Thermal analysis of additive manufactured parts by studying tool paths

Abstract

The invention relates to a method for determining the thermal behavior of a part for additive manufacturing production by means of at least one tool, comprising: for a set of points of the path of the tool to be used for said production: determining (S1) values of a set of main parameters relating to said additive manufacturing production; determining (S4, S5) values of a reduced set of dimensionless parameters from values of a set of main parameters and a correlation function linking the dimensionless parameters; generating (S6) a heat map of at least one layer of the component from the dimensionless parameters; determining at least one risk area in the heat map; and adjusting at least one parameter of the tool (200) according to at least one risk area, the at least one parameter optionally being a parameter of the path.

Description

TECHNICAL FIELD

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

[0002] Additive Manufacturing (AM) or 3D printing is a family of processes that produce parts by successive addition of material layers.

[0003] The produced parts can have different properties, different sizes and different complexities. Certain parts must also meet strict specifications and can require certification. By way of example, in the aeronautical field, additive manufacturing can involve high-pressure distributors or low-pressure distributors for turbomachines, turbomachine fairing blades, injectors, casings, heat exchangers, hydraulic blocks, etc.

[0004] In general, any additive manufacturing process that can consider the melting or consolidation of a material (metal, polymer, ceramic, etc.) by successive or simultaneous application of one or more heat sources provided by a tool along a given path can be considered. These tools can in particular be lasers.

[0005] Currently available processes include: - 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 laser powder bed fusion processes (SLM, LBM, LPBF, DMLS, etc.), parts are manufactured by laser fusion and solidification of a succession of powder layers.

[0007] For each layer, a doctor blade spreads a bed of metal powder of fixed thickness. Then, a laser whose movement is controlled melts only the surface corresponding to the cross section of the part to be built, scanning this surface along a path set by the operator (see below). This part of the operation is often referred to as "lasing". The molten powder resolidifies after the passage of the laser, thus creating a solid surface. The platform is then lowered by the thickness of the new powder layer to 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 (called "laser bead") when the laser passes.

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

[0009] The state of the material is strongly influenced by the thermal cycles imposed by the passage of the laser beam and the successive cooling. These thermal cycles therefore induce various defects in the material and in the manufactured part: porosity, cracks, non-planar surfaces, etc.

[0010] It has been proposed to determine the thermal behavior of a part during its manufacturing, in particular upstream of its manufacturing.

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

[0012] There is therefore a digital tool that makes it possible to finely simulate the thermal history of the process on the scale of a few beads, even on the scale of a layer, with a relatively high associated calculation time (from a few hours to several tens of hours per layer and per part). There are also tools that make it possible to estimate the macroscopic temperature field during the manufacturing in a few hours, but with simplified assumptions (such as a uniform heat source on the scale of a layer) that do not take into account the local effects that one wishes to analyze, and therefore do not allow to predict the anomalies of the product during the manufacturing with sufficient precision and fineness.

[0013] For example, mention can be made of patent application EP3318352, which describes a method of detecting areas of a thermal critical part.

[0014] This has the drawback of relying on the geometric description of the part to be manufactured. When the part is large and complex, the descriptive data become very cumbersome to manage and generate a calculation time that is not compatible with industrial constraints. In addition, relying on the geometric description of the part necessarily means that the simulation is valid only for this part, and therefore does not take into account several laser paths properly when several parts are manufactured simultaneously.

[0015] Furthermore, energy supply strategies (laser paths, the possible presence of several lasers, etc.) are not considered. Therefore, thermal modeling is very macroscopic and does not allow for accurate and efficient prediction of anomalies related to the thermal behavior of components within a limited modeling time that enables reductions in modeling and manufacturing cycle times.

[0016] Therefore, the current proposals require improvements to existing technologies. Summary of the Invention

[0017] For these purposes, according to a first aspect, the invention can be achieved by a method for determining the thermal behavior of a component for additive manufacturing using at least one tool, the method comprising, for a set of points on the path of the tool to be used in the production, the processing unit of an optimization device performing the following steps: - Determine the values ​​of a set of key parameters related to the additive manufacturing process; - Determine the value of the reduced set of dimensionless parameters based on the values ​​of the set of main parameters and the related functions linking the dimensionless parameters; - Generate a thermal map of at least one layer of the component based on the dimensionless parameters, the thermal map being recorded in a digital format and associated with values ​​representing temperature at the points; - Identify at least one risk zone within the heatmap; - Adjust at least one parameter of the tool (200) according to the at least one risk zone, wherein the at least one parameter is optionally a parameter of the path.

[0018] The invention presented here does not require the use of the geometric model of the part being analyzed (“heavy” data), but only the file describing the path taken by the tool during manufacturing (“light” data).

[0019] Therefore, this computational method faithfully integrates the manufacturing sequence of the produced parts without simplifying the energy deposition pattern (in other words, it considers the precise production pattern of the parts) and allows for thermal analysis within computation time compatible with industrial constraints. For example, thermal map calculations representing hot spots can be obtained in approximately 1 second per powder layer (for laser powder bed fusion processes).

[0020] Therefore, the proposed method makes it possible to generate thermal maps and thus perform diagnostics at the scale of the entire platform, and to improve or even optimize production via additive manufacturing by adjusting at least one parameter of the tool at the same scale. Thus, this method allows for a considerably larger scale of scaling compared to existing solutions (e.g., which typically only handle weld beads).

[0021] Finally, the calculation method can be described as universal, meaning it adapts to the specific conditions of the analyzed component in a self-compatible manner.

[0022] According to a preferred embodiment, the present invention includes one or more of the following features, which may be used alone, in partial or complete combination with each other: - The heatmap is generated based on the values ​​of a set of principal parameters and a reduced set of dimensionless parameters determined by modeling based on a set of representative basic volumes.

[0023] - The determination of the reduced set of dimensionless parameters includes determining a subset of dimensionless parameters based on the principal parameters, and determining a dimensionless parameter that depends on temperature rise based on the subset and the correlation function, and including the dimensionless parameter that depends on temperature rise in the determined reduced set of dimensionless parameters.

[0024] The correlation function is estimated by changing the values ​​of the main parameters in a set of main parameters and simulating the associated temperature rise.

[0025] The simulations are performed at a scale of a representative basic volume associated with each simulation point.

[0026] - The key parameters may specifically relate to the path provided for production, and / or the materials used in the production, and / or the at least one tool.

[0027] - The at least one tool is at least one laser, and the key parameters include the irradiance and / or cumulative exposure time and / or laser action time of the at least one laser and / or the depth of the dense material and / or the equivalent depth and / or the thermal conductivity and / or the thermal diffusivity.

[0028] - There are 3 of the aforementioned dimensionless parameters , , And the dimensionless parameter , , It is represented as: , in , It represents the temperature value at a point in the set, I abs It is the irradiance mentioned above. It depends on the characteristic diffusion length of the thermal diffusivity, k is the thermal conductivity, and b′ is the equivalent depth. It is the cumulative exposure time, and tscan It is the laser action time.

[0029] The key parameters also include the laser action speed and the feature radius of the tool.

[0030] - There are 5 of the aforementioned dimensionless parameters , , , , And the dimensionless parameter , , , , It is represented as:

[0031] in, , The value I represents the temperature at a point in the set. abs It is the irradiance mentioned above. It depends on the characteristic diffusion length of the thermal diffusivity, k is the thermal conductivity, and b′ is the equivalent depth. This refers to the cumulative exposure time. t scan R is the laser action time. L It is the characteristic radius, V L It is the speed at which the laser interacts.

[0032] - The adjustment is performed individually for at least one segment of the path.

[0033] - The adjustment includes adjusting one or more of the following parameters: the power of the laser of the tool, the laser speed, the pause time between two segments of the path, the order of multiple segments of the path, the length of the multiple segments, the arrangement of the path, and the geometry of the component.

[0034] The adjustments include modifications to the data structure representing the path, which is to be provided to the tool.

[0035] According to another aspect, the present invention relates to a computer program comprising instructions for implementing the method described above.

[0036] According to another aspect, the present invention relates to a system comprising a machine for producing by additive manufacturing using at least one tool, the machine being adapted to produce parts according to the path of the tool, and the system comprising an optimization device configured to perform the following steps: Determine the values ​​of a set of key parameters related to the additive manufacturing process; The value of the reduced set of dimensionless parameters is determined based on the values ​​of the set of main parameters and the related functions linking the dimensionless parameters; A thermal map of at least one layer of the component is generated based on the dimensionless parameters, the thermal map being recorded in a digital format and associated with values ​​representing temperature at the points; Identify at least one risk zone within the heatmap; Adjust at least one parameter of the machine according to the at least one risk zone, wherein the at least one parameter may optionally be a parameter of the path.

[0037] According to one embodiment, the machine is adapted to produce components for use in high-pressure or low-pressure distributors, turbine rectifier blades, injectors, housings, heat exchangers, hydraulic blocks, etc. of turbines.

[0038] Other features and advantages of the invention will become apparent upon reading the following description of preferred embodiments of the invention, given by way of example and with reference to the accompanying drawings. Attached Figure Description

[0039] The accompanying drawings illustrate the present invention: Figure 1 A system according to an embodiment of the present invention is illustrated schematically, comprising a machine for production via additive manufacturing.

[0040] Figure 2 A flowchart illustrating the steps of a method according to an embodiment of the present invention is shown schematically.

[0041] Figure 3a and Figure 3b An example of a representative basic volume is shown.

[0042] Figure 4 It is a very schematic illustration of a heatmap.

[0043] Figure 5 An example of the relevant function is shown. Detailed Implementation

[0044] The proposed method is applicable to various printing or additive manufacturing (or 3D printing) technologies. Typically, additive manufacturing involves the travel of one or more tools along a predetermined path (which may be referred to as a "tool path") to provide a point heat source on the material.

[0045] This method is particularly suitable for laser powder bed fusion processes, and more specifically, but not exclusively, for laser powder bed fusion (LPBF).

[0046] This method allows for the selective melting of components based on continuously stacked powder beds. It can manufacture lighter, more complex components, such as thin structures (lattice-type), and is therefore suitable for the aerospace industry.

[0047] It should be noted that the metallurgical and mechanical condition (existing phases, residual stress, etc.), material health (porosity, cracking, etc.), surface condition, and thus the thermomechanical properties of the resulting parts are primarily determined by the thermal cycles applied during the additive manufacturing process.

[0048] Therefore, it is essential to understand the impact of heating / cooling cycles on the thermal behavior observed in components in order to optimize manufacturing parameters as necessary to eliminate or reduce harmful effects.

[0049] In certain cases of the LPBF process, thermal cycling is controlled by a vectorized (or laser) path applied to each layer. Depending on these laser application strategies and the local geometry of the components, hot spots may arise, which are related to excessive local heat dissipation capacity relative to the energy input. This is, for example, in regions with small cross-sections and / or in regions with undercut overhanging powder agglomerates, where the laser makes multiple round trips in a relatively short time period, and where the undercut overhanging powder agglomerates have a relatively low thermal diffusivity compared to the thermal diffusivity of the dense material.

[0050] These "hot topics" should be avoided because: - Heat buildup in localized areas can cause coalescence in the molten pool, forming protrusions during solidification. When this localized excess thickness exceeds the thickness of the powder layer, the scraping system may collide with the part being manufactured, potentially leading to deterioration of the manufactured geometry or even manufacturing shutdown. This results in molten material loss and extended industrial cycle times. - Hot spots can promote cracking (solidification cracking or macroscopic cracking). Overheated areas can promote the formation of unstable keyholes, which can create voids in the component when they collapse.

[0051] To predict the emergence of these hotspots, it is proposed to conduct numerical modeling and simulation before actual manufacturing.

[0052] In fact, by simulating the heat or energy input in parts produced through additive manufacturing and considering vectorized (or laser) patterns, we can assess in advance the evolution of the thermal field during manufacturing. Therefore, the emergence of overheated zones can be predicted and potentially triggered corrective measures.

[0053] Therefore, the proposed method aims to identify risk areas that may become “hot spots” caused by precise laser application strategies on the parts to be produced, with computation time compatible with industrial constraints (i.e., at most a few hours per production platform).

[0054] The proposed method is based on a laser strategy or pattern, rather than on the geometry of the part to be manufactured, as some existing proposals do. This makes it possible to significantly reduce the required computation time while maintaining high accuracy in estimating the risk zone, and it also allows consideration of the entire production platform, which can comprise several parts, whereas previous proposals opted for a part-by-part approach. It is worth noting that since the laser pattern is generic across the entire production platform, the product-by-product approach inevitably introduces bias into the estimation.

[0055] Figure 1 The environment in which the proposed method is used is illustrated schematically.

[0056] A machine or printer 200 used for additive manufacturing consumes material 210 to produce one or more parts 220. The machine is parameterized by a set of parameters that specify its operation and can be modified during manufacturing: laser travel speed, laser power, etc.

[0057] In the aerospace field, machine 200 can be used to produce various components, such as high-pressure or low-pressure distributors for turbines, turbine rectifier blades, injectors, casings, heat exchangers, hydraulic blocks, etc.

[0058] An optimization apparatus 100 is also provided, which is adapted to simulate the thermal behavior of part 220 with regard to the production of part 220 by additive manufacturing using machine 200. The simulation is performed upstream of the production of the additive manufacturing machine and is designed to identify risk areas where hot spots are particularly likely to occur.

[0059] These risk areas can be indicated to the user. For example, a heat map can be displayed on the screen, potentially focusing on the risk areas.

[0060] Based on the risk zones identified in the thermal behavior of the part 220 to be produced, the user can intervene in the machine parameters to avoid or reduce the occurrence of these risk zones, or prevent these risk zones from actually becoming hot spots.

[0061] According to a specific embodiment, the simulation apparatus can be adapted to directly determine adjustments to the set of machine parameters in order to optimize the additive manufacturing process, thereby avoiding or minimizing the occurrence of hot spots. In particular, the heating and cooling cycles during additive manufacturing can thus be optimized using the results of the simulation phase.

[0062] The data structure describing the laser path or pattern can be modified before being transferred to the additive manufacturing tool. In particular, parameters associated with one or more segments constituting the path can be adjusted to reduce or eliminate the effects of hot spots detected by previous steps of the method.

[0063] Figure 2 A flowchart of the proposed method is shown schematically.

[0064] In step S1, values ​​of a set of key parameters are determined, relating to the path of one or more tools used to produce one or more parts, the material used for that production, and the one or more tools. In the case that the one or more tools are lasers, the one or more paths represent a laser pattern.

[0065] According to the proposed method, the principal parameters are chosen because they are identified as having a first-order effect on thermal behavior at a local scale.

[0066] These parameters are of different types. These parameters can relate to one or more lasers used and / or the materials used (especially these thermophysical properties) and / or the laser pattern.

[0067] Individually, these key parameters may not be sufficient to explain the thermal behavior of the parts to be manufactured, especially the possible occurrence of hot spots.

[0068] However, by combining these parameters through dimensional analysis to form a simplified set of dimensionless and independent parameters with physical meaning, it is possible to better describe the thermal behavior of the part at the scale of the laser pattern during its manufacturing.

[0069] At least one of these dimensionless parameters must be related to the temperature measured locally (along the path of the tool being analyzed, such as the path of the laser action being analyzed), while the other parameters characterize various factors that may contribute to local overheating (undercut area, relatively large vector concentration in the area, etc.).

[0070] Therefore, the dimensionless nature of these parameters makes it possible to infer from quantities that are specific to the vectorization being 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.

[0071] The determination of key parameters is based on the additive manufacturing process and the modeling of the associated laser pattern.

[0072] This modeling is performed at a mesoscopic scale. This mesoscopic scale lies between the macroscopic and microscopic scales; it is large enough to include a large number of particles (so that their statistical properties do not fluctuate significantly), while remaining fine enough to keep thermodynamic quantities (pressure, temperature, etc.) local (points on the macroscopic scale).

[0073] In particular, the mesoscopic scale can be defined by the effect of the laser on a point in the laser pattern and on points near that point, on the laser pattern, upstream or downstream.

[0074] Modeling can be based on a representative elementary volume (REV) associated with the point under consideration. Therefore, according to this embodiment, the values ​​of the set of principal parameters are determined from the modeling based on a set of representative elementary volumes.

[0075] Figure 3a and Figure 3b An example of a representative basic volume REV for a point M located on a laser pattern is shown.

[0076] The volume is characterized by a surface centered at the point M under consideration, the dimensions of which (in...) Figure 3a In the example, it is the diameter, in Figure 3b In the example, edge a).

[0077] The feature size (diameter, side, etc.) has a magnitude equivalent to several vector deviations (i.e., the distance between two consecutive vectors), for example, between 5 and 10 vector deviations, and the feature size includes the portion of the vector that has a thermal effect on point M. Therefore, the feature size can depend on different parameters related to the laser (power, etc.) and the material (thermal conductivity, etc.).

[0078] Figure 3a This shows all or part of the component 220 to be manufactured. The upper surface of the component is filled; these fill lines schematically represent the laser pattern.

[0079] The laser pattern can be viewed as a set of lines corresponding to the path of a laser beam (or other heat source) on the surface of a layer of the manufactured component.

[0080] The laser pattern or strategy primarily specifies the trajectory of the laser path and the bead spacing, which is the distance between two adjacent (and usually parallel) lines of the laser pattern. In the diagram, the lines are parallel, and the bead spacing corresponds to the distance between two lines of the hash marker.

[0081] The laser pattern consists of a set of segments; each segment can be represented by a set of parameters: starting coordinates, ending coordinates, laser speed, laser power, etc.

[0082] The laser pattern can be provided in a data structure that can be a table, in which each row corresponds to a segment, and columns correspond to different parameters associated with the segment (coordinates, laser speed, laser power, laser beam diameter, irradiance distribution, etc.).

[0083] Data structures can be provided by computer files. These files can be in various formats: TXT, G-code, CLI, CLI+, HDFS, OVF, etc.

[0084] Figure 3aAlso shown is a representative basic volume REV in hemispherical shape, which corresponds to region 221 of component 220 and is centered on point M belonging to the laser pattern.

[0085] This representative basic volume contains several vectors of the laser pattern. Here, the term "vector" refers to any straight line segment that discretizes the path of the laser on the surface. Therefore, the laser pattern is often also referred to as a "vectorization scheme." Curves used for laser action can be defined during the design phase, but these curves are typically discretized into a set of straight line segments or vectors.

[0086] The intersection of the laser pattern with the upper surface of the representative basic volume forms a set of segments between the entry and exit points (the laser pattern is oriented in the direction of the laser path).

[0087] therefore, Figure 3a The directional segments [1; 2], [3; 4], [5; 6], [7; 8], and [9; 10] are shown. According to the definition of representative basic volume, the passage of laser light through these different segments affects the thermal behavior of the material at point M (located in the middle of segment [5; 6]).

[0088] The representative basic volume can have different shapes: cube, hemisphere, semi-ellipsoid, etc., depending on its relevance to the thermal problem to be solved and the practical constraints that such a choice imposes on the implementation of the proposed method.

[0089] Figure 3b This illustrates another form of representative basic volume. Its cubic shape can be characterized by the characteristic edge a.

[0090] The aim of this method is to determine data representing the thermal behavior of the part to be produced. For example, this representative data could be a heat map of each layer of the part to be produced. This heat map can correlate values ​​of heat (or temperature) with each point M to which the quantity is to be evaluated. Based on the proposed modeling, it is assumed that the quantity depends on effective principal parameters (and is assumed to be constant) over a representative basic volume centered at the point M under consideration.

[0091] It is proposed to select a set of key parameters that allow for modeling to be as simple as possible while ensuring that the determined heatmaps (or more generally, data representing the thermal behavior of components) have good accuracy.

[0092] In other words, a set of key parameters can be selected so as not to exclude any important factors that may affect the thermal behavior of the material and the part to be produced.

[0093] Typically, these key parameters associated with additive manufacturing involve the predicted path of the tooling used in the production, the material, and the tooling used as a point heat source.

[0094] Therefore, in the case of lasers, this set of key parameters includes relative parameters: - A laser pattern planned for use in the production of one or more components; - Materials used in this production; - One or more lasers (e.g., power, speed, spot diameter, etc.).

[0095] Therefore, it should be noted that the key parameters are independent of the geometry of the part to be manufactured.

[0096] In practice, it has been observed that the geometry of the part to be produced can be extracted from the laser pattern (or more generally from the path of the tool used).

[0097] In practice, analyzing segments in a neighborhood makes it possible to have sufficient knowledge of the geometry of a part in that neighborhood, since segments only exist on parts of the part. The absence of segments in a region implicitly indicates that the region does not belong to the part to be manufactured.

[0098] This has the advantage of not having to consider documents describing the geometry of the part to be manufactured, which are often quite cumbersome; instead, only documents describing the laser's action need to be considered. These documents are much smaller and more structurally easier to manage, which can significantly improve performance.

[0099] The proposed method includes the previous step of determining a reduced set of dimensionless parameters from these principal parameters in step S2.

[0100] According to one embodiment, the values ​​of this reduced set of dimensionless parameters are determined based on modeling based on a set of representative basic volumes, the main parameters of which have previously been determined based on that set of representative basic volumes.

[0101] We also expect the number of dimensionless parameters to be minimized. In fact, the fewer the parameters, the simpler the problem and the easier it is to construct the graph, as shown below. Furthermore, according to the Vaschy-Buckingam theorem, the number of principal parameters must also be minimized.

[0102] A laser with incident irradiance I0 travels at a speed V L Travel across the upper surface of the representative basic volume. We can write: .

[0103] Where P is the laser power, R L 1 / e of the laser beam radius 2The constant “e” here represents e = exp(1). In this embodiment, we assume the laser is Gaussian, meaning the spatial distribution of irradiance follows a two-dimensional Gaussian curve centered at the impact point. 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 decreases to 13.5% (1 / e) of the maximum irradiance measured at the center of the spot. 2 =0.135).

[0104] Obviously, other types of spatial distribution of irradiance from a laser or more generally geothermal source around the point of impact can be envisioned, and this spatial distribution can be characterized by the radius characteristics of the focal spot or any other quantity or set of quantities.

[0105] The cumulative duration of laser exposure can be defined. The sum of the lengths of the vector portions contained in the representative basic volume, divided by the laser velocity. If the representative basic volume contains n vectors, and these vectors are parallel to one of its edges, then we can write: .

[0106] However, the continuous passage of the laser through the representative fundamental volume extends over time, and its duration corresponds to the instant t when the laser leaves the last vector in REV. out and the instant t when the laser reaches the first vector in REV in The difference between them.

[0107] exist Figure 3b In the example, instantaneous t in Corresponding to the instant when the laser arrives at point 1, and the instant t out This corresponds to the instant the laser leaves point 10. The laser's interaction time t, corresponding to the difference between these two instants, can be defined. scan : .

[0108] Each individual laser channel is actually separated from other laser channels by the laser action time outside the considered representative basic volume plus the jump time between two vectors (i.e., the travel time of the laser from the end of one vector to the beginning of the next). Therefore, and t scan Subject to the following inequalities: .

[0109] Furthermore, the representative basic volume includes a certain amount of dense material 223 for heat dissipation. Potentially, it also contains a complementary amount of powder 222 (not exposed to the laser), which acts as a thermal insulator. By further simplifying the problem, considering a unidirectional REV, b represents the depth of the dense material 223 located below the laser-treated surface. We can write: .

[0110] However, in the real part, the dense material portion in the REV is generally not unidirectional, especially in the draft and undercut regions. We can then consider the thickness b' of the thermally equivalent unidirectional element: .

[0111] V represents the volume of the dense material 223 contained in REV, and S represents the reference feature surface (e.g., the irradiated upper surface, the sum of surfaces in contact with the dense material, etc.). Furthermore, the dense material has an assumed constant thermal conductivity k and thermal diffusivity. Powder 222 is assumed to be a perfect insulator (insulating condition).

[0112] Finally, we can evaluate the results with respect to the variables. Considering the temperature rise at point M corresponding to REV: .

[0113] It is the characteristic temperature at point M generated by the vectorized sequence. This can be the maximum or average temperature observed during the exposure sequence, or any other uniform parameter at a temperature that can characterize the localized heating of the component. T0 is the reference temperature of the representative basic volume REV or layer.

[0114] The quantity determined for all points M This allows for the determination of a thermal map of one or more parts to be produced. Therefore, the thermal map can be associated with a value representing temperature, such as a temperature rise, by linking each point M of the tool's (here, a laser) path.

[0115] According to one embodiment, the heatmap is therefore based on the values ​​(e.g., temperature elements) associated with each representative basic volume (each REV centered at a point M associated with the value reported in the heatmap). )generate.

[0116] Therefore, according to this embodiment, p=7 main parameters are selected, which are: - Laser irradiance, I0 (or absorbed irradiance I) abs =I0.A, where A is the absorbance of the material); - Cumulative exposure time

[0117] - Laser application time t scan ; - The depth of dense material b, or the equivalent depth b(′); - Thermal conductivity k; - Thermal diffusivity ; - From the deviation from the reference temperature or the temperature rise .

[0118] As mentioned earlier, these parameters relate to the laser pattern ( , t scan b, b'), materials (k, (I0) and laser (I2). The main parameters are related to temperature rise, and these are the data points we are trying to determine.

[0119] Suppose these parameters are linked together by the mathematical function g().

[0120] These seven parameters depend on four basic units (mass, length, time, and temperature).

[0121] According to Vaschy-Buckingham's theorem (or (Theorem) If a physical equation involves p physical variables that depend on the basic unit u, then there is an equivalent equation involving pu dimensionless variables constructed from the original variables.

[0122] Therefore, in this embodiment, there exists a mathematical function h() equivalent to function g(), which involves pu = 3 independent dimensionless numbers, and can be expressed as: , , We can write it as: .

[0123] Subsequently, this function will be called the correlation function because it makes the dimensionless parameter , , The changes are interconnected.

[0124] Traditionally, by utilizing the properties of these three numbers, we can define: .

[0125] We can define The characteristic diffusion length makes: .

[0126] Then we can write the definition of the dimensionless parameter: .

[0127] Notice, It depends on the intensity I of the one-dimensional heat flux absorbed. abs The temperature T calculated at the surface of the semi-infinite medium 1D At Carslaw HJ, Jaeger, JC, Conduction of heat in solids The temperature is specifically described in Oxford University Press, 1959. It can be defined by the following expression: .

[0128] Then the definition of the dimensionless parameter can be rewritten: .

[0129] Therefore, the three dimensionless parameters obtained after dimensional analysis can be described as follows: It is proportional to the increase in normalized temperature. This quantity is unknown beforehand: it is the quantity we want to calculate along the laser pattern in order to obtain a thermal map.

[0130] It is proportional to the normalized diffusion length. This figure characterizes the component's ability to dissipate heat locally. It is related to the characteristic diffusion length. In contrast, the smaller the depth or equivalent depth b' of the dense material b, the smaller the component's ability to dissipate heat locally (all other things being equal). As mentioned above, considering that only the dense region is traversed by the vector, this value can be calculated solely from the data structure describing the laser pattern (e.g., in a file).

[0131] It is proportional to the normalized exposure time. The cumulative duration of laser exposure. The closer to laser time t scan The faster the local heat accumulates (all other things being equal), the more rapid the accumulation of heat. Similarly, this number can only be calculated based on the data structure describing the laser pattern.

[0132] Using the above equation , It can be represented as and A function to calculate the characteristic temperature rise along the laser pattern. : .

[0133] This expression shows that as temperature rises... With temperature T 1D Proportional, T 1DNormalized diffusion length and normalized exposure time The function weighting.

[0134] In step S3, which can be performed separately from simulation methods S1-S4-S5-S6 (e.g., upstream), the correlation function h() for estimating the dimensionless parameters of the link is sought.

[0135] This step can be called the calibration step because it involves correlating the known values ​​of a subset of dimensionless parameters with a correlation function to obtain the values ​​of the unknown parameters (i.e., parameters that depend on temperature rise).

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

[0137] According to one embodiment, the simulation is performed at a scale of a representative basic volume associated with each simulation point.

[0138] For example, this estimation can be performed by simulating the vectorization and thermal behavior associated with the scale of the representative basic volume REV by varying different key parameters of the additive manufacturing process within a range of values ​​related to the machine's capacity or the window of the additive manufacturing process being implemented. Thus, a space of relevant values ​​can be described, and for each n-tuple in the parameter space, dimensionless parameters can be obtained by computation or simulation. , , .

[0139] The goal is to create a numerical experimental design that constructs a response surface with dimensionless parameters. , , Correlation becomes possible. When the function h() is difficult to determine, a database can be constructed containing dimensionless parameters. , , Create a table.

[0140] In other words, based on p-tuples of these dimensionless parameter values, general rules can be determined (e.g., through linear approximation, etc.), or a table constituting a graph whose p-1 entries allow the determination of the final value of the p-tuple.

[0141] The simulation can be performed using different methods available in the art, such as the finite difference method, the finite element method, the finite volume method, and the discontinuous Galerkin (DG) method.

[0142] Simulating vectorization at the scale of the representative basic volume REV, to make the dimensionless parameters correlate with each other, rather than doing so at the scale of the entire layer, greatly reduces computation time. Therefore, simulating at REV may take only a few minutes compared to several hours or even tens of hours for the entire layer.

[0143] Figure 5 The results of this simulation set are shown. Each point represents a simulation and has an application on the x-axis. The value of the relevant function has an additional dimensionless parameter on the y-axis. The value of .

[0144] It will be noted that these points are approximately aligned for all parameter configurations, and especially for different materials (because during the simulation, the material type changes, thus changing the parameters k and ...). This is especially true. This verifies the universality of the scaling law derived therefrom. Therefore, if the experiment is well-designed, the simulation can be performed only once and repeated for different simulations of the thermal behavior of parts produced by additive manufacturing.

[0145] Therefore, the computational aspects of the simulation shift to the construction of this chart. These can be performed before use and can be shared for multiple purposes. These calculations no longer adversely affect the process of determining the thermal behavior of the parts to be manufactured.

[0146] Therefore, due to the universality of its values, this chart can be built upstream and used to simulate a set of thermal behaviors of the parts to be produced.

[0147] After determining the values ​​of the main parameters in step S1, calculations independent of temperature rise can be performed in step S4. The value of the dimensionless parameter.

[0148] In the above embodiments, these parameters are parameters and .

[0149] This calculation can be performed on all or part of the layers of the component to be manufactured.

[0150] Each layer under consideration is subdivided into representative basic volumes (REV). The feature dimensions of these and the distance between two representative basic volumes depend on the spatial and temporal resolution required for the analysis.

[0151] Each representative basic volume contains a portion of the laser pattern, forming a segment between the entry and exit points in the REV (therefore, as a reminder, Figure 3a The directional segments [1; 2], [3; 4], [5; 6], [7; 8], [9; 10] are shown.

[0152] Dimensionless parameters independent of the temperature rise for each REV can be calculated from these segments without using a geometric model.

[0153] Dimensionless parameters The calculation is straightforward: it depends on the duration. and t scan The values ​​of these durations depend only on the layer being considered.

[0154] Dimensionless parameters The calculation depends on a set of layers: it is necessary to aggregate the information contained in the previous layers at depth a of REV, and in particular, to sum all the lengths of the vector portion that allows the calculation of the volume of dense material.

[0155] In step S5, the value of the dimensionless parameter that depends on the temperature rise can be calculated.

[0156] This parameter This actually depends on other dimensionless parameters and on the relevant function h() determined in step S3.

[0157] In step S6, the additional dimensionless parameter can be used to determine the temperature increase. Calculate temperature rise .

[0158] Therefore, the thermal rise of a set of points M for the laser pattern The determined set of values ​​can provide a heatmap.

[0159] Figure 4 This is a very schematic illustration of this type of heatmap.

[0160] The diagram illustrates a virtual component 220 to be produced. It is assumed that the laser action is horizontal. The different filling patterns in zones 225, 226, and 227 correspond to different temperature rise values. For clarity, only three values ​​are shown in the graph, but in practice, the graph can have continuous values ​​(each value corresponds to a gray level in the graphical representation) or more discrete values.

[0161] In zone 225 (shown by dashed lines), heating is minimal because the laser travels a long distance within the component (or typically multiple components) before returning to the vicinity of the same point. Therefore, heat has time to dissipate substantially between two laser passes in the same neighborhood (according to a predefined laser pattern).

[0162] In zone 227 (indicated by bold shading), heating is intense because the laser travels a very short round trip through a component of very small size in the direction of laser action. Between two laser passes, the heat does not have sufficient time to dissipate, causing the temperature to rise.

[0163] Zone 226 (represented by a finer fill spacing) corresponds to the case between zones 225 and 227, where the zone is oriented at 45° relative to the laser pattern, such that the laser travel time in this zone is longer than in zone 227, but not long enough to allow sufficient heat dissipation.

[0164] This thermal mapping can be used to identify risk areas, which are areas where hotspots may occur, potentially leading to protrusions, cracks, cavities (keyholes), or other anomalies on the surface of the part to be manufactured.

[0165] These risk zones can be identified in various ways and are directly derived from the determination of heat maps.

[0166] For example, a threshold can be established, and temperature differences exceeding that threshold indicate a risk zone.

[0167] The detection of one or more risk areas can trigger several actions of the simulation device 100 on its components.

[0168] For example, these actions may include one or more of the following: - To warn users by highlighting one or more risk areas on the graphical representation of the heatmap; - This warning warns users against triggering additive manufacturing as is; - Trigger optimization of the configuration parameters of the additive manufacturing machine 200 in order to avoid or reduce the occurrence of these risk areas.

[0169] Therefore, simulation devices can be adapted to directly determine adjustments in this set of machine parameters to optimize heating and cooling cycles. In particular, this can address the issue of homogenizing heat input across layers without unduly extending manufacturing time.

[0170] According to one embodiment, adjustments are performed individually for one or more segments of the laser pattern. Therefore, the pattern can be adjusted segment by segment. For example, a single segment can be adjusted (where only that segment corresponds to a risk area), or different parameters can be adjusted for several segments, and so on.

[0171] The adjustable parameters used for this optimization include: - Laser power. The laser pattern can be preserved, but the power can be reduced on one or more segments of the laser pattern corresponding to the risk area.

[0172] - Laser application speed. The laser pattern can be preserved, but the laser speed can be increased on one or more segments corresponding to the risk zone.

[0173] - Pause time between two segments. For example, the laser pattern can be preserved, but a pause time can be added between two consecutive segments in or around the risk area to allow the area to cool down.

[0174] - Segment order. The laser pattern can be preserved, but one or more segments can be skipped in the risk zone and then returned to later so that the zone cools simultaneously. This option has a smaller negative impact on manufacturing time compared to introducing pause time.

[0175] - Segment length. In the case of a laser-guided strategy, the strip width can be increased to extend the time between two laser passes within the same area. If one of two adjacent segments is too short, the two adjacent segments can also be joined.

[0176] - Laser pattern, that is, the arrangement of the path in the entire laser pattern.

[0177] - The geometry of the part to be produced.

[0178] Such parameter adjustments can, for example, involve modifying the data structure representing the laser pattern. Laser action parameters (laser power, laser velocity, laser beam diameter, irradiance distribution, etc.) can be modified directly segment by segment within this data structure; the segment order can be changed, new rows can be added to insert pauses between two segments, etc.

[0179] According to one embodiment, the algorithm proposes several scenarios. Each scenario has advantages and disadvantages, which engineers decide based on other constraints present in its specifications.

[0180] For example, the first scenario could be to adjust the power (only) based on the length of the vector, such that the temperature at every point on the surface is below a previously set threshold. This adjustment is calculated automatically using the method presented here.

[0181] In this situation, the minimum power proposed by the algorithm may be incompatible with the metallurgical specifications of the alloy being produced. In such cases, the engineer can set a minimum power, which forces the algorithm to adjust a second parameter (e.g., the pause time between the two vectors) to meet the set temperature threshold.

[0182] Therefore, the engineers chose a hybrid approach with two adjustment variables (laser power and inter-vector pause time).

[0183] Another approach could be to add a pause time between all vectors. However, this solution could cause manufacturing times to exceed specifications. In this case, engineers could choose an alternative where the pause time is applied only to the shortest vector (with an undefined threshold) and the laser power and / or speed is adjusted for the other vectors.

[0184] In short, the algorithm must propose several scenarios, which engineers can then decide by navigating the different constraints imposed upon them. Each constraint imposed by the engineer (minimum power, maximum speed, etc.) is considered by the algorithm in a self-consistent manner, thereby adjusting its scenario accordingly.

[0185] Once modified, the data structure representing the "new" laser pattern can be provided to the tool, enabling the production of parts through additive manufacturing.

[0186] It should be noted that the description just given pertains to one embodiment. Many variations may be proposed.

[0187] In particular, the proposed dimensionless parameter , , It is not the only one, and other dimensionless parameters can be proposed, especially based on the primary parameters chosen to simulate the thermal behavior of the part to be produced. In fact, if the primary parameters are changed, dimensional analysis will provide a different set of dimensionless parameters.

[0188] In the above embodiments, the absorption process of the incident energy provided by the laser is considered a surface phenomenon. Therefore, the absorbed irradiance I abs This is considered the primary parameter. This assumption is particularly valid for metallic alloys irradiated by a YAG laser in “conduction” mode. Alternatively, it can be assumed that the irradiated material absorbs the incident radiation in volume (this is, for example, the case of ceramics irradiated by a YAG laser, or, as a first approximation, the case of metals in keyhole mode).

[0189] In this case, the absorbed irradiance I abs (in W / m) 2 (This can be represented by a volumetric heat source Q) abs (in W / m) 3 (This is used to represent) Through dimensional analysis, we can calculate three dimensionless parameters. , , : .

[0190] Q abs This can be considered as absorbed irradiance I. abs and volume absorption coefficient The product of makes The absorption thickness is uniform. Then we can write: , or: .

[0191] According to one embodiment, the volume absorption coefficient These can be considered as the primary parameters. Therefore, dimensional analysis can provide four dimensionless parameters. , , , These dimensionless parameters can be expressed as: .

[0192] Furthermore, in the above embodiments, the heat source (laser) is composed of only irradiance (I abs ) or only heat source (Q) abs Modeling.

[0193] However, depending on the application, the laser application speed V may need to be considered. L and the characteristic radius R of the energy source L The effect: In fact, laser scanning on a given surface is not strictly equivalent to the equivalent irradiance statically applied to the same surface.

[0194] Then five dimensionless parameters can be determined. , , , , : .

[0195] Similarly, step S3, which determines the relevant function h(), can be performed in a different manner.

[0196] Instead of the above simulation, accurate analytical resolution can be achieved, especially for simple geometric and thermal configurations.

[0197] Therefore, we can write the energy conservation equation for the surface of each representative fundamental volume: , Indicates the time t of the laser. scan The norm of the equivalent uniform heat flux absorbed at surface S of REV during this period makes the energy It is absorbed by the representative basic volume.

[0198] We can then derive from this equation: .

[0199] By making From the power density, we obtain: .

[0200] We can then assume that the behavior of each representative basic volume is analogous to a one-dimensional medium with an equivalent depth b' having an adiabatic edge. The average temperature rise can be calculated using the following formula: .

[0201] We use ierfc() to denote the integral function of the complementary error function of the Gaussian error function erfc().

[0202] Other analytical solutions can be obtained by setting different boundary conditions (Dirichlet temperature conditions, convection and radiation losses, etc.).

[0203] Combining the two equations above, we can obtain .

[0204] Finally, by making We obtain: , or , in: .

[0205] Compared to estimating the h() function through simulation, the advantage of analytical solutions is that they save computational costs. However, such exact analytical solutions represent simplified geometric configurations, and their boundary conditions are not very representative of the boundary conditions of this method.

[0206] Another way to do this is to use experimental data obtained during the manufacture of technical calibration test pieces (or samples) or complete parts, rather than numerical data (e.g., infrared thermal imaging measurements or any other field thermal measurements).

[0207] Compared to complete parts, technical test pieces have the advantage that they are designed with geometric features that represent those found on industrial parts that are being manufactured, while being less complex and less expensive to manufacture.

[0208] Therefore, thermal measurements can be correlated with dimensionless parameters along the laser pattern to estimate the correlation function h().

[0209] The advantage of experimental data over numerical solutions lies in their reliability (within the inherent limitations of measuring instruments). However, numerical simulations save on the materials and operating time of additive manufacturing machines.

[0210] Of course, the present invention is not limited to the examples and embodiments described and illustrated, but is defined by the claims. In particular, the examples and embodiments described and illustrated are capable of many variations available to those skilled in the art.

Claims

1. A method of determining the thermal behavior of a part for additive manufacturing production using at least one tool, the method comprising, for a set of points of a path of the tool to be used for the production, implementing by a processing unit of an optimization device (100) the following steps: determining (SI) values of a set of primary parameters related to the additive manufacturing production; determining (S4, S5) values of a reduced set of dimensionless parameters from the values of the set of primary parameters and a correlation function linking the dimensionless parameters; generating (S6) a thermal map of at least one layer of the part from the dimensionless parameters, the thermal map being recorded in a digital format and associating values representative of temperature to the points; determining at least one risk zone within the thermal map; adjusting at least one parameter of the tool (200), optionally a parameter of the path, from the at least one risk zone.

2. The method according to the preceding claim, wherein the determining values of a reduced set of dimensionless parameters comprises determining (S4) a subset of dimensionless parameters from the primary parameters and determining (S5) a dimensionless parameter depending on temperature rise from the subset and the correlation function, the dimensionless parameter depending on temperature rise being included in the determined reduced set of dimensionless parameters.

3. The method according to the preceding claim, wherein, The correlation function is estimated (S3) by varying the values of a primary parameter of the set of primary parameters and simulating an associated temperature rise.

4. The method according to any of the preceding claims, wherein, The at least one tool is at least one laser and the primary parameters include irradiance and / or cumulative exposure time and / or laser-on time and / or depth of dense material and / or equivalent depth and / or thermal conductivity and / or thermal diffusivity of the at least one laser.

5. The method according to the preceding claim, wherein, There are three said dimensionless parameters , , , and said dimensionless parameters , , are expressed as: wherein , is a value representative of the temperature at the point of the set, I abs is the irradiance, is a characteristic diffusion length depending on the thermal diffusivity, k is the thermal conductivity, b' is the equivalent depth, is the cumulative exposure time, and t scan is the laser action time.

6. The method of claim 4 or 5, wherein, The primary parameters further include laser-on speed and characteristic radius of the tool.

7. The method of any one of claims 1 to 4, wherein, There are five said dimensionless parameters , , , , , and said dimensionless parameters , , , , are expressed as: wherein, , is the value representative of the temperature at the point in the set, I abs is the irradiance, is a characteristic diffusion length dependent on the thermal diffusivity, k is the thermal conductivity, b' is the equivalent depth, is the cumulative exposure time, t scan is the laser action time, R L is the characteristic radius, V L is the laser action speed.

8. The method of any of the preceding claims, wherein, The determining of values of a set of primary parameters and values of a set of reduced dimensionless parameters is made according to a modeling based on a set of representative elementary volumes, the thermal map being generated from values associated with each representative elementary volume.

9. The method of any of the preceding claims, wherein, The simulation is performed on the scale of a representative elementary volume associated with each simulated point.

10. The method of any of the preceding claims, wherein, The adjustment is performed separately for at least one segment of the path.

11. The method according to the preceding claim, wherein, The adjustment includes an adjustment of one or more of the following parameters: power of a laser of the tool, laser-on speed, pause time between two segments of the path, order of segments of the path, length of segments of the path, arrangement of the path and geometry of the part.

12. The method of any of the preceding claims, wherein, The adjustment includes a modification of a data structure representing the path, the data structure to be provided to the tool.

13. A computer program comprising instructions for executing the method according to any one of the preceding claims.

14. A system comprising a machine (200) for additive manufacturing production using at least one tool, the machine being adapted to produce a part from a path of the tool, and the system comprising an optimization device configured to implement, for a set of points of the path, the following steps: determining values of a set of primary parameters related to the additive manufacturing production; determining values of a reduced set of dimensionless parameters from the values of the set of primary parameters and a correlation function linking the dimensionless parameters; generating a thermal map of at least one layer of the component from the dimensionless parameters, the thermal map being recorded in digital format and associating values representative of temperature with the points; determining at least one risk zone within the thermal map; adjusting at least one parameter of the machine (200), optionally a parameter of the path, from the at least one risk zone.

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