EP3417386A1 - Method, computer-readable data carrier, computer program, and simulator for determining stresses and shape deviations in an additively produced construction - Google Patents

Abstract

The invention relates to a method for determining production-related shape deviations (εl,i) and stresses in a construction (11) produced by means of an additive production method, which construction is produced by solidifying construction material in successive layers (12). The invention further relates to a use of said method to produce corrected production data (19) and to the application of said production data in an additive production system. The invention further relates to a computer-readable data carrier and to a computer program for performing said method and to a simulation in which such a computer program can run. In the method, superlayers (13) are used in order to reduce the computational complexity of the simulation. According to the invention, in order to ensure a simulation result of sufficient accuracy with justifiable computational complexity, effective shrinkage factors (αi or αl,i) are determined for the solidified construction material in order to calculate the effective thermal shrinkage (εl or εl,i) in each superlayer (13).

Description

description

METHOD, COMPUTER-READABLE DATA CARRIER, COMPUTER PROGRAM AND SIMULATOR FOR DETERMINING VOLTAGES AND FORM DEVIATIONS IN AN ADDITIVELY PRODUCED BUILDING STRUCTURE

The invention relates to a method for determining production-related shape deviations and stresses in a construction structure produced using an additive manufacturing method. This is to be produced by melting of building material in successive layers. Here, a processor uses data describing the geometry of the building structure to create a mesh of finite elements. The processor arranges the finite elements in such a way that they are each completely in superpositions, the superpositions each consisting of several layers of the building structure to be produced. For each super layer, the cooling behavior is determined by the processor. From the cooling behavior, the processor calculates the stresses and form deviations in the building structure resulting from thermal shrinkage using a finite element method (abbreviated to FEM below).

The method is suitable for calculating building structures produced by additive manufacturing processes that are obtained layer by layer by melting or sintering (generally solidifying). In this context, for example, laser melting, laser sintering, electron beam melting and laser deposition welding are mentioned. With these methods, a building structure can be produced for example in a powder bed or by direct application of powder material to the building structure under construction. The building structure comprises both the desired component and possibly auxiliary structures necessary for the production, such as support structures which engage the component and are removed after production. Also, the building structure may consist of several components which are manufactured in parallel on a building platform. To be able to produce the component, data describing the component (CAD model) are prepared for the selected additive manufacturing process. The data is converted into data of the component adapted to the production process for the production of instructions for the production plant, so that the suitable process steps for the successive production of the component can take place in the production plant. The data are processed in such a way that the geometric data are available for the respective layers (slices) of the component to be produced, which is also referred to as slicing.

Examples of additive manufacturing include selective laser sintering (also known as SLS for selective laser sintering), selective laser melting (also SLM for Slective Laser

Melting), the electron beam melting (also EBM for

Electrone Beam Melting), which are called laser powder deposition welding (also called LMD for Laser Metal Deposition). These methods are particularly suitable for the processing of metallic materials in the form of powders, with which

Construction components can be produced.

With the SLM, SLS and EBM, the components are produced in layers in a powder bed. These processes are therefore also referred to as powder bed-based additive manufacturing processes. In each case, a layer of the powder is produced in the powder bed, which is then locally melted or sintered by the energy source (laser or electron beam) in those areas in which the component is to be formed. Thus, the component is successively produced in layers and can be removed after completion of the powder bed.

With the LMD, the powder particles are fed directly to the surface on which a material application is to take place. With the LMD, the powder particles are melted by a laser directly in the point of impact on the surface and thereby form a layer of the component to be produced. SLS is also characterized in that the powder particles are not completely melted in these processes. With the SLS, care is taken when selecting the sintering temperature that this is below the melting temperature of the powder particles. In contrast, the SLM, EBM and LMD amount of the energy input deliberately so high that the powder particles are completely melted.

The aforementioned additive manufacturing processes are primarily intended for the processing of metals and metal alloys. This is carried out by fusion metallography, which means that a relatively small volume is melted by an energy beam, while the rest of the building structure under construction remains cold compared. After melting, a rapid cooling takes place, wherein the material solidifies again. Due to the associated thermal shrinkage strong local strain of the solidified material takes place, this process occurs repeatedly throughout the building structure. This creates stress and strain distributions in the building structure, which are difficult to predict due to their complexity. However, the stress and strain distribution in a manufactured building structure can disturb the dimensional stability and mechanical strength of the building structure so much that it must be discarded as broke. Possibly, several iterative modifications, in particular of a geometry describing the structure of the structure, and a repeated execution of the additive process are necessary in order to counteract a distortion of the building structure.

In this respect, there is a desire to simulate the component behavior during the additive manufacturing process in order to be able to predict stresses and strains in the building structure and to consider them already in the generation of the data sets describing the building structure. As described by B. Schoinochoritis et al. , "Simulation of metallic powder bed additive manufacturing processes with the finite element method: A critical review", Proc IMichE part B, J. Engineering Manufacture 1-22, 2015, there are already several different ones

Given approaches. However, these have in common that the main problem is that an FEM would have to process such a large amount of data that the necessary computation times would not be economically justifiable. Therefore, simplifying assumptions must be made in the FEM calculations, which, however, degrade the accuracy of the calculated results. An approach according to the method of the type specified, N. Keller et al. in "New method for fast predictions of residual stress and distortion of AM parts", Solid Freefrom Fabrication, 2014, pp. 1229-1237 In order to shorten the computation times, the idea is that instead of the individual layers to be produced, the As a result, fewer process steps can be calculated, whereby the complexity of the simulation is reduced The coefficient of expansion, which reflects the behavior of a specific material, is accepted, and the simplification of the simulation is increased in the interest of shorter calculation times.

The invention further relates to the use of the above-described method for generating corrected data describing the geometry of the building structure, the data being corrected such that any strains that occur are compensated by a geometry deviating from the desired geometry of the building structure in the data describing the geometry. In addition, the invention relates to a use of the method explained above to produce a building structure with the corrected data additively. Finally, the invention relates to a computer-readable data carrier, a computer program and a simulator for determining production-related form deviations and stresses in the building structure to be produced additively, the computer program, which may also be stored on the computer-readable data carrier, performing the above-mentioned method. In the simulator, for example, a computer, a processor may be programmed so that the above-mentioned method can be performed.

The object of the invention is to improve a method of the type specified at the beginning in such a way that it is connected with the least possible amount of computation during execution of the method, whereby the method can be used to calculate a calculation result for the stresses and shape deviations occurring in the building structure, which corresponds as closely as possible to the stresses and form deviations actually occurring during the implementation of the additive manufacturing process. It is another object of the invention to make this method accessible by uses in a method for generating corrected data describing the geometry of the building structure or a method for the additive production of the building structure with the above-mentioned properties. Finally, it is an object of the invention to provide a computer-readable data carrier, a computer program or a simulator for determining the production-related shape deviations and stresses in the building structure, in which said method is implemented.

According to the invention, the solution of the problem with the method specified at the outset succeeds in that the processor determines stresses and deviations in the structural structure caused by solidification by taking into account the superpositions in the order in which they are produced. This means that the

Tensions and shape deviations can be taken into account in each case already produced super layers in the superposition in production. The processor determines from the cooling behavior of the respective superposition (ie, the superposition currently being produced in the simulation, which is always referred to below as the superposition in question), has an average temperature ΤΊ of the superposition in question. In addition, the processor calculates the thermal shrinkage in the relevant superposition by the processor takes into account an effective shrinkage factor a ± or ι, ι for solidified building material. From this, the processor calculates a relative thermal shrinkage ει or ει, ± in the respective superposition taking into account the

Melting temperature Τ _{Ξ of} the building material and without consideration of other super layers using one of the following formulas (depending on a ± or ι, ι available). ει = o (i (T _B - Ti) or ει, ± i = _fi (T _B - Ti)

Finally, according to the invention, the processor calculates the resulting stresses and shape deviations in the relevant superposition, by the processor taking into account the stresses and shape deviations of already produced superpositions. These have an effect on the stresses and deviations in shape of the layer in question, since, due to the mechanical coupling, a transfer of stresses and resulting form deviations between the superpositions has to be taken into account in order to ensure a realistic simulation. According to the invention, the production process must be taken into account in such a way that already produced super layers influence the super layer in question and the super layer in question influences future superpositions to be produced in the future. In this way, the consideration of the superpositions succeeds in the order of their creation. In other words, the real manufacturing process is simulated by the simulation and the computational effort is reduced by the fact that instead of the real layers of production, the much thicker super layers are based on the FEM calculations.

From the result of the described method can be advantageously derived how the component is expected deform after its manufacture. If these deformations and stress states lie outside a tolerable range, a modification of the data describing the geometry of the structural structure can be made and the calculation can be carried out again according to the method described. This creates an iterative process for optimizing the geometry of the building structure to be produced in such a way that stresses and shape deviations are compensated. This advantageously takes place within a reasonable computing time, so that in comparison to the additive production of the real building structure, material expenditure and production time in the machine for additive production can be saved.

If the first superstructure of the building structure is calculated, it must also be taken into account that it is located on a building platform. The construction platform is to be considered as a boundary condition and behaves essentially like a previously created super layer. The calculation routines that can be used for the calculation of subsequent superpositions, taking into account already produced superpositions, therefore also apply to the construction platform. Possibly, a modulus of elasticity deviating from the superposition is to be taken into account here, which has an effect on a different rigidity of the construction platform.

After the form deviations of the building structure are known as a result of the implementation of the method, a correction of the data describing the geometry of the building structure can be carried out so that a shape deviation in the building structure in the opposite direction to the calculated shape deviations is provided. Since the quantitative effects of a modification of the geometry of the building structure is not completely predictable, a further accounting run can then be carried out by means of the method in order to be able to assess the effect of the measure.

According to an advantageous embodiment of the invention, the cooling behavior of the respective superposition by the Processor can be determined as follows. The processor takes into account for the cooling only already manufactured parts of the building structure under construction. The energy input into the building structure that is being created is averaged over the time frame of the production of the superlayer in question and evenly distributed over the surface area of the superlayer. This means that a uniform energy input over the entire surface of the superposition is assumed, which is equivalent to the actual energy input. Furthermore, a heat loss for the super layer in question during the period of production of this superposition is determined by the processor. Heat losses occur due to heat conduction within the building structure under construction, heat radiation from the building structure into the powder bed and the process chamber and by convection of the process gas. Finally, taking into account energy input and heat loss, the mean temperature i of the respective superposition is determined.

The thermal consideration of the already produced construction structure as a whole advantageously simplifies the thermal

Calculation of the component using the FEM method. It has been shown that the thermal processes in the building structure (after solidification of the building material) run so slowly that a simplification to a quasi-static behavior here have no great impact on the accuracy of the calculation result.

According to a further embodiment of the invention, it is therefore advantageously possible for the processor, when calculating the resulting voltages and shape deviations, to base a time-dependent continuous temperature profile Ti (t) in the relevant position, which runs from the melting temperature Τ _Ξ to the mean temperature i. The temperature difference in this case causes the shrinkage of the building structure and the resulting stresses and deviations in shape. This model advantageously simplifies the consideration of the time behavior of the temperature with sufficient approximation to the real conditions and therefore also simplifies the calculation with the consequence of reduced computing times. Of course, instead of a linear cooling behavior, a different cooling behavior (for example exponentially) can be assumed, if this better reflects the real cooling conditions.

According to another embodiment of the invention, it is provided that the shrinkage factor a ± is determined by producing a sample from the building material used and measuring the sample produced and making it accessible to the processor. This configuration of the method makes it possible to determine the shrinkage factor taking into account the real conditions (choice of the material of the building structure, conditions of the additive manufacturing plant, process parameters). This shrinkage factor is then assumed for the entire building structure. Alternatively, this shrinkage factor a ± can also be calculated by mathematically determining the behavior of the sample to be produced. For this purpose, known FEM methods can be used.

The experimental determination of the shrinkage factor a ± has the advantage that the real conditions can be taken into account without knowing exactly their interplay. The calculation of a sample by means of FEM method has the advantage that this is compared to the building structure small volume is set, so that the computational effort can be kept within limits.

According to a further embodiment of the method, it is provided that the processor or a processor corresponding to this processor has the shrinkage factor a ± (as already mentioned above) or the shrinkage factor ι, depending on the position in question, by calculating stresses and changes in shape in one calculated using the additive manufacturing process representative volume element (hereafter called RVE) with a FEM. When calculating the shrinkage factor, instead of the sample, an RVE is used, which has a specific geometry. The RVE For example, it may have the same height as the super layer in question. If the RVE is calculated individually for each superposition separately, the effects of already produced super layers on the shrinkage behavior can also be taken into account. As a result, the accuracy of the calculation result is advantageously improved, whereby the associated additional expenditure in the calculation is within reasonable limits. The calculation of the shrinkage factor may be performed by the processor or a processor corresponding to that processor. As a processor in the context of this application, a computing unit is to be understood, which is suitable for carrying out the method. This has an electronic circuit, which may be structurally housed in one or more processor cores. As a corresponding processor in the sense of this application, a computing unit is meant, which can perform calculations independently of the former processor, but can correspond to it for the purpose of exchanging data.

In other words, the method may be performed on one or more processors. If a "said processor" is referred to in the context of this application, this refers to one of these processors, the functional sequence of the method being ensured by corresponding multiple processors Corresponding processors are used, these are not mentioned individually, but all are referred to as corresponding processors.In this respect, the former processor in conjunction with other processors is a corresponding processor.

According to a particular embodiment of the invention, it is provided that the processor or the processor corresponding to this processor composes the RVE from a multiplicity of irradiation tracks which are superimposed in several layers, the course of the irradiation tracks corresponding to is defined in accordance with an intended for the additive manufacturing process irradiation pattern. In other words, the plurality of irradiation tracks produce a modeling of the actual planned exposure regime of the additive manufacturing process. Thus, the RVE behaves essentially as a volume corresponding to the RVE of the real component, in which case a distinction between the individual superpositions can be made. The effective shrinkage factor ±, ι can then be used for the entire superposition for calculating the stresses and strains.

If the additive manufacturing process consists of a SLM or an EBM, then the material is actually melted and thereby solidified. In this case, the traces of irradiation consist of the traces of welding, the material solidifying again after melting. In the case of SLS, the material is solidified by the laser beam by sintering, without resulting in a complete melting of the powder particles of the building material. However, the procedure is comparable. Advantageously, the irradiation coils in the respective layer (which forms part of the superposition) can run in a straight line and parallel to one another. This is a frequently used exposure regime, and thus a realistic assumption in most cases. Furthermore, it can be considered that the course of the irradiation coils are rotated from position to position at a certain angle. Again, this is a common irradiation strategy, in which there is a certain balance of stresses and strains in the component inside and thus in the RVE.

According to a specific embodiment of the invention, it is provided that the processor or the processor corresponding to this processor calculates all the irradiation traces under the boundary conditions, that these are applied in a straight line to already solidified building material of an adjacent irradiation track. Unlike the making of a real one cube-shaped sample can be assumed in the RVE namely that this is located inside the building structure to be produced. In this case, the irradiation traces lying on the edge of the RVE also have to be such that they behave like irradiation traces lying inside the component, in that adjacent irradiation traces are applied outside the RVE. The influence of adjacent irradiation tracks not belonging to the RVE therefore advantageously represents a more realistic approach.

It is furthermore advantageous that the processor or the processor corresponding to this processor has a temperature distribution in the irradiation tracks through a finite

Element method calculated. This means that the cooling behavior, in particular of the molten bath but also the cooling following the solidification of the molten bath, can be modeled close to reality. In this case, the molten bath can be modeled, for example, as a so-called Goldak heat source, this process already being described by Keller et al. has been described in the source cited above.

A further advantageous embodiment of the method is obtained if the processor or the processor corresponding to this processor at least one of the effective shrinkage factors a _1: ± determined such that its determination is based on a solidification of the building material on a substrate with a stiffness C ±. This has the advantage that the rigidity of a construction platform on which the building structure is built, can be taken into account. The method for taking into account the building board is analogous to the method of taking into account the super-layer lying under the superposition in question, except that the boundary conditions are dictated by the material and the temperature of the building board. Advantageously, the building board can be considered in particular in terms of their heat capacity in the subsequent calculations of the super layers, whereby also applied in this case the valid for the already produced super layers calculation methods analog can be. In the further course of the calculations, this is achieved by the processor or the processor corresponding to this processor for the superposition concerned effective for this situation effective shrinkage factor ι _, ι taking into account the rigidity Ci_i _, i of lying under the superposition superpositions (which the form previously produced building structure) determined.

The stiffness of each located under the respective superstructure structure therefore plays such a significant

Role, because this prevents unhindered shrinkage of the respective super layer. Rather, there is a tension between the respective super layer and the underlying super layer or the building platform or base, so that a portion of the change in shape generated due to the shrinkage behavior is omitted and instead a tension between the adjacent super layers is established.

In particular, this behavior can be computationally determined by the processor or the processor corresponding to this processor using the RVE with a height corresponding to the strength of the relevant superposition. For this purpose, the processor generates a finite element describing the respective superposition, which has the connection to a base having a stiffness Ci_i, i the super layer lying under the respective superposition (or in the case of the first super layer with the rigidity of the build platform C _± ). From this, the said processor calculates a relative tension of the building structure (or building platform) lying under the respective superposition, taking into account the

Lowering the temperature from the melting temperature Τ _Ξ to the temperature of the layer Ti through a FEM. For the superposition in question, said processor then determines the effective shrinkage factor ι _, ι, in that said processor generates a homogeneously solidified volume element (hereafter HVE) of the same material and the same dimensions as the relevant RVE. The PDB is thus a replacement volume element which does not have a heterogeneous structure has individual irradiation traces, but has a homogeneous, idealized microstructure of the corresponding material. This is used, that said processor adapts a thermal shrinkage factor of the PDB that the previously calculated for the RVE stresses and deformations present in an interface between the PDB and the building structure lying under the relevant Super location and this shrinkage factor equal _ι, ι puts. The last-mentioned calculation step advantageously achieves that the calculation can be simplified by adopting the PDB. Within the PDB, the effective shrinkage factor ι, ι applies homogeneously, with the aid of which the stresses and strains can advantageously be determined with further reduced computational effort.

To achieve the greatest possible reduction of the computational effort, the super layers must be as thick as possible. In order to ensure the greatest possible accuracy of the calculation result, the super layers must be as thin as possible. Here, it is important to find a compromise so that the calculation result can be calculated with sufficient accuracy and at the same time within a reasonable computing time. The compromise is advantageously achieved in particular when the super layers each consist of at least 10 and at most 20 layers of the building structure to be produced.

An advantageous good approximation for the energy input is obtained when the melting of building material with an energy beam and the processor or a processor corresponding to this processor the energy input Q as a product

 The power of the energy beam,

 • the difference between 1 and the reflectivity of the material and

• the quotient of a writing time in which the energy beam solidifies construction material and the total processing time of the respective superposition calculated. In this case, all significant influencing variables for the energy amount are taken into consideration in an advantageously comparatively simple manner, wherein it has been shown that due to the time behavior of the already produced building structure such an approximation enables a sufficiently accurate assessment of the temperature behavior of the building structure.

Of course, the power of the energy beam flows directly into the energy input Q. However, the part of the power which is reflected by the building material must not be taken into account, which comes through the difference between 1 and the reflectivity of the building material for discharge. Finally, the energy input is also reduced by the radiation breaks, in which no power of the energy beam is introduced into the building structure. This can be expressed by the quotient of a writing time, during which the power of the energy beam is introduced, in relation to the total processing time (including the writing pauses). According to another embodiment of the invention, it is provided that the processor or a processor corresponding to this processor calculates an additional thermal shrinkage of the building structure, due to a cooling down to a uniform temperature level, with a FEM. In doing so, the said processor takes into account the building structure with the determined solidified resulting stresses and shape deviations as a whole, ie after completion of their production. The building structure is subjected to a temperature profile which is set for this building structure when the cooling behavior of the last super layer of the building structure was determined. At this time, there is still residual heat in the finished building structure, which leads to a further shrinkage of the building structure as a whole when the building structure cools to a lower temperature level. The additional stresses and deviations in the form of the lowering of the temperature to the said temperature level are calculated by means of FEM and with the resulting stresses and shape deviations ascertained as a result of the production superimposed. The result is advantageously an analysis directed to the subsequent use of the component. The uniform temperature level can be at room temperature or a normal operating temperature for the operation of the building structure.

According to a particular embodiment of the method, it is provided that the processor or a processor corresponding to this processor subdivides at least one of the superpositions into volume segments, the volume segments together resulting in the volume of the superpositions. For the respective superposition, said processor calculates the cooling behavior for each of the volume segments individually. This refinement of the method will advantageously lead, with justifiable increase in computational complexity, to more refined results of the simulation calculation in cases in which the cooling behavior in the relevant superposition is too inhomogeneous in order to obtain a sufficient approximation of the simulation calculation. The refinement of the process by subdividing the respective superposition into volume segments does not have to be carried out for each of the superpositions of which the construction structure is composed. In order to keep the computational effort as low as possible, such a calculation can only be carried out for the critical superpositions.

The volume segments in the respective superposition can also be provided either with a constant size or can be provided as needed in areas of the superposition in question in which a homogeneous behavior exists, for example in the peripheral regions of the superlage, a relatively large-volume segment, while in areas close to the edge In the superlayer, where the influence of cooling due to heat radiation from the building structure plays a greater role, volume segments with a smaller volume are provided. For example, the volume segments may have the same dimensions as the RVE. In a particular embodiment of the invention, the superposition can also be divided exclusively from volume segments in the size of the RVE, where can occur in the peripheral layer of the building structure due to the outer contour and volume segments with a different geometry. In a further step, the said processor calculates the thermal shrinkage in the respective superposition, by this processor individually determining an effective shrinkage factor ι, ι for solidified building material for each of the volume segments. For each of the volume segments, said processor individually calculates a relative thermal

Shrinkage ει to ει ± segment in the volume, taking into account the melting temperature of the building material _Τ Ξ and excluding other layers and Super volume segments, ι = i o £ _fi (T _B - Ti).

The resulting stresses and shape deviations in each volume segment of the superpositions in question are then calculated by the processor by taking into account the stresses and shape deviations of already produced superpositions. The volume segments are treated in the same way as the entire super layer, so the individual treatment of super layers and volume segments of a super layer can be selected as needed.

According to the invention, the object specified at the outset is also achieved by the use of the above-described method for generating corrected data describing the geometry of a building structure, wherein the building structure can be produced with an additive manufacturing method by solidification, in particular melting, of building material in successive layers. In this case, the determined production-related shape deviations and voltages are taken into account by the processor or a processor corresponding to this processor when generating the corrected data describing the structure of the structure. The result is thus a data set for the production of the building structure, which improves the performance of the additive manufacturing process. serten building structure and thus advantageously improves their quality.

According to the invention, the object stated at the outset also solves the use of the above-described method in a method for the additive production of a building structure, in which the building structure is produced by solidifying building material in successive layers, using the above-mentioned corrected data describing the building structure ,

The object is also achieved by a computer-readable medium having stored thereon a computer program which executes the method described above when it is executed in one processor or a plurality of corresponding processors. This computer program, which is processed in a processor and thereby executes the method described above, solves the problem as well. The computer program or the computer-readable data carrier, on which this computer program is stored, represent here forms of expression of the invention, since the features of the method described above are implemented in the course of the program. Finally, the object stated at the outset also solves a simulator for determining production-related shape deviations and stresses in a building structure produced by an additive manufacturing method, which is produced by solidifying building material in successive layers, this simulator having a processor which is programmed to execute the above Method, so that the features essential to the invention are performed by the simulator. Further details of the invention are described below with reference to the drawing. The same or corresponding drawing elements are each provided with the same reference numerals and are only explained in detail insofar as There are differences between the individual figures. Show it

1 shows the sequence of an embodiment of the inventive method based on simplified intermediate results of the calculation method, and

2 to 5 selected process steps of an embodiment of the inventive method as

Flowcharts and

FIG. 6 shows an exemplary embodiment of the method according to the invention, implemented by a plurality of corresponding processors, which can run in a laser melting system.

FIG. 1 shows a turbine blade IIa as a building structure 11 to be produced, which has two support structures 11c parallel to a blade root IIb for the purpose of simplified manufacture. The actual component consists of the turbine blade IIa with the blade root IIb, while the support structures 11c belong to the building structure 11, but are removed after manufacture.

In the manufacturing step designated as U in FIG. 1, the building structure 11 is composed as a CAD model of finite elements FE. This description of the component is suitable for design purposes, but not for manufacturing the building structure 11, for example in a laser melting process (or other additive manufacturing process). For this purpose, the building structure 11 in a manufacturing step V in a conventional manner must be divided by slicing, ie that the geometric description of the building structure contains layers 12, which correspond exactly to the produced during laser melting layers of the building structure. However, this description of the component is too fine for the purposes of applying the method according to the invention, so that the computational effort too would lead to uneconomical computing times. For the purpose of applying the method according to the invention, it is therefore provided that the building structure 11 is subdivided in a step W into superpositions 13 which have a greater thickness than the layers 12 to be produced. Preferably, the super layers may each contain exactly one specific number of layers, for example between 10 and 20 layers 12.

For the following considerations, a coordinate system indicated in FIG. 1 is taken as a basis, the stacking sequence of the layers 12 or of the superpositions 13 taking place in the z-direction. Thus, the layers are spatially aligned in the x-y plane respectively. The super layers 13 are indicated in step W according to FIG. Their greater thickness compared to the layers 12 in step V can also be seen in FIG. In addition, it is shown that the superpositions 13 can in turn be subdivided into finite elements, preferably subdividing into representative volume elements RVE (shown in method step C).

The actual calculation procedure is performed by a program with four program modules A, B, C and D (optionally in step D additionally Dl and D.2). This program sequence is shown in FIG. 1 on the one hand on the basis of the model formation for the building structure 11 and in FIG. 2 on the basis of program steps. The four program modules allow a simplified view of the processes occurring in laser melts with sufficient accuracy and can be carried out independently of each other with suitable transfer of data, in which case the physical structure, ie the thermal and the mechanical problem of the considered the descriptive structure Continuum and the scaling of the consideration, ie a macro scale for the already established building structure and a mesoscale for the consideration of the processes in the molten bath or the newly melted track can be distinguished. In program module A, the thermal macro scale is calculated. In each case, the already produced building structure 11 is considered as a whole, for which purpose the model with the superpositions 13 is used. From this model, the geometric data of the respective superposition L (z) can be used as input data.

The calculation of the thermal mesoscale consists of a quasi-stationary solution of the heat equation With

p: density of the material

c _p : specific heat capacity

K: Thermal conductivity as shown in FIG. 2 (a). This is based on a completely homogenized heating power, which is detected by the energy input Q already explained above. For the long periods of time assumed in program module A, one proceeds approximately from the assumption that the energy input Q would be distributed on average over the entire surface of the super layer 13 being produced. The heating power is then calculated according to the relationship

(b) Q = P _laser . (1-R). (T _laser / T _work ) with

P _L aer: Laser power

 R: average reflectivity of the material at the selected laser wavelength

T _L aser: Laser writing time

T " ₀ rk: total time for processing

T _L aser and T _work can be calculated taking into account the process of laser melting. Here are also considers the time periods for applying the powder during which the laser remains switched off. To determine the ratio, a representative layer 12 of the superstrate 13 can be considered. It is also possible to form the ratio of viewing all the layers 12 in the superstrate 13.

Furthermore, the heat losses due to heat conduction in the building structure, convection in the process gas and heat radiation are taken into account. For this purpose, conventional FEM calculation models can be used, which are generally known in the art.

The calculation is performed on a comparatively small number of setup states of the building structure. At most as many setup states should be considered as are superpositions 13 in the building structure. For uniform building structures with a simple geometry, it is also possible to combine several superpositions, if the thermal behavior of the building structure in the relevant component area changes little. As a result, computational effort is saved.

The result of each calculation is a time-averaged temperature distribution in the relevant setup states. From this it is possible to determine a reference temperature ΤΊ, which is an averaged temperature of the superstrate 13, against which a molten bath of the laser melting has to cool. For this purpose, the reference temperature i is transferred to the program module B. Thus, the reference temperature i of the macroscale temperature simulation determined in the program module A functions as a thermal boundary condition for the cooling from the melt pool. For the

Melting bath, a corresponding calculation can be carried out, this calculation, for example, as in Keller et al. described can be performed. Optionally, different reference temperatures Ti for different superpositions 13 of the building structure are determined in program module A. calculates, so that the melt pool calculation in program step B for different reference temperatures ΤΊ must be performed. The calculation of the temperature distribution in the mesoscale, ie at the level of the molten bath takes place in program module B (see FIG. 2) and serves to determine the temperature distribution in the molten bath. For this purpose, a small section of the workpiece is considered, in which a thin layer of powder lies on an already consolidated metal layer. In the further course of the solidification of the powder, a system is also to be calculated in which the upper layer consists of partly already consolidated metal and partly still of powder, so that a metal trace is melted onto a step of consolidated material. The last-described configuration represents the predominant state in the construction of new layers 12. For their calculation, the heat conduction equation (a) is again to solve, but this time for the heating power Q a local energy input Qi is selected in the powder bed. Qi approximates in a simplified approach

(c) Qi = P _laser · (1-) For a more accurate approach, a temporally and spatially varying power profile of the laser can be assumed, such as: B. a Gaussian beam profile of the width w at a speed v in the x-direction and a Lambert-Beer attenuation in the material, ie z = 0.

With

 Q (r, t): local energy input

I ₀ : power density ß: Lambert-Beer attenuation factor of the radiation in the material

x, y, z: see coordinate system in FIG. 1

Instead of the heat equation (a) can be solved in the program module B in a preferred embodiment, an equivalent differential equation for the enthalpy, which results in With

 Η: Entalpie of the material The application of this differential equation is advantageous when calculating smelting processes because around the melting point the temperature remains almost constant with continuous enthalpy supply. Coupled with the solution of equation (a) or (e) for Qi, the fact must also be taken into account that the physical properties of powder and consolidated material change greatly as the powder undergoes an irreversible state change. In other words, with an increase in the powder temperature over the

Melting temperature addition, a conversion of powder to

Melting takes place, while after cooling, the solidified material has the properties of a solid. To take this fact into account, a phase field variable "state" is introduced, which depends on x and y (coordinates of the position being produced), z (depth of the melt bath) and t (temporal behavior), which corresponds in each considered area of the powder bed the historical maximum of the temperature T _max (optionally also the enthalpy) If this historical maximum lies above the

Melting temperature Τ _{Ξ of} the powder material, then the physical properties correspond to those of the consolidated

Body and no longer those of the powder. It should be noted that the heat dissipation in the consolidated Body makes a much higher amount than the heat dissipation into the powder, which is a poor conductor of heat. The heat dissipation into the powder can even be neglected to simplify the approach. The solution of equation (a) or (e) taking into account the equation for the

Phase field variable State (x, y, z, t) results as a result in a temperature distribution in the immediate vicinity of an irradiation track 14 as shown in Figure 1. This is referred to below as analytical fit function Ti _oc (t).

Ti _oc (t) is transferred to the program module C (see FIG. 2). In program module C, a mesoscale-oriented structural mechanical simulation is carried out. For this purpose, the analytical fit function Ti _oc (t) is adapted to the temperature distribution for a representative irradiation track 14, as assumed in program module B. As a simulation area, a representative volume element, RVE for short, is formed, which consists of a matrix of individual strips, as shown in FIG.

Each strip in the RVE represents an irradiation track for which the temperature behavior Ti _oc (t) holds. At the beginning of the simulation, all strips are in the powdery state.

Successively transferred from the program module B analytical fit function Ti _oc (t) runs for the temperature via a respective strip whose processing is being simulated. When the melting temperature is reached, the state of the strip changes from pulverulent to molten state. If, after passing through the strip in the strip, the temperature is again below the melting temperature, the material is present as a solid and the resulting stresses and strains due to the thermal shrinkage are calculated using the following equation system consisting of the equation of motion (f ) for a continuous medium, Hooke's law (g) and the linear thermal strain law (h). d ² u

 (f) p - V a = F

dt ² With

u: 3-dimensional displacement

σ: stress tensor

 F: Acting force

 C: stiffness tensor

The fit function Ti _oc (t) can be described as a temperature pulse that runs on the surface of the powder bed, for example in the x direction, and trailing a cooling irradiation track 14 behind it. As a solution of the equation (f) taking into account the equations (g), (h) gives as a solution, the self-adjusting stress distribution after the material solidifies when the temperature pulse of the considered subregion away. As indicated in a recursion loop 21 in FIG. 2, the explained calculation according to equations (f), (g), (h) can be repeated for the matrix of strips of the RVE in an analogous manner, so to speak the individual strips successively with the same, temporally shifted fit function for the temperature are applied. The resulting stress distribution in the RVE is calculated. This is a partial result of the mechanical

 Mesoscale calculation, which is performed in program module C (see Figure 2).

In the next step, a transfer of the mesoscale calculation to the building structure has to succeed. For this purpose, a mechanical macroscale calculation is carried out in the program module C, for which purpose a physically based model for the stress-strain distribution in the body produced by the laser melting, represented by the structure, must be formulated. However, for this purpose, the known stress distribution σ (χ, y, z), resulting from the Mesoscale calculation RVE on a rigid base 16 (see Figure 1), not suitable. Instead, an effective shrinkage factor a ± (c) is calculated, which is dependent on the rigidity of the pad 16. For this purpose, instead of the RVE, which preferably has the thickness of the superposition, a material with homogeneous layer properties is set with the volume of the RVE, which is referred to below as homogeneous volume element (abbreviated to HVE). Now, a calculation is carried out in which, instead of a matrix of individual vectors in the case of the RVE, the entire volume of the HVE cools from the melting temperature Τ _Ξ to the reference temperature ΤΊ. In this case, in the manner already described, the equation (f) is calculated globally for the whole HVE taking into account the equations (g), (h) and taking into account the rigidity C of the support 16. Instead of _the rm _a i, a value is used as the variation variable as an effective thermal shrinkage factor a ± and the calculation is carried out therewith. If the value for a ± is correctly selected, the mean tension of the base 16 or of the HVE at the boundary surface to the base is the same as the tension between the base and the RVE in the mesoscale calculation. In order to achieve this, several recursion loops with different o (i may be necessary If the correct effective shrinkage factor a ± is found, this is forwarded to the program module D, which is shown in FIG.

The program module D is used for the mechanical calculation of the building structure at the macroscale level, whereby a physically based model for the stress-strain distribution can be applied here. The macroscale model uses superpositions 13, which may have a thickness of 0.5 to 1 mm, which corresponds to a homogenization of 10 to 20 layers 12 each of a superposition. The macroscale calculation assumes that the building structure to be examined in the z-direction, ie the construction direction, can be divided into a corresponding number of superpositions 13, as can be deduced from the step W according to FIG. When considering the individual super layers 13 of the already constructed part 17 of the building structure 11 is taken into account.

In the macroscale calculation, it is further assumed that the superpositions are all in a state of melt at the beginning of the simulation. As part of the simulation, a fictitious temperature is lowered from the lowest temperature to the highest in each super layer successively from the melting temperature to the reference temperature ti determined in the program module A, assuming a continuous function (for example, linear or exponential) for the temperature profile. The thermal strain used in equation (h) is replaced by a ±, since the thermal problem has already been solved in the mesoscale calculation and is assumed to be given in the context of the macroscale calculation.

Different stiffnesses of the base, that is to say of the previously produced building structure or of the building platform in the case of the first produced super layer, also lead to different values of the effective thermal expansion ει. In macroscopic bodies, the cause of the different stiffness lies in their geometric structure. Thus, the building structure 11 which is being formed in different heights z may also have different stiffnesses Ci. This can be considered in a program module D.l, in which a calculation of the substrate rigidity Ci is made in layers. In this case, each superposition of the building structure to be calculated is assigned an effective rigidity Ci. For this purpose, all known methods for stiffness calculation can be applied.

For example, a stiffness estimation can be made with the program module D1 (compare FIG. 4) as follows. The method is based on the assumption that the relevant stiffness of a structure with respect to the forces resulting from the thermal shrinkage of the overlying superposition is determined by the relationship between force and output. elongation, the force acting in the direction of the center of gravity of the layer. For each superposition the position of the center of gravity is determined. If the superlayer is made up of several islands isolated from each other, each of these islands is assigned its own center of gravity. In the structure lying below the superposition, ie the already constructed construction structure, each point of the interface with the current superposition is loaded with a small test force F (eg 1 N) in the direction of the center of gravity S of the current superposition (see FIG. Hereby, the elastic equations (f) and (g) are solved, whereby an effective stiffness Ci can be determined for each superlayer by forming the ratio between test force F and average displacement. This rigidity of the layer can be used to determine the effective thermal expansion ε 1 or ε 1, in the program module D, by means of the equations (f), (g), (h).

In order to further refine the model, instead of a uniform temperature in the superlayer, a locally differentiated consideration of the shrinkage behavior can be carried out in the calculation of the effective shrinkage factor. For this purpose, in a program module D.2 (compare FIG. 5), the superposition 13 currently being considered is subdivided into volume segments 15 (see also L (z) from step W in step D.2 in FIG. 1). These can have a uniform volume, in particular the volume of the RVE and HVE, at least in inner regions of the superposition, but can also have different sizes depending on the temperature distribution which occurs in the x-y plane. For example, the entire interior area can be defined as a volume segment and the complete edge area, which cools down more rapidly due to the heat radiation, than a second volume segment.

The volume segments are denoted by Vi, i. As is indicated in FIG. 5, different effective shrinkage factors are therefore available for the different volume elements Vi, i. ren ι, ι, which can be considered individually in the calculation module D (compare Figure 3).

It can also be seen in FIG. 1 that the calculated strains ει or ει, ± from the program module D can be used in a program module E in order to determine the geometry 18 of the actually produced building structure, which, as indicated by dashed lines, does not correspond to the original geometry the building structure 11 corresponds. In a first recursion step U + 1, the geometry 19 of the building structure 11 to be produced can be adapted such that the shape deviations of a subsequent calculation step D + 1 lead as far as possible to the desired geometry of the building structure (which is illustrated in step U). This can be checked by a subsequent iteration step of the simulation.

FIG. 6 shows a system 31 for laser melting, which has a process chamber 32 with a process window 33 for a laser beam 34. This laser beam 34 is generated by a laser 35, whereby the building structure 11 can be produced in a powder bed 36. The powder bed 36 is filled via a powder reservoir 37, for which purpose a doctor 38 is used. So that the laser beam 34 in the powder bed 36 can write the building structure 11, a deflection mirror 39 is also provided.

The processes described are controlled by a machine control, which can process data records which were generated in method step V according to FIG.

For this purpose, the machine control has a processor 40. A further processor 41 is provided for producing the production data (slicen), ie for producing a model of the building structure 11 with layers 12. This processor 41 can receive the data required for this purpose from a processor 42 with which CAD data of the building structure can be generated. Alternatively, as shown in steps W, A, B, C, D, D1 and D2, these CAD data may be processed by a processor 43 using the program modes described above. are implemented. A calculation result for the strains ε 1 _, ± that occur can be transmitted from the processor 43 to the processor 42, so that a modification of the geometry can be carried out as illustrated in FIG. 1 under step E. The modified component can then be calculated by the processor 41, in order subsequently to carry out a division into super layers 13 by means of the processor 43 and, secondly, a production in the laser melting system 31 by the machine control 40.

The configuration of processors 40, 41, 42, 43 is shown here by way of example only. Functionalities can also be distributed to more than the processors shown in FIG. 6 or combined in fewer processors. The processor 43 primarily has the task of carrying out the simulation method according to the invention, but in this case it can be supported by corresponding processors, wherein according to FIG. 6 these are the processors 41 and 42. In this sense, the processor 43 is also to be understood as a corresponding processor.

Claims

claims 1. A method for determining production-related shape deviations and stresses in a building structure (11) produced by an additive manufacturing method, which is produced by melting building material in successive layers (12), in which a processor (41)  • the geometry of the building structure (11) uses descriptive data to create a mesh of finite elements, wherein the processor (41) arranges the finite elements so that they are respectively completely in superpositions (13), the superpositions (13 ) each consist of several layers to be produced (12) of the building structure (11), • For each super layer (13) determines the cooling behavior and  Calculated from the cooling behavior the stresses and shape deviations resulting from a thermal shrinkage in the building structure (11) by a finite element method (FEM), characterized, in that the processor (41) determines solidification-related stresses and form deviations in the building structure by taking into account the superpositions (13) in the order in which they are formed, wherein the processor (41) determines an average temperature ΤΊ of the relevant superstrate (13) from the cooling behavior of the relevant superstrate (13), the processor (41) calculates the thermal shrinkage in the respective superstrate (13) by the processor (41)  · Takes into account an effective shrinkage factor a ± or ι, ι for solidified building material and A relative thermal shrinkage ει or ει, ± calculated in the superposition (13) in consideration of the melting temperature Τ _{Ξ of} the building material and without taking into account other superpositions (13) ι = od (T _B - Ti) or ει, ± = i _fi (T _B - Ti), the processor (41) calculates the resulting stresses and shape deviations in the respective superstrate (13), the processor (41) takes into account the stresses and shape deviations of already produced super layers (13). 2. The method according to claim 1, characterized, in that the processor (41) determines the cooling behavior of the relevant superstrate (13) by the processor (41)  • takes into account for the cooling only already produced parts of the building structure (11) which is being created, · averages the energy input into the building structure (11) that is being built over the period of production of the superposition (13) concerned and over the surface area of the superposition (13 ) equally distributed,  • determined a heat loss for the super layer (13) in the period of manufacture of this super layer (13) and  • taking into account the energy input and heat loss, the mean temperature i of the super layer (13) determined. 3. Method according to one of the preceding claims, characterized, that the processor (41), when calculating the resulting stresses and shape deviations, uses a time-dependent, continuous temperature profile Ti (t) in the relevant position, which runs from the melting temperature Τ _Ξ to the mean temperature i. 4. Method according to one of the preceding claims, characterized, the shrinkage factor a ± is determined by producing a sample from the building material used and measuring the sample produced and making it accessible to the processor (41). 5. The method according to any one of claims 1 to 3, characterized, the processor (41) or a processor corresponding to this processor has the shrinkage factor a ± or ι, ι by calculating stresses and changes in shape in a representative volume element (RVE) produced by the additive manufacturing method using a finite element method (FEM ). 6. The method according to claim 5, characterized, in that the processor (41) or the processor corresponding to this processor composes the representative volume element (RVE) from a multiplicity of irradiation tracks (14) which lie one above the other in a plurality of layers, the course of the irradiation tracks (14) corresponding to one for the additive track Production process of the planned irradiation pattern. 7. The method according to claim 6, characterized, in that the irradiation tracks (14) in the respective position are rectilinear and parallel to one another. 8. The method according to claim 7, characterized, in that the processor (41) or the processor corresponding to this processor calculates all the irradiation tracks (14) under the boundary conditions that are applied in a straight line to already solidified construction material of an adjacent irradiation track (14). 9. The method according to any one of claims 6 to 8, characterized, in that the processor (41) or the processor corresponding to this processor calculates a temperature distribution in the irradiation tracks (14) by a finite element method. 10. The method according to any one of claims 5 to 9, characterized, that the processor (41) or the processor corresponding to this processor at least one of the effective Shrinkage factors a _1: ± determined in such a way that, when it is tempered, a hardening of the building material on a base with a stiffness C ± is used. 11. The method according to claim 10, characterized, in that the processor (41) or the processor corresponding to this processor determines, for the super layer (13) in question, an effective shrinkage factor oii, i taking into account the stiffness Ci_i, i of the building structure underlying the respective superposition (13) , 12. The method according to claim 11, characterized, that the processor (41) or the processor corresponding to this processor  The representative volume element (RVE) is used with a height corresponding to the strength of the superposition in question,  A network of finite elements describing the relevant superposition is produced, which has a connection to a base with the rigidity Ci_i, i of the building structure (11) lying under the respective superposition (13), A relative tension of the building structure (11) lying below the relevant superposition (13) is calculated taking into account the lowering of the temperature from the melting temperature Τ _Ξ to the temperature of the layer Ti by a finite element method (FEM) and  • emits the effective shrinkage factor ι, ι applicable for the superposition (13) in question, in that said processor produces a homogeneously solidified volume element (PDU) of the same material and the same dimension generates the relevant representative volume element (RVE),  and in that said processor has a thermal  Shrinkage factor of the homogeneously solidified volume elements (HVE) adjusted so that for the representative volume element (RVE) previously calculated tensions or shape changes in an interface between the homogeneously solidified volume element (HVE) and the underlying superstructure (13) lying structure. 13. Method according to one of the preceding claims, characterized in that the super layers (13) each consist of at least 10 and at most 20 layers (12) of the building structure (11) to be produced. 14. Method according to one of the preceding claims, characterized in that that the building material is solidified with an energy beam, and the processor (41) or a processor corresponding to this processor records the energy input Q as a product The power of the energy beam,  The difference between 1 and the reflectivity of the building material and the quotient of a writing time in which the energy beam solidifies building material, and • the total processing time of the respective superposition calculated. 15. Method according to one of the preceding claims, characterized in that in that the processor (41) or a processor corresponding to this processor calculates an additional thermal shrinkage of the building structure due to a cooling down to a uniform temperature level with a finite element method (FEM) by the said processor • takes into account the building structure (11) with the determined consolidation-related resulting stresses and shape deviations as a whole,  • the building structure (11) is subjected to a temperature profile which results for the building structure (11) after the cooling behavior of the last super layer (13) of the building structure has been determined,  • the additional stresses and deviations in shape when the temperature is lowered to the said temperature level are calculated and superimposed with the resulting stresses and shape deviations determined by the manufacturing process. 16. The method according to any one of claims 5 to 15, characterized, in that the processor (41) or a processor corresponding to this processor  • at least one of the super layers (13) in volume segments (15), wherein the volume segments (15) together give the volume of the superposition,  Calculated individually for the respective superposition (13) the cooling behavior for each of the volume segments (15), and said processor calculates the thermal shrinkage in the respective superstrate (13) by said processor  For each of the volume segments (15) individually determines an effective shrinkage factor ι, ι for solidified building material and · For each of the volume segments (15) individually calculated a relative thermal shrinkage ει, ± in the volume segment (15) taking into account the melting temperature Τ _{Ξ of} the building material and without taking into account other super layers (13) and volume segments (15) ει, ι = o il _fi (T _B - Ti) and said processor calculates the resulting stresses and shape deviations in each volume segment of the respective superstrate (13) by reducing the stresses and shape deviations. already prepared super layers (13). 17. Use of a method according to one of the preceding claims in a method for generating corrected data describing the geometry of a building structure (11), wherein the building structure (11) can be produced by an additive manufacturing method by solidifying building material in successive layers (12) and wherein the processor (41) or a processor corresponding to this processor takes into account the determined production-related shape deviations and stresses in generating the corrected data describing the construction structure (11). 18. Use of a method according to claim 17 in a method for the additive production of a building structure, in which the building structure is produced by solidifying building material in successive layers, wherein the method uses the corrected data describing the structure of the structure. 19. computer-readable data carrier, on which a computer program is stored, which carries out the method according to one of the preceding claims, when it is executed in a processor (41). 20. computer program, which is processed in a processor (41) and thereby carries out the method according to one of claims 1 to 18. 21. simulator for determining production-related shape deviations and stresses in a building structure (11) produced by an additive manufacturing method, which is produced by consolidating building material in successive layers (12), which has a processor (41) which is programmed to carry out the method according to one of claims 1 to 18.