium Pieces Obtained by Dry Turning Based on Taguchi Techniques and Statistical Tests

Magnesium is one of the lightest metallic materials and is used in industries such as aeronautics or aerospace because of its excellent weight to resistance ratio. The surface finish is a key quality characteristic in dry turning of magnesium pieces and is often affected by multiple factors within the machining process. Factors such as feed rate, cutting speed, tool coatings, and the interactions among these were investigated in this experimental study. The objectives of this work were to identify the main factors that influence the dry turning of magnesium and to select the optimal manufacturing conditions that result in minimum surface roughness. To achieve these objectives, the “smaller-the-better” characteristic from the Taguchi method was applied to the average roughness R a . Using an orthogonal experimental design approach, the signal-to-noise (S/N) ratio was used to quantify the amount of variation present in the surface roughness. Then, graphical exploratory data analysis was conducted, and the variability in the S/N ratio of surface roughness was modeled via analysis of variance (ANOVA) fixed-effect analysis and Snedecors F-tests. This statistical modeling, together with Least Significant Difference testing permitted different combinations of cutting conditions to be classified into two groups: (I) optimal combinations and (II) the remaining combinations.

Surface Roughness Analysis of Magnesium Pieces Obtained by Intermittent Turning

This paper presents an experimental study to analyze the surface roughness reached in pieces of UNS M11917 magnesium alloy obtained by intermittent turning. A design of experiments (DOE) was established to carry out the study. Namely, factors identified as posible sources of variation of the surface roughness and their levels, written between parentheses, are the following: depth of cut (1), feed rate (2), spindle speed (2), type of tool (2), quantity of lubrication (3), type of interruption (3), measurement length (3) and measurement generatrice (3). Due to the high number of possible combinations that can be generated with the set of factors and levels identified a combined design of experiments L4x32 was performed. Data are was analyzed by means of the analysis of variance (ANOVA) method. The main results of the statistical analysis highlight the great influence of the feed rate on surface roughness among the set of factors and their interactions considered. In addition, focusing on the intermittent cutting, type of interruption and its interaction with the type of tool used are also important sources of variation, but at a lower level than feed rate.

Analysis of Main Optimization Techniques in Predicting Surface Roughness in Metal Cutting Processes

This paper collects the main methodologies and tools employed for predicting the surface roughness. The goal of this work is to provide compact and adequate information that could be useful in metal cutting industries to select the techniques and optimization tools that best suit to their needs and particular requirements. Each approach, with its advantages and disadvantages, is outlined and the present and future trends are discussed. As result, a quick guide for using practitioners of mentioned industrial sector is provided in form of tables that relate: machining parameters, cutting tool properties, workpiece properties and cutting phenomena with the different techniques and optimization tools usually employed to analyze the different parameters and phenomena involved in the process of surface roughness generation.

Study of Surface Roughness of Pieces of Magnesium UNS M11311 Obtained by Dry Turning Using ANOVA

The work presents a study of surface roughness of pieces of magnesium UNS M11311 obtained by dry turning. The study is focused in repair operations of this type of materials when they are used as inserts of metalic hybrid components. Therefore, the main limitations of this research are the values of the cutting conditions used; especially low in comparison with the usually values of these parameters used in the production of the magnesium. The followed methodology consists of a series of tests of dry horizontally turning carried out with tools of different coatings and under different cutting conditions. The design of experiments has been made by means of fractional factorial orthogonal designs and the analysis of the results by the ANOVA method. The principal result is one ranking for the combinations of cutting conditions and tool coatings based on the surface roughness expected given by the mathematical model. As first conclusion, it is possible to affirm that, the best surface finishes are obtained for low feeds. Cutting tools used in the machining of other types of materials (steel, stainless steel) can be used obtaining a quality of the surface finish similar to that obtained with tools for specific use of non-ferrous metals.

Evaluation of extreme temperature events in northern Spain based on process control charts

Extreme climate events have recently attracted the attention of a growing number of researchers because these events impose a large cost on agriculture and associated insurance planning. This study focuses on extreme temperature events and proposes a new method for their evaluation based on statistical process control tools, which are unusual in climate studies. A series of minimum and maximum daily temperatures for 12 geographical areas of a Spanish region between 1931 and 2009 were evaluated by applying statistical process control charts to statistically test whether evidence existed for an increase or a decrease of extreme temperature events. Specification limits were determined for each geographical area and used to define four types of extreme anomalies: lower and upper extremes for the minimum and maximum anomalies. A new binomial Markov extended process that considers the autocorrelation between extreme temperature events was generated for each geographical area and extreme anomaly type to establish the attribute control charts for the annual fraction of extreme days and to monitor the occurrence of annual extreme days. This method was used to assess the significance of changes and trends of extreme temperature events in the analysed region. The results demonstrate the effectiveness of an attribute control chart for evaluating extreme temperature events. For example, the evaluation of extreme maximum temperature events using the proposed statistical process control charts was consistent with the evidence of an increase in maximum temperatures during the last decades of the last century.

Cutting Parameter Selection for Efficient and Sustainable Repair of Holes Made in Hybrid Mg–Ti–Mg Component Stacks by Dry Drilling Operations

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.

An alternative method to achieve metrological confirmation in measurement process

Metrological confirmation process must be designed and implemented to ensure that metrological characteristics of the measurement system meet metrological requirements of the measurement process. The aim of this paper is to present an alternative method to the traditional metrological requirements about the relationship between tolerance and measurement uncertainty, to develop such confirmation processes. The proposed way to metrological confirmation considers a given inspection task of the measurement process into the manufacturing system, and it is based on the Index of Contamination of the Capability, ICC. Metrological confirmation process is then developed taking into account the producer risks and economic considerations on this index. As a consequence, depending on the capability of the manufacturing process, the measurement system will be or will not be in adequate state of metrological confirmation for the measurement process.

Roundness and cylindricity verification of cylindrical workpieces of magnesium alloys obtained by intermittent dry machining

Magnesium is the lightest metal used in industry, above all for aerospace and automotive applications where weight reduction allows an improvement in the fuel efficiency and reducing CO2 emission. In this work, an experimental study was carried out in order to determine with which machining process, turning or milling, are obtained cylindrical bars of magnesium alloy UNS M11917 by intermittent dry cut with improved roundness and cylindricity finish.