RU2843999C2 - Method of weight reduction and/or design of additively fabricated article - Google Patents

Abstract

FIELD: chemistry.

SUBSTANCE: invention relates to additive manufacturing of an article. Such a result is achieved by filling and/or assembling each of one or more integral parts of the article with a quasi-crystalline structure. Additive manufactured article obtained by implementing the method comprises a quasi-periodic or aperiodic minimum surface filling and/or a quasi-periodic minimum or aperiodic surface design structure, wherein a quasi-crystalline structure is used as a frame.

EFFECT: maximization of product strength at minimization of product weight.

18 cl, 26 dwg

Description

Field of technology to which the invention relates

The present invention relates to a method for reducing the weight and/or design of an additively manufactured article. The invention further relates to a computer program product capable of implementing the method of the present invention, as well as to an additively manufactured article obtained by means of the method according to the present invention, in full accordance with the preambles of the independent claims.

State of the art

The ways in which a space-filling periodic lattice can be organized are limited by 213 general symmetric constructs called "space groups," which describe all combinatorial solutions to the problem of repeating a point in space using a sequence of copying operations such as translations, rotations, and reflections. However, there is an exception to this rule: infinite, non-periodic structures called "quasicrystals." Like lattices represented by one of the periodic space groups, quasicrystals are formed from one or more, but not infinite, types of fundamental cells. Because the repetition of these cells produces similar (or even identical) arrangements on a small scale that never repeat on a large scale, quasicrystals exhibit a property called "quasiperiodicity" (instead of "aperiodicity"). Quasicrystals can fill ("tile") space without repeating at all. While two-dimensional quasi-crystalline tiling arrangements (such as the famous Penrose tiling arrangement) consist of two or more types of rhombuses, three-dimensional quasicrystals are made of two or more rhombus-shaped cells.

There are two widely used methods for creating quasicrystals: the projection method, in which a six- or more-dimensional pattern is projected onto three-dimensional space, and the de Bruijn mesh method, in which three or more vectors in space create a sequence of families of planes that in turn result in a specification of the quasicrystal.

Minimal surfaces are curved, two-dimensional, space-occupying mathematical constructs that satisfy the requirement that at each point, the average of two perpendicularly measured curvatures is zero. Each point is therefore defined such that if the surface is curved by a certain amount in a certain direction, then the curvature measured perpendicular to that direction is the negative of the first curvature. Because minimal surfaces are the least curved surfaces connecting a given set of points, they constitute an ideal geometry that allows for the most efficient conductors of forces other than spheres and catenaries (the latter of which is a minimal surface itself). This makes a minimal surface ideal for distributing loads and forces in structures such as three-dimensionally printed parts, and indeed in every load-bearing structure. Minimal surfaces whose fundamental cells are structured in such a way that they can be repeated in all directions (thereby tiling an infinite space) are called "triple periodic minimal surfaces (TPMS)".

Additive manufacturing (AM, "three-dimensional printing", "rapid prototyping") is an umbrella term covering a wide range of computer-controlled manufacturing processes that enable the physical formation of products made from various materials. For the purposes of the present invention, it should be understood that additive manufacturing also includes robotic assembly of parts.

Before an object can be 3D printed, it must be defined in the form of a virtual computer model ("CAD model", "3D model") in which its geometry is represented as mathematical functions ("CAD surfaces"), through the coordinates of vertices, edges, faces and their interdependencies describing the space enclosed by the 3D model, or as a 3D voxel matrix ("voxel" is a combination word that combines "volume" and "pixel"). In most standardized 3D model interchange formats, the geometry of objects is represented as a polygonal mesh of triangles and/or quadrilaterals (the coordinates and interdependencies of vertices, edges and faces that form the volume). While the polygonal mesh representation is very flexible and can be used to (approximately) describe almost any shape without the need for mathematical analysis of its geometry (which is necessary when using the CAD surface representation), it is clearly error-prone and tends to result in large amounts of data and therefore high network traffic and computational load.

In most types of AM processes, the part is formed by the sequential, layer-by-layer application of either bonding, strengthening, or polymerization of one or more substances. The bonding, strengthening, or polymerization process may be called upon continuously, immediately after application or after each layer is processed, either at the end of the build process or in an entirely separate process outside the actual printing press. Preparing a 3D model for 3D printing therefore involves converting the spatial information contained in the 3D model (the "preprocessing") into "material/no-material" information packets for each layer (the "slices"). In most cases, the slices are simple bitmap images associated with the desired print layer height, with black representing "material" and white representing "no-material". On the one hand, each pixel in the slice corresponds to one minimum printing unit in the layer (e.g. depending on the characteristics of the printing machine; minimum diameter of the laser dot, laser path, etc.), and on the other hand, it represents one voxel in the printed product. In some cases, the slice contains additional control information related to printer-specific or product-specific parameters, such as laser energy or laser travel speed, which may differ for each layer or vary within a layer.

Other operations in pre-processing include global parameter adjustments based on the characteristics of the printing press and/or the printing process and/or their modeling and optimization, such as weight reduction ("lightweighting").

AM enables the formation of extremely complex parts that are very difficult, if not impossible, to assemble with classical manufacturing methods. Depending on the geometry of the part, the printing method and the material used, an external assembly support structure (“assembly support”) is necessary to ensure correct and error-free production of the part. Some methods and/or materials do not require assembly supports, as they are stabilized by the carrier itself during formation. However, most methods used to form parts from metals such as steel, aluminum, titanium, etc. require assembly supports not only to ensure error-free formation and correct print geometry, but also to dissipate excess heat. Removal of assembly supports during post-processing is often labor-intensive, and in cases where the assembly supports are internal or difficult to access due to the shape of the part, almost impossible or simply impossible without damaging the object.

Therefore, the more self-supporting the product is (the fewer the number of assembly supports required for a successful assembly process), the better. In order to maximize strength while minimizing weight, and since complex, "bionic" or amorphous geometries can be formed in AM without additional cost or effort, the shape of products is often parametrically optimized according to the minimum use of materials and the optimal shape that satisfies the structural and geometric requirements of the product. Compared to the initial design solution of the product (which in some cases is "classical" monolithic), such an optimized shape often has holes, branches, bulges and veins; the process leading to this shape is therefore called "topology optimization", since the topology of the product - the number of holes it has (its "genus") - is changed.

Such optimization is often part of the CAE (computer-aided engineering) process, in which geometric constraints, forces, stresses, and motions are modeled, often using a computer-aided technique called finite element modeling (FEM). Some products are designed and manufactured without the need or assistance of FEM modeling; these are often products that are not intended to be optimally optimized. Products in which the strength-to-weight ratio is critical (e.g. in aerospace or industrial applications), on the other hand, are always designed using FEM or similar techniques. Since forces tend to flow along the surface of an object rather than through its interior, the object can, in principle, be reduced to a thin skin. Naturally, a certain cross-section of the material must be maintained to conduct the forces, reveal the geometric integrity, and account for the material characteristics and stresses acting on the product.

In some cases, the addition of an internal structure connecting the skin sides significantly increases the overall stability, while not revealing the geometric integrity of the product under mechanical stress and during the assembly process. However, while this dilution of the "classically" formed or topologically optimized product results in reduced manufacturing time and cost, significant weight gains, and sometimes even increased stability, most products are still manufactured in solid form. This is due in part to the difficulty of machining large polygonal meshes, which are inherently error-prone, and the need to reveal the integrity of the form and geometry of the products, which may be subject to distortion, during the assembly process, in use, and under load if a coherent, carefully designed, and carefully modeled internal structure is not present.

A widely used hollowing out technique is the application of "infills", which are simple geometric lattice structures ("spatial grids") that complement the "interior" of the product. However, there are three major drawbacks to this technique: (1) the effective structural impact and infill efficiency are subject to unreasonable assumptions unless studied using FEM, (2) the infill geometry must be inherently extremely simple since it must be similar to the layout support structure (which, of course, can always be laid out without the need for an additional layout support), and (3) the infill structure significantly increases the number of polygons in the 3D model (thereby also increasing the computational load and response time), since it is very small-scale compared to the 3D model itself, but must be precisely defined. Because complex and/or sophisticated infills can increase the polygon count of a 3D model by one or more orders of magnitude, infills are typically analogous to layout supports: roughly shaped, coarse and fine, optimized more for printability than structural efficiency.

Therefore, there is a need to provide methods and means for pre-processing additively manufactured articles that overcome at least one known limitation.

Disclosure of the essence of the invention

It is therefore an object of the present invention to provide a method, a computer program product and an additively manufactured article that overcome at least one of the disadvantages of the prior art. A specific object of the present invention is to provide such a method, a computer program product or an article that provides weight reduction and/or design of an article with superior properties at least with respect to its geometric integrity and/or load-bearing structure compared to having an identical article conventionally designed and/or weight-reduced.

The present invention therefore relates to the production of additively manufactured articles and their pre-processing, whereby the article may comprise one or more integral parts of the article, each of which has an internal structure (“filling”) that provides increased stability, reduced weight and production support and/or assembly support.

The aim of the present invention is achieved by a method, a computer program product and an additively manufactured article according to the characteristic parts of the independent claims of the invention.

One aspect of the present invention is a method for lightening the weight and/or design of an additively manufactured article. The article comprises one or more integral parts of the article, each of which has a structure. The method comprises at least a step of filling and/or assembling each of the one or more integral parts of the article by means of a quasi-crystalline structure.

In a particular embodiment of the present invention, each or some of the one or more integral parts of the article comprises an internal structure, and lightening the weight refers to designing the internal structure in such a way that stability, weight, and manufacturing support, respectively, of the assembly support during the additive manufacturing process are affected by the method steps described herein.

In one particular embodiment, the article and/or one integral part of the article substantially consists of a structure.

In the context of the present invention, the filling according to the above step can be understood as a weight reduction step according to the present invention, whereas the assembly step above can be considered as a design step of the additively manufactured article according to the present invention. In the context of the present invention, the filling can be understood as providing an internal structure, which in the processed article according to the present invention is at least partially, preferably substantially, masked by the outer skin of the article. In contrast, the design is a relevant method when the structure is "open", i.e. the article is not covered by the outer skin. It will be obvious to those skilled in the art that a combination of both method steps can be applied to one specific article, for example with a plurality of integrally formed parts of the article, and the processed article resulting from the method according to the present invention can consist of parts that have a skin covering the filling and parts of the article for which the structure is accessible from the outside, with different degrees between them.

In the context of the present invention, a quasi-crystalline structure may be understood as a structure that is ordered but not periodic, as will be understood by those skilled in the art.

In a particular embodiment of the present invention, the quasi-crystalline structure is a three-dimensional quasicrystal made of two or more types of rhomboid-shaped cells.

In an alternative embodiment, the quasicrystalline structure is a three-dimensional crystal, i.e., regularly repeating units formed according to one of the space groups, namely, according to one of the 219 non-chiral or 11 chiral space groups.

In the context of the present invention, a cell in this rhomboid shape can be understood as a three-dimensional body with six transverse sides of parallelogram geometry.

In a particular embodiment of the present invention, the quasi-crystalline structure may be created by a projection method, for which a six- or more-dimensional pattern is projected onto a three-dimensional space. Alternatively or additionally, the quasi-crystalline structure may be created by applying a grid-based method, in which four or more vectors in space create a sequence of families of planes, which in turn lead to a specification of the quasi-crystal. Different methods for forming the quasi-crystalline structure may be used for the production of a single product, for example, for different parts of the product, or even subsequently as a verification step.

In a particularly preferred embodiment, the grid-based method is based on the diagonalization of de Bruijn (N. de Bruijn, Ned. Akad. Weten. Proc. Ser. A 43, 39 (1981); 43, 53 (1981).

In a particular embodiment of the present invention, the filling and/or arrangement of each of the one or more integral parts of the article is a filling and/or arrangement by means of a quasi-periodic minimum surface filling and/or a quasi-periodic minimum surface design structure and/or an aperiodic minimum surface design structure and/or an aperiodic minimum surface filling.

In a particularly preferred embodiment, the resulting infill and/or design solution comprises minimal surfaces, i.e., for example, surfaces for which, at each point on the surface, the average of two perpendicularly measured curvatures is zero or virtually zero.

In the context of the present invention, “virtually zero” may be understood as a curvature sufficient to substantially represent the minimum surface properties in the scale and shape of the design solution for the article and/or its filling, even more specifically, having a deviation from zero to +/- 0.0005 for the average of two perpendicularly measured curvatures on the surface.

In a particularly preferred embodiment, the resulting infill and/or design comprises periodic surfaces, such as, for example, three-dimensional crystalline surfaces.

One advantage of the minimal surfaces according to the present invention may be that they are ideal for distributing loads and forces within or through structures. In addition, these minimal surfaces may be ideal for creating objects for which large surfaces and/or surface-to-volume ratios are useful, such as in parts of an article that have applications in the field of construction engineering, catalysis, heat transfer, batteries, etc., or in any other field of application for which the surface-to-volume ratio is important. Without being bound by theory, the realized structural advantages may be due to the fact that minimal surfaces are the least curved surfaces connecting a certain set of points and therefore provide the ability to conduct forces between these points most efficiently.

In a particularly preferred embodiment, the method of the present invention is carried out by filling and/or arranging by means of a quasi-periodic minimum surface filling and/or a quasi-periodic minimum surface design structure and/or an aperiodic minimum surface design structure and/or an aperiodic minimum surface filling in such a way that an effective conductor of forces is provided through the article.

In a particular embodiment of the present invention, the method comprises an additional step of using the quasi-crystalline structure as a framework to form a quasi-periodic minimum surface filling and/or a quasi-periodic minimum surface design structure. In the context of the present invention, the framework may be a skeleton formation, for example, to achieve a definition of the kind of quasi-periodic minimum surface. In an alternative or additional embodiment of the present invention, the method comprises an additional step of using the quasi-crystalline structure as a framework to form an aperiodic minimum surface filling and/or an aperiodic minimum surface design structure.

In a particular embodiment of the present invention, the method further comprises a step of creating a quasicrystal geometry. This creation of the quasicrystal geometry may be performed, in particular, by a first step of inputting at least three primary vectors. In a further particular embodiment, the step is the input of 3-12 vectors. In the context of the present invention, the input may be understood as the selection and/or formation of a corresponding specific parameter in the computer program product. Such input may be performed, for example, by means of digital pre-processing and/or configuring pre-processing associated with the software and the device for additive manufacturing.

In this particular embodiment, the creation of the quasicrystal geometry may comprise, in particular, an additional step of creating a number of groups of parallel planes for each of the input primary vectors. Each group of parallel planes contains at least three planes.

In this particular embodiment, the number of parallel plane groups is limited only by the processing power and memory of the computer system used. However, it has been found that a number of parallel plane groups in the range between 3 and 1000 is particularly preferred, and in the range between 3 and 50 is even more preferred. The number of parallel plane groups together with the number of planes in each group can be selected by the user and defines the "resolution" of the quasicrystal. In the context of the present invention, the resolution can be understood as the number of cells in a specific predetermined volume of the article. Without being bound by theory, the number of planes selected by the user is set at the discretion of the user, but can be affected by or must necessarily be within certain threshold values for certain purposes or applications. For example, a specific number of planes can be set as required to achieve the desired stability or due to requirements due to limitations in the size of the article. As mentioned above, there are theoretically no limits to the upper number of planes selected, although in fact they can be limited by the processing power of the computers used for the method. However, it is possible that up to 100,000 planes can be processed using suitably powerful computers.

In a particular embodiment, the number of parallel plane groups corresponds to the number of input vectors. In a particularly preferred embodiment, the direction of the planes is specified by the vectors. Even more preferably, the direction of the planes is normal to the selected vector. In other words, each vector may be associated with a parallel plane group that spans an angle of 90° relative to the vector.

In a particular embodiment of the present invention, the planes in one particular group of parallel planes are uniformly spaced. In this context, "uniformly spaced" shall mean planes in one particular group, i.e., for example, the distance in a group of at least three planes corresponding to each other. In a particularly preferred embodiment, all planes of this particular group are uniformly spaced. This may be understood as all planes in this particular group having an identical distance in the normal direction corresponding to the plane relative to the previous neighboring plane and the next neighboring plane.

In a particular embodiment of the present invention, the planes in one particular group of parallel planes are randomly spaced. More particularly, all the planes in this particular group are randomly spaced. The random spacing may be specified at the time of generating the vectors. By inputting a vector, a certain number of randomly placed planes normal to this vector may be created, for example, each of which has a random distance relative to the other planes in the identical group.

In a particular embodiment of the present invention, the planes in one particular group of parallel planes are spaced according to a given pattern. In particular, it is advantageous if all the planes in one particular group are then arranged in this given pattern. In a particular embodiment, the spacing may be determined by means of the results of a particular FEM, i.e., finite element method, applied to design and/or fill the product with respect to the desired properties.

In a particular embodiment of the present invention, at least some planes in one particular group of parallel planes are equally spaced, and/or some planes of the planes are randomly spaced, and/or some planes are spaced according to a given pattern. As indicated above, the number of planes may be selected as an indicator of the resolution of the resulting quasicrystal geometry. In a further particular embodiment, one group of planes may be created using particular given rules. In the context of this example, the given rules may specify, for example, that if a number of ten planes are created in one particular group, for example, one input vector should have a number of ten parallel planes normal to said vector, in other words, covering an angle of 90° between the plane and the vector, then out of these ten planes, three planes are specified to be randomly spaced along the extent of the vector, four planes are arranged to be in an equally spaced arrangement corresponding to each other, i.e. where each plane is followed by a successive plane of four after a certain correct distance, and the resulting three planes in this group of planes are arranged according to a pattern, which may be, for example, 1:3, which means that the second plane comes after the first plane with a first distance, and the third plane comes after the second plane with a second distance, which is three times the first distance. It should be obvious to those skilled in the art that these variables can be subject to interdependent control methods by means of a rule, where, for example, a specific prescribed pattern is combined with equidistantly placed planes, so that all three requirements of "random", "prescribed" and "equally spaced" can be included in the creation of the geometry of one specific quasicrystal according to the present invention.

In a particular embodiment of the present invention, the method further comprises the step of bisecting the rhomboid-shaped cell(s) such that the faces resulting from the bisection have a hexagonal shape. In the context of the present invention, the bisection thereby results in an intersection that has a hexagonal shape.

In a particular embodiment, bisecting a rhomboid-shaped cell results in two equal monotruncated tetrahedra from the cell.

A truncated tetrahedron is a regular tetrahedron with four corners cut off. For the purposes of the present invention, a monotruncated tetrahedron is a new term defined for the purposes of illustrating the present invention and can be understood as a tetrahedron with only three of its four corners cut off. Compared to a truncated tetrahedron, it has seven faces instead of eight (Greek; "mono=one" and "tria=three").

In a particular embodiment of the present invention, the center of gravity of the rhomboid-shaped cell is in the plane of intersection resulting from dividing the rhomboid-shaped cell in half. This face has a hexagonal shape, as described above.

In a particular embodiment of the present invention, the bisection is performed across six edges of the cell of the diamond shape in question, preferably in the middle of the six segment lines in question.

In a particular embodiment of the present invention, the method comprises the additional step of assigning each monotritruncated tetrahedron to one of the two groups such that two labyrinths are formed from the two groups of monotritruncated tetrahedrons. In a particular embodiment, each of the monotritruncated tetrahedrons resulting from dividing the rhomboid-shaped cell in half is assigned to either of the two groups, i.e. the first group of monotritruncated tetrahedrons or the second group of monotritruncated tetrahedrons. The first group forms the first labyrinth, and the second group forms the second labyrinth. Preferably, the first and second labyrinths extend throughout the internal structure of the article and/or the integral part of the article.

In a particular embodiment, the method of the present invention comprises the additional step of inserting a skeleton graph into each of the types of rhomboid-shaped cells, in particular one skeleton graph into each monotritruncated tetrahedron in such a way that two interleaved skeleton graphs are created, spanning the entire quasicrystal without being interconnected at any point. These skeleton graphs extend through one of the two labyrinths formed by assigning each monotritruncated tetrahedron to one of the two groups, as described above. The skeleton graphs may be placed inside a monotritruncated tetrahedron in such a way that they extend through the surfaces of the tetrahedrons into neighboring tetrahedrons of the same group in such a way that all skeleton graphs in a particular group of monotritruncated tetrahedrons are connected to each other. In other words, the first skeleton graph extends through the first group of monotritruncated tetrahedrons, and the second skeleton graph extends through the second group of monotritruncated tetrahedrons.

In a particular embodiment of the present invention, for an article with more than one integral part of the article, each of which has a structure, the steps of selecting the number of planes are performed separately. One advantage of achieving this may be that it becomes possible to create zones of increased "resolution".

In a particular embodiment related to integral parts of an article with an internal structure, skeletal graphs may be scaled up and/or down to create locally dense skeletal graphs and/or less dense skeletal graphs. The scaling up and/or down may be dependent on a set of parameters, such as parameters selected from the group consisting of the following: three-dimensional geometry of the article, printer parameter(s), finite element modeling, etc.

In the context of the present invention, a skeleton graph, for example, can be formed by a plurality of trees, where each tree represents a fine-scale graph filling one monotritruncated tetrahedron and consisting of a plurality of segments. In particular, each tree comes with a mirror partner rotated by 60 degrees along the axis of the diagonal of the diamond cell of the corresponding monotritruncated tetrahedron.

In a particular embodiment, the up- and/or down-scaling may result in empty areas in integrally formed parts of the product with an internal structure. Accordingly, the method may further comprise a step of filling empty areas in integrally formed parts of the product with an internal structure resulting from the up- and/or down-scaling of the skeletal graphs. This may be achieved, for example, by extending the free ends of the skeletal graphs with additional trees.

By being able to dynamically and locally adapt the geometry, density and scale of the skeletal graphs, it becomes possible to create customizable and adaptive infills and/or design solutions. If the printing parameters are also taken into account, it may additionally become possible to make parts printable without the need for printed support structures for processes that previously required them and/or to print parts that are resistant to high forces. These objects are further characterized by the maximum mating surface in a given space and by using the least amount of material to achieve this. Possible applications may be as building blocks or as structures for heat exchangers, air conditioning, batteries, dialysis machines, other medical devices, filters, implants, nanoscale materials and metamaterials, microscale materials and metamaterials, etc. Since the labyrinths create two interleaved but separate continuous internal volumes, they can be used as impact-resistant containers for powders, grains, liquids and/or gases with special advantages in applications in which two components must be stored separately, i.e. before being mixed together during use. In addition, the resulting products are advantageously useful as containers for systems in which two components are stored separately and subsequently used together, such as fuels, adhesives or building materials. This represents only an approximate number of possible applications for the resulting products.

In a specific embodiment of the present invention, which may be an alternative or additional to the scaling of the skeleton graphs described above, a voxel-based three-dimensional pre-processing is performed, in which the internal structure is optimized based on the mechanical stress and automatically generated. In this embodiment, a pair of skeleton graphs may be generated as described above with an unscaled density, preferably with an unscaled density corresponding to the highest density required for a specific task depending on the mechanical stress/stretching and the shape of the product. In a further specific embodiment, the voxel-based three-dimensional pre-processing comprises FEM modeling. In yet another further specific embodiment, the shape of the product corresponds to said skeleton graphs with a homogeneous density. Based on the shape of the product and/or the layout parameters and/or the analysis of the mechanical stress/stretching, the skeleton graphs are thinned by removing individual segments and/or highways of the graphs, thereby creating locally denser and less dense regions.

In the context of the present invention, the unscaled density skeleton graph may be provided by the method of the present invention as described above, starting with rhomboid-shaped cells, bisecting the cells into monotritruncated tetrahedra, and creating skeleton graphs that continue through both groups of monotritruncated tetrahedra, as explained above, and encompassing various variations and alternatives as described above. Alternatively, the skeleton graph provided by the method of this embodiment may be provided by a pre-existing skeleton graph, such as from a triply periodic minimal surface known in the art.

One additional advantage of the present invention may be to provide an automated filling system by implementing the method according to the present invention. All this, taking into account the FEM modeling, the required resistance, geometry, size, weight, material and parameters of the devices, is discretionary from the corresponding printing task.

In a particular embodiment of the present invention, skeleton graphs are used to construct surfaces that are equidistant from both graphs and globally separate two mazes defined by the skeleton graphs.

In a further specific embodiment, a voxel-based Voronoi analysis is used to create a first approximation of a surface equidistant from both graphs.

In yet another further embodiment, by minimizing the mean square curvature of this surface, the minimum surface can be created as detailed above. Alternatively and/or additionally, the surface smoothing can be performed by methods selected from the group consisting of the following: smoothing by using the Laplace operator, LS3 subdivision of Loop and algorithms based on curvature flow, etc., or a combination of the above. In an alternative or additional embodiment, by minimizing the mean square curvature of this surface, an aperiodic minimum surface can be created, as detailed above.

In yet another embodiment, smoothing the surface equidistant from both graphs obtained by the Voronoi voxel analysis may be performed by repeatedly applying the following operations: (1) one iteration of the LS3 Loop subdivision weighted to improve regularity, (2) one to ten iterations, preferably three iterations, of smoothing by the Laplace operator using cotangent weighting, and (3) reducing the mesh resolution to 50% using a quadratic face collapse simplification algorithm or reducing the mesh resolution to 50%, or to 25%, or to 12.5%, or to 6.25%, or to 3.125%. Preferably, these operations are performed such that all triangles on the boundary(ies) of the surface remain non-touching.

By increasing the iterations, the minimal surface can be approximated with greater accuracy. This results in a smoother surface. The number of iterations may depend on the computer performance, the required accuracy and the available computation time, but two or three iterations are preferably performed.

In a particular embodiment of the present invention, the skeleton graphs, after minimizing and/or smoothing the curvature of the equidistant surface, create a triply periodic minimal surface selected from the group consisting of the following: disphenoidal Bracke surfaces of genus 31, 35, 43, 51, 55 and 67, hexaplanar Bracke surfaces of genus 6, 12, 18, 24 and 30, star-shaped Bracke surfaces of genus 31, 43, 47, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 99, 103, 115, triplanar Bracke surfaces of genus 3, 9, 15, 21, 27, 33, S-, C(S)-, Y- and C(Y)-surfaces Fischer-Koch, P3a-Lord-Mackay surface, Neovius surface and complementary P-Schoen surfaces of genus 15, 21, 27, 33, 39 and 45, Ж-shaped Shen surfaces of genus 25, 41 and 57 and pseudo-Ж-shaped Brakke surface, F-RD-, F-RD(r)-, P-, F-RD-, S'-S''|P- and S-S''-Schoen surfaces, GW-, I-WP-, I-WP(r)- and O-, CT-O-Schoen surfaces, gyroidal Shen surface, H'-T, H''-R, T'-R', H'-T|H''-R, T'-R'|H'-T and H''-R|T'-R'-Schoen surfaces, hybrid S-S'', S'-S''|P, H'-T, H''-R, T'-R', H'-T|H''-R, T'-R'|H'-T and H''-R|T'-R'-Schwarz surfaces, mantle Shen surfaces of genus 19, 35 and 51, RII-, RIII-, I-6-, I-8- and I-9-Schwarz surfaces, N14-, N26- and N38-Schwarz/Bracke surfaces, P-, D-, H-, CLP-Schwarz surfaces, complementary D-Schwarz surface and all derivatives of the above.

In particular, it is preferable if the skeletal graphs, after minimizing the mean square curvature of the equidistant surface or after smoothing by any other means as described above, create a triply periodic minimal surface selected from the group consisting of the following: a Schwartz type P-surface, a Schwartz type D-surface, a Shen type G-surface, a Fischer-Koch type S-surface, a Fischer-Koch type CY-surface, a Shen type GW-surface and/or a Lord-Mackay type P3a-surface.

Those skilled in the art will appreciate from the teachings of the present invention that the embodiment of the method described herein may result in a design solution and/or filling with a quasi-periodic and/or aperiodic minimum surface not previously characterized as represented in any of the above groups.

In a particular embodiment of the present invention, local adaptation of skeletal graphs as described above, i.e. by up-scaling and/or down-scaling and/or segment removal, results in a unique minimum surface optimized for a particular product.

One aspect of the present invention is the application of the described method in the design and pre-processing stage of additive manufacturing for lightening the weight and/or design of an article to be printed. Parameters for local adaptation and hyperbolic scaling of skeletal graphs are then determined based on the article geometry, finite element modeling of load cases, printing method parameters, etc., required by those skilled in the art for a specific printing task.

An additional aspect of the present invention is a computer program product for pre-processing an additively manufactured article, wherein the article comprises one or more parts of the article, each of which has a structure, in particular, whereby one of these structures is an internal structure. The computer program product is configured to implement the method according to the present invention, when executed on a computer.

An additional aspect of the present invention is an additively manufactured article obtainable by implementing the method of the present invention. The article comprises a quasi-crystalline and/or quasi-periodic minimum surface filling and/or a quasi-periodic minimum surface design structure and/or an aperiodic minimum surface filling and/or an aperiodic minimum surface design structure.

In a particular embodiment of the present invention, the additively manufactured article obtained by the method described above comprises an outer skin defining the shape of the article and a filling. The filling comprises a substantially quasi-periodic minimum surface. In the context of the present invention, the substantially quasi-periodic minimum surface may be an approximation of the minimum surface by performing smoothing, as described in the above embodiments of the method.

In a further specific embodiment, the additively manufactured article has a minimum surface filling that touches the outer skin in a substantially perpendicular direction. In the present context, "substantially perpendicular" can be understood as a tolerance of a potential deviation between 0.1 and 5 degrees from an angle of 90 degrees, whereby it provides an ideal conductor of loads from the skin of the article to the filling. In a specific embodiment, the minimum surface is aperiodic.

In a particular embodiment of the present invention, the additively manufactured article comprises a metal, even more preferably a metal used for selective laser melting.

By means of the present invention, a universal method for creating, specifying and sizing customized and optimized structures for additively manufactured articles is provided, which enables structuring and filling of these articles with a custom-made structure adapted to the geometric, structural and printer-specific requirements of the particular article, which must be specified by specialists in the art.

The present invention is illustrated below by means of drawings and specific examples, without being limited thereto. However, those skilled in the art should be able to derive additional advantageous embodiments and implementations of the invention by studying the corresponding examples.

It should be readily apparent to those skilled in the art that all of the above described embodiments may be included in the method, computer program product and/or article of manufacture according to the present invention in any combination, provided that they are not mutually exclusive.

Brief description of the drawings

Fig. 1a-1e schematically show how the structure or internal structure according to the present invention can be arranged;

Fig. 2a and Fig. 2b show exemplary structures obtainable by the method of the present invention;

Fig. 3a and Fig. 3b schematically show how downscaling according to the present invention can be performed for illustrative geometries;

Fig. 4a and Fig. 4d schematically show how an exemplary object may be filled with an adaptively scaled structure according to the present invention;

Fig. 5a-5e schematically show how an exemplary object may be filled with an adaptively scaled structure according to a further embodiment of the present invention.

Fig. 6a and 6b show an example of the present invention;

Fig. 7a and 7b show exemplary internal structures and/or structures according to the present invention, and

Fig. 8 shows an embodiment of the present invention based on the method according to Figs. 5a-5e;

Fig. 9 is an illustration of a product without outer skin, assembled according to the idea of the present invention.

Description of embodiments of the invention

Fig. 1a-1e serve to illustrate some steps of the method of the present invention for lightening the weight and/or design of an additively manufactured article by illustrating a step-by-step approach and a schematic progression through the various process steps that may lead to a structure according to the present invention, in a simplified example.

Fig. 1a shows a rhomboid-shaped cell 1, which can be used as a basic initial building block for implementing the method of the present invention. In a first step, a rhomboid-shaped cell 1 with six faces is provided, and in the present example it consists of six rhomboid-shaped faces connected by edges 11, ..., 22, having a total number of twelve edges 11, ..., 22. The rhomboid-shaped cell 1 in the present example forms a rhombohedron in which none of the angles between two adjacent edges 11, ..., 22 are located at a right angle. In the context of the present invention, a rhomboid should always be referred to as associated with a three-dimensional shape.

The rhomboid-shaped cell 1, as illustrated in Fig. 1a, is an exemplary representation of such a cell. In this example, the de Bruijn grid-based method is used by inputting four vectors as the primary input and creating a certain number of plane families (each consisting of a certain number of parallel planes). In the present example, the number of plane families corresponds to the number of vectors, i.e. four.

Additionally, with respect to the present example, each plane family has three planes. As already detailed in the general description, the number of planes may vary depending on the required resolution for the intended geometry of the resulting quasicrystalline structure and is essentially limited only by the processing power of the computer system used to design the product.

In this example, three planes are used for each plane family, and the spacing between the planes is chosen to be uniform, i.e. each plane is placed equidistant from the corresponding successive plane relative to the previous one. All these planes are normal to the vector. As already detailed above, the placement of the planes can be changed to random or to correspond to specific specified distances.

In the first step, the rhomboid-shaped cell 1 is divided in half. The bisection of the rhomboid-shaped cell 1 is performed by placing two tetrahedrons 30.1, 30.2 having identical volume in the rhomboid-shaped cell 1 in such a way that only the minimum volume of the corresponding tetrahedron 30.1, 30.2 remains outside the rhomboid-shaped cell 1 and none of the volume of the rhomboid-shaped cell 1 is covered by the corresponding tetrahedron 30.1, 30.2. In the illustration of Fig. 1a, the tetrahedrons 30.1, 30.2 are shown with a dotted line. The tetrahedrons 30.1, 30.2 are placed in the rhomboid-shaped cell 1 in such a way that each pyramidal tetrahedron is cut out from the edges of the tetrahedrons 30.1, 30.2. The contact face between two tetrahedrons 30.1, 30.2 shall form the intersection face F (see Fig. 1b). In the present example, the contact surface between two tetrahedrons 30.1, 30.2 cuts transverse edges 13, 14, 15, 17, 19, 20 in the middle of the corresponding edge length. The corners of the tetrahedrons 30.1, 30.2 are chosen so that they coincide with the corners of the rhomboid-shaped cell 1.

Additionally, the first tetrahedron 30.1 of the two of them is allocated to the first group A, while the second tetrahedron 30.2 is allocated to the second group B.

As shown in Fig. 1b, the bisection of the rhomboid cell 1 results in an intersection face F which is hexagonal, with each corner located on the corresponding transverse edge of the rhomboid cell 1 and, in the present example, exactly in the middle of said edge. The rhomboid cell 1 is bisected into two bodies of equal volume. For the purposes of the present invention, these two bodies are called "monotriatruncated tetrahedrons 2, 2'". As already indicated above, for the context of the present invention, a truncated tetrahedron can be understood as a regular tetrahedron with four corners cut out. A monootriatruncated tetrahedron, on the other hand, is a tetrahedron only three of whose four corners are cut out. Compared to a truncated tetrahedron, it has seven faces instead of eight.

The bisection therefore results in two monotriatruncated tetrahedra 2, 2' corresponding to the tetrahedron used for the bisection and suitable for the corresponding half of the rhomboid-shaped cell 1. Each of the monotriatruncated tetrahedra 2, 2' belongs to either the groups A or B. In the illustration of Fig. 1b, the monotriatruncated tetrahedron 2 on the left belongs to the group A, while the monotriatruncated tetrahedron 2' on the right belongs to the group B. It will be readily apparent to those skilled in the art that this division is purely arbitrary and, for the purposes of illustrating the teachings of the present invention, it is relevant if, based on any rhomboid-shaped cell, by bisecting the cell into two tetrahedra of equal volume, each of which is substantially located within a structure with a plurality of rhomboid-shaped cells, two groups A, B are created, each of which forms a labyrinth, as explained in more detail below.

For the present example, after initially selecting a monotriatruncated tetrahedron 2, 2' of either group A or B, one must in fact follow identical logic for all rhomboid-shaped cells within the same structure. In other words, if the half "on the left" is selected such that it belongs to group A, then in the full structure, all halves that are logically "left" halves must form a monotriatruncated tetrahedron 2 belonging to group A.

This allocation of monotriatruncated tetrahedra 2, 2' to one group already creates two interwoven continuous and quasi-periodic infinite polyhedra within the structure.

Fig. 1c illustrates an additional step of the method. In each of the resulting monotritruncated tetrahedrons 2, 2', a skeleton graph A', B' is inserted. The skeleton graphs A', B' illustrated in Fig. 1c are illustrative examples of how such skeleton graphs can be inserted into the corresponding monotritruncated tetrahedron 2, 2'. In this way, for each rhomboid-shaped cell of the corresponding structure, the skeleton graphs A', B' are extended, for example, in such a way that they span the entire volume of the structure. Each skeleton graph A', B' is connected to the skeleton graph(s) A', B' in the adjacent monotritruncated tetrahedron of the identical group. To illustrate the group attachment in the present example, the skeleton graphs are referred to with the same letter as the group to which they belong, i.e. the skeleton graph A' of Fig. 1c continues into the volume created by all monotriatruncated tetrahedra 2 belonging to group A.

In the present example, as illustrated in Fig. 1d, the skeleton graph A' branches from two internal nodes N1, N2. The internal nodes N1, N2 may be located within a particular region N within the volume of the monotritruncated tetrahedron 2 belonging to the group A. This may result in a "backbone" of the tree structure for the skeleton graph in the monotritruncated tetrahedron 2. The "backbone" has a varying size, up to a particular embodiment in which the first internal node N1 and the second internal node N2 are identical, i.e., are in the same spot, and the length of the "backbone" is zero.

In the present example, the first internal node N1 and the second internal node N2 are spaced apart and branch into three branches each. For the clarity of the drawings, the branching is illustrated by means of the mentioned example in the monotritruncated tetrahedron 2' belonging to the group B. Here, the first and second internal nodes are spaced apart and connected by the backbone b1. Each internal node branches into three branches, and these branches cut the surfaces of the monotritruncated tetrahedron 2' in specific zones. To construct the skeleton graph B' belonging to the group B, each monotritruncated tetrahedron 2' is connected to adjacent monotritruncated tetrahedrons and has a connecting node bi, ..., bl that touches the connecting node of the corresponding neighboring monotritruncated tetrahedron in a specific face G, ..., L of the node. For example, the branch of the first node of the skeleton graph B' in Fig. 1d extends through the face G of the knot and cuts this face at the connecting node bg. This connecting node bg is the point at which the corresponding branch of the adjacent skeleton graph connects to the skeleton graph of the monotriatruncated tetrahedron 2' of Fig. 1d.

The resulting skeletal graphs A', B' encompass or integrate the entire quasicrystal without being interconnected at any point. Fig. 1e illustrates the step of creating a minimal surface infill structure by constructing a surface equidistant from both skeletal graphs. This divides the volume of the overall structure, which is filled with infill or designed to be composed from the structure according to the present invention, into two separate volumes A, B. The structure can be dynamically adapted to adjust to varying product geometries, and since the rhomboid-shaped cell 1 of the present invention is specifically chosen to be simple in Figs. 1a-1e, it should be obvious to those skilled in the art that within the structure, there may be a certain number of compressed, expanded or distorted rhomboid-shaped cells. The construction of the surface equidistant from both skeletal graphs may comprise an approximation of the surface equidistant from both skeletal graphs.

In the present example, structure 10 is illustrated with two corresponding skeleton graphs A', B' and a corresponding interior volume A, B through which the skeleton graphs A', B' belonging to one particular group A or B are extended.

In this particular example, the minimization of the root-mean-square curvature of surfaces equidistant from both graphs is applied by means of computer FEM processes. Depending on the spatial, geometrical and mechanical constraints and load cases specified for the product, when using the present method, the structure is unique and, in particular, adapted to the product. Due to this most basic principle of the present invention, a method is provided by which an infinite number of products can be assembled, consisting of the above-described structure or containing the above-described structure as a filling and internal structure for load-bearing or other structural reasons. In addition, since the method of the present invention essentially ideally divides a given volume into two equal labyrinths, applications in which such a division of a volume into two compartments is required receive a significant benefit from the idea of the present invention.

Fig. 2a illustrates how the article 50 can be laid out with a plurality of rhomboid-shaped cells 1, 1', 1''. In the present example of Fig. 2a, a total of four rhomboid-shaped cells 1, 1', 1'' are shown for illustration, wherein two of these rhomboid-shaped cells 1'', 1'' are identical to each other, and two additional cells 1, 1' are different from each other and from the above-mentioned type of rhomboid-shaped cell 1'', 1''. As can be seen from Fig. 2a, the skeletal graph A', which extends through the volume A, which is separate from the volume B by the structure 10, encompasses each of the rhomboid-shaped cells 1, 1', 1''. The structure can be expanded with additional cells based on the specific needs of the article to be manufactured, and in Fig. 2b illustrates that no matter how large the product is formed and how many cells are added, the basic building blocks adhere to the same principle with the rhomboid-shaped cell 1, and the corresponding monotritruncated tetrahedra 2, 2' still form the basic building blocks and provide the placement of the corresponding skeletal graphs A', B', which continue through the internal volumes A, B and cover the entire volume of the product.

One advantageous concept of the present invention is illustrated in Fig. 3a and 3b. The method of the present invention can be easily adapted to accommodate varying product geometries and can result in structural integrity optimization and a load case for a large number of products by scaling the structure according to the product geometry.

Fig. 3a shows an example in which the filling for the front end of an article comprising an outer skin 23, wherein the skin 23 which defines the shape of the article is adapted by applying a hyperbolic scaling to the skeletal graph A'. An identical scaling is, of course, applied to the skeletal graph B' (however, it is not shown in this figure for the sake of transparency).

By starting with a tapered front end of the article, the internal structure is scaled by compacting the skeletal graph A' into a denser skeletal graph A''. This prevents a wedge-shaped geometry of the front end of the article having an internal structure that has weak points under the surface of the skin 23 at any point. By downward scaling the skeletal graph A', the resulting minimum surface structure providing the internal structure for the article is adapted to the geometry in such a way that optimal stability and infilling are provided in all geometries. This enables additive manufacturing of articles with optimized internal structure and infilling by using a smaller-scale infilling if the geometry requires it, or a larger-scale infilling (not shown in Fig. 3a) if it is preferred. The scaling may additionally not only be influenced by the three-dimensional geometry of the article, but also become dependent on the printer parameters or the load cases for the respective article.

In Fig. 3b an alternative example is illustrated in which a local densification is applied to the central portion of a virtually bar-shaped article. The skeletal graphs A' are hyperbolically scaled into densified skeletal graphs A''. This densified structure, by superimposing the form of the article on top of the skeletal graph, must be outside the article. By scaling, a more densified region is created, under which the skin 23 is supported by an internal structure that is denser, i.e. provides increased stability for the article.

Fig. 4a-4d illustrate an aspect of the present invention, in which a basic set of two connected skeletal graphs A', B', created by means of the method according to the present invention, is adapted as filling to an article having an article shape 25. The article shape 25 is essentially an L-shaped article; in a first step of this use of said several skeletal graphs A', B', the article shape 25 is superimposed on a grid formed by means of the two skeletal graphs A', B'.

Fig. 4a shows how such a product shape 25 is positioned when viewed from above.

In Fig. 4b, the product shape 25 is still shown in plan view, but for comparison, the skeletal graph A' is densified into a densified skeletal graph A'' by means of a hyperbolic scaling. For ease of presentation, the skeletal graph B' and its corresponding scaling into a densified skeletal graph B'' are omitted. It is evident that from left to right, the protrusion of the product shape 25 is filled with "comparatively more" skeletal graph than from the left. This results in a denser region providing better structural integrity and potentially skin support. However, it should be noted that the skeletal graph serves as a template or plan of a quasi-periodic minimal surface that divides the interior volume of the product shape 25 into two labyrinths A, B, which are to correspond to the skeletal graphs A', A'', respectively. The scaling of the skeletal graphs thereby results in a scaling of the quasi-periodic minimal surface additively fabricated into the resulting product as infill for the present exemplary product.

Fig. 4c shows an identical product with a condensed skeletal graph of group A in front view, i.e. with the projection continuing in the direction of the viewer.

In a similar manner, Fig. 4d illustrates the shape 25 of the product in a side view, in which, similarly to Fig. 4b, the densification of the skeletal graph A' into a densified skeletal graph A'' increases from left to right.

In all the above figures, the unscaled original skeleton graph A' is shown for reference and to illustrate the concept as a point skeleton graph.

Figs. 5a-5e illustrate an alternative method of adapting the infill to a specific product geometry and load-bearing needs, which, however, can also be used in addition to the above method. The illustration is intended to guide the method and is not intended to represent a real working example. For this reason, some simplifications are given in the drawings. One such simplification consists in illustrating only one skeleton graph A'. In a real implementation, of course, the following description of the thinning of the skeleton graphs must be applied to both graphs of the pair (created by the method illustrated in Fig. 1 above).

Fig. 5a illustrates how an article with article shape 25 is superimposed on an unscaled skeletal graph A' of substantially homogeneous density. The density is chosen to be as high as required for the present example and is most often determined by the expected load-bearing and geometrical needs of the article shape, i.e., not higher than the highest required final density in the article.

In Fig. 5b(s) the structure 25 of the product is subjected to a first analysis, in which the shape 25 of the product and the geometry dictate which regions are to be filled more densely and which may be filled less densely. For this purpose, the product is divided into cubes of such a size that each cube contains at least some skeletal graph backbones, preferably contains more than three backbones, even more preferably 5-8 backbones, even more preferably less than 100 backbones. Currently, a distinction is made between two types of cubes: the cube(s) supporting the layout process 45 and the cube(s) on the boundary 46 of the product. Depending on the definition of the cube type, the operation to remove skeletal graph units may be performed in a specific cube. In the context of the present invention, a skeletal graph unit is to be understood as a branch in one specific monotriatruncated tetrahedron. Of course, since they always come in pairs, this means removing two branches of the skeletal graphs, i.e. pairs in two monotriatruncated tetrahedra, originally belonging to an identical rhomboid-shaped cell.

Fig. 5b(q) illustrates a second analysis performed for the structure 25 of the product, wherein the analysis of the voxel load cases is again performed by means of cubes, wherein each cube covers a plurality of voxels, preferably each cube covers an identical number of voxels. This may be performed by sorting the cubes based on their stress/strain requirements and characteristics. In the present example, five types are distinguished: cube(s) 40 with zero stress, cube(s) 41 with a small positive stress (with compression), cube(s) 42 with a small negative stress (with tension), cube(s) 43 with a high positive stress (with compression) and cube(s) with a high negative stress (with tension). Depending on the characteristics, the specific operation can be pre-defined: for example, essentially all or most of the units can be removed in cube(s) 40 with zero mechanical stress, half of the units in cube(s) 41 with a slight positive mechanical stress (with compression), etc., depending on the parameters of the load case analysis. In the real case, of course, a much larger number of incremental steps and corresponding adaptations are carried out, and the cube(s) are(are) significantly smaller.

The resulting adapted skeletal graphs A''' (B''' omitted for clarity in the drawings) are generated separately for the analysis of the shape 25 of the product, resulting in a shape-corresponding partially thinned skeletal graph A'''(s) of group A, as shown in Fig. 5c(s), and in a load-corresponding partially thinned skeletal graph A'''(q) of group A, as illustrated in Fig. 5c(q).

The resulting combined scaled skeleton graph A''', achieved by unifying A'''(s) and A'''(q), is shown in Fig. 5d for the full product structure 25 and has low-density regions O''' (high-resolution sparse skeleton graphs) and high-density regions P''' (high-resolution skeleton graphs).

Fig. 5e shows the final step of the adjustment, the open-ended segments A'''(x), i.e. the segments that are not connected to further segments and end in a void, are removed. Additionally, from the outermost segment(s), i.e. the segments that must pass along the skin of the product, the parts A'''(o) outside the skin are removed and replaced by a mirror image A'''(m) of the part A'''(i) of the segment inside the product. Due to this, the mirror image is a mirror image of the part inside, which is mirrored with respect to the skin at the place where it is passed by the segment. After this adjustment step, the Voronoi analysis is performed as described above and a surface with zero mean curvature is calculated between the skeleton graphs. This reveals that the resulting minimum surface M (similar to the structure 10 of the previous examples) touches the surface of the article 50 in a substantially perpendicular direction, thereby providing an ideal conductor of loads from the surface to the filling. In the present context, "substantially perpendicular" can be understood as containing a deviation of between 1 and 5 degrees from an angle of 90 degrees.

Fig. 6a shows how a specific example of the present invention can be carried out for a manufacturing process with additive manufacturing of an article, which typically requires a plurality of build supports. The article 50 comprises an infill of a structure 10 based on a minimum surface obtained by means of the method of the invention. The structure is adapted to the shape 25 of the article and is constructed during advancement 62 from the build platform by adding printing layers 54.

Due to the present invention, it becomes possible to manufacture with a minimum number of assembly supports. This is approximately illustrated in Fig. 6b.

The currently used methods for additive manufacturing include building up the product from successive layers initially placed on a build platform 51. The methods using metal as the additive material of the prior art must cope with a maximum layer-to-layer angle of 45°, after which a build support is required to hold the layer during the build process in order to dissipate heat and prevent deformation of the product during production. For the purposes of this example, a selective laser melting rapid prototyping method is carried out for the additive manufacturing of a product with a shape 25 of the product that has an inclination on one part that is less than 45°, relative to the build support 53. The selective laser melting manufacturing method is carried out in a powder bed, in which the desired shape is selectively melted by using a laser, typically an ytterbium fiber laser, in one plane while successive layers of powder are applied to the shape synchronously with the operation of the laser.

In the present example of Fig. 6b, by way of illustration, the required support structures 52 according to the prior art are shown for comparison with only one required assembly support 53, which is sufficient to perform the additive manufacturing of the article 50 with a specific article shape 25. For this example, the article shape 25 corresponds to the outer skin of the article. Starting from the assembly support 53, a certain number of printing layers 54 are added in the direction of advance 62. Printing begins with the first layer of the contact zone 55 of the article 50, which is a resting zone that contacts the assembly support 53. The deposition of the layers 54 is performed in the direction of advance 62 of the assembly. As the assembly advances with the structure 10, the center of gravity 58, 59, 57 of the article shifts from the middle of the contact zone 55 to the left, i.e. in the direction of the protruding part on the left. The track 57 of the center of gravity is shown in Fig. 6b to illustrate the shift of the center of gravity 58, 59, 57, 60 as layers are added. For example, the center of gravity 58 shifts from the center of the contact area 55 after several layers of the projecting part on the left have been formed. The center of gravity 58, 59, 57, 60 moves further to the left, up to the center of gravity at a certain time 59, with a clear shift, and at time X, the center of gravity 60 reaches the vertical divider 56 of the contact area. Advancing beyond this delimitation 56 shifts the center of gravity beyond the contact area 55, after which the article 50 risks warping and distortion of shape when supports are not used at this given angle. The maximum angle of the prior art printing without the need for support structures, shown at the maximum angle of the prior art for an unsupported arrangement 61. It is essentially an angle of 45 °.

At time X, the top border of the product 60.1 is printed, and the center of gravity must pass the vertical divider 56.

For printing the article as illustrated, instead of having a plurality of arrangement supports 52, only one arrangement support 53 approximately at the upper limit at the time X in which the center of gravity of the article moves beyond or is located directly in the vertical divider of the contact zone is sufficient to support the article and provide sufficient stability for the extension of the projecting part to the left. The maximum angle of the prior art for an unsupported arrangement 61 is shown for reference. Due to the idea of the present invention, printing with steeper angles with less support than previously required becomes possible due to the filling structure 10 providing sufficient support.

In addition to providing a layout of products with steeper angles, the present invention and the method disclosed herein also provide advantages in selective laser melting by providing optimal heat dissipation within the layout structures. Since the minimum surfaces of the present invention always dissipate heat in an optimal path, the product is dissipated onto the layout platform more efficiently, which allows for increased printing speed and/or increased stability and/or smoothness of the melted surfaces.

For the present example, an EOS GmbH printer of the M290 type, equipped with a 400 W ytterbium fiber laser, is used. As an alloy, the maraging NEOS steel MS1/1, 2709, offered by EOS, is used with a grain size of 20-65 μm. The resulting products can take a shape as shown in Fig. 7a and 7b. In Fig. 7a, the outer skin (corresponding to the shape 25 of the product) is omitted to show the filling and internal structure of the product 50. The internal volume of the product is divided into two labyrinths A, B. The structure 10 represents the minimum surface structure and comprises an upwardly scaled zone O and a downwardly scaled zone P, whereby the hyperbolic scaling, as described above, is performed in order to achieve certain structural characteristics in these zones.

In contrast to Fig. 7a, the article 50 of Fig. 7b does not have an outer skin, and the surface of the article corresponds to the structure 10 itself. In fact, the rod-shaped article 50 also divides its volume into two labyrinths A, B. Also illustrated are an upwardly scaled zone O, in which the structure 10 is less dense, and a downwardly scaled zone P, in which the structure 10 is compacted, for example, in order to obtain a more stable surface as a result.

Fig. 8 shows an article obtained by the method described in Fig. 5a-5e, in which the thinning of the skeletal graph segments is performed based on the article shape and/or the layout parameters, and/or the analysis of mechanical stress/strain by removing individual segments and/or graph highways to create locally denser and less dense areas, illustrated in Fig. 8. The article shape 25 is shown without the outer skin, which is removed in order to better provide an internal view. If the article shape 25 is to be present, the article shape 25 should be substantially cubic.

The article has several regions that are found, depending on the analysis of the shape and/or load cases, to be printable with low-density infill or that are found to require high-density infill. In the article, an aperiodic minimal surface subdivides the volume into two labyrinths A and B, separated by a structure 10 that forms the infill. The structure 10 is a minimal surface M. A low-density zone O''', which is thinned out from the high-resolution skeletal graphs, is visible in the upper right corner of the article. In addition, a high-density zone P''', in which the original density of the high-resolution skeletal graphs is maintained, is visible to the left of O''', above the upper left corner of the article.

Fig. 9 is a photograph showing an article 50 printed according to the method of the present invention.

The articles obtained by the method of the present invention can be used in a large number of applications. One of the most basic applications is to use the article as shown in Fig. 9 as a building block for a lightweight assembly in which stability and weight are important factors. The method of the present invention shows that printing of metal structures is possible and provides articles with great stability, which are lightweight and have optimal heat dissipation when dividing the volume into two different and separate labyrinths.

In a further example of the present invention, the method and idea of the present invention are used as a pre-processing for an article intended for additive manufacturing by using computer software integrating an executable fragment adapted to perform the present invention. The general processing flows in the design and pre-processing during additive manufacturing include a first stage of forming a three-dimensional model. Most often, this is performed by CAD design, adaptation or interrogation of the corresponding model.

In the second step, the forces are simulated. This can be done by means of finite element modeling (FEM) and can additionally include a dimensioning and optimization step to adapt the design solution or change the topology if necessary by means of force modeling. The preparation for printing includes weight reduction and the use of simple infill, which increases the number of polygons in the modeling. The print simulation is then performed to check whether the print rule set can be printed or not. External and internal supports are also integrated in this step of the method if necessary. To perform the printing, a slicing is performed, which depends on the parameters of the nesting process and the printer settings, which are mainly determined by the hardware. The nesting step is then performed "layer by layer", which roughly corresponds to "slicing" depending on the previous slicing step of the additive manufacturing of the product.

The present invention comprises an alternative or additional tool for performing weight reduction and for providing filling as indicated in the above steps of the pre-treatment process.

Alternatively or additionally, the method of the present invention can also be used to create a structure from raw material. This means that the method of the present invention can be used to create a structure in which the filling formed by means of, as detailed above, is the structure itself.

Therefore, a further aspect of the present invention relates to an article obtainable by the method described above, having the characteristics as described above. Yet another further aspect also relates to a computer program product, which comprises control instructions and/or skeleton graphs required to apply a pre-processing to the article, based on the idea of the present invention.

Although the examples in this document are described with selective laser melting, those skilled in the art will readily appreciate that the method of the present invention is equally applicable to any other type of additive manufacturing technology, such as bath polymerization, material jetting, binder jetting, material extrusion, directed energy deposition, or sheet material layering, as required by the appropriate printer and for the purposes of the article in question.

The idea of the present invention provides a method and an article with superior characteristics and attributes that open up a new field of application for structural materials, as well as for the efficient printing of geometries, and require much less post-processing, such as the removal of burrs and/or support structures. The articles resulting from the method of the present invention can also be more easily evacuated from the material, since the surfaces divide the volume of the article into two complete labyrinths. As such, two small holes placed in the correct spot of the article can be sufficient to remove the material by draining or blowing.

Link positions

1 - rhomboid shaped cell

1' - the second cell in the shape of a rhomboid

1'' - the third cell in the shape of a rhomboid

2 - group A of a monotriatruncated tetrahedron

2' - group B of monotriatruncated tetrahedron

10 - structure

11 - first rib

12 - second rib

13 - third rib

14 - fourth rib

15 - fifth rib

16 - sixth rib

17 - seventh rib

18 - eighth rib

19 - ninth rib

20 - tenth rib

21 - eleventh rib

22 - the twelfth rib

23 - sheathing

24 - hyperbolic scaling

25 - product shape

30.1 - tetrahedron, group A

30.2 - tetrahedron, group B

40 - voxel with zero mechanical stress

41 - voxel with slight positive mechanical stress (with compression)

42 - voxel with slight negative mechanical stress (with tension)

43 - voxel with high positive mechanical stress (with compression)

44 - voxel with high negative mechanical stress (with tension)

45 - voxel supporting the compositing process

46 - voxel on the product boundary

50 - product

51 - assembly platform

52 - prior art assembly supports

53 - layout support

54 - printing layer

55 - contact zone

56 - vertical contact zone divider

57 - Center of gravity track (COG)

58 - COG of the product at time #1

58.1 - upper limit of the product at time #1

59 - COG product at time #4

59.1 - upper limit of the product at time #4

60 - COG of the product at X time

60.1 - upper limit of the product at time X (COG to move beyond the contact zone)

61 - Prior art maximum angle for unsupported layout

62 - promotion

A - labyrinth of the first group

A' is the skeleton graph of group A

A'' is the condensed skeleton graph of group A

A'''(s) is the corresponding partially thinned skeleton graph of group A

A'''(q) is the load-matched partially sparse skeleton graph of group A

A''' is a partially thinned skeleton graph of group A: unification of A'''(s) and A'''(q)

A'''(i) is the interior of the outermost segment of the partially thinned skeleton graph of group A

A'''(o) is the outer segment of the outermost segment of the partially thinned skeleton graph of group A

A'''(m) is a mirror image of the interior of the outermost segment of the partially thinned skeleton graph of group A

A'''(x) is an open-ended segment of the partially thinned skeleton graph of group A

B - labyrinth of the second group

B' is the skeleton graph of group B

B'' is the condensed skeleton graph of group B

F - intersection face

G - first edge of the knot

H - the second edge of the knot

I - the third edge of the knot

J - the fourth edge of the knot

K - the fifth edge of the knot

L - the sixth edge of the knot

M - minimum surface

N - variable area of internal nodes

N1 - first internal node (skeletal group A)

N2 - the second internal node (skeletal group A)

O - low density zone (upscaled skeletal graphs)

O''' - low density zone (high resolution sparse skeletal graphs)

P - high density zone (downscaled skeletal graphs)

P''' - high density zone (high resolution skeletal graphs)

S - analysis of product shape

Q - load case analysis (FEM modeling)

b1 - "highway"

bg - connecting node, first edge of the node

bh - connecting node, second edge of the node

bi - connecting knot, third edge of the knot

bj - connecting node, fourth edge of the node

bk - connecting knot, fifth edge of the knot

bl - connecting node, sixth edge of the node.

Claims (26)

1. A method for reducing the weight of an additively manufactured article, wherein the article comprises one or more integral parts of the article, wherein each or some of the one or more integral parts of the article has an internal structure, wherein the method includes the step of: - additively manufacture the product, - filling and/or assembling each of the one or more integral parts of the article by means of a quasi-crystalline structure, wherein the quasi-crystalline structure is a three-dimensional quasi-crystal made of two or more types of rhomboid-shaped cells, and the filling and/or assembling of each of the one or more integral parts of the article is filling and/or assembling by means of a quasi-periodic or aperiodic minimum surface filling and/or a quasi-periodic minimum or aperiodic surface design structure, wherein the method comprises an additional step of using the quasi-crystalline structure as a framework in order to form a quasi-periodic or aperiodic minimum surface filling and/or a quasi-periodic or aperiodic minimum surface design structure, - divide the rhomboid-shaped cell(s) in half in such a way that the faces resulting from the division in half have a hexagonal shape, thereby forming two equal mono-triatruncated tetrahedra from each cell. 2. The method according to claim 1, further comprising a step in which the geometry of the quasicrystal is created by performing steps in which: a. at least four primary vectors are introduced; b. create a number of parallel plane groups equal to the number of primary vectors input in step a., wherein each parallel plane group contains at least three parallel planes. 3. The method of claim 2, wherein all planes in one particular group of parallel planes are uniformly spaced. 4. The method of claim 2, wherein all planes in one particular group of parallel planes are randomly spaced. 5. The method according to claim 2, wherein all planes in one specific group of parallel planes are spaced according to a given pattern. 6. The method according to any one of claims 2 to 5, wherein at least some planes in one particular group of parallel planes are uniformly spaced, and/or some planes are randomly spaced, and/or some planes are spaced according to a given pattern. 7. The method according to claim 6, further comprising the step of assigning each monotriatruncated tetrahedron to one of two groups A or B such that two labyrinths A, B are formed. 8. The method according to any one of claims 1 to 7, further comprising the step of inserting one skeletal graph A', B' into each monotriatruncated tetrahedron such that two interleaved skeletal graphs A', B' are created spanning the entire quasicrystal without interconnection at any point. 9. The method according to claim 8, wherein each skeletal graph A', B' extends through one group of monotriatruncated tetrahedra. 10. The method according to any one of paragraphs 2-9, further comprising the step of selecting the number of planes in each group of planes as an indicator of resolution for the desired internal structure. 11. The method according to claim 10, wherein the selection is performed separately for any part of one or more integral parts of the product with an internal structure. 12. The method according to any one of claims 8-11, further comprising the step of down-scaling the skeletal graphs A', B' beyond one or more integral parts of the product, each of which has an internal structure, to create locally condensed skeletal graphs A'', B''. 13. The method according to any one of claims 1 to 12, wherein the quasi-crystalline structure is used to define a quasi-periodic minimal surface, and the skeletal graphs A', B'; A'', B'' are used to specify the minimal surface. 14. The method according to any one of claims 1 to 12, wherein the quasi-crystalline structure is used to define an aperiodic minimum surface, and the skeletal graphs A''', B''' are used to specify an adapted minimum surface after the segments are removed, according to an analysis of load cases and/or an analysis of the shape of the product. 15. The method according to item 1, wherein the method includes the steps of: a. provide two skeletal graphs A', B' extending through one group of monotritruncated tetrahedra in such a way that two interleaved skeletal graphs A', B' are created spanning the entire quasicrystal without interconnection at any point; b. remove units and/or segments from skeletal graphs A', B' depending on the local mechanical stress/strain analysis. 16. An additively manufactured lightweight article manufactured using the steps of the method of claim 1 and comprising integrally formed parts of the article with an internal structure, wherein the integrally formed parts of the article have a quasi-crystalline structure or a quasi-periodic minimum surface fill or a quasi-periodic minimum surface design structure or an aperiodic minimum surface fill or an aperiodic minimum surface design structure. 17. The article of claim 16, comprising an outer skin and a filling, and wherein the surface has a substantially zero mean curvature having a deviation from zero to +/- 0.0005 for the average of two perpendicularly measured curvatures on the surface, preferably a minimum surface, the filling touching the outer skin at a substantially perpendicular angle having a deviation between 0.1 and 5 degrees from an angle of 90 degrees. 18. An article according to any one of claims 16 or 17, comprising low-density zone(s) O, O''' and/or high-density zone(s) P'''.