JP2018062006A - Method of estimating hardness of casting of nodular graphite cast iron - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method of accurately estimating a hardness of a casting of nodular graphite cast iron by simulation.SOLUTION: A method of estimating a hardness of a casting of nodular graphite cast iron comprises an element creating step (S1) that creates an analytic model, a cooling history analysis step (S2) that chronologically analyzes a heat transmission in a casting element during a period from when a molten metal flows a casting element to be filled until when it is cooled and obtains a set of data of time and temperature of the casting element, a chemical composition value setting step (S3), a temperature setting step (S4) that gives a preset temperature for calculating a cooling rate, a maximum temperature calculation step (S5) that determines a maximum temperature of the casting element, a cooling rate calculation step (S6) that includes a process of calculating a cooling rate of eutectic solidification, a cooling rate after eutectic solidification and a cooling rate of eutectoid transformation on the basis of the preset temperature and the set of data, and a hardness calculation step (S7) that calculates a hardness of the casting element by a hardness estimation formula on the basis of the maximum temperature, the cooling rate of eutectic solidification, the cooling rate after eutectic solidification, the cooling rate of eutectoid transformation and chemical composition values.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a method for predicting the hardness of a spheroidal graphite cast iron casting.

  It is known that the strength and other mechanical properties of a metal material have a strong correlation with hardness. Regarding the method of predicting the hardness of spheroidal graphite cast iron castings frequently used as structural members for automobiles by simulation, for example, Patent Document 1 describes the cooling rate near the start of eutectic solidification in the casting element of the analytical model, the hardness of the casting, Are proportional to each other, suggesting that the hardness can be predicted by obtaining the cooling rate by analysis.

JP 2008-155230 A

  If the hardness of each part of the spheroidal graphite cast iron casting can be accurately predicted, it is possible to accurately predict the mechanical properties necessary for automobile parts such as tensile strength, proof stress, and elongation without performing actual casting. The development period can be shortened by reducing the number of prototypes. However, it has been found that the accuracy as described in Patent Document 1 is insufficient in the method of predicting the hardness by calculating only the cooling rate in a certain temperature range by simulation.

  Therefore, an object of the present invention is to provide a method for accurately predicting the hardness of a spheroidal graphite cast iron casting by simulation.

  The inventor carefully examined the relationship between the hardness of the spheroidal graphite cast iron casting actually measured and the solidification cooling temperature curve and chemical component value measured in the vicinity of the portion where the hardness was measured. Has found that there is a strong correlation with the cooling rate other than the cooling rate in the vicinity of eutectic solidification, the number of graphite grains, the chemical component value, and the like, and has reached the present invention. In the present invention, the cooling rate near eutectic solidification may be referred to as “eutectic solidification cooling rate” and the cooling rate near eutectoid transformation temperature may be referred to as “eutectoid transformation cooling rate”.

That is, the present invention is a method for predicting the hardness of a spheroidal graphite cast iron casting,
An element creation step (S1) for creating an analysis model including a casting element;
Analyzing the heat transfer of the casting element over time during the period from when the molten metal made of spheroidal graphite cast iron flows and fills the casting element and is cooled to a temperature lower than the eutectoid transformation temperature of the spheroidal graphite cast iron. , A cooling history analysis step (S2) for acquiring set data of time and temperature of the casting element;
A chemical component value setting step (S3) for giving a chemical component value of the spheroidal graphite cast iron;
A temperature setting step (S4) for providing a set temperature for calculating the cooling rate of the casting element;
A maximum temperature calculation step (S5) for obtaining a maximum temperature of the casting element based on the set data of the casting element;
Based on the set temperature and the set data, a first cooling rate calculation step (S61) for calculating a cooling rate for eutectic solidification, and a second cooling rate calculation step for calculating a cooling rate after eutectic solidification ( A cooling rate calculation step (S6) including S62) and a third cooling rate calculation step (S63) for calculating the cooling rate of the eutectoid transformation;
Based on the maximum temperature, the cooling rate of the eutectic solidification, the cooling rate after the eutectic solidification, the cooling rate of the eutectoid transformation, and the chemical component value This is a method for predicting the hardness of a spheroidal graphite cast iron casting having a calculation step (S7).

  In the present invention, the chemical component value given in the chemical component value setting step (S3) preferably includes at least C, Si, Cu and Mn as elements.

  In the present invention, the hardness calculation step (S7) calculates the number of graphite grains of the casting element based on the maximum temperature, the cooling rate of the eutectic solidification, and the chemical component value including at least C and Si as elements. It is preferable to include a graphite particle number calculating step (S71).

  In the present invention, the hardness calculation step (S7) preferably includes calculation of a relative value between the cooling rate of the eutectoid transformation and the cooling rate after eutectic solidification.

  Furthermore, the present invention preferably includes a hardness output step (S8) for outputting the hardness of the casting element calculated in the hardness calculation step (S7) as an image.

  The present invention provides a method for accurately predicting the hardness of each part of a spheroidal graphite cast iron casting by simulation. This makes it possible to accurately predict the mechanical properties necessary for designing cast parts for automobiles, such as the tensile strength and proof stress of spheroidal graphite cast iron castings, without performing actual casting. It becomes possible to shorten the development period by reducing man-hours.

It is a flowchart which shows the whole structure of this invention. It is a flowchart which shows the cooling history analysis process (S2) which comprises this invention. It is a flowchart which shows the cooling rate calculation process (S6) which comprises this invention. It is a flowchart which shows the 1st cooling rate calculation process (S61) which is one of the components of the cooling rate calculation process (S6) which comprises this invention. It is a flowchart which shows the hardness calculation process (S7) which comprises this invention. It is a figure which compares the predicted value of the hardness by the Example of this invention, and the actual value of the hardness of a real thing. It is a schematic diagram of the solidification cooling curve which shows the cooling history of spheroidal graphite cast iron. It is the example which measured the relationship between the cooling rate of a spheroidal graphite cast iron casting, and Brinell hardness, (a) is the relationship between the cooling rate near eutectoid transformation temperature and Brinell hardness, (b) is the eutectoid transformation temperature neighborhood. It is a figure which shows the relationship between ratio of a cooling rate and the cooling rate after eutectic solidification, and Brinell hardness. It is a figure which shows the example which measured the relationship between the graphite particle number of a spheroidal graphite cast iron casting, and Brinell hardness. It is a figure which shows the example which measured the relationship between the highest attained temperature in the stage of the molten metal poured in the casting mold of the spheroidal graphite cast iron, and the number of graphite grains. It is a figure which shows the example which measured the relationship between the cooling rate of the eutectic solidification temperature vicinity of a spheroidal graphite cast iron casting, and the number of graphite grains. It is a figure which compares the predicted value of the hardness by the comparative example which considered only the cooling rate of eutectoid transformation, and the actual value of the hardness of a real thing.

  As described above, the present inventor has carefully studied the relationship between the hardness of each part of an actual spheroidal graphite cast iron casting (hereinafter also referred to as a casting) and the measured solidification cooling temperature curve and chemical component value at that part. It was. As a result, the hardness is a function of the cooling history, chemical component value, and number of graphite grains of the part, and by setting the component parameters based on the cooling rate and the chemical component value, which are representative values of the cooling history, the experiment was performed. From the data, it was found that the hardness prediction formula and the graphite grain number prediction formula can be made with high accuracy. And from this knowledge, the cooling history of the casting element obtained by the simulation using CAE (Computer-aided Engineering), the chemical component value, the hardness prediction formula and the graphite grain number prediction formula created in advance based on the experimental data. As a result, the inventors have come up with a method for accurately predicting the hardness of each part of the casting.

  The present invention is a method for predicting the hardness of a spheroidal graphite cast iron casting, wherein an element creating step (S1) for creating an analysis model including a cast element, and a molten metal made of spheroidal graphite cast iron flows and fills the cast element. Cooling that analyzes the heat transfer of the casting element over time until it is cooled to a temperature lower than the eutectoid transformation temperature of the spheroidal graphite cast iron, and obtains time and temperature set data of the casting element A history analysis step (S2), a chemical component value setting step (S3) for giving a chemical component value of the spheroidal graphite cast iron, and a temperature setting step (S4) for giving a set temperature for calculating the cooling rate of the casting element A first temperature calculating step (S5) for obtaining a maximum temperature of the casting element based on the set data of the casting element, and a first rate of calculating a cooling rate for eutectic solidification based on the set temperature and the set data. Cooling rate meter Cooling rate calculation including a step (S61), a second cooling rate calculation step (S62) for calculating the cooling rate after eutectic solidification, and a third cooling rate calculation step (S63) for calculating the cooling rate of the eutectoid transformation Based on the step (S6), the maximum temperature, the cooling rate of the eutectic solidification, the cooling rate after the eutectic solidification, the cooling rate of the eutectoid transformation, and the chemical component value, the casting element according to the hardness prediction formula And a hardness calculation step (S7) for calculating the hardness. Hereinafter, although the detail of this invention is demonstrated, referring drawings, it is not limited to this.

  FIG. 1 is a flowchart showing the overall configuration of the present invention. The present invention includes an element creation step S1, a cooling history analysis step S2, a chemical component setting step S3, a temperature setting step S4, a maximum temperature calculation step S5, a cooling rate calculation step S6, and a hardness calculation step S7. The present invention may further include a hardness output step S8. The procedure of hardness prediction will be described later in order from the element creation step S1, but the details of the hardness prediction formula used in the hardness calculation step S7 will be described first.

(1) Hardness Prediction Formula and Graphite Grain Number Prediction Formula The inventor carefully examined the relationship between the actual casting hardness, the solidification cooling curve and the chemical component value measured at the site, and the following correlation was found. I found out.

FIG. 7 is a schematic diagram of the solidification cooling curve 1 showing the cooling history of the spheroidal graphite cast iron casting. Looking at the transition of the temperature T with time t in the solidification cooling curve 1, the molten spheroidal graphite cast iron poured into the mold is extracted from the maximum temperature T _{max as the} time elapses and the temperature rises. In the process, it solidifies while crystallization of graphite at the eutectic solidification temperature T _E , and the eutectoid transformation temperature T _A1 is accompanied by precipitation of a pearlite phase in the structure. In the vicinity of the eutectic solidification temperature T _{E and in the} vicinity of the eutectoid transformation temperature T _A1 , since the latent heat is released, the temperature drop becomes gentle. The cooling rate is generally defined by a value obtained by dividing a certain temperature section by the time required for it, but as shown in the solidification cooling curve 1, the cooling rate varies depending on the temperature section. For this reason, the present inventor analyzed the experimental data and examined the temperature interval in which the cooling rate showing a strong correlation with the hardness was obtained.

FIG. 8 shows an example in which the relationship between the cooling rate of the spheroidal graphite cast iron casting and the Brinell hardness is measured. FIG. 8A shows the relationship between the cooling rate near the eutectoid transformation temperature T _A1 and the Brinell hardness H _B (hereinafter also referred to as hardness). In this example, there is a strong correlation in which the hardness H _B increases as the cooling rate V _{740-710 in} the temperature range from 740 ° C. to 710 ° C. near the eutectoid transformation temperature T _A1 near the hardness measurement site increases. It was seen. The present inventor presumed that the hardness of the spheroidal graphite cast iron casting was strongly influenced by the cooling rate in the vicinity of the eutectoid transformation temperature accompanied by the precipitation of the pearlite phase in the structure. It was confirmed that the inference was valid as shown in.

Further, FIG. 8 (b), the cooling rate _{V 1100-1000} of eutectoid transformation temperature _{T A1} near the cooling rate _{V 740-710} and the temperature zone of 1000 ° C. from 1100 ° C. after eutectic solidification shown in Figure 7 This is an example in which the relationship between the relative value ratio V _740-710 / V _1100-1000 and hardness is measured. In this example, it was found that the hardness H _B decreased as V _740-710 / V _1100-1000 increased, but this correlation was found to be particularly strong for the thin portion of the casting. Thus, it was found that not only the cooling rate near the eutectoid transformation temperature but also the cooling rate after eutectic solidification greatly affects the hardness.

Moreover, FIG. 9 is a figure which shows the example which measured the relationship between the graphite particle number of a casting, and hardness. As the number of graphite grains _NG increases, the hardness H _B tends to increase, and it has been found that the hardness of the casting has a correlation not only with the cooling rate as described above but also with the number of graphite grains. FIG. 10 is a diagram showing an example in which the relationship between the maximum temperature T _max (hereinafter also referred to as the maximum temperature) at the stage of the molten metal in the mold and the number of graphite grains is actually measured. That is, the tendency for the number of graphite grains _NG to decrease as the maximum temperature T _max shown in FIG. 7 increases was found to be significant, indicating that the number of graphite grains has a strong correlation with the maximum temperature. Further, FIG. 11 is a diagram showing an example in which the relationship between the cooling rate near the eutectic solidification temperature and the number of graphite grains is measured. The number of graphite grains _{N G} with the eutectic solidification temperature _{T E} cooling rate _{V 1160-1100} from 1160 ° C. interval of 1100 ° C. vicinity shown in FIG. 7 increases also found that a strong tendency to increase. As described above, the hardness was also correlated with the number of graphite grains, and the number of graphite grains was also found to have a strong correlation with the maximum temperature and the cooling rate near the eutectic solidification temperature.

  And the hardness of a casting and the number of graphite grains are influenced also by the chemical component value to contain. For example, Cu and Mn are known to be component elements that increase the hardness of a casting because they promote the precipitation of a pearlite phase having a high hardness. It is also known that C and Si are component elements that promote crystallization of graphite. Therefore, it is preferable to consider the component parameters based on the chemical component values of these elements as variables.

Based on the above knowledge, the hardness prediction formula of the spheroidal graphite cast iron casting can be conceptually expressed as the following function F _{1 using} the plurality of cooling rates, the number of graphite grains, and the chemical component value as variables.
H _B = F ₁ (E ₁ , N _G , V ₂ , V ₃ ) (Formula 1)
Where H _B : Hardness
E ₁ : First variable based on chemical component values
N _G : Number of graphite grains
V ₂ : Cooling rate after eutectic solidification
V ₃ is the cooling rate of the eutectoid transformation.

Incidentally, for the number of graphite grains N _G the prediction equation as a function F _2, it can be conceptually represented as follows.
N _G = F ₂ (E ₂ , V ₁ , T _max ) (Formula 2)
Where E ₂ : second variable based on chemical component value
V ₁ : Cooling rate of eutectic solidification
T _max : Maximum temperature.

Since the number of graphite grains _NG represented by the function F ₂ is also a variable of the function F ₁ as described above, the hardness H _B is determined by the first variable E ₁ and the _first variable based on the chemical component value. Next, the function F ₁ having the variables E ₂ , the maximum temperature T _max , the cooling rate V ₁ of eutectic solidification, the cooling rate V ₂ after eutectic solidification, and the cooling rate V ₃ of eutectoid transformation as a variable It is also possible to express as follows.
H _B = F ₁ (E ₁ , E ₂ , T _max , V ₁ , V ₂ , V ₃ ) (Formula 3)

The above (Formula 1) to (Formula 3) are conceptual notations, but actual measurement data of chemical component values, cooling history (solidification cooling curve) in the vicinity of the hardness measurement site, hardness, and number of graphite grains for actual castings. Are collected, and a specific expression of the function F ₁ and the function F ₂ is created by performing regression analysis such as multiple regression analysis or trial and error iterative calculation for each of the above variables. It is possible.

The inventor sufficiently collects experimental data as shown in FIG. 8 to FIG. 11 and performs analysis to thereby obtain a hardness prediction formula (formula 4) and a graphite particle number prediction having a highly accurate function form shown below. Formula (Formula 5) was created. However, the hardness prediction formula and the graphite grain number prediction formula of the present invention are not limited to this function form. Note that the _NG term in the hardness prediction formula (Formula 4) does not necessarily have to be the value of _NG determined by the graphite grain number prediction formula (Formula 5), and the graphite grain number _NG is set as a constant value. Also good.

H _B = F ₁ (Cu _eq , _NG , V ₂ , V ₃ )
= Ω + α ₁ Cu _eq + α ₂ V ₃ + α _{3 NG} + α ₄ V ₃ / V ₂ (Formula 4)

N _G = F ₂ (D _CE , V ₁ , T _max )
= Ψ ₁ + D _CE (β ₁ V ₁ −ψ ₂ ) + β ₂ V ₁ + β ₃ T _max (Formula 5)

Here, Cu _eq in (Equation 4) is a component parameter referred to herein as Cu equivalent, which corresponds to the first variable E ₁ based on the chemical component value, and is set to Cu _eq = Cu% + ξ ₂ Mn%. Here, Cu% represents Cu, and Mn% represents mass% of Mn. Ξ ₂ is a constant indicating the contribution of Mn.

Further, the term of V ₃ / V ₂ in (Equation 4), that is, the ratio of the cooling rate V _{3 of the} eutectoid transformation and the cooling rate V ₂ after eutectic solidification is the result as illustrated in FIG. 8B. It is based on. As described above, since the accuracy of predicting the hardness of the thin-walled portion can be particularly improved, V ₃ / V ₂ is preferably incorporated in the function F ₁ as a process for obtaining this. In the example of (Equation 4), V ₃ / V ₂ is used, but since it is an indicator of the relative relationship between V ₂ and V ₃ , the reciprocal number V ₂ / V ₃ may be used. Note that the term V ₃ / V ₂ in (Equation 4) is not essential, and this term is excluded, or only the cooling rate V ₂ after eutectic solidification is incorporated as α ₄ V ₂ instead of V ₃ / V _2. But you can.

_DCE is referred to herein as the hypereutectic degree, and is a component parameter indicating a deviation from the eutectic composition of the spheroidal graphite cast iron to the hypereutectic side, and is a second variable E ₂ based on the chemical component value. The corresponding hypereutectic degree D _CE is set to D _CE = C _eq −φ = C% + ξ ₁ Si% −φ. Here, C _eq is a carbon equivalent generally referred to as a CE value, ξ ₁ is a constant indicating the contribution of Si, and ξ ₁ = 1/3 (0.33) is widely used. C% indicates C and Si% indicates mass% of Si. The constant φ is a value corresponding to the eutectic composition when viewed in terms of carbon equivalent C _eq , and generally φ = 4.5.

Further, ω, α _{1 to} α ₄ , β _{1 to} β _3, and ψ _{1 to} ψ ₂ are constants, and give weights (contributions) of the above variables to the hardness and the number of graphite grains. These constants often have different optimum values depending on the casting production conditions. Therefore, these constants are as probable as possible by sufficiently collecting actual measurement data and conducting appropriate analysis for each production line, foundry factory, or product to be manufactured for which the hardness is to be predicted. Is preferably obtained.

  A highly accurate hardness prediction formula can be created by the above method. Hereinafter, the steps of the present invention will be described in order with reference to the drawings.

(2) Element creation process (S1)
Element creation step S1 is a step of creating an analysis model. In this process, the shape data of the casting that is the product is created as three-dimensional CAD data, or the shape data prepared in advance is taken in, and the casting plan for the gate, runner, feeder, weir, etc. necessary for casting The shape data of the part and the shape data of the mold around the casting are created, and each of these shape data is divided into a plurality of microelements (hereinafter also referred to as elements) made of a polyhedron, and then these elements are cast or An analysis model is defined that includes n casting elements to be hardness-predicted, casting elements that are not to be hardness-predicted, and mold elements.

  To create a plurality of elements, a method of giving the position where the element is divided for each part as coordinates, an element creation program for automatically generating elements if a desired element size is given, or the like may be used. In creating the mold element, a simple mold element in which the thickness of the mold is defined only from the shape data of the casting may be arranged around the casting element.

  Various formats can be used as the format of the three-dimensional CAD data for taking in the shape of the casting created in advance. For example, an international standard IGES (Initial Graphics Exchange Specification) format, STL (Stereo Lithography) format, or the like can be used.

(3) Cooling history analysis step (S2)
FIG. 2 shows a flowchart of the cooling history analysis step S2. The cooling history analysis step S2 is shown in FIG. 7 after the first cooling history analysis step S21 at the stage where the analytical molten metal (hereinafter also referred to as molten metal) flows, and then after the molten metal stops flowing. The stage until reaching a predetermined temperature T _END that is equal to or lower than the eutectoid transformation temperature T _A1 is a step of executing the second cooling history analysis step S22, and a known hot water flow / solidification simulation method can be used. .

In the cooling history analysis step S2, and between the casting elements, analysis over time was analyzed, and time t _m on analysis for each n-number of the casting element, at time t _m heat transfer between the casting elements and the mold elements The set data (t _m , T _m ) of the upper temperature T _m is acquired and stored in electromagnetic storage means (hereinafter also referred to as storage means). Here, the subscript m represents a time step in analysis over time, and the time t _m means the time of the mth time step from the initial time t ₀ .

(3-1) First cooling history analysis step (S21)
The first cooling history analysis step S21 is a step using a molten metal flow analysis for calculating a behavior in which a molten metal is filled in a casting element. In the first cooling history analysis step S21, the inflow amount or the inflow pressure of the molten metal is applied to the gate element forming part of the casting element created in the element creation step S1, and the density, specific heat, thermal conductivity and After assigning physical properties such as viscosity coefficient, initial temperature and initial pressure, and heat transfer coefficient as the heat transfer condition between the casting element and the mold element, for example, using the Naviestokes formula, the molten metal in the casting element The position, temperature, pressure, etc. are obtained over time. In this process, the set data (t _m , T _m ) of time and temperature for each time step can be obtained for n casting elements.

(3-2) Second cooling history analysis step (S22)
The second cooling history analysis step S22 is a step of using heat conduction analysis for each element until the temperature drops to a predetermined temperature T _END equal to or lower than the eutectoid transformation temperature T _A1 after the flow of the molten metal stops. is there. In the second cooling history analysis step S22, the casting element and the mold element are provided with physical properties such as density, specific heat, thermal conductivity, latent heat of solidification, and the time when the flow is completed obtained in the first cooling history analysis step S21. After giving temperature set data and giving heat transfer coefficient etc. as a heat transfer condition between casting elements and mold elements, the time of n casting elements immediately after all the casting elements are filled with molten metal The set data (t _m , T _m ) with temperature is obtained over time.

The second cooling history analysis step S22 is the same as a technique widely used for the purpose of predicting shrinkage cavities of castings. When aiming at shrinkage cavities, the analysis is usually performed at the time when solidification of the casting is completed. Just finish. However, in the present invention, since the object is to determine the hardness of the casting when the temperature of the casting is sufficiently lowered, the analysis is continued until the temperature falls to the predetermined temperature T _END even after the solidification is completed.

The predetermined temperature T _END for ending the analysis is set to a temperature lower than the eutectoid transformation temperature T _A1 of the spheroidal graphite cast iron. This is because the great influence pearlite hardness is deposited on tissue of the casting in the process of passing through the eutectoid transformation temperature T _A1. In the temperature range lower than the eutectoid transformation temperature T _A1, the hardness of the spheroidal graphite cast iron casting does not change so much. Therefore, the analysis is performed until the hardness is lowered to at least a temperature lower than the eutectoid transformation temperature T _A1 . The eutectoid transformation temperature T _A1 of the spheroidal graphite cast iron is about 730 ° C. However, since the eutectoid transformation of the spheroidal graphite cast iron proceeds in a certain temperature range near the eutectoid transformation temperature, the predetermined temperature T _END for ending the analysis is The temperature is preferably 630 ° C. or lower, which is 100 ° C. or lower than the eutectoid transformation temperature.

  The value of the time step interval τ may be a value set in a normal molten metal flow / solidification simulation. The smaller the value of τ, the more accurately the cooling history can be analyzed, while the analysis time increases. For this reason, the value of τ may be changed according to each stage of the cooling history. For example, it is preferable to decrease the value of τ when the temperature change per time is large and increase the value of τ when the temperature change is small because the balance between the analysis accuracy and the analysis time is improved.

(4) Chemical component value setting step S3
The hardness of the spheroidal graphite cast iron casting also varies depending on its chemical component value. This is because the structure of the casting changes depending on the chemical component value. The structure of the spheroidal graphite cast iron casting is composed of a base composed of a soft ferrite phase and a hard pearlite phase, and spheroidal graphite dispersed in the base. The proportion of these phases constituting the structure varies depending on chemical components, and in particular, the ferrite phase also varies in its own hardness. In the chemical component value setting step S3, it is preferable to give chemical component values of at least C, Si, Cu, and Mn as elements that greatly affect the properties of these constituent phases. These chemical component values are preferably stored in the storage means in advance, and are read in the hardness calculation step S7 described later.

(5) Temperature setting step S4
In the temperature setting step S4, a cooling rate V _{1 for} eutectic solidification (hereinafter also referred to as a first cooling rate) and a cooling rate V ₂ after eutectic solidification (hereinafter referred to as a _second rate) in the cooling rate calculation step S6 described later. And a eutectoid transformation cooling rate V ₃ (hereinafter also referred to as a third cooling rate), and a temperature setting step for defining a temperature section. Hereinafter, description will be made again with reference to FIG.

(5-1) First temperature T1 and second temperature T2
The first temperature T1 and the second temperature T2 shown in FIG. 7 are for calculating the _first cooling rate V1, and satisfy T1> T2. Since the eutectic solidification temperature T _E of the spherical graphite cast iron is around 1150 ° C., the first temperature T1 is a value equal to or greater than 1150 ° C., when excessively high value prediction accuracy of the hardness and the number of graphite grains decreases Therefore, it shall be 1150 degreeC or more and 1200 degrees C or less. The first temperature T1 is preferably 1155 ° C. or higher and 1180 ° C. or lower, more preferably 1155 ° C. or higher and 1165 ° C. or lower. On the other hand, the presence of the eutectic solidification temperature T _E chemical composition and inoculation slightly or decreased by the production conditions such as heat removal conditions from ambient, it may or cause a slight supercooling 2 shown in FIG. For this reason, it is preferable that the second temperature T2 is 1145 ° C. or lower, which is a temperature lower than the temperature of the supercooling 2, but if it is an excessively low value, the accuracy of predicting the hardness and the number of graphite grains decreases, so 1145 C. or lower and 1080 C or higher. The second temperature T2 is preferably 1145 ° C. or lower and 1095 ° C. or higher.

(5-2) Third temperature T3 and fourth temperature T4
The third temperature T3 and the fourth temperature T4 are for calculating the _second cooling rate V2, and satisfy T3> T4. The third temperature T3 may be a temperature after completion of eutectic solidification. The second temperature is preferably equal to or lower than the second temperature T2. The fourth temperature T4 to a value larger than the eutectoid transformation temperature T _A1. The third temperature T3 and the fourth temperature T4 satisfy T3> T4, and are preferably T2 (° C.) or lower and 950 ° C. or higher, preferably T2 (° C.) or lower and 1000 ° C. or higher.

(5-3) Fifth temperature T5 and sixth temperature T6
The fifth temperature T5 and the sixth temperature T6 are for calculating the _third cooling rate V3, and satisfy T5> T6. The fifth temperature T5 is a temperature higher than the eutectoid transformation temperature T _A1 , and the sixth temperature T6 is a temperature lower than the eutectoid transformation temperature T _A1 . When the fifth temperature T5 is an excessively high value, or when the sixth temperature T6 is an excessively low value, the accuracy of predicting hardness decreases, so the fifth temperature T5 is 735 ° C. or more and 755 ° C. or less. The sixth temperature T6 is preferably 720 ° C. or lower and 700 ° C. or higher.

The above set temperature T1~T6 including the set temperature _{T END} of the foregoing analysis end is set so as to satisfy the _{T1 ≧ T E> T2 ≧ T3} > T4 ≧ T5> T A1>T6> T END. Each set temperature of T _END and T1 to T6 is preferably stored in the storage means in advance.

(6) Maximum temperature calculation step S5
The maximum temperature calculation step S5 is a step of obtaining the maximum temperature _Tmax that the casting element reaches from the set data of the time and temperature obtained in the cooling history analysis step S2. The time and temperature set data (t _m , T _m ) acquired in the cooling history analysis step S2 and stored in the storage means is read, and _the maximum value of T _{m is} set as the maximum temperature T _max of the element, and the time t _max The set data (t _max , T _max ) is stored in the storage means.

(7) Cooling rate calculation step S6
Next, the cooling rate calculation step S6 is executed. FIG. 3 is a flowchart showing the cooling rate calculation step S6. The cooling rate calculation step S6 includes a first cooling rate calculation step S61, a second cooling rate calculation step S62, and a third cooling rate calculation step S63, and includes the time and temperature obtained in the cooling history analysis step S2. While reading the set data (t _m , T _m ) and the set temperatures T1 to T6 set in the temperature setting step S4, the processes are executed in the order of S61, S62, and S63. Since the first to third cooling rate calculation steps S61 to S63 all have the same flow, only the first cooling rate calculation step S61 will be described in detail with reference to FIG. To do.

(7-1) First cooling rate calculation step S61
FIG. 4 shows a flowchart of the first cooling rate calculation step S61. In the cooling history analysis step S2, the jumping temperature _Tm is acquired for each time step, so the acquired temperature _Tm is completely equal to the first temperature T1 and the second temperature T2 set in the temperature setting step S4. There may be no value that matches. Accordingly, as the temperature used in the first calculation of the cooling rate _{V 1,} a first temperature T1 in place to a second temperature T2, using the first analysis temperature T1 _A second analysis temperature T2 _A. The first analysis temperature T1 _A is a temperature closest to the first temperature T1, and is a temperature at a time immediately before or immediately after reaching the first temperature T1. Also the same for the second analysis temperature T2 _A, and similarly for the third to sixth analysis temperature _T3 A to T6 _A to be described later.

First, a step of obtaining the first analysis temperature T1 _A is shown. Of the set data obtained in the cooling history analysis step S2, the first set data (t _m , T _m ) read in the first cooling rate calculation step S61 is obtained in the maximum temperature calculation step S6 which is the immediately preceding step. The set data (t _max , T _max ) = (t _m , T _m ) indicating the maximum temperature T _max is set to (t _{m + 1} , T _{m + 1} ) of the next time step. That is, (t _m , T _m ) is read with m = m + 1.

Then, by comparing the magnitude relation between the first temperature T1 set in a temperature T _m and the temperature setting step S4, successively repeating this as further m = m + 1 in the case of T1 <T _m. When T _m ≦ T1, the following operation is performed to store in the storage means as set data (t1, T1 _A ) of the first analysis temperature T1 _A and the time t1. That is, in the case of T _m <T1, the difference between T _m and T1 (T1−T _m ) and the difference between T _m−1 and T1 at the previous time t _m−1 (T _m−1 −T1) _but stored in the storage unit set data _{(t m-1, T m} -1) as (t1, T1 _a) when a _{(T m-1 -T1) ≦} (T1-T m). On the other hand, when T _m = T ₁ and (T _m−1 −T ₁ )> (T 1 −T _m ), the set data (t _m , T _m ) at time t _m is stored as (t 1, T 1 _A ). Store in the means. That is, to the closest temperature to the first temperature T1 first analysis temperature T1 _A of the temperature T _m.

Obtaining a second analysis temperature T2 _A to be executed and then also the same as obtaining a first analysis temperature T1 _A. That is, m = m + 1, that is, the set data in the time step immediately after the set data stored in the storage means in the step of acquiring the first analysis temperature T1 _A is read from the storage means, and set in the temperature setting step S4. while comparing the magnitude relation between the second temperature T2, successively repeating this until T2 ≦ T _m, set in the second analysis temperature T2 _a by the same method as for obtaining the first analysis temperature T1 _a Data (t2, T2 _A ) is acquired and stored in the storage means. In other words, the closest temperature to the second temperature T2 and the second analysis temperature T2 _A of the temperature _{T m.}

Then, calculating a first cooling rate _{V 1.} The set data (t1, T1 _A ) and (t2, T2 _A ) stored in the storage means are read, and the first cooling rate V is calculated by the calculation formula of V ₁ = (T1 _A −T2 _A ) / (t2−t1). ₁ is obtained and stored in the storage means.

(7-2) Second cooling rate calculation step S62 and third cooling rate calculation step S63
Subsequently, the second cooling rate calculation step S62 and the third cooling rate calculation step S63 are executed. Although both the second cooling rate calculation step S62 and the third cooling rate calculation step S63 are not shown, both m = m + 1 and in the time step after the set data stored in the storage means in the immediately preceding step. The set data is read from the storage means, and is performed in the same manner as in the first cooling rate calculation step S61. The second cooling speed calculation step S62, the set data in the third analysis temperature T3 _A (t3, T3 _A) and the fourth set data in the analysis temperature T4 _A of (t4, T4 _A) is obtained, then the second cooling rate V ₂ of are stored in the computed and the storage means. Then, the third cooling rate calculation step S63, the set data in the fifth analysis temperature T5 _A of (t5, T5 _A) and a sixth set data in the analysis temperature T6 _A of (t6, T6 _A) is obtained, the The cooling rate V3 of ₃ is calculated and stored in the storage means.

  The above-described maximum temperature calculation step S5 and the subsequent series of steps up to the cooling rate calculation step S6 are executed for n casting elements.

(8) Hardness calculation step S7
As a formula for predicting the hardness H _{B of the} casting element, a hardness prediction formula created in advance by regression calculation or the like based on experimental data as described above is applied. FIG. 5 is a flowchart showing the hardness calculation step S7. In FIG. 5, the process is divided into the graphite grain number calculation step S71 for executing the graphite grain number prediction formula and the step S72 for executing the hardness prediction formula, but the hardness prediction formula including the graphite grain number prediction formula is calculated. You may perform by one process. Hereinafter, the steps are divided into a graphite particle number calculation step S71 that executes the above-described (Equation 5) as a graphite particle number prediction equation, and a step S72 that executes a hardness prediction equation that uses the above-described (Equation 4) as a hardness prediction equation. This will be described with an example, but the present invention is not limited to this. For example, the _NG term of the hardness prediction formula (Formula 4) may set the graphite grain number _NG as a constant value (for example, 300 particles / mm ² ), but the graphite grain count prediction formula (Formula 5) If the graphite particle number calculation step S71 is executed, the accuracy of predicting the hardness can be improved.

First, the graphite particle number calculation step S71 is executed. That is, the maximum temperature T _max acquired up to the cooling rate calculation step S6 and stored in the storage means, the first cooling rate V ₁ and the C% and Si% set in the chemical component setting step S3 and stored in the storage means. Read and execute the graphite grain number prediction formula (Formula 5) to obtain the graphite grain number _NG . Next, a hardness prediction formula is executed (S72). That is, the graphite particle number N _G obtained by the graphite particle number prediction formula (Equation 5) in the graphite particle number calculation step S71, the second cooling rate V ₂ obtained in the cooling rate calculation step S6 and stored in the storage means The values of Cu% and Mn% set in the third cooling rate V ₃ and chemical component setting step S3 and stored in the storage means are read, and the hardness H _B is calculated by the hardness prediction formula (formula 4) and stored. Store in the means. The above-described steps S71 to S73 are executed for all n casting elements or a casting element at a necessary portion of the n casting elements. In the hardness prediction formula (Formula 4), the relative value between the cooling rate of the eutectoid transformation (third cooling rate V ₃ ) and the cooling rate after eutectic solidification (second cooling rate V ₂ ) is not necessarily limited. Although not necessarily included in the calculation, if the relative value of both cooling rates is included in the calculation as, for example, V ₃ / V ₂ , the accuracy of predicting the hardness of the thin portion can be particularly improved.

(9) Hardness output step S8
The hardness of all the n casting elements calculated in the hardness calculation step S7 and stored in the storage means, or the hardness of the casting elements in the necessary portions of the n casting parts, is determined by a three-dimensional model for each element using a post processor, for example. It is preferable to output as an image mapped to. For example, the hardness can be output as an image by using commercially available viewer software. By outputting the hardness as an image, the distribution of hardness for each part of the casting can be easily recognized visually.

  Hereinafter, examples in which the present invention is specifically implemented will be described with reference to the drawings and tables.

(Example 1) Foundry A, product A
Example 1 is an example in which the method of predicting the hardness of the present invention is applied to a product A (steering knuckle) that is a casting made of spheroidal graphite cast iron manufactured at a foundry A. Prediction equation is the formula of function form shown in equation (4) of the hardness _{H B} used in step S72 to perform the hardness prediction equation of hardness calculating step S7, i.e. _{H B = ω + α 1 Cu} eq + α 2 V 3 + α 3 N _G + α ₄ V ₃ / V ₂ (Formula 6)
age,
Similarly, the graphite particle number prediction formula used in the graphite particle number calculation step S71 of the hardness calculation step S7 is a functional equation of (Equation 5), that is, N _G = ψ ₁ + D _CE (β ₁ V ₁ −ψ ₂ ) + β ₂ V ₁ + β ₃ T _max (Equation 7)
It was.

Moreover, the value shown in Table 1 was used for the constant ξ ₂ of the formula Cu _eq = Cu% + ξ ₂ Mn% for obtaining the constants α _{1 to} α _4, ω and Cu _eq of (Formula 6). That is, α ₁ = 100, α ₂ = 250, α ₃ = −0.10, α ₄ = −50, ω = 120, and ξ ₂ = 0.3. Moreover, the constant β ₁ ~β _3, ψ _1, formula _D CE = constants _{C% + ξ 1 Si% -φ} ξ 1 and φ for obtaining the [psi ₂ and _{D CE,} the values shown in Table 2 (Formula 7) Using. That is, β ₁ = 300, β ₂ = 100, β ₃ = −1.0, ψ ₁ = 1000, ψ ₂ = 70, ξ ₁ = 0.33, and φ = 4.5.

  In the chemical component value setting step S3, the mass% values shown in Table 3 were used for C, Si, Cu and Mn as elements. That is, C% = 3.6, Si% = 2.4, Cu = 0.1, and Mn% = 0.2. In addition, the mass% of the element of Example 1 shown in Table 3 is a chemical component value aimed at in the manufacture of the product A manufactured in the foundry A.

  The values shown in Table 4 were used for the first temperature T1 to the sixth temperature T6 given in the temperature setting step S4. That is, T1 = 1160, T2 = 1100, T3 = 1100, T4 = 1000, T5 = 740, T6 = 710.

In addition, the value shown in Table 4, that is, T _END = 600, was also used as the predetermined temperature T _END for finishing the analysis in the cooling history analysis step S2.

FIG. 6 shows a comparison between the predicted value of hardness obtained by the example of the present invention using the above formulas and constants, and the actually measured value of the hardness of the actual casting, that is, the actual product. 6 (a) is a diagram showing a portion H1~H4 predicted and measured hardness in product A, Fig. 6 (b) and the predicted value of the hardness _{H B} at the site H1~H4 shown in FIG. 6 (a) It is the figure which compared measured value. Plots with open markers in FIG. 6B show the results of Example 1. In an actual casting containing 0.1% by mass of Cu, the soft ferrite phase becomes a relatively large structure and the hardness is low, but this was predicted by Example 1 where Cu% = 0.1 was set. The hardness and the measured hardness were in good agreement, and the present invention was able to accurately predict the hardness of the spheroidal graphite cast iron casting.

(Example 2) Foundry B, product A
Example 2 predicts the hardness of the present invention for a product A (steering knuckle), which is a casting made of spheroidal graphite cast iron having the same shape as Example 1 manufactured in a foundry B having a different production line from Example 1. This is an example of applying the method. As the hardness prediction formula and the graphite grain number prediction formula, (Formula 6) and (Formula 7) having the same function form as in Example 1 were used, respectively, but constants β ₂ , β ₃ , and ψ ₁ in (Formula 7) are shown in Table 2. As shown in FIG. 4, numerical values different from those in Example 1 were used. That is, β ₂ = 400, β ₃ = −0.1, and ψ ₁ = 500. The other constants shown in Table 2 and the constants shown in Table 1 were the same as in Example 1.

  In the chemical component value setting step S3, the mass% values shown in Table 3 were used for C, Si, Cu and Mn as elements. That is, C% = 3.7, Si% = 2.3, Cu = 0.4, and Mn% = 0.2. In addition, the mass% of the element of Example 2 shown in Table 3 is a chemical component value aimed at in the manufacture of the product A manufactured in the foundry B.

  As shown in Table 4, the same values as in Example 1 were used for the first temperature T1 to the sixth temperature T6 given in the temperature setting step S4.

The result of calculating the hardness according to Example 2 is also shown in accordance with FIG. 6B shown in Example 1. The parts H1 to H4 whose hardness was predicted and measured in Example 2 were the same as those shown in FIG. 6 (b) is a diagram of comparison between the predicted and measured values of the hardness H _B at the site H1-H4, plotted by solid black marker in the figure shows the results of Example 2. In an actual casting containing 0.4% by mass of Cu, the hardness becomes high due to the structure having a relatively large amount of hard pearlite phase, but this was predicted by Example 2 where Cu% = 0.4 was set. The hardness and the measured hardness were in good agreement, and the present invention was able to accurately predict the hardness of the spheroidal graphite cast iron casting.

  Here, comparing the hardness predicted in Example 1 and Example 2 with the hardness of the actual casting, the hardness of the actual casting is lower than that of the product A of the foundry A, and the product A of the foundry B The hardness is high. Moreover, even if it is the same product A, hardness differs with the site | parts. As can be seen from FIG. 6 (b), according to the method for predicting the hardness of the spheroidal graphite cast iron casting of the present invention, it is possible to accurately predict this, including the difference in the hardness of the casting, which differs depending on the foundry and location. Yes.

(Comparative example 1) Foundry A, product A
In Comparative Example 1, in applying the method of predicting the hardness of the present invention to the same product A (steering knuckle) manufactured in the same foundry A as in Example 1, the cooling rate of the eutectoid transformation (third This is an example in which the hardness is predicted considering only the cooling rate. In Comparative Example 1, the chemical component value setting step S3 and the maximum temperature calculation step S5 are not executed. In the temperature setting step S4, only the fifth temperature T5 and the sixth temperature T6 are set, and the cooling rate calculation step S6. Then, only the third cooling rate calculation step S63 was executed.

Further, in the hardness calculation step S7, the graphite particle number calculation step S71 is not executed, that is, the hardness prediction equation is executed without using the functional equation (Equation 7) of the graphite particle number prediction equation (Equation 5). Of the functional formula (formula 6) of the prediction formula (formula 4) of the hardness H _{B in} S72, the functional formula using only the constants ω and α ₂ and the third cooling rate V ₃ , that is, H _B = Ω + α ₂ V ₃ (Formula 8)
Was used to execute the hardness calculation step S7.

In Comparative Example 1, except that Table 1 and Table 2 the constants ω and alpha ₂ (Formula 8) was set in the same manner as in Example 1, all the constants of the equation (6) and (7) Not set. In addition, as shown in Table 3, the chemical component value setting step S3 was not executed, so the elements and the mass% of each element were not set. In the temperature setting step S4, only the fifth temperature T5 and the sixth temperature T6 used in the third cooling rate calculation step S63 were given, and the same values as in Example 1 were used as shown in Table 4. In addition, as the predetermined temperature T _END that ends the analysis in the cooling history analysis step S2, the same value as in Example 1 was used as shown in Table 4.

FIG. 12 shows a comparison between the predicted hardness value and the actual hardness measurement value in the comparative example in consideration of only the eutectoid transformation cooling rate (third cooling rate). The parts H1 to H4 whose hardness was predicted and measured in Comparative Example 1 were the same as those shown in FIG. Figure 12 is a view of comparing the predicted and measured values of the hardness H _B at the site H1-H4, are plotted by marker white in the figure shows the results of Comparative Example 1. The hardness predicted in Comparative Example 1 greatly deviated from the actually measured hardness, and the two did not match.

(Comparative example 2) Foundry B, product A
In Comparative Example 2, in applying the method of predicting the hardness of the present invention to the same product A (steering knuckle) manufactured in the same foundry B as in Example 2, the cooling rate of the eutectoid transformation (third This is an example in which the hardness is predicted considering only the cooling rate. In Comparative Example 2, as in Comparative Example 1, the chemical component value setting step S3 and the maximum temperature calculation step S5 are not executed, and only the fifth temperature T5 and the sixth temperature T6 are set in the temperature setting step S4. In the cooling rate calculation step S6, only the third cooling rate calculation step S63 was executed.

Further, in the hardness calculation step S7, the graphite particle number calculation step S71 is not executed, that is, the hardness prediction equation is executed without using the functional equation (Equation 7) of the graphite particle number prediction equation (Equation 5). hardness H equation functional form of the prediction equation of _B in the S72, and executes the hardness calculating step S7 using Comparative example 1 the same and the (equation 8).

As in Comparative Example 1, Comparative Example 2 is similar to Comparative Example 1 except that constants ω and α ₂ of (Equation 8) are set to be the same as those in Example 1, as shown in Table 1 and Table 2. All constants of 7) were not set. The mass% of the elements and each element as shown in Table 3 is not set, any given temperature T _END to end the fifth temperature T5 and temperature T6 and analysis of the sixth, as shown in Table 4 The same values as in Example 1 were used.

The result of calculating the hardness according to Comparative Example 2 is similarly shown in accordance with FIG. 12 shown in Comparative Example 1. The parts H1 to H4 whose hardness was predicted and measured in Comparative Example 2 were the same as those shown in FIG. Figure 12 is a view of comparing the predicted and measured values of the hardness H _B at the site H1-H4, are plotted by solid black marker in the figure shows the results of Comparative Example 2. The hardness predicted in Comparative Example 2 greatly deviated from the actually measured hardness, and the two did not match.

Here, comparing the hardness predicted in Comparative Example 1 and Comparative Example 2 with the hardness of the actual casting, the hardness of the actual casting is the hardness of the product A of the foundry A and the product A of the foundry B as described above. whereas there is a height difference, hardness predicted in Comparative example 1 and Comparative example 2 are both are contained in the hardness range of about 150～210H _B, not been able to predict the height difference between the hardness of the real casting . Moreover, the predicted value has a large deviation from the actually measured value. Thus, in the comparative example which considered only the cooling rate of the eutectoid transformation, the prediction accuracy of the actual casting hardness is low.

1 Solidification cooling curve 2 Supercooling

Claims (5)

A method for predicting the hardness of a spheroidal graphite cast iron casting,
An element creation step (S1) for creating an analysis model including a casting element;
Analyzing the heat transfer of the casting element over time during the period from when the molten metal composed of spheroidal graphite cast iron flows and fills the casting element and is cooled to a temperature lower than the eutectoid transformation temperature of the spheroidal graphite cast iron. , A cooling history analysis step (S2) for acquiring set data of time and temperature of the casting element;
A chemical component value setting step (S3) for giving a chemical component value of the spheroidal graphite cast iron;
A temperature setting step (S4) for providing a set temperature for calculating the cooling rate of the casting element;
A maximum temperature calculation step (S5) for obtaining a maximum temperature of the casting element based on the set data of the casting element;
Based on the set temperature and the set data, a first cooling rate calculation step (S61) for calculating a cooling rate for eutectic solidification, and a second cooling rate calculation step for calculating a cooling rate after eutectic solidification ( A cooling rate calculation step (S6) including S62) and a third cooling rate calculation step (S63) for calculating the cooling rate of the eutectoid transformation;
Based on the maximum temperature, the cooling rate of the eutectic solidification, the cooling rate after the eutectic solidification, the cooling rate of the eutectoid transformation, and the chemical component value A method of predicting the hardness of the spheroidal graphite cast iron casting, comprising a calculation step (S7).   The method for predicting the hardness of a spheroidal graphite cast iron casting according to claim 1, wherein the chemical component value given in the chemical component value setting step (S3) includes at least C, Si, Cu and Mn as elements.   The hardness calculation step (S7) is a graphite particle number calculation step of calculating the number of graphite particles of the casting element based on the maximum temperature, the eutectic solidification cooling rate, and the chemical component value including at least C and Si as elements. The method for predicting the hardness of the spheroidal graphite cast iron casting according to claim 1 or 2, comprising (S71).   The spheroidal graphite cast iron casting according to any one of claims 1 to 3, wherein the hardness calculation step (S7) includes calculation of a relative value between a cooling rate of the eutectoid transformation and a cooling rate after the eutectic solidification. Of predicting hardness.   The hardness of the spheroidal graphite cast iron casting according to any one of claims 1 to 4, further comprising a hardness output step (S8) for outputting the hardness of the cast element calculated in the hardness calculation step (S7) as an image. Method.

Images