Polyhedral Voronoi diagrams for additive manufacturing

International audienceA critical advantage of additive manufacturing is its ability to fabricate complex small-scale structures. These microstructures can be understood as a metamaterial: they exist at a much smaller scale than the volume they fill, and are collectively responsible for an average elastic behavior different from that of the base printing material making the fabricated object lighter and/or flexible along specific directions. In addition, the average behavior can be graded spatially by progressively modifying the microstructure geometry.The definition of a microstructure is a careful trade-off between the geometric requirements of manufacturing and the properties one seeks to obtain within a shape: in our case a wide range of elastic behaviors. Most existing microstructures are designed for stereolithography (SLA) and laser sintering (SLS) processes. The requirements are however different than those of continuous deposition systems such as fused filament fabrication (FFF), for which there is currently a lack of microstructures enabling graded elastic behaviors.In this work we introduce a novel type of microstructures that strictly enforce all the requirements of FFF-like processes: continuity, self-support and overhang angles. They offer a range of orthotropic elastic responses that can be graded spatially. This allows to fabricate parts usually reserved to the most advanced technologies on widely available inexpensive printers that also benefit from a continuously expanding range of materials

Explicit Topology Optimization of Conforming Voronoi Foams

Topology optimization is able to maximally leverage the high DOFs and mechanical potentiality of porous foams but faces three fundamental challenges: conforming to free-form outer shapes, maintaining geometric connectivity between adjacent cells, and achieving high simulation accuracy. To resolve the issues, borrowing the concept from Voronoi tessellation, we propose to use the site (or seed) positions and radii of the beams as the DOFs for open-cell foam design. Such DOFs cover extensive design space and have clear geometrical meaning, which makes it easy to provide explicit controls (e.g. granularity). During the gradient-based optimization, the foam topology can change freely, and some seeds may even be pushed out of the shape, which greatly alleviates the challenges of prescribing a fixed underlying grid. The mechanical property of our foam is computed from its highly heterogeneous density field counterpart discretized on a background mesh, with a much improved accuracy via a new material-aware numerical coarsening method. We also explore the differentiability of the open-cell Voronoi foams w.r.t. its seed locations, and propose a local finite difference method to estimate the derivatives efficiently. We do not only show the improved foam performance of our Voronoi foam in comparison with classical topology optimization approaches, but also demonstrate its advantages in various settings, especially when the target volume fraction is extremely low

Voronoi diyagramına dayalı bir yörünge planlama ve güncelleme algoritması

Coverage of an area is required for a large variety of robotics and manufacturing applications, such as environment monitoring, home cleaning, search and rescue operations, machining, delivery, additive manufacturing and even for 3D terrain reconstruction. In this work, we present a highly flexible algorithm that can be used for coverage and graph traversal. In addition to being applicable to diverse types of engineering problems, proposed method is advantageous to other algorithms, as it never turns around and traverses the edge it recently traversed. Although the method takes advantage of variable-sized Voronoi cells, by which regular, irregular and complex geometries can be easily composed, it is not limited to Voronoi diagrams and can be applied for any connected graph. Furthermore, path planning algorithm can update the path to deal with changes in the graph. In some applications, like 3D printing, path planning must be done for many instances. However, our algorithm calculates the path at the first layer, and performs only necessary changes at the subsequent layers, instead of calculating the whole path from scratch. This update mechanism makes the method very efficient as it is demonstrated with several test cases. In addition to the path planning algorithm, a G-code file encryption method is introduced, size of G-code files can be greatly reduced. As automation and robotics integrate into numerous areas everyday, proposed methods can be useful for many applications.Alan tarama işlemi robotik ve üretim alanlarında birçok uygulama için gereklidir. Çevreyi gözetlemek, ev temizligi, arama ve kurtarma operasyonları, parça işleme, teslim ve 3B arazi rekonstrüksiyonu buna örnek olarak verilebilir. Bu çalı¸smada, alan ve grafik tarama uygulamarında kullanılabilecek ve son derece esnek bir algoritma sunulmuştur. Farklı alanlarda birçok probleme uygulanabilir olmanın yanı sıra, algoritmanın diger yakla¸sımlardan üstün özellikleri bulunmaktadır. Örneğin, taramakta oldugu kenarı tekrar taramak yerine başka bir kenara devam etmektedir. Geliştirilen yöntem, düzenli ve düzensiz kafes yapılarını modellemek için rahatlıkla kullanılabilecek Voronoi hücrelerinden faydalanmaktadır. Öte yandan, yöntem yalnızca Voronoi grafikleriyle kısıtlı olmayıp herhangi bir baglı grafiğe de uygulanabilir. Algoritma, yörünge planlama dı¸sında, yörünge güncelleme özelligine de sahiptir. 3B üretim gibi, onlarca katman boyunca yörünge planlamanın gerekli olacagı bir senaryoda, algoritma ilk katman için bir yörünge planı oluşturup devam eden katmanlar için bu yörüngeyi güncellemektedir, her katmanda yörüngeyi baştan planlamamaktadır. Testlerle de gösterildigi üzere, bu planlama mekanizması algoritmayı son derece verimli yapmaktadır. Yörünge planlama dışında, G-kodu dosyalarıyla aynı veriyi çok daha az bir depolama alanıyla saklayan bir yöntem sunulmuştur. Otomasyon ve robotik teknolojilerinin sayısız alanda kullanılmasıyla birlikte sunulan yöntemler birçok uygulama için kullanışlı olacaktırM.S. - Master of Scienc

Design and mechanical characterization of voronoi structures manufactured by indirect additive manufacturing

Additive manufacturing (AM) is a production process for the fabrication of three-dimensional items characterized by complex geometries. Several technologies employ a localized melting of metal dust through the application of focused energy sources, such as lasers or electron beams, on a powder bed. Despite the high potential of AM, numerous burdens afflict this production technology; for example, the few materials available, thermal stress due to the focused thermal source, low surface finishing, anisotropic properties, and the high cost of raw materials and the manufacturing process. In this paper, the combination by AM of meltable resins with metal casting for an indirect additive manufacturing (I-AM) is proposed. The process is applied to the production of open cells metal foams, similar in shape to the products available in commerce. However, their cellular structure features were designed and optimized by graphical editor Grasshopper®. The metal foams produced by AM were cast with a lost wax process and compared with commercial metal foams by means of compression tests

The investigation of a method to generate conformal lattice structures for additive manufacturing

Additive manufacturing (AM) allows a geometric complexity in products not seen in conventional manufacturing. This geometric freedom facilitates the design and fabrication of conformal hierarchical structures. Entire parts or regions of a part can be populated with lattice structure, designed to exhibit properties that differ from the solid material used in fabrication. Current computer aided design (CAD) software used to design products is not suitable for the generation of lattice structure models. Although conceptually simple, the memory requirements to store a virtual CAD model of a lattice structure are prohibitively high. Conventional CAD software defines geometry through boundary representation (B-rep); shapes are described by the connectivity of faces, edges and vertices. While useful for representing accurate models of complex shape, the sheer quantity of individual surfaces required to represent each of the relatively simple individual struts that comprise a lattice structure ensure that memory limitations are soon reached. Additionally, the conventional data flow from CAD to manufactured part is arduous, involving several conversions between file formats. As well as a lengthy process, each conversion risks the generation of geometric errors that must be fixed before manufacture. A method was developed to specifically generate large arrays of lattice structures, based on a general voxel modelling method identified in the literature review. The method is much less sensitive to geometric complexity than conventional methods and thus facilitates the design of considerably more complex structures. The ability to grade structure designs across regions of a part (termed functional grading ) was also investigated, as well as a method to retain connectivity between boundary struts of a conformal structure. In addition, the method streamlines the data flow from design to manufacture: earlier steps of the data conversion process are bypassed entirely. The effect of the modelling method on surface roughness of parts produced was investigated, as voxel models define boundaries with discrete, stepped blocks. It was concluded that the effect of this stepping on surface roughness was minimal. This thesis concludes with suggestions for further work to improve the efficiency, capability and usability of the conformal structure method developed in this work

Three-dimensional virtual microstructure generation of porous polycrystalline ceramics

Various numerical methods have been recently employed to model microstructure of ceramics with different level of accuracy. The simplicity of the models based on regular morphologies results in a low computational cost, but these methods produce less realistic geometries with lower precision. Additional methods are able to reconstruct irregular structures by simulating the grain-growth kinetics but are restricted due to their high computational cost and complexity. In this paper, an innovative approach is proposed to replicate a three-dimensional (3D) complex microstructure with a low computational cost and the realistic features for porous polycrystalline ceramics. We present a package, written in MATLAB, that develops upon the basic Voronoi tessellation method for representing realistic microstructures to describe the evolution during the solid-state sintering process. The method is based on a cohesive prism that links the interconnect cells and thus simulates the neck formation. Spline surfaces are employed to represent more realistic features. The method efficiently controls shape and size and is able to reconstruct a wide range of microstructures composed of grains, grain boundaries, interconnected (open) and isolated (closed) pores. The numerical input values can be extracted from 2D imaging of real polished surfaces and through theoretical analysis. The capability of the method to replicate different structural properties is tested using some examples with various configurations

Designing Volumetric Truss Structures

We present the first algorithm for designing volumetric Michell Trusses. Our method uses a parametrization approach to generate trusses made of structural elements aligned with the primary direction of an object's stress field. Such trusses exhibit high strength-to-weight ratios. We demonstrate the structural robustness of our designs via a posteriori physical simulation. We believe our algorithm serves as an important complement to existing structural optimization tools and as a novel standalone design tool itself

An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles

We study a path-planning problem amid a set $\mathcal{O}$ of obstacles in $\mathbb{R}^2$, in which we wish to compute a short path between two points while also maintaining a high clearance from $\mathcal{O}$; the clearance of a point is its distance from a nearest obstacle in $\mathcal{O}$. Specifically, the problem asks for a path minimizing the reciprocal of the clearance integrated over the length of the path. We present the first polynomial-time approximation scheme for this problem. Let $n$ be the total number of obstacle vertices and let $\varepsilon \in (0,1]$. Our algorithm computes in time $O(\frac{n^2}{\varepsilon ^2} \log \frac{n}{\varepsilon})$ a path of total cost at most $(1+\varepsilon)$ times the cost of the optimal path.Comment: A preliminary version of this work appear in the Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithm