Thermal analysis of a part manufactured by additive manufacturing through the study of toolpaths

Abstract

A method for determining the thermal behavior of a part for production by additive manufacturing using at least one tool, comprising, for a set of points on a trajectory of said tool intended for production, the steps of: - determining (S1) values ​​of a set of primary parameters relating to production by additive manufacturing; - determining (S4, S5) values ​​of a reduced set of dimensionless parameters, as a function of the values ​​of the set of primary parameters and a correlation function linking the dimensionless parameters; - generating (S6) a thermal map for at least one layer of said part, as a function of said dimensionless parameters, the thermal map being recorded in digital format and associating a representative temperature value at these points. Figure for the abstract: Fig. 2

Description

Title of the invention: Thermal analysis for a part manufactured by additive manufacturing by the study of tool trajectories FIELD OF THE INVENTION

[0001] The present invention relates to additive manufacturing (or printing) and in particular to the simulation and optimization of the thermal behavior of a part produced by additive manufacturing.

[0002] Additive manufacturing (AM), or 3D printing, is a family of processes in which parts are produced by successively adding layers of materials.

[0003] The parts produced can be of different natures, different dimensions and varied complexity. Some parts must also meet strict specifications and may be subject to certifications. For example, in the aeronautical field, additive manufacturing can concern high or low pressure distributors for turbomachines, turbomachine rectifier vanes, injectors, casings, heat exchangers, hydraulic blocks, etc.

[0004] Generally speaking, we can consider any additive manufacturing process by melting or consolidating material (metallic, polymer, ceramic, etc.) by successive or simultaneous applications of one or more heat sources provided by tools following a given trajectory. These tools can in particular be lasers.

[0005] Among the methods currently available, we can notably cite - powder bed laser sintering processes, such as selective laser sintering (SLS), - laser powder bed fusion processes, such as selective laser melting (SLM), laser beam melting (LBM), laser powder bed fusion (LPBF), direct metal laser sintering (DMLS), etc. - electron beam powder bed fusion processes, such as electron beam melting (EBM), electron powder bed fusion (EPBF), etc.

[0006] In particular, in powder bed laser fusion processes (SLM, LBM, LPBF, DMLS, etc.), the parts are manufactured by laser fusion and solidification of a succession of powder layers.

[0007] For each layer, a scraper spreads a bed of metal powder of fixed thickness. Then a laser whose movement is controlled melts only the cor surface corresponding to the cutting of the part to be built, by scanning this surface along a path set by the operator (see below). This part of the operation is often called "lasing". The molten powder resolidifies after the laser passes over it and the solid surface is thus created. The plate is then lowered by the thickness of the new layer of powder that will be spread, and the process is repeated until the part is completely produced. The power, speed and focal plane of the laser are controlled throughout the process. These parameters determine the width and depth of the melted zone as the laser passes (called the "lasing bead").

[0008] The laser trajectory is also set by the operator. This laser trajectory is also called a laser pattern, or path, a scanning pattern, or a vectorization strategy. This trajectory is predefined during the manufacturing preparation phase (CAM for "computer-aided manufacturing").

[0009] The state of the material is strongly impacted by the thermal cycles imposed by the passage of the laser beam, and the successive coolings. These thermal cycles can thus cause various defects in the material and the part being manufactured: porosity, cracking, non-flat surface, etc.

[0010] Proposals have been made to determine the thermal behavior of a part during manufacture, particularly upstream of its manufacture.

[0011] However, tools for a priori evaluation of the thermal behavior of a part encounter limitations linked to the scale effects associated with additive manufacturing processes, and in particular with laser powder bed fusion processes such as the LPBF process.

[0012] Thus, there are digital tools capable of finely simulating the thermal history of the process at the scale of a few beads, or even at the scale of a layer, with relatively high associated calculation times (from a few hours to a few tens of hours per layer and per part). There are also tools that make it possible to estimate in a few hours the macroscopic temperature fields during manufacturing, but with simplifying assumptions (for example, a homogeneous heat source at the scale of a layer) which do not take into account the local effects that one wishes to analyze and therefore do not make it possible to anticipate anomalies of the product during manufacturing with sufficient precision and finesse.

[0013] As an example, we can cite patent application EP3318352 which describes a method for detecting thermally critical component areas.

[0014] This has the particular disadvantage of being based on the geometric description of the part to be manufactured. When the part is large and complex, the descriptive data can become very cumbersome to manage and generate calculation times incompatible with industrial constraints. In addition, the fact of basing itself on the geometric description of a part necessarily implies that the simulation is only valid for this part and therefore cannot correctly take into account the laser paths when several parts are manufactured simultaneously.

[0015] Furthermore, the energy supply strategy is not considered (lasing path, possible presence of several lasers, etc.). Thermal modeling is therefore very macroscopic and does not allow precise and efficient prediction of anomalies linked to the thermal behavior of the part, in a limited modeling time allowing a reduction in modeling and manufacturing cycle times.

[0016] There is therefore a need to improve the current state-of-the-art proposals. Summary of the invention

[0017] For these purposes, according to a first aspect, the present invention can be implemented by a method for determining the thermal behavior of a part with a view to production by additive manufacturing using at least one tool, comprising, for a set of points of a trajectory of said tool provided for said production, steps implemented by a processing unit of an optimization device: - determination of values ​​of a set of primary parameters relating to said production by additive manufacturing; - determination of values ​​of a reduced set of dimensionless parameters, as a function of the values ​​of said set of primary parameters and of a correlation function linking said dimensionless parameters; - generation of a thermal map for at least one layer of said part, as a function of said dimensionless parameters, said thermal map being recorded in digital format and associating a value representative of a temperature with said points

[0018] The invention proposed here does not necessarily exploit the geometric model of the part(s) analyzed (“heavy” data), but only the or all of the files describing the trajectories taken by the tool(s) during manufacturing (“light” data).

[0019] As a result, the calculation method faithfully integrates the manufacturing sequence of the manufactured part(s) without simplifying the energy deposition method (in other words, the exact production method of the parts is taken into account), and makes it possible to produce thermal analyses in calculation times compatible with industrial constraints. For example, a calculation of a thermal map representing the hot spot zones can be obtained in a time of approximately one second per layer of powder (for a laser fusion process on a powder bed).

[0020] Finally, the calculation method is said to be “universal”, that is to say that it adapts in a self-consistent manner to the particular conditions of the parts analyzed.

[0021] According to preferred embodiments, the invention comprises one or more of the following features which can be used separately or in partial combination with each other or in total combination with each other: - said determination of values ​​of a reduced set of dimensionless parameters comprises the determination of a subset of dimensionless parameters from said primary parameters, and the determination of a dimensionless parameter dependent on a temperature rise from said subset and the correlation function, said dimensionless parameter dependent on a temperature rise being included in the reduced set of dimensionless parameters thus determined. - said correlation function is estimated by varying values ​​for the primary parameters of said set of primary parameters and simulating an associated temperature rise. - Said primary parameters may in particular relate to said trajectory planned for production, and / or to the material used for this production, and / or to said at least one tool. - said at least one tool is at least one laser and said primary parameters comprise an irradiance of said at least one laser and / or a cumulative exposure time and / or a lasing duration and / or a dense material depth and / or an equivalent depth and / or a thermal conductivity and / or a thermal diffusivity. - the said dimensionless parameters, jri, ir2> ir3 are 3 in number, and are expressed: [Math.l] 2 711“ fcumu! i-expo '■scan

[0022] with — IabKë ], A being said value representing a temperature in a point of said set, Iabs being said irradiance, 3 being a characteristic diffusion length depending on said thermal diffusivity, k being said thermal conductivity, b' being said equivalent depth, t'expo1 being said cumulative exposure time, and being said laser duration. - said primary parameters further include a laser speed and a characteristic radius of said tool. - the said dimensionless parameters, jti, ir2> ir3, ir4j ir5 are 5 in number, and express themselves: [Math.2] t]D Æ2 “ 2 7 / fcumid '■expo t Vr hïMt'L ^4“ ô R, ^3 = “

[0023] with — I^ô f k.^ ■> A being said value representing a temperature in a point of said set, Iabs being said irradiance, ô being a characteristic diffusion length depending on said thermal diffusivity, k being said thermal conductivity, b' being said equivalent depth, being said cumulative exposure time, riron being said lasing duration, RL being said characteristic radius and VL being said lasing speed.

[0024] According to another aspect, the invention relates to a method of producing a part by additive manufacturing using a machine for additive manufacturing, comprising steps of - determination of a heat map by the method as previously described,

[0025]

[0026] - determination of at least one risk zone within said heat map, - adaptation of at least one parameter of said machine as a function of said at least one risk zone, said at least one parameter being able to be a parameter of said trajectory. According to another aspect, the invention relates to a computer program comprising instructions for implementing a method as previously described. According to another aspect, the invention relates to a system comprising a machine (200) for production by additive manufacturing using at least one tool, adapted to produce a part from a trajectory of said tool, and comprising an optimization device configured for implementing steps of: - determination of values ​​of a set of primary parameters relating to said production by additive manufacturing; - determination of values ​​of a reduced set of dimensionless parameters, as a function of the values ​​of said set of primary parameters and of a correlation function linking said dimensionless parameters; - generation of a thermal map for at least one layer of said part, according to said dimensionless parameters, said thermal map being recorded in digital format and associating a value representative of a temperature with said points

[0027] According to one embodiment, said machine is suitable for producing a part from among a high or low pressure distributor for a turbomachine, a turbomachine rectifier vane, an injector, a casing, a heat exchanger, a hydraulic block, etc.

[0028] Other characteristics and advantages of the invention will appear on reading the following description of a preferred embodiment of the invention, given by way of example and with reference to the appended drawings. BRIEF DESCRIPTION OF THE FIGURES

[0029] The attached drawings illustrate the invention: [Fig.l] schematically illustrates a system according to one embodiment of the invention, comprising a machine for production by additive manufacturing.

[0030] [Fig.2] schematically represents a flowchart of the steps of a method according to one embodiment of the invention.

[0031] [Fig.3a] and [Fig.3b] illustrate examples of elementary volumes represented sive. [Fig.4] illustrates a heat map very schematically. [Fig.5] illustrates an example of a correlation function.

[0032] DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[0033] The proposed method applies to various printing or manufacturing techniques. additive (or 3D printing). Generally speaking, additive manufacturing involves moving one or more tools along a predefined path (which may be called a "tool path") to provide a point source of heat on a material.

[0034] The method applies in particular to laser powder bed fusion processes, and more specifically, but not exclusively, to laser powder bed fusion (LPBF).

[0035] This process makes it possible to manufacture parts from the selective fusion of successively stacked powder bed layers. It allows the manufacture of lighter complex parts such as fine structures (lattice type), and is therefore applicable to the field of aeronautics.

[0036] It is found that the metallurgical and mechanical state (phases present, residual stresses, etc.), the health of the material (porosity rate, cracking, etc.), the state of the surface, and therefore, the thermomechanical properties of the resulting parts are determined to the first order by the thermal cycles imposed by the manufacturing process. additive building.

[0037] It is therefore essential to understand the influence of heating / cooling cycles on the thermal observed in the parts in order to be able, where appropriate, to optimize the manufacturing parameters to eliminate, or reduce, the harmful effects.

[0038] In the particular case of an LPBF process, the thermal cycles are controlled by the vectorization (or lasing) paths imposed on each layer. Depending on these lasing strategies and the local geometric configuration of the part, hot spots may develop, linked to an energy input that is too high compared to the part's capacity to evacuate heat locally. This is for example the case of areas with small sections where the laser makes numerous back-and-forth movements in a relatively short period of time and / or undercut areas overlooking powder masses which have a relatively low thermal diffusivity compared to that of the dense material.

[0039] These “hot spots” should be avoided because: - Heat accumulation in a localized area can cause coalescence of the molten pools, which form a protrusion during solidification. When this local excess thickness exceeds the thickness of the powder layer, the scraping system can collide with the part being manufactured, which can cause degradation of the manufactured geometry or even a manufacturing stoppage. As a result, the fused material is lost and industrial cycle times are extended. - Hot spots can promote cracking phenomena (solidification cracking or macroscopic cracking) - Overheating areas can promote the formation of unstable “keyholes” (keyhole cavities) which, when they collapse, form porosities in the part.

[0040] In order to anticipate the appearance of these hot spots, it is proposed to carry out digital modeling and simulations upstream of the actual manufacturing.

[0041] Indeed, by simulating the heat, or energy, input into a part produced by additive manufacturing, and by taking into account the vectorization (or lasing) schemes, we can evaluate a priori the evolution of the thermal field during manufacturing. We can thus anticipate the appearance of overheating zones, and possibly trigger corrective actions.

[0042] The proposed method thus aims to identify risk zones, which could possibly become “hot spots” and induced by the exact lasing strategy on the parts to be produced, and this with a calculation time compatible with industrial constraints (i.e. a few hours at most per production platform).

[0043] The proposed method is based on the laser strategy, or scheme, and not, like some prior art proposals, on the geometry of the parts to be produced. This makes it possible, on the one hand, to drastically reduce the necessary calculation times while maintaining high precision in the estimation of risk areas, and also to take into account the entire production tray, which may include several parts, whereas previous proposals opt for a part-by-part approach. It is important to note that since the laser scheme is common for the entire production tray, a product-by-product approach necessarily introduces a bias into the estimation.

[0044] [Fig.l] schematically illustrates a context of use of a proposed method.

[0045] A machine, or printer, 200 for additive manufacturing consumes materials 210 in order to produce one or more parts 220. This machine is parameterized by a set of parameters which specify its operation and which can be modified during manufacturing: laser movement speed, laser power, etc.

[0046] In the field of aeronautics, the machine 200 can be adapted to produce parts as varied as, for example, a high or low pressure distributor for turbomachines, a turbomachine rectifier vane, an injector, a casing, a heat exchanger, a hydraulic block, etc.

[0047] An optimization device 100 is also provided and adapted for simulating the thermal behavior of a part 220 with a view to its production by additive manufacturing using the machine 200. This simulation is implemented upstream of production by the machine for additive manufacturing and aims to determine risk zones which are in particular likely to give rise to hot spots.

[0048] These risk areas can be indicated to the user. For example, a heat map can be displayed on a screen, possibly highlighting the risk areas.

[0049] Depending on the risk zones determined in the thermal behavior of the part 220 to be produced, a user can intervene on the parameters of the machine in order to avoid, or reduce, the appearance of these risk zones, or else so that these risk zones actually become hot spots.

[0050] According to a particular embodiment, the simulation device can be adapted to directly determine adaptations in the parameter set of the machine in order to optimize the additive manufacturing process in order to avoid or minimize the appearance of hot spots. In particular, it is thus possible to optimize the heating and cooling cycles during additive manufacturing thanks to the results of the simulation phase.

[0051] [Fig.2] schematically illustrates a flowchart of the proposed method.

[0052] In a step SI, the values ​​of a set of primary parameters relating to the trajectory of the tool(s) planned for the production of one (or more) parts, to the material used for this production and to the tool(s) are determined. In the case where this or these tools are lasers, the trajectory(s) represent the lasing diagram.

[0053] According to the proposed method, primary parameters are selected because they are identified as having a first-order influence on the thermal at the local scale.

[0054] These parameters are of different natures. They may relate to the laser(s) used, and / or to the material used (in particular to its thermo-physical properties) and / or to the lasing scheme.

[0055] Taken individually, these primary parameters are not necessarily sufficient to explain the thermal behavior of the part to be produced, and, a fortiori, the possible appearance of hot spots.

[0056] However, thanks to a dimensional analysis, these parameters are combined together to form a reduced set of dimensionless and independent parameters, which have a physical meaning better able to describe the thermal behavior of the part during its manufacture on the scale of the laser diagram.

[0057] At least one of these dimensionless parameters must relate to the temperature measured locally (along the analyzed tool path, for example the analyzed laser path), while the others characterize the various factors likely to promote local overheating (undercut areas, relatively high concentration of vectors in an area, etc.).

[0058] The dimensionless nature of these parameters thus makes it possible to reason from quantities independent of the specificities of the vectorization analyzed. In other words, the values ​​of these parameters are valid regardless of the materials used or the parameters of the heat source (laser) used.

[0059] The determination of the primary parameters is based on modeling of the additive manufacturing process and the associated laser diagram.

[0060] This modeling is carried out at the mesoscopic scale. This mesoscopic scale is intermediate between the macroscopic and microscopic scales; it is sufficiently large to include a large number of particles (such that their statistical properties do not fluctuate significantly), while remaining sufficiently fine so that the thermodynamic quantities (pressure, temperature, etc.) remain local (point-like at the macroscopic scale).

[0061] In particular, the mesoscopic scale can be defined by the influence that the laser has on a point of the lasing pattern but also on the points close to this point, on this lasing pattern, upstream or downstream.

[0062] The modeling can be based on a Representative Elementary Volume (REV) associated with a point considered.

[0063] [Fig.3a] and [Fig.3b] illustrate examples of representative elementary volumes VER, for a point M located on the laser diagram.

[0064] This volume is characterized by a surface centered on this point M considered, by a dimension of this surface (diameter in the example of [Fig.3a], side a in the example of [Fig.3b].

[0065] The characteristic dimension (diameter, side, etc.) has a magnitude which is equivalent to a few vector deviations (i.e. distance between two consecutive vectors), for example between 5 and 10 vector deviations, and contains portions of the vectors which have a thermal influence on point M. This characteristic dimension can therefore depend on different parameters relating to the laser (power, etc.) and the material (thermal conductivity, etc.).

[0066] [Fig.3a] illustrates all or part of a part 220 to be produced. The upper surface of this part is hatched, these hatchings schematically represent the lasing diagram.

[0067] This laser pattern can be seen as a set of lines corresponding to the path of the laser beam (or other heat source) on the surface of the layer of the part being manufactured.

[0068] This lasing scheme, or strategy, mainly specifies the trajectory of the laser path and the inter-cord distance, i.e. the distance between two neighboring (and generally parallel) lines of the lasing scheme. In the figure, the lines are parallel and the inter-cord distance corresponds to the distance between two lines of the hash.

[0069] This lasing diagram is formed from a set of segments, each segment can be represented by a set of parameters: coordinates of a starting point, coordinates of an arrival point, laser speed, laser power, etc.

[0070] This lasing diagram can be provided in a data structure which can be tabular, in which each row corresponds to a segment and the columns correspond to the different parameters associated with the segments (coordinates, laser speed, laser power, laser beam diameter, irradiance profile, etc.)

[0071] This data structure can be provided by a computer file. The latter can be in different formats: TXT, G-code, CLI, CLI+, HDFS, OVF, etc.

[0072] [Fig.3a] also represents a representative elementary volume VER of hemispherical shape, corresponding to a zone 221 of the part 220, and centered on a point M belonging to the laser diagram.

[0073] This representative elementary volume contains several vectors of the laser pattern. Here, we call "vector" any rectilinear section which discretizes the path of the laser on the surface. The laser pattern is thus also commonly called "vectorization pattern". It is possible during the design to define curved lines for lasing, but these are generally discretized into a set of line segments, or vectors.

[0074] The intersection of the lasing pattern with the upper surface of the representative elementary volume forms a set of segments between an entry point and an exit point (the lasing pattern being oriented in the direction of the laser path).

[0075] Thus, in [Fig.3a], we observe the oriented segments [1; 2], [3; 4], [5; 6], [7; 8], [9, 10]. According to the definition of a representative elementary volume, the passage of the laser on these different segments can influence the thermal behavior of the material at point M (located in the middle of the segment [5; 6]).

[0076] The representative elementary volume can have different shapes: cube, hemisphere, hemi-ellipsoid, etc., depending on its relevance to the thermal problem that one wishes to resolve, and the practical constraints that this choice imposes on the implementation of the proposed method.

[0077] [Fig.3b] shows another form of representative elementary volume. Its cubic form can be characterized by a characteristic side a.

[0078] The method aims to determine data representative of the thermal behavior of the part to be produced. This representative data can for example be a thermal map for each layer of the part to be produced. This thermal map can associate a value of a thermal quantity (or temperature) with each point M at which this quantity is to be evaluated. It is assumed, according to the proposed modeling, that this quantity depends on valid primary parameters (and assumed to be constant) on the representative elementary volume centered on the point M considered.

[0079] It is proposed to select a set of primary parameters which makes it possible to simplify the modeling as much as possible while allowing good precision in the determined thermal map (or more generally of the data representative of the thermal behavior of the part).

[0080] In other words, the set of primary parameters can be chosen so as not to exclude any important factor likely to impact the thermal behavior of the material and the part to be produced.

[0081] Generally speaking, these primary parameters relating to production by additive manufacturing concern the planned trajectory of the tool for this production, the material and the tool(s) to be used as a point source of heat.

[0082] Thus, in the case of a laser, this set of primary parameters includes relative parameters: - the laser diagram planned for the production of one (or more) parts, - the material used for this production and - to the laser(s) (for example, power, speed, spot diameter, etc.)

[0083] It should be noted that the primary parameters do not relate to the geometry of the part to be produced.

[0084] It is in fact noted that the geometry of the part to be produced can be extracted from the laser diagram (or more generally from the trajectory of the tools used).

[0085] Indeed, the analysis of segments on a neighborhood allows to have sufficient knowledge of the geometry of the part on this neighborhood, since the segments are only present on parts of the part. The absence of a segment on an area indicates, implicitly, that the area does not belong to the part to be produced.

[0086] This has the advantage of not having to take into account the files describing the geometry of the parts to be produced, which are traditionally quite heavy, but only the file describing the lasing. The latter is substantially smaller in size and easier to manage in structure, which can allow a significant gain in performance.

[0087] The proposed method comprises a prior step of determining, in a step S2, a reduced set of adimensional parameters from these primary parameters.

[0088] We also want the number of dimensionless parameters to be minimal. Indeed, the fewer parameters there are, the simpler the problem is, and the simpler it is to construct an abacus as will be seen below. Also, by virtue of the Vaschy-Buckingam theorem, the number of primary parameters must also be minimal.

[0089] A laser of incident irradiance Io travels across the upper surface of a representative elementary volume at a speed VL. We can write:

[0090] [Math.3] j _ P

[0091] with P the laser power, RL the radius at 1 / e2 of the laser beam. The constant "e" here represents e=exp(l). In this embodiment, the laser is considered to be Gaussian, i.e. the spatial distribution of irradiance follows a two-dimensional Gaussian curve centered on the point of impact. For a Gaussian laser, the radius of the focal spot is arbitrarily defined as the radial distance from the optical axis such that the incident irradiance falls to 13.5% of the maximum irradiance, measured at the center of the spot (1 / e2 = 0.135).

[0092] Obviously, it is possible to envisage other types of spatial distribution of the irradiance of the laser, or more generally of the heat source, around a point of impact, and to characterize this spatial distribution by a characteristic radius of the focal spot, or any other quantity or set of quantities.

[0093] The cumulative laser exposure time can be defined as the sum of the lengths of the portions of vectors contained in the representative elementary volume, divided by this laser speed. If there are n vectors in the representative elementary volume- representative and that these are parallel to one of its sides, we can write:

[0094] [Math.4] fcumul — n JL texpo —

[0095] However, the successive passages of the laser in the representative elementary volume are spread out in time, over a duration which corresponds to the difference between the instant t exit at which the laser leaves the last vector in the VER, and the instant t entry at which the laser arrives on the first vector of the VER.

[0096] In the example of [Fig.3b], the instant tentre corresponds to the instant when the laser arrives at point 1, and the instant tsort;e corresponds to the instant when the laser leaves point 10. We can define the laser duration tscan corresponding to the difference between these two instants:

[0097] [Math.5] tscan — t output ” $ input

[0098] Each individual laser pass is in fact separated from the others by a lasing duration outside the representative elementary volume considered plus a jump time between two vectors (i.e. the time taken for the laser to move from the end of one vector to the beginning of the next vector). Thus and tscan are constrained by the following inequality:

[0099] [Math.6] 0, .cumul. lexpo — tscan

[0100] Furthermore, the representative elementary volume includes a certain quantity of dense material 223 which diffuses heat. Potentially, it also contains a complementary quantity of powder 222 (not exposed to the laser) which acts as a thermal insulator. Simplifying the problem further, considering a unidirectional VER, we denote by b the depth of dense material 223 located under the lasered surface. We can write:

[0101] [Math.7] b £ a

[0102] In a real part, however, the dense material portions in VERs are generally not unidirectional, particularly in the draft and undercut areas. The thickness of a thermally equivalent unidirectional element b' can then be considered:

[0103] [Math.8]

[0104] V represents the volume of dense material 223 contained in the VER and S represents the reference characteristic surface (for example the irradiated upper surface, the sum of the surfaces in contact with the dense material, etc.). Furthermore, the dense material has a thermal conductivity k and a thermal diffusivity a assumed constants, while powder 222 is assumed to be a perfect insulator (adiabatic conditions).

[0105] Finally, we can evaluate the temperature rise at point M corresponding to the VER considered by the variable A:

[0106] [Math.9]

[0107] is a characteristic temperature at point M, resulting from the vectorization sequence. It can be the maximum temperature or the average temperature seen during the exposure sequence or any other parameter homogeneous at a temperature, which can characterize local heating of the part. To is the reference temperature of the representative elementary volume, VER, or of the layer.

[0108] This quantity A determined for all the points M makes it possible to determine a thermal map of the part(s) to be produced. The thermal map can therefore associate with each point M of the trajectory of the tool (here the laser) a value representative of a temperature which can for example be a rise in temperature.

[0109] Thus, according to this embodiment, p=7 primary parameters are chosen, which are: - the irradiance of the laser, I0 (or the absorbed irradiance Iabs=I0.A with A the absorbance of the material); - the cumulative exposure time - the duration of the tscan age; - the depth of dense matter b, or the equivalent depth b'; - thermal conductivity k; - thermal diffusivity a; - the deviation from the reference temperature, or temperature rise, A

[0110] As previously indicated, these parameters are relative to the lasing pattern (texpc, tscan, b, b'), to the material (k, a), to the laser (Io). A primary parameter is relative to the temperature rise, which is the data that we seek to determine.

[0111] These parameters are assumed to be linked together by a mathematical function g().

[0112] These 7 parameters depend on 4 fundamental units (mass, length, time and temperature).

[0113] According to the Vaschy-Buckingham theorem (or theorem ji), if a physical equation involves p physical variables, these depending on u fundamental units, then there exists an equivalent equation involving pu dimensionless variables constructed from the original variables.

[0114] In the present embodiment, there therefore exists a mathematical function h() equivalent to the function g(), involving pu=3 independent dimensionless numbers, which can be noted jtb ir2, ir3. We can write:

[0115] [Math. 10] Æj^ / îO^TT,)

[0116] Subsequently, we will call this function the correlation function, since it allows us to correlate the variations of the dimensionless parameters jri, ir2, ir3.

[0117] In a classical way, by exploiting the properties of these 3 numbers, we can define:

[0118] [Math. 11] TTi — “ ——-

[0119] We can define <5 the characteristic diffusion length, such that:

[0120] [Math. 12] Ô = 2.^at,scan

[0121] The definition of the dimensionless parameters can then be written:

[0122] [Math. 13] 2k.àT'd „ 5 fCfimul -

[0123] It is noted that ^ depends on the temperature TiD calculated at the surface of a semi-infinite medium absorbing the intensity Iabs with a one-dimensional heat flow. This temperature is notably described in Carslaw HJ, Jaeger, JC, “Conduction of heat in solids”, Oxford University Press, 1959. It can be defined by the expression:

[0124] [Math. 14]

[0125] The definition of the dimensionless parameters can then be rewritten:

[0126] [Math. 15]

[0127] Thus, the 3 dimensionless parameters obtained after dimensional analysis can be described as follows:

[0128] 711 is proportional to a standardized temperature rise. This quantity is unknown a priori: this is the one we want to calculate along the laser diagram in order to obtain the thermal map.

[0129] æ2 is proportional to the normalized diffusion length. This number characterizes the part's ability to dissipate heat locally. The smaller the depth of dense material b, or the equivalent depth b', compared to the characteristic diffusion length ô, the less the part is able to dissipate heat locally (all other things being equal). As described previously, this value can be calculated solely from the data structure describing the lasing scheme (for example in a file), considering the fact that only dense areas are crossed by vectors.

[0130] 71 is proportional to the standardized exposure time. The higher the cumulative duration laser exposure texpo1 tends towards the duration of lasing and the faster the heat buildup locally (all other things being equal). Just as this number can be calculated only from the data structure describing the lasing pattern.

[0131] Thanks to the equation 711=11(¾ ; ir3), stated previously, we can express jti as a function of ir2 and ir3, so as to calculate the characteristic temperature rise A along the laser diagram:

[0132] [Math. 16] / s (cumul \

[0133] This expression shows that the temperature rise A is proportional to the temperature T1D, weighted by a function of the normalized diffusion length 15y / / and the normalized exposure time fexpo jt

[0134] In a step S3, which can be carried out separately (for example upstream) from the simulation method S1-S4-S5-S6, we seek to estimate the correlation function h() which links the dimensionless parameters.

[0135] This step can be called the calibration step, or calibration, since it involves relating the known values ​​of a subset of dimensionless parameters to a correlation function to obtain the value of the unknown parameter, i.e. the one which depends on the temperature rise.

[0136] Several methods can be used to obtain an estimate of this function.

[0137] For example, this estimation can be carried out by simulating the vectorization and the associated thermal behavior at the scale of the representative elementary volume, VER, by varying the different primary parameters of the additive manufacturing process within a range of values ​​relevant to the capabilities of the machines or the window of the additive manufacturing process implemented. We can thus describe a space of relevant values ​​and, for each n-tuple of the parameter space, we can obtain by calculation or simulation the dimensionless parameters jti, ir2, ir3.

[0138] This involves carrying out a numerical experiment plan with the aim of constructing a response surface allowing the adimensional parameters jrb ir2> ir3 to be correlated. When a function h() is difficult to determine, it is possible to construct a database in which the adimensional parameters jtb ir2> ir3 are tabulated.

[0139] In other words, from these p-tuples of adimensional parameter values, we can determine a general law (by linear or other approximation, for example), or a table constituting a sort of abacus whose knowledge of p-1 entries makes it possible to determine the last value of the p-tuple.

[0140] This simulation can be carried out by different methods of the state of the art such as for example the finite difference method, the finite element method, the finite volume method, the discontinuous Galerkin method (GD), etc.

[0141] Simulating the vectorization at the scale of the representative elementary volume, VER, to correlate the dimensionless parameters with each other, instead of doing it at the scale of an entire layer, makes it possible to considerably reduce the calculation times: thus, the simulation can take a few minutes for a VER compared to a few hours, or even a few tens of hours, for an entire layer.

[0142] [Fig.5] illustrates the result of such a simulation set. Each point re presents a simulation, and has as abscissa the value of the correlation function applied to the couple (ns ir3) and as ordinate the value of the dimensionless parameter ir b

[0143] We note that the points are approximately aligned for all parametric configurations, and in particular for different materials (since, during the simulations, the types of materials and therefore the parameters k and a were varied). This therefore validates the universal nature of the scaling law thus obtained. Therefore, if the experimental plan is well designed, this simulation can be carried out only once and reused for different simulations of the thermal behavior of a part for production by additive manufacturing.

[0144] Thus, the computational aspects of the simulation are transferred to the construction of this abacus. They can be carried out upstream of its use and be shared for several uses. These calculations therefore no longer penalize the processing of the determination of the thermal behavior of a part to be produced.

[0145] This abacus can therefore be created upstream and reused for a set of simulations of the thermal behavior of a part to be produced due to the universal nature of its values.

[0146] Following the determination of the values ​​of the primary parameters, in step S1, it is possible, in step S4, to calculate the values ​​of the dimensionless parameters which do not depend on the temperature rise A

[0147] In the embodiment previously described, these parameters are the parameters jt2 and JT3.

[0148] This calculation can be carried out for all or part of the layers of the part to be produced.

[0149] Each layer considered is subdivided into representative elementary volumes, VER. The characteristic dimension of these and the distance between two representative elementary volumes depend on the spatial and temporal resolution desired for the analysis.

[0150] Each representative elementary volume contains portions of the laser diagram, forming segments between an entry point and an exit point in the VER (Thus, as a reminder, in [Fig.3a], we observe the segments oriented [1; 2], [3; 4], [5; 6], [7; 8], [9, 10]).

[0151] The dimensionless parameters not dependent on the temperature rise can be calculated for each VER from these segments and without resorting to the geometric model.

[0152] The calculation of the dimensionless parameter ir3 is direct: it depends on the values ​​of the durations and tscan- The value of these durations depends only on the layer considered.

[0153] The calculation of the dimensionless parameter ir2 depends on a set of layers: it is necessary to aggregate the information contained in the previous layers in the depth a of the VER, in particular, to sum all the lengths of portions of vectors allowing the calculation of the volume of dense matter.

[0154] In a step S5, the value of the dimensionless parameter which depends on the temperature rise can be calculated.

[0155] This parameter, jti here, depends in fact on the other dimensionless parameters and on the correlation function h(), determined in step S3.

[0156] In a step S6, the temperature rise A T*M can be calculated, from this dimensionless parameter ^dependent on the temperature rise.

[0157] The set of values ​​determined for the thermal elevation AT^ for a set of points M of the laser diagram can thus provide a thermal map.

[0158] [Fig.4] illustrates such a heat map very schematically.

[0159] This figure represents a fictitious part to be produced 220. It is assumed that the lasing is carried out horizontally. The different filling patterns of the zones 225, 226, 227 correspond to distinct values ​​of the temperature rise AT Only 3 values ​​are represented for the clarity of the figure, but in practice, the map can present a continuity of values ​​(each corresponding to a gray level, in a graphical representation) or to a larger number of discrete values.

[0160] In zone 225 (shown in dotted lines), heating is minimal because the laser travels a long distance, within the part (or parts, in the general case) before returning to the vicinity of the same point. The heat therefore has time to dissipate substantially between two passes of the laser in the same vicinity (according to the predefined lasing pattern).

[0161] In zone 227 (represented by bold hatching), heating is strong because the laser makes very short back and forth movements in the part which, in this zone, has a very small dimension in the direction of the lasing. Between two passes of the laser, the heat does not have enough time to be evacuated, and the temperature rises.

[0162] Zone 226 (represented by finer hatching) corresponds to a situation intermediate to those of zones 225 and 227, in which the zone is oriented at 45° relative to the lasing pattern so that the travel time of the laser within this zone is longer than in zone 227, but not sufficiently to allow sufficient heat evacuation.

[0163] This thermal mapping can make it possible to determine risk areas, i.e. areas likely to give rise to hot spots which could lead to surface protrusions, cracks, cavities (“keyholes”), or other anomalies on the part to be produced.

[0164] The determination of these risk areas can be carried out in different ways and follows directly from the determination of the heat map.

[0165] For example, a threshold can be established beyond which a temperature difference is indicative of a risk zone.

[0166] The detection of one or more risk zones can trigger several actions on the part of the simulation device 100.

[0167] For example, these actions may include one or more of the following actions: - Alerting a user by highlighting the risk area(s) on a graphical representation of the heat map; - Alert the user so as to prevent the triggering of additive manufacturing as is; - Trigger an optimization of the configuration parameters of the additive manufacturing machine 200, in order to avoid, or reduce, the appearance of these risk areas.

[0168] Thus, the simulation device can be adapted to directly determine adaptations in the machine parameter set, in particular to optimize the heating and cooling cycles. In particular, it may involve homogenizing the heat input to the layers without (too much) penalizing the manufacturing times.

[0169] The parameters that can be adjusted for this optimization include: - The power of the laser. The laser pattern can be kept but the power can be reduced on one or more segments of the laser pattern that correspond to risk areas; - The laser speed. The laser pattern can be maintained, but the laser speed can be increased on one or more segments that correspond to risk areas. - Pause times between two segments. For example, you can keep the laser pattern, but add a pause time between two successive segments in or around a risk area to allow the area to cool. - The order of the segments. You can keep the laser pattern, but skip one or more segments in a risk area and then return to them later, in order to let the area cool down in the meantime. This option penalizes manufacturing time less than introducing pause times. - Segment length. In the case of a strip laser strategy, the width of the strips can be increased to increase the time between two laser passes in the same area. Two adjacent segments can also be joined together if one of them is too short. - The laser diagram, in its entirety. - The geometry of the part to be produced.

[0170] This adaptation of parameters may for example comprise the modification of the data structure expressing the lasing scheme. The lasing parameters (laser power, laser speed, laser beam diameter, irradiance profile, etc.) may be directly modified segment by segment in this data structure, the order of the segments may be modified, new lines may be added to insert a pause between two segments, etc.

[0171] According to one embodiment, the algorithm proposes several scenarios. Each scenario has advantages and disadvantages, which, for example, an engineer arbitrates according to the other constraints present in his specifications.

[0172] For example, a first scenario may be to modulate (only) the power according to the length of the vectors, so that the temperature at each point of the surface falls below the previously fixed threshold. This modulation is calculated automatically via the method presented here.

[0173] In this scenario, the minimum power proposed by the algorithm may be incompatible with the metallurgical specifications of the alloy being produced. In this case, the engineer may set a minimum power, which forces the algorithm to adjust a second parameter (e.g., pause times between two vectors), in order to respect the set temperature threshold.

[0174] Therefore, the engineer chooses a hybrid scenario, with two adjustment variables (the laser power, and the inter-vector pause time).

[0175] Another scenario could be to add pause times between all vectors. However, this solution may extend the manufacturing time beyond the specifications. In this case, the engineer can choose an alternative scenario, in which pause times are imposed only on the shortest vectors (with a threshold to be defined), and modulate the laser power and / or speed for the others.

[0176] In short, the algorithm must propose several scenarios, and the engineer can arbitrate by crossing the different constraints imposed on him. Each constraint imposed by the engineer (minimum power, maximum speed, etc.) is taken into account in a self-consistent manner by the algorithm, which adapts its scenarios accordingly.

[0177] It should be noted that the description which has just been given relates to one embodiment. Numerous variants can be proposed.

[0178] In particular, the proposed dimensionless parameters, jrb ir2, ir3 are not unique and other dimensionless parameters can be proposed, in particular depending on the primary parameters that are chosen to model the thermal behavior of the part to be produced. Indeed, if the primary parameters are changed, the dimensional analysis will provide a different set of dimensionless parameters.

[0179] In the embodiment described above, it was considered that the process of absorption of the incident energy provided by the laser was a surface phenomenon. The absorbed irradiance Iabs was therefore considered as the primary parameter. This hypothesis works particularly well for metal alloys irradiated by YAG lasers, in “conduction” mode. Alternatively, it can be considered that the irradiated material absorbs the incident radiation in volume (this is for example the case of ceramics irradiated by YAG lasers or, as a first approximation, that of metals in “keyhole” mode).

[0180] In this case, the absorbed irradiance Iabs (expressed in W / m2) can be replaced by a volumetric heat source Qabs (expressed in W / m3). After dimensional analysis, three dimensionless parameters ji'b ji'2, jt'3 can be calculated:

[0181] [Math.17] TT — / i — t V -■ hcan

[0182] We can consider that Qabs is expressed as the product of the absorbed irradiance Iabs and a volume absorption coefficient [3 such that 1 / P is homogeneous at a thickness absorption. We can then write:

[0183] [Math. 18] ' 2 Æl- IA -fiâ ^2 —' IT?

[0184] Or again:

[0185] [Math. 19] 1' _ 3^ Æ1 æ2 “ Æ2 = 7F3

[0186] According to one embodiment, the volume absorption coefficient P can be considered as a primary parameter. Therefore, the dimensional analysis can provide 4 dimensionless parameters, jt”b ir”2, jt”3, ir”4. These dimensionless parameters can be expressed as:

[0187] [Math.20] Æ2 = ^2 “ 4 tcumuf ' t (expa 7T =■ --- J} 'bucket ^4 = fi3

[0188] Furthermore, in the embodiments previously described, the heat source (laser) is modeled by an irradiance alone (Iabs) or a heat source alone (Qabs)•

[0189] However, depending on the application, it may be desirable to take into account the effect of the lasing speed VL and that of the characteristic radius RL of the energy source: in fact, a laser scan on a given surface is not strictly equivalent to an equivalent irradiance imposed statically on this same surface.

[0190] We can then determine five dimensionless parameters jtb ir2, ir3, ir4, ir5:

[0191] [Math.21] / v, Æ4- T~ Æ3 “ “

[0192] Similarly, step S3 of determining a correlation function h() can be carried out in different ways.

[0193] Instead of the previously described simulation, an exact analytical resolution can be implemented, in particular for simple geometric and thermal configurations.

[0194] To do this, we can write the energy conservation equation at the surface of each representative elementary volume: [DWS] =

[0196] <peq représente la norme du flux de chaleur homogène équivalent, absorbé à surface s ver pendant durée lasage tscan, telle que l’énergie ap pumulest absorbée l' ‘'expo by the representative elementary volume.

[0197] We can deduce from this equation that

[0198] [Math.23] — ^eq ~ S ' txam

[0199] By setting = APL / S, the power density, we obtain:

[0200] [Math.24] __ z àbs* tscan

[0201] We can then assume that each representative elementary volume behaves like a one-dimensional medium of equivalent depth b', with adiabatic edges. We can calculate the average temperature rise by the expression:

[0202] [Math.25] A Tw = T^o {( 2«Ç ) + ierfc (2 ( n + 1 ) Ç )}

[0203] We denote by ierfc() the integral function of the complementary error function of the Gaussian error function, erfc().

[0204] Other analytical solutions can be obtained by setting other different boundary conditions (Dirichlet conditions on temperature, convection and radiation losses, etc.).

[0205] By combining the two previous equations, we can obtain

[0206] [Math.26] a ) +^A'(2(«+OŸ ) )

[0207] Finally, by setting ' we obtain:

[0208] [Math.27] A T*M = T\d^ {ierfc ( 2n% ) + ierfc ( 2 ( n + 1 ) § )}

[0209] Or again

[0210] [Math.28] c fcumid \ y fa lscan l

[0211] With:

[0212] [Math.29] ( S fCUttlttl \ ■■■■■■■■■■■■ +Çltf'f'ttd u1 ■ 1 •• / ' / \ / yf \ x f. = +ierfe(2(n+ 1)| )}

[0213] The advantage of an analytical solution over estimation of the h() function by simulation is that it saves computational costs. However, this exact analytical solution represents a simplified geometric configuration with boundary conditions that are not very representative of those of the process.

[0214] Yet another way of doing this is to use experimental data instead of digital data (for example, measurements by infrared thermography, or any other in situ thermal measurement), acquired during the manufacture of technological calibration test pieces (or samples) or complete parts.

[0215] The advantage of technological test pieces compared to complete parts is that they are designed to present geometric characteristics representative of those found on the industrial parts that one seeks to manufacture, while being less complex and less expensive to manufacture than the latter.

[0216] Thus, it is possible to correlate the thermal measurements to the adimensional parameters along the lasing pattern and thus estimate a correlation function h().

[0217] The advantage of experimental data over numerical solutions is their reliability (within the limits inherent to the measuring instruments). However, numerical simulation saves material and time in using additive manufacturing machines.

[0218] Of course, the present invention is not limited to the examples and the embodiment described and shown, but is defined by the claims. It is in particular susceptible of numerous variants accessible to those skilled in the art.< / peq>

Claims

Claims

1. Method for determining the thermal behavior of a part for production by additive manufacturing using at least one tool, comprising, for a set of points of a trajectory of said tool intended for said production, steps implemented by a processing unit of an optimization device (100) of: - determining (S1) values ​​of a set of primary parameters relating to said production by additive manufacturing; - determining (S4, S5) values ​​of a reduced set of adimensional parameters, as a function of the values ​​of said set of primary parameters and of a correlation function linking said adimensional parameters; - generating (S6) a thermal map for at least one layer of said part, as a function of said adimensional parameters, said thermal map being recorded in digital format and associating a value representative of a temperature with said points.

2. Method according to the preceding claim, wherein said determining values ​​of a reduced set of adimensional parameters comprises determining (S4) a subset of adimensional parameters from said primary parameters, and determining (S5) a adimensional parameter dependent on a temperature rise from said subset and the correlation function, said adimensional parameter dependent on a temperature rise being included in the reduced set of adimensional parameters thus determined.

3. Method according to the preceding claim, wherein said correlation function is estimated (S3) by varying values ​​for the primary parameters of said set of primary parameters and simulating an associated temperature rise.

4. Method according to one of the preceding claims, wherein said at least one tool is at least one laser and said primary parameters comprise an irradiance of said at least one laser and / or a cumulative exposure time and / or a lasing duration and / or a dense material depth and / or an equivalent depth and / or a conductivity

5. thermal and / or thermal diffusivity. Method according to the preceding claim, in which said dimensionless parameters, jti, ir2> ir3 are 3 in number, and are expressed: [Math.30] • — 2 M Æ2“ 2 7?' ★cumul ■ 3 t lsam with TiD = 1 ATy being said value representing a temperature at a point of said set, Iabs being said irradiance, 5 being a characteristic diffusion length depending on said thermal diffusivity, k being said thermal conductivity, b' being said equivalent depth, f^pa being said cumulative exposure time, and ^scan being said laser duration.

6.

7. The method of claim 4 or 5, wherein said primary parameters further comprise a lasing speed and a characteristic radius of said tool. Method according to one of claims 1 to 4, in which said dimensionless parameters, jri, ir2> ir3, ir4j ir5 are 5 in number, and are expressed: [Math.31] 2 af^ ^'Tw _ _ 1 5 ^2 2'b' tewmd — .......... 714“ g ^3 = T withy^ = IabK,5 f A T'm being said value representing a tem temperature at a point of said set, Iabs being said irradiance, 5 being a characteristic diffusion length depending on said thermal diffusivity, k being said thermal conductivity, b' being said equivalent depth, t^o being said cumulative exposure time, tsam being said lasing duration, RL being said characteristic radius and VL being said lasing speed.

8.

9.

10. Method for producing a part by additive manufacturing using a machine (200) for additive manufacturing, comprising steps of - determination of a heat map by the method according to one of the preceding claims, - determination of at least one risk zone within said heat map, - adaptation of at least one parameter of said machine (200) as a function of said at least one risk zone, said at least one parameter being able to be a parameter of said trajectory. Computer program comprising instructions for implementing a method according to one of the preceding claims. System comprising a machine (200) for production by additive manufacturing using at least one tool, adapted to produce a part from a trajectory of said tool, and comprising an optimization device configured for, for a set of points of said trajectory, the implementation of steps of: determining values ​​of a set of primary parameters relating to said production by additive manufacturing; determining values ​​of a reduced set of adimensional parameters, as a function of the values ​​of said set of primary parameters and of a correlation function linking said adimensional parameters; generating a thermal map for at least one layer of said part, as a function of said dimensionless parameters, said thermal map being recorded in digital format and associating a value representative of a temperature with said points.