Analysis program and molten metal flow analysis method

Abstract

A viscosity coefficient μn of molten metal 11 at an integration point Pn is calculated on the basis of a provisional temperature gradient Tn' of the molten metal 11 set in an analysis region R, and an average viscosity coefficient μm of the molten metal 11 in the analysis region R is calculated by numerically integrating the viscosity coefficient μn. The calculation processing of the average viscosity coefficient μm of the molten metal 11 is repeated while changing the number of integration points Pn. In the repeated calculation processing of the average viscosity coefficient μm, the calculated average viscosity coefficient μm falls within a predetermined threshold, and the integration point Pn with the smallest number of integration points is set as an integration point Pn at the time of molten metal flow analysis. That is, the minimum necessary number of integration points which allow accurate calculation of the average viscosity coefficient μm of the molten metal 11, is preset before the molten metal flow analysis of the molten metal 11 is performed. Thus, the flow of the molten metal 11 in the analysis region R in the vicinity of a mold can be accurately analyzed in a short time.

Description

Analysis program and method for analyzing molten metal flow

[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.

[0002] A technique is known that predicts whether or not a casting defect 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 the 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 the 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] In particular, in recent years, there has been an increasing demand for large-scale casting equipment such as GigaPress and GigaCast. When analyzing such large molds, the mesh size used during analysis is likely to be larger. When a relatively large mesh is used, the method of calculating the viscosity coefficient based on the average temperature of the molten metal, as described above, will underestimate the viscosity of the molten metal in the analysis region near the mold. On the other hand, if the mesh size is reduced to accurately evaluate the viscosity of the molten metal in this region, the total number of meshes will increase, resulting in a longer calculation time.

[0006] Therefore, the present applicant has proposed a method for calculating the average viscosity coefficient of the molten metal by setting multiple integration points in the analysis region near the mold and numerically integrating the viscosity coefficient of the molten metal at those multiple integration points (see, for example, Non-Patent Document 1). This method makes it possible to accurately calculate the viscosity coefficient of the molten metal in the analysis region near the mold, even when a relatively large mesh is used. Therefore, the flow of the molten metal in this region can be analyzed with high accuracy.

[0007] Japanese Patent Application Laid-Open No. 10-137926 (for example, paragraphs 0012 to 0018, Figures 2 and 3)

[0008] Tanaka Tomoko, Minaka Nishi Shinji, Fukuda Tadao, Ozaki Koichi, "A Study on Evaluation Parameters for Die Cast Fusion Defects on the Extreme Surface," Japan Foundry Engineering Society, 174th National Lecture Conference Abstracts, September 2019, p. 94

[0009] However, when the viscosity coefficient of the molten metal is numerically integrated at multiple integration points as in the conventional technology described above, increasing the number of integration points allows for accurate calculation of the average viscosity coefficient of the molten metal, but the time required for calculation increases (the calculation load increases). On the other hand, reducing the number of integration points too much makes it impossible to accurately calculate the average viscosity coefficient of the molten metal, making it impossible to accurately analyze the flow of the molten metal in the analysis region near the mold. Therefore, there is a demand for a technology that can accurately analyze the flow of the molten metal in the analysis region near the mold in a short period of time.

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

[0011] In order to achieve this object, the analysis program and molten metal flow analysis method of the present invention cause a computer to execute the following steps: 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 integration points for molten metal flow analysis in an analysis region on the wall surface side of the mold in a first mesh among the plurality of meshes set in the analysis model setting step, the first mesh being adjacent to the mold; 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; 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. The method further causes the computer to execute the following steps: a provisional temperature setting step of setting a provisional temperature gradient of the molten metal in the analysis region; a provisional viscosity calculation step of calculating a viscosity coefficient of the molten metal at integration points set in the analysis region based on the provisional temperature gradient set in the provisional temperature setting step; a provisional average viscosity calculation step of calculating an average viscosity coefficient of the molten metal by numerically integrating the viscosity coefficient calculated in the provisional viscosity calculation step; and a repetition step of repeating the calculation process of calculating the average viscosity coefficient by the provisional viscosity calculation step and the provisional average viscosity calculation step while changing the number of integration points, and the integration point setting step sets, as an integration point for the molten metal flow analysis, an integration point where the calculated average viscosity coefficient falls within a predetermined threshold value and has the fewest number of integration points, among the calculation processes repeated in the repetition step.

[0012] According to the analysis program of claim 1 and the molten metal flow analysis method of claim 6, a provisional temperature gradient of the molten metal is set in an analysis region on the wall side of the mold (hereinafter referred to as the "analysis region near the mold") in a first mesh adjacent to the mold. Based on this provisional temperature gradient, the viscosity coefficient of the molten metal at integration points set in the analysis 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 this calculation process of the average viscosity coefficient of the molten metal is repeated while changing the number of integration points.

[0013] In this repeated calculation process of the average viscosity coefficient, the integration point where the calculated average viscosity coefficient falls within a predetermined threshold and has the fewest number of integration points is set as the integration point for the molten metal flow analysis. In other words, the minimum number of integration points necessary to accurately calculate the average viscosity coefficient of the molten metal is set in advance before the molten metal flow analysis is performed. This has the effect of enabling the molten metal flow in the analysis region near the mold to be analyzed accurately in a short time.

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

[0015] The analysis program of claim 3 achieves the following effect in addition to the effect achieved by the analysis program of claim 1: A mesh adjacent to a 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 opposite side of the second mesh is defined as a third mesh.

[0016] When defined in this way, the temperature gradient of the molten metal in the first mesh is approximated by a curve based on the temperature of the mold in the second mesh and the temperature of the molten metal in the third mesh. By calculating the viscosity coefficient of the molten metal at each integration point based on this curved-approximated temperature gradient, the average viscosity coefficient of the molten metal in the analysis region near the mold can be accurately calculated. This has the effect of enabling accurate analysis of the flow of the molten metal in this region.

[0017] The analysis program of claim 4 achieves the following effect in addition to the effect achieved by the analysis program of claim 1. When setting a provisional temperature gradient of the molten metal in the analysis region, the temperature at which the molten metal reaches its 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. This makes it possible to approximate the provisional temperature gradient used when setting the number of integration points to the actual temperature gradient used when performing a molten metal flow analysis. This makes it easier to set an appropriate number of integration points, which has the effect of enabling the flow of the molten metal in the analysis region near the mold to be analyzed accurately in a short period of time.

[0018] The analysis program of claim 5 achieves the following effect in addition to the effect achieved by the analysis program of claim 4. When setting a provisional temperature gradient of the molten metal in the analysis region, a temperature gradient is set in which the temperature of the molten metal decreases proportionally from the center of the first mesh to the surface of the mold. This has the effect of reducing the calculation load compared to, for example, approximating the provisional temperature gradient of the molten metal as a curve.

[0019] 1 is an external view of an analysis device showing how molten metal flow analysis is performed using an analysis model. (a) is a graph linearly approximating the temperature gradient of the molten metal during molten metal flow analysis in a molten metal mesh, (b) is a graph showing the provisional temperature gradient of the molten metal in the molten metal mesh, and (c) is a graph showing the relationship between the number of integration points set in the analysis domain and the average viscosity coefficient calculated at those integration points. (a) is a block diagram showing the electrical configuration of the analysis device, and (b) is a flowchart of the analysis process. (b) is a flowchart of the integration point number setting process. (c) is a flowchart of the molten metal flow analysis process. (c) is a graph curvedly approximating the temperature gradient of the molten metal during molten metal flow analysis in a molten metal mesh.

[0020] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. First, the overall configuration of an analysis device 1 will be described with reference to Fig. 1. Fig. 1 is an external view of the analysis device 1, showing how a flow analysis of a molten metal 11 is performed using an analysis model 10. In Fig. 1, the molten metal 11 flowing within a cavity 12a of a mold 12 is indicated by dotted hatching, and the cross section of the mold 12 is indicated by dotted 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) that divides a mold 12 defined in an analysis model 10 into a plurality of meshes 13 and analyzes the behavior of a molten metal 11 in the plurality of meshes 13.

[0022] The analytical model 10 is created based on a casting plan loaded into the analytical device 1 by a user. The casting plan is CAD data or the like of a mold 12 designed by a user, and is data on the mold 12 (hereinafter simply referred to as "data on the mold 12") including information such as the shape of the cavity 12a, the position and shape of the gate 12b (dam), and the cooling structure (e.g., the presence or absence of cooling pipes) not shown. The analytical device 1 creates the analytical model 10 by dividing the loaded data of the mold 12 into multiple meshes 13. The meshes 13 are polyhedral (hexahedral in this embodiment) solid elements.

[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 flow analysis of the molten metal 11. The analysis conditions input by the user include the above-mentioned data on the mold 12 as well as information on casting conditions such as the physical properties of the molten metal 11, the initial temperature, and the pouring rate.

[0024] The analysis device 1 analyzes (simulates) the flow and solidification process 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 the analysis results. The analysis results of the molten metal flow displayed on this display 4 make it possible to predict in advance the locations where casting defects are likely to occur in a casting produced in a mold 12 designed by the user.

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

[0026] In order to accurately predict defects that will occur 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 (wall surface of the mold 12) between the molten metal mesh 13c1 and the mold mesh 13d1.

[0027] Therefore, in this embodiment, a plurality of integration points P ｎ (In the example shown in the enlarged portion of FIG. 1, n=1, 2) are set, and the multiple integration points P ｎ Viscosity coefficient μ of the molten metal 11 ｎ By numerically integrating the above, the average viscosity coefficient μ of the molten metal 11 in the analysis region R is obtained. ｍ In this embodiment, the Gauss-Legendre integral formula is used for this numerical integration. This integration method will be explained below.

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

[0029] The Gauss-Legendre integral formula shown in the following Equation 2 is applied to Equation 1.

[0030] In order to make the integral interval of Equation 1 coincide with the integral interval [-1, 1] of Equation 2, the variable of Equation 1 is set to x=4y / h-1, and the following Equation 3 is obtained.

[0031] When the Gauss-Legendre integral formula of Equation 2 above is applied to Equation 3, the following Equation 4 is obtained.

[0032] In the Nth-order Gauss-Legendre integral formula, the equinox x ｉ and weight ω ｉ The value of is specified by the following formulas 5 and 6.

[0033]

[0034] P Ｎ (x) is the Legendre polynomial of degree N, and P Ｎ '(x) is its derivative. The function values ​​and derivatives of the Legendre polynomials can be calculated numerically using the recurrence formulas in Equations 7 to 9 below.

[0035]

[0036]

[0037] First, using the above formula 4, the integral point P ｎ The number of points is 2 (P ｎ =P １ , P ２ ) The average viscosity coefficient μ of the molten metal 11 when ｍ The calculation method of each integral point P １ , P ２ The distance to each １ , y ２ Then, y １= {(√3-1)h / 4√3}=(3-√3)h / 12,y ２ = {(√3+1)h / 4√3}=(3+√3)h / 12, x １ = -1 / √3, x ２ = 1 / √3, ω １ =ω ２ = 1. １ , x ２ , ω １ , ω ２ When the value of is substituted into the above-mentioned Equation 4, the average viscosity coefficient μ of the molten metal 11 in the analysis region R is ｍ can be approximated by the following Equation 10.

[0038] μ in this formula 10 １ and μ ２ is the integral point P １ , P ２ The viscosity coefficient μ of the molten metal 11 is １ and μ ２ The calculation method of the temperature gradient T of the molten metal 11 during the melt flow analysis in the molten metal mesh 13c1 will be described with reference to FIG. ｎ 1. The horizontal axis represents the distance y from the boundary B with the mold 12, and the vertical axis represents the temperature T of the molten metal 11.

[0039] As shown in FIG. 2(a), first, a flow analysis of the molten metal 11 is performed to determine the temperature T of the molten metal 11 at the boundary B with the mold 12 during the casting process. ａ and the temperature T of the molten metal 11 at the center C of the molten metal mesh 13c1. ｂ The temperature gradient T of the molten metal 11 is calculated. ｎ is linear (the temperature of the molten metal 11 decreases proportionally from the center C of the molten metal mesh 13c1 to the mold 12 side), the temperature T ｎ can be calculated using the following formula 11.

[0040] Then, from the boundary B with the mold 12 to the integration point P １ , P ２ Distance y to １ =(3-√3)h / 12,y ２= (3 + √3) h / 12 ​​into the above formula 11, each integration point P １ , P ２ The temperature T of the molten metal 11 １ , T ２ can be calculated using the following formulas 12 and 13.

[0041]

[0042] The relationship between the temperature of the molten metal 11 and the viscosity coefficient (a formula for calculating the viscosity coefficient from the temperature) is stored in the analysis device 1, and the temperature T １ and T ２ Based on this, the integral point P １ , P ２ Viscosity coefficient μ of the molten metal 11 １ and μ ２ is calculated. This calculated viscosity coefficient μ １ and μ ２ By substituting into the above-mentioned formula 10, the integral point P ｎ 2 points (P ｎ =P １ , P ２ ) The average viscosity coefficient μ of the molten metal 11 when ｍ can be calculated.

[0043] Integral point P ｎ 3 points (P ｎ =P １ , P ２ , P ３ ), the boundary B with the mold 12 to each integral point P １ , P ２ , P ３ The distance to each １ , y ２ , y ３ Then, y １ = {(√5-√3)h / 4√5}=(5-√15)h / 20, y ２ = h / 4, y ３ = {(√5+√3)h / 4√5}=(5+√15)h / 20, x １ = -√15 / 5, x ２ = 0, x ３ =√15 / 5, ω １ =ω ３ = 5 / 9, ω ２= 8 / 9. This x １ , x ２ , x ３ , ω １ , ω ２ , ω ３ When the value of is substituted into the above-mentioned Equation 4, the average viscosity coefficient μ of the molten metal 11 in the analysis region R is ｍ can be approximated by the following Equation 14.

[0044] Also, from the boundary B with the mold 12 to the integration point P １ , P ２ , P ３ Distance y to １ =(5-√15)h / 20,y ２ = h / 4, y ３ = (5 + √15) h / 20 into the above formula 11, each integration point P １ , P ２ , P ３ The temperature T of the molten metal 11 １ , T ２ , T ３ can be calculated using the following formulas 15 to 17.

[0045]

[0046]

[0047] The temperature T １ , T ２ , T ３ The viscosity coefficient μ of the molten metal 11 calculated from １ , μ ２ , μ ３ By substituting into Equation 14, the integral point P ｎ The average viscosity coefficient μ of the molten metal 11 when the three points are ｍ can be calculated.

[0048] Also, the integral point P ｎ 4 points (P ｎ =P １ , P ２ , P ３ , P ４ ) Similarly, the average viscosity coefficient μ of the molten metal 11 in the analysis region R ｍ can be approximated by the following Equation 18.

[0049] Then, at each integration point P １ , P ２ , P ３ , P ４ Viscosity coefficient μ of the molten metal 11 １ , μ ２ , μ ３ , μ ４ By substituting into Equation 18, the integral point P ｎ The average viscosity coefficient μ of the molten metal 11 when ｍ can be calculated.

[0050] In this way, multiple integration points P ｎ Viscosity coefficient μ of the molten metal 11 ｎ When numerically integrating, the integration point P ｎ The larger the number of ｍ However, when analyzing the flow of the molten metal 11, multiple integration points P ｎ Since it is necessary to perform integration at every minute elapsed time dt, ｎ If the number of integration points P is too large, the calculation load increases (calculation time becomes longer). ｎ If the number of is too small, the average viscosity coefficient μ of the molten metal 11 ｍ cannot be calculated accurately.

[0051] Therefore, in this embodiment, before starting the analysis of the flow of the molten metal 11 with the analysis device 1, an appropriate integration point P ｎ The number of integral points P ｎ 2(b) and 2(c), a method for setting the number of the molten metal 11 in the molten metal mesh 13c1 will be described. ｎ 2(c) is a graph showing the relationship between the integration point P and the temperature T of the molten metal 11. The horizontal axis indicates the distance y from the wall surface of the mold 12, and the vertical axis indicates the temperature T of the molten metal 11. ｎ and the number of integration points P ｎ The average viscosity coefficient μ calculated by ｍ 10 is a graph showing the relationship between

[0052] As shown in Figure 2(b), the appropriate integration point P ｎWhen the number of the temperature values ​​is set in advance, the virtual value T of the temperature of the molten metal 11 at the boundary B with the mold 12 is first set. ａ The temperature at which the molten metal 11 reaches the flow limit solid fraction is set as '. Also, the virtual value T ｂ ', the liquidus temperature (T ａ '<T ｂ ') to set it.

[0053] Next, the temperature T ａ ', T ｂ A provisional (virtual) temperature gradient T ′ is assumed to be linear. ｎ ', and this temperature gradient T ｎ ', the integral point P ｎ The average viscosity coefficient μ of the molten metal 11 is increased while increasing the number of ｍ We will calculate the following.

[0054] Specifically, first, the integral point P ｎ 1 point (P ｎ =P １ ) and the temperature gradient T ｎ Average viscosity coefficient μ of molten metal 11 based on ｍ Then, the integral point P ｎ 2 points (P ｎ =P １ , P ２ ) as the average viscosity coefficient μ of the molten metal 11 ｍ Calculate the average viscosity coefficient μ ｍ The calculation of the integral point P ｎ This is repeated until the number of the 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 changed (increased) while changing (increasing) the number of ｍ The integral point P when ｎ and viscosity coefficient ratio μ ｍ The relationship between the viscosity and the solid fraction 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 FIG. 2(c), the integral point P ｎ When the number of viscosity coefficients is small (for example, n = 1 to 6), the calculated viscosity coefficient ratio μ ｍ / μ0 (average viscosity coefficient μ of the molten metal 11 ｍ ) values ​​vary, while the integral point P ｎ When the number of viscous coefficients is increased (for example, when n ≥ 7), the calculated viscosity coefficient ratio μ ｍ Therefore, in this embodiment, the calculated viscosity coefficient ratio μ ｍ / μ0 (average viscosity coefficient μ of the molten metal 11 ｍ ) falls within a predetermined threshold and the number of integration points is the smallest. ｎ are set as integration points during the flow analysis.

[0057] Specifically, the integral point P ｎ When the number of is sufficiently larger than 1 (in this embodiment, n = 256), the average viscosity coefficient μ ｍ The reference viscosity coefficient μ ｍｓ The viscosity coefficient ratio in this case is the reference viscosity coefficient ratio μ ｍｓ / μ0, the calculated viscosity coefficient ratio μ ｍ / μ0 is the reference viscosity coefficient ratio μ ｍｓ Within ±0.1% of / μ0 (0.999μ ｍｓ ≦μ ｍ ≦1.001μ ｍｓ ) and the minimum number of integration points P ｎ (For example, n=7) is extracted. Then, when analyzing the flow of the molten metal 11, the extracted integration points P ｎ The average viscosity coefficient μ of the molten metal 11 ｍ Calculate.

[0058] In this way, the average viscosity coefficient μ of the molten metal 11 ｍ The minimum number of integration points P required to accurately calculate ｎ By setting in advance (before performing the flow analysis of the molten metal 11), the average viscosity coefficient μ of the molten metal 11 during the flow analysis ｍ That is, the flow of the molten metal 11 in the analysis region R can be analyzed with high accuracy in a short time.

[0059] In particular, when the mold 12 is used to produce large castings such as Giga Press (Giga Cast), the calculation load during the flow analysis of the molten metal 11 tends to be large. Therefore, as in this embodiment, an appropriate number of integration points P ｎ It is particularly preferable to preset

[0060] Also, the appropriate integration point P ｎ The provisional temperature gradient T of the molten metal 11 for evaluating the number of ｎ When setting the temperature T ′ (see FIG. 2B), ａ ' is set as the temperature at which the molten metal 11 reaches the flow limit solid phase fraction, and the temperature T ｂ The liquidus temperature of the molten metal 11 is set as '. ｎ ' is the temperature gradient T of the molten metal 11 during the melt flow analysis. ｎ Therefore, the integral point P ｎ Since it becomes easier to set an appropriate number, the flow of the molten metal 11 in the analysis region R can be analyzed accurately in a short time.

[0061] The temperature T at which the molten metal 11 reaches the flow limit solid phase ratio is ａ ' and the liquidus temperature T ｂ ' and the provisional temperature gradient T ｎ That is, the temperature gradient T ′ is set such that 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. ｎ ' is set, for example, the provisional temperature gradient T ｎ This reduces the calculation load compared to when ' is curve-approximated.

[0062] Also, the appropriate integration point P ｎ In case of evaluating the number of integral points P ｎ When performing a melt flow analysis of the molten metal 11, the average viscosity coefficient μ of the molten metal 11 is calculated using the Gauss-Legendre integral formula. ｍ As a result, a large number of integration points P ｎ The average viscosity coefficient μ of the molten metal 11 ｍEven when calculating the above, the calculation load can be reduced.

[0063] Next, the electrical configuration of the analysis device 1 and the analysis processing executed by the analysis device 1 will be described with reference to Fig. 3. 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 processing.

[0064] 3(a), the analysis device 1 has a CPU 5, a hard disk drive (HDD) 6, and a RAM 7, which are connected to an input / output port via a bus line 8. The above-mentioned mouse 2, keyboard 3, and display device 4 are also connected to the bus line 8.

[0065] The CPU 5 is a computing 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 executed by the CPU 5, fixed value data, etc. When the analysis program 6 a stored in the HDD 6 is executed by the CPU 5, an analysis process (see FIG. 3( b)) is performed.

[0066] The RAM 7 is a memory for rewritably storing various workpiece data, flags, etc. when the CPU 5 executes the analysis program 6a, and is provided with a viscosity coefficient memory 7a and an integral point number memory 7b. These memories 7a and 7b are used in the integral point number setting process (S3) and the molten metal flow analysis process (S4) of the analysis process shown in Figure 3(b), and details of these processes will be described later with reference to Figure 4. When an instruction to execute the analysis program 6a is input from the mouse 2 or keyboard 3, the analysis process is executed by the CPU 5.

[0067] As shown in FIG. 3( b), the analysis process begins with setting various analysis conditions (S1). The analysis conditions set here include the physical properties of the molten metal 11 (casting), the pouring speed of the molten metal 11, gravitational acceleration, data on the mold 12, and the size of the mesh 13. 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 of the molten metal 11. The data on the mold 12 includes the data on the structure of the mold 12 described above as well as information such as the density, specific heat, and thermal conductivity of the mold 12.

[0068] After the analysis conditions are set in step S1, initial conditions for the analysis are set in step S2 (S2). In setting these initial conditions, for example, initial temperatures of the molten metal 11 and the mold 12 and initial values ​​of the pressure inside the cavity 12a of the mold 12 (pressure depending on whether a vacuum is applied) are set. 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 proportion of the volume of the molten metal 11 to the volume of the mesh 13 (cavity 12a).

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

[0070] After the initial conditions are set in the process of S2, the appropriate integration points P are set by the integration point number setting process (S3). ｎ The number of integration points P ｎ The flow analysis process (S4) of the molten metal 11 is executed with the number of integration points set (S3), and the series of processes is completed. The processes of S3 and S4 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, a provisional temperature gradient T ｎ ' (see FIG. 2(b)) is set (S10).ｎ After setting ', the integration point P in the analysis region R ｎ is set at one point (n=1) (S11), and the provisional 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 is numerically integrated to obtain the average viscosity coefficient μ of the molten metal 11. 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 process of S14, the integral point P ｎ (S15), and the number of the integral point 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 processes of S12 to S16, the integral point P ｎ The average viscosity coefficient μ of the molten metal 11 is calculated 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 by using the Gauss-Legendre integral formula. ｍ is calculated, so many integration points P ｎ The average viscosity coefficient μ of the 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 the integral points P exceeds 256 (S16: Yes), ｎ The average viscosity coefficient μ of the molten metal 11 calculated when the number of ｍ (The reference viscosity coefficient ratio μ shown in FIG. 2(c) ｍｓ / μ0) is set as the reference value (S17). After the process of S17, the viscosity coefficient memory 7a is referenced and each integration point P ｎ The calculated average viscosity coefficient μ ｍ (viscosity coefficient ratio μ ｍ / μ0) is within the threshold of the reference value. ｎ is extracted (S18).

[0075] Then, the extracted integration point P ｎ Among them, the integration point P with the smallest number of integration points ｎ is stored in the integration point number memory 7b (S19), and the series of processes is terminated. By the process of S19, the average viscosity coefficient μ of the molten metal 11 is ｍ The minimum number of integration points P required to accurately calculate ｎ The number of the molten metal can be set in advance before the molten metal flow analysis process (S4) shown in FIG.

[0076] As shown in FIG. 5, in the molten metal flow analysis process (S4), first, the number of integration points in the molten metal mesh 13c1 is set to the integration point P ｎ After the process of S20, each integration point P ｎ The temperature T of the molten metal 11 ｎ (see FIG. 2(a)), the viscosity coefficient μ of the molten metal 11 ｎ is calculated (S21), and the integral point P ｎ Viscosity coefficient μ in ｎ By numerically integrating the above, the average viscosity coefficient μ of the molten metal in the analysis region R is obtained. ｍ At this time, the average viscosity coefficient μ of the molten metal 11 is calculated using the Gauss-Legendre integral formula (S22). ｍ is calculated, so many integration points P ｎ The average viscosity coefficient μ of the molten metal 11 ｍ Even when calculating the above, the calculation load can be reduced.

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

[0078] The methods for calculating the values ​​(analysis results) of the time increment dt, the flow velocity and pressure of the molten metal 11, and the temperature of the molten metal 11 in the processes of S23 to S26 are well-known techniques, and therefore detailed explanations thereof will be omitted. Examples of well-known calculation methods include the techniques disclosed in Japanese Patent Laid-Open Nos. 10-137926 and 06-122068.

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

[0080] In this way, according to the analysis program 8a (analysis method) of this embodiment, the average viscosity coefficient μ of the molten metal 11 ｍ The minimum number of integration points P required to accurately calculate ｎ The number of integral points is set in the integral point setting process (S3), and the minimum number of integral points P ｎ The average viscosity coefficient μ obtained by ｍ Based on this, a flow analysis of the molten metal 11 (processing of S21 to S28) is performed. This makes it possible to analyze the flow of the molten metal 11 in the analysis region R 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 ｎ In the above embodiment, the temperature T of the molten metal 11 during the flow analysis will be described. ｎIn the following modified example, the temperature gradient T of the molten metal 11 during the melt flow analysis is approximated as a straight line. ｎｃ１ 6 shows the temperature gradient T of the molten metal 11 during the melt flow analysis in the molten metal mesh 13c1. ｎｃ１ 1 is a graph showing a curve approximation of the above.

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

[0083] The central temperature of the molten metal mesh 13c1 calculated by the above-mentioned 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 , the central temperature of the mold mesh 13b2 is T ｄ２ The distance from the boundary B1 between the molten metal mesh 13c1 and the mold mesh 13d1 is defined as y ｃ１ Then, the temperature gradient T of the molten metal 11 in the molten metal mesh 13c1 is ｎｃ１ is expressed by the following Equation 19.

[0084] In this formula 19, c ０ , c １ , c ２ is a coefficient expressed by the following formulas 20 to 23, α is the heat transfer coefficient between the molten metal 11 and the mold 12, h is the element width described above, k ｃ is the thermal conductivity of the molten metal 11 (casting), k ｄ is the thermal conductivity of the mold 12.

[0085]

[0086]

[0087]

[0088] In addition, the distance from the boundary B2 between the molten metal mesh 13c2 and the molten metal mesh 13c1 is defined as y ｃ２Then, the temperature gradient T of the molten metal 11 in the molten metal mesh 13c2 is ｎｃ２ is expressed by the following Equation 24.

[0089] In addition, the distance from the boundary B1 between the mold mesh 13d1 and the molten metal mesh 13c1 is defined as y ｄ１ Then, the temperature gradient T of the mold 12 in the mold mesh 13d1 ｎｄ１ is expressed by the following Equation 25.

[0090] In this formula 25, d ０ , d １ , d ２ are coefficients expressed by the following equations 26 to 29.

[0091]

[0092]

[0093]

[0094] The distance from the boundary B3 between the mold mesh 13d2 and the mold mesh 13d1 is y ｄ２ Then, the temperature gradient T ｎｄ２ can be expressed by the following Equation 30.

[0095] From these formulas 19 to 30, the temperature gradient T of the molten metal 11 in the analysis region R is calculated. ｎｃ１ In the process of S21 of the above-mentioned molten metal flow analysis process (see FIG. 5), the curve-approximated temperature gradient T ｎｃ１ From each integration point P ｎ Viscosity coefficient μ of the molten metal 11 ｎ In the process of S22, each integral point P ｎ Viscosity coefficient μ in ｎ By numerically integrating by Gauss-Legendre integral, the average viscosity coefficient μ of the molten metal 11 in the analysis region R is obtained. ｍ is calculated.

[0096] In this manner, in the present 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 is calculated. 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 This allows for more accurate analysis of the flow of the molten metal 11 in the analysis region R than when linear approximation is used. Therefore, defects that occur 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 increased by one. ｍ By calculating the appropriate integral 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 Alternatively, an 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 Pｎ 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, an 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, the temporary temperature gradient T ｎ When approximating the temperature T ′ linearly, the temperature T ′ of the molten metal 11 on the boundary B side with the mold 12 is ａ ' is set as the temperature at which the molten metal 11 reaches the flow limit solid phase fraction, and the temperature T ｂ In the above description, the liquidus temperature of the molten metal 11 is set as T', but this is not necessarily limited to this. ａ T than ' ｂ If the temperature of ' is large, T ａ ' and T ｂ Other temperatures may be set for the temperature gradient T ｎｃ１ Similarly, the temporary temperature gradient T ｎ ' may be approximated by a curve.

[0102] REFERENCE SIGNS LIST 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 Provisional temperature setting step S12 Provisional viscosity calculation step S13 Provisional average viscosity calculation step S12-16 Repeating steps S20 Integration point setting step S21 Viscosity calculation step S22 Average viscosity calculation step S23-S28 Analysis steps

Claims

1. An analysis program that causes a computer to execute the following steps: 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 integration points for a molten metal flow analysis in an analysis domain on the wall surface side of the mold in a first mesh of 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 points 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; and an analysis step of analyzing the flow of the molten metal in the analysis domain based on the average viscosity coefficient calculated in the average viscosity calculation step, wherein the program comprises: an analysis program that causes a computer to execute the following steps: 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 integration points for a molten metal flow analysis in an analysis domain on the wall surface side of 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 points 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; and an analysis step of analyzing the flow of the molten metal in the analysis domain based on the average viscosity coefficient calculated in the average viscosity calculation step; an analysis program further causing the computer to execute a provisional average viscosity calculation step of calculating an average viscosity coefficient of the molten metal by numerically integrating the viscosity coefficient calculated in the provisional viscosity calculation step; and a repetition step of repeating the calculation process of calculating the average viscosity coefficient by the provisional viscosity calculation step and the provisional average viscosity calculation step while changing the number of integration points, wherein the integration point setting step sets, among the calculation processes repeated in the repetition step, an integration point at which the calculated average viscosity coefficient falls within a predetermined threshold and has the fewest number of integration points as an integration point during the molten metal flow analysis.

2. The analysis program according to claim 1, wherein the average viscosity calculation step and the provisional average viscosity calculation step calculate the average viscosity coefficient of the molten metal using the Gauss-Legendre integral formula.

3. The analysis program described in claim 1, further comprising: a temperature setting step in which, when a mesh adjacent to the first mesh on the wall side of the mold is defined as a second mesh and a mesh adjacent to the first mesh on the opposite side of the second mesh is defined as a third mesh, the computer is caused to execute a temperature setting step in which a temperature gradient of the molten metal in the first mesh is approximated in a curve based on the temperature of the mold in the second mesh and the temperature of the molten metal in the third mesh; and a viscosity calculation step in which the viscosity coefficient is calculated based on the temperature gradient approximated in a curve in the temperature setting step.

4. The analysis program described in claim 1, characterized in that the provisional temperature setting step sets the temperature at which the molten metal reaches the flow limit solid phase fraction as the temperature of the molten metal on the wall side of the mold, and sets the liquidus temperature of the molten metal as the temperature of the molten metal on the center side of the first mesh, thereby setting the provisional temperature gradient.

5. An analysis program as described in claim 4, characterized in that the provisional temperature setting step sets a provisional temperature gradient in which the temperature of the molten metal decreases proportionally from the center side of the first mesh to the surface side of the mold.

6. A method for analyzing molten metal flow, which causes a computer to execute the following steps: an analysis model setting step for setting an analysis model in which a model of a mold is divided into a plurality of meshes; an integration point setting step for setting integration points for molten metal flow analysis in an analysis region on the wall surface side of the mold in a first mesh of the plurality of meshes set in the analysis model setting step; a viscosity calculation step for calculating a viscosity coefficient of the molten metal based on the temperature of the molten metal at the integration points set in the integration point setting step; an average viscosity calculation step for calculating an average viscosity coefficient of the molten metal by numerically integrating the viscosity coefficient calculated in the viscosity calculation step; and an analysis step for analyzing the flow of the molten metal in the analysis region based on the average viscosity coefficient calculated in the average viscosity calculation step, a provisional average viscosity calculation step of calculating an average viscosity coefficient of the molten metal by numerically integrating the viscosity coefficient calculated in the provisional viscosity calculation step; and a repetition step of repeating the calculation process of calculating the average viscosity coefficient by the provisional viscosity calculation step and the provisional average viscosity calculation step while changing the number of integration points, wherein the integration point setting step sets, among the calculation processes repeated in the repetition step, an integration point at which the calculated average viscosity coefficient falls within a predetermined threshold and has the fewest number of integration points as an integration point for the molten metal flow analysis.

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