Three-dimensional shaping device

By predicting and correcting cutting data in a 3D modeling device, the deformation problem caused by thermal stress in 3D modeling is solved, achieving the effect of improving accuracy without increasing time during the modeling process.

CN121104134APending Publication Date: 2025-12-12MATSUURA MACHINERY CO LTD
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Patent Information

Application Number
CN202511302832.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Priority Date
2024-09-27
Filing Date
2025-09-12
Publication Date
2025-12-12

AI Technical Summary

Technical Problem

In existing 3D modeling technology, deformation caused by thermal stress still exists after repeated modeling and cutting, which affects the modeling accuracy. Furthermore, waiting for the thermal stress to dissipate before cutting will increase the time required.

Method used

The possible deformation after cutting is predicted by a three-dimensional modeling device, the cutting data is used to correct the cutting, and the deformation is predicted by combining simulation and database. The cutting data is then generated to perform cutting during the modeling process to avoid the influence of deformation.

Benefits of technology

It improves modeling accuracy without increasing modeling time, avoids deformation caused by thermal stress, and is applicable to various 3D modeling methods, including PBF and DED.

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Abstract

The invention relates to a three-dimensional shaping apparatus. The purpose of the present invention is to improve shaping accuracy in three-dimensional shaping in which a three-dimensional shaped object is formed by repeating shaping in which powder is melted and solidified and cutting thereof. In a powder bed type three-dimensional shaping device, metal powder is irradiated with laser light, the powder is melted and solidified to form thin layers, and the thin layers are laminated to perform three-dimensional shaping. At this time, each time a predetermined layer such as 10 layers is formed, the formed layer is cut, thereby improving the shaping accuracy of the shaped object. Cutting data defining a cutting shape uses a shape S3 obtained by reflecting a displacement d1 between a shape S1 to be obtained and a shape S2 deformed by simulation prediction in the shape S1. The deformation of the shape (S3) can be further predicted, the displacement of the displacement (d2) relative to the shape (S1) can be obtained, and the shape (S5) reflecting the displacement can be used as the cutting data. In this way, shaping and cutting are repeatedly performed using the cutting data generated on the basis of the deformation prediction, whereby shaping accuracy of the shaped object can be improved.
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Description

Technical Field

[0001] This invention relates to a technique for improving the accuracy of three-dimensional shaping, wherein the three-dimensional shaping is achieved by repeatedly melting and solidifying powder using lasers or electron beams, and by cutting the powder to form a three-dimensional object. Background Technology

[0002] As a technique for three-dimensional modeling, additive manufacturing is known to be performed by melting and solidifying powder using lasers or electron beams. Various methods are known within this approach, including Powder Bed Fusion (PBF) and Directed Energy Deposition (DED). In these three-dimensional models, residual stresses generated during melting and solidification can sometimes cause deformation of the model, making the improvement of modeling accuracy a challenge.

[0003] For example, Patent Document 1 discloses a technique for repeatedly shaping and cutting layers during the formation of a structure by stacking thin layers. Patent Document 2 discloses a technique in which, during the shaping of the laminate, deformation caused by residual thermal stress is assumed, each layer is formed larger than its original shape, and portions exposed from the original shape are formed with low strength, thereby facilitating cutting. In this way, by repeatedly performing shaping and cutting, an attempt is made to improve the accuracy of the three-dimensional shape.

[0004] Existing technical documents Patent documents Patent Document 1: Japanese Patent Application Publication No. 2020-82179 Patent Document 2: Japanese Patent Application Publication No. 2022-55792. Summary of the Invention

[0005] The problem that the invention aims to solve However, even with repeated shaping and cutting, the shaping accuracy cannot be maintained when the layers, after being finished by cutting, deform due to thermal stress. On the other hand, waiting until each layer has stopped deforming due to thermal stress before cutting leads to another problem: increased shaping time. These problems are unrelated to the method of stacking thin layers; they are common to all additional shaping processes. In view of the above-mentioned problems, the present invention aims to improve the accuracy of three-dimensional modeling while suppressing the increase of modeling time.

[0006] Solution for solving the problem This invention is a three-dimensional shaping device for shaping three-dimensional objects, wherein the three-dimensional shaping device comprises: The input unit reads in the shape data of the object. The shaping section melts and solidifies the powder, forming a portion of the object according to the shape data; A moving mechanism that moves the portion and the shaping part relative to each other, so as to attach the formed portion to form the next portion; The cutting section is used to cut the completed part; and The control unit controls the repeated execution of the shaping by the shaping unit and the moving mechanism, as well as the cutting by the cutting unit, thereby shaping the object. The control unit predicts the deformation that will occur in the portion after the cutting due to the stress accompanying the shaping, and performs the cutting based on cutting data that is corrected to fit the shape data in order to produce the deformation.

[0007] In this invention, a three-dimensional object is formed by repeatedly performing shaping and cutting based on shape data set without considering deformation that may occur during shaping. The cutting process can then correct the shape of the object based on deformation caused by stress during shaping. Therefore, even if the object deviates from its original shape during cutting, its original shape can be restored by subsequent deformation. Therefore, according to the present invention, cutting can be performed in a manner that achieves the shape of the object without waiting for deformation to occur in the part where the object has been formed. That is, the shaping accuracy can be improved while suppressing the increase in shaping time.

[0008] In three-dimensional modeling, it is also possible to consider cutting and finishing the object after all the modeling is completed. However, this method has the drawbacks of time required for cutting and increased strain on the tools. Furthermore, depending on the shape of the object, such as deep grooves, cutting with conventional tools after modeling is sometimes not feasible. In contrast, in this invention, since cutting is performed during the modeling process, it has the advantage of avoiding these problems.

[0009] This invention is applicable to various three-dimensional shaping methods that utilize the melting and solidification of powders, such as PBF (Powder Bed Fusion) and DED (Directed Energy Deposition). Shaping and cutting can be performed at any time. Cutting can also be performed after shaping has been repeated a specified number of times. In this invention, cutting data can be generated by a three-dimensional modeling device, or the operator can read the generated data into the three-dimensional modeling device. Alternatively, cutting data can also be generated by a device other than the three-dimensional modeling device.

[0010] In this invention, a cutting data generation unit may also be included, which generates the cutting data by simulating the deformation caused by the stress and reflecting the prediction result in the shape data.

[0011] If the deformation caused by stress is predicted based on the original shape of the object, and the shape that reflects the deformation in the opposite direction is used as cutting data, the result of the deformation is that the original shape of the object can be achieved. Alternatively, it is not necessary to directly reflect the deformation obtained through prediction; calculations such as multiplying by weighting coefficients can be performed to reflect it. Simulations that predict deformation can utilize a variety of well-known methods. The cutting data generation unit can be located within the 3D modeling device, or it can be located on a separate device, server, etc. The same applies to the following situations.

[0012] When using simulation as described above, the cutting data generation unit can also predict the deformation generated in the cutting data through the simulation and reflect the difference between the deformed shape and the shape data, thereby updating the cutting data.

[0013] Even when cutting data is set to reflect predicted deformation, various error factors may prevent the object from accurately achieving its shape after deformation. According to the method described above, if the predicted deformation based on cutting data fails to achieve the desired shape, the cutting data can be set to reflect this discrepancy. This allows for a higher degree of accuracy in achieving the object's shape after deformation. Furthermore, the updating of cutting data based on deformation prediction can be repeated not only once, but also more than twice. For example, the difference between the deformed shape and the original shape of the object can be repeatedly calculated until it converges to a specified range.

[0014] In addition to using simulation methods, the present invention may also include a cutting data generation unit that predicts the deformation caused by the stress based on a database and reflects the prediction result in the shape data to generate the cutting data. The database stores past shapes and the deformations in those shapes caused by the stress.

[0015] For example, cutting data can be generated by shaping the object without predicting deformation, measuring the deformation at the location using a three-dimensional measuring instrument, and then eliminating the deformation. In this way, by predicting deformation based on data generated from past models, cutting data can be set with high precision. Additionally, this can sometimes be achieved with a lighter load than the simulation. In addition, as a method that utilizes past data, deformation can also be predicted through statistical methods or machine learning.

[0016] In this invention, the control unit may also perform the cutting in the shaping process repeatedly performed by the shaping unit and the moving mechanism, excluding the portion generated by the shaping process of a predetermined number of steps from the previous step.

[0017] The part shaped in a previous process may be affected by heat due to further shaping in a subsequent process. Therefore, even if this part is cut, unexpected deformation may occur due to the new heat. According to the method described above, by performing the cutting without considering the amount from several previous processes, such effects can be avoided. The processes that should be excluded can be determined arbitrarily based on the three-dimensional modeling method or the model itself.

[0018] In this invention, the cutting part can also be a lollipop-shaped tool.

[0019] A lollipop-shaped tool refers to a tool with a spherical blade at the front end of the shaft, the diameter of which is larger than the diameter of the shaft. This allows for cutting even when a part of the object protrudes, avoiding interference and thus enabling improved cutting precision for a wider variety of objects. Lollipop shapes are particularly useful in situations where shaping is done in layers of thin material, and cutting is performed on the material that has been excluding the material from the most recent steps. In this case, when the thin layer that is not the material to be cut is protruding, cutting the layer below it is possible to avoid interference with the protruding layer if the tool is lollipop shaped.

[0020] In this invention, the shaping part is a mechanism in which powder is melted and solidified on a base plate for holding the shaped object to form a thin layer that is part of the shaped object. A heater is provided for heating the base plate. The control unit controls the heating by the heater so that the warpage of the base plate accompanying the shaping converges below a specified requirement value.

[0021] When shaping by stacking thin layers on a base plate, the base plate will warp, leading to a decrease in the precision of the shape. According to the above method, by appropriately heating the base plate with a heater, the warping on the base plate and the deformation of the shape can be suppressed. The above method can also be applied to make other deformations, such as warpage, of the shaped object after separation from the base plate below the required value.

[0022] In the above-described manner, the heating by the heater can be controlled by various methods. For example, heating conditions can be set to minimize warping based on past modeling data. These heating conditions can be set based on the warping of the base plate determined through simulation. The results can also be used in simulations predicting the deformation of the model, where the deformation of the base plate is also considered during analysis. Furthermore, since the warpage of the base plate is highly correlated with the heating conditions of the heater and the contact area with the object, their correlation can be represented in advance using functions, mappings, and tables. Based on this correlation, the heating conditions of the heater with warpage below the required value can be determined. In addition to considering the contact area of ​​the object, other parameters representing the size and shape of the object, such as height, can also be considered. Furthermore, strain sensors or other sensors for detecting other deformations can be installed on the base plate itself to provide feedback control of the heater's heating so that the warping detected by the sensor is below a required value.

[0023] In addition, the control unit can also set the cutting height range of the thin layer in the stacking direction based on the set temperature of the heater and the area of ​​the thin layer that is bonded to the base plate.

[0024] When thin layers are stacked, if the end faces of the thin layers are inconsistent, the end faces of the formed object may become rough. By cutting, the roughness of the end faces of the formed object can be suppressed, and the surface quality can be improved. However, in order to improve the surface quality of the end faces, it is preferable to consider the deformation generated during forming on the thin layers, the subsequent heat effect from the stacked thin layers, and the effect of deformation when performing cutting. The deformation of a thin layer can result in either primarily shrinkage or primarily expansion compared to the initial shaping. In the case of primarily shrinkage, if the thin layer shrinks after cutting, it may not be able to maintain its original shape; therefore, it is preferable to cut within a range where shrinkage is not expected to occur during subsequent shaping. On the other hand, in the case of primarily expansion, further expansion may occur on the cut thin layer as shaping progresses; therefore, it is sometimes preferable to re-cut the thin layer after it has been cut. It was found that the tendency of these deformations is affected by factors such as the temperature of the heater of the heated base plate and the area of ​​the thin layer bonded to the base plate. Therefore, in the above-described manner, by setting the cutting height range in the lamination direction according to these parameters, the surface quality can be improved based on the tendency of deformation generated in the thin layer.

[0025] The cutting height range can be set using various methods. For example, in cases where deformation with a tendency to shrink is expected based on parameters such as the heater temperature, the cutting height range can be defined as the lower side separated by a specified interval from the top of the existing thin layer. Conversely, in cases where deformation is expected to produce an expansion tendency, the previously cut layers can be included, with the cut height range defined from the topmost layer.

[0026] The various features of the present invention described above are not necessarily all present, and some may be omitted or combined appropriately. Furthermore, the present invention can be configured in various ways besides the three-dimensional shaping device described above. For example, a three-dimensional shaping method for shaping a three-dimensional object using a three-dimensional shaping device, wherein the three-dimensional shaping method comprises: (a) The step of reading in the shape data of the object; (b) The step of melting and solidifying the powder and forming a portion of the shape according to the shape data; (c) Repeat step (b) to attach steps to the completed portion to form the next portion; and (d) The steps for cutting the completed portion. Step (d) is a step that involves predicting the deformation of the portion that will occur in the portion after the cutting due to the stress accompanying the shaping, and performing the cutting based on cutting data that has been corrected in a manner that is suitable for the shape data in order to produce the deformation.

[0027] This three-dimensional modeling method can achieve the same effect as described in the three-dimensional modeling device. Furthermore, various features described in the three-dimensional modeling device can also be applied.

[0028] The present invention can also be configured as a computer program for controlling a three-dimensional modeling device via a computer. Alternatively, it can be configured as a computer program for generating cutting data, a major component of which is implemented by a computer. That is, it can also be a computer program that generates cutting data for a three-dimensional shaping device, which repeatedly performs the shaping of parts of a three-dimensional object by melting and solidifying powder and the cutting of the formed parts, thereby shaping the object. The computer performs the following functions: The function of reading the shape data of the object; and The function predicts the deformation of the portion due to the stress accompanying the shape after the cutting and generates cutting data, which is corrected in a manner suitable for the shape data based on the deformation.

[0029] Furthermore, it can be a computer program that generates cutting data for a three-dimensional shaping device, which repeatedly performs the shaping of parts of a three-dimensional object by melting and solidifying powder, and the cutting of the completed parts, thereby shaping the object. The computer performs the following functions: reading the shape data of the object; and... The function of generating cutting data by predicting deformation caused by said stress based on a database and reflecting the prediction results in the shape data, wherein the database stores past shapes and the deformation caused by said stress in the shapes. Attached Figure Description

[0030] Figure 1 This is an explanatory diagram schematically showing the structure of the three-dimensional shaping device in the embodiment. Figure 2 This is an explanatory diagram showing the shaping process in the embodiment. Figure 3 This is an explanatory diagram showing an example of the tool shape for the cutting part. Figure 4 This is a flowchart of the shaping process. Figure 5 This is an explanatory diagram showing the setting of the heater temperature. Figure 6 This is an explanatory diagram showing the method for generating cutting data. Figure 7 This is a flowchart of the cutting data generation and processing. Figure 8 This is an explanatory diagram showing the deformation that occurs in each layer. Figure 9 This is an explanatory diagram showing how to set the range of cutting heights for shrinkage tendency. Figure 10 This is an explanatory diagram showing how to set the range of cutting heights for expansion tendency. Figure 11 This is an explanatory diagram showing the results of the improved accuracy. Figure 12 This is an explanatory diagram showing the result of improved surface quality. Detailed Implementation

[0031] Regarding embodiments of the present invention, an example of shaping using powder bed fusion bonding will be described. The present invention is not only applicable to this method, but also to various shaping methods that melt and solidify powders, such as DED (Directed Energy Deposition) methods.

[0032] A. Device Structure: Figure 1 This is an explanatory diagram schematically showing the structure of the three-dimensional shaping device in the embodiment. The three-dimensional shaping apparatus 10 of this embodiment includes a shaping stage 14 for forming a shape and a powder spreader 13 that reciprocates thereon. A substrate, called a base plate, is provided on the shaping stage 14, and shaping is performed on it. Metal powder, which is the raw material for the shape, accumulates in a hopper 12. When the powder spreader 13 reciprocates during shaping, the surface of the base plate is covered with metal powder used for shaping to a substantially uniform thickness. The three-dimensional shaping device 10 includes a laser irradiation unit 11 as a mechanism for heating and melting the metal powder. The laser irradiation unit 11 includes a laser source and a mechanism for moving the irradiated area according to the shape of the object being shaped. In the area irradiated by the laser irradiation unit 11, the metal powder melts, then cools and solidifies, forming a thin layer that constitutes part of the object being shaped. All of the above parts can be collectively referred to as the shaping unit in the sense of the structure used to shape the thin layer. The three-dimensional shaping device 10 includes a moving mechanism 15 that moves the shaping stage 14 downward. After a thin layer is formed, the shaping stage 14 is moved downward by one layer. If metal is spread using the powder spreader 13 and melted and solidified using the laser irradiation section 11, a next layer can be stacked on top of the formed thin layer. The three-dimensional shaping device of the embodiment can shape three-dimensional objects on a base plate by repeatedly forming and stacking thin layers.

[0033] The three-dimensional shaping apparatus 10 of this embodiment alternately performs thin-layer shaping and cutting to improve accuracy. In the three-dimensional shaping apparatus 10, a cutting section 20 is provided as a cutting mechanism. During thin-layer shaping, the cutting section 20 retracts as shown in the figure, and then moves to the shaping table 14 for cutting during the cutting process.

[0034] The three-dimensional modeling device 10 is equipped with a control device 30 to control the aforementioned modeling and cutting. These can also be configured in hardware, but in this embodiment, they are configured in software by assembling computer programs that implement the drawing functions in a computer equipped with a CPU and memory.

[0035] The data input unit 31 reads the shape data of the object. During the shaping process, the shape of each layer that is stacked is required; therefore, the shape data can also serve as the shape data of each layer constituting the object. Alternatively, data representing the three-dimensional shape of the object can also be read, and the three-dimensional shaping device 10 generates shape data for each layer. The data input unit 31 also reads cutting data that defines the shape of the cut. As will be described later, in this embodiment, shape data and cutting data are different. Shape data is data that represents the shape of the object to be obtained, while cutting data is data used in the cutting process during the shaping process. In the case of three-dimensional shaping using the melting and solidification of powder, since thermal stress may sometimes cause the object to deform, the cutting data is set to estimate the deformation after cutting, and the result of the deformation is to achieve the desired shape. Cutting data can also be generated by the three-dimensional modeling device 10, but in this embodiment, it is assumed that it is generated by a separately prepared cutting data generation device 50. The structure of the cutting data generation device 50 will be described later.

[0036] The lamination control unit 35 forms a thin layer by controlling the supply of powder from the powder spreader 13 and the laser generated by the laser irradiation unit 11, and by utilizing the movement of the moving mechanism 15. The cutting control unit 34 controls the cutting unit 20 to perform cutting based on cutting data during the shaping process. The heater control unit 33 controls the heaters provided with the shaping stage 14 to bring the temperature of the shaping stage 14 to an appropriate level. It is known that the temperature of the shaping stage 14 affects the warping of the base plate, thereby affecting the accuracy of the shaped object. In this embodiment, the temperature of the shaping stage 14 is controlled so that the shaped object can maintain sufficient accuracy. The shaping control unit 32 integrates the heater control unit 33, the cutting control unit 34, and the stacking control unit 35 to shape the object based on the shape data.

[0037] As described above, in this embodiment, thin-layer shaping and cutting are repeatedly performed during the shaping process of the object. The cutting data defining the shape to be cut can also be generated by the three-dimensional shaping device 10, but in this embodiment, it is assumed that it is generated by the cutting data generation device 50. The cutting data generation device 50 is constructed in software by installing computer programs on a computer or server equipped with a CPU, memory, etc., to implement the functions illustrated. These functions can be implemented by a single computer or by multiple computers or servers connected via a network.

[0038] The shaping database 51 stores shaping data representing past shaping results. The content of the shaping data can be arbitrarily determined; for example, it can be the shape of the object, the cutting data during shaping, the magnitude of deformation generated in the object, etc. The shape of the object and the cutting data can use three-dimensional shapes, such as parameters like thickness in the stacking direction. The magnitude of deformation can also be represented by parameters such as deformation in the stacking direction and deformation within a layer.

[0039] The machine learning unit 53 uses the shape database 51 to generate a learning model through machine learning regression. The purpose of machine learning is to create a learning model that sets cutting data in a way that the deformation of a future object after cutting results in the desired shape. Therefore, machine learning is performed with shape, deformation, etc., as explanatory variables and cutting data as the objective variable. Machine learning can be performed using various algorithms. The generated learning model is stored by the machine learning unit 53. Alternatively, instead of the machine learning unit 53, a function can be set up to determine cutting data based on the shape database 51 using statistical methods. For example, a method can be used to statistically calculate the deformation generated in each direction of the three dimensions of the shape using parameters such as the planar shape of the thin layer and the thickness of each part of the shape.

[0040] The deformation prediction unit 52 functions to determine, through simulation or other means, how the object to be shaped will deform due to thermal stress or changes in microstructure. Regarding the simulation used for deformation prediction, since various methods are known, an appropriate method can be used.

[0041] The cutting data generation unit 54 generates cutting data based on the shape data of the object, reflecting the results obtained by the machine learning unit 53 and the deformation prediction unit 52. Either the machine learning unit 53 or the deformation prediction unit 52 can be used selectively, or the results of both can be used, depending on the object or the like. The generated cutting data is sent to the control device 30 for use in the cutting process.

[0042] Alternatively, the cutting data generation unit 54 can be structured by omitting either the machine learning unit 53 or the deformation prediction unit 52, using only the remaining one to generate the cutting data. Alternatively, the structure of the cutting data generation unit 54 can be integrated into the control device 30.

[0043] B. The process of three-dimensional modeling: Figure 2 This is an explanatory diagram illustrating the shaping process in an embodiment. In this embodiment, the shaping of thin layers is repeated (arrows SC1, SC2), and cutting is performed at predetermined time intervals (arrow SC3). This process will be described below. First, the forming of the thin layer (arrow SC1) will be explained. The figure shows the state in which the thin layer 1a is formed on the forming stage 14. In this state, metal powder is supplied while the powder spreader 13 moves in the direction of arrow A. Then, the laser 11L is irradiated, causing the powder to melt and solidify to form the thin layer 1b. As a result, a state in which the thin layer 1b is stacked on top of the thin layer 1a is formed. The above process is repeated several times (arrow SC2). In this embodiment, 10 layers are formed repeatedly. Afterward, the cutting part 20 moves on the forming object to cut the existing thin layer 1c (arrow SC3). When the cutting is completed, the forming of the thin layer is returned (arrow SC1). As described above, the three-dimensional modeling is achieved by repeatedly performing thin-layer shaping and cutting. In this embodiment, it is assumed that cutting is performed every 10 layers, but the timing of the cutting can be arbitrarily determined. In addition, in this embodiment, the deformation of the thin layer is predicted for cutting (hereinafter, this cutting is sometimes referred to as finishing cutting). However, in addition, intermediate cutting can also be added during the shaping process, that is, cutting with a margin for the original shape (hereinafter, this cutting is sometimes referred to as semi-finishing). In the following description, unless otherwise specified, cutting refers to finishing cutting, but this does not mean that semi-finishing is excluded.

[0044] Figure 3 This is an explanatory diagram showing an example of the tool shape for the cutting part. Figure 3 Figure (a) shows a perspective view of a cutting tool 40 mounted on the cutting section 20. As shown, the cutting tool 40 is so-called lollipop-shaped with a spherical cutting edge 41 formed at the front end of the shaft 42. Figure 3 (b) is a side view of the cutting tool 40. The diameter d2 of the spherical cutting edge 41 is greater than the diameter d1 of the shaft 42 (d1 < d2). In addition, a cutting edge is formed on the cutting edge 41 within the range of angle ANG. The angle ANG can be arbitrarily determined, but in this embodiment it is 220°. Figure 3 (c) schematically illustrates the advantages of the lollipop shape. When shaping by stacking thin layers L1 and L2 as in this embodiment, as shown in region S, sometimes the subsequently formed layer L1 protrudes beyond the existing layer L2. In such cases, when cutting the existing layer L2, if it is a lollipop shape, because the cutting edge 41 is formed at a large angle ANG, it is possible to avoid interference from layer L1 while cutting layer L2. The same applies when only layer L2 is cut when layer L1 does not protrude. In this embodiment, as described later, cutting is performed by excluding several layers from above. Therefore, the lollipop-shaped cutting tool 40 is particularly useful.

[0045] C. Shaping treatment: Next, the processing of shaping using the three-dimensional shaping device 10 of this embodiment will be described. Figure 4 This is a flowchart of the modeling process. It is the process executed by the control device 30 of the three-dimensional modeling device 10. When processing begins, the three-dimensional shaping device 10 first reads the shape data of the object (step S10). This shape data is the data that defines the shape of each thin layer when the object is constructed as a stack of thin layers. In the case where the shape data is the three-dimensional data of the object, the three-dimensional shaping device 10 needs to generate the shape data of the thin layers based on the three-dimensional data.

[0046] Next, the three-dimensional shaping device 10 controls the temperature of the heater of the heating base plate (step S11). Figure 5 This is an explanatory diagram showing the setting of the heater temperature. The horizontal axis represents the heater temperature, and the vertical axis represents the deformation of the base plate. Negative values ​​indicate upward convex deformation, and positive values ​​indicate downward convex deformation. During the forming process, various stresses are generated on the formed object, and the base plate sometimes deforms under their influence. The stress acting on the base plate is affected by the size of the object (strictly speaking, the contact area between the object and the base plate) and the temperature of the heater that heats the base plate. Points p1 to p3 in the diagram show the measured deformation results when the heater temperature changes for a certain object. Based on this example, the relationship between heater temperature and deformation can be roughly calculated as shown by the straight line L in the diagram. Therefore, for this object, the heater temperature at which the expected deformation is zero can be determined. The straight line L will differ depending on the shape. Furthermore, increasing the number of measurement points sometimes yields an approximate curve instead of a straight line. Therefore, the heater temperature can be set to determine the straight line L or an approximate curve based on past similar or identical shape results. return Figure 4 In step S11, the heater is controlled to reach the temperature set as described above.

[0047] Once the above processing is complete, the three-dimensional shaping device 10 begins the shaping process. First, an initial thin layer is formed (step S12). The method for forming the thin layer is as follows: Figure 2 As described, based on the shape data, a laser is irradiated to melt and solidify the metal powder. This process is repeated until the shaping of N layers (N is a natural number) is complete (step S13). Figure 2 As explained in the document, in this embodiment, it is assumed that N = 10.

[0048] When the shaping of layer N is completed (step S13), the 3D shaping device 10 performs cutting data generation processing (step S14) and performs cutting processing, that is, cutting the layer that becomes the object based on the cutting data (step S15). The 3D shaping device 10 repeats the above processing until the shaping is completed (step S16).

[0049] The cutting data generation process will be described later. In this embodiment, the cutting data is generated during the shaping process, but it can also be prepared in step S10 before the shaping begins. In the cutting process (S15), in this embodiment, a predetermined number of layers (hereinafter referred to as the "exclusion area") may be excluded starting from the layer following the shape, i.e., the topmost layer, and cutting may only be performed on the layers below it. Because the exclusion area is the upper region, it is easily affected by heat when subsequent thin layers are stacked. Even if the cutting is performed with good precision, deformation may occur during the period before the next cutting, resulting in steps sometimes forming on the cutting surface, i.e., the end face of the shape. If the exclusion area is thickened, the cut portion is less susceptible to the heat effect during the formation of subsequent layers. On the other hand, depending on the shape of the shape, if the exclusion area is thickened, it may protrude significantly, and cutting the layers below the exclusion area may become difficult. The exclusion area can be arbitrarily determined taking these factors into account. The method of determining this area will be described later. In addition, in the cutting process, not only finishing cutting can be performed, but semi-finishing cutting can also be performed.

[0050] D. Methods for generating cutting data: Next, the method for generating cutting data will be explained. This is related to the shaping process (…). Figure 4 The processing in step S14 is equivalent to the content of the previous step.

[0051] Figure 6 This is an explanatory diagram showing the method for generating cutting data. Figure 6 (a) shows an example of the shape S1 that a three-dimensional object should obtain. As shown in the examples, when performing three-dimensional shaping using the melting and solidification of powder, the shaped object may sometimes deform due to thermal stress generated during the shaping process. Figure 6 (b) shows an example of deformation. It shows an example where the left and right sidewalls shrink due to deformation from their original state as shown in shape S2. Due to the deformation, a displacement d1 is generated between the original and the desired shape. In the example shown in the figure, the deformation is schematically illustrated only on the left and right sides, but the deformation can occur in various ways depending on the shape of the object. Such deformation can be predicted through simulation. Based on the simulation, the displacement d1 caused by the deformation can be predicted.

[0052] Therefore, relative to the desired shape S1, the displacement d1 is reversed (shown as -d1 in the figure) to obtain shape S3. If a shape is generated with shape S3, then a deformation with displacement d1 is subsequently produced, and a shape of shape S1 is expected. From this point of view, shape S3 can be used as cutting data. In addition, the example in the figure shows an example of directly reflecting the displacement d1 in the opposite direction, but it can also be reflected after performing various operations such as multiplying the displacement d1 by a weighting coefficient or correcting it to make the displacement d1 change smoothly.

[0053] As mentioned above, shape S3 can be used as cutting data, but in this embodiment, further improvement in accuracy is sought. That is, the deformation prediction simulation is performed again on shape S3. If shape S1 is obtained through this simulation, there is no problem, but since the displacement d1 generated in shape S1 is not necessarily the same as the displacement generated in shape S3, therefore... Figure 6 As shown in (d) shape S4, sometimes a displacement d2 from shape S1 is produced. In the case where displacement d2 is generated, such as Figure 6 As shown in (e), shape S5, which reflects displacement d2 for shape S3, is used as cutting data. Therefore, compared with shape S3, the possibility of achieving shape S1 with high precision is increased.

[0054] Alternatively, the following process can be repeated: further simulate deformation prediction for shape S5, reflect the results and displacement of shape S1, and update the cutting data. By repeating this process until the simulation results of deformation prediction and the displacement of shape S1 converge within a specified range, the accuracy of the shaping can be further improved. The extent to which cutting data is updated based on deformation prediction simulation depends on the desired accuracy; alternatively, the initially obtained cutting data can be used. Figure 6 The shape of (c) is S3).

[0055] Figure 7 This is a flowchart of the cutting data generation and processing. It includes the cutting data generation device 50 (see reference). Figure 1 The processing performed is along... Figure 6 The idea described in the text is to generate cutting data processing.

[0056] When processing begins, the cutting data generation device 50 reads the shape data of the object (step S20). Next, the initial cutting data is set (step S21). The shape data can also be used directly as the initial value.

[0057] Next, the cutting data generation device 50 simulates the deformation prediction of the shape represented by the cutting data (step S22) and calculates the displacement relative to the shape data of the object (step S23). If referring to... Figure 6 Providing an explanation is equivalent to calculating the... Figure 6 The shape S1 of (a) predicts the deformation result. Figure 6 The processing of displacement d1 of (b)). If the displacement converges to less than the preset range (step S24), it is determined that the cutting data can be shaped with sufficient accuracy, and the process ends.

[0058] On the other hand, if the displacement has not converged, the cutting data is updated based on the displacement (step S25). If referring to... Figure 6 To explain, this is equivalent to using displacement d1 to determine shape S3. Then, the cutting data is subjected to deformation prediction simulation (step S22) and displacement calculation (step S23) again. If referring to... Figure 6 To provide an explanation is equivalent to obtaining... Figure 6 The shape S4 and displacement d2 of (d) are processed.

[0059] The cutting data generation device 50 repeats the above process until the displacement converges to the specified range (step S24). The cutting data generation device 50 also sets the cutting height range (step S26). As previously described in the cutting process ( Figure 4 As explained in step S15), in the cutting of this embodiment, not all of the shaped thin layer is always the cutting target; a certain exclusion area can also be set. The cutting height range refers to the range in the stacking direction that becomes the cutting target. The method for determining the cutting height range will be described later. The cutting data obtained through the above processing was used for the cutting processing of the three-dimensional modeling device 10 (see reference). Figure 4 Step S15).

[0060] As a variation, the deformation prediction simulation (step S22) and displacement calculation (step S23) in the cutting data generation and processing can also utilize the shaping database 51 (see reference) that stores past shaping results. Figure 1 The method. Specifically, displacement can be calculated using machine learning by referring to the shape database 51. Alternatively, machine learning can be used to generate cutting data reflecting the displacement. Besides using machine learning, displacement can also be calculated and cutting data generated through statistical processing of the shape database 51. Alternatively, the average displacement obtained through deformation prediction simulation and the average displacement obtained through machine learning or statistical methods can be used simultaneously to generate cutting data.

[0061] E. Method for setting the cutting height range: Next, the method for setting the cutting height range will be explained. This involves the cutting data generation and processing ( Figure 7 The processing content of step S26). First, after explaining how deformation occurs in each layer when shaping in stacked thin layers, the method for setting the cutting height range taking into account this deformation is explained. Figure 8 This is an explanatory diagram showing the deformation that occurs in each layer. The deformation that occurs in each layer varies depending on factors such as the temperature of the base plate. Figure 8 (a)~ Figure 8 (e) shows the deformation that occurs when the temperature of the base plate is low. Figure 8 (a) shows the state where layer LL2 is stacked on top of the completed layer LL1. Furthermore, layer LL1 can be a single thin layer formed in a single molding process, or it can be a region composed of multiple thin layers formed through multiple molding processes. In this embodiment, as in... Figure 4 As described in steps S12 and S13, cutting is performed after the N-layer is formed, so the amount of the N-layer can be considered to form layer LL1. When the temperature of the base plate is low, after the formation of layer LL2, over time, as... Figure 8 As shown in (b), layer LL2 shrinks. Furthermore, with this shrinkage, the upper surface of layer LL1 also shrinks, deforming into a trapezoidal shape with the upper base shorter than the lower base, as shown in layer LL1. In this state, as... Figure 8 As shown in (c), the end face of layer LL2 is cut to the desired shape (the part shown by the dashed line in the figure) using an end mill EM. Next, as... Figure 8 As shown in (d), layer LL3 is formed on layer LL2. Therefore, with... Figure 8 Similarly, as shown in (b), shrinkage occurs in layer LL3, and layer LL2 also deforms into a trapezoid. If this process is repeated, then when the base plate is at a low temperature, such as Figure 8 As shown in (e), the end face SL of the shape is not flush, but rather forms a rough state with overlapping concave and convex surfaces that extend downwards. Thus, sometimes the rough state is represented as low surface quality, and conversely, sometimes the absence of concave and convex surfaces is represented as high surface quality.

[0062] Figure 8 (f) Figure 8 (j) shows the deformation of the base plate when the temperature is high. Figure 8 (f) shows the state of layer LH2 stacked on top of the completed layer LH1. When the temperature of the base plate is high, after the formation of layer LH2, as time passes, such as Figure 8 As shown in (g), the microstructure of layer LH2 undergoes a martensitic phase transformation, resulting in expansion within layer LH2. Furthermore, the upper surface of layer LH1 also changes with the expansion of layer LH2, deforming into a trapezoidal shape with the upper base longer than the lower base, as shown in layer LH1. In this state, as... Figure 8 As shown in (h), the end face of layer LH2 is cut to the desired shape (the part shown by the dashed line in the figure) using an end mill EM. Next, as... Figure 8 As shown in (i), layer LH3 is formed on layer LH2. Therefore, with... Figure 8 Similarly, as shown in (g), expansion occurs in layer LH3, and layer LH2 also deforms into a trapezoid. If this process is repeated, then under conditions where the base plate temperature is high, such as... Figure 8 As shown in (j), the end face SH of the object is not flat, but rather forms a rough state with overlapping concave and convex surfaces that extend upwards.

[0063] The cutting of the end face is to suppress Figure 8 The unevenness shown is to improve surface quality. For example, in... Figure 8 As explained in the text, since the deformation generated in the layer varies depending on the temperature of the base plate, the cutting method is also preferably varied according to the temperature of the base plate.

[0064] Figure 9 This is an explanatory diagram showing how to set the range of cutting heights for shrinkage tendency. Figure 9 (a) shows the state where layer LL2 is stacked on top of the completed layer LL1. For example... Figure 9 As shown in (b), a semi-finishing process is performed on layer LL2 by cutting the end face with an end mill EM. During the semi-finishing, cutting is stopped while the shape still has a margin beyond the original dimensions. This has the advantages of reducing the amount of material removed during the finishing cut described later, and also suppressing deformation in layer LL2 caused by shrinkage. However, the semi-finishing process is not mandatory and can be omitted. like Figure 9 As shown in (c), when LL3 is formed along layer LL2, as Figure 9 As shown in (d), layer LL3 shrinks, and consequently, layer LL2 also deforms. Figure 9 As shown in (e), a semi-finishing process is performed on layer LL3.

[0065] After that, as Figure 9As shown in (f), finishing cutting involves cutting to maintain the original shape. Figure 9 In the process, since each layer mainly undergoes deformation with a tendency to shrink, for example, if the topmost layer LL3 is cut, it is possible that deformation will occur in layer LL3 during subsequent formation, and layer LL3 will become smaller than its original shape. To avoid this situation, it is preferable that the finishing cut is based on the topmost layer (0 in the figure) and has an upper limit of offset by a predetermined height HLS in the stacking direction. Furthermore, the cutting is preferably limited to reaching the height HLE of the layer unaffected by the shaping process. The portion below height HLE is the part where the finishing cut is completed, equivalent to the portion that does not require re-finishing, but it may also include this portion in the cutting process. Cutting can be performed from top to bottom or bottom to top. Furthermore, to ensure that the topmost layer LL3 remains intact during cutting, as shown in the figure, a lollipop-shaped end mill EM2 is preferably used.

[0066] In addition, Figure 9 In (f), the upper limit height HLS of the cutting height range indicates a state consistent with the upper surface of layer LL2, and the lower limit height HLE indicates a state consistent with the upper surface of layer LL1, but this is only an example. For example, deformation caused by subsequent shaping may not be limited to the uppermost layer LL3, but may sometimes also affect the layer LL2 below it. In this case, the upper limit height HLS is preferably set below layer LL2. Furthermore, even if no subsequent deformation occurs after the finishing cut of layer LL1 is completed, it is possible to eliminate the step at the boundary between layers LL1 and LL2 by cutting including layer LL1. From this perspective, the lower limit height HLE can also be set to overlap with the portion where the finishing cut has been completed.

[0067] Thus, if layer LL4 is formed after the finishing cut, it becomes... Figure 9 The state shown in (g) can be repeatedly executed. Figure 9 The processes (c) to (f). The above describes the finishing cuts for deformations that primarily tend to shrink. In cases of deformations that tend to shrink, the basic idea is to perform finishing cuts on layers that will not deform due to the shape.

[0068] Next, the finishing cutting during deformation that mainly produces an expansion tendency will be explained. Figure 10 This is an explanatory diagram showing how to set the range of cutting heights for expansion tendency. Figure 10 (a) shows the state in which layer LH2 is formed on layer LH1. As mentioned above, under relatively high temperature conditions on the substrate, such as Figure 10 As shown in (b), layer LH2 expands with the martensitic phase transformation. Consequently, layer LH1 also deforms. Therefore, as Figure 10 As shown in (c), finishing cutting is performed on layers LH1 and LH2. In this case, the finishing cutting is performed on the entire layer LH1 and LH2. That is, when the topmost layer of layer LH2 is taken as the reference (0 in the figure), the upper limit height HHS0 of the cutting height range can also be consistent with the reference. In addition, the lower limit height can be the height HHE of the lower surface of layer LH1, which is affected by deformation. After completing the finishing cut, as follows: Figure 10 As shown in (d), a layer LH3 is formed on it, which can be repeated. Figure 10 (b) Figure 10 The process shown in (c).

[0069] exist Figure 10 In (c), the cutting height range of the upper limit height HHS0 and the lower limit height HHS1 is illustrated, but the cutting height range can be set in various ways. For example, if deformation in layer LH2 is anticipated due to subsequent shaping, the cutting height range can also be set by excluding layer LH2. In this case, as... Figure 10 As shown in (c), the upper limit height HHS1 can be set. Furthermore, even if the layers below layer LH1 do not undergo deformation due to the shaping associated with layer LH2, the lower limit height HHE of the cutting height range can be set below layer LH1. This allows for a smoother boundary between layer LH1 and the layers below it. The above describes the finishing cuts used when deformations tend to expand. In cases of deformations that tend to expand, the basic idea is to re-perform finishing cuts on even layers that have only been temporarily finished, until no further deformation due to subsequent shaping occurs.

[0070] Setting the cutting height range ( Figure 7 In step S26), based on Figure 9 and Figure 10 The idea is as shown. For example, based on the heater temperature of the base plate and the contact area between the object and the base plate, it can be determined whether the deformation is likely to cause shrinkage or expansion. Past shaping results can be stored in a database and used as a basis for judgment. Moreover, in either case, it is possible to determine the extent to which the deformation caused by the shaping affects the existing area, based on... Figure 9 , Figure 10 The idea described in the text is to set the upper and lower limits of the height.

[0071] F. Effects and variations: According to the three-dimensional shaping device 10 and the shaping method based on the three-dimensional shaping device 10 described in the embodiments, the shaping accuracy of the object can be improved by using cutting data that predicts deformation, as described below. Figure 11 This is an explanatory graph showing the improvement in accuracy. In Figure 11 In (a), the shape is schematically shown. The Y-axis is defined in the upward direction of the shape, and the displacements XL and XR generated in the side surfaces SL and SR at various locations are measured.

[0072] Figure 11 (b) and (c) represent the displacement generated in the shape when the shape data of the shape is used directly for shaping and cutting without following the method of this embodiment. Figure 11 (b) represents the displacement XL produced on the left lateral side SL. Figure 11 (c) shows the displacement XR generated on the right side SR. Multiple measurements are shown, taken at multiple locations along the depth of the form. (e.g.) Figure 11 As shown in (b) and (c), it can be seen that the displacements XL and XR on the left and right sides SL and SR are greater as they move upwards.

[0073] Figure 11 (d) and (e) represent the displacement generated in the shape when the cutting data is generated in accordance with the method of this embodiment, i.e., when the displacement obtained from the deformation prediction is reflected. Figure 11 (d) represents the displacement XL produced on the left lateral side SL. Figure 11 (e) shows the displacement XR generated on the right-side side SR. For example... Figure 11 As shown in (d)(e), it can be seen that the left and right sides SL and SR have small displacements relative to the shape data at any location. Thus, it is confirmed that the three-dimensional shaping device 10 and the shaping method based on the three-dimensional shaping device 10 according to this embodiment can improve the accuracy of the shaped object.

[0074] According to the three-dimensional shaping device 10 and the shaping method based on the three-dimensional shaping device 10 described in the embodiment, the cutting height range of the finishing cutting is set based on the temperature of the base plate, thereby improving the surface quality of the end face of the shaped object. Figure 12 This is an explanatory diagram showing the result of improved surface quality. Figure 12 (a) schematically shows a shape that primarily exhibits a tendency to contract. As described above, the end face is a downwardly expanding trapezoid, creating an uneven surface. Figure 12(b) is a graphical representation of the state of its end face. With the base plate as the reference, the horizontal axis shows the position in the height direction. On the vertical axis, displacement in the outer direction of the end face is represented as positive, and displacement in the inner direction as negative. For example... Figure 12 As shown in (b), it can be seen that the position of the end face shifts from the outside to the inside as it moves upwards. At a certain moment, it discontinuously changes to an outward displacement, and then gradually shifts inwards again. That is, Figure 12 (b) means Figure 12 A graphical representation of the end face shape of (a). In this example, the surface roughness is calculated as Ra 1.00 μm.

[0075] Figure 12 (c) schematically illustrates a shape that primarily exhibits a tendency to expand. As described above, the end face is an upwardly expanding trapezoid, creating an uneven surface. Figure 12 (d) is a graphic representation of the state of its end face. For example... Figure 12 As shown in (d), it can be seen that the position of the end face shifts from the inside to the outside as it moves upwards. At a certain moment, it discontinuously changes to an inward displacement, and then gradually shifts outwards again. That is, Figure 12 (d) means Figure 12 The figure shows the shape of the end face of (c). In this example, the surface roughness is calculated as Ra 0.48 μm.

[0076] Figure 12 (e) represents the result of finishing cuts performed after setting the cutting height range, as in this embodiment. It can be seen that, compared to... Figure 12 Compared to (b) and (d), it clearly suppresses displacement variation. That is, in Figure 12 In example (e), it was confirmed that the unevenness of the sides of the object was suppressed, resulting in improved surface quality. Figure 12 In example (e), the surface roughness is calculated as Ra 0.24 μm. Thus, it has been confirmed that, according to this embodiment, by setting the cutting height range for finishing cuts based on factors such as the temperature of the base plate, the surface quality of the end face of the object can be improved.

[0077] The various features described in this embodiment do not necessarily need to be fully satisfied, and some of them may be omitted or combined appropriately. Furthermore, the present invention is not limited to this embodiment and can be configured in various variations. This invention is not limited to the powder bed method described in the embodiments, but can be applied to various shaping methods that melt and solidify powder.

[0078] Industrial availability This invention can be used to improve the accuracy of three-dimensional shaping, which is formed by repeatedly melting and solidifying powder and cutting it to create three-dimensional objects.

[0079] Explanation of reference numerals in the attached figures 10 Three-dimensional shaping devices 11 Laser Irradiation Section 12 hoppers 13 Powder Spreader 14 shaping tables 15 mobile mechanisms 20 Cutting section 30 control devices 31 Data Input Section 32 Shaping Control Department 33 Heater Control Section 34 Cutting Control Unit 35-layer control unit 40 cutting tools 41 blade 42 axes 50 Cutting Data Generation Device 51 Form Database 52 Deformation Prediction Department 53 Machine Learning Department 54. Cutting Data Generation Department.

Claims

1. A three-dimensional shaping device for shaping three-dimensional objects, wherein, The three-dimensional modeling device includes: The input unit reads in the shape data of the object. The shaping section melts and solidifies the powder, forming a portion of the object according to the shape data; A moving mechanism that moves the portion and the shaping part relative to each other, so as to attach the formed portion to form the next portion; The cutting section is used to cut the completed part; as well as The control unit controls the repeated execution of the shaping by the shaping unit and the moving mechanism, as well as the cutting by the cutting unit, thereby shaping the object. The control unit predicts the deformation that will occur in the portion after the cutting due to the stress accompanying the shaping, and performs the cutting based on cutting data that is corrected to fit the shape data in order to produce the deformation.

2. The three-dimensional shaping device according to claim 1, wherein, The device includes a cutting data generation unit that generates the cutting data by simulating the deformation caused by the stress and reflecting the prediction result in the shape data.

3. The three-dimensional shaping device according to claim 2, wherein, The cutting data generation unit uses the simulation to predict the deformation generated in the cutting data and reflects the difference between the deformed shape and the shape data, thereby updating the cutting data.

4. The three-dimensional shaping device according to claim 1, wherein, The device includes a cutting data generation unit that predicts the deformation caused by the stress based on a database and reflects the prediction result in the shape data to generate the cutting data. The database stores past shapes and the deformations in those shapes caused by the stress.

5. The three-dimensional shaping device according to claim 1, wherein, The control unit performs the cutting process by excluding the portion generated by the shaping process, which is repeated by the shaping unit and the moving mechanism, based on the number of steps specified from the previous step.

6. The three-dimensional shaping device according to claim 1, wherein, The shaping section is a mechanism that melts and solidifies the powder on a base plate for holding the shaped object to form a thin layer that is part of the shaped object. A heater is provided for heating the base plate. The control unit controls the heating by the heater so that the warpage of the base plate accompanying the shaping converges below a specified requirement value.

7. The three-dimensional shaping device according to claim 1, wherein, The shaping section is a mechanism that melts and solidifies the powder on a base plate for holding the shaped object to form a thin layer that is part of the shaped object. A heater is provided for heating the base plate. The control unit sets the cutting height range of the thin layer in the stacking direction based on the set temperature of the heater and the area of ​​the thin layer that is bonded to the base plate.

8. A three-dimensional modeling method for modeling a three-dimensional object using a three-dimensional modeling device, wherein, The three-dimensional modeling method has the following features: (a) The step of reading in the shape data of the object; (b) The step of melting and solidifying the powder and forming a portion of the shape according to the shape data; (c) Repeat step (b) to attach steps to the completed portion to form the next portion; and (d) The steps for cutting the completed portion. Step (d) is a step that involves predicting the deformation of the portion that will occur in the portion after the cutting due to the stress accompanying the shaping, and performing the cutting based on cutting data that has been corrected in a manner that is suitable for the shape data in order to produce the deformation.

9. A computer program that generates cutting data for use in a three-dimensional shaping apparatus, the three-dimensional shaping apparatus repeatedly performing the shaping of portions of a three-dimensional object by melting and solidifying powder, and the cutting of the completed portions thereby shaping the object, wherein... The following functions can be achieved using a computer: The function of reading the shape data of the object; and The function predicts the deformation of the portion due to the stress accompanying the shape after the cutting and generates cutting data, which is corrected in a manner suitable for the shape data based on the deformation.

10. A computer program that generates cutting data for use in a three-dimensional shaping apparatus, the three-dimensional shaping apparatus repeatedly performing the shaping of portions of a three-dimensional object by melting and solidifying powder, and the cutting of the formed portions thereby shaping the object, wherein... The following functions can be achieved using a computer: The function of reading the shape data of the object; and The function of using a database to predict stress-induced deformation and reflecting the prediction results in the shape data to generate data for the cutting, wherein the database stores past shapes and the deformations in those shapes caused by the stresses accompanying the shape.

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