JP2008188671A - Solidification analysis method and apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a solidification analysis method of a cast that can perform analysis by considering different latent heat emitting patterns according to the differences of the cooling speeds, and can predict a molten temperature drop history with fine precision. <P>SOLUTION: The solidification analysis method of a cast using an analysis model having a plurality of elements includes: stages (S21 to S27) where a cooling speed is calculated in each element by performing a calculation of heat transfer between the elements adjacent to each other; stages (S28 to S29) where a temperature fluctuation range is revised in each element when a temperature fluctuates from emission of solidification latent heat based on the calculated cooling speed and a predetermined fraction solid-temperature curve of a molten alloy; and a stage where a solidification analysis of the analysis model is performed by using the revised temperature fluctuation range. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a solidification analysis method for a cast product, and more particularly, to a solidification analysis method using a computer simulation and an analysis apparatus therefor.

  In order to produce a sound and inexpensive cast product, it is necessary to examine the shape of the cast product and the design policy for casting in advance. As one means for that purpose, casting analysis using an electronic computer (hereinafter referred to as “computer”) is widely used.

  There are various types of casting analysis, such as flow analysis, deformation analysis, and solidification analysis. In particular, solidification analysis is an important analysis method for predicting the location and size of shrinkage cavities.

In the solidification analysis, the solid fraction is calculated based on the idea that latent heat corresponding to the amount of heat lost at a temperature below the liquidus is released and the solid fraction increases due to the release of this latent heat. In calculating the solid phase rate by this method, a solid phase rate-temperature curve (hereinafter referred to as “solid phase rate-temperature curve”) is used for latent heat calculation, which is an important factor in the solidification process. (Non-Patent Document 1).
Prediction of solidification behavior of AC8C alloy by thermodynamic calculation, Kenichi Ohtsuki, Mayumi Shoji, Toshio Narita, Casting Engineering Vol.72 No.8

  By the way, in the conventional casting analysis method for cast products, the relationship between the solid phase rate and the temperature is constant and used for latent heat calculation regardless of the difference in cooling rate. Therefore, the analysis cannot be performed in consideration of the latent heat release pattern caused by the difference in cooling rate, and the molten metal temperature drop history cannot be accurately predicted.

  The present invention has been made in order to solve the above-described problems, and can perform analysis in consideration of different latent heat release patterns depending on the cooling rate, and can accurately predict the molten metal temperature drop history. An object of the present invention is to provide a solidification analysis method and an analysis apparatus for a cast product.

  In order to achieve the above object, a solidification analysis method for a cast product according to the present invention is a solidification analysis method for a cast product using an analysis model formed from a plurality of elements. Performing heat transfer calculation to calculate the cooling rate for each element, and based on the calculated cooling rate and a preset solid phase rate-temperature curve of the molten alloy, When the temperature fluctuates, the method includes a step of correcting the fluctuating temperature fluctuation width for each element, and a step of performing solidification analysis of the analysis model using the corrected temperature fluctuation width. .

  Further, a solidification analysis device for a cast product according to the present invention for achieving the above object is a solidification analysis device for a cast product using an analysis model formed from a plurality of elements, and the elements adjacent to each other Based on the cooling rate calculation means for calculating the cooling rate for each element, the calculated cooling rate and a preset solid phase rate-temperature curve of the molten alloy, When the temperature fluctuates due to the release of latent heat of solidification, correction means for correcting the fluctuation range of temperature fluctuation for each element, solidification analysis means for performing solidification analysis of the analysis model using the corrected temperature width, It is characterized by providing.

  According to the present invention, when the temperature fluctuates due to the release of the solidification latent heat by correcting the solid phase rate-temperature curve given in advance using the calculated cooling rate of the molten metal, the fluctuating temperature fluctuation range is set. The analysis is performed while correcting. Therefore, the analysis can be performed in consideration of the different latent heat release patterns depending on the cooling rate, and the temperature drop history and the solid phase rate change can be obtained with high accuracy.

  Hereinafter, a solidification analysis method for a cast product according to the present invention will be described in detail with reference to the drawings. FIGS. 1-6 is a figure where it uses for description of the solidification analysis method of the casting based on embodiment of this invention. FIG. 1 is a main flowchart showing a processing procedure for carrying out a solidification analysis method for a cast product according to the present invention, and FIG. 2 is a flowchart showing a subroutine showing a processing procedure of heat transfer / solidification calculation shown in FIG. It is. 3 to 5 are diagrams used for explaining the processing procedure shown in FIG.

  The processing procedure described below is executed by a computer (not shown) in which a program created according to this processing procedure performs a simulation (hereinafter referred to as “simulation”) of solidification analysis. This computer includes a CPU, a RAM, a ROM, a hard disk, a display, and an input device, which are connected to each other via a bus for exchanging signals. The computer used in this embodiment will be briefly described below.

  The computer is an electronic computer such as a personal computer, which performs heat transfer solidification analysis based on a solidification analysis simulation program, or processes and displays various information obtained from the analysis results. It functions as a cooling rate calculation means, a correction means, and a solidification analysis means.

  The CPU executes various arithmetic processes necessary for the control of each part and the heat transfer solidification analysis based on the simulation program.

  The RAM temporarily stores programs and data as a work area.

  The ROM stores various programs and parameters for controlling basic operations of the computer in advance.

  The hard disk stores an OS (operating system) and programs and parameters for controlling predetermined operations of the computer. The hard disk contains programs necessary for heat transfer and solidification analysis (preparation of analysis models, various physical properties necessary for heat transfer and solidification analysis, processing or display processing of information obtained from analysis results, and other general transmission Program required for thermal / solidification analysis) and solid phase rate-temperature curve showing the relationship between solid phase rate and temperature of alloy (solid phase rate-temperature curve according to cooling rate and according to characteristics of analysis target in analysis model) (Solid phase ratio-temperature curve) is stored in advance. Furthermore, the hard disk also functions as a storage area for storing analysis results. The program necessary for heat transfer / coagulation analysis may be stored in advance in a recording medium (for example, a recording medium such as a CD-ROM or DVD-ROM), and the program is directly read from this recording medium for transmission. The thermal coagulation analysis may be executed by a computer.

  The display is, for example, a CRT display or a liquid crystal display, and displays various types of information obtained from the analysis results.

  The input device is a pointing device such as a mouse, a keyboard, or a touch panel, and receives input from a user.

  Using the computer configured as described above, the coagulation analysis method according to the present embodiment is executed.

  Below, with reference to FIG. 1, the whole process sequence in the solidification analysis method of the casting based on this Embodiment is demonstrated in detail. FIG. 1 is a main flowchart showing a processing procedure for implementing a solidification analysis method for a cast product according to the present invention.

  As shown in FIG. 1, first, analysis data stored in advance in a computer is read (step S1). Here, the analysis data includes, for example, shape data, liquidus temperature TL, solidus temperature TS, element division number, and the like. The shape data is shape data for performing solidification analysis of the cast product such as the shape of the cast product to be analyzed, the design shape of the cast product, and the shape of the mold. The liquidus temperature TL and the solidus temperature TS differ depending on the metal used for casting. In general, the liquidus temperature TL is the equilibrium temperature between the melt and the initial phase of the crystal, and is the temperature above which no crystal exists, and the solidus temperature is the opposite, and the presence of the melt. Do not temperature. The solidification analysis method according to the present invention can analyze an alloy having a different latent heat release pattern depending on the difference in the cooling rate of the molten metal, and examples of the metal to be analyzed include AC2A. The number of element divisions is used to create an analysis model when performing simulation, and is equal to the number of cells (number of elements) in the analysis model. The number of element divisions is equal to the number of cells (number of elements) of the mesh model, and the element division is performed on the mesh model when the simulation is performed. The cell refers to each element of the analysis model used when performing the simulation. In the solidification analysis in the present embodiment, a method used for general solidification analysis such as a difference method or a finite element method can be appropriately used.

  Next, physical property values, initial conditions, boundary conditions, and calculation control information (necessary calculation control information according to the analysis method, such as counting the number of molten metal elements ns, setting of time increment dt, setting of calculation end time te), etc. Are set (step S2). Here, physical property values, initial conditions, and boundary conditions differ depending on the metal to be cast.

  Next, the mold initial temperature is set (step S3). The mold initial temperature is usually the mold initial temperature set in the casting process to be analyzed, but here, since it is a solidification analysis by simulation, it can be variously changed for evaluation.

  Then, after the heat transfer / solidification calculation process is performed (step S4), the process ends.

  Next, a processing procedure for heat transfer / solidification calculation will be described in detail.

  FIG. 2 is a subroutine chart showing the heat transfer / solidification calculation processing procedure of step S4 in FIG.

  As shown in FIG. 2, first, the heat transfer amount is calculated (heat transfer calculation) (step S21). The calculation of the amount of heat transfer is to obtain the amount of heat transfer for each cell (element) of a normal analysis model.

  Subsequently, the temperature TN at the target time of the target cell is calculated from the heat transfer amount (step S22). Here, the target temperature at a predetermined time (hereinafter referred to as “designated temperature”) is a temperature predicted after the time interval dt, and is calculated from heat transfer calculation between the cell of interest and its surrounding cells. .

  Subsequently, it is determined whether or not the attention cell is a molten metal element (step S23). Here, about the cell which is not a molten metal element, it progresses to step S30. Here, the fact that it is not a molten metal element indicates that the molten metal has not turned to the cell or has already solidified.

  On the other hand, for a cell determined to be a molten metal element, it is subsequently determined whether or not the solid phase ratio fs of the cell is 1.0. (Step S24). In this process, if the solid phase rate fs is 1.0 or more, the solid phase rate fs is regarded as 1.0 in the calculation, and the process proceeds. Here, if the solid phase ratio fs of the cell is 1.0, it can be determined that the cell is solidified, and the subsequent solidification calculation is terminated (step S25). On the other hand, if the solid phase ratio fs of the cell is not 1.0, it is next determined whether or not the specified temperature TN of the cell is lower than the liquidus temperature TL (step S26). Here, when the temperature of the cell is not lower than the liquidus temperature TL, it can be determined that all the cells are in the liquid phase, and the process proceeds to step S30.

  On the other hand, when the temperature of the cell is lower than the liquidus temperature TL, solidification is in progress, the cooling rate of the molten metal is calculated (step S27), and the solid phase rate fs is corrected (step S28). Based on the calculated cooling rate and the corrected solid phase rate fs, the designated temperature TN is corrected (step S29). Details of the processes in steps S27 to S29 will be described later.

  Finally, the corrected designated temperature TN is updated as the temperature T of each cell at the end of the processing so far (step S30).

  Next, with reference to FIG. 3, the processing of steps S27 to S29 will be described.

  FIG. 3 is a diagram schematically showing a solid phase ratio-temperature curve.

  As described above, at a temperature below the liquidus, latent heat corresponding to the amount of heat lost when the liquid phase solidifies as a solid phase is released, and the release of this latent heat increases the solid phase rate. In calculating the solid phase ratio, a solid phase ratio-temperature curve is used for latent heat calculation in the solidification process.

  In the solidification analysis method according to the present invention, according to the type of alloy to be analyzed, a solid phase rate-temperature curve as schematically shown in FIG. 3 is given in advance, and is given per predetermined time dt. Based on the temperature drop ΔT of the molten metal, the cooling rate v of the molten metal of the alloy to be analyzed is calculated. The method for calculating the cooling rate v is not particularly limited. For example, the cooling rate v can be calculated based on the descent time per predetermined temperature range, and the same applies to the following. Using this calculated cooling rate v, the solid phase rate-temperature curve is corrected as shown by the broken line in FIG. 3 to correct the temperature width that fluctuates in the direction in which the temperature recovers (hereinafter referred to as “temperature fluctuation width”). Analyzing while doing. As a result, the analysis can be performed in consideration of the latent heat release pattern corresponding to the cooling rate v, and the temperature drop history and the solid phase rate change can be obtained with high accuracy.

  The temperature correction is performed by paying attention to the fact that the temperature drop amount ΔT is obtained by heat transfer calculation, and solidification occurs if ΔT> 0, so that the temperature varies due to the release of latent heat. Specifically, referring to FIG. 2, in step S27, based on the molten metal temperature drop ΔT per predetermined time dt, the molten metal cooling rate v to be analyzed is calculated. Next, in step S28, using ΔT, the change amount Δfs of the solid phase ratio expressed by the following equation 1 is calculated.

  Here, in the above formula 1, Δfs is the change amount of the solid phase rate, Cp is the specific heat, ΔT is the temperature drop, and L is the latent heat.

  In step S29, when the temperature fluctuates due to the release of solidification latent heat, the designated temperature TN is corrected by correcting the fluctuating temperature fluctuation range. Specifically, the temperature fluctuation range is corrected for each cell based on the change rate Δfs of the solid phase ratio and the cooling rate v within a predetermined time. As a result, the analysis can be performed in consideration of different latent heat release patterns depending on the difference in the cooling rate v, and the temperature drop history and the solid phase rate change can be obtained with high accuracy.

  FIG. 4 is a diagram schematically showing two solid phase ratio-temperature curves with different cooling rates. FIG. 5 is a schematic model diagram of two solid phase ratio-temperature curves with different cooling rates. FIG. 4 schematically shows a schematic model diagram of the solid phase rate-temperature curve of FIG. 5, and is an enlarged view of a part extracted from the solid phase rate-temperature curve.

  With reference to FIGS. 4 and 5, in this embodiment, the temperature after recovery is calculated using the cooling rate v as a parameter at the time of temperature fluctuation in the solid phase ratio-temperature curve. The faster the cooling rate v, the smaller the fluctuation temperature range.

  As shown in FIG. 4, solid phase rate-temperature curves having different cooling rates are given, and the solid phase rate fs at a predetermined time t of the solid phase rate-temperature curve is used, depending on the cooling rate of the cell. A temperature T (fs) max obtained from the solid phase rate-temperature curve and a temperature T (fs) min obtained from another solid phase rate-temperature curve having a cooling rate faster than the one solid phase rate-temperature curve. A range of T (fs) is set in between. Then, within the range of T (fs), the target temperature of T (fs) is calculated by the following equation (2). In addition, the solid phase rate-temperature curve shown in FIG. 4 shows what the solid phase rate-temperature curve according to the alloy kind used as analysis object previously calculated | required by experiment, and each solid phase rate- Between the temperature curves, the range of T (fs) is set so that a solid phase ratio-temperature curve in the actual manufacturing process exists.

  Here, the above equation (2) is linearly interpolated. In the equation (2), the temperature at the cooling rate v1 is T (fs + Δfs) max, and the temperature at the cooling rate v2 is T (fs + Δfs). ) Min. According to the above formula 2, the analysis can be performed with higher accuracy in consideration of different latent heat release patterns depending on the difference in the cooling rate v, and the temperature drop history and the change in the solid phase ratio can be obtained with higher accuracy.

  In this embodiment, an example using two solid phase rate-temperature curves with different cooling rates has been described, but the present invention is not limited to this, and a plurality of solid phase rate-temperature curves are used. The target temperature of T (fs) may be calculated by interpolation approximation with a high-order linear polynomial, for example, interpolation approximation with a quadratic linear polynomial using three solid phase ratio-temperature curves. You may calculate by. That is, the target temperature of T (fs) is obtained by generalizing an equation for correcting the temperature predicted value from the solid phase rate-temperature curve that varies depending on the cooling rate, and T (fs) = f (T (fs) max , T (fs) min, v). This means that the target T (fs) can be calculated by using a function of “T (fs) max”, “T (fs) min”, and “v”. This means that any calculation method using the relationship of T (fs) = f (T (fs) max, T (fs) min, v) is included in the present invention when calculating T (fs). . Of course, other polynomials and spline interpolation can be used for this interpolation calculation.

  FIG. 6 is a diagram showing a melt temperature history.

  The melt temperature history as shown in FIG. 6 can be obtained by continuously calculating the temperature fluctuation range as described above over time. In FIG. 6, the solidification analysis method according to the present invention, the novel solidification analysis method according to the present invention, and the actual measurement data (when the solidification is slow (cooling rate is slow) and solidification is fast (cooling rate is fast)) (Actual) shows a molten metal temperature history. As shown in the figure, according to the new solidification analysis method according to the present invention, both the case where solidification is slow (cooling rate is slow) and the case where solidification is fast (cooling rate is fast) than the conventional solidification analysis method. It can also be seen that it is closer to the measured value data.

  The present invention is useful in the technical field related to solidification analysis of cast products.

It is a main flowchart which shows the process sequence for enforcing the solidification analysis method of the casting based on this invention. It is a subroutine chart which shows the process sequence of heat-transfer / solidification calculation. It is a figure which shows typically the curve of a solid-phase rate-temperature. It is a figure which shows typically the curve of two solid-phase rate-temperature from which a cooling rate differs. It is a schematic model figure of two solid-phase rate-temperature curves from which a cooling rate differs. It is a figure which shows a molten metal temperature log | history.

Claims (6)

A solidification analysis method for a cast product using an analysis model formed from a plurality of elements,
Performing a heat transfer calculation between the elements adjacent to each other to calculate a cooling rate for each element;
When the temperature fluctuates due to the release of latent heat of solidification, based on the calculated cooling rate and the preset solid phase rate-temperature curve of the molten alloy, the fluctuating temperature fluctuation range is corrected for each element. When,
Performing solidification analysis of the analytical model using the corrected temperature fluctuation range;
A solidification analysis method for a cast product, comprising:   The solidification rate-temperature curve of the molten metal of the alloy is set as the solidification rate-temperature curve corresponding to the cooling rate of the element. . The solid phase rate-temperature curve of the molten metal of the alloy includes solid phase rate-temperature curves with different cooling rates,
Performing the coagulation analysis comprises:
Using the solid phase ratio fs at the predetermined time t of the solid phase ratio-temperature curve, the temperature T (fs) max obtained from one solid phase ratio-temperature curve and the one according to the cooling rate of the element. Setting a range of T (fs) between the temperature T (fs) min obtained from another solid phase ratio-temperature curve whose cooling rate is faster than the solid phase ratio-temperature curve of
In the range of T (fs), calculating a target temperature of T (fs) according to the following equation (1):
The solidification analysis method for a cast product according to claim 1 or 2, characterized by comprising:
However, in the following formula 1, T is temperature, fs is a solid phase rate, and v is a cooling rate.
The equation 1 is
The solidification analysis method for a cast product according to claim 3, wherein:   The solidification analysis method for a cast product according to any one of claims 1 to 4, wherein the solidification analysis is executed by analyzing an alloy having a different latent heat release pattern in accordance with the cooling rate. A solidification analysis device for castings using an analysis model formed from a plurality of elements,
A cooling rate calculating means for calculating a cooling rate for each element by performing heat transfer calculation between the elements adjacent to each other;
When the temperature fluctuates due to the release of latent heat of solidification based on the calculated cooling rate and the solid phase rate-temperature curve of the molten alloy of the alloy set in advance, the correction for correcting the fluctuating temperature fluctuation range for each element Means,
Solidification analysis means for performing solidification analysis of the analysis model using the corrected temperature fluctuation range;
A solidification analysis device for a cast product, comprising: