JP2021188060A - Analyser and analysis method of laminated molding, as well as, molding system of laminated molding - Google Patents

Abstract

To make it possible to properly analyze a state of a laminated molding, in an analyzer of the laminated molding.SOLUTION: An analyzer 110 of a layered molding which predicts the temperature distribution during molding of a laminated molding 180 by numerical analysis is provided with analysis portions 104, 105 that predicts a temperature distribution during molding of a laminated molding 180, by using a heat source model expressed by the received superior Gaussian distribution parameter PS and a double elliptical parameter PE, the physical properties of the material used in the lamination molding, and a molding condition.SELECTED DRAWING: Figure 1

Description

The present invention relates to an analysis device and an analysis method for a laminated model, and a modeling system for a laminated model.

In recent years, laminated modeling technology using powder of metal material, wire, or the like has been researched and developed. In laminated modeling, since the material is repeatedly melted and solidified in a minute region, deformation of the entire modeled object due to residual stress becomes a problem. In addition, it has been confirmed that the mechanical properties are deteriorated due to the formation of voids and unhealthy microstructures inside the laminated model (hereinafter, may be simply referred to as a model). Therefore, it is required to understand the manufacturing method that can satisfy both the final shape and the required specifications of the mechanical characteristics.

In laminated modeling, the output of the heat energy source and the moving speed of the heat source differ greatly depending on the device method. For example, in a laminated molding of a type in which an electron beam is irradiated to a metal powder bed, the maximum output is about 3500 [W] and the maximum moving speed is about 8000 [m / s]. On the other hand, when the heat energy source is a laser, the maximum output is about 400 [W] and the maximum moving speed is about 7 [m / s]. Therefore, the distribution and shape of the heat energy taken into the modeled object varies depending on the laminated modeling method. In addition, the deformation of the modeled object and the internal structure are greatly affected by the heat input form.

Deformation and residual stress of a modeled object are generally analyzed by computer simulation using FEM (Finite Element Method). The simulation technique is also used for selecting the laminated modeling conditions, and various models for predicting the deformation after modeling and the state of the internal structure by numerical analysis have been proposed.
For example, in paragraph 0031 of Patent Document 1 below, "Next, an embodiment of the analysis device 10 will be described. In the embodiment, the shape of the partial model 12 is a rectangular parallelepiped having a length of 5 mm, a width of 5 mm, and a height of 2 mm. In addition, scanning with an electron beam was input as the laminated molding conditions. The heat source has a two-dimensional Gaussian distribution, the heat input amount is about 1000 J / m, the scanning speed is about 300 m / sec, and the laminated thickness is 80 μm. There is. "

Therefore, for example, by applying the technique of Patent Document 1 described above, the temperature distribution at the time of modeling is evaluated by the thermal elasto-plastic analysis using the heat source model of the Gaussian distribution, and the calculated intrinsic strain and the elastic analysis are combined. Therefore, it is considered that the residual stress and deformation of the entire model can be predicted.

Japanese Patent No. 6659407

In the process of manufacturing a modeled object by a laminated modeling method using a material such as a metal material, the heat input condition is important because it not only melts the material but also affects the deformation and internal structure change of the modeled object. It is positioned as a factor. If the amount of heat input is too small, the material may not be sufficiently melted, and unevenness on the surface of the modeled object or voids may be formed inside the modeled object. On the other hand, if the amount of heat input is too large, the molten metal may flow down to the surroundings without solidifying, and even when solidified, it may form a heat-affected layer around and change the internal structure. Further, there is a problem that the entire modeled object is deformed due to residual stress or the like due to the inflow and outflow of heat.

As a method of suppressing and controlling deformation and changes in the internal structure in the laminated modeling process, there is a method of always performing laminated modeling under optimum heat input conditions. If appropriate heat input conditions can be maintained to the extent that an abnormal portion is not formed in the surface state or internal structure, excessive heat energy is not applied to the modeled object and warpage after modeling is reduced. However, it is disadvantageous in that it takes time and cost to make a prototype of a laminated model for each type of material, modeling device, and shape of the model and examine the optimum modeling conditions.

Therefore, there is a demand for a simulation technique using numerical analysis that can efficiently search and examine appropriate modeling conditions. By applying the technique of Patent Document 1 described above, it is possible to numerically analyze the residual stress and deformation of the modeled object based on the heat source model of the two-dimensional Gaussian distribution. However, due to the diversification of laminated modeling methods, modeling devices having a heat input profile other than the Gaussian distribution that has been conventionally used have appeared. Further, depending on the combination of the output of the heat source and the moving speed, the shape of the molten pool changes, and the form of heat input to the modeled object changes. Therefore, an analysis technique based on a heat source model that can be applied to various laminated modeling methods that takes these influences into consideration is desired.

For example, assuming that the heat source has a Gaussian distribution, it may not be possible to properly analyze the state of the laminated model.
The present invention has been made in view of the above circumstances, and an object of the present invention is to provide an analysis device and an analysis method for a laminated model capable of appropriately analyzing the state of a laminated model, and a modeling system for the laminated model. ..

As a result of diligent research, the present inventors have newly found a method for predicting the temperature distribution of a modeled object in laminated modeling of materials with high accuracy in consideration of the molten pool shape and heat input distribution that change depending on the modeling method. .. That is, by expressing the spatial distribution of the input thermal energy with a combination of the dominant Gaussian distribution function and the double ellipse, a prediction model with high prediction accuracy and reproducibility of the temperature distribution of the modeled object is derived, and this prediction is made. We devised a method to use the model to calculate the temperature distribution of the laminated model.

That is, the analysis device for the laminated model according to the preferred embodiment is an analysis device for the laminated model that predicts the temperature distribution during the modeling of the laminated model by numerical analysis, and has a dominant Gaussian distribution parameter and a double elliptical parameter. It is characterized by including an analysis unit that predicts the temperature distribution during modeling of a laminated model using a heat source model expressed using the above, physical property values of materials used in laminated modeling, and modeling conditions. ..

As a result, when predicting the temperature distribution of the modeled object in the laminated modeling of materials by numerical analysis, the dominant Gaussian distribution function representing the spatial distribution of thermal energy and the double ellipse representing the heat input region of the modeled object are used. The heat source model can be used for numerical analysis to obtain the temperature distribution of the laminated model in the laminated model.

Further, the analysis method of the laminated model according to the preferred embodiment is an analysis method of the laminated model that predicts the temperature distribution during the modeling of the laminated model by numerical analysis, and has a dominant Gaussian distribution parameter and a double ellipse. Predicting the temperature distribution during modeling of a laminated model using a heat source model expressed using the parameter assignment process for setting parameters, the dominant Gaussian distribution parameter, and the double elliptical parameter. It is equipped with an analysis process.

Further, the modeling system for the laminated model according to the preferred embodiment includes a modeling device for laminating the laminated model, a measuring device for measuring the state of the laminated model, and an analysis device for the above-mentioned laminated model. The analysis device is characterized by having a modeling control unit that sets laminated modeling conditions for the modeling device based on a comparison result between the analysis result and the measurement result in the measuring device.

According to the present invention, the state of the laminated model can be appropriately analyzed.

FIG. 3 is a block diagram of an analysis system according to a preferred first embodiment. It is a figure which shows the example of the dominant Gaussian distribution function. It is a schematic diagram of the heat input region of a heat source model. It is a figure which shows an example of the temperature distribution data obtained by the analysis. It is a figure which shows the comparison result of the bead width by an experimental value and an analysis value. It is a figure which shows the comparison result of the bead depth by an experimental value and an analysis value. It is a block diagram of the modeling system according to a preferred second embodiment.

[Outline of Embodiment]
A preferred embodiment described below is intended to predict the temperature distribution of a modeled object during layered modeling with high accuracy in consideration of the influence of the molten pool shape and the heat input distribution that change variously depending on the layered modeling method. One of the features of these methods and devices is that the spatial distribution of thermal energy by the dominant distribution function and the setting of the heat input region considering the flow of the molten pool by the double ellipse are added to the heat source model. It is supposed to be. In the method for analyzing the temperature distribution of the laminated model, the analysis device, and the modeling system according to the preferred embodiment, the temperature distribution of the model can be predicted for each type of material used for the laminated model and the modeling conditions. The type of material to be predicted is not particularly limited as long as it is a material to be used for laminated modeling. Specific examples of the materials to be predicted include metal materials such as Ni-based alloys (718 alloys), but other alloys other than Ni-based alloys such as Fe-based alloys, Cu-based alloys, Al-based alloys and the like. May be.

[First Embodiment]
<Overall configuration of the first embodiment>
FIG. 1 is a block diagram of an analysis system 100 according to a preferred first embodiment.
The analysis system 100 is a system for analyzing the temperature distribution of the laminated model 180. In the initial state (before modeling), for example, only a flat plate-shaped substrate 186 is used. Then, a solidified layer is formed by spreading a metal material on the surface of the substrate 186, melting and solidifying, and repeating this to form a laminated body 188, and a laminated model 180 is formed. The metal material may be sprayed onto the modeling site to be melted and solidified. Here, the two axes orthogonal to each other on the plane along the surface of the substrate 186 are referred to as the x-axis and the y-axis. Further, the axis orthogonal to the x-axis and the y-axis is called the z-axis.

However, the laminated model 180 may be a processed product that is subjected to layered modeling in the manufacturing process. That is, the laminated model 180 may be a product manufactured by combining an arbitrary material other than the laminated model and an arbitrary processing method. Further, in the example shown in FIG. 1, the laminated model 180 has a substantially rectangular parallelepiped shape, but the laminated model 180 is not particularly limited by the shape to be processed and molded.

The modeling apparatus 172 has a function of spreading a metal material on the surface of the laminated model 180 and irradiating the spread metal material with a laser or the like. When irradiated with a laser or the like, a heat source 182 is formed on the portion of the metal material. Then, a molten pool 184 in which the metal material is melted is formed in and around the heat source 182. In the illustrated example, the molten pool 184 is larger than the heat source 182, but the molten pool 184 may be smaller than the heat source 182. When the modeling apparatus 172 moves the heat source 182, the molten pool 184 is cooled to solidify, and the portion of the laminated model 180 is formed.

The analysis system 100 includes an analysis device 110, an input device 132, and a display device 134. The analysis device 110 includes hardware as a general computer such as a CPU (Central Processing Unit), a RAM (Random Access Memory), and a storage device, and the storage device includes an OS (Operating System), an application program, and the like. Various data etc. are stored. Here, the storage device is a ROM (Read Only Memory), an SSD (Solid State Drive), a flash memory, a hard disk, an optical disk, or the like. The OS and application programs stored in the storage device are expanded in RAM and executed by the CPU.

In FIG. 1, the inside of the analysis device 110 shows a function realized by an application program or the like as a block. That is, the analysis device 110 includes a material model storage unit 101, a laminated modeling condition storage unit 102, a heat source model storage unit 103 (parameter addition process, parameter addition unit), and a heat conduction analysis unit 104 (analysis process, analysis unit). A temperature distribution extraction unit 105 (analysis step, analysis unit) and an evaluation unit 106 are provided.

The material model storage unit 101 stores the material model parameter PM. Further, the laminated modeling condition storage unit 102 stores the laminated modeling condition parameter PL. Further, the heat source model storage unit 103 stores the dominant distribution parameter PS and the bi-elliptic transfer parameter PE. The details of these parameters PM, PL, PS, and PE will be described later.

The heat conduction analysis unit 104 analyzes the heat conduction state in each part of the laminated model 180 by FEM (Finite Element Method) based on the above-mentioned parameters PM, PL, PS, and PE. Further, the temperature distribution extraction unit 105 calculates the temperature distribution in the laminated model 180 based on this heat conduction state. The evaluation unit 106 calculates the strain, deformation, residual stress, etc. generated in the laminated model 180 based on the temperature distribution, and predicts the quality of the laminated model 180. Thereby, the analysis device 110 can calculate the predicted value of the temperature distribution in the laminated modeling of the laminated model 180 for each type of the arbitrary laminated material and any arbitrary laminated modeling condition, and predict the quality thereof.

The input device 132 inputs the above-mentioned parameters PM, PL, PS, and PE to the analysis device 110. The input device 132 can be configured by, for example, various devices such as a keyboard, a mouse, a touch pad, and a trackball. The display device 134 displays the analysis result in the heat conduction analysis unit 104, the temperature distribution calculated by the temperature distribution extraction unit 105, the evaluation result in the evaluation unit 106, and the like. For example, various display devices such as a liquid crystal display, a plasma display, an organic EL display, and a cathode ray tube can be applied to the display device 134.

<Details of parameters>
Next, the details of the above-mentioned parameters PM, PL, PS, and PE will be described.
First, the material model parameter PM is a physical property value of the material applied to the laminated model 180, and includes, for example, the thermal conductivity, specific heat, density, and heat transfer coefficient of the material. By substituting the thermal conductivity, specific heat, and density into the heat conduction equation, the temperature distribution inside the model and its time change can be obtained. Further, by using the heat transfer coefficient, it is possible to analyze the heat conduction between the surface of the modeled body and the fluid around the modeled body. Further, the laminated modeling condition parameter PL includes the shape and modeling path of the model of the laminated modeling object 180, the energy input from the modeling device 172 to the heat source 182, the moving speed of the heat source 182, and the like. The shape of the model of the laminated model 180 includes the shape of the substrate 186, the shape of the laminated model 180 after modeling, and the like. Further, the "modeling path" is data indicating in what order the laminated modeling is performed from the state of only the substrate 186 at the start of modeling to the final shape of the laminated model 180 after modeling. The shape of the model determines the area in which the heat conduction analysis is performed. In addition, heat energy is input from a heat energy source such as a laser according to the modeling path, and the temperature distribution of the modeled object and its time change are calculated by analyzing the heat conduction equation each time.

Further, the dominant distribution parameter PS and the bi-elliptic transfer parameter PE are parameters that describe the model of the heat source 182, that is, the heat source model. The heat source model is expressed by the dominant Gaussian distribution function of the following equation (1) using the dominant Gaussian distribution parameter PS and the bi-elliptic transfer parameter PE.

However, in the formula (1), Q is the thermal energy density, k is the distribution parameter, β is the coefficient value Γ is the gamma function, a, b, and c are the radius lengths, η is the thermal efficiency, and W is the input energy from the modeling apparatus 172. Is. Thermal efficiency is determined by the combination of modeling equipment, materials of the model, and the type of heat energy source. Also, exp is a power of the Napier number.
Of the parameters in these equations (1), the radius lengths a, b, and c are included in the bi-elliptic transfer parameter PE. The radius lengths a, b, and c are parameters that determine the shape of the heat input region 301 (see FIG. 3), and the details thereof will be described later. Further, the distribution parameter k and the coefficient value β are included in the dominant distribution parameter PS. Further, the thermal efficiency η and the input energy W are included in the laminated molding condition parameter PL. In the formula (1), the spatial distribution of thermal energy can be optimized by changing the value of k.

The distribution parameter k shown in the formula (1) is used as the distribution parameters k1, k2, k3 (first, second, and third distribution parameters) corresponding to the x-axis, y-axis, and z-axis shown in FIG. 1, respectively. , May be set independently. In that case, the mathematical formula (1) becomes the following mathematical formula (2).

The distribution parameters k, k1, k2, and k3 in the formulas (1) and (2) are not particularly limited as long as they exceed "1". For example, the distribution parameters k, k1, k2, and k3 can be in the range of "1.2 or more and 100 or less".
The distribution parameter k shown in the formula (1) is independently set as the distribution parameters k1, k2, k3 (first, second, and third distribution parameters) corresponding to the x-axis, y-axis, and z-axis, respectively. As a result, the degree of freedom of the function is increased, and as a result, the reproduction accuracy of the heat source shape is improved. For example, when the thermal conductivity is different in the x-axis direction, the y-axis direction, and the z-axis direction, the distribution parameters k1, k2, and k3 can be set according to the thermal conductivity in each direction. Further, for example, in a thermal energy source using a laser, the formation position of the top hat shape can be arbitrarily manipulated by improving the beam forming technique.

Here, the top hat shape refers to a shape having a dominant distribution such as the characteristics LA2, LA5, LA10, and LA100 shown in FIG. Compared with the Gaussian distribution shown in the characteristic LA1, if the heat source is a top hat type, it is possible to clarify the distinction between the part that should be heated and the part that should not be heated, and it is considered that the degree of freedom of modeling is increased. Therefore, it is expected that the number of application examples will increase in the future. Therefore, the heat energy source such as a laser can correspond to a modeling device capable of generating a top hat type heat source having anisotropy, which is expected to increase in the future.

FIG. 2 is a diagram showing an example of a dominant Gaussian distribution function according to the mathematical formula (1).
The vertical axis of FIG. 2 is the thermal energy density Q, and the horizontal axis is the coordinate value x in the x-axis direction. Further, the coefficient value β in the mathematical formula (1) is “3”. The characteristic LA1 in the figure is an example of the characteristic by the Gaussian distribution function with “k = 1”, and is shown for reference. As shown in the figure, in the characteristic LA1, the distribution of the thermal energy density Q is such that it is localized at the position of the coordinate value x = 0. The characteristics LA2, LA5, LA10, and LA100 are examples of the characteristics based on the dominant Gaussian distribution function, in which "k = 2", "k = 5", "k = 10", and "k = 100", respectively. .. As shown in the figure, as the distribution parameter k becomes larger, the maximum value of the thermal energy density Q becomes smaller, but the thermal energy density Q becomes a characteristic that spreads over a wide range.
Assuming that the thermal energy density Q is a function of only the coordinate values x in the x-axis direction, the spatial distribution of the thermal energy density Q can be obtained by using the following mathematical formula (3).

In general, the Gaussian distribution has often been used in the FEM heat source model for analyzing welding phenomena. However, in laminated modeling, many volumes are formed in a short time, so the heat energy distribution is often adjusted so that heat reaches a relatively wide range. Therefore, since the shape in which the energy density spreads over a wide range matches as described above, the heat input phenomenon peculiar to the laminated molding can be appropriately expressed by introducing the dominant Gaussian distribution parameter PS into the heat source model.

Further, FIG. 2 shows a case where the radius length a is 1.5 [mm] as an example. In FIG. 2, when the coordinate value x exceeds the radius length a = 1.5 [mm], the thermal energy density sharply decreases. Therefore, the radius length a serves as a guideline for the heat input radius in the x direction. Further, the ratio Q (a) / Q (0) of the thermal energy density Q (a) when x = a and the thermal energy density Q (0) when x = 0 is always "1 / e ^β ". ("1 / e ³ " in the illustrated example). The coefficient value β is not limited to “3”, and any value can be applied. In the formula (3), the coefficient part "(2k3 ^{1 / 2k} / Γ (1 / 2k) a)" before the exponential function is when the thermal energy density is integrated over the entire interval (x is from 0 to infinity). The integral value of is set to 1. However, as a heat source model, when setting an integral section of thermal energy in a finite region, it is advisable to determine the coefficient portion so as to match the total heat energy input to the laminated model.

FIG. 3 is a schematic diagram of the heat input region 301 of the heat source model using the bi-elliptic transfer parameter PE.
In FIG. 3, the heat input region 301 is a range in which the heat energy input from the modeling apparatus 172 is applied in the laminated model 180 (see FIG. 1). The heat input region 301 has a shape in which a three-dimensional region whose surface satisfies ^{"x 2} / a ² + y ² / b ² + z ² / c ^{2 = 1" is divided in half along the xy plane.} .. Further, in the illustrated example, the heat source traveling direction DP is equal to the x-axis direction.

The projected shape 302 shown in FIG. 3 is a shape in which the heat input region 301 is projected onto the xy plane. Similarly, the projected shapes 303 and 304 are shapes in which the heat input region 301 is projected onto the xz plane and the yz plane, respectively. The projected shape 302 has an elliptical shape in which the radius length a is the semi-major axis and the radius length b is the semi-minor axis. The projected shape 303 has a shape of only the lower half of an ellipse having a radius length a as a semi-major axis and a radius length c as a semi-minor axis. Further, the projected shape 304 has only the lower half of an ellipse having a radius length b having a semi-major axis and a radius length c having a semi-minor axis. The shape of the heat input region 301 formed as described above is called a "double ellipse".

The radius lengths a, b, and c are set according to the region where the thermal energy is taken into the laminated model 180. In the welding phenomenon, the heat input region 301 extends in the heat source traveling direction DP due to the convection motion of the molten material and the movement of the heat source, so that the radius length a is generally larger than the radius length b. However, in laminated modeling, the heat source may move in a complicated manner according to the modeling path, and the present invention is not limited to the case where the radius length a is larger than the radius length b. Similarly, with respect to the relationships between the other radius lengths a, b, and c, there is no specific magnitude relationship. Therefore, it is advisable to set arbitrary values for each of the radius lengths a, b, and c according to the modeling conditions.

<Example>
Next, examples in this embodiment will be described.
In the embodiment, a laser beam was input to a substrate 186 (see FIG. 1) of a Ni-based alloy (718 alloy) to form a 50 mm linear bead accompanied by melting and solidification. The dimensions of the Ni-based alloy substrate 186 were 100 mm in length × 100 mm in width × 10 mm in thickness. Table 1 shows the output of the laser beam from the thermal energy source as four levels of 1.2 kW, 1.6 kW, 2.0 kW, and 2.4 kW, and the moving speed as three levels of 500 mm / min, 1000 mm / min, and 2000 mm / min. The six combination conditions shown were applied.

For the material model parameter PM (see FIG. 1), the physical property values calculated by the thermodynamic model from the composition of the 718 alloy, that is, the thermal conductivity, the specific heat, the density and the heat transfer coefficient were adopted. However, as the physical property value, an experimentally obtained database may be adopted.
Based on the heat conduction analysis results, the temperature distribution data of the substrate was extracted, and the bead shape formed by melting with a laser beam was measured. The boundary between the melted portion and the unmelted portion was the solid phase temperature of the 718 alloy composition. That is, in the laminated molding process, the region where the maximum temperature reached was equal to or higher than the solidus temperature was determined as a bead, and its shape was measured.

FIG. 4 is a diagram showing an example of temperature distribution data obtained by analysis.
In FIG. 4, the laminated model 420 is being modeled along the heat source traveling direction DP. In this laminated model 420, the temperature distribution at a certain timing is shown as, for example, the temperature distribution 401. On the other hand, in the cross section perpendicular to the heat source traveling direction DP, the bead width 403 and the bead depth 404 of the finally formed straight bead can be calculated by using the maximum temperature distribution data 402 of the laminated model 420. ..

FIG. 5 is a diagram showing a comparison result of bead widths based on experimental values and analytical values. Further, FIG. 6 is a diagram showing a comparison result of the bead depth based on the experimental value and the analytical value.
In FIGS. 5 and 6, the vertical axis of each is the bead width and the bead depth, and the horizontal axis of both figures is the unit heat input [J / mm] obtained by dividing the output by the velocity. The characteristics LB1 and LC1 in FIGS. 5 and 6 are examples of characteristics based on experimental values. On the other hand, the characteristics LB2 to LB5 and LC2 to LC5 are analysis results based on models M2 to M5 (not shown), respectively.

Here, the models M2 to M5 are the following models.
M2 (characteristics LB2, LC2): It has a dominant distribution (k> 1) and has a relationship of “a> b” in radius lengths a and b.
M3 (characteristics LB3, LC3): It has a dominant distribution (k> 1) and has a relationship of “a = b” in radius lengths a and b.
M4 (characteristics LB4, LC4): It has a Gaussian distribution (k = 1) and has a relationship of “a> b” in radius lengths a and b.
M5 (characteristics LB5, LC5): It has a Gaussian distribution (k = 1) and has a relationship of “a = b” in radius lengths a and b.
In the models M3 and M5 in which the radius lengths a and b have a relationship of "a = b", the projected shape 302 (see FIG. 3) with respect to the xy plane is circular. Further, for parameters other than those described above, a certain parameter set is applied to each model M2 to M5 so as to be closest to the characteristics LB1 and LC1 according to the experimental values.

In the model M5 (characteristics LB5 and LC5), the change in both the bead width and the bead depth becomes very steep with respect to the change in the unit heat input, and the tendency of the experimental values (characteristics LB1, LC1) is almost reproduced. No. It is considered that this is because the thermal energy density distribution in the corresponding model is localized in the center. Further, according to the characteristic LB3 of the model M3, the slope of the graph becomes more gentle with respect to the bead width, and the characteristic LB1 is closer to the experimental value than the characteristic LB5. However, according to the characteristic LC3, the model M3 shows almost no improvement in bead depth.

On the other hand, according to the model M2 (characteristics LB2, LC2) in which the dominant distribution and the heat input region of the double ellipse (a> b) are set, both the bead width and the bead depth are the experimental values in the characteristics LB1 and LC1. It best reproduces the trend of change. As described above, according to the analysis method according to the first embodiment, since the thermal energy density distribution by the dominant Gaussian distribution function characteristic in the laminated molding and the heat input region by the double ellipse are applied, various laminated molding conditions are applied. On the other hand, it is possible to obtain an analysis result that appropriately reproduces the experimental value.

Further, according to the present embodiment, a model having a Gaussian distribution and a model having a heat input region having a circular upper surface (a = b) can be expressed according to the specifications of the modeling device 172, so that various modeling devices 172 can be expressed. The temperature distribution in the laminated model 180 during modeling can be analyzed with. Further, according to the present embodiment, since the temperature distribution of the laminated model 180 under various laminated modeling conditions can be confirmed prior to the experiment, an appropriate laminated modeling for modeling the desired laminated model 180 can be confirmed. Conditions (eg, thermal energy source output, scanning speed, etc.) can be selected.

[Second Embodiment]
FIG. 7 is a block diagram of the modeling system 150 according to the preferred second embodiment. In the following description, the same reference numerals may be given to the parts corresponding to the respective parts of the first embodiment described above, and the description thereof may be omitted.
In FIG. 7, the modeling system 150 is a system that analyzes the state of the laminated model 180 based on the same principle as that of the first embodiment, determines the laminated modeling conditions based on the analysis result, and models the laminated model 180. be.

The modeling system 150 includes a modeling control device 120, an input device 132, a display device 134, a modeling device 172, and a measuring device 174. Similar to the analysis device 110 (see FIG. 1) of the first embodiment, the modeling control device 120 includes hardware as a general computer such as a CPU, RAM, and a storage device, and the storage device includes an OS. , Application programs, various data, etc. are stored.

In FIG. 7, the inside of the modeling control device 120 shows a function realized by an application program or the like as a block. That is, the modeling control device 120 includes a material model storage unit 101, a laminated modeling condition storage unit 102, a heat source model storage unit 103, a heat conduction analysis unit 104, a temperature distribution extraction unit 105, an evaluation unit 106, and a database. It includes 107 and a modeling control unit 162.

The measuring device 174 monitors the laminated model 180, and includes a camera that captures a moving image of the laminated model 180, an infrared thermography that measures the temperature distribution on the surface of the laminated model 180, and the like. The modeling system 150 can grasp the shape of the molten pool 184 and the like from the moving image. The functions of the heat conduction analysis unit 104 and the temperature distribution extraction unit 105 are the same as those of the analysis system 100 (see FIG. 1) of the first embodiment. That is, the heat conduction analysis unit 104 predicts the heat conduction state in each part of the laminated model 180 based on the parameters PM, PL, PS, and PE.

Further, the temperature distribution extraction unit 105 calculates a predicted value of the temperature distribution in the laminated model 180 based on the predicted heat conduction state. The database 107 stores the heat conduction state analyzed by the heat conduction analysis unit 104 in the past, the temperature distribution calculated by the temperature distribution extraction unit 105 in the past, and the like.

The evaluation unit 106 compares the predicted value of the temperature distribution calculated by the temperature distribution extraction unit 105 with the measured value of the temperature distribution measured by the measuring device 174. Then, the modeling control unit 162 controls the modeling device 172 while modifying the laminated modeling conditions based on the comparison result between the predicted value of the temperature distribution and the measured value.

In other words, in the modeling system 150, the process of setting the laminated modeling conditions of the laminated model 180 by the modeling control unit 162 and the temperature distribution during modeling of the laminated model 180 are predicted by the temperature distribution extraction unit 105 by numerical analysis. It is possible to execute a step, a step of modeling the laminated model 180 by the modeling device 172, and a step of monitoring the laminated model 180 by the measuring device 174.

In the step of setting the laminated modeling condition of the laminated model, at least the output of the heat source 182 and the moving speed of the heat source 182 are set as the laminated modeling condition. As the set values of the output and the moving speed of the heat source 182, the representative values corresponding to any modeling state such as the initial heat source output value at the start of the laminated modeling and the initial moving speed are set for each laminated modeling condition to be laminated. Can be set.

As described above, the temperature distribution of the laminated model 180 can be predicted by the temperature distribution extraction unit 105. However, since the heat conduction state, the temperature distribution, and the like analyzed in the past are stored in the database 107, the temperature distribution extraction unit 105 may predict the temperature distribution based on the data stored in the database 107. As described above, the modeling control unit 162 can obtain the laminated modeling conditions predicted to realize the desired temperature distribution by analysis in advance, or can be obtained based on the data stored in the database 107. .. Therefore, the modeling control unit 162 may set the laminated modeling conditions predicted to realize a desired temperature distribution as the initial laminated modeling conditions.

The modeling device 172 models the laminated model 180 based on the layered modeling conditions set by the modeling control unit 162. That is, the modeling apparatus 172 uses the set output and moving speed of the heat source 182 to perform laminated modeling on a material of the same type as the material to be predicted. As a result, the temperature distribution of the laminated model 180 becomes close to the predicted value. Then, the measuring device 174 measures the shape of the laminated model 180, the shape of the molten pool 184, the temperature distribution on the surface of the laminated model 180, and the like.

Then, the evaluation unit 106 compares the measurement result by the measuring device 174 with the analysis result predicted by the temperature distribution extraction unit 105, and the temperature distribution, the shape of the molten pool, etc. assumed by this, the actual temperature distribution, and the actual temperature distribution. The degree of deviation from the molten pool shape can be evaluated. For example, the evaluation unit 106 evaluates "the temperature distribution of the laminated model 180 is in a temperature range higher than the analysis result" or "the molten pool area is larger than the analysis result".

In response to such evaluation, the modeling control unit 162 searches past analysis data from the database 107, and outputs a heat source 182 that can realize a temperature distribution lower than the initially assumed temperature distribution and a small heat input region. Search for analysis data corresponding to the movement speed condition. Then, the modeling control unit 162 determines a new laminated modeling condition based on the searched analysis data, and instructs the modeling device 172 of the determined laminated modeling condition. The heat source condition, that is, the condition relating to the heat source 182 is not limited to the output and the moving speed, but may be a spatial distribution of heat energy corresponding to the dominant Gaussian distribution parameter.

As described above, the modeling system 150 of the present embodiment constantly compares the monitoring result by the measuring device 174 with the desired temperature distribution and the shape of the molten pool, and repeatedly resets the laminated modeling conditions as necessary. This makes it possible to control the temperature distribution of the laminated model 180 during modeling so as to approach a desired state.

[Effect of embodiment]
According to the preferred embodiment as described above, the layered model analysis device (110) and the model control device (120) predict the temperature distribution of the layered model (180) during modeling by numerical analysis. A heat source model expressed using a dominant distribution parameter (PS) and a double elliptical parameter (PE) in an object analysis device (110) and a modeling control device (120), and materials used in laminated modeling. It is provided with an analysis unit (104, 105) for predicting a temperature distribution during modeling of a laminated model (180) using physical property values and modeling conditions. Here, the double elliptical parameter PE is a parameter that defines a heat input region 301 in which ^{the heat energy density Q is at least a predetermined ratio (1 / e β} ) with respect to the maximum heat energy density Q (0) in the heat source model. Is.

Further, a preferred embodiment is, from another viewpoint, an analysis method (110) of the laminated model, which predicts the temperature distribution during modeling of the laminated model (180) by numerical analysis, and is a dominant Gaussian distribution parameter. It is expressed using a parameter assignment step (103) for setting (PS) and a double elliptical parameter (PE), a dominant Gaussian distribution parameter (PS), and a double elliptical parameter (PE). It comprises an analysis step (104, 105) for predicting the temperature distribution during modeling of the laminated model (180) using a heat source model.

Thereby, the state of the laminated model 180 can be appropriately analyzed. For example, in order to use a heat source model that takes into account the dominant Gaussian distribution parameter PS that expresses the thermal energy density distribution and the double elliptical parameter PE that expresses the heat input region that takes into account the flow of the molten metal for numerical analysis, it is laminated. The temperature distribution of the object 180 can be predicted with high accuracy. This makes it possible to study the laminated modeling conditions for each material type and modeling conditions without actually making a prototype of the laminated model 180, shortening the process design period and reducing the prototype cost. Can be done.

Further, the dominant Gaussian distribution parameter PS is an independent first, second and third distribution parameter (k1,) corresponding to each of the three-dimensional axial directions (x-axis direction, y-axis direction, z-axis direction). It is preferable to include k2 and k3). Thereby, when the thermal energy density distribution characteristic changes according to the three-dimensional axial direction, the state of the laminated model 180 can be analyzed more appropriately.

Further, it is more preferable that the heat source model is expressed by the above-mentioned mathematical formula (1) or mathematical formula (2). Thereby, in the model in which the heat input region of the double ellipse (a> b) is set, the tendency of the change in the characteristics of the experimental values can be appropriately reproduced.

Further, the physical property values of the materials used in the laminated molding include at least one of thermal conductivity, specific heat, density and heat transfer coefficient, and the molding conditions are the energy of the heat source at the time of molding and the moving speed of the heat source. It is preferable to include it. This makes it possible to more appropriately reproduce the tendency of changes in the characteristics of the experimental values.

Further, the modeling system (150) for the laminated model according to the preferred embodiment includes a modeling device (172) for laminating the laminated model (180) and a measuring device (174) for measuring the state of the laminated model (180). ) And the above-mentioned analysis device (110) for the laminated model, the analysis device (110) is based on the comparison result between the analysis result and the measurement result in the measurement device (174), and the modeling device (172). ), It has a modeling control unit (162) that sets the laminated modeling conditions. Thereby, the laminated modeling conditions can be appropriately adjusted according to the actual situation of the laminated model 180.

[Modification example]
The present invention is not limited to the above-described embodiment, and various modifications are possible. The above-described embodiments are exemplified for the purpose of explaining the present invention in an easy-to-understand manner, and are not necessarily limited to those having all the configurations described. Further, it is possible to replace a part of the configuration of one embodiment with the configuration of another embodiment, and it is also possible to add the configuration of another embodiment to the configuration of one embodiment. Further, it is possible to delete a part of the configuration of each embodiment, or add / replace another configuration. In addition, the control lines and information lines shown in the figure show what is considered necessary for explanation, and do not necessarily show all the control lines and information lines necessary for the product. In practice, it can be considered that almost all configurations are interconnected. Possible modifications to the above embodiment are, for example, as follows.

(1) The material model storage unit 101, the laminated modeling condition storage unit 102, the heat source model storage unit 103, the database 107, etc. (see FIGS. 1 and 7) in each of the above embodiments may be, for example, a cloud or the like on a network (not shown). ), And it does not necessarily have to be included in the analysis device 110 or the modeling control device 120.

(2) Since the hardware of the analysis device 110 or the modeling control device 120 in the above embodiment can be realized by a general computer, a program or the like for executing the above-mentioned various processes is stored in a storage medium or via a transmission path. You may distribute it.

(3) Each of the above-mentioned processes has been described as a software-like process using a program in the above embodiment, but a part or all of them may be an ASIC (Application Specific Integrated Circuit) or an FPGA (Field). It may be replaced with hardware-like processing using Programmable Gate Array) or the like.

103 Heat source model storage unit (parameter application process, parameter application unit)
104 Heat conduction analysis unit (analysis process, analysis unit)
105 Temperature distribution extraction unit (analysis process, analysis unit)
110 Analytical device 150 Modeling system 162 Modeling control unit 172 Modeling device 174 Measuring device 180 Laminated model PE Double ellipse parameter PS Superior Gaussian distribution parameter k1, k2, k3 Distribution parameter (1st, 2nd and 3rd distribution parameters) )

Claims (11)

It is an analysis device for laminated objects that predicts the temperature distribution during modeling of laminated objects by numerical analysis.
Predicting the temperature distribution during modeling of a laminated model using a heat source model expressed using a dominant Gaussian distribution parameter and a double ellipse parameter, physical property values of materials used in laminated modeling, and modeling conditions. An analysis device for laminated objects, characterized by having an analysis unit. The analysis of the laminated model according to claim 1, wherein the dominant distribution parameter includes independent first, second, and third distribution parameters corresponding to each of the three-dimensional axial directions. Device. The heat source model is expressed by the following mathematical formula (1).

In the formula (1), Q is the heat energy density, k is the distribution parameter, β is the coefficient value, Γ is the gamma function, x is the coordinate value in the x-axis direction, which is the traveling direction of the heat source, and y is along the laminated model. The coordinate values in the y-axis direction orthogonal to the x-axis direction, z are the coordinate values in the x-axis direction and the z-axis direction orthogonal to the y-axis direction, and a, b, and c are the x-axis direction and the y-axis direction, respectively. , The radius length in the z-axis direction, η is the thermal efficiency, W is the input energy from the modeling device, a, b, c are included in the double elliptical parameter, and the coefficient value β and the distribution parameter k are the dominant Gaussian characteristics. The analyzer for analyzing a laminated model according to claim 1, wherein the device is included in a distribution parameter. The heat source model is expressed by the following mathematical formula (2).

In the formula (2), Q is the heat energy density, β is the coefficient value, Γ is the gamma function, x is the coordinate value in the x-axis direction which is the traveling direction of the heat source, and y is the x-axis direction along the laminated model. The coordinate values in the y-axis direction orthogonal to the x-axis direction, z are the coordinate values in the x-axis direction and the z-axis direction orthogonal to the y-axis direction, and a, b, and c are the x-axis direction, the y-axis direction, and the z-axis direction, respectively. The radius length, k1, k2, and k3 are the first, second, and third distribution parameters in the x-axis direction, the y-axis direction, and the z-axis direction, respectively, η is the thermal efficiency, and W is the input energy from the modeling device. The analyzer for analyzing a laminated model according to claim 2, wherein a, b, and c are included in the double elliptical parameter, and the coefficient value β is included in the dominant distribution parameter. The physical property values of the materials used in the laminated molding include at least one of thermal conductivity, specific heat, density and heat transfer coefficient.
The modeling conditions include the energy of the heat source at the time of modeling and the moving speed of the heat source.
The analysis device for a laminated model according to any one of claims 1 to 4, characterized in that. It is an analysis method of a laminated model that predicts the temperature distribution during modeling of a laminated model by numerical analysis.
A parameter assignment process for setting the dominant distribution parameter and the bi-elliptic transfer parameter,
It is characterized by comprising an analysis step of predicting a temperature distribution during modeling of a laminated model using a heat source model expressed using the dominant Gaussian distribution parameter and the double ellipse parameter. Analysis method of laminated model. The method for analyzing a laminated model according to claim 6, wherein the dominant distribution parameter includes independent first, second, and third distribution parameters corresponding to each of the three-dimensional axial directions. .. The heat source model is expressed by the following mathematical formula (1).

In the formula (1), Q is the heat energy density, k is the distribution parameter, β is the coefficient value, Γ is the gamma function, x is the coordinate value in the x-axis direction, which is the traveling direction of the heat source, and y is along the laminated model. The coordinate values in the y-axis direction orthogonal to the x-axis direction, z are the coordinate values in the x-axis direction and the z-axis direction orthogonal to the y-axis direction, and a, b, and c are the x-axis direction and the y-axis direction, respectively. , The radius length in the z-axis direction, η is the thermal efficiency, W is the input energy from the modeling device, a, b, c are included in the double elliptical parameter, and the coefficient value β and the distribution parameter k are the dominant Gaussian characteristics. The method for analyzing a laminated model according to claim 6, wherein the layered object is included in the distribution parameter. The heat source model is expressed by the following mathematical formula (2).

In the formula (2), Q is the heat energy density, β is the coefficient value, Γ is the gamma function, x is the coordinate value in the x-axis direction which is the traveling direction of the heat source, and y is the x-axis direction along the laminated model. The coordinate values in the y-axis direction orthogonal to the x-axis direction, z are the coordinate values in the x-axis direction and the z-axis direction orthogonal to the y-axis direction, and a, b, and c are the x-axis direction, the y-axis direction, and the z-axis direction, respectively. The radius length, k1, k2, and k3 are the first, second, and third distribution parameters in the x-axis direction, the y-axis direction, and the z-axis direction, respectively, η is the thermal efficiency, and W is the input energy from the modeling device. The method for analyzing a laminated model according to claim 7, wherein a, b, and c are included in the double elliptical parameter, and the coefficient value β is included in the dominant distribution parameter. The analysis step is
The physical property values of the materials used in the laminated molding include at least one of thermal conductivity, specific heat, density and heat transfer coefficient.
The method for analyzing a laminated model according to any one of claims 6 to 9, wherein the energy of the heat source at the time of modeling and the moving speed of the heat source are used as the modeling conditions. A modeling device that laminates and models laminated objects,
A measuring device that measures the state of the laminated model, and
The device for analyzing a laminated model according to any one of claims 1 to 5 is provided.
The analysis device is characterized by having a modeling control unit for setting laminated modeling conditions for the modeling device based on a comparison result between the analysis result and the measurement result of the measuring device. system.

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