JPH1034320A - Method for analyzing fluid solidification of molten metal, instrument therefor and recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve the reliability of alloy casting, etc., in a mold casting and to reduce the cost by dividing molten metal into fine elements and analyzing a molten metal model in the element in each passing time. SOLUTION: The molten metal for casting into the mold is divided into plural fine elements according to a mold shape and the modeling is executed to the molten metal model in each element with a temp. changing according to the solidified state variable showing the plural condition and the soluble element concn. in the solid phase and the liquid phase. To this analyzing model, the thermal condition and the solute shifting are analyzed in each passing time between the fine elements, and at least one of the variable showing the temp. and the phase condition and the solute element concn. of the liquid phase is renewed and outputted in each passing time based on the analyzed results. This fluid solidification analyzing calculation ST8 is repeated through a time step addition ST7 until it is judged that the solidification completes with the nineth step ST9. In the case, segregation position and segregation quantity are in the desirable range with the eleventh step ST11 and it is judged that there is no other defect, a casting plan is made.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for manufacturing an alloy casting, in order to prevent shrinkage porosity defects and macrosegregation defects of alloy components caused by solidification shrinkage of molten metal (casting). The present invention relates to a flow solidification analysis method for analyzing a solidification process of a casting and predicting the occurrence of shrinkage cavities and macrosegregation defects according to the shape of the casting. Further, the present invention relates to a flow solidification analysis device for predicting the occurrence of shrinkage cavities and macrosegregation defects, and a recording medium storing a flow solidification analysis program.

[0002]

2. Description of the Related Art In recent years, with the development of computer hardware and cost reduction, a method using solidification simulation has been frequently used to create a casting plan for die casting.

Many of them qualitatively predict the position of a shrinkage defect caused by coagulation contraction. That is,
This shrinkage porosity defect prediction method is based on modeling the molten metal (casting) and mold and its surrounding area, calculating the heat transfer, and determining the solidification rate distribution uniquely determined from the temperature distribution and physical property data of the casting. Was calculated, and a temperature gradient, a solidification rate gradient, and a solidification rate calculated as a result were used as parameters to predict a position where a shrinkage porosity defect due to coagulation shrinkage was likely to occur.

On the other hand, by evaluating the amount of coagulation shrinkage, the flow in the coexistence region of the molten metal and the solid-liquid during the coagulation is calculated,
Calculation methods for quantitatively predicting the occurrence of shrinkage cavities have also been attempted (for example, research report 70 issued by the Japan Foundry Association in 1994).
"Study on hot water flow simulation and optimization of hot water method", page 104, by Kimiyoshi Nakayama. Methods of predicting shrinkage cavities using these solidification analysis techniques and using the results to create an optimal casting plan have met with numerous successes.

[0005] Incidentally, as a defect that needs to be controlled in addition to the shrinkage porosity defect in the die casting of the alloy, there is a segregation defect of the alloy component. The segregation of alloy components is a phenomenon in which the component ratio of the main component (solvent element) of the alloy to the added element (solute element) differs depending on the location. Are different from each other in solubility.

For example, in an Al-Si alloy, the maximum amount of Si element that can be dissolved in the solid phase (α phase) of Al is about 1.6% by weight, and a molten metal having a Si concentration exceeding 2% by weight is solidified. If so, S in the molten metal in a portion exceeding 1.6% by weight
The i element is discharged from the solidification interface between the solid phase and the liquid phase to the liquid phase during solidification. Therefore, as the solidification progresses and the solid phase of the Al—Si alloy having the Si concentration of 1.6% by weight spreads, the Si concentration in the liquid phase increases. As a result, the Si concentration in the solid phase portion that solidifies later, particularly the Si concentration near the local solidification in the final stage, may suddenly increase. Such a scale (period) in which the concentration of the alloy component is high or low on the order of the dendrite secondary arm interval is referred to as microsegregation, which is normally found in a sound casting structure.

On the other hand, a phenomenon in which a portion having a high or low alloy component concentration exists continuously over a wide range beyond the dendrite secondary arm interval is called macrosegregation,
The occurrence of this macro segregation causes the material properties to be significantly reduced. V segregation seen in steel ingots, etc.
It is a kind of macro segregation. In addition, center segregation, which is not mold casting but is found in continuous casting, can also be included in the category of macro segregation.

As a method for controlling the macro-segregation using solidification analysis for the purpose of improving the quality of a product, there has been a horizontal continuous casting method disclosed in, for example, Japanese Patent Application Laid-Open No. 6-79421.

[0009]

The conventional macro-segregation prediction based on solidification analysis is applied to the case of continuous casting performed under normal pressure without a complicated product shape. In this case, the prediction of the segregation position is not performed. It is possible and has achieved some results. However, when the product shape is complicated, the casting is generally manufactured by die casting, but even if an attempt is made to apply the macro-segregation control method effective in the continuous casting method to the die casting, in the case of a complicated product shape, The solidification process is complicated, and there is a problem that it is difficult to predict the generation position and the degree of segregation.

[0010] For example, there is a mold casting method such as melt forging or medium pressure casting in which external pressure is applied during solidification to suppress shrinkage cavities due to solidification shrinkage. In these mold castings, the product shape is often complicated and the types of products are many as compared with the continuous casting and ingot casting described above. In addition, the position and degree of generation of macrosegregation are completely different depending on each product shape. Therefore, if it is possible to easily analyze the generation position and the degree of macro-segregation before actually manufacturing a product, it is easy to optimize the manufacturing parameters.

It has been reported that this segregation is likely to be generated near the final solidification position as well as the shrinkage cavities (Hiroshi Terauchi, Kazuhiko Yamashita: Casting 66 (1994), page 922). However, unlike the shrinkage porosity defect that appears almost certainly at the final solidification position, the segregation defect is located near the final solidification part but definitely at a different position from the final solidification part. It is hard to say that the techniques and techniques for determining In particular, at present, no solidification analysis method has been established for a solidification analysis method for predicting segregation of an alloy component such as an Al-Si alloy in mold casting that takes a complicated solidification process.

The present invention has been made in view of such circumstances, and when a casting plan is created by controlling macrosegregation, alloy component segregation and shrinkage cavity position in mold casting are predicted by solidification analysis. Newly devised a flow solidification analysis method,
It is an object of the present invention to provide a fluid coagulation analysis method, a fluid coagulation analysis device, and a recording medium in which a program for fluid coagulation analysis is stored.

[0013]

SUMMARY OF THE INVENTION In order to solve the above-mentioned problems of the prior art and to achieve the above object, the present inventors investigated the segregation positions of high-pressure cast castings of various shapes, and investigated Numerical calculations were performed using an analytical model consisting of the molten metal in the cavity of the mold. As a result of considering them, the present inventors have found that the generation of component segregation in high-pressure cast castings is caused by the movement of molten metal (casting) in the solid-liquid coexistence region caused by external pressure and solidification shrinkage. Knew. More specifically, in areas where the flow velocity of the molten metal (casting) in the solid-liquid coexistence region is high, the alloy components of the molten metal are likely to be concentrated, and the concentrated molten metal is not solidified around the final solidified part. It may flow toward the part, and it is known that the final solidification position of the concentrated molten metal is a position where segregation defects appear in the product.

The flow solidification analysis method of the present invention has been devised based on this finding. As an analysis model of the flow solidification of the molten metal, a plurality of minute molten metals are cast according to the shape of the die. The model of the molten metal in each element is divided into a temperature that changes according to the solidification state, at least a variable indicating the phase state consisting of the solid phase and the liquid phase, the solute element concentration in the solid phase, and the A modeling step represented by the solute element concentration, and analyzing the heat conduction and solute transfer between the microelements with respect to each elapsed time with respect to the analysis model, based on the analysis result of the heat conduction and solute transfer, And a flow solidification analysis step of updating and outputting at least one of a variable indicating the phase state and a solute element concentration of the liquid phase over time.

In the flow solidification analysis, it is considered that a flow (flow) between the solid phase and the liquid phase elements occurs due to solidification shrinkage, and solute elements move along the flow. In order to further improve the accuracy, it is necessary to quantitatively estimate the void amount at the time of solidification shrinkage, which causes flow. In the fluid solidification analysis method of the present invention in which this flow is considered, in the modeling step, as a variable representing the phase state, a solid phase ratio indicating a ratio of a solid phase occupying in each element, and a solidification shrinkage in each element by solidification shrinkage. The porosity, which indicates the ratio of voids generated in each element, represents the molten metal model, and in the flow solidification analysis step, inter-element flow of solid phase and liquid phase that compensates for voids generated in each element due to solidification shrinkage Analyze, the flow between the elements of the solid phase and the liquid phase, based on the analysis results of the heat conduction and the solute transfer, the solid phase ratio, the porosity, the temperature, at least the solute element concentration of the liquid phase Another feature is that any one is updated and output every elapsed time.

In these solidification analysis methods, the microelements of the analysis model are grasped from the solid phase and the liquid phase (voids), and the temperature and the solute element concentration for each phase are used as time-dependent parameters. The concentration and average concentration of the concentrated molten liquid (liquid phase) can be calculated, and the macro-segregation position can be easily predicted at, for example, the position of the element that has been concentrated most by the end. In addition, since the coagulation time at each position can be known from the coagulation rate (solid phase rate) for each elapsed time, the final coagulation position can be known, whereby the shrinkage cavity position can be easily predicted. Further, the shrinkage cavity position and the shrinkage cavity size can be easily predicted from the final porosity of each element.

In pressure casting, in which the molten metal is easily moved by pressurization and mainly prevents the occurrence of shrinkage cavities, the diffusion coefficient of the solute transfer equation depends on, for example, the solid phase ratio during flow solidification analysis. May be changed appropriately. In the former method that does not consider the flow, the solute transfer coefficient representing the ease of solute transfer, for example, according to the solid fraction, when pressure is applied to the molten metal during solidification when pressure is not applied After setting a larger value, a solute transfer analysis may be performed.

On the other hand, in the latter method taking flow into consideration, first, a porosity generated by solidification shrinkage is estimated, and a flow generated to compensate for shrinkage by pressurization is calculated. It is preferable to solve the solute transfer equation using the results (for example, pressure and flow velocity), and obtain changes over time in the solid fraction, the porosity, the temperature, and the solute element concentration for the entire analysis model. Specifically, in order to reflect the result of the flow calculation on the solute transfer, for example, the pressure applied to the molten metal during solidification obtained by performing the flow calculation (solid-phase and liquid-phase inter-element flow analysis) is calculated. The diffusion coefficient of the solute transfer equation may be appropriately changed and set depending on the size, the magnitude and direction of the flow velocity, the magnitude of the solid fraction, and the magnitude and direction of the solid fraction gradient. In addition, by changing the magnitude of the pressure, the magnitude and direction of the flow velocity, the magnitude of the solid fraction, and the magnitude of the solid fraction gradient, the ratio of the amount of movement between the solid phase and the liquid phase due to the flow is appropriately changed. Thus, the diffusion coefficient may be set.

In the fluid solidification analyzer of the present invention, as an analysis model of the fluid solidification of the molten metal, the molten metal cast into the mold is divided into a plurality of minute elements according to the shape of the mold, and each element is subjected to temperature, Modeling means represented by at least a variable indicating a phase state consisting of a solid phase and a liquid phase, a solute element concentration in a solid phase, and a time-varying parameter consisting of a solute element concentration in a liquid phase, and the position of each element according to the type. The element parameters relating to the size and the time-varying parameters are input from the modeling means, and based on the input parameters, the heat conduction and the solute movement are analyzed for each elapsed time between the elements, and the heat conduction and the solute transfer are analyzed. Analyzing means for updating and outputting the time-varying parameter based on the analysis result of the movement. Further, in the present fluid coagulation analyzer considering a flow, the modeling means includes, as variables representing the phase state, a solid phase ratio indicating a ratio of the solid phase occupying in each element, and solidification shrinkage in each element by solidification shrinkage. The porosity, which indicates the ratio of the generated voids to each element, represents each element, and the analysis means analyzes the inter-element flow of the solid phase and the liquid phase to compensate for the voids generated in each element due to solidification shrinkage. Another feature is that the time-varying parameter including the porosity and the solid fraction is updated and output based on the analysis results of the flow between the elements, the heat conduction, and the solute transfer.

The recording medium for flow solidification analysis of the present invention is characterized in that the procedure of the above-mentioned flow solidification analysis method is stored as a program.

[0021]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a flow solidification analysis method and a flow solidification analysis apparatus according to the present invention will be described in detail with reference to the drawings.

First Embodiment FIG. 1 is a schematic configuration diagram of a coagulation analyzer according to the present invention. The fluid solidification analyzer 1 prepares an analysis shape model, executes a preprocessor 2 for inputting physical property values and casting conditions necessary for analysis, and executes heat conduction and mass transfer analysis on the manufactured shape model. It comprises a main processor 3 as a solver and a post processor 4 for outputting an analysis result. Main processor 3
Is composed of a heat conduction analyzing means 5, a parameter updating means 6, and a solute movement analyzing means 7. Specific functions and operations of the processors 2, 3, 4 and the means 5, 6, 7 will be described in the following description of the flow coagulation analysis method.

Hereinafter, the flow solidification analysis method of the present invention will be described with reference to the flowchart of FIG. 3 by taking as an example the case where component segregation control in high-pressure casting is performed using this method. First, in preparing an analysis shape model by the preprocessor 2, in a first step ST1, an analysis model (micro element data)
Input. That is, as in the conventional case, the analysis target is divided into mesh-like fine elements, and the size and position of each element are defined.

In the next second step ST2, it is determined whether or not the flow analysis is used as the initial condition of the analysis model. If so, the flow analysis calculation is performed in the third step ST3. This flow analysis calculation is also performed by the preprocessor 4, and as a result, for example, in a case where a two-dimensional model is created and analyzed using the direct difference method, a model as illustrated in FIG. 4 is created.

When it is determined in the second step ST2 that flow analysis is not to be performed, or after the end of the third step ST3, an initial condition is set in a fourth step ST4, and a time step Δt is set in a fifth step. These settings are also performed by the preprocessor 4. Of these, as the initial conditions set in the fourth step ST4, initial values of temperature and concentration are given for each element in addition to various casting conditions and physical property data, as in the conventional case.

FIG. 5 schematically shows the condition for each element in the present invention in comparison with the conventional case. As shown in the figure, the feature of the flow solidification analysis method of the present invention is that each element N _i is analyzed so that analysis of alloy component enrichment of the molten metal can be performed.
The concentration grasped between solid and liquid phases in accordance with the solidification rate fs _i, further, for example in the case of binary alloys, for each of which the solid and liquid phases of each element, and the solvent element to be mainly, this Temperature and concentration with the solute element dissolved in the steel. Therefore, in the initial setting in the fourth step ST4, each element is divided into a solid phase and a liquid phase in accordance with this model, and the process is performed for each solvent element and solute element. That is, where the temperature T _i of each element N _i,
Initially, the solid phase concentration Cs and the liquid phase concentration Cl are set.
In the fifth step ST5, the value of the time step Δt is determined.

When the above modeling and setting of conditions have been completed, finally, from the sixth step ST6, the main processor 3 in FIG. Be executed. That is, after the initialization of the time (sixth step ST6) and the addition of the first time step (seventh step ST7), the flow solidification analysis calculation is executed in the eighth step ST8. This flow solidification analysis calculation is repeated through time step addition (seventh step ST7) until it is determined in step 9 that the solidification is completed. The details of the flow solidification analysis calculation will be described later for each calculation step.

If it is determined in the ninth step ST9 that the coagulation has been completed, the final concentration distribution and coagulation time distribution are confirmed (first).
0 step ST10), and if it is determined from the result in the eleventh step ST11 that the segregation position and the segregation amount are within a desired range, the presence or absence of another defect is similarly confirmed (twelfth step ST12). Further, if it is determined in the next thirteenth step ST13 that there is no other defect, the fourteenth step ST14
Then, a casting plan is created based on the above analysis results.

On the other hand, if the segregation position or the like is not within the desired range in the eleventh step ST11, or if there is another defect in the thirteenth step ST13, the fifteenth step ST11 is executed.
If it is determined in 15 that changes in the analysis model, etc. are necessary,
After the analysis model or the initial conditions are changed in the sixteenth step ST16, the process returns to the step before the fifth step ST5, and the flow solidification analysis is executed again. By the judgment of the fifteenth step ST15,
If there is no need to change the analysis model or the like, a casting plan is created in a fourteenth step ST14.

Hereinafter, the contents of the solidification analysis calculation in the eighth step ST8 will be described in detail. FIG. 6 is a flowchart showing the contents of the eighth step ST8 in FIG. 3 in more detail, and FIG.
It is a correlation diagram of the calculated value which shows the flow of each calculation of coagulation analysis.
The purpose of this solidification analysis calculation is to predict the position of segregation and the position of shrinkage cavities, as described above, which is calculated from the concentration distribution of the casting in which the alloy component is concentrated and the final solidification position. It is. In the determination of the position of the deviation of the molten metal, for example, since the average concentration gradually changes, the distribution of the average concentration is obtained, and the position where the average concentration is the highest can be finally determined as the position of the deviation. Further, an equal coagulation time is obtained from the relationship between the coagulation rate and time, and a position requiring the longest coagulation time can be determined as a shrinkage cavity position. Furthermore, since there is a certain relationship between the temperature and the solidification rate, the shrinkage cavity position can be determined from the temperature distribution. Further, the size of the shrinkage cavity can be determined from the final porosity.

[0031] In view of the above, in this solidification analysis calculations, as shown in FIG. 7, the enthalpy H _i defined for each element N _i at any time t, the temperature T _i, the solidification rate fs
_{From i} and the liquid phase concentration Cl, the heat conduction equation and the solute transfer equation between the adjacent elements _Ni and _Nj (corresponding to the elements _Ni-1 and _{Ni + 1} in FIG. 5) are solved, and a new equation is obtained. Temperature T
_i, is set to be calculated coagulation factor fs _i and liquid concentrations Cl.

Calculation of Heat Diffusion (ST801) First, the following formula (1) showing Fourier's law (heat conduction equation) is used to calculate the amount of heat transferred between each element per unit time and per unit sectional area. qj _ij = −K _ij (T _j −T _i ) × Δt × S _ij / Δr _ij (1) Here, _{q j ij} is the amount of heat flowing from element _Ni to element N _j during the minute time step Δt. , K _ij elements N _i and element N _j reciprocal falls variable-constant thermal resistance between, T _i is the temperature of the element N _i, T _j is temperature factors N _j, Delta] t is very small time step, S _ij elements the contact area between N _i and element N _j, [Delta] r _ij is the distance between the elements N _i and element N _j.

K _ij is, for example, the thermal conductivity between the elements and is a physical property value specific to the material of the element. When the two elements in contact with each other are different substances, the average thermal conductivity between the two elements is It will be used, and in some cases, it will be determined in consideration of the contact thermal resistance (heat transfer coefficient) between the two substances.
The calculation of qj _ij is performed for each of all two adjacent elements. The following calculations are also performed between all elements or for all elements unless otherwise specified.

Calculation of Effective Transfer Cross-Section Rate (ST802) The effective transfer cross-section rate is one parameter indicating the ease of movement of a solute element. For example, the following equations (2-1) to (2-3) Is calculated. fc _ij = 1−fs _i ... (2-1) fc _ij = 1−max (fs _i , fs _j )... (2-2) fc _ij = 1− (fs _i + fs _j ) / 2 (2) 3) here, fc _ij is effective moves sectional area ratio between the elements N _i and element N _j, fs _i, fs _j are each elements N _i, the solidification rate of the elements N _j, max (x, y) is x And the larger value of y.

In this example, it is assumed that the solute moves only in the liquid phase. Therefore, the effective moving area ratio fc _ij is calculated as a value correlated with the solid phase ratio (in this example, the complement of the liquid phase ratio). Further, the effective moving area ratio fc _ij is defined between two elements that are in contact with each other, and as shown in the above equations (2-1) to (2-3), the solid phase ratio is one of the two elements, the maximum value or the average value. Any of the values may be used. Incidentally, if it is assumed that the transfer of the solute occurs similarly in both the liquid phase and the solid phase, the effective transfer cross-sectional area ratio fc _ij is fc _ij irrespective of the above equations (2-1) to (2-3). =
It may be set to 1. In some cases, another value may be defined as fc _ij regarding the movement of the solute and the movement of the liquid phase and the solid phase.

Calculation of Solute Transfer Coefficient between Elements (ST803) In this embodiment, it is assumed that solute transfer is proportional to the concentration of two elements that are in contact with each other, as described in ST804 described below. Defined as coefficient D _ij . Therefore, the solute transfer coefficient D _ij between the elements is
Represents the ease of movement of the solute element, similarly to the effective movement cross-sectional area fc _ij . In this example, as shown in the following equation (3), and the solute transport coefficient D _ij solidification rate fs _i elements, the time t from the start of casting, as a function of coagulation time tf. D _ij = D (fs _i , t, tf) (3)

More specifically, the solute transfer coefficient D _ij under the pressurized condition as in the present embodiment is expressed by the following equations (3-1) to (3-4). D2> D1, D2>
Three solute transfer coefficients D1, D2, D3 having the relationship of D3
Can be expressed separately. _Dij = D1 (t <t1, fs <f1) (3-1) _Dij = D2 (t <t1, f1 <fs <f2) ... (3-2) _Dij = D3 (t> t1 or fs) > F2) ... (3-3) _Dij = D3 (t> tf, but only applied to some elements in the thin portion) ... (3-4) where t1 is the pressurization end time and tf is thin The local coagulation time at which coagulation ends at each element constituting the part, f1 and f2 are constants indicating specific coagulation rates.

[0038] That is, in terms of solidification rates fs _i, if this is small (Formula (3-1)) or greater when (3-3) in solute difficult to move, within certain specific coagulation factor (formula ( 3-2) The solute moves easily in). Also, within a certain period of time from the start of casting, the solute is likely to move depending on the solidification rate due to the application of pressure (Equation (3-2)), but after the pressurization end time t1, the solute generally does not easily move. Further, after the local solidification time tf of the thinnest part, even at a solidification rate within a specific range, the solute becomes more difficult to move at element positions constituting a part of the thin part far from the gate (Equation (3) -2)).

Calculation of solute transfer between elements (ST804) The solute transfer cj _ij between elements is calculated using the effective transfer cross-sectional area ratio fc and solute transfer coefficient D obtained in ST802 and ST803. The calculation is performed in three steps ST3, or in a fourth step ST4 in the same figure, using the liquid phase concentration Cl preset in accordance with the solute transfer equation of the following equation (4). _{cj ij = -D ij × fc ij} × (Cl j -Cl i) / Δr ij × Δt × S ij ... (4) Here, cj _ij is between the minute time step Delta] t, the element N _i to the element N _j Inflowing mass, Cl _i is the element N _i
, And Cl _j indicates the liquid phase concentration of the element _Nj . In this example, the transfer of the solute occurs only in the liquid phase, but the same equation may be defined in the solid phase.

[0040] In the calculation (ST 805) the present embodiment of the enthalpy H _i, as a heat transfer solidification calculation method, and using the enthalpy method, enthalpy H _i of the casting element, wherein
It is calculated by the following equation (5) using the thermal diffusion amount qj _ij between each element in ST801. ^{_{H i t = H i t-}} 1 + Σqj / ρ i / U i ... (5) where, H _i ^t is the enthalpy at time t value,
H _i ^t−1 indicates the value of the enthalpy at time t 2. Σ is the sum of all elements in contact with element N _i , ρ _i is the density of element N _i ,
U _i denotes the volume of the element N _i. Note that a temperature recovery method may be used as another method.

Calculation of Average Concentration (ST806) The average concentration is calculated by the following equation (6) using the solute transfer amount cj obtained in ST804. ^{Cav t = Cav t-1 +} Σcj / U i ... (6) where, Cav ^t is the average concentration of elements N _i at time t, sigma is the sum of all the elements in contact with the element N _i.

Calculation of Liquidus Temperature and Solidus Temperature (ST807) In this embodiment, the liquidus temperature Tl and solidus temperature Ts of each element are assumed to be functions of the average concentration of each element. In this case, the liquidus temperature Tl and the solidus temperature Ts are, for example, the following equation (7)
-1) and (7-2). _{Tl i = (Tlc0 -Tlce) ×} (Cav-Ce) / (Ce -C0) + Tlce ... (7-1) Ts i = (Tsc0 -Tsce) × (Cav-Ce) / (Ce -C0) + Tsce ... ( 7-2) where Tl is the local liquidus temperature, C0 and Ce are constants indicating an arbitrary concentration, Tlc0 is the liquidus temperature at the concentration C0,
Tlce is the liquidus temperature at the concentration Ce. Ts is the local solidus temperature, Tsc0 is the solidus temperature at the concentration C0, and Tsce is the solidus temperature at the concentration Ce.

[0043] Calculation of the coagulation rate (ST 808) fraction solid (solidification rate) fs _i includes enthalpy Hl _i of the liquid phase in an element (casting element) N _i liquidus temperature Tl _i, solidus temperature solid phase and enthalpy Hs _i of at ts _i, can be determined from the average enthalpy H _i of the element N _i. That is, the solidification rate fs _i, as the following equation (8), each of enthalpy H _i, Hs _i, is defined by the arbitrary function fn of Hl _i. However, as defined by equation (8), the state of the elements N _i is limited to semi-solid state between the liquidus and solidus. _{fs i = fn (H i,} Hs i, Hl i) ... (8) for example, specifically coagulation factor fs _i and the enthalpy H _i,
If Hs _i, and the Hl _i was a linear relationship, equation (8) can be expressed by the following equation (8-1). fs _i = 1− (Hs−H) / (Hs−Hl) (8-1)

Calculation of Temperature Field (ST809) The temperature T _i of each element N _i in the coexisting state of the liquid phase is determined by the ST
And enthalpy H _i of each element N _i determined in 805, the ST
The liquidus temperature Tl _i and the solidus temperature Ts _i obtained in 807
When using a solidification rate fs _i determined in the ST 808, the following equation (9
Calculated by -1). _{T i = Ts i + (1} -fs i) × (Tl i -Ts i) ... (9-1) In the case of solid and liquid phase, the following equations (9-2),
It calculates the temperature T _i of each element N _i by (9-3). _{T i = H i / cp i} ( solid _{phase) ... (9-2) T i =} (H i + L) / cp i ( liquid phase) (9-3) where, cp _i is the specific heat, L is the latent heat It is.

The liquid phase concentration, calculated (ST 810) a liquid phase concentration of solid concentration, the solid phase concentration calculations are performed using the coagulation rate fs _i calculated in ST 808, an average concentration Cav which has been determined by the ST806. In the present embodiment, the solid phase concentration Cs is constant regardless of the average density Cav and liquid phase concentrations Cl ^t. For this reason, the liquid phase concentration Clt at the time ^t is determined by the previously calculated solidification rate fs.
It is uniquely determined by substituting _i and the average density Cav into the following equation (10). ^{_{Cav = Cs × fs i t +}} Cl t × (1-fs i t) ... (10) As a method other than this, a method of obtaining defines the ratio of the liquid phase concentration Cl and the solid concentration Cs as the distribution coefficient There is.

Calculation of eutectic amount ( eutectic ratio) (ST811) When the liquid phase concentration Cl exceeds the eutectic composition, a solid phase having the eutectic composition is crystallized. ) fse ^t is,
It is calculated by the following equation (11). ^{fse t = fse t-1 +} (Cl t-1 -Ce) × (1-fs t) / (Ce -Cs) ... (11) where KyoAkiraritsu in FSE ^t is the time t, FSE ^t-1 KyoAkiraritsu of time t immediately before (one time step previous), the liquid phase concentration of Cl ^t-1 at time t immediately before (one time step previous), Cs is the solid phase concentration, Ce the eutectic concentration, fs _i ^t is This is the solidification rate at time t.

The calculation order of each of the above ST801 to ST811 is not limited to the flowchart of FIG. 5, and the 16th step ST1 of FIG.
6 can be rearranged. For example, first, ST80
After step 1, the enthalpy of ST805 and the solidification rate of ST808 are calculated, and then the calculation is performed in the order of ST802 to ST804 and ST806. Then, the liquidus temperature of ST807 is calculated. Finally, ST807 and ST808 are calculated. From the results, the temperature field of ST809 and ST81
A calculation such as a liquid phase concentration of 0 may be performed.

The main processor 3 of the flow solidification analyzer 1 executes the analysis using the direct difference method, but the finite element method or another method can be used as the analysis calculation method. Further, the division mode of the minute elements is not limited to the orthogonal mesh shown in FIG. 4, and another division mode suitable for the analysis means can be used.

Second Embodiment This embodiment is directed to a case in which a flow due to movement of a solid phase and a liquid phase due to coagulation contraction is considered. FIG. 8 is a schematic configuration diagram of the main processor 3 in the present embodiment. As compared with FIG. 2 of the first embodiment described above, a flow analysis means 8 for solving a flow equation is added.

FIG. 9 is an explanatory diagram showing each parameter defined in the analysis model of this embodiment. As shown in FIG. 9, the feature of the flow solidification analysis method in the present embodiment is that each element is composed of a solid phase and a liquid phase (solid phase ratio) so that the analysis of the enrichment of the alloy component of the molten metal and the formation of the cavity can be performed. fs, liquid phase ratio fl) and the voids (porosity por), and, for example, in the case of a binary alloy, the concentration of solute elements in the solid phase and liquid phase of each element is determined by the liquid phase The eutectic ratio fse and the eutectic composition Ce are obtained by making the concentration Cl and the solid phase concentration Cs, and, if necessary, making a part of the solid phase eutectic. P, speed v.

The flowchart showing the entire flow of the analysis method is the same as that of FIG. 2 except for the contents of the eighth step ST8. However, in the initial setting of the fourth step ST4, the liquid phase, the liquid phase,
Performed on solid phase, voids and, if necessary, eutectic. In other words, in this case, the temperature T of each element N _i, enthalpy H, solid fraction fs, the liquid phase ratio fl, KyoAkiraritsu FSE, porosity por,
Initially, a solid phase concentration Cs, a liquid phase concentration Cl, a eutectic composition Ce, and an average concentration Cav are set.

Hereinafter, the contents of the flow solidification analysis calculation in the eighth step ST8 will be described in detail. FIG. 6 shows the eighth step in this case.
FIG. 7 is a flowchart detailing the contents of ST8, and FIG. 7 is a correlation diagram of the calculated values of the flow solidification analysis. In this solidification analysis calculation,
As shown in FIG. 7, enthalpy is defined in each concentration N _i at any time t H _i, the temperature T _i, the solidification rate fs
_i , liquid phase concentration Cl _i , average concentration Cav, porosity por
Solve the heat conduction law equation, flow equation, solute transfer equation,
The pressure P, velocity v, parameter D _ij , parameter SI, etc. are determined as intermediate variables, and new enthalpies H _i , temperatures T _i , solidification rates f _i , liquid phase concentrations C _{i i} , average concentrations C av,
And the porosity por are calculated. In the following, in the steps overlapping with the above-described first embodiment, only the correspondence of step codes is shown (... ST8XX), and the description thereof will be omitted. In addition, when the contents partially overlap, or when the calculation methods are different, only the different portions are described after indicating the correspondence of the codes.

Calculation of heat transfer between elements (ST821)
… ST801

Calculation of enthalpy and mold temperature of casting element
As (ST822) ... ST805 heat transfer solidification calculation method, and using the enthalpy method as in the first embodiment, the enthalpy H _i of the casting element,
It is calculated by the above equation (5). On the other hand, the temperature of the element whose temperature changes other than the casting element is similarly calculated by the following equation (2-4). T _j ^t = T _j ^{t -1} + (Σq _j ) / ρ _j / cp _j / U _j (2-4) where T _j is an element N _i (in this case, an element other than a casting)
Is the sum of the elements that touch the element N _j , cp _j
Denotes the specific heat of the elements N _j.

Calculation of solid fraction (coagulation rate) (ST823)
... ST 808 solid fraction (solidification rate) fs _i is an element enthalpy of the liquid phase in the (casting element) N _i liquidus temperature Tl _i Hl (Tl _i,
Cav _i ), the solid phase enthalpy Hs (Ts _i , Cav _i ) at the solidus temperature Ts _i , and the average enthalpy H _{i of the} element. _{fs i = (Hl (Tl i} , Cav i) -H i) / (Hl (Tl i, Cav i) -Hs (Ts i, Cav i)) ... (3-5) here, fs _i elements N solid fraction of _i (solidification rate), H _i is the enthalpy of the elements N _i, Tl _i, the element N _i liquidus temperature, Ts _i is the solidus temperature of the element N _i, Cav _i elements N _i
Average _{density, Hl (Tl i, Cav i} ) the enthalpy of the liquid phase average density Cav _i at temperature _{Tl i, Hs (Ts i,} Ca of
v _i) denotes the enthalpy of the solid phase of the average density Cav _i at temperature Ts _i.

Calculation of solid / liquid phase / void / eutectic volume fraction,
Calculation of shrinkage speed (ST824) When solidification progresses and the liquid phase changes to a solid phase, voids are generated due to condensation and shrinkage. The volume fraction vos of the solid phase of each element, the volume fraction vol of the liquid phase, the volume fraction por of the void generated in each element
Can be calculated by the following equation. vos = gt × fs / ρ _s (4-1) vol = gt × (1-fs) (4-2) por = 1−vos−vol (4-3) where vos is an element , Vol is the volume ratio of the liquid phase in the element, por is the volume ratio of the void in the element, and gt is the element defined as gt = 1 when the liquid phase ratio of the element is 1. Ρ _s indicates the specific gravity of the solid phase when the specific gravity of the liquid phase is 1. The contraction speed during the time step Δt is obtained by the following equation. ^{fv = (por t -por t-} 1) × U / Δt ... (4-4) where, fv is the volumetric shrinkage rate, porosity in por ^t time t, por ^t-1 time t just before time The porosity in, U indicates the volume of the element.

Calculation of effective moving area ratio (ST825)
... ST 802 expression for the effective movement cross-sectional area ratio fc _ij between the elements N _i and element N _j of the first embodiment (2-1) to (2-3), each element obtained above ST824 solid phase It can be expressed by the following equation using the volume ratio vos. fc _ij = 1−vos _i or 1−vos _j (5-1) fc _ij = 1−max (vos _i , vos _j ) (5-2) fc _ij = 1− (vos _i + vos _j ) / 2… (5-3)

The liquid phase concentration, solid phase concentration, eutectic ratio and average concentration
Calculation (ST826 ) ST806, ST810, ST811 In the present embodiment, the solid phase concentration is constant regardless of the temperature, concentration, position, time, and the like. Liquid phase concentration Cl ^t at time t is calculated and solidification rate fs ^t at time t, solidification rate fs ^t-1 of the previous time (one time step before time), from the liquid phase concentration Cl ^t-1 by the following formula I do. ^{Cl t = Cl t-1 +} (Cl t-1 -Cs) × (fs t -fs t-1) / (1-fs) ... (6-1) , where the liquid phase concentration of Cl ^t time t , Clt ^-1 represents the value of the liquid phase concentration immediately before time t, and Cs represents the solid phase concentration (in the present embodiment, a constant). In the calculation of the above equation (6-1), when the liquid phase concentration exceeds the preset concentration, it can be assumed that the solid phase corresponding to the excess portion crystallizes as a eutectic having a high concentration. In this case, the ratio of the solid phase crystallized as a eutectic (eutectic rate fse) can be calculated by the following equation. ^{fse t = fse t-1 +} (Cl t-1 -Ce) × (1-fs t) / (Ce -Cs) ... (6-2) where KyoAkiraritsu in FSE ^t is the time t, FSE ^{t -1} is the eutectic ratio at the time immediately before time t (one time step before), C
e indicates a eutectic concentration (a constant in the present embodiment). Using the results of the above equations (6-1) and (6-2), the average density Cav of each element can be obtained by the following equation (6-3). Cav = Cs × (fs−fse) + Ce × fse + Cl × (1−fs) (6-3) In the present embodiment, the solid phase concentration Cs and the eutectic concentration Ce are constants, but some relational expression is added. By doing so, it can be treated as a variable. For example, the solid phase concentration Cs
Can be obtained as Cs = ke × Cl (6-4) as an effective partition coefficient ke between the liquid phase and the solid phase.

Calculation of Flow Velocity and Pressure (ST827) The flow calculation performed in this flow solidification analysis is a flow for compensating for solidification shrinkage, and is a flow in which a solid phase and a liquid phase coexist.
There are several examples of flow analysis under these conditions, but in this embodiment, the calculation time is relatively short, and the flow in the actual solid-liquid coexistence region must be accurately represented. Was treated as a Darcy flow. The basic equation of Darcy flow is shown in the following equation (7-3). ▽ P = −Ak · V (7-3) where ▽ P is a pressure gradient (vector), V is a velocity (vector), and Ak is a parameter consisting of transmittance, viscosity, and liquid phase rate. The variables that form Ak can be expressed in terms of solid phase fraction fs in terms of permeability, viscosity, and liquid phase fraction in the flow handled in this analysis.
Handle in the form of (7-4). Ak = fnl (fs) (7-4) Here, fnl represents an arbitrary function, and the following equation (7-5) is employed in the present embodiment as an example of the form of fnl. fnl (fs) = 0.01 (flim + 0.1−fs) / (flim + 0.1)… (7-5) Furthermore, as a relational expression of material preservation of fluid, if the following expression (7-6) is not satisfied No. ▽ · V = fv (7-5) Here, ▽ · V indicates the start of the velocity component, and fv is expressed by the formula (4
-4) This is the shrinkage speed obtained in. The speed and pressure are given by the equation (7
It can be obtained by solving -3) and (7-5) simultaneously. In addition to the present embodiment, there is a method of assuming another flow as a flow equation such as the Navier-Stokes equation. Further, in the present embodiment, the analysis is performed ignoring the gravity, but the analysis can be performed in the same manner even if the analysis is performed in consideration of the gravity and the convection.

The solid-liquid phase transfer coefficient between the elements (parameter S
Calculation of I) (ST828) The flow of the casting during solidification was analyzed in ST827. Essentially, this flow is a liquid phase flow. However, during solidification of an actual casting, not only the liquid phase but also the solid phase may move. In this analysis, a solid-phase liquid phase transfer coefficient (parameter SI) was introduced as a means for estimating the movement of the solid phase by simple means. The parameter SI represents the ratio of the movement amount of the liquid phase and the solid phase in the flow. When SI = 0, only the liquid phase moves, and when SI = 1, the liquid phase and the solid phase When the volume ratio moves at the same ratio and the SI takes an intermediate value between 0 and 1, the ratio between the moving solid phase and the liquid phase is changed according to the SI value. The detailed formula will be described later (ST832). In the present embodiment, SI is a function of the velocity V, the solidification rate fs of the element, the effective moving area ratio fc (corresponding to the solidification rate and the liquid phase rate), the pressure, and the solidification rate gradient. The format is as follows (8-
2) SI _ij = fn2 (V, fs, fc, P, ...) (8-2)

The solute transfer coefficient (parameter D) between elements
Calculation (ST829) ... ST803 In the first embodiment, the transfer coefficient D representing the ease of movement of the solute element is expressed as a function of the solidification rate fs, the time t from the start of casting, and the solidification time tf (formula ( 3)). In the present embodiment, as shown in the following equation (9-4), the solute transfer coefficient D
Is a function of the flow velocity ∨, the effective moving area ratio fc (corresponding to the solidification rate and the liquid phase rate), the pressure P, and the parameter SI shown in ST828. D = fn3 (V, fs, fc, P, SI,...) (9-4) To further explain, the solute transfer coefficient D is a comparison of the flow in a solid phase, which is the flow during solidification. It is a correction coefficient for correcting an error when approximated by a simple flow equation. In other words, in a region where the flow is fast, the phenomenon corresponds to a phenomenon that a solution having a high concentration is concentrated so as to be squeezed out from a portion having a high coagulation rate to a portion having a low coagulation rate. In addition, if it is assumed that the solute does not move in proportion to such a concentration difference and the solute is concentrated only by the movement of the liquid phase and the solid phase by the flow, D = 0 may be set in this calculation.

Calculation of solute transfer amount between elements (ST830)
… ST804

Recalculation of liquid phase concentration, solid phase concentration and average concentration (S
T831) ... ST806, ST810 Since the amount of solute transfer between the elements was calculated in ST830, the element concentrations changed as a result. In this step, the concentration of each phase is recalculated (updated) before calculating the movement of the solid phase and the liquid phase in the next step ST832. In this embodiment, the concentration of the solid phase is constant, and the ST830 does not consider the transfer of solute in the solid phase. The liquid phase concentration is given by the following equation (11-
The average concentration is recalculated (updated) according to the equation (1) and the equation (6-3) of ST826. C _i ^t = C _i ^{t -1} + (Σc j) / U _i / vol _i (11-1) where C l _i ^t is the liquid phase concentration at time t of element N _i , and C l _i ^t-1 is the element Liquid phase concentration immediately before time t of Ni, _i
Is the sum of the elements in contact with the element N _i , and U _i is the element N _i
Volume, vol _i denotes the volume fraction of the liquid phase component N _i.

Calculation of solid / liquid phase transfer between elements (ST832) Calculation of solid / liquid phase transfer between elements is based on the velocity ∨ determined in ST827 and the effective transfer area ratio determined in ST825. fc _ij
And the solid-liquid phase transfer coefficient (parameter S
I). That is, when the parameter SI = 0, only the liquid phase flows, but when SI> 0,
Depending on the value of SI, both the liquid phase and the solid phase move. SS _ij = v _ij × fc _ij × S _ij × Δt × SI _ij × vos _ij / (1-por _ij ) (12-1) SF _ij = v _ij × fc _ij × S _ij × Δt −SS _ij (( _{12-2) SE ij = SS ij ×} (fse ij / fs ij) ... (12-3) wherein, SS _ij is between the minute time (= time step) Delta] t, by the flow from the element N _i to the element N _j the amount of movement to the solid phase (by volume), v _ij elements N _i and element N interface in a direction perpendicular velocity component at the interface between the _j, SF _ij is between the minute time (= time step) Delta] t, the element N _i From the element N _j
The amount of liquid phase to be moved by the flow (volume), the between SE _ij is the short time (= time step) Delta] t, indicates the amount of eutectic moving by the flow from the element N _i in the element N _j (volume). Vos _ij , por _ij , fse _ij , fs _ij are
Each solid phase volume ratio, porosity, KyoAkiraritsu, is a solid fraction, either, since the value on the boundary of the element N _i and element N _j, of the average of the elements N _i and element N _j It is preferable to reduce the error by using a value, or by using a value of the element N _i when v _ij is positive and using a value of the element N _j when v _ij is negative.

The liquid phase concentration, solid phase concentration, average concentration, liquid phase ratio,
Solid phase ratio, eutectic ratio, liquid phase volume ratio, solid phase volume ratio, eutectic volume
Recalculation of the porosity and porosity (ST833) Because the movement of the liquid phase and the solid phase between each element was calculated in ST832, the solid phase volume ratio vos and the liquid phase volume ratio vol of each element were compared with those before ST832. Crystal volume fraction vose, porosity por, solid fraction f
s, liquid phase ratio fl, and eutectic ratio fse change. Also,
The solute also moves in a form accompanying the movement of the liquid phase and solid phase,
The liquid phase concentration Cl and the average concentration Cav also change. The formula for calculating and recalculating (updating) each value is as follows:
3-1) to (13-8). vose = vos × (fse / fs ) + (ΣSE) ... (13-1) vos t = vos t-1 + (ΣSS) / U ... (13-2) vol t = vol t-1 + (ΣSF) / U ... (13-3) por = 1 -vol -vos ... (13-4) Cl t = ((Cl t-1 × vol t-1) + (ΣSF × Cl t-1)) / vol t ... ( ^{13-5) fs t = vos × ρ} s / (vos × ρ s + vol) ... (13-6) fse = (vose / vos) × fs ... (13-7) Cav = Cs × (fs-fse) + Ce × fse + Cl × (1-fs) (13-8) Expression (13-8) is the same as Expression (11-2). Although ignored in the present embodiment, it is considered that the enthalpy changes due to the movement of the solid phase and the liquid phase.
In this case, it is preferable to estimate the amount of movement and recalculate (update) the enthalpy in the same manner as calculated in this step.

Calculation of Packing Density (ST834) In this flow solidification analysis, it is assumed that solidification progresses and solidification shrinkage occurs when the liquid phase changes to a solid phase. this is,
That is, it means that there is a difference in density between the solid phase and the liquid phase. As calculated in ST832 and ST833, the solid phase and the liquid phase moved between the elements, and the amounts of the liquid phase and the solid phase of each element changed, so that the density gt of each element changed. The density gt of each element is given by the following equation (14). _{gt = vos × ρ s + vol} ... (14) where, gt denotes the specific gravity of the elements, the liquid phase volume ratio of the element
When vol = 1, gt = 1 is defined. ρ _s is the specific gravity of the solid phase, and the liquid phase is 1.

Storage of coagulation time (ST835)
… ST807 One of the important information obtained from the results of the flow solidification analysis is
The clotting time. The solidification time is defined as the time required for the solidification rate of a certain element to reach ff. Where ff is
It is a constant that satisfies 0.0 <ff ≦ 1.0, and is usually defined by default before analysis calculation. An element N _i is the analysis end time point, with at most one of the values tf _i as clotting time. Time in current on analysis is t, if the solidification rate of the element N _i is, if satisfying the relation fs _i ^t-1 <ff and ^{_{fs i t ≧ ff ... (15-1}} ), the In the step, data of tf _i = t (15-2) is recorded. Here, tf _i is an element N _i
Shows the coagulation time.

Calculation of liquidus temperature and solidus temperature (ST836)
... ST807 In this embodiment, it is assumed that the liquidus temperature Tl and the solidus temperature Ts of each element are functions of the average concentration of the element. These are calculated by the following equations (16-1) and (16-2). _{Tl i = (Tl (C2)} -Tl (Cl)) × (Cav i -C2) / (C2 -C1) + Tl (C2) ... (16-1) Ts i = (Ts (C2) -Ts (Cl) _{) × (Cav i -C2) /} (C2 -C1) + Ts (C2) ... (16-2) wherein, Tl _i is the liquidus temperature of the element N _i, Ts _i is the solidus temperature of the elements N _i , C1, C2 are arbitrary concentrations (however, C
1 ≠ C2), Cav _i is the average concentration of elements N _i, Tl (Cl) is the liquidus temperature of the case of the average concentration Cl, Tl (C2) is the liquidus temperature of the case of the average concentration C2, Ts (Cl ) Is the solidus temperature when the average concentration is Cl, and the other conditions are the same. Ts (C2) indicates the solidus temperature at the average concentration C2.

Recalculation of solidification rate (ST837) Since the movement of the solid phase and the liquid phase was considered in ST832 and ST833,
There is a contradiction in the relation between the solid fraction fs and the enthalpy H in each element. Although not considered in this embodiment,
In the case where the movement of enthalpy H is considered in ST832 and ST833, the relationship between the solid fraction fs and the enthalpy H is similarly contradictory. Therefore, in the present embodiment, it is assumed that the solid fraction fs is updated in accordance with the enthalpy H. The solid phase fraction fs is
It is obtained from (17-1) to (17-3). · H _i> Hl _i (if enthalpy element N _i H _i is greater than _{Hl i) fs i = 0.0 ...} (17-1) · H i <Hs i ( element N _i enthalpy H _i of less than Hs _{i If) fs i = 1.0 ... (17-2} ) · Hs i <H i < If Hl _i (H _i is the intermediate value of Hl _i and _{Hs i) fs i = (Hl} i -H i) / (Hl _i -Hs _i) ... (17-3) _{However, H i = Hl (Tl i} ) = cp i × Tl i + L ... (17-4) Hs i = Hs (Ts i) = cp i × Ts i ... ( 17-5) here, Hl _i is the element N _i, the concentration of that time
Enthalpy of (Cav _i) and liquidus temperature liquid phase at (Tl _i), Hs _i is the element N _i, the concentration at that time
(Cav _i ) and the enthalpy of the solid phase at the solidus temperature (Ts _i ). Tl _i is the element N _i, liquidus temperature at a concentration Cav _i at that time, Ts _i is the element N _i, a solidus temperature of a concentration Cav _i at that time. fs
_i is the solid phase ratio of the elements N _i (coagulation factor), T _i is the temperature of the element N _i, the cp _i shows the specific heat of element N _i. Equation (17-3)
Indicates the same content as in the above formula (3-5), although the expression form is different.

Calculation of temperature (ST838)
... ST809 The temperature T is calculated from the enthalpy obtained up to ST833, and is given by the following equations (18-1) and (18-2). However, in an element in which the solid phase and the liquid phase coexist, the temperature T is the liquidus temperature Tl, the solidus temperature Ts, and the solidus fraction (solidification rate) fs
Using the solid phase ratio fs updated in ST837, the liquidus temperature Tl and the solidus temperature Ts calculated in ST836, and an arbitrary function fn3, (18-3)
Is required in the form · H _i> Hl _i (enthalpy H _i of the element N _i is higher than _{Hl i) T i = (H} i -L) / cp i ... (18-1) · H i <Hs i ( element N _i enthalpy H if _i is less than Hs _i) T _i = if _{H i / cp i ... (18-2} ) · Hs i <H i <Hl i (H i is the intermediate value of Hl _i and Hs _i) T _i = Ts _i + f n4 (fs _i , T l _i , Ts _i ) (18-3) Here, as an example of an arbitrary function fn4, the following equations (18-4) and (18-
5) is often used. _{T i = Ts i + (1.0} -fs i) n × (Tl i -Ts i) n ... (18-4) fn4 (fs i, Tl i, Ts i) = (1.0 -fs i) n × (Tl _i− Ts _i ) ⁿ … (18-5)

Note that the calculation order of ST821 to ST838 is not limited to the flowchart of FIG. 10 and can be rearranged as long as the relationship of FIG. 11 using the previous result is satisfied. As in the first embodiment, there is no limitation on the element division mode.

[0072]

【Example】

Hereinafter, examples of the present invention will be described more specifically. First Example In this example, the coagulation analyzer 1 described in the first embodiment was used.
As shown in FIG. 4, a casting having two thin portions is subjected to solidification analysis using a solidification analysis method. Analysis model performs elements divided into orthogonal Meshu shape as shown in FIG. 4, defining the parameters of each element N _i in FIG. At this time, the gate of the casting was set on the right side of FIG. 4 (the left side in FIG. 5), and the pressurization was performed only for the first 3 seconds after the injection of the molten metal.

Under these conditions, using the coagulation analyzer 1 shown in FIGS. 1 and 2 and performing coagulation analysis according to the flowcharts shown in FIGS. 3 and 6, the average concentration C shown in FIG.
The distribution map of av was output. Since such an output diagram is obtained, the final segregation position by the present apparatus 2 can be easily determined. FIG. 12 is a first output example of the density distribution. The highest concentration range of 8.4 to 8.8% covers a wide area,
If the final segregation position cannot be specified at this stage, the analysis model and conditions are re-input according to the analysis method shown in the flowchart of FIG. 3 described above, and the interval between the display scales of the concentration is further reduced. Analysis will be repeated.

FIG. 13 shows an output result of the temperature distribution T _i . Under the conditions in this example, the final coagulation (shrinkage cavity) position was not specified from the temperature distribution.

In the present embodiment, the distribution of equicoagulation time was such that the final coagulation (shrinkage cavity) position could be easily specified. FIG. 14 shows the output result of the uniform coagulation time distribution in comparison with the case of the conventional coagulation analysis method. FIG. 15 shows a photograph of a cast product actually manufactured after the above analysis and an explanatory diagram thereof. From the viewpoint that shrinkage cavities are formed at the final coagulation position,
In the isocoagulation time distribution according to the conventional analysis shown in FIG.
As shown in FIG. 15, it can be seen that an actual shrinkage cavity is formed at a position which cannot be predicted from the final solidification position indicated by A0 on the side of the wick, as shown in FIG.

On the other hand, in the isocoagulation time distribution of FIG. 14A obtained by using the method of the present invention, actual shrinkage cavities are also generated near the final coagulation positions A1 and A2 on the side of the gate. And predicts its location. In addition, the position and shape of the segregation position are accurately predicted. From these results, the effectiveness of the present invention was confirmed.

SECOND EXAMPLE In this example, the same analysis as in the first example is performed using the coagulation analyzer and the coagulation analysis method described in the second embodiment. When the analysis model and the casting conditions are the same as those in the first embodiment, and the solidification analysis is performed using the solidification analysis apparatus 1 shown in FIGS. 1 and 8 according to the flowcharts in FIGS. 3 and 10, the average as shown in FIG. 16 is obtained. Concentration C
The distribution map of av was output.

In FIG. 16, the region A3 having the highest concentration of 8.5% or more substantially corresponds to the segregation position in the actual cast product shown in FIG. As a result, the analysis method of the second embodiment in which the flow of the solid phase and the liquid phase due to coagulation shrinkage is considered has improved analysis accuracy compared to the analysis method of the first embodiment in which this flow is not considered. Was confirmed.

Third Example In this example, an example is shown in which the apparatus and the analysis method of the first embodiment are used to reduce the segregation of the scroll scroll of the compressor component. FIG. 17 is a schematic configuration diagram of a scroll spiral. This scroll scroll 10 is made of JI
It is an S8 standard AC8C alloy cast by squeeze casting.

In the casting method in which the gate position shown in FIG. 17 (b) is set to B, the center of the spiral of the casting is shown in FIG.
The segregation shown in the photograph was seen in (a). Therefore, when the solidification analysis device 2 and the solidification analysis method of the first embodiment are used to perform solidification analysis of the gate position B and the gate position C shown in FIG. 17B to predict the segregation position, In the case of C, the segregation was smaller in the central portion. Based on this result, when the scroll spiral body 10 was actually cast using the casting method with the gate position C, and the cross section was observed, as shown in the photograph in FIG. .

[0081]

According to the prior art, there has been provided a method for preparing a plan for avoiding only the results such as shrinkage cavities, poor running of the hot water or hot water. According to the flow solidification analysis apparatus and the flow solidification analysis method according to the present invention described above, when a casting plan is created, in addition to these defects, segregation and shrinkage cavities of solute elements in die casting are analyzed by solidification. Thus, the prediction can be made with high accuracy. This makes it possible to control the segregation position, the amount of segregation, and the shrinkage cavity position, and to create an appropriate casting plan in which these are within a desirable range.

When a computer is used as the analysis means of the present invention, since the present invention uses a simple mass transfer analysis algorithm, the time and load required for the analysis calculation can be kept low. Save money. Furthermore, conventionally, it took time to obtain the optimum casting plan by repeating the casting plan creation and the actual casting prototype, but according to the present invention, the labor and cost of the casting prototype can be significantly reduced. . Therefore, according to the present invention, improvement of reliability and cost reduction of alloy casting in die casting are further advanced.

[Brief description of the drawings]

FIG. 1 is a schematic configuration diagram of a flow coagulation analyzer according to a first embodiment of the present invention.

FIG. 2 is a schematic configuration diagram showing details of a main processor in the fluid coagulation analyzer of FIG. 1;

FIG. 3 is a flowchart showing an overall flow of a flow solidification analysis method according to the first embodiment of the present invention.

FIG. 4 is an element division diagram of an analysis model according to the embodiment of the present invention and first and second examples.

FIGS. 5A and 5B are explanatory diagrams showing parameters defined in the elements of the analysis model. FIG. 5A shows the case of the related art, and FIG. 5B shows the case of the first embodiment.

FIG. 6 is a flowchart showing the details of the coagulation analysis (eighth step ST8 in FIG. 3).

FIG. 7 is a correlation diagram of calculated values showing a flow of each calculation in FIG. 6;

FIG. 8 is a schematic configuration diagram showing details of a main processor in a fluid coagulation analyzer according to a second embodiment of the present invention.

FIG. 9 is an explanatory diagram showing parameters defined in elements of an analysis model in the second embodiment.

FIG. 10 shows a coagulation analysis (eighth in FIG. 3) in the second embodiment.
It is a flowchart which shows the content of step ST8) in more detail.

11 is a correlation diagram of calculated values showing the flow of each calculation in FIG.

FIG. 12 is an average density distribution diagram showing an output example according to the first embodiment of the present invention.

FIG. 13 is a temperature distribution diagram at the end of solidification showing another output example in the first embodiment.

FIGS. 14A and 14B are distribution diagrams of isocoagulation time showing still another output example in the first embodiment. FIG. 14A shows a conventional case, and FIG. 14B shows a case of the present embodiment.

FIG. 15A is a photograph of a cross section of an actual cast product in the example, and FIG. 10B is an explanatory view.

FIG. 16 is an average density distribution diagram showing an output example according to the second embodiment of the present invention.

17A and 17B show a schematic configuration of a scroll scroll according to a third embodiment of the present invention, wherein FIG. 17A is a side view and FIG. 17B is a top view.

18 is a cross-sectional photograph of the center of the scroll scroll shown in FIG. 17, and FIG. 18A shows a case where the gate position is B;
FIG. 6B shows the case where the gate position is C.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Coagulation analyzer, 2 ... Preprocessor (initial setting means), 3 ... Main processor (coagulation analysis means), 4 ... Postprocessor, 5 ... Heat conduction analysis means, 6 ... Parameter determination means, 7 ... Solute movement analysis means , 10 ... scroll spiral, A0 ... conventional expected segregation position, A1, A2, A3 ... expected segregation position of the present invention, B, C ... gate position, cj ... solute transfer amount, C ... concentration, Cl ... liquid phase concentration . Cs ... solid concentration, the average concentration of Cav ... elements, D ... solute transport coefficient, fs ... solid fraction (wt%), i-th element of N _i ... solidification model, P ... melt pressure, ▽ P ... pressure gradient (Vector), qj: calorific value, SI: solid-liquid phase transfer coefficient, parameter SI (ratio of transfer amount), T: temperature, v: flow velocity, V: flow velocity vector, pore: porosity, SS: by flow Movement amount (volume) of solid phase, SF ... Movement amount (volume) of liquid phase due to flow.

Claims (9)

[Claims] 1. A method for analyzing the flow solidification of a molten metal for predicting the position of alloy component segregation or shrinkage cavities in die casting of a molten metal containing a solute element. The molten metal cast into the mold is divided into a plurality of minute elements according to the mold shape, and the molten metal model in each element is formed of a temperature that changes according to a solidification state, at least a solid phase and a liquid phase. Modeling process represented by variables indicating the phase state, solute element concentration in the solid phase, and solute element concentration in the liquid phase; and analyzing the heat conduction and solute transfer between each microelement for each elapsed time for the analysis model Then, based on the analysis results of the heat conduction and the solute transfer, the temperature, the variable indicating the phase state, at least one of the solute element concentration of the liquid phase is updated every time, Flow coagulation analyzing method of molten metal having a flow solidification analyzing step of force, the. 2. In the modeling step, as a variable representing the phase state, a solid phase ratio indicating a ratio of a solid phase occupying in each element, and a void generated in each element due to solidification shrinkage occupies each element. The porosity indicating the ratio represents the molten metal model, In the flow solidification analysis step, the inter-element flow of the solid phase and the liquid phase that compensates for voids generated in each element due to solidification shrinkage is analyzed, and the solid phase and the liquid are analyzed. Based on the analysis results of the inter-phase flow of the phase, the heat conduction and the solute transfer, the solid fraction,
The flow solidification analysis method for a molten metal according to claim 1, wherein at least one of the porosity, the temperature, and the solute element concentration in the liquid phase is updated and output for each elapsed time. 3. When performing the analysis of solute transfer, the solute transfer coefficient representing the ease of solute transfer is made larger when pressure is applied to the solidifying metal melt than when no pressure is applied. 3. The method according to claim 1, wherein the solute transfer analysis is performed after the setting. 4. The pressure applied to the molten metal during solidification, the speed of movement between the elements, and the solid fraction are calculated as analysis results of the inter-element flow, and the magnitude and direction of the calculated pressure are calculated. 3. The molten metal according to claim 2, wherein the solute transfer analysis is performed after changing the solute transfer coefficient according to the magnitude and direction of the velocity, the magnitude of the solid fraction, or the magnitude and direction of the solid fraction gradient. Flow solidification analysis method. 5. The pressure applied to the molten metal during solidification, the speed of movement between the elements, and the solid fraction are calculated as the analysis results of the inter-element flow, and the magnitude and direction of the calculated pressure are calculated. According to the magnitude and direction of the velocity, the magnitude of the solid fraction, or the magnitude and orientation of the solid fraction gradient, the ratio of the solid phase and the liquid phase moving between the elements is changed. After changing the solute transfer coefficient,
3. The method according to claim 2, wherein the analysis of the solute movement is performed. 6. A flow solidification analyzer for molten metal for predicting alloy component segregation or shrinkage cavity position in die casting of molten metal containing a solute element, the analytical model of flow solidification of the molten metal. The metal melt cast into the mold is divided into a plurality of fine elements according to the shape of the mold, and each element is divided into a temperature, a variable indicating at least a phase state consisting of a solid phase and a liquid phase, a solute element in the solid phase. Modeling means represented by a time-varying parameter consisting of a concentration and a solute element concentration in a liquid phase, and element parameters relating to the position and size of each element according to the type, and the time-varying parameter are input from the modeling means. , Based on both parameters entered,
Analysis means for analyzing heat conduction and solute movement for each elapsed time between each element, updating and outputting the time-varying parameter based on the analysis result of the heat conduction and solute movement, and Analysis device. 7. The modeling means includes, as variables representing the phase state, a solid phase ratio indicating a ratio of a solid phase occupying each element, and a void generated in each element due to solidification shrinkage in each element. The porosity indicates a ratio, and each element is expressed. The analysis means analyzes the inter-element flow of the solid phase and the liquid phase that compensates for the void generated in each element due to solidification shrinkage, and calculates the inter-element flow and the heat. The flow solidification analysis apparatus for a molten metal according to claim 6, wherein the time-varying parameter including the porosity and the solid phase rate is updated and output based on the analysis result of the conduction and the solute transfer. 8. A method for predicting the position of alloy component segregation or shrinkage cavities in die casting of a molten metal containing a solute element, wherein the molten metal cast into a mold is used as an analytical model of the flow solidification of the molten metal. Is divided into a plurality of minute elements according to the mold shape, and the molten metal model in each element is changed at a temperature that changes according to the solidification state, at least a variable indicating a phase state consisting of a solid phase and a liquid phase, The solute element concentration in the liquid phase and the solute element concentration in the liquid phase are modeled. Based on the analysis model, the heat conduction and solute transfer between each of the microelements are analyzed for each elapsed time. A program for updating and outputting at least one of the temperature, the variable indicating the phase state, and the solute element concentration in the liquid phase based on the analysis result every time has been stored. Flow coagulation analysis recording medium of the metal melt. 9. In the modeling, as a variable representing the phase state, a solid phase ratio indicating a ratio of a solid phase in each element and a ratio of a void generated in each element due to solidification shrinkage in each element. Representing the molten metal model with a porosity indicating, In the flow solidification analysis, analyze the inter-element flow of the solid and liquid phases to compensate for the voids generated in each element due to solidification shrinkage,
This solid-phase and liquid-phase inter-element flow, based on the analysis results of the heat conduction and the solute transfer, the solid phase ratio, the porosity, the temperature, at least one of the solute element concentration of the liquid phase, 9. An output which is updated and output for each elapsed time.
3. A recording medium for flow solidification analysis of a molten metal according to item 1.