JP2010110792A - Solidification analysis method for alloy molten metal and solidification analysis program thereof - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a solidification analysis method for an alloy molten metal in consideration of an supercooled state. <P>SOLUTION: The solidification analysis method for the alloy molten metal includes a solidification analysis process comprising: a solidification property defining step where supercooling solidification properties showing the correlation between the solid phase ratio or eutectic solidification temperature and the cooling velocity of an alloy molten metal are defined; and a solidification analysis step where, based on the supercooling solidification properties, a solidification process through which the alloy molten metal is solidified in a packed element as a cavity element packed with the alloy molten metal is calculated with the lapse of time. By performing simulation in consideration of such supercooled state, solidification analysis with higher precision can be relatively easily performed on various alloy molten metals. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a solidification analysis method for molten alloy that can be used for die casting simulation and the like, and a solidification analysis program thereof.

  When mass producing a member made of an aluminum (Al) alloy, a magnesium (Mg) alloy, or the like, die casting (die casting) that is excellent in dimensional stability and provides a clean casting surface is frequently used. In this die-casting, a large pressure of about 20 to 80 MPa is usually applied to pour molten metal into a mold cavity and rapidly cooled to produce a casting.

  However, even in die casting, the solidification state of the molten metal in each part of the cavity differs depending on the route from the molten metal supply site, the shape of the cavity, and the like, and the occurrence of shrinkage defects due to solidification shrinkage can be a problem. Conventionally, in order to eliminate this defect, optimum conditions were determined by repeating trial and error such as changing the cooling conditions of the mold.

  Such a method is naturally costly and has low development efficiency. Therefore, without trial and error using the actual product, it is possible to predict the flow and solidification of the molten metal during die casting in advance by computer simulation, and to efficiently search for appropriate die casting conditions. is there.

  However, conventional simulations often use an equilibrium solidification model or a local equilibrium solidification model that considers solute partitioning and segregation assuming a local equilibrium between a solid and a liquid. In such a (quasi-) static model, the supercooling solidification phenomenon occurring during actual casting is not taken into consideration, and the accuracy of solidification analysis by simulation is not necessarily high.

Then, the dynamic model which enabled dynamic handling is considered, for example, the following patent document 1 or nonpatent literature 1 is mentioned. These documents include a description of a solidification analysis method based on a nucleation / solidification growth model using a cellular automaton method. Here, the nucleation amount of the nucleation model and the crystal growth rate of the solidification growth model are treated as a function of the degree of supercooling, and attention is paid to the difference between the solidification latent heat release amount calculated from the crystal growth rate and the heat transfer amount to the surroundings. The subcooling solidification phenomenon is taken into consideration.
JP 2003-33864 A JP-A-5-96343 “A Three-Dimensional Cellular Automation-Finite Element Model for the Predication of Solidification Grain Structures” (Metaradical, And, Materials, Transaction A, Volume 30 December (1999), 3153]

  However, the amount of nucleation when solids nucleate from the molten metal is not a solidification characteristic value that is accurately determined by experiment. For this reason, in the analysis method using the cellular automaton method described above, parameters relating to the amount of nucleation are empirically given, and as a result, the degree of supercooling during supercooling solidification cannot be accurately taken into the simulation. difficult.

  In addition, in the above-mentioned Patent Document 2, although it is not a die casting simulation, there is a description relating to a casting simulation using cast iron. In this simulation, the supercooling solidification phenomenon is taken into account using (i) the cooling rate dependence of the number of graphite grains in the nucleation model and (ii) the increase rate of the graphite radius in the crystal growth model. In this case, since the number of graphite grains is a solidification characteristic value that is experimentally obtained with good reproducibility, it is possible to perform solidification analysis with high accuracy in consideration of supercooling solidification. However, this object is limited to castings such as spheroidal graphite cast iron capable of measuring the number of graphite grains or CV cast iron having a high spheroidization rate, and is not applicable to die casting of Al alloys and Mg alloys that are frequently used industrially.

  The present invention has been made in view of such circumstances. That is, the present invention aims to provide a solidification analysis method and a solidification analysis program that can be widely applied to die casting including die casting and can accurately analyze the supercooling solidification phenomenon of molten alloy during casting on a computer. .

  As a result of extensive research and trial and error, the present inventor has newly found that the eutectic solidification temperature of the molten alloy has a correlation with the cooling rate during overcooling (during continuous cooling). . By using a supercooling solidification model that incorporates the cooling rate dependence of the eutectic solidification temperature into the solid phase rate, etc., the supercooling solidification phenomenon of the molten alloy during casting was successfully simulated on a computer. . And by developing this result, the present inventor has completed various inventions described below.

<Solidification analysis method of molten alloy>
(1) That is, the solidification analysis method for molten alloy according to the present invention is a model for setting a mold model in which a mold constituting a cavity filled with a molten alloy that is a molten metal containing an alloy element is modeled on a coordinate system. A setting step, and a filling analysis step for sequentially calculating a filling process in which the molten alloy is filled into the cavity in the set mold model,
In a solidification analysis method for a molten alloy comprising a solidification analysis step for sequentially calculating a solidification process in which the filled molten alloy solidifies,
The model setting step includes a model formation step of positioning and forming the mold model on a coordinate system, an element creation step of creating a large number of minute elements obtained by finely dividing a region in the formed mold model, An element defining step of defining a microelement corresponding to a cavity region in the mold model as a cavity element among the created microelements and defining a microelement corresponding to the mold region in the mold model as a mold element. Prepared,
The solidification analysis step shows a correlation between a solid phase ratio that is a solidification ratio of the molten alloy or a eutectic solidification temperature that is a temperature at which a eutectic starts to crystallize from the molten alloy, and a temperature and a cooling rate of the molten alloy. A solidification characteristic defining step for defining a supercooling solidification characteristic, and a solidification process in which the molten alloy solidifies in a filling element that is a cavity element filled with the molten alloy is calculated over time based on the supercooling solidification characteristic. A coagulation analysis step.

(2) In the solidification analysis method for a molten alloy according to the present invention, a subcooling solidification characteristic indicating a correlation between a solid phase rate or a eutectic solidification temperature and a cooling rate is defined in the solidification characteristic definition step of the solidification analysis step. The next solidification analysis step is performed based on the cold solidification characteristics. As a result, compared to the conventional solidification analysis performed assuming an equilibrium state, in the present invention, the solidification analysis reflecting the undercooling solidification phenomenon is performed, and more accurate than the actual casting is matched. High coagulation analysis results can be obtained.
In particular, in the present invention, since the undercooled solidification phenomenon is taken into account using characteristic values that can be experimentally verified, the conventional solidification analysis method can be used without much change, and high-speed and high-precision solidification analysis can be performed. This is possible relatively easily.

In the case of the present invention, for example, the solid phase ratio at the time of supercooling solidification is calculated not only as a function of only the temperature assuming an equilibrium state but also taking into account the cooling rate. By doing so, it is possible to easily reflect the supercooling solidification phenomenon in the solid phase rate generally used for solidification analysis, and it is efficient while using conventional casting analysis software etc. Highly accurate analysis is possible. And as long as the analysis method of the present invention is adopted, there is basically no limitation due to the type of molten alloy.
Furthermore, by applying the present invention, it becomes possible to predict casting defects and the like that occur in the case of supercooling and solidification relatively easily with high accuracy. Further, a suitable mold shape, casting conditions, injection conditions, etc. can be determined efficiently, leading to a reduction in the development cost of the molded product.

(3) The supercooling solidification characteristic of the present invention is sufficient if a factor relating to the cooling rate is incorporated or reflected in the mathematical expression or database used when calculating the solid phase ratio. Although the method is not limited, for example, when specifying or defining the cooling rate dependency of the solid phase ratio, it is effective to use the cooling rate dependency of the eutectic solidification temperature of the molten alloy in a supercooled state. . Specifically, the correlation between the eutectic solidification temperature in the supercooled state and the cooling rate is shown in the equilibrium solidification characteristic that shows the correlation between the temperature of the molten alloy in the equilibrium state and the solid phase rate that is the solidification rate. Taking into account the cooling rate dependence of the eutectic solidification temperature, the supercooling solidification characteristic can be calculated.

By the way, the “cooling rate” in the present invention is a change with time of the temperature of the molten alloy, but particularly pays attention to the cooling rate immediately above the liquidus temperature, and the cooling rate R = T _{N + 1} −T _N (T _N : temperature obtained by calculation step N).
In this specification, Al alloy molten metal and Mg alloy molten metal are exemplified as representative examples of molten alloy, and die casting is often taken up as a representative example of casting. However, the concept of the present invention itself is not limited to a specific molten alloy or a specific casting method. In addition, it is natural that the specific aspect of the supercooling and solidification characteristics may vary depending on the type of the molten alloy and the casting method.

<Other forms of the present invention>
The present invention is not limited to the above-described “method” invention, but can be grasped as a “product” invention. That is, the present invention may be a solid alloy analysis program for a molten alloy, which is characterized by executing the above-described solidification analysis method for a molten alloy by causing a computer to function.

  If the program is not grasped as “thing”, it can be grasped as a computer-readable recording medium on which the program is recorded. Furthermore, it can be grasped as a solidification analysis device for molten alloy that executes the program. In these cases, the “process” in the present invention may be read as “means”. That is, the model setting process may be replaced with the model setting means, the filling analysis process of the present invention may be replaced with the filling analysis means, and the solidification analysis process may be replaced with the solidification analysis means.

  The present invention will be described in more detail with reference to embodiments of the invention. For convenience, the present specification mainly describes the “solidification analysis method of molten alloy” of the present invention, but the contents described in this specification are not only the solidification analysis method but also a program ( It should be noted that the present invention can be applied as appropriate to a molten alloy solidification analysis program). Also, it should be noted that which embodiment is the best depends on the target, required performance, and the like.

  As shown in FIG. 1, the solidification analysis method of the present invention comprises a model setting step, a filling analysis step, and a solidification analysis step. Hereinafter, each of these steps will be described sequentially. Each process and each step described below can be executed by means set as logic on a computer.

(1) Model setting process The model setting process is a process of setting a mold model in which a mold constituting a cavity filled with molten alloy is modeled on a coordinate system. The model setting process includes, for example, a model formation step, an element creation step, an element definition step, and an inflow position setting step as shown in FIG.

(A) Model formation step The model formation step is a step of forming a mold model by positioning the shape of the mold on the coordinate system. When the mold is composed of a plurality of mold members, the mold model does not require that the shape of each mold member be individually positioned on the coordinate system, and the shape of the entire mold is on the coordinate system. If it is positioned in, it is enough.

  Positioning of the shape (particularly the outer shape) of the mold or mold member on the coordinate system can be performed by converting the shape into numerical data. If the shape of the mold already exists as CAD data or the like, it is efficient to use it. Of course, the acquisition of numerical data is not limited to CAD data, but can also be obtained using CAE, a coagulation analysis simulation device, or the like. Furthermore, it is also possible to convert the shape of an actual mold or die-cast product prototyped using a three-dimensional scanner or the like into numerical data, and form a mold model from the numerical data.

  Incidentally, the coordinate system to be used is generally a Cartesian coordinate system, but is not limited thereto, and it is preferable to select an appropriate coordinate system according to the shape of the mold and the analysis method such as a cylindrical coordinate system and a spherical coordinate system.

(B) Element creation step The element creation step is a step of creating a large number of minute elements obtained by dividing the region in the mold model formed in the model formation step. That is, it is a step of subdividing the type model positioned on the coordinate system into microelements for analysis. By this step, the space on the coordinate system partitioned by the mold model is divided into a large number of microelements made of a polyhedron. The number of divisions or the division width may be appropriately set in consideration of analysis accuracy, calculation time, and the like.

  The divided shape of the elements is arbitrary, and may be an orthogonal hexahedron as employed in the finite difference method, or may be a polyhedron corresponding to the mold shape as in the finite element method. However, when the finite difference method is used, there is an advantage that the division into small elements is easy and the analysis becomes mathematically simple. Further, the sizes of the microelements do not have to be the same, and it is possible to improve the analysis accuracy by setting the microelements finely locally. For example, fine elements may be set finely in a portion where the molten metal flow of the molten alloy is poor or a portion where gas defects are likely to occur during casting.

  It is not always necessary to divide the microelements over the entire region (space) in the mold model, but it is necessary to form a range necessary for the filling analysis step or the solidification analysis step, that is, a cavity region and its boundary. It is also possible to do it only in the range.

(C) Element definition step The element definition step defines at least a microelement corresponding to the cavity region in the mold model among the many microelements created in the element creation step as a cavity element and also molds in the mold model This is a step of defining a microelement corresponding to a region as a mold element. In this step, for example, a cavity element that is not filled with molten alloy is defined as a void element, a cavity element that is filled with molten alloy is defined as a filled element, or the interface between the cavity element and the mold element is a surface element. Or is defined. In short, the element definition step is a step of defining attributes of each microelement for the filling analysis process or the solidification analysis process.

  Here, in the case of mold casting, a coolant (cooling water or the like) may be brought into contact with the outer wall surface of the mold to be rapidly solidified. In particular, in the case of die casting, a series of casting processes must be completed within a short period of time to efficiently mass-produce castings, so that the mold is often forcedly cooled continuously. In such a case, a passage through which the refrigerant passes may be defined as a cooling path element or the like separately from the mold element. In addition, even if the cooling path is not defined as a special element, a specific type element that contacts the cooling path is selected, and attributes such as temperature are separately defined for the selected selected type element. Also good. In any case, it is only necessary to make a setting close to the actual die casting conditions so as to achieve a highly accurate die casting simulation.

  This element definition step is a step performed after the above-described element creation step, but it is not necessary to perform the element definition step after all the minute elements have been created in the element creation step. That is, every time one or more microelements are created in the element creation step, an element definition step for defining the attribute may be performed, and this operation may be repeated.

  The “mold region” in the present specification is a region where the mold itself is formed, and is a portion where molten alloy is not injected. The “cavity region” is a portion where a molten alloy is injected and a molded product such as a casting is finally formed. Further, the interface between the “mold region” and the “cavity region” may be used as the boundary region. Further, a part of the “mold region” may be the cooling path region described above.

  A method for defining each microelement as a cavity element or a mold element is not particularly limited. An example is shown in FIGS. In the following, for convenience, the mold model and the minute elements will be described two-dimensionally, but the same is true in the case of three-dimensional.

  FIG. 3 shows a case where orthogonal coordinates are employed and the microelement 1 is a square (three-dimensionally a polyhedral shape such as a rectangular parallelepiped or a cube). The wavy line on the coordinates is the boundary of the cavity. When the center of gravity 2 of each microelement 1 exists in the mold area (shaded portion), the microelement 1 is defined as a mold element, and when it exists in the cavity area, the microelement is defined as a cavity element.

  FIG. 4 shows a state where each microelement 1 is defined as a mold element or a cavity element. A case where the center of gravity 2 exists in the mold region is represented by a white circle ◯, and a case where the center of gravity 2 exists in the cavity region is represented by ●. In addition, it is good to prescribe | regulate that the microelement 1 which does not correspond to any of a type | mold area | region and a cavity area | region does not become a calculation load.

(D) Inflow position setting step The inflow position setting step is a step of setting the pressurized inflow position of the molten alloy to a selected cavity element selected from the cavity elements near the plunger that presses the molten alloy. Usually, the pressure inflow position is defined by a point in the cavity element near the die-matching surface on the front surface of the plunger. The molten alloy is blown out at the point where the pressure inflow position is set. The number of the selected cavity elements may be one, but usually a plurality of the selected cavity elements are provided according to the plunger shape. A weighting factor may be given to a plurality of selected cavity elements according to the actual pressurization state of the molten alloy. The inflow position may be set so as to move together with the plunger that pressurizes the molten alloy.

(2) Filling analysis step The filling analysis step is a step of sequentially calculating the filling process in which the molten alloy is filled into the cavity in the set mold model. As a result, the physical behavior of the molten alloy injected into the cavity is analyzed on a minute element basis for each minute time.

  A specific calculation method is not particularly limited, and a known or commonly used method can be used. For example, VOF (Volume of Fluid), SOLA, FAN, or an improved calculation method thereof can be used. As basic equations used in these analyses, as shown in FIG. 5, (1-1) continuity equation, (1-2) Navier-Stokes equation, (1-3) VOF (interface There is a formula of (tracking). This filling analysis step includes, for example, a flow velocity / pressure calculation step, a molten alloy moving step, and an element flag changing step as shown in FIG.

(A) Flow velocity / pressure calculation step In the flow velocity / pressure calculation step, the flow velocity is calculated from the Navia-Stokes equation and the continuous equation for the filling element and the surface element. The “pressure” here is the pressure of the molten alloy.

(B) Molten Alloy Movement Step In the molten alloy movement step, the amount of fluid that moves in a minute time is calculated from the VOF equation. Thereby, the filling degree of each cavity element is expressed by a filling rate (fluid rate). For example, when the filling rate is 0 or less, it is a void element, and when the filling rate> 0, it is a filling element. As described above, in this specification, a minute element (a cavity element having a filling rate larger than 0 and equal to or smaller than 1) filled with a molten alloy is referred to as a “filling element”. Conversely, a minute element with a filling rate = 0 is referred to as a “gap element”.

(C) Element Flag Change Step In the element flag change step, for example, a void pressure (atmospheric pressure in the cavity) is applied to the surface element as a boundary condition.
These steps are repeated until the filling of the molten alloy is completed. The completion of the filling is determined by examining the type of the cavity element and determining whether 90% or more of the cavity elements have become the filling elements. Alternatively, it may be determined when the filling time calculated in advance from the initial molten metal amount and the cavity volume is exceeded. At this time, when there is an unfilled element, the temperature of the unfilled element may be sequentially applied to the temperature of the adjacent element.

(3) Solidification analysis step The solidification analysis step is a step of sequentially calculating the solidification process in which the filled alloy melt solidifies. This solidification analysis process includes, for example, a solidification characteristic definition step and a solidification analysis step as shown in FIG. In this solidification analysis process, each step is sequentially advanced every minute reference time set in advance, and the solidification behavior of the molten alloy is analyzed for each step. In this way, solidification analysis at an arbitrarily set time becomes possible.

(A) Solidification characteristic definition step The solidification characteristic definition step is a eutectic which is a solid phase ratio, which is a solidification ratio of the molten alloy, or a temperature at which the eutectic starts to crystallize from the molten alloy, depending on the type of the molten alloy. This is a step of defining supercooling solidification characteristics indicating a correlation between the solidification temperature and the cooling rate of the molten alloy.
In this supercooling solidification characteristic, for example, the solid phase ratio may be given as a function of temperature and cooling rate, or each variable may be given as a database of numerical groups corresponding to each variable. Below, the case where a solid-phase rate can be expressed as a function of temperature and a cooling rate (Formula (2-1) of FIG. 8) as a supercooling solidification characteristic is demonstrated.

(i) Modeling of cooling rate dependency of eutectic solidification temperature First, the present inventor used a general ADC12 alloy (JIS) as an Al alloy for die casting, during continuous cooling during which a supercooled state may occur. The cooling rate dependence of eutectic solidification temperature was investigated. As a result, a correlation between the eutectic solidification temperature and the cooling rate as shown in FIG. 12 was obtained. The chemical composition of the ADC12 alloy and the derivation process of FIG. 12 will be described later.
From FIG. 12, the eutectic solidification temperature in the range where the cooling rate is small substantially coincides with 568.4 ° C. which is the eutectic solidification temperature in the equilibrium state of the ADC12 alloy. However, it was found that the eutectic solidification temperature in the range where the cooling rate is large decreases with an increase in the cooling rate, and greatly deviates from the eutectic solidification temperature in the equilibrium state. In addition, when the cooling rate is displayed logarithmically, the eutectic solidification temperature and the cooling rate are in a relationship displayed on a substantially straight line. From this, using the coefficients a and b, the eutectic solidification temperature T _E ^ne during continuous cooling is expressed as follows using the cooling rate R.
^{_{T E ne = aR b (3-1}} )

  Here, in order to determine the above-described coefficients a and b, it is necessary to consider a measurement error. As a result of intensive studies by the inventor, as shown in FIG. 12, in the case of the straight line A having the lowest eutectic solidification temperature during continuous cooling, a was about 600 and b was about −0.0178. On the contrary, in the case of the straight line C having the highest eutectic solidification temperature during continuous cooling, a was about 623 and b was about -0.0223. When performing solidification analysis in consideration of undercooling solidification as in the present invention, numerical values of the coefficients a and b are selected within these ranges and the equation (3-1) may be determined. Specifically, for example, coefficients a = 589.7 and b = −0.01046 (corresponding to the broken line B in FIG. 12) obtained by approximating experimental values by the least square method may be used.

(ii) Modeling of undercooling solidification characteristics incorporating cooling rate dependence Next, the present inventor also incorporated cooling rate as a function of solid fraction and temperature using the above equation (3-1). In order to express the cooling rate dependence of the solid phase rate, an attempt was made to model the supercooling solidification characteristics. This method will be described with reference to FIGS.
9 and 10 schematically show that the solid phase ratio in the above-described ADC12 alloy depends on the temperature and the cooling rate.

The solid line (i) in the figure indicates the solid phase ratio in the equilibrium state. In this case, since the solid phase ratio is a physical property value of the ADC12 alloy, it is a function of only the temperature without depending on the cooling rate. Accordingly, the solid fraction in the equilibrium state of a solid line _(i) (f s) by using the temperature (T) of the molten alloy, is expressed as follows.
f _s = f _s (T) (3-2)

On the other hand, the solid line (ii) in the figure indicates the solid phase ratio in the supercooled state. The solid phase ratio in this case is a function depending on not only the temperature but also the cooling rate, as can be seen from FIG. Accordingly, the solid fraction in the equilibrium state of a solid line _(ii) (f s) by using the temperature (T) and the cooling rate of the molten alloy (R) of the molten alloy, is expressed as follows.
f _s ^ne = f _s ^ne (R, T) (3-3)

Here, as shown in FIGS. 9 and 10, when the solid phase ratio is f _s0 , _assuming that the temperature in the equilibrium state is T ₀ and the temperature in the supercooled state is T ₀ ^ne , the equations (3-2) and From (3-3), it becomes as follows.
^{_{f s0 = f s ne (R}} , T 0 ne) = f s (T 0) (3-4)

  In order to perform the solidification analysis in the supercooled state with high accuracy, it is necessary to determine the formula (3-3) that indicates the solid phase ratio in the supercooled state as accurately as possible. However, there is usually not much experimental data that can directly specify the formula (3-3) itself. For this reason, it is difficult to directly determine the equation (3-3) that indicates the solid phase ratio in the supercooled state.

On the other hand, regarding the solid phase ratio in the equilibrium state, there are abundant past thermal analysis data and thermodynamic data. By using these, it becomes possible to specify the expression (3-2) with high accuracy. In addition, the present inventor has obtained an index (Equation (3-1)) indicating a relatively high cooling rate dependency with respect to the eutectic solidification temperature.
Therefore, the present inventor considered that the function of the expression (3-3) can be specified with relatively high accuracy by combining the expression (3-1) and the expression (3-2). Specifically, it was considered that Equation (3-3) can be determined by using proportional calculation as shown in FIGS. The reason for approximation by proportional calculation is that in the case of ADC12 alloy, most of the latent heat of solidification is released during eutectic solidification.
Hereinafter, the specific method of Formula (3-3) is demonstrated concretely.

First, the case of T ₀ ^ne > T _E ^ne will be described with reference to FIG. In Figure 9, T _L is the liquidus temperature, T _E is the eutectic solidification temperature at equilibrium.
The temperature difference between the liquidus temperature T _L to each temperature respectively put as follows.
p = T _L −T ₀
q = _T L -T _E
p ^ne = T _L −T ₀ ^{ne
_{q ne = T L -T E ne}} = T L -aR b ( formula (3-1) from)
Here, the proportional relationship between the equilibrium state and the supercooled state is considered as follows.
p: q = p ^ne : q ^ne
Substituting the above formulas and rearranging them gives the following.
_{T 0 = T L - (T} L -T E) (T L -T 0 ne) / (T L -aR b) (3-5)

Here liquidus temperature T _L and eutectic solidification temperature T _E of the equilibrium state is a physical property value, the coefficients a and b can be identified from the experimental values as described above. Therefore, when the temperature T ₀ ^ne during continuous cooling and the cooling rate R are specified, T _{0 of the} equation (3-4) is obtained from the equation (3-5), and f is obtained from the functional equation of the solid phase ratio in the equilibrium state. The solid phase ratio in the supercooled state (R, T ₀ ^ne ) is obtained by _s (T ₀ ) = f _s0 .
Next, also in the case of T ₀ ^ne <T _E ^ne , as is apparent from FIG. 10, r: s = r ^ne : s ^ne , so that the following equation is obtained.
_{T 0 = T E - (T} E -T S) (T E -T 0 ne) / (aR b -T S) (3-6)

Incidentally, _{T S} in FIG. 10 and Formula (3-6) is the solidus temperature. As with this case was also described above, the solidus temperature T _S and the eutectic solidification temperature T _E of the equilibrium state is a physical property value, the coefficients a and b can be identified from the experimental values as described above. Therefore, when the temperature T ₀ ^ne during continuous cooling and the cooling rate R are specified, T _{0 of the} equation (3-4) is obtained from the equation (3-5), and f is obtained from the functional equation of the solid phase ratio in the equilibrium state. _{By s} (T ₀ ) = f _s0 , the solid phase ratio in the supercooled state is obtained.
Is as follows when the last ^{_T 0 ne} _{= T} ^E ne.
T ₀ = T _E (3-7)
At this time, the solid phase ratio in the supercooled state is obtained as f _s0 = f _s (T _E ).

  By modeling the supercooling solidification characteristics as described above, it is possible to proceed with solidification analysis in consideration of supercooling solidification. In the present embodiment, the modeling of the supercooling solidification characteristics using the proportional calculation method is shown, but this modeling is not limited to the proportional calculation method, and other methods can be used if the supercooling state can be skillfully taken in. May be used.

(B) Solidification analysis step The solidification analysis step is a step of calculating with time the solidification process in which the molten alloy in the filling element, which is a cavity element filled with molten alloy, solidifies based on the supercooling solidification characteristics. The solidification analysis step includes, for example, small steps that sequentially repeat the latent heat release amount, temperature, cooling rate, solid phase rate, and the like for the filling element filled with the molten alloy. Thus, the physical behavior of the molten alloy for each minute time is analyzed for each minute cavity element. Specifically, heat transfer (heat conduction, heat transfer) between each filling element or between the outermost surface of the mold and the filling element in contact therewith is analyzed, and the temperature of the molten alloy of each filling element is changed over time. Calculated. At this time, in the present invention, the analysis proceeds based on the supercooling solidification characteristic defined in the solidification characteristic value defining step.

  In the present invention, the basic solidification analysis method itself of the molten alloy is not particularly limited. For example, an energy conservation law (formula (2-2) in FIG. 8) is used as a basic formula for heat transfer analysis. As a numerical solution method of this differential equation, for example, a known or commonly used method such as a forward Euler method, a backward Euler method, a crank-Nicholson method, a Runge-Kutta method, or a method obtained by improving them is used.

As a method for handling solidification, a known or commonly used method such as a temperature recovery method, an equivalent specific heat method, an enthalpy method, or a method obtained by improving them is used. In particular, when the temperature recovery method is used, the basic equation of the equation (2-2) described above is transformed into the equation (2-3a) in FIG. 8, and the solidification is expressed by the equation (2-3b) expressing the temperature recovery method. May be used. By the way, the temperature recovery method is a method of solving the heat transfer basic equation in two stages. That is, first, the basic equation of Formula (2-3a) is solved without considering solidification, and then a solidification latent heat release amount and a temperature recovery amount corresponding thereto are obtained.
The solid phase ratio calculated in this way is expressed by mass% of the solid phase when the entire molten alloy filled in the cavity element is 100 mass%.

The present invention will be described more specifically with reference to examples.
<Cooling rate dependency>
First, the cooling rate dependency of the eutectic solidification temperature required for performing the die casting simulation of the present invention was investigated. Specifically, a die casting experiment and a pouring experiment were performed using an Al alloy for casting (JIS: ADC12), and temperature changes until solidification at the time of continuous cooling were measured. The chemical composition of the Al alloy (ADC12) used was Cu: 2.89%, Si: 11.62%, Mg: 0.21%, Zn: 0.93%, Fe: 0.88%, Mn : 0.34%, Ni: 0.05%, Al: remainder (unit: mass%).

(1) Die Casting Experiment A tool steel (JIS: SKD61) mold having a cavity with a product part (cavity) size of 100 mm × 100 mm × thickness 10 mm was installed in a vertical die casting machine. A highly responsive alumel chromel thermocouple having a tip diameter of 0.1 mm and a response time of 0.05 s or less was attached to the cavity of this mold.
A molten Al alloy obtained by melting the Al alloy in an electric resistance furnace was poured into an injection sleeve connected to the cavity. When the molten metal temperature reached 610 ° C., 640 ° C. or 670 ° C., the Al alloy molten metal was filled in the cavity. The casting pressure (plunger pressure) at this time was 50 MPa.

The pouring temperature when injecting the Al alloy melt was 670 ° C., and the temperature change until the Al alloy melt was completely solidified was recorded. This is shown in FIG.
First, when the plunger displacement shown in FIG. 11 is observed, it can be seen that the change almost disappears in the vicinity of 0.95 s, and the molten metal is filled in the cavity of the mold. At this time, after the temperature of the molten metal once reached the maximum (point A in FIG. 11), the temperature dropped rapidly, and a gentle portion with a very small temperature change appeared (B in FIG. 11). point). This portion is a portion where eutectic solidification is proceeding, and the initial temperature at this time was defined as the eutectic solidification temperature during continuous cooling. This eutectic solidification temperature is 540 ° C., which is lower than the eutectic solidification temperature (568.4 ° C.) of the Al alloy (ADC12) in an equilibrium state. Therefore, in the case of this experiment, it is clear that the eutectic crystallizes in the supercooled solidified state.

(2) Casting pouring experiment The Al alloy (ADC12) melted in an electric resistance furnace was poured into various molds, and the temperature change until solidification was completed was the same as the thermocouple described above (diameter: 0). 0.1 mm). The reason why the various molds were used is to change the cooling rate of the molten Al alloy. The molds used were a copper mold (50 × 150 × 100 mm) and a shell mold (φ40 × 50 mm). The temperature of the Al alloy melt poured into each mold was 650 ° C. for all.

The eutectic solidification temperature was read from the measurement results in each case in the same manner as in the above-described die casting experiment.
When using a copper mold, the cooling rate is about 840 ° C./s, the eutectic solidification temperature is 548.3 ° C., and when using the shell mold, the cooling rate is about 14.9 ° C./s and the eutectic solidification temperature is 564.5 ° C. The low cooling rate was close to the equilibrium eutectic solidification temperature (568.4 ° C.), but the high cooling rate was lower than the equilibrium eutectic solidification temperature.

(3) Dependence of eutectic solidification temperature and cooling rate on cooling rate The eutectic solidification temperature is combined with the eutectic solidification temperature measured in the above-mentioned die casting experiment and pouring experiment and the eutectic solidification temperature described in the literature. The correlation between temperature and cooling rate is shown in FIG. And after calculating | requiring the coefficient a and b of Formula (3-1) mentioned above from this FIG. 12, using the Formula (3-5)-(3-7), the solid-phase rate and temperature of each cooling rate Sought a relationship. The result is shown in FIG.

<< Test 1 >>
<Manufacture of die castings>
(1) Mold A test mold having the shape shown in FIG. 14 was prepared. The shape of the product part (casting part) corresponds to the cavity shape (region) in the present invention. The size of each part is as follows.
Product part: 100x100x wall thickness 2 (mm)
Gate: width 25 x thickness 2 (mm)
Runner: 10x20x50 (mm)
Sleeve: φ60x300 (mm)

(2) Die-casting The actual die-casting was manufactured using a 135-ton die-casting machine using the above mold. At this time, the molten alloy being filled was prevented from entraining air in the cavity. Specifically, the plunger was moved at a low speed (injection speed: 0.01 m / s) for 0.1 s and then switched to a high speed (injection speed: 0.4 m / s) to fill the molten alloy.

  A plunger having a size of φ60 × 300 (mm) was used as the plunger for pressurizing and filling the molten alloy into the mold cavity. The gas in the cavity was discharged from the gas discharge hole, and the pressure in the cavity was reduced to 50 torr (actual measurement value in the cavity). The pouring temperature was about 670 ° C. in a holding furnace. In this way, a flat plate test piece (die casting with a product part thickness of 2 mm) made of an aluminum alloy (ADC12 alloy described above) was obtained.

  During this die casting, the temperature change from the filling of the molten metal into the mold cavity corresponding to the product portion to the completion of solidification was measured with an alumel chromel thermocouple having a diameter of 0.1 mm as described above. . The state of this temperature change is shown in FIG.

<Die-casting simulation>
A die casting simulation according to the solidification analysis method of the molten alloy according to the present invention was performed, and the result was compared with the above measurement result to evaluate the compatibility between them. The details will be described below.
(1) Model setting process Using the CAD data created at the time of designing the mold shown in FIG. 14, a mold model used for die casting simulation was formed (model formation step). Then, the mold model was divided into minute elements (element creation step). The division method was a mesh division with rectangular elements. Furthermore, each element was defined as a cavity element or a mold element (element definition step). A cavity element in the vicinity of the inner wall surface of the plunger was selected, and a pressurized inflow position was set in the selected cavity element (inflow position setting step).

(2) Filling analysis step and solidification analysis step Solidification analysis of the molten alloy into the cavity element (void element) of the above-mentioned mold model follows the steps shown in FIG. 6 described above in consideration of actual casting conditions. I went. Completion of filling was judged when 90% or more of the cavity elements became filling elements, and completion of solidification was judged when the solid phase ratio of the cavity elements became 1. The simulation is completed when the solidification is completed.

By the way, when performing this simulation, the relationship between the solid phase ratio and temperature depending on the cooling rate shown in FIG. 13 (see formula (1)) was defined as the supercooling solidification characteristic (solidification characteristic definition step). In addition, a solidification analysis step was performed based on the energy conservation law (see formula (2-3a)) and the temperature recovery method (see formula (2-3b)).
For comparison, a simulation including a conventional solidification analysis process in which the above-described solidification characteristic definition step is omitted was also performed. As solidification characteristic values required at this time, physical property values in an equilibrium state were used.

<Evaluation>
Regarding the temperature change at the time of die casting, the actual measurement value described above and the analysis result obtained from the above simulation are shown together in FIG.
The measured eutectic solidification temperature was about 540 ° C. The eutectic solidification temperature of the analysis result according to the present invention started from about 542 ° C. and changed so as to overlap with the measured value soon after. From this, it was confirmed that the simulation according to the present invention agrees very well with the actual experimental results.
On the other hand, it was confirmed that the eutectic solidification temperature obtained by the conventional analysis method started from 568.4 ° C. and greatly deviated from the actual experimental results.

<< Test 2 >>
The thickness of the product part of the die cast product described above was changed from 2 mm to 10 mm, and in the same manner as in the case of Test 1, actual die casting and die casting simulation were performed to check the temperature change. These results are shown in FIG.

  By increasing the thickness of the product portion, the cooling rate of the cavity portion (or cavity element) corresponding to the temperature measurement point becomes slow. For this reason, the measured eutectic solidification temperature was about 550 ° C., which was about 10 ° C. higher than that in Test 1. The eutectic solidification temperature of the analysis result obtained from the simulation according to the present invention started from about 544 ° C., which is a little lower than the actual measurement value, but soon moved closer to the actual measurement value. From this, it was confirmed that the simulation according to the present invention can obtain a result that agrees very well with the actual experimental result even when the cooling rate changes due to a change in the cavity shape or the like.

On the other hand, the eutectic solidification temperature obtained by the conventional analysis method started from 568.4 ° C., and remained unchanged from the actual measurement value and did not approach the actual measurement value.
As is clear from the above, it was confirmed that according to the simulation according to the present invention, an analysis result reproducing the actual experimental result with higher accuracy can be obtained.

It is a main flowchart which shows the process sequence of the solidification analysis method of the molten alloy of this invention. It is a subflowchart which detailed the model setting process in the main flowchart. It is a schematic diagram which shows a mode that the type | mold model was divided | segmented into the microelement. It is a schematic diagram which shows a mode that the divided | segmented microelement was defined as a mold element or a cavity element. It is a figure which shows the basic equation used by the filling analysis. It is a subflowchart which explained the filling analysis process in the main flowchart in detail. It is a sub-flowchart which explained in detail the solidification analysis process in the main flow chart. It is a figure which shows the basic equation used by the solidification analysis. It is a schematic diagram which shows the relationship between the solid-phase rate used for modeling of a supercooling solidification characteristic, and temperature. It is a schematic diagram which shows the relationship between the solid-phase rate used for modeling of a supercooling solidification characteristic, and temperature. It is the graph which recorded the measured value which shows the temperature change of a molten alloy. It is a graph which shows the cooling rate dependence of eutectic solidification temperature. It is a graph which shows the correlation (supercooling solidification characteristic) with the solid-phase rate by temperature difference, and temperature. It is a figure which shows the shape of the product model of die-casting, and the type | mold model of die-casting simulation. It is the graph which contrasted the case of the actual measurement, and the case of simulation about the relationship between the temperature of molten alloy when the thickness of a product part is 2 mm, and time. It is the graph which compared the case where it measured, and the case where it simulated about the relationship between the temperature of molten alloy, and time when the thickness of a product part was 10 mm.

Claims (5)

A model setting step for setting a mold model in which a mold constituting a cavity filled with a molten alloy that is a molten metal containing an alloy element is modeled on a coordinate system;
A filling analysis step for sequentially calculating a filling process in which the molten alloy is filled into the cavity in the set mold model;
In a solidification analysis method for a molten alloy comprising a solidification analysis step for sequentially calculating a solidification process in which the filled molten alloy solidifies,
The model setting step includes
A model forming step of positioning and forming the mold model on a coordinate system;
An element creating step for creating a large number of minute elements obtained by finely dividing a region in the formed mold model;
An element defining step of defining a microelement corresponding to a cavity region in the mold model as a cavity element among the created microelements and defining a microelement corresponding to the mold region in the mold model as a mold element; With
The solidification analysis step includes
Define a solidification ratio that is a solidification ratio of the molten alloy or a eutectic solidification temperature that is a temperature at which eutectic starts to crystallize from the molten alloy and a supercooling solidification characteristic that indicates a correlation between a cooling rate of the molten alloy. A solidification characteristic definition step;
A solidification analysis step for calculating over time a solidification process in which the molten alloy solidifies in a filling element that is a cavity element filled with the molten alloy based on the undercooling solidification characteristics;
A solidification analysis method for molten alloy, comprising:   The supercooling solidification characteristic is a correlation between the eutectic solidification temperature in the supercooled state and the cooling rate in the equilibrium solidification characteristic indicating the correlation between the temperature of the molten alloy in the equilibrium state and the solid phase ratio as the solidification rate. The solidification analysis method for molten alloy according to claim 1, wherein the solidification analysis is calculated taking into account the cooling rate dependence of the eutectic solidification temperature.   3. The solidification analysis method for molten alloy according to claim 1, wherein the molten alloy is an molten Al alloy made of an aluminum (Al) alloy or a molten Mg alloy made of a magnesium (Mg) alloy.   The solidification analysis method for molten alloy according to claim 3, wherein the molten Al alloy contains 10 to 13% of silicon (Si) when the whole is 100 mass%.   5. A solidification analysis program for molten alloy according to claim 1, wherein the solidification analysis method for molten alloy is executed by causing a computer to function.

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