Toward G1-continuous multi-strip path-planning for 5-axis flank CNC machining of free-form surfaces with conical tools
Kanika Rajain BCAM | Jun 12, 2023. Existing flank milling path-planning methods typically lead to tiny gaps or overlaps between neighboring paths, which causes artifacts and imperfections in the workpiece. We propose a new multi-strip path-planning method for 5-axis flank milling of free-form surfaces which targets G1 (tangent-plane) continuity of the neighboring strips along shared boundaries. While for some geometries one cannot achieve G1 continuity and high approximation quality at the same time, our optimization framework offers a good trade-off between machining accuracy in terms of distance error and the G1 connection of neighboring strips. We demonstrate our algorithm on synthetic free-form surfaces as well as on industrial benchmark datasets, showing that we are able to meet fine industrial tolerances and simultaneously significantly reduce the kink angle of adjacent strips, and consequently to improve the surface finish in terms of smoothness.
Kernel-based Construction Operators for Boolean Sum and Ruled Geometry
Haitham Fadila  Technion | Jun 5,2023. Boolean sum and ruling are two well-known construction operators for both parametric surfaces and trivariates. In many cases, the input freeform curves in  R2 orsurfaces in Rare complex, and as a result, these construction operators might fail to build the parametric geometry so that it has a positive Jacobian throughout the domain.
In this work, we focus on cases in which those constructors fail to build parametric geometries with a positive Jacobian throughout while the freeform input has a kernel point. We show that in the limit, for high enough degree raising or enough refinement, our construction scheme must succeed if a kernel exists. In practice, our experiments, on quadratic, cubic and quartic Bézier and B-spline curves and surfaces show that for a reasonable degree raising and/or refinement, the vast majority of construction examples are successful.
 Implicit Functionally Graded Conforming Microstructures
Q Youn Hong  Hanyan University at Ansan, Korea | May 22, 2023. The tensor product parametric representations are the most commonly used representation in geometric modeling. Yet, other representations have advantages in certain aspects, and in this work, we focus on employing implicit representations in the construction of microstructures. An implicit function, either functionally precise, or spline trivariate-based, is used to populate a macro-shape trivariate parametric form, and construct a conforming microstructure. Either the implicit tile or the macro-shape can be functionally graded or be heterogeneous, carrying graded properties such as material, translucency, or color alongside the geometry. Further, the implicit tiles can be parametrized and hence their geometry can vary across the macro-shape. The representation is locally precise and we demonstrate that in a slicing process that employs no (piecewise-linear) approximation. Finally, we demonstrate this framework on several 3D printed heterogeneous models.
 Inverse Mold Design in Injection Molding
Florian Zwicke  TU Wien | Dec 19, 2022. Molding and casting processes present some difficulties when it comes to achieving the intended part shape. These manufacturing processes have in common that a hot liquid material is cooled down in a mold so that it solidifies. This solidification can lead to inhomogeneous material properties. E.g., when considering injection molding with semi-crystalline polymers, crystallization leads to residual stresses in the material. Such stresses, combined with the inhomogeneous cooling behavior, can lead to local variances in the thermally-induced shrinkage of the material. This, in turn, causes warpage, which means that the shape of the finished part does not correspond exactly to the shape of the mold cavity. There are multiple aspects of the process that can be adjusted to improve the results. Options are, for instance, the design of the cooling system or various process parameters. Another approach is to compensate for the anticipated shrinkage and warpage by designing the mold cavity to be different than the desired part shape. This approach can be treated as a shape optimization problem. In order to apply numerical optimization techniques, certain ingredients are required. One of these is a low-dimensional parameterization of the cavity shape that yields a CAD-suitable geometry. Another one is an objective function that expresses the suitability of an output shape as a scalar number and fulfills certain criteria that yield a well-posed optimization problem. An alternative approach to solve this design problem is based on an inverse formulation of the equations used in the simulation model. Depending on the material, the final process steps can lend themselves to a purely elastic description. In this case, it is possible to exchange the roles of the initial and equilibrium configurations and apply certain approximations to the initial values of certain fields. Such an approach promises much higher efficiency than
an iterative optimization method, but poses certain limitations on the simulation model..
 Planar Hoberman-like Mechanisms along General B-spline Curves
Gershon Elber  Technion | Nov 28, 2022. The Hoberman mechanism requires no introduction. This expandable truss mechanisms is traditionally defined over constant curvature geometries, namely circles and spheres. In this work, we present a similar expandable solution for general planar B-spline curves. The freeform curve is decomposed into small enough segments, each of which is fitted with a proper scissors mechanisms for the specific curvature of that segment. 3D printing and fabrication considerations are discussed and assemblies of such generalized mechanisms are demonstrated.
 Geometric construction of auxetic metamaterials
Georges-Pierre Bonneau  INRIA | May 02, 2022. This talk is devoted to a category of metamaterials called auxetics, identified by their negative Poisson’s ratio. Our work consists in exploring geometrical strategies to generate irregular auxetic structures. More precisely we seek to reduce the Poisson’s ratio (PR) by pruning an irregular network based solely on geometric criteria. We introduce a strategy combining a pure geometric pruning algorithm followed by a physics-based testing phase to determine the resulting PR of our structures. We propose an algorithm that generates sets of irregular auxetic networks. Our contributions include geometrical characterization of auxetic networks, development of a pruning strategy, generation of auxetic networks with low PR, as well as validation of our approach. We provide statistical validation of our approach on large sets of irregular networks, and we additionally laser-cut auxetic networks in sheets of rubber. The findings reported here show that it is possible to reduce the Poisson’s ratio by geometric pruning, and that we can generate irregular auxetic networks at lower processing times than a physics-based approach.
 Detection and computation of conservative kernels of models consisting of freeform curves and surfaces, using inequality constraints
Q Youn Hong  Technion | Apr 25, 2022. The kernel of a closed domain is the loci of points that are internal to the domain and visible to every point on the boundary of the domain at the same time. In this talk, we present an algorithm to compute a tight-as-needed conservative approximation of the kernel domain of freeform curves in R2 and freeform surfaces in R3. Inequality constraints to detect the interior of the kernel domain are formulated as multivariates, and solved with a subdivision-based approach to find the domains in R2 or R3 that satisfy the inequalities and are therefore in the kernel. The convex hull of the computed domains is also included in the kernel, and adopted as approximated kernel domains. The proposed algorithm can be applied to detect the kernel domains of not only C1 continuous closed regular curves and surfaces, but also the kernel domains of multiple piecewise C1 continuous regular freeform curves and surfaces. Further, we apply the presented algorithm to find the gamma-kernel as well as the kernel domain of open curves and surfaces, under some assumptions. We demonstrate our experimental results using various freeform curves and surfaces, and compare them with the previous kernel computation algorithm based on equality constraints.
 Curve-guided 5-axis CNC flank milling of free-form surfaces using custom-shaped tools
Kanika Rajain   BCAM | Apr 04, 2022.  A new method for 5-axis flank milling of free-form surfaces is proposed. Existing flank milling path-planning methods typically use on-market milling tools whose shape is cylindrical or conical, and is therefore not well-suited for meeting fine tolerances for manufacturing of benchmark free-form surfaces like turbine blades, gears, or blisks. In contrast, our optimization-based framework incorporates the shape of the tool into the optimization cycle and looks not only for the milling paths, but also for the shape of the tool itself. Given a free-form reference surface and a guiding path that roughly indicates the motion of the milling tool, tangential movability of quadruplets of spheres centered along a straight line is analyzed to indicate possible shapes and their motions. This results in $G^1$ Hermite data in the space of rigid body motions that are interpolated and further optimized, both in terms of the motion and the shape of the milling tool itself. We demonstrate our algorithm on synthetic free-form surfaces and industrial benchmark datasets, showing that the use of custom-shaped tools is capable of meeting fine industrial tolerances and outperforms the use of classical, on-market tools.
 Dimensional metrology, artifacts and others
Silvia de la Maza  Trimek | Mar 03, 2022.  A brief introduction will be made on the company Trimek and its products
and services. Relevance of artifacts and calibration. Implementation of Adam2.
 Shape Optimization of CAD-Compliant Microstructured Geometries
Jacques Zwar  TU Wien | Feb 17, 2022.  Recent advances in modern production techniques have opened up a vast realm of previously unthinkable design possibilities. These new geometries cannot be adequately designed using classical engineering methods, which is why numerical design techniques are becoming increasingly valuable. In this context, this work aims to present concepts that exploit the emerging design space and facilitate numerical optimization.
The proposed framework is based on a microstructured components, whose geometry is constructed via composition of two splines. More specifically, a macro-spline determines the outer geometry and a micro-spline defines the internal structure of the individual building blocks [Elber, 2017]. This approach opens up a broad design space, since both geometric components can be altered individually. The representation uses volume splines, providing full compatibility with CAD/CAM and further facilitates the use of Isogeometric Analysis (IGA).
We will present first results for the concrete example of a heat exchanger around an extrusion die. Here, we aim to impose a specific temperature profile on the flow channel. This temperature profile is chosen in such a way that it supports a homogeneous material distribution. Special emphasis is placed on the definition of a suitable, low-dimensional design space for shape optimization.
 New algorithms for computing surface intersections and self-intersections
Youngjin Park  Seoul National University | Nov 24, 2021.  We present an efficient and robust algorithm for computing the intersection curve of two freeform surfaces and the self-intersection curve of a freeform surface, using a Bounding Volume Hierarchy where the leaf nodes contain osculating toroidal patches. The hierarchy of simple bounding volumes accelerates the geometric search for the potential pairs of surface patches that may generate some intersection curve segments. Furthermore, a union of tightly fitting toroidal patches greatly simplifies the geometric operations involved in the surface intersection computation. We demonstrate the effectiveness and robustness of our algorithms by using test examples, including some highly non-trivial examples.
 Shell-lattice construction based on regular and semi-regular tiling via functional composition
Sumita Dahiya  Technion | Nov 03, 2021.  In this talk, we present a methodology and algorithm for the design process of shell-lattice structures based on dual regular and semi-regular planar shapes. We introduce a 2-manifold, parametric freeform shell type of tiling to tessellate the domain of any given bivariate deformation map and hence obtain freeform shell-lattice structures in 3-space. Any primal regular or semi-regular pattern, results into a variety of tiling that differs in both aesthetic appearance and final manifestation.
 A New Approach in the Design of Microstructured Ultralight Components to Achieve Maximum Functional Performance
Haizea González  UPV | Oct 27, 2021.  In the energy and aeronautics industry, some components need to be very light but with high strength. For instance, turbine blades and structural components under rotational centrifugal forces, or internal supports, ask for low weight, and in general, all pieces in energy turbine devices will benefit from weight reductions. In space applications, a high ratio strength/weight is even more important. Light components imply new optimal design concepts, but to be able to be manufactured is the real key enable technology. Additive manufacturing can be an alternative, applying radical new approaches regarding part design and components’ internal structure. Here, a new approach is proposed using the replica of a small structure (cell) in two or three orders of magnitude. Laser Powder Bed Fusion (L-PBF) is one of the most well-known additive manufacturing methods of functional parts (and prototypes as well), for instance, starting from metal powders of heat-resistant alloys. The working conditions for such components demand high mechanical properties at high temperatures, Ni-Co superalloys are a choice. The work here presented proposes the use of “replicative” structures in different sizes and orders of magnitude, to manufacture parts with the minimum weight but achieving the required mechanical properties. Printing process parameters and mechanical performance are analyzed, along with several examples.
 Conformal Microstructure Synthesis in Trimmed Trivariate based V-reps
Q Youn Hong  Technion | Sep 22, 2021.  In this talk, we present a microstructure tiling scheme for V-rep models consisting of trimmed trivariates. Trimmed trivariates are formed by hierarchically applying Boolean operations to full tensor-product trivariates. An existing tiling method is employed to tile individual primitive tensor product trivariates in a conformal way, only to handle the intersection of the microstructure tiles with the trimming surfaces of the trivariates. One-to-one and two-to-one bridging tiles are then constructed along the trimmed zones, while tile-clipping is completely avoided. We consider Boolean operation cases of subtraction, intersection and union. The result is a set of, regular in the interior, possibly heterogeneous, trivariates, that defines the whole microstructure arrangement. This result is fully compatible with iso-geometric analysis as well as heterogeneous additive manufacturing. Examples are presented, including of 3D printed heterogeneous microstructures.
 The role and the integration of micro-structures for Digital Anatomy 3D printed models
Ido Bitan  Stratasys | Sep 14, 2021.  In order to properly mimic actual human organs through 3D printing, one has to account for various structural behavior characteristics as well as the look and feel of the actual organs. Complex micro-structures which allow to mimic real human tissues are at the backbone of this process. These structures allow users to manipulate the internal core of the printed part and to define the bio-mechanical properties of the target organ. The ability to change material ratios, methods of material deposition and thickness of each layer allows us to reach a wide variety of medical applications according to the measured behavior such as compression values, compliance, tensile strength, isotropic structure and more. During the presentation we will demonstrate how various organs are mimicked through specifically selected micro structures and blending mechanisms.
 Application of a new paradigm to microstructured based design. Implementation of the WP1 deliverables in an industrial code
Benjamin Thomas  Hutchinson | June 30, 2021. A first code based on the work done in the Technion about microstructure generation and assembly was developped by Hutchinson. A comparison is made on the possibilities of a commercial CAD software and the proposed code to construct academic but not so simple structures based on elementary tiles with specific acoustic or mechanical properties. This work will end up with a report presenting a workflow on structures that we plan to directly 3D print using the outputs of the program.
 The role of Analysis in the design process of micro-structured geometries
Thibaut Hirschler  EPFL | June 16, 2021. The first letter of the project acronym ADAM^2 stands for Analysis. But what does it consists in? We give in this presentation an overview of computer simulation and its role in a design-to-manufacturing cycle. We discuss more specifically the computational design of micro-structured geometries and the challenges arising from this multiscale problem (from an analysis perspective). We present our developed approaches dedicated to ADAM^2 types of structures and discuss what is yet to come in order to build compact and user-friendly ADAM tools for Microstructures.
 Precise Hausdorff Distance Computation for Freeform Surfaces Based on Computations with Osculating Toroidal Patches
Sang-Hyun Son  Seoul National University | June 2, 2021. We present an efficient algorithm for computing the precise Hausdorff Distance (HD) between two freeform surfaces. The algorithm is based on a hybrid Bounding Volume Hierarchy (BVH), where osculating toroidal patches (stored in the leaf nodes) provide geometric properties essential for the HD computation in high precision. Intrinsic features from the osculating geometry resolve computational issues in handling the cross-boundary problem for composite surfaces, which leads to the acceleration of HD algorithm with a solution (within machine precision) to the exact HD. The HD computation for general freeform surfaces is discussed, where we focus on the computational issues in handling the local geometry across surface boundaries or around surface corners that appear as the result of gluing multiple patches together in the modeling of generic composite surfaces. We also discuss how to switch from an approximation stage to the final step of computing the precise HD using numerical improvements and confirming the correctness of the HD computation result. The main advantage of our algorithm is in the high precision of HD computation result. As the best cases of the proposed torusbased approach, we also consider the acceleration of HD computation for freeform surfaces of revolution and linear extrusion, where we can support real-time computation even for deformable surfaces. The acceleration is mainly due to a fast biarc approximation to the planar profile curves of the simple surfaces, each generated by rotating or translating a planar curve. We demonstrate the effectiveness of the proposed approach using experimental results.
 Geometry and tool motion planning for curvature adapted CNC machining
Oleksii Sliusarenko  BCAM | May 26, 2021. CNC machining is the leading subtractive manufacturing technology. Although it is in use since decades, it is far from fully solved and still a rich source for challenging problems in geometric computing. We demonstrate this at hand of 5-axis machining of freeform surfaces, where the degrees of freedom in selecting and moving the cutting tool allow one to adapt the tool motion optimally to the surface to be produced. We aim at a high-quality surface finish, thereby reducing the need for hard-to-control post-machining processes such as grinding and polishing. Our work is based on a careful geometric analysis of curvature-adapted machining via so-called second order line contact between tool and target surface.On the geometric side, this leads to a new continuous transition between “dual” classical results in surface theory concerning osculating circles of surface curves and osculating cones of tangentially circumscribed developable surfaces. Practically, it serves as an effective basis for tool motion planning. Unlike previous approaches to curvature-adapted machining, we solve locally optimal tool positioning and motion planning within a single optimization framework and achieve curvature adaptation even for convex surfaces. This is possible with a toroidal cutter that contains a negatively curved cutting area. The effectiveness of our approach is verified at hand of digital models, simulations and machined parts, including a comparison to results generated with commercial software.

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