JP2007125589A - Apparatus and method for analyzing casting process - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an apparatus and a method for analyzing a casting process, by which apparatus and method, the position and size of a shrinkage cavity generated in a cast product in solidification can be accurately estimated. <P>SOLUTION: A cast product is manufactured by pouring molten metal into a cavity formed in a metallic die, and by applying a pressure to the molten metal from an injection device, and by solidifying the molten metal in the state that the pressure is held. The method for analyzing the casting process analyzes the shrinkage cavities of the cast product as follows. The zone filled with the molten metal is divided into a plurality of elements (8a, 8b), and the flow speed u of the molten metal flowing between the respective neighboring elements (8a, 8b) is calculated. In calculating the flow speed u, it is assumed that the molten metal in the solid-liquid coexisting state in the respective elements (8a, 8b) integratedly flow in solidification. In this case, an apparent coefficient μ<SB>e</SB>of viscosity is calculated based on a solid phase rate fs, and the flow speed u of the molten metal is calculated based on the calculated coefficient μ<SB>e</SB>of viscosity. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  According to the present invention, the molten metal filled in the space formed in the mold is held by applying pressure from the injection device, and the shrinkage generated in the cast product obtained by solidifying the molten metal in this state is analyzed by computer analysis. The present invention relates to a casting analysis apparatus and a casting analysis method for outputting, in particular, a casting analysis capable of accurately analyzing the flow of molten metal during solidification and accurately predicting the position and size of shrinkage cavities in the space. The present invention relates to an apparatus and a casting analysis method.

  When casting, such as die casting, the molten metal is injected into the space including the cavity formed in the mold and the filling is completed. Shrinkage can occur. The shrinkage cavity of the cast product may cause various problems such as strength and aesthetic appearance of the product.

  Therefore, in order to reduce shrinkage cavities, the molten metal is filled in the space including the cavity formed in the mold by using an injection device, and pressure is further applied to the molten metal after filling from the injection device. A casting method is generally employed in which the molten metal is solidified while being held. Even after the molten metal is completely filled in the cavity in this way, the molten metal is pressurized using the injection device, so even if the molten metal starts to solidify and contract in the cavity, a part of the molten metal that can flow is included in this molten metal. Since (pushing hot water) flows into the space that becomes the shrinkage cavity and is replenished, the occurrence of the shrinkage cavity of the cast product can be suppressed.

  However, even if pressure is applied to the molten metal after it has been filled into the cavity, it is difficult to completely eliminate the shrinkage nest from the cast product, even if the number of shrinkage nests decreases and the nest becomes smaller. Depending on the location and size of the nest, the problem as described above cannot be completely solved. Therefore, in order to predict the occurrence position and the size of such a shrinkage cavity and perform an optimum casting method, casting analysis on the shrinkage cavity is performed by CAE (Computer Aided Engineering). As an example of this casting analysis, it is a flow solidification analysis method that divides into a plurality of minute elements according to the mold shape and analyzes the heat conduction and solute movement for each elapsed time between each minute element, When calculating the flow velocity and pressure of the molten metal in the analysis of solute movement, the flow velocity (flow velocity) of the molten metal is calculated using the basic equation of Darcy flow. From this flow velocity, the solid phase between the elements Calculate the total moving volume of the liquid phase, calculate the ratio of the solid phase to the liquid phase flowing out of the total volume using the solid phase liquid phase transfer coefficient, and analyze the shrinkage state based on this result A fluidized solidification analysis method has been proposed (see Patent Document 1).

JP-A-10-34320

  However, even if an analysis is performed by such an analysis method, it is impossible to predict the exact position of the shrinkage nest and its size. In other words, the basic equation of Darcy flow (Darcy law) used in the analysis method described above is generally that the solid phase in the solid-liquid coexistence state is porous at the time of metal solidification, and the inside of this porous solid phase is the liquid phase. It is known as an equation constructed to calculate the flow velocity of this liquid phase, but in actual casting, the above-mentioned pressurization to the molten metal is performed under high pressure conditions. In general, this is not a phenomenon where the liquid phase flows in the porous solid phase, but rather a phenomenon where the liquid phase and the solid phase flow together. Conceivable. Further, when an aluminum casting alloy for die casting (for example, JIS standard: ADC12) generally used as a casting material for a molten metal is used, this material has a short solidification time and takes a skin forming type solidification form. For this material, it is considered that the assumption of Darcy's law that only the liquid phase flows does not hold.

  Therefore, although the analysis method as described in Patent Document 1 changes the ratio of the solid phase to the liquid phase to move depending on the value of the solid phase liquid phase transfer coefficient, the total amount of movement between the solid phase and the liquid phase is Since the amount depends on the speed obtained by the Darcy law shown in Fig. 1, the total amount of movement is not obtained by faithfully reproducing the phenomenon that the liquid phase and the solid phase flow together as shown above. As a result, even if the analysis is performed by this casting method, an analysis result of a shrinkage nest having a position and a size different from that of the shrinkage nest actually generated is obtained.

  Furthermore, since such an analysis method obtains the flow rate of the molten metal from Darcy's law, and further obtains the amount of movement between the solid phase and the liquid phase from the solid phase liquid phase transfer coefficient, the analytical programming becomes complicated, At the time of analysis, a considerable calculation load is applied to the apparatus, and time is required for analysis.

  The present invention has been made to solve the above-described problems, and its object is to quickly increase the flow rate of the molten metal during solidification in a space filled with the molten metal in a pressurized state. Another object of the present invention is to provide a casting analysis apparatus and a casting method capable of accurately and predicting the position and size of a shrinkage cavity of a cast product generated during solidification with high accuracy.

  In order to achieve the above-mentioned object, the present inventors have conducted intensive investigations. As a result, when pressure is applied to the molten metal to prevent shrinkage, the pressure acting on the molten metal is high. Therefore, it was considered that the melt in the solid-liquid coexistence state, that is, the melt containing the solid phase and the liquid phase, was flowing together during solidification, and this phenomenon should be reflected in the analysis.

  Therefore, the inventors compared the melt in the solid-liquid coexistence state with the melt in the liquid phase only, and focused on the viscosity coefficient as an important physical property value for calculating the flow rate of the melt. As a result of casting analysis using the apparent viscosity coefficient when the melt in the solid-liquid coexisting state flows together during solidification, the occurrence position of the shrinkage nest of the cast product and without complicating the formula used for the calculation The knowledge that the size can be predicted quickly and accurately was obtained.

  The present invention is based on the above-mentioned new knowledge obtained by the present inventors, the casting analysis method according to the present invention fills the molten metal using an injection device in the space formed in the mold, With respect to a cast product obtained by solidifying the molten metal in a state in which the molten metal is further held by applying pressure from the injection device, the space filled with the molten metal is divided into a plurality of elements, and the molten metal in each element is divided. By calculating at least the pressure and the solid phase ratio, and calculating the flow rate of the molten metal flowing between adjacent elements based on the pressure and solid phase ratio of the molten metal, the state of the shrinkage cavity of the cast product is calculated by a computer. A casting analysis method for analyzing, wherein the casting analysis method assumes that, in the calculation, the solid-liquid coexisting molten metal in each element flows integrally during solidification, and the solid-liquid coexisting molten metal flows Do The apparent viscosity of the interleaf calculated based on the fraction solid, is characterized by calculating the flow velocity of the molten metal based on 該見 seat viscosity.

  Here, the “solid-liquid coexisting molten metal” according to the present invention refers to a molten metal containing a solid phase and a liquid phase, and “the solid-liquid coexisting molten metal flows integrally during solidification” When the molten metal is supplied to the voids generated by the solidification shrinkage and the shrinkage, the molten metal containing not only the liquid phase but also the solid phase flows together.

  In this way, first, the viscosity coefficient (apparent viscosity coefficient) that changes in accordance with the solid phase ratio or liquid phase ratio when the molten metal containing the solid phase and the liquid phase flows together during solidification is calculated. Since the flow rate of the molten metal is calculated based on the viscosity coefficient, it is possible to accurately capture the molten metal flow phenomenon under the actual machine conditions. As a result, the molten metal flow during solidification is analyzed accurately, and the molten metal is solidified. It is possible to quickly and accurately predict the position and size of the shrinkage cavity of the casting that occurs at times. Based on this prediction, it is possible to obtain an optimum mold design and optimum casting conditions by CAE so that no shrinkage occurs. Here, the apparent viscosity coefficient is obtained based on the solid phase ratio, but the apparent viscosity coefficient may be obtained based on the liquid phase ratio, and these give the same result.

Further, the flow rate of this molten metal is u, the apparent viscosity coefficient is μ _e , the pressure difference between adjacent elements is ΔP, the center-to-center distance between adjacent elements is Δx, and it passes between adjacent elements. When the transmittance of the molten metal is K ₀ ,

として演算されることがより好ましい。この数１は、従来のダルシーの基礎方程式の液相の粘性係数（一定値）に、先に示した固液共存状態の見掛け粘性係数μ_ｅを、透過率（固相率の関数により表された値）に、一定値として透過率Ｋ_０を適用したものである。なお、この「隣接する要素間の中心間距離」とは、隣接する各要素の中心位置（重心となる位置）を結んだ距離をいう。

More preferably, it is calculated as This number 1 is expressed by the permeability (function of the solid phase ratio), the apparent viscosity coefficient μ _e of the solid-liquid coexistence state shown above in the viscosity coefficient (constant value) of the liquid phase of the conventional Darcy basic equation. The transmittance K ₀ is applied as a constant value. The “center distance between adjacent elements” refers to a distance connecting the center positions (positions that become the center of gravity) of adjacent elements.

  Thus, not only can the shrinkage nest be predicted more accurately by calculating the flow rate of the molten metal in the solid-liquid coexistence state using a simplified formula as shown in Equation 1 using Darcy's law, It is possible to minimize the change of the program in the analysis processing, and to shorten the calculation time. In addition, when calculating the flow velocity of such a melt, it is not limited to the equation such as Equation 1, but for example, an equation representing the flow of the melt during solidification used for this type of shrinkage nest analysis is used. The apparent viscosity coefficient may be applied. For example, when analyzing a cast product having a simple cylindrical shape, the apparent viscosity coefficient may be calculated using the Hagen-Poiseuille equation.

  Furthermore, it is more preferable that this apparent viscosity coefficient is calculated using the applied pressure from the injection device. In general, since the viscosity of molten metal decreases as the pressure acting on the molten metal increases, the apparent viscosity coefficient is determined based on the pressure applied from the injection device (casting pressure) in consideration of the pressure dependence of this viscosity. By calculating, the flow rate of the molten metal during solidification can be calculated with higher accuracy. Here, for the sake of simple calculation, the apparent viscosity coefficient is calculated using the pressure of the injection device, but at the time of this casting analysis, the calculated pressure of the molten metal in each element is used for each calculation. The apparent viscosity coefficient for the molten metal of the element may be calculated. Furthermore, when the pressure in the element hardly changes, as in low-pressure casting, this apparent viscosity coefficient is made to depend only on the change in the solid fraction. It may be.

The apparent viscosity coefficient calculating means is configured so that the apparent viscosity coefficient is μ _e , the viscosity coefficient μ _{0 of} only the liquid phase of the molten metal is fs, the solid phase ratio is fs, and the coefficient relating to the pressure applied from the injection device is A. Viscosity coefficient μ _e

として演算することがより好ましい。さらに、この解析精度を向上させるためには、この射出装置からの加圧力に依存した係数Ａは、実際に鋳造を行う材料の固液共存状態の溶湯に対する固相率、加圧力、粘性係数を常法により測定し、この得られた実測値に基づいて決定されることが好ましい。

It is more preferable to calculate as Furthermore, in order to improve the analysis accuracy, the coefficient A that depends on the applied pressure from the injection device is determined by the solid phase ratio, the applied pressure, and the viscosity coefficient for the melt in the solid-liquid coexistence state of the material that is actually cast. It is preferable to measure by a conventional method and determine based on the obtained actual measurement value.

Equation 2 for calculating the apparent viscosity coefficient μ _e reproduces the phenomenon in which the apparent viscosity coefficient of the melt in a solid-liquid coexistence state changes exponentially when the solid phase ratio is increased at a constant rate in actual casting. Therefore, the flow rate of the molten metal during solidification can be calculated more accurately. As another method of calculating the apparent viscosity coefficient μ _e , the values of the apparent viscosity coefficient with respect to the solid phase ratio and the applied pressure obtained by the above actual measurement are stored in a table, and the apparent viscosity coefficient μ _e may be read out, or such an exponential function may be approximated to a polyline, and the apparent viscosity coefficient μ _e may be calculated using the polyline approximation formula.

  Furthermore, as an apparatus that can effectively carry out the above casting analysis method, the present invention fills the molten metal into the space formed in the mold using the injection apparatus, and the filled molten metal from the injection apparatus. Further, with respect to a cast product obtained by solidifying the molten metal in a state where it is held by applying pressure, the space filled with the molten metal is divided into at least a plurality of elements, and the state of the shrinkage nest of the cast product in the space is calculated by a computer In order to analyze, at least the molten metal pressure and the solid phase ratio in each of the divided elements are calculated, and the flow velocity of the molten metal flowing between adjacent elements is calculated based on the molten metal pressure and solid phase ratio. A casting analysis apparatus comprising at least computing means for performing the computation, wherein the computing means assumes that the solid-liquid coexisting molten metal in each element flows together during solidification, and the solid-liquid Casting analysis, comprising: means for calculating an apparent viscosity coefficient when the molten metal in an existing state flows based on the solid phase ratio; and means for calculating the flow rate of the molten metal based on the apparent viscosity coefficient An apparatus is also disclosed. With such an apparatus configuration, the flow rate of the molten metal of each element during solidification can be analyzed quickly and accurately, and the position and size of the shrinkage cavity of the cast product can be accurately and predicted.

More preferably, the flow rate calculating means u is the flow rate of the molten metal u, the apparent viscosity coefficient is μ _e , the pressure difference between adjacent elements is ΔP, the center-to-center distance between adjacent elements is Δx, and between adjacent elements When the transmittance K ₀ of the molten metal is,

として演算し、さらに、この前記見掛け粘性係数演算手段は、射出装置からの加圧力を用いて前記見掛け粘性係数を演算することが好ましい。

Further, it is preferable that the apparent viscosity coefficient calculating means calculates the apparent viscosity coefficient using the pressure applied from the injection device.

Further, the apparent viscosity coefficient calculating means has an apparent viscosity coefficient of μ _e , a viscosity coefficient μ _{0 of} only the liquid phase of the molten metal, a solid phase ratio of fs, and a coefficient related to the pressure applied from the injection device as A, The apparent viscosity coefficient μ _e is

として演算することが好ましい。

It is preferable to calculate as

  ADVANTAGE OF THE INVENTION According to this invention, the flow speed of the molten metal at the time of solidification can be analyzed rapidly and accurately, and the position and size of the shrinkage cavity generated in the cast product can be accurately and predicted. Based on this prediction, it is possible to obtain an optimum mold design and optimum casting conditions that can reduce the occurrence of shrinkage.

  Exemplary embodiments of a casting analysis apparatus and a method thereof according to the present invention will be described below in detail with reference to the accompanying drawings.

  FIG. 1 is a diagram for explaining an example of an analysis model for performing a casting analysis method according to the present invention, and FIG. 2 is a diagram for explaining an apparatus configuration for analyzing the analysis model of FIG. FIG. 3 is an analysis block diagram showing an example of the casting analysis apparatus of FIG. 2, and FIG. 4 explains the details of the calculation of the apparent viscosity coefficient and the calculation of the flow rate of the molten metal shown in FIG. FIG. 5 is a diagram for explaining the apparent viscosity coefficient calculated using the equation shown in FIG.

  As shown in FIG. 1, in the casting analysis method according to the present embodiment, the molten metal 9 is filled in the space 8 including the cavity 8A formed in the mold 2 of the casting apparatus 1 by using the injection apparatus 5. Further, pressure is applied to the molten metal 9 from the hydraulic unit 5C constituting the injection device 5 via the plunger 5B and the molten metal 9 is solidified in this state to analyze the shrinkage generated in the cast product. To do. Specifically, in the casting analysis method of the present embodiment, a mold 2 comprising a fixed mold 2A and a movable mold 2B (including a sleeve 5A constituting the injection apparatus 5 when a large amount of molten metal has been introduced into the injection apparatus 5 is included. In order to set the shape of the space 8 filled with the molten metal 9 formed by the above method as an analysis model and perform analysis by an analysis method such as a finite element method or a difference method, the modeled space 8 is divided into a plurality of elements. Each element is given conditions such as material conditions, boundary conditions, and initial conditions to be described later, and based on these conditions, the speed, pressure, temperature, and temperature of the melt in each element during solidification The solid phase ratio is calculated, and based on the calculation result, the state of the shrinkage nest of the solidified molten metal 9 (cast product) in the space 8 is analyzed.

  2 and 3 show an example of a casting analysis apparatus suitable for performing such casting analysis. As shown in FIG. 2, the casting analysis apparatus 10 mainly includes a storage unit 30 having a RAM and a ROM, and a calculation unit (calculation means) 40 having a CPU. The storage unit 30 receives input data from the input device 20. Based on the stored data, the calculation unit 40 flows during solidification in the space 8 filled with the molten metal formed in the mold 2 including the fixed mold 2A and the movable mold 2B. The behavior of the molten metal 9 is analyzed, and the state of the shrinkage nest of the molten metal 9 filled in the space 8 is output to the display device 50 based on the result.

  Specifically, as illustrated in FIG. 3, the storage unit 30 stores data input from the input device 20 and outputs the stored data to the calculation unit 40 as necessary. The storage unit 30 includes a shape of a space divided into elements, material conditions (such as physical properties of molten metal, a mold, and an injection device), boundary conditions (such as heat transfer coefficients of the mold and the molten metal), and initial conditions (such as metal molds). The initial temperature of the mold, the injection device, and the molten metal), the pressure of the casting apparatus (so-called casting pressure), the viscosity coefficient when the molten metal is only in the liquid phase, and the like, and each means 41 constituting the calculation unit 40 described later. These data are output to .about.44. As the data to be input to the storage unit 30, the space 8 filled with the molten metal 9 has already been divided into a plurality of elements, but this space 8 is input from the input device 20 to the storage unit 30. Then, the calculation unit 40 may divide the space 8 into a plurality of elements before the following calculation.

  The calculation unit 40 includes a heat / solidification calculation means 41 for calculating the amount of heat (temperature) of the molten metal and a solidification rate in the divided elements of the space 8 filled with the molten metal, and a pressure calculation means for calculating the pressure of the molten metal. 42, apparent viscosity coefficient calculating means 43 for calculating the apparent viscosity coefficient of the molten metal in the coexisting state of solid and liquid, flow speed calculating means 44 for calculating the flow speed of the molten metal, and for analyzing the shrinkage nest from the molten metal filled in each element A nest analysis unit 45; and a solidification determination unit 46 that determines whether the molten metal is solidified from the temperature or the solidification rate.

  The heat / solidification calculating means 41 calculates the amount of heat (temperature) of the molten metal with time change and the solidification rate. For example, using a general heat conduction equation such as Fourier's law, The temperature of the molten metal in each element is calculated from the amount of heat transferred. From this molten metal temperature, the solid phase rate is 0% in the region above the liquidus temperature, the solid phase rate is 100% below the solidus temperature, and the solid liquid is above the solidus temperature and below the liquidus temperature. In the coexistence region, the solid phase ratio is calculated so as to be a value between them.

  The pressure calculation means 42 and the flow velocity calculation means 44 are calculated by using a differential method based on the pressure at which the injection device 5 pressurizes the molten metal 9, the solid phase ratio of the molten metal, etc. Thus, the molten metal pressure between the elements and the flow rate of the molten metal flowing between the adjacent elements are calculated.

  Further, the shrinkage nest analyzing means 45 calculates the amount of movement of the molten metal between the elements from the flow velocity in each element determined by the flow velocity calculating means 44, and calculates the amount of the molten metal in each element from the amount of movement of the molten metal. The position and size of the shrinkage nest in the space 8 filled with the molten metal 9 including the region of the cavity 8A are analyzed.

  Further, the solidification determining means 46 determines whether or not the molten metal in each element is solidified and cannot flow, and when it is determined that the molten metal in each element is not flowable. When the shrinkage nest analysis result shown above is output to the display device 50 and the molten metal can flow, a predetermined time step is given to repeat the series of calculations so far. The calculation result is input to the heat / solidification calculation means 41. In addition, since the calculation by the calculation means 41 and 42 shown so far, the analysis by the analysis means 45, and the determination by the determination means 46 are general methods in casting analysis that can be performed by those skilled in the art, a detailed description will be given. Omitted.

And in this embodiment, the apparent viscosity coefficient calculating means 43 is further provided, and this flow velocity calculating means 44 calculates the flow velocity of the molten metal based on the calculated apparent viscosity coefficient. Specifically, as shown in FIG. 4 (a), the apparent viscosity coefficient calculating means 43 includes an infinite number of solid phases (hatched portions) in the elements 8a and 8b between the adjacent elements 8a and 8b. Assuming that the melt in the solid-liquid coexistence state including the liquid phase (outlined part) between the solid phases flows together during solidification, the apparent viscosity coefficient when the melt in the coexistence state of solid-liquid flows first The calculation is based on the solid phase ratio calculated. Then, the flow rate calculation means 44 performs a process of calculating the flow rate of the molten metal based on this apparent viscosity coefficient. More specifically, as shown in FIG. 4 (a), the apparent viscosity coefficient calculating means 43 calculates the apparent viscosity coefficient using the applied pressure (casting pressure) from the casting apparatus. Specifically, The apparent viscosity coefficient is the above-mentioned apparent viscosity coefficient μ _e , the viscosity coefficient of only the liquid phase of the molten metal is μ ₀ , the solid phase ratio of the molten metal in the element is fs, and the coefficient depending on the pressure of the molten metal in the element is A, When using the following formula,

演算される。この見掛け粘性係数の演算にあたっては、事前に射出装置からの加圧力に依存した係数Ａを、実際に鋳造を行う材料の固液共存状態の溶湯に対する固相率、加圧力、粘性係数を常法により測定し、この得られた実測値に基づいて決定されている。この結果、溶湯圧力に依存した係数Ａは、図５に示すよう、圧力が高いと小さい値となるように設定されることになり、例えば、ダイカスト用アルミニウム鋳造合金（ＪＩＳ規格：ＡＤＣ１２）の場合には、固相率と加圧力に対する見掛け粘性係数は、図５に示すような結果となり、この係数Ａは、その加圧力に合わせて１〜１０の範囲に設定されることになる。なお、このダイカスト用アルミニウム鋳造合金の場合には、液相の粘性係数μ_０は、２．７ＭＰａ・Ｓであるため、この値を数５に代入して計算を行う。

Calculated. In calculating the apparent viscosity coefficient, the coefficient A depending on the applied pressure from the injection device is used in advance, and the solid phase ratio, the applied pressure, and the viscosity coefficient for the melt in the solid-liquid coexistence state of the material to be actually cast are used in the usual manner And is determined based on the actually measured value obtained. As a result, as shown in FIG. 5, the coefficient A depending on the molten metal pressure is set to be a small value when the pressure is high. For example, in the case of an aluminum casting alloy for die casting (JIS standard: ADC12) The apparent viscosity coefficient with respect to the solid phase ratio and the applied pressure is as shown in FIG. 5, and the coefficient A is set in the range of 1 to 10 in accordance with the applied pressure. In the case of this aluminum casting alloy for die casting, since the viscosity coefficient μ ₀ of the liquid phase is 2.7 MPa · S, this value is substituted into Equation 5 for calculation.

  Such an expression of the apparent viscosity coefficient reproduces the phenomenon that the viscosity decreases as the pressure at which the molten metal acts on the molten metal and the phenomenon that the viscosity increases exponentially as the solid phase ratio increases. Therefore, by using this equation, the flow rate of the molten metal shown below can be calculated with higher accuracy, and as a result, the exact position and size of the shrinkage can be analyzed and predicted.

Based on the calculated apparent viscosity coefficient μ _e , the flow velocity calculating means 44 sets the apparent viscosity coefficient μ _e , the pressure difference between adjacent elements ΔP, and the center distance between adjacent elements Δx , When the permeability of the molten metal in a solid-liquid coexistence state between adjacent elements (a constant value) K ₀ ,

として演算している。この数６は、図４（ｂ）に示すダルシー流れの基礎方程式の粘性係数μ_０に見かけ粘性係数μ_ｅを、固相率の関数となる透過率Ｋに、一定値の透過率Ｋ_０を用いたものであり、金属凝固時において固液共存状態の固相を多孔質とし、この多孔質の固相内を液相のみが流動する（図４（ｂ）参照）と仮定しているダルシー流れの基礎方程式を、要素内における固液共存状態の溶湯が凝固時に一体となって流動する（図４（ａ）参照）と仮定したモデル式にしたものである。

Is calculated as This equation 6 is obtained by setting the apparent viscosity coefficient μ _e to the viscosity coefficient μ ₀ of the basic equation of Darcy flow shown in FIG. 4B, the transmittance K ₀ as a function of the solid phase ratio, and the constant transmittance K ₀ . Darcy assumes that the solid phase in the solid-liquid coexistence state is porous at the time of metal solidification, and that only the liquid phase flows in the porous solid phase (see FIG. 4B). The basic equation of the flow is a model equation that assumes that the solid-liquid coexisting molten metal in the element flows together during solidification (see FIG. 4A).

  In this way, the flow velocity calculating means 44 is an arithmetic process that faithfully captures the phenomenon in which the solid phase and the liquid phase flow together under high pressure conditions in an actual machine, so the molten metal flow is accurately analyzed, The position and size of the shrinkage cavity of the cast product generated when the molten metal is solidified can be predicted quickly and accurately. In addition, by using a simplified formula using Darcy's basic equations, it is possible not only to predict shrinkage more accurately, but also to minimize program changes in analysis processing, Calculation time can be shortened.

  FIG. 6 shows an example of a calculation flow chart when the position and size of the shrinkage cavity of the cast product are analyzed by a computer using the apparatus configured as described above. First, in step 61 (S61) of FIG. 6, the shape of the space 8 filled with the molten metal formed by the mold 2 and the injection device 5 is input from the input device 20 to the storage unit 30 of the casting analysis device 10. Here, the input data of the space 8 is data obtained by dividing the space 8 into a plurality of elements in accordance with the shape of the space filled with the molten metal formed by the mold 2. Next, in step 62, material conditions necessary for the analysis, material conditions (such as physical properties of the molten metal, mold, and injection device), boundary conditions (such as heat transfer coefficients of the mold and molten metal), and initial conditions (mold) The data of the mold, the injection device, the initial temperature of the molten metal, etc.) and the pressure (casting pressure) of the injection device 5 are input from the input device 20 to the storage unit 30, and the process proceeds to step 63.

  In step 63, based on these input data, the heat / solidification calculating means 41 calculates the amount of heat (temperature) and the solidification rate of the molten metal with time. In step 64, the pressure calculating means 42 calculates the pressure of the molten metal in each element based on the calculated temperature of the molten metal, the solidification rate, the applied pressure from the injection device 5, and the like. Further, in step 65, the apparent viscosity coefficient calculating means 43 obtains the apparent viscosity coefficient from the solid phase ratio of each element and the pressure applied by the injection device by the method shown in FIG. 4 (a). In step 66, this apparent viscosity coefficient is obtained. Based on the viscosity coefficient and the calculated melt pressure, solid phase ratio, etc., the flow rate calculation means 44 calculates the flow rate of the melt in each element by the method as shown in FIG. In step 67, the shrinkage analysis means 45 calculates the amount of movement of the molten metal flowing between adjacent elements from the flow rate of the molten metal, and in step 68, the shrinkage cavity analysis means 45 calculates the amount of movement of the molten metal. Then, the position and size of the shrinkage nest in the space 8 including the cavity 8A is analyzed, and the process proceeds to step 69.

  In step 69, when the solidification determining means 46 determines whether or not the molten metal in each element is completely solidified and cannot flow, and determines that the molten metal in each element cannot flow. Proceeds to step 70. In step 70, the analysis result of the shrinkage nest shown above is output to the display device 50. If the molten metal can flow, the process proceeds to step 71. Then, the process proceeds to step 63 to repeat the series of calculations. Here, as the determination of the end of the calculation, the determination is made based on whether or not the molten metal in each element is completely solidified. However, for example, the calculation may be ended based on the accumulation of given time steps. .

Examples of performing casting analysis using the above-described casting analysis apparatus of the present embodiment will be described below.
Example 1
As shown in FIG. 7, a product part (cast part in the cavity) 81 in which nine protrusions 81b having a size of 25 mm × 25 mm and a height of 5 mm are formed on a flat plate 81a of 150 mm × 150 mm × thickness 5 mm, and casting A shrinkage cavity analysis was performed using a casting product 80 composed of a biscuit portion 82, which is a surplus material sometimes generated, as an analysis model. Specifically, the shape of the space filled with the molten metal to be the cast product was input and divided into a plurality of elements. Next, as shown in Table 1 below, as material conditions, the material of the molten metal is an aluminum casting alloy for die casting (JIS standard: ADC12), the material of the mold is an alloy tool steel (JIS standard: SKD61), The physical property values when the material of the liner (planar head portion) was a cast iron product (JIS standard: FC230) were input.

Furthermore, the initial conditions of the analysis are a molten metal temperature of 923K and a plunger pressure (casting pressure) of 5 MPa, and the boundary conditions are a range of 2000 to 10,000 W / m ² · K in terms of the thermal conductivity of the mold and the molten metal according to the site. Entered in The result of analyzing the shrinkage nest based on the input data is shown in the column 1 of the embodiment of FIG. In addition, the analysis result of FIG. 8 is AA sectional drawing of the analysis model shown in FIG.

  Furthermore, the same aluminum alloy was actually cast using a casting apparatus under the same conditions as the analysis conditions, and the shrinkage cavities of the obtained castings were observed. This result is also shown in the column 1 of the reference example in FIG. In addition, as this observation result, it is the result of having scanned the center cross section (AA arrow cross section as FIG. 7) of a casting.

(Example 2)
Analysis was performed in the same manner as in Example 1. The difference from the first embodiment is that the applied pressure (casting pressure) of the plunger is set to 50 MPa at the time of analysis. The result of analyzing the shrinkage nest based on the input data is shown in the column 2 of the embodiment of FIG. Further, under the same conditions as the analysis conditions of Example 2, an aluminum alloy was actually cast using a casting apparatus, and the observation result of the shrinkage nest at the same position of the obtained cast product was shown in Reference Example 2 of FIG. Shown in the column.

(Comparative Example 1)
Analysis was performed in the same manner as in Example 1. The difference from the first embodiment is that when calculating the flow velocity of the molten metal in each element, a basic equation of Darcy flow (see FIG. 4 (b) instead of an equation using an apparent viscosity coefficient (see FIG. 4 (a)). ))). The results are shown in column 1 of the comparative example in FIG.

(Comparative Example 2)
Analysis was performed in the same manner as in Example 2. The difference from the second embodiment is that the basic equation of Darcy flow is used instead of the equation using the apparent viscosity coefficient when calculating the flow velocity of the molten metal in each element. The results are shown in the column 2 of the comparative example in FIG.

(result)
The shrinkage nest portion (shaded portion) in the analysis results of Examples 1 and 2 is less than the shrinkage nest portion (shaded portion) in the analysis result of the comparative example, and the shrinkage nest portion (shaded portion) in Examples 1 and 2 is The positions of the shrinkage nests (broken line encircled parts) in the actual castings (Reference Examples 1 and 2) corresponding to this were substantially the same, and the size of the shrinkage nests was similar. Furthermore, the size of the shrinkage nest portion of Example 2 was closer to the shrinkage nest generated during actual casting than the shrinkage nest portion of Example 1.

(Discussion)
In the analysis in Comparative Examples 1 and 2, the basic equation of Darcy flow in which only the molten metal flows is used as the flow rate of the molten metal between adjacent elements during casting. In actual casting, as in Examples 1 and 2, Since the solid phase and the liquid phase are considered to flow together, the calculation results using the apparent viscosity coefficient of the molten metal in the solid-liquid coexistence state as in Examples 1 and 2 are more effective than the actual casting shrinkage. It is thought that the result was close to. Furthermore, since the result of the shrinkage nest at the time of high-pressure (50 MPa) casting in Example 2 was close to the shrinkage nest portion in the actual casting, the melt in a solid-liquid coexisting state was solidified at the time of actual high-pressure casting. This is thought to be due to the assumption that sometimes it flows together.

  As mentioned above, although one Embodiment of this invention was explained in full detail, this invention is not limited to the said embodiment, For example, if the analysis of a shrinkage nest could be performed, it showed to Embodiment The procedure of each step of the flow diagram may be interchanged. In the examples, the molten metal was used, but the material of the molten metal is not limited to the aluminum alloy, and the molten metal is in a semi-solid and semi-molten state. However, the same effect can be obtained.

The figure for demonstrating an example of the analysis model for performing the casting analysis method which concerns on this invention. The figure for demonstrating the apparatus structure for performing the analysis based on the analysis model of FIG. The analysis block diagram which showed an example of the casting analysis apparatus of FIG. It is a figure for demonstrating the detail of calculation of the apparent viscosity coefficient shown in FIG. 3, and the calculation of the flow velocity of a molten metal, (a) is for demonstrating the calculation of the apparent viscosity coefficient and flow velocity of a molten metal in this embodiment. It is a figure, (b) is a conceptual diagram for demonstrating the calculation of the flow rate of the molten metal using the conventional Darcy law. The figure for demonstrating the value of the apparent viscosity coefficient at the time of calculating using the type | formula shown in FIG. The flowchart for demonstrating the analysis step which the casting analysis apparatus shown in FIG. 3 performs. The figure for demonstrating the analysis model in Examples 1, 2 and Comparative Examples 1,2. The figure which showed the analysis result at the time of performing the casting analysis by Example 1, 2 and the comparative examples 1 and 2, and the casting result at the time of actual casting using the analysis model shown in FIG.

Explanation of symbols

  1: casting apparatus, 2: mold, 2A: fixed mold, 2B: movable mold, 5: injection apparatus, 5B: plunger, 8: space filled with molten metal, 8A: cavity, 8a, 8b: element, 8a: Element: 9: Molten metal, 10: Casting analysis device, 20: Input device, 30: Storage unit, 40: Calculation unit (calculation unit), 41: Thermal / solidification calculation unit, 42: Pressure calculation unit, 43: Flow rate Calculation means 43: Apparent viscosity coefficient calculation means 44: Flow velocity calculation means 45: Shrinkage analysis means 46: Solidification determination means 47: Solidification determination means 50: Display device 80: Cast product 81a: Flat plate , 81b: protrusion, 82: biscuit part

Claims (8)

About a cast product obtained by filling a molten metal in a space formed in a mold using an injection device, and solidifying the molten metal in a state where pressure is further applied to the filled molten metal from the injection device and the molten metal is solidified. The filled space is divided into a plurality of elements, and at least the melt pressure and the solid phase ratio in each element are calculated, and the molten metal that flows between adjacent elements based on the melt pressure and the solid phase ratio A casting analysis method for calculating the flow rate of the casting by computer analysis of the state of the shrinkage cavity of the casting,
The casting analysis method assumes that in the calculation, the solid-liquid coexisting molten metal in each element flows integrally during solidification, and the apparent viscosity coefficient when the solid-liquid coexisting molten metal flows is calculated as a solid phase. A casting analysis method characterized by calculating based on a rate and calculating a flow rate of the molten metal based on the apparent viscosity coefficient. The flow rate of the molten metal is u, the apparent viscosity coefficient is μ _e , the pressure difference between adjacent elements is ΔP, the center-to-center distance between adjacent elements is Δx, and the molten metal that permeates between adjacent elements. When the transmittance is K ₀ ,

The casting analysis method according to claim 1, wherein   The casting analysis method according to claim 1, wherein the apparent viscosity coefficient is calculated using a pressing force from an injection device. The apparent viscosity coefficient is μ _e , the viscosity coefficient of only the liquid phase of the molten metal is μ ₀ , the solid phase ratio of the molten metal in the element is fs, and the coefficient depending on the pressure applied from the injection device is A , And when

The casting analysis method according to claim 3, wherein the casting analysis method is calculated as follows. About a cast product obtained by filling a molten metal in a space formed in a mold using an injection device, and solidifying the molten metal in a state where pressure is further applied to the filled molten metal from the injection device and the molten metal is solidified. In order to divide the filled space into at least a plurality of elements and to perform a computer analysis of the state of the shrinkage cavity of the casting in the space, at least the melt pressure and the solid phase ratio in each of the divided elements are calculated. A casting analysis apparatus comprising at least computing means for computing the flow rate of the molten metal flowing between adjacent elements based on the pressure and solid phase ratio of the molten metal,
The calculation means assumes that the melt in the solid-liquid coexistence state in each element flows integrally during solidification, and the apparent viscosity coefficient when the melt in the coexistence state of solid-liquid flows is based on the solid phase ratio. A casting analysis apparatus comprising: means for calculating; and means for calculating a flow rate of the molten metal based on the apparent viscosity coefficient. The flow rate calculation means includes a flow rate of molten metal u, an apparent viscosity coefficient μ _e , a pressure difference between adjacent elements ΔP, a center-to-center distance between adjacent elements Δx, and a molten metal flow between adjacent elements. When the transmittance is K ₀ ,

The casting analysis apparatus according to claim 5, wherein   The casting analysis apparatus according to claim 5 or 6, wherein the apparent viscosity coefficient calculating means calculates the apparent viscosity coefficient using a pressing force from an injection device. The apparent viscosity coefficient calculating means has the apparent viscosity coefficient μ _e , the viscosity coefficient μ _{0 of} only the liquid phase of the molten metal, the solid phase rate fs, and the coefficient related to the pressure applied from the injection device A. Viscosity coefficient μ _e

The casting analysis apparatus according to claim 7, wherein

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