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Title:
METHOD AND SYSTEM FOR THE ADDICTIVE GENERATION OF OBJECTS
Document Type and Number:
WIPO Patent Application WO/2018/025181
Kind Code:
A1
Abstract:
The method (M) for the additive generation of objects comprises the following phases: a first phase (PHI) for the preparation of a physical domain (DF) or of a plurality of physical sub-domains (SDF); a second phase (PH2) for the slicing of the physical domain (DF) or of each of said physical sub-domains (SDF) prepared during the first phase (PHI), for the generation of a plurality of layers for the physical domain (DF) or for each of the physical sub-domains (SDF); a third phase (PH3) for the definition of machine instructions, starting from the generated layers, for the print of the physical domain (DF) or of each of the physical sub-domains (SDF) by means of a technology for the additive manufacturing; wherein the first phase (PHI) comprises a step (ST1.6, ST1.9) for the identification of a first main surface (SPl) and of a second main surface (SP2) of the physical domain (DF) or of each of the physical sub-domains (SDF); the second phase (PH2) comprises a step (ST2.3) for the definition of a plurality of pairs of points (P(1)n,m,d, P(2)n,m,d) on the first main surface (SPl) and on the second main surface (SP2), respectively; the second phase (PH2) comprises a step (ST2.4) for the construction of a plurality of guide curves (yn,m,d) that join the pairs of points (P(1)n,m,d, P(2)n,m,d); the second phase (PH2) comprises a step (ST2.5) for the identification of a plurality of points (Qp,n,m,d) on each of the guide curves (γn, m,d); the second phase (PH2) comprises a step (ST2.6) for the grouping of a plurality of the points (Qp,n,m,d) belonging to different guide curves (yn,m,d) for the generation of a plurality of surfaces (∑r,d), i.e. of the layers.

Inventors:
ROSA, Francesco (Piazza Leonardo da Vinci 32, Milano, 20133, IT)
GRAZIOSI, Serena (Piazza Leonardo da Vinci 32, Milano, 20133, IT)
Application Number:
IB2017/054703
Publication Date:
February 08, 2018
Filing Date:
August 01, 2017
Export Citation:
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Assignee:
POLITECNICO DI MILANO (Piazza Leonardo da Vinci 32, Milano, 20133, IT)
International Classes:
B29C67/00; B33Y50/02
Other References:
BIN HUANG ET AL: "Curved Layer Adaptive Slicing (CLAS) for fused deposition modelling", RAPID PROTOTYPING JOURNAL, vol. 21, no. 4, 15 June 2015 (2015-06-15), GB, pages 354 - 367, XP055371962, ISSN: 1355-2546, DOI: 10.1108/RPJ-06-2013-0059
SARAT SINGAMNENI ET AL: "Modeling and evaluation of curved layer fused deposition", JOURNAL OF MATERIALS PROCESSING TECHNOLOGY, ELSEVIER, NL, vol. 212, no. 1, 3 August 2011 (2011-08-03), pages 27 - 35, XP028103130, ISSN: 0924-0136, [retrieved on 20110809], DOI: 10.1016/J.JMATPROTEC.2011.08.001
XIUZHI QU ET AL: "A 3D surface offset method for STL-format models", RAPID PROTOTYPING JOURNAL, vol. 9, no. 3, 1 August 2003 (2003-08-01), GB, pages 133 - 141, XP055372382, ISSN: 1355-2546, DOI: 10.1108/13552540310477436
Attorney, Agent or Firm:
GRANA, Daniele (Via Scaglia Est 19-31, Modena, 41126, IT)
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Claims:
CLAIMS

1) Method (M) for the additive generation of objects, comprising at least the following phases:

a first phase (PHI) for the preparation of a physical domain (DF) or of a plurality of physical sub-domains (SDF);

a second phase (PH2) for the slicing of said physical domain (DF) or of each of said physical sub-domains (SDF) prepared during said first phase (PHI), for the generation of a plurality of layers for said physical domain (DF) or for each of said physical sub-domains (SDF);

- a third phase (PH3) for the definition of machine instructions, starting from said generated layers, for the print of said physical domain (DF) or of each of said physical sub-domains (SDF) by means of a technology for the additive manufacturing;

characterized by the fact that:

- said first phase (PHI) comprises at least one step (ST1.6, ST1.9) for the identification of a first main surface (SPl) and of a second main surface (SP2) of said physical domain (DF) or of each of said physical sub-domains (SDF);

said second phase (PH2) comprises at least one step (ST2.3) for the definition of a plurality of pairs of points (P(1)n,m,d, P(2)n,m,d) on at least one part of said first main surface (SPl) and on at least one part of said second main surface (SP2), respectively;

said second phase (PH2) comprises at least one step (ST2.4) for the construction of a plurality of guide curves (yn,m,d) that join said pairs of points (P(1)n,m,d, P(2)

said second phase (PH2) comprises at least one step (ST2.5) for the identification of a plurality of points (QP,n,m,d) on each of said guide curves (γη, m,d);

said second phase (PH2) comprises at least one step (ST2.6) for the grouping of a plurality of said points (QP,n,m,d) belonging to different guide curves (yn,m,d) for the generation of a plurality of surfaces (∑r,d), i.e. of said layers.

2) Method according to claim 1, characterized by the fact that said second phase (PH2) comprises at least one step (ST2.1) for the definition of a first family of curves (λ(1 ) on said first main surface (SP1) and of a second family of curves (λ(¾) on said second main surface (SP2), and at least one step (ST2.3) for the definition of a plurality of pairs of points (P(1)n,m,d, P(2)n,m,d) on at least one part of said first family of curves (λ(1½) and on at least one part of said second family of curves (λ(¾), respectively.

3) Method according to one or more of the preceding claims, characterized by the fact that said first phase (PHI) comprises one step (ST 1.1) for the selection of an orientation of said physical domain (DF) with respect to a predefined print axis.

4) Method (M) according to one or more of the preceding claims, characterized by the fact that said first phase (PHI) comprises one step (ST1.3) for the definition of at least one support of said physical domain (DF) or of at least one of said physical sub-domains (SDF).

5) Method (M) according to one or more of the preceding claims, characterized by the fact that said first phase (PHI) comprises one step (ST1.5) for the division of a physical domain (DF) into said plurality of physical sub-domains (SDF).

6) Method (M) according to one or more of the preceding claims, characterized by the fact that said first phase (PHI) comprises at least one step (ST1.7) for the identification of at least one boundary surface (SC) for each of said physical sub-domains (SDF), in which said boundary surface (SC) is constituted by at least one portion of the border of the physical sub-domain (SDF) that separate the same from other physical sub-domains (SDF) and which belong neither to said first main surface (SP1), nor to said second main surface (SP2), nor to the border of the physical domain DF. 7) Method (M) according to one or more of the preceding claims, characterized by the fact that said first phase (PHI) comprises at least one step (ST1.8, ST 1.10) for the identification of at least one external surface (SE) of said physical domain (DF) or of at least one border portion of each of said physical sub-domains (SDF) that are also part of the border of said physical domain (DF).

8) Method (M) according to one or more of the preceding claims, characterized by the fact that said second phase (PH2) comprises at least one step (ST2.2) for the extraction of a finite number (M) of curves ( (1)m,d, (2)m,d) from each of said first family of curves (λ(1½) and said second family of curves (λ(¾).

9) Method (M) according to one or more of the preceding claims, characterized by the fact that said second phase (PH2) comprises at least one step (ST2.3) for the definition of a plurality of pairs of points (P(1)n,m,d P(2)n,m,d) of each of said pairs of curves ( (1)m,d and (2)m,d).

10) Method (M) according to one or more of the preceding claims, characterized by the fact that said second phase (PH2) comprises at least one step (ST2.3) for the definition of pairs of versors normal to said first and second main surfaces (SP1, SP2) at said points (P(1)n,m,d, P(2)n,m,d)-

11) Method (M) according to one or more of the preceding claims, characterized by the fact that said third phase (PH3) comprises one step (ST3.1) for the sorting of said surfaces (∑r,d) according to a print order, and the grouping of these surfaces (∑r,d) for the definition of limit surfaces (Eq).

12) Method (M) according to one or more of the preceding claims, characterized by the fact that said third phase (PH3) comprises one step (ST3.2) for the definition of a plurality of atlases (Aq) for the re-mapping of each limit surface (Eq) of a curved layer on a domain of a two-dimensional Euclidean space (Xq).

13) Method (M) according to one or more of the preceding claims, characterized by the fact that said third phase (PH3) comprises one step (ST3.4) for the generation of the volumes to be printed. 14) Method (M) according to one or more of the preceding claims, characterized by the fact that said third phase (PH3) comprises, for each domain (Xq), one step (ST3.5) for the definition of the deposition trajectories of the material.

15) Method (M) according to one or more of the preceding claims, characterized by the fact that said third phase (PH3) comprises at least one step (ST3.6) for the generation of the machine parameters necessary to adjust the addition of material.

16) Method (M) according to one or more of the preceding claims, characterized by the fact that it comprises at least one optimization step (ST3.7) for the generation of final instructions.

17) System for the additive generation of objects, characterized by the fact that it comprises at least one processing unit having:

first means for the processing of said first phase (PHI) for the preparation according to one or more of the preceding claims;

- second means for the processing of said second phase (PH2) for the slicing according to one or more of the preceding claims;

third means for the processing of said third phase (PH3) for the definition of machine instructions according to one or more of the preceding claims.

Description:
METHOD AND SYSTEM FOR THE ADDITIVE GENERATION OF OBJECTS

Technical Field

The present invention relates to a method and a system for the additive generation of objects.

Background Art

With reference to additive production technologies, the so-called "plane slicing" technique is known, which involves splitting an object into parallel layers having the same or different thicknesses in the direction "Z", or in a direction perpendicular to the printing plane.

First of all, it should be noted that the material of the objects made using such technique is non-isotropic. The properties of the material in the plane of the single layer are in fact different from those measured in a direction orthogonal to such plane. Hence a first limitation of such technique appears: it does not allow the complete control of the properties of the material in relation to the functional needs of the object, since the choice of print direction is generally based on considerations relating to the printing process (reduction of time and costs) and on the capacities of the additive technology itself (such as, for example, the need to minimize the presence of overhanging parts).

Secondly, such technique, though relatively easy to implement and widely disseminated even at a commercial level, determines the creation of an object whose external surface is characterized by a stepped aspect.

In order to overcome such drawback, a subsequent finishing phase of the surface of the object is required in order to eliminate the stepped aspect. Such finishing process requires longer times and higher costs in order to obtain an object which complies with technical and aesthetic requirements.

In order to reduce as much as possible both the "aesthetic" and/or functional damage generated by the presence of such stepped aspect and the need for further processing, algorithms have been developed called "adaptive slicing", i.e., algorithms capable of automatically generating layers with reduced thickness in the proximity of details of particular interest and/or significant variations in the curvature of the surface of the object.

Nevertheless, although these techniques are effective in reducing the aesthetic and functional impact of the "stepped aspect", they constrain in any case the orientation of the material and may also result in an increase in the number of layers to be printed.

Given the limits of such techniques, the development and optimization of which has in any case never stopped, research has also begun exploring the development of slicing techniques based on non-planar layers.

In particular, the increasing interest is known in the development of slicing techniques based on curved layer.

More specifically, it is known that for the development of a slicing technique based on curved layers, a number of considerations need be made, including: how to define the geometry of the curved layer in relation to the geometry of the object to be printed and/or in relation to other purposes of a technical and functional nature (such as, for example, the generation of objects with particular mechanical properties in specific directions); what thickness of the layer to adopt to generate the object; how to ensure the continuity between one layer and the next.

With respect to the thickness of the layer, it is well known that most curved slicing techniques of conventional type provide for the generation of layers characterized by a constant thickness. Such aspect constitutes a considerable limitation of such techniques, since the possibility of generating curved layers having a variable thickness could add a further degree of freedom to the design of the internal and external characteristics of the material.

Furthermore, most of the known curved slicing techniques commonly use a reference surface as the starting point for the definition of the geometry of the curved layer.

Most curved slicing techniques also refer to the additive technology of filament deposition (FDM - Fused Deposition Modelling).

In general, the slicing techniques which use solid tesselated geometry as a starting input, or a digital model in STL (Stereo Lithography interface format) of the solid to be generated, also have the limit that the curved surfaces are approximated by a series of flat stretches. In this format, in fact, the solid is represented roughly by triangular flat faces and relative normal ones.

In order to correctly identify the state of the art, a number of documents are mentioned and briefly described which make reference to known types of techniques.

The document "Extruder path generation for Curved Layer Fused Deposition Modeling" (Chakraborty, D., Aneesh Reddy, B., Roy Choudhury, A. (2008), CAD Computer Aided Design, 40 (2), pp. 235-243) describes a technique based on the concept of depositing material along curvilinear trajectories and proposes an algorithm for depositing the material on curved layers studied both to ensure adequate overlap and adhesion between the various filaments of material and to obtain a better correspondence between printed object and digital model.

The study described in document "An experimental demonstration of effective Curved Layer Fused Filament Fabrication utilising a parallel deposition robot" (Allen, R.J.A., Trask, R.S. (2015), Additive Manufacturing, 8, pp. 78-87) proposes a development and the relative experimental validation of the technique of depositing along curvilinear trajectories by the use of a suitably modified "delta" type commercial machine. The technique involves printing the structure that will serve as a support for depositing the curved layer using the conventional planar slicing procedure. The authors also show that such a technique can also be used to create sandwich structures. The technique proposed in this study also provides information about the stage of creation of the supports. However, this technique is only applicable to solids sub-dividable into rectangular sub-domains.

The document "Curved layer adaptive slicing (CLAS) for fused deposition modelling" (Huang, B., Singamneni, S.B. (2015), Rapid Prototyping Journal, 21 (4), pp. 354-367) describes a hybrid approach that integrates adaptive slicing techniques, which allows the generation of planar layers having variable thicknesses, and the deposition technique along curvilinear trajectories. However, it seems that the generation of curved layers occurs mainly as an "offset" of a reference surface.

The document "Application of curved layer manufacturing for preservation of randomly located minute critical surface features in rapid prototyping" (Patel, Y., Kshattriya, A., Singamneni, S.B., Choudhury, A.R. (2015), Rapid Prototyping Journal, 21 (6), pp. 725-734) describes a curved slicing technique that allows taking into consideration the critical features of the solid to be printed by identifying points defined as fundamental and/or critical. Furthermore, this technique is based on the creation of layers with constant thickness, albeit adaptive, and therefore obtained as offset of a surface taken as reference.

The solution described in document US 2015/0266244 Al envisages the creation of an inner core using the traditional technique of slicing on planes. This inner portion is subsequently coated by depositing the material following the desired curved surface. The purpose of this operation is, on the one hand, to improve the aesthetic finish and, on the other hand, to establish a closer bond between the different layers.

This document also shows the creation of generically curved internal layers. Nevertheless, no details are given as to how these surfaces can be defined.

Description of the Invention

The main aim of the present invention is to provide a method and a system for the additive generation of objects which allows for the creation of curved layers the shape and thickness of which can vary with continuity from one layer to the other, thus adapting to the specific case.

Another object of the present invention is to provide a method and a system for the additive generation of objects, which allows to overcome the mentioned drawbacks of the prior art within the ambit of a simple, rational, easy, effective to use and low cost solution.

The above mentioned objects are achieved by the present method for the additive generation of objects according to claim 1.

The above mentioned objects are also achieved by the present system for the additive generation of objects according to claim 17. Brief Description of the Drawings

Other characteristics and advantages of the present invention will become more evident from the description of a preferred, but not exclusive, embodiment of a method and a system for the additive generation of objects, illustrated by way of an indicative, but non-limiting example in the accompanying drawings, wherein:

- Figure 1 shows schematically the method according to the invention;

- Figures from 2 to 14 show a first phase of the method according to the invention;

- Figures from 15 to 24 show a second phase of the method according to the invention;

- Figures from 25 to 39 show a third phase of the method according to the invention.

Embodiments of the Invention

With particular reference to Figure 1, globally indicated with M is a method for the additive generation of objects.

In particular, the method M according to the invention can be used for any additive manufacturing technology (Additive Manufacturing) whether the latter envisages the deposition of the material, using any technology, or is based on the solidification of layers of material inside a bath or sintering/melting inside a powder bed, according to any surface, provided that this is able to vary during the deposition process.

As schematically illustrated in Figure 1, the method M according to the invention comprises the following phases:

- a first phase PHI for the preparation of a physical domain DF and, possibly, of several physical sub-domains SDF;

a second phase PH2 for the slicing of the physical domain DF or of each physical sub-domains SDF prepared during the first phase PHI;

- a third phase PH3 for the definition of machine instructions for the print of the physical domain DF or of each physical sub-domains SDF.

In particular, the first phase PHI consists in preparing the three-dimensional model of the object that has to be printed.

Reference to this model will be made below by calling it physical domain DF. By extension, physical quantities will be defined (e.g., the coordinates) which refer to the space wherein is defined the physical domain DF.

It should be noted that the boundary of this physical domain can be defined both by continuous surfaces (i.e., e.g., those defined within a CAD system), as well as tessellated surfaces (i.e., defined, e.g., by STL format).

The steps that characterize this first phase PHI of the method M are discussed below and are illustrated schematically in figure 2.

The first phase PHI comprises a step ST1.1 for the selection of the orientation of the physical domain DF with respect to the print axis.

In particular, said print axis is defined according to the reference rules for the selected technology suitably expanded in the light of the method M found, and generally coincides with the axis Z of the machine used for printing.

Since the method M according to the invention is relatively flexible, it is not necessary to choose a particular normal direction from among the infinite number that can be defined for each surface described or introduced herein below. This freedom can therefore be exploited to optimize other aspects of the printing, such as: reduction of supports or print time; the minimization of stepped aspect on other surfaces; the reduction of the risk of contact between the head (or other parts of the machine) and already printed portions of the object. Once the print direction (step ST1.1) has been chosen, if necessary (step ST1.2), the method M envisages a possible step ST1.3 for the definition of the necessary supports.

Such definition of the supports can be carried out by applying the procedures and the indications known in literature, suitably expanded in the light of the described method M, and varying in relation to the print technology and to the material to be used to make the object.

Figures 6 to 10 illustrate by way of example how the method M can be used both to print the physical domain DF and to print the support of the physical domain itself. In particular, figure 6 shows a schematic view of a possible object to be printed. Figure 7 on the other hand shows a possible example of adaptive slicing of the object with a conventional approach performed on the planes (state of the art). It can also be noted that the method M introduces a new type of support which is not necessarily functional to supporting overhanging parts (figure 10), but is intended to provide a better aesthetic finish and/or functional performance to the product.

Advantageously, as shown in figure 2, the method M therefore allows choosing whether to divide the physical domain DF into appropriate physical sub- domains SDF (step ST1.4), i.e., into portions of the same in which to independently define the layers. Such subdivision could also facilitate the assignment of different materials in different areas of the product while preserving the ability of the print technology to operate in that direction.

In the event of the physical domain DF being subdivided into physical sub- domains SDF, the method M envisages therefore one step ST1.5 for the division of the physical domain DF into a plurality of physical sub-domains SDF.

For example, as shown purely by way of example in figure 4, the physical domain DF may be subdivided into a first physical sub-domain SDFd and into a second physical sub-domain SDFd + i.

For the sake of simplicity, it has been imagined that the subdivision into different physical sub-domains meets the requirement that each surface forming part of the border of a generic physical sub-domain SDF not be in contact with more than one other sub-domain except through an edge.

In this regard, it is pointed out that in the present treatise, by the term "edge" is meant the intersection curve between two adjacent SC or SE surfaces (such SC and SE surfaces are defined below).

It is pointed out, however, that the method M according to the invention may also be applied even if this requirement is not met.

By way of example, figure 11 shows a possible physical domain DF, while figures 12, 13 and 14 show possible subdivisions into physical sub-domains.

For example, in figure 12, the subdivision does not meet the above requirement because the surface SC (belonging to the sub-domain SDF1) which separates the first physical sub-domain SDF1 on the left from the other two physical sub- domains SDF2 and SDF3 is in contact with two surfaces belonging to the border of two different physical sub-domains SDF2, SDF3.

In figures 13 and 14, however, the subdivisions meet the requirement.

In particular, in fig. 14, such requirement is met because all the physical sub- domains SDF3-SDF7 are in contact with each other only through a single edge, indicated by the reference S in the illustration.

The first phase PHI of the method M allows, depending on the outcome of step ST1.4, defining a pair of main surfaces SPl, SP2 for each physical domain DF (step ST1.9) or SDF (step ST1.6), i.e., those surfaces which are to be used as a guide for layer definition.

The typical criteria for identifying the main surfaces SPl, SP2 comprise, for example, the need to orient the fibers of the material for structural purposes, or to identify those surfaces on which no steps are wanted for both aesthetic and functional reasons. The use of further possible selection criteria cannot however be ruled out.

The choice of such main surfaces SPl and SP2 is completely free and can be exploited to better manage the layer distribution in the physical sub-domain SDF or in the entire domain DF.

It must however be noted that this choice cannot ignore the obvious necessity of being able to add material to the surfaces to be defined and that such material must be able to adhere to that already deposited without undergoing significant displacements due to its own weight.

Such main surfaces SPl, SP2 can be portions of the border of the physical domain DF or of the individual SDF, and in this case they are called limit surfaces SLl and SL2. For example, figure 5 shows a sub-domain SDFd and the respective first limit surface SLl and second limit surface SL2 identified according to step ST1.6.

More generally, the main surfaces can be defined ad hoc by the user, as shown in the example of figure 29. In particular, figure 29 shows an example of application of the method M wherein the first main surface SP1 is not a portion of the border of the physical domain DF (delimited in figure 29 by the continuous line), but an external surface suitably defined for the purpose of orienting the layers that will be generated inside the physical domain itself. The second main surface SP2 in this case is also considered as limit surface SL2 because it coincides with the "lower" portion of the border of the DF in the figure orientation. In other words, in this case, the method M is applied to the extended domain delimited by the "lower" portion of the border of the physical domain DF (continuous line in figure 29) and by virtual surfaces (portion defined by the short mixed type lines in figure 29), which fully contains the physical domain DF.

A physical sub-domain SDF may also thus appear as a volume delimited by a first limit surface SLI and by a second limit surface SL2, as well as possibly by other portions of surfaces which connect them (figure 3).

Without thereby wanting to limit the generality of the approach, but for greater display clarity and simplicity, herein below reference will generally be made to a preferred embodiment, wherein both the main surfaces SP1 and SP2 belong to the border of a physical domain DF or of a physical sub-domain SDF, and so will both be defined as limit surfaces SLI and SL2.

The application cannot however be ruled out of the method M with different main surfaces SP1 and SP2.

The flexibility of the method M also makes it applicable in the event of the limit surfaces SLI and SL2 being the only two surfaces completely delimiting the physical sub-domain SDF (e.g., when these are both two spherical caps).

In the event of its having been decided, at step ST 1.4, to subdivide the domain DF into a plurality of sub-domains SDF, after the step ST1.5, the method M provides for the repetition of the steps ST1.6, ST1.7 and ST1.8 for each of the physical sub-domains SDF identified (for each SDFd with d = 1, D). In steps ST1.7 and ST1.8 are identified:

- the boundary surfaces SC (step ST1.7), i.e., the other portions of the border of the physical sub-domain SDF which separate it from other physical sub- domains SDF, and which do not belong either to the first limit surface SL1 nor to the second limit surface SL2, if present. Two physical sub-domains SDF may in fact also be in contact through the first limit surface SL1 or the second limit surface SL2, if existing;

- the external surfaces SE of the physical sub-domain SDF (step ST1.8), i.e., the border portions of each physical sub-domain SDF which also form part of the border of the physical domain DF.

Figure 8 shows a first example of application of the method M wherein the lower part SDF1 has the sole purpose of supporting the upper part SDF 2, corresponding to the object to be made and represented in figure 6.

Figure 9 shows a second example of application of the method M wherein the object is subdivided into two arbitrary physical sub-domains SDF1, SDF2, in order to show how it is possible to act on the different geometric parameters to orient the fibers in relation to specific requirements.

It should also be noted that the individual curved layers are oriented so as to be normal to each external surface SE. This way, a more accurate interpolation of the external surfaces SE is obtained.

Figure 10 shows a third example in which the supports have been introduced on the assumption that the external surface SE1.S is not self-supporting or on the assumption that the purpose of the support is to give the object particular aesthetic and/or functional characteristics. In particular, it is shown how it is possible to use the method described herein to generate supports and how the limit surfaces SLl.S, SL2.S need not necessarily be in contact with other physical sub-domains. The limit surfaces SLl .S and SL2.S are in fact only used to shape the layers while it is the external surfaces SE1.S and SE2.S which are in contact with another physical sub-domain (SDF1) and with the piece-holding table respectively. Taking into account the given limit surface SL1.2, the other limit surfaces (SL1.1, SLl.S, SL2.S) have been defined so as to facilitate the generation of continuous and tangent curved layers at the external surface SE1.S.

With reference to figure 2, in the event of the subdivision of the physical domain DF into several physical sub-domains SDF not being envisaged, the first phase PHI of the method M provides for a step ST 1.9 for the detection of the border portions of the physical domain DF which make up the first main surface SP1 and the second main surface SP2 of the physical domain itself. Subsequently, the external surfaces SE of the physical domain DF (step ST 1.10) are identified.

The second phase PH2 of the method M according to the invention comprises the steps leading to the creation of the layers for the physical domain DF or for each defined physical sub-domain SDF, including in the latter also the supports. The second phase PH2 is repeated for each physical sub-domain SDF to be printed.

Furthermore, it is pointed out that the description of the second phase PH2 shown below with reference to a physical sub-domain SDF is quite similar to a single physical domain DF in the case of no partitions of the latter being performed.

The steps that characterize this second phase PH2 of the method M are discussed below and shown in the diagram of Figure 15 and in figures 16 to 24. First of all, once the physical sub-domain SDF to be operated on has been selected, at step ST2.1 is defined a family of curves (1) d and λ ( ¾ on both the main surfaces SP1 and SP2. In particular, a first family of curves λ (1 ι is defined on the first limit surface SL1 and a second family of curves λ ( ¾, on the second limit surface SL2.

It is pointed out that, with particular reference to the present description, each family of curves is indicated by the term (l) d, where i indicates the i-th main surface SP and d indicates the d-th physical sub-domain SDF.

It is further stated that the definition of such families of curves represents one of the possible solutions adapted to allow the definition of the geometric elements used in the method M. However, such geometric elements, in particular the points P (l) n,m,d and the versors associated with them, and which will be defined below, can be defined in many other ways.

Such families of curves λ ( ¾ and λ ( ¾ must each cover the entire surface on which they are defined. Thus, each point of the limit surfaces SL1 and SL2 must belong to one and only one curve of the respective families of curves λ (1 ι and λ ( ¾.

Furthermore, the two families of curves λ (1 ι and λ ( ¾ preferably have similar orientation and shape.

The curves of such families λ ( ¾ and λ ( ¾ must not intersect, nor must two curves of a same family (1) d or λ ( ¾ intersect one another.

The families of curves λ (1) d and λ (2) d can be defined in numerous ways, e.g.: by exploiting the parametric curves used to describe the respective limit surface SL1 or SL2; following the directions of the main curvatures; following particular conformations of the physical domain DF to give the object particular properties.

As shown by way of example in figure 21, in the event of a limit surface SL1.1 of a first physical sub-domain SDF1 having a border portion A (curve belonging to a boundary surface SC) coinciding with a border portion curve of a limit surface SL1.2 of a second physical sub-domain SDF2, then the extremes of each of the curves of the two families of curves λ (1 and λ (1) 2 (each belonging to a limit surface SL1 of a different sub-domain SDF1 or SDF2) must coincide at the curve A common to the two limit surfaces.

As shown in the diagram of figure 15, once the families of curves (1) d and λ ( ¾ have been defined, the second phase PH2 envisages a step ST2.2 for the extraction of a finite number M of curves (1) m ,d and (2) m ,d from each of such families.

It is pointed out that, with particular reference to the present description, each curve is indicated by the wording (l) m ,d, where i indicates the i-th main surface SP, d indicates the d-th physical sub-domain SDF and m=l,...,M indicates the m-th curve of the family λ¾.

At the step ST2.3, on each of the M pairs of curves of the families λ ( ¾ and λ ( ¾ are then defined N m pairs of points P (1) n , m ,d and P (2) n , m ,d (in general, the number Nm can differ for each pair of curves) and pairs of normal versors at the limit surfaces SL1 and SL2 at such points, excepting the points belonging to a boundary surface SC or to an external surface SE.

It is pointed out that, with particular reference to the present description, each of the points is indicated with the wording P (l) n , m ,d, where i indicates the i-th main surface SP, d indicates the d-th physical sub-domain SDF, m=l,...,M indicates the m-th curve of the family λ¾ and n=l,...,N m indicates the n-th point of the curve.

As shown in the figures 16 and 18, if the points P (1) n , m ,d and/or P (2) n , m ,d also belong to a boundary surface SC or to an external surface SE, the respective normal versor will instead be defined by the versor of the straight line intersection between the plane IIsc tangent with the boundary surface SC or with the external surface SE in the point itself and the normal plane ITj in the same point at the curve φ intersection between the limit surface (SL1 or SL2) and the boundary surface SC or the external surface SE. Such solution permits also managing the situations wherein the two limit surfaces (SL1 or SL2) belonging to two adjacent physical sub-domains SDF do not have a common tangent plane along their intersection with the corresponding boundary surface SC.

After performing step ST2.3 at disposal for each physical sub-domain SDF are ∑^ = 1 N m pairs of points P (1) n , m ,d and P (2) n , m ,d and∑^ = 1 N m pairs of respective versors, each paired with a specific point.

The pairs of points P (1) n , m ,d and P (2) n , m ,d and the respective versors being known, at step ST2.4 the method M envisages the construction of ∑m= i N m guide curves, indicated in figure 18 with the reference y n ,m,d, which unite the pairs of points P (1) n,m,d and P (2) n , m ,d and which there have tangent versor coinciding with the versor associated with each point.

It is pointed out that, with particular reference to the present description, each of such curves is indicated with the wording y n ,m,d, where n indicates the n-th pair of points of the m-th pair of curves (1) m ,d and (2) m ,d and d indicates the d-th physical sub-domain SDF.

Preferably, if the points P (1) n , m ,d and P (2) n , m ,d belong to a boundary surface SC it is advisable that the respective guide curve y n ,m,d also belong to the same boundary surface SC. In this case, such y n ,m,d is shared by the two adjacent physical sub-domains SDF. This permits avoiding the formation of discontinuity between adjacent physical sub-domains SDF.

If the points P (1) n , m ,d and P (2) n , m ,d belong to two boundary surfaces SC at the same time, i.e., when they belong to an "edge" of a physical sub-domain SDF, the "edge" itself will represent the guide curve y n ,m,d.

The guide curves y n ,m,d being known, at step ST2.5 the method M provides for the identification of P(m,n,d) points, indicated in figure 18 by the reference Qp,n,m,d, on each of the guide curves y n ,m,d.

It is pointed out that, with particular reference to the present description, each of the points is indicated by the wording Q p , n ,m,d, where d indicates the d-th physical sub-domain SDF, m=l,...,M indicates the m-th pair of curves of the families λ ( ¾ and λ ( ¾, n=l,...,N indicates the n-th points of the curves and p=l,...,P(m,n,d) indicates the p-th point of the guide curve y n , m ,d.

The numbering of the points is such that Qi, n , m ,d c SL1 and Qp( m ,n,d),n, m ,d c SL2. Such points are identified so as to ensure between them a distance d p , n ,m,d compatible with the selected technology, but which can in any case be varied locally in order to convey particular local properties to the product.

At step ST2.6, the second phase PH2 of the method M envisages the grouping together of the points Q P , n ,m,d with same "p", or with other criterion tied to the optimization or to the management of the print, and the generation of the R surfaces ∑ r ,d, i.e., curved layers, for each physical sub-domain SDF, interpolating the points belonging to each of the groups of points just defined. It is pointed out that, with particular reference to the present description, each of the surfaces is indicated with the wording∑ r ,d, where r=l,...,R indicates the r-th surface and d indicates the d-th physical sub-domain SDF.

Such grouping is shown by way of example in figure 19 and in the respective front view of figure 20.

In the creation of each surface∑ r ,d the perpendicularity must be ensured, as far as possible, between the surface itself and each guide curve at the points Q P , n ,m,d. In the event of the number of points on the guide curves y n , m ,d not coinciding, the extension of the surfaces ∑ r ,d will be limited to the portion of physical sub- domain SDF affected by the guide curves y n ,m,d with higher number of points. It must be observed that in defining the surface ∑ r ,d also participate the points of the immediately adjacent guide curves y n ,m,d which lie on the second limit surface SL2.

In this respect, figure 22 shows an example of definition of the surfaces that delimit the curved layers∑ r ,d.

After having defined the five guide curves yi, m ,d, Y2,m,d, Y3,m,d, Y4,m,d, Y5, m ,d the opportune points are extracted on each. In the case shown in the illustration, five points have been extracted on the first guide curve Yi, m ,d, seven on the second guide curve Y2, m ,d, ten on the third guide curve Y3, m ,d, seven on the fourth guide Curve Y4,m,d and six on the fifth guide curve Y5, m ,d. Up to r=5, the surface∑ r ,d is generated considering a point for each guide curve Yi, m ,d, Y2, m ,d, Y3, m ,d, Y4, m ,d, Y5,m,d. For r=6 as well, a point is used for each guide curve Yi, m ,d, Y2, m ,d, Y3, m ,d, Y4,m,d, Y5,m,d, but for the first guide curve Yi, m ,d, the point Q5,i, m ,d is again used, corresponding to the point P (2) i, m ,d, this being immediately adjacent to the second guide curve Y2, m ,d which has a point Q6,2, m ,d that does not belong to the limit surface SL2. When, instead, r>7 we proceed in a similar way. Because the third guide curve Y3, m ,d is however the only one to have more than seven points, each ∑ r ,d will be defined by the corresponding point on the third guide curve Y3,m,d and by the two end points and Q7,4 ,m,d— P4,m,d of the two adjacent guide curves Y2, m ,d and Y4, m ,d.

If necessary, the local contribution of material to obtain the desired thickness can be suitably regulated.

By way of example and with reference to the filament print technologies, wherein a regulation of the thickness of the deposited material also involves a variation in the width of the deposit itself, it will also be necessary to regulate by consequence the distance between the successive generated strokes as schematically shown in figure 23.

In particular, figure 23 shows two stripes of material deposited in two successive strokes on a single layer. If, by regulating the thickness of the deposited layer, i.e., by varying its height from 2h to 2h' or vice versa, the deposition technology automatically involves a reduction in the width of the deposited material from w' to w, in generating the trajectories of deposition of the material on the single layer, it will be necessary to regulate the step so that the two "successive strokes" are in any case in the correct relative position to produce the adhesion of the one to the other.

Alternatively, a nozzle could be used, the end part of which is specifically shaped so as to laterally distribute the deposited material.

Finally, the definition of such points must be done so as to avoid the generation of steps between layers belonging to adjacent physical sub-domains SDF.

The surfaces∑ r ,d must be topological manifolds, where by the term "topological manifold" is meant a topological space wherein each element possesses an isomorphic surround of an open sub-assembly of a numerable base n- dimensional Euclidean space.

In order to ensure such property, formulations can be exploited of the guide curves y n ,m,d with more parameters than those which it is possible to determine univocally with the above-introduced conditions only. Such formulations can also be exploited to ensure that the guide curves y n ,m,d next to the boundary surfaces SC or to the external surfaces SE follow an opportune conformation (Figure 24).

In particular, figure 24 shows an example of subdivision of the physical domain DF wherein the guide curves y n ,m,d next to an external surface SE (the trace of which on the section, shown in Figure 24, is the curve yi,m,d) of the physical domain DF are defined by a higher number of points Q P , n ,m,d so as to obtain a greater detail, from the point of view of the slicing of the physical domain DF, at a specific area of the physical domain itself.

The third phase PH3 of the method M according to the invention defines the operations to be performed for the generation of the machine instructions of each identified curved layer ∑ r ,d and of all those as a whole for printing the entire physical sub-domain SDF.

The steps that characterize such phase PH3 of the method M are discussed below and are schematically shown in the flow chart of figure 25.

As shown in figure 26, a first step ST3.1 of the third phase PH3 envisages ordering the surfaces ∑ r ,d according to the print sequence and their possible grouping together for the definition of the Q limit surfaces E q of each single curved layer.

In particular, figure 28 shows an example of definition of the surfaces E q , where

E q =∑r,d ∑r',d+l .

At step ST3.2, the method M envisages the definition of Q atlases A q , by using which it is possible to remap the surface defining the limit surface E q of a curved layer on a portion (domain) X q of a two-dimensional Euclidean space (plane) R 2 (figure 35).

The domains X q are used to define the trajectories according to which to add materials in the subsequent phases.

In the event of the q-th domain X q being broken down into two or more disconnected sub-domains, these will be treated like two separate "islands".

In this respect, in the figures 29 and 30, an example is shown of how a single surface ∑ r ,d can give rise to two disjointed sub-domains and to their transformation into the Euclidean space R 2 .

If the q-th domain X q has empty areas, i.e., not to be filled with material, these can be treated using the usual techniques of deposition of the material on flat layers.

In this respect, the figures 31 and 32 show an example of how a single surface E q can give rise to a physical sub-domain SDF with an inside cavity and how its transformation can be made into the space R 2 . The definition of the path for the deposition of the material on this example layer can be made with the techniques usually adopted for a flat layer, being defined in the flat domain X q . The knowledge of the points Q P , n ,m,d on each surface∑r,d and therefore for each surface E q which delimits the curved layer, permits maintaining the correspondence between them, in order to build inner gridded, honeycomb, or in any case only partially filled structures.

Considering that the method M according to the invention can also be used in the event of gridded structures being present in the physical domain DF, the figures 33 and 34 show how the method M for the generation of the curved layers can also be used to define gridded structures inside the product.

In detail, the figures 33 and 34 show a section of a physical domain DF split into three physical sub-domains SDF1, SDF2 and SDF3. The first physical sub- domain SDF1 is completely filled, while in the second physical sub-domain SDF2 are identified only a number of areas in which to deposit material, i.e., those indicated by the background. The different directions of the backgrounds also highlight the possibility of printing the single areas using different materials.

Because, in the second physical sub-domain SDF2, the areas in which to define the material have been identified with the aid of the surfaces E q , it is possible to always deposit the material following a single surface as shown in figure 34. In particular, such illustration shows an intermediate phase of the building of the grid, during which the material will be deposited on the surface Ξ 2 .

In particular, the method M envisages a step ST3.3 for the generation of special surfaces T g , generated by means of the interpolation of a group of curves y n ,m,d. By way of example, figure 27 shows a surface T g containing the curves y n -i,m,d, Yn,m,d, Yn+i,m,d and portions of the curves (1) m ,d and (2) m ,d. The complete definition of such surfaces obviously requires other parameters to be defined by the user in relation to the specific needs of the application.

At step ST3.4, the volumes are therefore generated to be printed in the physical domain DF, i.e., the physical domain DF is split into volumes in which to deposit or not material. More specifically, such volumes are generated by means of the surfaces E q and by means of the specific surfaces T g .

The third phase PH3 of the method M therefore envisages a fifth step ST3.5 of generation in the domains X q of the trajectories according to which the addition will occur of a portion of material, if necessary modified to take into account both the effects due to the variation in quantity of added material aimed at regulating its thickness, the final aesthetic quality and/or the technical and functional properties of the product, and any increases in the distance between such trajectories which the mapping in the physical space (step ST3.5) might introduce.

The definition of the quantity of material to be added locally and therefore of the consequent adjustments to be implemented to the printing machine will be based on the local thickness of the layer to be made. For example, in the case of filament print technologies, this translates into the definition of the relative vertical shift (in direction Z) between the nozzle and the table, and of its inclination (in the event of the technology and the adopted machine permitting it), the flow of the material and the movement speed of the nozzle.

If the adopted technology does not permit changing the thickness of the material with continuity, it will be possible to regulate it locally breaking the stretches that could be defined with a single command so as to be able to define the thickness to be made on short stretches.

Such step ST3.5 also envisages the optimization of the instructions for the deposition of the material and the consequent transformation into physical coordinates.

In particular, therefore, the step ST3.5 comprises reverse mapping, transforming the coordinates on the layer of each of the points identified in the writing of the individual machine instructions, into physical coordinates.

By way of example, figure 35 shows a possible one-to-one correspondence between the points of the surface E q , on which are defined the coordinates (ξ#,ζ#) of the atlas A q , and the points on the domain X q , wherein are defined the coordinates (x (X) q ,y (X) q ).

The surface E q belongs to the physical domain DF and therefore its coordinates are the physical coordinates (Χ,Υ,Ζ), in which the portion of machine code written in the domain X q must be transformed.

Furthermore, by way of example and relating to the filament print technology, the figures from 36 to 39 show, in sequence, an example of paths of the extruder on a number of curved layers.

During this transformation, it will also be necessary to perform an optimization of the instructions for the addition of the material. Finally, the method M envisages a step ST3.6 for the generation of the machine parameters and a final step ST3.7 for the optimization of the process adapted to generate the final instructions.

The generated instructions can be ordered so as to minimize the risk of knocks with previously printed parts, envisaging, where necessary, suitable trajectories, and inserting, always where necessary, the instructions for printing the supports (for which it is possible to adopt both the traditional approach and the approach described above) at the most suitable height.

The conceived method M permits the generation, the union and the integration of machine instructions for the additive generation of products, obtained using different slicing techniques (on planes and/or surfaces).

Finally, the use is envisaged of a system for processing the method according to the invention.

In particular, the system used for the additive generation of objects comprises at least one processing unit having:

first means for the processing of the first phase PHI for the preparation; second means for the processing of the second phase PH2 for the slicing; third means for the processing of the third phase PH3 for the definition of machine instructions.

More specifically, the processing unit can consist of one or more dedicated electronic processors, while the first, second and third processing means can consist of dedicated software modules and/or of a suitable dedicated hardware. It has in practice been ascertained how the described invention achieves the proposed objects.

In particular, the following is underlined.

Compared to common slicing techniques on flat layers, the method and the system forming the subject of the present patent permit obtaining the following advantages:

- eliminating/reducing the stair-step effects;

- considerably increasing the accuracy of the geometry of the printed part, preserving details considered critical; - locally and/or globally managing the arrangement/orientation of the deposited material, so as to control its mechanical-physical-chemical characteristics, among which the improvement of the adhesion between the individual layers;

- managing surfaces with double curvatures and solids with complex surfaces (e.g., with "holes" and borders of any shape);

- facilitating the definition of the areas to be made with different materials;

- providing a new method for the generation of supports.

The method and the system according to the invention, furthermore, permit defining internal grids with orientation connectable to the external surfaces and to the curved layers. This capacity, among the other numerous applications, also permits making sandwich structures.

Compared to the techniques of known type which envisage the reduction in the thickness of the flat layer to more accurately reproduce curved surfaces, the current method and system permit greater accuracy.

Furthermore, compared to the currently known techniques which make use of curved layers, the method and the system according to the invention differ because the layers are not obtained by translation of preceding or subsequent curved layers.

In fact, in an innovative way, the method and the system according to the invention permit creating parametric-associative curved layers, the shape of which can vary with continuity from one layer to another, and adapt to the specific case.

Furthermore, such approach permits generating layers with locally optimized curvatures so as to give the component local functional and/or aesthetic properties.

Furthermore, the method and the system according to the invention can be used on commercial machines and integrate well with current slicing techniques: a physical sub-domain can in fact be printed with flat layers and an adjacent one with curved layers.

The method and the system according to the invention can also be used on the most recent machines; e.g., in the case of filament print technologies, the method M can also be applied to machines which permit varying the inclination of the nozzle and/or of the table during printing. In particular, in this case, the above-expounded technique is able to provide even more accurate results, because it is possible to deposit the material in a direction orthogonal to the previously-deposited layer.

The method and the system according to the invention also include the slicing technique on planes: to obtain them, it is enough to define the guide curves so that the surfaces∑ r ,d are flat.

Furthermore, the method and the system according to the invention permit defining the supports not only to sustain overhanging parts "from below", but also to permit a better definition of the curved surfaces, without the need to make curved supports with other typically sub tractive technologies.

Finally, the method and the system according to the invention permit using suitably shaped nozzles so as to be able to better "spread" the deposited material.