Implementation of reengineering technology to ensure the predefined geometric accuracy of a light aircraft keel

The subject of this research is the technology of reengineering and control of parts of aircraft objects (AOs) and technological equipment for their manufacture. The predefined accuracy of the keel of a light aircraft and molding surfaces of technological equipment for its manufacture has been ensured by using reengineering technology and CAD systems. A portrait of the actual physically existing keel of a light aircraft was built in the *.stl file format using the software Artec Studio (USA). The control and comparison of the geometry of the shapes of the analytical standard with the actual physically existing keel of a light aircraft based on its portrait have been implemented. The methods used are the analysis and synthesis of the experimental geometry of shapes, the method of expert evaluations. The following results were obtained: based on the analysis and synthesis, the presence of significant errors in the accuracy of the manufacture of the keel for a light aircraft in the range from −5.26 mm to +5.39 mm was detected. It has been shown that the key factor is the keel's relative plane indicator, which is outside the tolerance margin and is 85 %. It was decided to fabricate new technological equipment from another material – organic plastics. Control of the technological equipment made from organic plastics for the keel of a light aircraft showed that the shape-forming surfaces of the equipment have appropriate shapes and sizes corresponding to the existing analytical standard and are devoid of inaccuracies that occurred in the previous version. The range of keel margins that was made using the new technological equipment from organic plastics is from –0.51 mm to +0.34 mm while the relative plane of the keel outside the tolerance margin does not exceed 15 %. The study results showed the adequacy of the decisions taken, ensuring the predefined accuracy for the keel of a light aircraft and molding surfaces of technological equipment for its manufacture.

Optimization of the Cutting Tool for Internal Flash Removing Operations in the Production of Electric-Welded Tubes

The article considers the structural optimization results for the process of mechanic removing inside flash during the production of longitudinal electric-welded pipes with a diameter of 60.3 ... 89.0 mm. Mechanical processing was performed with a pipe electric welding unit, designed for the manufacture of pipes with a diameter of 60.0 ... 178.0 mm, using various cutting tools and grades of hard alloys. The influence of the parameters of chip formation and cutting forces on the quality of inside flash removing in a longitudinal electric-welded pipe is found. The experiments were carried out using both the basic and experimental geometry of the cutting tool. The dependence of the tool durability at the operation of flash removing on the hardness of the alloy and the wear resistance of the coating has been studied. The analysis of the results of the study of annular inserts made of a three-carbide hard alloy with a multilayer wear-resistant coating showed the possibility of reducing the consumption of cutting tools and emergency stops of the mill, improving the quality of processing and the rate of yield.

Constrained geometrical analysis of complete K-line patterns for calibrationless auto-indexing

Indexing of Kikuchi and Kossel lines is a crucial step in K-line pattern analysis. Previous approaches mostly rely on the knowledge of unit-cell parameters and experimental geometry. An auto-indexing procedure is introduced that is able to find the unknown lattice, its orientation and the indices of the lines. To achieve this, the unbiased extraction of the precise conical geometrical information from the patterns is combined with existing auto-indexing procedures developed in the field of crystallography. A subsequent lattice-constrained refinement of all lines to the experimental pattern yields reliable lattice and experimental parameters simultaneously. Beyond providing detailed mathematical formulae, the procedure is also demonstrated on an experimental Kossel line pattern.

Formação continuada de professores de matemática e o ensino de geometria: um panorama das pesquisas dos últimos anosContinuing education of mathematics teachers and the geometry teaching: an overview of research in recent years

ResumoEste artigo apresenta um mapeamento da produção cientifica realizada entre os anos de 2003 e 2019, acerca da temática formação continuada de professores de matemática e o ensino de geometria. Este estudo, sob uma perspectiva exploratória, apresenta 21 trabalhos divididos entre teses e dissertações, que tiveram como lócus, ambientes de formação continuada de professores com ênfase nos objetos geométricos. Como resultados, destacamos a existência de duas tendências didático-pedagógicas emergentes nesses espaços de formação continuada: geometria experimental e geometria computacional. Para além dessas tendências, as pesquisas foram classificadas, ainda de acordo com seus objetos de estudo, buscando fornecer coordenadas relevantes e contributivas a novas pesquisas sobre esta temática.Palavras-chave: Formação continuada, Ensino de geometria, Professores de matemática.AbstractThis article presents a mapping of scientific production carried out between 2003 and 2019, on the theme of continuing education for mathematics teachers and the teaching of geometry. This study, from an exploratory perspective, presents 21 works divided between theses and dissertations, which had as their locus, environments of continuing education for teachers with an emphasis on geometric objects. As a result, we highlight the existence of two didactic-pedagogical trends emerging in these spaces of continuing education: experimental geometry and computational geometry. Besides these trends, research was further classified, according to its objects of study, seeking to provide relevant and contributory coordinates to new research on this topic.Keywords: Continuing education, Teaching geometry, Mathematics teachers.ResumenEste artículo presenta un mapeo de la producción científica realizada entre 2003 y 2019, sobre la formación continua de profesores de matemáticas y la enseñanza de la geometría. Este estudio, desde una perspectiva exploratoria, presenta 21 trabajos divididos entre tesis y disertaciones, que tenían como locus entornos de educación continua para docentes con énfasis en objetos geométricos. Como resultado, destacamos la existencia de dos tendencias pedagógico-didácticas emergentes en los espacios de educación continua: geometría experimental y geometría computacional. Además de estas tendencias, dado que la investigación aún se clasifica, de acuerdo con sus objetos de estudio, con la intención de proporcionar coordenadas relevantes y contribuyentes para nuevas investigaciones sobre este tema.Palabras clave: Educación continua, Enseñanza de geometría, Profesores de matemáticas.

Microstructured Fibers Based on Tellurite Glass for Nonlinear Conversion of Mid-IR Ultrashort Optical Pulses

Compact fiber-based sources generating optical pulses with a broadband spectrum in the mid-IR range are in demand for basic science and many applications. Laser systems producing tunable Raman solitons in special soft-glass fibers are of great interest. Here, we report experimental microstructured tellurite fibers and demonstrate by numerical simulation their applicability for nonlinear soliton conversion in the mid-infrared (-IR) range via soliton self-frequency shift. The fiber dispersion and nonlinearity are calculated for experimental geometry. It is shown numerically that there are two zero dispersion wavelengths for the core size of 2 μm and less. In such fibers, efficient Raman soliton tuning is attained up to a central wavelength of 4.8 μm using pump pulses at 2.8 μm.

Electrically powered motions of toron crystallites in chiral liquid crystals

Malleability of metals is an example of how the dynamics of defects like dislocations induced by external stresses alters material properties and enables technological applications. However, these defects move merely to comply with the mechanical forces applied on macroscopic scales, whereas the molecular and atomic building blocks behave like rigid particles. Here, we demonstrate how motions of crystallites and the defects between them can arise within the soft matter medium in an oscillating electric field applied to a chiral liquid crystal with polycrystalline quasi-hexagonal arrangements of self-assembled topological solitons called “torons.” Periodic oscillations of electric field applied perpendicular to the plane of hexagonal lattices prompt repetitive shear-like deformations of the solitons, which synchronize the electrically powered self-shearing directions. The temporal evolution of deformations upon turning voltage on and off is not invariant upon reversal of time, prompting lateral translations of the crystallites of torons within quasi-hexagonal periodically deformed lattices. We probe how these motions depend on voltage and frequency of oscillating field applied in an experimental geometry resembling that of liquid crystal displays. We study the interrelations between synchronized deformations of the soft solitonic particles and their arrays, and the ensuing dynamics and giant number fluctuations mediated by motions of crystallites, five–seven defects pairs, and grain boundaries in the orderly organizations of solitons. We discuss how our findings may lead to technological and fundamental science applications of dynamic self-assemblies of topologically protected but highly deformable particle-like solitons.

From experimental to theoretical geometry in new pedagogical movements at the turn of the 19th and 20th centuries (1872-1906)

There exist many historical works on the new pedagogical movements in the beginning of the 20th century, at the level of one country and at the international level also. Our purpose is to focus on teaching of geometry with comparing situations in four countries: United Kingdom, France, Germany and United States. We show that, behind the agreements, there are deep differences in relation with questions posed by geometrical teaching. We use two kinds of materials, discussions and textbooks, and we specially examine the questions on parallels definitions and their introduction in teaching. Keywords: laboratory method, concrete geometry, experimental geometry, intuitive geometry, practical geometry, rational geometry, Émile Borel, Carlo Bourlet, John Dewey, George Halsted, Julius Henrici, Adelia Hornbrook, Jules Houël, Charles Méray, Eliakim Moore, John Perry, Peter Treutlein.

Intuitive and experimental geometry: circulation of international proposals

The late 19th and early 20th centuries are marked by the international circulation of new methodologies for the teaching of geometry. The aim of the present study is to analyze geometry and pedagogy textbooks for elementary education which circulated in countries such as France, Germany, the United States and Brazil. The paper seeks to answer the question: what are the supporting pillars for the formulation of an intuitive and experimental geometry read in the different textbooks? The circulation and appropriations of various protagonists are identified in search of the production of an intuitive and modernizing geometry, in contrast to the abstract, deductive and logical character of Euclidean geometry.

Computational framework chinook for angle-resolved photoemission spectroscopy

We have developed the numerical software package chinook for the simulation of photoemission matrix elements. This quantity encodes a depth of information regarding the orbital structure of the underlying wavefunctions from which photoemission occurs. Extraction of this information is often nontrivial, owing to the influence of the experimental geometry and photoelectron interference, precluding straightforward solutions. The chinook code has been designed to simulate and predict the ARPES intensity measured for arbitrary experimental configuration, including photon-energy, polarization, and spin-projection, as well as consideration of both surface-projected slab and bulk models. This framework then facilitates an efficient interpretation of the ARPES, allowing for a deeper understanding of the electronic structure in addition to the design of new experiments which leverage the matrix element effects towards the objective of selective photoemission from states of particular interest.