Overflow optimization design method aimed at preventing gas entrapment defects

Abstract

To provide an optimal design system that in order to completely discharge the molten metal in the product part that has entrained gas, estimates the flow direction of the molten metal during filling, and thereby, automatically designs the position and volume of the overflow.SOLUTION: For the purpose of preventing gas entrainment defects when manufacturing predetermined die casting products by casting, an optimal overflow design method performs calculations by computational fluid dynamics (CFD) using a computer. The method includes the following steps (1) and (2): an overflow position determination step (1) of determining an installation point of overflow of the die casting product; and an overflow volume determination step (2) of determining, after determining an initial shape of the overflow, a volume and shape of the overflow whose volume corresponding to a volume that is based on an evaluation (2-1) of the overflow gate and an evaluation (2-2) of the inside of the product.SELECTED DRAWING: Figure 19

Description

Technical Field

[0001] The present invention relates to an overflow optimal design method for preventing gas entrainment defects.

Background Art

[0002] In die casting, if gas is not discharged well during injection molding and is trapped in the product part, casting defects such as casting cavities occur, deteriorating the product quality. Therefore, exhaust schemes such as exhaust runners and overflows are designed to try to discharge gas to the outside of the mold as much as possible. At that time, due to the constraints of mold design, the installation range of the exhaust runner is limited, but the overflow has a high degree of design freedom and a wide installation range. Therefore, the importance of appropriately designing its position and size is high. Generally, the positions where overflows are installed are recommended to be (1) the final filling position of the molten metal, (2) the part where the molten metals merge, (3) the part with a low mold temperature, and (4) the part where the molten metal stagnates and becomes a dead angle (Non-Patent Document 1). Also, regarding the volume, it is considered desirable to install a plurality of small overflows rather than one large overflow (Non-Patent Documents 1 to 3). In recent years, research has been conducted on the optimization of die-casting mold shapes by combining optimization theory and computational fluid dynamics (hereinafter referred to as "CFD") (Non-Patent Documents 4 to 8). For example, El-Fotouh et al. have optimized the gate positions of a single overflow and runner using the experimental design method to minimize porosity (Non-Patent Document 7). Also, Tsukada et al. have optimized the gate positions of a plurality of overflows and runners to minimize the amount of gas entrainment, etc. (Non-Patent Document 8).

Prior Art Documents

Non-Patent Documents

[0003]

Non-Patent Document 1

Non-Patent Document 2

[0004] However, optimizing only the overflow location can lead to gas trapping in the product section or excessive molten metal discharge due to volume deficiencies or excesses. Furthermore, methods involving these iterative calculations are difficult to apply to the design of exhaust systems that analyze the entire mold, especially for products with complex shapes, due to computation time constraints. Therefore, the inventors proposed a method to automatically design the optimal exhaust gate without iterative calculations by quantitatively evaluating the molten metal filling time (Non-Patent Literature 9). However, optimizing only the exhaust gate is insufficient to completely discharge the molten metal containing gas from the product section, making the establishment of an appropriate overflow design method a challenge. This invention has been made in view of the above problems, and its purpose is to provide an optimal overflow design system that automatically designs the position of molten metal containing gas by considering the remaining position of the molten metal containing gas, and automatically designs the volume by estimating the flow direction of the molten metal containing gas during filling, in order to completely discharge the molten metal containing gas from the product section. [Means for solving the problem]

[0005] The inventors of this invention have diligently studied and, as a result of solving the above problems, have essentially completed the present invention. Thus, the overflow optimization design method according to the present invention aims to prevent gas entrapment defects when manufacturing a predetermined die-cast product by casting, and includes the following steps (1) and (2), and is an overflow optimization design method that performs calculations by computational fluid dynamics (CFD) calculations using a computer, (1) An overflow position determination step in which the installation point of the overflow of the die-cast product is determined, (2) After determining the initial shape of the overflow, an overflow volume determination step is performed to determine the volume and shape of the overflow corresponding to that volume, based on the evaluations in (2-1) and (2-2) below. In the (1) overflow location determination step, the molten metal flow is determined by CFD without providing an overflow, the remaining location of molten metal with gas entrained above a predetermined threshold is determined, and candidate overflow installation points Pc are determined from the distance from a point within a set range to the point where the gas entrained molten metal is located, the fluid residence time Tr is calculated for these candidate installation points, and the candidate installation point with the longest residence time Tr is set as the overflow installation point. In the (2) overflow volume determination step, a provisional volume of one overflow is determined, (2-1) In the overflow gate evaluation step, the fluid volume Vfr and air entrainment volume Var of the molten metal passing through the inspection surface set in the overflow gate are measured, and the air entrainment volume fraction Va is calculated. If Va is smaller than a predetermined threshold, the next internal evaluation step is performed. (2-2) In the internal evaluation step, which involves evaluating the inside of the product, only the molten metal cells containing gas around the overflow inside the product are extracted, the velocity vectors of each extracted cell are combined to obtain the vector [V] of the molten metal flow direction, the molten metal flow direction and the overflow position are expressed mathematically, and the following equation (3) is calculated for the vector [PfG] connecting point Pf on the normal and the centroid G, the vector [PfPv] connecting point Pf and point Pv which has moved from the centroid G to the tip of the molten metal flow direction, and the vector [PfPd] connecting point Pf and the overflow installation point Pd,

[0006]

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[0007] When the calculated value is 0 or more, it is determined that the molten metal flow direction is towards the installation point of the overflow, and the molten metal is discharged to the overflow. On the other hand, when the calculated value is negative, it is determined that the molten metal flow direction is not towards the overflow, and the discharge of the molten metal to the overflow is stopped. (2 - 3) Next, from the inspection volume at the time of molten metal filling when discharging to the overflow that satisfies the above (2 - 1) and (2 - 2), the filling rate Fr of the overflow measured and the initial volume V0 of the overflow, the required volume V'(=V0×Fr) is calculated, and the volume of the overflow is changed to V' in shape. Each time the volume and shape of each overflow are changed, the above (2 - 1) to (2 - 3) are repeated, and finally, optimization is performed until the volume and shape of all overflows satisfy the conditions.

[0008] Also, the software according to another invention is for implementing the overflow optimal design method described above. In the above invention, the threshold value of the amount of gas entrained is not particularly limited, but is 0.5 to 0.9, preferably 0.6 to 0.8, and more preferably about 0.7. The threshold value can be appropriately changed depending on whether it is for obtaining the installation point of the overflow or for obtaining the volume (for example, 0.9 can be used for the former and 0.7 for the latter). Not only can the threshold value be changed for position and volume, but it can also be changed according to the importance of each part of the product, etc. For example, it can be set to 0.5 at a position where it is difficult to perform processing to remove defects of the product such as a sliding surface, and 0.9 at a position where some defects can be tolerated. However, in the following embodiments, since it is desired to remove molten metal with a Va value of 0.7 or more from the entire product, it is set to 0.7 for all.

Effect of the Invention

[0009] According to the present invention, in order to completely discharge the molten metal in the product part that has entrapped gas, by estimating the flow direction of the molten metal during filling, an optimal design system that automatically designs the overflow position and volume can be provided. According to the present invention, it becomes possible to automatically design a die-casting plan that simultaneously prevents wasteful discharge of molten metal and gas entrapment defects.

Brief Description of the Drawings

[0010] [Figure 1] This is a diagram showing the visualization of only the molten metal with a Va value of 0.7 or more and the repeated design results of overflow using CFD analysis. (a) The shape designed using an exhaust runner, (b) The shape designed with an additional overflow (the positions of the overflows in the figure are indicated by 1 and 2), and (c) The shape designed with a third overflow are shown respectively. The color display of the molten metal is shown as the air entrainment volume ratio (Va value), with the minimum value being 0 (blue) and the maximum value being 0.7 (red, and values of 0.7 or more are also red) (the same applies in FIGS. 15 and 16). [Figure 2] This is a diagram showing the result of extracting the cells of the molten metal that has entrapped gas in the product part (air entrainment volume ratio of 0.7 or more). In the figure, the range surrounded by a semi-circle indicates the extraction range. (a) The overflow on the upper side in the y-axis direction, (b) The overflow on the lower side in the y-axis direction are shown. G in the figure indicates the center of gravity coordinates, and Pd indicates the installation point of the overflow. Also, the arrows indicate the velocity vectors of the molten metal in each cell. [Figure 3] This is a diagram showing the estimated result of the flow direction of the molten metal. (a) and (b) show the states when viewed from different positions. The small arrows in the figure indicate the velocity vectors of the molten metal in each cell, and the large arrow (orange color) indicates the vector [V] of the flow direction V obtained by synthesizing the velocity vectors of each cell. [Figure 4] This is a diagram showing the evaluation result of the relationship between the flow direction of the molten metal and the overflow setting position. (a) shows the state when the calculation result of Equation (3) is 0 or more, and (b) shows the state when the calculation result of Equation (3) is negative. [Figure 5]This diagram shows the mold shape for the target product. The product extends from the center to the left and right, and has a pair of holes on both sides. Molten metal flows in from the runner on the bottom of the product. There are six overflows shown in the diagram. Air is exhausted through the exhaust runner to the air vent. [Figure 6] This figure shows the molten metal flow behavior excluding overflow. (a) shows the behavior after 0.08 seconds, (b) after 0.10 seconds, and (c) after 0.12 seconds. Molten metal with high Va values, indicated in red, is observed around the left and right holes of the product (after 0.08 and 0.10 seconds) and below the right hole (after 0.12 seconds). [Figure 7] This figure shows the results of defining the designable area and acquiring candidate design points. (a) The area enclosed by the rectangle indicates the designable area, and (b) the candidate points Pc for overflow placement. [Figure 8] This figure shows the results of determining the installation points for the overflow. (a) shows the installation points shown in the XZ plane, and (b) shows the installation points shown in the perspective view. [Figure 9] This is a perspective view showing the initial shape of the overflow as generated by a CFD simulator. Numbers 1-11 in the figure indicate the location and shape of the overflows. In the CFD simulator, it is necessary to set the inspection volume for the entire overflow and the measurement surface for each overflow gate. [Figure 10] (a) A figure showing the results of gate evaluation using the measurement surface, and (b) A graph showing the relationship between time and Va for each overflow gate. In graph (b), the Va of gate 1 becomes smaller than 0.7 first, and then the Va of the other gates also becomes smaller than 0.7. [Figure 11]This figure shows three operations in the internal evaluation of the product: (a) a figure showing that Va is 0.7 or higher throughout the entire product section, (b) a figure showing cells extracted from the overflow installation point where the product section evaluation is performed within a minimum distance Lmin, (c) a figure showing cells that satisfy 26 connections from the extracted cells, and (d) a figure showing that the value of the air-entrained volume of the region is equal to or greater than the set value. [Figure 12] This figure shows the product evaluation results for the second overflow. [Figure 13] This figure shows the product evaluation results for item number 3, which experienced overflow. [Figure 14] This graph shows the relationship between fluid volume and time within each overflow. [Figure 15] This figure shows the molten metal flow behavior when using the conventional shape. (a) shows the behavior after 0.08 seconds, (b) after 0.11 seconds, and (c) after 0.14227 seconds, respectively. After 0.08 seconds, red areas with high Va values ​​begin to appear around the left and right holes, and after 0.11 seconds, these areas increase significantly (the lower part of the left hole and the area around the right hole). After 0.14227 seconds, red areas are clearly visible around the left hole and in the overflow area. [Figure 16] This figure shows the molten metal flow behavior when using the proposed shape of this embodiment. (a) shows the behavior after 0.08 seconds, (b) after 0.11 seconds, (c) after 0.14001 seconds, and (d) after 0.16633 seconds, respectively. After 0.08 seconds, red areas with high Va values ​​begin to appear around the left and right holes, and after 0.11 seconds, these areas increase significantly (the lower part of the left hole and the area around the right hole), and after 0.14227 seconds, red areas are clearly visible around the left hole and in the overflow. After 0.08 seconds, red areas begin to appear around the left and right holes, and after 0.11 seconds, these areas increase significantly (the lower part of the left hole and the area around the right hole), but after 0.14001 seconds, the red areas move to each overflow, and after 0.16633 seconds, most of the red areas are collected in the overflow. [Figure 17]This figure shows the CFD analysis results when only molten metal with a Va value of 0.7 or higher is visualized and a conventional shape is used. A large amount of red area is observed around the left-hand hole (especially the lower left side of the hole). [Figure 18] This figure shows the CFD analysis results when only molten metal with a Va value of 0.7 or higher is visualized and the proposed shape of this embodiment is used. Although a small amount of red is visible in the lower left of the left-side hole, there is almost no red area overall. Furthermore, Figures 17 and 18 show that by analyzing whether the overflow is filled with molten metal, it is possible to determine whether the molten metal containing gas is being discharged into the overflow without unnecessary discharge. [Figure 19] This graph compares the air-entrained volume within products with an air-entrained volume ratio of 0.7 or higher. [Figure 20] This is a flowchart of the overflow optimization design system of this embodiment. [Modes for carrying out the invention]

[0011] Next, embodiments of the present invention will be described with reference to the figures and tables, but the technical scope of the present invention is not limited to these embodiments, and it can be implemented in various forms without changing the gist of the invention. <Challenges in overflow design> Traditionally, if casting defects occurred during prototype manufacturing, the overflow design was often repeatedly redesigned. In such cases, to completely drain the molten metal containing trapped gas from the product, additional overflows were added to problematic locations or their volume was increased. However, this often resulted in unnecessary overflow. Furthermore, this unnecessary overflow design could potentially hinder the complete drainage of the molten metal containing trapped gas. To clarify the problems in this iterative design, a simplified molten metal flow analysis was performed. While many computational software programs can be used for molten metal flow analysis, in this embodiment, Flow Science's FLOW-3D was used (Non-Patent Literature 10). Furthermore, an air entrainment model (Non-Patent Literature 11, 12) was used as an indicator of gas entrainment. The mesh cell size in the CFD analysis was set to 1 mm. The molten metal was ADC12, an aluminum alloy commonly used in die casting, and the mold material was SKD61, a hot-work tool steel.

[0012] Figure 1 shows the results of iterative design. Here, molten metal containing gas is defined as a fluid with a Va value of 0.7 or greater, calculated from the air entrainment volume fraction (Va) of the air entrainment model based on the results of casting experiments in previous research (Non-Patent Literature 9), and is shown in red. In Figure 1(a), only the exhaust runner is used to discharge gas and molten metal containing gas. However, a significant amount of molten metal containing gas was observed remaining within the blue frame on the right side of the product. Therefore, an overflow was installed as shown in Figure 1(b) to discharge the remaining molten metal containing gas on the right side of the product. However, residual molten metal containing gas was observed within the green frame on the upper right side of the product, so an additional overflow was installed as shown in Figure 1(c). As a result, most of the molten metal containing gas was discharged from the product, but new residual molten metal containing gas was observed in a location where it was not present in Figure 1(b). In the diagram, at the location of residual molten metal containing gas at the top of the product (1), the additional design increased the discharge of excess molten metal to the overflow at the bottom of the product. This resulted in a delay in filling the product section, preventing the delayed discharge of the gas-entrained molten metal. Similarly, at the location of residual molten metal containing gas at the right side of the product (2), the additional design reduced the flow towards the larger overflow at the bottom of the product (as it was before the design), causing it to clash with the flow towards the exhaust runner. As a result, the gas-entrained molten metal could not be discharged and remained. Thus, attempting to discharge molten metal containing gas through excessive overflow leads to increased discharge of excess molten metal, causing flow resistance and stagnation between the overflows. As a result, the molten metal containing gas remains in the product without being discharged. This is undesirable as it also reduces yield. In other words, to properly discharge molten metal containing gas from the product, it is important to avoid discharging excess molten metal and to design an overflow with the minimum necessary size (volume) at the appropriate location.

[0013] <Hot water flow estimation algorithm> This study proposes a molten metal flow estimation algorithm that determines which overflow point should be used for molten metal discharge by estimating the flow direction of the gas-entrained molten metal, thereby completely discharging the gas-entrained molten metal from the product section without excess discharge. Ultimately, we will develop an overflow optimization design system incorporating this algorithm. The molten metal flow estimation algorithm will be explained in three calculation steps using a schematic diagram of the mold. 1. Extraction of molten metal with gas incorporated. To estimate the flow direction of molten metal containing gas, target molten metal cells were extracted. Instead of extracting all gas-containing molten metal cells within the mold, as shown in Figure 2, only the gas-containing molten metal cells around the overflow area were extracted. This allowed for the estimation of molten metal flow directions corresponding to different parts of the product, and the required overflow volume, which varies depending on the location. Here, point Pd is the connection point between the overflow gate and the product section in the plane where the overflow is designed. The area shown in blue is the extraction range, and the red cells are the cells of molten metal containing the extracted gas. In Figure 2(a), the decision is made whether to discharge the molten metal for the overflow in the upper y-axis direction, and in Figure 2(b), the decision is made for the overflow in the lower y-axis direction.

[0014] 2. Estimation of the flow direction of molten metal To estimate the flow direction of the molten metal containing the gas extracted in step 1 above, the velocity vectors of each cell in the extracted molten metal were combined, as shown in Figure 3, to determine the flow direction [V] in the xy-plane. The flow direction [V] was defined as shown in equation (1).

[0015]

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[0016] 3. Evaluation of the relationship between the molten metal flow direction and the overflow installation point. The relationship between the molten metal flow direction and the overflow installation point was expressed mathematically, and the overflow that should discharge molten metal containing gas was determined. First, using equation (2), we derived the equation of the normal line f(x) to the equation of the slope V, passing through the centroid coordinates (Gx, Gy, 0) on the xy-plane, shown by the blue line in Figures 4(a) and 4(b).

[0017]

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[0018]

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[0019] <Overflow Optimal Design System> In this study, we developed an overflow optimization design system incorporating the aforementioned molten metal flow estimation algorithm. This section describes the overflow optimization design system using a real product as an example. A flowchart of the overflow optimization design system is shown in Figure 20. The product studied in this research was a crankcase, a component of a motorcycle engine, with dimensions of 250mm (height), 600mm (width), and 100mm (depth). The molten metal was aluminum alloy ADC12, and the mold material was hot-work tool steel SKD61. The computer used for the analysis had an Intel Core i9-10850K CPU (clock speed 3.6GHz) and 32GB of memory. The analysis mesh size was 3mm, with a mesh count of 2,001,348. Under these conditions, the analysis until filling was complete took approximately one hour. In this study, the overflow designed using a general method is referred to as the conventional shape. Figure 5 shows the mold shape including the sprue configuration, exhaust runner, and the conventional overflow shape.

[0020] 1. Optimal overflow position design considering the location of molten metal containing gas. It is believed that if the overflow point is located far enough from the location of the molten metal containing the gas, excess discharge will increase. Therefore, it is important to install the overflow point close to the location of the molten metal containing the gas, in a position that allows for more efficient discharge. First, by performing an analysis excluding overflow, the residual location of molten metal containing gases from the product section that could not be discharged by the exhaust runner was identified, and the appropriate installation point was automatically determined. Figure 6 shows the molten metal flow behavior inside the mold at 0.02s intervals until the completion of filling, when overflow is excluded. Figures 6(a) and 6(b) show that in the circular section on the left side of the product, molten metal with a high Va value was converging from above and below. However, because the exhaust runner on the left side of the product is designed to be located at the top of the product, away from the circular section, it could not discharge the molten metal, and it remained in the product even after filling was complete, as shown in Figure 6(c). In addition, molten metal containing gas was also trapped in the lower right side of the product and could not be discharged by the exhaust runner, remaining there as well. Furthermore, molten metal with a high Va value became clogged in the pin section on the right side of the product and could not be discharged, remaining there.

[0021] Next, to determine the installation point from a position where overflow is designable, a designable range was specified. At this time, in order to determine an installation point close to the molten metal location where gas was entrained, the designer considered the results of the CFD analysis without overflow mentioned above and specified a location near the molten metal location where gas was entrained. Then, the coordinates Pp of the product surface within the specified range were obtained. Furthermore, in the CFD analysis results without overflow, the molten metal location of the product part with a Va value of 0.7 or greater was defined as Pa. Then, in order to minimize the distance from point Pp within the set range to point Pa, which is the molten metal location where gas was entrained, candidate installation points Pc that satisfy the conditions were determined using equation (4).

[0022]

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[0023]

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[0024] In the formula, Lmin represents the minimum distance between the overflow installation points Pd, and is set appropriately by the designer to avoid contact between the overflows. In this case, it was set to 70 mm. The determined installation points are shown in Figure 8. Furthermore, in the mold shape of this embodiment, the positions where the residence time Tr is 0.08 s or more and the positions where the air-entrained volume fraction Va is 0.7 or more roughly coincide, indicating that the molten metal containing entrained gas remains trapped at the molten metal retention points inside the product. By using the residence time Tr as an evaluation value for determining the installation point, it is thought that not only will the discharge of molten metal containing entrained gas be improved, but the flow of molten metal inside the product will also be improved. Comparing Figure 6(c) and Figure 8, it was confirmed that the 11 determined installation points were located near the positions where molten metal containing gas remained, as shown in the molten metal flow analysis results excluding overflow.

[0025] 2. Optimal overflow volume design considering the flow of molten metal with gases involved. In the volumetric design system, the volume of each overflow was determined through the following three-stage evaluation. Each evaluation was performed in parallel with the analysis, at each time step of the molten metal filling time. The step size was set to 0.0005s. (1) Evaluation of the gate section by the measurement surface (2) Internal product evaluation using a hot water flow estimation algorithm (3) Evaluation of molten metal volume in overflow based on inspection volume and modification of overflow shape

[0026] First, the simulator was configured. Here, the simulator refers to the space to be calculated using CFD, specifically a suitable three-dimensional space (preferably a rectangular prism with minimum and maximum values ​​in the X, Y, and Z directions) containing the product and all overflows. Since the required volume for each overflow is unknown, as shown in Figure 9, a sufficiently large overflow shape was set as the initial shape, taking into account the constraints of the equipment relative to the determined installation point. Furthermore, the CFD simulator required setting the inspection volume for the entire overflow and the measurement surface for each overflow gate. Here, the 11 overflows were numbered 1 through 11, as shown in Figure 9. In the first evaluation, the molten metal passing through the gate section was evaluated. Because the calculation time required for the product section evaluation in the next step is long, the calculation cost was reduced by evaluating the molten metal passing through the gate section to understand the flow of gas-entrained molten metal. Specifically, as shown in Figure 10(a), the fluid volume Vfr and air-entrained volume Var of the molten metal passing through the inspection surface set in the overflow gate section were measured, and the air-entrained volume fraction Va was calculated using equation (8).

[0027]

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[0028] Firstly, to avoid evaluating molten metal flowing towards an overflow other than the one being evaluated, cells are extracted that have a Va value of 0.7 or greater in the product area and are located within a spherical range with a radius equal to the minimum distance Lmin between the installation points of the overflow to be evaluated, as shown in Figures 11(a) to 11(b). Secondly, in order to estimate the molten metal flow, the molten metal was divided into coherent individual regions for evaluation. As shown in Figures 11(b) to 11(c), the acquired cell groups were labeled using MathWorks' MATLAB, and cells satisfying the "26-connection" condition were obtained (Non-Patent Literature 13). "26-connection" means that the cells are connected if their faces, edges, or corners are in contact in the 3D image. Thirdly, the regions extracted in the second operation include minute areas, and evaluating all of them could potentially increase unnecessary emissions. Therefore, we select the regions to evaluate. Thus, as shown in Figures 11(c) to 11(d), we calculated the air entrainment volume of each extracted region using equation (9), and evaluated the region if its value was greater than or equal to a set value. In this study, the set value was 0.50 cm³. 3 That's what I decided.

[0029]

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[0030] The three operations described above were performed, and the molten metal flow estimation algorithm was applied. As an example, when the volume of all overflows is undetermined, the left side of the product is used as the installation point, and the results of determining two adjacent overflows are shown in Figures 12 and 13. In Figure 12, one region shown in green is extracted, and since the judgment formula of the hot water flow estimation algorithm is greater than or equal to 0, discharge to the overflow continues. On the other hand, in Figure 13, two regions shown in green and blue are extracted, and since the judgment formula of the hot water flow estimation algorithm is less than 0 in both regions, discharge to the overflow is stopped. In the third evaluation, the required volume V' is calculated using equation (10) from the overflow filling rate Fr, measured from the inspected volume at the time of molten metal filling when the discharge to the overflow is stopped, and the initial volume V0 of the overflow. Up to this point, we have stated that the discharge of molten metal to the overflow is stopped, which means that the discharge is stopped by changing the initial volume V0 to the required volume V'.

[0031]

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[0032]

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[0033] <Verification of effectiveness by CFD analysis> In order to verify the effectiveness of the overflow designed by the proposed method, the molten metal flow analysis was carried out and compared between the case of using the conventional shape and the case of using the proposed shape. The molten metal flow behavior in the mold every 0.03 s until the filling completion time in each of the conventional shape and the proposed shape is shown in Figs. 15 and 16. As shown in Fig. 15, in the conventional shape, the molten metal with a high Va value could not be discharged at the circular part on the left side of the product and flowed out to the right side of the product where the filling was slow, remaining in the central part of the product. Also, at the lower right part of the product which was the final filling part, the volume of the overflow was insufficient, so the molten metal with a high Va value could not be discharged and remained. In addition, no overflow was designed at the pin part on the right side of the product, so the molten metal with a high Va value was clogged at the tip. On the other hand, as shown in Fig. 16, in the proposed shape, the molten metal with a high Va value merged from above and below at the circular part on the left side of the product in the same way as in the case of using the conventional shape. However, since the volume of the overflow at that position was designed to be larger by the molten metal flow estimation algorithm, the molten metal with a high Va value could be actively discharged. Also, sufficient volumes of overflows were designed for the right side and the pin part of the product, eliminating the remaining of the molten metal with a high Va value in the conventional shape. In addition, the sizes of the volumes of each overflow could be confirmed, and the necessary volume according to the installation point could be designed.

[0034] Also, in order to confirm whether the molten metal entraining gas could be completely discharged without excessive discharge, the molten metal with a Va value of 0.7 or more in the product part was colored red, and the molten metal with a Va value of 0.7 or more other than that was colored blue. Figs. 17 and 18 show the visualized analysis results at the filling completion time. Furthermore, Figures 17 and 18 allow us to analyze whether the overflow is filled with molten metal, which can be used to determine whether the molten metal containing gas is being discharged into the overflow without unnecessary discharge. Specifically, Figure 17 shows that in the conventional shape, the volume of the overflow was insufficient, and molten metal containing red gas remained throughout the entire product. On the other hand, Figure 18 shows that in the proposed shape, a small amount of molten metal containing red gas can be seen remaining in the circular area on the left side of the product, but it was almost completely discharged throughout the entire product. Thus, it was confirmed that the molten metal containing blue gas was sufficiently discharged in the overflow area, and no unnecessary discharge occurred. Comparisons were made using evaluation values ​​J where the Va value calculated using equation (9), which is considered to numerically indicate a higher likelihood of casting defects compared to conventional experiments, is 0.7 or higher. The comparison results are shown in Figure 19. Analysis results using the conventional overflow shape showed 97.34 cm 3 The volume of air entrainment was confirmed. In contrast, the analysis results using the overflow in this embodiment showed that the volume of air entrainment was 0.68 cm³. 3 The molten metal containing gas can be discharged until it reaches a certain state, a 99.3% reduction compared to conventional designs. Therefore, the method of this embodiment achieves an optimal overflow design that prevents the retention of molten metal containing gas.

[0035] <Flowchart of the Overflow Optimal Design System> Next, referring to Figure 20, we will explain the flowchart of the overflow optimization system. Since the details of each step are described above, we will briefly explain what each step does here. First, the analysis results before the overflow design are obtained (CFD results (without overflow). Step to obtain CFD results without overflow: S100), the designer inputs the design conditions (Initial setting. Initial setup step: S110), the system is started and the overflow placement points are determined (Overflow design positions. Overflow position determination step: S120). Next, a sufficiently large overflow, taking into account the constraints of the device, is designed as the initial shape for the determined installation point, and a CFD simulator is constructed. Here, the designer inputs the design conditions (Initial setting, second initial setting step: S130), starts the system (Start), and determines the optimal overflow volume for each installation point (Overflow volume, overflow volume determination step: S200). In S200, the overall shape of the overflow, for which the volume has been determined, is modified so that no more molten metal than the determined volume is discharged (Change of overflow shape step: S240). Specifically, after determining the volume of one overflow, CFD analysis is performed using the overflow with the shape corresponding to the determined volume (CFD analysis step: S210), the overflow gate is evaluated (Evaluation of overflow gate step: S220), and the inside of the product is evaluated (Evaluation inside the product step: S230). S220 is repeated until the Va value becomes smaller than a predetermined threshold (0.7 in this embodiment). S220 and S230 are repeated for each overflow. Next, the overflow shape modification step S240 is performed to evaluate how many overflow volumes have been determined (Evaluation step: S250). These steps S210 to S250 are repeated each time the volume and shape of the overflow change. If all overflow volumes have been determined, the overall evaluation is performed again using the automatically designed overflows (Evaluation, final evaluation step: S300), and the proposed shape is presented (End).

[0036] <Summary> This study proposes an algorithm to estimate the molten metal flow of a product under analysis, including gas entrainment, and to evaluate its relationship with the overflow placement point. An optimal design system incorporating this algorithm was then constructed, and the optimal overflow placement was optimized within a limited number of analysis iterations to prevent gas entrainment defects. As a result, the overflow designed using the proposed system significantly reduced the air-entrained volume of the product compared to the analysis results using a conventional overflow design. Therefore, designing the overflow using the proposed system is expected to suppress defect occurrence. Thus, according to this embodiment, in order to completely discharge the molten metal from the product section containing gas, we were able to provide an optimal design system that automatically designs the location and volume of overflow by estimating the flow direction of the molten metal during filling.

Claims

1. The purpose of this overflow optimization design method is to prevent gas entrapment defects when manufacturing a specified die-cast product by casting, and includes the following steps (1) and (2): the object is decomposed into mesh cells, and computational fluid dynamics (CFD) calculations are performed for each cell using a computer, wherein the designer sets and inputs the design conditions in advance. (1) An overflow position determination step in which the installation point of the overflow of the die-cast product is determined, (2) After determining the initial shape of the overflow, an overflow volume determination step is performed to determine the volume and shape of the overflow corresponding to that volume, based on the evaluations in (2-1) and (2-2) below. In the (1) overflow location determination step, the molten metal flow is determined by CFD without providing an overflow, the remaining location of molten metal with gas entrained above a predetermined threshold is determined, and candidate overflow installation points Pc are determined from the distance from a point within a set range to the point where the gas entrained molten metal is located, the fluid residence time Tr is calculated for these candidate installation points, and the installation point with the longest residence time Tr is set as the overflow installation point. In the (2) overflow volume determination step, the overflow obtained at the overflow installation point is determined to be a sufficiently large overflow, taking into account the constraints of the device, as the initial shape. (2-1) In the overflow gate evaluation step, in which the overflow gate section is evaluated, an inspection volume is set for the entire overflow and a measurement surface is set for each overflow gate, and the fluid volume Vfr and air entrainment volume Var of the molten metal passing through the inspection surface set for the overflow gate section are measured. The air-entrained volume ratio Va is calculated using the following formula (8), and only cells with a value of 0.7 or greater under the first condition are extracted. [Math 1] If Va becomes less than 0.7, proceed to the next internal evaluation step. (2-2) In the internal evaluation step, which evaluates the inside of the product, only the molten metal cells containing gas around the overflow inside the product are extracted, the velocity vectors of each extracted cell are combined to obtain the vector [V] of the molten metal flow direction, the molten metal flow direction and the overflow position are expressed mathematically, and the following equation (3) is calculated for the vector [PfG] connecting point Pf on the normal and the centroid G, the vector [PfPv] connecting point Pf and point Pv which has moved from the centroid G to the tip of the molten metal flow direction, and the vector [PfPd] connecting point Pf and the overflow installation point Pd, [Math 2] If the calculated value is 0 or greater, it is determined that the molten metal flow direction is towards the overflow installation point, and the molten metal is discharged into the overflow. On the other hand, if the calculated value is negative, it is determined that the molten metal flow direction is not towards the overflow, and the discharge of molten metal into the overflow is stopped. (2-3) Next, the required volume V' (= V0 × Fr) is calculated from the overflow filling rate Fr measured from the inspection volume at the time of molten metal filling when discharge to the overflow is stopped, satisfying the conditions of (2-1) and (2-2) above, and the initial volume of the overflow V0. The shape is then modified according to the following formula (11) so that the volume of the overflow becomes V'. [Math 3] In the formula, the length of the overflow in the initial shape is l0, the width is W0, and the thickness is t0, while the length of the overflow after the shape change is l', the width is W', and the thickness is t'. An overflow optimization design method characterized by repeating steps (2-1) to (2-3) above each time the volume and shape of each overflow are changed, and optimizing until the volume and shape of all overflows finally satisfy the above conditions.

2. Software for implementing the overflow optimization design method described in claim 1.

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