Euclidean Offset and Bisector Approximations of Curves over Freeform Surfaces

The computation of offset and bisector curves/surfaces has always been considered a challenging problem in geometric modeling and processing. In this work, we investigate a related problem of approximating offsets of curves on surfaces (OCS) and bisectors of curves on surfaces (BCS). While at times the precise geodesic distance over the surface between the curve and its offset might be desired, herein we approximate the Euclidean distance between the two. The Euclidean distance OCS problem is reduced to a set of under-determined non-linear constraints, and solved to yield a univariate approximated offset curve on the surface. For the sake of thoroughness, we also establish a bound on the difference between the Euclidean offset and the geodesic offset on the surface and show that for a C2 surface with bounded curvature, this difference vanishes as the offset distance is diminished. In a similar way, the Euclidean distance BCS problem is also solved to generate an approximated bisector curve on the surface. We complete this work with a set of examples that demonstrates the effectiveness of our approach to the Euclidean offset and bisector operations

Modelling and path planning for additive manufacturing of continuous fiber composites

Material-extrusion based Additive Manufacturing (AM) is one of the leading (AM) technologies, which produces three-dimensional (3D) parts by extrusion of molten thermoplastic polymers layer by layer. However, its applications are limited due to the low strength and stiffness of the parts produced by this technology. One of the ways to improve the mechanical properties of the parts is to use a reinforced thermoplastic polymer with a filler such as chopped or continuous fibers. The resulting additively manufactured continuous fiber reinforced thermoplastic (CFRTP) composites could have superior mechanical properties and hence can be used in high-performance applications such as for aerospace and automotive industries. This thesis is divided into two sections. The first section is related to the modeling of additively manufactured continuous fiber composites for evaluation of the mechanical properties. The current studies for evaluating the mechanical properties of additively manufactured CFRTP composites are based on experimental results. Therefore, there is very limited study available to determine and optimize the process parameters. In this section, a finite element based study is presented to determine the effect of process parameters such as nozzle diameter, layer thickness, volume fraction and infill percentage on elastic properties of additively manufactured CFRTP composite structures. The second section presents the development of a continuous path planning algorithm for additive manufacturing of continuous fiber composites. The existing path planning algorithms used in material extrusion-based processes cause discontinuities in the material deposition if complex shapes are manufactured. Moreover, they cannot be used for continuous fiber composite printing, since the use of continuous fiber as a reinforcement requires continuous deposition of material throughout the printing process. In this thesis, a novel path planning algorithm has been developed to generate continuous deposition path for 3D printing of continuous fiber composites. The algorithm has been implemented for various complex geometries to generate continues deposition paths for the designed complex parts. The research conducted in this thesis can expand to the additive manufacturing of CFRTP composites with various reinforcing materials. The developed continuous path planning algorithm can be coupled with the optimized process parameters obtained from modeling results to produce v highly complex shape functional composite parts that could replace the conventional metal parts and processes by providing light-weight solutions for various industrial applications

Оброблення криволінійних поверхонь на п`ятиосьових верстатах з ЧПК

На сьогоднішній день в машинобудуванні широко використовують скла-дно-профільні поверхні в геометрії деталей. Прикладом можуть бути: копіри, матриці, пуансони штампів, лопатки турбін і т.д. Такі деталі зазвичай мають високі вимоги до точності та шорсткості і як наслідок велика трудомісткість виготовлення. До складно-профільних поверхонь можна віднести ті поверхні, в точках яких відсутній напрям з нульовим значенням індикатриси кривизни, а рівняння самої індикатриси відрізняються від рівняння окружності. Згідно з цим визначенням околиці точок складно - профільної поверхні характеризуються значеннями її головних радіусів кривизни - максимального і мінімального (гауссовою кривизною) або орієнтацією її головних січних площин, в яких лежать зазначених радіусах. Сучасним методом обробки таких деталей є обробка кінцевими сферичними фрезами на верстатах з ЧПК з 3 або 5 керуючими координатами. Але при такому способі обробки виникає проблема залишкового гребінця, оскільки геометрія інструменту не дозволяє усунути весь шар припуску за один прохід, що значно збільшує час обробки. Тому актуальною проблемою є відсутність розроблених ефективних траєкторій, що враховують геометрію фрези, які б дозволили отримати деталі із заданою точністю та шорсткістю

Trajectoire de type spirale adaptative pour l'usinage haute vitesse des cavités

Ce travail de recherche étudie le comportement des nouvelles trajectoires spiralées, adaptées à l'usinage haute vitesse de pochettes, dans le domaine de l'aéronautique. Principalement, il sera question de vérifier comment réagissent les trajectoires spiralées lorsqu'elles s'adaptent au contour géométrique de la cavité. À cet effet, un programme prototype a été développé en Visual Basic afin de générer automatiquement les parcours d'outils adaptés à des pochettes de formes variables. Les paramètres entrant dans la définition de ces trajectoires ont démontré un impact sur les conditions d'usinage. Les résultats obtenus à partir d'essais expérimentaux révèlent le comportement des trajectoires spiralées adaptatives, et illustrent leur potentiel concernant la réduction du temps d'usinage d'environ 15% pour les opérations d'ébauche. La contribution de ces travaux a favorisé l'implantation des tactiques de coupe spiralées et de nouveaux types d'approche hélicoidales utilisables dans les logiciels de CFAO. L'algorithme prend également en considération les murs inclinés, ce qui accroît la quantité de matériel retirée

Calidad geométrica en el mecanizado de superficies curvas en titanio para aplicaciones médicas

El objetivo del presente estudio, es determinar la influencia de la velocidad de corte, avance por diente y la estrategia de mecanizado; sobre la calidad geométrica de la superficie mecanizada en el fresado con herramienta de punta esférica del titanio grado quirúrgico Ti6Al4V (En este trabajo, se considera calidad geométrica a los parámetros de rugosidad superficial, precisión dimensional y tolerancia de forma). Para ello, las probetas se mecanizaron, por medio de fresado con herramienta de punta esférica. El análisis de la influencia de los factores se realizó, por medio de un diseño experimental factorial 23. Por otra parte, un ANOVA (análisis de la varianza) se realizó, considerando geometrías esféricas cóncavas y convexas del mismo radio; para determinar la influencia de este sobre la calidad geométrica de la superficie mecanizada. Adicionalmente, se realizó; un ANOVA entre geometrías esféricas convexas de radio diferente, con la intención de determinar la influencia sobre la calidad geométrica de la superficie mecanizada. Los resultados del diseño experimental factorial 23 mostraron que el factor interacción velocidad de corte-avance por diente tiene efecto sobre los parámetros de rugosidad superficial Ra y Rt. Por otra parte, el ANOVA para las geometrías esféricas cóncavas y convexas del mismo radio, muestra que el cambio de geometría cóncava a convexa tiene efecto sobre la precisión dimensional. Por último, el ANOVA para geometrías esféricas convexas, muestra que el cambio de radio tiene efecto sobre los parámetros de rugosidad superficial Ra, Rt y la precisión dimensional.Abstract. The objective of this study, is to determine the influence of the cutting speed, feed per tooth and machining strategy; on geometric quality of the machined surface, in the ball milling tool of the surgical grade titanium Ti6Al4V (In this paper, geometrical quality, is considered; parameters of surface roughness, dimensional accuracy and shape tolerance). The samples were machined by means of ball milling tool. Analysis of the influence of the factors was performed by means of a 23 factorial experimental design. Further, an ANOVA (analysis of variance) was performed between concave and convex spherical geometries of the same radius, to determine the influence on the geometric quality of the machined surface. Additionally, an ANOVA was performed; between convex spherical geometries different radius to determine the influence on the geometric quality of the machined surface. The factorial experimental design results showed that factor 23 interaction cutting speed-feed per tooth has an effect on surface roughness parameters Ra and Rt. Furthermore, ANOVA for concave and convex spherical geometries of the same radius, shows that the change of a convex concave geometry has an effect on the dimensional accuracy. Finally, ANOVA for convex spherical geometries shows that the radius change has an effect on surface roughness parameters Ra, Rt, and the dimensional accuracy.Maestrí

Automated Process Planning for Five-Axis Point Milling of Sculptured Surfaces

Ph.DDOCTOR OF PHILOSOPH

Fibre-reinforced additive manufacturing: from design guidelines to advanced lattice structures

In pursuit of achieving ultimate lightweight designs with additive manufacturing (AM), engineers across industries are increasingly gravitating towards composites and architected cellular solids; more precisely, fibre-reinforced polymers and functionally graded lattices (FGLs). Control over material anisotropy and the cell topology in design for AM (DfAM) offer immense scope for customising a part’s properties and for the efficient use of material. This research expands the knowledge on the design with fibre-reinforced AM (FRAM) and the elastic-plastic performance of FGLs. Novel toolpath strategies, design guidelines and assessment criteria for FRAM were developed. For this purpose, an open-source solution was proposed, successfully overcoming the limitations of commercial printers. The effect of infill patterns on structural performance, economy, and manufacturability was examined. It was demonstrated how print paths informed by stress trajectories and key geometric features can outperform conventional patterns, laying the groundwork for more sophisticated process planning. A compilation of the first comprehensive database on fibre-reinforced FGLs provided insights into the effect of grading on the elastic performance and energy absorption capability, subject to strut-and surface-based lattices, build direction and fibre volume fraction. It was elucidated how grading the unit cell density within a lattice offers the possibility of tailoring the stiffness and achieving higher energy absorption than ungraded lattices. Vice versa, grading the unit cell size of lattices yielded no effect on the performance and is thus exclusively governed by the density. These findings help exploit the lightweight potential of FGLs through better informed DfAM. A new and efficient methodology for predicting the elastic-plastic characteristics of FGLs under large strain deformation, assuming homogenised material properties, was presented. A phenomenological constitutive model that was calibrated based upon interpolated material data of uniform density lattices facilitated a computationally inexpensive simulation approach and thus helps streamline the design workflow with architected lattices.Open Acces