JP2651296B2 - Phase transformation analyzer - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a mesh dividing means for dividing a shape of an object into a plurality of meshes, and an analysis for solving a heat conduction equation for each mesh divided by the mesh dividing means and analyzing a phase transformation. And a phase transformation analysis device.

[0002]

2. Description of the Related Art Conventionally, this type of casting solidification analyzing apparatus has a mesh dividing means for dividing the shape of an object into a plurality of meshes, and solves a heat conduction equation for each of the meshes divided by the mesh dividing means. And analysis means for performing a phase transformation analysis.

[0003]

In recent years, it has been desired to provide an apparatus for analyzing a plurality of phase transformations. For example, in the case of cast products, as a container for transporting radioactive waste, in special cases such as the production of thick-walled ductile cast iron of standard products or higher, sufficient strength should be provided in case of an accident during transportation. In order to make the material spherical, it is necessary to ferrite all the bases while making the graphite spheroidal, such as when performing austempering treatment or pearlite treatment or a mixed treatment of these materials according to the purpose, It is necessary to analyze not only the solidification transformation but also the _Ar1 transformation. However, the above-mentioned conventional technique has a drawback that it is difficult to quickly produce a high-quality casting plan because the plurality of analyzes cannot be performed, so that the analysis must be performed based on actual experimental data. Therefore, in order to analyze a plurality of phase transformations, it is conceivable to configure a phase transformation analysis device by providing analysis means for performing a single phase transformation analysis in a plurality of stages. Each time, it is determined whether or not the transformation temperature of the transformation to be analyzed has been reached for all the meshes, and the transformation analysis is performed on the corresponding mesh. Was. Furthermore, the physical property value of the analysis object may change on the way, as occurs in the actual casting process. For example, when a steel ingot is taken out from an ingot case, a substance in contact with the inner wall of the case changes from the steel ingot to air. In such a case, analysis must be performed after a new boundary condition or initial condition is input from that point in time. An object of the present invention is to eliminate the above-mentioned conventional disadvantages.

[0004]

In order to achieve this object, a phase transformation analyzing apparatus according to the present invention is characterized in that the analyzing means comprises: a first analyzing means for solving a heat conduction equation for each mesh; A second analysis unit configured to divide the mesh into a plurality of groups corresponding to transitions of each phase based on a temperature obtained as a result of one analysis unit and perform a predetermined transformation analysis for each group. . It is preferable that a replacement means for changing a substance or a temperature of a specific portion of the mesh during analysis by the analysis means is provided.

[0005]

The first analysis means derives the temperature for each mesh by solving the heat conduction equation for all meshes based on the analysis conditions. The second analysis means first divides each mesh into a plurality of groups set corresponding to the transition of each phase based on the temperature of each mesh set under the initial condition, and registers them. After that, necessary analysis processing and subdivision processing are performed for each group. The analysis processing means, for example, the calculation of the release of latent heat of solidification in the case of solidification analysis, and the subdivision processing means that when the temperature of the mesh for which analysis processing has been completed deviates from the temperature range of the group, the mesh is returned to another group. To register. When it is necessary to change the physical property value of the analysis target during the analysis by the analysis means (for example, when analyzing the temperature change of the case after removing the steel ingot from the ingot case), By replacing the substance or temperature of a specific portion of the mesh with new data by means, the subsequent analysis is continuously performed without interruption.

[0006]

According to the phase transformation analyzer of the present invention, a plurality of phase transformation analyzes can be performed at high speed. As a result, for example, it has become possible to quickly create a high-quality casting plan that also takes into account the _Ar1 transformation. In addition, even if the physical property value of the analysis object may change in the middle by the replacement means, the analysis can be continuously performed, so that the analysis time,
The labor has been greatly improved. For example, if applied to cast products, analysis of continuous casting of molds, analysis of ingot case ingot removal, and analysis of long-time casting of centrifugal rolls in centrifugal casting can be performed. Casting can be produced very efficiently.

[0007]

Embodiments will be described below. As shown in FIG.
The casting solidification analysis apparatus for a casting includes a pre-processor 1 for generating a shape model to be analyzed, an analysis means 2 for executing a heat conduction analysis on the shape model, and a post-processor 3 for outputting an analysis result. It is composed. The pre-processor 1 includes an input device 1A such as a mouse and a keyboard for inputting a shape of a casting mold and a casting to be cast by the mold, a storage unit 1B for storing the input shape as a shape file, A CRT for displaying the shape, a processor functioning as a mesh dividing unit 1C for dividing the input shape into a two-dimensional or three-dimensional orthogonal lattice mesh, and a storage unit 1D for storing the generated mesh as a mesh file. Analytical conditions and meshes, which are constituted by the constituent materials of each mesh (for example, the material of the mold and the composition of the molten metal to be input) input from the input device 1A, initial conditions such as initial temperature, and boundary conditions. An analysis data file is generated from the data and stored in the storage unit 1F. The pre-processor 1 further specifies a region in units of each mesh with respect to the generated mesh, and inputs and specifies replacement data for changing the material or temperature of the specified region from an arbitrary time. There is provided a replacement data generating means 1E for editing and combining replacement data for an area with the analysis data file. The analysis means 2 handles a two-stage phase transformation, as shown by a characteristic curve A shown in FIG. 6, and solves a heat conduction equation by a direct difference method for each mesh of the analysis data file, thereby obtaining an unsteady nonlinear nonlinearity. The first analysis means 2B for performing the heat conduction analysis and the latent heat analysis of the solidification transformation and the _Ar1 transformation in the cooling process during the period from the phase transformation start temperature input as the analysis condition to the end temperature are performed by the temperature recovery method. A second analyzing means 2C to be used and executed; a replacing means 2D for changing a substance or a temperature of a specific portion of the mesh during the execution of the first analyzing means 2B; A means for calculating and deriving an evaluation index indicating the degree of conversion is stored in the storage means 2A as a result file. As an example of the analysis results, a cooling curve as shown in FIG. Incidentally, the phase transformation start temperature and the end temperature are different depending on the content of the Fe-C alloy and other elements contained therein, and values actually obtained in advance from experimental results are set in the analysis data file. is there. As shown in FIG. 2, the first analysis unit 2B sets a difference equation for the cast product divided by the mesh division unit 1C and the minute elements (for example, A and B in the figure) of the mold. The solution will be described in detail below.

The amount of heat Q accumulated in the nodal region (referred to as the above-mentioned minute element) during the minute time Δt is expressed by the following equation (1).

[0009]

(Equation 1)

[0010] amount of heat flowing by heat conduction from the surface S _a in contact without nodal region a and the thermal resistance of the same material is expressed by the number from the Fourier's law 2.

[0011]

(Equation 2)

Here, λ _ia is the average thermal conductivity between nodes _ia (meaning the center of the circumcircle of the microelement), and l _ia is the node i
It is the distance between a.

[0013]

(Equation 3)

[0014] Also, the heat flow Q _inb flowing from the surface S _b when in contact with a mold or the like and heat resistance r _b in terms S _b are expressed by the number 4.

[0015]

(Equation 4)

Here, l _i1 and l _b1 are connected from the nodes i and b to the surface S
_In the distance to _{b ,} l _i1 / λ _i and l _b1 / λ _b indicate thermal resistance due to heat conduction. The heat resistance r _b is the heat transfer coefficient h
You can use the _b, a r _b = 1 / h _b. External temperature T _c, the inflow amount of heat of the heat transfer coefficient h _c is the known boundary surface S _c is the number _{4 l b1 = 0, r b} = 1 / h c, T b = T c, S b
= It may be used as the S _c. Also, the boundary surface S for which the heat flux q _d is known
The heat flow Q _ind from _d is represented by _Equation 5.

[0017]

(Equation 5)

Furthermore, the thermal energy Q _inc entering from the environment of the temperature (T _c +273.15) to the boundary surface S _c of the thermal emissivity epsilon _c is expressed by Equation 6.

[0019]

(Equation 6)

[0020] Here, T _sc is the surface temperature of the surface S _c. If the above inflowing heat amount is equalized to the accumulated amount Q, Equation 7 is obtained.

[0021]

(Equation 7)

When the time step Δt is large and the influence of a region farther than the adjacent node region becomes a problem, a remarkable error occurs. Therefore, the time step Δt has a certain limit, as shown in Expression 8. A value less than or equal to the value must be adopted.

[0023]

(Equation 8)

As shown in FIG. 3, the temperature recovery method is a method of calculating latent heat release, and is handled as follows during solidification transformation. First, a thermal analysis without considering the release of latent heat is performed. Assuming that the amount of temperature decrease is ΔT, the heat transfer amount Q is: Q = ρCpVΔT Next, if ΔT is recovered by releasing latent heat ΔL, Q = ρVΔL ΔL = CpΔT Therefore, the temperature T during the solidification transformation is the solid phase ratio Using fs, T = T (liq) − (T (liq) −T (sol)) fs fs = ΣΔL / L Here, ρ is density, Cp is specific heat, and V is volume. Also, in the A _r1 transformation, the liquidus temperature T (li
q) is the A _r1 transformation onset temperature, and the solidus temperature T (sol) is A
_r1 transformation end temperature, solid fraction fs is _Ar1 transformation rate, latent heat is _Ar1
The same can be performed by using the transformation latent heat. The post processor 3 includes a processor that generates a graph (for example, divided into a plurality of areas according to a temperature range and different display colors for each area) and a document from the data of the result file. And an output device 3B such as a printer for outputting the contents.

The main operation of the casting solidification analyzing apparatus will be described below with reference to the flowchart shown in FIG. From the analysis data file, casting elements are extracted from the entire mesh according to the initial temperature, and the element numbers of the mesh are registered in the corresponding groups in order to divide each casting element into the groups shown in FIG. 5 <# 1>. Transient non-linear heat conduction calculation is performed on all meshes using the direct difference method. At this time, the calculation is set to be performed at appropriate time intervals in order to avoid the divergence of the solution caused by affecting the other mesh by jumping over the influence on the adjacent mesh <# 2>. .
That is, step <# 2> is the first analysis means. If the presence of elements of group 1 is detected and present (at the beginning, almost all casting elements are at or above the liquidus temperature), the temperature of each element is changed to the solidification transformation based on the result of step <# 2>. It is determined whether or not the temperature has decreased, and if the temperature has decreased, the element is transferred to group 2 <# 3>, <# 4>. If the presence of an element of group 2 or 3 (during solidification transformation) is detected and present, solidification latent heat analysis is performed by the above-mentioned temperature recovery method, and step <# 4 is performed based on the result of step <# 2>. > Perform grouping processing in the same manner as <># 5
>, <# 6>. Subsequently, if present by detecting the presence of elements of Groups 4 or 5, performs A _r1 latent analysis for a group 5, and Step <# 4> based on step <# 2> Results Similarly, grouping processing is performed <# 7>, <# 8>, <# 9>, <# 10>. That is, steps <# 3> to <# 10> constitute the second analysis means. As a result, when all meshes reach the freezing point,
Based on the analysis results, an evaluation index indicating the degree of spheroidization of the contained graphite is calculated and derived <# 11>, <# 12>. In detail, the evaluation index is [Evaluation index] = [Chemical component coefficient] × [Coagulation time coefficient] ×
It is represented by (concentration factor), the greater the "evaluation index" is greater than a predetermined value determined based on past experimental data, the higher the probability of occurrence of flaky graphite such as chunky graphite, The smaller the smaller, the lower the probability of generation of flaky graphite such as chunky graphite, and therefore, the higher the spheroidization rate of graphite is evaluated. That is, step <# 9> constitutes the evaluation means 2E. As a result of the evaluation, if the “evaluation index” is larger than the predetermined value, an element that may increase the cooling rate or increase the content of the element that promotes the spheroidization of graphite or hinders the spheroidization of graphite Create a plan to lower the content rate of and evaluate it again. “Chemical component coefficient” refers to other elements contained in the Fe—C alloy, for example, Ti, Pb, Al, B
It is expressed by adding each product of the composition (% by weight) of i, Ce, etc., and the composition coefficient obtained from the accumulated past experimental data, and is set with particular emphasis on the contribution of Ce. It is. The “coagulation time coefficient” is a coefficient determined by whether the time required for coagulation obtained as a result of the analysis is longer or shorter than the set time obtained from the past experimental data. Is a value smaller than 1 in a function using as a variable, and "a value larger than 1 in a function using a coagulation time as a variable" if it is longer than a set time. That is, attention is paid to the tendency that the longer the solidification time is, the lower the spheroidization rate of graphite is. The "concentration factor" is the product of the ratio of the volume of the solidified region and the volume of the unsolidified region of the casting at regular intervals until the whole obtained from the analysis is solidified, that is, the enrichment is a variable It focuses on the tendency that the spheroidization of graphite decreases as the concentration increases. In this way, the solidification time, temperature distribution history, cooling curve, etc. of each part of the cast product are obtained based on a plurality of sets of initial conditions and boundary conditions, and the spheroidization of graphite and shrinkage cavity prediction are performed. For a radioactive material shielding container made of ductile, a casting method will be examined to secure desired specifications while securing a sufficient cooling rate.
As shown in FIG. 4, before the process of the step <# 2>, it is further determined from the plurality of replacement data set by the replacement means 1F in the analysis data file whether or not it is time to replace. <# 01>, if it is time to replace, data to replace the corresponding mesh, that is, the material or temperature (for example, from cast steel to air) constituting the mesh is changed <# 02>, <# 03. >. Here, if any or none of the substance and the temperature is not specified, the data immediately before that is adopted <# 04>.

Hereinafter, another embodiment of the present invention will be described. In the previous embodiment, an example of analyzing the phase transformation in the cooling process of the casting was described.However, the present invention is not limited to this, and the analysis of the phase transformation of any substance such as a gas phase, a liquid phase, and a solid phase is performed. It can be carried out. In the above embodiment, the mesh dividing means is described as being divided into orthogonal lattice meshes. However, the mesh may be divided arbitrarily according to the solution of the heat conduction equation. Many other methods such as the Macneal et al. Network method and the Saeki, Iwaki et al. Hodgkins method can be applied, and the method is not limited to the direct difference method but may be any method such as the finite element method. Available. The shrinkage cavity prediction described in the above embodiment can be performed by any method such as a solid phase gradient method, an isothermal curve method, and a temperature gradient method.
By using the replacement means described in the previous embodiment, analysis of continuous casting of a mold, analysis of taking out a steel ingot from an ingot case, and analysis of long-time casting of a centrifugal roll in centrifugal casting can be performed. Further, by simultaneously dealing with the phase transformations of a plurality of materials, it is possible to analyze a two-layer alloy (BI-METAL).

In the claims, reference numerals are provided for convenience of comparison with the drawings, but the present invention is not limited to the configuration shown in the attached drawings.

[Brief description of the drawings]

FIG. 1 is a block diagram of a phase transformation analyzer.

FIG. 2 is a plan view of a casting to be divided into meshes.

FIG. 3 is an explanatory diagram of latent heat release.

FIG. 4 is a flowchart.

FIG. 5 is a mesh group split table.

FIG. 6 is a characteristic diagram showing a cooling curve.

[Explanation of symbols]

 1C mesh division means 2 analysis means 2B first analysis means 2C second analysis means

 ────────────────────────────────────────────────── ─── Continuing from the front page (72) Inventor Yukihiro Matsunaga 1-1-1 Hama, Amagasaki-shi, Hyogo Inside Kubota Technology Development Laboratory Co., Ltd.

Claims (2)

(57) [Claims] 1. A mesh dividing means (1C) for dividing the shape of an object into a plurality of meshes, and an analyzing means for solving a heat conduction equation and analyzing a phase transformation for each of the meshes divided by the mesh dividing means (1C). (2) a phase transformation analysis device, wherein the analysis means (2) comprises: a first analysis means (2B) for solving a heat conduction equation for each mesh; and a first analysis means (2).
A second analysis means (2C) configured to divide the mesh into a plurality of groups corresponding to the transition of each phase based on the temperature obtained as a result of B) and to perform a predetermined transformation analysis for each group; Transformation analyzer. 2. The phase transformation analysis device according to claim 1, further comprising a replacement unit (2D) for changing a substance or a temperature of a specific portion of the mesh during the analysis by the analysis unit (2).