Numerical analysis apparatus, method, and program

Abstract

To provide a numerical analysis device capable of drastically reducing the calculation amount required for numerical analysis while taking phase transformation of steel material into consideration when carrying out numerical analysis on physical quantity of steel material during quenching.SOLUTION: A numerical analysis device 10 calculates a characteristic curve showing a relation between a cooling index correlated with the cooling rate of the steel material and the transformation rate of the steel material by using a continuous cooling transformation diagram showing a phase of transformation of the steel material, calculates a position distribution of the transformation rate from a position distribution of the cooling indices by using the characteristic curve, and calculates a time change or a position distribution of a physical quantity by using the position distribution of the transformation rate.SELECTED DRAWING: Figure 1

Description

【Technical Field】 【0001】 The present invention relates to a numerical analysis apparatus, method, and program for performing numerical analysis on physical quantities of a steel material during quenching. 【Background Art】 【0002】 Conventionally, a technique for performing numerical analysis using computer simulation has been known. Patent Document 1 discloses a method for setting quenching conditions of a steel material and simulating changes in physical quantities (for example, hardness distribution) of the steel material during quenching. More specifically, FIG. 1 of the same document schematically shows solving by connecting three models including a heat transfer model, an elastoplastic model, and a phase transformation kinetics model. 【Prior Art Document】 【Patent Document】 【0003】 【Patent Document 1】 Japanese Patent No. 2772707 【Summary of the Invention】 【Problems to be Solved by the Invention】 【0004】 However, in the method disclosed in Patent Document 1, since the finite element method is applied to both the heat transfer model and the elastoplastic model, there is a problem that the amount of calculation and the required time for obtaining a transient solution or a steady state solution of physical quantities increase dramatically. 【0005】 The present invention has been made in view of such problems, and an object thereof is to provide a numerical analysis apparatus, method, and program capable of significantly reducing the amount of calculation required for numerical analysis while considering the phase transformation of a steel material when performing numerical analysis on physical quantities of the steel material during quenching. 【Means for Solving the Problems】 【0006】 A numerical analysis apparatus according to a first aspect of the present invention is an apparatus for performing numerical analysis on physical quantities of a steel material during quenching, comprising: a first calculation unit that uses a continuous cooling transformation diagram showing the transformation pattern of the steel material to calculate a characteristic curve showing the relationship between a cooling index correlated with the cooling rate of the steel material and the transformation rate of the steel material; a second calculation unit that uses the characteristic curve calculated by the first calculation unit to calculate the position distribution of the transformation rate from the position distribution of the cooling index; and a third calculation unit that uses the position distribution of the transformation rate calculated by the second calculation unit to calculate the time change or position distribution of the physical quantity. 【0007】 In the numerical analysis apparatus according to the second aspect of the present invention, the characteristic curve is a curve common to any part of the steel material. 【0008】 A numerical analysis method in a third aspect of the present invention is a method for performing numerical analysis on physical quantities of a steel material during quenching, comprising: a first calculation step of calculating a characteristic curve showing the relationship between a cooling index correlated with the cooling rate of the steel material and the transformation rate of the steel material, using a continuous cooling transformation diagram showing the transformation pattern of the steel material; a second calculation step of calculating the position distribution of the transformation rate from the position distribution of the cooling index using the calculated characteristic curve; and a third calculation step of calculating the time change or position distribution of the physical quantity using the calculated position distribution of the transformation rate, performed by one or more computers. 【0009】 A numerical analysis program in a fourth aspect of the present invention is a program that performs numerical analysis on the time change of physical quantities of steel material during quenching, and causes one or more computers to perform the following steps: a first calculation step of calculating a characteristic curve showing the relationship between a cooling index correlated with the cooling rate of the steel material and the transformation rate of the steel material using a continuous cooling transformation diagram showing the transformation pattern of the steel material; a second calculation step of calculating the position distribution of the transformation rate from the position distribution of the cooling index using the calculated characteristic curve; and a third calculation step of calculating the time change or position distribution of the physical quantities using the calculated position distribution of the transformation rate. [Effects of the Invention] 【0010】 According to the present invention, when performing numerical analysis on the physical quantities of steel material during quenching, the amount of computation required for numerical analysis can be significantly reduced while taking into account the phase transformation of the steel material. [Brief explanation of the drawing] 【0011】 [Figure 1] This is a block diagram of a numerical analysis device in one embodiment of the present invention. [Figure 2] Figure 1 is a flowchart illustrating an example of the analysis operation performed by the numerical analysis device. [Figure 3] This figure shows an example of a continuous cooling transformation diagram (CCT diagram) for steel. [Figure 4] This figure shows the characteristic curve calculated from the CCT diagram in Figure 3. [Figure 5] This figure shows an example of a method for calculating heat flux due to radiation. [Figure 6] This figure shows an example of a method for evaluating the hardness distribution of steel materials. [Modes for carrying out the invention] 【0012】 Embodiments of the present invention will be described below with reference to the attached drawings. To facilitate understanding of the description, the same reference numerals are used for identical components in each drawing whenever possible, and redundant explanations are omitted. 【0013】 [Configuration of the numerical analysis device 10] Figure 1 is an overall configuration diagram of a numerical analysis device 10 in one embodiment of the present invention. The numerical analysis device 10 is a computer for performing numerical analysis on physical quantities (e.g., metal structure and hardness distribution) of steel material during quenching. Note that "steel material" refers to, for example, iron with a carbon content of 2.0% by weight or less, and contains trace amounts of silicon, manganese, phosphorus, sulfur, etc. as impurities. Specifically, the numerical analysis device 10 comprises a communication unit 12, an input unit 14, an output unit 16, a control unit 18, and a storage unit 20. 【0014】 The communication unit 12 is an interface for sending and receiving electrical signals to and from external devices. This allows the numerical analysis device 10 to receive various information, including model information 34, from external devices (not shown), and to transmit analysis result information 40 that it generates to external devices. 【0015】 The input unit 14 consists of input devices including a mouse, keyboard, touch sensor, or microphone. The output unit 16 consists of output devices including a display and speakers. A graphical user interface (GUI) is constructed by combining the input function of the input unit 14 with the display function of the output unit 16. 【0016】 The control unit 18 is composed of a CPU (Central Processing Unit) or MPU (Micro-Processing Unit) processor. The control unit 18 functions as a characteristic curve creation unit 22 (corresponding to the "first calculation unit"), a numerical analysis unit 24, and an output instruction unit 26 by reading and executing a numerical analysis program stored in the memory unit 20. 【0017】 The characteristic curve creation unit 22 uses a continuous cooling transformation diagram (hereinafter also called a "CCT diagram") that shows the transformation pattern of the steel material to calculate a characteristic curve that shows the relationship between an index correlated with the cooling rate of the steel material (hereinafter referred to as the "cooling index") and the transformation rate of the steel material. This "cooling index" corresponds to the index when the temperature of the steel material decreases exponentially during the cooling period from the first temperature to the second temperature. This index may be the so-called cooling rate, or it may be the reciprocal of the cooling rate (i.e., the time required for cooling). 【0018】 The numerical analysis unit 24 performs numerical analysis on the physical quantities of the steel material during quenching. For this numerical analysis, the "finite element method" is used, which divides the analysis target, which is a continuum, into a large number of model elements and solves them. The shape, size, arrangement, or combination thereof of the model elements is appropriately selected according to the shape of the steel material, etc. More specifically, the numerical analysis unit 24 functions as a conversion unit 28 (corresponding to the "second calculation unit"), a calculation unit 30, and an evaluation unit 32 (corresponding to the "third calculation unit"). 【0019】 The output instruction unit 26 instructs the output of the analysis result information 40 generated by the numerical analysis unit 24. This "output" includes, in addition to the case where the analysis result information 40 is output to the output unit 16 of the numerical analysis device 10, the case where data including the analysis result information 40 is transmitted from the communication unit 12 to an external device. 【0020】 The storage unit 20 is non-transitory and is composed of a computer-readable storage medium. Here, the computer-readable storage medium is a storage device such as a magneto-optical disk, ROM, CD-ROM, a portable medium such as a flash memory, or a hard disk built into a computer system. 【0021】 The storage unit 20 stores programs and data necessary for the control unit 18 to control each component. Specifically, the storage unit 20 stores model information 34, CCT data 36, characteristic data 38, and analysis result information 40, respectively. 【0022】 The model information 34 includes information on a heat transfer model that describes the heat transfer of the steel material. The model information includes [1] "shape information" regarding the shape of the model elements in the finite element method, [2] "arrangement information" regarding the arrangement of the model elements, [3] "temperature information" regarding the temperature constraint conditions, or [4] "physical property information" regarding the physical properties of the model elements, etc. 【0023】 The CCT data 36 is data for specifying the continuous cooling transformation diagram (hereinafter also referred to as the "CCT diagram") of steel materials. The CCT diagram is a diagram showing the start point and end point of the phase transformation according to the cooling rate in order to represent the transformation process of steel materials during the continuous cooling process. Examples of the types of phase transformations include austenite transformation, ferrite transformation, pearlite transformation, bainite transformation, martensite transformation, and the like. Since this CCT diagram varies depending on the type of steel material (alloy composition), the CCT data 36 is provided for each type. 【0024】 The characteristic data 38 is data for specifying a curve (that is, a characteristic curve) showing the relationship between the cooling index and the transformation rate of steel materials, and is generated by the characteristic curve creation unit 22. The characteristic data 38 may be a data set or may be a coefficient for specifying the shape of an approximate function. 【0025】 The analysis result information 40 includes the analysis result of the steel material and is generated by the numerical analysis unit 24. Examples of the analysis result include [1] the time change of temperature, [2] the position distribution of temperature, [3] the position distribution of hardness, [4] the metal structure, and the like. 【0026】 [Operation of the Numerical Analysis Device 10] The numerical analysis device 10 in one embodiment of the present invention is configured as described above. Subsequently, the analysis operation by this numerical analysis device 10 will be described while referring to the flowchart of FIG. 2 and FIGS. 3 to 6. 【0027】 <SP10: Acquisition Step> In step SP10, the control unit 18 acquires the model information 34 indicating the heat transfer model to be analyzed through reading 3D CAD (Computer Aided Design) data or an input operation by an operator. 【0028】 <SP12: Acquisition Step> In step SP12, the control unit 18 uses the model information 34 obtained in step SP10 to acquire a continuous cooling transformation diagram (i.e., CCT diagram) corresponding to the type of steel material to be analyzed. If the corresponding CCT data 36 is not stored in the storage unit 20, the characteristic curve creation unit 22 may newly create a CCT diagram using a time-temperature transformation diagram (hereinafter also referred to as a "TTT diagram"). 【0029】 FIG. 3 is a diagram showing an example of a continuous cooling transformation diagram (CCT diagram) of a steel material. The horizontal axis of the graph shows the logarithmic value of time (unit: second), and the vertical axis of the graph shows temperature (unit: °C). In this figure, starting from the upper side to the lower side, the start lines of ferrite transformation, pearlite transformation, bainite transformation, and martensite transformation are drawn. 【0030】 <SP14: Calculation Step> In step SP14 of FIG. 2, the characteristic curve creation unit 22 uses the CCT diagram obtained in step SP12 to calculate a characteristic curve showing the relationship between the cooling index and the transformation rate. Specifically, the characteristic curve creation unit 22 calculates the transformation rate corresponding to the cooling index by integrating the change amount of the phase fraction for each time along a virtual cooling curve starting from the start temperature of cooling. Here, the "virtual cooling curve" means a virtual curve assuming that the temperature decreases exponentially. When this virtual cooling curve is represented on a semi-logarithmic graph, the slope of the straight line corresponds to the cooling index, that is, "v" in exp(-vt). Thus, by sequentially changing the value of the cooling index (v) and obtaining the transformation rate respectively, the characteristic curve illustrated in FIG. 4 described later can be obtained. 【0031】 FIG. 4 is a diagram showing characteristic curves calculated from the CCT diagram of FIG. 3. The horizontal axis of the graph indicates the logarithmic value of time (unit: second), and the vertical axis of the graph indicates the phase fraction (unit: %). In this case, the cooling index corresponds to the logarithmic value of the required time until cooling from the first temperature (for example, 800°C) to the second temperature (for example, 500°C). In this figure, the phase fractions of martensite transformation, bainite transformation, ferrite transformation, and pearlite transformation are shown. As can be understood from this figure, by calculating the cooling index of the steel material for each time, the time change of the transformation rate (that is, the phase fraction) can be obtained. 【0032】 <SP16: Selection Step> In step SP16 of FIG. 2, the arithmetic unit 30 selects the time point to be calculated (hereinafter, also referred to as the "sampling time point"). When the initial state is defined as t = 0, the first sampling time point is selected as t = Δt. 【0033】 <SP18: Construction Step> In step SP18, the arithmetic unit 30 constructs the heat conduction equation for each model element at the sampling time point (t = Δt) selected in step SP16. For example, the heat transfer equation in the cylindrical coordinate system (r, θ, z) is expressed by the following equation (1). 【0034】 【Equation】 【0035】 Usually, when performing numerical calculations, the partial differential equation shown in equation (1) is approximated by differences and transformed into a difference equation. As methods of transformation, for example, the explicit method, the implicit method, the ADI (Alternating Direction Implicit) method, etc. can be mentioned. 【0036】 Incidentally, with the occurrence of the phase transformation of the steel material, heat exchange according to the phase fraction is performed between the surrounding parts. Therefore, the conversion unit 28 calculates the distribution of the phase fraction from the distribution of the cooling index using a previously calculated characteristic curve, and converts it into the heat exchange amount for each part. By incorporating this heat exchange amount into the heat transfer equation, the calculation unit 30 can perform a calculation considering the occurrence of the phase transformation. 【0037】 Also, when calculating the amount of heat transfer (or heat flux) by radiation between the steel material and the cooling oil, a predetermined heat transfer function is used. As this heat transfer function, various one-logarithmic functions applied to the heat treatment of the steel material are used. For example, a two-logarithmic function assuming a boiling heat transfer phenomenon may be used. 【0038】 FIG. 5 is a diagram showing an example of a method for calculating the heat flux caused by radiation. The horizontal axis of the graph shows the logarithmic value of the temperature difference (unit: °C), and the vertical axis of the graph shows the logarithmic value of the heat flux (unit: W / m 2 ). This curve has a function shape in which the heat flux increases linearly as the temperature difference increases and has a peak (heat flux B) centered on the temperature difference A. 【0039】 <SP20: Analysis step> In step SP20 of FIG. 2, the calculation unit 30 solves the heat conduction equation constructed in step SP18 by联立 or 連成. As a result, the temperature at each position (that is, the temperature distribution) at the first sampling time point (t = Δt) is obtained. 【0040】 <SP22: Judgment step> In step SP22, the calculation unit 30 determines whether or not the temperature distribution obtained in step SP20 satisfies the end condition of the iterative calculation. This "end condition" is, for example, that the temperatures in n (1 < n ≤ N) of the N model elements match the target temperature during cooling or are sufficiently close to the target temperature. Since the end condition is not satisfied at the first sampling time point (step SP22: NO), the calculation unit 30 returns to step SP16. 【0041】 It should be noted that there may be some inaccuracies in the translation of technical terms. For the correct understanding of the content, it is recommended to refer to relevant technical materials and professional knowledge. <Repeated execution of steps SP16 to SP20> Returning to step SP16 in FIG. 2, the calculation unit 30 updates the sampling time point. As a result, the second sampling time point is selected as t = 2Δt. Hereinafter, the calculation unit 30 repeatedly executes steps SP16 to SP20 to obtain the temperature distribution at each sampling time point (t = mΔt; m is a natural number). 【0042】 As the temperature distribution becomes uniform over time and satisfies the above-described end condition (step SP20: YES), the calculation unit 30 proceeds to step SP24 instead of returning to step SP16. 【0043】 <SP24: Evaluation step> In step SP24, the evaluation unit 32 evaluates the hardness distribution of the steel material using the time change of the temperature distribution obtained by repeatedly executing step SP18. The hardness of the steel material is empirically determined in relation to the cooling index. 【0044】 FIG. 6 is a diagram showing an example of a method for evaluating the hardness distribution of a steel material. The horizontal axis of the graph indicates time (unit: second), and the vertical axis of the graph indicates temperature (unit: °C). Here, it is assumed that the time change of the temperature (i.e., the cooling curve) is different depending on the portions P1 and P2 of the steel material. Regarding the cooling curves at the portions P1 and P2, it is assumed that the times required to reach 500°C starting from quenching at 800°C (cooling indices) are t1 and t2, respectively. In this case, the hardnesses of the portions P1 and P2 are obtained as H1 and H2 (unit: HV) corresponding to t1 and t2, respectively. By obtaining the hardness for each portion of the steel material in this way, the hardness distribution of the steel material is obtained. 【0045】 <SP26: Output step> In step SP26, the output instruction unit 26 instructs the output of the analysis result information 40 generated through the evaluation in step SP24. For example, the output instruction unit 26 generates a display signal including the analysis result information 40 and supplies the obtained display signal to the output unit 16. As a result, the analysis results are visualized and displayed on the display screen of the output unit 16. This allows the operator to judge the appropriateness of the hardening conditions while visually confirming the visualized analysis results. 【0046】 [Summary of Embodiments] As described above, the numerical analysis device 10 in this embodiment is one or more computers that perform numerical analysis on physical quantities possessed by steel material during quenching. The numerical analysis device 10 includes a first calculation unit (here, a characteristic curve creation unit 22) that uses a continuous cooling transformation diagram showing the transformation pattern of the steel material to calculate a characteristic curve showing the relationship between a cooling index correlated with the cooling rate of the steel material and the transformation rate of the steel material; a second calculation unit (here, a conversion unit 28) that uses the characteristic curve calculated by the characteristic curve creation unit 22 to calculate the position distribution of the transformation rate from the position distribution of the cooling index; and a third calculation unit (here, an evaluation unit 32) that uses the position distribution of the transformation rate calculated by the conversion unit 28 to calculate the time change or position distribution of physical quantities. 【0047】 Furthermore, according to the numerical analysis method and program in this embodiment, one or more computers perform the following steps: a first calculation step (SP14 in Figure 2) in which a continuous cooling transformation diagram showing the transformation of steel material is used to calculate a characteristic curve showing the relationship between a cooling index correlated with the cooling rate of the steel material and the transformation rate of the steel material; a second calculation step (SP18) in which the calculated characteristic curve is used to calculate the position distribution of the transformation rate from the position distribution of the cooling index; and a third calculation step (SP24) in which the calculated position distribution of the transformation rate is used to calculate the time change or position distribution of a physical quantity. 【0048】 In this way, a characteristic curve is calculated using a continuous cooling transformation diagram that shows the transformation process of steel, and the positional distribution of the transformation rate is calculated from the positional distribution of the cooling index using this characteristic curve. As a result, the transformation rate at each part of the steel can be easily determined. This significantly reduces the amount of computation required for numerical analysis of the physical quantities of steel during quenching, while still considering the phase transformation of the steel. 【0049】 In particular, by using characteristic curves common to any part of the steel material, the positional distribution of the transformation rate can be calculated more quickly, regardless of the three-dimensional shape of the steel material being analyzed. 【0050】 [Differentiation] It should be noted that the present invention is not limited to the embodiments described above, and can be freely modified without departing from the spirit of the invention. Alternatively, the various components may be combined in any way that does not create a technical inconsistency. Alternatively, the execution order of each step constituting the flowchart may be changed as long as it does not create a technical inconsistency. 【0051】 In the embodiment described above, a general-purpose computer was described as executing a numerical analysis program for the purpose of computer simulation, but the configuration of the apparatus is not limited to this. For example, a controller that constitutes part of the heat treatment apparatus may execute this numerical analysis program. [Explanation of symbols] 【0052】 10... Numerical analysis device (computer), 22... Characteristic curve calculation unit (first calculation unit), 24... Numerical analysis unit, 28... Conversion unit (second calculation unit), 32... Evaluation unit (third calculation unit), SP14... Creation step (first calculation step), SP18... Construction step (second calculation step), SP24... Evaluation step (third calculation step)

Claims

[Claim 1] A numerical analysis device that constructs a single finite element model to describe the heat transfer and phase transformation of steel material during quenching, and performs numerical analysis on the physical quantities of the steel material using the finite element model, A first calculation unit calculates a characteristic curve common to any part of the steel material, which shows the relationship between the cooling index, which correlates with the cooling rate of the steel material within the finite element model, and the phase fraction of the steel material, using a continuous cooling transformation diagram that shows the transformation pattern of the steel material. A second calculation unit calculates the position distribution of the phase fraction from the position distribution of the cooling index within the finite element model using the characteristic curve calculated by the first calculation unit, A third calculation unit calculates the time change or position distribution of the physical quantity using the position distribution of the phase fraction calculated by the second calculation unit, A numerical analysis device characterized by comprising the following features. [Claim 2] The numerical analysis apparatus according to claim 1, characterized in that the physical quantity is temperature, hardness, or metal structure. [Claim 3] A numerical analysis method comprising constructing a single finite element model that describes the heat transfer and phase transformation of steel material during quenching, and performing a numerical analysis on the physical quantities of the steel material using the finite element model, A first calculation step involves using a continuous cooling transformation diagram showing the transformation pattern of the steel material to calculate a characteristic curve common to any part of the steel material, which shows the relationship between the cooling index correlated with the cooling rate of the steel material within the finite element model and the phase fraction of the steel material. A second calculation step involves using the calculated characteristic curve to calculate the position distribution of the phase fraction from the position distribution of the cooling index within the finite element model, A third calculation step involves using the calculated positional distribution of the phase fraction to calculate the time change or positional distribution of the physical quantity, A numerical analysis method characterized by being performed by one or more computers. [Claim 4] A numerical analysis program that constructs a single finite element model to describe the heat transfer and phase transformation of steel material during quenching, and performs numerical analysis on the time evolution of physical quantities of the steel material using the finite element model, A first calculation step involves using a continuous cooling transformation diagram showing the transformation process of the steel material to calculate a characteristic curve common to any part of the steel material, which shows the relationship between the cooling index, which correlates with the cooling rate of the steel material, and the phase fraction of the steel material. A second calculation step involves using the calculated characteristic curve to calculate the position distribution of the phase fraction from the position distribution of the cooling index within the finite element model, A third calculation step involves using the calculated positional distribution of the phase fraction to calculate the time change or positional distribution of the physical quantity within the finite element model, A numerical analysis program characterized by being executed on one or more computers.

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