Analysis program and casting analysis method

Abstract

Since the multiple layers of mold meshes 15 arranged along the cavity 120 and the cooling structure 121 of the mold 12 are set to the bond-prohibited mesh, the entire cavity 120 and the cooling structure 121 can be covered with the multiple layers of bond-prohibited meshes. Then, the multiple mold meshes 15 excluding the bond-prohibited meshes are bonded to the primary bonded mesh 150, so that multiple layers of relatively fine mold meshes 15 can be left in the heat exchange regions R1 and R2, while the coarse primary bonded mesh 150 can be arranged in the region away from them. Therefore, the heat transfer calculation in the heat exchange regions R1 and R2 can be performed accurately, and the load of the heat transfer calculation in the region away from them can be reduced. Therefore, the temperature change of the mold 12 can be analyzed accurately in a short time.

Description

Technical Field

[0001] The present invention relates to an analysis program and a casting analysis method, and particularly to an analysis program and a casting analysis method capable of accurately analyzing the temperature change of a mold in a short time.

Background Art

[0002] There is a known technique for predicting in advance whether or not casting defects will occur in a casting by dividing a mold model into a plurality of meshes (elements) and analyzing the flow of molten metal and the solidification process in the meshes. In order to accurately analyze the flow of molten metal, it is necessary to accurately perform heat transfer calculations in a region where the temperature gradient is large in the vicinity of the cavity of the mold and the cooling structure (hereinafter referred to as the "heat exchange region"). If the heat exchange region is divided into fine meshes, the heat transfer calculation in the region can be made accurate. On the other hand, if the entire mold is divided into fine meshes, the total number of meshes increases and the time required for analysis becomes long.

[0003] Particularly in recent years, the demand for large-scale casting equipment such as gigapresses and gigacasts has been increasing. In addition to the casting (cavity), if such a large mold is divided into fine meshes, the analysis time becomes extremely long. Therefore, a technique using a so-called non-uniformly divided mesh, in which the mesh size is reduced in the heat exchange region of the mold while the mesh size is increased in the region far from it, has attracted attention.

[0004] As a technique using this type of non-uniformly divided mesh, for example, in Patent Document 1, after generating primary meshes for a model of a substrate having a copper wiring 50, the primary meshes including the copper wiring 50 are left without being combined, while secondary meshes are generated by combining the primary meshes not including the copper wiring 50. According to this technique, the warping of the substrate can be accurately analyzed in the region including the copper wiring 50, and the calculation load can be reduced in the region far from the copper wiring 50.

Prior Art Documents

Patent Documents

[0005] [Patent Document 1] Japanese Patent Publication No. 2005-050137 (e.g., paragraphs 0023-0043, Figures 4-6) [Overview of the project] [Problems that the invention aims to solve]

[0006] In the technology described in Patent Document 1, the mesh on the copper wiring 50, or the mesh adjacent to the mesh on the copper wiring 50, is combined as a secondary mesh (see Figure 6 in Patent Document 1). When this technology from Patent Document 1 is applied to a mold model, a secondary mesh (combined mesh) is also placed in the heat exchange region, making it impossible to accurately perform heat transfer calculations in that region. Therefore, there was a problem in that the temperature changes of the mold could not be analyzed with accuracy.

[0007] This invention was made to solve the above-mentioned problems, and aims to provide an analysis program and a casting analysis method that can analyze temperature changes in a mold quickly and accurately. [Means for solving the problem]

[0008] To achieve this objective, the present invention provides an analysis program and casting analysis method which involves causing a computer to execute the following steps: a model generation step of generating an analysis model of a mold having a heat exchange section consisting of a cavity or cooling structure; a mesh generation step of generating a plurality of meshes on the analysis model generated in the model generation step; a setting step of setting meshes that are not to be joined as non-joining meshes from among the plurality of meshes generated in the mesh generation step; a joining step of generating an unequal division mesh by excluding the non-joining meshes set in the setting step and joining the meshes located on the mold; and a casting analysis step of performing a casting analysis using the unequal division mesh generated in the joining step, wherein in the setting step, a plurality of layers of meshes arranged along the heat exchange section are generated.and the multiple layers of the mesh overlap in a direction away from the heat exchange section. By setting the connection-prohibiting mesh to this setting, the heat exchange section is covered by multiple layers of the connection-prohibiting mesh. [Effects of the Invention]

[0009] According to the analysis program described in claim 1 and the casting analysis method described in claim 7, a plurality of mesh layers are arranged along the heat exchange section of the mold. Therefore, multiple layers of mesh overlap in a direction away from the heat exchange section. The system includes a setting step to set a non-joining mesh, allowing the entire heat exchange section to be covered with multiple layers of non-joining mesh. In the joining step, the meshes on the mold, excluding the non-joining mesh, are joined together. This allows multiple layers of relatively fine mesh to remain in the area adjacent to the heat exchange section (hereinafter referred to as the "heat exchange area"), while a coarser joined mesh can be placed in areas further away. Therefore, heat transfer calculations in the heat exchange area can be performed accurately, while the load on heat transfer calculations in areas further away can be reduced. This has the effect of enabling accurate analysis of the mold temperature change in a short amount of time.

[0010] According to the analysis program described in claim 2, in addition to the effects of the analysis program described in claim 1, in the coupling step, the coupling mesh is generated sequentially from a starting point away from the heat exchange section toward the heat exchange section. Therefore, even if fine meshes that cannot be coupled remain, these fine meshes can be placed near the heat exchange region. Thus, it is possible to accurately calculate heat transfer in the heat exchange region while reducing the load on heat transfer calculations in regions far from it.

[0011] The analysis program described in claim 3 provides the following effects in addition to those of the analysis program described in claim 1. In the setting step and the joining step, the process of setting joined meshes adjacent to a joined-prohibited mesh as joined-prohibited meshes, and then joining joined meshes excluding the joined-prohibited meshes, is repeated multiple times. As a result, the joined mesh can be gradually coarsened as it moves away from the heat exchange region. Therefore, it is possible to perform heat transfer calculations accurately in the heat exchange region and reduce the load on heat transfer calculations in regions far from it.

[0012] According to the analysis program described in claim 4, in addition to the effects of the analysis program described in claim 3, in the setting step, meshes that could not be joined and remained unjoined in the joining step are set as meshes that should not be joined, making it easier to search for meshes that should be joined. Therefore, there is an effect of reducing the processing load associated with that search.

[0013] The analysis program described in claim 5 provides the following effects in addition to those of the analysis program described in claim 1. When a fine mesh and a coarser mesh adjacent to the fine mesh and coarser than the fine mesh are formed in an unequal division mesh, the following steps are performed in the casting analysis step.

[0014] Specifically, in the virtual joining step, adjacent fine meshes to a coarse mesh are virtually joined and defined as a virtual joined mesh, and in the virtual division step, the coarse mesh is virtually divided into fine meshes of the same size and defined as a virtual divided mesh. In the temperature calculation step, the temperature of the virtual divided mesh is calculated based on the temperatures of the virtual joined mesh and other coarse meshes arranged around the coarse mesh, and in the heat transfer calculation step, heat transfer calculations are performed between the fine meshes and the virtual divided mesh based on their temperatures. This allows for more accurate heat transfer calculations between the meshes compared to simply calculating heat transfer based on the temperatures of the fine mesh and the coarse mesh. Therefore, it has the effect of being able to analyze the temperature changes of the mold with high accuracy.

[0015] The analysis program described in claim 6 provides the following effects in addition to those of the analysis program described in claim 1: Removes the meshes that are prohibited from joining, which were set in the setting step. Kume The system includes an adjustment step that adjusts the number of meshes based on the number of meshes, and in this adjustment step, the number of meshes is adjusted to reduce the number of unjoinable meshes that cannot be joined in the joining step. This has the effect of suppressing the generation of unjoinable meshes in the joining step, thereby enabling the proper generation of unequal subdivision meshes. [Brief explanation of the drawing]

[0016] [Figure 1] This is an external view of the analysis device showing how it performs casting analysis of molten metal using an analytical model. [Figure 2] (a) is a schematic diagram of the analysis model showing the state in which template meshes other than those prohibited from joining have begun to be joined to the primary joined mesh, and (b) is a schematic diagram of the analysis model showing the state in which the generation of the primary joined mesh has been completed. [Figure 3] (a) is a schematic diagram of the analysis model showing a state in which some non-connectable meshes and some primary connected meshes are designated as meshes that cannot be connected, and (b) is a schematic diagram of the analysis model showing a state in which primary connected meshes are connected to generate secondary connected meshes. [Figure 4] This is a schematic diagram of an analysis model showing a state where some non-connectable meshes and secondary connected meshes are designated as meshes that cannot be connected. [Figure 5] (a) is a graph showing the calculated heat flux when four layers of mold mesh are placed outside the molten metal mesh, and (b) is a graph showing the calculated heat flux when two layers of mold mesh are placed outside the molten metal mesh. [Figure 6] This is an explanatory diagram for performing a two-dimensional heat transfer calculation between a template mesh and a primary bonded mesh. [Figure 7] (a) is a block diagram showing the electrical configuration of the analysis device, and (b) is a flowchart of the analysis process. [Figure 8]This is a flowchart of the unequal division mesh generation process.

Embodiments for Carrying out the Invention

[0017] 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 and solidification analysis (hereinafter referred to as "casting analysis") of the molten metal 11 are performed in the analysis model 10. In FIG. 1, the molten metal 11 flowing in the cavity 120 of the mold 12 and the cooling structure 121 of the mold 12 are provided with dot-like hatching.

[0018] As shown in FIG. 1, the analysis device 1 is an information processing device (personal computer) that divides the mold 12 defined in the analysis model 10 into a molten metal mesh 13, a cooling mesh 14, and a mold mesh 15, and analyzes the temperature changes of the molten metal 11 and the mold 12 in each of these meshes 13 to 15.

[0019] 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 including information such as the shape of the cavity 120, the presence or absence of the cooling structure 121 (for example, cooling pipes), and the position and shape of the pouring gate (weir). The analysis device 1 divides the created analysis model 10 into each of the meshes 13 to 15. Each of these meshes 13 to 15 is a solid element of a polyhedron (in this embodiment, a hexahedron).

[0020] The analysis device 1 is provided with a mouse 2 and a keyboard 3 (input devices) for the user to input conditions for casting analysis, etc. The analysis conditions input by the user are information regarding casting conditions such as the physical properties, initial temperature, pouring speed, etc. of the molten metal 11 in addition to the data of the mold 12 described above.

[0021] The analysis device 1 performs casting analysis based on the analysis conditions entered by the user and the temperature changes of the molten metal 11 and the mold 12. The analysis device 1 is equipped with a display 4 for displaying the analysis results. Based on the casting analysis results displayed on this display 4, the user can predict in advance the areas where casting defects are likely to occur in the castings manufactured using the mold 12 designed by the user.

[0022] The molten metal mesh 13 located on the cavity 120 of the mold 12 is positioned on the interior side of the cavity 120 relative to the wall surface of the mold 12, and the cooling mesh 14 located on the cooling structure 121 is positioned on the interior side of the cooling structure 121 relative to the boundary between the mold 12 and the cooling structure 121. In other words, these molten metal meshes 13 and cooling meshes 14 are meshes that do not include (or are in contact with) the edges of the cavity 120 or the cooling structure 121.

[0023] On the other hand, the mold mesh 15 is the mesh located on the mold 12 other than the molten metal mesh 13 and the cooling mesh 14. The heat exchange regions R1 and R2 (areas with hatched areas in Figure 1) near the molten metal mesh 13 (cavity 120) and the cooling mesh 14 (cooling structure 121) tend to have large temperature gradients. Therefore, in order to accurately predict defects occurring on the surface of the casting, it is important to perform accurate heat transfer calculations in the mold mesh 15 located in these regions R1 and R2. On the other hand, in areas far from the heat exchange regions R1 and R2, the temperature gradient is relatively small, and rigorous heat transfer calculations are not necessary.

[0024] Therefore, in this embodiment, a fine mold mesh 15 is generated in the heat exchange regions R1 and R2, while a primary bonded mesh 150 is generated outside of it by joining the mold meshes 15 together. Furthermore, a secondary bonded mesh 151 is generated outside of the primary bonded mesh 150 by joining the primary bonded meshes 150 together, and a tertiary bonded mesh 152 is generated further outside by joining the secondary bonded meshes 151 together.

[0025] Because the casting analysis is performed using the unequally divided mold mesh 15 and each of the connected meshes 150-152, heat transfer calculations can be performed accurately in the heat exchange regions R1 and R2 with large temperature gradients, while the load of heat transfer calculations can be reduced in regions with small temperature gradients that are far from these regions.

[0026] The method for generating this unequal division mesh will be explained with reference to Figures 2 to 4. Figure 2(a) is a schematic diagram of the analysis model 10 showing the state in which the template meshes 15 other than the meshes that are not to be joined have begun to be joined to the primary joined mesh 150, and Figure 2(b) is a schematic diagram of the analysis model 10 showing the state in which the generation of the primary joined mesh 150 has been completed.

[0027] Figure 3(a) is a schematic diagram of the analysis model 10 showing a state in which some of the unconnectable meshes 153 and primary connected meshes 150 are designated as meshes that cannot be connected, and Figure 3(b) is a schematic diagram of the analysis model 10 showing a state in which the primary connected meshes 150 are connected to generate secondary connected meshes 151. Figure 4 is a schematic diagram of the analysis model 10 showing a state in which some of the unconnectable meshes 153 and secondary connected meshes 151 are designated as meshes that cannot be connected.

[0028] As shown in Figure 2(a), when generating an unequal division mesh, first, multiple meshes 13 to 15 of a very small size (for example, with sides of 0.5 mm) are generated on the model of the mold 12. All of these meshes 13 to 15 are the same size. Next, among the multiple mold meshes 15, the multiple layers of mold mesh 15 placed within the heat exchange regions R1 and R2 are designated as non-connecting meshes. In Figure 2(a), the mold meshes 15 designated as non-connecting meshes are given a dot-like hatching that is denser than that of the molten metal mesh 13 and cooling mesh 14 (the same applies in subsequent figures).

[0029] In this embodiment, multiple layers of mold mesh 15, including all mold meshes 15 adjacent to the molten metal mesh 13 and cooling mesh 14, are designated as non-binding meshes, extending outward from the mold 12 (away from each mesh 13 and 14). Note that the number of non-binding mesh layers may be other than three.

[0030] After designating the template mesh 15 on the heat exchange regions R1 and R2 as a non-joinable mesh, a primary joined mesh 150 is generated by joining 2×2×2 (8 in total) template meshes 15, as shown in the lower right portion of Figure 2(a) (in Figure 2(a), the analysis model 10 is shown in two dimensions, so the joining of the 2×2 template meshes 15 is illustrated).

[0031] Thus, in this embodiment, since the multiple layers of mold mesh 15 arranged along the cavity 120 of the mold 12 and the cooling structure 121 (molten metal mesh 13 and cooling mesh 14) are set as bond-preventing meshes, the entire cavity 120 and cooling structure 121 can be covered with multiple layers of bond-preventing mesh.

[0032] Furthermore, by removing the non-binding meshes, multiple template meshes 15 are joined together in the primary bonding mesh 150. This allows multiple layers of relatively fine template meshes 15 to remain in the heat exchange regions R1 and R2, while coarser primary bonding meshes 150 can be placed in regions further away. Therefore, heat transfer calculations in the heat exchange regions R1 and R2 can be performed accurately, while the load on heat transfer calculations in regions further away can be reduced. Consequently, the temperature change of the template 12 can be analyzed accurately in a short amount of time.

[0033] The starting point for generating the primary combined mesh 150 can be set arbitrarily, but in this embodiment, the generation of the primary combined mesh 150 is started from the starting point P (the edge of the analysis model 10) furthest from the heat exchange regions R1 and R2. More specifically, a plurality of template meshes 15, including a template mesh 15 touching the starting point P, are joined to the primary combined mesh 150, and then a plurality of template meshes 15 touching the joined primary combined mesh 150 are joined to the primary combined mesh 150.

[0034] This bonding process is carried out sequentially from the starting point P toward the heat exchange regions R1 and R2. Figure 2(a) illustrates the case where primary bonded meshes 150 are sequentially generated toward the left side (towards the heat exchange region R1) from the starting point P. After the bonding of this row of primary bonded meshes 150 is completed, the template mesh 15 located one row above (closest to the starting point P) is sequentially bonded to the primary bonded meshes 150 toward the left side from the starting point P.

[0035] Alternatively, the primary connected mesh 150 may be generated sequentially upwards from the starting point P. Alternatively, after generating the primary connected mesh 150 including the starting point P, all adjacent template meshes 15 may be simultaneously joined to the primary connected mesh 150. That is, the primary connected mesh 150 may be generated simultaneously at two locations, to the left and above the primary connected mesh 150 including the starting point P, as shown in Figure 2(a). Figure 2(b) illustrates the state after the generation of such primary connected meshes 150 has been completed.

[0036] As shown in Figure 2(b), depending on the number of template meshes 15 from the edge (starting point P) of the analysis model 10 to the heat exchange regions R1 and R2, and the number of template meshes 15 between the heat exchange regions R1 and R2, some unconnectable meshes 153 that cannot be connected as primary connected meshes 150 remain.

[0037] Therefore, in a configuration where, for example, primary connected meshes 150 are sequentially generated starting from the heat exchange regions R1 and R2 and moving away from those regions R1 and R2, unconnected meshes 153 remain at positions far from the heat exchange regions R1 and R2.

[0038] In contrast, in this embodiment, a starting point P is set at a location away from the heat exchange regions R1 and R2, and a primary bonded mesh 150 is sequentially generated from the starting point P toward the heat exchange regions R1 and R2. This allows for the placement of a coarser primary bonded mesh 150 in locations away from the heat exchange regions R1 and R2, while leaving relatively small unbonded meshes 153 (template meshes 15) in the vicinity of the heat exchange regions R1 and R2. Therefore, heat transfer calculations in the heat exchange regions R1 and R2 can be performed accurately, while the load on heat transfer calculations in areas far from them can be reduced.

[0039] Here, in the intermediate region R3 located at the upper end of Figure 2(b), which is sandwiched between the heat exchange regions R1 and R2, two primary bonded meshes 150a are arranged side by side, and a total of four non-bonded meshes 153a are arranged on either side of these two primary bonded meshes 150a. Therefore, in the state before the primary bonded meshes 150a are generated in this intermediate region R3, there are 2 × 6 template meshes 15 in two dimensions, so it is actually possible to form three primary bonded meshes 150 in this intermediate region R3.

[0040] However, performing such processing causes the center positions of the three primary connected meshes 150 generated in the intermediate region R3 and the other primary connected meshes 150 adjacent to those three primary connected meshes 150 (located on the lower side of Figure 2(b)) to shift laterally. Such a shift makes heat transfer calculations between meshes complicated.

[0041] In contrast, in this embodiment, since the four template meshes 15 in the intermediate region R3 are left as non-connectable meshes 153a, the primary connected meshes 150a arranged in the same region R3 can be aligned vertically with the other primary connected meshes 150 (the center positions of each primary connected mesh 150 are aligned vertically and horizontally). By aligning all the primary connected meshes 150 in a grid in this way, heat transfer calculations between those meshes can be easily performed.

[0042] As shown in Figure 3(a), the unconnectable mesh 153 that could not be connected as a primary connected mesh 150 is designated as a non-connectable mesh. In addition, among the primary connected meshes 150, primary connected meshes 150 adjacent to non-connectable meshes (template mesh 15 and unconnectable mesh 153) are also designated as non-connectable meshes.

[0043] Note that Figure 3(a) illustrates the case where a single-layer primary mesh 150 adjacent to a mesh that cannot be joined is designated as a mesh that cannot be joined. However, two or more layers of primary meshes 150 can also be designated as meshes that cannot be joined (the same applies when generating the tertiary mesh 152 described later).

[0044] Next, as shown in Figure 3(b), the 2x2x2 (8 in total) primary mesh 150, excluding the meshes that cannot be joined, are joined to generate a secondary mesh 151. Even when generating the secondary mesh 151, the secondary mesh 151 is generated sequentially starting from a starting point P that is far from the heat exchange regions R1 and R2. Therefore, the unjoinable meshes 153 that could not be joined as secondary mesh 151 can be placed in a position close to the heat exchange regions R1 and R2.

[0045] Note that the 2x2 primary mesh 150b enclosed by the thick line in Figure 3(b) can actually be joined as a secondary mesh 151. However, if these primary meshes 150b are joined, a secondary mesh will be generated at a position offset from the other secondary meshes 151. Therefore, in this embodiment, these primary meshes 150b are intentionally left unjoined (remaining as unjoinable meshes 153). This allows all secondary meshes 151 to be aligned in a grid pattern.

[0046] Next, as shown in Figure 4, the unconnectable meshes 153 that could not be connected as secondary connected meshes 151 are designated as non-connectable meshes. In addition, among the secondary connected meshes 151, those adjacent to the non-connectable meshes (primary connected meshes 150 and unconnectable meshes 153) are designated as non-connectable meshes. Then, excluding the non-connectable meshes, the 2x2x2 (8 in total) secondary connected meshes 151 are connected to generate a tertiary connected mesh 152 (see Figure 1).

[0047] Thus, in this embodiment, when a secondary combined mesh 151 is generated, a primary combined mesh 150 adjacent to a mesh that is prohibited from being combined (template mesh 15 or uncombinable mesh 153) is designated as a mesh that is prohibited from being combined, and the primary combined mesh 150 excluding that prohibited mesh is combined with the secondary combined mesh 151. Similarly, when a tertiary combined mesh 152 is generated, a secondary combined mesh 151 adjacent to a mesh that is prohibited from being combined is designated as a mesh that is prohibited from being combined.

[0048] By employing this joining method, the mesh size can be gradually increased in the following order: template mesh 15, primary joined mesh 150, secondary joined mesh 151, and tertiary joined mesh 152. More specifically, every primary joined mesh 150 (if it is an n-th order joined mesh, then n=1) is always adjacent to either a primary joined mesh 150 or a secondary joined mesh 151 (n-th order joined mesh or n+1-th order joined mesh). In other words, a tertiary joined mesh 152 (n+2-th order joined mesh) is never placed next to a primary joined mesh 150.

[0049] In this way, by gradually increasing the coarseness of the mold mesh 15 as you move away from the heat exchange regions R1 and R2, it is possible to accurately calculate heat transfer in the heat exchange regions R1 and R2, while reducing the load on heat transfer calculations in regions further away.

[0050] While generating such an unequal division mesh allows for accurate analysis of the temperature change of the mold 12 in a short time, it tends to complicate heat transfer calculations between meshes of different sizes (for example, at the boundary between the mold mesh 15 and the primary bonded mesh 150). A method for accurately performing these heat transfer calculations will be explained with reference to the enlarged portion of Figure 4.

[0051] As shown in the enlarged section of Figure 4, among the mold mesh 15, the one placed in the third layer from the molten metal mesh 13 side will be described as mold mesh 15a, and the one placed outside of mold mesh 15a will be described as mold mesh 15b. Furthermore, among the primary bond mesh 150, the one placed outside of mold mesh 15b will be described as primary bond mesh 150c, and the one placed outside of primary bond mesh 150c will be described as primary bond mesh 150d.

[0052] First, we will explain the case where heat transfer calculations between the mold mesh 15b and the primary bonded mesh 150c are performed in one dimension. In this one-dimensional heat transfer calculation, the two layers of mold meshes 15a and 15b are virtually joined and defined as a virtual bonded mesh 15e. The boundary between this virtual bonded mesh 15e and the primary bonded mesh 150c is set to ξ=0, and the temperature Te (average temperature; the same applies below) of the virtual bonded mesh and the temperatures Tc and Td of the primary bonded meshes 150c and 150d are approximated by, for example, the following quadratic function, Equation 1.

[0053]

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[0055]

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[0062] Figure 5(a) is a graph showing the calculation results of the heat flux from the mold mesh 15b to the primary bonded mesh 150c (virtual divided mesh 150f). In Figure 5(a), the vertical axis represents the magnitude q of the heat flux, and the horizontal axis represents the elapsed time t(s) during the casting analysis (the same applies to Figure 5(b), which will be described later). The solid line graph in Figure 5(a) is the exact solution of the heat flux from the mold mesh 15b to the primary bonded mesh 150c, and the dashed line graph shows the magnitude of the heat flux qb→f calculated by the above equation 9.

[0063] Furthermore, the dashed-dotted line in Figure 5(a) shows the heat flux qb→c from the template mesh 15b to the primary bonded mesh 150c, calculated simply based on the temperatures Tb and Tc of those meshes, as shown in equation 10 below.

[0064]

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[0065] As mentioned above, the temperature gradient of the mold 12 becomes larger the closer it is to the heat exchange regions R1 and R2. For this reason, if, for example, the two layers of mold mesh 15g and 15h (see Figure 4) located inside the mold meshes 15a and 15b are omitted, and the mold meshes 15a and 15b are placed adjacent to the molten metal mesh 13 (i.e., the two layers of mold mesh 15a and 15b are placed outside the molten metal mesh 13), the temperature Ta of the mold mesh 15a may temporarily become very large compared to the temperature Tb of the mold mesh 15b.

[0066] In a situation with such a large temperature gradient, if the temperature Te of the virtual combined mesh 15e (Te=(Ta+Tb) / 2) is calculated from the average temperatures Ta and Tb of the mold mesh 15a and 15b, and the temperature Tf of the virtual divided mesh 150f is calculated from this temperature Te of the virtual combined mesh 15e, the temperature Tf of the virtual divided mesh 150f may be estimated to be higher than the temperature Tb of the mold mesh 15b. In this case, the heat flux qb→f from the mold mesh 15b to the virtual divided mesh 150f is calculated as a negative value. This phenomenon will be referred to as undershoot below, and will be explained with reference to Figures 5(a) and 5(b).

[0067] Figure 5(a) is a graph showing the calculated heat flux when four layers of mold mesh 15a, 15b, 15g, and 15h are placed outside the molten metal mesh 13 as in this embodiment, and Figure 5(b) is a graph showing the calculated heat flux when two layers of mold mesh 15a and 15b are placed outside the molten metal mesh 13.

[0068] As shown in Figure 5(b), when two layers of mold mesh 15a and 15b are placed outside the molten metal mesh 13, no undershoot occurs in the heat flux qb→c value, shown by the dashed line, while an undershoot occurs in the heat flux qb→f value, shown by the dashed line. This undershoot of the heat flux qb→f occurs in a very short time during the initial stage of the casting analysis (the stage when heat input from the molten metal mesh 13 to the mold mesh 15a and 15b begins). Therefore, although the impact of the undershoot of the heat flux qb→f on the accuracy of the casting analysis is small, it is preferable that such an undershoot does not occur.

[0069] Therefore, as shown in Figure 4, it is preferable to arrange about four layers of mold mesh 15a, 15b, 15g, and 15h on the outside of the molten metal mesh 13. This allows the heat transfer calculation between the mold mesh 15b and the primary bond mesh 150c to be performed in a region with a relatively small temperature gradient, thereby suppressing undershoot in the heat flux qb→f value, as shown in Figure 5(a). Consequently, the temperature change of the mold 12 can be analyzed with high accuracy.

[0070] Next, with reference to Figure 6, we will explain the case where heat transfer calculations between the mold mesh 15 and the primary bonded mesh 150c are performed in two dimensions. Figure 6 is an explanatory diagram of the case where heat transfer calculations between the mold mesh 15 and the primary bonded mesh 150c are performed in two dimensions.

[0071] As shown in Figure 6, the primary bonded mesh 150c may have a mold mesh 15 adjacent to its left side and two sides above and below it (a total of three sides). In this case, when performing a two-dimensional heat transfer calculation between the mold mesh 15 and the primary bonded mesh 150c, the mold mesh 150c is virtually divided (divided into four parts) to the same size as the mold mesh 15 and defined as virtual divided meshes 150ia to 150id. Then, the corner of the virtual divided mesh 150ia (the intersection of the two sides adjacent to the mold mesh 15) is taken as the origin O, and the temperature distribution of the mesh relative to this origin O is assumed to be, for example, as shown in equation 11 below.

[0072]

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[0073] Furthermore, let Tn and Tp be the temperatures of two primary joined meshes 150 that are in contact with (share an angle with) the primary joined mesh 150c. Let TO and Tq be the temperatures of a 2x2 template mesh 15 that is in contact with (shares an angle with) the primary joined mesh 150c.

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[0079] Thus, in this embodiment, when performing heat transfer calculations between the mold mesh 15 and the primary combined mesh 150 (fine mesh and coarse mesh), the following processes are executed: a process in which the mold mesh 15 is virtually combined and defined as a virtual combined mesh (virtual combination step), and a process in which the primary combined mesh 150 (coarse mesh) is virtually divided into the same size as the mold mesh 15 and defined as a virtual divided mesh (virtual division step).

[0080] Furthermore, the process includes calculating the temperature of the virtual divided mesh based on the temperatures (temperature distribution) of the virtual joined mesh and the primary joined mesh 150 arranged around the virtual divided mesh (temperature calculation step), and performing heat transfer calculations between the meshes based on the temperatures of the template mesh 15 and the virtual divided mesh (heat transfer calculation step). This enables accurate heat transfer calculations between meshes 15 and 150 of different sizes.

[0081] In the above explanation, we have illustrated how to perform heat transfer calculations between the mold mesh 15 and the primary bonded mesh 150 in one or two dimensions, but similar heat transfer calculations can be performed in three dimensions. Furthermore, similar heat transfer calculations can be performed between other relatively fine meshes (e.g., the primary bonded mesh 150) and meshes that are coarser than the fine mesh (e.g., the secondary bonded mesh 151).

[0082] Next, the analysis process performed by the analysis device 1 will be described with reference to Figures 7 and 8. Figure 7(a) is a block diagram showing the electrical configuration of the analysis device 1, and Figure 7(b) is a flowchart of the analysis process.

[0083] As shown in Figure 7(a), the analysis device 1 has a CPU 5, an HDD (hard disk drive) 6, and RAM 7, which are connected to input / output ports via a bus line 8. The aforementioned mouse 2, keyboard 3, and display 4 are also connected to the bus line 8.

[0084] The CPU 5 is an arithmetic unit that controls each part 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 6a stored in the HDD 6 is executed by the CPU 5, the analysis process (see Figure 7(b)) is performed.

[0085] RAM7 is a memory that the CPU5 uses to store various work data and flags in a rewritable format when executing the analysis program 6a. RAM7 is equipped with a join flag 7a used in the unequal division mesh generation process (S2). This join flag 7a is set for each template mesh 15 and each join mesh 150-152, and is used to determine whether or not a mesh is prohibited from joining. When an instruction to execute the analysis program 6a is input from the mouse 2 or keyboard 3, the CPU 5 executes the analysis process.

[0086] As shown in Figure 7(b), the analysis process first involves setting various analysis conditions (S1). These analysis conditions include the physical properties of the molten metal 11 (casting), the pouring speed of the molten metal 11, the acceleration due to gravity, the data of the mold 12, and the size of each mesh 13-15. The physical properties of the molten metal 11 include information such as the density, specific heat, and thermal conductivity of the molten metal 11, while the data of the mold 12 includes the data on the structure of the mold 12 as described above, as well as information such as the density, specific heat, and thermal conductivity of the mold 12.

[0087] The conditions set in process S1 are mainly entered by the user, but some of these settings may be performed automatically by the analysis program 6a. Once the various analysis conditions are set in process S1, an analysis model 10 is generated, and after the generation of this analysis model 10, the unequal mesh generation process (S2) is executed. This process will be explained with reference to Figure 8. Figure 8 is a flowchart of the unequal mesh generation process (S2).

[0088] As shown in Figure 8, the unequal division mesh generation process (S2) first generates multiple meshes 13 to 15 on the mold 12 of the analysis model 10 (S10). At this time, each mesh 13 to 15 is assigned a member number indicating that it is located on the mold 12, cavity 120, or cooling structure 121. Next, the molten metal mesh 13 and cooling mesh 14 are identified (searched) based on the member number, and the value of the joining flag 7a for these meshes 13 and 14 is set to 0, indicating that they are not joined meshes (S11). Next, the number of times the mold mesh 15 is joined is set to N (S12). This number of joins N may be set by the user or automatically by the analysis program 6a.

[0089] In the above embodiment, the template mesh 15 is joined three times (N=3), and the case where it is joined up to a cubic joined mesh 152 (n=1,2,3 if it is an n-th order joined mesh) was described. However, the number of joins can be one or more (N is an integer of 1 or more, and if it is joined up to an n-th order joined mesh, then n=1,2,3...).

[0090] After processing in S12, the value of the join flag 7a for all template meshes 15 is set to 1, indicating that it is a mesh to be joined (S13), and the number of layers of meshes that are not to be joined is set (S14). The number of layers of meshes that are not to be joined may also be set by the user, or it may be set automatically by the analysis program 6a.

[0091] After processing in S14, the value of the join flag 7a for the join-prohibited mesh is set to 0 (S15). Next, in the join process in the following S17, the number of layers of the template mesh 15 is adjusted so that as few unjoinable meshes 153 as possible are generated (S16). Specifically, the number of template meshes 15 excluding the join-prohibited mesh set in S14 is checked in three dimensions, and the total number of meshes is adjusted to reduce the number of unjoinable meshes 153 generated in the subsequent join process, based on the number of meshes to be joined (whether 2x2x2 meshes are joined or 3x3x3) and the number of joins performed (how many order of joined meshes are generated).

[0092] Examples of such processing include adding a template mesh 15 with one or more layers (columns) to the edge of the analysis model 10 (for example, the right edge of Figure 2(a)), or reducing the number of layers of meshes that are not to be joined. This mesh number adjustment process may be performed only once before generating the primary joined mesh 150, or it may be performed when generating the nth-order joined mesh (for example, the secondary joined mesh 151), by adjusting the number of n-1th-order joined meshes (for example, the primary joined mesh 150).

[0093] By performing the mesh count adjustment process in S16, when mesh joining is started from a starting point P far from the heat exchange regions R1 and R2, it is possible to suppress the remaining unjoinable meshes 153 in the vicinity of the R1 and R2 regions. Therefore, the intended number of layers of template mesh 15 can be placed on the heat exchange regions R1 and R2. Also, when mesh joining is started from the heat exchange regions R1 and R2, it is possible to suppress the remaining unjoinable meshes 153 in areas far from that point. In this way, by suppressing the generation of unjoinable meshes 153, an unequal division mesh can be appropriately generated.

[0094] After processing in S16, the system searches for template meshes 15 with the join flag 7a set to 1, and the searched template meshes 15 are joined together to generate a primary joined mesh 150 (S17). In the above embodiment, the case in which 2 × 2 × 2 template meshes 15 are joined to the primary joined mesh 150 has been described, but 3 × 3 × 3 or more template meshes 15 may also be joined to the primary joined mesh 150 (the same applies when joining an n-th order joined mesh to an n+1-th order joined mesh).

[0095] Furthermore, the number of meshes to be joined may differ depending on whether an n-th order joined mesh is generated or an n+1-th order joined mesh is generated. An example of such a configuration is one in which 2x2x2 primary joined meshes 150 are joined to generate a secondary joined mesh 151, while 4x4x4 secondary joined meshes 151 are joined to generate a tertiary joined mesh 152.

[0096] After processing in S17, it is checked whether the number of mesh joins has reached N (S18). In processing S18, if the number of joins has not reached N (S18: No), the join flag 7a of the unjoinable mesh 153 that could not be joined as the primary joined mesh 150 is set to 0 (S19), and the process returns to S14.

[0097] In the second S14 process, the number of layers to be designated as meshes that should not be joined among the primary joined meshes 150 is set, and the join flag 7a of the meshes that should not be joined is set to 0 (S15). Next, the number of layers of the primary joined meshes 150 is adjusted (S16), or the S16 process is skipped, and primary joined meshes 150 with the join flag 7a set to 1 are joined together to generate a secondary joined mesh 151 (S17). At this time, since the join flag 7a of all meshes that should not be joined, including the unjoinable mesh 153, is set to 0, the primary joined meshes 150 that should be joined can be easily found.

[0098] After processing in S17, it is checked whether the number of mesh joins has reached N (S18). If the number of joins has not reached N (S18: No), the join flag 7a of the unjoinable mesh 153 that could not be joined as a secondary joined mesh 151 is set to 0 (S19), and the process returns to S14. This process from S14 to S19 is repeated, and the template mesh 15 is joined N times, generating up to an nth-order joined mesh. As a result, an unequal division mesh is generated on the template 12 of the analysis model 10 (see Figure 1).

[0099] On the other hand, if the number of mesh joining cycles in the S18 process reaches N (S18: Yes), the series of processes is terminated and the casting analysis process (S3) is executed (see Figure 7(b)). A detailed explanation of the method for analyzing the flow of the molten metal 11 in this casting analysis process (S3) is omitted as known techniques can be used, but examples of known analysis methods include the techniques described in Japanese Patent Publication No. 10-137926 and Japanese Patent Publication No. 06-122068.

[0100] In the casting analysis process (S3), the unequal mesh described above (see Figure 1) is used, which allows for accurate heat transfer calculations in the heat exchange regions R1 and R2 while reducing the load of heat transfer calculations in regions far from these regions. Furthermore, equations 1 to 16 above are used for heat transfer calculations between meshes of different sizes (for example, calculating the heat flux qb → f), thus enabling accurate heat transfer calculations in such cases.

[0101] Although the present invention has been described above based on the above embodiments, it can be easily inferred that the present invention is not limited in any way to the above embodiments, and that various modifications and improvements are possible without departing from the spirit of the present invention.

[0102] In the above embodiment, the case in which each connected mesh 150, 151 is sequentially generated from a starting point P away from the heat exchange regions R1, R2 toward the same regions R1, R2 was described, but the embodiment is not necessarily limited to this. For example, each connected mesh 150, 151 may be sequentially generated toward the heat exchange regions R1, R2.

[0103] Furthermore, if an intermediate region exists between heat exchange regions, the center of that intermediate region (the midpoint between each heat exchange region flanking the intermediate region) may be used as the starting point, and the coupled mesh may be sequentially generated from that starting point toward each heat exchange region. This allows for the placement of a coarser coupled mesh towards the center of the intermediate region, while allowing for the placement of fine meshes that could not be coupled (uncoupled meshes) near the heat exchange regions. An example of such an intermediate region is the intermediate region R3 described in the above embodiment (see Figure 2(b)). Also, for example, if another heat exchange region R4 exists on the opposite side of the starting point P from heat exchange region R1 (to the right in Figure 2), the region between these heat exchange regions R1 and R4 is the intermediate region.

[0104] In the above embodiment, the case in which the heat flux qb→f is calculated from the temperatures Tb and Tf of the mold mesh 15b and the virtual divided mesh 150f was described. However, the heat flux qb→c from the mold mesh 15b to the primary combined mesh 150c may also be calculated from the temperatures Tb and Tc of those meshes. [Explanation of Symbols]

[0105] 1. Analysis device (computer) 6a Analysis Program 10. Analysis Models 11 Molten metal 12 molds 120 Cavity (heat exchange section) 121 Cooling structure (heat exchange section) 13 Molten metal mesh 14 Cooling Mesh 15, 15g, 15h mold mesh 15a Mold mesh (fine mesh) 15b Mold mesh (fine mesh) 15e Virtual Joined Mesh 150, 150a, 150b Primary combined mesh (combined mesh) 150c Primary combined mesh (coarse mesh, combined mesh) 150d Primary Joined Mesh (Coarse Mesh, Joined Mesh) 150f virtual subdivided mesh 151 Secondary joined mesh (joined mesh) 152 tertiary joined mesh (joined mesh) 153,153a Unconnectable mesh S14,17 Setup Steps S15 Bonding step S16 Adjustment Step S3 Casting Analysis Process (Casting Analysis Step) P starting point

Claims

1. A model generation step for generating an analytical model of a mold having a heat exchange section consisting of a cavity or cooling structure, A mesh generation step that generates multiple meshes on the analysis model generated in the model generation step, A setting step in which, among the multiple meshes generated in the mesh generation step, meshes that are not to be joined are set as non-joining meshes, A joining step to generate an unequal division mesh by joining the meshes located on the template, excluding the meshes that are not to be joined as set in the setting step, A casting analysis program that causes a computer to perform a casting analysis step using the unequal division mesh generated in the coupling step, The analysis program is characterized in that, in the setting step, the heat exchange section is covered by the multiple layers of the non-connecting mesh, by setting the multiple layers of the mesh arranged along the heat exchange section, which overlap in a direction away from the heat exchange section, as the non-connecting mesh.

2. The analysis program according to claim 1, characterized in that the coupling step starts at a position away from the heat exchange section and sequentially generates the coupling mesh from that starting point toward the heat exchange section.

3. The setting step and the coupling step are repeated multiple times. The setting step involves setting the mesh adjacent to the mesh that is prohibited from joining as a mesh that is prohibited from joining. The analysis program according to claim 1, wherein the joining step further joins the joined meshes excluding the meshes that are prohibited from joining.

4. The analysis program according to claim 3, characterized in that the setting step sets the unjoinable meshes that remained unjoined in the joining step as the joining prohibited meshes.

5. The aforementioned unequal division mesh has a fine mesh and a coarser mesh adjacent to the fine mesh that is coarser than the fine mesh. In the aforementioned casting analysis step, A virtual joining step is performed to virtually join adjacent fine meshes to the aforementioned coarse mesh and define them as a virtual joined mesh. A virtual partitioning step in which the coarse mesh is virtually divided into the same size as the fine mesh and defined as a virtual partitioned mesh, A temperature calculation step of calculating the temperature of the virtual divided mesh based on the temperatures of the virtual combined mesh and other coarse meshes arranged around the coarse mesh, The analysis program according to claim 1, characterized in that it performs a heat transfer calculation step of performing a heat transfer calculation between the fine mesh and the virtual divided mesh based on the temperatures of the fine mesh and the virtual divided mesh.

6. The computer is further instructed to perform an adjustment step to adjust the number of meshes based on the number of meshes excluding the meshes that are prohibited from joining, as set in the setting step. The analysis program according to claim 1, characterized in that the adjustment step adjusts the number of meshes so as to reduce the number of unconnectable meshes that cannot be connected in the connection step.

7. A model generation step for generating an analytical model of a mold having a heat exchange section consisting of a cavity or cooling structure, A mesh generation step that generates multiple meshes on the analysis model generated in the model generation step, A setting step in which, among the multiple meshes generated in the mesh generation step, meshes that are not to be joined are set as non-joining meshes, A joining step to generate an unequal division mesh by joining the meshes located on the template, excluding the meshes that are not to be joined as set in the setting step, A casting analysis method comprising: a casting analysis step in which a computer performs a casting analysis using the unequal division mesh generated in the aforementioned joining step, The method for analyzing casting is characterized in that, in the setting step, the heat exchange portion is covered by the multiple layers of the non-binding mesh, by setting the multiple layers of the mesh arranged along the heat exchange portion, which overlap in a direction away from the heat exchange portion, as the non-binding mesh.

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