Analysis program and method for analyzing hot water flow

Abstract

The provisional temperature gradient T of the molten metal 11 set in the analysis area R n 'Based on the integral point P n Viscosity coefficient μ of molten metal 11 at n is calculated, and the viscosity coefficient μ n By numerically integrating the above, the average viscosity coefficient μ of the molten metal 11 in the analysis region R is obtained. m The average viscosity coefficient μ of the molten metal 11 is calculated. m The calculation process is performed at the integral point P n The number of iterations is changed, and the average viscosity coefficient μ m Among the calculation processes, the calculated average viscosity coefficient μ m is within a predetermined threshold and the number of integration points is the smallest. n Integration point P during molten metal flow analysis n That is, the average viscosity coefficient μ of the molten metal 11 is set as follows: m The minimum number of integration points necessary to accurately calculate the above is set in advance before performing the flow analysis of the molten metal 11. This allows the flow of the molten metal 11 in the analysis region R near the mold to be analyzed accurately in a short time.

Description

[Technical field]

[0001] The present invention relates to an analysis program and a method for analyzing molten metal flow, and more particularly to an analysis program and a method for analyzing molten metal flow that can analyze the flow of molten metal in an analysis region near a mold in a short time with high accuracy. [Background technology]

[0002] A technique is known that predicts whether or not casting defects will occur in a casting by dividing a mold model into multiple meshes (elements) and analyzing the flow and solidification process of molten metal in those meshes. In order to accurately predict casting defects that will occur on the surface of a casting, it is important to accurately analyze the flow of molten metal near the wall of the mold, which is easily affected by heat.

[0003] As an example of this type of technology, Patent Document 1 describes a technology in which the viscosity coefficient of a molten metal is calculated from the temperature of the molten metal and the flow of the molten metal is analyzed based on the calculated viscosity coefficient. This viscosity coefficient of the molten metal is generally calculated based on the average temperature of the molten metal in the mesh.

[0004] However, during actual casting, the temperature of the molten metal decreases (the viscosity coefficient increases) as it approaches the wall of the mold. Therefore, the method of calculating the viscosity coefficient based on the average temperature of the molten metal in the mesh as described above will underestimate the viscosity of the molten metal in the analysis region between the center of the mesh and the wall of the mold (hereinafter referred to as the "analysis region near the mold"), making it impossible to accurately analyze the flow of the molten metal.

[0005] Particularly in recent years, the demand for large-scale casting equipment such as gigapresses and gigacastings has been increasing. When analyzing such large molds, it is conceivable that the mesh used in the analysis will also become larger. When using a relatively large mesh, in the method of calculating the viscosity coefficient based on the average temperature of the molten metal as described above, the viscosity of the molten metal in the analysis region near the mold will be estimated to be lower. On the other hand, if the mesh size is reduced to accurately evaluate the viscosity of the molten metal in the same region, the total number of meshes will increase and the calculation will require a lot of time.

[0006] Therefore, the applicant of the present application has proposed a method of calculating the average viscosity coefficient of the molten metal by setting a plurality of integration points in the analysis region near the mold and numerically integrating the viscosity coefficients of the molten metal at the plurality of integration points (for example, Non-Patent Document 1). According to this method, even when using a relatively large mesh, the viscosity coefficient of the molten metal in the analysis region near the mold can be accurately calculated. Therefore, the flow of the molten metal in the same region can be accurately analyzed.

Prior Art Documents

Patent Documents

[0007]

Patent Document 1

Non-Patent Documents

[0008]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0009] However, when numerically integrating the viscosity coefficient of the molten metal at a plurality of integration points as in the above-described conventional technology, although the average viscosity coefficient of the molten metal can be accurately calculated by increasing the number of integration points, the time required for the calculation becomes long (the calculation load becomes large). On the other hand, if the number of integration points is reduced too much, the average viscosity coefficient of the molten metal cannot be accurately calculated, so the flow of the molten metal in the analysis region near the mold cannot be accurately analyzed. Therefore, there is a need for a technology that can accurately analyze the flow of the molten metal in the analysis region near the mold in a short time.

[0010] The present invention has been made to meet this requirement, and an object thereof is to provide an analysis program and a molten metal flow analysis method that can accurately analyze the flow of the molten metal in the analysis region near the mold in a short time.

Means for Solving the Problems

[0011] To achieve this object, the analysis program and the molten metal flow analysis method of the present invention include an analysis model setting step of setting an analysis model in which a model of a mold is divided into a plurality of meshes, and among the plurality of meshes set in the analysis model setting step, in a first mesh adjacent to the mold, an integration point setting step of setting an integration point in an analysis region on the wall surface side of the mold for molten metal flow analysis, a viscosity calculation step of calculating the viscosity coefficient of the molten metal based on the temperature of the molten metal at the integration point set in the integration point setting step, an average viscosity calculation step of numerically integrating the viscosity coefficient calculated in the viscosity calculation step to calculate the average viscosity coefficient of the molten metal, and an analysis step of analyzing the flow of the molten metal in the analysis region based on the average viscosity coefficient calculated in the average viscosity calculation step, which are to be executed by a computer, and setting a virtual temperature gradient in the analysis region virtuality temperature setting step, and a virtuality viscosity calculation step of calculating the viscosity coefficient of the molten metal at the integration point set in the analysis region based on the virtual temperature gradient set in the virtuality temperature setting step, and the virtuality virtual temperature gradient virtuality viscosity calculation step, and the virtualityNumerically integrate the viscosity coefficient calculated in the viscosity calculation step to calculate the average viscosity coefficient of the molten metal virtuality An average viscosity calculation step, and the above virtuality Viscosity calculation step and the above virtuality The computer is further made to execute a repetition step of repeating the calculation process of calculating the average viscosity coefficient by the viscosity calculation step and the average viscosity calculation step while changing the number of integration points. The integration point setting step is such that among the calculation processes repeated in the repetition step, the calculated average viscosity coefficient falls within a predetermined threshold value and the integration point with the fewest number of integration points is set as the integration point during the molten metal flow analysis The virtual temperature setting step sets the virtual temperature gradient such that the temperature of the molten metal gradually decreases from the center side of the first mesh to the wall side of the mold. Do.

Effect of the Invention

[0012] According to the analysis program described in claim 1 and the molten metal flow analysis method described in claim 6, in the first mesh adjacent to the mold, an analytical region on the wall surface side of the mold (hereinafter referred to as "analytical region near the mold") has a molten metal virtuality Typical temperature gradient is set. The virtual temperature gradient is a temperature gradient in which the temperature of the molten metal gradually decreases from the center side of the first mesh to the wall side of the mold. This virtuality Based on this typical temperature gradient, the viscosity coefficient of the molten metal at the integration points set in the analytical region near the mold is calculated. By numerically integrating this viscosity coefficient, the average viscosity coefficient of the molten metal in the same region is calculated, and the calculation process of this average viscosity coefficient of the molten metal is repeated while changing the number of integration points.

[0013] Among the calculation processes of the average viscosity coefficient repeated in this way, the calculated average viscosity coefficient falls within a predetermined threshold value and the integration point with the fewest number of integration points is set as the integration point during the molten metal flow analysis. That is, the minimum number of integration points necessary to accurately calculate the average viscosity coefficient of the molten metal is preset before performing the molten metal flow analysis. As a result, there is an effect that the flow of the molten metal in the analytical region near the mold can be accurately analyzed in a short time.

[0014] According to the analysis program described in claim 2, in addition to the effects of the analysis program described in claim 1, when calculating the average viscosity coefficient of the molten metal in the analysis region near the mold, the Gauss-Legendre integration formula is used. Therefore, even when calculating the average viscosity coefficient of the molten metal from a large number of integration points, the calculation load can be reduced. Thus, there is an effect that the flow of the molten metal in the analysis region near the mold can be accurately analyzed in a short time.

[0015] According to the analysis program described in claim 3, in addition to the effects of the analysis program described in claim 1, the following effects are achieved. Mesh adjacent to the first mesh on the wall side of the mold is defined as the second mesh, and mesh adjacent to the first mesh on the side opposite to the second mesh is defined as the third mesh.

[0016] When defined in this way, based on the temperature of the mold in the second mesh and the temperature of the molten metal in the third mesh, the temperature gradient of the molten metal in the first mesh is approximately represented in a curve. By calculating the viscosity coefficient of the molten metal at each integration point based on the temperature gradient approximately represented in a curve in this way, the average viscosity coefficient of the molten metal in the analysis region near the mold can be accurately calculated. Thus, there is an effect that the flow of the molten metal in the same region can be accurately analyzed.

[0017] According to the analysis program described in claim 4, in addition to the effects of the analysis program described in claim 1, the following effects are achieved. When setting an ideal temperature gradient of the molten metal in the analysis region, the temperature at which the molten metal reaches the flow limit solid fraction is set as the temperature of the molten metal on the wall side of the mold, and the liquidus temperature of the molten metal is set as the temperature of the molten metal on the center side of the first mesh. Thereby, the ideal temperature gradient when setting the number of integration points can be approximated to the actual temperature gradient when performing the molten metal flow analysis. Therefore, it becomes easier to set the integration points to an appropriate number, and there is an effect that the flow of the molten metal in the analysis region near the mold can be accurately analyzed in a short time. virtuality When setting an ideal temperature gradient of the molten metal in the analysis region, the temperature at which the molten metal reaches the flow limit solid fraction is set as the temperature of the molten metal on the wall side of the mold, and the liquidus temperature of the molten metal is set as the temperature of the molten metal on the center side of the first mesh. Thereby, the ideal temperature gradient when setting the number of integration points can be approximated to the actual temperature gradient when performing the molten metal flow analysis. Therefore, it becomes easier to set the integration points to an appropriate number, and there is an effect that the flow of the molten metal in the analysis region near the mold can be accurately analyzed in a short time. virtuality When setting an ideal temperature gradient of the molten metal in the analysis region, the temperature at which the molten metal reaches the flow limit solid fraction is set as the temperature of the molten metal on the wall side of the mold, and the liquidus temperature of the molten metal is set as the temperature of the molten metal on the center side of the first mesh. Thereby, the ideal temperature gradient when setting the number of integration points can be approximated to the actual temperature gradient when performing the molten metal flow analysis. Therefore, it becomes easier to set the integration points to an appropriate number, and there is an effect that the flow of the molten metal in the analysis region near the mold can be accurately analyzed in a short time.

[0018] According to the analysis program of claim 5, in addition to the effects of the analysis program of claim 4, the following effects are achieved: virtuality When setting a general temperature gradient, the temperature of the mold is measured from the center of the first mesh. wall A temperature gradient is set so that the temperature of the molten metal decreases proportionally from the surface side. virtuality This has the advantage of reducing the calculation load compared to when the general temperature gradient is approximated as a curve. [Brief description of the drawings]

[0019] [Figure 1] FIG. 1 is an external view of an analysis device showing how molten metal flow analysis is performed using an analysis model. [Figure 2] (a) is a graph that linearly approximates the temperature gradient of the molten metal during the flow analysis in the molten metal mesh, (b) is a graph that shows the virtual temperature gradient of the molten metal in the molten metal mesh, and (c) is a graph that shows the relationship between the number of integration points set in the analysis region and the average viscosity coefficient calculated at those integration points. [Figure 3] 1A is a block diagram showing the electrical configuration of the analysis device, and FIG. 1B is a flowchart of the analysis process. [Figure 4] 10 is a flowchart of an integration point number setting process. [Figure 5] 10 is a flowchart of a molten metal flow analysis process. [Figure 6] 10 is a graph showing a curved approximation of the temperature gradient of the molten metal during a melt flow analysis in the molten metal mesh. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings. First, the overall configuration of the analysis device 1 will be described with reference to FIG. 1. FIG. 1 is an external view of the analysis device 1 showing a state in which the molten metal flow analysis of the molten metal 11 is performed by the analysis model 10. In FIG. 1, the molten metal 11 flowing in the cavity 12a of the mold 12 is provided with dot-shaped hatching, and the cross-section of the mold 12 is provided with dot-shaped hatching that is denser (darker) than the molten metal 11.

[0021] As shown in FIG. 1, the analysis device 1 is an information processing device (personal computer) for dividing the mold 12 defined in the analysis model 10 into a plurality of meshes 13 and analyzing the behavior of the molten metal 11 in the plurality of meshes 13.

[0022] The analysis model 10 is created based on the casting plan read by the user into the analysis device 1. The casting plan is CAD data of the mold 12 designed by the user, etc., and is data of the mold 12 (hereinafter simply referred to as "data of the mold 12") including information such as the shape of the cavity 12a, the position and shape of the sprue 12b (weir), and the cooling structure (for example, the presence or absence of cooling pipes) not shown. The analysis device 1 divides the read data of the mold 12 into a plurality of meshes 13 to create the analysis model 10. The mesh 13 is a solid element of a polyhedron (a hexahedron in this embodiment).

[0023] The analysis device 1 is provided with a mouse 2 and a keyboard 3 (input devices) for the user to input conditions for the molten metal flow analysis of the molten metal 11. The analysis conditions input by the user are information related to casting conditions such as the physical properties of the molten metal 11, the initial temperature, and the pouring speed, in addition to the data of the mold 12 described above.

[0024] The analysis device 1 analyzes (simulates) the flow and solidification processes of the molten metal 11 in each mesh 13 of the analysis model 10 based on the analysis conditions input by the user. The analysis device 1 is provided with a display 4 (display device) for displaying this analysis result. Based on the analysis result of the flow of the molten metal displayed on this display 4, it is possible to predict in advance the locations in the casting manufactured with the mold 12 designed by the user where casting defects are likely to occur.

[0025] As shown in the enlarged portion of FIG. 1, in the following description, the mesh 13 adjacent to the wall surface (inner surface) of the mold 12 is referred to as the molten metal mesh 13c1, and the mesh 13 disposed on the mold 12 adjacent to the molten metal mesh 13c1 is described as the mold mesh 13d1.

[0026] In order to accurately predict the defects occurring on the surface of the casting, it is important to accurately analyze the flow of the molten metal 11 in the analysis region R between the center C of the molten metal mesh 13c1 and the boundary B (the wall surface of the mold 12) between the molten metal mesh 13c1 and the mold mesh 13d1.

[0027] Therefore, in the present embodiment, a plurality of integration points P n (in the example shown in the enlarged portion of FIG. 1, n = 1, 2) are set in the analysis region R near the mold 12, and the viscosity coefficient μ n of the molten metal 11 at the plurality of integration points P n is numerically integrated to calculate the average viscosity coefficient μ m of the molten metal 11 in the analysis region R. In this numerical integration, the Gaussian-Legendre integration formula is used in the present embodiment. This integration method will be described below.

[0028] First, assuming that the element width of the molten metal mesh 13c1 is h and the distance from the boundary B with the mold mesh 13d1 is y (for example, the distance from the boundary B to the integration point P1 is y1), the average viscosity coefficient μ m of the molten metal 11 in the analysis region R can be calculated by the following mathematical formula 1.

[0029]

Equation

[0030]

number

[0031]

number

[0032]

number

[0033]

number

[0034]

number

[0035]

number

[0036]

number

[0037]

Number

[0038]

Number

[0039] As shown in FIG. 2(a), first, through the molten metal flow analysis of the molten metal 11, the temperature T a of the molten metal 11 at the boundary B with the mold 12 during the casting process and the temperature T b of the molten metal 11 at the center C of the molten metal mesh 13c1 are obtained. Assuming that the temperature gradient T n of this molten metal 11 is linear (the temperature of the molten metal 11 decreases proportionally from the center C of the molten metal mesh 13c1 toward the mold 12 side), the temperature T n of the molten metal 11 in the analysis region R can be obtained by the following Equation 11.

[0040]

Number

[0041]

Number

[0042]

Number

[0043] When the integration point P n is three points (P n = P1, P2, P3), if the distances from the boundary B with the mold 12 to each integration point P1, P2, and P3 are y1, y2, and y3 respectively, then y1 = {(√5 - √3)h / 4√5} = (5 - √15)h / 20, y2 = h / 4, y3 = {(√5 + √3)h / 4√5} = (5 + √15)h / 20, x1 = -√15 / 5, x2 = 0, x3 = √15 / 5, ω1 = ω3 = 5 / 9, ω2 = 8 / 9. Substituting the values of x1, x2, x3, ω1, ω2, and ω3 into the above formula 4, the average viscosity coefficient μ of the molten metal 11 in the analysis region R m can be approximated by the following formula 14.

[0044]

Number

[0045]

number

[0046]

number

[0047]

number

[0048] Also, the integral point P n 4 points (P n Similarly, when P1, P2, P3, P4) are set, the average viscosity coefficient μ of the molten metal 11 in the analysis region R is m can be approximated by the following Equation 18.

[0049]

number

[0050] In this way, multiple integration points P nThe viscosity coefficient μ of the molten metal 11 n When numerically integrating, the integration point P n The larger the number of points, the more accurately the average viscosity coefficient μ of the molten metal 11 in the analysis region R can be calculated. However, when analyzing the molten metal flow of the molten metal 11, it is necessary to perform quadrature at each integration point P m for each minute elapsed time dt. Therefore, if the number of integration points P n is too large, the calculation load increases (the calculation time becomes long). Also, if the number of integration points P n is too small, the average viscosity coefficient μ of the molten metal 11 n cannot be accurately calculated. m

[0051] Therefore, in this embodiment, before starting the analysis of the flow of the molten metal 11 by the analysis device 1, the number of appropriate integration points P n is set in advance. The method for setting the number of these integration points P n will be described with reference to FIGS. 2(b) and 2(c). FIG. 2(b) is a graph showing the virtuality approximate temperature gradient T n ' of the molten metal 11 in the molten metal mesh 13c1. The horizontal axis represents the distance y from the wall surface of the mold 12, and the vertical axis represents the temperature T of the molten metal 11. FIG. 2(c) is a graph showing the relationship between the number of integration points P n set in the analysis region R and the average viscosity coefficient μ n calculated at that integration point P m .

[0052] As shown in FIG. 2(b), when setting the number of appropriate integration points P n in advance, first, as the virtual value T a ' of the temperature of the molten metal 11 at the boundary B with the mold 12, the temperature at which the molten metal 11 reaches the flow limit solid fraction is set. Also, as the virtual value T b ' of the temperature of the molten metal 11 at the center C (y = h / 2) of the molten metal mesh 13c1, the liquidus temperature of the molten metal 11 (T a ' < T b ') is set.

[0053] Next, the temperature T a ' of this molten metal 11, T​b Assuming the slope of ' is linear, Tata Thoughts Something like that temperature gradient T n Set this temperature gradient T n ', and the integral point P n The average viscosity coefficient μ of the molten metal 11 is m We will calculate the following.

[0054] Specifically, first, the integral point P n 1 point (P n = P1), and the temperature gradient T n Average viscosity coefficient μ of molten metal 11 based on m Then, calculate the integral point P n 2 points (P n = P1, P2) and the average viscosity coefficient μ of the molten metal 11 m Calculate the average viscosity coefficient μ m Calculation of the integral point P n This is repeated until the number of is sufficiently larger than 1 (for example, n = 256). Note that this average viscosity coefficient μ m The calculation of is performed using the Gauss-Legendre integral (see Equations 1 to 18) described above.

[0055] In this way, the integral point P n The average viscosity coefficient μ of the molten metal 11 is m The integration point P when n and the viscosity coefficient ratio μ m The relationship between the solid fraction and the viscosity of the molten metal 11 is shown in the graph of FIG. 2(c), where μ is the viscosity coefficient of the molten metal 11 at which the solid fraction is 0.

[0056] As shown in Figure 2(c), the integral point P n When the number of is small (for example, n = 1 to 6), the calculated viscosity coefficient ratio μ m / μ0 (average viscosity coefficient μ of molten metal m ) values vary, while the integration point P n When the number of viscosities increases (for example, when n ≥ 7), the calculated viscosity coefficient ratio μ m Therefore, in this embodiment, the calculated viscosity coefficient ratio μm / μ0 (the average viscosity coefficient μ of the molten metal 11 m ) falls within a predetermined threshold value, and the integration point P with the fewest number of integration points n is set as the integration point during the molten metal flow analysis.

[0057] Specifically, when the number of integration points P n is sufficiently larger than 1 (in this embodiment, n = 256), the average viscosity coefficient μ m is used as the reference viscosity coefficient μ ms , and when the viscosity coefficient ratio in that case is the reference viscosity coefficient ratio μ ms / μ0, if the calculated viscosity coefficient ratio μ m / μ0 is within ±0.1% of the reference viscosity coefficient ratio μ ms / μ0 (0.999μ ms ≦μ m ≦1.001μ ms ), and the integration point P with the fewest number of integration points n (for example, n = 7) is extracted. Then, during the molten metal flow analysis of the molten metal 11, the average viscosity coefficient μ n of the molten metal 11 is calculated at the extracted integration point P m .

[0058] In this way, by presetting the integration point P m that can accurately calculate the average viscosity coefficient μ of the molten metal 11 with the minimum necessary precision n (before performing the molten metal flow analysis of the molten metal 11), it is possible to accurately calculate the average viscosity coefficient μ m of the molten metal 11 during the molten metal flow analysis while reducing the calculation load. That is, the flow of the molten metal 11 in the analysis region R can be accurately analyzed in a short time.

[0059] In particular, when the mold 12 is for manufacturing a large-sized casting such as a gigapress (gigacast), the calculation load during the molten metal flow analysis of the molten metal 11 tends to increase. Therefore, it is particularly preferable to preset an appropriate number of integration points P n as in this embodiment.

[0060] Also, for evaluating the appropriate number of integration points P n , the molten metal 11 for virtualityTypical temperature gradient T n When setting the temperature T a ' (see Fig. 2(b)) of the molten metal 11 on the boundary B side with the mold 12, a as the temperature T b ' at which the molten metal 11 reaches the flow limit solid fraction is set, and the temperature T n ' of the molten metal 11 on the center C side of the molten metal mesh 13c1 b is set as the liquidus temperature of the molten metal 11. Thereby, the virtuality typical temperature gradient T n of the molten metal 11 n can be approximated to the temperature gradient T n of the molten metal 11 during the molten metal flow analysis. Therefore, it becomes easier to set the integration point P n to an appropriate number, n and thus the flow of the molten metal 11 in the analysis region R can be accurately analyzed in a short time. n

[0061] Also, by linearly connecting the temperature T a ' at which the molten metal 11 reaches the flow limit solid fraction and the liquidus temperature T b ' of the molten metal 11, the a typical temperature gradient T n of the molten metal 11 b is set. That is, since the temperature gradient T n ' in which the temperature of the molten metal 11 decreases proportionally from the center C side of the molten metal mesh 12c1 to the mold 12 side is set, for example, compared with the case of virtuality curvilinearly approximating the typical temperature gradient T n of the molten metal 11, n the computational load can be reduced. n virtuality typical temperature gradient T n n

[0062] Also, when evaluating the number of appropriate integration points P n in advance or when performing the molten metal flow analysis of the molten metal 11 at the integration point P n , the average viscosity coefficient μ m of the molten metal 11 n is calculated using the above Gaussian-Legendre integration formula. Thereby, even when calculating the average viscosity coefficient μ m of the molten metal 11 from a large number of integration points P n , n m the computational load can be reduced. n m

[0063] ​​​​​​Next, with reference to FIG. 3, the electrical configuration of the analysis device 1 and the analysis process executed by the analysis device 1 will be described. FIG. 3(a) is a block diagram showing the electrical configuration of the analysis device 1, and FIG. 3(b) is a flowchart of the analysis process.

[0064] As shown in FIG. 3(a), the analysis device 1 includes a CPU 5, an HDD (hard disk drive) 6, and a RAM 7, which are connected to an input / output port via a bus line 8. Further, the mouse 2, the keyboard 3, and the display device 4 described above are connected to the bus line 8.

[0065] The CPU 5 is an arithmetic device that controls each unit connected by the bus line 8, and the HDD 6 is a rewritable non-volatile storage device that stores programs, fixed-value data, etc. to be executed by the CPU 5. When the analysis program 6a stored in the HDD 6 is executed by the CPU 5, an analysis process (see FIG. 3(b)) is executed.

[0066] The RAM 7 is a memory for the CPU 5 to store various work data, flags, etc. in a rewritable manner during the execution of the analysis program 6a, and a viscosity coefficient memory 7a and an integration point memory 7b are provided. These memories 7a and 7b are used in the integration point setting process (S3) and the hot flow analysis process (S4) of the analysis process shown in FIG. 3(b), and the details of these processes will be described later with reference to FIG. 4. When an execution instruction of the analysis program 6a is input from the mouse 2 or the keyboard 3, the CPU 5 executes the analysis process.

[0067] As shown in Fig. 3(b), in the analysis process, first, various analysis conditions are set (S1). The analysis conditions set here include the physical properties of the molten metal 11 (casting), the pouring speed of the molten metal 11, the gravitational acceleration, the data of the mold 12, the size of the mesh 13, etc. The physical properties of the molten metal 11 include information such as the density, specific heat, thermal conductivity, solidus temperature, liquidus temperature, data showing the relationship between the solid fraction and temperature, latent heat of solidification, viscosity coefficient (data showing the relationship between temperature and viscosity coefficient), and surface tension. The data of the mold 12 includes information such as the density, specific heat, and thermal conductivity of the mold 12 in addition to the data related to the structure of the mold 12 described above.

[0068] After the analysis conditions are set in the process of S1, the initial conditions for the analysis are set in the process of S2 (S2). In setting these initial conditions, for example, the initial temperatures of the molten metal 11 and the mold 12, and the initial value of the pressure in the cavity 12a of the mold 12 (pressure according to the presence or absence of vacuum pumping) are set. Also, in setting the initial conditions, the initial velocity and fluid fraction of the molten metal 11 are set to zero. The fluid fraction of the molten metal 11 is the ratio of the volume occupied by the molten metal 11 in the volume of the mesh 13 (cavity 12a).

[0069] Note that the conditions set in these processes of S1 and S2 are mainly input by the user using the mouse 2 and the keyboard 3, but a part of the setting may be automatically performed by the analysis program 6a.

[0070] After the initial conditions are set in the process of S2, the appropriate number of integration points P n is set by the integration point number setting process (S3), and the molten metal flow analysis process (S4) of the molten metal 11 is executed with the set number of integration points P n , and a series of processes are terminated. These processes of S3 and 4 will be described with reference to Figs. 4 and 5. Fig. 4 is a flowchart of the integration point number setting process (S3), and Fig. 5 is a flowchart of the molten metal flow analysis process (S4).

[0071] As shown in Fig. 4, in the integration point number setting process (S3), first, the approximate temperature gradient T virtuality of the molten metal 11 in the analysis region R of the molten metal mesh 13c1n ' (see FIG. 2(b)) is set (S10). virtuality Typical temperature gradient T n After setting ', integration point P in analysis region R n was set to one point (n=1) (S11) and set in the analysis region R. virtuality Typical temperature gradient T n 'Based on the integral point P n Viscosity coefficient μ in n After the process of S12, the integral point P n Viscosity coefficient μ in n The average viscosity coefficient μ of the molten metal 11 is calculated by numerically integrating m is calculated (S13), and the calculated average viscosity coefficient μ m (viscosity coefficient ratio μ m / μ0) is stored in the viscosity coefficient memory 7a (S14).

[0072] After the processing of S14, the integral point P n Add 1 to the number of integration points P n It is checked whether the number of integration points P exceeds 256 (S16). n If the number does not exceed 256 (S16: No), the process from S12 onwards is repeated.

[0073] That is, in the processing of S12 to S16, the integral point P n The average viscosity coefficient μ of the molten metal 11 until the number of m The process of calculating the average viscosity coefficient μ m (viscosity coefficient ratio μ m / μ0) is stored in the viscosity coefficient memory 7a. At this time, the average viscosity coefficient μ of the molten metal 11 is calculated using the Gauss-Legendre integral formula. m is calculated, so many integration points P n The average viscosity coefficient μ of molten metal 11 m Even when calculating the above, the calculation load can be reduced.

[0074] On the other hand, in the process of S16, the integral point P n If the number of points exceeds 256 (S16: Yes), the integration point Pn The average viscosity coefficient μ of the molten metal 11 calculated when the number is 256 m (The reference viscosity coefficient ratio μ ms / μ0 shown in Fig. 2(c)) is set as the reference value (S17). After the process of S17, referring to the viscosity coefficient memory 7a, each integration point P n Among them, the calculated average viscosity coefficient μ m (Viscosity coefficient ratio μ m / μ0) is within the threshold value of the reference value, and the integration point P n is extracted (S18).

[0075] And among the extracted integration points P n , the integration point P n with the fewest number of integration points is stored in the integration point number memory 7b (S19), and a series of processes are terminated. By the process of S19, the number of integration points P m required to accurately calculate the average viscosity coefficient μ of the molten metal 11 n can be preset before the molten metal flow analysis process (S4) shown in Fig. 5.

[0076] As shown in Fig. 5, in the molten metal flow analysis process (S4), first, as the number of integration points in the molten metal mesh 13c1, the integration point P n stored in the integration point number memory 7b is set (S20). After the process of S20, based on the temperature T n of the molten metal 11 at each integration point P n (see Fig. 2(a)), the viscosity coefficient μ n of the molten metal 11 is calculated (S21), and the viscosity coefficient μ n at that integration point P n is numerically integrated to calculate the average viscosity coefficient μ m of the molten metal in the analysis region R (S22). At this time, since the average viscosity coefficient μ m of the molten metal 11 is calculated using the Gauss-Legendre integration formula, even when calculating the average viscosity coefficient μ n of the molten metal 11 from a large number of integration points P m , the calculation load can be reduced.

[0077] After the process of S22, a time increment dt is determined, and the time in the analysis process is advanced by a small time (S23), and the flow velocity and pressure of the molten metal 11 are calculated by using the Navier-Stokes equations and the continuity equation (S24). After the process of S24, the flow velocity on the surface of the molten metal 11 is calculated (S25), and the temperature of the molten metal 11 is calculated (S26). As the temperature of the molten metal 11 calculated in this S26, for example, the temperature T at the boundary B with the mold mesh 13d1 a or the temperature T at the center C of the molten metal mesh 13c1 b is exemplified.

[0078] Since the calculation methods of values (analysis results) such as the time increment dt, the flow velocity and pressure of the molten metal 11, and the temperature of the molten metal 11 in these processes of S23 to S26 are known techniques, detailed descriptions thereof are omitted. Note that, as known calculation methods, the techniques disclosed in JP-A-10-137926 and JP-A-06-122068 are exemplified.

[0079] After the process of S26, the analysis result (intermediate progress) is output to the display device 4 (S27), and it is confirmed whether the mold 12 is filled with the molten metal 11 (S28). If the mold 12 is not filled with the molten metal 11 (S28: No), the processes of S21 and below (molten metal flow analysis) are repeated, while if the mold 12 is filled with the molten metal 11 (S28: Yes), the series of processes is terminated.

[0080] As described above, according to the analysis program 8a (analysis method) of the present embodiment, the minimum necessary number of integration points P m for accurately calculating the average viscosity coefficient μ of the molten metal 11 n is set in the integration point setting process (S3), and based on the average viscosity coefficient μ n obtained at the minimum necessary number of integration points P m the molten metal flow analysis (processes of S21 to S28) of the molten metal 11 is performed. Thereby, the flow of the molten metal 11 in the analysis region R can be analyzed in a short time with high accuracy.

[0081] Next, referring to FIG. 6, the temperature gradient T of the molten metal 11 in the analysis region R nA modified example of the calculation method will be described. In the above embodiment, the case where the temperature T of the molten metal 11 during the molten metal flow analysis is linearly approximated has been described. However, in the following modified example, the case where the temperature gradient T of the molten metal 11 during the molten metal flow analysis is curve approximated will be described. n Although the case where it is linearly approximated has been described, in the following modified example, the case where the temperature gradient T of the molten metal 11 during the molten metal flow analysis is curve approximated will be described. nc1 FIG. 6 is a graph in which the temperature gradient T of the molten metal 11 during the molten metal flow analysis in the molten metal mesh 13c1 is curve approximated. nc1 is a graph in which the temperature gradient T of the molten metal 11 during the molten metal flow analysis in the molten metal mesh 13c1 is curve approximated.

[0082] As shown in FIG. 6, in the following description, the mesh 13 adjacent to the molten metal mesh 13c1 on the side opposite to the mold mesh 13d1 will be referred to as the molten metal mesh 13c2, and the mesh 13 adjacent to the mold mesh 13d1 on the side opposite to the molten metal mesh 13c1 will be referred to as the mold mesh 13d2 for description.

[0083] The central temperature of the molten metal mesh 13c1 calculated by the above-described molten metal flow analysis process (see FIG. 5) is T c1 , the central temperature of the molten metal mesh 13c2 is T c2 , the central temperature of the mold mesh 13d1 is T d1 , and the central temperature of the mold mesh 13b2 is T d2 are defined. Also, if the distance from the boundary B1 with the mold mesh 13d1 in the molten metal mesh 13c1 is y c1 , then the temperature gradient T of the molten metal 11 in the molten metal mesh 13c1 nc1 is expressed by the following Equation 19.

[0084]

Equation

[0085]

Equation

[0086]

Number

[0087]

Number

[0088]

Number

[0089]

Number

[0090]

Number

[0091]

Number

[0092]

Number

[0093]

Number

[0094]

number

[0095]

number

[0096] In this manner, in this embodiment (the temperature gradient setting step executed before the process of S21), the temperature T d1 and the temperature T of the molten metal 11 in the molten metal mesh 13c2 c2 Based on this, the temperature gradient T of the molten metal 11 in the molten metal mesh 13c2 nc1 is approximated as a curve. nc1 Based on the average viscosity coefficient μ of the molten metal 11 in the analysis region R m By calculating the temperature gradient T n Compared with the case where the flow of the molten metal 11 is linearly approximated, the flow of the molten metal 11 in the analysis region R can be analyzed with high accuracy. Therefore, defects occurring at the boundary between the molten metal 11 and the mold 12 (on the surface of the casting) can be accurately predicted.

[0097] The present invention has been described above based on the above embodiment, but the present invention is not limited to the above form in any way, and it can be easily inferred that various modifications and improvements are possible within the scope that does not deviate from the spirit of the present invention.

[0098] In each of the above embodiments, the average viscosity coefficient μ of the molten metal 11 in the analysis region R m Although the case where is calculated using the Gauss-Legendre integral formula has been described, it is not necessarily limited to this. For example, other known integral formulas such as the Newton-Cotes method may also be used.

[0099] In each of the above embodiments, the integral point P n The average viscosity coefficient μ of the molten metal 11 is calculated by increasing the number of m By calculating the appropriate integration point P n However, this is not necessarily limited to this. For example, n The average viscosity coefficient μ of the molten metal 11 is calculated by increasing the number of m You can also calculate the integral point P n Numerical integration begins at the integration point P n The average viscosity coefficient μ of the molten metal 11 is decreased. m may be calculated.

[0100] In each of the above embodiments, the integral point P n The average viscosity coefficient μ calculated while increasing m When determining whether or not is within a predetermined threshold, as a specific example of the threshold, the integral point P n The average viscosity coefficient μ m (Reference average viscosity coefficient μ ms ) is exemplified as a range of ±0.1% of the integral point P. However, it is not necessarily limited to this. The threshold value may be within a range of at least ±1%, but the narrower the range of the threshold value, the more appropriate the integral point P. n Therefore, it is preferable that the range is within ±0.5%, and more preferably within ±0.1%.

[0101] In the above embodiment, for the virtuality approximate linear temperature gradient T n ’ of the molten metal 11, the temperature T a ’ of the molten metal 11 on the boundary B side with the mold 12 is set to the temperature at which the molten metal 11 reaches the flow limit solid fraction, and the temperature T b ’ of the molten metal 11 on the center C side of the molten metal mesh 13c1 is set to the liquidus temperature of the molten metal 11. However, it is not necessarily limited to this. If the temperature of T a ’ is higher than that of T b ’, other temperatures may be set for T a ’ and T b ’. Also, similar to the temperature gradient T nc1 of the molten metal 11 during the above-described molten metal flow analysis, the virtuality approximate temperature gradient T n ’ of the molten metal 11 may be approximated curvilinearly.

Explanation of Reference Numerals

[0102] 1 Analysis device (computer) 6a Analysis program 10 Analysis model 11 Molten metal 12 Mold 13 Mesh 13c1 Molten metal mesh (first mesh) 13c2 Molten metal mesh (third mesh) 13d1 Mold mesh (second mesh) P n Integration point R Analysis region S1 Analysis model setting step S10 virtuality Temperature setting step S12 virtuality Viscosity calculation step S13 virtuality Average viscosity calculation step S12~16 Repetition step S20 Integration point setting step S21 Viscosity calculation step S22 Average viscosity calculation step S23~S28 Analysis step

Claims

1. An analysis model setting step of setting an analysis model in which a model of a mold is divided into a plurality of meshes; An integration point setting step of setting an integration point for an analysis area on the wall surface side of the mold in a first mesh adjacent to the mold among the plurality of meshes set in the analysis model setting step when performing a molten metal flow analysis; A viscosity calculation step of calculating a viscosity coefficient of the molten metal based on the temperature of the molten metal at the integration point set in the integration point setting step; An average viscosity calculation step of numerically integrating the viscosity coefficient calculated in the viscosity calculation step to calculate an average viscosity coefficient of the molten metal; In an analysis program for causing a computer to execute: an analysis step of analyzing a flow of the molten metal in the analysis area based on the average viscosity coefficient calculated in the average viscosity calculation step; A virtual temperature setting step of setting a virtual temperature gradient of the molten metal in the analysis area; A virtual viscosity calculation step of calculating a viscosity coefficient of the molten metal at the integration point set in the analysis area based on the virtual temperature gradient set in the virtual temperature setting step; A virtual average viscosity calculation step of numerically integrating the viscosity coefficient calculated in the virtual viscosity calculation step to calculate an average viscosity coefficient of the molten metal; A repetition step of repeating a calculation process of calculating the average viscosity coefficient by the virtual viscosity calculation step and the virtual average viscosity calculation step while changing the number of integration points, and further causing the computer to execute; In the integration point setting step, among the calculation processes repeated in the repetition step, an integration point at which the calculated average viscosity coefficient falls within a predetermined threshold value and the number of integration points is the smallest is set as the integration point for the molten metal flow analysis; The virtual temperature setting step is characterized by setting the virtual temperature gradient in which the temperature of the molten metal gradually decreases from the center side of the first mesh toward the wall surface side of the mold. An analysis program.

2. The analysis program according to claim 1, wherein the average viscosity calculation step and the virtual average viscosity calculation step calculate the average viscosity coefficient of the molten metal by a Gauss-Legendre integration formula.

3. When a mesh adjacent to the first mesh on the wall surface side of the mold is defined as a second mesh, and a mesh adjacent to the first mesh on the side opposite to the second mesh is defined as a third mesh, further causing the computer to execute a temperature setting step of curvilinearly approximating a temperature gradient of the molten metal in the first mesh based on the temperature of the mold in the second mesh and the temperature of the molten metal in the third mesh; 2. The analysis program according to claim 1, wherein the viscosity calculation step calculates the viscosity coefficient based on the temperature gradient that is approximated to a curve in the temperature setting step.

4. 2. The analysis program according to claim 1, wherein the virtual temperature setting step sets the virtual temperature gradient by setting a temperature at which the molten metal has a flow limit solid phase fraction as the temperature of the molten metal on the wall surface side of the mold, and setting a liquidus temperature of the molten metal as the temperature of the molten metal on the center side of the first mesh.

5. 5. The analysis program according to claim 4, wherein the virtual temperature setting step sets the virtual temperature gradient such that the temperature of the molten metal decreases proportionally from the center side of the first mesh to the wall side of the mold.

6. an analysis model setting step in which an analysis model is set by dividing the mold model into a plurality of meshes; an integration point setting step of setting integration points for a molten metal flow analysis in an analysis region on a wall surface side of the mold in a first mesh adjacent to the mold among the plurality of meshes set in the analysis model setting step; a viscosity calculation step of calculating a viscosity coefficient of the molten metal based on the temperature of the molten metal at the integration point set in the integration point setting step; an average viscosity calculation step of calculating an average viscosity coefficient of the molten metal by numerically integrating the viscosity coefficient calculated in the viscosity calculation step; an analyzing step of analyzing a flow of the molten metal in the analysis region based on the average viscosity coefficient calculated in the average viscosity calculating step, a virtual temperature setting step of setting a virtual temperature gradient of the molten metal in the analysis region; a virtual viscosity calculation step of calculating a viscosity coefficient of the molten metal at an integration point set in the analysis region based on the virtual temperature gradient set in the virtual temperature setting step; a virtual average viscosity calculation step of calculating an average viscosity coefficient of the molten metal by numerically integrating the viscosity coefficient calculated in the virtual viscosity calculation step; The computer is further caused to execute a repetition step of repeating the calculation process for calculating the average viscosity coefficient by the virtual viscosity calculation step and the virtual average viscosity calculation step while changing the number of integration points. The integration point setting step sets, as the integration point during the molten metal flow analysis, the integration point at which the calculated average viscosity coefficient falls within a predetermined threshold value and the number of integration points is the smallest among the calculation processes repeated in the repetition step. The virtual temperature setting step is characterized in that a virtual temperature gradient in which the temperature of the molten metal gradually decreases is set from the center side of the first mesh toward the wall surface side of the mold in the method for analyzing the molten metal flow.