Iterative surface warping to shape craters in micro-EDM simulation

This paper introduces a new method for simulating the micro-EDM process in order to predict both the tool’s wear and the workpiece’s roughness. The tool and workpiece are defined by NURBS patches whose shapes result from an iterative crater-by-crater deformation technique driven by physical parameters. Through hundreds of thousands of local surface warping, the method is able to compute the global as well as the local shapes of the tool and workpiece. At each step, the warping vector and function are computed so as to be able to generate a spherical crater whose volume is also controlled. While acting very locally to simulate the real physical phenomenon, not only the method can evaluate the tool’s wear from the overall final shape at a low resolution level, but it can also estimate the workpiece’s roughness from the high resolution level. The simulation method is validated through a comparison with experimental data. Different simulations are presented with an increase in computation accuracy in order to study its influence on the results and their deviation from expected values

Iterative surface warping to shape craters in micro‐EDM simulation

This paper introduces a new method for simulat- ing the micro-EDM process in order to predict both the tool’s wear and the workpiece’s roughness. The tool and workpiece are de ned by NURBS patches whose shapes result from an iterative crater-by-crater deformation technique driven by physical parameters. Through hundreds of thousands of local surface warping, the method is able to compute the global as well as the local shapes of the tool and workpiece. At each step, the warping vector and function are computed so as to be able to generate a spherical crater whose volume is also controlled. While acting very locally to simulate the real physical phenomenon, not only the method can evaluate the tool’s wear from the overall nal shape at a low resolu- tion level, but it can also estimate the workpiece’s roughness from the high resolution level. The simulation method is validated through a comparison with experimental data. Dif- ferent simulations are presented with an increase in compu- tation accuracy in order to study its in uence on the results and their deviation from expected values

On the family of B-spline surfaces obtained by knot modification

B-spline surfaces are piecewisely defined surfaces where the section points of the domain of definition are called knots. In [2] the authors proved some theorems in terms of knot modification of B-spline curves. Here we generalize these results for one- and two-parameter family of surfaces. An additional result concerning a higher order contact of these surfaces and an envelope is also proved

Integrated modeling and analysis methodologies for architecture-level vehicle design.

In order to satisfy customer expectations, a ground vehicle must be designed to meet a broad range of performance requirements. A satisfactory vehicle design process implements a set of requirements reflecting necessary, but perhaps not sufficient conditions for assuring success in a highly competitive market. An optimal architecture-level vehicle design configuration is one of the most important of these requirements. A basic layout that is efficient and flexible permits significant reductions in the time needed to complete the product development cycle, with commensurate reductions in cost. Unfortunately, architecture-level design is the most abstract phase of the design process. The high-level concepts that characterize these designs do not lend themselves to traditional analyses normally used to characterize, assess, and optimize designs later in the development cycle. This research addresses the need for architecture-level design abstractions that can be used to support ground vehicle development. The work begins with a rigorous description of hierarchical function-based abstractions representing not the physical configuration of the elements of a vehicle, but their function within the design space. The hierarchical nature of the abstractions lends itself to object orientation - convenient for software implementation purposes - as well as description of components, assemblies, feature groupings based on non-structural interactions, and eventually, full vehicles. Unlike the traditional early-design abstractions, the completeness of our function-based hierarchical abstractions, including their interactions, allows their use as a starting point for the derivation of analysis models. The scope of the research in this dissertation includes development of meshing algorithms for abstract structural models, a rigid-body analysis engine, and a fatigue analysis module. It is expected that the results obtained in this study will move systematic design and analysis to the earliest phases of the vehicle development process, leading to more highly optimized architectures, and eventually, better ground vehicles. This work shows that architecture level abstractions in many cases are better suited for life cycle support than geometric CAD models. Finally, substituting modeling, simulation, and optimization for intuition and guesswork will do much to mitigate the risk inherent in large projects by minimizing the possibility of incorporating irrevocably compromised architecture elements into a vehicle design that no amount of detail-level reengineering can undo

Procedurally generated models for Isogeometric Analysis

Increasingly powerful hard- and software allows for the numerical simulation of complex physical phenomena with high levels of detail. In light of this development the definition of numerical models for the Finite Element Method (FEM) has become the bottleneck in the simulation process. Characteristic features of the model generation are large manual efforts and a de-coupling of geometric and numerical model. In the highly probable case of design revisions all steps of model preprocessing and mesh generation have to be repeated. This includes the idealization and approximation of a geometric model as well as the definition of boundary conditions and model parameters. Design variants leading to more resource-efficient structures might hence be disregarded due to limited budgets and constrained time frames. A potential solution to above problem is given with the concept of Isogeometric Analysis (IGA). Core idea of this method is to directly employ a geometric model for numerical simulations, which allows to circumvent model transformations and the accompanying data losses. Basis for this method are geometric models described in terms of Non-uniform rational B-Splines (NURBS). This class of piecewise continuous rational polynomial functions is ubiquitous in computer graphics and Computer-Aided Design (CAD). It allows the description of a wide range of geometries using a compact mathematical representation. The shape of an object thereby results from the interpolation of a set of control points by means of the NURBS functions, allowing efficient representations for curves, surfaces and solid bodies alike. Existing software applications, however, only support the modeling and manipulation of the former two. The description of three-dimensional solid bodies consequently requires significant manual effort, thus essentially forbidding the setup of complex models. This thesis proposes a procedural approach for the generation of volumetric NURBS models. That is, a model is not described in terms of its data structures but as a sequence of modeling operations applied to a simple initial shape. In a sense this describes the "evolution" of the geometric model under the sequence of operations. In order to adapt this concept to NURBS geometries, only a compact set of commands is necessary which, in turn, can be adapted from existing algorithms. A model then can be treated in terms of interpretable model parameters. This leads to an abstraction from its data structures and model variants can be set up by variation of the governing parameters. The proposed concept complements existing template modeling approaches: templates can not only be defined in terms of modeling commands but can also serve as input geometry for said operations. Such templates, arranged in a nested hierarchy, provide an elegant model representation. They offer adaptivity on each tier of the model hierarchy and allow to create complex models from only few model parameters. This is demonstrated for volumetric fluid domains used in the simulation of vertical-axis wind turbines. Starting from a template representation of airfoil cross-sections, the complete "negative space" around the rotor blades can be described by a small set of model parameters, and model variants can be set up in a fraction of a second. NURBS models offer a high geometric flexibility, allowing to represent a given shape in different ways. Different model instances can exhibit varying suitability for numerical analyses. For their assessment, Finite Element mesh quality metrics are regarded. The considered metrics are based on purely geometric criteria and allow to identify model degenerations commonly used to achieve certain geometric features. They can be used to decide upon model adaptions and provide a measure for their efficacy. Unfortunately, they do not reveal a relation between mesh distortion and ill-conditioning of the equation systems resulting from the numerical model

Avaliação do consumo de energia em etapas iniciais do projeto : um estudo associando interfaces físicas e digitais como elemento qualificador do processo projetual

Modelos físicos possibilitam a manipulação rápida e intuitiva da forma na fase de concepção e exploração do envoltório edificado. Por outro lado, modelos digitais de desempenho oferecem resultados quantitativos que podem contribuir com a tomada de decisões durante a exploração empírica da forma. O diálogo entre ferramentas computacionais e atividades de projeto – desenhar, executar modelos físicos, analisar e testar – envolvem escolhas, por exemplo, quanto à eficiência energética, que podem ser auxiliadas por ferramentas de aprendizagem que explorem a interação entre modelos físicos e digitais. Este trabalho associa a manipulação da forma ao conhecimento sobre seu desempenho energético usando, simultaneamente, dois modelos, físico e digital. O modelo físico apoia a manipulação da composição volumétrica e da fenestração, enquanto o modelo digital permite avaliar o impacto ambiental das escolhas através da simulação do consumo energético. Para capturar a posição dos elementos físicos que compõem o envoltório, o modelo físico utilizou uma câmera e marcadores para capturar a translação e rotação destes elementos. A alteração das dimensões das fenestrações foi controlada, em meio físico, por meio de potenciômetros que gerenciaram a proporção dos planos translúcidos das fachadas com auxílio da plataforma Arduino O modelo físico conectou-se ao modelo digital através das ferramentas computacionais Rhinoceros e Grasshopper, com auxílio do plug-in Firefly e da plataforma ReactVision. O modelo digital simulou o desempenho energético utilizando o software EnergyPlus e os plug-ins do Grasshopper, Ladybug e Honeybee. Como prova de conceito, foi concebido um exercício de exploração da forma, tendo como parâmetro a minimização do consumo de energia para aquecimento e refrigeração do ambiente interno de uma edificação de uso comercial composta por dois prismas regulares. O experimento, que contou com a participação de alunos de graduação de curso de arquitetura e urbanismo, mensurou transformações geométricas, quantidade e desempenho das soluções geradas vis a vis tempo de manipulação (trinta minutos). Relacionando as ações projetuais dos estudantes aos resultados de desempenho da forma, observou-se redução do consumo de energia. Foi possível concluir que o uso do modelo físico associado ao modelo digital pode aumentar a segurança do estudante ao escolher alternativas de projeto ao tomar decisões sobre o desempenho energético de edificações, assim como, pode aumentar a fixação de conteúdos que relacionam forma arquitetônica e desempenho ambiental durante processos de ensino e aprendizagem.Physical models allow quick and intuitive shape’s manipulation during design and exploration phases of the building’s envelope. On the other hand, digital performance models offer quantitative results, which may contribute to decision making throughout empirical exploration of the shape. The dialogue between computational tools and design activities – drawing, run physical models, analyzing and testing – involves choices, for example, regarding energy efficiency, that be able to aided by learning tools who exploring the interaction between physical and digital models. This work associates shape exploration with the knowledge about the project’s energy performance, apply simultaneously, two models, physical and digital. The physical model supports fenestration and shape composition manipulation, while the digital model allows evaluate the environmental impact of choices through energy consumption simulation. To capture the position of physical elements that make up the building envelope, the physical model used a camera and markers to capture the translation and rotation position of these elements. The manipulation of fenestration dimensions was controlled, in physical media, by means of potentiometers that managed the proportion of façade translucent planes, with support from Arduino platform The physical model connected to the digital model by means of computational tools: Rhinoceros and Grasshopper, with support from Firefly plug-in and the ReactVision platform. The digital model simulated the energy performance using the software EnergyPlus and the Grasshopper plug-ins: Ladybug and Honeybee. As proof of concept, a shape exploration exercise was designed, with as a parameter the energy consumption minimization to heating and cooling the internal environment of a commercial building, composed of two regular prisms. The experiment, that had the undergraduate architecture and urbanism students’ participation, measured geometric transformations, quantity and the performance of generated solutions in relation to manipulation time (thirty minutes). Relating the students’ activities and shape performance results, reduction of energy consumption was observed. It was possible to conclude that using physical models associated with digital models can increase the student reliability when choosing project alternatives, during the building energy performance decision making, as well as, may increase the ability to fix contents that relate architectural shape and environmental performance, during learning and teaching processes